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Mathematical Description (mathematical + description)
Selected AbstractsInfluence of crop edges on movement of generalist predators: a diffusion approachAGRICULTURAL AND FOREST ENTOMOLOGY, Issue 1 2002Riccardo Bommarco Abstract 1,Diffusion models were applied to recapture data for the generalist predator Pterostichus cupreus (Coleoptera: Carabidae) moving between two adjacent crop habitats (perennial ley and annual barley) first excluding, and then including, terms in the model quantifying the influences of edges on beetle movements. 2,Adult beetles were released at the centre of experimental 3 × 3 m plots that overlapped the edge separating perennial ley (mixed perennial crop of grass and clover) and annual barley crops, both early and later in the growing season. 3,Mathematical description of the data improved when the attractive or repulsive effects of habitat edges on dispersal were considered in the model. 4,Early in the season, when a sharp habitat edge was present, P. cupreus beetles appeared ,attracted' to ley. 5,Diffusion rates were consistently higher in barley than in ley early in the season, and vice versa late in the season. These patterns were probably linked to variation in prey availability. 6,Despite the risk of experiencing food limitation in the annual crop, our analyses suggest that these beetles regularly move from ley into the early barley habitat and then continue to disperse within the barley, providing opportunities for enhanced biological control of pest species. [source] Kinetics of intra- and intermolecular zymogen activation with formation of an enzyme,zymogen complexFEBS JOURNAL, Issue 1 2005Matilde Esther Fuentes A mathematical description was made of an autocatalytic zymogen activation mechanism involving both intra- and intermolecular routes. The reversible formation of an active intermediary enzyme,zymogen complex was included in the intermolecular activation route, thus allowing a Michaelis,Menten constant to be defined for the activation of the zymogen towards the active enzyme. Time,concentration equations describing the evolution of the species involved in the system were obtained. In addition, we have derived the corresponding kinetic equations for particular cases of the general model studied. Experimental design and kinetic data analysis procedures to evaluate the kinetic parameters, based on the derived kinetic equations, are suggested. The validity of the results obtained were checked by using simulated progress curves of the species involved. The model is generally good enough to be applied to the experimental kinetic study of the activation of different zymogens of physiological interest. The system is illustrated by following the transformation kinetics of pepsinogen into pepsin. [source] The importance of being persistent: heterogeneity of bacterial populations under antibiotic stressFEMS MICROBIOLOGY REVIEWS, Issue 4 2009Orit Gefen Abstract While the DNA sequence is largely responsible for transmitting phenotypic traits over evolutionary time, organisms are also considerably affected by phenotypic variations that persist for more than one generation, with no direct change in the organisms' DNA sequence. In contrast to genetic variation, which is passed on over many generations, the phenotypic variation generated by nongenetic mechanisms is difficult to study due to the inherently limited life time of states that are not encoded in the DNA sequence, but makes it possible for the ,memory' of past environments to influence future organisms. One striking example of phenotypic variation is the phenomenon of bacterial persistence, whereby genetically identical bacterial populations respond heterogeneously to antibiotic treatment. Our aim is to review several experimental and theoretical approaches to the study of persistence. We define persistence as a characteristic of a heterogeneous bacterial population that is taken as a generic example through which we illustrate the approach and study the dynamics of population variability. The clinical and evolutionary implications of persistence are discussed in light of the mathematical description. This approach should be of relevance to the study of other phenomena in which nongenetic variability is involved, such as cellular differentiation or the response of cancer cells to treatment. [source] On the Application of Inductive Machine Learning Tools to Geographical AnalysisGEOGRAPHICAL ANALYSIS, Issue 2 2000Mark Gahegan Inductive machine learning tools, such as neural networks and decision trees, offer alternative methods for classification, clustering, and pattern recognition that can, in theory, extend to the complex or "deep" data sets that pervade geography. By contrast, traditional statistical approaches may fail, due to issues of scalability and flexibility. This paper discusses the role of inductive machine learning as it relates to geographical analysis. The discussion presented is not based on comparative results or on mathematical description, but instead focuses on the often subtle ways in which the various inductive learning approaches differ operationally, describing (1) the manner in which the feature space is partitioned or clustered, (2) the search mechanisms employed to identify good solutions, and (3) the different biases that each technique imposes. The consequences arising