scholarly journals Fundamental Problems of the Electrodynamics of Heterogeneous Media with Boundary Conditions Corresponding to the Total-Current Continuity

10.5772/16937 ◽  
2011 ◽  
Author(s):  
N.N. Grinchik ◽  
O.P. Korogoda ◽  
M.S. Khomich ◽  
S.V. Ivanova ◽  
V.I. Terechov ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Heterogeneous Media ◽  
Total Current

scholarly journals Thermostatics vs. Electrodynamics

2020 ◽  
Author(s):  
Robert S. Eisenberg
Keyword(s):  
Dielectric Constant ◽  
Boundary Conditions ◽  
Maxwell Equations ◽  
Displacement Current ◽  
Total Current ◽  
Thermal Dynamics ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Classical Formulation ◽  
Low Pass

Thermodynamics has been the foundation of many models of biological and technological systems. But thermodynamics is static and is misnamed. A more suitable name is thermostatics. Thermostatics does not include time as a variable and so has no velocity, flow or friction. Indeed, as usually formulated, thermostatics does not include boundary conditions. Devices require boundary conditions to define their input and output. They usually involve flow and friction. Thermostatics is an unsuitable foundation for understanding technological and biological devices. A time dependent generalization of thermostatics that might be called thermal dynamics is being developed by Chun Liu and collaborators to avoid these limitations. Electrodynamics is not restricted like thermostatics, but in its classical formulation involves drastic assumptions about polarization and an over-approximated dielectric constant. Once the Maxwell equations are rewritten without a dielectric constant, they are universal and exact. Conservation of total current, including displacement current, is a restatement of the Maxwell equations that leads to dramatic simplifications in the understanding of one dimensional systems, particularly those without branches, like the ion channel proteins of biological membranes and the two terminal devices of electronic systems. The Brownian fluctuations of concentrations and fluxes of ions become the spatially independent total current, because the displacement current acts as an unavoidable low pass filter, a consequence of the Maxwell equations for any material polarization. Electrodynamics and thermal dynamics together form a suitable foundation for models of technological and biological systems.

3D finite-difference dynamic-rupture modeling along nonplanar faults

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. SM123-SM137 ◽  
Author(s):  
Víctor M. Cruz-Atienza ◽  
Jean Virieux ◽  
Hideo Aochi
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Heterogeneous Media ◽  
Slip Rate ◽  
Quantitative Agreement ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Weight Functions ◽  
Dynamic Rupture ◽  
Fault Surface

Proper understanding of seismic emissions associated with the growth of complexly shaped microearthquake networks and larger-scale nonplanar fault ruptures, both in arbitrarily heterogeneous media, requires accurate modeling of the underlying dynamic processes. We present a new 3D dynamic-rupture, finite-difference model called the finite-difference, fault-element (FDFE) method; it simulates the dynamic rupture of nonplanar faults subjected to regional loads in complex media. FDFE is based on a 3D methodology for applying dynamic-rupture boundary conditions along the fault surface. The fault is discretized by a set of parallelepiped fault elements in which specific boundary conditions are applied. These conditions are applied to the stress tensor, once transformed into a local fault referenceframe. Numerically determined weight functions multiplying particle velocities around each element allow accurate estimates of fault kinematic parameters (i.e., slip and slip rate) independent of faulting mechanism. Assuming a Coulomb-like slip-weakening friction law, a parametric study suggests that the FDFE method converges toward a unique solution, provided that the cohesive zone behind the rupture front is well resolved (i.e., four or more elements inside this zone). Solutions are free of relevant numerical artifacts for grid sizes smaller than approximately [Formula: see text]. Results yielded by the FDFE approach are in good quantitative agreement with those obtained by a semianalytical boundary integral method along planar and nonplanar parabola-shaped faults. The FDFE method thus provides quantitative, accurate results for spontaneous-rupture simulations on intricate fault geometries.

scholarly journals Equivalent Boundary Conditions for Heterogeneous Acoustic Media

