scholarly journals A derivation of the Liouville equation for hard particle dynamics with non-conservative interactions

2020 ◽  
pp. 1-35
Author(s):  
Benjamin D. Goddard ◽  
Tim D. Hurst ◽  
Mark Wilkinson
Keyword(s):  
Liouville Equation ◽  
Particle Dynamics ◽  
Fundamental Importance ◽  
Continuum Models ◽  
Hard Particle ◽  
Interacting Particles ◽  
Weak Formulation ◽  
Physical Systems ◽  
Physical Particle

The Liouville equation is of fundamental importance in the derivation of continuum models for physical systems which are approximated by interacting particles. However, when particles undergo instantaneous interactions such as collisions, the derivation of the Liouville equation must be adapted to exclude non-physical particle positions, and include the effect of instantaneous interactions. We present the weak formulation of the Liouville equation for interacting particles with general particle dynamics and interactions, and discuss the results using two examples.

scholarly journals Search for dynamical origin of social networks

2016 ◽  
Author(s):  
Michail Zak
Keyword(s):  
Social Networks ◽  
Social Network ◽  
Power Law ◽  
Liouville Equation ◽  
Quantum Algorithms ◽  
Intelligent Agent ◽  
Second Law Of Thermodynamics ◽  
Complete Problems ◽  
Proposed Model ◽  
Physical Particle

The challenge of this work is to re-define the concept of intelligent agent as a building block of social networks by presenting it as a physical particle with additional non-Newtonian properties. The proposed model of an intelligent agent described by a system of ODE coupled with their Liouville equation has been introduced and discussed. Following the Madelung equation that belongs to this class, non-Newtonian properties such as superposition, entanglement, and probability interference typical for quantum systems have been described. Special attention was paid to the capability to violate the second law of thermodynamics, which makes these systems neither Newtonian, nor quantum. It has been shown that the proposed model can be linked to mathematical models of livings as well as to models of AI. The model is presented in two modifications. The first one is illustrated by the discovery of a stochastic attractor approached by the social network; as an application, it was demonstrated that any statistics can be represented by an attractor of the solution to the corresponding system of ODE coupled with its Liouville equation. It was emphasized that evolution to the attractor reveals possible micro-mechanisms driving random events to the final distribution of the corresponding statistical law. Special attention is concentrated upon the power law and its dynamical interpretation: it is demonstrated that the underlying micro- dynamics supports a “violent reputation” of the power-law statistics. The second modification of the model of social network associated with a decision-making process and applied to solution of NP-complete problems known as being unsolvable neither by classical nor by quantum algorithms. The approach is illustrated by solving a search in unsorted database in polynomial time by resonance between external force representing the address of a required item and the response representing the location of this item.

scholarly journals DECONFINEMENT AND COLD ATOMS IN OPTICAL LATTICES

2006 ◽  
Vol 20 (30n31) ◽  
pp. 5169-5178
Author(s):  
M. A CAZALILLA ◽  
A. F. HO ◽  
T. GIAMARCHI
Keyword(s):  
Optical Lattices ◽  
Cold Atoms ◽  
Three Dimensional ◽  
Optical Traps ◽  
High Dimensional ◽  
Interacting Particles ◽  
Controllable System ◽  
One Dimensional ◽  
Physical Systems ◽  
The One

Despite the fact that by now one dimensional and three dimensional systems of interacting particles are reasonably well understood, very little is known on how to go from the one dimensional physics to the three dimensional one. This is in particular true in a quasi-one dimensional geometry where the hopping of particles between one dimensional chains or tubes can lead to a dimensional crossover between a Luttinger liquid and more conventional high dimensional states. Such a situation is relevant to many physical systems. Recently cold atoms in optical traps have provided a unique and controllable system in which to investigate this physics. We thus analyze a system made of coupled one dimensional tubes of interacting fermions. We explore the observable consequences, such as the phase diagram for isolated tubes, and the possibility to realize unusual superfluid phases in coupled tubes systems.

Simulation of three Dimensional Defect Images in Transmission Electron Microscopy

1976 ◽  
Vol 34 ◽  
pp. 470-471
Author(s):  
W. D. Cooper ◽  
C. S. Hartley ◽  
J. J. Hren
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Three Dimensional ◽  
Crystalline Lattice ◽  
Continuum Models ◽  
Thin Foils ◽  
Transmission Electron ◽  
Microscope Images ◽  
General Computer Program ◽  
General Computer

Interpretation of electron microscope images of crystalline lattice defects can be greatly aided by computer simulation of theoretical contrast from continuum models of such defects in thin foils. Several computer programs exist at the present time, but none are sufficiently general to permit their use as an aid in the identification of the range of defect types encountered in electron microscopy. This paper presents progress in the development of a more general computer program for this purpose which eliminates a number of restrictions contained in other programs. In particular, the program permits a variety of foil geometries and defect types to be simulated.The conventional approximation of non-interacting columns is employed for evaluation of the two-beam dynamical scattering equations by a piecewise solution of the Howie-Whelan equations.

