Accumulation of embedded solitons in systems with quadratic nonlinearity

Previous numerical studies have revealed the existence of embedded solitons (ESs) in a class of multiwave 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 Wentzel-Kramers-Brillouin 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, -65, and a fairly good approximation for the numerical factor in front of the scaling term.     

Discussion on Weakly Bound States of Three-Body Systems

The equivalent two-body method for a three-body system has been generalized to an arbitrary three-body system with short-range two-body interactions. An analytical expression for the long-range effective potential is obtained for the Gaussian potential, the Yukawa potential and the exponential potential. The asymptotic behavior of the effective potential at very large distance is found to be universal and an explanation on the significance of universality is given. The weakly bound excited state for the system is first obtained although there is no bound state for two-body subsystems.     

Existence and Asymptotic Stability of Periodic Solutions of the Reaction–Diffusion Equations in the Case of a Rapid Reaction

A singularly perturbed periodic in time problem for a parabolic reaction-diffusion equation in a two-dimensional domain is studied. The case of existence of an internal transition layer under the conditions of balanced and unbalanced rapid reaction is considered. An asymptotic expansion of a solution is constructed. To justify the asymptotic expansion thus constructed, the asymptotic method of differential inequalities is used. The Lyapunov asymptotic stability of a periodic solution is investigated.     

Free energy of quenched binary alloys and the time evolution of their structure function

An idea about the free energy of a binary alloy system under phase separation at low temperatures is discussed. Slow asymptotic decays in the structure functions for both a conserved and a non-conserved order parameter are studied.     

Quadratic maps without asymptotic measure

An interval map is said to have an asymptotic measure if the time averages of the iterates of Lebesgue measure converge weakly. We construct quadratic maps which have no asymptotic measure. We also find examples of quadratic maps which have an asymptotic measure with very unexpected properties, e.g. a map with the point mass on an unstable fix point as asymptotic measure. The key to our construction is a new characterization of kneading sequences.     

On the current-voltage characteristic of the oxide process

The transport equations that simulate the passage of the ionic current through an oxide layer under Steady-state conditions have been investigated. These equations are integrated by the method of matched asymptotic expansions. An analysis of the current-voltage characteristic of the system has revealed a region with negative differential conductivity. On this basis, it has been argued that the system is characterized by an instability of the initially uniform distribution of the electric current, which, in turn, leads to the appearance of “current filaments.” The threshold value of this instability is determined.     

There are no Magnetically Charged Particle-like Solutions of the Einstein Yang-Mills Equations for Models with an Abelian Residual Group

We prove that there are no magnetically charged particle-like solutions for any model with an Abelian residual group in Einstein Yang-Mills, but for the non-Abelian models the possibility remains open. An analysis of the Lie algebraic structure of the Yang-Mills fields is essential to our results. In one key step of our analysis we use invariant polynomials to determine which orbits of the gauge group contain the possible asymptotic Yang-Mills field configurations. Together with a new horizontal/vertical space decomposition of the Yang-Mills fields this enables us to overcome some obstacles and complete a dynamical system existence theorem for asymptotic solutions with nonzero total magnetic charge. We then prove that these solutions cannot be extended globally for Abelian models and begin an investigation of the details for non-Abelian models.     

Mass Transfer Induced by a Wave Perturbation on the Surface of the Velocity Field Tangential Discontinuity

An analytical asymptotic model of relative mass transfer in a system of two ideal immiscible unmixed liquids with a capillary gravitational periodic wave propagating over the interface has been constructed.     

Observation of laser speckle effects and nonclassical kinetics in an elementary chemical reaction

An experimental demonstration is provided for memory-based, nonclassical reaction kinetics in a homogeneous system with an elementary reaction, A+B-->C. A new reaction-kinetics regime is observed which is a direct consequence of speckles in the laser beam. However, in spite of the nonrandom, speckled initial distribution of reactant B, the long-time regime gives the first experimental demonstration of the asymptotic self-segregation ("Zeldovich") effect. Monte Carlo simulation results are consistent with the experiments.     

Synchronization of hyperchaotic Chen systems: a class of the adaptive control approach

The synchronization of hyperchaotic Chen systems is considered. An adaptive synchronization approach and a cascade adaptive synchronization approach are presented to synchronize a drive system and a response system. By utilizing an adaptive controller based on the dynamic compensation mechanism, exact knowledge of the systems is not necessarily required, and the synchronous speed is controllable by tuning the controller parameters. Sufficient conditions for the asymptotic stability of the two synchronization schemes are derived. Numerical simulation results demonstrate that the adaptive synchronization scheme with four control inputs and the cascade adaptive synchronization scheme with only one control signal are effective and feasible in chaos synchronization of hyperchaotic systems.     

基于观测器的混沌广义同步解析设计

提出用改进的状态观测器研究混沌广义同步问题.采用解析法求得了混沌广义同步的响应系统.从状态观测器理论，得到驱动和响应系统全局渐进线性广义同步的充分条件.以超混沌R?ssler系统为例，数值研究了该同步方法.结果表明了它的有效性. 关键词： 混沌 广义同步 状态观测器 R?ssler系统     

Structure of modes of smoothly irregular three-dimensional integrated optical four-layer waveguide

An asymptotic method is used for researching an integrated optical multilayer waveguide satisfying the condition of the smooth modification of the shape of the studied three-dimensional structure. Three-dimensional fields of smoothly deforming modes of the integrated optical waveguide are described analytically. An evident dependence of the contributions that the first order of smallness makes to the amplitudes of the electrical and magnetic fields of the quasi-waveguide modes is obtained. The canonical type of equations describing the propagation of quasi-TE and quasi-TM modes in the smoothly irregular part of a four-layer integrated optical waveguide is represented for an asymptotic method. With the help of the method of coupled waves and the perturbation theory method, the shifts of complex propagation constants for quasi-TE and quasi-TM modes are obtained in an explicit form. The elaborated theory is applicable for an analysis of similar structures of dielectric materials, magnetic materials, and metamaterials over a wide enough range of electromagnetic wavelengths.     

