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A family of arbitrarily high-order fully discrete space-time finite element methods are proposed for the nonlinear Schrödinger equation based on the scalar auxiliary variable formulation, which consists of a Gauss collocation temporal discretization and the finite element spatial discretization. The proposed methods are proved to be well-posed and conserving both mass and energy at the discrete level. An error bound of the form O(hp + τk+1) in the L∞(0, T; H¹)-norm is established, where h and τ denote the spatial and temporal mesh sizes, respectively, and (p, k) is the degree of the space-time finite elements. Numerical experiments are provided to validate the theoretical results on the convergence rates and conservation properties. The effectiveness of the proposed methods in preserving the shape of a soliton wave is also demonstrated by numerical results. [ABSTRACT FROM AUTHOR]

This paper presents a new narrow-stencil finite difference method for approximating viscosity solutions of Hamilton--Jacobi--Bellman equations. The proposed finite difference scheme naturally extends the Lax--Friedrichs scheme for first order fully nonlinear PDEs to second order fully nonlinear PDEs which are approximated by Lax--Friedrichs-like numerical operators. The crux for constructing such a numerical operator is to introduce a stabilization term, which is called a "numerical moment" and corresponds to the numerical viscosity term in the original Lax--Friedrichs scheme for first order PDEs. It is proved that the proposed Lax--Friedrichs-like scheme has a unique solution and is stable in both the ℓ²-norm and the ℓ∞-norm. Moreover, the convergence of the proposed finite difference scheme to the viscosity solution of the underlying Hamilton--Jacobi--Bellman equation is also established using a novel discrete comparison argument. [ABSTRACT FROM AUTHOR]

The crystal-metal interfacial free energy for a six-site model of succinonitrile [N=C–(CH2)2–C=N] has been calculated using molecular-dynamics simulation from the power spectrum of capillary fluctuations in interface position. The orientationally averaged magnitude of the interfacial free energy is determined to be (7.0±0.4)×10-3 J m-2. This value is in agreement (within the error bars) with the experimental value [(7.9±0.8)×10-3 J m-2] of Maraşli et al. [J. Cryst. Growth 247, 613 (2003)], but is about 20% lower than the earlier experimental value [(8.9±0.5)×10-3 J m-2] obtained by Schaefer et al. [Philos. Mag. 32, 725 (1975)]. In agreement with the experiment, the calculated anisotropy of the interfacial free energy of this body-centered-cubic material is small. In addition, the Turnbull coefficient from our simulation is also in agreement with the experiment. This work demonstrates that the capillary fluctuation method of Hoyt et al. [Phys. Rev. Lett. 86, 5530 (2001)] can be successfully applied to determine the crystal-melt interfacial free energy of molecular materials. [ABSTRACT FROM AUTHOR]

This paper develops an analogue (or counterpart) to discontinuous Galerkin (DG) methods for approximating a general class of calculus of variations problems. The proposed method, called the discontinuous Ritz (DR) method, constructs a numerical solution by minimizing a discrete energy over DG function spaces. The discrete energy includes standard penalization terms as well as the DG Finite element (DG-FE) numerical derivatives developed recently by Feng, Lewis, and Neilan in [7]. It is proved that the proposed DR method converges and that the DG-FE numerical derivatives exhibit a compactness property which is desirable and crucial for applying the proposed DR method to problems with more complex energy functionals. Numerical tests are provided on the classical p-Laplace problem to gauge the performance of the proposed DR method. [ABSTRACT FROM AUTHOR]

This article concerns finite element approximations of a quasi-static poroelasticity model in displacementpressure formulation, which describes the dynamics of poro-elastic materials under an applied mechanical force on the boundary. To better describe the multiphysics process of deformation and diffusion for poroelastic materials, we first present a reformulation of the original model by introducing two pseudo-pressures. We then propose a time-stepping algorithm that decouples the reformulated partial differential equation (PDE) problem at each time step into two sub-problems: one of which is a generalized Stokes problem for the displacement vector field (of the solid network of the poroelastic material) along with one pseudopressure field, and the other is a diffusion problem for the other pseudo-pressure field (of the solvent of the material). To make this multiphysics approach feasible numerically, two critical issues must be resolved: the first one is the uniqueness of the generalized Stokes problem and the other is to find a good boundary condition for the diffusion equation, so that it also becomes uniquely solvable. To address the first issue, we discover certain conserved quantities for the PDE solution that provide ideal candidates for a needed boundary condition for the pseudo-pressure field. The solution to the second issue is to use the generalized Stokes problem to generate a boundary condition for the diffusion problem. A practical advantage of the time-stepping algorithm allows one to use any convergent Stokes solver (and its code) together with any convergent diffusion equation solver (and its code) to solve the poroelasticity model. In this article, the Taylor-Hood mixed finite element method combined with the P1 -conforming finite element method is used as an example to demonstrate the viability of the proposed multiphysics approach. It is proved that the solutions of the fully discrete finite element methods fulfill a discrete energy law, which mimics the differential energy law satisfied by the PDE solution and converges optimally in the energy norm. Moreover, it is showed that the proposed formulation also has a built-in mechanism to overcome so-called 'locking phenomenon' associated with the numerical approximations of the poroelasticity model. Numerical experiments are presented to show the performance of the proposed approach and methods, and to demonstrate the absence of 'locking phenomenon' in our numerical experiments. This article also presents a detailed PDE analysis for the poroelasticity model, especially it is proved that this model converges to the well-known Biot's consolidation model from soil mechanics as the constrained specific storage coefficient tends to zero. As a result, the proposed approach and methods are robust under such a limit process. [ABSTRACT FROM AUTHOR]

