scholarly journals Topological supersymmetry breaking: The definition and stochastic generalization of chaos and the limit of applicability of statistics

2016 ◽  
Vol 30 (08) ◽  
pp. 1650086 ◽  
Author(s):  
Igor V. Ovchinnikov ◽  
Robert N. Schwartz ◽  
Kang L. Wang
Keyword(s):  
Steady State ◽  
Ground State ◽  
Initial Conditions ◽  
Probability Distributions ◽  
Total Probability ◽  
Dynamical Chaos ◽  
Infinite Memory ◽  
Spontaneous Breakdown ◽  
Stochastic Chaos ◽  
Independent Probability

The concept of deterministic dynamical chaos has a long history and is well established by now. Nevertheless, its field theoretic essence and its stochastic generalization have been revealed only very recently. Within the newly found supersymmetric theory of stochastics (STS), all stochastic differential equations (SDEs) possess topological or de Rahm supersymmetry and stochastic chaos is the phenomenon of its spontaneous breakdown. Even though the STS is free of approximations and thus is technically solid, it is still missing a firm interpretational basis in order to be physically sound. Here, we make a few important steps toward the construction of the interpretational foundation for the STS. In particular, we discuss that one way to understand why the ground states of chaotic SDEs are conditional (not total) probability distributions, is that some of the variables have infinite memory of initial conditions and thus are not “thermalized”, i.e., cannot be described by the initial-conditions-independent probability distributions. As a result, the definitive assumption of physical statistics that the ground state is a steady-state total probability distribution is not valid for chaotic SDEs.

Steady-State Dynamic Response of a Limited Slip System

1968 ◽  
Vol 35 (2) ◽  
pp. 322-326 ◽  
Author(s):  
W. D. Iwan
Keyword(s):  
Steady State ◽  
Dynamic Response ◽  
Slip System ◽  
External Load ◽  
Initial Conditions ◽  
Viscous Damping ◽  
Steady State Response ◽  
Response Curves ◽  
State Response ◽  
System Nonlinearity

The steady-state response of a system constrained by a limited slip joint and excited by a trigonometrically varying external load is discussed. It is shown that the system may possess such features as disconnected response curves and jumps in response depending on the strength of the system nonlinearity, the level of excitation, the amount of viscous damping, and the initial conditions of the system.

SPECKLE STATISTICS IN THE PHOTON LOCALIZATION TRANSITION

2010 ◽  
Vol 24 (12n13) ◽  
pp. 1950-1988 ◽  
Author(s):  
Azriel Z. Genack ◽  
Jing Wang
Keyword(s):  
Steady State ◽  
Probability Distributions ◽  
Speckle Pattern ◽  
Frequency Variation ◽  
Localization Transition ◽  
Classical Waves ◽  
Speckle Patterns ◽  
The Many ◽  
Photon Localization ◽  
State Propagation

We review the statistics of speckle in the Anderson localization transition for classical waves. Probability distributions of local and integrated transmission and of the evolution of the structure of the speckle pattern are related to their corresponding correlation functions. Steady state and pulse transport can be described in terms of modes whose speckle patterns are obtained by decomposing the frequency variation of the transmitted field. At the same time, transmission can be purposefully manipulated by adjusting the incident field and the eigenchannels of the transmission matrix can be found by analyzing sets of speckle patterns for different inputs. The many aspects of steady state propagation are reflected in diverse, but simply related, parameters so that a single localization parameter encapsulates the character of transport on both sides of the divide separating localized from diffusive waves.

scholarly journals Calculating the Energy Spectrum of Complex Low-Dimensional Heterostructures in the Electric Field

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Svetlana N. Khonina ◽  
Sergey G. Volotovsky ◽  
Sergey I. Kharitonov ◽  
Nikolay L. Kazanskiy
Keyword(s):  
Steady State ◽  
Electric Field ◽  
Ground State ◽  
State Energy ◽  
Airy Functions ◽  
Piecewise Constant ◽  
Matrix Rank ◽  
The Matrix ◽  
Constant Potential ◽  
Low Dimensional

