Inverse problem method for the perturbed nonlinear Schrödinger equation

A scattering matrix is defined for eq. (1), and a complete set of equations, governing the time evolution of the scattering parameters, is derived by a general method. These equations form a basis for the perturbation theory.     

Algebraic method applied to the pairing interaction

The algebraic approach to the theory of collective motion is applied to the pairing interaction with two or three non-degenerate levels of arbitrary degeneracy each. A closed set of non-linear algebraic equations for observables referring to the lowest-lying levels of even nuclei is derived from the relevant quasispin algebra and from the equations of motion. Number conservation and blocking can both be taken into account. The solutions agree remarkably well with exact solutions even for small systems.     

Lattice effects in the quasiparticle dynamics and kinetics

In this work we present a full selfconsistent set of nonlinear equations which unifies the nonlinear elasticity theory equations, the Boltzmannn transport theory and the Maxwell equations for quasiparticles with arbitrary dispersion laws in nonstationarily deformed crystals with arbitrary (but linear) constitutive relations. Transformations to replace the Galilean ones are obtained, the quasiparticle mechanics in a Hamiltonian form is deduced, and a Boltzmann-type transport equation (valid in the whole Brillouin zone) is derived. The theory may be applied to metals, semiconductors, quantum crystals, low-dimensional structures etc. Received 20 October 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: dipushk@issp.bas.bg     

Electrodynamics of the band-edge in a direct gap semiconductor

A set of equations is derived which can describe resonant interaction of a two band semiconductor with intense radiation. The theory comprises as limiting cases: (1) Bloch equation treatment of localized two level atoms; (2) Lindhard's dielectric theory of free electrons; (3) a linear band to band transition theory equivalent to that of Elliott.     

The critical supersaturations predicted by nucleation theory

A general set of equations is derived for calculating the supersaturation required to obtain a given rate of nucleation. This set is general enough to encompass all the present theories, the classical theory, the Lothe-Pound theory, the Reiss-Katz-Cohen theory, a recent theory by H. Reiss, and any other theory which includes a size-dependent correction to the classical theory. Comparison of these predictions is made for various substances.     

圆柱开槽波导FEM放大器数值研究

以圆柱开槽波导、螺旋摇摆器为模型,考虑了电子初始速度零散、引导磁场等效应对放大器饱和特性的影响,导出了自洽的注波互作用三维非线性方程组.并在此基础上编制了相应的计算软件,通过数值分析的方法研究了圆柱开槽波导自由电子激光放大器的饱和效率、频带宽度等高频特性.     

Nonlinear Study on FEM Amplifier with a Novel Elliptic-Groove Guide

FEM amplifier with a novel elliptic-groove guide is proposed and three-dimensional nonlinear theory for the elliptic-groove guide FEM amplifier is developed. A set of coupled nonlinear differential equations is derived and the characteristics of this FEM amplifier are numerically analyzed in detail including the evolution of power, efficiency and bandwidth. The effects on saturation efficiency due to electron momentum spread and wiggler taper are also studied.     

On the Partial Regularity of a 3D Model of the Navier-Stokes Equations

We study the partial regularity of a 3D model of the incompressible Navier-Stokes equations which was recently introduced by the authors in [11]. This model is derived for axisymmetric flows with swirl using a set of new variables. It preserves almost all the properties of the full 3D Euler or Navier-Stokes equations except for the convection term which is neglected in the model. If we add the convection term back to our model, we would recover the full Navier-Stokes equations. In [11], we presented numerical evidence which seems to support that the 3D model develops finite time singularities while the corresponding solution of the 3D Navier-Stokes equations remains smooth. This suggests that the convection term play an essential role in stabilizing the nonlinear vortex stretching term. In this paper, we prove that for any suitable weak solution of the 3D model in an open set in space-time, the one-dimensional Hausdorff measure of the associated singular set is zero. The partial regularity result of this paper is an analogue of the Caffarelli-Kohn-Nirenberg theory for the 3D Navier-Stokes equations.     

Quantum mechanical treatment of electron-positron excitations in heavy ion collisions with nuclear contact

A general theory is formulated of electron-positron excitations in heavy ion collisions with nuclear contact, treating the nuclear relative motion quantum mechanically. A set of coupled channel equations for the electronic occupation amplitudes is derived, which is formally very similar to the semiclassical theory based on a classical nuclear trajectory, and reduces to the latter in the JWKB approximation. The new coupled equations contain all the quantum mechanical information on the details of the nuclear scattering during nuclear contact. The importantce of this formulation for a quantitative theory of spontaneous positron creation in supercritical systems with nuclear time delay is pointed out. The possibility of line structures in the positron spectrum, as predicted semiclassically and recently discovered experimentally, is discussed in the framework of the DWBA approximation. For light-particle scattering off a nuclear resonance, the Blair formula for vacancy production is recovered in the same approximation.     

On the geometry of relativistic magnetofluid flows

This paper deals with the construction of “magnetic vorticity” vector using Greenberg's theory of spacelike congruences for the trajectories of magnetic fields. A set of propagation equations is derived for the geometrical invariants associated with the congruences of magnetic field lines and fluid flow lines. Some applications of these propagation equations are made. A generalization of Ferraro's law of isorotation is obtained employing the propagation equation forω ² along the magnetic field lines.     

A virial approach to soliton-like solutions of coupled non-linear differential equations including the ’t-Hooft-Polyakov monopole equations

A virial theorem for solitons derived by Friedberg, Lee and Sirlin is used to reduce a system of second order equations to an equivalent first order set. It is shown that this theorem, when used in conjunction with our earlier observation that soliton-like solutions lie on the separatrix, helps in obtaining soliton-like solutions of theories involving coupled fields. The method is applied to a system of equations studied extensively by Rajaraman. The ’t-Hooft-Polyakov monopole equations are then studied and we obtain the well-known monopole solutions in the Prasad-Sommerfeld limit (λ=0); for the case λ≠0, we succeed in obtaining a non-trivial algebraic constraint between the fields of the theory.     

