Effect of an external action on a pair distribution function in a steady state

An external action that reduces a two-component equilibrium thermodynamic system to a nonequilibrium steady state with scalar fluxes has been studied. A system of integrodifferential equations for pair correlation functions has been obtained. These equations coincide with the second equations of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, but with different effective temperatures. Thus, ordinary integrodifferential equations for a pair correlation function with effective temperatures expressed in terms of the perturbed (nonequilibrium) Maxwellian momentum distribution function can be used to calculate the structural and thermodynamic properties of such a system.     

Painlevé Integrability of Nonlinear Schrödinger Equations with bothSpace- and Time-Dependent Coefficients

We investigate the Painlevé integrability of nonautonomous nonlinearSchrödinger (NLS) equations with both space- and time-dependent dispersion, nonlinearity, and external potentials. The Painlevé analysis is carried out without using the Kruskal's simplification, which results in more generalized form of inhomogeneous equations. The obtained equations are shown to be reducible to the standard NLS equation by using a point transformation. We also construct the corresponding Lax pair and carry out its Kundu-type reduction to the standard Lax pair. Special cases of equations from choosing limited form of coefficients coincide with the equations from the previous Painlevé analyses and/or become unknown new equations.     

On perturbations of solutions of the Einstein-Maxwell equations

By using the expressions for the solutions of the Einstein-Maxwell equations in terms of potentials, valid in the case where the spacetime admits a shear-free geodesic null congruence and the electromagnetic field is aligned to it, we show that a pair of complex potentials generates simultaneous perturbations of the gravitational and the electromagnetic fields. We also show that if the background electromagnetic field is null, then the pair of complex potentials is determined by a pair of coupled, linear, second-order differential equations.     

The C-number treatment for one-photon absorptive optical bistability in Fabry-Perot cavity

The problem of optical bistability in a standing wave cavity in the steady state leads to a pair of coupled, nonlinear, ordinary differential equations for the forward and backward waves. Here an approach different from the truncation of hierarchy and spatial average is applied to obtain this pair of equations. The results are compared with those obtained from the other approaches.     

Rogue-wave pair and dark-bright-rogue wave solutions of the coupled Hirota equations

Novel explicit rogue wave solutions of the coupled Hirota equations are obtained by using the Darboux transformation.In contrast to the fundamental Peregrine solitons and dark rogue waves, we present an interesting rogue-wave pair that involves four zero-amplitude holes for the coupled Hirota equations. It is significant that the corresponding expressions of the rogue-wave pair solutions contain polynomials of the fourth order rather than the second order. Moreover, dark-brightrogue wave solutions of the coupled Hirota equations are given, and interactions between Peregrine solitons and dark-bright solitons are analyzed. The results further reveal the dynamical properties of rogue waves for the coupled Hirota equations.     

Dynamical behaviour of transverse plasmons in pair plasmas

This paper analytically investigates the nonlinear behaviour of transverse plasmons in pair plasmas on the basis of the nonlinear governing equations obtained from Vlasov--Maxwell equations. It shows that high frequency transverse plasmons are modulationally unstable with respect to the uniform state of the pair plasma. Such an instability would cause wave field collapse into a localized region. During the collapse process, ponderomotive expulsion is greatly enhanced for the increase of wave field strength, leading to the formation of localized density cavitons which are significant for the future experimental research in the interaction between high frequency electromagnetic waves and pair plasmas.     

The appearance and development of turbulence in a flow past a sphere: Problems and the existing approaches to their solution

The results of the direct numerical integration of the Navier-Stokes equations and integration of the pair functions theory equations are evaluated against experimental data for the problem of a flow past a hard sphere at rest in an unstable regime. Calculations based on the Navier-Stokes equations satisfactorily reproduced three stable medium states observed for a flow past a sphere. In agreement with experiment, each of these three states begins to develop after stability loss in its own direction different from those characteristic of the other states. Calculations were, however, incapable of reproducing any of the three directions of turbulence development recorded experimentally. Most likely, the reason for this is the Navier-Stokes equations themselves. The possibility is discussed that the assumption made in the derivation of the Boltzmann equation, namely, the molecular chaos hypothesis (Stosszahlansatz), may be responsible for the failure of classic hydrodynamics. This assumption is a closure to the Boltzmann equation that allows hydrodynamics to be constructed on the lower three hydrodynamic values. The inaccuracy mentioned introduced no substantial error into stable flow calculations. The error, however, increased rapidly after stability loss. We suggest the use of hydrodynamic equations based on pair functions theory as an alternative to the Navier-Stokes equations for unstable modes. These equations are derived without invoking any additional assumptions such as the Stosszahlansatz hypothesis. As distinct from classic hydrodynamics equations, pair functions theory equations predict the direction of turbulence development close to that observed experimentally.     

Direct calculation of ionization energies

The advantages of the propagator formalism, as a direct method of calculating ionization energies, are stressed. The propagator equations are derived for closed-shell systems using an operator method instead of the usual diagrammatic derivations. The equations enable the development of an interpretation of the ionization energies in terms of conceptually simple quantities, such as pair correlation energies and associated relaxation effects, and retain the idea of orbital ionization. Infinite summations appearing in the self-energy terms are replaced by finite expressions involving functions satisfying uncoupled inhomogeneous differential equations. Certain high-order propagator equations are derived, and a connection with the Bethe-Goldstone formulation of pair correlation is made. Several computational procedures are advocated as forming the basis for balanced calculations of atomic and molecular ionization energies.     

