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We consider the quantum inverse scattering method for several mixed integrable models based on the rational SU(N) R-matrix with general toroidal boundary conditions. This includes systems whose Hilbert spaces are invariant by the discrete representations of the group SU(2) and the non-compact group SU(1,1) as well as the conjugate representation of the SU(N) symmetry. Introducing certain transformations on the quantum spaces we are able to solve generalizaed impurity problems including those related to singular matrices.
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arxiv:nlin/0406021
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We introduce a simple method to estimate the system parameters in continuous dynamical systems from the time series. In this method, we construct a modified system by introducing some constants (controlling constants) into the given (original) system. Then the system parameters and the controlling constants are determined by solving a set of nonlinear simultaneous algebraic equations obtained from the relation connecting original and modified systems. Finally, the method is extended to find the form of the evolution equation of the system itself. The major advantage of the method is that it needs only a minimal number of time series data and is applicable to dynamical systems of any dimension. The method also works extremely well even in the presence of noise in the time series. This method is illustrated for the case of Lorenz system.
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arxiv:nlin/0406027
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We discuss the quasiclassical approximation for the equations of motions of a nonlinear chain of phonons and electrons having phonon mediated hopping. Describing the phonons and electrons as even and odd grassmannian functions and using the continuum limit we show that the equations of motions lead to a Zakharov-like system for bosonic and fermionic fields. Localised and nonlocalised solutions are discussed using the Hirota bilinear formalism. Nonlocalised solutions turn out to appear naturally for any choice of wave parameters. The bosonic localised solution has a fermionic dressing while the fermionic one is an oscillatory localised field. They appear only if some constraints on the dispersion are imposed. In this case the density of fermions is a strongly localised travelling wave. Also it is shown that in the multiple scales approach the emergent equation is linear. Only for the resonant case we get a nonlinear fermionic Yajima-Oikawa system. Physical implications are discussed.
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arxiv:nlin/0406045
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We report a remarkable type of bifurcation: by varying real parameters, unstable complex orbits may become stable over wide parameter ranges. Thus, phase diagrams obtained by analizing solely the stability of real solutions may be incomplete.
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arxiv:nlin/0407004
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The semiclassical limit of the algebraic Bethe Ansatz for the Izergin-Korepin 19-vertex model is used to solve the theory of Gaudin models associated with the twisted $A_{2}^{(2)}$ R-matrix. We find the spectra and eigenvectors of the $N-1$ independents Gaudin Hamiltonians. We also use the off-shell Bethe Ansatz method to show how the off-shell Gaudin equation solves the associated trigonometric system of Knizhnik-Zamolodchikov equations.
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arxiv:nlin/0407041
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Chaos often represents a severe obstacle for the set-up of many-body experiments, e.g., in fusion plasmas or turbulent flows. We propose a strategy to control chaotic diffusion in conservative systems. The core of our approach is a small apt modification of the system which channels chaos by building barriers to diffusion. It leads to practical prescriptions for an experimental apparatus to operate in a regular regime (drastic enhancement of confinement). The experimental realization of this control on a Travelling Wave Tube opens the possibility to practically achieve the control of a wide range of systems at a low additional cost of energy.
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arxiv:nlin/0407048
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This paper describes the security weaknesses of a recently proposed secure communication method based on chaotic masking using projective synchronization of two chaotic systems. We show that the system is insecure and how to break it in two different ways, by high-pass filtering and by generalized synchronization.
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arxiv:nlin/0407058
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We present a nonparametric way to retrieve a system of differential equations in embedding space from a single time series. These equations can be treated with dynamical systems theory and allow for long term predictions. We demonstrate the potential of our approach for a modified chaotic Chua oscillator.
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arxiv:nlin/0408003
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Atmospheric wind speeds and their fluctuations at different locations (onshore and offshore) are examined. One of the most striking features is the marked intermittency of probability density functions (PDF) of velocity differences -- no matter what location is considered. The shape of these PDFs is found to be robust over a wide range of scales which seems to contradict the mathematical concept of stability where a Gaussian distribution should be the limiting one. Motivated by the instationarity of atmospheric winds it is shown that the intermittent distributions can be understood as a superposition of different subsets of isotropic turbulence. Thus we suggest a simple stochastic model to reproduce the measured statistics of wind speed fluctuations.
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arxiv:nlin/0408005
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We present a general holistic theory for the organization of complex networks, both human-engineered and naturally-evolved. Introducing concepts of value of interactions and satisfaction as generic network performance measures, we show that the underlying organizing principle is to meet an overall performance target for wide-ranging operating or environmental conditions. This design or survival requirement of reliable performance under uncertainty leads, via the maximum entropy principle, to the emergence of a power law vertex degree distribution. The theory also predicts exponential or Poisson degree distributions depending on network redundancy, thus explaining all three regimes as different manifestations of a common underlying phenomenon within a unified theoretical framework.
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arxiv:nlin/0408007
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Very recently Willis et al. [Phys. Rev. E {\bf 69}, 056612 (2004)] have used a collective variable theory to explain the appearance of a nonzero energy current in an ac driven, damped sine-Gordon equation. In this comment, we prove rigorously that the time-averaged energy current in an ac driven nonlinear Klein-Gordon system is strictly zero.
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arxiv:nlin/0410021
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A two-dimensional fluid, stirred at high wavenumbers and damped by both viscosity and linear friction, is modeled by a statistical field theory. The fluid's long-distance behavior is studied using renormalization-group (RG) methods, as begun by Forster, Nelson, and Stephen [Phys. Rev. A 16, 732 (1977)]. With friction, which dissipates energy at low wavenumbers, one expects a stationary inverse energy cascade for strong enough stirring. While such developed turbulence is beyond the quantitative reach of perturbation theory, a combination of exact and perturbative results suggests a coherent picture of the inverse cascade. The zero-friction fluctuation-dissipation theorem (FDT) is derived from a generalized time-reversal symmetry and implies zero anomalous dimension for the velocity even when friction is present. Thus the Kolmogorov scaling of the inverse cascade cannot be explained by any RG fixed point. The beta function for the dimensionless coupling ghat is computed through two loops; the ghat^3 term is positive, as already known, but the ghat^5 term is negative. An ideal cascade requires a linear beta function for large ghat, consistent with a Pad\'e approximant to the Borel transform. The conjecture that the Kolmogorov spectrum arises from an RG flow through large ghat is compatible with other results, but the accurate k^{-5/3} scaling is not explained and the Kolmogorov constant is not estimated. The lack of scale invariance should produce intermittency in high-order structure functions, as observed in some but not all numerical simulations of the inverse cascade. When analogous RG methods are applied to the one-dimensional Burgers equation using an FDT-preserving dimensional continuation, equipartition is obtained instead of a cascade--in agreement with simulations.
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arxiv:nlin/0410050
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In this paper the path integral technique is applied to the quantum motion on the Hermitian hyperbolic space HH(2). The Schr\"odinger equation on this space separates in 12 coordinate systems which are closely related to the coordinate systems on the two-dimensional hyperboloid. For six coordinate systems out of the twelve it is possible to find a path integral solution.
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arxiv:nlin/0411053
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In this work we study the interactions between stabilized Townes solitons. By means of effective Lagrangian methods, we have found that the interactions between these solitons are governed by central forces, in a first approximation. In our numerical simulations we describe different types of orbits, deflections, trapping and soliton splitting. Splitting phenomena are also described by finite dimensional reduced models. All these effects could be used for potential applications of stabilized solitons.
