Until now, a comprehensive textbook covering both ordinary differential equations (ODEs) and partial differential equations (PDEs) didnt exist. We propose a neural network based approach for extracting models from dynamic data using ordinary and partial differential equations. Ordinary and Partial Differential Equations Proceedings of the Fourth Conference Held at Dundee, Scotland March 30 - April 2, 1976 E.g. This textbook can be tailored for courses in numerical differential equations and numerical analysis as well as traditional courses in ordinary and/or partial differential equations. 6) (vi) Nonlinear Differential Equations and Stability (Ch. Intended primarily for engineering and science students. Maple is the world leader in finding exact solutions to ordinary and partial differential equations. An ordinary differential equation involves a derivative over a single variable, usually in an univariate context, whereas a partial differential equation involves several (partial) derivatives ...
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From 1870, Sophus Lies work put the theory of differential equations on a more satisfactory foundation. He showed that the integration theories of the older mathematicians can, by the introduction of what are now called Lie groups, be referred to a common source, and that ordinary differential equations that admit the same infinitesimal transformations present comparable difficulties of integration. He also emphasized the subject of transformations of contact. Lies group theory of differential equations has been certified, namely: (1) that it unifies the many ad hoc methods known for solving differential equations, and (2) that it provides powerful new ways to find solutions. The theory has applications to both ordinary and partial differential equations.[18]. A general approach to solve DEs uses the symmetry property of differential equations, the continuous infinitesimal transformations of solutions to solutions (Lie theory). Continuous group theory, Lie algebras, and differential geometry ...
From 1870, Sophus Lies work put the theory of differential equations on a more satisfactory foundation. He showed that the integration theories of the older mathematicians can, by the introduction of what are now called Lie groups, be referred to a common source, and that ordinary differential equations that admit the same infinitesimal transformations present comparable difficulties of integration. He also emphasized the subject of transformations of contact. Lies group theory of differential equations has been certified, namely: (1) that it unifies the many ad hoc methods known for solving differential equations, and (2) that it provides powerful new ways to find solutions. The theory has applications to both ordinary and partial differential equations.[18] A general approach to solve DEs uses the symmetry property of differential equations, the continuous infinitesimal transformations of solutions to solutions (Lie theory). Continuous group theory, Lie algebras, and differential geometry ...
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The first contemporary textbook on ordinary differential equations (ODEs) to include instructions on MATLAB , Mathematica , and MapleTM, A Course in Ordinary Differential Equations focuses on applications and methods of analytical and numerical solutions, emphasizing approaches used in the typical engineering, physics, or mathematics students field of study.Stressing applications wherever possible, the authors have written this text with the applied math, engineer, or science major in mind. It includes a number of modern topics that are not commonly found in a traditional sophomore-level text. For example, Chapter 2 covers direction fields, phase line techniques, and the Runge-Kutta method; another chapter discusses linear algebraic topics, such as transformations and eigenvalues. Chapter 6 considers linear and nonlinear systems of equations from a dynamical systems viewpoint and uses the linear algebra insights from the previous chapter; it also includes modern applications like epidemiological models
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Introduction to Ordinary Differential Equations from Korea Advanced Institute of Science and Technology. In this introductory course on Ordinary Differential Equations, we first provide basic terminologies on the theory of differential equations ...
Many problems in physics and engineering, but also, for example, biology, and other fields are modeled using partial differential equations. Waves motion and forest management are some of the examples of these applications. In this course, an introduction to the theory of the first and second-order equations is presented. The focus is on specific methods showing how to solve the partial differential equations, but it is also accompanied with analytical theory of PDEs. At the end, a brief overview of numerical solution methods is given.. ...
TY - JOUR. T1 - Mathematical equation of fusion index of tetanic contraction of skeletal muscles. AU - Watanabe, Shogo. AU - Kitawaki, T.. AU - Oka, Hisao. PY - 2010/4. Y1 - 2010/4. N2 - The fusion index (FI) is an index that can evaluate the tetanic progression of the skeletal muscles. Although the FI-frequency curve (FFC), which is obtained by changing the stimulation frequency, is greatly affected by muscle fiber type and fiber compositions, there are no reports of a mathematical equation that can express the FFC. In this study, the FFC was measured for the gastrocnemius, vastus intermedius, and soleus muscles of rats, and the mathematical equation (FFC-equation) was proposed. The FFC-equation (FI(f)) was proportional to the h-th power of f, and was in inverse proportion to the sum of the h-th power of k and the h-th power of f. f was the stimulation frequency, k was the stimulation frequency at 50% of FI, and h reflected the gradient of FFC. As a result, the approximated curve produced by ...
