Semi-analytical solution of multilayer diffusion problems with time-varying boundary conditions and general interface conditions

We develop a new semi-analytical method for solving multilayer diffusion problems with time-varying external boundary conditions and general internal boundary conditions at the interfaces between adjacent layers. The convergence rate of the semi-analytical method, relative to the number of eigenvalues, is investigated and the effect of varying the interface conditions on the solution behaviour is explored. Numerical experiments demonstrate that solutions can be computed using the new semi-analytical method that are more accurate and more efficient than the unified transform method of Sheils [Appl. Math. Model., 46:450-464, 2017]. Furthermore, unlike classical analytical solutions and the unified transform method, only the new semi-analytical method is able to correctly treat problems with both time-varying external boundary conditions and a large number of layers. The paper is concluded by replicating solutions to several important industrial, environmental and biological applications previously reported in the literature, demonstrating the wide applicability of the work.Comment: 24 pages, 8 figures, accepted version of paper published in Applied Mathematics and Computatio

Fast computation of effective diffusivities using a semi-analytical solution of the homogenization boundary value problem for block locally-isotropic heterogeneous media

Direct numerical simulation of diffusion through heterogeneous media can be difficult due to the computational cost of resolving fine-scale heterogeneities. One method to overcome this difficulty is to homogenize the model by replacing the spatially-varying fine-scale diffusivity with an effective diffusivity calculated from the solution of an appropriate boundary value problem. In this paper, we present a new semi-analytical method for solving this boundary value problem and computing the effective diffusivity for pixellated, locally-isotropic, heterogeneous media. We compare our new solution method to a standard finite volume method and show that equivalent accuracy can be achieved in less computational time for several standard test cases. We also demonstrate how the new solution method can be applied to complex heterogeneous geometries represented by a grid of blocks. These results indicate that our new semi-analytical method has the potential to significantly speed up simulations of diffusion in heterogeneous media.Comment: 29 pages, 4 figures, 5 table

Numerical investigation into coarse-scale models of diffusion in complex heterogeneous media

Computational modelling of diffusion in heterogeneous media is prohibitively expensive for problems with fine-scale heterogeneities. A common strategy for resolving this issue is to decompose the domain into a number of non-overlapping sub-domains and homogenize the spatially-dependent diffusivity within each sub-domain (homogenization cell). This process yields a coarse-scale model for approximating the solution behaviour of the original fine-scale model at a reduced computational cost. In this paper, we study coarse-scale diffusion models in block heterogeneous media and investigate, for the first time, the effect that various factors have on the accuracy of resulting coarse-scale solutions. We present new findings on the error associated with homogenization as well as recommendations for choosing the number of homogenization cells and the type of boundary condition imposed on the homogenization cells to produce accurate coarse-scale solutions.Comment: 19 pages, 10 figures, submitte

BISON: bio-interface for the semi-global analysis of network patterns

BACKGROUND: The large amount of genomics data that have accumulated over the past decade require extensive data mining. However, the global nature of data mining, which includes pattern mining, poses difficulties for users who want to study specific questions in a more local environment. This creates a need for techniques that allow a localized analysis of globally determined patterns. RESULTS: We developed a tool that determines and evaluates global patterns based on protein property and network information, while providing all the benefits of a perspective that is targeted at biologist users with specific goals and interests. Our tool uses our own data mining techniques, integrated into current visualization and navigation techniques. The functionality of the tool is discussed in the context of the transcriptional network of regulation in the enteric bacterium Escherichia coli. Two biological questions were asked: (i) Which functional categories of proteins (identified by hidden Markov models) are regulated by a regulator with a specific domain? (ii) Which regulators are involved in the regulation of proteins that contain a common hidden Markov model? Using these examples, we explain the gene-centered and pattern-centered analysis that the tool permits. CONCLUSION: In summary, we have a tool that can be used for a wide variety of applications in biology, medicine, or agriculture. The pattern mining engine is global in the way that patterns are determined across the entire network. The tool still permits a localized analysis for users who want to analyze a subportion of the total network. We have named the tool BISON (Bio-Interface for the Semi-global analysis Of Network patterns)

Bose-Einstein condensates in standing waves: The cubic nonlinear Schroedinger equation with a periodic potential