An algorithm for solving the steady-state Schrödinger equation for a complex piecewise-constant potential in the presence of theE-field is developed and implemented. The algorithm is based on the consecutive matching of solutions given by the Airy functions at the band boundaries with the matrix rank increasing by no more than two orders, which enables the characteristic solution to be obtained in the convenient form for search of the roots. The algorithm developed allows valid solutions to be obtained for the electric field magnitudes larger than the ground-state energy level, that is, when the perturbation method is not suitable.

scholarly journals Fluorescent chemosensors for metal ions based on 3-(2-benzoxazol-5-yl)alanine skeleton

2010 ◽  
Vol 8 (3) ◽  
pp. 674-686 ◽  
Author(s):  
Magda Milewska ◽  
Katarzyna Guzow ◽  
Wiesław Wiczk
Keyword(s):  
Steady State ◽  
Fluorescence Spectroscopy ◽  
Metal Ions ◽  
Ground State ◽  
Transition Metal Ions ◽  
Fluorescent Chemosensors ◽  
Time Resolved Fluorescence ◽  
Absorption Bands ◽  
Time Resolved ◽  
Ratiometric Sensors

AbstractThe ability of new chelate ligands, benzoxazol-5-yl-alanine derivatives substituted in position 2 by heteroaromatic substituent, to form complexes with selected metal ions in acetonitrile are studied by means of absorption and steady-state and time-resolved fluorescence spectroscopy. Among the ligands studied, only azaaromatic derivatives form stable complexes with transition metal ions in the ground state. Their absorption bands are bathochromically shifted enabling to use those ligands as ratiometric sensors. The fluorescence of each ligand is quenched by metal ions, however, in the presence of Cd(II) and Zn(II) ions a new red shifted emission band is observed.

Exact Dynamics in a Model of the Bimolecular Reaction A+B→ 0

1992 ◽  
Vol 290 ◽  
Author(s):  
Eric Clément ◽  
Patrick Leroux-Hugon ◽  
Leonard M. Sander
Keyword(s):  
Exact Solution ◽  
Steady State ◽  
Initial Conditions ◽  
Finite Size ◽  
Bimolecular Reaction ◽  
Reaction Model

AbstractWe have previously given an exact solution [1] for the steady state of a model of the bimolecular reaction model A+B→ 0 due to Fichthorn et al. [2]. The dimensionality of the substrate plays a central role, and below d=2 segregation on macroscopic scales becomes important: above d=2 saturation sets in for finite size systems. Here we extend our treatment to give an exact account of the dynamics and show how various initial conditions develop into the segregated and saturated regimes. In certain conditions we find logarithmic relaxation which is related to the dimensionality.

Numerical simulation of soliton gas within the Korteweg-de Vries type equations

2019 ◽  
pp. 52-66
Author(s):  
Екатерина Геннадьевна Диденкулова ◽  
Анна Витальевна Кокорина ◽  
Алексей Викторович Слюняев
Keyword(s):  
Numerical Scheme ◽  
Initial Conditions ◽  
Probability Distributions ◽  
Scattering Problem ◽  
Spectral Composition ◽  
Computation Time ◽  
Qualitative Description ◽  
Statistical Characteristics ◽  
De Vries ◽  
Pseudo Spectral Method

Приведены детали численной схемы и способа задания начальных условий для моделирования нерегулярной динамики ансамблей солитонов в рамках уравнений типа Кортевега-де Вриза на примере модифицированного уравнения Кортевега-де Вриза с фокусирующим типом нелинейности. Дано качественное описание эволюции статистических характеристик для ансамблей солитонов одной и разных полярностей. Обсуждаются результаты тестовых экспериментов по столкновению большого числа солитонов. The details of the numerical scheme and the method of specifying the initial conditions for the simulation of the irregular dynamics of soliton ensembles within the framework of equations of the Korteweg - de Vries type are given using the example of the modified Korteweg - de Vries equation with a focusing type of nonlinearity. The numerical algorithm is based on a pseudo-spectral method with implicit integration over time and uses the Crank-Nicholson scheme for improving the stability property. The aims of the research are to determine the relationship between the spectral composition of the waves (the Fourier spectrum or the spectrum of the associated scattering problem) and their probabilistic properties, to describe transient processes and the equilibrium states. The paper gives a qualitative description of the evolution of statistical characteristics for ensembles of solitons of the same and different polarities, obtained as a result of numerical simulations; the probability distributions for wave amplitudes are also provided. The results of test experiments on the collision of a large number of solitons are discussed: the choice of optimal conditions and the manifestation of numerical artifacts caused by insufficient accuracy of the discretization. The numerical scheme used turned out to be extremely suitable for the class of the problems studied, since it ensures good accuracy in describing collisions of solitons with a short computation time.