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Mechanistic within-host models integrating blood anti-malarial drug concentrations with the parasite-time profile provide a valuable decision tool for determining dosing regimens for anti-malarial treatments, as well as a formative component of population-level drug resistance models. We reviewed published anti-malarial pharmacokinetic-pharmacodynamic models to identify the challenges for these complex models where parameter estimation from clinical field data is limited. The inclusion of key pharmacodynamic processes in the mechanistic structure adopted varies considerably. These include the life cycle of the parasite within the red blood cell, the action of the anti-malarial on a specific stage of the life cycle, and the reduction in parasite growth associated with immunity. With regard to estimation of the pharmacodynamic parameters, the majority of studies simply compared descriptive summaries of the simulated outputs to published observations of host and parasite responses from clinical ...
Estimation of fluxes through metabolic networks from redistribution patterns of (13)C has become a well developed technique in recent years. However, the approach is currently limited to systems at metabolic steady-state; dynamic changes in metabolic fluxes cannot be assessed. This is a major impediment to understanding the behaviour of metabolic networks, because steady-state is not always experimentally achievable and a great deal of information about the control hierarchy of the network can be derived from the analysis of flux dynamics. To address this issue, we have developed a method for estimating non-steady-state fluxes based on the mass-balance of mass isotopomers. This approach allows multiple mass-balance equations to be written for the change in labelling of a given metabolite pool and thereby permits over-determination of fluxes. We demonstrate how linear regression methods can be used to estimate non-steady-state fluxes from these mass balance equations. The approach can be used to
Ionic polymer-metal composites (IPMCs) generate electrical potential under deformation and can be used as sensors. Recently, Zhu et al. have proposed a sensor model which describes distribution of cations, water molecules and electrical potential under bending deformation. In this paper, we discuss a simplification of the multi-physical sensor model, which is represented by a set of nonlinear partial differential equations. The nonlinear partial differential equations are simplified and approximated into a set of linear ordinary differential equations, i.e., a state-space equation model. At the end, the simplified model is validated by comparing the simulation results with those of the partial differential equation model ...
It is well understood that populations cannot grow without bound and that it is competition between individuals for resources which restricts growth. Despite centuries of interest, the question of how best to model density dependent population growth still has no definitive answer. We address this question here through a number of individual based models of populations expressed using the process algebra WSCCS. The advantage of these models is that they can be explicitly based on observations of individual interactions. From our probabilistic models we derive equations expressing overall population dynamics, using a formal and rigorous rewriting based method. These equations are easily compared with the traditionally used deterministic Ordinary Differential Equation models and allow evaluation of those ODE models, challenging their assumptions about system dynamics. Further, the approach is applied to epidemiology, combining population growth with disease spread ...
In this paper, an efficient computational solution technique based on the energy balance equations is presented for the dynamic analysis of shear-frames, as an example of a multi-degree-of-freedom system. After deriving the dynamic energy balance equations for these systems, a new mathematical solution technique which is called Elimination of Discontinuous Velocities is proposed to solve a set of coupled quadratic algebraic equations. The method will be illustrated for the free vibration of a two-story structure. Subsequently, the damped dynamic response of a three-story shear-frame which is subjected to harmonic loading is considered. Finally the analysis of a three-story shear-building under horizontal earthquake load, as one of the most common problems in Earthquake Engineering, is studied. The results show that this method has acceptable accuracy in comparison with other techniques, but is not only faster compared with modal analysis but also does not require adjusting and calibrating the stability
Mathematical modeling and computer simulations have become an integral part of modern biological research. The strength of theoretical approaches is in the simplification of complex biological systems. We here consider the general problem of receptor-ligand binding in the context of antibody-antigen binding. On the one hand, we establish a quantitative mapping between macroscopic binding rates of an ordinary differential equation model and their microscopic equivalents as obtained from simulating the spatio-temporal binding kinetics by agent-based models. On the other hand, we investigate the impact of various receptor properties - such as their dimensionality of motion, morphology and binding valency - on the receptor-ligand binding kinetics. To this end, we implemented an algorithm that simulates antigen binding by B cell derived receptors with a Y-shaped morphology that can move in different dimensionalities, i.e. either as membrane-anchored receptors or as soluble receptors. The mapping of the
Recently, epigenetic-mediated mechanisms - which involve heritable changes in gene expression in the absence of alterations in DNA sequences - have been proposed as contributing to asthma. In this issue of the JCI, Hollingsworth and colleagues report on the effect of prenatal maternal dietary intake of methyl donors on the risk of allergic airway disease in offspring in mice and show that these effects involve epigenetic regulation (see the related article beginning on page 3462). Supplementation of the maternal diet with methyl donors was associated with greater airway allergic inflammation and IgE production in F1 and, to some extent, F2 progeny. Site-specific differences in DNA methylation and reduced transcriptional activity were detected. If these findings are confirmed, a new paradigm for asthma pathogenesis may be emerging. ...
