TY - JOUR
TI - Electric-Field Effects on Optical Absorption near Thresholds in Solids
AU - Aspnes, David E.
T2 - Physical Review
AB - The weak-field effective-mass-approximation calculations of the absorption coefficient in the presence of an electric field for direct and indirect transitions at a normal (${M}_{0}$) threshold are extended to an arbitrary orientation of the electric field in an anisotropic solid. To do this, a systematic method of evaluating density-of-states integrals arising in the electroabsorption or Franz-Keldysh effect is presented. Certain integrals obtained in prior calculations at the ${M}_{0}$ threshold which have not been previously evaluated are given in closed form. This method is also used to derive the change in absorption coefficient, $\ensuremath{\Delta}\ensuremath{\alpha}(\mathcal{E})$, occuring at the saddle-point edges ${M}_{1}$ and ${M}_{2}$, as well as the edge ${M}_{3}$, for an arbitrary field direction in an anisotropic solid. It is shown that there is a direct correlation between $\ensuremath{\Delta}\ensuremath{\alpha}(\mathcal{E})$ for the ${M}_{0}$ and ${M}_{3}$ edges, and also for the ${M}_{1}$ and ${M}_{2}$ thresholds. Reduced masses of opposite signs, as in the ${M}_{1}$ and ${M}_{2}$ edges, give rise to two branches in $\ensuremath{\Delta}\ensuremath{\alpha}(\mathcal{E})$.
DA - 1966/7/15/
PY - 1966/7/15/
DO - 10.1103/physrev.147.554
VL - 147
IS - 2
SP - 554-566
J2 - Phys. Rev.
LA - en
OP -
SN - 0031-899X
UR - http://dx.doi.org/10.1103/physrev.147.554
DB - Crossref
ER -
TY - JOUR
TI - ON FORMULATION AND ITERATIVE SOLUTION OF SMALL STRAIN PLASTICITY PROBLEMS
AU - HAVNER, KS
T2 - QUARTERLY OF APPLIED MATHEMATICS
AB - This paper is concerned with a general method of formulation and iterative solution of small displacement plasticity problems, using the Hencky-Nadai hardening law as mathematical model for the material behavior. Beginning with a minimum energy principle for small thermal-mechanical strains under simple external loading, quasi-linear partial differential equations are formulated and a method of iteration by successive solutions is proposed. A finite-difference discretization of the equations (in two dimensions) is obtained through minimization of the total potential energy function, leading to positive definite symmetric matrices for general boundary configurations.
DA - 1966///
PY - 1966///
DO - 10.1090/qam/99938
VL - 23
IS - 4
SP - 323-&
SN - 0033-569X
ER -
TY - JOUR
TI - On energy balance criteria in ductile fracture
AU - Havner, K. S.
AU - Glassco, J. B.
T2 - International Journal of Fracture Mechanics
DA - 1966///
PY - 1966///
VL - 2
SP - 506-525
ER -