Search

The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet for fluid problems it only achieves first-order spatial accuracy near embedded boundaries for the velocity field and fails to converge pointwise for elements of the stress tensor. In a previous work we introduced the Immersed Boundary Smooth Extension (IBSE) method, a variation of the IB method that achieves high-order accuracy for elliptic PDE by smoothly extending the unknown solution of the PDE from a given smooth domain to a larger computational domain, enabling the use of simple Cartesian-grid discretizations. In this work, we extend the IBSE method to allow for the imposition of a divergence constraint, and demonstrate high-order convergence for the Stokes and incompressible Navier–Stokes equations: up to third-order pointwise convergence for the velocity field, and second-order pointwise convergence for all elements of the stress tensor. The method is flexible to the underlying discretization: we demonstrate solutions produced using both a Fourier spectral discretization and a standard second-order finite-difference discretization. [ABSTRACT FROM AUTHOR]

We present a spectrally accurate embedded boundary method for solving linear, inhomogeneous, elliptic partial differential equations (PDE) in general smooth geometries in two dimensions, focusing in this manuscript on the Poisson, modified Helmholtz, and Stokes equations. Unlike several recently proposed methods which rely on function extension, we propose a method which instead utilizes function intension , or the smooth truncation of known function values. Similar to those methods based on extension, once the inhomogeneity is truncated we may solve the PDE using any of the many simple, fast, and robust solvers that have been developed for regular grids on simple domains. Function intension is inherently stable, as are all steps in the proposed solution method, and can be used on domains which do not readily admit extensions. We pay a price in exchange for improved stability and flexibility: in addition to solving the PDE on the regular domain, we must additionally (1) solve the PDE on a small auxiliary domain that is fitted to the boundary, and (2) ensure consistency of the solution across the interface between this auxiliary domain and the rest of the physical domain. We show how these tasks may be accomplished efficiently (in both the asymptotic and practical sense), and compare convergence to two recent high-order embedded boundary schemes. Finally, to demonstrate the wide applicability of the method, we solve a nonlinear predator-prey model, achieving rapid convergence in both space and time. • Embedded boundary scheme for inhomogeneous PDE in general smooth 2D geometries. • Spectrally accurate, stable, and efficient: same scaling as FFT based methods. • Uses 'function intension', i.e. smooth truncation, instead of function extension. • Function intension is stable; solutions converge rapidly to near machine precision. • Demonstrations for Poisson, modified Helmholtz, Stokes, and predator-prey equations. [ABSTRACT FROM AUTHOR]

The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet it only achieves first-order spatial accuracy near embedded boundaries. In this paper, we introduce a new high-order numerical method which we call the Immersed Boundary Smooth Extension (IBSE) method. The IBSE method achieves high-order accuracy by smoothly extending the unknown solution of the PDE from a given smooth domain to a larger computational domain, enabling the use of simple Cartesian-grid discretizations (e.g. Fourier spectral methods). The method preserves much of the flexibility and robustness of the original IB method. In particular, it requires minimal geometric information to describe the boundary and relies only on convolution with regularized delta-functions to communicate information between the computational grid and the boundary. We present a fast algorithm for solving elliptic equations, which forms the basis for simple, high-order implicit-time methods for parabolic PDE and implicit–explicit methods for related nonlinear PDE. We apply the IBSE method to solve the Poisson, heat, Burgers', and Fitzhugh–Nagumo equations, and demonstrate fourth-order pointwise convergence for Dirichlet problems and third-order pointwise convergence for Neumann problems. [ABSTRACT FROM AUTHOR]

