reaction-diffusion system with fractional derivatives
Directory of Open Access Journals (Sweden)
Kamel Haouam
2006-01-01
Full Text Available We give some necessary conditions for local and global existence of a solution to reaction-diffusion system of type (FDS with temporal and spacial fractional derivatives. As in the case of single equation of type (STFE studied by M. Kirane et al. (2005, we prove that these conditions depend on the behavior of initial conditions for large |x|.
Nonlinear analysis of a reaction-diffusion system: Amplitude equations
Energy Technology Data Exchange (ETDEWEB)
Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)
2012-10-15
A reaction-diffusion system with a nonlinear diffusion term is considered. Based on nonlinear analysis, the amplitude equations are obtained in the cases of the Hopf and Turing instabilities in the system. Turing pattern-forming regions in the parameter space are determined for supercritical and subcritical instabilities in a two-component reaction-diffusion system.
Pulses in singularly perturbed reaction-diffusion systems
Veerman, Frederik Willem Johan
2013-01-01
In this thesis, the existence and stability of pulse solutions in two-component, singularly perturbed reaction-diffusion systems is analysed using dynamical systems techniques. New phenomena in very general types of systems emerge when geometrical techniques are applied.
Analytically solvable models of reaction-diffusion systems
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Zemskov, E P; Kassner, K [Institut fuer Theoretische Physik, Otto-von-Guericke-Universitaet, Universitaetsplatz 2, 39106 Magdeburg (Germany)
2004-05-01
We consider a class of analytically solvable models of reaction-diffusion systems. An analytical treatment is possible because the nonlinear reaction term is approximated by a piecewise linear function. As particular examples we choose front and pulse solutions to illustrate the matching procedure in the one-dimensional case.
Turing instability in reaction-diffusion systems with nonlinear diffusion
Energy Technology Data Exchange (ETDEWEB)
Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)
2013-10-15
The Turing instability is studied in two-component reaction-diffusion systems with nonlinear diffusion terms, and the regions in parametric space where Turing patterns can form are determined. The boundaries between super- and subcritical bifurcations are found. Calculations are performed for one-dimensional brusselator and oregonator models.
Distribution in flowing reaction-diffusion systems
Kamimura, Atsushi
2009-12-28
A power-law distribution is found in the density profile of reacting systems A+B→C+D and 2A→2C under a flow in two and three dimensions. Different densities of reactants A and B are fixed at both ends. For the reaction A+B, the concentration of reactants asymptotically decay in space as x-1/2 and x-3/4 in two dimensions and three dimensions, respectively. For 2A, it decays as log (x) /x in two dimensions. The decay of A+B is explained considering the effect of segregation of reactants in the isotropic case. The decay for 2A is explained by the marginal behavior of two-dimensional diffusion. A logarithmic divergence of the diffusion constant with system size is found in two dimensions. © 2009 The American Physical Society.
Existence of Solutions for a Quasilinear Reaction Diffusion System
Tian, Canrong
2012-01-01
The degenerate reaction diffusion system has been applied to a variety of physical and engineering problems. This paper is extended the existence of solutions from the quasimonotone reaction functions (e.g., inhibitor-inhibitor mechanism) to the mixed quasimonotone reaction functions (e.g., activator-inhibitor mechanism). By Schauder fixed point theorem, it is shown that the system admits at least one positive solution if there exist a coupled of upper and lower solutions. This result is appl...
Nonlinear dynamics of reaction-diffusion systems: Analysis and computations
International Nuclear Information System (INIS)
Wilhelmsson, H.
1991-01-01
Equilibria and dynamics of reaction-diffusion systems are studied by means of analysis and computations based on a central expansions method for radially symmetric as well as angularly asymmetric distributions. Effects of boundary conditions are included. The interplay between the different processes in the evolution of the system is considered. The investigation provides a unified description in one, two and three dimensions. A particular application concerns the time evolution of temperature profiles in a fusion reactor plasma. (au)
Parametric spatiotemporal oscillation in reaction-diffusion systems.
Ghosh, Shyamolina; Ray, Deb Shankar
2016-03-01
We consider a reaction-diffusion system in a homogeneous stable steady state. On perturbation by a time-dependent sinusoidal forcing of a suitable scaling parameter the system exhibits parametric spatiotemporal instability beyond a critical threshold frequency. We have formulated a general scheme to calculate the threshold condition for oscillation and the range of unstable spatial modes lying within a V-shaped region reminiscent of Arnold's tongue. Full numerical simulations show that depending on the specificity of nonlinearity of the models, the instability may result in time-periodic stationary patterns in the form of standing clusters or spatially localized breathing patterns with characteristic wavelengths. Our theoretical analysis of the parametric oscillation in reaction-diffusion system is corroborated by full numerical simulation of two well-known chemical dynamical models: chlorite-iodine-malonic acid and Briggs-Rauscher reactions.
Global Bifurcation for a Reaction-Diffusion System with Inclusions
Czech Academy of Sciences Publication Activity Database
Eisner, Jan; Kučera, Milan; Väth, M.
2009-01-01
Roč. 28, č. 4 (2009), s. 373-409 ISSN 0232-2064 R&D Projects: GA AV ČR IAA100190506 Institutional research plan: CEZ:AV0Z10190503 Keywords : global bifurcation * degree * stationary solutions * reaction-diffusion system * Laplace operator Subject RIV: BA - General Mathematics Impact factor: 0.371, year: 2009 http://www.ems-ph.org/journals/show_abstract.php?issn=0232-2064&vol=28&iss=4&rank=1
Control of transversal instabilities in reaction-diffusion systems
Molnos, Sonja; Löber, Jakob; Totz, Jan Frederik; Engel, Harald
2015-01-01
In two-dimensional reaction-diffusion systems, local curvature perturbations in the shape of traveling waves are typically damped out and disappear in the course of time. If, however, the inhibitor diffuses much faster than the activator, transversal instabilities can arise, leading from flat to folded, spatio-temporally modulated wave shapes and to spreading spiral turbulence. For experimentally relevant parameter values, the photosensitive Belousov-Zhabotinsky reaction (PBZR) does not exhib...
Global dynamics of a reaction-diffusion system
Directory of Open Access Journals (Sweden)
Yuncheng You
2011-02-01
Full Text Available In this work the existence of a global attractor for the semiflow of weak solutions of a two-cell Brusselator system is proved. The method of grouping estimation is exploited to deal with the challenge in proving the absorbing property and the asymptotic compactness of this type of coupled reaction-diffusion systems with cubic autocatalytic nonlinearity and linear coupling. It is proved that the Hausdorff dimension and the fractal dimension of the global attractor are finite. Moreover, the existence of an exponential attractor for this solution semiflow is shown.
Periodic solutions to systems of reaction-diffusion equations
Rosen, G.
1976-01-01
Necessary and sufficient conditions are derived for the existence of temporally periodic 'dissipative structure' solutions in weak diffusion with the reaction rate terms dominant in a generic system of reaction-diffusion differential equations. The enumerator index i of the equations denotes the density or concentration of the ith participating molecular or biological species, and D sub i is the diffusivity constant for the ith species while Q sub i (c), an algebraic function of the n-tuple c, expresses the local rate of production of the ith species due to chemical reactions or biological interactions.
A discrete model to study reaction-diffusion-mechanics systems.
Weise, Louis D; Nash, Martyn P; Panfilov, Alexander V
2011-01-01
This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.
A discrete model to study reaction-diffusion-mechanics systems.
Directory of Open Access Journals (Sweden)
Louis D Weise
Full Text Available This article introduces a discrete reaction-diffusion-mechanics (dRDM model to study the effects of deformation on reaction-diffusion (RD processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material. Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.