Recently, epigenetic-mediated mechanisms - which involve heritable changes in gene expression in the absence of alterations in DNA sequences - have been proposed as contributing to asthma. In this issue of the JCI, Hollingsworth and colleagues report on the effect of prenatal maternal dietary intake of methyl donors on the risk of allergic airway disease in offspring in mice and show that these effects involve epigenetic regulation (see the related article beginning on page 3462). Supplementation of the maternal diet with methyl donors was associated with greater airway allergic inflammation and IgE production in F1 and, to some extent, F2 progeny. Site-specific differences in DNA methylation and reduced transcriptional activity were detected. If these findings are confirmed, a new paradigm for asthma pathogenesis may be emerging. ...
Abstract , References , Similar Articles , Additional Information Abstract: This paper considers the problem of stabilizing a control system governed by a combination of partial and ordinary differential equations. The partial differential equations govern the evolution of the system in the interior of some spatial domain, and the ordinary differential equations describe the evolution of the boundary data; the control enters through the boundary ordinary differential equations in a bilinear fashion. We provide sufficient conditions for feedback stabilization of such ``hybrid systems. Two examples to wave equations with dynamic boundary conditions are provided ...
TY - JOUR. T1 - Tumor growth dynamics with nutrient limitation and cell proliferation time delay. AU - Alsheri, Ahuod. AU - Alzahrani, Ebraheem O.. AU - Asiri, Asim. AU - El-Dessoky, Mohamed M.. AU - Kuang, Yang. PY - 2017/12/1. Y1 - 2017/12/1. N2 - It is known that avascular spherical solid tumors grow monotonically, often tends to a limiting final size. This is repeatedly confirmed by various mathematical models consisting of mostly ordinary differential equations. However, cell growth is limited by nutrient and its proliferation incurs a time delay. In this paper, we formulate a nutrient limited compartmental model of avascular spherical solid tumor growth with cell proliferation time delay and study its limiting dynamics. The nutrient is assumed to enter the tumor proportional to its surface area. This model is a modification of a recent model which is built on a two-compartment model of cancer cell growth with transitions between proliferating and quiescent cells. Due to the limitation of ...
Research in this group spans a broad spectrum underpinned by the rigorous treatment and analysis of linear and nonlinear partial differential equations (PDEs).. This ranges from PDEs arising in geometry, physics and mechanics to those in control theory, finance and material sciences.. A core of our activities is on calculus of variations and geometric and harmonic analysis and there are subgroups with major interests in geometric measure theory, spectral theory, function spaces, dynamical systems, fluid mechanics, nonlinear elasticity and homogenisation.. For details see the Research tab.. ...
Oscar A Linares,1 William E Schiesser,2 Jeffrey Fudin,3–6 Thien C Pham,6 Jeffrey J Bettinger,6 Roy O Mathew,6 Annemarie L Daly7 1Translational Genomic
Attempts to formulate realistic models of the development of the human oculomotor control system have led to the conclusion that evolutionary factors play a crucial role. Moreover, even rather coarse simulations of the biological evolutionary processes result in adaptable control systems that are considerably more efficient than those designed by human researchers. In this paper I shall describe some of the aspects of these biological models that are likely to be useful for building robot control systems. In particular, I shall consider the evolution of appropriate innate starting points for learning/adaptation, patterns of learning rates that vary across different system components, learning rates that vary during the systems lifetime, and the relevance of individual differences across the evolved populations.. ...
We present a concise optimal control optimization approach to continuous-depth deep learning models by discussing ideas and algorithms derived from the optimality conditions of the powerful Pontryagins Maximum Principle. The new emerging field of constant memory cost models, however, is vulnerable to adversarial attacks. Apart from highlighting the inconsistency of neural networks theoretically, we experiment with adversarial deformations for neural ordinary differential equations on MNIST and compare our results to convolutional neural-network based architectures.
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Mathematics is a very helpful tool that can be used to describe naturally arising phenomena, quantity, structure, shape, change, and relationships.What constitutes the notion of useless anyway? Mathematical equations are simply there to state the relationship of two expressions. There is also an infinite amount of mathematical equations, so you could not possibly write all the useless ones here anyway. Because mathematical equations can be created indiscriminately, there will be infinite numbers of useless mathematical equations and infinite numbers of useful mathematical equations depending on your definition of useless ...
Mathematics is a very helpful tool that can be used to describe naturally arising phenomena, quantity, structure, shape, change, and relationships.What constitutes the notion of useless anyway? Mathematical equations are simply there to state the relationship of two expressions. There is also an infinite amount of mathematical equations, so you could not possibly write all the useless ones here anyway. Because mathematical equations can be created indiscriminately, there will be infinite numbers of useless mathematical equations and infinite numbers of useful mathematical equations depending on your definition of useless ...
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Membranes are the most common cellular structures in both plants and animals. They are now recognized as being involved in almost all aspects of cellular activity ranging from motility and food entrapment in simple unicellular organisms, to energy transduction, immunorecognition, nerve conduction and biosynthesis in plants and higher organisms. This functional diversity is reflected in the wide variety of lipids and particularly of proteins that compose different membranes. An understanding of the physical principles that govern the molecular organization of membranes is essential for an understanding of their physiological roles since structure and function are much more interdependent in membranes than in, say, simple chemical reactions in solution. We must recognize, however, that the word understanding means different things in different disciplines, and nowhere is this more apparent than in this multidisciplinary area where biology, chemistry and physics meet ...
