TY - JOUR
T1 - Nonlinear dielectrics
T2 - Electrostatics of random media and propagation of electromagnetic waves in a homogeneous slab
AU - Blumenfeld, Raphael
AU - Bergman, David J.
PY - 1989/5/1
Y1 - 1989/5/1
N2 - We study nonlinear dielectrics obeying D = ε{lunate}(E2)β/2E. The solution to the eletrostatic equations is found to be unique for ∞ α = 1/(β + 1) 1/(d - 1). We find the electrostatic fields produced by a point charge and by an infinite charged slab in such a medium. Two definitions of the effective dielectric constant, ε{lunate}eff, are shown to coincide. For the case where ε{lunate} varies in space we show that the differential equation for the first correction to the potential field is dipolar in scaled coordinates. We use the first correction to bound ε{lunate}eff. Finally we formulate the explicit time dependent equations that describe the dynamic behavior of the magnetic and electric fields in such materials.
AB - We study nonlinear dielectrics obeying D = ε{lunate}(E2)β/2E. The solution to the eletrostatic equations is found to be unique for ∞ α = 1/(β + 1) 1/(d - 1). We find the electrostatic fields produced by a point charge and by an infinite charged slab in such a medium. Two definitions of the effective dielectric constant, ε{lunate}eff, are shown to coincide. For the case where ε{lunate} varies in space we show that the differential equation for the first correction to the potential field is dipolar in scaled coordinates. We use the first correction to bound ε{lunate}eff. Finally we formulate the explicit time dependent equations that describe the dynamic behavior of the magnetic and electric fields in such materials.
UR - http://www.scopus.com/inward/record.url?scp=0039054838&partnerID=8YFLogxK
U2 - 10.1016/0378-4371(89)90339-7
DO - 10.1016/0378-4371(89)90339-7
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AN - SCOPUS:0039054838
SN - 0378-4371
VL - 157
SP - 428
EP - 436
JO - Physica A: Statistical Mechanics and its Applications
JF - Physica A: Statistical Mechanics and its Applications
IS - 1
ER -