Global exponential convergence to variational traveling waves in cylinders

We prove, under generic assumptions, that the special variational traveling wave that minimizes the exponentially weighted Ginzburg-Landau functional associated with scalar reaction-diffusion equations in infinite cylinders is the long-time attractor for the solutions of the initial value problems with front-like initial data. The convergence to this traveling wave is exponentially fast. The obtained result is mainly a consequence of the gradient flow structure of the considered equation in the exponentially weighted spaces and does not depend on the precise details of the problem. It strengthens our earlier generic propagation and selection result for "pushed" fronts.Comment: 23 page

Si/SiGe bound-to-continuum quantum cascade emitters

Si/SiGe bound-to-continuum quantum cascade emitters designed by self-consistent 6-band k.p modeling and grown by low energy plasma enhanced chemical vapour deposition are presented demonstrating electroluminescence between 1.5 and 3 THz. The electroluminescence is Stark shifted by an electric field and demonstrates polarized emission consistent with the design. Transmission electron microscopy and x-ray diffraction are also presented to characterize the thick heterolayer structure

Large-time Behavior of Solutions to the Inflow Problem of Full Compressible Navier-Stokes Equations

Large-time behavior of solutions to the inflow problem of full compressible Navier-Stokes equations is investigated on the half line $R^+ =(0,+\infty)$. The wave structure which contains four waves: the transonic(or degenerate) boundary layer solution, 1-rarefaction wave, viscous 2-contact wave and 3-rarefaction wave to the inflow problem is described and the asymptotic stability of the superposition of the above four wave patterns to the inflow problem of full compressible Navier-Stokes equations is proven under some smallness conditions. The proof is given by the elementary energy analysis based on the underlying wave structure. The main points in the proof are the degeneracies of the transonic boundary layer solution and the wave interactions in the superposition wave.Comment: 27 page

On the chromatic numbers of 3-dimensional slices

We prove that for an arbitrary $\varepsilon > 0$ holds $$\chi (\mathbb{R}^3 \times [0,\varepsilon]^6) \geq 10,$$ where $\chi(M)$ stands for the chromatic number of an (infinite) graph with the vertex set $M$ and the edge set consists of pairs of monochromatic points at the distance 1 apart

A PROSPECTIVE CONTROLLED STUDY OF LOW BACK SCHOOL IN THE GENERAL POPULATION

There are no data on the efficacy of a back school in primary prevention of back pain in the general population or on the characteristics of the population who volunteers. After announcement in the local press, 494 healthy adults volunteered and paid for a back school course in Switzerland. A total of 371 controls were matched for sex, age, profession, nationality and back pain. A statistically significant decrease in numbers of doctor's visits was found by the participants during the following 6 months compared with the controls. However, there were no significant between-group differences in the four remaining parameters (presence and intensity of back pain, drug intake and sick leave). Three-quarters of participants changed their attitudes after the back school. Volunteering for a back pain prevention programme was associated with the presence of back pain problems. Reasons for volunteering are further discussed. Overall, the results of this study showed that a back school for the general population may not solve the problem of low back pain, but improves self-help in a subgroup of the populatio

Describing the set of words generated by interval exchange transformation

Let $W$ be an infinite word over finite alphabet $A$. We get combinatorial criteria of existence of interval exchange transformations that generate the word W.Comment: 17 pages, this paper was submitted at scientific council of MSU, date: September 21, 200

Response of Seven Crystallographic Orientations of Sapphire Crystals to Shock Stresses of 16 to 86 GPa

Shock-wave profiles of sapphire (single-crystal Al2O3) with seven crystallographic orientations were measured with time-resolved VISAR interferometry at shock stresses in the range 16 to 86 GPa. Shock propagation was normal to the surface of each cut. The angle between the c-axis of the hexagonal crystal structure and the direction of shock propagation varied from 0 for c-cut up to 90 degrees for m-cut in the basal plane. Based on published shock-induced transparencies, shock-induced optical transparency correlates with the smoothness of the shock-wave profile. The ultimate goal was to find the direction of shock propagation in sapphire that is most transparent as a window. Particle velocity histories were recorded at the interface between a sapphire crystal and a LiF window. In most cases measured wave profiles are noisy as a result of heterogeneity of deformation. Measured values of Hugoniot Elastic Limits (HELs) depend on direction of shock compression and peak shock stress. The largest HEL values were recorded for shock loading along the c-axis and perpendicular to c along the m-direction. Shock compression along the m- and s-directions is accompanied by the smallest heterogeneity of deformation and the smallest rise time of the plastic shock wave. m- and s-cut sapphire most closely approach ideal elastic-plastic flow, which suggests that m- and s-cut sapphire are probably the orientations that remains most transparent to highest shock pressures. Under purely elastic deformation sapphire has very high spall strength, which depends on load duration and peak stress. Plastic deformation of sapphire causes loss of its tensile strength.Comment: 18 pages, 18 figure

Flame Enhancement and Quenching in Fluid Flows

We perform direct numerical simulations (DNS) of an advected scalar field which diffuses and reacts according to a nonlinear reaction law. The objective is to study how the bulk burning rate of the reaction is affected by an imposed flow. In particular, we are interested in comparing the numerical results with recently predicted analytical upper and lower bounds. We focus on reaction enhancement and quenching phenomena for two classes of imposed model flows with different geometries: periodic shear flow and cellular flow. We are primarily interested in the fast advection regime. We find that the bulk burning rate v in a shear flow satisfies v ~ a*U+b where U is the typical flow velocity and a is a constant depending on the relationship between the oscillation length scale of the flow and laminar front thickness. For cellular flow, we obtain v ~ U^{1/4}. We also study flame extinction (quenching) for an ignition-type reaction law and compactly supported initial data for the scalar field. We find that in a shear flow the flame of the size W can be typically quenched by a flow with amplitude U ~ alpha*W. The constant alpha depends on the geometry of the flow and tends to infinity if the flow profile has a plateau larger than a critical size. In a cellular flow, we find that the advection strength required for quenching is U ~ W^4 if the cell size is smaller than a critical value.Comment: 14 pages, 20 figures, revtex4, submitted to Combustion Theory and Modellin