A NEW APPROACH TO NONEQUILIBRIUM STATISTICAL MECHANICS OF GASES
Gas dynamics - nonequilibrium statistical mechanics
RAREFIED GAS DYNAMICS↗
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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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The application of statistical mechanics of nonequilibrium processes to astrophysics and the determination of galactic mass distribution and gravitational potential Final report
Application of statistical mechanics of nonequilibrium processes to astrophysics and determination of galactic mass distribution and gravitational potential
NONEQUILIBRIUM↗
Strongly magnetized classical plasma models
Discrete particle processes in the presence of a strong external magnetic field were investigated. These processes include equations of state and other equilibrium thermodynamic relations, thermal relaxation phenomena, transport properties, and microscopic statistical fluctuations in such quantities as the electric field and the charge density. Results from the equilibrium statistical mechanics of two-dimensional plasmas are discussed, along with nonequilibrium statistical mechanics of the electrostatic guiding-center plasma (a two-dimensional plasma model).
Montgomery, D.↗
Statistical mechanics of neocortical interactions - Dynamics of synaptic modification
A recent study has demonstrated that several scales of neocortical interactions can be consistently analyzed with the use of methods of modern nonlinear nonequilibrium statistical mechanics. The formation, stability, and interaction of spatial-temporal patterns of columnar firings are explicitly calculated, to test hypothesized mechanisms relating to information processing. In this context, most probable patterns of columnar firings are associated with chemical and electrical synaptic modifications. It is stressed that synaptic modifications and shifts in most-probable firing patterns are highly nonlinear and interactive sets of phenomena. A detailed scenario of information processing is calculated of columnar coding of external stimuli, short-term storage via hysteresis, and long-term storage via synaptic modification.
Ingber, L.↗
Strongly magnetized classical plasma models
The class of plasma processes for which the so-called Vlasov approximation is inadequate is investigated. Results from the equilibrium statistical mechanics of two-dimensional plasmas are derived. These results are independent of the presence of an external dc magnetic field. The nonequilibrium statistical mechanics of the electrostatic guiding-center plasma, a two-dimensional plasma model, is discussed. This model is then generalized to three dimensions. The guiding-center model is relaxed to include finite Larmor radius effects for a two-dimensional plasma.
Montgomery, D. C.↗
Kinetic theory of a two-dimensional magnetized plasma.
Several features of the equilibrium and nonequilibrium statistical mechanics of a two-dimensional plasma in a uniform dc magnetic field are investigated. The charges are assumed to interact only through electrostatic potentials. The problem is considered both with and without the guiding-center approximation. With the guiding-center approximation, an appropriate Liouville equation and BBGKY hierarchy predict no approach to thermal equilibrium for the spatially uniform case. For the spatially nonuniform situation, a guiding-center Vlasov equation is discussed and solved in special cases. For the nonequilibrium, nonguiding-center case, a Boltzmann equation, and a Fokker-Planck equation are derived in the appropriate limits. The latter is more tractable than the former, and can be shown to obey conservation laws and an H-theorem, but contains a divergent integral which must be cut off on physical grounds. Several unsolved problems are posed.
Vahala, G.↗
Transport phenomena in gases.
Nonequilibrium statistical mechanics of nonreacting gases, discussing transport phenomena in dilute and moderately dense gases
Curtiss, C. F.↗
A functional random-walk model of the many- particle system
Generalized random walk method presented as master equation in nonequilibrium statistical mechanics
Hosokawa, I.↗
The closure approximation in the hierarchy equations.
The expectation of the solution process in a stochastic operator equation can be obtained from averaged equations only under very special circumstances. Conditions for validity are given and the significance and validity of the approximation in widely used hierarchy methods and the ?self-consistent field' approximation in nonequilibrium statistical mechanics are clarified. The error at any level of the hierarchy can be given and can be avoided by the use of the iterative method.
Adomian, G.↗
Time-correlation-function expressions for linear and nonlinear transport coefficients.
