Kinetic Decomposition of Homogenization Problems
نویسنده
چکیده
We develop an analytical tool which is adept for detecting shapes of oscillatory functions, is useful in decomposing homogenization problems into limit-problems for kinetic equations. and provides an efficient framework for the validation of multi-scale asymptotic expansions. We apply it first to a hyperbolic homogenization problem and transform it to a hyperbolic limit problem for a kinetic equation. We establish conditions determining an effective equation and counterexamples for the case that such conditions fail. Second, when the kinetic decomposition is applied to the problem of enhanced diffusion, it leads to a diffusive limit problem for a kinetic equation that in turn yields the effective equation for enhanced diffusion.
منابع مشابه
Kinetic Decomposition for Periodic Homogenization Problems
Abstract. We develop an analytical tool which is adept for detecting shapes of oscillatory functions, is useful in decomposing homogenization problems into limit-problems for kinetic equations, and provides an efficient framework for the validation of multi-scale asymptotic expansions. We apply it first to a hyperbolic homogenization problem and transform it to a hyperbolic limit problem for a ...
متن کاملKinetic Study and Thermal Decomposition Behavior of Magnesium-Sodium Nitrate Based on Hydroxyl-Terminated Polybutadiene
This paper has been utilizing the simultaneous ThermoGravimetric analysis and Differential Scanning Calorimetry (TG–DSC) to investigate the thermal decomposition of magnesium-sodium nitrate pyrotechnic composition based HTPB resin. The thermal behaviors of different samples with various fuel-oxidizer ratio contents were determined. Decomposition kinetic was investigated by evaluating the in...
متن کاملError Control Based Model Reduction for Parameter Optimization of Elliptic Homogenization Problems
In this work we are considered with parameter optimization of elliptic multiscale problems with macroscopic optimization functionals and microscopic material design parameters. An efficient approximation is obtained by the reduced basis approach. A posteriori error estimates for the reduced forward problem are obtained in the periodic homogenization setting, using the so called two scale weak f...
متن کاملNumerical Homogenization of Elliptic Multiscale Problems by Subspace Decomposition
Numerical homogenization tries to approximate solutions of elliptic partial differential equations with strongly oscillating coefficients by the solution of localized problems over small subregions. We develop and analyze a rapidly convergent iterative method for numerical homogenization that shares this feature with existing approaches and is modeled after the Schwarz method. The method is hig...
متن کاملA KINETIC STUDY OF THE DECOMPOSITION OF PYRIDINE CHROMIUM (VI) PEROXIDE WITH ALCOHOLS
A kinetic study of the decomposition of pyridine chromium peroxide with methanol, ethanol, propanol and isopropanol has been made over the temperature range 25 to 40°C. It is found that the ligand exchange stage is the rate determining step in the oxidation process. The activation parameters E , ?H‡ and ?S‡ for the reactions are determined. It is believed that the peroxide linkage is primaril...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006