A dynamical test of phase transition order: New things in old places or old wine in new bottles

We first discuss nonlinear aspects of phase transition theory applied to a particular liquid crystal phase transition. A simple derivation is given to show how two coupled Goldstone modes (one appearing as gauge fluctuations of the ordered phase) can force a phase transition, against all expectations, to take place discontinuously (theory of Halperin, Lubensky, and Ma)-but the discontinuity may be immeasurably small. Then, we describe a new dynamical test of phase transition order, developed by Cladiset al., that turns out to be more sensitive than x-ray diffraction and adiabatic calorimetry. Quantitative data found by this new method are in excellent agreement with the measurements of adiabatic calorimetry and x-ray diffraction as well as expectations implicit in the predictions of HLM.This is the text of an after-banquet talk given at the CNLS Workshop on the Dynamics of Concentrated Systems.     

Rehabilitation of the Gauss-Jordan algorithm

Summary In this paper a Gauss-Jordan algorithm with column interchanges is presented and analysed. We show that, in contrast with Gaussian elimination, the Gauss-Jordan algorithm has essentially differing properties when using column interchanges instead of row interchanges for improving the numerical stability. For solutions obtained by Gauss-Jordan with column interchanges, a more satisfactory bound for the residual norm can be given. The analysis gives theoretical evidence that the algorithm yields numerical solutions as good as those obtained by Gaussian elimination and that, in most practical situations, the residuals are equally small. This is confirmed by numerical experiments. Moreover, timing experiments on a Cyber 205 vector computer show that the algorithm presented has good vectorisation properties.     

Growth studies of m-GaN layers on LiAlO2 by MOCVD

This paper reports that the m-plane GaN layer is grown on （200）-plane LiAlO2 substrate by metal-organic chemical wpour deposition （MOCVD） method. Tetragonal-shaped crystallites appear at the smooth surface. Raman measurement illuminates the compressive stress in the layer which is released with increasing the layer＇s thickness. The high transmittance （80%）, sharp band edge and excitonic absorption peak show that the GaN layer has good optical quality. The donor acceptor pair emission peak located at -3.41 eV with full-width at half maximum of 120 meV and no yellow peaks in the photoluminescence spectra partially show that no Li incorporated into GaN layer from the LiAlO2 substrate.     

Conjugate addition of pyrroles to α,β-unsaturated ketones using copper bromide as a catalyst

Copper bromide was used as a catalyst for the addition of pyrroles to enones. When both the reactants were used in equimolar amounts, mono and dialkylated products were obtained. However, the use of excess enone furnished only dialkylated products. Thus, copper bromide was shown to be an efficient catalyst for the dialkylation of pyrroles.     

A triangular map with homoclinic orbits and no infinite ω-limit set containing periodic points

Recently, Forti, Paganoni and Smítal constructed an example of a triangular map of the unite square, F(x,y)=(f(x),g(x,y)), possessing periodic orbits of all periods and such that no infinite ω-limit set of F contains a periodic point. In this note we show that the above quoted map F has a homoclinic orbit. As a consequence, we answer in the negative the problem presented by A.N. Sharkovsky in the eighties whether, for a triangular map of the square, existence of a homoclinic orbit implies the existence of an infinite ω-limit set containing a periodic point. It is well known that, for a continuous map of the interval, the answer is positive.     

Ground-state properties of LiV2O4 and Li1-xZnx(V1-yTiy)2O4

We present susceptibility, microwave resistivity, NMR and heat-capacity results for Li_1-xZn_x(V_1-yTi_y)₂O₄ with 0 ? x ? 0.3 and 0 ? y ? 0.3. For all doping levels the susceptibility curves can be fitted with a Curie-Weiss law. The paramagnetic Curie-Weiss temperatures remain negative with an average value close to that of the pure compound Θ≈ - 36 K. Spin-glass anomalies are observed in the susceptibility, heat-capacity and NMR measurements for both type of dopants. From the temperature dependence of the spin-lattice relaxation rate we found critical-dynamic behavior in the Zn doped compounds at the freezing temperatures. For the Ti-doped samples two successive freezing transitions into disordered low-temperature states can be detected. The temperature dependence of the heat capacity for Zn-doped compounds does not resemble that of canonical spin glasses and only a small fraction of the total vanadium entropy is frozen at the spin-glass transitions. For pure LiV₂O₄ the spin-glass transition is completely suppressed. The temperature dependence of the heat capacity for LiV₂O₄ can be described using a nuclear Schottky contribution and the non-Fermi liquid model, appropriate for a system close to a spin-glass quantum critical point. Finally an ( x / y , T )-phase diagram for the low-doping regime is presented. Received 16 March 2001 and Received in final form 30 October 2001     

Research of spatial resolution in external electro-optic probing

A new method, based on zero point of longitudinal electric field, was used to determine the spatial resolution of external electro-optic (EO) probing equipment. Considering the diffraction of Gauss beam, the result of external EO probing was simulated which was in accordance with the experiment. A spatial resolution <1 μm was demonstrated initially in our equipment using 650 nm laser diode as probe beam and semi-insulating GaP as probe tip.     

Feedback controlled periodic states for different kinds of photorefractive nonlinear response

We investigate analytically and numerically the influence of the type of the photorefractive nonlinear response on the periodic states (attractors) which occur during feedback controlled 2W-coupling and correspond to almost 100% diffraction efficiency of the dynamic index grating. In addition to the case of the local response typical, for example, for LiNbO₃ crystals we consider the cases of nonlocal (diffusive) response (BaTiO₃, SBN) and resonant response (DC-biased BSO, BTO, and BGO crystals). It is shown that the conditions for the transition to the periodic states and their apparent characteristics are strongly different for the two limiting cases above. Received 16 July 2002 / Received in final form 29 October 2002 Published online 4 March 2003     

Ultraslow phonon-assisted collapse of tubular image states

We predict ultraslow collapse of “tubular image states” (TIS) on material surfaces. TIS are bound Rydberg-like electronic states formed at large distances (∼30 nm) from the surfaces of suspended circularly-symmetric nanowires, such as metallic C nanotubes. The states are formed in potential wells, resulting from a combination of the TIS-electron attraction to image charges in the nanotube and its centrifugal repulsion, caused by spinning around the tube. We demonstrate that TIS can collapse on the tube surface by passing their angular momentum l to circularly polarized flexural phonons excited in the tube. Our analysis shows that for highly detached TIS with l ? 6 the relaxation lifetimes are of the order of 10 ns-1 μs, while for l < 6 these lifetimes are reduced by several orders of magnitude.     

Synthesis and Crystal Structure of a Novel Organic Adduct Nonlinear Optical Material: 3,5-Dinitrobenzonic Acid·ethanolamine (3,5-DNBEA)

The title compound (C2H7NO·C7H4N2O6) has been obtained by the reaction of etha- nolamine with 3,5-dinitrobenzoic acid in deionized water at room temperature. The crystal crystal- lizes in orthorhombic, space group P212121 with a = 6.048(2), b = 9.146(3), c = 21.955(7)(A), C9H11N3O7, Mr = 273.21, Z = 4, V = 1214.3(7)(A)3, Dc = 1.494 g/cm3, F(000) = 568, μ(MoKα) = 0.131 mm-1, R1 = 0.0338 and wR2 = 0.0497. The new organic adduct is composed of one ethanolamine and one 3,5-dinitrobenzoic acid, which are linked up by O-H…O and N-H…O types of hydrogen bonds to form a nine-membered ring and an eleven-membered ring, extending into a one-dimensional network structure.