Derivation of quantum Maxwell equations from relativistic particle Hamiltonian

Given the Hamiltonian forN relativistic particles with charges and intrinsic magnetic moments interacting via pair potentials and self-interactions, we derive not only the particle equations, but also the full set of Maxwell's equations, thereby testing the consistency of particle equations, currents, and field equations in the Heisenberg picture.     

非线性激发的磁激子对的振荡特性

通过分析放置于微波谐振腔中的磁有序晶体中的磁激子对激励过程，推导出了磁激子对的运动方程，发现磁激子对不能被认为是两个单个的磁激子的一般组成，而是可以整体的看作为一个具有非线性行为的单模谐振子.依据微波谐振腔与磁激子对集体形成的谐振器之间的耦合作用的机理，可以定性解释在有关磁激子对激励实验中所出现的双峰现象.     

Constraints and Soliton Solutions for KdV Hierarchy and AKNS Hierarchy

It is well-known that the finite-gap solutions of the KdV equationcan be generated by its recursion operator.We generalize the result to a special form of Lax pair,from which a method to constrain the integrable system to alower-dimensional or fewer variable integrable system is proposed.A direct result is that the n-soliton solutions of the KdV hierarchy can be completely depictedby a series of ordinary differential equations (ODEs), which may be gotten by a simple but unfamiliar Lax pair. Furthermore the AKNS hierarchy is constrained to a series of univariate integrable hierarchies. The key is a special form of Lax pair for the AKNS hierarchy. It is proved that under the constraints all equations of the AKNS hierarchy are linearizable.     

Relativistic Two-Boson System in Presence of Electromagnetic Plane Wave

The relativistic two-body problem is considered for spinless particles subject to an external electromagnetic field. When this field is made of the monochromatic superposition of two counter-propagating plane waves (and provided the mutual interaction between particles is known), it is possible to write down explicitly a pair of coupled wave equations (corresponding to a pair of mass-shell constraints) which takes into account also the field contribution. These equations are manifestly covariant; constants of the motion are exhibited, so one ends up with a reduced problem involving five degrees of freedom.     

Invasion and Extinction in the Mean Field Approximation for a Spatial Host-Pathogen Model

We derive the mean field equations of a simple spatial host-pathogen, or predator-prey, model that has been shown to display interesting evolutionary properties. We compare these equations, and the equations including pair-correlations, with the low-density approximations derived by other authors. We study the process of invasion by a mutant pathogen, both in the mean field and in the pair approximation, and discuss our results with respect to the spatial model. Both the mean field and pair correlation approximations do not capture the key spatial behaviors—the moderation of exploitation due to local extinctions, preventing the pathogen from causing its own extinction. However, the results provide important hints about the mechanism by which the local extinctions occur.     

Manakov solitons in biased photorefractive polymer

The coupled equations for the incoherently coupled soliton pairs in biased photorefractive polymer are provided. It is shown that the coupled soliton equations reduce to Manakov equations when the total intensity of two coupled solitons is much lower than the background illumination. The bright-bright, dark-dark, and grey-grey soliton pair solutions of these Manakov equations are obtained, and the characteristics of these Manakov solitons are also discussed.     

Kinetische Herleitung verallgemeinerter NERNST-PLANCK-Gleichungen. II.

The equations of motion derived in part I contain three terms, which don't allow the immediate application of these equations: The pressure tensors, the collective force in the equation of the pair distributions, and the term containing the short range interaction. The latter can be transformed, with the help of an assumption concerning the macroscopic state of the system, into the first moments of Boltzmann collision operators. These operators and the pressure tensors are evaluated in the hydrodynamic approximation. From the assumption concerning the macroscopic state it follows that the three particle densities are functionals of the pair distributions. Thus one has a closed system of equations for the densities, the pairdensities, the mean velocities and the correlation velocities.     

Does the “two-level atom” picture of a josephson junction have a theoretical foundation in BCS?

Yes, except that the rigorous equations are nonlocal and involve the internal pair coordinates.     

Inflationary Brans-Dicke universe andG

In a recent paper, Mathiazhagan and Johri reduced the field equations for an isotropic, homogeneous, and almost flat universe with a constant vacuum-energy density by Brans-Dicke theory to a pair of coupled differential equations. They also obtained a particular solution of these equations. Further, they used this particular solution of the equations to estimate the value of the gravitational constant. Here we obtain the complete set of solutions of the above-mentioned coupled differential equations and improved the estimate of Mathiazhagan and Johri of the gravitational constant.     

System of differential equations in the momentum space for a three-body problem

A form of three-boson Skornyakov-Ter-Martirosyan equations differential in the momentum space is proposed. This form makes it possible to directly use the Danilov condition for self-adjointness of the three-particle Hamiltonian with zero-range pair interactions. The numerical solution for the system of differential equations of the Heun class is compared with the solutions for the Faddeev equations for the problem of determining the helium trimer spectrum.