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arxiv:nlin/0412014
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We investigate the large-scale statistics of a passive scalar transported by a turbulent velocity field. At scales larger than the characteristic lengthscale of scalar injection, yet smaller than the correlation length of the velocity, the advected field displays persistent long-range correlations due to the underlying turbulent velocity. These induce significant deviations from equilibrium statistics for high-order scalar correlations, despite the absence of scalar flux.
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arxiv:nlin/0501007
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An explicit reciprocal transformation between a 2-component generalization of the Camassa-Holm equation, called the 2-CH system, and the first negative flow of the AKNS hierarchy is established, this transformation enables one to obtain solutions of the 2-CH system from those of the first negative flow of the AKNS hierarchy. Interesting examples of peakon and multi-kink solutions of the 2-CH system are presented.
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arxiv:nlin/0501028
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The energy gradient method has been proposed with the aim of better understanding the mechanism of flow transition from laminar flow to turbulent flow. In this method, it is demonstrated that the transition to turbulence depends on the relative magnitudes of the transverse gradient of the total mechanical energy which amplifies the disturbance and the energy loss from viscous friction which damps the disturbance, for given imposed disturbance. For a given flow geometry and fluid properties, when the maximum of the function K (a function standing for the ratio of the gradient of total mechanical energy in the transverse direction to the rate of energy loss due to viscous friction in the streamwise direction) in the flow field is larger than a certain critical value, it is expected that instability would occur for some initial disturbances. In this paper, using the energy gradient analysis, the equation for calculating the energy gradient function K for plane Couette flow is derived. The result indicates that K reaches the maximum at the moving walls. Thus, the fluid layer near the moving wall is the most dangerous position to generate initial oscillation at sufficient high Re for given same level of normalized perturbation in the domain. The critical value of K at turbulent transition, which is observed from experiments, is about 370 for plane Couette flow when two walls move in opposite directions (anti-symmetry). This value is about the same as that for plane Poiseuille flow and pipe Poiseuille flow (385-389). Therefore, it is concluded that the critical value of K at turbulent transition is about 370-389 for wall-bounded parallel shear flows which include both pressure (symmetrical case) and shear driven flows (anti-symmetrical case).
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arxiv:nlin/0501048
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It has recently been emphasized again that the very existence of stationary stable localized structures with short range interactions might allow to store information in non-equilibrium media, opening new perspectives on information storage. We show how to use generalized topological entropies to measure aspects of the quantities of storable and non-storable information. This leads us to introduce a measure of the long term stably storable information. As a first example to illustrate these concepts, we revisit a mechanism for the appearance of stationary stable localized structures that is related to the stabilization of fronts between structured and unstructured states (or between differently structured states).
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arxiv:nlin/0503011
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We study the dynamics of moving discrete breathers in an interfaced piecewise DNA molecule. This is a DNA chain in which all the base pairs are identical and there exists an interface such that the base pairs dipole moments at each side are oriented in opposite directions. The Hamiltonian of the Peyrard--Bishop model is augmented with a term that includes the dipole--dipole coupling between base pairs. Numerical simulations show the existence of two dynamical regimes. If the translational kinetic energy of a moving breather launched towards the interface is below a critical value, it is trapped in a region around the interface collecting vibrational energy. For an energy larger than the critical value, the breather is transmitted and continues travelling along the double strand with lower velocity. Reflection phenomena never occur. The same study has been carried out when a single dipole is oriented in opposite direction to the other ones. When moving breathers collide with the single inverted dipole, the same effects appear. These results emphasize the importance of this simple type of local inhomogeneity as it creates a mechanism for the trapping of energy. Finally, the simulations show that, under favorable conditions, several launched moving breathers can be trapped successively at the interface region producing an accumulation of vibrational energy. Moreover, an additional colliding moving breather can produce a saturation of energy and a moving breather with all the accumulated energy is transmitted to the chain.
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arxiv:nlin/0503062
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The Fermi-Pasta-Ulam (FPU) paradox consists of the nonequipartition of energy among normal modes of a weakly anharmonic atomic chain model. In the harmonic limit each normal mode corresponds to a periodic orbit in phase space and is characterized by its wave number $q$. We continue normal modes from the harmonic limit into the FPU parameter regime and obtain persistence of these periodic orbits, termed here $q$-Breathers (QB). They are characterized by time periodicity, exponential localization in the $q$-space of normal modes and linear stability up to a size-dependent threshold amplitude. Trajectories computed in the original FPU setting are perturbations around these exact QB solutions. The QB concept is applicable to other nonlinear lattices as well.
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arxiv:nlin/0504036
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This work is concerned with the formulation of the boundary quantum inverse scattering method for the xxz Gaudin magnet coupled to boundary impurities with arbitrary exchange constants. The Gaudin magnet is diagonalized by taking a quasi-classical limit of the inhomogeneous lattice. Using the method proposed by Babujian, the integral representation for the solution of the Knizhnik-Zamolodchikov equation is explictly constructed and its rational limit discussed.
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arxiv:nlin/0504060
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Our technologies complexify our environments. Thus, new technologies need to deal with more and more complexity. Several efforts have been made to deal with this complexity using the concept of self-organization. However, in order to promote its use and understanding, we must first have a pragmatic understanding of complexity and self-organization. This paper presents a conceptual framework for speaking about self-organizing systems. The aim is to provide a methodology useful for designing and controlling systems developed to solve complex problems. First, practical notions of complexity and self-organization are given. Then, starting from the agent metaphor, a conceptual framework is presented. This provides formal ways of speaking about "satisfaction" of elements and systems. The main premise of the methodology claims that reducing the "friction" or "interference" of interactions between elements of a system will result in a higher "satisfaction" of the system, i.e. better performance. The methodology discusses different ways in which this can be achieved. A case study on self-organizing traffic lights illustrates the ideas presented in the paper.
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arxiv:nlin/0505009
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Previous numerical studies have revealed the existence of embedded solitons (ESs) in a class of multi-wave systems with quadratic nonlinearity, families of which seem to emerge from a critical point in the parameter space, where the zero solution has a fourfold zero eigenvalue. In this paper, the existence of such solutions is studied in a three-wave model. An appropriate rescaling casts the system in a normal form, which is universal for models supporting ESs through quadratic nonlinearities. The normal-form system contains a single irreducible parameter $\epsilon $, and is tantamount to the basic model of type-I second-harmonic generation. An analytical approximation of WKB type yields an asymptotic formula for the distribution of discrete values of $\epsilon $ at which the ESs exist. Comparison with numerical results shows that the asymptotic formula yields an exact value of the scaling index, -6/5, and a fairly good approximation for the numerical factor in front of the scaling term.
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arxiv:nlin/0505012
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New Cellular Automata associated with the Schroedinger discrete spectral problem are derived. These Cellular Automata possess an infinite (countable) set of constants of motion.
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arxiv:nlin/0505033
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We develop a uniform semiclassical trace formula for the density of states of a three-dimensional isotropic harmonic oscillator (HO), perturbed by a term $\propto r^4$. This term breaks the U(3) symmetry of the HO, resulting in a spherical system with SO(3) symmetry. We first treat the anharmonic term in semiclassical perturbation theory by integration of the action of the perturbed periodic HO orbits over the manifold $\mathbb{C}$P$^2$ which characterizes their 4-fold degeneracy. Then we obtain an analytical uniform trace formula which in the limit of strong perturbations (or high energy) asymptotically goes over into the correct trace formula of the full anharmonic system with SO(3) symmetry, and in the limit $\epsilon$ (or energy) $\to 0$ restores the HO trace formula with U(3) symmetry. We demonstrate that the gross-shell structure of this anharmonically perturbed system is dominated by the two-fold degenerate diameter and circular orbits, and {\it not} by the orbits with the largest classical degeneracy, which are the three-fold degenerate tori with rational ratios $\omega_r:\omega_\phi=N:M$ of radial and angular frequencies. The same holds also for the limit of a purely quartic spherical potential $V(r)\propto r^4$.
