11 research outputs found
Piecewise continuous partition function method in the theory of wave perturbations of inhomogeneous gas
The problem of wave disturbance propagation in rarefied gas in gravity field
is explored. The system of hydrodynamic-type equations for a stratified gas in
gravity field is derived from BGK equation by method of piecewise continuous
partition function. The obtained system of the equations generalizes the
Navier-Stokes at arbitrary density (Knudsen numbers). The verification of the
model is made for a limiting case of a homogeneous medium. Results are in the
good agreement with experiment and former theories at arbitrary Knudsen
numbers.Comment: 12 pages, 5 figure
Piecewise continuous distribution function method: Fluid equations and wave disturbances at stratified gas
Wave disturbances of a stratified gas are studied. The description is built
on a basis of the Bhatnagar -- Gross -- Krook (BGK) kinetic equation which is
reduced down the level of fluid mechanics. The double momenta set is introduced
inside a scheme of iterations of the equations operators, dividing the velocity
space along and opposite gravity field direction. At both half-spaces the local
equilibrium is supposed. As the result, the momenta system is derived. It
reproduce Navier-Stokes and Barnett equations at the first and second order in
high collision frequencies. The homogeneous background limit gives the known
results obtained by direct kinetics applications by Loyalka and Cheng as the
recent higher momentum fluid mechanics results of Chen, Rao and Spiegel. The
ground state declines from exponential at the Knudsen regime. The WKB solutions
for ultrasound in exponentially stratified medium are constructed in explicit
form, evaluated and plotted.Comment: 20 pages, 7 figures, 14 ISNA conference, 199
Counting and computing regions of -decomposition: algebro-geometric approach
New methods for -decomposition analysis are presented. They are based on
topology of real algebraic varieties and computational real algebraic geometry.
The estimate of number of root invariant regions for polynomial parametric
families of polynomial and matrices is given. For the case of two parametric
family more sharp estimate is proven. Theoretic results are supported by
various numerical simulations that show higher precision of presented methods
with respect to traditional ones. The presented methods are inherently global
and could be applied for studying -decomposition for the space of parameters
as a whole instead of some prescribed regions. For symbolic computations the
Maple v.14 software and its package RegularChains are used.Comment: 16 pages, 8 figure
Finite Automata with Generalized Acceptance Criteria
We examine the power of nondeterministic finite automata with acceptance of an input word defined by a leaf language, i.e., a condition on the sequence of leaves in the automaton's computation tree. We study leaf languages either taken from one of the classes of the Chomsky hierarchy, or taken from a time- or space-bounded complexity class. We contrast the obtained results with those known for leaf languages for Turing machines and Boolean circuits