Formulation and optimization of the energy-based blended quasicontinuum method

We formulate an energy-based atomistic-to-continuum coupling method based on blending the quasicontinuum method for the simulation of crystal defects. We utilize theoretical results from Ortner and Van Koten (manuscript) to derive optimal choices of approximation parameters (blending function and finite element grid) for microcrack and di-vacancy test problems and confirm our analytical predictions in numerical tests

A mathematical formalization of the parallel replica dynamics

The purpose of this article is to lay the mathematical foundations of a well known numerical approach in computational statistical physics and molecular dynamics, namely the parallel replica dynamics introduced by A.F. Voter. The aim of the approach is to efficiently generate a coarse-grained evolution (in terms of state-to-state dynamics) of a given stochastic process. The approach formally consists in concurrently considering several realizations of the stochastic process, and tracking among the realizations that which, the soonest, undergoes an important transition. Using specific properties of the dynamics generated, a computational speed-up is obtained. In the best cases, this speed-up approaches the number of realizations considered. By drawing connections with the theory of Markov processes and, in particular, exploiting the notion of quasi-stationary distribution, we provide a mathematical setting appropriate for assessing theoretically the performance of the approach, and possibly improving it

Development of an Optimization-Based Atomistic-to-Continuum Coupling Method

Atomistic-to-Continuum (AtC) coupling methods are a novel means of computing the properties of a discrete crystal structure, such as those containing defects, that combine the accuracy of an atomistic (fully discrete) model with the efficiency of a continuum model. In this note we extend the optimization-based AtC, formulated in arXiv:1304.4976 for linear, one-dimensional problems to multi-dimensional settings and arbitrary interatomic potentials. We conjecture optimal error estimates for the multidimensional AtC, outline an implementation procedure, and provide numerical results to corroborate the conjecture for a 1D Lennard-Jones system with next-nearest neighbor interactions.Comment: 12 pages, 3 figure

Electronic density of states for incommensurate layers

We prove that the electronic density of states (DOS) for 2D incommensurate layered structures, where Bloch theory does not apply, is well-defined as the thermodynamic limit of finite clusters. In addition, we obtain an explicit representation formula for the DOS as an integral over local configurations. Next, based on this representation formula, we propose a novel algorithm for computing electronic structure properties in incommensurate heterostructures, which overcomes limitations of the common approach to artificially strain a large supercell and then apply Bloch theory

Incommensurate heterostructures in momentum space

To make the investigation of electronic structure of incommensurate heterostructures computationally tractable, effective alternatives to Bloch theory must be developed. In [Multiscale Model. Simul., 15(2017), pp. 476--499] we developed and analyzed a real space scheme that exploits spatial ergodicity and near-sightedness. In the present work, we present an analogous scheme formulated in momentum space, which we prove has significant computational advantages in specific incommensurate systems of physical interest, e.g., bilayers of a specified class of materials with small rotation angles. We use our theoretical analysis to obtain estimates for improved rates of convergence with respect to total CPU time for our momentum space method that are confirmed in computational experiments

A Multifaceted Mathematical Approach for Complex Systems

Applied mathematics has an important role to play in developing the tools needed for the analysis, simulation, and optimization of complex problems. These efforts require the development of the mathematical foundations for scientific discovery, engineering design, and risk analysis based on a sound integrated approach for the understanding of complex systems. However, maximizing the impact of applied mathematics on these challenges requires a novel perspective on approaching the mathematical enterprise. Previous reports that have surveyed the DOE's research needs in applied mathematics have played a key role in defining research directions with the community. Although these reports have had significant impact, accurately assessing current research needs requires an evaluation of today's challenges against the backdrop of recent advances in applied mathematics and computing. To address these needs, the DOE Applied Mathematics Program sponsored a Workshop for Mathematics for the Analysis, Simulation and Optimization of Complex Systems on September 13-14, 2011. The workshop had approximately 50 participants from both the national labs and academia. The goal of the workshop was to identify new research areas in applied mathematics that will complement and enhance the existing DOE ASCR Applied Mathematics Program efforts that are needed to address problems associated with complex systems. This report describes recommendations from the workshop and subsequent analysis of the workshop findings by the organizing committee

