Numerical simulation of particle dynamics in a storage ring by using BETACOOL program

The BETACOOL program, developed by electron cooling group of the Joint Institute for Nuclear Research (JINR), is a set of algorithms based on common format of input and output files. The program is oriented toward simulation of the ion beam dynamics in a storage ring in the presence of cooling and heating effects. The version presented in this report includes three basic algorithms: simulation of root-mean-square (rms) parameters of the particle distribution function evolving in time, simulation of the distribution function evolution using the Monte Carlo method, and a tracking algorithm based on a molecular dynamics technique. The general processes investigated with the program are intrabeam scattering in the ion beam, electron cooling, and interaction with residual gas and an internal target.     

Algorithms for Brownian dynamics

We derive a class of efficient and stable algorithms of Brownian dynamics using a formula, derived by Suzuki, to express time-ordered operators. These algorithms are simpler than those derived by Helfand from Runge-Kutta algorithms and, like Helfand algorithms, can be combined with SHAKE to describe the Brownian dynamics of constrained systems.     

Mesoscopic Modeling for Continuous Spin Lattice Systems: Model Problems and Micromagnetics Applications

In this paper we derive deterministic mesoscopic theories for model continuous spin lattice systems both at equilibrium and non-equilibrium in the presence of thermal fluctuations. The full magnetic Hamiltonian that includes singular integral (dipolar) interactions is also considered at equilibrium. The non-equilibrium microscopic models we consider are relaxation-type dynamics arising in kinetic Monte Carlo or Langevin-type simulations of lattice systems. In this context we also employ the derived mesoscopic models to study the relaxation of such algorithms to equilibrium     

An adaptive template method for analyzing crystal structures and defects in molecular dynamics simulations of high-rate deformations

The paper presents a review and comparative analysis of several algorithms for the recognition of crystal structures and defects of various types used in molecular dynamics simulations of materials. A new algorithm called the adaptive template analysis is suggested. Unlike the other algorithms, it is iterative. The algorithms considered were tested in molecular dynamics calculations taking into account temperature changes and high-rate deformation in shock waves.     

3D simulation of the ion-beam transport in bending magnets and electrostatic deflectors

The equations and algorithms for calculating the charged-particle-beam dynamics in bending magnets and electrostatic deflectors, which are used in the ion-beam transport lines and spectrometers, are presented. Calculations of the electromagnetic field 3D maps are illustrated. The value of the electromagnetic-field nonlinearities and their effect on the particle dynamics are analyzed. The simulation of the ion dynamics in the axial injection beam line of the DC-280 cyclotron and GALS spectrometer created at the JINR Laboratory of Nuclear Reactions (FLNR) is described.     

Diffusion generated motion using signed distance functions

We describe a new class of algorithms for generating a variety of geometric interfacial motions by alternating two steps: Construction of the signed distance function (i.e. redistancing) to the interface, and convolution with a suitable kernel. These algorithms can be seen as variants of Merriman, Bence, and Osher’s threshold dynamics [25]. The new algorithms proposed here preserve the computational efficiency of the original threshold dynamics algorithm. However, unlike threshold dynamics, the new algorithms also allow attaining high accuracy on uniform grids, without adaptive refinement.     

Liapunov exponents and the reversibility of molecular dynamics algorithms

We study the phenomenon of lack of reversibility in molecular dynamics algorithms for the case of Wilson's lattice QCD. We demonstrate that the classical equations of motion that are employed in these algorithms are chaotic in nature. The leading Liapunov exponent is determined in a range of coupling parameters. We consider the consequences of the breakdown of reversibility due to round-off errors.     

