scholarly journals A New Criterion Beyond Divergence for Determining the Dissipation of a System: Dissipative Power

2021 ◽  
Vol 9 ◽  
Author(s):  
Xiaoliang Gan ◽  
Haoyu Wang ◽  
Ruoshi Yuan ◽  
Ping Ao
Keyword(s):  
Dynamical Systems ◽  
Lyapunov Function ◽  
Classical Mechanics ◽  
Dynamic Structure ◽  
Phase Space Volume ◽  
New Feature ◽  
New Criterion ◽  
The Relationship ◽  
Planar Dynamical Systems ◽  
Space Volume

Divergence is usually used to determine the dissipation of a dynamical system, but some researchers have noticed that it can lead to elusive contradictions. In this article, a criterion, dissipative power, beyond divergence for judging the dissipation of a system is presented, which is based on the knowledge of classical mechanics and a novel dynamic structure by Ao. Moreover, the relationship between the dissipative power and potential function (or called Lyapunov function) is derived, which reveals a very interesting, important, and apparently new feature in dynamical systems: to classify dynamics into dissipative or conservative according to the change of “energy function” or “Hamiltonian,” not according to the change of phase space volume. We start with two simple examples corresponding to two types of attractors in planar dynamical systems: fixed points and limit cycles. In judging the dissipation by divergence, these two systems have both the elusive contradictions pointed by researchers and new ones noticed by us. Then, we analyze and compare these two criteria in these two examples, further consider the planar linear systems with the coefficient matrices being the four types of Jordan’s normal form, and find that the dissipative power works when divergence exhibits contradiction. Moreover, we also consider another nonlinear system to analyze and compare these two criteria. Finally, the obtained relationship between the dissipative power and the Lyapunov function provides a reasonable way to explain why some researchers think that the Lyapunov function does not coexist with the limit cycle. Those results may provide a deeper understanding of the dissipation of dynamical systems.

scholarly journals Solitons, Peakons, and Periodic Cuspons of a Generalized Degasperis-Procesi Equation

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Jiangbo Zhou ◽  
Lixin Tian
Keyword(s):  
Dynamical Systems ◽  
Bifurcation Theory ◽  
Soliton Solutions ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
The Relationship ◽  
Planar Dynamical Systems ◽  
Explicit Expressions

We employ the bifurcation theory of planar dynamical systems to investigate the exact travelling wave solutions of a generalized Degasperis-Procesi equationut−uxxt+4uux+γ(u−uxx)x=3uxuxx+uuxxx. The implicit expression of smooth soliton solutions is given. The explicit expressions of peaked soliton solutions and periodic cuspon solutions are also obtained. Further, we show the relationship among the smooth soliton solutions, the peaked soliton solutions, and the periodic cuspon solutions. The physical relevance of the found solutions and the reason why these solutions can exist in this equation are also given.

The Non-Causal Character of Renormalization Group Explanations

2018 ◽  
Author(s):  
Margaret Morrison
Keyword(s):  
Probability Theory ◽  
Renormalization Group ◽  
Dynamical Systems ◽  
Recent Literature ◽  
Mathematical Explanation ◽  
Causal Status ◽  
Physical Information ◽  
The Relationship ◽  
Structural Aspects

After reviewing some of the recent literature on non-causal and mathematical explanation, this chapter develops an argument as to why renormalization group (RG) methods should be seen as providing non-causal, yet physical, information about certain kinds of systems/phenomena. The argument centres on the structural character of RG explanations and the relationship between RG and probability theory. These features are crucial for the claim that the non-causal status of RG explanations involves something different from simply ignoring or “averaging over” microphysical details—the kind of explanations common to statistical mechanics. The chapter concludes with a discussion of the role of RG in treating dynamical systems and how that role exemplifies the structural aspects of RG explanations which in turn exemplifies the non-causal features.

scholarly journals Deservingness for "Family 500 +" Benefit in Poland: Qualitative Study of Internet Debates