The reconstruction of gene regulatory networks from time series gene expression data is one of the most difficult problems in systems biology. This is due to several reasons, among them the combinatorial explosion of possible network topologies, limited information content of the experimental data with high levels of noise, and the complexity of gene regulation at the transcriptional, translational and post-translational levels. At the same time, quantitative, dynamic models, ideally with probability distributions over model topologies and parameters, are highly desirable. We present a novel approach to infer such models from data, based on nonlinear differential equations, which we embed into a stochastic Bayesian framework. We thus address both the stochasticity of experimental data and the need for quantitative dynamic models. Furthermore, the Bayesian framework allows it to easily integrate prior knowledge into the inference process. Using stochastic sampling from the Bayes posterior distribution,
ABSTRACT:We consider a minimal cascade model previously proposed ~1 for the mitotic oscillator driving the embryonic cell division cycle. The model is based on a bicyclic phosphorylation-dephosphorylation cascade involving cyclin and cdc2 kinase. By constructing stability diagrams showing domains of periodic behavior as a function of the maximum rates of the kinases and phosphatases involved in the two cycles of the cascade, we investigate the role of these converter enzymes in the oscillatory mechanism. Oscillations occur when the balance of kinase and phosphatase rates in each cycle is in a range bounded by two critical values. The results suggest ways to arrest the mitotic oscillator by altering the maximum rates of the converter enzymes. These results bear on the control of cell proliferation. The original paper reference is cited below: Arresting the mitotic oscillator and the control of cell proliferation: insights from a cascade model for cdc2 kinase activation, Goldbeter, A. and ...
ABSTRACT:We consider a minimal cascade model previously proposed ~1 for the mitotic oscillator driving the embryonic cell division cycle. The model is based on a bicyclic phosphorylation-dephosphorylation cascade involving cyclin and cdc2 kinase. By constructing stability diagrams showing domains of periodic behavior as a function of the maximum rates of the kinases and phosphatases involved in the two cycles of the cascade, we investigate the role of these converter enzymes in the oscillatory mechanism. Oscillations occur when the balance of kinase and phosphatase rates in each cycle is in a range bounded by two critical values. The results suggest ways to arrest the mitotic oscillator by altering the maximum rates of the converter enzymes. These results bear on the control of cell proliferation. The original paper reference is cited below: Arresting the mitotic oscillator and the control of cell proliferation: insights from a cascade model for cdc2 kinase activation, Goldbeter, A. and ...
Title: Stochastic and deterministic spatial models for complex systems Abstract: Interacting particle models are often employed to gain understanding of the emergence of macroscopic phenomena from microscopic laws of nature. These individual-based models capture fine details, including randomness and discreteness of individuals, that are not considered in continuum models such as partial differential equations (PDE) and integral-differential equations. The challenge, which is fundamental in any multi-scale modeling approach for complex systems, is how to simultaneously retain key information in microscopic models as well as efficiency and robustness of macroscopic models. In this talk, I will discuss how this challenge can be overcome by elucidating the probabilistic connections between particle models and PDE, in particular, why naively adding diffusion terms to ordinary differential equations might fail to account for spatial dynamics in population models. These connections also explain how ...
Title: Stochastic and deterministic spatial models for complex systems Abstract: Interacting particle models are often employed to gain understanding of the emergence of macroscopic phenomena from microscopic laws of nature. These individual-based models capture fine details, including randomness and discreteness of individuals, that are not considered in continuum models such as partial differential equations (PDE) and integral-differential equations. The challenge, which is fundamental in any multi-scale modeling approach for complex systems, is how to simultaneously retain key information in microscopic models as well as efficiency and robustness of macroscopic models. In this talk, I will discuss how this challenge can be overcome by elucidating the probabilistic connections between particle models and PDE, in particular, why naively adding diffusion terms to ordinary differential equations might fail to account for spatial dynamics in population models. These connections also explain how ...