导热系数的分子动力学模拟研究及相关问题的探讨

对于采用分子动力学方法研究导热系数的背景、研究现状及存在的问题进行了综述和分析。总结了通过分子动力学模拟方法求得导热系数的物理模型和基本算法。讨论了目前在微尺度导热问题的研究中引入分子动力学模拟方法需要考察的影响因素和几个重要问题。     

Dynamics of heuristic optimization algorithms on random graphs

In this paper, the dynamics of heuristic algorithms for constructing small vertex covers (or independent sets) of finite-connectivity random graphs is analysed. In every algorithmic step, a vertex is chosen with respect to its vertex degree. This vertex, and some environment of it, is covered and removed from the graph. This graph reduction process can be described as a Markovian dynamics in the space of random graphs of arbitrary degree distribution. We discuss some solvable cases, including algorithms already analysed using different techniques, and develop approximation schemes for more complicated cases. The approximations are corroborated by numerical simulations. Received 14 March 2002 Published online 31 July 2002     

Structure and dynamics of a dense dipolar system in an electric field and their relevance to electrorheological fluids

Results of computer simulations of a dense system of dipolar spheres in an electric field are summarized. Dissipative and Hamiltonian dynamics algorithms have been used to find energy minima of the system for varying particle densities. The structures obtained by these simulations are in reasonable agreement with experimentally observed structures in electrorheological (ER) fluids. Qualitative agreement is also obtained with the limited available experimental observations on the dynamics of ER fluids.     

Optimal UAV Formation Tracking Control with Dynamic Leading Velocity and Network-Induced Delays

With the rapid development of UAV technology, the research of optimal UAV formation tracking has been extensively studied. However, the high maneuverability and dynamic network topology of UAVs make formation tracking control much more difficult. In this paper, considering the highly dynamic features of uncertain time-varying leader velocity and network-induced delays, the optimal formation control algorithms for both near-equilibrium and general dynamic control cases are developed. First, the discrete-time error dynamics of UAV leader–follower models are analyzed. Next, a linear quadratic optimization problem is formulated with the objective of minimizing the errors between the desired and actual states consisting of velocity and position information of the follower. The optimal formation tracking problem of near-equilibrium cases is addressed by using a backward recursion method, and then the results are further extended to the general dynamic case where the leader moves at an uncertain time-varying velocity. Additionally, angle deviations are investigated, and it is proved that the similar state dynamics to the general case can be derived and the principle of control strategy design can be maintained. By using actual real-world data, numerical experiments verify the effectiveness of the proposed optimal UAV formation-tracking algorithm in both near-equilibrium and dynamic control cases in the presence of network-induced delays.     

Mesoscale simulations: Lattice Boltzmann and particle algorithms

I introduce two mesoscale algorithms, lattice Boltzmann and stochastic rotation dynamics, and show how they can be used to investigate the hydrodynamics of complex fluids. For each method I describe the algorithm, show that it solves the Navier–Stokes equations, and then discuss physical problems where it is particularly applicable. For lattice Boltzmann the examples I choose are phase ordering in a binary fluid and drop dynamics on a chemically patterned surface. For stochastic rotation dynamics I consider the hydrodynamics of dilute polymer solutions, concentrating on shear thinning and translocation across a barrier.     

Control Meets Inference: Using Network Control to Uncover the Behaviour of Opponents

Using observational data to infer the coupling structure or parameters in dynamical systems is important in many real-world applications. In this paper, we propose a framework of strategically influencing a dynamical process that generates observations with the aim of making hidden parameters more easily inferable. More specifically, we consider a model of networked agents who exchange opinions subject to voting dynamics. Agent dynamics are subject to peer influence and to the influence of two controllers. One of these controllers is treated as passive and we presume its influence is unknown. We then consider a scenario in which the other active controller attempts to infer the passive controller’s influence from observations. Moreover, we explore how the active controller can strategically deploy its own influence to manipulate the dynamics with the aim of accelerating the convergence of its estimates of the opponent. Along with benchmark cases we propose two heuristic algorithms for designing optimal influence allocations. We establish that the proposed algorithms accelerate the inference process by strategically interacting with the network dynamics. Investigating configurations in which optimal control is deployed. We first find that agents with higher degrees and larger opponent allocations are harder to predict. Second, even factoring in strategical allocations, opponent’s influence is typically the harder to predict the more degree-heterogeneous the social network.     

