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A solution for the two-dimensional transport equation for photons and electrons in a rectangular domain by the Laplace transform technique

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International Journal of Nuclear Energy Science and Technology 2010年第1期5卷 25-40页

作者： Do Amaral Rodriguez, Bárbara D. Vilhena, Marco Túllio Borges, Volnei Instituto de Matemática Estatística e Física Universidade Federal Do Rio Grande - FURG Campus Carreiros Av. Itália Km 8 s/n Rio Grande Rio Grande do Sul Brazil Pure and Applied Mathematics Department Universidade Federal Do Rio Grande Do sul - UFRGS Avenida Bento Gonçalves 9500 Porto Alegre Rio Grande do Sul Brazil Mechanical Engineering Post-Graduation Program Universidade Federal Rio Grande Do sul - UFRGS Rua Sarmento Leite 425 sala 314 Porto Alegre Rio Grande do Sul Brazil

In the first part of this paper, we describe a review in the Laplace transform technique applied to SN two-dimensional transport equation in a rectangular domain considering Compton scattering. In Compton scattering the incident photon interacts with an electron of the irradiated medium, giving the electron kinetic energy, and also producing a scattered photon. In order to track that electron, in the second part of this paper, we apply the P N approximation to X,Y-geometry electron transport problems. In this derivation, the energy deposited by the free electron is taken into account. To reach this objective we solve two model problems: the first one for the transport of photons, assuming the Klein-Nishina scattering kernel as the scattering differential cross-section as well as the multigroup model in the energy variable;and the second one for the transport of free electrons considering the screened Rutherford scattering kernel. The results are presented under absorbed energy form in several points of interest. We report numerical simulations and comparisons with results obtained by using the Geant4 version 9.1 program which applies the Monte Carlo's technique to low energy libraries for both two-dimensional problems. Copyright © 2010 Inderscience Enterprises Ltd.

关键词： Photons

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Exact constructions of a family of dense periodic packings of tetrahedra

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Physical Review E 2010年第4期81卷 041310-041310页

作者： S. Torquato Y. Jiao Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08540 USA Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08544 USA

The determination of the densest packings of regular tetrahedra (one of the five Platonic solids) is attracting great attention as evidenced by the rapid pace at which packing records are being broken and the fascinating packing structures that have emerged. Here we provide the most general analytical formulation to date to construct dense periodic packings of tetrahedra with four particles per fundamental cell. This analysis results in six-parameter family of dense tetrahedron packings that includes as special cases recently discovered “dimer” packings of tetrahedra, including the densest known packings with density ϕ=40004671=0.856347…. This study strongly suggests that the latter set of packings are the densest among all packings with a four-particle basis. Whether they are the densest packings of tetrahedra among all packings is an open question, but we offer remarks about this issue. Moreover, we describe a procedure that provides estimates of upper bounds on the maximal density of tetrahedron packings, which could aid in assessing the packing efficiency of candidate dense packings.

关键词： constructions family tetrahedra tetrahedrons family Dense Platonic solid

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Dislocation climb strengthening in systems with immobile obstacles: Three-dimensional level-set simulation study

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Physical Review B 2010年第5期81卷 054104-054104页

作者： Zi Chen Kevin T. Chu David J. Srolovitz Jeffrey M. Rickman Mikko P. Haataja Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08540 USA Princeton Institute for the Science and Technology of Materials (PRISM) Princeton University Princeton New Jersey 08540 USA Vitamin D Inc. Menlo Park California 94025 USA Institute of High Performance Computing Singapore Singapore Department of Materials Science and Engineering Lehigh University Bethlehem Pennsylvania 18015 USA Department of Physics Lehigh University Bethlehem Pennsylvania 18015 USA Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08540 USA

We employ a parallel, three-dimensional level-set code to simulate the dynamics of isolated dislocation lines and loops in an obstacle-rich environment. This system serves as a convenient prototype of those in which extended, one-dimensional objects interact with obstacles and the out-of-plane motion of these objects is key to understanding their pinning-depinning behavior. In contrast to earlier models of dislocation motion, we incorporate long-ranged interactions among dislocation segments and obstacles to study the effect of climb on dislocation dynamics in the presence of misfitting penetrable obstacles/solutes, as embodied in an effective climb mobility. Our main observations are as follows. First, increasing climb mobility leads to more effective pinning by the obstacles, implying increased strengthening. Second, decreasing the range of interactions significantly reduces the effect of climb. The dependence of the critical stress on obstacle concentration and misfit strength is also explored and compared with existing models. In particular, our results are shown to be in reasonable agreement with the Friedel-Suzuki theory. Finally, the limitations inherent in the simplified model employed here, including the neglect of some lattice effects and the use of a coarse-grained climb mobility, are discussed.

