Analysis of flow dynamics on Buslaev contour networks

Traffic flow models on networks are relevant because of exponential growth of road transport in megalopolises worldwide. But there are not enough adequate approaches to describe such processes. Buslaev A.P. with co-authors had introduced networks of contours with common nodes, local particles movement on each contour in given direction and competition resolution rules in common nodes. The problem is to study limit system behavior in dependence on initial conditions. In mathematical models of communication systems and computer networks, particles correspond to messages or information blocks (message packages). Behavior of particles on a contour chain with two cells on each contour is similar to behavior of Ising model used in quantum mechanics. In particular, Ising model is used for modeling of behavior of experimental computers based on principles of quantum mechanics. Contour network models can be used for study of spectral quantization. We study a behavior contour networks of Buslaev type for regular cases depending on rules of competition resolutions in common nodes. Exact results were obtained for closed chain with opposite and odd-even resolution rules, and stochastic version of left-priority rule with non-zero probability of indecisive movement

Spectrum of continuous two-contours system

A deterministic continuous dynamical system is considered. This system contains two contours. The length of the ith contour equals ci, i = 1, 2. There is a moving segment (cluster) on each contour. The length of the cluster, located on the ith contour, equals li , i = 1, 2. If a cluster moves without delays, then the velocity of the cluster is equal to 1. There is a common point (node) of the contours. Clusters cannot cross the node simultaneously, and therefore delays of clusters occur. A set of repeating system states is called a spectral cycle. Spectral cycles and values of average velocities of clusters have been found. The system belongs to a class of contour systems. This class of dynamical systems has been introduced and studied by A.P. Buslaev

Computational investigations of single-chain nanoparticles: novel synthesis routes, complex flow behavior and reversible gel formation.

167 p.Las llamadas nanopartículas unicadena ("single-chain nanoparticles", SCNPs) se obtienen mediante enlazamiento puramente intramolecular de precursores poliméricos. Hay un interés creciente en estos sistemas debido a sus prometedoras aplicaciones en catálisis, biomedicina, sensores, nanocompuestos, etc. El conocimiento de su estructura y dinámica, que controlan en gran parte su respuesta al entorno, es aún escaso. Esta tesis supone un importante avance en dicho conocimiento al investigar tres problemas de interés fundamental y práctico aún inexplorados. Mediante técnicas de simulación computacional se estudia y demuestra: 1) La posibilidad de controlar la topología (en particular la compacidad) de las SCNPs usando anillos como precursores en disoluciones concentradas de anillos inertes (con interacciones puramente estéricas). 2) La respuesta de las SCNPs al flujo de cizalla, cubriendo todo el intervalo desde alta dilución hasta disolución concentrada. Las SCNPs muestran una respuesta independiente de su topología concreta, únicamente ligada a su arquitectura de tipo red polimérica. A diferencia del caso simple de cadenas lineales, la respuesta es diferente a ambos lados de la concentración de solapamiento, este efecto estando ligado a las interacciones topológicas que evitan la concatenación de los anillos presentes en su arquitectura. 3) La competición entre enlaces intra- e intermoleculares en disoluciones de SCNPs con enlaces reversibles, y la obtención de geles reversibles basados en SCNPs, con redes estables altamente dinámicas y evitando la separación de fases a concentraciones de interés.CFM:Materials Physics Cente

Computational investigations of single-chain nanoparticles: novel synthesis routes, complex flow behavior and reversible gel formation.

167 p.Las llamadas nanopartículas unicadena ("single-chain nanoparticles", SCNPs) se obtienen mediante enlazamiento puramente intramolecular de precursores poliméricos. Hay un interés creciente en estos sistemas debido a sus prometedoras aplicaciones en catálisis, biomedicina, sensores, nanocompuestos, etc. El conocimiento de su estructura y dinámica, que controlan en gran parte su respuesta al entorno, es aún escaso. Esta tesis supone un importante avance en dicho conocimiento al investigar tres problemas de interés fundamental y práctico aún inexplorados. Mediante técnicas de simulación computacional se estudia y demuestra: 1) La posibilidad de controlar la topología (en particular la compacidad) de las SCNPs usando anillos como precursores en disoluciones concentradas de anillos inertes (con interacciones puramente estéricas). 2) La respuesta de las SCNPs al flujo de cizalla, cubriendo todo el intervalo desde alta dilución hasta disolución concentrada. Las SCNPs muestran una respuesta independiente de su topología concreta, únicamente ligada a su arquitectura de tipo red polimérica. A diferencia del caso simple de cadenas lineales, la respuesta es diferente a ambos lados de la concentración de solapamiento, este efecto estando ligado a las interacciones topológicas que evitan la concatenación de los anillos presentes en su arquitectura. 3) La competición entre enlaces intra- e intermoleculares en disoluciones de SCNPs con enlaces reversibles, y la obtención de geles reversibles basados en SCNPs, con redes estables altamente dinámicas y evitando la separación de fases a concentraciones de interés.CFM:Materials Physics Cente

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum

On linear, fractional, and submodular optimization

In this thesis, we study four fundamental problems in the theory of optimization. 1. In fractional optimization, we are interested in minimizing a ratio of two functions over some domain. A well-known technique for solving this problem is the Newton– Dinkelbach method. We propose an accelerated version of this classical method and give a new analysis using the Bregman divergence. We show how it leads to improved or simplified results in three application areas. 2. The diameter of a polyhedron is the maximum length of a shortest path between any two vertices. The circuit diameter is a relaxation of this notion, whereby shortest paths are not restricted to edges of the polyhedron. For a polyhedron in standard equality form with constraint matrix A, we prove an upper bound on the circuit diameter that is quadratic in the rank of A and logarithmic in the circuit imbalance measure of A. We also give circuit augmentation algorithms for linear programming with similar iteration complexity. 3. The correlation gap of a set function is the ratio between its multilinear and concave extensions. We present improved lower bounds on the correlation gap of a matroid rank function, parametrized by the rank and girth of the matroid. We also prove that for a weighted matroid rank function, the worst correlation gap is achieved with uniform weights. Such improved lower bounds have direct applications in submodular maximization and mechanism design. 4. The last part of this thesis concerns parity games, a problem intimately related to linear programming. A parity game is an infinite-duration game between two players on a graph. The problem of deciding the winner lies in NP and co-NP, with no known polynomial algorithm to date. Many of the fastest (quasi-polynomial) algorithms have been unified via the concept of a universal tree. We propose a strategy iteration framework which can be applied on any universal tree