Simulating mesoscopic reaction-diffusion systems using the Gillespie algorithm
Energy Technology Data Exchange (ETDEWEB)
Bernstein, David
2004-12-12
We examine an application of the Gillespie algorithm to simulating spatially inhomogeneous reaction-diffusion systems in mesoscopic volumes such as cells and microchambers. The method involves discretizing the chamber into elements and modeling the diffusion of chemical species by the movement of molecules between neighboring elements. These transitions are expressed in the form of a set of reactions which are added to the chemical system. The derivation of the rates of these diffusion reactions is by comparison with a finite volume discretization of the heat equation on an unevenly spaced grid. The diffusion coefficient of each species is allowed to be inhomogeneous in space, including discontinuities. The resulting system is solved by the Gillespie algorithm using the fast direct method. We show that in an appropriate limit the method reproduces exact solutions of the heat equation for a purely diffusive system and the nonlinear reaction-rate equation describing the cubic autocatalytic reaction.
Hopping transport in hostile reaction-diffusion systems
Missel, Andrew R.; Dahmen, Karin A.
2009-02-01
We investigate transport in a disordered reaction-diffusion model consisting of particles which are allowed to diffuse, compete with one another (2A→A) , give birth in small areas called “oases” (A→2A) , and die in the “desert” outside the oases (A→0) . This model has previously been used to study bacterial populations in the laboratory and is related to a model of plankton populations in the oceans. We first consider the nature of transport between two oases: In the limit of high growth rate, this is effectively a first passage process, and we are able to determine the first passage time probability density function in the limit of large oasis separation. This result is then used along with the theory of hopping conduction in doped semiconductors to estimate the time taken by a population to cross a large system.
Attractor for a Reaction-Diffusion System Modeling Cancer Network
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Xueyong Chen
2014-01-01
Full Text Available A reaction-diffusion cancer network regulated by microRNA is considered in this paper. We study the asymptotic behavior of solution and show the existence of global uniformly bounded solution to the system in a bounded domain Ω⊂Rn. Some estimates and asymptotic compactness of the solutions are proved. As a result, we establish the existence of the global attractor in L2(Ω×L2(Ω and prove that the solution converges to stable steady states. These results can help to understand the dynamical character of cancer network and propose a new insight to study the mechanism of cancer. In the end, the numerical simulation shows that the analytical results agree with numerical simulation.
Decay to Equilibrium for Energy-Reaction-Diffusion Systems
Haskovec, Jan
2018-02-06
We derive thermodynamically consistent models of reaction-diffusion equations coupled to a heat equation. While the total energy is conserved, the total entropy serves as a driving functional such that the full coupled system is a gradient flow. The novelty of the approach is the Onsager structure, which is the dual form of a gradient system, and the formulation in terms of the densities and the internal energy. In these variables it is possible to assume that the entropy density is strictly concave such that there is a unique maximizer (thermodynamical equilibrium) given linear constraints on the total energy and suitable density constraints. We consider two particular systems of this type, namely, a diffusion-reaction bipolar energy transport system, and a drift-diffusion-reaction energy transport system with confining potential. We prove corresponding entropy-entropy production inequalities with explicitly calculable constants and establish the convergence to thermodynamical equilibrium, first in entropy and later in L norm using Cziszár–Kullback–Pinsker type inequalities.
Reaction-diffusion mechanisms and quantum spin systems
Schütz, Gunter M.
We present a brief tutorial introduction into the quantum Hamiltonian formalism for stochastic many-body systems defined in terms of a master equation for their time evolution. These models describe interacting classical particle systems where particles hop on a lattice and may undergo reactions such as A+A→0. The quantum Hamiltonian formalism for the master equation provides a convenient general framework for the treatment of such models which, by various mappings, are capable of describing a wide variety of phenomena in non-equilibrium physics and in random media. The formalism is particularly useful if the quantum Hamiltonian has continuous global symmetries or if it is integrable, i.e. has an infinite set of conservation laws. This is demonstrated in the case of the exclusion process and for a toy model of tumor growth. Experimental applications of other integrable reaction-diffusion models in various areas of polymer physics (gel electrophoresis of DNA, exciton dynamics on polymers and the kinetics of biopolymerization on RNA) are pointed out.
Pattern formation in reaction-diffusion and ferrofluid systems
Ytreberg, Frederick Martin
2000-11-01
The study of pattern forming systems has been of growing interest to biologists, chemists and physicists in recent years. Generally, these pattern forming systems involve competing interactions that lead to instabilities, driving the system to form a pattern. In this project, we look at two such pattern forming systems. The first is a reaction-diffusion system, where the competition is between the activator and the inhibitor, and the second is a thin layer of ferrofluid which exhibits pattern formation due to a competition between magnetic and surface energies. Numerical simulation of the Gierer-Meinhardt model for reaction and diffusion is used to study the sequence of transitions from islands of high activator concentration to stripes of high activator concentration to wells of depleted activator. This sequence can occur by activator saturation or by inhibitor depletion. Four quantitative measures are introduced which display different trends depending upon whether the transition is driven by activator saturation or inhibitor depletion. These four measures characterize the transitions, and enhance understanding of the system. A model for the Helmholtz free energy is derived to predict aggregate spacing in thin layers of ferrofluid. When a drop of ferrofluid is confined between two glass plates and subjected to an external magnetic field, the particles in the ferrofluid aggregate, forming a hexagonal array. This theoretical model, once fully developed, is used to predict aggregate spacing for this hexagonal pattern as a function of external magnetic field, the ramping rate of the external magnetic field, and plate separation. The results of this model are then compared to experimental data, demonstrating excellent agreement.
A priori L∞ estimates for solutions of a class of reaction-diffusion systems.
Du, Zengji; Peng, Rui
2016-05-01
In this short paper, we establish a priori L∞-norm estimates for solutions of a class of reaction-diffusion systems which can be used to model the spread of infectious disease. The developed technique may find applications in other reaction-diffusion systems.
Distributed order reaction-diffusion systems associated with Caputo derivatives
Saxena, R. K.; Mathai, A. M.; Haubold, H. J.
2014-08-01
This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation of distributed order associated with the Caputo derivatives as the time-derivative and Riesz-Feller fractional derivative as the space-derivative. The solution is derived by the application of the joint Laplace and Fourier transforms in compact and closed form in terms of the H-function. The results derived are of general nature and include the results investigated earlier by other authors, notably by Mainardi et al. ["The fundamental solution of the space-time fractional diffusion equation," Fractional Calculus Appl. Anal. 4, 153-202 (2001); Mainardi et al. "Fox H-functions in fractional diffusion," J. Comput. Appl. Math. 178, 321-331 (2005)] for the fundamental solution of the space-time fractional equation, including Haubold et al. ["Solutions of reaction-diffusion equations in terms of the H-function," Bull. Astron. Soc. India 35, 681-689 (2007)] and Saxena et al. ["Fractional reaction-diffusion equations," Astrophys. Space Sci. 305, 289-296 (2006a)] for fractional reaction-diffusion equations. The advantage of using the Riesz-Feller derivative lies in the fact that the solution of the fractional reaction-diffusion equation, containing this derivative, includes the fundamental solution for space-time fractional diffusion, which itself is a generalization of fractional diffusion, space-time fraction diffusion, and time-fractional diffusion, see Schneider and Wyss ["Fractional diffusion and wave equations," J. Math. Phys. 30, 134-144 (1989)]. These specialized types of diffusion can be interpreted as spatial probability density functions evolving in time and are expressible in terms of the H-function in compact forms. The convergence conditions for the double series occurring in the solutions are investigated. It is interesting to observe that the double series comes out to be a special case of the Srivastava-Daoust hypergeometric function of two variables
Cherniha, Roman
2017-01-01
This book presents several fundamental results in solving nonlinear reaction-diffusion equations and systems using symmetry-based methods. Reaction-diffusion systems are fundamental modeling tools for mathematical biology with applications to ecology, population dynamics, pattern formation, morphogenesis, enzymatic reactions and chemotaxis. The book discusses the properties of nonlinear reaction-diffusion systems, which are relevant for biological applications, from the symmetry point of view, providing rigorous definitions and constructive algorithms to search for conditional symmetry (a nontrivial generalization of the well-known Lie symmetry) of nonlinear reaction-diffusion systems. In order to present applications to population dynamics, it focuses mainly on two- and three-component diffusive Lotka-Volterra systems. While it is primarily a valuable guide for researchers working with reaction-diffusion systems and those developing the theoretical aspects of conditional symmetry conception,...