Non-ergodicity of Nose-Hoover dynamics

The numerical integration of the Nose-Hoover dynamics gives a deterministic method that is used to sample the canonical Gibbs measure. The Nose-Hoover dynamics extends the physical Hamiltonian dynamics by the addition of a "thermostat" variable, that is coupled nonlinearly with the physical variables. The accuracy of the method depends on the dynamics being ergodic. Numerical experiments have been published earlier that are consistent with non-ergodicity of the dynamics for some model problems. The authors recently proved the non-ergodicity of the Nose-Hoover dynamics for the one-dimensional harmonic oscillator. In this paper, this result is extended to non-harmonic one-dimensional systems. It is also shown for some multidimensional systems that the averaged dynamics for the limit of infinite thermostat "mass" have many invariants, thus giving theoretical support for either non-ergodicity or slow ergodization. Numerical experiments for a two-dimensional central force problem and the one-dimensional pendulum problem give evidence for non-ergodicity

Pax6 Expression Is Sufficient to Induce a Neurogenic Fate in Glial Progenitors of the Neonatal Subventricular Zone

The forebrain subventricular zone (SVZ) of neonatal mammals contains a large, heterogeneous population of migratory and proliferating precursors of interneurons and glia. These cell types are produced in large numbers in the immediate postnatal period, the glioblasts populating the hemispheres with astrocytes and oligodendrocytes, the neuroblasts migrating to the olfactory bulb to become interneurons. How cell fate decisions are determined or stabilized in this mixed population is not clear, although previous studies indicate the importance of two transcription factors, Pax6 in neurons and Olig2 in glia, and suggest there may be reciprocal repression between these genes.In examining the SVZ of neonatal mouse and rat brain, we find that the very large majority of SVZ cells express either Pax6 or Olig2, but few express both. We have used in vivo retro- and lenti-virus injections into the neonatal SVZ and in vitro gene transfer to demonstrate that pax6 over-expression is sufficient to down-regulate olig2 and to promote a neuronal lineage development and migration pattern in olig2-expressing cells. Furthermore, we provide evidence that Pax6 binds to the olig2 promoter and that an HEB sequence in the promoter is required for the Pax6 repression of olig2 transcription. Lastly, we constructed a lentivirus to target olig2-expressing cells in the SVZ to trace their fates, and found that the very large majority developed into glia.We provide evidence for a direct repression of olig2 by Pax6. Since SVZ cells can display developmental plasticity in vitro, the cross-repression promotes a stabilization of cell fates. This repression may be critical in a germinal zone in which immature cells are highly migratory and are not organized into an epithelium

Atovaquone Compared with Dapsone for the Prevention of Pneumocystis carinii Pneumonia in Patients with HIV Infection Who Cannot Tolerate Trimethoprim, Sulfonamides, or Both

BACKGROUND Patients with human immunodeficiency virus (HIV) infection and latent tuberculosis are at substantial risk for the development of active tuberculosis. As a public health measure, prophylactic treatment with isoniazid has been suggested for HIV-infected persons who have anergy and are in groups with a high prevalence of tuberculosis. METHODS We conducted a multicenter, randomized, double-blind, placebo-controlled trial of six months of prophylactic isoniazid treatment in HIV-infected patients with anergy who have risk factors for tuberculosis infection. The primary end point was culture-confirmed tuberculosis. RESULTS The study was conducted from November 1991 through June 1996. Over 90 percent of the patients had two or more risk factors for tuberculosis infection, and nearly 75 percent of patients were from greater New York City. After a mean follow-up of 33 months, tuberculosis was diagnosed in only 6 of 257 patients in the placebo group and 3 of 260 patients in the isoniazid group (risk ratio, 0.48; 95 percent confidence interval, 0.12 to 1.91; P=0.30). There were no significant differences between the two groups with regard to death, death or the progression of HIV disease, or adverse events. CONCLUSIONS Even in HIV-infected patients with anergy and multiple risk factors for latent tuberculosis infection, the rate of development of active tuberculosis is low. This finding does not support the use of isoniazid prophylaxis in high-risk patients with HIV infection and anergy unless they have been exposed to active tuberculosis