Screening in ionic systems: simulations for the Lebowitz length

Simulations of the Lebowitz length, xiL (T, rho), are reported for the restricted primitive model hard-core (diameter a) 1:1 electrolyte for densities rho approximately < 4rho(c) and T(c) approximately < T approximately < 40T(c). Finite-size effects are elucidated for the charge fluctuations in various subdomains that serve to evaluate xiL. On extrapolation to the bulk limit for T approximately > 10T(c) the exact low-density expansions are seen to fail badly when rho > 1/10 rho(c) (with rho(c)a3 approximately = 0.08). At higher densities xiL rises above the Debye length, xiD proportional to square root(T/rho), by 10%-30% (up to rho approximately =1.3rho(c)); the variation is portrayed fairly well by the generalized Debye-Hückel theory. On approaching criticality at fixed rho or fixed T, xiL (T, rho) remains finite with xiL(c) approximately = 0.30a approximately = 1.3xiD(c) but displays a weak entropylike singularity.     

Particle chaos in the Earth's magnetotail

Nonlinear particle dynamics is studied both in current sheets and near neutral lines. The parameter governing particle chaos in a current sheet with a constant normal component, B(n), is kappa=(R(min)/rho(max))(1/2), where R(min) is the minimum field line radius of curvature and rho(max) is the maximum gyroradius. In such a current sheet, motion can be viewed as a combination of a component normal to the current sheet and a tangential component. The parameter kappa represents the ratio of the characteristic time scale of the normal component to the tangential, and thus, particle chaos is maximized for kappa approximately 1. For kappa<1, the slow motion preserves the action integral of the fast motion, J(z), except near the separatrix, the phase space boundary separating motion that crosses the current sheet midplane from that which does not. Near a linear neutral line, it is found that the parameter b(n), which is the ratio of the characteristic vertical and horizontal field strengths, rather than kappa governs particle chaos. In the limit b(n)<1, the slow motion again preserves J(z), and J(z) has the same analytic form as in a constant B(n) current sheet. In the limit of b(n)<1, the structure of x-p(x) phase space is controlled by the stable and unstable manifolds associated with the unstable fixed point orbit at (x,p(x))=(0,0), and this structure lies along a contour of constant J(z).     

R(1rho) relaxation for two-site chemical exchange: general approximations and some exact solutions

Analytic expressions for the nuclear magnetic spin relaxation rate constant for magnetization spin-locked in the rotating reference frame under an applied radiofrequency field, R(1rho), are obtained for two-site chemical exchange. The theoretical approach is motivated by Laguerre's method and obtains R(1rho) as the root of a (p1,q1) Padé approximant. The general formula for R(1rho) obtained by this approach is substantially simpler than existing expressions and is equally or slightly more accurate, in most cases. In addition, particular solutions for the R(1rho) rate constant are presented for two special cases: equal populations of the two exchanging sites, or placement of the radiofrequency carrier at the average resonance frequency of the two sites. The solutions are exact when the R1 and R2 relaxation rate constants are identical, and nearly exact under realistic experimental conditions.     

Precise simulation of near-critical fluid coexistence

We present a novel method to derive liquid-gas coexisting densities, rho(+/-)(T), from grand canonical simulations (without knowledge of T(c) or criticality class). The minima of Q(L) identical with (2)(L)/(L) in an LxLxL box with m=rho-(L) are used to generate recursively an unbiased universal finite-size scaling function. Monte Carlo data for a hard-core square-well fluid and for the restricted primitive model electrolyte yield rho(+/-) to +/-1%-2% of rho(c) down to 1 part in 10(4)-10(3) of T(c) (and confirm well Ising character). Pressure mixing in the scaling fields is unequivocally revealed and indicates Yang-Yang ratios R(mu)=-0.04(4) and 0.2(6) for the two models, respectively.     

Multispecies pair annihilation reactions

We consider diffusion-limited reactions A(i)+A(j)--> (1< or =i2 and d> or =2, we argue that the asymptotic density decay for such mutual annihilation processes with equal rates and initial densities is the same as for single-species pair annihilation A+A-->. In d=1, however, particle segregation occurs for all q< infinity. The total density decays according to a q dependent power law, rho(t) approximately t(-alpha(q)). Within a simplified version of the model alpha(q)=(q-1)/2q can be determined exactly. Our findings are supported through Monte Carlo simulations.     