International Nuclear Information System (INIS)
Moore, Peter K.
2003-01-01
Solving systems of reaction-diffusion equations in three space dimensions can be prohibitively expensive both in terms of storage and CPU time. Herein, I present a new incomplete assembly procedure that is designed to reduce storage requirements. Incomplete assembly is analogous to incomplete factorization in that only a fixed number of nonzero entries are stored per row and a drop tolerance is used to discard small values. The algorithm is incorporated in a finite element method-of-lines code and tested on a set of reaction-diffusion systems. The effect of incomplete assembly on CPU time and storage and on the performance of the temporal integrator DASPK, algebraic solver GMRES and preconditioner ILUT is studied
Stochastic modeling and simulation of reaction-diffusion system with Hill function dynamics.
Chen, Minghan; Li, Fei; Wang, Shuo; Cao, Young
2017-03-14
Stochastic simulation of reaction-diffusion systems presents great challenges for spatiotemporal biological modeling and simulation. One widely used framework for stochastic simulation of reaction-diffusion systems is reaction diffusion master equation (RDME). Previous studies have discovered that for the RDME, when discretization size approaches zero, reaction time for bimolecular reactions in high dimensional domains tends to infinity. In this paper, we demonstrate that in the 1D domain, highly nonlinear reaction dynamics given by Hill function may also have dramatic change when discretization size is smaller than a critical value. Moreover, we discuss methods to avoid this problem: smoothing over space, fixed length smoothing over space and a hybrid method. Our analysis reveals that the switch-like Hill dynamics reduces to a linear function of discretization size when the discretization size is small enough. The three proposed methods could correctly (under certain precision) simulate Hill function dynamics in the microscopic RDME system.
Trend to equilibrium for a reaction-diffusion system modelling reversible enzyme reaction
Elias, Jan
2016-01-01
20 pages; A spatio-temporal evolution of chemicals appearing in a reversible enzyme reaction and modelled by a four component reaction-diffusion system with the reaction terms obtained by the law of mass action is considered. The large time behaviour of the system is studied by means of entropy methods.
Trend to Equilibrium for a Reaction-Diffusion System Modelling Reversible Enzyme Reaction.
Eliaš, Ján
2018-01-01
A spatio-temporal evolution of chemicals appearing in a reversible enzyme reaction and modelled by a four-component reaction-diffusion system with the reaction terms obtained by the law of mass action is considered. The large time behaviour of the system is studied by means of entropy methods.
Traveling wave solutions for reaction-diffusion systems
DEFF Research Database (Denmark)
Lin, Zhigui; Pedersen, Michael; Tian, Canrong
2010-01-01
This paper is concerned with traveling waves of reaction–diffusion systems. The definition of coupled quasi-upper and quasi-lower solutions is introduced for systems with mixed quasimonotone functions, and the definition of ordered quasi-upper and quasi-lower solutions is also given for systems...... with quasimonotone nondecreasing functions. By the monotone iteration method, it is shown that if the system has a pair of coupled quasi-upper and quasi-lower solutions, then there exists at least a traveling wave solution. Moreover, if the system has a pair of ordered quasi-upper and quasi-lower solutions...
Pattern formation mechanisms in reaction-diffusion systems.
Vanag, Vladimir K; Epstein, Irving R
2009-01-01
In systems undergoing chemical reaction and diffusion, a remarkable variety of spatially structured patterns, stationary or moving, local or global, can arise, many of them reminiscent of forms and phenomena seen in living systems. Chemical systems offer the advantage that one can often control the parameters that determine the patterns formed and can thereby probe fundamental issues about pattern formation, with possible insights into biologically relevant phenomena. We present experimental examples and discuss several mechanisms by which such spatiotemporal structure may arise, classifying the mechanisms according to the type of instability that results in pattern formation. In some systems, the pattern that emerges depends not only on the chemical and physical parameters but also on the initial state of the system. Interactions between instabilities can result in particularly complex patterns.
Phase-Reduction Approach to Synchronization of Spatiotemporal Rhythms in Reaction-Diffusion Systems
Nakao, Hiroya; Yanagita, Tatsuo; Kawamura, Yoji
2014-04-01
Reaction-diffusion systems can describe a wide class of rhythmic spatiotemporal patterns observed in chemical and biological systems, such as circulating pulses on a ring, oscillating spots, target waves, and rotating spirals. These rhythmic dynamics can be considered limit cycles of reaction-diffusion systems. However, the conventional phase-reduction theory, which provides a simple unified framework for analyzing synchronization properties of limit-cycle oscillators subjected to weak forcing, has mostly been restricted to low-dimensional dynamical systems. Here, we develop a phase-reduction theory for stable limit-cycle solutions of reaction-diffusion systems with infinite-dimensional state space. By generalizing the notion of isochrons to functional space, the phase-sensitivity function—a fundamental quantity for phase reduction—is derived. For illustration, several rhythmic dynamics of the FitzHugh-Nagumo model of excitable media are considered. Nontrivial phase-response properties and synchronization dynamics are revealed, reflecting their complex spatiotemporal organization. Our theory will provide a general basis for the analysis and control of spatiotemporal rhythms in various reaction-diffusion systems.
Scaling of morphogenetic patterns in reaction-diffusion systems.
Rasolonjanahary, Manan'Iarivo; Vasiev, Bakhtier
2016-09-07
Development of multicellular organisms is commonly associated with the response of individual cells to concentrations of chemical substances called morphogens. Concentration fields of morphogens form a basis for biological patterning and ensure its properties including ability to scale with the size of the organism. While mechanisms underlying the formation of morphogen gradients are reasonably well understood, little is known about processes responsible for their scaling. Here, we perform a formal analysis of scaling for chemical patterns forming in continuous systems. We introduce a quantity representing the sensitivity of systems to changes in their size and use it to analyse scaling properties of patterns forming in a few different systems. Particularly, we consider how scaling properties of morphogen gradients forming in diffusion-decay systems depend on boundary conditions and how the scaling can be improved by passive modulation of morphogens or active transport in the system. We also analyse scaling of morphogenetic signal caused by two opposing gradients and consider scaling properties of patterns forming in activator-inhibitor systems. We conclude with a few possible mechanisms which allow scaling of morphogenetic patterns. Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.
Global existence of solutions for some coupled systems of reaction-diffusion equations
Salem, Abdelmalek; Amar, Youkana
2010-01-01
The aim of this work is to study the global existence of solutions for some coupled systems of reaction diffusion which describe the spread within a population of infectious disease. We consider a triangular matrix diffusion and we show that we can prove global existence of classical solutions for the nonlinearities of weakly exponential growth.
Czech Academy of Sciences Publication Activity Database
Eisner, J.; Väth, Martin
2016-01-01
Roč. 135, April (2016), s. 158-193 ISSN 0362-546X Institutional support: RVO:67985840 Keywords : reaction-diffusion system * turing instability * global bifurcation Subject RIV: BA - General Mathematics Impact factor: 1.192, year: 2016 http://www.sciencedirect.com/science/article/pii/S0362546X16000146
Stochastic reaction-diffusion systems with H\\"older continuous multiplicative noise
Kunze, Markus C.
