On the infinite Prandtl number limit in two-dimensional magneto-convection

In this paper, the infinite limit of the Prandtl number is justified for the two-dimensional incompressible magneto-convection, which describes the nonlinear interaction between the Rayleigh-B$\rm\acute{e}$nard convection and an externally magnetic field. Both the convergence rates and the thickness of initial layer are obtained. Moreover, based on the method of formal asymptotic expansions, an effective dynamics is constructed to simulate the motion within the initial layer

On the vanishing resistivity limit and the magnetic boundary-layers for one-dimensional compressible magnetohydrodynamics

We consider an initial-boundary value problem for the one-dimensional equations of compressible isentropic viscous and non-resistive magnetohydrodynamic flows. The global well-posedness of strong solutions with general large data is established. Moreover, the vanishing resistivity limit is justified and the thickness of magnetic boundary layers is analyzed. The proofs of these results are based on a full use of the so-called "effective viscous flux", the material derivative and the structure of the equations

Global well-posedness for the two-dimensional equations of nonhomogeneous incompressible liquid crystal flows with nonnegative density

In this paper, the authors first establish the global well-posedness of strong solutions of the simplified Ericksen-Leslie model for nonhomogeneous incompressible nematic liquid crystal flows in two dimensions if the initial data satisfies some smallness condition. It is worth pointing out that the initial density is allowed to contain vacuum states and the initial velocity can be arbitrarily large. We also present a Serrin's type criterion, depending only on $\nabla d$, for the breakdown of local strong solutions. As a byproduct, the global strong solutions with large initial data are obtained, provided the macroscopic molecular orientation of the liquid crystal materials satisfies a natural geometric angle condition (cf. [19])Comment: 19 pages, 0 figure

Center of Mass Momentum Dependent Interaction Between Ultracold Atoms

We show that a new type of two-body interaction, which depends on the momentum of the center of mass (CoM) of these two particles, can be realized in ultracold atom gases with a laser-modulaed magnetic Feshbach resonance (MFR). Here the MFR is modulated by two laser beams propagating along different directions, which can induce Raman transition between two-body bound states. The Doppler effect causes the two-atom scattering length to be strongly dependent on the CoM momentum of these two atoms. As a result, the effective two-atom interaction is CoM-momentum dependent, while the one-atom free Hamiltonian is still the simple kinetic energy ${\bf p}^2/(2m)$.Comment: Main paper: 5 pages, 3 figures. Supplemental material: 9 pages, 4 figur

Suppression of two-body collisional loss in an ultracold gas via the Fano effect

The Fano effect (U. Fano, Phys. Rev. \textbf{15},1866 (1961) shows that an inelastic scattering process can be suppressed when the output channel (OC) is coupled to an isolated bound state. In this paper we investigate the application of this effect for the suppression of two-body collisional losses of ultracold atoms. The Fano effect is originally derived via a first-order perturbation treatment for coupling between the incident channel (IC) and the OC. We generalize the Fano effect to systems with arbitrarily strong IC--OC couplings. We analytically prove that, in a system with one IC and one OC, when the inter-atomic interaction potentials are real functions of the inter-atomic distance, the exact s-wave inelastic scattering amplitude can always be suppressed to \emph{zero} by coupling between the IC or the OC (or both of them) and an extra isolated bound state. We further show that when the low-energy inelastic collision between two ultracold atoms is suppressed by this effect, the real part of the elastic scattering length between the atoms is still possible to be much larger than the range of inter-atomic interaction.In addition, when open scattering channels are coupled to two bound states, with the help of the Fano effect, independent control of the elastic and inelastic scattering amplitudes of two ultracold atoms can be achieved. Possible experimental realizations of our scheme are also discussed.Comment: 14 pages,4 figure

Retrieving Reed-Solomon coded data under interpolation-based list decoding

A transform that enables generator-matrix-based Reed-Solomon (RS) coded data to be recovered under interpolation-based list decoding is presented. The transform matrix needs to be computed only once and the transformation of an element from the output list to the desired RS coded data block incurs $k^{2}$ field multiplications, given a code of dimension $k$.Comment: 10 pages. Submitted to IEEE information theory for possible publicatio

Locally Orthogonal Training Design for Cloud-RANs Based on Graph Coloring

We consider training-based channel estimation for a cloud radio access network (CRAN), in which a large amount of remote radio heads (RRHs) and users are randomly scattered over the service area. In this model, assigning orthogonal training sequences to all users will incur a substantial overhead to the overall network, and is even impossible when the number of users is large. Therefore, in this paper, we introduce the notion of local orthogonality, under which the training sequence of a user is orthogonal to those of the other users in its neighborhood. We model the design of locally orthogonal training sequences as a graph coloring problem. Then, based on the theory of random geometric graph, we show that the minimum training length scales in the order of $\ln K$, where $K$ is the number of users covered by a CRAN. This indicates that the proposed training design yields a scalable solution to sustain the need of large-scale cooperation in CRANs. Numerical results show that the proposed scheme outperforms other reference schemes.Comment: 10 pages, 9 figures, submitted to IEEE Trans. Wireless Commu

Nearly MDS expander codes with reduced alphabet size

Recently, Roth and Skachek proposed two methods for constructing nearly maximum-distance separable (MDS) expander codes. We show that through the simple modification of using mixed-alphabet codes derived from MDS codes as constituent codes in their code designs, one can obtain nearly MDS codes of significantly smaller alphabet size, albeit at the expense of a (very slight) reduction in code rate

New sufficient conditions of signal recovery with tight frames via l1l_1-analysis

The paper discusses the recovery of signals in the case that signals are nearly sparse with respect to a tight frame $D$ by means of the $l_1$-analysis approach. We establish several new sufficient conditions regarding the $D$-restricted isometry property to ensure stable reconstruction of signals that are approximately sparse with respect to $D$. It is shown that if the measurement matrix $\Phi$ fulfils the condition $\delta_{ts}<t/(4-t)$ for $0<t<4/3$, then signals which are approximately sparse with respect to $D$ can be stably recovered by the $l_1$-analysis method. In the case of $D=I$, the bound is sharp, see Cai and Zhang's work \cite{Cai and Zhang 2014}. When $t=1$, the present bound improves the condition $\delta_s<0.307$ from Lin et al.'s reuslt to $\delta_s<1/3$.Comment: 15 page

A sharp sufficient condition of block signal recovery via l2/l1l_2/l_1-minimization

This work gains a sharp sufficient condition on the block restricted isometry property for the recovery of sparse signal. Under the certain assumption, the signal with block structure can be stably recovered in the present of noisy case and the block sparse signal can be exactly reconstructed in the noise-free case. Besides, an example is proposed to exhibit the condition is sharp. As byproduct, when $t=1$, the result improves the bound of block restricted isometry constant $\delta_{s|\mathcal{I}}$ in Lin and Li (Acta Math. Sin. Engl. Ser. 29(7): 1401-1412, 2013).Comment: 16 page