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arxiv:nlin/0505060
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We present a theorem that allows to simplify linear stability analysis of periodic and quasiperiodic nonlinear regimes in N-particle mechanical systems (both conservative and dissipative) with different kinds of discrete symmetry. This theorem suggests a decomposition of the linearized system arising in the standard stability analysis into a number of subsystems whose dimensions can be considerably less than that of the full system. As an example of such simplification, we discuss the stability of bushes of modes (invariant manifolds) for the Fermi-Pasta-Ulam chains and prove another theorem about the maximal dimension of the above mentioned subsystems.
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arxiv:nlin/0506013
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The degree of synchronization and the amount of dynamical cluster formation in electroencephalographic (EEG) signals are characterized by employing two order parameters introduced in the context of coupled chaotic systems subject to external noise. These parameters are calculated in EEG signals from a group of healthy subjects and a group of epileptic patients, including a patient experiencing an epileptic crisis. The evolution of these parameters shows the occurrence of intermittent synchronization and clustering in the brain activity during an epileptic crisis. Significantly, the existence of an instantaneous maximum of synchronization previous to the onset of a crisis is revealed by this procedure. The mean values of the order parameters and their standard deviations are compared between both groups of individuals.
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arxiv:nlin/0506014
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We prove Nishida's 1971 conjecture stating that almost all low-energetic motions of the anharmonic Fermi-Pasta-Ulam lattice with fixed endpoints are quasi-periodic. The proof is based on the formal computations of Nishida, the KAM theorem, discrete symmetry considerations and an algebraic trick that considerably simplifies earlier results.
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arxiv:nlin/0506024
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Logistic growth of diffusing reactants on spatial domains with long range competition is studied. The bifurcations cascade involved in the transition from the homogenous state to a spatially modulated stable solution is presented, and a distinction is made between a modulated phase, dominated by single or few wavenumbers, and the spiky phase, where localized colonies are separated by depleted region. The characteristic defects in the periodic structure are presented for each phase, together with the invasion dynamics in case of local initiation. It is shown that the basic length scale that controls the bifurcation is the width of the Fisher front, and that the total population grows as this width decreases. A mix of analytic results and extensive numerical simulations yields a comprehensive examination of the possible phases for logistic growth in the presence of nonlocal competition.
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arxiv:nlin/0506046
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The Lax representation for the nonstationary Schr\"odinger equation with rather arbitrary potential is proposed. Some examples of the construction of exact solutions are given by means of Darboux Transformation method.
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arxiv:nlin/0507013
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Pointing out the difference between the Discrete Nonlinear Schr\"odinger equation with the classical power law nonlinearity-for which solutions exist globally, independently of the sign and the degree of the nonlinearity, the size of the initial data and the dimension of the lattice-we prove either global existence or nonexistence in time, for the Discrete Klein-Gordon equation with the same type of nonlinearity (but of ``blow-up'' sign), under suitable conditions on the initial data, and some times on the dimension of the lattice. The results, consider both the conservative and the linearly damped lattice. Similarities and differences with the continuous counterparts, are remarked. We also make a short comment, on the existence of excitation thresholds, for forced solutions of damped and parametrically driven, Klein-Gordon lattices.
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arxiv:nlin/0507044
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We propose a new cryptosystem by combing the Lissajous map, which is the asymptotic model of deterministic randomness, with the one-way coupled map lattice (OCML) system. The key space, the encryption efficiency, and the security are investigated. We find that the parameter sensitivity can reach the computational precision when the system size is only three, all the lattice outputs can be treated as key stream parallelly, and the system is resistible against various attacks including the differential-like chosen cipher attack. The findings of this paper are a strong indication of the importance of deterministic randomness in secure communications.
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arxiv:nlin/0507063
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The advection of passive tracers in an oscillating vortex chain is investigated. It is shown that by adding a suitable perturbation to the ideal flow, the induced chaotic advection exhibits two remarkable properties compared with a generic perturbation : Particles remain trapped within a specific domain bounded by two oscillating barriers (suppression of chaotic transport along the channel), and the stochastic sea seems to cover the whole domain (enhancement of mixing within the rolls).
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arxiv:nlin/0508032
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${\rm CaRuO_3}$ is a paramagnetic metal and since its low temperature resistivity is described by $\rho=\rho_0+AT^\gamma $ with $\gamma \sim 1.5$, it is also considered a non-Fermi liquid (NFL) metal. We have performed extensive magnetoresistance and Hall effect measurements of untwinned epitaxial films of ${\rm CaRuO_3}$. These measurements reveal that ${\rm CaRuO_3}$ exhibits uniaxial magnetocrystalline anisotropy. In addition, the low-temperature NFL behavior is most effectively suppressed when a magnetic field is applied along the easy axis, suggesting that critical spin fluctuations, possibly due to proximity of a quantum critical phase transition, are related to the NFL behavior.
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arxiv:nlin/0508038
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The Darboux--Dressing Transformations are applied to the Lax pair associated to the system of nonlinear equations describing the resonant interaction of three waves in 1+1 dimensions. We display explicit solutions featuring localized waves whose profile vanishes at the spacial boundary plus and minus infinity, and which are not pure soliton solutions. These solutions depend on an arbitrary function and allow to deal with collisions of waves with various profiles.
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arxiv:nlin/0509038
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Stationary bifurcations in several nonlinear models of fluid conveying pipes fixed at both ends are analyzed with the use of Lyapunov-Schmidt reduction and singularity theory. Influence of gravitational force, curvature and vertical elastic support on various properties of bifurcating solutions are investigated. In particular the conditions for occurrence of supercritical and subcritical bifurcations are presented for the models of Holmes, Thurman and Mote, and Paidoussis.
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arxiv:nlin/0509056
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A lattice model of interacting q-oscillators, proposed in [V. Bazhanov, S. Sergeev, arXiv:hep-th/0509181], is the quantum mechanical integrable model in 2+1 dimensional space-time. Its layer-to-layer transfer-matrix is a polynomial of two spectral parameters, it may be regarded in the terms of quantum groups both as a sum of sl(N) transfer matrices of a chain of length M and as a sum of sl(M) transfer matrices of a chain of length N for reducible representations. The aim of this paper is to derive the Bethe Ansatz equations for the q-oscillator model entirely in the framework of 2+1 integrability providing the evident rank-size duality.
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arxiv:nlin/0510048
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Multivariate time series analysis is extensively used in neurophysiology with the aim of studying the relationship between simultaneously recorded signals. Recently, advances on information theory and nonlinear dynamical systems theory have allowed the study of various types of synchronization from time series. In this work, we first describe the multivariate linear methods most commonly used in neurophysiology and show that they can be extended to assess the existence of nonlinear interdependences between signals. We then review the concepts of entropy and mutual information followed by a detailed description of nonlinear methods based on the concepts of phase synchronization, generalized synchronization and event synchronization. In all cases, we show how to apply these methods to study different kinds of neurophysiological data. Finally, we illustrate the use of multivariate surrogate data test for the assessment of the strength (strong or weak) and the type (linear or nonlinear) of interdependence between neurophysiological signals.
