SYNERGISM IN ORDER FORMATION FROM UNSTABLE FLUCTUATIONS

2012 ◽  
Vol 26 (01) ◽  
pp. 1250001 ◽  
Author(s):  
MASUO SUZUKI
Keyword(s):  
Stochastic Analysis ◽  
Statistical Physics ◽  
Random Noise ◽  
Synergetic Effect ◽  
Planck Equation ◽  
New Order ◽  
Stochastic Integrals ◽  
Simple Derivation ◽  
General Aspects ◽  
Unstable States

The present paper reviews some general aspects of the stochastic analysis performed by the author in the field of statistical physics, particularly concerning the order formation from unstable states. First, a brief review and some new results are given on the generalization of the Itô-type and Stratonovich-type stochastic integrals. Their physical meaning is also discussed form the viewpoint of symmetry. Secondly, Kubo's stochastic Liouville equation is presented from the viewpoint of separation of procedures, to give a simple derivation of the Fokker–Planck equation. Thirdly, the scaling theory of order formation from the unstable point is re-formulated by introducing here a new order parameter to characterize macroscopic order formation and to clarify the synergetic effect of the initial fluctuation, random noise and nonlinearity. Finally, some discussions are given, particularly concerning applications of the Hida calculus based on the Gelfand triplet space.

BIASED RANDOM WALKS, PARTIAL DIFFERENTIAL EQUATIONS AND UPDATE SCHEMES

2013 ◽  
Vol 55 (2) ◽  
pp. 93-108 ◽  
Author(s):  
JACK D. HYWOOD ◽  
KERRY A. LANDMAN
Keyword(s):  
Statistical Physics ◽  
Planck Equation ◽  
Step Length ◽  
Physical Object ◽  
Cell Diameter ◽  
Agent Based Models ◽  
Time Step ◽  
Partial Differential ◽  
Agent Based ◽  
Random Walkers

AbstractThere is much interest within the mathematical biology and statistical physics community in converting stochastic agent-based models for random walkers into a partial differential equation description for the average agent density. Here a collection of noninteracting biased random walkers on a one-dimensional lattice is considered. The usual master equation approach requires that two continuum limits, involving three parameters, namely step length, time step and the random walk bias, approach zero in a specific way. We are interested in the case where the two limits are not consistent. New results are obtained using a Fokker–Planck equation and the results are highly dependent on the simulation update schemes. The theoretical results are confirmed with examples. These findings provide insight into the importance of updating schemes to an accurate macroscopic description of stochastic local movement rules in agent-based models when the lattice spacing represents a physical object such as cell diameter.

scholarly journals Hybrid Threats: Essence, Characteristics, Preconditions for Escalation

2021 ◽  
Vol 3 (49) ◽  
pp. 16-21
Author(s):  
N. H. Kalyuzhna ◽  
◽  
T. K. Kovtun ◽  
Keyword(s):  
Synergetic Effect ◽  
Weak States ◽  
Economic Interests ◽  
Trade Relations ◽  
Global Pandemic ◽  
Key Characteristics ◽  
Economic Sphere ◽  
Hybrid Threats ◽  
General Aspects ◽  
National Economies

The article aims at clarifying the essence of hybrid threats through systematizing their key characteristics and determining preconditions for conflict escalation. Common definitions of hybrid threats are considered and the lack of a unified approach to their interpretation is emphasized given their diversity and comprehensive nature. The high destructive potential of hybrid threats due to their hidden nature and focus on the most vulnerable aspects of the hybrid aggression object are substantiated. The specifics of carrying out hybrid threats in the economic sphere is analyzed, and the example of foreign trade relations between Ukraine and the Russian Federation shows that the economic sphere serves as a space for hiding and deformalizing a hybrid conflict. The essence of the synergetic effect made by the synchronous realization of hybrid threats in different confrontation areas is considered. It is demonstrated that the key feature of hybrid conflicts is their staying outside the legally justified intervention of other states and international organizations. Emphasis is placed on the rapid spread of hybrid threats in the economic sphere and on the special risks that conflicts hybridization creates for economically weak states. Another important feature of hybrid threats is identified, namely, the high probability of their escalation due to unforeseen events, the global pandemic COVID-19 in particular. It is substantiated that the expected risk of the post-pandemic period is the transition of most national economies to protectionist policies, which will inevitably increase the risk of hybrid threats escalation for economically weak states due to the desire of more powerful states to protect their national economic interests. Having analyzed the specifics of hybrid threats and understanding hybridity as a result of combining different forms, the authors identify the key characteristics of hybrid threats and further combine them into the following groups according to their essence: general aspects; specifics of methods and tools; areas of implementation; prerequisites for efficiency.

