Converging shocks in elastic-plastic solids

We present an approximate description of the behavior of an elastic-plastic material processed by a cylindrically or spherically symmetric converging shock, following Whitham's shock dynamics theory. Originally applied with success to various gas dynamics problems, this theory is presently derived for solid media, in both elastic and plastic regimes. The exact solutions of the shock dynamics equations obtained reproduce well the results obtained by high-resolution numerical simulations. The examined constitutive laws share a compressible neo-Hookean structure for the internal energy e = e_(s)(I_1)+e_(h)(ρ,ς), where e_(s) accounts for shear through the first invariant of the Cauchy–Green tensor, and e_(h) represents the hydrostatic contribution as a function of the density ρ and entropy ς. In the strong-shock limit, reached as the shock approaches the axis or origin r=0, we show that compression effects are dominant over shear deformations. For an isothermal constitutive law, i.e., e_(h) = e_(h)(ρ), with a power-law dependence e_(h) ∝ ρ_(α), shock dynamics predicts that for a converging shock located at r=R(t) at time t, the Mach number increases as M ∝ [log(1/R)]^α, independently of the space index s, where s=2 in cylindrical geometry and 3 in spherical geometry. An alternative isothermal constitutive law with p(ρ) of the arctanh type, which enforces a finite density in the strong-shock limit, leads to M ∝ R^(−(s−1)) for strong shocks. A nonisothermal constitutive law, whose hydrostatic part eh is that of an ideal gas, is also tested, recovering the strong-shock limit M∝R^(−(s−1)/n(γ)) originally derived by Whitham for perfect gases, where γ is inherently related to the maximum compression ratio that the material can reach, (γ+1)/(γ−1). From these strong-shock limits, we also estimate analytically the density, radial velocity, pressure, and sound speed immediately behind the shock. While the hydrostatic part of the energy essentially commands the strong-shock behavior, the shear modulus and yield stress modify the compression ratio and velocity of the shock far from the axis or origin. A characterization of the elastic-plastic transition in converging shocks, which involves an elastic precursor and a plastic compression region, is finally exposed

U(1) Noncommutative Gauge Fields and Magnetogenesis

The connection between the Lorentz invariance violation in the lagrangean context and the quantum theory of noncommutative fields is established for the U(1) gauge field. The modified Maxwell equations coincide with other derivations obtained using different procedures. These modified equations are interpreted as describing macroscopic ones in a polarized and magnetized medium. A tiny magnetic field (seed) emerges as particular static solution that gradually increases once the modified Maxwell equations are solved as a self-consistent equations system.Comment: 4 page

Continuum variational and diffusion quantum Monte Carlo calculations

This topical review describes the methodology of continuum variational and diffusion quantum Monte Carlo calculations. These stochastic methods are based on many-body wave functions and are capable of achieving very high accuracy. The algorithms are intrinsically parallel and well-suited to petascale computers, and the computational cost scales as a polynomial of the number of particles. A guide to the systems and topics which have been investigated using these methods is given. The bulk of the article is devoted to an overview of the basic quantum Monte Carlo methods, the forms and optimisation of wave functions, performing calculations within periodic boundary conditions, using pseudopotentials, excited-state calculations, sources of calculational inaccuracy, and calculating energy differences and forces

Scattering of surface plasmons by one-dimensional periodic nanoindented surfaces

In this work, the scattering of surface plasmons by a finite periodic array of one-dimensional grooves is theoretically analyzed by means of a modal expansion technique. We have found that the geometrical parameters of the array can be properly tuned to achieve optimal performance of the structure either as a Bragg reflector or as a converter of surface plasmons into light. In this last case, the emitted light is collimated within a few degrees cone. Importantly, we also show that a small number of indentations in the array are sufficient to fully achieve its functional capabilities.Comment: 5 pages, 5 figures; changed sign convention in some definition