A multidimensional subdiffusion model： An arbitrage-free market

<正>To capture the subdiffusive characteristics of financial markets,the subordinated process,directed by the inverse Q-stale subordinator S_α(t) for 0 <α< 1,has been employed as the model of asset prices.In this article,we introduce a multidimensional subdiffusion model that has a bond and K correlated stocks.The stock price process is a multidimensional subdiffusion process directed by the inverse Q-stable subordinator.This model describes the period of stagnation for each stock and the behavior of the dependency between multiple stocks.Moreover,we derive the multidimensional fractional backward Kolmogorov equation for the subordinated process using the Laplace transform technique.Finally, using a martingale approach,we prove that the multidimensional subdiffusion model is arbitrage-free,and also gives an arbitrage-free pricing rule for contingent claims associated with the martingale measure.     

基于分数阶环境热浴的非各态历经判据研究

本文从分数阶谱形式的气固耦合模型出发, 理论推导出具有幂律记忆核的广义朗之万方程. 研究气体分子在自由场和简谐势场中的动力学演化和长时渐进行为, 着重分析三种各态历经判据: Khinchin判据、Lee判据以及内在判据和外在表现的适用性. 研究结果表明: Khinchin判据适用于广义朗之万方程描述的所有扩散和输运过程; Lee判据并不适用于布朗运动, 只能用来区分不同类型的扩散过程; 而内在判据和外在表现不仅能够把非各态历经分为两类, 同时可以揭示非各态历经的物理内在根源.     

Burgers equation with self-similar gaussian initial data: Tail probabilities

The statistical properties of solutions of the one-dimensional Burgers equation in the limit of vanishing viscosity are considered when the initial velocity potential is fractional Brownian motion (FBM). We establish the asymptotic power-law order for log-probability of large values, both velocity and shock (amplitude of velocity discontinuity). This confirms the conjecture of U. Frisch and his collaborators. Rigorous results for this problem were previously derived for the case of Brownian motion using Markov techniques. Our approach is based on the intrinsic properties of FBM and the theory of extreme values for Gaussian processes.     

On the Time Fractional Generalized Fisher Equation:Group Similarities and Analytical Solutions

In this letter,the Lie point symmetries of the time fractional Fisher(TFF) equation have been derived using a systematic investigation.Using the obtained Lie point symmetries,TFF equation has been transformed into a different nonlinear fractional ordinary differential equations with the Erd′elyi–Kober fractional derivative which depends on the parameter α.After that some invariant solutions of underlying equation are reported.     

端面抽运Tm,Ho:YLF激光器热转换系数及热透镜效应的研究

根据激光二极管纵向抽运Tm,Ho:YLF激光器的能级跃迁和能量传递过程，在考虑能量传递上转换和基态重吸收的前提下，建立了准三能级速率方程理论模型.给出了Tm,Ho:YLF激光器的热转换系数的解析表达式，讨论了抽运光斑半径与激光束腰半径的比值对热转换系数的影响.实验上得到了热焦距随抽运功率的变化关系，并将其与理论结果进行了对比，发现符合较好. 关键词： Tm Ho:YLF晶体 能量传递上转换 速率方程 热转换系数     

Directed transport in equilibrium: A model study

It is generally believed that sustained directed transport in mechanical systems is not achievable under equilibrium conditions. In this article, by analyzing a simple model, we will show that directed motion under equilibrium conditions can take place and is not inconsistent with conservation of energy and the second law of thermodynamics. Our model demonstrates a novel symmetry breaking mechanism sustainable under equilibrium conditions and average uniform motion of the center of mass is a consequence of the sustained broken symmetry. The most important consequence of our results is that, no current condition for mechanical equilibrium is possibly non-universal.     