2012-01-01
We prove pathwise uniqueness and strong existence of solutions for stochastic reaction-diffusion systems with locally Lipschitz continuous reaction term of polynomial growth and H\\"older continuous multiplicative noise. Under additional assumptions on the coefficients, we also prove positivity of the solutions.
Czech Academy of Sciences Publication Activity Database
Eisner, J.; Väth, Martin
2016-01-01
Roč. 135, April (2016), s. 158-193 ISSN 0362-546X Institutional support: RVO:67985840 Keywords : reaction -diffusion system * turing instability * global bifurcation Subject RIV: BA - General Mathematics Impact factor: 1.192, year: 2016 http://www.sciencedirect.com/science/article/pii/S0362546X16000146
Stability results for a reaction-diffusion system with a single measurement
Energy Technology Data Exchange (ETDEWEB)
Ramoul, Hichem [Centre universitaire de Khenchela, Route de Batna, BP 1252, Liberte, 40004 Khenchela (Algeria); Gaitan, Patricia [Laboratoire d' analyse, topologie, probabilites CNRS UMR 6632, Marseille (France) and Universite Aix-Marseille II (France); Cristofol, Michel [Laboratoire d' analyse, topologie, probabilites CNRS UMR 6632, Marseille, France and Universite Aix-Marseille III (France)
2007-06-15
For a two by two reaction-diffusion system on a bounded domain we give a simultaneous stability result for one coefficient and for the initial conditions. The key ingredient is a global Carleman-type estimate with a single observation acting on a subdomain.
Stability Analysis of a Reaction-Diffusion System Modeling Atherogenesis
Ibragimov, Akif
2010-01-01
This paper presents a linear, asymptotic stability analysis for a reaction-diffusionconvection system modeling atherogenesis, the initiation of atherosclerosis, as an inflammatory instability. Motivated by the disease paradigm articulated by Ross, atherogenesis is viewed as an inflammatory spiral with a positive feedback loop involving key cellular and chemical species interacting and reacting within the intimal layer of muscular arteries. The inflammatory spiral is initiated as an instability from a healthy state which is defined to be an equilibrium state devoid of certain key inflammatory markers. Disease initiation is studied through a linear, asymptotic stability analysis of a healthy equilibrium state. Various theorems are proved, giving conditions on system parameters guaranteeing stability of the health state, and a general framework is developed for constructing perturbations from a healthy state that exhibit blow-up, which are interpreted as corresponding to disease initiation. The analysis reveals key features that arterial geometry, antioxidant levels, and the source of inflammatory components (through coupled third-kind boundary conditions or through body sources) play in disease initiation. © 2010 Society for Industrial and Applied Mathematics.
International Nuclear Information System (INIS)
Mittal, R.C.; Rohila, Rajni
2016-01-01
In this paper, we have applied modified cubic B-spline based differential quadrature method to get numerical solutions of one dimensional reaction-diffusion systems such as linear reaction-diffusion system, Brusselator system, Isothermal system and Gray-Scott system. The models represented by these systems have important applications in different areas of science and engineering. The most striking and interesting part of the work is the solution patterns obtained for Gray Scott model, reminiscent of which are often seen in nature. We have used cubic B-spline functions for space discretization to get a system of ordinary differential equations. This system of ODE’s is solved by highly stable SSP-RK43 method to get solution at the knots. The computed results are very accurate and shown to be better than those available in the literature. Method is easy and simple to apply and gives solutions with less computational efforts.
On the uniform boundedness of the solutions of systems of reaction-diffusion equations
Directory of Open Access Journals (Sweden)
L. Melkemi
2005-12-01
Full Text Available We consider a system of reaction-diffusion equations for which the uniform boundedness of the solutions can not be derived by existing methods. The system may represent, in particular, an epidemic model describing the spread of an infection disease within a population. We present an $L^{p}$ argument allowing to establish the global existence and the uniform boundedness of the solutions of the considered system.
Flow-induced symmetry reduction in two-dimensional reaction-diffusion system
Hu, Hai Xiang; Li, Xiao Chun; Li, Qian Shu
2009-03-01
The influence of uniform flow on the pattern formation is investigated in a two-dimensional reaction-diffusion system. It is found that the convective flow plays a key role on pattern modulation. Both traveling and stationary periodic patterns are obtained. At moderate flow rates, the perfect hexagon, phase-shifted hexagon and stable square, which are essentially unstable in unperturbed reaction-diffusion systems, are obtained. These patterns move downstream. If the flow rate is increased further, the stationary flow-oriented stripes develop and compete with the spots. If the flow rate exceeds some critical value, the system is convectively unstable and the stationary stripes prevail against the traveling spots. The above patterns all have the same critical wavenumber associated with Turing bifurcation, which indicates that Turing instability produces the patterns while the flow induces the symmetry reduction, i.e., from six-fold symmetry to four-fold one, and to two-fold one ultimately.
Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains
Madzvamuse, Anotida
2009-08-29
By using asymptotic theory, we generalise the Turing diffusively-driven instability conditions for reaction-diffusion systems with slow, isotropic domain growth. There are two fundamental biological differences between the Turing conditions on fixed and growing domains, namely: (i) we need not enforce cross nor pure kinetic conditions and (ii) the restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Our theoretical findings are confirmed and reinforced by numerical simulations for the special cases of isotropic linear, exponential and logistic growth profiles. In particular we illustrate an example of a reaction-diffusion system which cannot exhibit a diffusively-driven instability on a fixed domain but is unstable in the presence of slow growth. © Springer-Verlag 2009.
STEPS: Modeling and Simulating Complex Reaction-Diffusion Systems with Python
Wils, Stefan; Schutter, Erik De
2009-01-01
We describe how the use of the Python language improved the user interface of the program STEPS. STEPS is a simulation platform for modeling and stochastic simulation of coupled reaction-diffusion systems with complex 3-dimensional boundary conditions. Setting up such models is a complicated process that consists of many phases. Initial versions of STEPS relied on a static input format that did not cleanly separate these phases, limiting modelers in how they could control the simulation and b...
Czech Academy of Sciences Publication Activity Database
Baltaev, J.I.; Kučera, Milan; Väth, Martin
2012-01-01
Roč. 57, č. 2 (2012), s. 143-165 ISSN 0862-7940 R&D Projects: GA AV ČR IAA100190805 Institutional research plan: CEZ:AV0Z10190503 Keywords : reaction -diffusion system * unilateral condition * variational inequality Subject RIV: BA - General Mathematics Impact factor: 0.222, year: 2012 http://www.springerlink.com/content/e1km86727356pl88/
Bifurcation points for a reaction-diffusion system with two inequalities
Czech Academy of Sciences Publication Activity Database
Eisner, J.; Kučera, Milan; Väth, M.
2010-01-01
Roč. 365, č. 1 (2010), s. 176-194 ISSN 0022-247X R&D Projects: GA AV ČR IAA100190805 Institutional research plan: CEZ:AV0Z10190503 Keywords : global bifurcation * degree * stationary solutions * reaction -diffusion system * variational inequality * Signorini boundary condition * Laplace operator Subject RIV: BA - General Mathematics Impact factor: 1.174, year: 2010 http://www.sciencedirect.com/science/article/pii/S0022247X09008579
Location of bifurcation points for a reaction-diffusion system with Neumann-Signorini conditions
Czech Academy of Sciences Publication Activity Database
Eisner, J.; Väth, Martin
2011-01-01
Roč. 11, č. 4 (2011), s. 809-836 ISSN 1536-1365 R&D Projects: GA AV ČR IAA100190805 Institutional research plan: CEZ:AV0Z10190503 Keywords : global bifurcation * stationary solutions * reaction -diffusion system Subject RIV: BA - General Mathematics Impact factor: 0.644, year: 2011 http://www.advancednonlinearstudies.com/Archive/V11N4/ANLS_V11N4_pg809-836.pdf
Externally controlled anisotropy in pattern-forming reaction-diffusion systems.
