On the convergence of dual-Schur partitioned time integrators

Partitioned time-integrators have often been used in computational science and engineering for solving coupled multidomain problems and even for single-domain problems with multiple spatial and/or temporal scales. Partitioning based on dual-Schur domain decomposition allows single-domain problems in solid and structural dynamics to be decomposed into nonoverlapping subdomains that can be solved independently using different time integration schemes and then coupled back together for greater computational efficiency. The coupling is achieved by using Lagrange multipliers to enforce continuity of the solution across the interface between the subdomains. It has been documented, through many numerical examples, that this coupling method preserves the accuracy and stability properties of the underlying time-integrators used within the individual subdomains. In this research, for the first time, we conduct a rigorous error analysis for such dual-Schur coupling methods and quantify the local and global truncation errors to show that partitioned time integrators preserve the theoretical rates of convergence within each individual subdomain and the global problem domain. We focus on a multitime-step method which allows one to couple subdomains that are solved with different time steps and time integrators from the Newmark family of schemes. We show that the second-order convergence rate enjoyed by the Newmark method for single domain problems is also preserved for partitioned systems with any time-step ratio between the two subdomains. Several numerical examples are shown to support this fact. This result lends a strong theoretical basis to the results observed only numerically heretofore in the literature and establishes an a priori error measure of error for dual-Schur partitioned numerical time integrators

Embedded symmetric positive semi-definite machine-learned elements for reduced-order modeling in finite-element simulations with application to threaded fasteners

We present a machine-learning strategy for finite element analysis of solid mechanics wherein we replace complex portions of a computational domain with a data-driven surrogate. In the proposed strategy, we decompose a computational domain into an "outer" coarse-scale domain that we resolve using a finite element method (FEM) and an "inner" fine-scale domain. We then develop a machine-learned (ML) model for the impact of the inner domain on the outer domain. In essence, for solid mechanics, our machine-learned surrogate performs static condensation of the inner domain degrees of freedom. This is achieved by learning the map from (virtual) displacements on the inner-outer domain interface boundary to forces contributed by the inner domain to the outer domain on the same interface boundary. We consider two such mappings, one that directly maps from displacements to forces without constraints, and one that maps from displacements to forces by virtue of learning a symmetric positive semi-definite (SPSD) stiffness matrix. We demonstrate, in a simplified setting, that learning an SPSD stiffness matrix results in a coarse-scale problem that is well-posed with a unique solution. We present numerical experiments on several exemplars, ranging from finite deformations of a cube to finite deformations with contact of a fastener-bushing geometry. We demonstrate that enforcing an SPSD stiffness matrix is critical for accurate FEM-ML coupled simulations, and that the resulting methods can accurately characterize out-of-sample loading configurations with significant speedups over the standard FEM simulations

Recursive Multi-Time-Step Coupling of Multiple Subdomains

The need for efficient computation methods for modeling of large-scale structures has become critically important over the past few years. Efficient means of analysis often involve coupling in space through domain decomposition and multi scale methods in time. The multi-time-step coupling method is a coupling method in time which allows for efficient analysis of large-scale problems for structural dynamics where a large structural model is decomposed into smaller subdomains that are solved independently and then coupled back together to obtain the global solution. For coupling of more than two subdomains that are solved at different timesteps, we employ recursive methods. Currently a constraint on this recursive coupling is that subdomains with the same time step must be coupled first before coupling with other subdomains of different time steps. In this research, we develop a computational algorithm to overcome this constraint and allow the user to specify general coupling orders for the different subdomains. Our efforts till now have been directed towards coding the recursive coupling of multi-subdomain models and we have verified that the equations that will allow us to overcome coupling constraint are correct. We are in the process of implementing these equations into our codes. Once in place, these sets of codes will allow users to conduct simulation of structural dynamics in a very efficient manner

Anomalous Heat Conduction and Anomalous Diffusion in Low Dimensional Nanoscale Systems

Thermal transport is an important energy transfer process in nature. Phonon is the major energy carrier for heat in semiconductor and dielectric materials. In analogy to Ohm's law for electrical conductivity, Fourier's law is a fundamental rule of heat transfer in solids. It states that the thermal conductivity is independent of sample scale and geometry. Although Fourier's law has received great success in describing macroscopic thermal transport in the past two hundreds years, its validity in low dimensional systems is still an open question. Here we give a brief review of the recent developments in experimental, theoretical and numerical studies of heat transport in low dimensional systems, include lattice models, nanowires, nanotubes and graphenes. We will demonstrate that the phonon transports in low dimensional systems super-diffusively, which leads to a size dependent thermal conductivity. In other words, Fourier's law is breakdown in low dimensional structures

SKA2 regulated hyperactive secretory autophagy drives neuroinflammation-induced neurodegeneration

