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1.
We construct an asymptotic theory that describes the kinetics of first-order phase transitions. The theory is a considerable
refinement of the well-known Lifshits-Slezov theory. The main difference between the two is that the Lifshits—Slezov theory
uses for the first integral of the kinetic equation an approximate solution of the characteristic equation, which is valid
in the entire range of sizes except for the blocking point, i.e., it uses a nonuniformly applicable approximation. At the
same time, the behavior of the characteristic solution near the blocking point determines the asymptotic behavior of the size
distribution function of the nuclei for the new phase. Our theory uses a uniformly applicable solution of the characteristic
equation, a solution valid at long times over the entire range of sizes. This solution is used to find the asymptotic behavior
of all basic properties of first-order phase transitions: the size distribution function, the average nucleus size, and the
nucleus density.
Zh. éksp. Teor. Fiz. 113, 2193–2208 (June 1998) 相似文献
2.
The Hirota-Satsuma coupled KdV equations associated 2×2 matrix spectral problem is discussed by the dressing method, which is based on the factorization of integral operator on a line into a product of two Volterra integral operators. A new solution is obtained by choosing special kernel of integral operator. 相似文献
3.
The initial value problem of fractional differential equations and its solving method are studied in this paper. Firstly,
for easy understanding, a different version of the initialized operator theory is presented for Riemann-Liouville’s fractional-order
derivative, addressing the initial history in a straightforward form. Then, the initial value problem of a single-term fractional
differential equation is converted to an equivalent integral equation, a form that is easy for both theoretical and numerical
analysis, and two illustrative examples are given for checking the correctness of the integral equation. Finally, the counter-example
proposed in a recent paper, which claims that the initialized operator theory results in wrong solution of a fractional differential
equation, is checked again carefully. It is found that solving the equivalent integral equation gives the exact solution,
and the reason behind the result of the counter-example is that the calculation therein is based on the conventional Laplace
transform for fractional-order derivative, not on the initialized operator theory. The counter-example can be served as a
physical model of creep phenomena for some viscoelastic materials, and it is found that it fits experimental curves well. 相似文献
4.
This paper deals with the mass operator representing multiple-scattering effects in the theory of wave scattering from a slightly random surface. By means of the stochastic-functional approach, a recurrence equation for the mass operator is obtained in the form of an iterative integral. However, its solution oscillates in a non-physical manner against the number of iterations. Next, the recurrence equation may be regarded as a nonlinear integral equation, when the number of iterations goes to infinity. An analytical solution of the nonlinear integral equation is presented for a special case in which the roughness spectrum is the Dirac delta function. Then, the nonlinear integral equation is solved numerically for the Gaussian roughness spectrum by iteration, starting from such an analytical solution. It is shown that only a few iterations are required to obtain the mass operator, even when the correlation distance is small. Effects of the mass operators on the coherent reflection coefficient and the incoherent scattering cross section are calculated and shown in figures. 相似文献
5.
基于多尺度的思想,将小波多分辨分析和多尺度方法结合,构造了小波多尺度反演方法,并应用于一维双相介质孔隙率的反演.利用小波变换,将原始反问题分解为不同尺度上的一系列子反问题,并按照尺度从粗到细的顺序依次求解.在每一个尺度上,都采用稳定、收敛快的正则化高斯牛顿法求解,次一级尺度上求出的“全局最优解”作为上一级的初始解,依次类推,直到求出原始问题的真正的全局最优解.将小波多尺度方法归结为三种不同算子(分解算子、求解算子、插入算子)的交替应用,给出了小波多尺度反演算法的基本流程图,并推导出当采用Daubechie
关键词:
双相介质
反演
小波多尺度方法
孔隙率 相似文献
6.