PDE #10 Partial Differential Equation in Hindi|Form of PDE By Eliminating Arbitray Function|NP Bali Hello student welcome to JK SMART CLASSES , I will be discuss Engineering Mathematics 3 Partial differential equations in Hindi .Now in this video I will briefly explained PDE #10 Formation Partial Differential Equation in Hindi By Eliminating Arbitary Function|PTU|NP BALI|JK Smart Classes for B.tech and m.tech student whose study in various universities like Punjab Technical university (PTU), Gujarat Technological University (GTU), Visvesvaraya Technological University (vtu), Rajasthan Technical University (RTU), kurukshetra university (KU) and Mumbai university etc.for exam point of view Partial differential equations in Hindi chapter for engineering mathematics 3 in very important chapter for pass point of view as well as for getting good marks in Engg math 3.so student please more focus on Partial differential equations in Hindi chapter for success in exam So
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Physiologically-based pharmacokinetic (PBPK) modelling is traditionally employed to predict drug concentration-time profiles in plasma and tissues using information from physiology / biology, in vitro experiments and in silico predictions. Model-based analysis of population pharmacokinetic (PK) data is rarely performed in such a mechanistic framework, as empirical compartmental models are mainly utilised for this purpose. However, the combination of traditional PBPK methodologies with parameter estimation techniques and non-linear mixed effects modelling is an approach with progressively increasing impact due to the significant advantages it offers. Therefore, the general aim of this thesis is to illustrate, explore and thus further facilitate the application of physiologically-based pharmacokinetic models in the context of population data analysis.In order to pursue this aim, this work firstly particularly focuses on the population pharmacokinetics of simvastatin (SV) and its active metabolite, ...
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TY - JOUR. T1 - Stability of stationary solutions for a scalar non-local reaction-diffusion equation. AU - Frettas, Pedro. PY - 1995/11. Y1 - 1995/11. N2 - The stability of stationary solutions of the non-local reaction-diffusion equation with homogeneous Neumann boundary conditions is studied. Depending on a, bounds on the dimension of the unstable manifold of a stationary solution are given. In particular, it is shown that only constant or monotone stationary solutions may be stable. For the specific case of a cubic like f, the existence of a Hopf bifurcation is proven. Finally, some related equations are discussed. © 1995 Oxford University Press.. AB - The stability of stationary solutions of the non-local reaction-diffusion equation with homogeneous Neumann boundary conditions is studied. Depending on a, bounds on the dimension of the unstable manifold of a stationary solution are given. In particular, it is shown that only constant or monotone stationary solutions may be stable. For the ...
TY - BOOK. T1 - Recent progress on reaction-diffusion systems and viscosity solutions. AU - Du, Yihong. AU - Ishii, Hitoshi. AU - Lin, Wei Yueh. PY - 2009/1/1. Y1 - 2009/1/1. N2 - This book consists of survey and research articles expanding on the theme of the International Conference on Reaction-Diffusion Systems and Viscosity Solutions, held at Providence University, Taiwan, during January 3-6, 2007. It is a carefully selected collection of articles representing the recent progress of some important areas of nonlinear partial differential equations. The book is aimed for researchers and postgraduate students who want to learn about or follow some of the current research topics in nonlinear partial differential equations. The contributors consist of international experts and some participants of the conference, including Nils Ackermann (Mexico), Chao-Nien Chen (Taiwan), Yihong Du (Australia), Alberto Farina (France), Hitoshi Ishii (Japan), N Ishimura (Japan), Shigeaki Koike (Japan), Chu-Pin ...
In this paper we investigate additional regularity properties for global and trajectory attractors of all globally defined weak solutions of semi-linear parabolic differential reaction-diffusion equations with discontinuous nonlinearities, when initial data uτ ∈ L2(Ω). The main contributions in this paper are: (i) sufficient conditions for the existence of a Lyapunov function for all weak solutions of autonomous differential reaction-diffusion equations with discontinuous and multivalued interaction functions; (ii) convergence results for all weak solutions in the strongest topologies; (iii) new structure and regularity properties for global and trajectory attractors. The obtained results allow investigating the long-time behavior of state functions for the following problems: (a) a model of combustion in porous media; (b) a model of conduction of electrical impulses in nerve axons; (c) a climate energy balance model; (d) a parabolic feedback control problem. ...
This book deals with equations that have played a central role in the interplay between partial differential equations and probability theory. Most of this material has been treated elsewhere, but it is rarely presented in a manner that makes it readily accessible to people whose background is probability theory. Many results are given new proofs designed for readers with limited expertise in analysis. The author covers the theory of linear, second order, partial differential equations of parabolic and elliptic types. Many of the techniques have antecedents in probability theory, although the book also covers a few purely analytic techniques. In particular, a chapter is devoted to the De Giorgi-Moser-Nash estimates, and the concluding chapter gives an introduction to the theory of pseudodifferential operators and their application to hypoellipticity, including the famous theorem of Lars Hormander. ...
|p style=text-indent:20px;|In this paper, we present a multiscale model reduction framework within Generalized Multiscale Finite Element Method (GMsFEM) for nonlinear elliptic problems. We consider an exemplary problem, which consists of nonlinear p-Laplacian with heterogeneous coefficients. The main challenging feature of this problem is that local subgrid models are nonlinear involving the gradient of the solution (e.g., in the case of scale separation, when using homogenization). Our main objective is to develop snapshots and local spectral problems, which are the main ingredients of GMsFEM, for these problems. Our contributions can be summarized as follows. (1) We re-cast the multiscale model reduction problem onto the boundaries of coarse cells. This is important and allows capturing separable scales as discussed. (2) We introduce nonlinear eigenvalue problems in the snapshot space for these nonlinear harmonic functions. (3) We present convergence analysis and numerical results, which show that
The (asymptotic) behaviour of the second moment of solutions to stochastic differential equations is treated in mean-square stability analysis. This property is discussed for approximations of infinite-dimensional stochastic differential equations and necessary and sufficient conditions ensuring mean-square stability are given. They are applied to typical discretization schemes such as combinations of spectral Galerkin, finite element, Euler-Maruyama, Milstein, Crank-Nicolson, and forward and backward Euler methods. Furthermore, results on the relation to stability properties of corresponding analytical solutions are provided. Simulations of the stochastic heat equation illustrate the theory.