2014 ◽  
Vol 15 (3) ◽  
pp. 301
Author(s):  
Manuela Longoni De Castro ◽  
Julien Diaz ◽  
Victor Perón
Keyword(s):  
Boundary Conditions ◽  
Seismic Waves ◽  
Heterogeneous Media ◽  
Absorbing Boundary Conditions ◽  
Computational Domain ◽  
Absorbing Boundary ◽  
Equivalent Boundary ◽  
Artificial Boundaries ◽  
Acoustic Media ◽  
Propagation Of Waves

In this work, we have worked on possibilities to model artificial boundaries needed in the simulation of wave propagation in acoustic heterogeneous media.  Our motivation is to restrict the computational domain in the simulation of seismic waves that are propagated from the earth and transmitted to the stratified heterogeneous media composed by ocean and atmosphere. Two possibilities were studied and compared in computational tests: the use of absorbing boundary conditions on an artificial boundary in the atmosphere layer and the elimination of the atmosphere layer using an equivalent boundary condition that mimics the propagation of waves through the atmosphere. <br />

Electrodynamics of layered media with boundary conditions corresponding to the total-current continuum

2009 ◽  
Vol 82 (4) ◽  
pp. 810-819 ◽  
Author(s):  
N. N. Grinchik ◽  
A. P. Dostanko ◽  
I. A. Gishkelyuk ◽  
Yu. N. Grinchik
Keyword(s):  
Boundary Conditions ◽  
Layered Media ◽  
Total Current

scholarly journals Vacuum fermionic currents in braneworld models on AdS bulk with a cosmic string

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
S. Bellucci ◽  
W. Oliveira dos Santos ◽  
E.R. Bezerra de Mello ◽  
A.A. Saharian
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Current Density ◽  
Cosmic String ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Vacuum State ◽  
Total Current ◽  
De Sitter ◽  
Proper Distance

Abstract We investigate the effects of a brane and magnetic-flux-carrying cosmic string on the vacuum expectation value (VEV) of the current density for a charged fermionic field in the background geometry of (4+1)-dimensional anti-de Sitter (AdS) spacetime. The brane is parallel to the AdS boundary and the cosmic string is orthogonal to the brane. Two types of boundary conditions are considered on the brane that include the MIT bag boundary condition and the boundary conditions in Z2-symmetric braneworld models. The brane divides the space into two regions with different properties of the vacuum state. The only nonzero component of the current density is along the azimuthal direction and in both the regions the corresponding VEV is decomposed into the brane- free and brane-induced contributions. The latter vanishes on the string and near the string the total current is dominated by the brane-free part. At large distances from the string and in the region between the brane and AdS horizon the decay of the brane-induced current density, as a function of the proper distance, is power-law for both massless and massive fields. For a massive field this behavior is essentially different from that in the Minkowski bulk. In the region between the brane and AdS boundary the large-distance decay of the current density is exponential. Depending on the boundary condition on the brane, the brane-induced contribution is dominant or subdominant in the total current density at large distances from the string. By using the results for fields realizing two inequivalent irreducible representations of the Clifford algebra, the vacuum current density is investigated in C - and P -symmetric fermionic models. Applications are given for a cosmic string in the Randall-Sundrum-type braneworld model with a single brane.

RADIATION BOUNDARY CONDITIONS FOR VERTICALLY HETEROGENEOUS ACOUSTIC MEDIA

1993 ◽  
Vol 01 (03) ◽  
pp. 321-333 ◽  
Author(s):  
GONGQIN LI ◽  
JOSEPH E. MURPHY ◽  
STANLEY A. CHIN-BING
Keyword(s):  
Boundary Conditions ◽  
Heterogeneous Media ◽  
Plane Waves ◽  
Reflection Coefficients ◽  
Radiation Boundary Conditions ◽  
Media Comparison ◽  
Acoustic Media ◽  
Radiation Boundary ◽  
Radiation Conditions ◽  
Effective Reflection Coefficient

Several radiation boundary conditions for inhomogeneous acoustic media are investigated. Previous investigators have developed various approximate radiation conditions and have studied their accuracy by calculating an effective reflection coefficient for plane waves incident on such radiating boundaries. In this paper, it is shown that effective reflection coefficients can be calculated for a class of parabolic approximations to the Helmholtz equation. These results are valid for vertically heterogeneous media. Comparison of these radiation conditions is given through numerical examples.

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