This paper is concerned with finite element approximations of W2,p strong solutions of second-order linear elliptic partial differential equations (PDEs) in non-divergence form with continuous coefficients. A nonstandard (primal) finite element method, which uses finite-dimensional subspaces consisting of globally continuous piecewise polynomial functions, is proposed and analyzed. The main novelty of the finite element method is to introduce an interior penalty term, which penalizes the jump of the flux across the interior element edges/faces, to augment a non-symmetric piecewise defined and PDE-induced bilinear form. Existence, uniqueness and error estimate in a discrete W2,p energy norm are proved for the proposed finite element method. This is achieved by establishing a discrete Calderon-Zygmund-type estimate and mimicking strong solution PDE techniques at the discrete level. Numerical experiments are provided to test the performance of proposed finite element methods and to validate the convergence theory. [ABSTRACT FROM AUTHOR]

The key obstacle to the use of consumer cameras in computer vision and computer graphics applications is the lack of synchronization hardware. We present a stroboscope based synchronization approach for the charge-coupled device (CCD) consumer cameras. The synchronization is realized by first aligning the frames from different video sequences based on the smear dots of the stroboscope, and then matching the sequences using a hidden Markov model. Compared with current synchronized capture equipment, the proposed approach greatly reduces the cost by using inexpensive CCD cameras and one stroboscope. The results show that our method could reach a high accuracy much better than the frame-level synchronization of traditional software methods. [ABSTRACT FROM AUTHOR]

This paper studies finite element approximations of the stochastic Allen--Cahn equation with gradient-type multiplicative noise that is white in time and correlated in space. The sharp interface limit--as the diffuse interface thickness vanishes--of the stochastic Allen--Cahn equation is formally a stochastic mean curvature flow which is described by a stochastically perturbed geometric law of the deterministic mean curvature flow. Two fully discrete finite element methods which are based on different time-stepping strategies for the nonlinear term are proposed. Strong convergence with sharp rates for both fully discrete finite element methods is proved. This is done with the crucial help of the Holder continuity in time with respect to the spatial L2-norm and H¹-seminorm for the strong solution of the stochastic Allen--Cahn equation. It also relies on the fact that high moments of the strong solution are bounded in various spatial and temp oral norms. Numerical experiments are provided to gauge the performance of the proposed fully discrete finite element methods and to study the interplay of the geometric evolution and gradient-type noise. [ABSTRACT FROM AUTHOR]

This paper proposes and analyzes two fully discrete mixed interior penalty discontinuous Galerkin (DG) methods for the fourth order nonlinear Cahn-Hilliard equation. Both methods use the backward Euler method for time discretization and interior penalty DG methods for spatial discretization. They differ from each other on how the nonlinear term is treated; one of them is based on fully implicit time-stepping and the other uses energy-splitting time-stepping. The primary goal of the paper is to prove the convergence of the numerical interfaces of the DG methods to the interface of the Hele-Shaw flow. This is achieved by establishing error estimates that depend on ϵ-1 only in some low polynomial orders, instead of exponential orders. Similar to [X. Feng and A. Prohl, Numer. Math., 74 (2004), pp. 47-84], the crux is to prove a discrete spectrum estimate in the discontinuous Galerkin finite element space. However, the validity of such a result is not obvious because the DG space is not a subspace of the (energy) space HM1(Ω) and it is larger than the finite element space. This difficulty is overcome by a delicate perturbation argument which relies on the discrete spectrum estimate in the finite element space proved by Feng and Prohl. Numerical experiment results are also presented to gauge the theoretical results and the performance of the proposed fully discrete mixed DG methods. [ABSTRACT FROM AUTHOR]