Escala, Dario M; Guiu-Souto, Jacobo; Muñuzuri, Alberto P
2015-06-01
The effect of centrifugal forces is analyzed in a pattern-forming reaction-diffusion system. Numerical simulations conducted on the appropriate extension of the Oregonator model for the Belousov-Zhabotinsky reaction show a great variety of dynamical behaviors in such a system. In general, the system exhibits an anisotropy that results in new types of patterns or in a global displacement of the previous one. We consider the effect of both constant and periodically modulated centrifugal forces on the different types of patterns that the system may exhibit. A detailed analysis of the patterns and behaviors observed for the different parameter values considered is presented here.
Existence and exponential stability of traveling waves for delayed reaction-diffusion systems
Hsu, Cheng-Hsiung; Yang, Tzi-Sheng; Yu, Zhixian
2018-03-01
The purpose of this work is to investigate the existence and exponential stability of traveling wave solutions for general delayed multi-component reaction-diffusion systems. Following the monotone iteration scheme via an explicit construction of a pair of upper and lower solutions, we first obtain the existence of monostable traveling wave solutions connecting two different equilibria. Then, applying the techniques of weighted energy method and comparison principle, we show that all solutions of the Cauchy problem for the considered systems converge exponentially to traveling wave solutions provided that the initial perturbations around the traveling wave fronts belong to a suitable weighted Sobolev space.
Basin of Attraction of Solutions with Pattern Formation in Slow-Fast Reaction-Diffusion Systems.
Ambrosio, B; Aziz-Alaoui, M A
2016-12-01
This article is devoted to the characterization of the basin of attraction of pattern solutions for some slow-fast reaction-diffusion systems with a symmetric property and an underlying oscillatory reaction part. We characterize some subsets of initial conditions that prevent the dynamical system to evolve asymptotically toward solutions which are homogeneous in space. We also perform numerical simulations that illustrate theoretical results and give rise to symmetric and non-symmetric pattern solutions. We obtain these last solutions by choosing particular random initial conditions.
Simulations of pattern dynamics for reaction-diffusion systems via SIMULINK.
Wang, Kaier; Steyn-Ross, Moira L; Steyn-Ross, D Alistair; Wilson, Marcus T; Sleigh, Jamie W; Shiraishi, Yoichi
2014-04-11
Investigation of the nonlinear pattern dynamics of a reaction-diffusion system almost always requires numerical solution of the system's set of defining differential equations. Traditionally, this would be done by selecting an appropriate differential equation solver from a library of such solvers, then writing computer codes (in a programming language such as C or Matlab) to access the selected solver and display the integrated results as a function of space and time. This "code-based" approach is flexible and powerful, but requires a certain level of programming sophistication. A modern alternative is to use a graphical programming interface such as Simulink to construct a data-flow diagram by assembling and linking appropriate code blocks drawn from a library. The result is a visual representation of the inter-relationships between the state variables whose output can be made completely equivalent to the code-based solution. As a tutorial introduction, we first demonstrate application of the Simulink data-flow technique to the classical van der Pol nonlinear oscillator, and compare Matlab and Simulink coding approaches to solving the van der Pol ordinary differential equations. We then show how to introduce space (in one and two dimensions) by solving numerically the partial differential equations for two different reaction-diffusion systems: the well-known Brusselator chemical reactor, and a continuum model for a two-dimensional sheet of human cortex whose neurons are linked by both chemical and electrical (diffusive) synapses. We compare the relative performances of the Matlab and Simulink implementations. The pattern simulations by Simulink are in good agreement with theoretical predictions. Compared with traditional coding approaches, the Simulink block-diagram paradigm reduces the time and programming burden required to implement a solution for reaction-diffusion systems of equations. Construction of the block-diagram does not require high-level programming
Mielke, Alexander; Mittnenzweig, Markus
2018-04-01
We discuss how the recently developed energy dissipation methods for reaction diffusion systems can be generalized to the non-isothermal case. For this, we use concave entropies in terms of the densities of the species and the internal energy, where the importance is that the equilibrium densities may depend on the internal energy. Using the log-Sobolev estimate and variants for lower-order entropies as well as estimates for the entropy production of the nonlinear reactions, we give two methods to estimate the relative entropy by the total entropy production, namely a somewhat restrictive convexity method, which provides explicit decay rates, and a very general, but weaker compactness method.
Global existence and blowup for free boundary problems of coupled reaction-diffusion systems
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Jianping Sun
2014-05-01
Full Text Available This article concerns a free boundary problem for a reaction-diffusion system modeling the cooperative interaction of two diffusion biological species in one space dimension. First we show the existence and uniqueness of a local classical solution, then we study the asymptotic behavior of the free boundary problem. Our results show that the free boundary problem admits a global solution if the inter-specific competitions are strong, while, if the inter-specific competitions are weak, there exist the blowup solution and a global fast solution.
The entropy dissipation method for spatially inhomogeneous reaction-diffusion-type systems
Di Francesco, M.
2008-12-08
We study the long-time asymptotics of reaction-diffusion-type systems that feature a monotone decaying entropy (Lyapunov, free energy) functional. We consider both bounded domains and confining potentials on the whole space for arbitrary space dimensions. Our aim is to derive quantitative expressions for (or estimates of) the rates of convergence towards an (entropy minimizing) equilibrium state in terms of the constants of diffusion and reaction and with respect to conserved quantities. Our method, the so-called entropy approach, seeks to quantify convergence to equilibrium by using functional inequalities, which relate quantitatively the entropy and its dissipation in time. The entropy approach is well suited to nonlinear problems and known to be quite robust with respect to model variations. It has already been widely applied to scalar diffusion-convection equations, and the main goal of this paper is to study its generalization to systems of partial differential equations that contain diffusion and reaction terms and admit fewer conservation laws than the size of the system. In particular, we successfully apply the entropy approach to general linear systems and to a nonlinear example of a reaction-diffusion-convection system arising in solid-state physics as a paradigm for general nonlinear systems. © 2008 The Royal Society.
International Nuclear Information System (INIS)
Owolabi, Kolade M.
2016-01-01
The aim of this paper is to examine pattern formation in the sub— and super-diffusive scenarios and compare it with that of classical or standard diffusive processes in two-component fractional reaction-diffusion systems that modeled a predator-prey dynamics. The focus of the work concentrates on the use of two separate mathematical techniques, we formulate a Fourier spectral discretization method as an efficient alternative technique to solve fractional reaction-diffusion problems in higher-dimensional space, and later advance the resulting systems of ODEs in time with the adaptive exponential time-differencing solver. Obviously, the fractional Fourier approach is able to achieve spectral convergence up to machine precision regardless of the fractional order α, owing to the fact that our approach is able to give full diagonal representation of the fractional operator. The complexity of the dynamics in this system is theoretically discussed and graphically displayed with some examples and numerical simulations in one, two and three dimensions.
Oscillatory pulses and wave trains in a bistable reaction-diffusion system with cross diffusion.
Zemskov, Evgeny P; Tsyganov, Mikhail A; Horsthemke, Werner
2017-01-01
We study waves with exponentially decaying oscillatory tails in a reaction-diffusion system with linear cross diffusion. To be specific, we consider a piecewise linear approximation of the FitzHugh-Nagumo model, also known as the Bonhoeffer-van der Pol model. We focus on two types of traveling waves, namely solitary pulses that correspond to a homoclinic solution, and sequences of pulses or wave trains, i.e., a periodic solution. The effect of cross diffusion on wave profiles and speed of propagation is analyzed. We find the intriguing result that both pulses and wave trains occur in the bistable cross-diffusive FitzHugh-Nagumo system, whereas only fronts exist in the standard bistable system without cross diffusion.