A. V. Manzhirov 《Doklady Physics》2017,62(7):344-349
The plane contact problem with wear for an elastic foundation with a longitudinally nonuniform (surface nonuniform) coating and a rigid punch with a flat foundation has been solved for the first time. The case of linear wear is considered. The nonuniformity of the coating is described by a rapidly changing function. This strong nonuniformity arises when coatings are deposited using modern additive manufacturing technologies. The problem is reduced to the solution of an integral equation with two different integral operators: a compact self-adjoint positively defined operator with respect to the coordinate and the non-selfadjoint integral Volterra operator with respect to time. The solution is obtained in series using author’s projection method. The efficiency of the proposed approach for constructing a high-accuracy approximate solution to the problem (with only a few expansion terms retained) is demonstrated. A simple engineering formula for estimating the contact stresses under a punch for large values of times is proposed. 相似文献
7.
基于多尺度的思想,将小波多分辨分析和多尺度方法结合,构造了小波多尺度反演方法,并应用于一维双相介质孔隙率的反演.利用小波变换,将原始反问题分解为不同尺度上的一系列子反问题,并按照尺度从粗到细的顺序依次求解.在每一个尺度上,都采用稳定、收敛快的正则化高斯牛顿法求解,次一级尺度上求出的“全局最优解”作为上一级的初始解,依次类推,直到求出原始问题的真正的全局最优解.将小波多尺度方法归结为三种不同算子(分解算子、求解算子、插入算子)的交替应用,给出了小波多尺度反演算法的基本流程图,并推导出当采用Daubechie 相似文献
8.
Completeness of the system of eigenvectors of off-diagonal operator matrices and its applications in elasticity theory
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This paper deals with off-diagonal operator matrices and their applications in elasticity theory.Two kinds of completeness of the system of eigenvectors are proven,in terms of those of the compositions of two block operators in the off-diagonal operator matrices.Using these results,the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed.Moreover,we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation. 相似文献
9.
S. V. Izvekov 《Physics of the Solid State》1997,39(9):1383-1388
A nonlocal dynamic coherent-potential approximation is formulated as a further development of the dynamic coherent-potential
method. The nonlocal dynamic coherent-potential approximation is an efficient method of determining the one-exciton Green’s
function in a model with the Hamiltonian in the strong-coupling approximation, where a spectrum of optical phonons is assumed,
and the exciton-phonon interaction operator is linear or quadratic in the phonon operators. A system of recursion equations
is derived, from which the coherent potential is found as a function of the energy E and the wave vector k. An analytical expression is derived for the one-exciton Green’s function in the case of narrow (in comparison with the phonon
energy) exciton bands and exciton-phonon interaction linear in the phonon operators. For broader exciton bands and more complex
exciton-phonon interaction the system of equations determining the coherent potential represents a recursion algorithm, which
can be effectively implemented by numerical means.
Fiz. Tverd. Tela (St. Petersburg) 39, 1560–1563 (September 1997) 相似文献
10.
Joseph Polchinski 《Nuclear Physics B》1981,179(3):509-540
We study the euclidean Green functions of the 't Hooft vortex operator, primarily for abelian gauge theories. The operator is written in terms of elementary fields, with emphasis on a form in which it appears as the exponential of a surface integral. We explore the requirement that the Green functions depend only on the boundary of this surface. The Dirac veto problem appears in a new guise. We present a two-dimensional “solvable model” of a Dirac string, which suggests a new solution of the veto problem. The renormalization of the Green functions of the abelian Wilson loop and abelian vortex operator is studied with the aid of the operator product expansion. In each case, an overall multiplication of the operator makes all Green functions finite; a surprising cancellation of divergences occurs with the vortex operator. We present a brief discussion of the relation between the nature of the vacuum and the cluster properties of the Green functions of the Wilson and vortex operators, for a general gauge theory. The surface-like cluster property of the vortex operator in an abelian Higgs theory is explored in more detail. 相似文献
11.