Coexistence and criticality in size-asymmetric hard-core electrolytes

Liquid-vapor coexistence curves and critical parameters for hard-core 1:1 electrolyte models with diameter ratios lambda = sigma(-)/sigma(+) = 1 to 5.7 have been studied by fine-discretization Monte Carlo methods. Normalizing via the length scale sigma(+/-) = 1 / 2(sigma(+)+sigma(-)), relevant for the low densities in question, both T(*)(c) ( = k(B)T(c)sigma(+/-)/q(2)) and rho(*)(c) ( = rho(c)sigma(3)(+/-)) decrease rapidly (from approximately 0.05 to 0.03 and 0.08 to 0.04, respectively) as lambda increases. These trends, which unequivocally contradict current theories, are closely mirrored by results for tightly tethered dipolar dimers (with T(*)(c) lower by approximately 0%-11% and rho(*)(c) greater by 37%-12%).     

A lot of strange attractors: chaotic or not?

Iterations on R given by quasiperiodic displacement are closely linked with the quasiperiodic forcing of an oscillator. We begin by recalling how these problems are related. It enables us to predict the possibility of appearance of strange nonchaotic attractors (SNAs) for simple increasing maps of the real line with quasiperiodic displacement. Chaos is not possible in this case (Lyapounov exponents cannot be positive). Studying this model of iterations on R for larger variations, beyond critical values where it is no longer invertible, we can get chaotic motions. In this situation we can get a lot of strange attractors because we are able to smoothly adjust the value of the Lyapounov exponent. The SNAs obtained can be viewed as the result of pasting pieces of trajectories, some of which having positive local Lyapounov exponents and others having negative ones. This leads us to think that the distinction between these SNAs and chaotic attractors is rather weak.     

Topology of electronic charge density and energetics of planar faults in fcc metals

Using ab initio calculations we have studied the energetics and the evolution of the electronic charge density with shear in three fcc metals exhibiting different deformation properties, aluminum, silver, and iridium. The charge redistribution described by the change in character of specific charge density critical points (cps), is ascertained from the values of the charge density, rho(0), and its three principal curvatures, rho( parallel parallel), rho(hh), and rho(vv), respectively. The change in character of cps correlates with the energetics. For all three metals, rho(hh) vanishes near the unstable stacking configuration. The symmetry or asymmetry of the charge redistribution, measured by rho(hh)/rho(vv), may be an important factor determining stacking fault energies.     

Distribution of fixed-point energies of a quasiperiodic Hamiltonian flow

Energy distributions rho(+/-)(E) for the elliptic and hyperbolic fixed points of the Hamiltonian H(x,y)= summation operator (k=0) (4) cos [x cos(2pik/5)+y sin(2pik/5)] are calculated as integrals over a one-dimensional manifold M(E) in five-dimensional space. Singular points of M(E) produce three logarithmic singularities of rho(+/-)(E), and vanishing of connected components of M(E) gives rise to three discontinuities. The strengths of the singularities and discontinuities of rho(+/-)(E) are determined analytically, and the distributions are evaluated numerically for representative points in the nonsingular intervals. The calculation provides an explicit realization of general theorems concerning the critical points of infinitely smooth functions defined on an n-dimensional torus and restricted to a k-dimensional linear subset. Formally the calculation resembles the determination of the density of states of a dynamical system with one degree of freedom on a 2-torus, but with important differences due to topology and symmetry.     

Computation of hierarchical renormalization-group fixed points and their ε-expansions

We compute hierarchical renormalization-group fixed points as solutions to an algebraic equation for the coupling constants. This method does not rely on an iteration of renormalization-group transformations and therefore avoids the problem of fine tuning. We solve truncated versions of the fixed-point equation numerically for different values of the dimension parameter in the range 2<d<4 and different orders of truncations. The method is well suited even for multicritical fixed points with any number of unstable directions. Precise numerical data are presented for the first three nontrivial fixed points and their critical indices. We also develop an -expansion for the hierarchical models using computer algebra. The numerical results are compared with the -expansion.     

