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On the relationship between r and R₀ and its role in the bifurcation of stable equilibria of Darwinian matrix models

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Journal of Biological Dynamics 2011年第3期5卷 277-297页

作者： Cushing, J.M. Department of Mathematics Interdisciplinary Program in Applied Mathematics University of Arizona Tucson AZ 85721 United States

If the demographic parameters in a matrix model for the dynamics of a structured population are dependent on a parameter u, then the population growth rate r = r(u) and the net reproductive number R₀ = R₀(u) are functions of u. For a general matrix model, we showthat r and R₀ share critical values and extrema at values u = u^* for which r(u^*) = R₀(u^*) = 1. This allows us to re-interpret, in terms of the more analytically tractable quantity R₀, a fundamental bifurcation theorem for non-linear Darwinian matrix models from the evolutionary game theory that concerns the destabilization of the extinction equilibrium and creation of positive equilibria. Two illustrations are given: a theoretical study of trade-offs between fertility and survivorship in the evolution of an evolutionarily stable strategies and an application to an experimental study of the evolution to a genetic polymorphism. © 2011 Taylor & Francis.

关键词： Bifurcation Darwinian matrix models Equilibria Net reproductive number The evolutionary game theory

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Shear flow, phase change and matched asymptotic expansions: Pattern formation in mushy layers

Shear flow, phase change and matched asymptotic expansions: ...

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作者： Neufeld, Jerome A. Wettlaufer, J.S. Institute of Theoretical Geophysics Department of Applied Mathematics and Theoretical Physics University of Cambridge CMS Wilberforce Road Cambridge CB3 0WA United Kingdom Department of Geology and Geophysics Yale University New Haven CT 06520 United States Department of Physics Yale University New Haven CT 06520 United States Program in Applied Mathematics Yale University New Haven CT 06520 United States

In many scientific and engineering problems the solidification of an alloy leads to a highly convoluted crystalline matrix modeled as a thermodynamically controlled reactive porous medium called a mushy layer. We analyze the interaction of an external shear flow with a solidifying mushy layer through a corrugated mushliquid interface. We find that the external flow can drive forced convective motions within the mushy layer resulting in the formation of a pattern of dissolution and solidification features transverse to the overall flow. Here we seek to lay bare the underlying processes through a systematic comparison of matched asymptotic expansions and numerical solutions. The success of our modeling effort draws substantially upon understanding gleaned from the fluid mechanics of boundary layers and the theory of multi-component solidification. The results have a broad range of implications in geophysics and materials science. © 2010 Elsevier B.V. All rights reserved.

关键词： Shear flow

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59.1: Invited paper: LTPS backplane technologies for AMLCDs and AMOLEDs

59.1: Invited paper: LTPS backplane technologies for AMLCDs ...

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作者： Kim, Chi Woo Jung, Jin Goo Choi, Jae Beom Kim, Deok Hui Yi, Chung Kim, Hye Dong Choi, Yun Ho Im, James Process Development Team 1 Samsung Mobile Display Co. Ltd. Cheonan-City Chungcheongnam-Do Korea Republic of Program in Materials Science and Engineering Department of Applied Physics and Applied Mathematics Columbia University New York NY 10027 United States

In this paper, we review various LTPS backplane technologies based on laser-crystallization and other related methods that have been applied to AMLCD and AMOLED displays. The TFT performances obtained by different melt-mediated crystallization methods with excimer laser and solid phase crystallization will be compared. The technical issues of the image quality and the resolution will be discussed. © 2011 SID.

关键词： Excimer lasers

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Minimum time control of helicopter UAVs using computational dynamic optimization

Minimum time control of helicopter UAVs using computational ...

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9th IEEE International Conference on Control and Automation, ICCA 2011

作者： Tang, K. Wang, B. Kang, W. Chen, B. Internship Program Naval Postgraduate School Monterey CA 93943 United States Department of Electrical and Computer Engineering National University of Singapore Singapore 117576 Singapore Department of Applied Mathematics Naval Postgraduate School Monterey CA 93943 United States

ISBN: (纸本)9781457714757

This paper focuses on the problem of minimum time trajectory planning for helicopter UAVs. It is formulated as a nonlinear optimal control subject to the dynamics and limitations of helicopter UAVs. The dynamical system is defined by a set of fifteen states nonlinear differential equations developed for HeLion, a UAV helicopter constructed in National University of Singapore (NUS). The problem is then solved numerically using pseudospectral method for dynamic optimization. The results show that minimum time trajectories are highly nonlinear that require complicated maneuvering. © 2011 IEEE.

