arXiv subjects

Ping Zhang

Publications and source records attributed to Ping Zhang.

At least 523 records · Page 29Linked to original sources

arXiv2013

Global large solutions to 3-D inhomogeneous Navier-Stokes system with one slow variable

In this paper, we are concerned with the global wellposedness of 3-D inhomogeneous incompressible Navier-Stokes equations \eqref{1.3} in the critical Besov spaces with the norm of which are invariant by the scaling of the equations and under a nonlinear smallness condition on the isentropic critical Besov norm to the fluctuation of the initial density and the critical anisotropic Besov norm of the horizontal components of the initial velocity which have to be exponentially small compared with the critical anisotropic Besov norm to the third component of the initial velocity. The novelty of this results is that the isentropic space structure to the homogeneity of the initial density function is consistent with the propagation of anisotropic regularity for the velocity field. In the second part, we apply the same idea to prove the global wellposedness of \eqref{1.3} with some large data which are slowly varying in one direction.

math.AP↗

arXiv2013

On the global well-posedness of 2-D density-dependent Navier-Stokes system with variable viscosity

Given solenoidal vector $u_0\in H^{-2\d}\cap H^1(\R^2),$ $\r_0-1\in L^2(\R^2),$ and $\r_0 \in L^\infty\cap\dot{W}^{1,r}(\R^2)$ with a positive lower bound for $\d\in (0,\f12)$ and $2<r<\f{2}{1-2\d},$ we prove that 2-D incompressible inhomogeneous Navier-Stokes system \eqref{1.1} has a unique global solution provided that the viscous coefficient $μ(\r_0)$ is close enough to 1 in the $L^\infty$ norm compared to the size of $\d$ and the norms of the initial data. With smoother initial data, we can prove the propagation of regularities for such solutions. Furthermore, for $1<p<4,$ if $(\r_0-1,u_0)$ belongs to the critical Besov spaces $\dB^{\f2p}_{p,1}(\R^2)\times \bigl(\dB^{-1+\f2p}_{p,1}\cap L^2(\R^2)\bigr)$ and the $\dB^{\f2p}_{p,1}(\R^2)$ norm of $\r_0-1$ is sufficiently small compared to the exponential of $\|u_0\|_{L^2}^2+\|u_0\|_{\dB^{-1+\f2p}_{p,1}},$ we prove the global well-posedness of \eqref{1.1} in the scaling invariant spaces. Finally for initial data in the almost critical Besov spaces, we prove the global well-posedness of \eqref{1.1} under the assumption that the $L^\infty$ norm of $\r_0-1$ is sufficiently small.

math.AP↗

arXiv2013

Global unique solvability of inhomogeneous Navier-Stokes equations with bounded density

In this paper, we prove the global existence and uniqueness of solution to d-dimensional (for $d=2,3$) incompressible inhomogeneous Navier-Stokes equations with initial density being bounded from above and below by some positive constants, and with initial velocity $u_0\in H^s(\R^2)$ for $s>0$ in 2-D, or $u_0\in H^1(\R^3)$ satisfying $|u_0|_{L^2}|\na u_0|_{L^2}$ being sufficiently small in 3-D. This in particular improves the most recent well-posedness result in [10], which requires the initial velocity $u_0\in H^2(\R^d)$ for the local well-posedness result, and a smallness condition on the fluctuation of the initial density for the global well-posedness result.

math.AP↗

arXiv2012

Global solutions to 2-d inhomogeneous navier-stokes system with general velocity

In this paper, we are concerned with the global wellposedness of 2-D density-dependent incompressible Navier-Stokes equations with variable viscosity, in a critical functional frame- work which is invariant by the scaling of the equations and under a non-linear smallness condition on fluctuation of the initial density which has to be doubly exponential small compared with the size of the initial velocity. In the second part of the paper, we apply our methods combined with the techniques of R. Danchin and P. B. Mucha to prove the global existence of solutions to inhomogeneous Navier-Stokes system with piecewise constant initial density which has small jump at the interface and is away from vacuum. In particular, this latter result removes the smallness condition for the initial velocity in a corresponding theorem of R. Danchin and P. B. Mucha.

math.AP↗

arXiv2012

Global wellposedness to incompressible inhomogeneous fluid system with bounded density and non-Lipschitz velocity

In this paper, we first prove the global existence of weak solutions to the d-dimensional incompressible inhomogeneous Navier-Stokes equations with initial data in critical Besov spaces, which satisfies a non-linear smallness condition. The regularity of the initial velocity is critical to the scaling of this system and is general enough to generate non-Lipschitz velocity field. Furthermore, with additional regularity assumption on the initial velocity or on the initial density, we can also prove the uniqueness of such solution. We should mention that the classical maximal regularity theorem for the heat kernel plays an essential role in this context.

