The Experts below are selected from a list of 139134 Experts worldwide ranked by ideXlab platform
Abraham Nitzan - One of the best experts on this subject based on the ideXlab platform.
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upside downside statistical mechanics of nonequilibrium brownian motion i distributions moments and correlation functions of a Free Particle
arXiv: Statistical Mechanics, 2019Co-Authors: Galen T Craven, Abraham NitzanAbstract:Statistical properties of Brownian motion that arise by analyzing, separately, trajectories over which the system energy increases (upside) or decreases (downside) with respect to a threshold energy level, are derived. This selective analysis is applied to examine transport properties of a nonequilibrium Brownian process that is coupled to multiple thermal sources characterized by different temperatures. Distributions, moments, and correlation functions of a Free Particle that occur during upside and downside events are investigated for energy activation and energy relaxation processes, and also for positive and negative energy fluctuations from the average energy. The presented results are sufficiently general and can be applied without modification to standard Brownian motion. This article focuses on the mathematical basis of this selective analysis. In subsequent articles in this series we apply this general formalism to processes in which heat transfer between thermal reservoirs is mediated by activated rate processes that take place in a system bridging them.
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upside downside statistical mechanics of nonequilibrium brownian motion i distributions moments and correlation functions of a Free Particle
Journal of Chemical Physics, 2018Co-Authors: Galen T Craven, Abraham NitzanAbstract:Statistical properties of Brownian motion that arise by analyzing, separately, trajectories over which the system energy increases (upside) or decreases (downside) with respect to a threshold energy level are derived. This selective analysis is applied to examine transport properties of a nonequilibrium Brownian process that is coupled to multiple thermal sources characterized by different temperatures. Distributions, moments, and correlation functions of a Free Particle that occur during upside and downside events are investigated for energy activation and energy relaxation processes and also for positive and negative energy fluctuations from the average energy. The presented results are sufficiently general and can be applied without modification to the standard Brownian motion. This article focuses on the mathematical basis of this selective analysis. In subsequent articles in this series, we apply this general formalism to processes in which heat transfer between thermal reservoirs is mediated by activated rate processes that take place in a system bridging them.
Yeechung Jin - One of the best experts on this subject based on the ideXlab platform.
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mps mesh Free Particle method for multiphase flows
Computer Methods in Applied Mechanics and Engineering, 2012Co-Authors: Ahmad Shakibaeinia, Yeechung JinAbstract:Abstract By treating the multiphase system as a multi-density multi-viscosity fluid, a straightforward model has been proposed in this paper based on the Moving Particle Semi-implicit (MPS) mesh-Free Particle method for incompressible multiphase flow. The weakly-compressible MPS (WC-MPS) formulation (developed by the authors) is used to solve a single set of equations for all of the phases. In the model, the multiphase forces are introduced in a straightforward way. Dealing with multi-viscosity systems, different methods for defining the viscosity, by which Particles of different phases interact, is examined. To evaluate the accuracy of each of these methods, a stratified multi-viscosity Poiseuille flow test case is used and model results are compared with the analytical solution. The results show that selection of this interaction viscosity has an important role in the accuracy of the results. The model is then validated and applied to two basic hydrodynamic instability cases (Rayleigh–Taylor and Kelvin–Helmholtz instabilities). The results are then compared to a mesh-based model (with volume of fluid interface tracing method) to examine the ability of the model to deal with the multi-density systems. Comparisons show the model has reasonable accuracy. The results of this work offer the potential of modeling of multiphase incompressible immiscible systems in an extensive range of conditions using MPS.
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mps based mesh Free Particle method for modeling open channel flows
Journal of Hydraulic Engineering, 2011Co-Authors: Ahmad Shakibaeinia, Yeechung JinAbstract:Dealing with large deformation and fragmentation of geometries and interfaces (e.g., Free surfaces), the regular mesh-based Eulerian methods, such as finite-element and finite-difference methods, have difficulties in fluid-flow modeling. Recently, studies have focused on a new generation of numerical methods called mesh-Free Particle (Lagrangian) methods. In this study, a mesh-Free Particle method based on the moving-Particle semi-implicit (MPS) Particle-interaction model has been developed for simulation of open-channel flow. The model is able to simulate viscous fluid flow with large deformation and fragmentation of Free surface in practical fields. Moreover, the model is capable of modeling open-channel problems with both inflow and outflow and inconstant numbers of Particles. The model has been validated and applied to some common sample problems. The results show the reasonable accuracy of the model. The final model is capable of modeling Free-surface deformation and fragmentation as well as accurate...