from these issues, when considering complex geographic feature spaces, are then described in detail. The overall aim is to provide a foundation upon which reliable inductive analysis methods can be constructed, instead of depending on piecemeal or haphazard experimentation with the various operational criteria that inductive learning tools call for. Often, it would appear that these criteria are not well understood by practitioners in the geographic sphere, which can lead to difficulties in configuration and operation, and ultimately to poor performance. [source] Mathematical simulation of calcimine deliming in the production of gelatinAICHE JOURNAL, Issue 7 2010Karel Kolomazník Abstract Calcimine is a valuable by-product originating during the processing of cured hide into leather. It is used as raw material in the production of gelatin and biodegradable sheets. For further usage, it is necessary to remove calcium hydroxide from calcimine by chemical deliming, which is, from the environmental protection point of view, the most important stage of the entire deliming process. In this article, a mathematical description of chemical deliming is proposed, based on the unreacted nucleus approach. Numerical solution of the model is found, concentration fields of the reacting chemicals described, and the evolution of the acido-basic boundary inside calcimine shown. The model is used to justify a simplified way to determine the effective diffusion coefficient of the deliming agent. The model can also be used as a basis for optimization of the deliming process. © 2010 American Institute of Chemical Engineers AIChE J, 2010 [source] Modeling of turbulent precipitation: A transported population balance-PDF methodAICHE JOURNAL, Issue 4 2010Giovanni di Veroli Abstract Turbulent precipitation is a complex problem, whose mathematical description of precipitation requires a coupling of fluid dynamics with the population balance equation (PBE). In the case of turbulent flow, this coupling results in unclosed equations due to the nonlinear nature of precipitation kinetics. In this article, we present a methodology for modeling turbulent precipitation using the concept of the transported probability density function (PDF) in conjunction with a discretized PBE, simulated via a Lagrangian stochastic method. The transported PBE-PDF approach resolves the closure problem of turbulent precipitation for arbitrarily complex precipitation kinetics, while retrieving the full particle size distribution (PSD). The method is applied to the precipitation of BaSO4 in a turbulent pipe flow and comparisons are made with the experimental results of Baldyga and Orciuch (Chem Eng Sci. 2001;56:2435-2444) showing excellent agreement, while insight is drawn into the mechanisms that determine the evolution of the product PSD. © 2009 American Institute of Chemical Engineers AIChE J, 2010 [source] A kriging method for the solution of nonlinear programs with black-box functionsAICHE JOURNAL, Issue 8 2007Eddie Davis Abstract In this article, a new methodology is developed for the optimization of black-box systems lacking a closed-form mathematical description. To properly balance the computational cost of building the model against the probability of convergence to global optimum, a hybrid methodology is proposed. A kriging approach is first applied to provide information about the global behavior of the system considered, whereas a response surface method is considered close to the optimum to refine the set of candidate local optima and find the global optimum. The kriging predictor is a global model employing normally distributed basis functions, so both an expected sampling value and its variance are obtained for each test point. The presented work extends the capabilities of existing response surface techniques to address the refinement of optima located in regions described by convex asymmetrical feasible regions containing arbitrary linear and nonlinear constraints. The performance of the proposed algorithm is compared to previously developed stand-alone response surface techniques and its effectiveness is evaluated in terms of the number of function calls required, number of times the global optimum is found, and computational time. © 2007 American Institute of Chemical Engineers AIChE J, 2007 [source] High-Pressure Polymerization of Ethylene in Tubular Reactors: A Rigorous Dynamic Model Able to Predict the Full Molecular Weight DistributionMACROMOLECULAR REACTION ENGINEERING, Issue 7 2009Mariano Asteasuain Abstract A rigorous dynamic model of the high-pressure polymerization of ethylene in tubular reactors is presented. The model is capable of predicting the full molecular weight distribution (MWD), average branching indexes, monomer conversion and average molecular weights as function of time and reactor length. The probability generating function method is applied to model the MWD. This technique allows easy and efficient calculation of the MWD, in spite of the complex mathematical description of the process. The reactor model is used to analyze the dynamic responses of MWD and other process variables under different transition policies, as well as to predict the effects of process perturbations. The influence of the material recycle on the process dynamics is also shown. [source] Qualitative model of concrete acidification due to cathodic protection,MATERIALS AND