Dynamics of structural defects and plasticity: models and numerical implementation for dynamical problems

We report the plasticity model with explicit description of kinetics of the material defects (dislocations, grain boundaries). This method becomes especially effective for computation of the dynamical deformation of materials at high strain rates because it allows for a simple accounting of the strain rate effects. The equation system is written out and discussed; its implementation is demonstrated for the problem of the plastic flow localization

Generalized Green Functions and current correlations in the TASEP

We study correlation functions of the totally asymmetric simple exclusion process (TASEP) in discrete time with backward sequential update. We prove a determinantal formula for the generalized Green function which describes transitions between positions of particles at different individual time moments. In particular, the generalized Green function defines a probability measure at staircase lines on the space-time plane. The marginals of this measure are the TASEP correlation functions in the space-time region not covered by the standard Green function approach. As an example, we calculate the current correlation function that is the joint probability distribution of times taken by selected particles to travel given distance. An asymptotic analysis shows that current fluctuations converge to the ${Airy}_2$ process.Comment: 46 pages, 3 figure

Exact Domain Integration in the Boundary Element Method for 2D Poisson Equation

Boundary value problems for Poisson equation often appear in electrical engineering applications, such as magnetic and electric field modeling and so on. In such context, effective techniques of solving such equations are subject of continuous development. This article reports an exact formula for domain integral in boundary-integral form of 2D Poisson Equation. This formula is derived for rectangle domain element

Statistics of layered zigzags: a two-dimensional generalization of TASEP

A novel discrete growth model in 2+1 dimensions is presented in three equivalent formulations: i) directed motion of zigzags on a cylinder, ii) interacting interlaced TASEP layers, and iii) growing heap over 2D substrate with a restricted minimal local height gradient. We demonstrate that the coarse-grained behavior of this model is described by the two-dimensional Kardar-Parisi-Zhang equation. The coefficients of different terms in this hydrodynamic equation can be derived from the steady state flow-density curve, the so called `fundamental' diagram. A conjecture concerning the analytical form of this flow-density curve is presented and is verified numerically.Comment: 5 pages, 4 figure

Total coloring of 1-toroidal graphs of maximum degree at least 11 and no adjacent triangles

A {\em total coloring} of a graph $G$ is an assignment of colors to the vertices and the edges of $G$ such that every pair of adjacent/incident elements receive distinct colors. The {\em total chromatic number} of a graph $G$, denoted by \chiup''(G), is the minimum number of colors in a total coloring of $G$. The well-known Total Coloring Conjecture (TCC) says that every graph with maximum degree $\Delta$ admits a total coloring with at most $\Delta + 2$ colors. A graph is {\em $1$-toroidal} if it can be drawn in torus such that every edge crosses at most one other edge. In this paper, we investigate the total coloring of $1$-toroidal graphs, and prove that the TCC holds for the $1$-toroidal graphs with maximum degree at least~$11$ and some restrictions on the triangles. Consequently, if $G$ is a $1$-toroidal graph with maximum degree $\Delta$ at least~$11$ and without adjacent triangles, then $G$ admits a total coloring with at most $\Delta + 2$ colors.Comment: 10 page

Mechanical characteristics, as well as physical-and-chemical properties of the slag-filled concretes, and investigation of the predictive power of the metaheuristic approach

Our article is devoted to development and verification of the metaheuristic optimisation algorithm in the course of selection of the compositional proportions of the slag-filled concretes. The experimental selection of various compositions and working modes, which ensure one and the same fixed level of a basic property, is the very labour-intensive and time-consuming process. This process cannot be feasible in practice in many situations, for example, in the cases, where it is necessary to investigate composite materials with equal indicators of resistance to aggressive environments or with equal share of voids in the certain range of dimensions. There are many similar articles in the scientific literature. Therefore, it is possible to make the conclusion on the topicality of the above-described problem. In our article, we will consider development of the methodology of the automated experimental-and-statistical determination of optimal compositions of the slag-filled concretes. In order to optimise search of local extremums of the complicated functions of the multi-factor analysis, we will utilise the metaheuristic optimisation algorithm, which is based on the concept of the swarm intelligence. Motivation in respect of utilisation of the swarm intelligence algorithm is conditioned by the absence of the educational pattern, within which it is not necessary to establish a certain pattern of learning as it is necessary to do in the neural-network algorithms. In the course of performance of this investigation, we propose this algorithm, as well as procedure of its verification on the basis of the immediate experimental verification. Open Access. © 2019 K. Borodin and N. Zhangabayuly Zhangabay, published by De Gruyter

Temperature, pressure and density of Venus' atmosphere according to measurement data of the AIS Venera-4

Atmospheric temperature, pressure, and density of Venus according to measurements obtained by AIS Venera-

Changing Bases: Multistage Optimization for Matroids and Matchings

This paper is motivated by the fact that many systems need to be maintained continually while the underlying costs change over time. The challenge is to continually maintain near-optimal solutions to the underlying optimization problems, without creating too much churn in the solution itself. We model this as a multistage combinatorial optimization problem where the input is a sequence of cost functions (one for each time step); while we can change the solution from step to step, we incur an additional cost for every such change. We study the multistage matroid maintenance problem, where we need to maintain a base of a matroid in each time step under the changing cost functions and acquisition costs for adding new elements. The online version of this problem generalizes online paging. E.g., given a graph, we need to maintain a spanning tree $T_t$ at each step: we pay $c_t(T_t)$ for the cost of the tree at time $t$, and also $| T_t\setminus T_{t-1} |$ for the number of edges changed at this step. Our main result is an $O(\log m \log r)$-approximation, where $m$ is the number of elements/edges and $r$ is the rank of the matroid. We also give an $O(\log m)$ approximation for the offline version of the problem. These bounds hold when the acquisition costs are non-uniform, in which caseboth these results are the best possible unless P=NP. We also study the perfect matching version of the problem, where we must maintain a perfect matching at each step under changing cost functions and costs for adding new elements. Surprisingly, the hardness drastically increases: for any constant $\epsilon>0$, there is no $O(n^{1-\epsilon})$-approximation to the multistage matching maintenance problem, even in the offline case

Finding the Median (Obliviously) with Bounded Space

We prove that any oblivious algorithm using space $S$ to find the median of a list of $n$ integers from $\{1,...,2n\}$ requires time $\Omega(n \log\log_S n)$. This bound also applies to the problem of determining whether the median is odd or even. It is nearly optimal since Chan, following Munro and Raman, has shown that there is a (randomized) selection algorithm using only $s$ registers, each of which can store an input value or $O(\log n)$-bit counter, that makes only $O(\log\log_s n)$ passes over the input. The bound also implies a size lower bound for read-once branching programs computing the low order bit of the median and implies the analog of $P \ne NP \cap coNP$ for length $o(n \log\log n)$ oblivious branching programs