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arxiv:nlin/0510077
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This paper extends the results of the previous paper designated I hereafter in which the one- and two-soiton solutions of the Degasperis-Procesi(DP) equation were obtained and their peakon limit was considered. Here, we present the general N-soliton solution of the DP equation and investigate its property. We show that it has a novel structure expressed by a parametric representation in terms of the BKP tau-functions. A purely algebraic proof of the solution is given by establishing various identities among the tau-functions. The large time asymptotic of the solution recovers the formula for the phase shift which was derived in I by a different method. Finally, the structure of the N-soliton solution is discussed in comparison with that of the Camassa-Holm shallow water wave equation.
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arxiv:nlin/0511029
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A transition from asymmetric to symmetric patterns in time-dependent extended systems is described. It is found that one dimensional cellular automata, started from fully random initial conditions, can be forced to evolve into complex symmetrical patterns by stochastically coupling a proportion $p$ of pairs of sites located at equal distance from the center of the lattice. A nontrivial critical value of $p$ must be surpassed in order to obtain symmetrical patterns during the evolution. This strategy is able to classify the cellular automata rules -with complex behavior- between those that support time-dependent symmetric patterns and those which do not support such kind of patterns.
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arxiv:nlin/0512017
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I construct a complete asymptotic expansion of solutions to the problem of linear stability of three-dimensional steady space-periodic magnetohydrodynamic states to perturbations involving large periods. Eddy diffusivity tensor is derived for parity-invariant steady states. I present numerical evidences that if perturbations of the flow are permitted, then the effect of negative eddy diffusivity emerges at much larger magnetic molecular diffusivities than in the kinematic dynamo problem (where no perturbations of the flow are assumed).
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arxiv:nlin/0512076
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We demonstrate that an array of discrete waveguides on a slab substrate, both featuring the $\chi^{2}$ nonlinearity, supports stable solitons composed of discrete and continuous components. Two classes of fundamental composite solitons are identified: ones consisting of a discrete fundamental-frequency (FF) component in the waveguide array, coupled to a continuous second-harmonic (SH) component in the slab waveguide, and solitons with an inverted FF/SH structure. Twisted bound states of the fundamental solitons are found too. In contrast with usual systems, the \emph{intersite-centered} fundamental solitons and bound states with the twisted continuous components are stable, in an almost entire domain of their existence.
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arxiv:nlin/0601041
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We consider the Lagrangian formalism of the deformations of Whitham systems having Dubrovin-Zhang form. As an example the case of modulated one-phase solutions of the non-linear "V-Gordon" equation is considered.
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arxiv:nlin/0601050
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Process of the nonlinear deformation of the shallow water wave in a basin of constant depth is studied. The characteristics of the first breaking are analyzed in details. The Fourier spectrum and steepness of the nonlinear wave is calculated. It is shown that spectral amplitudes can be expressed through the wave front steepness, and this can be used for practical estimations.
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arxiv:nlin/0601052
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The results of modeling of radiation defects formation and evolution on the surface and in the volume of a crystal are presented in this article. Statistical properties are calculated for the investigated system. It is revealed that defects structure is a multifractal and system entropy decreases, while observing self-organization of the physical system.
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arxiv:nlin/0601064
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The surrogate data method is widely applied as a data dependent technique to test observed time series against a barrage of hypotheses. However, often the hypotheses one is able to address are not those of greatest interest, particularly for system known to be nonlinear. In the review we focus on techniques which overcome this shortcoming. We summarize a number of recently developed surrogate data methods. While our review of surrogate methods is not exhaustive, we do focus on methods which may be applied to experimental, and potentially nonlinear, data. In each case, the hypothesis being tested is one of the interests to the experimental scientist.
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arxiv:nlin/0603004
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Persistence of stationary and traveling single-humped localized solutions in the spatial discretizations of the nonlinear Schrodinger (NLS) equation is addressed. The discrete NLS equation with the most general cubic polynomial function is considered. Constraints on the nonlinear function are found from the condition that the second-order difference equation for stationary solutions can be reduced to the first-order difference map. The discrete NLS equation with such an exceptional nonlinear function is shown to have a conserved momentum but admits no standard Hamiltonian structure. It is proved that the reduction to the first-order difference map gives a sufficient condition for existence of translationally invariant single-humped stationary solutions and a necessary condition for existence of single-humped traveling solutions. Other constraints on the nonlinear function are found from the condition that the differential advance-delay equation for traveling solutions admits a reduction to an integrable normal form given by a third-order differential equation. This reduction also gives a necessary condition for existence of single-humped traveling solutions. The nonlinear function which admits both reductions defines a two-parameter family of discrete NLS equations which generalizes the integrable Ablowitz--Ladik lattice.
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arxiv:nlin/0603022
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New approach in classification of integrable hydrodynamic chains is established. This is the method of the Hamiltonian hydrodynamic reductions. Simultaneously, this approach yields explicit Hamiltonian hydrodynamic reductions of the Hamiltonian hydrodynamic chains. The concept of reducible Poisson brackets is established. Also this approach is useful for non-Hamiltonian hydrodynamic chains. The deformed Benney hydrodynamic chain is considered.
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arxiv:nlin/0603057
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We conduct an experimental investigation of nonlinearity management in optics using femtosecond pulses and layered Kerr media consisting of glass and air. By examining the propagation properties over several diffraction lengths, we show that wave collapse can be prevented. We corroborate these experimental results with numerical simulations of the (2 + 1)-dimensional focusing cubic nonlinear Schr\"odinger equation with piecewise constant coefficients and a theoretical analysis of this setting using a moment method.
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arxiv:nlin/0604031
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Most evolution equations %or wave equations are partially integrable and, in order to explicitly integrate all possible cases, there exist several methods of complex analysis, but none is optimal. The theory of Nevanlinna and Wiman-Valiron on the growth of the meromorphic solutions gives predictions and bounds, but it is not constructive and restricted to meromorphic solutions. The Painleve' approach via the a priori singularities of the solutions gives no bounds but it is often (not always) constructive. It seems that an adequate combination of the two methods could yield much more output in terms of explicit (i.e. closed form) analytic solutions. We review this question, mainly taking as an example the chaotic equation of Kuramoto and Sivashinsky nu u''' + b u'' + mu u' + u^2/2 +A=0, nu nonzero, with nu,b,mu,A constants.
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arxiv:nlin/0604063
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A simple class of chaotic systems in a random environment is considered and the fluctuation theorem is extended under the assumption of reversibility.
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arxiv:nlin/0605001
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We show that space-time evolution of one-dimensional fermionic systems is described by nonlinear equations of soliton theory. We identify a space-time dependence of a matrix element of fermionic systems related to the {\it Orthogonality Catastrophe} or {boundary states} with the $\tau$-function of the modified KP-hierarchy. The established relation allows to apply the apparatus of soliton theory to the study of non-linear aspects of quantum dynamics. We also describe a {\it bosonization in momentum space} - a representation of a fermion operator by a Bose field in the presence of a boundary state.
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arxiv:nlin/0605006
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In this paper we find the inverse and direct recursion operator for the intrinsic generalized sine-Gordon equation in any number $n > 2$ of independent variables. Among the flows generated by the direct operator we identify a higher-dimensional analogue of the pmKdV equation.
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arxiv:nlin/0605015
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Turbulent boundary layers exhibit a universal structure which nevertheless is rather complex, being composed of a viscous sub-layer, a buffer zone, and a turbulent log-law region. In this letter we present a simple analytic model of turbulent boundary layers which culminates in explicit formulae for the profiles of the mean velocity, the kinetic energy and the Reynolds stress as a function of the distance from the wall. The resulting profiles are in close quantitative agreement with measurements over the entire structure of the boundary layer, without any need of re-fitting in the different zones.