Nonequilibrium system representation by statistical mechanical ensemble expressing time correlation function for linear/nonlinear transport coefficients
Andrews, F. C.↗
Statistical physics and physiology: monofractal and multifractal approaches
Even under healthy, basal conditions, physiologic systems show erratic fluctuations resembling those found in dynamical systems driven away from a single equilibrium state. Do such "nonequilibrium" fluctuations simply reflect the fact that physiologic systems are being constantly perturbed by external and intrinsic noise? Or, do these fluctuations actually, contain useful, "hidden" information about the underlying nonequilibrium control mechanisms? We report some recent attempts to understand the dynamics of complex physiologic fluctuations by adapting and extending concepts and methods developed very recently in statistical physics. Specifically, we focus on interbeat interval variability as an important quantity to help elucidate possibly non-homeostatic physiologic variability because (i) the heart rate is under direct neuroautonomic control, (ii) interbeat interval variability is readily measured by noninvasive means, and (iii) analysis of these heart rate dynamics may provide important practical diagnostic and prognostic information not obtainable with current approaches. The analytic tools we discuss may be used on a wider range of physiologic signals. We first review recent progress using two analysis methods--detrended fluctuation analysis and wavelets--sufficient for quantifying monofractual structures. We then describe recent work that quantifies multifractal features of interbeat interval series, and the discovery that the multifractal structure of healthy subjects is different than that of diseased subjects.
NASA Discipline Cardiopulmonary↗
Upgrade of PARC2D to include real gas effects
This paper presents a description of the changes and additions to the perfect gas PARC2D code to include chemical equilibrium effects, resulting in a code called PARCEQ2D. The work developed out of a need to have the capability of more accurately representing the flowfield surrounding the aeroassist flight experiment (AFE) vehicle. Use is made of the partition function of statistical mechanics in the evaluation of the thermochemical properties. This approach will allow the PARC code to be extended to thermal nonequilibrium when this task is undertaken in the future. The transport properties follow from formulae from the kinetic theory of gases. Results are presented for a two-dimensional AFE that compare perfect gas and real gas solutions at flight conditions, showing vast differences between the two cases.
Saladino, Anthony↗
Simulation and Modeling of Hypersonic Turbulent Boundary Layers Subject to Favorable Pressure Gradients due to Streamline Curvature
Direct numerical simulations (DNS) of favorable-pressure-gradient turbulent boundary layers are presented for a nominal freestream Mach number of 5, with the objective of assessing the limitations of the currently available Reynolds-averaged Navier-Stokes (RANS) models.The wall geometry and flow conditions of the DNS are representative of the experimental data for a Mach 4.9 turbulent boundary layer that was tested on a two-dimensional planar convexwall model in the high-speed blow-down wind tunnel located at the National Aerothermochemistry Laboratory at Texas A&M University. The favorable pressure gradient is induced bythe streamwise surface curvature. The DNS results will be compared with experimental measurements and RANS computations for the same flow conditions and wall geometry. The DNS datasets will also be analyzed to provide an improved physical understanding of hypersonic boundary-layer turbulence subject to mechanical nonequilibrium, including the validity of Morkovin’s hypothesis and the various available compressibility transformations, as well as to obtain turbulence statistics that are relevant to RANS modeling, including the distribution ofeddy viscosity, the budgets of turbulent kinetic energy and Reynolds stresses, and the velocity-temperature correlations. The RANS predictions will be obtained by using both the commonly used one- and two-equation models that assume a constant turbulent Prandtl number and an algebraic, variable Prandtl number model for the turbulent energy flux.
turbulent boundary layers↗
On the bulk viscosity of relativistic matter
It is shown that the Kubo formulation leads to an expression for bulk viscosity involving the differences of the trace equilibrium and nonequilibrium hydrodynamic tensors just as in the Boltzmann formulation. It is argued that, if a dense system is represented by a quantum field, the field-theoretic energy-momentum tensor and, therefore, the hydrodynamic tensor should always have a vanishing trace in the limit of high energies. This bulk viscosity should vanish in the same limit. Finally, it is noted that the explicit use of well-known statistical mechanical formulation can be considered as a justification of Weinberg's intuitive argument from a fundamental point of view.