This paper develops and analyses two fully discrete interior penalty discontinuous Galerkin (IP-DG) methods for the Allen–Cahn equation, which is a nonlinear singular perturbation of the heat equation and originally arises from phase transition of binary alloys in materials science, and its sharp interface limit (the mean curvature flow) as the perturbation parameter tends to zero. Both fully implicit and energy-splitting time-stepping schemes are proposed. The primary goal of the paper is to derive sharp error bounds which depend on the reciprocal of the perturbation parameter ∈ (also called 'interaction length') only in some lower polynomial order, instead of exponential order, for the proposed IP-DG methods. The derivation is based on a refinement of the nonstandard error analysis technique first introduced in Feng & Prohl (2003, Numerical analysis of the Allen–Cahn equation and approximation for mean curvature flows. Numer. Math., 2003, 94, 33–65). The centrepiece of this new technique is to establish a spectrum estimate result in totally discontinuous DG finite element spaces with the help of a similar spectrum estimate result in the conforming finite element spaces which was established in Feng & Prohl. As a nontrivial application of the sharp error estimates, they are used to establish convergence, and the rates of convergence of the zero-level sets of the fully discrete IP-DG solutions to the classical and generalized mean curvature flow. Numerical experiment results are also presented to gauge the theoretical results and the performance of the proposed fully discrete IP-DG methods. [ABSTRACT FROM AUTHOR]

While a more integrated central counterparty (CCP) network via interoperability will provide users more cost efficient clearing and settlement services, it also increases the default transmission through the system. Using epidemic spreading model, it is found that a vertically interoperated CCP network is more robust compared with a horizontally interoperated one when certain condition is satisfied. Variation of the different transmission rates from both internal and external sources leads to different equilibrium. The safe range which is free from the crisis explosion state is identified and can be reached with certain policy coordination among nations. [ABSTRACT FROM AUTHOR]

This paper develops and analyzes an interior penalty discontinuous Galerkin (IPDG) method using piecewise linear polynomials for the indefinite time harmonic Maxwell equations with the impedance boundary condition in the three-dimensional space. The main novelties of the proposed IPDG method include the following: first, the method penalizes not only the jumps of the tangential component of the electric field across the element faces but also the jumps of the tangential component of its vorticity field; second, the penalty parameters are taken as complex numbers of negative imaginary parts. For the differential problem, we prove that the sesquilinear form associated with the Maxwell problem satisfies a generalized weak stability (i.e., inf-sup condition) for star-shaped domains. Such a generalized weak stability readily infers wave-number explicit a priori estimates for the solution of the Maxwell problem, which plays an important role in the error analysis for the IPDG method. For the proposed IPDG method, we show that the discrete sesquilinear form satisfies a coercivity for all positive mesh size h, wave number k, and for general domains including nonstar-shaped ones. In turn, the coercivity estimate easily yields the well-posedness and stability estimates (i.e., a priori estimates) for the discrete problem without imposing any mesh constraint. Based on these discrete stability estimates, by adapting a nonstandard error estimate technique of [X. Feng and H. Wu, SIAM J. Numer. Anal., 47 (2009), pp. 2872-2896, X. Feng and H. Wu, Math. Comp., 80 (2011), pp. 1997-2024], we derive both the energy-norm and the L²-norm error estimates for the IPDG method in all mesh parameter regimes including preasymptotic regime (i.e., k²h ≳ 1). Numerical experiments are also presented to gauge the theoretical results and to numerically examine the pollution effect (with respect to k) in the error bounds. [ABSTRACT FROM AUTHOR]

Background and methods: In addition to possess cross drug resistance characteristic, emerging evidences have shown that multiple-drug resistance (MDR) cancer cells exhibit aberrant metastatic capacity when compared to parental cells. In this study, we explored the contribution of c-Jun N-terminal kinases (JNK) signaling to the mesenchymal phenotypes and the aberrant motile capacity of MDR cells utilizing a well characterized MDR cell line KB/VCR, which is established from KB human epidermoid carcinoma cells by vincristine (VCR), and its parental cell line KB. Results: Taking advantage of experimental strategies including pharmacological tool and gene knockdown, we showed here that interference with JNK signaling pathway by targeting JNK1/2 or c-Jun reversed the mesenchymal properties of KB/VCR cells to epithelial phenotypes and suppressed the motile capacity of KB/VCR cells, such as migration and invasion. These observations support a critical role of JNK signaling in maintaining the mesenchymal properties of KB/VCR cells. Furthermore, we observed that JNK signaling may control the expression of both snail and twist1 in KB/VCR cells, indicating that both snail and twist1 are involved in controlling the mesenchymal characteristics of KB/VCR cells by JNK signaling. Conclusion: JNK signaling is required for maintaining the mesenchymal phenotype of KB/VCR cells; and JNK signaling may maintain the mesenchymal characteristics of KB/VCR cells potentially through snail and twist1. [ABSTRACT FROM AUTHOR]