Dynamics of Dual-Cell Series Miura-Ori Structures With Different Types of Inter-Cell Connections

2021 ◽  
Author(s):  
Hai Zhou ◽  
Haiping Wu ◽  
Jian Xu ◽  
Hongbin Fang
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Theoretical Basis ◽  
Initial Conditions ◽  
Cell Structure ◽  
Dynamic Responses ◽  
Complex Environment ◽  
Current State ◽  
Different Types ◽  
Cell Series

Abstract Origami-inspired structures and materials have shown remarkable properties and performances originating from the intricate geometries of folding. Origami folding could be a dynamic process and origami structures could possess rich dynamic characteristics under external excitations. However, the current state of dynamics of origami has mostly focused on the dynamics of a single cell. This research has performed numerical simulations on multi-stable dual-cell series Miura-Ori structures with different types of inter-cell connections based on a dynamic model that does not neglect in-plane mass. We introduce a concept of equivalent constraint stiffness k* to distinguish different types of inter-cell connections. Results of numerical simulations reveal the multi-stable dual-cell structure will exhibit a variety of complex nonlinear dynamic responses with the increasing of connection stiffness because of the deeper energy well it has. The connection stiffness has a strong effect on the steady-state dynamic responses under different excitation amplitudes and a variety of initial conditions. This effect makes us able to adjust the dynamic behaviors of dual-cell series Miura-Ori structure to our needs in a complex environment. Furthermore, the results of this research could provide us a theoretical basis for the dynamics of origami folding and serve as guidelines for designing dynamic applications of origami metastructures and metamaterials.

Nonlinear Rolling Motion of a Statically Biased Ship Under the Effect of External and Parametric Excitation

1993 ◽  
Author(s):  
Isaac Esparza ◽  
Jeffrey Falzarano
Keyword(s):  
Steady State ◽  
Parametric Excitation ◽  
Poincaré Map ◽  
Initial Conditions ◽  
Global Analysis ◽  
Wave Train ◽  
Periodic Wave ◽  
Rolling Motion ◽  
Poincare Map ◽  
Safe Basin

Abstract In this work, global analysis of ship rolling motion as effected by parametric excitation is studied. The parametric excitation results from the roll restoring moment variation as a wave train passes. In addition to the parametric excitation, an external periodic wave excitation and steady wind bias are also included in the analysis. The roll motion is the most critical motion for a ship because of the possibility of capsizing. The boundaries in the Poincaré map which separate initial conditions which eventually evolve to bounded steady state solutions and those which lead to unbounded capsizing motion are studied. The changes in these boundaries or manifolds as effected by changes in the ship and environmental conditions are analyzed. The region in the Poincaré map which lead to bounded steady state motions is called the safe basin. The size of this safe basin is a measure of the vessel’s resistance to capsizing.

scholarly journals Two-phonon structures for beta-decay theory

2018 ◽  
Vol 194 ◽  
pp. 02008
Author(s):  
A.P. Severyukhin ◽  
N.N. Arsenyev ◽  
I.N. Borzov ◽  
R.G. Nazmitdinov ◽  
S. Åberg
Keyword(s):  
Random Matrix ◽  
Single Particle ◽  
Ground State ◽  
Matrix Theory ◽  
Decay Rates ◽  
Total Probability ◽  
Phonon Coupling ◽  
Skyrme Interaction ◽  
Β Decay ◽  
Gamow Teller

The β-decay rates of 60Ca have been studied within a microscopic model, which is based on the Skyrme interaction T45 to construct single-particle and phonon spaces. We observe a redistribution of the Gamow–Teller strength due to the phonon-phonon coupling, considered in the model. For 60Sc, the spin-parity of the ground state is found to be 1+. We predict that the half-life of 60Ca is 0.3 ms, while the total probability of the βxn emission is 6:1%. Additionally, the random matrix theory has been applied to analyze the statistical properties of the 1+ spectrum populated in the β-decay to elucidate the obtained results.

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