Local structure-preserving methods for the generalized Rosenau-RLW-KdV equation with power law nonlinearity

Local structure-preserving algorithms including multi-symplectic, local energy-and momentum-preserving schemes are proposed for the generalized Rosenau–RLW–Kd V equation based on the multi-symplectic Hamiltonian formula of the equation. Each of the present algorithms holds a discrete conservation law in any time–space region. For the original problem subjected to appropriate boundary conditions, these algorithms will be globally conservative. Discrete fast Fourier transform makes a significant improvement to the computational efficiency of schemes. Numerical results show that the proposed algorithms have satisfactory performance in providing an accurate solution and preserving the discrete invariants.     

Bright and dark solitons of the Rosenau-Kawahara equation with power law nonlinearity

In this paper, the topological (dark) as well as non-topological (bright) soliton solutions to the Rosenau-Kawahara equation with power law nonlinearity are obtained by the solitary wave ansatz method. A couple of conserved quantities are also calculated for the case of bright soliton solution.     

Some extensions on the soliton solutions for the Novikov equation with cubic nonlinearity

In this paper, by using the bifurcation method of dynamical systems, we derive the traveling wave solutions of the nonlinear equation UU_τyy ? U_yU_τy + U²U_τ + 3U_y = 0. Based on the relationship of the solutions between the Novikov equation and the nonlinear equation, we present the parametric representations of the smooth and nonsmooth soliton solutions for the Novikov equation with cubic nonlinearity. These solutions contain peaked soliton, smooth soliton, W-shaped soliton and periodic solutions. Our work extends some previous results.     

Exact stationary solution of the master equation for systems far from thermal equilibrium in detailed balance

If the master equation (Chapman-Kolmogorov equation) has a unique solution and fulfills the principle of detailed balance it may be solved explicitly by mere summations or, in the continuous case, by quadratures.     

Analyticity of the scattering operator for the nonlinear Klein-Gordon equation with cubic nonlinearity

The wave and scattering operators for the equation $$\left( {\square + m^2 } \right)\varphi + \lambda \varphi ^2 = 0$$ withm>0 and λ>0 on four-dimensional Minkowski space are analytic on the space of finite-energy Cauchy data, i.e.L ₂ ¹ (R ³)⊕L ₂(R ³).     

Exact and explicit solutions to the discrete nonlinear Schrödinger equation with a saturable nonlinearity

We analyze the discrete nonlinear Schrödinger equation with a saturable nonlinearity through the (G^′/G)-expansion method to present some improved results. Three types of analytic solutions with arbitrary parameters are constructed; hyperbolic, trigonometric, and rational which have not been explicitly computed before.     

An alternative construction of the Percus-Yevick equation based on the equilibrium BBGKY hierarchy

The existing derivations of the Percus-Yevick equation are not readily extendable into the nonequilibrium domain. In particular, the elegant Percus functional construction relies on a test particle theorem which lacks an exact nonequilibrium generalization. We propose here a new construction which utilizes some elementary ideas of functional expansions together with the equilibrium BBGKY hierarchy of equations. Also, we feel this new construction provides fresh insight into the physical basis of the equilibrium Percus-Yevick equation.This research was supported in part by a grant from the Faculty Research Award Program of the City University of New York.     

Return to thermal equilibrium by the solution of a quantum Langevin equation

A quantum-mechanical treatment of the evolution of an anharmonic oscillator coupled to a heat bath is given. It is shown that for a certain class of anharmonic potentials the heat bath drives the oscillator to an equilibrium state, close to the quantum Gibbs state associated to the potential. Thus a partial proof is provided for a conjecture of R. Benguria and M. Kac.This paper contains part of the author's Ph.D. work, done at the Institute for Theoretical Physics of Groningen State University, Groningen, the Netherlands.     

A two-tail version of the PPS distribution with application to current account balance data

The double Pareto-positive stable (dPPS) distribution is introduced as a new model for describing countries’ global current account balance data. The dPPS distribution provides a flexible model for fitting the entire range of a set of current account data (both surplus and deficit), where zero and unimodality are possible, and the double-sided Pareto distribution is included as a particular case. Expressions for the cumulative distribution, probability density and quantile functions are given. An estimation method is discussed and a simple graphical method for studying the adequacy of the data to model is given. Finally, we consider the fit of countries’ global current account balance data for several years. The new distribution is compared with four classical models: Normal, Skew Normal, Asymmetric Laplace and Hyperbolic distributions. In all the data sets considered, the dPPS distribution outperforms the fits of these four distributions.     