CORROSION/WERKSTOFFE UND KORROSION, Issue 2 2008W. H. A. Peelen In this paper a mathematical description and numerical implementation for ion transport in concrete due to current passage is developed, in which the heterogeneous equilibrium between Ca2+, OH, and the solid Ca(OH)2 is incorporated. The description is based on the Nernst,Planck equation for ion transport, and reaction terms for the dissolution/precipitation of Ca(OH)2. This description was implemented in the finite element package Comsol Multiphysics. In this way Ca(OH)2 depletion in a zone at a CP anode adjacent to a bulk of concrete with Ca(OH)2 could be modelled in one calculation. Drawback of this model is that the kinetic parameters in the reaction terms are not known, and must be chosen high to ensure the dissolution of Ca(OH)2 to be in equilibrium. This proved numerically challenging and sometimes caused long calculation times. The growth rate of the zone without solid depends on the current density applied, concrete cover, the pore liquid composition and the diffusion constants of Ca2+ and OH,. This rate must be evaluated numerically. This qualitative model of anode acidification shows no participation of Na+; therefore transport properties of this ion do not affect the acidification rate of concrete. The same would hold for any other ion included in the model, which is not involved in electrochemical or chemical reactions. [source] Weak solutions of a phase-field model for phase change of an alloy with thermal propertiesMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 14 2002José Luiz Boldrini The phase-field method provides a mathematical description for free-boundary problems associated to physical processes with phase transitions. It postulates the existence of a function, called the phase-field, whose value identifies the phase at a particular point in space and time. The method is particularly suitable for cases with complex growth structures occurring during phase transitions. The mathematical model studied in this work describes the solidification process occurring in a binary alloy with temperature-dependent properties. It is based on a highly non-linear degenerate parabolic system of partial differential equations with three independent variables: phase-field, solute concentration and temperature. Existence of weak solutions for this system is obtained via the introduction of a regularized problem, followed by the derivation of suitable estimates and the application of compactness arguments. Copyright © 2002 John Wiley & Sons, Ltd. [source] Non-centrosymmetric section forming shoulders in packaging machinesPACKAGING TECHNOLOGY AND SCIENCE, Issue 2 2006Yi-Jie Zhou Abstract The mathematical description of a non-centrosymmetric section, trapezoid shoulder is presented and the equations of the bending curve, the shoulder curved surface and the fringe curve are developed. Triangular, flat-round, rectangular and round shoulders are discussed as special cases of the non-centrosymmetric shoulder. To confirm the validity of the mathematical description, 3-D shoulders are modelled on computer, and actual shoulders are manufactured by rapid manufacturing machine. Copyright © 2005 John Wiley & Sons, Ltd. [source] Spatial and temporal evolution of the photo initiation rate for thick polymer systems illuminated on both sidesPOLYMER INTERNATIONAL, Issue 10 2005Nicole Stephenson Abstract Photopolymerizations of thick systems are inherently non-uniform and much more complex than polymerizations of films and coatings. This contribution presents a mathematical description of the evolution of the photoinitiation rate profile for a thick photopolymerization system illuminated on two sides. Simulation results revealed that when two lamps of equal intensity are used, the spatial and temporal evolution of the photoinitiation rate profile follows a characteristic progression from a bimodal distribution to a unimodal shape with a maximum in the center of the sample. The addition of a second light source can lead to an initiation profile that is more uniform throughout the sample. System variables such as the initiator concentration, molar absorptivity and monomer absorptivity determine how the photoinitiation rate profile evolves. For example, increasing initiator concentration results in sharper initiation fronts which move through the sample more slowly. A reflective boundary condition, a special case of two-sided illumination using only one lamp, was found to enhance the initiation rate and uniformity for some reaction systems. This model provides the fundamental understanding needed to ensure proper selection of reaction components for effective photoinitiation in thick systems, including the possibility of a second light source as an additional design variable. Copyright © 2005 Society of Chemical Industry [source] A framework for describing correlated excitation of solar p-modesASTRONOMISCHE NACHRICHTEN, Issue 5 2008W. J. Chaplin Abstract In a previous paper we suggested that, for a given p mode, the excitation function is the same as the component of the solar background noise that has an identical surface spherical harmonic projection (over the corresponding range of temporal frequency). An important consequence of this surmise is that the excitation of overtones of a given angular degree and azimuthal order will be correlated in time. In this note, we introduce the basic principles and a mathematical description of correlated mode excitation. We use simple, illustrative examples, involving two modes. Our treatment suggests that in the real observations, any signatures of the correlation would not appear as a correlation of the output amplitudes of overtones, but rather as subtle modifications to the power spectral density at frequencies between the central frequencies of the overtones. These modifications give a contribution to the observed peak asymmetries. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Development of a Transient Segregated Mathematical Model of the Semicontinuous Microbial Production Process of DihydroxyacetoneBIOTECHNOLOGY PROGRESS, Issue 1 2006Rüdiger Bauer For the mathematical description of the semicontinuous two-stage repeated-fed-batch fermentation of dihydroxyacetone (DHA), a novel segregated model incorporating transient growth rates was developed. The fermentation process was carried out in two stages. A viable, not irreversibly product-inhibited culture was maintained in the first reactor stage until a predetermined DHA threshold value was reached. In the second reactor stage, high final product concentrations of up to 220 g L,1 were reached while the culture was irreversibly product-inhibited. The experimentally observed changes of the physiological state of the culture due to product inhibition were taken into account by introducing a segregation into the mathematical model. It was shown that the state of the cells was dependent on the current environment and on the previous history. This phenomenon was considered in the model by utilizing delay time equations for the specific rates of growth on the primary and the secondary substrate. A comparison with reproducible measurements gave a good correlation between computation and experiment. The mathematical model was validated using independent own experimental data. A comparison with a stationary and nonsegregated model demonstrated the essential improvements of the novel model. It was deduced from the model calculations that high product formation rates of 3.3,3.5 g L,1 h,1 as well as high final DHA concentrations of 196,215 g L,1 can be obtained with a residual broth volume in the first reactor stage of 2% and a DHA threshold value in the range of 100,110g L,1. [source] Experiment and Mathematical Modeling of Solid Formation at Spray DryingCHEMICAL ENGINEERING & TECHNOLOGY (CET), Issue 5 2004P. Seydel The process of solid formation during spray drying has been described many times in the literature, however, a detailed mathematical description of the time-dependent process concerning the structure of the particles as a function of substance and process parameters is still not available. In the present work, a time-dependent and local modeling of the mass and energy transport processes during solid formation inside the droplet was carried out. The model was validated against reproducible experiments performed in a vertical pipe with single drop generation. [source] Groundwater Banking in Aquifers that Interact With Surface Water: Aquifer Response Functions and Double-Entry Accounting,JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION, Issue 6 2009Bryce A. Contor Contor, Bryce A., 2009. Groundwater Banking in Aquifers That Interact With Surface Water: Aquifer Response Functions and Double-Entry Accounting. Journal of the American Water Resources Association (JAWRA) 45(6):1465-1474. Abstract:, Increasing worldwide demands for water call for mechanisms to facilitate storage of seasonal supplies and mechanisms to facilitate reallocation of water. Markets are economically efficient reallocation and incentive mechanisms when market conditions prevail, but special hydrologic and administrative conditions of water use and allocation interfere with required market conditions. Water banking in general can bring market forces to bear on water storage and reallocation, improving economic efficiency and therefore the welfare of society as a whole. Groundwater banking can utilize advantages of aquifers as storage vessels with vast capacity, low construction cost, and protection of stored water. For groundwater banking in aquifers that interact with surface water, an accounting system is needed that addresses the depletion of stored volumes of water as water migrates to surface water. Constructing such a system requires integration of hydrologic, economic, and legal principles with principles of financial accounting. Simple mass-balance accounting, even with allowances for depletion, is not adequate in these aquifers. Aquifer response functions are mathematical descriptions of the impact that aquifer pumping or recharge events have upon hydraulically connected surface water bodies. Double-entry accounting is a financial accounting methodology for tracking asset inventories and ownership claims upon assets. The powerful innovation of linking aquifer response functions with double-entry accounting technologies allows application of groundwater banking to aquifers where deposits can be depleted by migration to hydraulically connected surface water. It honors the hydrologic realities of groundwater/surface water interaction, the legal requirements of prior appropriation water law, and the economic requirements for equitable and efficient allocation of resources. 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