This article surveys the recent developments in computational methods for second order fully nonlinear partial differential equations (PDEs), a relatively new subarea within numerical PDEs. Due to their ever increasing importance in mathematics itself (e.g., differential geometry and PDEs) and in many scientific and engineering fields (e.g., astrophysics, geostrophic fluid dynamics, grid generation, image processing, optimal transport, meteorology, mathematical finance, and optimal control), numerical solutions to fully nonlinear second order PDEs have garnered a great deal of interest from the numerical PDE and scientific communities. Significant progress has been made for this class of problems in the past few years, but many problems still remain open. This article intends to introduce these current advancements and new results to the SIAM community and generate more interest in numerical methods for fully nonlinear PDEs. [ABSTRACT FROM AUTHOR]

The negative externalities from an individual bank failure to the whole system can be huge. One of the key purposes of bank regulation is to internalize the social costs of potential bank failures via capital charges. This study proposes a method to evaluate and allocate the systemic risk to different countries/regions using a Susceptible-Infected-Removable (SIR) type of epidemic spreading model and the Shapley value (SV) in game theory. The paper also explores features of a constructed bank network using real globe-wide banking data. [ABSTRACT FROM AUTHOR]

This paper concerns discontinuous finite element approximations of a fourth-order bi-wave equation arising as a simplified Ginzburg-Landau-type model for d-wave superconductors in the absence of an applied magnetic field. In the first half of the paper, we construct a variant of the Morley finite element method, which was originally developed for approximating the fourth-order biharmonic equation, for the bi-wave equation. It is proved that, unlike the biharmonic equation, it is necessary to impose a mesh constraint and to include certain penalty terms in the method to guarantee convergence. Nearly optimal order (off by a factor ∣ln h∣) error estimates in the energy norm and in the H¹-norm are established for the proposed Morley-type nonconforming method. In the second half of the paper, we develop a symmetric interior penalty discontinuous Galerkin method for the bi-wave equation using general meshes and prove optimal order error estimates in the energy norm. Finally, numerical experiments are provided to gauge the efficiency of the proposed methods and to validate the theoretical error bounds. [ABSTRACT FROM AUTHOR]

In this paper we develop and analyze some interior penalty hpdiscontinuous Galerkin (hp-DG) methods for the Helmholtz equation with first order absorbing boundary condition in two and three dimensions. The proposed hp-DG methods are defined using a sesquilinear form which is not only mesh-dependent (or h-dependent) but also degree-dependent (or p-dependent). In addition, the sesquilinear form contains penalty terms which not only penalize the jumps of the function values across the element edges but also the jumps of the first order tangential derivatives as well as jumps of all normal derivatives up to order p. Furthermore, to ensure the stability, the penalty parameters are taken as complex numbers with positive imaginary parts, so essentially and practically no constraint is imposed on the penalty parameters. It is proved that the proposed hp-discontinuous Galerkin methods are stable (hence, well-posed) without any mesh constraint. For each fixed wave number k, sub-optimal order (with respect to h and p) error estimates in the broken H1-norm and the L2-norm are derived without any mesh constraint. The error estimates as well as the stability estimates are improved to optimal order under the mesh condition k3h2p-2 ⩽ C0 by utilizing these stability and error estimates and using a stability-error iterative procedure, where C0 is some constant independent of k, h, p, and the penalty parameters. To overcome the difficulty caused by strong indefiniteness (and non-Hermitian nature) of the Helmholtz problems in the stability analysis for numerical solutions, our main ideas for stability analysis are to make use of a local version of the Rellich identity (for the Laplacian) and to mimic the stability analysis for the PDE solutions given in [19, 20, 33], which enable us to derive stability estimates and error bounds with explicit dependence on the mesh size h, the polynomial degree p, the wave number k, as well as all the penalty parameters for the numerical solutions. [ABSTRACT FROM AUTHOR]

This paper concerns discontinuous finite element approximations of a fourth-order bi-wave equation arising as a simplified Ginzburg-Landau-type model for $ d$ $ \vert\mathrm{ln} h\vert$-norm are established for the proposed Morley-type nonconforming method. In the second half of the paper, we develop a symmetric interior penalty discontinuous Galerkin method for the bi-wave equation using general meshes and prove optimal order error estimates in the energy norm. Finally, numerical experiments are provided to gauge the efficiency of the proposed methods and to validate the theoretical error bounds. [ABSTRACT FROM AUTHOR]