math.AP↗

arXiv2012

Electron correlation and spin-orbit coupling effects in US3 and USe3

A systematic density functional theory (DFT)+U study is conducted to investigate the electron correlation and spin-orbit coupling (SOC) effects in US3 and USe3. Our calculations reveal that inclusion of the U term is essential to get energy band gaps for them, indicating the strong correlation effects for uranium 5f electrons. Taking consideration of the SOC effect results in small reduction on the electronic band gaps of US3 and USe3, but largely changes the energy band shapes around the Fermi energy. As a result, US3 has a direct band gap while USe3 has an indirect one. Our calculations predict that both US3 and USe3 are antiferromagnetic insulators, in agreement with corresponding experimental results. Based on our DFT+U calculations, we systematically present the ground-state electronic, mechanical, and Raman properties for US3 and USe3.

cond-mat.str-el↗

arXiv2012

Quantum molecular dynamics simulations of thermophysical properties of fluid ethane

We have performed first-principles molecular-dynamics simulations based on density-functional theory to study the thermophysical properties of ethane under extreme conditions. We present new results for the equation of state of fluid ethane in the warm dense region. The optical conductivity is calculated via the Kubo-Greenwood formula from which the dc conductivity and optical reflectivity are derived. The close correlation between the nonmetal-metal transition of ethane and its decomposition, that ethane dissociates significantly into molecular and/or atomic hydrogen and some long alkane chains, has been systematically studied by analyzing the optical conductivity spectra, pair correlation functions, electronic density of states and charge density distribution of fluid ethane.

cond-mat.mtrl-sci↗

arXiv2012

Elasticity behavior, phonon spectra, and the pressure-temperature phase diagram of HfTi alloy: A density-functional theory study

The pressure-induced phase transition, elasticity behavior, thermodynamic properties, and $P\mathtt{-}T$ phase diagram of $α$, $ω$, and $β$ equiatomic HfTi alloy are investigated using first-principles density-functional theory (DFT). The simulated pressure-induced phase transition of the alloy follows the sequence of $α\mathtt{\rightarrow}ω\mathtt{\rightarrow}β$, in agreement with the experimental results of Hf and Ti metals. Our calculated elastic constants show that the $α$ and $ω$ phases are mechanically stable at ambient pressure, while the $β$ phase is unstable, where a critical pressure of 18.5 GPa is predicted for its mechanical stability. All the elastic constants, bulk modulus, and shear modulus increase upon compression for the three phases of HfTi. The ductility of the alloy is shown to be well improved with respect to pure Hf and Ti metals. The Mulliken charge population analysis illustrates that the increase of the d-band occupancy will stabilize the $β$ phase under pressure. The phonon spectra and phonon density of states are studied using the supercell approach for the three phases, and the stable nature of $α$ and $ω$ phases at ambient pressure are observed, while the $β$ phase is only stable along the [110] direction. With the Gibbs free energy calculated from DFT-parametrized Debye model as a function of temperature and pressure, the phase transformation boundaries of the $α$, $ω$, and $β$ phases of HfTi are identified.

cond-mat.mtrl-sci↗

arXiv2012

Electronic, mechanical, and thermodynamic properties of americium dioxide

By performing density functional theory (DFT) +$U$ calculations, we systematically study the electronic, mechanical, tensile, and thermodynamic properties of AmO$_{2}$. The experimentally observed antiferromagnetic insulating feature [J. Chem. Phys. 63, 3174 (1975)] is successfully reproduced. It is found that the chemical bonding character in AmO$_{2}$ is similar to that in PuO$_{2}$, with smaller charge transfer and stronger covalent interactions between americium and oxygen atoms. The valence band maximum and conduction band minimum are contributed by 2$p-5f$ hybridized and 5$f$ electronic states respectively. The elastic constants and various moduli are calculated, which show that AmO$_{2}$ is less stable against shear forces than PuO$_{2}$. The stress-strain relationship of AmO$_{2}$ is examined along the three low-index directions by employing the first-principles computational tensile test method. It is found that similar to PuO$_{2}$, the [100] and [111] directions are the strongest and weakest tensile directions, respectively, but the theoretical tensile strengths of AmO$_{2}$ are smaller than those of PuO$_{2}$. The phonon dispersion curves of AmO$_{2}$ are calculated and the heat capacities as well as lattice expansion curve are subsequently determined. The lattice thermal conductance of AmO$_{2}$ is further evaluated and compared with attainable experiments. Our present work integrally reveals various physical properties of AmO$_{2}$ and can be referenced for technological applications of AmO$_{2}$ based materials.