Background Obesity currently affects more than a third of the United States population and is associated with increased surgical complications. Compared to all other subspecialties, colorectal surgery is the most affected by the increasing trend in obese surgical patients. Operative time has been found to have the greatest impact on hospital costs and physician workload. This study was conducted to determine whether obesity has a direct impact on operative time in elective colorectal procedures using a high-powered, nationally representative patient sample. Methods A retrospective analysis was conducted on 45,362 patients who underwent open and laparoscopic ileocolic resections, partial colectomies, and low pelvic anastomoses using American College of Surgeons National Surgical Quality Improvement Program data from 2005-2009. Operative time was the main outcome variable, whereas body mass index (BMI) was the main independent variable. BMI was divided into three classes as follows: normal (<25), overweight and/or obese (25-35), and morbidly obese (>35). A univariate linear model was used to analyze the relationship while controlling for confounding factors such as demographics and preoperative conditions. Statistical significance was established at P ≤ 0.05. Results Morbidly obese patients were found to have longer operative times than did normal patients across each individual colorectal procedure (P < 0.001), ranging from a mean difference of 17.8 min for open ileocolic resections to 56.6 min for laparoscopic low pelvic anastomoses with colostomies. Conclusions BMI, as an objective measure of obesity, is a direct, statistically significant independent predictor of operative time across elective colorectal procedures. [ABSTRACT FROM AUTHOR]

Abstract: Dengue virus (DEN) is a major public health problem worldwide and causes a spectrum of diseases, for which no antiviral treatments exist. Peptide-conjugated phosphorodiamidate morpholino oligomers (P-PMOs) complementary to the DEN 5′ stem–loop (5′SL) and to the DEN 3′ cyclization sequence (3′CS) inhibit DEN replication, presumably by blocking critical RNA–RNA or RNA–protein interactions involved in viral translation and/or RNA synthesis. Here, a third P-PMO, complementary to the top of the 3′ stem–loop (3′SLT), inhibited DEN replication in BHK cells. Using a novel DEN2 reporter replicon and a DEN2 reporter mRNA, we determined that the 5′SL P-PMO inhibited viral translation, the 3′CS P-PMO blocked viral RNA synthesis but not viral translation, and the 3′SLT P-PMO inhibited both viral translation and RNA synthesis. These results show that the 3′CS and the 3′SL domains regulate DEN translation and RNA synthesis and further demonstrate that P-PMOs are potentially useful as antiviral agents. [Copyright &y& Elsevier]

• A fast, spectrally accurate algorithm for computing the Bingham closure. • Chebyshev interpolation provides a controllable error/efficiency tradeoff. • The algorithm enables large-scale continuum simulations of apolar particle suspensions. Continuum kinetic theories provide an important tool for the analysis and simulation of particle suspensions. When those particles are anisotropic, the addition of a particle orientation vector to the kinetic description yields a 2 d − 1 dimensional theory which becomes intractable to simulate, especially in three dimensions or near states where the particles are highly aligned. Coarse-grained theories that track only moments of the particle distribution functions provide a more efficient simulation framework, but require closure assumptions. For the particular case where the particles are apolar, the Bingham closure has been found to agree well with the underlying kinetic theory; yet the closure is non-trivial to compute, requiring the solution of an often nearly-singular nonlinear equation at every spatial discretization point at every timestep. In this paper, we present a robust, accurate, and efficient numerical scheme for evaluating the Bingham closure, with a controllable error/efficiency tradeoff. To demonstrate the utility of the method, we carry out high-resolution simulations of a coarse-grained continuum model for a suspension of active particles in parameter regimes inaccessible to kinetic theories. Analysis of these simulations reveals that inaccurately computing the closure can act to effectively limit spatial resolution in the coarse-grained fields. Pushing these simulations to the high spatial resolutions enabled by our method reveals a coupling between vorticity and topological defects in the suspension director field, as well as signatures of energy transfer between scales in this active fluid model. [ABSTRACT FROM AUTHOR]

Abstract: West Nile virus (WNV) genome cyclization is mediated by two pairs of long-distance RNA/RNA interactions: the 5′CS/3′CSI (conserved sequence) and the 5′UAR/3′UAR (upstream AUG region) base pairings. Antisense peptide-conjugated phosphorodiamidate morpholino oligomers (PPMOs), designed to interfere with the 5′CS/3′CSI or 5′UAR/3′UAR base pairings, were previously shown to inhibit WNV. In this study, we selected and characterized WNVs resistant to a PPMO targeting the 3′UAR (3′UAR-PPMO). All resistant viruses accumulated one-nucleotide mutations within the 3′UAR, leading to a single-nucleotide mismatch or a weakened base-pairing interaction with the 3′UAR-PPMO. Remarkably, a one-nucleotide mutation within the 5′UAR was correspondingly co-selected; the 5′UAR mutation restored the base pairing with the 3′UAR mutation. Mutagenesis of WNV demonstrated that the single-nucleotide change within the 3′UAR-PPMO-target site conferred the resistance. RNA binding analysis indicated that the single-nucleotide change reduced the ability of 3′UAR-PPMO to block the RNA/RNA interaction required for genome cyclization. The results suggest a mechanism by which WNV develops resistance to 3′UAR-PPMO, through co-selection of the 5′UAR and 3′UAR, to create a mismatch or a weakened base-pairing interaction with the PPMO, while maintaining the 5′UAR/3′UAR base pairings. [Copyright &y& Elsevier]

