Efficient one-pot synthesis of substituted 2-amino-1,3,4-oxadiazoles

A convenient one-pot method for the preparation of substituted 2-amino-1,3,4-oxadiazoles has been developed. The method is a significant improvement over previously reported syntheses. Reaction of carboxylic acids with thiosemicarbazides afforded the corresponding oxadiazoles in moderate to good yields. In general, the products precipitated from the reaction mixture, and were collected by filtration. In most of the cases, no chromatographic separations were required. To explore the scope and limitations of this reaction, various aliphatic, aromatic, and heteroaromatic carboxylic acids were reacted with different substituted thiosemicarbazides. The influence of R¹ and R² substituents on the reaction yield and additional results demonstrating the versatility of this method are presented.     

Melting of microinclusions close packed in an elastic matrix

A novel representation is proposed of the liquid state in a microcavity, the collective nature of that state being taken into account. In this case a microinclusion undergoing melting is described as a single two-level system. The phase transition of melting in a close-packed system of such inclusions embedded in an elastic medium is described rigorously within the framework of the self-consistent approach. When an additional intermediate premelting state is taken into account, the curve of the steady-state phase transition with a critical point that happens on the phase diagram can be transformed in different ways, depending on the values of the specific parameters. In the simplest case shortening of the straight line takes place; bending is also possible. There is a region of the parameters where the critical line is split. In the latter case the existence of the triple point is also possible. The results obtained are in agreement with the experimental data.     

Computerized Developments in Design,Generation, Simulation of Meshing,and Stress Analysis of Gear Drives

The paper represents new computerized developments in design, generation, simulation of meshing, and stress analysis of gear drives. The main contents of the paper are: (i) application of a predesigned parabolic function of transmission errors for reduction of noise, (ii) computerized simulation of noise caused by transmission errors, (iii) modification of the basic algorithm of tooth contact analysis, and (iv) application of approaches developed for enhanced design and simulation of meshing of the following gear drives: (a) spiral bevel gear drives, (b) face-gear drives (including an approach for grinding), and (c) modified helical gear drives. The developed theory is illustrated with numerical examples.     

Chiral stationary phases for separation of intermedine and lycopsamine enantiomers from Symphytum uplandicum

Enantioseparation of the pyrrolizidine alkaloid isomers intermedine and lycopsamine, isolated from Symphytum uplandicum, is discussed. The separatory power of two immobilized carbohydrate‐based chiral HPLC columns, Chiralpak IA and IC, in different chromatographic conditions is compared. The study demonstrated the importance of solvent and column selection while developing such chiral HPLC separation methods. The baseline HPLC separation of the two alkaloid isomers in preparatory scale is reported for the first time. The optimized separations were achieved on a Chiralpak IA column with mobile phases of ACN/methanol (80:20) and methanol/methyl‐t‐butyl ether (90:10), both containing 0.1% diethylamine.     

Strongly Focused Gravitational Waves

This paper contains a new proof of the formation of trapped spheres, in vacuum spacetimes, by the focusing of gravitational waves, from generic data. The first such result was obtained by Christodoulou (Zurich: Eur Math Soc, 2009). We exploit the same physical mechanism, but give a logically independent construction of these spacetimes.     

Phase-sensitive measurements of order parameters for ultracold atoms through two-particle interferometry

Nontrivial symmetry of order parameters is crucial in some of the most interesting quantum many-body states of ultracold atoms as well as condensed matter systems. Examples in cold atoms include p-wave Feshbach molecules and d-wave paired states of fermions that could be realized in optical lattices in the Hubbard regime. Identifying these states in experiments requires measurements of the relative phase of different components of the entangled pair wave function. We propose and discuss two schemes for such phase-sensitive measurements, based on two-particle interference revealed in atom-atom or atomic density correlations. Our schemes can also be used for relative phase measurements for nontrivial particle-hole order parameters, such as d-density wave order.     

Relaxation of fermionic excitations in a strongly attractive Fermi gas in an optical lattice

We theoretically study the relaxation of high energy single particle excitations into molecules in a system of attractive fermions in an optical lattice, both in the superfluid and the normal phase. In a system characterized by an interaction scale U and a tunneling rate t, we show that the relaxation rate scales as ～Ctexp[-αU(2)/t(2)ln(U/t)] in the large U/t limit. We obtain explicit expressions for the temperature and density dependent exponent α, both in the low temperature superfluid phase and the high temperature phase with pairing but no coherence between the molecules. We find that the relaxation rate decreases both with temperature and deviation of the fermion density from half filling. We show that quasiparticle and phase degrees of freedom are effectively decoupled within experimental time scales allowing for observation of ordered states even at high total energy of the system.     

Competition between pairing and ferromagnetic instabilities in ultracold Fermi gases near Feshbach resonances

We study the quench dynamics of a two-component ultracold Fermi gas from the weak into the strong interaction regime, where the short time dynamics are governed by the exponential growth rate of unstable collective modes. We obtain an effective interaction that takes into account both Pauli blocking and the energy dependence of the scattering amplitude near a Feshbach resonance. Using this interaction we analyze the competing instabilities towards Stoner ferromagnetism and pairing.