Nonlinear Kac model: Spatially homogeneous solutions and the Tjon effect

We study Kac's nonlinear model of the Boltzmann equation when the cross section() does not satisfy the special symmetry condition()=(-). We determine a differential system for the Laguerre moments of the odd and even velocity parts of the solutions. We consider the spatially homogeneous model in 1+1 dimensions (velocityv and timet) when the even velocity part of the solution is provided by the Bobylev-Krook-Wu closed solutions and study the associated odd velocity part. We find that the solutions depend on the microscopic models of(). For one class of(), which has sums of exponential terms for the Laguerre moments, we establish the relations allowing the construction of the time-dependent solutions associated with any initial distribution. We find sufficient conditions on() and on the even part such that the Laguerre series of the odd part converges. We establish a criterion for a well-defined linear combination of the moments cross section, and we check its validity for different numerical examples. We find that if the relaxation time for the even part is smaller than the corresponding one for the odd part and if the initial distribution has a narrow peak, then the Tjon effect exists for the complete B.K.W. solution (even+odd parts).     

Quantum carpets: efficiently probing fractional revivals in position-dependent mass systems

Position-dependent-mass systems are of great importance in many physical situations,such as the transport of charge carriers in semiconductors with non-uniform composition and in the theory of many-body interactions in condensed matter.Here we investigate,numerically and analytically,the phenomenon of fractional revivals in such systems,which is a generic characteristic manifested by the wave-packet evolution in bounded Hamiltonian systems.Identifying the fractional revivals using specific probe...     

Operating principles of the cerebral cortex as a six-layered network in primates: beyond the classic canonical circuit model

The cerebral cortex performs its computations with many six-layered fundamental units, collectively spreading along the cortical sheet. What is the local network structure and the operating dynamics of such a fundamental unit? Previous investigations of primary sensory areas revealed a classic “canonical” circuit model, leading to an expectation of similar circuit organization and dynamics throughout the cortex. This review clarifies the different circuit dynamics at play in the higher association cortex of primates that implements computation for high-level cognition such as memory and attention. Instead of feedforward processing of response selectivity through Layers 4 to 2/3 that the classic canonical circuit stipulates, memory recall in primates occurs in Layer 5/6 with local backward projection to Layer 2/3, after which the retrieved information is sent back from Layer 6 to lower-level cortical areas for further retrieval of nested associations of target attributes. In this review, a novel “dynamic multimode module (D3M)” in the primate association cortex is proposed, as a new “canonical” circuit model performing this operation.     

Stationary velocity distribution in an external field: A one-dimensional model

The velocity distribution of a charged hard rod coupled to an external field and moving in a neutral equilibrium hard rod gas is studied on the basis of Boltzmann's equation. The exact stationary solution is found. Above a threshold value the field becomes effective in the high-velocity region slowing down the decay of the velocity distribution. The drift velocity and the mean kinetic energy are discussed as functions of the field.     

Three-dimensional parabolic equation model for seismo-acoustic propagation: Theoretical development and preliminary numerical implementation

A three-dimensional(3D) parabolic equation(PE) model for sound propagation in a seismo-acoustic waveguide is developed in Cartesian coordinates, with x, y, and z representing the marching direction, the longitudinal direction, and the depth direction, respectively. Two sets of 3D PEs for horizontally homogenous media are derived by rewriting the 3D elastic motion equations and simultaneously choosing proper dependent variables. The numerical scheme is for now restricted to the y-independent bathymetry. Accuracy of the numerical scheme is validated, and its azimuthal limitation is analyzed. In addition, effects of horizontal refraction in a wedge-shaped waveguide and another waveguide with a polyline bottom are illustrated. Great efforts should be made in future to provide this model with the ability to handle arbitrarily irregular fluid-elastic interfaces.     

The kinetic Ising model: Exact susceptibilities of two simple examples

The susceptibility of a modified version of the one-dimensional kinetic Ising model is obtained and compared with the susceptibility of the Glauber version of this model. Spin-flip rates in the new model are picked so no spin-flip rate vanishes as the temperature vanishes. Despite the more rapid spin flips, the new model exhibits an infinitely slow approach to equilibrium in the low-temperature limit which is similar to the slowing down exhibited in the Glauber model. The new model also exhibits two different decay rates toward equilibrium, which are called the transient and slow decay rates. The Glauber model is characterized by only a single decay rate toward equilibrium.Work supported in part by National Science Foundation grant DMR 78-03408.     