Single particle dynamics of supercooled water and the kinetic glass transition

1998 ◽  
Vol 08 (PR6) ◽  
pp. Pr6-109-Pr6-113
Author(s):  
P. Gallo ◽  
F. Sciortino ◽  
P. Tartaglia ◽  
S.-H. Chen
Keyword(s):  
Glass Transition ◽  
Single Particle ◽  
Supercooled Water ◽  
Particle Dynamics

Emerging Cyber-Physical Systems : An Overview

2018 ◽  
pp. 306-316
Author(s):  
Okolie S.O. ◽  
Kuyoro S.O. ◽  
Ohwo O. B
Keyword(s):  
Health Care ◽  
Economic Benefit ◽  
Physical World ◽  
Cyber Physical Systems ◽  
Cyber Physical System ◽  
Economic Sectors ◽  
Strategic Research ◽  
Physical Systems ◽  
Security Issues ◽  
Wide Range

Cyber-Physical Systems (CPS) will revolutionize how humans relate with the physical world around us. Many grand challenges await the economically vital domains of transportation, health-care, manufacturing, agriculture, energy, defence, aerospace and buildings. Exploration of these potentialities around space and time would create applications which would affect societal and economic benefit. This paper looks into the concept of emerging Cyber-Physical system, applications and security issues in sustaining development in various economic sectors; outlining a set of strategic Research and Development opportunities that should be accosted, so as to allow upgraded CPS to attain their potential and provide a wide range of societal advantages in the future.

The Common as Body Without Organs

2010 ◽  
Vol 4 (supplement) ◽  
pp. 46-63
Author(s):  
Vidar Thorsteinsson
Keyword(s):  
The Body ◽  
Fundamental Importance ◽  
Recent Book ◽  
Social Production ◽  
Deleuze And Guattari ◽  
Political Thinking ◽  
Conceptual Apparatus ◽  
Body Without Organs ◽  
Social Factory ◽  
The Common

The paper explores the relation of Michael Hardt and Antonio Negri's work to that of Deleuze and Guattari. The main focus is on Hardt and Negri's concept of ‘the common’ as developed in their most recent book Commonwealth. It is argued that the common can complement what Nicholas Thoburn terms the ‘minor’ characteristics of Deleuze's political thinking while also surpassing certain limitations posed by Hardt and Negri's own previous emphasis on ‘autonomy-in-production’. With reference to Marx's notion of real subsumption and early workerism's social-factory thesis, the discussion circles around showing how a distinction between capital and the common can provide a basis for what Alberto Toscano calls ‘antagonistic separation’ from capital in a more effective way than can the classical capital–labour distinction. To this end, it is demonstrated how the common might benefit from being understood in light of Deleuze and Guattari's conceptual apparatus, with reference primarily to the ‘body without organs’ of Anti-Oedipus. It is argued that the common as body without organs, now understood as constituting its own ‘social production’ separate from the BwO of capital, can provide a new basis for antagonistic separation from capital. Of fundamental importance is how the common potentially invents a novel regime of qualitative valorisation, distinct from capital's limitation to quantity and scarcity.

Family Concerns inThe Vampire Diaries

2019 ◽  
Vol 21 (2) ◽  
pp. 209-222
Author(s):  
Antonio Sanna
Keyword(s):  
Fundamental Importance ◽  
Familial Relationships ◽  
Familial Bonds ◽  
Television Medium ◽  
Precious Stones

This paper examines the TV series The Vampire Diaries to show how the programme responds to traditional gothic tropes and transforms them for the television medium. Vampires and humans shall be read as both preoccupied with the ties of family, in story arcs that explore complex and often dark familial relationships. Especially in the early seasons of the series, objects such as magic rings, compasses, precious stones and magical devices are given fundamental importance for the development of the plot, the interactions among the characters, and the representation of familial bonds. Specifically, the search for and retrieval of the heirlooms shall be interpreted as instrumental to the representation of the characters’ relationships with their respective families, which I argue is a characteristic theme of gothic fictions at large.

Sign in / Sign up

Export Citation Format

Share Document