Abstract: The genus Alphavirus contains members that threaten human health, both as natural pathogens and as potential biological weapons. Peptide-conjugated phosphorodiamidate morpholino oligomers (PPMO) enter cells readily and can inhibit viral replication through sequence-specific steric blockade of viral RNA. Sindbis virus (SINV) has low pathogenicity in humans and is regularly utilized as a model alphavirus. PPMO targeting the 5′-terminal and AUG translation start site regions of the SINV genome blocked the production of infectious SINV in tissue culture. PPMO designed against corresponding regions in Venezuelan equine encephalitis virus (VEEV) were likewise found to be effective in vitro against several strains of VEEV. Mice treated with PPMO before and after VEEV infection were completely protected from lethal outcome while mice receiving only post-infection PPMO treatment were partially protected. Levels of virus in tissue samples correlated with animal survival. Uninfected mice suffered no apparent ill-effects from PPMO treatment. Thus, PPMO appear promising as candidates for therapeutic development against alphaviruses. [Copyright &y& Elsevier]

Abstract: West Nile virus (WNV) genome cyclization and replication require two pairs of long-distance RNA interactions. Besides the previously reported 5′CS/3′CSI (conserved sequence) interaction, a 5′UAR/3′UAR (upstream AUG region) interaction also contributes to genome cyclization and replication. WNVs containing mutant 5′UARs capable of forming the 5′/3′ viral RNA interaction were replicative. In contrast, WNV containing a 5′UAR mutation that abolished the 5′/3′ viral RNA interaction was non-replicative; however, the replication defect could be rescued by a single-nucleotide adaptation that restored the 5′/3′ RNA interaction. The 5′UAR/3′UAR interaction is critical for RNA synthesis, but not for viral translation. Antisense oligomers targeting the 5′UAR/3′UAR interaction effectively inhibited WNV replication. Phylogenic analysis showed that the 3′UAR could alternate between pairing with the 5′UAR or with the 3′ end of the flaviviral genome. Therefore, the 5′UAR/3′UAR pairing may release the 3′ end of viral genome (as a template) during the initiation of minus-strand RNA synthesis. [Copyright &y& Elsevier]

• High-order numerical scheme for the solution of the dissolution and Stefan problems. • Accurate computation of surface shear stress and solute concentration gradients at solid-liquid interface. • Numerical exploration and investigation of the onset of surface patterning. • Immersed Boundary Smooth Extension method for moving interface problems. The dissolution of solids has created spectacular geomorphologies ranging from centimeter-scale cave scallops to the kilometer-scale "stone forests" of China and Madagascar. Mathematically, dissolution processes are modeled by a Stefan problem, which describes how the motion of a phase-separating interface depends on local concentration gradients, coupled to a fluid flow. Simulating these problems is challenging, requiring the evolution of a free interface whose motion depends on the normal derivatives of an external field in an ever-changing domain. Moreover, density differences created in the fluid domain induce self-generated convecting flows that further complicate the numerical study of dissolution processes. In this contribution, we present a numerical method for the simulation of the Stefan problem coupled to a fluid flow. The scheme uses the Immersed Boundary Smooth Extension method to solve the bulk advection-diffusion and fluid equations in the complex, evolving geometry, coupled to a θ - L scheme that provides stable evolution of the boundary. We demonstrate 3rd-order temporal and pointwise spatial convergence of the scheme for the classical Stefan problem, and 2nd-order temporal and pointwise spatial convergence when coupled to flow. Examples of dissolution of solids that result in high-Rayleigh number convection are numerically studied, and qualitatively reproduce the complex morphologies observed in recent experiments. [ABSTRACT FROM AUTHOR]