This paper proposes and analyzes some fully discrete (multiphysics) finite element methods for a displacement-pressure model which describes swelling dynamics of polymer gels under mechanical constraints. By introducing an "elastic pressure" we first present a reformulation of the original model. We then propose a time-stepping scheme which decouples the PDE system at each time step into two subproblems, one of which is a Stokes-like problem for the displacement vector field (of the solid network of the gel) and the other is a diffusion problem for a "pseudopressure" field (of the solvent of the gel). To make such a multiphysics approach feasible, it is vital to find admissible constraints to resolve the uniqueness issue for the Stokes-like problem and to construct a good boundary condition for the diffusion equation so that it also becomes uniquely solvable. The key to the first difficulty is to discover certain conserved quantities for the PDE solution, and the solution to the second difficulty is to use the Stokes-like problem to generate a boundary condition for the diffusion problem. The time-stepping scheme allows one to use any convergent Stokes solver (and its code) together with any convergent diffusion equation solver (and its code) to solve the polymer gel model. In the paper, the Taylor-Hood mixed finite element method combined with the continuous linear finite element method are chosen as an example to present the ideas and to demonstrate the viability of the proposed multiphysics approach. It is proved that, under a mesh constraint, both the semidiscrete (in space) and fully discrete methods enjoy some discrete energy laws which mimic the differential energy law satisfied by the PDE solution. Optimal order error estimates in various norms are established for both semidiscrete and fully discrete methods. Numerical experiments are also presented to show the performance of the proposed approach and methods. [ABSTRACT FROM AUTHOR]

Although recently there are extensive research on currency network using minimum spanning trees approach, the knowledge about the actual evolution of a currency web in Asia is still limited. In the paper, we study the structural evolution of an Asian network using daily exchange rate data. It was found that the correlation between Asian currencies and US Dollar, the previous regional key currency has become weaker and the intra-Asia interactions have increased. This becomes more salient after the exchange rate reform of China. Different from the previous studies, we further reveal that it is the trade volume, national wealth gap and countries growth cycle that has contributed to the evolutionary topology of the minimum spanning tree. These findings provide a valuable platform for theoretical modeling and further analysis. [ABSTRACT FROM AUTHOR]

Divergence- L q and divergence-measure tensor fields are introduced and their properties are analyzed. These measure-theoretic tools are then used to study the gradient flow of linear growth functionals of maps into the unit sphere. A BV-solution concept is introduced and the existence of such a solution is established for the flow using the energy method together with a regularization and a penalization technique. Based on the analytical results, practical fully discrete finite element methods are then proposed for computing weak solutions of the gradient flow, and the convergence of the proposed numerical method is also proved. [ABSTRACT FROM AUTHOR]

This paper concerns with the finite element approximation of a nonlinear second order parabolic system which describes the L2-gradient flow for a class of linear growth energy functionals. Besides their appeals in differential geometry and calculus of variations, linear growth energy functionals and their gradient flows also arise naturally from emerging applications of image processing such as color image denoising. In this paper, we introduce a family of variational models for color image denoising which minimize linear growth energy functionals of maps into the unit sphere in R3. These models generalize the popular 1-harmonic map model which has been studied intensively in recent years. To compute the solutions of the variational models, we first derive their L2-gradient flow equations and then introduce some fully discrete implicit finite element method for the gradient flow equations. It is proved that the proposed finite element method is uniquely solvable and absolutely stable, and the finite element solution converges to the PDE solution as the mesh sizes tend to zero. Numerical experiments are presented to demonstrate the effectiveness of the proposed variational models for color image denoising and to show the efficiency of the proposed finite element method. A numerical comparison of the proposed models with the channel-by-channel model is also presented. [ABSTRACT FROM AUTHOR]

This paper studies mixed finite element approximations of the viscosity solution to the Dirichlet problem for the fully nonlinear Monge-Ampère equation det(D²u0) = f (> 0) based on the vanishing moment method which was proposed recently by the authors in [X. Feng and M. Neilan, J. Scient. Comp., DOI 10.1007/s10915-008-9221-9, 2008]. In this approach, the second-order fully nonlinear Monge-Amp`ere equation is approximated by the fourth order quasilinear equation -ϵΔ²uϵ + detD²uϵ = f. It was proved in [X. Feng, Trans. AMS, submitted] that the solution ue converges to the unique convex viscosity solution u0 of the Dirichlet problem for the Monge-Ampère equation. This result then opens a door for constructing convergent finite element methods for the fully nonlinear second-order equations, a task which has been impracticable before. The goal of this paper is threefold. First, we develop a family of Hermann-Miyoshi-type mixed finite element methods for approximating the solution uϵ of the regularized fourth-order problem, which computes simultaneously ue and the moment tensor σϵ := D²uϵ . Second, we derive error estimates, which track explicitly the dependence of the error constants on the parameter ϵ, for the errors uϵ - uϵ h and σ0 - σϵ h . Finally, we present a detailed numerical study on the rates of convergence in terms of powers of e for the error u0 -uϵ h and σϵ -σϵh , and numerically examine what is the "best" mesh size h in relation to e in order to achieve these rates. Due to the strong nonlinearity of the underlying equation, the standard perturbation argument for error analysis of finite element approximations of nonlinear problems does not work for the problem. To overcome the difficulty, we employ a fixed point technique which strongly relies on the stability of the linearized problem and its mixed finite element approximations. [ABSTRACT FROM AUTHOR]

