scholarly journals Symmetry Breaking in Stochastic Dynamics and Turbulence

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1193
Author(s):  
Michal Hnatič ◽  
Juha Honkonen ◽  
Tomáš Lučivjanský

Symmetries play paramount roles in dynamics of physical systems. All theories of quantum physics and microworld including the fundamental Standard Model are constructed on the basis of symmetry principles. In classical physics, the importance and weight of these principles are the same as in quantum physics: dynamics of complex nonlinear statistical systems is straightforwardly dictated by their symmetry or its breaking, as we demonstrate on the example of developed (magneto)hydrodynamic turbulence and the related theoretical models. To simplify the problem, unbounded models are commonly used. However, turbulence is a mesoscopic phenomenon and the size of the system must be taken into account. It turns out that influence of outer length of turbulence is significant and can lead to intermittency. More precisely, we analyze the connection of phenomena such as behavior of statistical correlations of observable quantities, anomalous scaling, and generation of magnetic field by hydrodynamic fluctuations with symmetries such as Galilean symmetry, isotropy, spatial parity and their violation and finite size of the system.

2021 ◽  
Vol 20 (5) ◽  
pp. 1-34
Author(s):  
Edward A. Lee

This article is about deterministic models, what they are, why they are useful, and what their limitations are. First, the article emphasizes that determinism is a property of models, not of physical systems. Whether a model is deterministic or not depends on how one defines the inputs and behavior of the model. To define behavior, one has to define an observer. The article compares and contrasts two classes of ways to define an observer, one based on the notion of “state” and another that more flexibly defines the observables. The notion of “state” is shown to be problematic and lead to nondeterminism that is avoided when the observables are defined differently. The article examines determinism in models of the physical world. In what may surprise many readers, it shows that Newtonian physics admits nondeterminism and that quantum physics may be interpreted as a deterministic model. Moreover, it shows that both relativity and quantum physics undermine the notion of “state” and therefore require more flexible ways of defining observables. Finally, the article reviews results showing that sufficiently rich sets of deterministic models are incomplete. Specifically, nondeterminism is inescapable in any system of models rich enough to encompass Newton’s laws.


1990 ◽  
Vol 215 ◽  
Author(s):  
Josef Jäckle

AbstractIt is shown that diffusion in the hard-square and hard-octahedron lattice gases at high particle concentration has cooperative properties resembling molecular relaxation in undercooled liquids near the glass transition. For these models a characteristic length of cooperativity is introduced by an underlying percolation problem, which determines whether permanently blocked particles exist in lattices of finite size. The percolation problem belongs to a general class of bootstrap percolation models. Salient Monte Carlo results for the concentration and size dependence of self diffusion in the hard-square lattice gas are presented. Similarities with the n-spin facilitated kinetic Ising models are also pointed out.


2016 ◽  
Vol 61 (2) ◽  
pp. 365-379 ◽  
Author(s):  
Piotr Gospodarczyk

Abstract This paper presents a methodology for modeling work of a coal shearer work in low longwall coal seams where the wall height does not exceed 1.5 m. In such conditions, an important issue is the process of loading the ore from shearer cutting drum on an armored face conveyor and selection of appropriate kinematic parameters to avoid choking. Discrete element method was used to model coal seam. This method allows for efficient simulation of physical systems composed of many separate components. Methods and algorithms based on existing theoretical models were developed to imitate coal cutting process. Main focus of analysis was put on coal stream movement for different variants of the shearer construction and kinematic parameters.