Canuto, V.↗
A pseudo-sound constitutive relationship for the dilatational covariances in compressible turbulence: An analytical theory
The mathematical consequences of a few simple scaling assumptions about the effects of compressibility are explored using a simple singular perturbation idea and the methods of statistical fluid mechanics. Representations for the pressure-dilation and dilatational dissipation covariances appearing in single-point moment closures for compressible turbulence are obtained. While the results are expressed in the context of a second-order statistical closure they provide some interesting and very clear physical metaphors for the effects of compressibility that have not been seen using more traditional linear stability methods. In the limit of homogeneous turbulence with quasi-normal large-scales the expressions derived are - in the low turbulent Mach number limit - asymptotically exact. The expressions obtained are functions of the rate of change of the turbulence energy, its correlation length scale, and the relative time scale of the cascade rate. The expressions for the dilatational covariances contain constants which have a precise and definite physical significance; they are related to various integrals of the longitudinal velocity correlation. The pressure-dilation covariance is found to be a nonequilibrium phenomena related to the time rate of change of the internal energy and the kinetic energy of the turbulence. Also of interest is the fact that the representation for the dilatational dissipation in turbulence, with or without shear, features a dependence on the Reynolds number. This article is a documentation of an analytical investigation of the implications of a pseudo-sound theory for the effects of compressibility.
Ristorcelli, J. R.↗
Hierarchical Statistical 3D ' Atomistic' Simulation of Decanano MOSFETs: Drift-Diffusion, Hydrodynamic and Quantum Mechanical Approaches
When MOSFETs are scaled to deep submicron dimensions the discreteness and randomness of the dopant charges in the channel region introduces significant fluctuations in the device characteristics. This effect, predicted 20 year ago, has been confirmed experimentally and in simulation studies. The impact of the fluctuations on the functionality, yield, and reliability of the corresponding systems shifts the paradigm of the numerical device simulation. It becomes insufficient to simulate only one device representing one macroscopical design in a continuous charge approximation. An ensemble of macroscopically identical but microscopically different devices has to be characterized by simulation of statistically significant samples. The aims of the numerical simulations shift from predicting the characteristics of a single device with continuous doping towards estimating the mean values and the standard deviations of basic design parameters such as threshold voltage, subthreshold slope, transconductance, drive current, etc. for the whole ensemble of 'atomistically' different devices in the system. It has to be pointed out that even the mean values obtained from 'atomistic' simulations are not identical to the values obtained from continuous doping simulations. In this paper we present a hierarchical approach to the 'atomistic' simulation of aggressively scaled decanano MOSFETs. A full scale 3D drift-diffusion'atomostic' simulation approach is first described and used for verification of the more economical, but also more restricted, options. To reduce the processor time and memory requirements at high drain voltage we have developed a self-consistent option based on a thin slab solution of the current continuity equation only in the channel region. This is coupled to the Poisson's equation solution in the whole simulation domain in the Gummel iteration cycles. The accuracy of this approach is investigated in comparison with the full self-consistent solution. At low drain voltage only single solution of the nonlinear Poisson equation is sufficient to extract the current with satisfactory accuracy. A pilot version of a hydrodynamic 'atomistic' simulator has been developed in order to study the effect of the nonequilibrium, non local transport in decanano MOSFETs on the random dopant induced current fluctuations. For the first time we have also applied the density gradient approach in 3D to investigate the effect of the quantum confinement on the threshold voltage fluctuations. The developed 'atomistic' simulation techniques have been applied to study various fluctuation resistant MOSFET architectures including epitaxial and delta doped devices.
Asenov, Asen↗