We present a new family of stationary solutions to the cubic nonlinear Schroedinger equation with a Jacobian elliptic function potential. In the limit of a sinusoidal potential our solutions model a dilute gas Bose-Einstein condensate trapped in a standing light wave. Provided the ratio of the height of the variations of the condensate to its DC offset is small enough, both trivial phase and nontrivial phase solutions are shown to be stable. Numerical simulations suggest such stationary states are experimentally observable.Comment: 4 pages, 4 figure

Augmented Reality Technician Assistance Program

The Augmented Reality Technician Assistance Program is a proof-of-concept project for allowing a remote expert to communicate with and assist a field technician in completing procedures with which the technician may be unfamiliar. For example, an expert in Navy aircraft maintenance could advise an Air Force flight mechanic about performing repairs or maintenance on Navy aircraft. The end goal of our Cedarville computer science capstone project is to create an experimental prototype to deliver to the Air Force Research Laboratory. In our prototype the expert uses a Microsoft Surface Pro tablet to communicate via marked up still images with a Hololens-enabled field technician. As a wearable computer, the Hololens provides the technician a hands-free advantage over traditional devices, because it’s interface does not use typical input devices such as a mouse and keyboard. The advantage of the Surface Pro is that it allows the expert to mark up instructional images naturally with the stylus, providing better precision for the annotations

Fabrication of low-cost, large-area prototype Si(Li) detectors for the GAPS experiment

A Si(Li) detector fabrication procedure has been developed with the aim of satisfying the unique requirements of the GAPS (General Antiparticle Spectrometer) experiment. Si(Li) detectors are particularly well-suited to the GAPS detection scheme, in which several planes of detectors act as the target to slow and capture an incoming antiparticle into an exotic atom, as well as the spectrometer and tracker to measure the resulting decay X-rays and annihilation products. These detectors must provide the absorption depth, energy resolution, tracking efficiency, and active area necessary for this technique, all within the significant temperature, power, and cost constraints of an Antarctic long-duration balloon flight. We report here on the fabrication and performance of prototype 2"-diameter, 1-1.25 mm-thick, single-strip Si(Li) detectors that provide the necessary X-ray energy resolution of $\sim$4 keV for a cost per unit area that is far below that of previously-acquired commercial detectors. This fabrication procedure is currently being optimized for the 4"-diameter, 2.5 mm-thick, multi-strip geometry that will be used for the GAPS flight detectors.Comment: Accepted for publication at Nuclear Instrumentation and Methods A, 12 pages, 11 figure

Pleiotropic phenotypes of a Yersinia enterocolitica flhD mutant include reduced lethality in a chicken embryo model

<p>Abstract</p> <p>Background</p> <p>The <it>Yersinia enterocolitica </it>flagellar master regulator FlhD/FlhC affects the expression levels of non-flagellar genes, including 21 genes that are involved in central metabolism. The sigma factor of the flagellar system, FliA, has a negative effect on the expression levels of seven plasmid-encoded virulence genes in addition to its positive effect on the expression levels of eight of the flagellar operons. This study investigates the phenotypes of <it>flhD </it>and <it>fliA </it>mutants that result from the complex gene regulation.</p> <p>Results</p> <p>Phenotypes relating to central metabolism were investigated with Phenotype MicroArrays. Compared to the wild-type strain, isogenic <it>flhD </it>and <it>fliA </it>mutants exhibited increased growth on purines and reduced growth on N-acetyl-D-glucosamine and D-mannose, when used as a sole carbon source. Both mutants grew more poorly on pyrimidines and L-histidine as sole nitrogen source. Several intermediates of the tricarboxylic acid and the urea cycle, as well as several dipeptides, provided differential growth conditions for the two mutants. Gene expression was determined for selected genes and correlated with the observed phenotypes. Phenotypes relating to virulence were determined with the chicken embryo lethality assay. The assay that was previously established for <it>Escherichia coli </it>strains was modified for <it>Y. enterocolitica</it>. The <it>flhD </it>mutant caused reduced chicken embryo lethality when compared to wild-type bacteria. In contrast, the <it>fliA </it>mutant caused wild-type lethality. This indicates that the virulence phenotype of the <it>flhD </it>mutant might be due to genes that are regulated by FlhD/FlhC but not FliA, such as those that encode the flagellar type III secretion system.</p> <p>Conclusion</p> <p>Phenotypes of <it>flhD </it>and <it>fliA </it>mutants are related to central metabolism and virulence and correlate with gene regulation.</p