Closed-form solutions for a rectangular layer with central crack under anti-plane shear stress

We consider the problem of determining the stress distributionin a finite rectangular elastic layer containing a Griffithcrack which is opened by internal shear stress acting alongthe length of the crack. The mode III crack is assumed to belocated in the middle plane of the rectangular layer. The followingtwo problems are considered: (A) the central crack is perpendicularto the two fixed lateral surfaces and parallel to the othertwo stress-free surfaces; (B) all the lateral surfaces of therectangular layer are clamped and the central crack is parallelto the two lateral surfaces. By using Fourier transformations,we reduce the solution of each problem to the solution of dualintegral equations with sine kernels and a weight function whichare solved exactly. Finally, we derive closed-form expressionsfor the stress intensity factor at the tip of the crack andthe numerical values for the stress intensity factor at theedges of the cracks are presented in the form of tables.     

Essay: The Quantum Gravitational Black Hole Is Neither Black Nor White

Understanding the end state of black hole evaporation, the microscopic origin of black hole entropy, the information loss paradox, and the nature of the singularity arising in gravitational collapse - these are outstanding challenges for any candidate quantum theory of gravity. Recently, a midisuperspace model of quantum gravitational collapse has been solved using a lattice regularization scheme. It is shown that the mass of an eternal black hole follows the Bekenstein spectrum, and a related argument provides a fairly accurate estimate of the entropy. The solution also describes a quantized mass-energy distribution around a central black hole, which in the WKB approximation, is precisely Hawking radiation. The leading quantum gravitational correction makes the spectrum non-thermal, thus providing a plausible resolution of the information loss problem.     

Equivariant Spectral Triples on the Quantum SU(2) Group

We characterize all equivariant odd spectral triples for the quantum SU(2) group acting on its L ₂-space and having a nontrivial Chern character. It is shown that the dimension of an equivariant spectral triple is at least three, and given any element of the K-homology group of SU_q(2), there is an equivariant odd spectral triple of dimension 3 inducing that element. The method employed to get equivariant spectral triples in the quantum case is then used for classical SU(2), and we prove that for p < 4, there does not exist any equivariant spectral triple with nontrivial K-homology class and dimension p acting on the L ₂-space.The first author would like to acknowledge support from the National Board of Higher Mathematics, India.     

Use of ultrafine-dispersed nanodiamond for selective deposition of boron-doped diamond films

A suspension of ultrafine-dispersed nanodiamond was used for introducing (in particular, selectively) high-density centers of diamond nucleation on various substrates. High-quality doped diamond films to be used as electrochemistry electrodes were deposited from the gas phase in a microwave discharge on certain substrates treated using ultrafine-dispersed nanodiamond. A uniform distribution of nucleation centers with concentrations greater than 10¹⁰ cm^-2 on silicon substrates was obtained. Electrochemical current-potential curves were measured for continuous films. Diamond meshes of different transparency were grown using selective nucleation. Successful production of high-quality doped diamond meshes gives grounds to consider them the most promising electrodes for use in electrochemistry.     

Microstructure and mechanical characteristics of nanodiamond-SiC compacts

Superhard nanodiamond-SiC ceramics are prepared by infiltrating liquid Si into porous nanodiamond compacts under pressure. Synthesized samples are 2.2 mm thick and 3–4 mm in diameter. The effect of particle size of dynamically synthesized nanodiamond powders on silicon infiltration and SiC phase formation is studied. It is established that silicon does not penetrate into the pores of nanodiamond powders if the original particle size is smaller than 0.5–1.0 μm. The critical pore size for infiltration is 100–200 nm. A study of the microstructure of the samples showed the presence of the nanometer-and submicron-scale SiC phase. The ultrasound velocities are measured in the prepared compacts, and the elastic moduli are calculated. __________ Translated from Fizika Tverdogo Tela, Vol. 46, No. 4, 2004, pp. 734–736. Original Russian Text Copyright ? 2004 by Ekimov, Gromnitskaya, Mazalov, Pal’, Pichugin, Gierlotka, Palosz, Kozubowski.     