This paper develops a posteriori error estimates of residual type for conforming and mixed finite element approximations of the fourth order Cahn-Hilliard equation ut + Δ(εΔu - ε-1 if(u)) = 0. It is shown that the a posteriori error bounds depends on ε-1 only in some low polynomial order, instead of exponential order. Using these a posteriori error estimates, we construct an adaptive algorithm for computing the solution of the Cahn-Hilliard equation and its sharp interface limit, the Hele-Shaw flow. Numerical experiments are presented to show the robustness and effectiveness of the new error estimators and the proposed adaptive algorithm. [ABSTRACT FROM AUTHOR]

Motivated by emerging applications from imaging processing, this paper studies the heat flow of a generalized p-harmonic map into spheres for the whole spectrum, 1 ≤ p < ∞, in a unified framework. The existence of global weak solutions is established for the flow using the energy method together with a regularization and a penalization technique. In particular, a BV -solution concept is introduced and the existence of such a solution is proved for the 1-harmonic map heat flow. The main idea used to develop such a theory is to exploit the properties of measures of the forms A · ∇v and A Λ ∇v, which pair a divergence-L¹, or a divergence-measure, tensor field A and a BV -vector field v. Based on these analytical results, a practical fully discrete finite element method is then proposed for approximating weak solutions of the p-harmonic map heat flow, and the convergence of the proposed numerical method is also established. [ABSTRACT FROM AUTHOR]

The Ericksen-Leslie model describes dynamics of low molar-mass nematic liquid crystals, where the spatiotemporal distribution of defects defining texture is represented by the director unit vector field d : ΩT → S2. It consists of the Navier-Stokes equations with an extra viscous stress tensor, and a convective harmonic map heat flow equation to govern the dynamics of the director field. Two fully discrete finite element methods, for a regularized system using the Ginzburg-Landau regularization and for the limiting Ericksen-Leslie model, are proposed, and well-posedness and related discrete energy laws are established. For the regularized model, unconditional convergence of finite element solutions towards weak solutions of the continuum model as well as convergence towards measure-valued solutions of the limiting Ericksen-Leslie model are verified when the mesh parameters and the regularization parameter successively tend to zero. Computational experiments are also presented to show the importance of balancing numerical and regularization parameters, to compare regularized and direct approaches, and to show numerically the finite-time formation, annihilation, and evolution of point defects. [ABSTRACT FROM AUTHOR]

Three fully discrete finite element methods are developed for approximating wave maps into the sphere based on two different approaches. The first method is an explicit scheme and the numerical solution satisfies the sphere-constraint exactly at every node. The second and third methods are implicit schemes which are based on a penalization approach, their numerical solutions satisfy the sphere-constraint approximately, and the quality of approximations is controlled by a small penalization parameter. Discrete energy conservation laws which mimic the underlying differential conservation law are established, and convergence of all proposed methods is proved. Computational experiments are also provided to validate the proposed methods and to present numerical evidence for possible finite-time blow-ups of the wave maps. [ABSTRACT FROM AUTHOR]

This paper develops and analyzes some fully discrete finite element methods for a parabolic system consisting of the Navier-Stokes equations and the Cahn-Hilliard equation, which arises as a diffuse interface model for the flow of two immiscible and incompressible fluids. In the model the two sets of equations are coupled through an extra phase induced stress term in the Navier-Stokes equations and a fluid induced transport term in the Cahn-Hilliard equation. Fully discrete mixed finite element methods are proposed for approximating the coupled system, it is shown that the proposed numerical methods satisfy a mass conservation law, and a discrete energy law which is analogous to the basic energy law for the phase field model. The convergence of the numerical solutions to the solutions of the phase field model and its sharp interface limit is established by utilizing the discrete energy law. As a by-product, the convergence result also provides a constructive proof of the existence of weak solutions to the Navier-Stokes-Cahn-Hilliard phase field model. Numerical experiments are also presented to validate the theory and to show the effectiveness of the combined phase field and finite element approach. [ABSTRACT FROM AUTHOR]