关键词： Nonlinear equations

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Ice-lens formation and geometrical supercooling in soils and other colloidal materials

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Physical Review E 2011年第4期84卷 041402-041402页

作者： Robert W. Style Stephen S. L. Peppin Alan C. F. Cocks J. S. Wettlaufer Department of Geology and Geophysics Department of Physics and Program in Applied Mathematics Yale University New Haven Connecticut USA and NORDITA Roslagstullsbacken 23 SE-10691 Stockholm Sweden

We present a physically intuitive model of ice-lens formation and growth during the freezing of soils and other dense, particulate suspensions. Motivated by experimental evidence, we consider the growth of an ice-filled crack in a freezing soil. At low temperatures, ice in the crack exerts large pressures on the crack walls that will eventually cause the crack to split open. We show that the crack will then propagate across the soil to form a new lens. The process is controlled by two factors: the cohesion of the soil and the geometrical supercooling of the water in the soil, a new concept introduced to measure the energy available to form a new ice lens. When the supercooling exceeds a critical amount (proportional to the cohesive strength of the soil) a new ice lens forms. This condition for ice-lens formation and growth does not appeal to any ad hoc, empirical assumptions, and explains how periodic ice lenses can form with or without the presence of a frozen fringe. The proposed mechanism is in good agreement with experiments, in particular explaining ice-lens pattern formation and surges in heave rate associated with the growth of new lenses. Importantly for systems with no frozen fringe, ice-lens formation and frost heave can be predicted given only the unfrozen properties of the soil. We use our theory to estimate ice-lens growth temperatures obtaining quantitative agreement with the limited experimental data that are currently available. Finally we suggest experiments that might be performed in order to verify this theory in more detail. The theory is generalizable to complex natural-soil scenarios and should therefore be useful in the prediction of macroscopic frost-heave rates.

关键词： SOIL absorption & adsorption SOIL freezing ICE formation & growth SUPERCOOLING CRACK propagation (Fracture mechanics) THEORY

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Estimating functional agent-based models: An application to bid shading in online markets format 11

Estimating functional agent-based models: An application to ...

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13th Annual Genetic and Evolutionary Computation Conference - Companion Publication, GECCO 2011 Companion

作者： Guo, Wei Jank, Wolfgang Rand, William Applied Mathematics and Statistics and Scientific Computation Program Department of Mathematics University of Maryland College Park MD United States Department of Decision Operations and Information Technology Robert H. Smith School of Business University of Maryland College Park MD United States Department of Marketing Robert H. Smith School of Business University of Maryland College Park MD United States

ISBN: (纸本)9781450306904

Bid shading is a common strategy in online auctions to avoid the "winner's curse". While almost all bidders shade their bids, at least to some degree, it is impossible to infer the degree and volume of shaded bids directly from observed bidding data. In fact, most bidding data only allows us to observe the resulting price process, i.e. whether prices increase fast (due to little shading) or whether they slow down (when all bidders shade their bids). In this work, we propose an agent-based model that simulates bidders with different bidding strategies and their interaction with one another. We calibrate that model (and hence estimate properties about the propensity and degree of shaded bids) by matching the emerging simulated price process with that of the observed auction data using genetic algorithms. From a statistical point of view, this is challenging because we match functional draws from simulated and real price processes. We propose several competing fitness functions and explore how the choice alters the resulting ABM calibration. We apply our model to the context of eBay auctions for digital cameras and show that a balanced fitness function yields the best results. © 2011 ACM.

关键词： Calibration

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The Transmission Line Matrix method applied to the sound propagation through a 3D reconstructed vocal tract using Magnetic Resonance images

The Transmission Line Matrix method applied to the sound pro...