Photodegradation of a herbicide derivative, 2,4-dichlorophenoxy acetic acid in aqueous suspensions of titanium dioxide

The photocatalytic degradation of a herbicide derivative, 2,4-dichlorophenoxy acetic acid (2,4-D, 1), has been investigated in aqueous suspensions of titanium dioxide. The degradation was studied by monitoring the change in substrate concentration employing UV spectroscopic analysis and decrease in Total Organic Carbon (TOC) content as a function of irradiation time in the presence of UV light source. The degradation kinetics was investigated under a variety of conditions, such as different types of TiO₂, pH, catalyst and substrate concentrations. Higher photonic efficiencies were observed with Degussa P25 as compared with other photocatalysts. The degradation products were analysed by GC-MS and probable pathways for the formation of different products were proposed.     

Critical Behavior of Two Interacting Linear Polymer Chains in a Good Solvent

A model of two interacting (chemically different) linear polymer chains is solved exactly using the real-space renormalization group transformation on a family of Sierpinski gasket type fractals and on a truncated 4-simplex lattice. The members of the family of the Sierpinski gasket-type fractals are characterized by an integer scale factorb which runs from 2 to ∞. The Hausdorff dimensiond _F of these fractals tends to 2 from below asb → ∞. We calculate the contact exponenty for the transition from the State of segregation to a State in which the two chains are entangled forb = 2-5. Using arguments based on the finite-size scaling theory, we show that forb→∞, y = 2 - v(b) d _F, wherev is the end-toend distance exponent of a chain. For a truncated 4-simplex lattice it is shown that the system of two chains either remains in a State in which these chains are intermingled in such a way that they cannot be told apart, in the sense that the chemical difference between the polymer chains completely drop out of the thermodynamics of the system, or in a State in which they are either zipped or entangled. We show the region of existence of these different phases separated by tricritical lines. The value of the contact exponenty is calculated at the tricritical points.     

Low-temperature specific heat of crystalline and amorphous Eu2(MoO4)3

The specific heat C _total of crystalline and amorphous Eu₂(MoO₄)₃ is measured in the temperature interval 4.5–30 K. The amorphous state is obtained by applying pressure ∼7 GPa at room temperature. It is found that the specific heat of the crystal at T⩽7.5 K is described by a cubic function of temperature, while the specific heat of the amorphous sample has a strongly non-Debye character in the entire experimental temperature interval. The curve of C _total for amorphous europium molybdate is analyzed in a model of soft atomic potentials, and it is shown that it agrees well with universal low-temperature anomalies of the specific heat of classical glasses obtained by quenching from the liquid. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 8, 623–627 (25 October 1998)     

Influence of exciton-exciton interaction with spin paired charge carriers and exciton-lattice interaction on the surface properties of crystalline solids

Applying tight-binding approximation and spin pairing of like charge carriers in a pair of excitons created in a lattice, the possibility of forming a bound exciton-exciton state is studied. It is found that, provided there exists strong exciton-lattice interaction, such a bound state may be formed and its energy may lie within the valence band deforming the material into a crystalline solid with no energy gap. Lowering of the energy is calculated in naphthalene and anthracene crystals where some experimental results are known. The excess energy released after the formation of such bound state can be adequate, depending on the material, to desorb neutral atoms or eject of electrons from surfaces.     

Study of the peak effect phenomenon in single crystals of 2H-NbSe2

The weakly pinned single crystals of the hexagonal 2H-NbSe₂ compound have emerged as prototypes for determining and characterizing the phase boundaries of the possible order-disorder transformations in the vortex matter. We present here a status report based on the ac and dc magnetization measurements of the peak effect phenomenon in three crystals of 2H-NbSe₂, in which the critical current densities vary over two orders of magnitude. We sketch the generic vortex phase diagram of a weakly pinned superconductor, which also utilizes theoretical proposals. We also establish the connection between the metastability effects and pinning.