Stress of worm under flow

Source: https://figshare.com/articles/dataset/cervantes_data23_shun_newmicron_shun_042717_flowworm_5X_4_/7523426/2

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Jun 28, 2018
06/18

by
Shun Zhang

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In this paper, a MATLAB package bdm_mfem for a linear Brezzi-Douglas- Marini (BDM) mixed finite element method is provided for the numerical solution of elliptic diffusion problems with mixed boundary conditions on unstructured grids. BDM basis functions defined by standard barycentric coordinates are used in the paper. Local and global edge ordering are treated carefully. MATLAB build-in functions and vectorizations are used to guarantee the erectness of the programs. The package is simple and...

Topics: Mathematics, Numerical Analysis

Source: http://arxiv.org/abs/1508.06445

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Sep 23, 2013
09/13

by
Shun Zhang; Gensun Fang

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We consider the asymptotic behaviour of the approximation, Gelfand and Kolmogorov numbers of compact embeddings between 2-microlocal Besov spaces with weights defined in terms of the distance to a $d$-set $U\subset \mathbb{R}^n$. The sharp estimates are shown in most cases, where the quasi-Banach setting is included.

Source: http://arxiv.org/abs/1105.3021v1

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Sep 18, 2013
09/13

by
Shun Zhang; Gensun Fang

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We study the asymptotic behaviour of the approximation, Gelfand and Kolmogorov numbers of the compact embeddings of weighted function spaces of Besov and Triebel-Lizorkin type in the case where the weights belong to a large class. We obtain the exact estimates in almost all nonlimiting situations where the quasi-Banach setting is included. At the end we present complete results on related widths for polynomial weights with small perturbations, in particular the sharp estimates in the case...

Source: http://arxiv.org/abs/1102.0681v2

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5.0

Jun 28, 2018
06/18

by
Zhiqiang Cai; Shun Zhang

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For elliptic interface problems in two- and three-dimensions, this paper establishes a priori error estimates for Crouzeix-Raviart nonconforming, Raviart-Thomas mixed, and discontinuous Galerkin finite element approximations. These estimates are robust with respect to the diffusion coefficient and optimal with respect to local regularity of the solution. Moreover, we obtain these estimates with no assumption on the distribution of the diffusion coefficient.

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1509.08166

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3.0

Jun 29, 2018
06/18

by
Erich Novak; Shun Zhang

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We study optimal quadrature formulas for arbitrary weighted integrals and integrands from the Sobolev space $H^1([0,1])$. We obtain general formulas for the worst case error depending on the nodes $x_j$. A particular case is the computation of Fourier coefficients, where the oscillatory weight is given by $\rho_k(x) = \exp(- 2 \pi i k x)$. Here we study the question whether equidistant nodes are optimal or not. We prove that this depends on $n$ and $k$: equidistant nodes are optimal if $n \ge...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1609.01146

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Sep 18, 2013
09/13

by
Shun Zhang; Gensun Fang

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In this paper we study the Gelfand and Kolmogorov numbers of Sobolev embeddings between weighted function spaces of Besov and Triebel-Lizorkin type with polynomial weights. The sharp asymptotic estimates are determined in the so-called non-limiting case.

Source: http://arxiv.org/abs/1102.0677v2

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3.0

Jun 30, 2018
06/18

by
Zhiqiang Cai; Shun Zhang

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We introduced and analyzed robust recovery-based a posteriori error estimators for various lower order finite element approximations to interface problems in [9, 10], where the recoveries of the flux and/or gradient are implicit (i.e., requiring solutions of global problems with mass matrices). In this paper, we develop fully explicit recovery-based error estimators for lower order conforming, mixed, and non- conforming finite element approximations to diffusion problems with full coefficient...

Topics: Mathematics, Numerical Analysis

Source: http://arxiv.org/abs/1407.4377

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Jun 29, 2018
06/18

by
Zhiqiang Cai; Cuiyu He; Shun Zhang

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In this paper, we study a modified residual-based a posteriori error estimator for the nonconforming linear finite element approximation to the interface problem. The reliability of the estimator is analyzed by a new and direct approach without using the Helmholtz decomposition. It is proved that the estimator is reliable with constant independent of the jump of diffusion coefficients across the interfaces, without the assumption that the diffusion coefficient is quasi-monotone. Numerical...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1603.01024

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Jun 28, 2018
06/18

by
Zhiqiang Cai; Cuiyu He; Shun Zhang

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In \cite{CaZh:09}, we introduced and analyzed an improved Zienkiewicz-Zhu (ZZ) estimator for the conforming linear finite element approximation to elliptic interface problems. The estimator is based on the piecewise "constant" flux recovery in the $H(div;\Omega)$ conforming finite element space. This paper extends the results of \cite{CaZh:09} to diffusion problems with full diffusion tensor and to the flux recovery both in piecewise constant and piecewise linear $H(div)$ space.