We consider complex-valued acoustic and elastic Helmholtz equations with the first order absorbing boundary condition in a star-shaped domain in ℜN for N ≥ 2. It is known that the elliptic regularity coefficients depend on the frequency ω, and have singularities for both zero and infinite frequency. In this paper, we obtain sharp estimates for the coefficients with respect to large frequencies. It is proved that the elliptic regularity coefficients are bounded by first or second order polynomials in ω for large ω. The crux of our analysis is to establish and make use of Rellich identities for the solutions to the acoustic and elastic Helmholtz equations. Our results improve the earlier estimates of Refs. 10 and 11, which were carried out based on layer potential representations of the solutions of the Helmholtz equations. [ABSTRACT FROM AUTHOR]

A 6-site succinonitrile force field has been developed. The model has produced proper proportions of the three succinonitrile conformers, which is necessary to avoid the thermal contraction of the plastic crystal phase around the melting point. The solid and liquid densities are about 1% lower or higher than the experimental values. The melting point of the model has been adjusted using the Gibbs-Duhem integration method. The theoretical melting point is in good agreement with experiment. [ABSTRACT FROM AUTHOR]

This paper presents a heterogeneous finite element method for a fluid–solid interaction problem. The method, which combines a standard finite element discretization in the fluid region and a mixed finite element discretization in the solid region, allows the use of different meshes in fluid and solid regions. Both semi‐discrete and fully discrete approximations are formulated and analysed. Optimal order a priori error estimates in the energy norm are shown. The main difficulty in the analysis is caused by the two interface conditions which describe the interaction between the fluid and the solid. This is overcome by explicitly building one of the interface conditions into the finite element spaces. Iterative substructuring algorithms are also proposed for effectively solving the discrete finite element equations. [ABSTRACT FROM PUBLISHER]

We present some two-level nonoverlapping and overlapping additive Schwarz methods for a discontinuous Galerkin method for solving second order elliptic problems. It is shown that the condition numbers of the preconditioned systems are of the order O(H/h) for the nonoverlapping Schwarz methods and of the order O(H/δ) for the overlapping Schwarz methods, where h and H stand for the fine-mesh size and the coarse-mesh size, respectively, and δ denotes the size of the overlaps between subdomains. Numerical experiments are provided to gauge the efficiency of the methods and to validate the theory. [ABSTRACT FROM AUTHOR]

Modeling the variation propagation based on the stream of variation (SoV) methodology for multistage machining processes (MMPs) has been investigated intensively in the past two decades; however, little research is conducted on the variation reduction and the existing work fails to be applied to irregular features caused by the machining-induced variation varying with the positions of the contour points on the machined surface. This paper proposes a novel error compensation method for MMPs by modifying the tool path to reduce variation for general features. The method based on differential motion vector (DMV) sets of multiple contour points is presented to represent the deviation of the irregular feature. Then, the conventional stream of variation (SoV) model is further extended to more accurately describe variation propagation for irregular features considering the actual datum-induced variations and the varying machining-induced variations, especially the deformation errors for the low stiffness workpiece. Based on the extended SoV model and error equivalence mechanism, the datum error and fixture error are transformed to the equivalent tool path error. Then, the original tool path is modified through shifting the machine zero points of machine tools with no need for changing the original G code and workpiece setup. A real cutting experiment validates the effectiveness of the proposed error compensation method for MMPs with an average precision improvement of over 60%. The application of the extended SoV model significantly contributes to compensating more complex error sources for MMPs, such as the clamp force, the internal residual stress, etc. [ABSTRACT FROM AUTHOR]

Modeling the variation propagation based on the stream of variation (SoV) methodology for multistage machining processes (MMPs) has been investigated intensively in the past two decades; however, little research is conducted on the variation reduction and the existing work fails to be applied to irregular features caused by the machining-induced variation varying with the positions of the contour points on the machined surface. This paper proposes a novel error compensation method for MMPs by modifying the tool path to reduce variation for general features. The method based on differential motion vector (DMV) sets of multiple contour points is presented to represent the deviation of the irregular feature. Then, the conventional stream of variation (SoV) model is further extended to more accurately describe variation propagation for irregular features considering the actual datum-induced variations and the varying machining-induced variations, especially the deformation errors for the low stiffness workpiece. Based on the extended SoV model and error equivalence mechanism, the datum error and fixture error are transformed to the equivalent tool path error. Then, the original tool path is modified through shifting the machine zero points of machine tools with no need for changing the original G code and workpiece setup. A real cutting experiment validates the effectiveness of the proposed error compensation method for MMPs with an average precision improvement of over 60%. The application of the extended SoV model significantly contributes to compensating more complex error sources for MMPs, such as the clamp force, the internal residual stress, etc. [ABSTRACT FROM AUTHOR]