2021 ◽  
Author(s):  
Piotr Michoń
Keyword(s):  
Future Research ◽  
Online Forums ◽  
Time Data ◽  
Social Surveys ◽  
Cash Benefit ◽  
Internet Forums ◽  
Welfare Attitudes ◽  
New Criterion ◽  
First Time ◽  
The Relationship

AbstractThe need for qualitative research of deservingness perception is strongly emphasised in the literature. This article studies the perception of deservingness for a "Family 500 +"—cash benefit in Poland. For the first time, data from online forums was used in the studies of deservingness and welfare attitudes. It allowed to avoid numerous limitations associated with social surveys. The qualitative analysis showed how participants of Internet debates perceive the criteria of deservingness: control, attitude, reciprocity, identity, need, and what are the relations between the criteria. The impurity of all deservingness criteria was indicated and a new criterion “adequacy” was proposed. Moreover due to the fact that the study concerned a concrete, non-abstract family cash benefit addressed the relationship between the perceived deservingness of children and their parents was pointed out. The vast majority of posts on Internet forums referred to deservingness of parents, not children. This is particularly evident in relation to the criteria of control and reciprocity. Presenting the hypothesis of jealousy and scapegoat strategy, the article also shows the direction of future research on deservingness.

Phase-space volume based control of semibatch reactors

2010 ◽  
Vol 88 (3) ◽  
pp. 320-330 ◽  
Author(s):  
José-Manuel Zaldívar ◽  
Fernanda Strozzi
Keyword(s):  
Phase Space ◽  
Phase Space Volume ◽  
Space Volume

scholarly journals A Hierarchical Probabilistic Framework for Recognizing Learners’ Interaction Experience Trends and Emotions

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Imène Jraidi ◽  
Maher Chaouachi ◽  
Claude Frasson
Keyword(s):  
Emotional Responses ◽  
Dynamic Bayesian Network ◽  
Dynamic Structure ◽  
Emotional Reactions ◽  
Probabilistic Framework ◽  
Interactive Learning Environment ◽  
Predictive Variables ◽  
Current Context ◽  
And Performance ◽  
The Relationship

We seek to model the users’ experience within an interactive learning environment. More precisely, we are interested in assessing the relationship between learners’ emotional reactions and three trends in the interaction experience, namely,flow: the optimal interaction (a perfect immersion within the task),stuck: the nonoptimal interaction (a difficulty to maintain focused attention), andoff-task: the noninteraction (a dropout from the task). We propose a hierarchical probabilistic framework using a dynamic Bayesian network to model this relationship and to simultaneously recognize the probability of experiencing each trend as well as the emotional responses occurring subsequently. The framework combines three modalitydiagnostic variablesthat sense the learner’s experience including physiology, behavior, and performance,predictive variablesthat represent the current context and the learner’s profile, and adynamic structurethat tracks the evolution of the learner’s experience. An experimental study, with a specifically designed protocol for eliciting the targeted experiences, was conducted to validate our approach. Results revealed that multiple concurrent emotions can be associated with the experiences of flow, stuck, and off-task and that the same trend can be expressed differently from one individual to another. The evaluation of the framework showed promising results in predicting learners’ experience trends and emotional responses.

scholarly journals Almost additive entropy

2014 ◽  
Vol 11 (05) ◽  
pp. 1450040 ◽  
Author(s):  
Nikos Kalogeropoulos
Keyword(s):  
Phase Space ◽  
Shannon Entropy ◽  
Power Law ◽  
Physical Significance ◽  
Small Deviations ◽  
Phase Space Volume ◽  
Composition Property ◽  
Flat Manifolds ◽  
Special Case ◽  
Space Volume

We explore consequences of a hyperbolic metric induced by the composition property of the Harvda–Charvat/Daróczy/Cressie–Read/Tsallis entropy. We address the special case of systems described by small deviations of the non-extensive parameter q ≈ 1 from the "ordinary" additive case which is described by the Boltzmann/Gibbs/Shannon entropy. By applying the Gromov/Ruh theorem for almost flat manifolds, we show that such systems have a power-law rate of expansion of their configuration/phase space volume. We explore the possible physical significance of some geometric and topological results of this approach.

Sign in / Sign up

Export Citation Format

Share Document