Contribution to harmonic balance calculations of self-sustained periodic oscillations with focus on single-reed instruments

The harmonic balance method (HBM) was originally developed for finding periodic solutions of electronical and mechanical systems under a periodic force, but has been adapted to self-sustained musical instruments. Unlike time-domain methods, this frequency-domain method does not capture transients and so is not adapted for sound synthesis. However, its independence of time makes it very useful for studying any periodic solution, whether stable or unstable, without care of particular initial conditions in time. A computer program for solving general problems involving nonlinearly coupled exciter and resonator, HARMBAL, has been developed based on the HBM. The method as well as convergence improvements and continuation facilities are thoroughly presented and discussed in the present paper. Applications of the method are demonstrated, especially on problems with severe difficulties of convergence: the Helmholtz motion (square signals) of single-reed instruments when no losses are taken into account, the reed being modeled as a simple spring.     

Influence of octupole photoionization transitions on the angular distribution of photoelectrons from solids with account for elastic scattering

Using the transport theory approach, equations are derived for the angular dependence of XPS intensities from semi-infinite solids taking into account elastic scattering of photoelectrons and non-dipolar transitions up the second-order corrections. The unpolarized excitation source is considered. The elastic scattering is the main term smearing the non-dipolar contribution in complete analogy with smearing of dipole contribution. Some additional terms are shown to be negligible in comparison with the main term for complete sets of emission and azimuth angles, three representative single scattering albedo values and several representative sets of the second-order non-dipolar parameters. The photoelectron angular distributions are calculated for Al 2s and Ag 3d lines using transport theory and Monte-Carlo simulation. The Monte-Carlo calculations are in agreement with transport theory approach.     

Trend to equilibrium of weak solutions of the Boltzmann equation in a slab with diffusive boundary conditions

Recently R. Illner and the author proved that, under a physically realistic truncation on the collision kernel, the Boltzmann equation in the one-dimensional slab [0, 1] with general diffusive boundary conditions at 0 and 1 has a global weak solution in the traditional sense. Here it is proved that when the Maxwellians associated with the boundary conditions atx=0 andx=1 are the same MaxwellianM _w , then the solution is uniformly bounded and tends toM _w fort.     

An equation to calculate the equilibrium constant of 1:1 complexes from dielectric relaxation measurements

The dielectric measurements of 1:1 mixture of acetates, namely ethyl acetate, butyl acetate and benzyl acetate and phenol and n-butyl alcohol in carbon tetrachloride at 9.8 GHz microwave frequency were carried out. A method has been proposed to calculate the equilibrium constant of 1:1 hydrogen bonded complexes. These values are in close agreement to the values obtained using the Few and Smith method.     

Metrics for probability distributions and the trend to equilibrium for solutions of the Boltzmann equation

This paper deals with the trend to equilibrium of solutions to the spacehomogeneous Boltzmann equation for Maxwellian molecules with angular cutoff as well as with infinite-range forces. The solutions are considered as densities of probability distributions. The Tanaka functional is a metric for the space of probability distributions, which has previously been used in connection with the Boltzmann equation. Our main result is that, if the initial distribution possesses moments of order 2+, then the convergence to equilibrium in his metric is exponential in time. In the proof, we study the relation between several metrics for spaces of probability distributions, and relate this to the Boltzmann equation, by proving that the Fourier-transformed solutions are at least as regular as the Fourier transform of the initial data. This is also used to prove that even if the initial data only possess a second moment, then _v>R f(v, t) v² dv0 asR, and this convergence is uniform in time.     

A superconducting direct-current limiter with a power of up to 8 MVA

A resistive switching superconducting fault current limiter (SFCL) for DC networks with a nominal voltage of 3.5 kV and a nominal current of 2 kA was developed, produced, and tested. The SFCL has two main units—an assembly of superconducting modules and a high-speed vacuum circuit breaker. The assembly of superconducting modules consists of nine (3 × 3) parallel–series connected modules. Each module contains four parallel-connected 2G high-temperature superconducting (HTS) tapes. The results of SFCL tests in the short-circuit emulation mode with a maximum current rise rate of 1300 A/ms are presented. The SFCL is capable of limiting the current at a level of 7 kA and break it 8 ms after the current-limiting mode begins. The average temperature of HTS tapes during the current-limiting mode increases to 210 K. After the current is interrupted, the superconductivity recovery time does not exceed 1 s.