Automatic simplification of systems of reaction-diffusion equations by a posteriori analysis.
Maybank, Philip J; Whiteley, Jonathan P
2014-02-01
Many mathematical models in biology and physiology are represented by systems of nonlinear differential equations. In recent years these models have become increasingly complex in order to explain the enormous volume of data now available. A key role of modellers is to determine which components of the model have the greatest effect on a given observed behaviour. An approach for automatically fulfilling this role, based on a posteriori analysis, has recently been developed for nonlinear initial value ordinary differential equations [J.P. Whiteley, Model reduction using a posteriori analysis, Math. Biosci. 225 (2010) 44-52]. In this paper we extend this model reduction technique for application to both steady-state and time-dependent nonlinear reaction-diffusion systems. Exemplar problems drawn from biology are used to demonstrate the applicability of the technique. Copyright © 2014 Elsevier Inc. All rights reserved.
Dynamics of interface in three-dimensional anisotropic bistable reaction-diffusion system
International Nuclear Information System (INIS)
He Zhizhu; Liu, Jing
2010-01-01
This paper presents a theoretical investigation of dynamics of interface (wave front) in three-dimensional (3D) reaction-diffusion (RD) system for bistable media with anisotropy constructed by means of anisotropic surface tension. An equation of motion for the wave front is derived to carry out stability analysis of transverse perturbations, which discloses mechanism of pattern formation such as labyrinthine in 3D bistable media. Particularly, the effects of anisotropy on wave propagation are studied. It was found that, sufficiently strong anisotropy can induce dynamical instabilities and lead to breakup of the wave front. With the fast-inhibitor limit, the bistable system can further be described by a variational dynamics so that the boundary integral method is adopted to study the dynamics of wave fronts.
An observer for an occluded reaction-diffusion system with spatially varying parameters
Kramer, Sean; Bollt, Erik M.
2017-03-01
Spatially dependent parameters of a two-component chaotic reaction-diffusion partial differential equation (PDE) model describing ocean ecology are observed by sampling a single species. We estimate the model parameters and the other species in the system by autosynchronization, where quantities of interest are evolved according to misfit between model and observations, to only partially observed data. Our motivating example comes from oceanic ecology as viewed by remote sensing data, but where noisy occluded data are realized in the form of cloud cover. We demonstrate a method to learn a large-scale coupled synchronizing system that represents the spatio-temporal dynamics and apply a network approach to analyze manifold stability.
Vorticity field, helicity integral and persistence of entanglement in reaction-diffusion systems
Energy Technology Data Exchange (ETDEWEB)
Trueba, J L; Arrayas, M [Area de Electromagnetismo, Universidad Rey Juan Carlos, Camino del Molino s/n, 28943 Fuenlabrada, Madrid (Spain)
2009-07-17
We show that a global description of the stability of entangled structures in reaction-diffusion systems can be made by means of a helicity integral. A vorticity vector field is defined for these systems, as in electromagnetism or fluid dynamics. We have found under which conditions the helicity is conserved or lost through the boundaries of the medium, so the entanglement of structures observed is preserved or disappears during time evolution. We illustrate the theory with an example of knotted entanglement in a FitzHugh-Nagumo model. For this model, we introduce new non-trivial initial conditions using the Hopf fibration and follow the time evolution of the entanglement. (fast track communication)
Stability and Hopf Bifurcation of a Reaction-Diffusion Neutral Neuron System with Time Delay
Dong, Tao; Xia, Linmao
2017-12-01
In this paper, a type of reaction-diffusion neutral neuron system with time delay under homogeneous Neumann boundary conditions is considered. By constructing a basis of phase space based on the eigenvectors of the corresponding Laplace operator, the characteristic equation of this system is obtained. Then, by selecting time delay and self-feedback strength as the bifurcating parameters respectively, the dynamic behaviors including local stability and Hopf bifurcation near the zero equilibrium point are investigated when the time delay and self-feedback strength vary. Furthermore, the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are obtained by using the normal form and the center manifold theorem for the corresponding partial differential equation. Finally, two simulation examples are given to verify the theory.
Asymptotic behavior of equilibrium states of reaction-diffusion systems with mass conservation
Chern, Jann-Long; Morita, Yoshihisa; Shieh, Tien-Tsan
2018-01-01
We deal with a stationary problem of a reaction-diffusion system with a conservation law under the Neumann boundary condition. It is shown that the stationary problem turns to be the Euler-Lagrange equation of an energy functional with a mass constraint. When the domain is the finite interval (0 , 1), we investigate the asymptotic profile of a strictly monotone minimizer of the energy as d, the ratio of the diffusion coefficient of the system, tends to zero. In view of a logarithmic function in the leading term of the potential, we get to a scaling parameter κ satisfying the relation ε : =√{ d } =√{ log κ } /κ2. The main result shows that a sequence of minimizers converges to a Dirac mass multiplied by the total mass and that by a scaling with κ the asymptotic profile exhibits a parabola in the nonvanishing region. We also prove the existence of an unstable monotone solution when the mass is small.
Critical behavior in reaction-diffusion systems exhibiting absorbing phase transition
Ódor, G
2003-01-01
Phase transitions of reaction-diffusion systems with site occupation restriction and with particle creation that requires n>1 parents and where explicit diffusion of single particles (A) exists are reviewed. Arguments based on mean-field approximation and simulations are given which support novel kind of non-equilibrium criticality. These are in contradiction with the implications of a suggested phenomenological, multiplicative noise Langevin equation approach and with some of recent numerical analysis. Simulation results for the one and two dimensional binary spreading 2A -> 4A, 4A -> 2A model display a new type of mean-field criticality characterized by alpha=1/3 and beta=1/2 critical exponents suggested in cond-mat/0210615.
Numerical solution and asymptotic behavior for a nonlocal reaction-diffusion coupled systems
Chin, Pius W. M.
2017-07-01
This paper is considered on a class of nonlocal systems of reaction-diffusion equations with coefficients which are Lipschitz-continuous positive functions. In this model, we are concerned with designing a coupling technique consisting of the non-standard finite difference(NSFD) and finite element method(FEM) both in time and space respectively. We prove theoretically that the schemes designed by the above technique converges optimally in some specified norms for given conditions. Furthermore, we show that the numerical solutions of the said schemes replicates the decaying properties of the exact solutions. Numerical experiments are presented to justify the above theory and some practical studies are carried out for the asymptotic behavior of the schemes under consideration.
Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources
Directory of Open Access Journals (Sweden)
Ida de Bonis
2017-09-01
Full Text Available We discuss the existence of a class of weak solutions to a nonlinear parabolic system of reaction-diffusion type endowed with singular production terms by reaction. The singularity is due to a potential occurrence of quenching localized to the domain boundary. The kind of quenching we have in mind is due to a twofold contribution: (i the choice of boundary conditions, modeling in our case the contact with an infinite reservoir filled with ready-to-react chemicals and (ii the use of a particular nonlinear, non-Lipschitz structure of the reaction kinetics. Our working techniques use fine energy estimates for approximating non-singular problems and uniform control on the set where singularities are localizing.
STEPS: modeling and simulating complex reaction-diffusion systems with Python
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Stefan Wils
2009-06-01
Full Text Available We describe how the use of the Python language improved the user interface of the program STEPS. STEPS is a simulation platform for modeling and stochastic simulation of coupled reaction-diffusion systems with complex 3-dimensional boundary conditions. Setting up such models is a complicated process that consists of many phases. Initial versions of STEPS relied on a static input format that did not cleanly separate these phases, limiting modelers in how they could control the simulation and becoming increasingly complex as new features and new simulation algorithms were added. We solved all of these problems by tightly integrating STEPS with Python, using SWIG to expose our existing simulation code.
Bursting regimes in a reaction-diffusion system with action potential-dependent equilibrium.
