Traveling Wave Solutions in an Integrodifference Equation with Weak Compactness

This article studies the existence of traveling wave solutions in an integrodifference equation with weak compactness. Because of the special kernel function that may depend on the Dirac function, traveling wave maps have lower regularity such that it is difficult to directly look for a traveling wave solution in the uniformly continuous and bounded functional space. In this paper, by introducing a proper set of potential wave profiles, we can obtain the existence and precise asymptotic behavior of nontrivial traveling wave solutions, during which we do not require the monotonicity of this model.     

Revisiting finite-scale Navier–Stokes theory: Order-of-magnitude results,new critical values,and connections to Stokesian fluids

We return to Ref. [7] and present, as well as note the implications stemming from, a rigorous order-of-magnitude-based derivation of the governing system considered therein. The system in question models the ‘piston problem’ for the case of a viscous, but thermally non-conducting, gas with constant transport coefficients under the generalization of the Navier–Stokes (NS) equations known as the finite-scale Navier–Stokes (FSNS) equations. Our analysis also provides a rigorous derivation of the FSNS system considered in Ref. [12], highlights links between FSNS theory and Stokesian fluids, and examines the possible applicability of generalizations of the perfect gas law to finite-scale theory. We conclude with a brief discussion regarding new critical values of the averaging length scale.     

Sharp estimates for the spreading speeds of the Lotka-Volterra diffusion system with strong competition

This paper is concerned with the classical two-species Lotka-Volterra diffusion system with strong competition. The sharp dynamical behavior of the solution is established in two different situations: either one species is an invasive one and the other is a native one or both are invasive species. Our results seem to be the first that provide a precise spreading speed and profile for such a strong competition system. Among other things, our analysis relies on the construction of new types of supersolution and subsolution, which are optimal in certain sense.     

High-power diffraction-limited phase-locked GaAs/GaAlAs semiconductor laser array

High-power diffraction-limited phase-locked gallium-arsenide (GaAs)/ gallium-aluminum-arsenide (GaAlAs) semiconductor laser arrays have been fabricated using the LPE technique, the standard photolithographic technique, wet etching, and proton bombardment. The tailored gain-guided arrays are made by varying the width of the channels of the lasers while keeping the spacing between them constant. The array consists of six lasers. Its optical output power per facet is 300 mW at 2.71_th with single-mode continuous wave (CW) operation and single lobe far-field pattern with full width at half maximum (FWHM) of 1.90°.