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18th International Congress on Sound and Vibration 2011, ICSV 2011

作者： Brandão, Alexandre S. Cataldo, Edson Leta, Fabiana R. Mechanical Engineering Department Mechanical Engineering Post-Graduation Program Universidade Federal Fluminense 24210-240 São Domingos Niterói RJ Brazil Applied Mathematics Department Universidade Federal Fluminense 24020-140 Valonguinho Niterói RJ Brazil

ISBN: (纸本)9781618392596

In this paper, the Transmission Line Method (TLM) is applied to generate a voice signal by simulating the acoustic propagation of a glottal signal, obtained by inverse filtering of the voice signal, through an /a/ vowel shaped vocal tract uniform TLM mesh. The vocal tract TLM mesh is constructed over a segmented Magnetic Resonance(MR) volume image. The tools for segmentation, mesh extraction and the TLM itself were implemented as part of the ModaVox program, which is an open source application constructed during the research presented here. The methodology was validated, firstly, simulating the acoustic propagation of a probe signal through tube model meshes. Then, the same probe signal was used as the input for the vocal tract TLM mesh and the resonant frequencies obtained by simulation were compared with those of the real vocal tract. Finally, the glottal signal is used as input for the vocal tract mesh and the reflective boundary conditions of the vocal tract walls were designed to reproduce the consistency of the soft tissues. The voice signal simulated was then compared with the original voice signal generated by the subject when his vocal tract was imaged.

关键词： Magnetic resonance

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Characterization of heterogeneous response of Al bicrystal subject to micro scale laser shock peening

Characterization of heterogeneous response of Al bicrystal s...

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作者： Vukelic, S. Noyan, I.C. Kysar, J.W. Yao, Y.L. Mechanical Engineering Department Bucknell University Pennsylvania PA 17837 United States Program in Materials Science Department of Applied Physics and Applied Mathematics Columbia University New York NY 10027 United States Mechanical Engineering Department Columbia University New York NY 10027 United States

This letter shows the ability to perform character-ization of the strain field in an aluminium bicrystal subject to plane strain condition induced by micro scale laser shock peening. Intensity contrast method, previously used in topographic measurements of strain fields in thin films is employed here. Our results show that this method is applicable for measurements of the plastically deformed bulk materials. Moreover, heterogeneous response of the grain boundary is observed as periodic nature of deformation. © Society for Experimental Mechanics 2010.

关键词： X ray diffraction

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Characterization of heterogeneous response of Al bicrystal subject to micro scale laser shock peening

Characterization of heterogeneous response of Al bicrystal s...

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作者： Vukelic, S. Noyan, I.C. Kysar, J.W. Yao, Y.L. Mechanical Engineering Department Bucknell University Pennsylvania. PA 17837 United States Program in Materials Science Department of Applied Physics and Applied Mathematics Columbia University New York NY 10027 United States Mechanical Engineering Department Columbia University New York NY 10027 United States

This letter shows the ability to perform characterization of the strain field in an aluminium bicrystal subject to plane strain condition induced by micro scale laser shock peening. Intensity contrast method, previously used in topographic measurements of strain fields in thin films is employed here. Our results show that this method is applicable for measurements of the plastically deformed bulk materials. Moreover, heterogeneous response of the grain boundary is observed as periodic nature of deformation. © Society for Experimental Mechanics 2010.

关键词： X ray diffraction

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Competitive outcomes changed by evolution

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Journal of Biological Dynamics 2011年第3期5卷 227-252页

作者： Rael, R.C. Vincent, T.L. Cushing, J.M. Interdisciplinary Program in Applied Mathematics University of Arizona Tucson AZ United States Aerospace and Mechanical Engineering University of Arizona Tucson AZ United States Department of Mathematics and Interdisciplinary Program in Applied Mathematics University of Arizona Tucson AZ United States

When evolution plays a role, population dynamic models alone are not sufficient for determining the outcome of multi-species *** an expansion of Maynard Smith's concept of an evolutionarily stable strategy, evolutionary game theory (EGT) combines population and evolutionary dynamics so that natural selection becomes a dynamic game with phenotypic traits as strategies. Using EGT,we showhowevolution can change the outcome of the interaction between two competing *** are particularly interested in situations where the interaction changes from one of competitive exclusion to one of coexistence and where the interaction changes from the exclusion of one species to the exclusion of the other. There are two crucial factors that determine whether or not such events can occur: the rate of evolution (which is proportional to the amount of variability in phenotypic traits within a species) and what we term the boxer effect, a phenomenon that concerns how the intensity of interspecies competition relates to species' trait differences. We apply the theory to data from two historical competition experiments involving species of flour beetle from the genus Tribolium. In both applications, we show how EGT can explain certain seemingly 'anomalous' experimental results. © 2011 Taylor & Francis.

关键词： Competition Competitive coexistence Competitive exclusion Evolutionarily stable strategy Evolutionary game theory

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