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a mesh Free Particle model for simulation of mobile bed dam break
Advances in Water Resources, 2011Co-Authors: Ahmad Shakibaeinia, Yeechung JinAbstract:Mesh-Free Particle (Lagrangian) methods such as Moving Particle Semi-Implicit (MPS) and Smoothed Particle Hydrodynamics (SPH) are the latest generation of methods in the field of computational fluid dynamics that attracts lots of attention in modeling applications where large interfacial deformations and fragmentations exist. Due to their mesh-Free nature, these methods are capable of simulating any kind of boundary/interface deformation and fragmentations. This study aims to develop a new mesh-Free Particle model based on the weakly compressible MPS (WC-MPS) formulation for modeling of a dam break over a mobile bed, which is a highly erosive and transient flow problem. A multiphase model, capable of handling the density and viscosity discontinuity and in which the solid (sediment) phase is treated as a non-Newtonian fluid, is introduced. The resulting model is first validated using a two-phase dam break problem and is then applied to the mobile-bed dam break problem with different conditions, comparing the results to those obtained from some experimental works.
Nick Laskin - One of the best experts on this subject based on the ideXlab platform.
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fractional quantum mechanics
2018Co-Authors: Nick LaskinAbstract:A path integral approach to quantum physics has been developed. Fractional path integrals over the paths of the L\'evy flights are defined. It is shown that if the fractality of the Brownian trajectories leads to standard quantum and statistical mechanics, then the fractality of the L\'evy paths leads to fractional quantum mechanics and fractional statistical mechanics. The fractional quantum and statistical mechanics have been developed via our fractional path integral approach. A fractional generalization of the Schr\"odinger equation has been found. A relationship between the energy and the momentum of the nonrelativistic quantum-mechanical Particle has been established. The equation for the fractional plane wave function has been obtained. We have derived a Free Particle quantum-mechanical kernel using Fox's H function. A fractional generalization of the Heisenberg uncertainty relation has been established. Fractional statistical mechanics has been developed via the path integral approach. A fractional generalization of the motion equation for the density matrix has been found. The density matrix of a Free Particle has been expressed in terms of the Fox's H function. We also discuss the relationships between fractional and the well-known Feynman path integral approaches to quantum and statistical mechanics.
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fractals and quantum mechanics
Chaos, 2000Co-Authors: Nick LaskinAbstract:A new application of a fractal concept to quantum physics has been developed. The fractional path integrals over the paths of the Levy flights are defined. It is shown that if fractality of the Brownian trajectories leads to standard quantum mechanics, then the fractality of the Levy paths leads to fractional quantum mechanics. The fractional quantum mechanics has been developed via the new fractional path integrals approach. A fractional generalization of the Schrodinger equation has been discovered. The new relationship between the energy and the momentum of the nonrelativistic fractional quantum-mechanical Particle has been established, and the Levy wave packet has been introduced into quantum mechanics. The equation for the fractional plane wave function has been found. We have derived a Free Particle quantum-mechanical kernel using Fox’s H-function. A fractional generalization of the Heisenberg uncertainty relation has been found. As physical applications of the fractional quantum mechanics we have studied a Free Particle in a square infinite potential well, the fractional “Bohr atom” and have developed a new fractional approach to the QCD problem of quarkonium. We also discuss the relationships between fractional and the well-known Feynman path integral approaches to quantum mechanics.
S Mignemi - One of the best experts on this subject based on the ideXlab platform.
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classical and quantum mechanics of the nonrelativistic snyder model in curved space
Classical and Quantum Gravity, 2012Co-Authors: S MignemiAbstract:The Snyder–de Sitter (SdS) model is a generalization of the Snyder model to a spacetime background of constant curvature. It is an example of noncommutative spacetime admitting two fundamental scales besides the speed of light, and is invariant under the action of the de Sitter group. Here, we consider its nonrelativistic counterpart, i.e. the Snyder model restricted to a three-dimensional sphere, and the related model obtained by considering the anti-Snyder model on a pseudosphere, that we call anti-Snyder–de Sitter (aSdS). By means of a nonlinear transformation relating the SdS phase-space variables to canonical ones, we are able to investigate the classical and the quantum mechanics of a Free Particle and of an oscillator in this framework. In their flat space limit, the SdS and aSdS models exhibit rather different properties. In the SdS case, a lower bound on the localization in position and momentum spaces arises, which is not present in the aSdS model. In the aSdS case, instead, a specific combination of position and momentum coordinates cannot exceed a constant value. We explicitly solve the classical and the quantum equations for the motion of the Free Particle and of the harmonic oscillator. In both the SdS and aSdS cases, the frequency of the harmonic oscillator acquires a dependence on the energy. Moreover, in the aSdS model only a finite number of states is present.
