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Applied Mathematics (applied + mathematics)
Selected AbstractsOn pressure separation algorithms (PSepA) for improving the accuracy of incompressible flow simulationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2009S. Turek Abstract We investigate a special technique called ,pressure separation algorithm' (PSepA) (see Applied Mathematics and Computation 2005; 165:275,290 for an introduction) that is able to significantly improve the accuracy of incompressible flow simulations for problems with large pressure gradients. In our numerical studies with the computational fluid dynamics package FEATFLOW (www.featflow.de), we mainly focus on low-order Stokes elements with nonconforming finite element approximations for the velocity and piecewise constant pressure functions. However, preliminary numerical tests show that this advantageous behavior can also be obtained for higher-order discretizations, for instance, with Q2/P1 finite elements. We analyze the application of this simple, but very efficient, algorithm to several stationary and nonstationary benchmark configurations in 2D and 3D (driven cavity and flow around obstacles), and we also demonstrate its effect to spurious velocities in multiphase flow simulations (,static bubble' configuration) if combined with edge-oriented, resp., interior penalty finite element method stabilization techniques. Copyright © 2008 John Wiley & Sons, Ltd. [source] Parasites in food webs: the ultimate missing linksECOLOGY LETTERS, Issue 6 2008Kevin D. Lafferty Abstract Parasitism is the most common consumer strategy among organisms, yet only recently has there been a call for the inclusion of infectious disease agents in food webs. The value of this effort hinges on whether parasites affect food-web properties. Increasing evidence suggests that parasites have the potential to uniquely alter food-web topology in terms of chain length, connectance and robustness. In addition, parasites might affect food-web stability, interaction strength and energy flow. Food-web structure also affects infectious disease dynamics because parasites depend on the ecological networks in which they live. Empirically, incorporating parasites into food webs is straightforward. We may start with existing food webs and add parasites as nodes, or we may try to build food webs around systems for which we already have a good understanding of infectious processes. In the future, perhaps researchers will add parasites while they construct food webs. Less clear is how food-web theory can accommodate parasites. This is a deep and central problem in theoretical biology and applied mathematics. For instance, is representing parasites with complex life cycles as a single node equivalent to representing other species with ontogenetic niche shifts as a single node? Can parasitism fit into fundamental frameworks such as the niche model? Can we integrate infectious disease models into the emerging field of dynamic food-web modelling? Future progress will benefit from interdisciplinary collaborations between ecologists and infectious disease biologists. [source] Extension of a combined analytical/numerical initial value problem solver for unsteady periodic flowINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2002Lawrence J. De Chant Abstract Here we describe analytical and numerical modifications that extend the Differential Reduced Ejector/ mixer Analysis (DREA), a combined analytical/numerical, multiple species ejector/mixing code developed for preliminary design applications, to apply to periodic unsteady flow. An unsteady periodic flow modelling capability opens a range of pertinent simulation problems including pulse detonation engines (PDE), internal combustion engine ICE applications, mixing enhancement and more fundamental fluid dynamic unsteadiness, e.g. fan instability/vortex shedding problems. Although mapping between steady and periodic forms for a scalar equation is a classical problem in applied mathematics, we will show that extension to systems of equations and, moreover, problems with complex initial conditions are more challenging. Additionally, the inherent large gradient initial condition singularities that are characteristic of mixing flows and that have greatly influenced the DREA code formulation, place considerable limitations on the use of numerical solution methods. Fortunately, using the combined analytical,numerical form of the DREA formulation, a successful formulation is developed and described. Comparison of this method with experimental measurements for jet flows with excitation shows reasonable agreement with the simulation. Other flow fields are presented to demonstrate the capabilities of the model. As such, we demonstrate that unsteady periodic effects can be included within the simple, efficient, coarse grid DREA implementation that has been the original intent of the DREA development effort, namely, to provide a viable tool where more complex and expensive models are inappropriate. Copyright © 2002 John Wiley & Sons, Ltd. [source] Inverse problems in quantum chemistryINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 11 2009Jacek Karwowski Abstract Inverse problems constitute a branch of applied mathematics with well-developed methodology and formalism. A broad family of tasks met in theoretical physics, in civil and mechanical engineering, as well as in various branches of medical and biological sciences has been formulated as specific implementations of the general theory of inverse problems. In this article, it is pointed out that a number of approaches met in quantum chemistry can (and should) be classified as inverse problems. Consequently, the methodology used in these approaches may be enriched by applying ideas and theorems developed within the general field of inverse problems. Several examples, including the RKR method for the construction of potential energy curves, determining parameter values in semiempirical methods, and finding external potentials for which the pertinent Schrödinger equation is exactly solvable, are discussed in detail. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009 [source] The radial basis functions method for identifying an unknown parameter in a parabolic equation with overspecified dataNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2007Mehdi Dehghan Abstract Parabolic partial differential equations with overspecified data play a crucial role in applied mathematics and engineering, as they appear in various engineering models. In this work, the radial basis functions method is used for finding an unknown parameter p(t) in the inverse linear parabolic partial differential equation ut = uxx + p(t)u + ,, in [0,1] × (0,T], where u is unknown while the initial condition and boundary conditions are given. Also an additional condition ,01k(x)u(x,t)dx = E(t), 0 , t , T, for known functions E(t), k(x), is given as the integral overspecification over the spatial domain. The main approach is using the radial basis functions method. In this technique the exact solution is found without any mesh generation on the domain of the problem. We also discuss on the case that the overspecified condition is in the form ,0s(t)u(x,t)dx = E(t), 0 < t , T, 0 < s(t) < 1, where s and E are known functions. Some illustrative examples are presented to show efficiency of the proposed method. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 [source] Craniofacial imaging informatics and technology developmentORTHODONTICS & CRANIOFACIAL RESEARCH, Issue 2003MW Vannier Structured Abstract Author, Vannier MW Purpose , ,Craniofacial imaging informatics' refers to image and related scientific data from the dentomaxillofacial complex, and application of ,informatics techniques' (derived from disciplines such as applied mathematics, computer science and statistics) to understand and organize the information associated with the data. Method , Major trends in information technology determine the progress made in craniofacial imaging and informatics. These trends include industry consolidation, disruptive technologies, Moore's law, electronic atlases and on-line databases. Each of these trends is explained and documented, relative to their influence on craniofacial imaging. Results , Craniofacial imaging is influenced by major trends that affect all medical imaging and related informatics applications. The introduction of cone beam craniofacial computed tomography scanners is an example of a disruptive technology entering the field. An important opportunity lies in the integration of biologic knowledge repositories with craniofacial images. Conclusion , The progress of craniofacial imaging will continue subject to limitations imposed by the underlying technologies, especially imaging informatics. Disruptive technologies will play a major role in the evolution of this field. [source] Modeling, Analysis, and Simulation of Biofilm Formation and DecayPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003HJ Eberl Dr. In this article, we give a brief overview of our recent work on continuum mechanical modelling and simulation of microbial films. This comprises some classical tasks of applied mathematics such as computational fluid dynamics, analysis of partial differential equations, and mathematical biology. [source] Models for Bounded Systems with Continuous DynamicsBIOMETRICS, Issue 3 2009Amanda R. Cangelosi Summary Models for natural nonlinear processes, such as population dynamics, have been given much attention in applied mathematics. For example, species competition has been extensively modeled by differential equations. Often, the scientist has preferred to model the underlying dynamical processes (i.e., theoretical mechanisms) in continuous time. It is of both scientific and mathematical interest to implement such models in a statistical framework to quantify uncertainty associated with the models in the presence of observations. That is, given discrete observations arising from the underlying continuous process, the unobserved process can be formally described while accounting for multiple sources of uncertainty (e.g., measurement error, model choice, and inherent stochasticity of process parameters). In addition to continuity, natural processes are often bounded; specifically, they tend to have nonnegative support. Various techniques have been implemented to accommodate nonnegative processes, but such techniques are often limited or overly compromising. This article offers an alternative to common differential modeling practices by using a bias-corrected truncated normal distribution to model the observations and latent process, both having bounded support. Parameters of an underlying continuous process are characterized in a Bayesian hierarchical context, utilizing a fourth-order Runge,Kutta approximation. [source] | |||||||||||||