A deflation by restriction scheme is developed for the inverse-free preconditioned Krylov subspace method for computing a few extreme eigenvalues of the definite symmetric generalized eigenvalue problem Ax = λBx. The convergence theory for the inverse-free preconditioned Krylov subspace method is generalized to include this deflation scheme and numerical examples are presented to demonstrate th...

We propose an unconditionally stable numerical scheme for a 2D dynamic Q-tensor model of nematic liquid crystals. This dynamic Q-tensor model is a L2 gradient flow generated by the liquid crystal free energy that contains a cubic term, which is physically relevant but makes the free energy unbounded from below, and for this reason, has been avoided in other numerical studies. The unboundedness ...

In the continuation of [DF], we study reversible reaction-diffusion equations via entropy methods (based on the free energy functional) in two situations of degeneracy: Firstly, for a two species system, we show explicit exponential convergence to the unique constant steady state when spatial diffusion of one specie vanishes but the system still obeys the same steady state. Secondly, for a syst...

We study the thermodynamics of massless φ-theory using screened perturbation theory, which is a way to systematically reorganise the perturbative series. The free energy and pressure are calculated through four loops in a double expansion in powers of g and m/T , where m is a thermal mass of order gT . The result is truncated at order g. We find that the convergence properties are significantly...

We study the convergence of a diffusive interface model to a sharp interface model. The model consists of the conservation of mass and momentum, where the mass undergoes a phase transition. The equations were considered in [W3] and in the diffuse case consist of the compressible Navier– Stokes system coupled with an Allen–Cahn equation. In the sharp interface limit a jump in the mass density as...

We study a free energy computation procedure, introduced in [4, 7], which relies on the long-time behavior of a nonlinear stochastic differential equation. This nonlinearity comes from a conditional expectation computed with respect to one coordinate of the solution. The long-time convergence of the solutions to this equation has been proved in [10], under some existence and regularity assumpti...

Nonlinear conjugate gradient method is well known in solving large-scale unconstrained optimization problems due to it’s low storage requirement and simple to implement. Research activities on it’s application to handle higher dimensional systems of nonlinear equations are just beginning. This paper presents a Threeterm Conjugate Gradient algorithm for solving Large-Scale systems of nonlinear e...

The new version of differential quadrature (DQ) method is extended to analyze the free vibration of thin sector orthotropic plates on the Pasternak elastic foundation with various sector angles and elastic parameters. Detailed formulations are given. Comparisons are made with existing analytical and/or numerical data. Numerical results indicate that convergence can be achieved with increasing i...

Let L be the class of limiting laws associated with sequences in the second Wiener chaos. We exhibit a large subset L0 ⊂ L satisfying that, for any F∞ ∈ L0, the convergence of only a finite number of cumulants suffices to imply the convergence in law of any sequence in the second Wiener chaos to F∞. This result is in the spirit of the seminal paper [12], in which Nualart and Peccati discovered ...

In this paper we consider a free boundary problem which describes contact angle dynamics on inhomogeneous surface. We obtain an estimate on convergence rate of the free boundaries to the homogenization limit in periodic media. The method presented here also applies to more general class of free boundary problems with oscillating boundary velocities.