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arxiv:nlin/0606035
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The superintegrability of the non-periodic Toda lattice is explained in the framework of systems written in action-angles coordinates. Moreover, a simpler form of the first integrals is given.
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arxiv:nlin/0606072
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This article examines how diseases on random networks spread in time. The disease is described by a probability distribution function for the number of infected and recovered individuals, and the probability distribution is described by a generating function. The time development of the disease is obtained by iterating the generating function. In cases where the disease can expand to an epidemic, the probability distribution function is the sum of two parts; one which is static at long times, and another whose mean grows exponentially. The time development of the mean number of infected individuals is obtained analytically. When epidemics occur, the probability distributions are very broad, and the uncertainty in the number of infected individuals at any given time is typically larger than the mean number of infected individuals.
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arxiv:nlin/0607039
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Parametric energy-level correlation describes the response of the energy-level statistics to an external parameter such as the magnetic field. Using semiclassical periodic-orbit theory for a chaotic system, we evaluate the parametric energy-level correlation depending on the magnetic field difference. The small-time expansion of the spectral form factor $K(\tau)$ is shown to be in agreement with the prediction of parameter dependent random-matrix theory to all orders in $\tau$.
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arxiv:nlin/0607070
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We consider the question of existence of periodic solutions (called breather solutions or discrete solitons) for the Discrete Nonlinear Schr\"odinger Equation with saturable and power nonlinearity. Theoretical and numerical results are proved concerning the existence and nonexistence of periodic solutions by a variational approach and a fixed point argument. In the variational approach we are restricted to DNLS lattices with Dirichlet boundary conditions. It is proved that there exists parameters (frequency or nonlinearity parameters) for which the corresponding minimizers satisfy explicit upper and lower bounds on the power. The numerical studies performed indicate that these bounds behave as thresholds for the existence of periodic solutions. The fixed point method considers the case of infinite lattices. Through this method, the existence of a threshold is proved in the case of saturable nonlinearity and an explicit theoretical estimate which is independent on the dimension is given. The numerical studies, testing the efficiency of the bounds derived by both methods, demonstrate that these thresholds are quite sharp estimates of a threshold value on the power needed for the the existence of a breather solution. This it justified by the consideration of limiting cases with respect to the size of the nonlinearity parameters and nonlinearity exponents.
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arxiv:nlin/0609023
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Adler's lattice equation has acquired the status of a master equation among 2D discrete integrable systems. In this paper we derive what we believe are the first explicit solutions of this equation. In particular it turns out necessary to establish a non-trivial seed solution from which soliton solutions can subsequently be constructed using the B\"acklund transformation. As a corollary we find the corresponding solutions of the Krichever-Novikov equation which is obtained from Adler's equation in a continuum limit.
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arxiv:nlin/0609044
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The influence of an external flow on the relaxation dynamics of a single polymer is investigated theoretically and numerically. We show that a pronounced dynamical slowdown occurs in the vicinity of the coil-stretch transition, especially when the dependence on polymer conformation of the drag is accounted for. For the elongational flow, relaxation times are exceedingly larger than the Zimm relaxation time, resulting in the observation of conformation hysteresis. For random smooth flows hysteresis is not present. Yet, relaxation dynamics is significantly slowed down because of the large variety of accessible polymer configurations. The implications of these results for the modeling of dilute polymer solutions in turbulent flows are addressed.
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arxiv:nlin/0609055
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We refute an often invoked theorem which claims that a periodic orbit with an odd number of real Floquet multipliers greater than unity can never be stabilized by time-delayed feedback control in the form proposed by Pyragas. Using a generic normal form, we demonstrate that the unstable periodic orbit generated by a subcritical Hopf bifurcation, which has a single real unstable Floquet multiplier, can in fact be stabilized. We derive explicit analytical conditions for the control matrix in terms of the amplitude and the phase of the feedback control gain, and present a numerical example. Our results are of relevance for a wide range of systems in physics, chemistry, technology,and life sciences, where subcritical Hopf bifurcations occur.
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arxiv:nlin/0609056
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This paper presents an application of partial contraction analysis to the study of global synchronization in discrete chaotic systems. Explicit sufficient conditions on the coupling strength of networks of discrete oscillators are derived. Numerical examples and applications to simple systems are presented. Previous researches have shown numerically that the systems under study, when arranged in a network, exhibits rich and complex patterns that can dynamically change in response to variations in the environment. We show how this ``adaptation'' process strongly depends on the coupling characteristics of the network. Other potential applications of synchronized chaotic oscillators are discussed.
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arxiv:nlin/0609064
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We study turbulence and Bose-Einstein condensation (BEC) within the two-dimensional Gross-Pitaevski (GP) model. In the present work, we compute decaying GP turbulence in order to establish whether BEC can occur without forcing and if there is an intensity threshold for this process. We use the wavenumber-frequency plots which allow us to clearly separate the condensate and the wave components and,therefore, to conclude if BEC is present. We observe that BEC in such a system happens even for very weakly nonlinear initial conditions without any visible threshold. BEC arises via a growing phase coherence due to anihilation of phase defects/vortices. We study this process by tracking of propagating vortex pairs. The pairs loose momentum by scattering the background sound, which results in gradual decrease of the distance between the vortices. Occasionally, vortex pairs collide with a third vortex thereby emitting sound, which can lead to more sudden shrinking of the pairs. After the vortex anihilation the pulse propagates further as a dark soliton, and it eventually bursts creating a shock.
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arxiv:nlin/0610016
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This paper presents a systematic investigation of the integrability conditions for nonautonomous quad-graph maps, using the Lax pair approach, the ultra-local singularity confinement criterion and direct construction of conservation laws. We show that the integrability conditions derived from each of the methods are the one and the same, suggesting that there exists a deep connection between these techniques for partial difference equations.
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arxiv:nlin/0611019
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Dynamics of information flow in adaptively interacting stochastic processes is studied. We give an extended form of game dynamics for Markovian processes and study its behavior to observe information flow through the system. Examples of the adaptive dynamics for two stochastic processes interacting through matching pennies game interaction are exhibited along with underlying causal structure.
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arxiv:nlin/0611032
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In the work a nonlinear Duffing oscillator is considered under impulse excitation with two ways of introduction of the random additive term simulating noise, - with help of amplitude modulation and modulation of period of impulses sequence. The scaling properties both in the Feigenbaum scenario and in the tricritical case are shown.
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arxiv:nlin/0611040
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A previously unknown bright N-soliton solution for an intermediate nonlinear Schr\"{o}dinger equation of focusing type is presented. This equation is constructed as a reduction of an integrable system related to a Sato equation of a 2-component KP hierarchy for certain differential--difference dispersion relations. Bright soliton solutions are obtained in the form of double Wronskian determinants.
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arxiv:nlin/0612031
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We have performed numerical analysis of the two-dimensional (2D) soliton solutions in Bose-Einstein condensates with nonlocal dipole-dipole interactions. For the modified 2D Gross-Pitaevski equation with nonlocal and attractive local terms, we have found numerically different types of nonlinear localized structures such as fundamental solitons, radially symmetric vortices, nonrotating multisolitons (dipoles and quadrupoles), and rotating multisolitons (azimuthons). By direct numerical simulations we show that these structures can be made stable.