Crystalline ground states for classical particles

Pair interactions whose Fourier transform is non-negative and vanishes above a wave number K(0) are shown to give rise to periodic and aperiodic infinite volume ground state configurations (GSCs) in any dimension d. A typical three-dimensional example is an interaction of asymptotic form cosK(0)r/r(4). The result is obtained for densities rho > or = rho(d), where rho(1) = K(0)/2(pi), rho(2) = (sq.rt(3)/8)(K(0)/pi)(2), and rho(3) = (1/8sq.rt(2)) x (K(0)/pi)(3). At rho(d) there is a unique periodic GSC which is the uniform chain, the triangular lattice, and the bcc lattice for d = 1,2,3, respectively. For rho > rho(d), the GSC is nonunique and the degeneracy is continuous: Any periodic configuration of density rho with all reciprocal lattice vectors not smaller than K(0), and any union of such configurations, is a GSC. The fcc lattice is a GSC only for rho > or = (1/6 sq.rt(3)) x (K(0)/pi)(3).     

Heteroclinic primary intersections and codimension one Melnikov method for volume-preserving maps

We study families of volume preserving diffeomorphisms in R(3) that have a pair of hyperbolic fixed points with intersecting codimension one stable and unstable manifolds. Our goal is to elucidate the topology of the intersections and how it changes with the parameters of the system. We show that the "primary intersection" of the stable and unstable manifolds is generically a neat submanifold of a "fundamental domain." We compute the intersections perturbatively using a codimension one Melnikov function. Numerical experiments show various bifurcations in the homotopy class of the primary intersections. (c) 2000 American Institute of Physics.     

Dynamical symmetry breaking as the origin of the zero-dc-resistance state in an ac-driven system

Under a strong ac drive the zero-frequency linear response dissipative resistivity rho(d)(j=0) of a homogeneous state is allowed to become negative. We show that such a state is absolutely unstable. The only time-independent state of a system with a rho(d)(j=0)<0 is characterized by a current which almost everywhere has a magnitude j(0) fixed by the condition that the nonlinear dissipative resistivity rho(d)(j(2)(0))=0. As a result, the dissipative component of the dc-electric field vanishes. The total current may be varied by rearranging the current pattern appropriately with the dissipative component of the dc-electric field remaining zero. This result, together with the calculation of Durst et al., indicating the existence of regimes of applied ac microwave field and dc magnetic field where rho(d)(j=0)<0, explains the zero-resistance state observed by Mani et al. and Zudov et al.     

Plasmons in Finite Three-Tile Quasiperiodic Superlattices: On-Site Model

We investigate the plasmon spectrum of a finite semiconductor superlattice in which the quantum wells are located at periodic sites but the electron densities are arranged in a three-tile quasiperiodic sequence. It is found that the branching rule of the on-site model is different from that of the transfer model. The quasiperiodic arrangement of the electron densities results in a number of surface modes. The localization of the modes is discussed.     

Shock Fluctuations for the Hammersley Process

We consider the Hammersley interacting particle system starting from a shock initial profile with densities \(\rho ,\lambda \in {\mathbb R}\) (\( \rho < \lambda \)). The microscopic shock is taken as the position of a second-class particle initially at the origin, and the main results are: (i) a central limit theorem for the shock; (ii) the variance of the shock equals \(2[\lambda \rho (\lambda - \rho )]^{-1}t + O(t^{2/3})\). By using the same method of proof, we also prove similar results for first-class particles.     

