Convergence Rate for a Parabolic Equation with Supercritical Nonlinearity

We study the behavior of solutions of the Cauchy problem for a diffusion equation with supercritical nonlinearity. It is shown that if two solutions are initially close enough near the spatial infinity, then these solutions approach each other. Under some conditions, we determine the exact convergence rate, which turns out to depend on initial data.     

Elastic scattering of 56 MeV polarized deuterons on 4He

The differential cross section and the vector and tensor analyzing powers A_y, A_xx, A_yy and A_xz were measured for the d-⁴He elastic scattering at 56 MeV. The measurement of A_xz was performed using a deuteron beam polarized in the horizontal plane. An optical-model analysis of the experimental data was carried out. The magnitude of the tensor analyzing powers could not be reproduced without the tensor potential. By including the T_R type tensor potential, the optical-model calculations give a reasonable reproduction of the experimental data at θ_c.m. < 120°. The obtained T_R tensor potential was much stronger than that predicted by the folding model. The strength of the real T_R potential was roughly in accordance with that obtained from the optical-model analysis of d-⁴He elastic scattering at 20.2 MeV.     

Visible nonlinear band-edge luminescence in ZnSe and CdS excited by a mid-infrared free-electron laser

Visible nonlinear band-edge luminescence in ZnSe and CdS bulk crystals was observed upon excitation by a mid-infrared free-electron laser (mid-IR FEL) at approximately 9 mm. The emission intensity is proportional to the 74th and 45th powers of the excitation intensity for ZnSe and CdS, respectively. For ZnSe, the temporal profile of the emission intensity does not follow the profile of the excitation macropulse of the FEL, but sharply rises and decays only at the maximum of the macropulse profile. These features are in marked contrast to those of a previous report, where the emission profile follows that of the macropulse, and the emission intensity scales with the 4th power of the excitation intensity. The experimental observations were reproduced by a numerical simulation based on impact ionization and avalanche ionization by electrons accelerated by the optical electric field of the FEL. The large nonlinearity in the bandedge emission comes from the macropulse temporal structure, which consists of micropulses densely spaced to allow excited carriers to survive when the next micropulse arrives. They work as seed carriers in the next carrier multiplication step.     

Palladium-catalyzed silylation of alcohols with hexamethyldisilane

The combination of hexamethyldisilane and a catalytic amount of [PdCl(eta3-C3H5)]2-PPh3 was found to be effective for the trimethylsilylation of alcohols, where both of the two trimethylsilyl groups of hexamethyldisilane were transferred to alcohols without coproduction of any stoichiometric amount of byproduct but H2.     

Maximization of the total population in a reaction–diffusion model with logistic growth

This paper is concerned with a nonlinear optimization problem that naturally arises in population biology. We consider the effect of spatial heterogeneity on the total population of a biological species at a steady state, using a reaction–diffusion logistic model. Our objective is to maximize the total population when resources are distributed in the habitat to control the intrinsic growth rate, but the total amount of resources is limited. It is shown that under some conditions, any local maximizer must be of “bang–bang” type, which gives a partial answer to the conjecture addressed by Ding et al. (Nonlinear Anal Real World Appl 11(2):688–704, 2010). To this purpose, we compute the first and second variations of the total population. When the growth rate is not of bang–bang type, it is shown in some cases that the first variation becomes nonzero and hence the resource distribution is not a local maximizer. When the first variation becomes zero, we prove that the second variation is positive. These results implies that the bang–bang property is essential for the maximization of total population.     

A Remark on the Global Existence of a Third Order Dispersive Flow into Locally Hermitian Symmetric Spaces

We prove time-global existence of solutions to the initial value problem for a third order dispersive flow into compact locally Hermitian symmetric spaces. The equation under consideration generalizes two-sphere-valued completely integrable systems modeling the motion of vortex filament. Unlike one-dimensional Schrödinger maps, our third order equation is not completely integrable under the curvature condition on the target manifold in general. The idea of our proof is to exploit two conservation laws and an “almost conserved quantity” which prevents the formation of a singularity in finite time.