scholarly journals The Feynman–Kac Representation and Dobrushin–Lanford–Ruelle States of a Quantum Bose-Gas

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1683
Author(s):  
Yuri Suhov ◽  
Mark Kelbert ◽  
Izabella Stuhl
Keyword(s):  
Boundary Condition ◽  
Particle System ◽  
Quantum Particle ◽  
Hard Core ◽  
Infinite Volume ◽  
Quantum Gas ◽  
Finite Range ◽  
System A ◽  
Energy Part ◽  
Quantum Analog

This paper focuses on infinite-volume bosonic states for a quantum particle system (a quantum gas) in Rd. The kinetic energy part of the Hamiltonian is the standard Laplacian (with a boundary condition at the border of a ‘box’). The particles interact with each other through a two-body finite-range potential depending on the distance between them and featuring a hard core of diameter a>0. We introduce a class of so-called FK-DLR functionals containing all limiting Gibbs states of the system. As a justification of this concept, we prove that for d=2, any FK-DLR functional is shift-invariant, regardless of whether it is unique or not. This yields a quantum analog of results previously achieved by Richthammer.

scholarly journals Deployment/Retrieval Modeling of Cable-Driven Parallel Robot

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Q. J. Duan ◽  
J. L. Du ◽  
B. Y. Duan ◽  
A. F. Tang
Keyword(s):  
Mathematical Model ◽  
Boundary Condition ◽  
Steady State ◽  
Differential Equations ◽  
Parallel Robot ◽  
Lumped Mass ◽  
Dynamic Motion ◽  
Long Span ◽  
System A ◽  
Lumped Mass Method

A steady-state dynamic model of a cable in air is put forward by using some tensor relations. For the dynamic motion of a long-span Cable-Driven Parallel Robot (CDPR) system, a driven cable deployment and retrieval mathematical model of CDPR is developed by employing lumped mass method. The effects of cable mass are taken into account. The boundary condition of cable and initial values of equations is founded. The partial differential governing equation of each cable is thus transformed into a set of ordinary differential equations, which can be solved by adaptive Runge-Kutta algorithm. Simulation examples verify the effectiveness of the driven cable deployment and retrieval mathematical model of CDPR.

The hard core quantum gas at high temperatures

1968 ◽  
Vol 27 (6) ◽  
pp. 377-378 ◽  
Author(s):  
P.C. Hemmer
Keyword(s):  
High Temperatures ◽  
Hard Core ◽  
Quantum Gas

scholarly journals Formale Mehrkanal-Streutheorie

1960 ◽  
Vol 15 (4) ◽  
pp. 311-319
Author(s):  
Gerald Gbawert ◽  
Joachim Petzold
Keyword(s):  
Quantum Mechanics ◽  
Particle System ◽  
Formal Theory ◽  
Exclusion Principle ◽  
Alternative Formulation ◽  
Matrix Formalism ◽  
Nonrelativistic Quantum ◽  
System A ◽  
S Matrix ◽  
Nonrelativistic Quantum Mechanics

An alternative formulation is presented of the formal theory of multi-channel scattering in nonrelativistic quantum mechanics. We start by defining spaces of state vectors, where two particles either stay together or separate in the limit t →+∞ (or — ∞), when the state vector develops in time by e–i H t (H is the complete Hamiltonian of the n-particle system). A channel is defined as a space of state vectors with the following property: Developing in time by e-i H t they asymptotically describe a state of the n-particle system, where the particles are grouped in fragments. Defining a Hamiltonian Hγ for each channel, in which—compared to H—the interactions acting between particles from different fragments are missing, it is physically plausible that lim eiH e—iHt Ψ exists for vectors Ψ in the channel. Having discussed the limit vectors (asymptotic states), the S-matrix formalism can be introduced as usual. Finally the introduction of the exclusion principle is discussed.

Heat and sweat transport in fibrous media with radiation

2014 ◽  
Vol 25 (3) ◽  
pp. 307-327 ◽  
Author(s):  
JILU WANG ◽  
WEIWEI SUN
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Parabolic System ◽  
Radiative Heat ◽  
Radiation Transport ◽  
Fibrous Media ◽  
Strongly Coupled ◽  
System A ◽  
Nonlinear Parabolic ◽  
Non Local

The paper is concerned with heat and sweat transport in porous textile media with a non-local thermal radiation and phase change. The model, based on a combination of these classical heat transfer mechanisms (convection, conduction and radiation), is governed by a nonlinear, degenerate and strongly coupled parabolic system. The thermal radiative flow is described by a radiation transport equation and characterized by the thermal absorptivity and emissivity of fibre. A conservative boundary condition is introduced to describe the radiative heat flux interacting with environment. With the conservative boundary condition, we prove the global existence of positive/non-negative weak solutions of a nonlinear parabolic system. A typical clothing assembly with a polyester batting material sandwiched in two laminated covers is investigated numerically. Numerical results show that the contribution of radiative heat transfer is comparable with that of conduction/convection in the sweating system.

Research on Flame Simulation Based on Improved Particle System and the Texture Mapping

2010 ◽  
Vol 44-47 ◽  
pp. 3601-3605
Author(s):  
Jian Ni ◽  
Hong Xia Liu
Keyword(s):  
Computer Graphics ◽  
Computational Modeling ◽  
Dynamic Equation ◽  
Particle System ◽  
Texture Mapping ◽  
System A ◽  
Particle Mixing ◽  
Mixing Effects ◽  
Simulation Based ◽  
Flame Simulation

Flame simulation in computer graphics has been the most challenging problems. According to the key problem of real time and reality in flame simulation based on particle system, a new flame model based on improved particle system and the texture mapping is proposed in this paper. This article uses specific geometric shape as the elementary particles and combines treatment of derivatives based on the flame of the original particle system to simplify some of the dynamic equation, to reduce the difficulty of computational modeling and improve rendering speed; Through texture mapping and particle mixing effects to achieve flame changes color in different regions and reflect the temperature difference between them; In addition, the method also reflects the dynamic field of the particle system.

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