On Singularity Formation of a Nonlinear Nonlocal System

We investigate the singularity formation of a nonlinear nonlocal system. This nonlocal system is a simplified one-dimensional system of the 3D model that was recently proposed by Hou and Lei in [13] for axisymmetric 3D incompressible Navier-Stokes equations with swirl. The main difference between the 3D model of Hou and Lei and the reformulated 3D Navier-Stokes equations is that the convection term is neglected in the 3D model. In the nonlocal system we consider in this paper, we replace the Riesz operator in the 3D model by the Hilbert transform. One of the main results of this paper is that we prove rigorously the finite time singularity formation of the nonlocal system for a large class of smooth initial data with finite energy. We also prove the global regularity for a class of smooth initial data. Numerical results will be presented to demonstrate the asymptotically self-similar blow-up of the solution. The blowup rate of the self-similar singularity of the nonlocal system is similar to that of the 3D model.Comment: 28 pages, 9 figure

No association of CTLA-4 polymorphisms with susceptibility to Behcet disease

Background: Cytotoxic T lymphocyte-associated antigen 4 (CTLA-4) is a key negative regulator of T lymphocytes and has been shown to be associated with a number of autoimmune diseases. The present study was performed to assess the association between CTLA-4 polymorphisms and Behcet disease (BD) in Chinese patients. Methods: Two hundred and twenty-eight BD patients and 207 controls were analysed for four single nucleotide polymorphisms (SNPs) (21661A/G, 2318C/T, + 49G/A and CT60G/A) in the CTLA-4 gene by PCR-restriction fragment length polymorphism (RFLP) analysis. The association between SNP +49A/G and BD in Chinese population as well as other ethnic groups was analysed by meta-analysis. Results: No association could be detected between CTLA-4 SNPs or haplotypes and BD. Also, no association was observed between CTLA-4 polymorphisms and BD subgroups, stratified by clinical features. A meta-analysis showed that there was no heterogeneity between studies (p = 0.60, I-2 = 0%) and that CTLA-4 SNP + 49 was not associated with BD (overall effect: Z = 0.26, p = 0.79). Conclusion: This study and a meta-analysis failed to demonstrate any association between the tested CTLA-4 polymorphisms and B

Wave spectra of 2D dusty plasma solids and liquids

Brownian dynamics simulations were carried out to study wave spectra of two-dimensional dusty plasma liquids and solids for a wide range of wavelengths. The existence of a longitudinal dust thermal mode was confirmed in simulations, and a cutoff wavenumber in the transverse mode was measured. Dispersion relations, resulting from simulations, were compared with those from analytical theories, such as the random-phase approximation (RPA), quasi-localized charged approximation (QLCA), and harmonic approximation (HA). An overall good agreement between the QLCA and simulations was found for wide ranges of states and wavelengths after taking into account the direct thermal effect in the QLCA, while for the RPA and HA good agreement with simulations were found in the high and low temperature limits, respectively.Comment: 26 pages, 9 figure

Analytical solutions of the lattice Boltzmann BGK model

Analytical solutions of the two dimensional triangular and square lattice Boltzmann BGK models have been obtained for the plain Poiseuille flow and the plain Couette flow. The analytical solutions are written in terms of the characteristic velocity of the flow, the single relaxation time $\tau$ and the lattice spacing. The analytic solutions are the exact representation of these two flows without any approximation.Comment: 10 pages, no postscript figure provide

Window on Higgs Boson: Fourth Generation b′b^\prime Decays Revisited

Direct and indirect searches of the Higgs boson suggest that 113 GeV $\lesssim m_H \lesssim$ 170 GeV is likely. With the LEP era over and the Tevatron Run II search via $p\bar p \to WH+X$ arduous, we revisit a case where $WH$ or $ZH +$ jets could arise via strong $b^\prime\bar b^\prime$ pair production. In contrast to 10 years ago, the tight electroweak constraint on $t^\prime$--$b^\prime$ (hence $t^\prime$--$t$) splitting reduces FCNC $b^\prime\to bZ$, $bH$ rates, making $b^\prime\to cW$ naturally competitive. Such a "cocktail solution" is precisely the mix that could evade the CDF search for $b^\prime\to bZ$, and the $b^\prime$ may well be lurking below the top. In light of the Higgs program, this two-in-one strategy should be pursued.Comment: 4 pages, RevTex, 4 eps figures, One more figure, version to be published in Phys. Rev.

Evolution of the single-hole spectral function across a quantum phase transition in the anisotropic-triangular-lattice antiferromagnet

We study the evolution of the single-hole spectral function when the ground state of the anisotropic-triangular-lattice antiferromagnet changes from the incommensurate magnetically-ordered phase to the spin-liquid state. In order to describe both of the ground states on equal footing, we use the large-N approach where the transition between these two phases can be obtained by controlling the quantum fluctuations via an 'effective' spin magnitude. Adding a hole into these ground states is described by a t-J type model in the slave-fermion representation. Implications of our results to possible future ARPES experiments on insulating frustrated magnets, especially Cs$_2$CuCl$_4$, are discussed.Comment: 8 pages, 7 figure

An alternative non-Markovianity measure by divisibility of dynamical map

Identifying non-Markovianity with non-divisibility, we propose a measure for non-Markovinity of quantum process. Three examples are presented to illustrate the non-Markovianity, measure for non-Markovianity is calculated and discussed. Comparison with other measures of non-Markovianity is made. Our non-Markovianity measure has the merit that no optimization procedure is required and it is finite for any quantum process, which greatly enhances the practical relevance of the proposed measure.Comment: 6 pages, 3 figue

Tevatron Mass Limits for Heavy Quarks Decaying via Flavor Changing Neutral Current

The dimuon and dielectron data from the Tevatron $\bar pp$ collider are used to probe for heavy quarks, which decay dominantly via flavour changing neutral current. Depending on whether the $FCNC$ decay occurs at the tree or loop level, one gets a lower mass limit of 85 or 75 GeV. The former applies to singlet, vector doublet and mirror type quarks while the latter applies to a lefthanded quark doublet of the fourth generation.Comment: 13 pages, TIFR/TH/92-58, Two figures to be supplied on reques

Direct CP Violation in Angular Distribution of B→J/ψK∗B\to J/\psi K^{*} Decays

We show that the study of certain observables in the angular distribution in $B\to J/\psi K^*$ provide clear test for CP vioaltion beyond the Standard Model. These observables vanish in SM, but in models beyond SM some of them can be large enough to be measured at B factories.Comment: 7 pages, Revte