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Critical dynamics in multicomponent lipid membranes

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Physical Review E 2009年第2期80卷 020902(R)-020902(R)页

作者： Mikko Haataja Department of Mechanical and Aerospace Engineering Princeton Institute for the Science and Technology of Materials (PRISM) and Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08544 USA

The formation and dynamics of spatially extended compositional domains in multicomponent lipid membranes both in vivo and in vitro lie at the heart of many important biological and biophysical phenomena. While the thermodynamic basis for domain formation has been explored extensively in the past, the roles of membrane and exterior fluid hydrodynamics on domain formation kinetics have received less attention. A case in point is the impact of hydrodynamics on the dynamics of compositional heterogeneities in lipid membranes in the vicinity of a critical point. In this Rapid Communication it is argued that the asymptotic dynamic behavior of a lipid membrane system in the vicinity of a critical point is strongly influenced by hydrodynamic interactions. More specifically, a mode-coupling argument is developed which predicts a scaling behavior of lipid transport coefficients near the critical point for both symmetric and asymmetric bilayers immersed in a bulk fluid.

关键词： Hydrodynamics

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Connector faculty: A friendly face for early engineering students

Connector faculty: A friendly face for early engineering stu...

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2009 ASEE Annual Conference and Exposition

作者： Briedis, Daina Buch, Neeraj Collins-Eaglin, Jan Ehrlich, Nathaniel Fleming, Denise Hinds, Timothy Sticklen, Jon Urban-Lurain, Mark Wolff, Thomas Department of Chemical Engineering and Materials Science Michigan State University United States Department of Civil and Environmental Engineering Michigan State University United States Cornerstone Engineering and Residential Experience Program Michigan State University United States Michigan State University United States United States College of Engineering Michigan State University United States Michigan State University College of Engineering Undergraduate Studies Department of Mechanical Engineering United States Applied Engineering Sciences College of Engineering Michigan State University United States Computer Science and Engineering Department Michigan State University United States Division of Science and Mathematics Education College of Natural Science Michigan State University United States Engineering for Undergraduate Studies Michigan State University United States

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Optimal packings of superballs

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Physical Review E 2009年第4期79卷 041309-041309页

作者： Y. Jiao F. H. Stillinger S. Torquato Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08540 USA

Dense hard-particle packings are intimately related to the structure of low-temperature phases of matter and are useful models of heterogeneous materials and granular media. Most studies of the densest packings in three dimensions have considered spherical shapes, and it is only more recently that nonspherical shapes (e.g., ellipsoids) have been investigated. Superballs (whose shapes are defined by |x1|2p+|x2|2p+|x3|2p≤1) provide a versatile family of convex particles (p≥0.5) with both cubic-like and octahedral-like shapes as well as concave particles (0

关键词： Temperature

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Dense packings of polyhedra: Platonic and Archimedean solids

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Physical Review E 2009年第4期80卷 041104-041104页

作者： S. Torquato Y. Jiao Department of Chemistry Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08540 USA Department of Mechanical and Aerospace Engineering Princeton University Princeton New Jersey 08544 USA

Understanding the nature of dense particle packings is a subject of intense research in the physical, mathematical, and biological sciences. The preponderance of previous work has focused on spherical particles and very little is known about dense polyhedral packings. We formulate the problem of generating dense packings of nonoverlapping, nontiling polyhedra within an adaptive fundamental cell subject to periodic boundary conditions as an optimization problem, which we call the adaptive shrinking cell (ASC) scheme. This optimization problem is solved here (using a variety of multiparticle initial configurations) to find the dense packings of each of the Platonic solids in three-dimensional Euclidean space R3, except for the cube, which is the only Platonic solid that tiles space. We find the densest known packings of tetrahedra, icosahedra, dodecahedra, and octahedra with densities 0.823…, 0.836…, 0.904…, and 0.947…, respectively. It is noteworthy that the densest tetrahedral packing possesses no long-range order. Unlike the densest tetrahedral packing, which must not be a Bravais lattice packing, the densest packings of the other nontiling Platonic solids that we obtain are their previously known optimal (Bravais) lattice packings. We also derive a simple upper bound on the maximal density of packings of congruent nonspherical particles and apply it to Platonic solids, Archimedean solids, superballs, and ellipsoids. Provided that what we term the “asphericity” (ratio of the circumradius to inradius) is sufficiently small, the upper bounds are relatively tight and thus close to the corresponding densities of the optimal lattice packings of the centrally symmetric Platonic and Archimedean solids. Our simulation results, rigorous upper bounds, and other theoretical arguments lead us to the conjecture that the densest packings of Platonic and Archimedean solids with central symmetry are given by their corresponding densest lattice packings. This can be regarded to be

关键词： Optimization

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Pre-heated substrate effects on melt-mediated laser crystallization of NiTi thin films

Pre-heated substrate effects on melt-mediated laser crystall...