Beyond modified mean field: a case for a stochastic grain growth model

ABSTRACT

We address the basic mechanism of grain growth in two and three dimensions in single phase metallic systems. It is argued, a comprehensive grain growth model is best based on a stochastic process described by a Fokker Planck equation. This concept is sufficient to determine almost all features of grain growth in general terms. The existence of the von Neumann law and its counterpart in three dimensions enables us to provide an explicit form of the Fokker Planck equation and thus determine many features of grain growth in great detail. Finally, we illustrate this model by determining the salient features of grain growth in three dimensions in the long time limit, and comparing them with experimental and computational results.     

Phase stability of the penetrable-square-well model: an integral equation approach

We present an extensive investigation, based on the hypernetted-chain integral equation, of the topology of mechanically stable and unstable regions of the thermodynamic plane for the penetrable-square-well fluid. The results obtained are in qualitative agreement with Monte Carlo numerical simulation [R. Fantoni, A. Malijevský, A. Santos, and A. Giacometti, Europhys. Lett. 93, 26002 (2011)] and confirm the existence of a fluid–fluid transition between thermodynamically metastable phases. Moreover, we were able to investigate regimes where simulation is impractical, and showed that as the width of the attractive well vanishes, the metastable fluid–fluid transition disappears.     

Three-dimensional Lorentz model in a magnetic field: Exact and Chapman–Enskog solutions

We derive the exact solution of the Boltzmann kinetic equation for the three-dimensional Lorentz model in the presence of a constant and uniform magnetic field. The velocity distribution of the electrons reduces exponentially fast to its spherically symmetric component. In the long time hydrodynamic limit there remains only the diffusion process governed by an anisotropic diffusion tensor. The systematic way of building the Chapman–Enskog solutions is described.     

A spatiotemporal master equation model of morphogen transport: Local accumulation times,noise measurement and diffusion force

Morphogen, a class of signaling molecules to direct and control pattern formation of cell and tissue, is first synthesized in a local region and then conveyed to other regions or degraded. In the previous studies, this transport process was modeled by deterministic models of ordinary differential equations. In microcosmic environments, however, the process is often affected by stochastic fluctuations (or the noise). It remains unclear how this noise affects morphogen gradients. Here, we build a spatiotemporal master equation model for the process of morphogen transport in a finite developmental field, from which we derive the first-order moment equations of this master equation. We derive the analytical expression of the local accumulation time that the morphogens reach a steady state, and find that this time is nonlinear with respect to the cell positions. We also derive the approximate expressions of the steady-state variances, the Fano factors and the local accumulation time of the variance. Interestingly, we find that the local accumulation time for the variance of the morphogen number is shorter than that of its corresponding second-order moment. Moreover, the noise in the morphogen number is almost not affected by the distance from the cellular position to morphogen source. In addition, we further study some quantities (e.g., potential energy and diffusion force) from the view of physical-chemical mechanisms, and uncover that the diffusion force is a key factor for the formation of the morphogen gradient. Our results provide insights on morphogen diffusion.     

Reversible diffusion-influenced reactions: comparison of theory and simulation for a simple model

Computer simulations of a simple model of a reversible diffusion-influenced reaction are used to test various approximate theoretical treatments. The model is a random walk in continuous time ofN particles on a one-dimensional lattice. The particles can be trapped reversibly at the origin. They move independently, except that only one particle at a time can occupy the origin. The theory is formulated in general terms using master equations for the probability distribution of occupancy numbers of different lattice sites. The general theoretical problem is not solved, although some exact consequences are presented. Several approximation schemes are described and tested by comparison with the simulations.