Phase transition in the generalized Ising-Kosterlitz-Thouless model

The features of the phase transition are considered in a model that is a combination of the Ising and Kosterlitz-Thouless models. It is shown that one or two successive phase transitions may occur in such a system, depending on the relation between parameters. An asymptotic formula is derived for the Ising-type phase transition temperature.     

近场光学理论初探

给出了非辐射场积分式的逐渐逼近表达式，阐明了非辐射场与辐射场一样受到光学信息传递系统的制约，同时阐明了图像畸变的原因．还给出了该系统信息传输自由度的计算公式，阐明了分辨率与光信息传输自由度的关系． 关键词：     

ASYMPTOTIC APPROACH FOR NON-LINEAR PERIODICAL VIBRATIONS OF CONTINUOUS STRUCTURES

An asymptotic approach for determining periodic solutions of non-linear vibration problems of continuous structures (such as rods, beams, plates, etc.) is proposed. Starting with the well-known perturbation technique, the independent displacement and frequency is expanded in a power series of a natural small parameter. It leads to infinite systems of interconnected non-linear algebraic equations governing the relationships between modes, amplitudes and frequencies. A non-trivial asymptotic technique, based on the introduction of an artificial small parameter is used to solve the equations. An advantage of the procedure is the possibility to take into account a number of vibration modes. As examples, free longitudinal vibrations of a rod and lateral vibrations of a beam under cubically non-linear restoring force are considered. Resonance interactions between different modes are investigated and asymptotic formulae for corresponding backbone curves are derived.     

Rotational friction coefficient of a permeable cylinder in a viscous fluid

An exact expression is derived for the rotational friction coefficient of a cylinder of infinite length and constant permeability immersed in an incompressible viscous fluid. An asymptotic expression for the translational friction coefficient of a permeable cylinder moving in a sheet of viscous fluid embedded on both sides in a fluid of much lower viscosity is also given.     

Theory of formation of second-phase particles as a result of diffusive saturation of solid solutions

A complete system of canonical equations, which describes the precipitation of new-phase particles as a result of diffusive saturation, is formulated. An asymptotic solution of this system of equations with respect to time is obtained in the general form. The volume of the precipitated new phase and the motion of the boundary of a two-phase region at a given point in the crystal is found for sufficiently large times to be independent of the nucleation mechanism and of the mechanism of mass to the particles of the precipitated phase.     

Asymptotic Entanglement Sudden Death in Two Atoms with Dipole–Dipole and Ising Interactions Coupled to a Radiation Field at Non-Zero Detuning

We investigate the time evolution and asymptotic behavior of a system of two two-level atoms (qubits) interacting off-resonance with a single mode radiation field. The two atoms are coupled to each other through dipole–dipole as well as Ising interactions. An exact analytic solution for the system dynamics that spans the entire phase space is provided. We focus on initial states that cause the system to evolve to entanglement sudden death (ESD) between the two atoms. We find that combining the Ising and dipole–dipole interactions is very powerful in controlling the entanglement dynamics and ESD compared with either one of them separately. Their effects on eliminating ESD may add up constructively or destructively depending on the type of Ising interaction (Ferromagnetic or anti-Ferromagnetic), the detuning parameter value, and the initial state of the system. The asymptotic behavior of the ESD is found to depend substantially on the initial state of the system, where ESD can be entirely eliminated by tuning the system parameters except in the case of an initial correlated Bell state. Interestingly, the entanglement, atomic population and quantum correlation between the two atoms and the field synchronize and reach asymptotically quasi-steady dynamic states. Each one of them ends up as a continuous irregular oscillation, where the collapse periods vanish, with a limited amplitude and an approximately constant mean value that depend on the initial state and the system parameters choice. This indicates an asymptotic continuous exchange of energy (and strong quantum correlation) between the atoms and the field takes place, accompanied by diminished ESD for these chosen setups of the system. This system can be realized in spin states of quantum dots or Rydberg atoms in optical cavities, and superconducting or hybrid qubits in linear resonators.     

Soliton Asymptotics of Solutions of the Sine-Gordon Equation

An asymptotic analysis of the Marchenko integral equation for the sine-Gordon equation is presented. The results are used for a construction of soliton asymptotics of decreasing and some non-decreasing solutions of the sine-Gordon equation. The soliton phases are shown to have an additional shift with respect to the reflectionless case caused by the non-zero reflection coefficient of the corresponding Dirac operator. Explicit formulas for the phases are also obtained. The results demonstrate an interesting phenomenon of splitting of non-decreasing solutions into an infinite series of asymptotic solitons.     

A hyperchaotic system stabilization via inverse optimal control and experimental research

In this paper, some basic dynamical properties of a four-dimensional autonomous hyperchaotic system are investigated by means of Poincar′e mapping, Lyapunov exponents and bifurcation diagram. The dynamical behaviours of this new hyperchaotic system are proved not only by performing numerical simulation and brief theoretical analysis but also by conducting an electronic circuit experiment. An efficient approaching is developed for global asymptotic stabilization of this four-dimensional hyperchaotic system. Based on the method of inverse optimal control for nonlinear systems, a linear state feedback is electronically implemented. It is remarkably simple as compared with other chaos control ways, like nonlinear state feedback.