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ICALEO 2008 - 27th International Congress on Applications of Lasers and Electro-Optics

作者： Birnbaum, Andrew J. Chung, Ui-Jin Huang, Xu Ramirez, Ainissa G. Im, James S. Yao, Y. Lawrence Mechanical Engineering Department Columbia University New York NY 10027 United States Program in Materials Science Department of Applied Physics and Applied Mathematics Columbia University New York NY 10027 United States Mechanical Engineering Department Yale University New Haven CT 06511 United States

Amorphous sputter-deposited NiTi thin films were subjected to pulsed, melt-mediated laser crystallization techniques to engineer their microstructure. The effects of laser processing of pre-heated films are examined. Laser processing of films at an elevated temperature has a significant effect on the rate with which solidification occurs and therefore may be used as an added parameter to control the resulting microstructure. It is seen that the temperature at which processing is carried out has significant implications for the resulting phase and microstructure, and therefore mechanical properties. Furthermore, the microstructural effects of varying incident laser energy density are examined via atomic force microscopy (AFM), scanning electron microscopy (SEM) and x-ray diffraction (XRD), and mechanical/shape memory properties are characterized via nanoindentation.

关键词： Microstructure

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Domain Formation in the Plasma Membrane: Roles of Nonequilibrium Lipid Transport and Membrane Proteins

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Physical Review Letters 2008年第17期100卷 178102-178102页

作者： Jun Fan Maria Sammalkorpi Mikko Haataja Department of Mechanical and Aerospace Engineering Princeton Institute for the Science and Technology of Materials (PRISM) and Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08544 USA

Compositional lipid domains (“lipid rafts”) in plasma membranes are believed to be important components of many cellular processes. The mechanisms by which cells regulate the sizes and lifetimes of these spatially extended domains are poorly understood at the moment. Here we show that the competition between phase separation in an immiscible lipid system and active cellular lipid transport processes naturally leads to the formation of such domains. Furthermore, we demonstrate that local interactions with immobile membrane proteins can spatially localize the rafts and lead to further clustering.

关键词： Lipids

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How to match theoretical and experimental boundary conditions of a cantilever beam 7

How to match theoretical and experimental boundary condition...

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7th European Conference on Structural Dynamics, EURODYN 2008

作者： Ritto, Thiago Aguiar, Romulo Sampaio, Rubens Cataldo, Edson Mechanical Engineering Department PUC-Rio Rua Marquês de São Vicente Rua Marque͉ de São Vicente 225 Gávea22453-900 Brazil Graduate Program in Telecommunications Engineering Applied Mathematics Department Rua Mário Santos Braga S/N Centro Niterói24020-140 Brazil

ISBN: (纸本)9780854328826

The purpose of this paper is to describe how to match experimental and theoretical frequencies of a cantilever beam through a prescribed error tolerance. In some cases there is a clear difference between a clamped boundary condition in a real system or in an experiment (called in this article as e-clamped condition) and the clamped condition as regularly modeled in theory (the t-clamped condition). In such occasions the e-clamped (experimental) might not follow the t-clamped (theoretical) condition. Actually, it hardly will. Depending on the e-clamped boundary condition the error between the natural frequencies of t-clamped and e-clamped might be greater than 10%. This work presents a theoretical model that relaxes the boundary condition of zero rotation. One parameter, a torsional stiffness at the fixed end of the beam, is used in order to fit the natural frequencies of the numerical simulations with the experimental data. The idea is to identify the torsional stiffness that minimizes the error between the numerical and experimental frequencies. For the numerical simulations, the Finite Element Method (with Timoshenko beam element) is used, and for the experiments, multiple rubber layers are mounted to the clamped side of the beam so that different e-clamped conditions can be analyzed and reproduced if necessary. The numerical and the experimental results show excellent agreement.

关键词： Boundary conditions

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