Integrals, partitions, and cellular automata

We prove that

where is the decreasing function that satisfies , for . When is an integer and we deduce several combinatorial results. These include an asymptotic formula for the number of integer partitions not having consecutive parts, and a formula for the metastability thresholds of a class of threshold growth cellular automaton models related to bootstrap percolation.

     

Deterministic automata simulation, universality and minimality

Finite automata have been recently used as alternative, discrete models in theoretical physics, especially in problems related to the dichotomy between endophysical/intrinsic and exophysical/ extrinsic perception (see, for instance [3, 6, 18–21]). These studies deal with Moore experiments; the main result states that it is impossible to determine the initial state of an automaton, and, consequently, a discrete model of Heisenberg uncertainty has been suggested. For this aim the classical theory of finite automata — which considers automata with initial states — is not adequate, and a new approach is necessary. A study of finite deterministic automata without initial states is exactly the aim of this paper. We will define and investigate the complexity of various types of simulations between automata. Minimal automata will be constructed and proven to be unique up to an isomorphism. We will build our results on an extension of Myhill-Nerode technique; all constructions will make use of “automata responses” to simple experiments only, i.e., no information about the internal machinery will be considered available.     

Ergodicity of quantum cellular automata

We define a class of dynamical maps on the quasi-local algebra of a quantum spin system, which are quantum analoges of probabilistic cellular automata. We develop criteria for such a system to be ergodic, i.e., to posses a unique invariant state. Intuitively, ergodicity obtains if the local transition operators exhibit sufficiently large disorder. The ergodicity criteria also imply bounds for the exponential decay of correlations in the unique invariant state. The main technical tool is a quantum version of oscillation norms, defined in the classical case as the sum over all sites of the variations of an observable with respect to local spin flips.     

双车道元胞自动机NS和WWH交通流混合模型的研究

考虑不同车辆的驾驶员有不同的驾驶方式和习惯，具体表现为不同的驾驶员采用适合自己行车特点的交通流模型在道路上驾车行驶，在一维元胞自动机交通流NS模型和WWH模型的基础上，建立了双车道元胞自动机NS和WWH交通流混合模型. 通过计算机模拟，给出了混合比例系数f_NS对混合交通流的速度-密度和流量-密度图以及车辆转道频率影响的结果. 关键词： 双车道 元胞自动机 混合交通流模型 计算机数值模拟     

On the uniaxial compression behavior of regular shaped cellular metals

The numerical simulation of random cellular metals is still connected to many unsolved problems due to their stochastic structure. Therefore, a periodic model of a cellular metal is developed for fundamental studies of the mechanical behavior and is numerically investigated under uniaxial compression. The influence of differing hardening behaviors and differing boundary conditions on the characteristics of the material is investigated. Recommendations for the numerical simulation are derived. In contrast to common models, experimental samples of the same geometry are easy to manufacture and the results of the experiments show good agreement with the finite element calculations. Based on the proposed concept of a unit cell with periodic boundary conditions, it is possible to derive constitutive equations of cellular materials under complex loading conditions.     

固定闭塞系统下列车运行限速区段交通流特性分析

针对铁路交通中四显示固定自动闭塞系统下的限速区段，建立了元胞自动机模型，对限速区段的交通流进行了模拟，分析了限速区段长度、发车时间间隔和限速值对交通流的影响，模拟结果表明减少限速区段长度、适当增加发车时间间隔和提高限速区段限速值都可增加列车在绿灯下的运行时间. 关键词： 四显示固定自动闭塞 元胞自动机 交通流     

A Monte Carlo ray tracing study of polarized light propagation in liquid foams

A Monte Carlo ray tracing scheme is used to investigate the propagation of an incident collimated beam of polarized light in liquid foams. Cellular structures like foam are expected to change the polarization characteristics due to multiple scattering events, where such changes can be used to monitor foam dynamics. A statistical model utilizing some of the recent developments in foam physics is coupled with a vector Monte Carlo scheme to compute the depolarization ratios via Stokes-Mueller formalism. For the simulations, the incident Stokes vector corresponding to horizontal linear polarization and right circular polarization are considered. It is observed that bubble size and the polydispersity parameter have a significant effect on the depolarization ratios. This is partially owing to the number of total internal reflection events in the Plateau borders. The results are discussed in terms of applicability of polarized light as a diagnostic tool for monitoring foams.     

Cellular automaton model for evacuation process with obstacles

A bidimensional cellular automaton model is used to simulate the process of evacuation of pedestrians in a room with fixed obstacles. A floor field is defined so that moving to a cell with lower floor field means approaching an exit door. The model becomes non-deterministic by introducing a “panic” parameter, given by a probability of not moving, and by a random choice to resolve conflicts in the update of pedestrian positions. Two types of exit doors are considered: single (where only one person can pass) and double (two persons can pass simultaneously). For a double door, the longest evacuation time turns out to occur for a very traditional location of the door. The optimum door position is determined. Replacing the double door by two single doors does not improve evacuation times noticeably. On the other hand, for a room without obstacles, a simple scaling law is proposed to model the dependence of evacuation time with the number of persons and exit width. This model fails when obstacles are present, as their presence introduces local bottlenecks whose effect outweighs the benefits of increasing door width beyond a certain threshold.     

Framework Nucleic Acids for Cell Imaging and Therapy

Over the past decade,structural DNA nanotechnology has been well developed to be a promising and powerful technique to generate various nanostructures with programmability,spatial organization and biocompatibi-lity.With the advent of computer-aided tools,framework nucleic acids have been employed in a series of biomedical applications,ranging from biosensing,bioimaging,diagnosis,to therapeutics.In this review,we summarized recent advances in the construction of precisely assembled DNA nanostructures,and DNA-engineered biomimetics.We also outlined the challenges and opportunities for the translational applications of framework nucleic acids.     

Modeling framework for optimal evacuation of large-scale crowded pedestrian facilities

The paper presents a simulation–optimization modeling framework for the evacuation of large-scale pedestrian facilities with multiple exit gates. The framework integrates a genetic algorithm (GA) and a microscopic pedestrian simulation–assignment model. The GA searches for the optimal evacuation plan, while the simulation model guides the search through evaluating the quality of the generated evacuation plans. Evacuees are assumed to receive evacuation instructions in terms of the optimal exit gates and evacuation start times. The framework is applied to develop an optimal evacuation plan for a hypothetical crowded exhibition hall. The obtained results show that the model converges to a superior optimal evacuation plan within an acceptable number of iterations. In addition, the obtained evacuation plan outperforms conventional plans that implement nearest-gate immediate evacuation strategies.