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Abstract: The main bottleneck when performing computational fluid dynamics (CFD) simulations of combustion systems is the computation and integration of the highly non-linear and stiff chemical source terms. In recent times, machine learning has emerged as a promising tool to accelerate combustion chemistry, involving the use of regression models to predict the chemical source terms as functions of the thermochemical state of the system. However, combustion is a highly nonlinear phenomenon, and this often leads to divergence from the true solution when the neural network representation of chemical kinetics is integrated in time. This is because these approaches minimize the error during training without guaranteeing successful integration with ordinary differential equation (ODE) solvers. In this work, a novel neural ODE approach to combustion modeling, ChemNODE, is developed to address this issue. The source terms predicted by the neural network are integrated during training, and by ...
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In this article we present a system of coupled bulk-surface reaction-diffusion equations on exponentially evolving volumes. Detailed linear stability analysis of the homogeneous steady state is carried out. It turns out that due to the nature of the coupling (linear Robin-type boundary conditions) the characterisation of the dispersion relation in the absence and presence of spatial variation (i.e. diffusion), can be decomposed as a product of the dispersion relation of the bulk and surface models thereby allowing detailed analytical tractability. As a result we state and prove the conditions for diffusion-driven instability for systems of coupled bulk-surface reaction-diffusion equations. Furthermore, we plot explicit evolving parameter spaces for the case of an exponential growth. By selecting parameter values from the parameter spaces, we exhibit pattern formation in the bulk and on the surface in complete agreement with theoretical predictions.. ...
The contaminant transport equation is solved in three dimensions using the Eulerian-Lagrangian Localized Adjoint Method (ELLAM). Trilinear and finite volume test functions defined by the characteristics of the governing equation are employed and compared. Integrations are simplified by forward tracking of integration points along the characteristics. The resulting equations are solved using a preconditioned conjugate gradient method. The algorithm is coupled to a block-centered finite difference approximation of the groundwater flow equation similar to that used in the popular MODFLOW code. The ELLAM is tested by comparison with 1D and 3D analytic solutions. The method is then applied with random, spatially correlated hydraulic conductivities in a simulation of a tracer experiment performed on Cape Cod, Massachusetts. The linear test function ELLAM was found to perform better than the finite volume ELLAM. Both ELLAM formulations were found to be robust, computationally efficient and relatively ...
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Spirit shares I Ching wisdom. Todays situation is expressed and explained in Hexagram 26 - Great Accumulation Continuous movement is a fundamental principle of the way of I Ching and way of Life. There is no stagnation in the sense of non-movement. Situations are always either improving or they are deteriorating. Energy moves, one way…
Title I: Fundamental Principles (Art. 1-9) Article 1: The Bolivarian Republic of Venezuela is irrevocably free and independent, basing its moral property and values of freedom, equality, justice and international peace on the doctrine of Simón Bolívar, the Liberator. Independence, liberty, sovereignty, immunity, territorial integrity and national self-determination are unrenounceable rights of the Nation. Article 2: Venezuela constitutes itself as a Democratic and Social State of Law and Justice, which holds as superior values of its legal order and actions those of life, liberty, justice, equality, solidarity, democracy, social responsibility and, in general, the preeminence of human rights, ethics and political pluralism. Article 3: The essential purposes of the State are the protection and development of the individual and respect for the dignity of the individual, the democratic exercise of the will of the people, the building of a just and peace-loving society, the furtherance of the ...
en] Biological systems and, in particular, cellular signal transduction pathways are characterised by their high complexity. Mathematical models describing these processes might be of great help to gain qualitative and, most importantly, quantitative knowledge about such complex systems. However, a detailed mathematical description of these systems leads to nearly unmanageably large models, especially when combining models of different signalling pathways to study cross-talk phenomena. Therefore, simplification of models becomes very important. Different methods are available for model reduction of biological models. Importantly, most of the common model reduction methods cannot be applied to cellular signal transduction pathways. Using as an example the epidermal growth factor (EGF) signalling pathway, we discuss how quantitative methods like system analysis and simulation studies can help to suitably reduce models and additionally give new insights into the signal transmission and processing ...
We study systems of two nonlinear reaction-diffusion partial differential equations undergoing diffusion driven instability. Such systems may have spatially inhomogeneous stationary solutions called Turing patterns. These solutions are typically non-unique and it is not clear how many of them exists. Since there are no analytical results available, we look for the number of distinct stationary solutions numerically. As a typical example, we investigate the reaction-diffusion system designed to model coat patterns in leopard and jaguar ...
