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Chun Liu

Publications and source records attributed to Chun Liu.

At least 145 records · Page 8Linked to original sources
arXiv2013

Finite time singularities for hyperbolic systems

In this paper, we study the formation of finite time singularities in the form of super norm blowup for a spatially inhomogeneous hyperbolic system. The system is related to the variational wave equations as those in [18]. The system posses a unique $C^1$ solution before the emergence of vacuum in finite time, for given initial data that are smooth enough, bounded and uniformly away from vacuum. At the occurrence of blowup, the density becomes zero, while the momentum stays finite, however the velocity and the energy are both infinity.

math.AP↗
arXiv2013

On the Cauchy-Born Approximation at Finite Temperature

We address several issues regarding the derivation and implementation of the Cauchy-Born approximation of the stress at finite temperature. In particular, an asymptotic expansion is employed to derive a closed form expression for the first Piola-Kirchhoff stress. For systems under periodic boundary conditions, a derivation is presented, which takes into account the translational invariance and clarifies the removal of the zero phonon modes. Also revealed by the asymptotic approach is the role of the smoothness of the interatomic potential. Several numerical examples are provided to validate this approach.

math-ph↗
arXiv2013

Dark Matter and Gauge Coupling Unification in A Supersymmetry Model with Vector-like Matter

WIMP dark matter and gauge coupling unification are considered in an R-parity violating MSSM with vector-like matter. Dark matter is contained in an additional vector-like SU(2)$_L$ doublet which possesses a new U(1) gauge symmetry. The Higgs fields are extended to be in a ${\bf 5\oplus \bar{5}}$ representation of SU(5). The stability of dark matter is a result of gauge symmetries, and the mass of the dark matter particle is between (1.1-1.5) TeV. Dark matter has a very small cross section with nucleis, thus the model is consistent with current dark matter direct detection experiments such as Xenon100. The model also predicts new charged and colored particles to be observed at LHC.

hep-ph↗
arXiv2013

Phenomenological Aspects of R-parity Violating Supersymmetry with A Vector-like Extra Generation

Phenomenological analysis to the R-parity violating supersymmetry with a vector-like extra generation is performed in detail. It is found that, via the trilinear couplings, the correct neutrino spectrum can be obtained. The Higgs mass rises to 125 GeV by new up-type Yukawa couplings of vector-like quarks with no need of very heavy superpartners. Phenomena of new heavy fermions at LHC are predicted.

hep-ph↗
arXiv2013

A Conservative Finite Difference Scheme for Poisson-Nernst-Planck Equations

A macroscopic model to describe the dynamics of ion transport in ion channels is the Poisson-Nernst-Planck(PNP) equations. In this paper, we develop a finite-difference method for solving PNP equations, which is second-order accurate in both space and time. We use the physical parameters specifically suited toward the modelling of ion channels. We present a simple iterative scheme to solve the system of nonlinear equations resulting from discretizing the equations implicitly in time, which is demonstrated to converge in a few iterations. We place emphasis on ensuring numerical methods to have the same physical properties that the PNP equations themselves also possess, namely conservation of total ions and correct rates of energy dissipation. We describe in detail an approach to derive a finite-difference method that preserves the total concentration of ions exactly in time. Further, we illustrate that, using realistic values of the physical parameters, the conservation property is critical in obtaining correct numerical solutions over long time scales.

math.NA↗
arXiv2013

$θ_{13}$ and the Higgs mass from high scale supersymmetry

In the framework in which supersymmetry is used for understanding fermion masses rather than stabilizing the electroweak scale, we elaborate the phenomenological analysis for the neutrino physics. A relatively large $\sin{θ_{13}}$ is the natural result. The model further predicts vanishingly small CP violation in neutrino oscillations. And $θ_{23}$ is not necessarily maximal. While the high scale supersymmetry generically results in a Higgs mass of about 141 GeV, our model reduces this mass via introducing SU(2)$_L$ triplet fields which also contribute to neutrino masses.

hep-ph↗
arXiv2012

On the General Ericksen-Leslie System: Parodi's Relation, Well-posedness and Stability

In this paper we investigate the role of Parodi's relation in the well-posedness and stability of the general Ericksen-Leslie system modeling nematic liquid crystal flows. First, we give a formal physical derivation of the Ericksen-Leslie system through an appropriate energy variational approach under Parodi's relation, in which we can distinguish the conservative/dissipative parts of the induced elastic stress. Next, we prove global well-posedness and long-time behavior of the Ericksen-Leslie system under the assumption that the viscosity $μ_4$ is sufficiently large. Finally, under Parodi's relation, we show the global well-posedness and Lyapunov stability for the Ericksen-Leslie system near local energy minimizers. The connection between Parodi's relation and linear stability of the Ericksen-Leslie system is also discussed.

