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Patrick Jenny - One of the best experts on this subject based on the ideXlab platform.

  • a fokker planck based kinetic model for diatomic rarefied gas flows
    Physics of Fluids, 2013
    Co-Authors: Hossein Miladi Gorji, Patrick Jenny
    Abstract:

    A Fokker–Planck based kinetic model is presented here, which also accounts for internal energy modes characteristic for diatomic gas molecules. The model is based on a Fokker–Planck approximation of the Boltzmann equation for monatomic molecules, whereas phenomenological principles were employed for the derivation. It is shown that the model honors the Equipartition Theorem in equilibrium and fulfills the Landau–Teller relaxation equations for internal degrees of freedom. The objective behind this approximate kinetic model is accuracy at reasonably low computational cost. This can be achieved due to the fact that the resulting stochastic differential equations are continuous in time; therefore, no collisions between the simulated particles have to be calculated. Besides, because of the devised energy conserving time integration scheme, it is not required to resolve the collisional scales, i.e., the mean collision time and the mean free path of molecules. This, of course, gives rise to much more efficient ...

  • a fokker planck based kinetic model for diatomic rarefied gas flows
    Physics of Fluids, 2013
    Co-Authors: Hossein Miladi Gorji, Patrick Jenny
    Abstract:

    A Fokker–Planck based kinetic model is presented here, which also accounts for internal energy modes characteristic for diatomic gas molecules. The model is based on a Fokker–Planck approximation of the Boltzmann equation for monatomic molecules, whereas phenomenological principles were employed for the derivation. It is shown that the model honors the Equipartition Theorem in equilibrium and fulfills the Landau–Teller relaxation equations for internal degrees of freedom. The objective behind this approximate kinetic model is accuracy at reasonably low computational cost. This can be achieved due to the fact that the resulting stochastic differential equations are continuous in time; therefore, no collisions between the simulated particles have to be calculated. Besides, because of the devised energy conserving time integration scheme, it is not required to resolve the collisional scales, i.e., the mean collision time and the mean free path of molecules. This, of course, gives rise to much more efficient simulations with respect to other particle methods, especially the conventional direct simulation Monte Carlo (DSMC), for small and moderate Knudsen numbers. To examine the new approach, first the computational cost of the model was compared with respect to DSMC, where significant speed up could be obtained for small Knudsen numbers. Second, the structure of a high Mach shock (in nitrogen) was studied, and the good performance of the model for such out of equilibrium conditions could be demonstrated. At last, a hypersonic flow of nitrogen over a wedge was studied, where good agreement with respect to DSMC (with level to level transition model) for vibrational and translational temperatures is shown.

Hossein Miladi Gorji - One of the best experts on this subject based on the ideXlab platform.

  • a fokker planck based kinetic model for diatomic rarefied gas flows
    Physics of Fluids, 2013
    Co-Authors: Hossein Miladi Gorji, Patrick Jenny
    Abstract:

    A Fokker–Planck based kinetic model is presented here, which also accounts for internal energy modes characteristic for diatomic gas molecules. The model is based on a Fokker–Planck approximation of the Boltzmann equation for monatomic molecules, whereas phenomenological principles were employed for the derivation. It is shown that the model honors the Equipartition Theorem in equilibrium and fulfills the Landau–Teller relaxation equations for internal degrees of freedom. The objective behind this approximate kinetic model is accuracy at reasonably low computational cost. This can be achieved due to the fact that the resulting stochastic differential equations are continuous in time; therefore, no collisions between the simulated particles have to be calculated. Besides, because of the devised energy conserving time integration scheme, it is not required to resolve the collisional scales, i.e., the mean collision time and the mean free path of molecules. This, of course, gives rise to much more efficient ...