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classical and quantum mechanics of the nonrelativistic snyder model in curved space
arXiv: High Energy Physics - Theory, 2011Co-Authors: S MignemiAbstract:The Snyder-de Sitter (SdS) model is a generalization of the Snyder model to a spacetime background of constant curvature. It is an example of noncommutative spacetime admitting two fundamental scales besides the speed of light, and is invariant under the action of the de Sitter group. Here we consider its nonrelativistic counterpart, i.e. the Snyder model restricted to a three-dimensional sphere, and the related model obtained by considering the anti-Snyder model on a pseudosphere, that we call anti-Snyder-de Sitter (aSdS). By means of a nonlinear transformation relating the SdS phase space variables to canonical ones, we are able to investigate the classical and the quantum mechanics of a Free Particle and of an oscillator in this framework. As in their flat space limit, the SdS and aSdS models exhibit rather different properties. In the SdS case, a lower bound on the localization in position and momentum space arises, which is not present in the aSdS model. In the aSdS case, instead, a specific combination of position and momentum coordinates cannot exceed a constant value. We explicitly solve the classical and the quantum equations for the motion of the Free Particle and of the harmonic oscillator. In both the SdS and aSdS cases, the frequency of the harmonic oscillator acquires a dependence on the energy.
Ahmad Shakibaeinia - One of the best experts on this subject based on the ideXlab platform.
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mps mesh Free Particle method for multiphase flows
Computer Methods in Applied Mechanics and Engineering, 2012Co-Authors: Ahmad Shakibaeinia, Yeechung JinAbstract:Abstract By treating the multiphase system as a multi-density multi-viscosity fluid, a straightforward model has been proposed in this paper based on the Moving Particle Semi-implicit (MPS) mesh-Free Particle method for incompressible multiphase flow. The weakly-compressible MPS (WC-MPS) formulation (developed by the authors) is used to solve a single set of equations for all of the phases. In the model, the multiphase forces are introduced in a straightforward way. Dealing with multi-viscosity systems, different methods for defining the viscosity, by which Particles of different phases interact, is examined. To evaluate the accuracy of each of these methods, a stratified multi-viscosity Poiseuille flow test case is used and model results are compared with the analytical solution. The results show that selection of this interaction viscosity has an important role in the accuracy of the results. The model is then validated and applied to two basic hydrodynamic instability cases (Rayleigh–Taylor and Kelvin–Helmholtz instabilities). The results are then compared to a mesh-based model (with volume of fluid interface tracing method) to examine the ability of the model to deal with the multi-density systems. Comparisons show the model has reasonable accuracy. The results of this work offer the potential of modeling of multiphase incompressible immiscible systems in an extensive range of conditions using MPS.
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mps based mesh Free Particle method for modeling open channel flows
Journal of Hydraulic Engineering, 2011Co-Authors: Ahmad Shakibaeinia, Yeechung JinAbstract:Dealing with large deformation and fragmentation of geometries and interfaces (e.g., Free surfaces), the regular mesh-based Eulerian methods, such as finite-element and finite-difference methods, have difficulties in fluid-flow modeling. Recently, studies have focused on a new generation of numerical methods called mesh-Free Particle (Lagrangian) methods. In this study, a mesh-Free Particle method based on the moving-Particle semi-implicit (MPS) Particle-interaction model has been developed for simulation of open-channel flow. The model is able to simulate viscous fluid flow with large deformation and fragmentation of Free surface in practical fields. Moreover, the model is capable of modeling open-channel problems with both inflow and outflow and inconstant numbers of Particles. The model has been validated and applied to some common sample problems. The results show the reasonable accuracy of the model. The final model is capable of modeling Free-surface deformation and fragmentation as well as accurate...
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a mesh Free Particle model for simulation of mobile bed dam break
Advances in Water Resources, 2011Co-Authors: Ahmad Shakibaeinia, Yeechung JinAbstract:Mesh-Free Particle (Lagrangian) methods such as Moving Particle Semi-Implicit (MPS) and Smoothed Particle Hydrodynamics (SPH) are the latest generation of methods in the field of computational fluid dynamics that attracts lots of attention in modeling applications where large interfacial deformations and fragmentations exist. Due to their mesh-Free nature, these methods are capable of simulating any kind of boundary/interface deformation and fragmentations. This study aims to develop a new mesh-Free Particle model based on the weakly compressible MPS (WC-MPS) formulation for modeling of a dam break over a mobile bed, which is a highly erosive and transient flow problem. A multiphase model, capable of handling the density and viscosity discontinuity and in which the solid (sediment) phase is treated as a non-Newtonian fluid, is introduced. The resulting model is first validated using a two-phase dam break problem and is then applied to the mobile-bed dam break problem with different conditions, comparing the results to those obtained from some experimental works.