High-field quasiparticle tunneling in Bi2Sr2CaCu2O(8+delta): negative magnetoresistance in the superconducting state

We report on the c-axis resistivity rho(c)(H) in Bi(2)Sr(2)CaCu(2)O(8+delta) that peaks in quasistatic magnetic fields up to 60 T. By suppressing the Josephson part of the two-channel (Cooper pair/quasiparticle) conductivity sigma(c)(H), we find that the negative slope of rho(c)(H) above the peak is due to quasiparticle tunneling conductivity sigma(q)(H) across the CuO2 layers below H(c2). At high fields (a) sigma(q)(H) grows linearly with H, and (b) rho(c)(T) tends to saturate ( sigma(c) not equal0) as T-->0, consistent with the scattering at the nodes of the d-wave gap. A superlinear sigma(q)(H) marks the normal state above T(c).     

Multistability of twisted states in non-locally coupled Kuramoto-type models

A ring of N identical phase oscillators with interactions between L-nearest neighbors is considered, where L ranges from 1 (local coupling) to N/2 (global coupling). The coupling function is a simple sinusoid, as in the Kuramoto model, but with a minus sign which has a profound influence on its behavior. Without the limitation of the generality, the frequency of the free-running oscillators can be set to zero. The resulting system is of gradient type, and therefore, all its solutions converge to an equilibrium point. All so-called q-twisted states, where the phase difference between neighboring oscillators on the ring is 2πq/N, are equilibrium points, where q is an integer. Their stability in the limit N → ∞ is discussed along the line of Wiley et al. [Chaos 16, 015103 (2006)] In addition, we prove that when a twisted state is asymptotically stable for the infinite system, it is also asymptotically stable for sufficiently large N. Note that for smaller N, the same q-twisted states may become unstable and other q-twisted states may become stable. Finally, the existence of additional equilibrium states, called here multi-twisted states, is shown by numerical simulation. The phase difference between neighboring oscillators is approximately 2πq/N in one sector of the ring, -2πq/N in another sector, and it has intermediate values between the two sectors. Our numerical investigation suggests that the number of different stable multi-twisted states grows exponentially as N → ∞. It is possible to interpret the equilibrium points of the coupled phase oscillator network as trajectories of a discrete-time translational dynamical system where the space-variable (position on the ring) plays the role of time. The q-twisted states are then fixed points, and the multi-twisted states are periodic solutions of period N that are close to a heteroclinic cycle. Due to the apparently exponentially fast growing number of such stable periodic solutions, the system shows spatial chaos as N → ∞.     

p-adic dynamics

The quadratic map overp-adic numbers is studied in some detail. We prove that near almost all indifferent fixed points it is topologically conjugate to a quasiperiodic linear map. We also establish the existence of chaotic behavior and describe it using symbolic dynamics.     

Stochastic Transport of Magnetic Field Lines in the Symmetric Tokamap

The topological structure and the statistical properties of stochastic magnetic fields are investigated on the basis of the so called tokamap. First, a monotonic safety factor (q‐profile) is assumed. As it is demonstrated, the transition from the continuous model to the discrete mapping in its symmetric form is essential, not only for the symplectic structure, but also for the precise values characterizing the transition to chaos (e.g. the break‐up of the KAM surfaces) in applications. Statistical properties of the symmetric tokamap, such as escape rates and anomalous diffusion properties, are being presented. By a systematic procedure the stable and unstable manifolds of the periodic hyperbolic fixed points and the resulting homoclinic tangles (stochastic layers) are determined. The latter are important for the magnetic field line transport. For a non‐monotonic q‐profile, the differences between the symmetric and non‐symmetric revtokamap become also significant. The symmetric revtokamap represents an open nonlinear dynamical system which is characterized here with the relevant tools. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

New perspective on cosmic coincidence problems

Cosmological data suggest that we live in an interesting period in the history of the universe when rho(Lambda) approximately rho(M) approximately rho(R). The occurrence of any epoch with such a "triple coincidence" is puzzling, while the question of why we happen to live during this special epoch is the "Why now?" problem. We introduce a framework which makes the triple coincidence inevitable; furthermore, the "Why now?" problem is transformed and greatly ameliorated. The framework assumes that the only relevant mass scales are the electroweak scale M(EW), and the Planck scale M(Pl) and requires rho(1/4)(Lambda) approximately M(2)(EW)/M(Pl) parametrically. Assuming that the true vacuum energy vanishes, we present a simple model, where a false vacuum energy yields a cosmological constant of this form.