  • a fokker planck based kinetic model for diatomic rarefied gas flows
    Physics of Fluids, 2013
    Co-Authors: Hossein Miladi Gorji, Patrick Jenny
    Abstract:

    A Fokker–Planck based kinetic model is presented here, which also accounts for internal energy modes characteristic for diatomic gas molecules. The model is based on a Fokker–Planck approximation of the Boltzmann equation for monatomic molecules, whereas phenomenological principles were employed for the derivation. It is shown that the model honors the Equipartition Theorem in equilibrium and fulfills the Landau–Teller relaxation equations for internal degrees of freedom. The objective behind this approximate kinetic model is accuracy at reasonably low computational cost. This can be achieved due to the fact that the resulting stochastic differential equations are continuous in time; therefore, no collisions between the simulated particles have to be calculated. Besides, because of the devised energy conserving time integration scheme, it is not required to resolve the collisional scales, i.e., the mean collision time and the mean free path of molecules. This, of course, gives rise to much more efficient simulations with respect to other particle methods, especially the conventional direct simulation Monte Carlo (DSMC), for small and moderate Knudsen numbers. To examine the new approach, first the computational cost of the model was compared with respect to DSMC, where significant speed up could be obtained for small Knudsen numbers. Second, the structure of a high Mach shock (in nitrogen) was studied, and the good performance of the model for such out of equilibrium conditions could be demonstrated. At last, a hypersonic flow of nitrogen over a wedge was studied, where good agreement with respect to DSMC (with level to level transition model) for vibrational and translational temperatures is shown.

Hong Zhao - One of the best experts on this subject based on the ideXlab platform.

  • violation of the virial Theorem and generalized Equipartition Theorem for logarithmic oscillators serving as a thermostat
    Scientific Reports, 2017
    Co-Authors: Kai Chen, Hong Zhao
    Abstract:

    A logarithmic oscillator has been proposed to serve as a thermostat recently since it has a peculiar property of infinite heat capacity according to the virial Theorem. In order to examine its feasibility in numerical simulations, a modified logarithmic potential has been applied in previous studies to eliminate the singularity at the origin. The role played by the modification has been elucidated in the present study. We argue that the virial Theorem is practically violated in finite-time simulations of the modified log-oscillator illustrated by a linear dependence of kinetic temperature on energy. Furthermore, as far as a thermalized log-oscillator is concerned, our calculation based on the canonical ensemble average shows that the generalized Equipartition Theorem is broken if the temperature is higher than a critical temperature. Finally, we show that log-oscillators fail to serve as thermostats for their incapability of maintaining a nonequilibrium steady state even though their energy is appropriately assigned.

  • violation of the virial Theorem and generalized Equipartition Theorem for logarithmic oscillators serving as a thermostat
    arXiv: Statistical Mechanics, 2016
    Co-Authors: Kai Chen, Hong Zhao
    Abstract:

    A logarithmic oscillator has been proposed recently to serve as a thermostat recently since it has a peculiar property of infinite heat capacity according to the virial Theorem. In order to examine its feasibility by numerical simulations, a modified logarithmic potential has been applied in previous studies to eliminate the singularity at origin. The role played by the modification has been elucidated in the present study. We argue that the virial Theorem is practically violated for the modified log-oscillator illustrated by a linear dependence of kinetic temperature on energy. Furthermore, as far as a thermalized log-oscillator is concerned, the generalized Equipartition Theorem with respect to the position coordinate is broken if the temperature is higher than a critical temperature. Finally, we show that log-oscillators fail to serve as thermostats for its incapability of maintaining a nonequilibrium steady state even though their energy is appropriately assigned.

Mark G. Raizen - One of the best experts on this subject based on the ideXlab platform.

  • testing the maxwell boltzmann distribution using brownian particles
    Optics Express, 2015
    Co-Authors: Akarsh Simha, Simon Kheifets, Mark G. Raizen
    Abstract:

    We report on shot-noise limited measurements of the instantaneous velocity distribution of a Brownian particle. Our system consists of a single micron-sized glass sphere held in an optical tweezer in a liquid in equilibrium at room temperature. We provide a direct verification of a modified Maxwell-Boltzmann velocity distribution and modified energy Equipartition Theorem that account for the kinetic energy of the liquid displaced by the particle. Our measurements confirm the distribution over a dynamic range of more than six orders of magnitude in count-rate and five standard deviations in velocity.

