Research ArticleOpen accessIn the keywordsConstructing Gibbs Measure in a Rigorous WayFarida Kachapova, Ilias KachapovEquilibrium statistical mechanics studies mathematical models for physical systems with many particles interacting with an external force and with one another. In this paper we describe an interaction model that generalizes several of these models in one model. An infinite model is constructed as the limiting case of finite interaction models, that is as a thermodynamic limit. The key point … …Journal of Mathematics and Statistics, Vol. 15, Issue 1 · 29 Oct 2019 · 6,591 accessesView PDFCite
Research ArticleOpen accessIn the keywordsInteraction Model in Statistical MechanicsFarida Kachapova, Ilias KachapovStatistical mechanics considers several models such as Ising model, Potts model, Heisenberg model etc. A rigorous mathematical approach based on the axiomatic foundation of probability would benefit the study and applications of these models. In this paper we use this approach to generalize some of these models into one construction named an interaction model. We introduce a mathematically rigorous definition … …Journal of Mathematics and Statistics, Vol. 13, Issue 4 · 4 Nov 2017 · 7,054 accessesView PDFCite
EditorialOpen accessIn the abstractThe Proton Radius PuzzleG. M. HuberOccasionally,“revolutions” are caused in physics when new measurement techniques becomeavailable and cause us to rethink what we thought we knew. This has recently happenedin the field of proton structure physics, where researchers have had to revisitfundamental assumptions used in their determinations of the proton's meanelectric charge radius. Until 2010, ourknowledge of the proton's electric charge radius came exclusively fromelectron-proton interactions. … …Physics International, Vol. 6, Issue 1 · 12 Sep 2015 · 8,321 accessesView PDFCite
Research ArticleOpen accessIn the abstractLaser-Induced Breakdown and Detonation in Particle-Laden SystemsKonstantin VolkovSimulation of the interaction of a laser pulse with gas-droplet and gas-particle mixtures plays an important role in environmental and engineering applications. The injection of liquid droplets or metal particle causes optical breakdown on the individual droplet or particle and leads to a drop of the detonation minimum pulse energy of the mixture. Mathematical models of various stages of the … …American Journal of Applied Sciences, Vol. 12, Issue 1 · 4 Mar 2015 · 7,348 accessesView PDFCite
Research ArticleOpen accessIn the abstractEffect of Impact Level and Fruit Properties on Golden Delicious Apple BruisingArzhang Javadi, Ebrahim Ahmadi, Mohammad Hossein Abbaspour-Fard et al.Problem Statement: Bruise damage is a major cause of fruit quality loss. Bruises occur under dynamic and static loading when stress induced in the fruit exceeds the failure stress of the fruit tissue. Statistical bruise estimation models were constructed to calculate Golden Delicious apple bruise volume with respect to fruit properties. Approach: The regression models were built based upon impact … …American Journal of Agricultural and Biological Sciences, Vol. 5, Issue 2 · 30 Jun 2010 · 9,259 accessesView PDFCite