Bayesian estimation for stochastic dynamic equations via Fokker–Planck equation

2020 ◽  
pp. 2150055
Author(s):  
Bin Yu ◽  
Guang-Yan Zhong ◽  
Jiang-Cheng Li ◽  
Nian-Sheng Tang
Keyword(s):  
Statistical Physics ◽  
Planck Equation ◽  
Dynamic Equations ◽  
Stochastic Dynamic ◽  
Computational Accuracy ◽  
Unknown Parameters ◽  
Bayesian Estimates ◽  
Fokker Planck Equation ◽  
Mh Algorithm ◽  
Fokker Planck

A Bayesian approach is proposed to estimate unknown parameters in stochastic dynamic equations (SDEs). The Fokker–Planck equation from statistical physics method is adopted to calculate the quasi-stationary probability density function. A hybrid algorithm combining the Gibbs sampler and the Metropolis–Hastings (MH) algorithm is proposed to obtain Bayesian estimates of unknown parameters in SDEs. Three simulation studies of SDEs are conducted to investigate the performance of the proposed methodologies. Empirical results evidence that the proposed method performs well in the sense that Bayesian estimates of unknown parameters are quite close to their corresponding true values and their corresponding standard divinations are quite small, and the computational accuracy of normalization parameters strongly affects the accuracy of the proposed Bayesian estimates.

Mathematical programming in economics by physical analogies

SIMULATION ◽  
1969 ◽  
Vol 13 (1) ◽  
pp. 25-42 ◽  
Author(s):  
Ole I Franksen
Keyword(s):  
Mathematical Programming ◽  
Economic Model ◽  
Statistical Physics ◽  
Perfect Competition ◽  
Electrical Network ◽  
Economic Production ◽  
Demand Curves ◽  
The One ◽  
General Aspects ◽  
Physical Analogy

REVIEW OF PART I AND PREVIEW OF PART II This article is the second of a series of three in which we establish and solve a physical analogy of the economic model underlying mathematical programming. Basically, the first article (published in SIMULATION last month) was a reexamination of the fundamental assumptions underlying quasi-static models in economics and engineering, with a view to the establishment of a conceptual framework common to both disciplines. At the microscopic level it was demonstrated that the assumptions of perfect competition can be cast in a form analogous to the one used in statistical physics. At the macroscopic level it was shown that measure ments in economics and physics can be classified in iden tical manners with the result that derived relationships, like Ohm's law and demand curves or electric power and total revenue, can be made analogous concepts. On this basis it was then asserted that underlying economics we find two basic laws which, apart from a single change in sign, are completely analogous to the well-known First and Second Laws of thermodynamics. The present article is primarily a reformulation of the Walrasian economic model, which underlies mathemati cal programming, into an analogue electrical network. In accordance with the tradition of physics, the Wal rasian system of equations is derived from the postulates of the First and Second Laws of economics. The advan tage of this approach, which differs from conventional economic expositions, is that it permits a nearly auto matic establishment, term for term, of the corresponding electrical network model. The constraints and state-functions of the electrical analogue are formulated by modern network techniques in order to separate, in the economic formulation of the Walrasian system, the analytical aspects from those more general aspects which are involved in the design of an economic production system.

