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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. ...

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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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###### Analysis and simulations of coupled bulk-surface reaction-diffusion systems on exponentially evolving volumes : Sussex...

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.. ...

###### A forward particle tracking Eulerian-Lagrangian Localized Adjoint Method for solution of the contaminant transport equation in...

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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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 ...

###### Reduction of mathematical models of signal transduction networks: simulation-based approach applied to EGF receptor signalling....

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 ...

###### DML-CZ - Czech Digital Mathematics Library: On the number of stationary patterns in reaction-diffusion systems

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 ...

###### An Algorithm for the Numerical Solution of Two-Sided Space-Fractional Partial Differential Equations : Computational Methods in...

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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###### Reaction-diffusion equations with fractional diffusion on non-smooth domains with various boundary conditions

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
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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 ...

###### A High-Performance Cellular Automaton Model of Tumor Growth with Dynamically Growing Domains

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###### Understanding lung function and disease through mathematical modeling and experiment | SMB 2021

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

###### Development of a Five-Degree-of-Freedom Seated Human Model and Parametric Studies for Its Vibrational Characteristics

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.

###### Frontiers | Validation and Trustworthiness of Multiscale Models of Cardiac Electrophysiology | Physiology

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

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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 ...

###### Mechanistic analysis of multi-omics datasets to generate kinetic parameters for constraint-based metabolic models | BMC...

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

###### A bistable reaction-diffusion system in a stretching flow - Nottingham ePrints

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 for one-dimensional steady state diffusion - Wikipedia

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 ...

###### 博客來-Advanced Spatial Modeling With Stochastic Partial Differential Equations Using R and Inla

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###### Understanding biological variability in susceptibility to respiratory disease<...

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

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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

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Free outflow boundary conditions have been widely adopted in hemodynamic model studies, they, however, intrinsically lack the ability to account for the regulatory mechanisms of systemic hemodynamics and hence carry a risk of producing incorrect results when applied to vascular segments with multiple outlets. In the present study, we developed a multiscale model capable of incorporating global cardiovascular properties into the simulation of blood flows in local vascular segments. The multiscale model was constructed by coupling a three-dimensional (3D) model of local arterial segments with a zero-one-dimensional (0-1-D) model of the cardiovascular system. Numerical validation based on an idealized model demonstrated the ability of the multiscale model to preserve reasonable pressure/flow wave transmission among different models. The multiscale model was further calibrated with clinical data to simulate cerebroarterial hemodynamics in a patient undergoing carotid artery operation. The results ...

###### Non-equilibrium thermodynamic sensitivity of oxidative phosphorylation | Proceedings of the Royal Society of London B:...

A new method was developed to analyse the dynamic properties of oxidative phosphorylation, in particular the sensitivity of the phosphate potential with respect to fluctuating cellular ATP utilization. This treatment is based on the eigenvalue sensitivity analysis of an experimentally supported non-equilibrium thermodynamic model of oxidative phosphorylation. Such an analysis allows direct access to the kinetic information, while circumventing the awkward conventional numerical integration of a set of nonlinear differential equations. This procedure revealed, for the parameters characteristic for liver of starved rats in vivo, that the sensitivity of oxidative phosphorylation to a fluctuating ATP utilization is minimal at a degree of coupling q = 0.95. This means that the phosphate potential is highly buffered with respect to fluctuating energy demands at that degree of coupling. This value of q agrees well with the degree of coupling qecf, at which net ATP production of oxidative ...

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The purposes of the research are to determine the main factors affecting the business success of agri-based exporting firms in Thanh Hoa Province. To achieve these research objectives, quantitative and qualitative method were used concurrently. 275 questionnaire survey was sent out, but only 180 respondents replied suitably for the quantitative analysis through SPSS 20.0 software. Cronbachs Alpha, EFA, and regression are taken to confirm the research result further. The research finding shows that external factors have much more affecting than others internal one on the business success of exporting SMEs, in which external factors have much effect on the Business Success of Agri-based Exporting Small and Medium-Sized Enterprises in Thanh Hoa Province than internal factors.

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###### Simplified models for the nonlinear evolution of two fast-particle-driven modes near the linear stability threshold

An analytical model that is based on purely differential equations of the nonlinear dynamics of two plasma modes driven resonantly by high-energy ions near the instability threshold is presented here. The well-known integro-differential model of Berk and Breizman (BB) extended to the case of two plasma modes is simplified here to a system of two coupled nonlinear differential equations of fifth order. The effects of the Krook, diffusion and dynamical friction (drag) relaxation processes are considered, whereas shifts in frequency and wavenumber between the modes are neglected. In spite of these simplifications the main features of the dynamics of the two plasma modes are retained. The numerical solutions to the model equations show competition between the two modes for survival, oscillations, chaotic regimes and blow-up behavior, similar to the BB model.

###### Smooth Particle methods page on SklogWiki - a wiki for statistical mechanics and thermodynamics

Smooth Particle Applied Mechanics (SPAM) and Smoothed Particle Hydrodynamics (SPH) are numerical methods for solving the equations of continuum mechanics (the continuity equation, the equation of motion, and the energy equation) with particles. This approach was originated by independently by Lucy [1] and by Gingold and Monaghan [2] in 1977 for astrophysical applications, and has since been applied to many challenging problems in fluid and solid mechanics. The main advantage of smooth-particle methods is that the partial differential equations (continuity, motion, energy) are replaced by ordinary differential equations (like molecular dynamics) describing the motion of particles. The particles can be of any size, from the microscopic to the astrophysical, and can obey any chosen constitutive equation. The main disadvantages are the difficulties in treating sharp surfaces or interfaces with discrete particles and in avoiding the instabilities that can result for materials under tension. Some ...

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The MIT Biology Department core courses, 7.012, 7.013, and 7.014, all cover the same core material, which includes the fundamental principles of biochemistry, genetics, molecular biology, and cell biology. Biological function at the molecular level is particularly emphasized and covers the structure and regulation of genes, as well as, the structure and synthesis of proteins, how these molecules are integrated into cells, and how these cells are integrated into multicellular systems and organisms. In addition, each version of the subject has its own distinctive material. 7.014 focuses on the application of the fundamental principles toward an understanding of human biology. Topics include genetics, cell biology, molecular biology, disease (infectious agents, inherited diseases and cancer), developmental biology, neurobiology and evolution ...