Anomalous Diffusion Equations with Multiplicative Acceleration

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.     

Anomalous Diffusion in a Linear Plasma Generator

Plasma production and particle transport of the magnetized plasma in the linear device PSI‐2 are investigated by analyzing the radial density and electron temperature pro.les obtained from Langmuir probe measurements. Additional information on the atomic (H) and proton temperatures is obtained from high resolution Doppler spectroscopy. The density profiles are found to be hollow, but do extend radially far beyond the visible rim with an exponential decay length of 3 cm. They can be explained by parallel and perpendicular diffusion in combination with a cylindrical source extending along the magnetic field all over the device. A large perpendicular diffusion coefficient in the range of 5 m²/s is inferred from the experimental results. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

纳米颗粒在复杂生物介质中的反常扩散

由于生物微环境中存在各向异性等复杂物理因素影响,纳米颗粒在其中的扩散运动表现出反常的特征.反常扩散与生物微环境的功能实现有重要的关联,同时也是流体力学在微纳尺度方向的重要扩展.该综述系统介绍了近年来反常扩散研究的进展,从物理模型、数值模拟、测量方法及实验现象等方面揭示了纳米颗粒在复杂生物介质中的反常扩散机理及特征.该问题在微纳尺度流体力学、生物物理等领域是研究的热点,在理论上和实验时仍有重大挑战,有待进一步深入研究.      

Detection of Anomalous Diffusion with Deep Residual Networks

Identification of the diffusion type of molecules in living cells is crucial to deduct their driving forces and hence to get insight into the characteristics of the cells. In this paper, deep residual networks have been used to classify the trajectories of molecules. We started from the well known ResNet architecture, developed for image classification, and carried out a series of numerical experiments to adapt it to detection of diffusion modes. We managed to find a model that has a better accuracy than the initial network, but contains only a small fraction of its parameters. The reduced size significantly shortened the training time of the model. Moreover, the resulting network has less tendency to overfitting and generalizes better to unseen data.     

On Nonlinear Functionals of Random Spherical Eigenfunctions

We prove central limit theorems and Stein-like bounds for the asymptotic behaviour of nonlinear functionals of spherical Gaussian eigenfunctions. Our investigation combines asymptotic analysis of higher order moments for Legendre polynomials and, in addition, recent results on Malliavin calculus and total variation bounds for Gaussian subordinated fields. We discuss applications to geometric functionals like the defect and invariant statistics, e.g., polyspectra of isotropic spherical random fields. Both of these have relevance for applications, especially in an astrophysical environment.     

Anomalous Diffusion Limit Induced on a Kinetic Equation

Using a compactness argument based on the velocity averaging lemma of Golse et al., it is shown that the limiting behavior of a kinetic (linearized BGK) gas model confined between two plates with Maxwell boundary conditions, when the distance between the plates goes to zero, under a suitable anomalous scaling, is diffusive. We do not require the use of central limit theorems as in the method of Börgers et al.     

Anomalous Dimension in the Solution of a Nonlinear Diffusion Equation

A new method is used to obtain the anomalous dimension in the solution of the nonlinear diffusion equation.The result is the same as that in the renormalization group (RG) approach.It gives us an insight into the anomalous dimension in the solution of the nonlinear diffusion equation in the RG approach.Based on this discussion,we can see anomalous dimension appears naturally in this system.``     

Anomalous Dimension in the Solution of a Nonlinear Diffusion Equation

A new method is used to obtain the anomalous dimension in the solution of the nonlinear diffusion equation.The result is the same as that in the renormalization group (RG) approach.It gives us an insight into the anomalous dimension in the solution of the nonlinear diffusion equation in the RG approach.Based on this discussion,we can see anomalous dimension appears naturally in this system.     

Anomalous Diffusion in a Model with a Variable Percolation Radius

Anomalous diffusion models for random 1-D cluster and comb structures of length L = 100 with finite fingers and different boundary conditions are considered. The effect of electric field on anomalous diffusion is discussed. The cases with different percolation radii are compared. The comb-structure model with periodic boundary conditions is shown to be useful in studying various types of anomalous diffusion. A new diffusion type, where the average rate is higher than the typical rate, is predicted. Physical causes for this diffusion are revealed.     

反常扩散:定向通过一个势能鞍点

考虑一个处于非Ohmic环境下的系统定向通过一个倒谐振子势鞍点的输运过程,给出了通过几率的解析式。结果表明在欠扩散情况下,时间有关的通过几率出现一个很强的超前峰和回流,这可能有助于理解重核熔合系统的激发函数随质心能量的慢增长机制。Directional transport of a particle in a non-Ohmic environment passing over the saddle point of a potential is considered and the analytical expression of the passing probability is obtained. Our results has shown that both overshooting and backflow are observed in the case of subdiffusion. This is a possible for understanding slow increasing of the fusion probability with the center-of-mass energy.     

On the Nuclear Effects of Valence Quark Distributions and Sea Quark Distributions

In this paper we present a method which may be used to get the nuclear effect functions R_υ^A(x_t) and R_s^A(x_t) for valence quark distributions and sea quark distributions in the light of the data of 1-A deep inelastic scattering and nuclear Drell-Yan process. Both the functions may be used to test the theoretical models explaining the nuclear effects. With nuclei Fe, Ca and C as examples, the results are shown.     

On Summability of Distributions and Spectral Geometry

Modulo the moment asymptotic expansion, the Cesáro and parametric behaviours of distributions at infinity are equivalent. On the strength of this result, we construct the asymptotic analysis for spectral densities arising from elliptic pseudodifferential operators. We show how Cesáro developments lead to efficient calculations of the expansion coefficients of counting number functionals and Green functions. The bosonic action functional proposed by Chamseddine and Connes can more generally be validated as a Cesáro asymptotic development. Received: 10 February 1997 / Accepted: 8 May 1997     

On the Anomalous Acceleration of Pioneer Spacecrafts

The anomalous acceleration of Pioneer 10 and 11 spacecrafts of (8.74± 1.33) × 10⁻⁸ cm s⁻² fits with a theoretical prediction of a minimal acceleration in nature of 7.61× 10⁻⁸ cm s⁻².     

On Spin Distributions for Generic p-Spin Models

Journal of Statistical Physics - We provide an alternative formula for spin distributions of generic p-spin glass models. As a main application of this expression, we write spin statistics as...     

A Multi-Scale Entropy Approach to Study Collapse and Anomalous Diffusion in Shared Mobility Systems

In this paper, we study the phenomena of collapse and anomalous diffusion in shared mobility systems. In particular, we focus on a fleet of vehicles moving through a stations network and analyse the effect of self-journeys in system stability, using a mathematical simplex under stochastic flows. With a birth-death process approach, we find analytical upper bounds for random walk and we monitor how the system collapses by super diffusing under different randomization conditions. Using the multi-scale entropy metric, we show that real data from a bike-sharing fleet in the city of Salamanca (Spain) present a complex behaviour with more of a 1/f signal than a disorganized system with a white noise signal.