Two independent weak-coupling expansions are developed for the Liouville quantum field theory on a circle. In the first, the coupling of the nonzero modes is treated as a perturbation on the exact solution to the zero-mode problem (quantum mechanics with an exponential potential). The second approach is a weak-coupling approximation to an explicit operator solution which expresses various Liouville operators as functions of a free massless field using a Bäcklund transformation. It is shown that the free state space associated with the latter solution must be restricted to the sector which is odd with respect to a type of “parity.” Various matrix elements are computed to order g10 using both approaches, yielding identical results. 相似文献
12.
本文基于积分方程法研究并建立了一种模拟横向同性介质中任意各向异性异常 体三维电磁响应的高阶广义扩展Born近似(Ho-GEBA)算法. 首先利用逐次迭代技术给出积分方程的广义级数展开解, 为保证其收敛性, 引入一种各向异性条件下满足压缩映射的迭代算子. 然后利用异常体区域分解技术, 并结合扩展Born近似原理, 得到各向异性介质三维电磁响应的Ho-GEBA解. 为提高效率, 计算过程中采用并矢Green函数的解析表达式. 最后通过数值计算实例对比验证了本文算法的有效性.
关键词:
高阶广义扩展Born近似
积分方程
电磁模拟
解析Green函数 相似文献
13.
S. Mudaliar 《Waves in Random and Complex Media》1999,9(4):521-536
This paper deals with scattering from a random-medium layer with rough boundaries. The fluctuations of the surface heights and medium permittivity are assumed to be small and smooth. All random quantities are assumed to be stationary and independent of each other. After the introduction of approximate boundary conditions, the system of partial differential equations is transformed into an integral equation where the fluctuations of the problem are represented as a zero-mean random operator. Employing smoothing, integral equations for the coherent fields are obtained. Use of the Helmholtz operator leads to solution for the coherent propagation constant while the boundary operators lead to coherent Fresnel coefficients. The characteristics of the results are illustrated by considering several examples. 相似文献
14.
15.
O. V. Soloviev 《Radiophysics and Quantum Electronics》1998,41(5):392-402
In this paper, we develop further the analytical and numerical method of solving three-dimensional problems in the theory
of radio wave propagation, including three-dimensional local inhomogeneities (ionospheric disturbances or Earth’s surface
irregularities). To model the Earth-ionosphere waveguide, we use the surface impedance concept, by which the irregularity
extending beyond one waveguide wall has an arbitrary smooth shape, and its surface can be described by the impedance. In the
scalar approximation, this problem is reduced to a two-dimensional integral equation for the irregularity surface, which,
by asymptotic (kr ≫ 1) integration over the coordinate transverse to the propagation path (with allowance for terms of the
order of (kr)−1), is reduced to a one-dimensional integral equation, in which the integration contour is the linear contour of the irregularity.
The equation is solved numerically, combining the inversion of a Volterra integral operator and successive approximations.
By reducing the computer times, this method enables one to study both small-scale and large-scale irregularities. The results
of numerical simulation of radio wave propagation in the presence of a powerful three-dimensional ionospheric disturbance
are presented as an example.
State University, St. Petersburg, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No.
5, pp. 588–604, May, 1998. 相似文献
16.
S.É. Derkachov J.A. Gracey A.N. Manashov 《The European Physical Journal C - Particles and Fields》1998,2(3):569-579
We compute the anomalous dimensions of a set of composite operators which involve derivatives at four loops in in theory as a function of the operator moment . These operators are similar to the twist-2 operators which arise in QCD in the operator product expansion in deep inelastic
scattering. By regarding their inverse Mellin transform as being equivalent to the DGLAP splitting functions we explore to
what extent taking a restricted set of operator moments can give a good approximation to the exact four loop result.
Received: 12 May 1997 / Published online: 20 February 1998 相似文献
17.