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Stephen R Meier
Full Text Available The equilibrium Nernst potential plays a critical role in neural cell dynamics. A common approximation used in studying electrical dynamics of excitable cells is that the ionic concentrations inside and outside the cell membranes act as charge reservoirs and remain effectively constant during excitation events. Research into brain electrical activity suggests that relaxing this assumption may provide a better understanding of normal and pathophysiological functioning of the brain. In this paper we explore time-dependent ionic concentrations by allowing the ion-specific Nernst potentials to vary with developing transmembrane potential. As a specific implementation, we incorporate the potential-dependent Nernst shift into a one-dimensional Morris-Lecar reaction-diffusion model. Our main findings result from a region in parameter space where self-sustaining oscillations occur without external forcing. Studying the system close to the bifurcation boundary, we explore the vulnerability of the system with respect to external stimulations which disrupt these oscillations and send the system to a stable equilibrium. We also present results for an extended, one-dimensional cable of excitable tissue tuned to this parameter regime and stimulated, giving rise to complex spatiotemporal pattern formation. Potential applications to the emergence of neuronal bursting in similar two-variable systems and to pathophysiological seizure-like activity are discussed.
Traveling and Pinned Fronts in Bistable Reaction-Diffusion Systems on Networks
Kouvaris, Nikos E.; Kori, Hiroshi; Mikhailov, Alexander S.
2012-01-01
Traveling fronts and stationary localized patterns in bistable reaction-diffusion systems have been broadly studied for classical continuous media and regular lattices. Analogs of such non-equilibrium patterns are also possible in networks. Here, we consider traveling and stationary patterns in bistable one-component systems on random Erdös-Rényi, scale-free and hierarchical tree networks. As revealed through numerical simulations, traveling fronts exist in network-organized systems. They represent waves of transition from one stable state into another, spreading over the entire network. The fronts can furthermore be pinned, thus forming stationary structures. While pinning of fronts has previously been considered for chains of diffusively coupled bistable elements, the network architecture brings about significant differences. An important role is played by the degree (the number of connections) of a node. For regular trees with a fixed branching factor, the pinning conditions are analytically determined. For large Erdös-Rényi and scale-free networks, the mean-field theory for stationary patterns is constructed. PMID:23028746
Parallel Solutions for Voxel-Based Simulations of Reaction-Diffusion Systems
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Daniele D’Agostino
2014-01-01
Full Text Available There is an increasing awareness of the pivotal role of noise in biochemical processes and of the effect of molecular crowding on the dynamics of biochemical systems. This necessity has given rise to a strong need for suitable and sophisticated algorithms for the simulation of biological phenomena taking into account both spatial effects and noise. However, the high computational effort characterizing simulation approaches, coupled with the necessity to simulate the models several times to achieve statistically relevant information on the model behaviours, makes such kind of algorithms very time-consuming for studying real systems. So far, different parallelization approaches have been deployed to reduce the computational time required to simulate the temporal dynamics of biochemical systems using stochastic algorithms. In this work we discuss these aspects for the spatial TAU-leaping in crowded compartments (STAUCC simulator, a voxel-based method for the stochastic simulation of reaction-diffusion processes which relies on the Sτ-DPP algorithm. In particular we present how the characteristics of the algorithm can be exploited for an effective parallelization on the present heterogeneous HPC architectures.
Czech Academy of Sciences Publication Activity Database
Eisner, Jan; Kučera, Milan; Väth, Martin
2016-01-01
Roč. 61, č. 1 (2016), s. 1-25 ISSN 0862-7940 R&D Projects: GA ČR GA13-12580S Institutional support: RVO:67985904 ; RVO:67985840 Keywords : reaction-diffusion system * unlateral condition * variational inequality Subject RIV: EG - Zoology; BA - General Mathematics (MU-W) Impact factor: 0.618, year: 2016
Mean field effects for counterpropagating traveling wave solutions of reaction-diffusion systems
International Nuclear Information System (INIS)
Bernoff, A.J.; Kuske, R.; Matkowsky, B.J.; Volpert, V.
1995-01-01
In many problems, one observes traveling waves that propagate with constant velocity and shape in the χ direction, say, are independent of y, and z and describe transitions between two equilibrium states. As parameters of the system are varied, these traveling waves can become unstable and give rise to waves having additional structure, such as traveling waves in the y and z directions, which can themselves be subject to instabilities as parameters are further varied. To investigate this scenario the authors consider a system of reaction-diffusion equations with a traveling wave solution as a basic state. They determine solutions bifurcating from the basic state that describe counterpropagating traveling wave in directions orthogonal to the direction of propagation of the basic state and determine their stability. Specifically, they derive long wave modulation equations for the amplitudes of the counterpropagating traveling waves that are coupled to an equation for a mean field, generated by the translation of the basic state in the direction of its propagation. The modulation equations are then employed to determine stability boundaries to long wave perturbations for both unidirectional and counterpropagating traveling waves. The stability analysis is delicate because the results depend on the order in which transverse and longitudinal perturbation wavenumbers are taken to zero. For the unidirectional wave they demonstrate that it is sufficient to consider the cases of (1) purely transverse perturbations, (2) purely longitudinal perturbations, and (3) longitudinal perturbations with a small transverse component. These yield Eckhaus type, zigzag type, and skew type instabilities, respectively
Existence of global solutions to reaction-diffusion systems via a Lyapunov functional
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Said Kouachi
2001-10-01
Full Text Available The purpose of this paper is to construct polynomial functionals (according to solutions of the coupled reaction-diffusion equations which give $L^{p}$-bounds for solutions. When the reaction terms are sufficiently regular, using the well known regularizing effect, we deduce the existence of global solutions. These functionals are obtained independently of work done by Malham and Xin [11].
Directory of Open Access Journals (Sweden)
M.H. Tiwana
2017-04-01
Full Text Available This work investigates the fractional non linear reaction diffusion (FNRD system of Lotka-Volterra type. The system of equations together with the boundary conditions are solved by Homotopy perturbation transform method (HPTM. The series solutions are obtained for the two cases (homogeneous and non-homogeneous of FNRD system. The effect of fractional parameter on the mass concentration of two species are shown and discussed with the help of 3D graphs.
Fatima, T Tasnim; Muntean, A Adrian; Aiki, T
2012-01-01
This paper treats the solvability of a semilinear reaction-diffusion system, which incorporates transport (diffusion) and reaction effects emerging from two separated spatial scales: $x$ - macro and $y$ - micro. The system's origin connects to the modeling of concrete corrosion in sewer concrete pipes. It consists of three partial differential equations which are mass-balances of concentrations, as well as, one ordinary differential equation tracking the damage-by-corrosion. The system is sem...
International Nuclear Information System (INIS)
Wu Shiliang; Li Wantong
2009-01-01
This paper deals with the global asymptotic stability and uniqueness (up to translation) of bistable traveling fronts in a class of reaction-diffusion systems. The known results do not apply in solving these problems because the reaction terms do not satisfy the required monotone condition. To overcome the difficulty, a weak monotone condition is proposed for the reaction terms, which is called interval monotone condition. Under such a weak monotone condition, the existence and comparison theorem of solutions is first established for reaction-diffusion systems on R by appealing to the theory of abstract differential equations. The global asymptotic stability and uniqueness (up to translation) of bistable traveling fronts are then proved by the elementary super- and sub-solution comparison and squeezing methods for nonlinear evolution equations. Finally, these abstract results are applied to a two species competition-diffusion model and a system modeling man-environment-man epidemics.
Simultaneous and non-simultaneous blow-up and uniform blow-up profiles for reaction-diffusion system
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Zhengqiu Ling
2012-11-01
Full Text Available This article concerns the blow-up solutions of a reaction-diffusion system with nonlocal sources, subject to the homogeneous Dirichlet boundary conditions. The criteria used to identify simultaneous and non-simultaneous blow-up of solutions by using the parameters p and q in the model are proposed. Also, the uniform blow-up profiles in the interior domain are established.
