Decay of solutions for 2D Navier–Stokes equations posed on Lipschitz and smooth bounded and unbounded domains

Initial–boundary value problems for 2D Navier–Stokes equations posed on bounded and unbounded rectangles as well as on bounded and unbounded smooth domains were considered. The existence and uniqueness of regular global solutions in bounded rectangles and bounded smooth domains as well as exponential decay of solutions on bounded and unbounded domains were established.     

A comparison of μSR and thermopower in Hg 1:2:0:1 high‐Tc cuprates

We present the results of μSR measurements of the transverse field relaxation rate below T_c for seven samples of HgBa₂ CuO_4+\delta, spanning the underdoped, optimally doped, and nominally overdoped regions of the superconducting phase. On comparison with the “anomalous” thermopower data for these compounds, we find that nominally “overdoped” Hg 1:2:0:1 resembles underdoped compounds in certain respects. This revised version was published online in August 2006 with corrections to the Cover Date.     

On a system of Klein-Gordon type equations with acoustic boundary conditions

We prove the existence, uniqueness and uniform stabilization of global solutions for a generalized system of Klein-Gordon type equations with acoustic boundary conditions on a portion of the boundary and the Dirichlet boundary condition on the rest.     

Transition from a one-dimensional to a quasi-one-dimensional state in interacting quantum wires

Upon increasing the electron density in a quantum wire, the one-dimensional electron system undergoes a transition to a quasi-one-dimensional state. In the absence of interactions between electrons, this corresponds to filling up the second subband of transverse quantization, and there are two gapless excitation modes above the transition. On the other hand, strongly interacting one-dimensional electrons form a Wigner crystal, and the transition corresponds to it splitting into two chains (zigzag crystal). We show that the soft mode driving the transition to the zigzag state is gapped, and only one gapless mode exists above the transition. Furthermore, we establish that in the vicinity of the transition already arbitrarily weak interactions open a gap in the second mode. We then argue that only one gapless mode exists near the transition at any interaction strength.     

Identification of the high-energy conformer of octa-1,3,5,7-tetraene detected in the one-photon excitation fluorescence spectrum

Scaled quantum-mechanical force field (SQM-FF) vibrational analyses at the HF/6-31G//HF/6-31G computational level of the gauche, Trans,trans,Trans,trans-, gauche,Trans,trans,Cis,trans-, trans,Trans,gauche,Trans,trans-, and trans,Cis,trans,Trans,trans-conformers of octa-1,3,5,7-tetraene were used to identify the rotational isomer observed in the one-photon excitation fluorescence spectrum of this conjugated molecule (Ackerman et al. in J Chem Phys 80:39–44, 1984) as the gauche,Trans,trans,Trans,trans (gTtTt)-conformer. The analysis was performed by comparing the RMS deviations of the 14 fundamental wavenumbers assigned to the high-energy conformer of octa-1,3,5,7-tetraene in the fluorescence spectrum with those calculated for these conformers. Some reassignments of the wavenumbers, originally suggested by experimental observations, were required for the current analysis. The non-planar structure of gTtTt-octa-1,3,5,7-tetraene was calculated to have the terminal –CH=CH₂ moiety rotated by ~30.5° with respect to the remainder of the nearly planar skeleton using both the HF/6-31G and MP2(FC)/aug-cc-pVDZ computational levels. The barriers to rotation of the –CH=CH₂ moiety at the MP2(FC)/aug-cc-pVDZ level were as follows: rotation from the lowest-energy planar all-trans conformer to the non-planar gTtTt-conformer was 31.4 kJ/mol; rotation from the gTtTt-conformer to the planar all-trans conformer was 18.0 kJ/mol; and the barrier between the two equivalent gTtTt-octa-1,3,5,7-tetraene conformers was only 1.4 kJ/mol.     

Correlation Analysis of Wideband Electromagnetic Radiation in Millimeter and Submillimeter Wave Bands

We describe an informatively alternative algorithm to the known algorithm of Hilbert transform spectrometry of incoherent radiation in millimeter and submillimeter wave bands. The synthesized algorithm for measuring autocorrelation functions of incoherent radiation is based on the use of manifestation of the ac Josephson effect in superconducting junctions irradiated by the radiation studied. As compared to the Hilbert transform spectroscopy algorithm the synthesized correlation analysis algorithm is characterized by a high accuracy and functional simplicity.     

Vortices in high temperature superconductors: the statistical mechanics and dynamics of strings

We briefly discuss a selection of the most pertinent features in the phenomenology of high temperature superconductors. We concentrate on the continuous anisotropic case with results appropriate for YBCO.     

A further optimal property of natural polynomial splines

A minimum mean-square-error principle is used to define optimality of rules appropriate for the estimation of linear functionals of certain nonnegative functions. It is shown that, just as in the usual linear estimation problem where nonnegativity is not a constraint, limiting forms of these optimal rules are “best” in the sense of Sard.     

Muon spin relaxation and susceptibility studies of the pure and diluted spin 1/2 kagomé-like lattice system (CuxZn(1-x))3V2O7(OH2) 2H2O

Muon spin relaxation and magnetic susceptibility measurements have been performed on the pure and diluted spin 1/2 kagomé system (CuxZn(1-x))3V2O7(OH)2 2H2O. In the pure x=1 system we found a slowing down of Cu spin fluctuations with decreasing temperature towards T approximately 1 K, followed by slow and nearly temperature-independent spin fluctuations persisting down to T=50 mK, indicative of quantum fluctuations. No indication of static spin freezing was detected in either of the pure (x=1.0) or diluted samples. The observed magnitude of fluctuating fields indicates that the slow spin fluctuations represent an intrinsic property of kagomé network rather than impurity spins.     

Nonlinear fluctuation phenomena in the transport properties of superconductors

There exists a wide temperature region $(GiT < T - T_c < T\sqrt {Gi} )$ where the influence of fluctuations on the thermodynamic properties of superconductors can be taken into account in the linear (Gaussian) approximation, while their influence on the kinetic properties is strongly nonlinear. The Maki-Thompson contribution to the conductivity saturates in this region. However, the Aslamazov-Larkin contribution becomes even more singular. This enhancement is related to the fact that nonlinear effects increase the lifetime of fluctuating pairs. The pair breaking and energy relaxation processes can decrease the nonlinear effects.