Mathematical model of a heterogeneous medium consisting of a matrix and spherical inclusions

1999 ◽  
Vol 40 (4) ◽  
pp. 704-711
Author(s):  
S. P. Kiselev ◽  
V. M. Fomin
Keyword(s):  
Mathematical Model ◽  
Heterogeneous Medium ◽  
Spherical Inclusions

The mathematical model of fluid filtration to the well of drift type in stress heterogeneous medium

2013 ◽  
Author(s):  
B. T. Zhumagulov ◽  
N. T. Azhikhanov ◽  
Zh. K. Masanov ◽  
K. T. Bissembaeva
Keyword(s):  
Mathematical Model ◽  
Heterogeneous Medium ◽  
Fluid Filtration ◽  
The Mathematical Model

scholarly journals Fundamental Problems of the Electrodynamics of Heterogeneous Media

2012 ◽  
Vol 2012 ◽  
pp. 1-28 ◽  
Author(s):  
N. N. Grinchik ◽  
Yu. N. Grinchik
Keyword(s):  
Mathematical Model ◽  
Electric Double Layer ◽  
Layered Medium ◽  
Heterogeneous Media ◽  
Heterogeneous Medium ◽  
Surface Current ◽  
Charge Carriers ◽  
Thermal Fields ◽  
Dirichlet Theorem ◽  
Generalized Wave Equation

The consistent physic-mathematical model of propagation of an electromagnetic wave in a heterogeneous medium is constructed using the generalized wave equation and the Dirichlet theorem. Twelve conditions at the interfaces of adjacent media are obtained and justified without using a surface charge and surface current in explicit form. The conditions are fulfilled automatically in each section of counting schemes for calculations. A consistent physicomathematical model of interaction of nonstationaly electric and thermal fields in a layered medium with allowance or mass transfer is constructed. The model is based on the methods of thermodynamics and on the equations of an electromagnetic field and is formulated without explicit separation of the charge carriers and the charge of an electric double layer.

A MOVING BOUNDARY PROBLEM IN A STOCHASTIC MEDIUM

1999 ◽  
Vol 02 (02) ◽  
pp. 179-202 ◽  
Author(s):  
BERNT ØKSENDAL ◽  
GJERMUND VÅGE
Keyword(s):  
Mathematical Model ◽  
Variational Inequalities ◽  
White Noise ◽  
Boundary Problem ◽  
Moving Boundary ◽  
Heterogeneous Medium ◽  
Moving Boundary Problem ◽  
Stochastic Variational Inequalities ◽  
Stochastic Medium ◽  
White Noise Functional

Suppose a fluid is pumped into a heterogeneous medium in ℝd at a known rate and that there is a known initial wet region D(0) (region filled with fluid) at time t=0. What is the wet region, D(t), at a later time t and what is the pressure, p(t,x), at this time and at the point x∈D(t)? We propose a mathematical model for this problem when the region is stochastic, i.e. has a stochastic permeability represented by some (positive) white noise functional. The model has the form of a family of stochastic variational inequalities. We show that there is a unique stochastic, weak (in Baiocchi sense) solution of this problem and we discuss its properties.

Observation of dislocations in dynamically loaded Cu-SiO2

1986 ◽  
Vol 44 ◽  
pp. 424-425
Author(s):  
D. S. Pritchard
Keyword(s):  
Electron Microscope ◽  
Strain Rate ◽  
Single Crystal ◽  
Transmission Electron Microscope ◽  
Volume Fraction ◽  
Screw Dislocations ◽  
Spherical Inclusions ◽  
Transmission Electron ◽  
Crystal Dispersion ◽  
Strain Rate Loading

The effect of varying the strain rate loading conditions in compression on a copper single crystal dispersion-hardened with SiO2 particles has been examined. These particles appear as small spherical inclusions in the copper lattice and have a volume fraction of 0.6%. The structure of representative crystals was examined prior to any testing on a transmission electron microscope (TEM) to determine the nature of the dislocations initially present in the tested crystals. Only a few scattered edge and screw dislocations were viewed in those specimens.

The microstructure change of low-carbon electrical steels by residual aluminum

1989 ◽  
Vol 47 ◽  
pp. 286-287
Author(s):  
C.K. Hou ◽  
C.T. Hu ◽  
Sanboh Lee
Keyword(s):  
Annealing Treatment ◽  
Low Carbon ◽  
Electrical Steels ◽  
Vacuum Degassing ◽  
Spherical Inclusions ◽  
Residual Aluminum ◽  
Average Grain Size ◽  
The Matrix ◽  
Fine Size ◽  
To Come

The fully processed low-carbon electrical steels are generally fabricated through vacuum degassing to reduce the carbon level and to avoid the need for any further decarburization annealing treatment. This investigation was conducted on eighteen heats of such steels with aluminum content ranging from 0.001% to 0.011% which was believed to come from the addition of ferroalloys.The sizes of all the observed grains are less than 24 μm, and gradually decrease as the content of aluminum is increased from 0.001% to 0.007%. For steels with residual aluminum greater than 0. 007%, the average grain size becomes constant and is about 8.8 μm as shown in Fig. 1. When the aluminum is increased, the observed grains are changed from the uniformly coarse and equiaxial shape to the fine size in the region near surfaces and the elongated shape in the central region. SEM and EDAX analysis of large spherical inclusions in the matrix indicate that silicate is the majority compound when the aluminum propotion is less than 0.003%, then the content of aluminum in compound inclusion increases with that in steel.

Mathematical model of hit phenomena and its application to movie advertisement

2008 ◽  
Author(s):  
Ishii Akira ◽  
Yoshida Narihiko ◽  
Hayashi Takafumi ◽  
Umemura Sanae ◽  
Nakagawa Takeshi
Keyword(s):  
Mathematical Model

Dynamics of conflict: Mathematical model of the interactions between two actors

2008 ◽  
Author(s):  
Larry Liebovitch ◽  
Vincent Naudot
Keyword(s):  
Mathematical Model

A mathematical model for brightness and contour perception

1976 ◽  
Author(s):  
Jiro Hamada
Keyword(s):  
Mathematical Model ◽  
Contour Perception

T-cell vaccination: Insights and questions raised by a mathematical model

1997 ◽  
Vol 56 (1-3) ◽  
pp. 172
Author(s):  
J Borghans
Keyword(s):  
Mathematical Model ◽  
T Cell ◽  
T Cell Vaccination
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