High levels of proinflammatory cytokines induce neurotoxicity and catalyze inflammation-driven neurodegeneration, but the specific release mechanisms from microglia remain elusive. Here we show that secretory autophagy (SA), a non-lytic modality of autophagy for secretion of vesicular cargo, regulates neuroinflammation-mediated neurodegeneration via SKA2 and FKBP5 signaling. SKA2 inhibits SA-dependent IL-1β release by counteracting FKBP5 function. Hippocampal Ska2 knockdown in male mice hyperactivates SA resulting in neuroinflammation, subsequent neurodegeneration and complete hippocampal atrophy within six weeks. The hyperactivation of SA increases IL-1β release, contributing to an inflammatory feed-forward vicious cycle including NLRP3-inflammasome activation and Gasdermin D-mediated neurotoxicity, which ultimately drives neurodegeneration. Results from protein expression and co-immunoprecipitation analyses of male and female postmortem human brains demonstrate that SA is hyperactivated in Alzheimer's disease. Overall, our findings suggest that SKA2-regulated, hyperactive SA facilitates neuroinflammation and is linked to Alzheimer's disease, providing mechanistic insight into the biology of neuroinflammation

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead

Coupling Peridynamics with Finite-Elements for Fast, Stable and Accurate Simulations of Crack Propagation

While FE methods are computationally very efficient, they are fraught with issues such as mesh dependent solutions, ill-conditioning, slow convergence under large deformations, and limitations associated with the underlying material fracture models. An alternative to a classical solid mechanics approach is the non-local continuum theory of peridynamics (PD), which is better suited for problems involving fracture and fragmentation. However, PD is computationally very intensive, and so in general it is not feasible to simulate large problems with PD without the use of a very powerful workstation. One method to reduce computational costs is to use domain decomposition (DD) to break down large domains in space. This approach, when used in conjunction with the multi-time-step (MTS) method, enables the decoupling of the temporal scales of each subdomain as well, which gives rise to significant savings in computational cost. A critical consideration with MTS methods is maintaining the stability and accuracy of the solution. In this research, an error analysis of the MTS method is conducted to ensure convergence of the coupled solution. Analytical error measures for the MTS solution are presented using the truncated Taylor series approach. These results rigorously prove, for the first time, that the MTS method retains the convergence rate of the underlying Newmark method. One limitation of the state of the art of MTS methods is that most implementations are limited to two subdomains. While this is a convenient simplification for theory and implementation, it places a hard limit on the amount of savings that can be achieved using a MTS approach. Thus, a generalized MTS implementation is presented which enables any number of subdomains to be coupled together, and addresses some of the issues with the existing approaches to couple multiple MTS subdomains. As mentioned above, PD is a good choice for modeling crack initiation and propagation. However, the computational costs can be prohibitively expensive. Thus, the DD and MTS approaches previously used in classical solid mechanics are investigated for coupling multiple PD domains as well. In addition to several numerical studies, the theoretical computational cost, convergence, and accuracy of this new method are also investigated. The final goal of this research is the development of a new MTS approach which leverages the strengths of both the PD and FE methods. This is acomplished by first dividing the problem domain into FE and PD subdomains using DD, and then allowing the subdomains to be integrated with different time steps using MTS. This approach allows one to use PD with a small time step for subdomains within regions of interest, such as critical regions containing crack-tips, and use FE methods with large time steps for the remainder of the problem domain to keep the total computational cost low

Comparative evaluation of commercially available point-of-care heartworm antigen tests using well-characterized canine plasma samples

Abstract Background Dirofilaria immitis is a worldwide parasite that is endemic in many parts of the United States. There are many commercial assays available for the detection of D. immitis antigen, one of which was modified and has reentered the market. Our objective was to compare the recently reintroduced Witness® Heartworm (HW) Antigen test Kit (Zoetis, Florham Park, NJ) and the SNAP® Heartworm RT (IDEXX Laboratories, Inc., Westbrook, ME) to the well-based ELISA DiroChek® Heartworm Antigen Test Kit (Zoetis, Florham Park, NJ). Methods Canine plasma samples were either received at the Auburn Diagnostic Parasitology Laboratory from veterinarians submitting samples for additional heartworm testing (n = 100) from 2008 to 2016 or purchased from purpose-bred beagles (n = 50, presumed negative) in 2016. Samples were categorized as “positive,” “borderline” or “negative” using our established spectrophotometric cutoff value with the DiroChek® assay when a sample was initially received and processed. Three commercially available heartworm antigen tests (DiroChek®, Witness® HW, and SNAP® RT) were utilized for simultaneous testing of the 150 samples in random order as per their package insert with the addition of spectrophotometric optical density (OD) readings of the DiroChek® assay. Any samples yielding discordant test results between assays were further evaluated by heat treatment of plasma and retesting. Chi-square tests for the equality of proportions were utilized for statistical analyses. Results Concordant results occurred in 140/150 (93.3%) samples. Discrepant results occurred in 10/150 samples tested (6.6%): 9/10 occurring in the borderline heartworm (HW) category and 1/10 occurring in the negative HW category. The sensitivity and specificity of each test compared to the DiroChek® read by spectrophotometer was similar to what has been reported previously (Witness®: sensitivity 97.0% [94.1–99.4%], specificity 96.4% [95.5–100.0%]; SNAP® RT: sensitivity 90.9% [78.0–100.0%], specificity 98.8% [96.0–100.0%]). There were significant differences detected when comparing the sensitivities of the SNAP® RT and the Witness® HW to the DiroChek® among the 150 total samples (p = 0.003) and the 50 “borderline” samples (p = 0.001). Conclusions In this study, the sensitivity of the Witness® HW was higher than the sensitivity of the SNAP® RT when compared with the DiroChek® test results prior to heat treatment of samples