Topics: Mathematics, Numerical Analysis

Source: http://arxiv.org/abs/1508.00191

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Jun 30, 2018
06/18

by
Zhiqiang Cai; Rob Falgout; Shun Zhang

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The first-order system LL* (FOSLL*) approach for general second-order elliptic partial differential equations was proposed and analyzed in [10], in order to retain the full efficiency of the L2 norm first-order system least-squares (FOSLS) ap- proach while exhibiting the generality of the inverse-norm FOSLS approach. The FOSLL* approach in [10] was applied to the div-curl system with added slack vari- ables, and hence it is quite complicated. In this paper, we apply the FOSLL* approach to the...

Topics: Mathematics, Numerical Analysis

Source: http://arxiv.org/abs/1407.4558

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Jun 28, 2018
06/18

by
Zhiqiang Cai; Cuiyu He; Shun Zhang

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For elliptic interface problems, this paper studies residual-based a posteriori error estimations for various finite element approximations. For the conforming and the Raviart-Thomas mixed elements in two-dimension and for the Crouzeix-Raviart nonconforming and the discontinuous Galerkin elements in both two- and three-dimensions, the global reliability bounds are established with constants independent of the jump of the diffusion coefficient. Moreover, we obtain these estimates with no...

Topics: Numerical Analysis, Mathematics

Source: http://arxiv.org/abs/1510.06481

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Sep 23, 2013
09/13

by
Shun Zhang; Gensun Fang; Fanglun Huang

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We consider the Gelfand and Kolmogorov numbers of compact embeddings between weighted function spaces of Besov and Triebel-Lizorkin type with polynomial weights in the non-limiting case. Our main purpose here is to complement our previous results in \cite{ZF10} in the context of the quasi-Banach setting, $0 < p, q \le \infty$. In addition, sharp estimates for their approximation numbers in several cases left open in Skrzypczak (JAT, 2005) are provided.

Source: http://arxiv.org/abs/1105.5499v3

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6.0

Jun 30, 2018
06/18

by
Shang-Shun Zhang; Jinwu Ye; Wu-Ming Liu

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Magnetic ordering of itinerant fermionic systems is at the forefront of condensed matter physics dating back to Stoner's instability. Spin-orbit coupling (SOC) which couples two essential ingredients of an itinerant fermionic system, namely spin and orbital motion, opens up new horizons to this long-standing problem. Here we report that the itinerant ferromagnetism is absent in 3D Fermi gas with a Weyl SOC and various itinerant spin density waves emerge instead, which is deeply rooted in the...

Topics: Quantum Gases, Materials Science, Strongly Correlated Electrons, Condensed Matter

Source: http://arxiv.org/abs/1403.7031

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Jun 29, 2018
06/18

by
Hongxiang Xie; Feifei Gao; Shun Zhang; Shi Jin

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This paper proposes a new channel estimation scheme for the multiuser massive multiple-input multiple-output (MIMO) systems in time-varying environment. We introduce a discrete Fourier transform (DFT) aided spatial-temporal basis expansion model (ST-BEM) to reduce the effective dimensions of uplink/downlink channels, such that training overhead and feedback cost could be greatly decreased. The newly proposed ST-BEM is suitable for both time division duplex (TDD) systems and frequency division...

Topics: Information Theory, Computing Research Repository, Mathematics

Source: http://arxiv.org/abs/1610.09437

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Jun 28, 2018
06/18

by
Hongxiang Xie; Feifei Gao; Shun Zhang; Shi Jin

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This paper proposes a new transmission strategy for the multiuser massive multiple-input multiple-output (MIMO) systems, including uplink/downlink channel estimation and user scheduling for data transmission. A discrete Fourier transform (DFT) aided spatial basis expansion model (SBEM) is first introduced to represent the uplink/downlink channels with much few parameter dimensions by exploiting angle reciprocity and the physical characteristics of the uniform linear array (ULA). With SBEM, both...

Topics: Information Theory, Computing Research Repository, Mathematics

Source: http://arxiv.org/abs/1511.04841

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Sep 21, 2013
09/13

by
Shang-Shun Zhang; Heng Fan; Wu-Ming Liu

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We investigate the quantum anomalous Hall effect in a mixture of ultra-cold neutral bosons and fermions held on a hexagonal optical lattice. In the strong atom-atom interaction limit, composite fermions composed of one fermion with bosons or bosonic holes in the mixture are formed. Such composite fermions have already been generated successfully in experiment [Nat. Phys. {\bf 7}, 642 (2011)]. Here we predict that this kind of composite fermions may provide a realization of the quantum anomalous...

Source: http://arxiv.org/abs/1204.4050v4

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Jun 28, 2018
06/18

by
Shang-Shun Zhang; Wu-Ming Liu; Han Pu

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How ferromagnetic phases emerge in itinerant systems is an outstanding problem in quantum magnetism. Here we consider a repulsive two-component Fermi gas confined in a two dimensional isotropic harmonic potential and subject to a large Rashba spin-orbit (SO) coupling, whose single-particle dispersion can be tailored by adjusting the SO coupling strength. We show that the interplay among SO coupling, correlation effects and mean-field repulsion leads to a competition between ferromagnetic and...