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arxiv:nlin/0612055
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We consider the q-Painlev\'e equation of type $A_4^{(1)}$ (a version of q-Painlev\'e V equation) and construct a family of solutions expressible in terms of certain basic hypergeometric series. We also present the determinant formula for the solutions.
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arxiv:nlin/0701001
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We study fluctuations of the Wigner time delay for open (scattering) systems which exhibit mixed dynamics in the classical limit. It is shown that in the semiclassical limit the time delay fluctuations have a distribution that differs markedly from those which describe fully chaotic (or strongly disordered) systems: their moments have a power law dependence on a semiclassical parameter, with exponents that are rational fractions. These exponents are obtained from bifurcating periodic orbits trapped in the system. They are universal in situations where sufficiently long orbits contribute. We illustrate the influence of bifurcations on the time delay numerically using an open quantum map.
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arxiv:nlin/0701025
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We consider and compare four Hamiltonian formulations of thermostated mechanics, three of them kinetic, and the other one configurational. Though all four approaches ``work'' at equilibrium, their application to many-body nonequilibrium simulations can fail to provide a proper flow of heat. All the Hamiltonian formulations considered here are applied to the same prototypical two-temperature "phi-4" model of a heat-conducting chain. This model incorporates nearest-neighbor Hooke's-Law interactions plus a quartic tethering potential. Physically correct results, obtained with the isokinetic Gaussian and Nose-Hoover thermostats, are compared with two other Hamiltonian results. The latter results, based on constrained Hamiltonian thermostats, fail correctly to model the flow of heat.
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arxiv:nlin/0701041
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Two novel classes of many-body models with nonlinear interactions "of goldfish type" are introduced. They are solvable provided the initial data satisfy a single constraint (in one case; in the other, two constraints): i. e., for such initial data the solution of their initial-value problem can be achieved via algebraic operations, such as finding the eigenvalues of given matrices or equivalently the zeros of known polynomials. Entirely isochronous versions of some of these models are also exhibited: i.e., versions of these models whose nonsingular solutions are all completely periodic with the same period.
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arxiv:nlin/0701046
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n this paper we formulate necessary conditions for the integrability in the Jacobi sense of Newton equations $\ddot \vq=-\vF(\vq)$, where $\vq\in\C^n$ and all components of $\vF$ are polynomial and homogeneous of the same degree $l$. These conditions are derived from an analysis of the differential Galois group of the variational equations along special particular solutions of the Newton equations. We show that, taking all admissible particular solutions, we restrict considerably the set of Newton's equations satisfying the necessary conditions for the integrability. Moreover, we apply the obtained conditions for a detailed analysis of the Newton equations with two degrees of freedom (i.e., $n=2$). We demonstrate the strength of the obtained results analyzing general cases with $\deg F_i =l< 4$. For $l=3$ we found an integrable case when the Newton equations have two polynomial first integrals and both of them are of degree four in the momenta $p_1=\dot q_1$, and $p_2=\dot q_2$. Moreover, for an arbitrary $k$, we found a family of Newton equations depending on one parameter $\lambda$. For an arbitrary value of $\lambda$ one quadratic in the momenta first integral exist. We distinguish infinitely many values of $\lambda$ for which the system is integrable or superintegrable with additional polynomial first integrals which seemingly can be of an arbitrarily high degree with respect to the momenta.
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arxiv:nlin/0701058
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We investigate the quantization of a free particle coupled linearly to a harmonic oscillator. This system, whose classical counterpart has clearly separated regular and chaotic regions, provides an ideal framework for studying the quantization of mixed systems. We identify key signatures of the classically chaotic and regular portions in the quantum system by constructing Husimi distributions and investigating avoided level crossings of eigenvalues as functions of the strength and range of the interaction between the system's two components. We show, in particular, that the Husimi structure becomes mixed and delocalized as the classical dynamics becomes more chaotic.
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arxiv:nlin/0702025
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A future goal of robot teams and agent-based models (ABMs) is to field organizations and systems based on first principles derived from human counterparts. Forestalling that opportunity, the failure of traditional organizational theory has at the same time opened the way to innovative theories of organizations and change. Inspired by Bohr and Heisenberg about the application of interdependent uncertainty in the interaction between action and observation, making organizations bistable, we have begun to construct a theory of organizations based on the uncertainty of energy level (resources) and belief/action consensus, leading to preliminary metrics of organizational performance that we have discovered in field studies. Our goal in this project is to address the problem posed by organizations with: the development of new theory; field tests of new metrics for organizations; and the development of quantum ABMs set within a social circuit as a building block for an organization. Should we be successful, our research would represent a fundamental departure from traditional observational methods of social science by forming the basis of a predictive science of organizations. We expect that replacing the traditional method of observation with a predictive science must account for when cognitive observations work and when they do not (illusions).
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arxiv:nlin/0702053
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Cardiac arrhythmias such as ventricular tachycardia (VT) or ventricular fibrillation (VF) are the leading cause of death in the industrialised world. There is a growing consensus that these arrhythmias arise because of the formation of spiral waves of electrical activation in cardiac tissue; unbroken spiral waves are associated with VT and broken ones with VF. Several experimental studies have been carried out to determine the effects of inhomogeneities in cardiac tissue on such arrhythmias. We give a brief overview of such experiments, and then an introduction to partial-differential-equation models for ventricular tissue. We show how different types of inhomogeneities can be included in such models, and then discuss various numerical studies, including our own, of the effects of these inhomogeneities on spiral-wave dynamics. The most remarkable qualitative conclusion of our studies is that the spiral-wave dynamics in such systems depends very sensitively on the positions of these inhomogeneities.
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arxiv:nlin/0703048
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The influence of uniaxial small-scale anisotropy on the stability of the scaling regimes and on the anomalous scaling of the structure functions of a passive scalar advected by a Gaussian solenoidal velocity field with finite correlation time is investigated by the field theoretic renormalization group and operator product expansion within one-loop approximation. Possible scaling regimes are found and classified in the plane of exponents $\epsilon-\eta$, where $\epsilon$ characterizes the energy spectrum of the velocity field in the inertial range $E\propto k^{1-2\epsilon}$, and $\eta$ is related to the correlation time of the velocity field at the wave number $k$ which is scaled as $k^{-2+\eta}$. It is shown that the presence of anisotropy does not disturb the stability of the infrared fixed points of the renormalization group equations which are directly related to the corresponding scaling regimes. The influence of anisotropy on the anomalous scaling of the structure functions of the passive scalar field is studied as a function of the fixed point value of the parameter $u$ which represents the ratio of turnover time of scalar field and velocity correlation time. It is shown that the corresponding one-loop anomalous dimensions, which are the same (universal) for all particular models with concrete value of $u$ in the isotropic case, are different (nonuniversal) in the case with the presence of small-scale anisotropy and they are continuous functions of the anisotropy parameters, as well as the parameter $u$. The dependence of the anomalous dimensions on the anisotropy parameters of two special limits of the general model, namely, the rapid-change model and the frozen velocity field model, are found when $u\to \infty$ and $u\to 0$, respectively.
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arxiv:nlin/0703063
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The linear stability of pipe flow implies that only perturbations of sufficient strength will trigger the transition to turbulence. In order to determine this threshold in perturbation amplitude we study the \emph{edge of chaos} which separates perturbations that decay towards the laminar profile and perturbations that trigger turbulence. Using the lifetime as an indicator and methods developed in (Skufca et al, Phys. Rev. Lett. {\bf 96}, 174101 (2006)) we show that superimposed on an overall $1/\Re$-scaling predicted and studied previously there are small, non-monotonic variations reflecting folds in the edge of chaos. By tracing the motion in the edge we find that it is formed by the stable manifold of a unique flow field that is dominated by a pair of downstream vortices, asymmetrically placed towards the wall. The flow field that generates the edge of chaos shows intrinsic chaotic dynamics.
