Krylov implicit integration factor discontinuous Galerkin methods on sparse grids for high dimensional reaction-diffusion equations

Computational costs of numerically solving multidimensional partial differential equations (PDEs) increase significantly when the spatial dimensions of the PDEs are high, due to large number of spatial grid points. For multidimensional reaction-diffusion equations, stiffness of the system provides additional challenges for achieving efficient numerical simulations. In this paper, we propose a class of Krylov implicit integration factor (IIF) discontinuous Galerkin (DG) methods on sparse grids to solve reaction-diffusion equations on high spatial dimensions. The key ingredient of spatial DG discretization is the multiwavelet bases on nested sparse grids, which can significantly reduce the numbers of degrees of freedom. To deal with the stiffness of the DG spatial operator in discretizing reaction-diffusion equations, we apply the efficient IIF time discretization methods, which are a class of exponential integrators. Krylov subspace approximations are used to evaluate the large size matrix exponentials resulting from IIF schemes for solving PDEs on high spatial dimensions. Stability and error analysis for the semi-discrete scheme are performed. Numerical examples of both scalar equations and systems in two and three spatial dimensions are provided to demonstrate the accuracy and efficiency of the methods. The stiffness of the reaction-diffusion equations is resolved well and large time step size computations are obtained

The diversification of the lynx lineage during the Plio-Pleistocene-evidence from a new small Lynx from Longdan, Gansu Province, China

Altres ajuts: CERCA Programme/Generalitat de CatalunyaA new small-sized lynx from Longdan, Gansu Province, China, Lynx hei sp. nov., is described in this study. The new species displays the characteristic Lynx generic traits, such as distinct buccal grooves in the upper canine, presence of an anterior groove in the upper canine, absence of upper premolar 2, and a moderately developed mastoid process, but it is markedly smaller than the previously described Lynx issiodorensis specimens from the same site and is also smaller overall than most living species, comparable to Lynx rufus in size. The new species has a relatively wide and deep zygomatic arch, similar to that of living Lynx lynx, Lynx pardinus and Lynx canadensis but wider than that of Lynx rufus. Our phylogenetic analyses suggest that Lynx hei falls within the crown group Lynx, being the sister to Lynx rufus or, less probably, a sister to Lynx issiodorensis + three other living species of Lynx. The Plio-Pleistocene Lynx issiodorensis is supported as the ancestor of Lynx lynx, Lynx pardinus and Lynx canadensis. Our phylogenetic study suggests that Lynx diversification over the Plio-Pleistocene was achieved initially by body size differentiation, putatively forced by intraspecific competition with other carnivorans, followed by morphological divergence

Modeling yeast cell polarization induced by pheromone gradients

Yeast cells respond to spatial gradients of mating pheromones by polarizing and projecting up the gradient toward the source. It is thought that they employ a spatial sensing mechanism in which the cell compares the concentration of pheromone at different points on the cell surface and determines the maximum point, where the projection forms. Here we constructed the first spatial mathematical model of the yeast pheromone response that describes the dynamics of the heterotrimeric and Cdc42p G-protein cycles, which are linked in a cascade. Two key performance objectives of this system are (1) amplification-converting a shallow external gradient of ligand to a steep internal gradient of protein components and (2) tracking-following changes in gradient direction. We used simulations to investigate amplification mechanisms that allow tracking. We identified specific strategies for regulating the spatial dynamics of the protein components (i.e. their changing location in the cell) that would enable the cell to achieve both objectives

The Antimicrobial Peptide Mastoparan X Protects Against Enterohemorrhagic Escherichia coli O157:H7 Infection, Inhibits Inflammation, and Enhances the Intestinal Epithelial Barrier

Escherichia coli can cause intestinal diseases in humans and livestock, destroy the intestinal barrier, exacerbate systemic inflammation, and seriously threaten human health and animal husbandry development. The aim of this study was to investigate whether the antimicrobial peptide mastoparan X (MPX) was effective against E. coli infection. BALB/c mice infected with E. coli by intraperitoneal injection, which represents a sepsis model. In this study, MPX exhibited no toxicity in IPEC-J2 cells and notably suppressed the levels of interleukin-6 (IL-6), tumor necrosis factor-alpha (TNF-α), myeloperoxidase (MPO), and lactate dehydrogenase (LDH) released by E. coli. In addition, MPX improved the expression of ZO-1, occludin, and claudin and enhanced the wound healing of IPEC-J2 cells. The therapeutic effect of MPX was evaluated in a murine model, revealing that it protected mice from lethal E. coli infection. Furthermore, MPX increased the length of villi and reduced the infiltration of inflammatory cells into the jejunum. SEM and TEM analyses showed that MPX effectively ameliorated the jejunum damage caused by E. coli and increased the number and length of microvilli. In addition, MPX decreased the expression of IL-2, IL-6, TNF-α, p-p38, and p-p65 in the jejunum and colon. Moreover, MPX increased the expression of ZO-1, occludin, and MUC2 in the jejunum and colon, improved the function of the intestinal barrier, and promoted the absorption of nutrients. This study suggests that MPX is an effective therapeutic agent for E. coli infection and other intestinal diseases, laying the foundation for the development of new drugs for bacterial infections

