33 research outputs found
Eigenvalue Problem in Two Dimensions for an Irregular Boundary II: Neumann Condition
We formulate a systematic elegant perturbative scheme for determining the
eigenvalues of the Helmholtz equation (\bigtriangledown^{2} + k^{2}){\psi} = 0
in two dimensions when the normal derivative of {\psi} vanishes on an irregular
closed curve. Unique feature of this method, unlike other perturbation schemes,
is that it does not require a separate formalism to treat degeneracies.
Degenerate states are handled equally elegantly as the non-degenerate ones. A
real parameter, extracted from the parameters defining the irregular boundary,
serves as a perturbation parameter in this scheme as opposed to earlier schemes
where the perturbation parameter is an artificial one. The efficacy of the
proposed scheme is gauged by calculating the eigenvalues for elliptical and
supercircular boundaries and comparing with the results obtained numerically.
We also present a simple and interesting semi-empirical formula, determining
the eigenspectrum of the 2D Helmholtz equation with the Dirichlet or the
Neumann condition for a supercircular boundary. A comparison of the
eigenspectrum for several low-lying modes obtained by employing the formula
with the corresponding numerical estimates shows good agreement for a wide
range of the supercircular exponent.Comment: 26 pages, 12 figure
Two distinct pathways for the invasion of Streptococcus pyogenes in non-phagocytic cells
Smoothed particle hydrodynamics modeling of linear shaped charge with jet formation and penetration effects
Modified Kocks-Mecking-Estrin Model to Account Nonlinear Strain Hardening
The dislocation density-based model after Kocks-Mecking-Estrin (KME) is widely used to characterize the thermally activated plastic deformation and dislocation kinetics. According to the model, the slope of the stress-strain curve decreases linearly with stress, which contradicts the experimental observation. In the current study, the evolution of dislocation density in the model is generalized to account for the nonlinearity of the slope.11Nsciescopu