Partial differential equations and stochastic methods in molecular dynamics

Acta Numerica ◽  
2016 ◽  
Vol 25 ◽  
pp. 681-880 ◽  
Author(s):  
Tony Lelièvre ◽  
Gabriel Stoltz
Keyword(s):  
Molecular Dynamics ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Statistical Physics ◽  
Stochastic Dynamics ◽  
Planck Equation ◽  
Stochastic Methods ◽  
High Dimensions ◽  
Partial Differential ◽  
Long Time

The objective of molecular dynamics computations is to infer macroscopic properties of matter from atomistic models via averages with respect to probability measures dictated by the principles of statistical physics. Obtaining accurate results requires efficient sampling of atomistic configurations, which are typically generated using very long trajectories of stochastic differential equations in high dimensions, such as Langevin dynamics and its overdamped limit. Depending on the quantities of interest at the macroscopic level, one may also be interested in dynamical properties computed from averages over paths of these dynamics.This review describes how techniques from the analysis of partial differential equations can be used to devise good algorithms and to quantify their efficiency and accuracy. In particular, a crucial role is played by the study of the long-time behaviour of the solution to the Fokker–Planck equation associated with the stochastic dynamics.

Wick Calculus of Generalized Operators and its Applications to Quantum Stochastic Calculus

1998 ◽  
Vol 01 (03) ◽  
pp. 455-466 ◽  
Author(s):  
Zhiyuan Huang ◽  
Shunlong Luo
Keyword(s):  
Differential Equations ◽  
White Noise ◽  
Stochastic Analysis ◽  
Stochastic Calculus ◽  
Stochastic Integrals ◽  
Algebra Structure ◽  
Quantum Stochastic Calculus ◽  
Fundamental Properties ◽  
White Noise Calculus ◽  
Wick Calculus

A nonlinear and stochastic analysis of free Bose field is established in the framework of white noise calculus. Wick algebra structure is introduced in the space of generalized operators generated by quantum white noise, some fundamental properties of the calculus based on the Wick algebra are investigated. As applications, quantum stochastic integrals and quantum stochastic differential equations are treated from the viewpoint of Wick calculus.

scholarly journals Statistical Physics of the Inflaton Decaying in an Inhomogeneous Random Environment

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Z. Haba
Keyword(s):  
Free Energy ◽  
Statistical Physics ◽  
Probability Distributions ◽  
Planck Equation ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Stochastic Evolution Equation ◽  
Stochastic Evolution ◽  
Stochastic Wave Equation ◽  
Diffusive System

We derive a stochastic wave equation for an inflaton in an environment of an infinite number of fields. We study solutions of the linearized stochastic evolution equation in an expanding universe. The Fokker-Planck equation for the inflaton probability distribution is derived. The relative entropy (free energy) of the stochastic wave is defined. The second law of thermodynamics for the diffusive system is obtained. Gaussian probability distributions are studied in detail.

Analysis of Stochastic Resonance Phenomenon in Wind Induced Vibration of a Girder

2014 ◽  
Vol 617 ◽  
pp. 285-290
Author(s):  
Stanislav Pospíšil ◽  
Jiří Náprstek
Keyword(s):  
Stochastic Resonance ◽  
Random Noise ◽  
Cross Flow ◽  
Planck Equation ◽  
Resonance Phenomenon ◽  
Periodic Force ◽  
Amplitude Increase ◽  
Special Stand ◽  
Non Linear Oscillator ◽  
Wind Induced Vibration

We study the response of a dynamic system to additive random noise and external determin- istic periodic force to investigate vibration of a slender prismatic beam in a cross flow with a turbulence component. The aim of the study is to find such parameter combinations, which should be avoided in practice to eliminate response amplitude increase due to the effect of the stochastic resonance. We assume the non-linear oscillator (beam) with one generalized degree of freedom in the divergence-like regime. It is described by the version of the Duffing equation. We conduct the theoretical investigation with the use of relevant Fokker-Planck equation together with verification by numerical simulation of corresponding stochastic differential system. Real characteristics of a sectional model, fixed in the special stand allowing the snap-through effect, in the wind tunnel are employed.

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