To process real-world datasets, modern data-parallel systems often require extremely large amounts of memory, which are both costly and energy inefficient. Emerging non-volatile memory (NVM) technologies offer high capacity compared to DRAM and low energy compared to SSDs. Hence, NVMs have the potential to fundamentally change the dichotomy between DRAM and durable storage in Big Data processing. However, most Big Data applications are written in managed languages and executed on top of a managed runtime that already performs various dimensions of memory management. Supporting hybrid physical memories adds a new dimension, creating unique challenges in data replacement. This article proposes Panthera, a semantics-aware, fully automated memory management technique for Big Data processing over hybrid memories. Panthera analyzes user programs on a Big Data system to infer their coarse-grained access patterns, which are then passed to the Panthera runtime for efficient data placement and migration. For Big Data applications, the coarse-grained data division information is accurate enough to guide the GC for data layout, which hardly incurs overhead in data monitoring and moving. We implemented Panthera in Open- JDK and Apache Spark. Based on Big Data applications' memory access pattern, we also implemented a new profiling-guided optimization strategy, which is transparent to applications. With this optimization, our extensive evaluation demonstrates that Panthera reduces energy by 32--53% at less than 1% time overhead on average. To show Panthera's applicability, we extend it to QuickCached, a pure Java implementation of Memcached. Our evaluation results show that Panthera reduces energy by 28.7% at 5.2% time overhead on average. [ABSTRACT FROM AUTHOR]

An explicit fully discrete finite element method, which satisfies the nonconvex side constraint at every node, is developed for approximating the p-harmonic flow for p ϵ (1, ∞). Convergence of the method is established under certain conditions on the domain and mesh. Computational examples are presented to demonstrate finite-time blow-ups and qualitative geometric changes of weak solutions of the p-harmonic flow. [ABSTRACT FROM AUTHOR]

Nowadays, the condition-based maintenance (CBM), in which repairs are triggered by the heuristic symptoms of the component faults, is finding increasing applications in the industrial fields. However, for the high-precision machine tools, the conventional CBM might not be the optimal option, which is uneconomic and incapable of ensuring their machining accuracy. In order to overcome these shortcomings, this paper propose the manufacturing-error-based maintenance (MEBM), where the repairs are initiated based on the manufacturing errors instead of the heuristic symptoms. In MEBM, repairs are taken properly at the occurrence of the excessive machining errors, and therefore, the premature and redundant maintenance can be avoided and the maintenance cost can be minimized; what is more, the machining errors are controlled in the closed loops, and therefore, the machining accuracy can be guaranteed. Based on the principles of the MEBM, a prototype maintenance system--the transient backlash error (TBE)-based maintenance system--is established. To achieve this aim, first, the width of the backlash in the mechanical chain is measured by utilizing the built-in encoders and the analytical mapping relationship between the backlash width and the TBE is derived. Relying on these foundations, the TBE can be indirectly estimated. Then, the warning threshold of the TBE is customized according to the permissible roundness error of the workpiece. Thus, the maintenance actions can be precisely implemented: when the monitored TBE exceeds its warning threshold, maintenance workers will be notified to lessen the backlash width, and meanwhile, the permissible maximal size for the backlash will also be informed. [ABSTRACT FROM AUTHOR]

A new optical metal ion sensor based on diffusion followed by an immobilizing reaction has been developed. The current sensor is based on a model that unifies two fundamental processes which a metal analyte undergoes when it is exposed to a porous, ligand-grafted monolith: (a) diffusion of metal ions to the binding sites and (b) metal-ligand (MIn) complexation. A slow diffusion of the metal ions is followed by their fast immobilizing reaction with the ligands in the monolith to give a complex. Inside the region where the ligands have been saturated, the diffusion of the metal ions reaches a steady state with a constant external metal ion concentration (Co). If the complex MLn, could be observed spectroscopically, the absorbance of the product Ap follows: Ap = Kt1/2, K = 2√2&epsiv;p(LoCoD)1/2. D = diffusion constant of the metal ions inside the porous solid; Lo = concentration of the ligands grafted in the monolith; and t time. This equation is straightforward to use, and the Kvs Co1/2 plot provides the correlations with the concentrations (Co) of the metal ions. This is a rare optical sensor for quantitative metal ion analysis. The use of the model in a mesoporous sol-gel monolith containing grafted amine ligands for quantitative Cu2+ sensing is demonstrated. This model may also be used in other chemical sensors that depend on diffusion of analytes followed by immobilizing reactions in porous sensors containing grafted/encapsulated functional groups/molecules. [ABSTRACT FROM AUTHOR]