共查询到20条相似文献,搜索用时 15 毫秒
1.
We present a spectral representation of the mean-square solution of the fractional kinetic equation (also known as fractional diffusion equation) with random initial condition. Gaussian and non-Gaussian limiting distributions of the renormalized solution of the fractional-in-time and in-space kinetic equation are described in terms of multiple stochastic integral representations. 相似文献
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Broadbridge Phil Kolesnik Alexander D. Leonenko Nikolai Olenko Andriy 《Journal of statistical physics》2019,177(5):889-916
Journal of Statistical Physics - The paper starts by giving a motivation for this research and justifying the considered stochastic diffusion models for cosmic microwave background (CMB) radiation... 相似文献
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In this paper, we study the fractional number operator as an analog of the finite-dimensional fractional Laplacian. An important relation with the Ornstein-Uhlenbeck process is given. Using a semigroup approach, the solution of the Cauchy problem associated to the fractional number operator is presented. By means of the Mittag-Leffler function and the Laplace transform, we give the solution of the Caputo time fractional diffusion equation and Riemann-Liouville time fractional diffusion equation in infinite dimensions associated to the fractional number operator. 相似文献
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This paper presents the second- and higher-order spectral densities of stationary (in space) random fields arising as approximations of rescaled solutions of the heat and fractional heat equations with singular initial conditions. The development is based on the diagram formalism and the Riesz composition formula. Our results are the first step to full parametrization of higher-order spectra of some classes of fractional random fields. 相似文献
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We study the Fisher-KPP equation where the Laplacian is replaced by the generator of a Feller semigroup with power decaying kernel, an important example being the fractional Laplacian. In contrast with the case of the standard Laplacian where the stable state invades the unstable one at constant speed, we prove that with fractional diffusion, generated for instance by a stable Lévy process, the front position is exponential in time. Our results provide a mathematically rigorous justification of numerous heuristics about this model. 相似文献
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This paper studies a system of semi-linear fractional diffusion equations
which arise in competitive predator-prey models by replacing the second-order derivatives
in the spatial variables with fractional derivatives of order less than two. Moving
finite element methods are proposed to solve the system of fractional diffusion equations
and the convergence rates of the methods are proved. Numerical examples are
carried out to confirm the theoretical findings. Some applications in anomalous diffusive
Lotka-Volterra and Michaelis-Menten-Holling predator-prey models are studied. 相似文献
8.
V. V. Saenko 《Journal of Experimental and Theoretical Physics》2018,126(4):462-478
A generalization of the model of Lévy walks with traps is considered. The main difference between the model under consideration and the already existing models is the introduction of multiplicative particle acceleration at collisions. The introduction of acceleration transfers the consideration of walks to coordinate–momentum phase space, which allows both the spatial distribution of particles and their spectrum to be obtained. The kinetic equations in coordinate–momentum phase space have been derived for the case of walks with two possible states. This system of equations in a special case is shown to be reduced to ordinary Lévy walks. This system of kinetic equations admits of integration over the spatial variable, which transfers the consideration only to momentum space and allows the spectrum to be calculated. An exact solution of the kinetic equations can be obtained in terms of the Laplace–Mellin transform. The inverse transform can be performed only for the asymptotic solutions. The calculated spectra are compared with the results of Monte Carlo simulations, which confirm the validity of the derived asymptotics. 相似文献
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Süleyman Demir 《International Journal of Theoretical Physics》2013,52(1):105-116
In this paper, the Maxwell-Proca type field equations of linear gravity are formulated in terms of hyperbolic octonions (split octonions). A hyperbolic octonionic gravitational wave equation with massive gravitons and gravitomagnetic monopoles is proposed. The real gravitoelectromagnetic field equations are recovered and written in compact form from an octonionic potential. In the absence of charges, this reduces to the Klein-Gordon equation of motion for the massive graviton. The analogy between massive gravitational theory and electromagnetism is shown in terms of the present formulation. 相似文献
12.
A numerical study is given on the spectral methods and the high order
WENO finite difference scheme for the solution of linear and nonlinear hyperbolic
partial differential equations with stationary and non-stationary singular sources.
The singular source term is represented by the $δ$-function. For the approximation
of the $δ$-function, the direct projection method is used that was proposed in [6].
