Global Solutions for Incompressible Viscoelastic Fluids

We prove the existence of both local and global smooth solutions to the Cauchy problem in the whole space and the periodic problem in the n-dimensional torus for the incompressible viscoelastic system of Oldroyd-B type in the case of near equilibrium initial data. The results hold in both two and three dimensional spaces. The results and methods presented in this paper are also valid for a wide range of elastic complex fluids, such as magnetohydrodynamics, liquid crystals and mixture problems.Comment: We prove the existence of global smooth solutions to the Cauchy problem for the incompressible viscoelastic system of Oldroyd-B type in the case of near equilibrium initial dat

The unusual electronic structure of the "pseudo-ladder" compound CaCu2O3

Experimental and theoretical studies of the unoccupied electronic structure of CaCu2O3 single crystals have been performed using polarization-dependent x-ray absorption spectroscopy and band structure calculations. The measured hole distribution shows an unusual large number of holes in orbitals parallel to the interlayer direction which is in agreement with the theoretical analysis. CaCu2O3 deviates significantly from the standard pd-sigma cuprate picture. The corresponding strong interlayer exchange is responsible for the missing spin gap generic for other two-leg ladder cuprates.Comment: 4 pages, 3 figures include

Ground-state phase diagram of the one-dimensional half-filled extended Hubbard model

We revisit the ground-state phase diagram of the one-dimensional half-filled extended Hubbard model with on-site (U) and nearest-neighbor (V) repulsive interactions. In the first half of the paper, using the weak-coupling renormalization-group approach (g-ology) including second-order corrections to the coupling constants, we show that bond-charge-density-wave (BCDW) phase exists for U \approx 2V in between charge-density-wave (CDW) and spin-density-wave (SDW) phases. We find that the umklapp scattering of parallel-spin electrons disfavors the BCDW state and leads to a bicritical point where the CDW-BCDW and SDW-BCDW continuous-transition lines merge into the CDW-SDW first-order transition line. In the second half of the paper, we investigate the phase diagram of the extended Hubbard model with either additional staggered site potential \Delta or bond alternation \delta. Although the alternating site potential \Delta strongly favors the CDW state (that is, a band insulator), the BCDW state is not destroyed completely and occupies a finite region in the phase diagram. Our result is a natural generalization of the work by Fabrizio, Gogolin, and Nersesyan [Phys. Rev. Lett. 83, 2014 (1999)], who predicted the existence of a spontaneously dimerized insulating state between a band insulator and a Mott insulator in the phase diagram of the ionic Hubbard model. The bond alternation \delta destroys the SDW state and changes it into the BCDW state (or Peierls insulating state). As a result the phase diagram of the model with \delta contains only a single critical line separating the Peierls insulator phase and the CDW phase. The addition of \Delta or \delta changes the universality class of the CDW-BCDW transition from the Gaussian transition into the Ising transition.Comment: 24 pages, 20 figures, published versio

A Variant of EFICA Algorithm with Adaptive Parametric Density Estimator

Abstract: FastICA is a popular method for Independent Component Analysis used for separation of linearly mixed independent sources. The separation proceeds through optimization of a contrast function that is based on kurtosis or other entropy approximations using a nonlinear function. The EFICA algorithm is a recently proposed version of this algorithm that is asymptotically efficient when all source distributions are from the Generalized Gaussian family. It is known that the optimal nonlinearity for entropy estimation is the score function of the source distribution. For its evaluation the knowledge of the probability density function (pdf) of the source signals is necessary. Because these pdfs are unknown, the EFICA algorithm assumes that the distribution is Generalized Gaussian Distribution, calculates its parameter α for each source and selects one nonlinearity from the available set for fine tuning of the sources. This paper proposes to modify the EFICA algorithm by parametric estimation of the real score function, which is subsequently used as the contrast function in fine tuning iterations. The algorithm is tested on artificial data; the results are compared to original EFICA, FastICA and JADE. I