Discontinuous travelling wave solutions for certain hyperbolic systems

In an earlier paper on a malignant cell invasion model (Marchantet al., SIAM J. Appl. Math, 60, 2000) we introduced a novelform of discontinuous travelling wave solution. These solutionscould be studied easily by combining behaviour within a phaseplane with the Rankine–Hugoniot shock conditions, whichdescribe properties (such as the ratio of the jump discontinuitiesto the speed of propagation) that solutions may possess. Theseresults were new for several reasons. The shock conditions relateto hyperbolic equations (which the model is) but were appliedin a travelling wave ordinary differential equation phase planeusing techniques that usually apply to parabolic reaction–diffusionsystems. In addition the solutions possess singular behaviournear several points in the phase plane but in spite of thisthere exists a robust and stable family of physically interestingsolutions. In this paper we discuss two previously studied models, oneof detonation theory and one of angiogenesis. We show that eachof these models also possesses a family of discontinuous travellingwave solutions which was not previously discovered. Of particularinterest is the solution which has a blunt interface at thefront of the invading profile. In all three models it is thissolution that is seen to stably evolve from physically relevantinitial data, and for physically relevant parameter values. This work confirms the robustness of these novel travellingwave solutions and their applicability to a wider range of mathematicalmodelling situations.     

Excitonic detectors of infrared and submillimeter radiation

The theory of new type detectors based on the quenching of secondary emission in direct-gap semiconductors (lines of Raman light scattering due to interaction between free and bound excitons in the crystal, and also bands of edge radiation) caused by IR or submillimeter radiation is proposed. The results obtained are confirmed by the experiment performed for CdS crystal excited by ultraviolet radiation of mercury lamp, at liquid helium temperature.     

Searching for gravitational waves with the LIGO and Virgo interferometers

The first generation of ground-based interferometric gravitational wave detectors, LIGO, GEO, and Virgo, have operated and taken data at their design sensitivities over the last few years. The data has been examined for the presence of gravitational wave signals. Presented here is a comprehensive review of the most significant results. The network of detectors is currently being upgraded and extended, providing a large likelihood for observations. These future prospects will also be discussed.     

The Hard Rod Fluid in a Uniform Gravitational Field

Abstract

The system of hard rods in an external, uniform gravitational field is studied and exact expressions obtained for the partition functions, and the one- and two-particle distributions. In principle all higher order distributions can be exactly expressed as finite sums and the Laplace transforms of the one-particle density and pressure for a semi-infinite system are reducible to single integrals. Limiting cases of weak field and small rod diameters are examined. In the former case, these results agree with Percus and Lebowitz's local density expansion. In the latter case, corrections to the barometric pressure and density laws are obtained. Finally some mathematical difficulties involved in the calculation of the virial expansion and distribution of roots of the grand partition function are mentioned.     

On the response of LR-115 plastic track detector to 10 20 Ne-ion

The track etch rates of ₁₀ ²⁰ Ne-ion in cellulose nitrate (LR-115) have been measured for different temperatures and the activation energy is determined. The experimental results show that both the track etch rate and the normalized track etch rate depend on the energy loss as well as on etching temperature. The maximum etched track length of ₁₀ ²⁰ Ne-ion agrees with the theoretically computed range. The experimental results show that there is no sharp threshold, at least in CN(LR-115).     

表面约束稳态装置中高频离子声波的激发特性

高频离子声波由于Landau阻尼很大,一般难以激发。本文研究了表面约束稳态装置上高频离子声波的激发特性。实验表明,仔细控制放电参数可以激发起纯离子声波,密度涨落n/n_o最大可以达到7.5％。     

Edge-wave-driven durable variations in the thickness of the surfactant film and concentration of surface floats

By employing a simple model for small-scale linear edge waves propagating along a homogeneous sloping beach, we demonstrate that certain combinations of linear wave components may lead to durable changes in the thickness of the surfactant film, equivalently, in the concentration of various substances (debris, litter) floating on the water surface. Such changes are caused by high-amplitude transient elevations that resemble rogue waves and occur during dispersive focusing of wave fields with a continuous spectrum. This process can be treated as an intrinsic mechanism of production of patches in the surface layer of an otherwise homogeneous coastal environment impacted by linear edge waves.     

Epitaxial growth of cobalt clusters on the bare and the oxide film grown on NiAl(1 0 0) surfaces

The structure of the nano-sized cobalt clusters on bare NiAl(1 0 0) and an oxidized NiAl(1 0 0) surfaces have been investigated by AES, LEED and RHEED. The deposition of Co onto bare NiAl(1 0 0) at room temperature led to small crystalline Co grains and surface asperities of substrate. The latter is likely induced by replacement of surface Al, Ni atoms by Co deposit. At 800 K Co particles aggregate to form clusters, but incorporation of Co into bulk NiAl(1 0 0) could occur upon annealing at 900 K. On the other hand, pure face-centered cubic (fcc) phase of Co crystallites of ≈1 nm in diameter with inclusion of smaller-sized particles (D < 1 nm) are observed on Θ-Al₂O₃ after Co deposition at room temperature. After annealing the Co nano-clusters grow larger at expense of small particles (D ≈ 3 nm), where the [1 1 0] and [−1 1 0] axis of the Co(0 0 1) facets are parallel to the [1 0 0] and [0 1 0] directions of (0 0 1)oxide, respectively. The in-plane lattice constant of Co clusters is ca. 4% larger than that of bulk Co, yielding less strain at the Co/oxide interface. A 15° ± 10% random orientation of the normal to (0 0 1) facet of Co clusters with respect to (0 0 1)oxide surface was deduced from the “arc”-shape reflection spots in RHEED. These results suggest that both orientation and phase of Co clusters are strongly affected by the nature and structure of oxide surface.