Asymptotic behaviour of regular solutions

2000 ◽  
pp. 49-70
Author(s):  
Vojislav Marić
Keyword(s):  
Asymptotic Behaviour ◽  
Regular Solutions

Thin structure of heterogeneous and multiphase fluid flows

2012 ◽  
Vol 9 (1) ◽  
pp. 175-180
Author(s):  
Yu.D. Chashechkin
Keyword(s):  
Large Scale ◽  
Fundamental System ◽  
Fluid Flows ◽  
Regular Solutions ◽  
Flow Models ◽  
Group Methods ◽  
Wide Range ◽  
Thin Structure ◽  
Multiphase Fluid ◽  
Complete Solutions

According to the results of visualization of streams, the existence of structures in a wide range of scales is noted: from galactic to micron. The use of a fundamental system of equations is substantiated based on the results of comparing symmetries of various flow models with the usage of theoretical group methods. Complete solutions of the system are found by the methods of the singular perturbations theory with a condition of compatibility, which determines the characteristic equation. A comparison of complete solutions with experimental data shows that regular solutions characterize large-scale components of the flow, a rich family of singular solutions describes formation of the thin media structure. Examples of calculations and observations of stratified, rotating and multiphase media are given. The requirements for the technique of an adequate experiment are discussed.

A discussion on equations of phase equilibrium between two regular binary phases

1981 ◽  
Vol 46 (6) ◽  
pp. 1433-1438
Author(s):  
Jan Vřešťál
Keyword(s):  
Phase Equilibrium ◽  
Linear Function ◽  
Concentration Dependence ◽  
Absolute Temperature ◽  
Enthalpy Change ◽  
Independent Parameter ◽  
Free Enthalpy ◽  
Regular Solutions ◽  
Regular Model ◽  
Concentration Dependences

The conditions of the existence of extreme on the concentration dependences of absolute temperature (x are mole fractions) T = Tα(xkα) and T = Tβ(xkβ) denoting equilibrium between two binary regular solutions are generally developed under two assumptions: 1) Free enthalpy change of pure components k = i, j at transition from phase α to β is a linear function of temperature. 2) Concentration dependence of excess free enthalpy (identical with enthalpy) of solutions α and β, respectively, is described in regular model by one concentration and temperature independent parameter for each individual phase.

Asymptotic behaviour of sample weighted circuits representing recurrent Markov chains

1990 ◽  
Vol 27 (03) ◽  
pp. 545-556 ◽  
Author(s):  
S. Kalpazidou
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Asymptotic Behaviour ◽  
Probabilistic Interpretation ◽  
Stationary Markov Chain

The asymptotic behaviour of the sequence (𝒞 n (ω), wc,n (ω)/n), is studied where 𝒞 n (ω) is the class of all cycles c occurring along the trajectory ωof a recurrent strictly stationary Markov chain (ξ n ) until time n and wc,n (ω) is the number of occurrences of the cycle c until time n. The previous sequence of sample weighted classes converges almost surely to a class of directed weighted cycles (𝒞∞, ω c ) which represents uniquely the chain (ξ n ) as a circuit chain, and ω c is given a probabilistic interpretation.

Entropy numbers of embedding maps between Besov spaces with an application to eigenvalue problems

1981 ◽  
Vol 90 (1-2) ◽  
pp. 63-70 ◽  
Author(s):  
Bernd Carl
Keyword(s):  
Banach Space ◽  
Asymptotic Behaviour ◽  
Besov Spaces ◽  
Eigenvalue Problems ◽  
Function Spaces ◽  
Sequence Spaces ◽  
Entropy Numbers ◽  
Diagonal Operators

SynopsisIn this paper we determine the asymptotic behaviour of entropy numbers of embedding maps between Besov sequence spaces and Besov function spaces. The results extend those of M. Š. Birman, M. Z. Solomjak and H. Triebel originally formulated in the language of ε-entropy. It turns out that the characterization of embedding maps between Besov spaces by entropy numbers can be reduced to the characterization of certain diagonal operators by their entropy numbers.Finally, the entropy numbers are applied to the study of eigenvalues of operators acting on a Banach space which admit a factorization through embedding maps between Besov spaces.The statements of this paper are obtained by results recently proved elsewhere by the author.

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