Monte Carlo techniques for real-time quantum dynamics

The stochastic-gauge representation is a method of mapping the equation of motion for the quantum mechanical density operator onto a set of equivalent stochastic differential equations. One of the stochastic variables is termed the “weight”, and its magnitude is related to the importance of the stochastic trajectory. We investigate the use of Monte Carlo algorithms to improve the sampling of the weighted trajectories and thus reduce sampling error in a simulation of quantum dynamics. The method can be applied to calculations in real time, as well as imaginary time for which Monte Carlo algorithms are more-commonly used. The Monte-Carlo algorithms are applicable when the weight is guaranteed to be real, and we demonstrate how to ensure this is the case. Examples are given for the anharmonic oscillator, where large improvements over stochastic sampling are observed.     

A scalable framework for the solution of stochastic inverse problems using a sparse grid collocation approach

Experimental evidence suggests that the dynamics of many physical phenomena are significantly affected by the underlying uncertainties associated with variations in properties and fluctuations in operating conditions. Recent developments in stochastic analysis have opened the possibility of realistic modeling of such systems in the presence of multiple sources of uncertainties. These advances raise the possibility of solving the corresponding stochastic inverse problem: the problem of designing/estimating the evolution of a system in the presence of multiple sources of uncertainty given limited information.A scalable, parallel methodology for stochastic inverse/design problems is developed in this article. The representation of the underlying uncertainties and the resultant stochastic dependant variables is performed using a sparse grid collocation methodology. A novel stochastic sensitivity method is introduced based on multiple solutions to deterministic sensitivity problems. The stochastic inverse/design problem is transformed to a deterministic optimization problem in a larger-dimensional space that is subsequently solved using deterministic optimization algorithms. The design framework relies entirely on deterministic direct and sensitivity analysis of the continuum systems, thereby significantly enhancing the range of applicability of the framework for the design in the presence of uncertainty of many other systems usually analyzed with legacy codes. Various illustrative examples with multiple sources of uncertainty including inverse heat conduction problems in random heterogeneous media are provided to showcase the developed framework.     

Computer simulation studies of magnetic phase transitions

The advancements which have been made in the use of computer simulations to study magnetic-phase transitions and critical phenomena are reviewed. We describe how the use of a combination of sophisticated Monte Carlo simulation algorithms and reweighting (histogram) techniques have allowed the determination of the static critical behavior with unprecedented precision. The study of “dynamic” critical behavior in simple spin models by both Monte Carlo and spin dynamics methods is also reviewed. Recent estimates for dynamic critical exponents are given including those for true dynamics.     

Point Symmetries of Controlled Systems and Their Applications

Abstract

A problem of finding point symmetries of controlled systems is discussed, basic theorems and algorithms are formulated. The application to some problems of flight dynamics is suggested.     

Multiscale entropy analysis of complex physiologic time series

There has been considerable interest in quantifying the complexity of physiologic time series, such as heart rate. However, traditional algorithms indicate higher complexity for certain pathologic processes associated with random outputs than for healthy dynamics exhibiting long-range correlations. This paradox may be due to the fact that conventional algorithms fail to account for the multiple time scales inherent in healthy physiologic dynamics. We introduce a method to calculate multiscale entropy (MSE) for complex time series. We find that MSE robustly separates healthy and pathologic groups and consistently yields higher values for simulated long-range correlated noise compared to uncorrelated noise.     

Community detection using global and local structural information

Community detection is of considerable importance for understanding both the structure and function of complex networks. In this paper, we introduced the general procedure of the community detection algorithms using global and local structural information, where the edge betweenness and the local similarity measures respectively based on local random walk dynamics and local cyclic structures were used. The algorithms were tested on artificial and real-world networks. The results clearly show that all the algorithms have excellent performance in the tests and the local similarity measure based on local random walk dynamics is superior to that based on local cyclic structures.