Statistical equilibrium solutions of the shallow water equations

A statistical method for calculating equilibrium solutions of the shallow water equations, a model of essentially 2D fluid flow with a free surface, is described. The model contains a competing acoustic turbulent direct energy cascade, and a 2D turbulent inverse energy cascade. It is shown, nonetheless that, just as in the corresponding theory of the inviscid Euler equation, the infinite number of conserved quantities constrains the flow sufficiently to produce nontrivial large-scale vortex structures which are solutions to a set of explicitly derived coupled nonlinear partial differential equations.     

Meixner basis functions in the problem of diffraction by a disk

A basis to solve the problem of diffraction by a disk in the axisymmetric case is constructed. A set of functions that satisfy the well-known Meixner condition on an edge, admit of analytical calculation of encountered integrals, and exhibit the orthogonality property in corresponding Hilbert spaces is derived for the first time. A theory of integral equations of diffraction by a disk is developed.     

Transient Decay of Longitudinal Magnetization in Heterogeneous Spin Systems under Selective Saturation. IV. Reformulation of the Spin-Bath-Model Equations by the Redfield-Provotorov Theory

Alternative formulations to the conventional Bloch equations for the RF saturation of the solid component in heterogeneous spin systems according to a spin-bath model are derived using the concept of spin temperature as suggested by Redfield and Provotorov. These formulations and the resulting equations derived by the projection-operator technique provide an analytical and explicit solution to the general problem of solid saturation under continuous RF irradiation. Using the Provotorov theory, a set of generalized (non-Markovian) equations of motions is derived. The solutions to these generalized equations approach those of the conventional Bloch formulation at one extreme when the applied RF is weak and the Redfield formulation at another when the applied RF is strong. In short, this development provides a simple alternative which removes the restriction of the lineshape function used to represent the solid component; the latter is well known to be non-Lorentzian, contrary to the tacit assumption made in the conventional Bloch formulation. Experimental verification of the generalized theory is provided by transient and steady-state longitudinal magnetization data acquired from cross-linked bovine serum albumin under selective saturation by continuous off-resonance RF irradiation.     

Formulation of the theory of turbulence in an incompressible fluid

The theory of turbulence in an incompressible fluid is formulated using methods similar to those of quantum field theory. A systematic perturbation theory is set up, and the terms in the perturbation series are shown to be in one to one correspondence with certain diagrams analogous to Feynman diagrams. From a study of the diagrams it is shown that the perturbation series can be rearranged and partially summed in such a way as to reduce the problem to the solution of three simultaneous integral equations for three functions, one of which is the second order velocity correlation function. The equations have the form of infinite power series integral equations, and the first few terms in the power series are derived from an analysis of the diagrams to sixth order. Truncation of the integral equations at the lowest nontrivial order yields Chandrasekhar's equation, and truncation at a higher order yields the equations discussed by Kraichnan.     

Colloidal glass transition: beyond mode-coupling theory

A new theory for the dynamics of concentrated colloidal suspensions and the colloidal glass transition is proposed. The starting point is the memory function representation of the density correlation function. The memory function can be expressed in terms of a time-dependent pair-density correlation function. An exact, formal equation of motion for this function is derived and a factorization approximation is applied to its evolution operator. In this way a closed set of equations for the density correlation function and the memory function is obtained. The theory predicts an ergodicity breaking transition similar to that predicted by mode-coupling theory, but at a higher density.     

The Becker–Döring Equations and the Lifshitz–Slyozov Theory of Coarsening

In this paper the relation between the kinetic set of Becker–Döring (BD) equations and the classical Lifshitz–Slyozov (LS) theory of coarsening is studied. A model that resembles the LS theory but keeps some of the nucleation effects is derived. For this model a solution is described that shows how the kinetic effects explain the particular solution selected in the LS theory. By means of a renormalization procedure, a discrete group of transformations is shown to play an important role in describing the structure of the solution near the critical size of the LS theory.     

用衍射相位元件分离并聚焦偏振光

通过相位恢复的原理,设计了在平行光的照明下单轴双折射晶体做成的衍射相位元件以实现分离并聚焦ｏ偏振光和ｅ偏振光,讨论了相位量化对结果的影响。理论计算表明：这种方法可成功地实现偏振光的分离和聚焦。     

Theory of switching of multiaxial ferroelectrics (the main stages)

The kinetics of switching of multiaxial ferroelectric crystals with 180° and 90° domains under conditions of normal and layer-by-layer domain growth is studied using the multidimensional theory of first-order phase transitions. The main stages of the process of switching of a multiaxial ferroelectric are considered under the assumption that repolarized cylinder-shaped domains grow three-dimensionally. A closed set of equations describing the kinetics of switching is derived with allowance for a change in repolarization in the course of the phase transition. Equations for the time-dependent switching current are derived. The main characteristics of switching are compared qualitatively with the experimental data on barium titanate.     

Two-dimensional multi-channel acousto-optic diffraction

In this paper, we have investigated the interaction between acoustic waves generated by an incident light beam propagating through two-dimensional transducers. A set of coupled mode equations for two-dimensional multi-channel acousto-optic inter-modulation are derived, and the solutions are obtained. A new type of two-dimensional multi-channel Bragg acousto-optic modulator is designed by analyzing two-dimensional multi-channel acousto-optic inter-modulation based on the coupled mode theory, and its performance has also been experimentally characterized. The experimental results are in accordance with our theoretical analysis.