We introduce an algorithm for solving two-sided space-fractional partial differential equations. The space-fractional derivatives we consider here are left-handed and right-handed Riemann-Liouville fractional derivatives which are expressed by using Hadamard finite-part integrals. We approximate the Hadamard finite-part integrals by using piecewise quadratic interpolation polynomials and obtain a numerical approximation of the space-fractional derivative with convergence order ...
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We investigate the long term behavior in terms of finite dimensional global attractors and (global) asymptotic stabilization to steady states, as time goes to infinity, of solutions to a non-local semilinear reaction-diffusion equation associated with the fractional Laplace operator on non-smooth domains subject to Dirichlet, fractional Neumann and Robin boundary conditions.
The global sensitivity analysis of a complex numerical model often calls for the estimation of variance-based importance measures, named Sobol indices. Metamodel-based techniques have been developed in order to replace the CPU time-expensive computer code with an inexpensive mathematical function, which predicts the computer code output. The common metamodel-based sensitivity analysis methods are well suited for computer codes with scalar outputs. However, in the environmental domain, as in many areas of application, the numerical model outputs are often spatial maps, which may also vary with time. In this paper, we introduce an innovative method to obtain a spatial map of Sobol indices with a minimal number of numerical model computations. It is based upon the functional decomposition of the spatial output onto a wavelet basis and the metamodeling of the wavelet coefficients by the Gaussian process. An analytical example is presented to clarify the various steps of our methodology. This ...
Tumor growth from a single transformed cancer cell up to a clinically apparent mass spans many spatial and temporal orders of magnitude. Implementation of cellular automata simulations of such tumor growth can be straightforward but computing performance often counterbalances simplicity. Computationally convenient simulation times can be achieved by choosing appropriate data structures, memory and cell handling as well as domain setup. We propose a cellular automaton model of tumor growth with a domain that expands dynamically as the tumor population increases. We discuss memory access, data structures and implementation techniques that yield high-performance multi-scale Monte Carlo simulations of tumor growth. We discuss tumor properties that favor the proposed high-performance design and present simulation results of the tumor growth model. We estimate to which parameters the model is the most sensitive, and show that tumor volume depends on a number of parameters in a non-monotonic
The COVID-19 pandemic and its impact on respiratory system has highlighted the exigent needs to research pulmonary mechanics. This mini-symposium aims to showcase some recent studies using mathematical models to examine lung development, normal lung function, diseased lung conditions and functional deterioration. These research explorations provide insights to diseases such as asthma, tuberculosis, cystic fibrosis and treatment of lung infection. They have also advanced pulmonary tissue characterization and understanding of age related alterations in lung function. Lung diseases often leads to reduced lung function and poor quality of life and mathematical models can provide excellent avenues to unravel the complex dynamics that orchestrate lung decline in various health conditions. The models employed in these works cut across different areas of mathematical and computational mathematics, including reaction-diffusion models, partial differential equation models, agent-based models, image-based analyses
This study focuses on the biodynamic responses of a seated human model to whole-body vibrations in a vehicle. Five-degree-of-freedom nonlinear equations of motion for a human model were derived, and human parameters such as spring constants and damping coefficients were extracted using a three-step optimization processes that applied the experimental data to the mathematical human model. The natural frequencies and mode shapes of the linearized model were also calculated. In order to examine the effects of the human parameters, parametric studies involving initial segment angles and stiffness values were performed. Interestingly, mode veering was observed between the fourth and fifth human modes when combining two different spring stiffness values. Finally, through the frequency responses of the human model, nonlinear characteristics such as frequency shift and jump phenomena were clearly observed.
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Computational models of cardiac electrophysiology have a long history in basic science applications and device design and evaluation, but have significant potential for clinical applications in all areas of cardiovascular medicine, including functional imaging and mapping, drug safety evaluation, disease diagnosis, patient selection, and therapy optimisation or personalisation. For all stakeholders to be confident in model-based clinical decisions, cardiac electrophysiological (CEP) models must be demonstrated to be trustworthy and reliable. Credibility, that is, the belief in the predictive capability, of a computational model is primarily established by performing validation, in which model predictions are compared to experimental or clinical data. However, there are numerous challenges to performing validation for highly complex multi-scale physiological models such as CEP models. As a result, credibility of CEP model predictions is usually founded upon a wide range of distinct factors, including
We present a method for orientation-selective edge detection and enhancement based on the irradiance transport equation. The proposed technique distinguishes the sign of the derivative of the intensity pattern along an arbitrarily selected direction. The method is based on the capacity of liquid-crystal displays to generate simultaneously a contrast reverted replica of the image displayed on it. When both images (the original one and its replica) are imagined across a slightly defocused plane, one obtains an image with enhanced first derivatives. Unlike most Fourier methods, the proposed technique works well with a low-coherence light source, and it does not require precise alignment. The proposed method does not involve numerical processing, and thus it could be potentially useful for processing large images in real-time applications. Validation experiments are presented.. © 2010 Optical Society of America. Full Article , PDF Article ...