  • observation of brownian motion in liquids at short times instantaneous velocity and memory loss
    Science, 2014
    Co-Authors: Simon Kheifets, Akarsh Simha, Kevin Melin, Tongcang Li, Mark G. Raizen
    Abstract:

    Measurement of the instantaneous velocity of Brownian motion of suspended particles in liquid probes the microscopic foundations of statistical mechanics in soft condensed matter. However, instantaneous velocity has eluded experimental observation for more than a century since Einstein’s prediction of the small length and time scales involved. We report shot-noise–limited, high-bandwidth measurements of Brownian motion of micrometer-sized beads suspended in water and acetone by an optical tweezer. We observe the hydrodynamic instantaneous velocity of Brownian motion in a liquid, which follows a modified energy Equipartition Theorem that accounts for the kinetic energy of the fluid displaced by the moving bead. We also observe an anticorrelated thermal force, which is conventionally assumed to be uncorrelated.

  • Measurement of the Instantaneous Velocity of a Brownian Particle
    Science, 2010
    Co-Authors: Simon Kheifets, David Medellin, Mark G. Raizen
    Abstract:

    Brownian motion of particles affects many branches of science. We report on the Brownian motion of micrometer-sized beads of glass held in air by an optical tweezer, over a wide range of pressures, and we measured the instantaneous velocity of a Brownian particle. Our results provide direct verification of the energy Equipartition Theorem for a Brownian particle. For short times, the ballistic regime of Brownian motion was observed, in contrast to the usual diffusive regime. We discuss the applications of these methods toward cooling the center-of-mass motion of a bead in vacuum to the quantum ground motional state.

Kai Chen - One of the best experts on this subject based on the ideXlab platform.

  • violation of the virial Theorem and generalized Equipartition Theorem for logarithmic oscillators serving as a thermostat
    Scientific Reports, 2017
    Co-Authors: Kai Chen, Hong Zhao
    Abstract:

    A logarithmic oscillator has been proposed to serve as a thermostat recently since it has a peculiar property of infinite heat capacity according to the virial Theorem. In order to examine its feasibility in numerical simulations, a modified logarithmic potential has been applied in previous studies to eliminate the singularity at the origin. The role played by the modification has been elucidated in the present study. We argue that the virial Theorem is practically violated in finite-time simulations of the modified log-oscillator illustrated by a linear dependence of kinetic temperature on energy. Furthermore, as far as a thermalized log-oscillator is concerned, our calculation based on the canonical ensemble average shows that the generalized Equipartition Theorem is broken if the temperature is higher than a critical temperature. Finally, we show that log-oscillators fail to serve as thermostats for their incapability of maintaining a nonequilibrium steady state even though their energy is appropriately assigned.

  • violation of the virial Theorem and generalized Equipartition Theorem for logarithmic oscillators serving as a thermostat
    arXiv: Statistical Mechanics, 2016
    Co-Authors: Kai Chen, Hong Zhao
    Abstract:

    A logarithmic oscillator has been proposed recently to serve as a thermostat recently since it has a peculiar property of infinite heat capacity according to the virial Theorem. In order to examine its feasibility by numerical simulations, a modified logarithmic potential has been applied in previous studies to eliminate the singularity at origin. The role played by the modification has been elucidated in the present study. We argue that the virial Theorem is practically violated for the modified log-oscillator illustrated by a linear dependence of kinetic temperature on energy. Furthermore, as far as a thermalized log-oscillator is concerned, the generalized Equipartition Theorem with respect to the position coordinate is broken if the temperature is higher than a critical temperature. Finally, we show that log-oscillators fail to serve as thermostats for its incapability of maintaining a nonequilibrium steady state even though their energy is appropriately assigned.