《Physics letters. [Part B]》1999,456(1):38-47
We propose a modification of the Faddeev–Popov procedure to construct a path integral representation for the transition amplitude and the partition function for gauge theories whose orbit space has a non-Euclidean geometry. Our approach is based on the Kato–Trotter product formula modified appropriately to incorporate the gauge invariance condition, and thereby equivalence to the Dirac operator formalism is guaranteed by construction. The modified path integral provides a solution to the Gribov obstruction as well as to the operator ordering problem when the orbit space has curvature. A few explicit examples are given to illustrate new features of the formalism developed. The method is applied to the Kogut–Susskind lattice gauge theory to develop a nonperturbative functional integral for a quantum Yang–Mills theory. Feynman's conjecture about a relation between the mass gap and the orbit space geometry in gluodynamics is discussed in the framework of the modified path integral. 相似文献
18.
O. V. Soloviev 《Radiophysics and Quantum Electronics》2000,43(7):557-568
This paper presents a further development of the numerical-analytical method for the solution of three-dimensional problems
in the theory of radio wave propagation. We consider a vector problem of the electromagnetic field of a vertical electric
dipole in a plane Earth-ionosphere waveguide with a local large-scale irregularity on the anisotropic ionosphere wall. The
possibility of lowering (elevating) of the local region of the upper waveguide wall with respect to the regular ionosphere
level is taken into account. The field components on the boundary surfaces obey the Leontovich impedance conditions. The problem
is reduced to a system of two-dimensional integral equations taking into account the overexcitation and depolarization of
the field scattered by the irregularity. Using asymptotic (with respect to the parameter kr ≫1) integration along the direction
perpendicular to the ray path, we transform this system to a system of one-dimensional integral equations. The system is solved
numerically in the diagonal approximation, combining direct inversion of the Volterra integral operator and the subsequent
iterations. The proposed method reduces the computer time required for solving the problem and is useful for the study of
both small-scale and large-scale irregularities. We obtained estimates of the TE field components that are not excited by
the source considered and originate entirely from field scattering by a three-dimensional irregularity disturbing the geometric
regularity of the ionospheric waveguide wall.
State University of St. Petersburg, Russia Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No.
7, pp. 617–629, July, 2000. 相似文献
19.
We consider the problem of the relaxation of an arbitrary initial distribution function of a gas of long-wave acoustic phonons scattered by isotopic impurities embedded in a crystalline medium with cubic symmetry. The spectral decomposition of the collision integral of the suitable Boltzmann-Peierls equation is obtained. The spectrum of the collision operator is purely discrete and in addition to the eigenvalue 0 consists of three other eigenvalues. Explicit analytic expressions for these eigenvalues are obtained. Within the Chapman-Enskog approximation we derive the diffusion equation for the density of phonons and obtain the explicit expression for the diffusion coefficient. The dependency of the eigenvalues of the collision operator and the diffusion coefficient on the elastic constants of the medium is studied. 相似文献
20.
J. Uhlig J.C. Lemm A. Weiguny 《The European Physical Journal A - Hadrons and Nuclei》1998,2(4):343-354
Abstact: Three variants of mean field methods for atomic and nuclear reactions are compared with respect to both conception and applicability:
The time–dependent Hartree–Fock method solves the equation of motion for a Hermitian density operator as initial value problem,
with the colliding fragments in a continuum state of relative motion. With no specification of the final state, the method
is restricted to inclusive reactions. The time–dependent mean field method, as developed by Kerman, Levit and Negele as well
as by Reinhardt, calculates the density for specific transitions and thus applies to exclusive reactions. It uses the Hubbard–Stratonovich
transformation to express the full time-development operator with two–body interactions as functional integral over one–body
densities. In stationary phase approximation and with Slater determinants as initial and final states, it defines non–Hermitian,
time–dependent mean field equations to be solved self–consistently as boundary value problem in time. The time–independent
mean field method of Giraud and Nagarajan is based on a Schwinger–type variational principle for the resolvent. It leads to
a set of inhomogeneous, non-Hermitian equations of Hartree–Fock type to be solved for given total energy. All information
about initial and final channels is contained in the inhomogeneities, hence the method is designed for exclusive reactions.
A direct link is established between the time–dependent and time–independent versions. Their relation is non–trivial due to
the non–linear nature of mean field methods.
Received: 7 January 1998 / Revised version: 20 April 1998 相似文献