Krylov SSP Integrating Factor Runge–Kutta WENO Methods

Weighted essentially non-oscillatory (WENO) methods are especially efficient for numerically solving nonlinear hyperbolic equations. In order to achieve strong stability and large time-steps, strong stability preserving (SSP) integrating factor (IF) methods were designed in the literature, but the methods there were only for one-dimensional (1D) problems that have a stiff linear component and a non-stiff nonlinear component. In this paper, we extend WENO methods with large time-stepping SSP integrating factor Runge–Kutta time discretization to solve general nonlinear two-dimensional (2D) problems by a splitting method. How to evaluate the matrix exponential operator efficiently is a tremendous challenge when we apply IF temporal discretization for PDEs on high spatial dimensions. In this work, the matrix exponential computation is approximated through the Krylov subspace projection method. Numerical examples are shown to demonstrate the accuracy and large time-step size of the present method

A Study on Stable Regularized Moving Least-Squares Interpolation and Coupled with SPH Method

The smoothed particle hydrodynamics (SPH) method has been popularly applied in various fields, including astrodynamics, thermodynamics, aerodynamics, and hydrodynamics. Generally, a high-precision interpolation is required to calculate the particle physical attributes and their derivatives for the boundary treatment and postproceeding in the SPH simulation. However, as a result of the truncation of kernel function support domain and irregular particle distribution, the interpolation using conventional SPH interpolation experiences low accuracy for the particles near the boundary and free surface. To overcome this drawback, stable regularized moving least-squares (SRMLS) method was introduced for interpolation in SPH. The surface fitting studies were performed with a variety of polyline bases, spatial resolutions, particle distributions, kernel functions, and support domain sizes. Numerical solutions were compared with the results using moving least-squares (MLS) and three SPH methods, including CSPH, K2SPH, and KGFSPH, and it was found that SRMLS not only has nonsingular moment matrix, but also obtains high-accuracy result. Finally, the capability of the algorithm coupled with SRMLS and SPH was illustrated and assessed through several numerical tests

Fixed-point iterative sweeping methods for static Hamilton-Jacobi equations

Fast sweeping methods utilize the Gauss-Seidel iterations and alternating sweeping strat-egy to achieve the fast convergence for computations of static Hamilton-Jacobi equations. They take advantage of the properties of hyperbolic PDEs and try to cover a family of characteristics of the corresponding Hamilton-Jacobi equation in a certain direction simul-taneously in each sweeping order. The time-marching approach to steady state calculation is much slower than the fast sweeping methods due to the CFL condition constraint. But this kind of fixed-point iterations as time-marching methods have explicit form and do not involve inverse operation of nonlinear Hamiltonian. So it can solve general Hamilton-Jacobi equations using any monotone numerical Hamiltonian and high order approximations eas-ily. In this paper, we adopt the Gauss-Seidel idea and alternating sweeping strategy to the time-marching type fixed-point iterations to solve the static Hamilton-Jacobi equations. Ex-tensive numerical examples verify at least a 2 ∼ 5 times acceleration of convergence even on relatively coarse grids. The acceleration is even more when the grid is further refined. More-over the Gauss-Seidel philosophy and alternating sweeping strategy improves the stability, i.e., a larger CFL number can be used. Also the computational cost is exactly the same as the time-marching scheme at each time step

Application Research of an Efficient and Stable Boundary Processing Method for the SPH Method

The boundary truncation of the kernel function affects the numerical accuracy and calculation stability of the smooth particle hydrodynamics (SPH) method and has been one of the key research fields for this method. In this paper, an efficient and stable boundary processing method for the SPH method was introduced by adopting an improved boundary interpolation method (i.e., the improved Shepard method) which needs only the sum of direct accumulation for fixed-boundary particles to improve the numerical stability and computational efficiency of the fixed ghost particle method. The improvement effect of the method was demonstrated by comparing it with different interpolation methods using the cases of still water, a wave generated by dam-breaking, and a solitary wave attacking problem with fixed walls and a moveable wall. The results showed that the new boundary processing method for SPH can help remarkably improve the efficiency of calculation and reduce the oscillations of pressure when simulating various flows