The $δ$-function is constructed in a consistent way to the derivative operator. Nonlinear
sine-Gordon equation with a stationary singular source was solved with the
Chebyshev collocation method. The $δ$-function with the spectral method is highly
oscillatory but yields good results with small number of collocation points. The
results are compared with those computed by the second order finite difference
method. In modeling general hyperbolic equations with a non-stationary singular
source, however, the solution of the linear scalar wave equation with the non-stationary
singular source using the direct projection method yields non-physical
oscillations for both the spectral method and the WENO scheme. The numerical
artifacts arising when the non-stationary singular source term is considered on the
discrete grids are explained. 相似文献
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In this paper, we study the global regularity for the Navier-Stokes-Maxwell system with fractional diffusion. Existence and uniqueness of global strong solution are proved for \(\alpha \geqslant \frac {3}{2}\). When 0 < α < 1, global existence is obtained provided that the initial data \(\|u_{0}\|_{H^{\frac {5}{2}-2\alpha }}+\|E_{0}\|_{H^{\frac {5}{2}-2\alpha }}+\|B_{0}\|_{H^{\frac {5}{2}-2\alpha }}\) is sufficiently small. Moreover, when \(1<\alpha <\frac {3}{2}\), global existence is obtained if for any ε >?0, the initial data \(\|u_{0}\|_{H^{\frac {3}{2}-\alpha +\varepsilon }}+\|E_{0}\|_{H^{\frac {3}{2}-\alpha +\varepsilon }}+\|B_{0}\|_{H^{\frac {3}{2}-\alpha +\varepsilon }}\) is small enough. 相似文献
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Journal of Statistical Physics - In this paper, we consider the random dichotomous fluctuations on both mass and damping in a fractional oscillator, which is subjected to an additive fractional... 相似文献
17.
Spectral estimation plays a significant role in gravitational wave data analysis. We provide a brief introduction to multi-taper methods which use multiple orthogonal tapers (or windows) to provide spectral estimators with excellent bias and variance properties. Multi-taper methods are also extremely powerful for the estimation and removal of sharp spectral peaks in the presence of noise such as arise due to power line harmonics or suspension resonances. We present examples of these methods using the GRASP (Gravitational Radiation Analysis and Simulation Package) software package. 相似文献
18.
C. Hoenselaers 《International Journal of Theoretical Physics》2007,46(5):1096-1099
We study soliton solutions of the Sinh–Gordon equation. It is also shown that the Cosh–Gordon equation, whilst being integrable,
does not admit pure solitons. 相似文献
19.
In this paper we use a Renormalization Group (RG) method to study the long-time asymptotics of nonlinear diffusion equations with time-dependent diffusion coefficients and nonlinearities which are marginal (or critical) with respect to the RG operator. These equations describe the time evolution of the average concentration of a passive scalar being advected by a random velocity field. We prove that, besides the expected diffusive behavior, there is an extra logarithmic correction which is the imprint of the critical nonlinearity. 相似文献
20.
如何从海量或高维数据中“提纯”出有用的信息,这是当前数据分析面临的一个巨大的挑战,也是当前研究的一个热点。变量筛选技术能够从众多、复杂的量测数据中提取出特征信息变量,达到简化多元模型乃至提高模型预测性能等目的。在光谱分析中,来自噪声等诸多因素的影响,量测数据会不可避免地包含干扰和无关信息变量,以及变量间存在的多重共线性,这些都会影响模型的稳健性和预测能力。近年来变量(波长)筛选方法在光谱解析领域的研究与应用中取得了较大的进展。结合国内外相关研究文献和作者的研究体会,不仅仅综述了近红外光谱,还综述了中红外光谱、拉曼光谱等众多筛选变量的方法的提出、特点、发展、类别、比较和近五年来在不同领域的应用进展。其中,评价变量重要性的参数及其标准或阈值的选择、搜索变量的策略和途径是变量筛选方法的关键。而且每种方法都具有各自的优势和局限性,实际使用中要根据方法自身特点结合目标体系的特征选择合适的方法。重点内容:(1)对比了光谱数据分析中常用的波长筛选和波段筛选方法;(2)对比了基于PLS模型参数的不同变量筛选方法的原理和特点;(3)根据搜索和筛选变量策略的不同将变量筛选方法进行分类评述。最后,围绕在解析实际复杂体系中变量筛选方法出现的过拟合、不稳定等问题进行了讨论并提出相应的解决措施,同时对变量筛选方法的研究趋势、发展前景和应用方向进行了展望。其中,新的评价变量重要性的判据和搜索变量的策略等工作仍需要展开深入地研究。期望本综述能够对光谱变量筛选的后续研究及应用起到积极的推动作用。 相似文献