Topics: Quantum Gases, Condensed Matter

Source: http://arxiv.org/abs/1509.04095

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Sep 23, 2013
09/13

by
Xiao-Lu Yu; Shang-Shun Zhang; Wu-Ming Liu

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We investigate normal state properties of spin-orbit coupled Fermi gases with repulsive s-wave interaction, in the absence of molecule formation, i.e., in the so-called "upper branch". Within the framework of random phase approximation, we derive analytical expressions for the quasi-particle lifetime $\tau_s$, the effective mass $m_s^*$, and the Green's function renormalization factor $Z_s$ in the presence of Rashba spin-orbit coupling. In contrast to spin-orbit coupled electron gas...

Source: http://arxiv.org/abs/1212.0420v5

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5.0

Jun 30, 2018
06/18

by
Shang-Shun Zhang; Nitin Kaushal; Elbio Dagotto; Cristian D. Batista

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We study the effect of spin-orbit interaction on one-dimensional U(1)-invariant frustrated magnets with dominant critical nematic fluctuations. The spin-orbit coupling explicitly breaks the U(1) symmetry of arbitrary global spin rotations about the high-symmetry axis down to $Z_2$ (invariance under a $\pi$-rotation). Given that the nematic order parameter is invariant under a $\pi$-rotation, it is relevant to ask if other discrete symmetries can be spontaneously broken. Here we demonstrate that...

Topics: Strongly Correlated Electrons, Quantum Gases, Condensed Matter

Source: http://arxiv.org/abs/1703.03881

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Oct 21, 2014
10/14

by
Yong, Yang; Kai, He; Bao-Shun, Zhang; Xue-Gang, LI

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This article is from Pharmacognosy Magazine , volume 10 . Abstract In this study, the fluorescence analysis was used to reveal the interaction between berberine derivatives and plasmid DNA. The results showed that berberine (C0) and its 8-alkyl derivatives can enhance the fluorescent intensity of plasmid DNA. Compared with 8-dodecyl- (C12) and 8-hexadecyl- (C16) berberine, 8-alkylberberine with shorter alkyl group, such as 8-ethyl (C2), 8-butyl (C4), 8-hexyl (C6), and 8-octyl (C8) berberine...

Source: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4048568

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Sep 23, 2013
09/13

by
Shang-Shun Zhang; Xiao-Lu Yu; Jinwu Ye; Wu-Ming Liu

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We investigate the collective modes in the spin-orbit coupled Fermi gas with repulsive s-wave interaction. The interplay between spin-orbit coupling and atom-atom interactions plays the crucial role in the collective behaviors of Fermi gas. In contrast with ordinary Fermi liquid, spin-orbit coupled Fermi gas has strongly correlated spin and density excitations. Within the scheme of random phase approximation, we classify collective modes based on the symmetry group and determine their...

Source: http://arxiv.org/abs/1212.0424v3

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Sep 21, 2013
09/13

by
Cheng-Jie Zhang; Yong-Sheng Zhang; Shun Zhang; Guang-Can Guo

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Separability problem, to decide whether a given state is entangled or not, is a fundamental problem in quantum information theory. We propose a powerful and computationally simple separability criterion, which allows us to detect the entanglement of many bound entangled states. The criterion is strictly stronger than the dV criterion, the computable cross-norm or realignment criterion and its optimal nonlinear entanglement witnesses. Furthermore, this criterion can be generalized to an analogue...

Source: http://arxiv.org/abs/0709.3766v6

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Sep 18, 2013
09/13

by
Jian-Ming Cai; Zheng-Wei Zhou; Shun Zhang; Guang-Can Guo

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We consider an arbitrary d_{1}\otimes d_{2}\otimes ... \otimes d_{N} composite quantum system and find necessary conditions for general m-party subsystem states to be the reduced states of a common N-party state. These conditions will lead to various monogamy inequalities for bipartite quantum entanglement and partial disorder in multipartite states. Our results are tightly connected with the measures of multipartite entanglement.

Source: http://arxiv.org/abs/quant-ph/0611224v6

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Sep 18, 2013
09/13

by
Cheng-Jie Zhang; Yong-Sheng Zhang; Shun Zhang; Guang-Can Guo

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We show that the entanglement witnesses based on local orthogonal observables which are introduced in [S. Yu and N.-L. Liu, Phys. Rev. Lett. 95, 150504 (2005)] and [O. G\"uhne, M. Mechler, G. T\'oth and P. Adam, Phys. Rev. A 74, 010301 (2006)] in linear and nonlinear forms can be optimized, respectively. As applications, we calculate the optimal nonlinear witnesses of pure bipartite states and show a lower bound on the I-concurrence of bipartite higher dimensional systems with our method.

Source: http://arxiv.org/abs/0705.1832v3