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Constraint-based modeling uses mass balances, flux capacity, and reaction directionality constraints to predict fluxes through metabolism. Although transcriptional regulation and thermodynamic constraints have been integrated into constraint-based modeling, kinetic rate laws have not been extensively used. In this study, an in vivo kinetic parameter estimation problem was formulated and solved using multi-omic data sets for Escherichia coli. To narrow the confidence intervals for kinetic parameters, a series of kinetic model simplifications were made, resulting in fewer kinetic parameters than the full kinetic model. These new parameter values are able to account for flux and concentration data from 20 different experimental conditions used in our training dataset. Concentration estimates from the simplified kinetic model were within one standard deviation for 92.7% of the 790 experimental measurements in the training set. Gibbs free energy changes of reaction were calculated to identify reactions that
We examine the evolution of a bistable reaction in a one-dimensional stretching flow, as a model for chaotic advection. We derive two reduced systems of ordinary differential equations (ODEs) for the dynamics of the governing advection-reaction-diffusion partial differential equations (PDE), for pulse-like and for plateau-like solutions, based on a non-perturbative approach. This reduction allows us to study the dynamics in two cases: first, close to a saddle-node bifurcation at which a pair of nontrivial steady states are born as the dimensionless reaction rate (Damkoehler number) is increased, and, second, for large Damkoehler number, far away from the bifurcation. The main aim is to investigate the initial-value problem and to determine when an initial condition subject to chaotic stirring will decay to zero and when it will give rise to a nonzero final state. Comparisons with full PDE simulations show that the reduced pulse model accurately predicts the threshold amplitude for a pulse ...
Finite volume method in computational fluid dynamics is a discretization technique for partial differential equations that arise from physical conservation laws. These equations can be different in nature, e.g. elliptic, parabolic, or hyperbolic. First well-documented use was by Evans and Harlow (1957) at Los Alamos. The general equation for steady diffusion can be easily be derived from the general transport equation for property Φ by deleting transient and convective terms.[1] General Transport equation can be define as ...
書名:Advanced Spatial Modeling With Stochastic Partial Differential Equations Using R and Inla,語言:英文,ISBN:9781138369856,頁數:298,作者:Krainski, Elias T./ Go´mez-rubio, Virgilio/ Bakka, Haakon/ Lenzi, Amanda/ Castro-camilo, Daniela,出版日期:2018/12/19,類別:自然科普
TY - JOUR. T1 - Understanding biological variability in susceptibility to respiratory disease. AU - Levitt, Roy C.. PY - 1991/11. Y1 - 1991/11. UR - http://www.scopus.com/inward/record.url?scp=0026254568&partnerID=8YFLogxK. UR - http://www.scopus.com/inward/citedby.url?scp=0026254568&partnerID=8YFLogxK. U2 - 10.1097/00008571-199111000-00006. DO - 10.1097/00008571-199111000-00006. M3 - Article. C2 - 1726951. AN - SCOPUS:0026254568. VL - 1. SP - 94. EP - 97. JO - Pharmacogenetics and Genomics. JF - Pharmacogenetics and Genomics. SN - 1744-6872. IS - 2. ER - ...
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Physical Principles and Techniques of Protein Chemistry, Part A deals with the principles and application of selected physical methods in protein chemistry evaluation. This book is organized into nine chapters that cover microscopic, crystallographic, and electrophoretic techniques for protein conformational perturbations evaluation. This text first presents a general account of electron microscopy, its specimen preparation, optimum conditions for high resolution, measurement of electron micrographs, and illustrative examples of protein study. This book then examines the different types of maps from X-ray methods and the diffraction data from fibrous proteins. The subsequent chapters cover discussions on UV spectroscopy of proteins; luminescence properties of proteins and related compounds; and perturbation and flow methods for evaluation of proteins dynamic properties and rate constants. Other chapters deal with the evaluation of proteins dielectric properties using dielectric relaxation, electric
Physical Principles and Techniques of Protein Chemistry, Part A deals with the principles and application of selected physical methods in protein chemistry evaluation. This book is organized into nine chapters that cover microscopic, crystallographic, and electrophoretic techniques for protein conformational perturbations evaluation. This text first presents a general account of electron microscopy, its specimen preparation, optimum conditions for high resolution, measurement of electron micrographs, and illustrative examples of protein study. This book then examines the different types of maps from X-ray methods and the diffraction data from fibrous proteins. The subsequent chapters cover discussions on UV spectroscopy of proteins; luminescence properties of proteins and related compounds; and perturbation and flow methods for evaluation of proteins dynamic properties and rate constants. Other chapters deal with the evaluation of proteins dielectric properties using dielectric relaxation, electric