Scaling Limits in Models of Statistical Mechanics

This conference (part of a long running series) aims to cover the interplay between probability and mathematical statistical mechanics. Specific topics addressed during the 22 talks include: Universality and critical phenomena, disordered models, Gaussian free field (GFF), random planar graphs and unimodular planar maps, reinforced random walks and non-linear σ-models, non-equilibrium dynamics. Less stress is given to topics which have running series of Oberwolfach conferences devoted to them specifically, such as random matrices or integrable models and KPZ universality class. There were 50 participants, including 9 postdocs and graduate students, working in diverse intertwining areas of probability, statistical mechanics and mathematical physics

MATHEMATICAL MODELING OF THE SEQUENCE OF MACHINING SECTIONS OF COMPLEX SURFACES WHEN MILLING ON A TRIAXIAL CNC MACHINE TOOL

The idle running times of the working units of a machine tool are the sum of the idle running times for the tool change and for changing the area uder treatment. The paper presents mathematical models, establishing the relationship between the additional time for performing the technological operations with the parameters of both the technological equipment and the object under treatment. The mathematical models for minimizing the idle moves when a tool passes from one machined section to another, allows to reduce the additional treatment time, which, in turn, leads to an increase in the productivity of the process of actual milling

Model Selection in Overlapping Stochastic Block Models

Networks are a commonly used mathematical model to describe the rich set of interactions between objects of interest. Many clustering methods have been developed in order to partition such structures, among which several rely on underlying probabilistic models, typically mixture models. The relevant hidden structure may however show overlapping groups in several applications. The Overlapping Stochastic Block Model (2011) has been developed to take this phenomenon into account. Nevertheless, the problem of the choice of the number of classes in the inference step is still open. To tackle this issue, we consider the proposed model in a Bayesian framework and develop a new criterion based on a non asymptotic approximation of the marginal log-likelihood. We describe how the criterion can be computed through a variational Bayes EM algorithm, and demonstrate its efficiency by running it on both simulated and real data.Comment: articl

An "All Possible Steps" Approach to the Accelerated Use of Gillespie's Algorithm

Many physical and biological processes are stochastic in nature. Computational models and simulations of such processes are a mathematical and computational challenge. The basic stochastic simulation algorithm was published by D. Gillespie about three decades ago [D.T. Gillespie, J. Phys. Chem. {\bf 81}, 2340, (1977)]. Since then, intensive work has been done to make the algorithm more efficient in terms of running time. All accelerated versions of the algorithm are aimed at minimizing the running time required to produce a stochastic trajectory in state space. In these simulations, a necessary condition for reliable statistics is averaging over a large number of simulations. In this study I present a new accelerating approach which does not alter the stochastic algorithm, but reduces the number of required runs. By analysis of collected data I demonstrate high precision levels with fewer simulations. Moreover, the suggested approach provides a good estimation of statistical error, which may serve as a tool for determining the number of required runs.Comment: Accepted for publication at the Journal of Chemical Physics. 19 pages, including 2 Tables and 4 Figure

WEST-3 wind turbine simulator development

The software developed for WEST-3, a new, all digital, and fully programmable wind turbine simulator is given. The process of wind turbine simulation on WEST-3 is described in detail. The major steps are, the processing of the mathematical models, the preparation of the constant data, and the use of system software generated executable code for running on WEST-3. The mechanics of reformulation, normalization, and scaling of the mathematical models is discussed in detail, in particulr, the significance of reformulation which leads to accurate simulations. Descriptions for the preprocessor computer programs which are used to prepare the constant data needed in the simulation are given. These programs, in addition to scaling and normalizing all the constants, relieve the user from having to generate a large number of constants used in the simulation. Also given are brief descriptions of the components of the WEST-3 system software: Translator, Assembler, Linker, and Loader. Also included are: details of the aeroelastic rotor analysis, which is the center of a wind turbine simulation model, analysis of the gimbal subsystem; and listings of the variables, constants, and equations used in the simulation

Analysis of Reforming Gas Combustion in Internal Combustion Engine

Abstract The present paper deals with the study of the combustion of reforming gas in a small size Internal Combustion Engine. Therefore, mathematical models of both reforming process and internal combustion engine were implemented. In particular, steams reforming of glycerol to produce synthesis gas and spark ignition four strokes ICE were studied. The reforming process mathematical model was verified using experimental data. Synthesis gas was used to feed the ICE with different syngas and engine configuration. On the basis of the comparison with the experimental results, it is possible to state that the mathematical model is validated. Engine performance and pollutant emission evaluation was carried out using the integrated mathematical models with reference to the engine running on standard commercial fuel. The results highlight a reduction in engine performance and, at the same time a reduction of pollutant emissions in terms of CO and CO 2