cond-mat.mtrl-sci↗

arXiv2012

Fractional quantum Hall effect in topological insulators: The role of Zeeman effect

We study the role of Zeeman effect in fractional quantum Hall effect (FQHE) on the surface of topological insulators (TIs). We show that the effective pseudopotentials of the Coulomb interaction are reformed due to Zeeman effect, which are quite different from those in graphene. By exactly diagonalizing the many-body Hamiltonian in the sphere geometry, we find that the ground state energies and the excitation gaps at $ν$=1/3 FQHE between the $n$=$\pm1$ Landau levels (LLs) render asymmetry, and the FQHE state at the $n$=1 LL is more robust than that at $n$=-1 LL since the excitation gap at $n$=1 LL is larger than that at $n$=-1 LL.

cond-mat.str-el↗

arXiv2012

An intermediate distribution between Gaussian and Cauchy distributions

In this paper, we construct an intermediate distribution linking the Gaussian and the Cauchy distribution. We provide the probability density function and the corresponding characteristic function of the intermediate distribution. Because many kinds of distributions have no moment, we introduce weighted moments. Specifically, we consider weighted moments under two types of weighted functions: the cut-off function and the exponential function. Through these two types of weighted functions, we can obtain weighted moments for almost all distributions. We consider an application of the probability density function of the intermediate distribution on the spectral line broadening in laser theory. Moreover, we utilize the intermediate distribution to the problem of the stock market return in quantitative finance.

physics.data-an↗

arXiv2012

Phonon dispersion curves and thermodynamic properties of α-Pu2O3

A recent inelastic x-ray scattering study [Manley et al., Phys. Rev. B 85, 132301 (2012)] reveals that the phonon dispersion curves of PuO2 is considerably consistent with our previous density functional +$U$ results [Zhang et al., Phys. Rev. B 82, 144110 (2010)]. Here in the present work, using the same computational methods, we further obtain the phonon dispersion curves for α-Pu2O3. We find that the Pu-O bonding is weaker in α-Pu2O3 than in fluorite PuO2, and subsequently a frequency gap appears between the vibrations of oxygen and plutonium atoms. Based on the phonon dispersion curves and Helmholtz free energies of PuO2 and α-Pu2O3, we systematically calculate the reaction energies for the transformations between Pu, PuO2, and α-Pu2O3. It is revealed that the thermodynamic equilibrium of the system is dependent on temperature as well as on the chemical environment. High temperature and insufficient oxygen environment are in favor of the formation of α-Pu2O3.

cond-mat.mtrl-sci↗

arXiv2012

First-principles study of surface properties of PuO2: Effects of thickness and O-vacancy on surface stability and chemical activity

The (111), (110), and (001) surfaces properties of PuO2 are studied by using density-functional theory+U method. The total-energy static calculations determine the relative order of stability for low-index PuO2 surfaces, namely, O-terminated (111) > (110) > defective (001) > polar (001). The effect of thickness is shown to modestly modulate the surface stability and chemical activity of the (110) surface. The high work function of 6.19 eV indicates the chemical inertia of the most stable (111) surface, and the surface O-vacancy with concentration C_V=25% can efficiently lower the work function to 4.35 eV, which is a crucial indicator of the difference in the surface chemical activities between PuO2 and α-Pu2O3. For the polar (001) surface, 50% on-surface O-vacancy can effectively quench the dipole moment and stabilize the surface structure, where the residual surface oxygen atoms are arranged in a zigzag manner along the <100> direction. We also investigate the relative stability of PuO2 surfaces in an oxygen environment. Under oxygen-rich conditions, the stoichiometric O-terminated (111) is found to be the most stable surface. Whereas under O-reducing conditions, the on-surface O-vacancy of C_V = 1/9 is stable, and for high reducing conditions, the (111) surface with nearly one monolayer subsurface oxygen removed (C_V = 8/9) becomes most stable.

cond-mat.mtrl-sci↗

arXiv2012

The environmental dependence of redox energetics of PuO2 and α-Pu2O3: A quantitative solution from DFT+U calculations