math.AP↗
arXiv2012

A blow-up criterion for 3-D compressible visco-elasticity

In this paper, we shall prove a blow-up criteria in terms of the upper bound of the density, deformation tensor and the gradient of deformation tensor for 3D compressible visco-elasticity. Based on the structure of deformation tensor, we find a cancelation in higher order derivatives, which brings us the desired results.

math.AP↗
arXiv2012

Supersymmetric Extension of the Minimal Dark Matter Model

The minimal dark matter model is given a supersymmetric extension. A super SU(2)L quintuplet is introduced with its fermionic neutral component still being the dark matter, the dark matter particle mass is about 19.7 GeV. Mass splitting among the quintplet due to supersymmetry particles is found to be negligibly small compared to the electroweak corrections. Other properties of this supersymmetry model are studied, it has the solutions to the PAMELA and Fermi-LAT anomaly, the predictions in higher energies need further experimental data to verify.

hep-ph↗
arXiv2012

LHCb $\bigtriangleup A_{CP}$ of $D$ meson and R-Parity Violation

LHCb collaboration has recently announced a measurement of the difference of time-integrated CP asymmetries between $D\rightarrow K^+K^-$ and $D \rightarrow π^+π^-$. This result provides the evidence of large direct CP violation in $D$ meson and reveals some important implications on underlying new physics. It is shown that the direct CP violation in $D$ meson can be enhanced by R-parity violating supersymmetry, while CP violations in $K$ and $B$ mesons are suppressed by this new physics, which is in consistence with previous experiments. Constraints on the model parameters and some consequences are also discussed.

hep-ph↗
arXiv2011

$Ω_b$ semi-leptonic weak decays

$Ω_b \rightarrow Ω_c^{(*)}$ semi-leptonic decays are studied in details. Relevant helicity amplitudes are written down. Both unpolarized and polarized $Ω_b$ cases are considered. Decay angular distributions, asymmetry parameters and semileptonic decay rates are calculated, with numerical results using leading order results of the large $N_c$ and heavy quark effective theory(HQET).

hep-ph↗
arXiv2011

On Supersymmetries

After reviewing electroweak (EW) scale supersymmetry (susy) and split susy, as well as their implications in very high energy cosmic rays, I present a high scale susy model for fermion masses. An O(0.1) nu_e-nu_{tau} mixing is expected.

hep-ph↗
arXiv2011

MINOS Anomaly as A Signal of Lorentz Violation

Recently, the MINOS collaboration reported an anomaly that the mass-squared difference and mixing angle of $\barν_μ$ $\leftrightarrow$ $\barν_τ$ are both different from that of $ν_μ$ $\leftrightarrow$ $ν_τ$. In this paper, based on the framework of neutrino oscillations, terms that break the Lorentz symmetry are used as perturbation to explain this anomaly and satisfactory results are got. Remarkably, some surprising conclusions, one of which is that in the high energy limit (hundreds of GeV) neutrino oscillation pattern will be independent of energy, are also arrived.

hep-ph↗
arXiv2011

Two-phase flow problem coupled with mean curvature flow

We prove the existence of generalized solution for incompressible and viscous non-Newtonian two-phase fluid flow for spatial dimension 2 and 3. The phase boundary moves along with the fluid flow plus its mean curvature while exerting surface tension force to the fluid. An approximation scheme combining the Galerkin method and the phase field method is adopted.

math.AP↗
arXiv2011

A Model of Electrodiffusion and Osmotic Water Flow and its Energetic Structure

We introduce a model for ionic electrodiffusion and osmotic water flow through cells and tissues. The model consists of a system of partial differential equations for ionic concentration and fluid flow with interface conditions at deforming membrane boundaries. The model satisfies a natural energy equality, in which the sum of the entropic, elastic and electrostatic free energies are dissipated through viscous, electrodiffusive and osmotic flows. We discuss limiting models when certain dimensionless parameters are small. Finally, we develop a numerical scheme for the one-dimensional case and present some simple applications of our model to cell volume control.

q-bio.CB↗
arXiv2010

Asymptotic Behavior for a Nematic Liquid Crystal Model with Different Kinematic Transport Properties

We study the asymptotic behavior of global solutions to hydrodynamical systems modeling the nematic liquid crystal flows under kinematic transports for molecules of different shapes. The coupling system consists of Navier-Stokes equations and kinematic transport equations for the molecular orientations. We prove the convergence of global strong solutions to single steady states as time tends to infinity as well as estimates on the convergence rate both in 2D for arbitrary regular initial data and in 3D for certain particular cases.

math.AP↗