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arxiv:nlin/0703067
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Kinetic energies of light fragments A <= 10 from the decay of target spectators in 197Au 197Au collisions at 1000 MeV per nucleon have been measured with high-resolution telescopes at backward angles. Except for protons and apart from the observed evaporation components, the kinetic-energy spectra exhibit slope temperatures of about 17 MeV, independent of the particle species, but not corresponding to the thermal or chemical degrees of freedom at breakup. It is suggested that these slope temperatures may reflect the intrinsic Fermi motion and thus the bulk density of the spectator system at the instant of becoming unstable. PACS numbers: 25.70.Pq, 21.65.+f, 25.70.Mn
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arxiv:nucl-ex/0003005
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Radiative decay of 21 resonances in the 55Mn(p,g)56Fe reaction was studied in the proton beam energy region Ep = 1.3 - 1.8 MeV. Branching of decay to many low lying bound states up to excitation energy Ex ~ 8 MeV was measured. Exact energy of all resonances has been established what pointed out that five of the resonances are very close doublets. For all studied resonances were determined their spin-parity charakteristics. Assignment of some resonances as isobaric analogues of the states in the 56Mn nucleus was discused and short note about energy systematics of isobaric analogue resonances was shown.
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arxiv:nucl-ex/0007008
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Experimental data from the reaction of an 8.0 GeV/c pi- beam incident on a 197Au target have been analyzed in order to investigate the integrated breakup time scale for hot residues. Alpha-particle energy spectra and particle angular distributions supported by a momentum tensor analysis suggest that at large excitation energy, above 3-5 MeV/nucleon, light-charged particles are emitted prior to or at the same time as the emission of the heavy fragments. Comparison with the SMM and GEMINI models is presented. A binary fission-like mechanism fits the experimental data at low excitation energies, but seems unable to reproduce the data at excitation energies above 3-5 MeV/nucleon.
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arxiv:nucl-ex/0009012
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As a tool for studying the structure of nuclei far off stability the technique of gamma-ray spectroscopy after low-energy single-nucleon transfer reactions with radioactive nuclear beams in inverse kinematics was investigated. Modules of the MINIBALL germanium array and a thin position-sensitive parallel plate avalanche counter (PPAC) to be employed in future experiments at REX-ISOLDE were used in a test experiment performed with a stable 36S beam on deuteron and 9Be targets. It is demonstrated that the Doppler broadening of gamma lines detected by the MINIBALL modules is considerably reduced by exploiting their segmentation, and that for beam intensities up to 10^6 particles/s the PPAC positioned around zero degrees with respect to the beam axis allows not only to significantly reduce the gamma background by requiring coincidences with the transfer products but also to control the beam and its intensity by single particle counting. The predicted large neutron pickup cross sections of neutron-rich light nuclei on 2H and 9Be targets at REX-ISOLDE energies of 2.2 MeV A are confirmed.
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arxiv:nucl-ex/0010005
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Production cross sections of charged pions, kaons and antikaons have been measured in C+C and C+Au collisions at beam energies of 1.0 and 1.8 AGeV for different polar emission angles. The kaon and antikaon energy spectra can be described by Boltzmann distributions whereas the pion spectra exhibit an additional enhancement at low energies. The pion multiplicity per participating nucleon M(pi+)/A_part is a factor of about 3 smaller in C+Au than in C+C collisions at 1.0 AGeV whereas it differs only little for the C and the Au target at a beam energy of 1.8 AGeV. The K+ multiplicities per participating nucleon M(K+)/A_part are independent of the target size at 1 AGeV and at 1.8 AGeV. The K- multiplicity per participating nucleon M(K-)/A_part is reduced by a factor of about 2 in C+Au as compared to C+C collisions at 1.8 AGeV. This effect might be caused by the absorption of antikaons in the heavy target nucleus. Transport model calculations underestimate the K-/K+ ratio for C+C collisions at 1.8 AGeV by a factor of about 4 if in-medium modifications of K mesons are neglected.
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arxiv:nucl-ex/0011010
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The dynamics of heavy-ion reactions at Fermi energies is dominated by a dissipative mechanism modified by the concurrent emission of non-statistical nucleons, light particles, and nuclear clusters. Experimental observables are available to monitor the relaxation processes driving the evolution of an interacting nuclear system towards equilibrium. Isospin degrees of freedom provide interesting new access to fundamental information on the reaction mechanism and the effective in-medium nucleonic interactions.
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arxiv:nucl-ex/0012003
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A kinematically complete measurement was made of the Coulomb dissociation of 8B nuclei on a Pb target at 83 MeV/nucleon. The cross section was measured at low relative energies in order to infer the astrophysical S factor for the 7Be(p,gamma)8B reaction. A first-order perturbation theory analysis of the reaction dynamics including E1, E2, and M1 transitions was employed to extract the E1 strength relevant to neutrino-producing reactions in the solar interior. By fitting the measured cross section from Erel = 130 keV to 400 keV, we find S17(0) = 17.8 (+1.4, -1.2) eV b.
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arxiv:nucl-ex/0101010
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This paper describes measurements of the hyperfine structure of two antiprotonic atoms that are planned at the Antiproton Decelerator (AD) at CERN. The first part deals with antiprotonic helium, a three-body system of alpha-particle, antiproton and electron that was previously studied at LEAR. A measurement will test existing three-body calculations and may - through comparison with these theories - determine the magnetic moment of the antiproton more precisely than currently available, thus providing a test of CPT invariance. The second system, antihydrogen, consisting of an antiproton and a positron, is planned to be produced at thermal energies at the AD. A measurement of the ground-state hyperfine splitting, which for hydrogen is one of the most accurately measured physical quantities, will directly yield a precise value for the magnetic moment of the antiproton, and also compare the internal structure of proton and antiproton through the contribution of the magnetic size of the antiproton to the ground state hyperfine splitting.
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arxiv:nucl-ex/0102002
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We present a measurement of the pseudorapidity density of primary charged particles near mid-rapidity in Au+Au collisions at sqrt(s_NN) = 130 GeV as a function of the number of participating nucleons. These results are compared to models in an attempt to discriminate between competing scenarios of particle production in heavy ion collisions.
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arxiv:nucl-ex/0105011
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The first results from Au-Au collisions at $\sqrt{s_{NN}}$=130 GeV obtained with the PHENIX detector in the Year 2000 run at RHIC are presented. The mid-rapidity charged particle multiplicity and transverse energy per participating nucleon rise steadily with the number of participants, such that transverse energy per charged particle remains relatively constant as a function of centrality. Identified charged hadron spectra as well as $\bar{p}/p$ and $K^+/K^-$ ratios are discussed. Charged particle and neutral pion transverse momentum distributions in peripheral nuclear collisions are consistent with point-like scaling. The spectra at high $p_t$ from central collisions are significantly suppressed when compared to a simple superposition of binary nucleon-nucleon collisions.
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arxiv:nucl-ex/0105017
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It is shown that it is just Dubna that possesses the priority both in the recent synthesis of a superheavy nucleus with charge Z = 114 (Flerov Laboratory of Nuclear Reactions, JINR) and in its theoretical prediction (Bogoliubov Laboratory of Theoretical Physics, JINR) made 33 years ago. Possible sizes of the island of stability of superheavy nuclei are discussed.