We report a comprehensive density functional theory (DFT) + $U$ study of the energetics of charged and neutral oxygen defects in both PuO$_{2}$ and $α$-Pu$_{2}$O$_{3}$, and present a quantitative determination of the equilibrium compositions of reduced PuO$_{2}$ (PuO$_{2-x}$) as functions of environmental temperature and partial pressure of oxygen, which shows fairly agreement with corresponding high-temperature experiments. Under ambient conditions, the endothermic reduction of PuO$_{2}$ to $α$-Pu$_{2}$O$_{3} $ is found to be facilitated by accompanying volume expansion of PuO$_{2-x}$ and the possible migration of O-vacancy, whereas further reduction of $α$-Pu$_{2}$O$_{3}$ is predicted to be much more difficult. In contrast to the endothermic oxidation of PuO$_{2}$,\ the oxidation of $α$-Pu$_{2} $O$_{3}$ is a stable exothermic process.

cond-mat.mtrl-sci↗

arXiv2012

Theory of multiple magnetic scattering for quasiparticles on a gapless topological insulator surface

We develop a general low-energy multiple-scattering partial-wave theory for gapless topological insulator (TI) surfaces in the presence of magnetic impurities. As applications, we discuss the differential cross section (CS) $dΛ/dφ$, the total CS $Λ_{tot}$, the Hall component of resistivity $Ω$, and inverse momentum relaxation time $Γ_{M}$ for single- and two-centered magnetic scattering. We show that differing from the nonmagnetic impurity scattering, $s\mathtt{-}$wave approximation is not advisable and convergent in the present case. The symmetry of CS is reduced and the backscattering occurs and becomes stronger with increasing the effective magnetic moment $M$ of single magnetic impurity. We show a non-zero perpendicular resistivity component $Ω$, which may be useful for tuning the Hall voltage of the sample. Consistent with the analysis of $dΛ/dφ$, by comparing $Γ_{M}$ with $Λ_{tot}$, we can determine different weights of backscattering and forward scattering. Similar to CS, $Ω$ and $Γ_{M}$ also exhibit oscillating behavior for multiple magnetic scattering centers due to interference effect.

cond-mat.mes-hall↗

arXiv2012

Excitonic condensation for the surface states of topological insulator bilayers

We propose a generic topological insulator bilayer (TIB) system to study the excitonic condensation with self-consistent mean-field (SCMF) theory. We show that the TIB system presents the crossover behavior from the Bardeen-Cooper-Schrieffer (BCS) limit to Bose-Einstein condensation (BEC) limit. Moreover, by comparison with traditional semiconductor systems, we find that for the present system the superfluid property in the BEC phase is more sensitive to electron-hole density imbalance and the BCS phase is more robust. Applying this TIB model into Bi$_{2}$Se$_{3}$-family material, we find that the BEC phase is most probable to be observed in experiment. We also calculate the critical temperature for Bi$_{2}$Se$_{3}$-family TIB system, which is $\mathtt{\sim}100$ K. More interestingly, we can expect this relative high-temperature excitonic condensation since our calculated SCMF critical temperature is approximately equal to the Kosterlitz-Thouless transition temperature.

cond-mat.mes-hall↗

arXiv2012

Pseudo-magnetoexcitons in strained graphene bilayers without external magnetic fields

The structural and electronic properties of graphene leads its charge carriers to behave like relativistic particles, which is described by a Dirac-like Hamiltonian. Since graphene is a monolayer of carbon atoms, the strain due to elastic deformations will give rise to so-called `pseudomagnetic fields (PMF)' in graphene sheet, and that has been realized experimentally in strained graphene sample. Here we propose a realistic strained graphene bilayer (SGB) device to detect the pseudo-magnetoexcitons (PME) in the absence of external magnetic field. The carriers in each graphene layer suffer different strong PMFs due to strain engineering, which give rise to Landau quantization. The pseudo-Landau levels (PLLs) of electron-hole pair under inhomogeneous PMFs in SGB are analytically obtained in the absence of Coulomb interactions. Based on the general analytical optical absorption selection rule for PME, we show that the optical absorption spectrums can interpret the corresponding formation of Dirac-type PME. We also predict that in the presence of inhomogeneous PMFs, the superfluidity-normal phase transition temperature of PME is greater than that under homogeneous PMFs.}

cond-mat.mes-hall↗

arXiv2012

Superfluidity and effective mass of magnetoexcitons in topological insulator bilayers: Effect of inter-Landau-level Coulomb interaction

The effective mass and superfluidity-normal phase transition temperature of magnetoexcitons in topological insulator bilayers are theoretically investigated. The intra-Landau-level Coulomb interaction is treated perturbatively, from which the effective magnetoexciton mass is analytically discussed. The inclusion of inter-Landau-level Coulomb interaction by more exact numerical diagonalization of the Hamiltonian brings out important modifications to magnetoexciton properties, which are specially characterized by prominent reduction in the magnetoexciton effective mass and promotion in the superfluidity-normal phase transition temperature at a wide range of external parameters.

cond-mat.mes-hall↗