scholarly journals Momentum jump condition for deformable Newtonian interfaces: Rigorous derivation

2020 ◽  
Vol 84 ◽  
pp. 367-445
Author(s):  
Suat Canberk Ozan ◽  
Hugo Atle Jakobsen
Keyword(s):  
Jump Condition ◽  
Rigorous Derivation

The Simplest Patterns of Interpenetrated Honeycomb Layers – Counter examples to the Minimal Transitivity Principle?

2018 ◽  
Author(s):  
Igor Baburin
Keyword(s):  
Crystal Engineering ◽  
Structural Chemistry ◽  
Broad Context ◽  
Rigorous Derivation ◽  
New Approach

The paper calls attention to the most symmetric interpenetration patterns of honeycomb layers. To the best of my knowledge, such patterns remained unknown so far. In my contribution a rigorous derivation of such patterns is given that makes use of a new approach to interpenetrating nets. The results are presented in a broad context of structural chemistry and crystal engineering.

Rigorous derivation of reaction path degeneracy in transition state theory

1992 ◽  
Vol 193 (1-3) ◽  
pp. 181-184 ◽  
Author(s):  
Andrew J. Karas ◽  
Robert G. Gilbert ◽  
Michael A. Collins
Keyword(s):  
Transition State ◽  
Transition State Theory ◽  
Reaction Path ◽  
State Theory ◽  
Rigorous Derivation

scholarly journals Modeling of a diffusion with aggregation: rigorous derivation and numerical simulation

2018 ◽  
Vol 52 (2) ◽  
pp. 567-593 ◽  
Author(s):  
Li Chen ◽  
Simone Göttlich ◽  
Stephan Knapp
Keyword(s):  
Particle System ◽  
Rigorous Derivation ◽  
Uniform Estimates ◽  
Estimates Of Solutions ◽  
Delta Potential ◽  
Intermediate Particle ◽  
Stochastic Particle System ◽  
Aggregation Equation ◽  
Discretization Schemes ◽  
Theoretical Results

In this paper, a diffusion-aggregation equation with delta potential is introduced. Based on the global existence and uniform estimates of solutions to the diffusion-aggregation equation, we also provide the rigorous derivation from a stochastic particle system while introducing an intermediate particle system with smooth interaction potential. The theoretical results are compared to numerical simulations relying on suitable discretization schemes for the microscopic and macroscopic level. In particular, the regime switch where the analytic theory fails is numerically analyzed very carefully and allows for a better understanding of the equation.

scholarly journals Homogenization of composite ferromagnetic materials

2015 ◽  
Vol 471 (2182) ◽  
pp. 20150365 ◽  
Author(s):  
François Alouges ◽  
Giovanni Di Fratta
Keyword(s):  
Free Energy ◽  
Ferromagnetic Material ◽  
Energy Functional ◽  
Ferromagnetic Materials ◽  
Rigorous Derivation ◽  
Free Energy Functional ◽  
Landau Free Energy ◽  
Ferromagnetic Body ◽  
The Media

The objective of this paper is to perform, by means of Γ - convergence and two-scale convergence , a rigorous derivation of the homogenized Gibbs–Landau free energy functional associated with a composite periodic ferromagnetic material, i.e. a ferromagnetic material in which the heterogeneities are periodically distributed inside the media. We thus describe the Γ -limit of the Gibbs–Landau free energy functional, as the period over which the heterogeneities are distributed inside the ferromagnetic body shrinks to zero.

On the estimation of a harmonic component in a time series with stationary dependent residuals

1973 ◽  
Vol 5 (02) ◽  
pp. 217-241 ◽  
Author(s):  
A. M. Walker
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Least Squares Method ◽  
Harmonic Component ◽  
Asymptotic Distributions ◽  
Finite Variance ◽  
Rigorous Derivation ◽  
Image Position ◽  
Vector Valued ◽  
Special Case

Let observations (X 1, X 2, …, Xn ) be obtained from a time series {Xt } such that where the ɛt are independently and identically distributed random variables each having mean zero and finite variance, and the gu (θ) are specified functions of a vector-valued parameter θ. This paper presents a rigorous derivation of the asymptotic distributions of the estimators of A, B, ω and θ obtained by an approximate least-squares method due to Whittle (1952). It is a sequel to a previous paper (Walker (1971)) in which a similar derivation was given for the special case of independent residuals where gu (θ) = 0 for u > 0, the parameter θ thus being absent.

Variational Iteration Method for a Nonlinear Reaction-Diffusion Process

2008 ◽  
Vol 6 (1) ◽  
Author(s):  
Shu-Qiang Wang ◽  
Ji-Huan He
Keyword(s):  
Exact Solution ◽  
Diffusion Process ◽  
Iteration Method ◽  
Unknown Parameter ◽  
Reaction Diffusion ◽  
Variational Iteration Method ◽  
Rigorous Derivation ◽  
Variational Iteration ◽  
Nonlinear Reaction ◽  
The Given

An extremely simple and elementary, but rigorous derivation of temperature distribution of a reaction-diffusion process is given using the variational iteration method. In this method, a trial function (an initial solution) is chosen with some unknown parameter, which is identified after a few iterations according to the given boundary conditions. Comparison with the exact solution shows that the method is very effective and convenient.

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