Rapid crack growth in a thermoelastic solid under mixed-mode thermomechanical loading

A two-dimensional steady-sate analysis of semi-infinite brittlecrack growth at a constant subcritical rate in an unboundedfully-coupled thermoelastic solid under mixed-mode thermomechanicalloading is made. The loading consists of normal and shear tractionsand heat fluxes applied as point sources (line loads in theout-of-plane direction). A related problem is solved exactly in an integral transformspace, and robust asymptotic forms used to reduce the originalproblem to a set of integral equations. The equations are partiallycoupled and exhibit operators of both Cauchy and Abel types,yet can be solved analytically. The temperature change field at a distance from the moving crackedge is then constructed, and its dominant term is found tobe controlled by the imposed heat fluxes. The role of this termis, indeed, enhanced if the heat fluxes serve to render thecrack as a net heat source/sink for the solid, as opposed tobeing a transmitter of heat across its plane. More generally,the influence of the thermoelastic coupling on this field, aswell as other functions, is found to increase with crack speed.     

Homogeneous and inhomogeneous manifolds

All metaLindelöf, and most countably paracompact, homogeneous manifolds are Hausdorff. Metacompact manifolds are never rigid. Every countable group can be realized as the group of autohomeomorphisms of a Lindelöf manifold. There is a rigid foliation of the plane.

     

Graph-like compacta: Characterizations and Eulerian loops

A compact graph-like space is a triple $\left(X,V,E\right)$, where $X$ is a compact, metrizable space, $V\subseteq X$ is a closed zero-dimensional subset, and $E$ is an index set such that $X⧹V\cong \text{◂+▸}E\times \left(0,1\right)$. New characterizations of compact graph-like spaces are given, connecting them to certain classes of continua, and to standard subspaces of Freudenthal compactifications of locally finite graphs. These are applied to characterize Eulerian graph-like compacta.     

Measurements of opacity and temperature of warm dense matter heated by focused soft X-ray laser irradiation

The transmission of plasma-based soft X-ray lasers through thin targets can be used to measure the target opacity. Measurements of warm dense matter transmission obtained using a focused 59 eV photon energy laser irradiation on thin targets of polyimide (C₂₂H₁₀N₂O₅) and aluminum are shown to produce simultaneous heating and probing enabling opacity and temperature measurements of warm dense matter. It is shown that the opacity of the warm dense matter considered in the experiments follows closely tabulated cold ‘room temperature’ opacities at temperatures below ～10 eV. Transmission measurements of thin iron targets which are highly opaque to the X-ray laser radiation are also presented.     

Spaces with property pp

This paper continues the study of pp spaces. It is shown that under a wide variety of circumstances, pp spaces are paracompact. However, examples of pp non-paracompact spaces are given, some have strong separation and covering properties, other examples fail dramatically to be paracompact. The stability of pp is examined and contrasted with paracompactness. Various strengthenings of pp are briefly examined.     

Synthetic magnetic opals

We present studies of novel nanocomposites of BiNi impregnated into the structure of opals as well as inverse opals. Atomic force microscopy and high resolution elemental analyses show a highly ordered structure and uniform distribution of the BiNi filler in the matrix. These BiNi-based nanocomposites are found to exhibit distinct ferromagnetic-like ordering with transition temperature of about 675 K. As far as we know there exists no report in literature on any BiNi compound which is magnetic.     

Extreme ultraviolet interferometry of warm dense matter in laser plasmas

We demonstrate that interferometric probing with extreme ultraviolet (EUV) laser light enables determination of the degree of ionization of the "warm dense matter" produced between the critical and ablation surfaces of laser plasmas. Interferometry has been utilized to measure both transmission and phase information for an EUV laser beam at the photon energy of 58.5 eV, probing longitudinally through laser-irradiated plastic (parylene-N) targets (thickness 350 nm) irradiated by a 300 ps duration pulse of wavelength 438 nm and peak irradiance 10(12) W cm(-2). The transmission of the EUV probe beam provides a measure of the rate of target ablation, as ablated plasma becomes close to transparent when the photon energy is less than the ionization energy of the predominant ion species. We show that refractive indices η below the solid parylene N (η(solid) = 0.946) and expected plasma values are produced in the warm dense plasma created by laser irradiation due to bound-free absorption in C(+).     

All Finite Distributive Lattices Occur as Intervals Between Hausdorff Topologies

It is shown that a finite lattice L is isomorphic to the interval betweentwo Hausdorff topologies on some set if and only if L is distributive. Thecorresponding results had previously been shown in ZFC for intervals between T₁ topologies and, assuming the existence of infinitely manymeasurable cardinals, for intervals between T₃ topologies.     

Ubiquity of Free Subgroups

Necessary and sufficient conditions are given for a Polish topologicalgroup to be ‘almost free’. It is deduced that theexistence of one free subgroup of a Polish group can lead tothe existence of many free subgroups of maximal rank. Applicationsare given to permutation groups, profinite groups, Lie groupsand unitary groups. 2000 Mathematics Subject Classification22F50, 20E05, 54H05 (primary), 12F10, 20B27, 20B30, 20E18 (secondary).     

Coupled flow phenomena in thin free-surface films

The flow of aqueous salt solutions in thin free-surface films is analyzed with a simple physico-chemical model. In addition to gravity, gradients in temperature, solute concentration and electric potential act as forces on the film. Through surface-tension gradients, electro-kinetic effects and thermal diffusion, a non-equilibrium thermodynamic coupling between the four forces and their respective fluxes is established. A global treatment of the Onsager thermodynamics is used to describe the cross-coupling, the physicochemical model used is shown to satisfy the Onsager reciprocal theorem and the relative importance of the various surface phenomena occurring in the film is acessed.