2017 ◽  
Vol 31 (10) ◽  
pp. 1742010 ◽  
Author(s):  
C. R. K. Windows-Yule

Driven granular media — assemblies of discrete, macroscopic elements exposed to a source of mechanical energy — represent inherently out-of-equilibrium systems. Although granular media are ubiquitous in both nature and industry, due to their dissipative nature and resultant complex behaviors they remain startlingly poorly understood as compared to classical, thermodynamic systems. Nonetheless, in recent years it has been observed that the behaviors of granular media can, under certain circumstances, closely resemble those of equilibrium systems. One of the most important contemporary questions in the field of granular physics is whether these similarities are merely superficial, or whether the parallels run deep enough that the behaviors of these nonequilibrium systems can in fact be successfully captured using analogs to existing theoretical models developed for classical systems. In this review, we draw together the findings of a variety of recent studies where this question has been addressed, comparing and contrasting the results and conclusions presented. We focus our attention on vibrated and vibrofluidized granular beds, which provide a canonical system representative of various equilibrium and nonequilibrium physical systems, and whose simple dynamics offer a valuable testing ground for exploring the fundamental physics of the granular state.


OALib ◽  
2016 ◽  
Vol 03 (09) ◽  
pp. 1-6
Author(s):  
Malkhaz Mumladze

Econometrics ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 46
Author(s):  
George Judge

In this paper, we borrow some of the key concepts of nonequilibrium statistical systems, to develop a framework for analyzing a self-organizing-optimizing system of independent interacting agents, with nonlinear dynamics at the macro level that is based on stochastic individual behavior at the micro level. We demonstrate the use of entropy-divergence methods and micro income data to evaluate and understand the hidden aspects of stochastic dynamics that drives macroeconomic behavior systems and discuss how to empirically represent and evaluate their nonequilibrium nature. Empirical applications of the information theoretic family of power divergence measures-entropic functions, interpreted in a probability context with Markov dynamics, are presented.


2017 ◽  
Vol 72 (6) ◽  
pp. 493-525 ◽  
Author(s):  
Jochem Hauser ◽  
Walter Dröscher

AbstractThis article provides a review of the latest experimental results in quantum physics and astrophysics, discussing their repercussions on the advanced physical theories that go beyond both the SMs (standard models) of particle physics and cosmology. It will be shown that many of the essential concepts of the advanced theoretical models developed over the past 40 years are no longer tenable because they are contradicting the novel data. Most recent results (December 2016) from the Large Hadron Collider revealed no new matter particles up to particle masses of 1.6 TeV/c2, which is in accordance with recent ACME experimental data (2014) that saw no electric dipole moment for the electron as predicted by these theories. Moreover, the LUX experiment (since 2013) did not see any dark matter particles either, thus independently supporting LHC and ACME measurements. Furthermore, experimental particle physics seems to be telling us that dark matter particles (LHC results) do not exist, suggesting that dark matter particles either are more exotic or are more difficult to detect than had been predicted in the past decades (less likely with recent LHC results). Astrophysical observations since 1933, starting with Caltech astronomer Zwicky, however, have provided irrefutable evidence for the existence of dark matter, for instance, based on the phenomenon of gravitational lensing as well as observed rotational velocities of stars orbiting the galactic center that are deviating from Newton’s law. Surprisingly, recent astronomical observations by Bidin, ESO (2010, 2012, 2014), seem to indicate the absence of dark matter within galaxies. In addition, cosmology at present has no explanation for about 68 % of the energy in the Universe that comes in the form of dark energy. Recently, measured data from three entirely different types of experiments both on earth and in space (2006–2011) are hinting at completely novel features of gravity that, if confirmed, must be outside Einstein’s general relativity. Extreme gravitomagnetic and gravity-like fields may have been observed at cryogenic temperatures generated by a rotating ring or disk. However, these experimental results are not conclusive so far. The strength of these extreme fields has been calculated and, according to the respective equations, should be sufficient to serve as a basis for a gravitational technology that, for example, could establish long sought field propulsion (i.e. propulsion without fuel), actively researched by physicists and rocket engineers in the 1960s and 1990s. This article concludes with an outlook on the novel technology of gravitational engineering that might follow from gravity-like fields and discusses the novel physical concepts resulting from the existence of these extreme gravitomagnetic fields.


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