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arxiv:nucl-ex/0105021
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The recent experimental program with the out-of-plane spectrometer system (OOPS) at MIT-Bates encompassed an extensive set of $\mathrm{d}(\vec\mathrm{e},\mathrm{e}'\mathrm{p})$ measurements, investigations of the $\mathrm{N}\to\Delta$ transition using $\mathrm{p}(\vec\mathrm{e},\mathrm{e}'\mathrm{p})\pi^0$ and $\mathrm{p}(\vec\mathrm{e},\mathrm{e}'\pi^+)\mathrm{n}$ reaction channels, and studies of virtual Compton scattering (VCS) $\mathrm{p}(\mathrm{e},\mathrm{e}'\mathrm{p})\gamma$ below the pion threshold. Preliminary results are presented.
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arxiv:nucl-ex/0107010
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Multifragmentation (MF) results from 1A GeV Au on C have been compared with the Copenhagen statistical multifragmentation model (SMM). A large number of observables, including the fragment charge yield distributions, fragment multiplicity distributions, caloric curve, critical exponents, and the critical scaling function are explored in this comparison. The nature of the phase transition in SMM is studied as a function of the remnant mass and charge using the microcanonical equation of state. For light remnants $A \leq $ 100, backbending is observed indicating negative specific heat, while for $A \geq$ 170 the effective latentheat approaches zero. Thus for heavier systems this transition can be identified as a continuous thermal phase transition.
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arxiv:nucl-ex/0107015
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The effect of limiting the acceptance in rapidity on event-by-event multiplicity fluctuations in nucleus-nucleus collisions has been investigated. Our analysis shows that the multiplicity fluctuations decrease when the rapidity acceptance is decreased. We explain this trend by assuming that the probability distribution of the particles in the smaller acceptance window follows binomial distribution. Following a simple statistical analysis we conclude that the event-by-event multiplicity fluctuations for full acceptance are likely to be larger than those observed in the experiments, since the experiments usually have detectors with limited acceptance. We discuss the application of our model to simulated data generated using VENUS, a widely used event generator in heavy-ion collisions. We also discuss the results from our calculations in presence of dynamical fluctuations and possible observation of these in the actual data.
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arxiv:nucl-ex/0108011
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We report the first measurement of inclusive antiproton production at mid-rapidity in Au+Au collisions at 130 GeV by the STAR experiment at RHIC. The antiproton transverse mass distributions in the measured transverse momentum range of 0.25 < pT < 0.95 GeV/c are found to fall less steeply for more central collisions. The extrapolated antiproton rapidity density is found to scale approximately with the negative hadron multiplicity density.
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arxiv:nucl-ex/0110009
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The cross section for the $^3$He(e, e$'$d)p reaction has been measured as a function of the missing momentum $p_m$ in q$\omega$ -constant kinematics at beam energies of 370 and 576 MeV for values of the three-momentum transfer $q$ of 412, 504 and 604 \mevc. The L(+TT), T and LT structure functions have been separated for $q$ = 412 and 504 \mevc. The data are compared to three-body Faddeev calculations, including meson-exchange currents (MEC), and to calculations based on a covariant diagrammatic expansion. The influence of final-state interactions and meson-exchange currents is discussed. The $p_m$-dependence of the data is reasonably well described by all calculations. However, the most advanced Faddeev calculations, which employ the AV18 nucleon-nucleon interaction and include MEC, overestimate the measured cross sections, especially the longitudinal part, and at the larger values of $q$. The diagrammatic approach gives a fair description of the cross section, but under(over)estimates the longitudinal (transverse) structure function.
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arxiv:nucl-ex/0201011
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Cross sections and polarization transfer observables in the $^{16}$O$(p,p')$ reactions at 392 MeV were measured at several angles between $\theta_{lab}=$ 0$^\circ$ and 14$^\circ$. The non-spin-flip (${\Delta}S=0$) and spin-flip (${\Delta}S=1$) strengths in transitions to several discrete states and broad resonances in $^{16}$O were extracted using a model-independent method. The giant resonances in the energy region of $E_x=19-$27 MeV were found to be predominantly excited by ${\Delta}L=1$ transitions. The strength distribution of spin-dipole transitions with ${\Delta}S=1$ and ${\Delta}L=1$ were deduced. The obtained distribution was compared with a recent shell model calculation. Experimental results are reasonably explained by distorted-wave impulse approximation calculations with the shell model wave functions.
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arxiv:nucl-ex/0202015
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We present the results of the analysis of the hard photon production in the $^{129}${Xe}+$^{\rm nat}${Sn} at 50{\it A} MeV system studied in the GANIL E300 experiment. The energy and angular hard photon distributions confirm the existence of a thermal component which follows the recently measured thermal bremsstrahlung systematics. Exploiting the performances of our complete detection system, consisting of TAPS and 3 charged particle multidetectors, we have also measured the hard photon multiplicity as a function of the charged particle multiplicity.
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arxiv:nucl-ex/0202027
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Data from Au + Au interactions at sqrt(s_NN) = 130 GeV, obtained with the PHENIX detector at RHIC, are used to investigate local net charge fluctuations among particles produced near mid-rapidity. According to recent suggestions, such fluctuations may carry information from the Quark Gluon Plasma. This analysis shows that the fluctuations are dominated by a stochastic distribution of particles, but are also sensitive to other effects, like global charge conservation and resonance decays.
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arxiv:nucl-ex/0203014
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Two particle azimuthal correlation functions are presented for charged hadrons produced in Au + Au collisions at RHIC sqrt(s_NN) = 130 GeV. The measurements permit determination of elliptic flow without event-by-event estimation of the reaction plane. The extracted elliptic flow values v_2 show significant sensitivity to both the collision centrality and the transverse momenta of emitted hadrons, suggesting rapid thermalization and relatively strong velocity fields. When scaled by the eccentricity of the collision zone, epsilon, the scaled elliptic flow shows little or no dependence on centrality for charged hadrons with relatively low p_T. A breakdown of this epsilon scaling is observed for charged hadrons with p_T > 1.0 GeV/c for the most central collisions.
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arxiv:nucl-ex/0204005
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Differential cross sections for Compton scattering from the deuteron were measured at MAX-lab for incident photon energies of 55 MeV and 66 MeV at nominal laboratory angles of $45^\circ$, $125^\circ$, and $135^\circ$. Tagged photons were scattered from liquid deuterium and detected in three NaI spectrometers. By comparing the data with theoretical calculations in the framework of a one-boson-exchange potential model, the sum and difference of the isospin-averaged nucleon polarizabilities, $\alpha_N + \beta_N = 17.4 \pm 3.7$ and $\alpha_N - \beta_N = 6.4 \pm 2.4$ (in units of $10^{-4}$ fm$^3$), have been determined. By combining the latter with the global-averaged value for $\alpha_p - \beta_p$ and using the predictions of the Baldin sum rule for the sum of the nucleon polarizabilities, we have obtained values for the neutron electric and magnetic polarizabilities of $\alpha_n= 8.8 \pm 2.4$(total) $\pm 3.0$(model) and $\beta_n = 6.5 \mp 2.4$(total) $\mp 3.0$(model), respectively.
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arxiv:nucl-ex/0204014
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Using mainly $\vec{p}$ p $\to$ p ${\pi^+}X$ and $\vec{p}$ p $\to$ p$_{f}$~p$_{s}$ X reactions, narrow baryonic structures were observed in the mass range 950$\le$ M $\le$ 1800 MeV.
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arxiv:nucl-ex/0207004
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