Mahara, Hitoshi; Okada, Koichi; Nomura, Atsushi; Miike, Hidetoshi; Sakurai, Tatsunari
2009-07-01
We found a rotating global structure induced by the dynamical force of local chemical activity in a thin solution layer of excitable Belousov-Zhabotinsky reaction coupled with diffusion. The surface flow and deformation associated with chemical spiral waves (wavelength about 1 mm) represents a global unidirectional structure and a global tilt in the entire Petri dish (100 mm in diameter), respectively. For these observations, we scanned the condition of hierarchal pattern selection. From this result, the bromomalonic acid has an important role to induce the rotating global structure. An interaction between a reaction-diffusion process and a surface-tension-driven effect leads to such hierarchal pattern with different scales.
Cluster geometry and survival probability in systems driven by reaction-diffusion dynamics
Energy Technology Data Exchange (ETDEWEB)
Windus, Alastair; Jensen, Henrik J [The Institute for Mathematical Sciences, 53 Prince' s Gate, South Kensington, London SW7 2PG (United Kingdom)], E-mail: h.jensen@imperial.ac.uk
2008-11-15
We consider a reaction-diffusion model incorporating the reactions A{yields}{phi}, A{yields}2A and 2A{yields}3A. Depending on the relative rates for sexual and asexual reproduction of the quantity A, the model exhibits either a continuous or first-order absorbing phase transition to an extinct state. A tricritical point separates the two phase lines. While we comment on this critical behaviour, the main focus of the paper is on the geometry of the population clusters that form. We observe the different cluster structures that arise at criticality for the three different types of critical behaviour and show that there exists a linear relationship for the survival probability against initial cluster size at the tricritical point only.
Directory of Open Access Journals (Sweden)
Felicia Shirly Peace
2014-01-01
Full Text Available A mathematical model of the dynamics of the self-ignition of a reaction-diffusion system is studied in this paper. An approximate analytical method (modified Adomian decomposition method is used to solve nonlinear differential equations under steady-state condition. Analytical expressions for concentrations of the gas reactant and the temperature have been derived for Lewis number (Le and parameters β, γ, and ϕ2. Furthermore, in this work, the numerical simulation of the problem is also reported using MATLAB program. An agreement between analytical and numerical results is noted.
Paul, Shibashis; Ghosh, Shyamolina; Ray, Deb Shankar
2018-02-01
We consider a reaction-diffusion system with linear, stochastic activator-inhibitor kinetics where the time evolution of concentration of a species at any spatial location depends on the relative average concentration of its neighbors. This self-regulating nature of kinetics brings in spatial correlation between the activator and the inhibitor. An interplay of this correlation in kinetics and disparity of diffusivities of the two species leads to symmetry breaking non-equilibrium transition resulting in stationary pattern formation. The role of initial noise strength and the linear reaction terms has been analyzed for pattern selection.
New mechanism of spiral wave initiation in a reaction-diffusion-mechanics system.
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Louis D Weise
Full Text Available Spiral wave initiation in the heart muscle is a mechanism for the onset of dangerous cardiac arrhythmias. A standard protocol for spiral wave initiation is the application of a stimulus in the refractory tail of a propagating excitation wave, a region that we call the "classical vulnerable zone." Previous studies of vulnerability to spiral wave initiation did not take the influence of deformation into account, which has been shown to have a substantial effect on the excitation process of cardiomyocytes via the mechano-electrical feedback phenomenon. In this work we study the effect of deformation on the vulnerability of excitable media in a discrete reaction-diffusion-mechanics (dRDM model. The dRDM model combines FitzHugh-Nagumo type equations for cardiac excitation with a discrete mechanical description of a finite-elastic isotropic material (Seth material to model cardiac excitation-contraction coupling and stretch activated depolarizing current. We show that deformation alters the "classical," and forms a new vulnerable zone at longer coupling intervals. This mechanically caused vulnerable zone results in a new mechanism of spiral wave initiation, where unidirectional conduction block and rotation directions of the consequently initiated spiral waves are opposite compared to the mechanism of spiral wave initiation due to the "classical vulnerable zone." We show that this new mechanism of spiral wave initiation can naturally occur in situations that involve wave fronts with curvature, and discuss its relation to supernormal excitability of cardiac tissue. The concept of mechanically induced vulnerability may lead to a better understanding about the onset of dangerous heart arrhythmias via mechano-electrical feedback.
Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems
Woolley, Thomas E.
2012-05-22
Cellular gene expression is a complex process involving many steps, including the transcription of DNA and translation of mRNA; hence the synthesis of proteins requires a considerable amount of time, from ten minutes to several hours. Since diffusion-driven instability has been observed to be sensitive to perturbations in kinetic delays, the application of Turing patterning mechanisms to the problem of producing spatially heterogeneous differential gene expression has been questioned. In deterministic systems a small delay in the reactions can cause a large increase in the time it takes a system to pattern. Recently, it has been observed that in undelayed systems intrinsic stochasticity can cause pattern initiation to occur earlier than in the analogous deterministic simulations. Here we are interested in adding both stochasticity and delays to Turing systems in order to assess whether stochasticity can reduce the patterning time scale in delayed Turing systems. As analytical insights to this problem are difficult to attain and often limited in their use, we focus on stochastically simulating delayed systems. We consider four different Turing systems and two different forms of delay. Our results are mixed and lead to the conclusion that, although the sensitivity to delays in the Turing mechanism is not completely removed by the addition of intrinsic noise, the effects of the delays are clearly ameliorated in certain specific cases. © 2012 American Physical Society.
Lagzi, István; Ueyama, Daishin
2009-01-01
The pattern transition between periodic precipitation pattern formation (Liesegang phenomenon) and pure crystal growth regimes is investigated in silver nitrate and potassium dichromate system in mixed agarose-gelatin gel. Morphologically different patterns were found depending on the quality of the gel, and transition between these typical patterns can be controlled by the concentration of gelatin in mixed gel. Effect of temperature and hydrodynamic force on precipitation pattern structure was also investigated.
Spirals in a reaction-diffusion system: Dependence of wave dynamics on excitability
Mahanta, Dhriti; Das, Nirmali Prabha; Dutta, Sumana
2018-02-01
A detailed study of the effects of excitability of the Belousov-Zhabotinsky (BZ) reaction on spiral wave properties has been carried out. Using the Oregonator model, we explore the various regimes of wave activity, from sustained oscillations to wave damping, as the system undergoes a Hopf bifurcation, that is achieved by varying the excitability parameter, ɛ . We also discover a short range of parameter values where random oscillations are observed. With an increase in the value of ɛ , the frequency of the wave decreases exponentially, as the dimension of the spiral core expands. These numerical results are confirmed by carrying out experiments in thin layers of the BZ system, where the excitability is changed by varying the concentrations of the reactant species. Effect of reactant concentrations on wave properties like time period and wavelength are also explored in detail. Drifting and meandering spirals are found in the parameter space under investigation, with the excitability affecting the tip trajectory in a way predicted by the numerical studies. This study acts as a quantitative evidence of the relationship between the excitability parameter, ɛ , and the substrate concentrations.
Existence of global solutions for systems of reaction-diffusion equations on unbounded domains
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Salah Badraoui
2002-08-01
Full Text Available We consider, an initial-value problem for the thermal-diffusive combustion system $$displaylines{ u_t=aDelta u-uh(v cr v_t=bDelta u+dDelta v+uh(v, }$$ where $a>0$, $d>0$, $beq 0$, $xin mathbb{R}^n$, $ngeq 1$, with $h(v=v^m$, $m$ is an even nonnegative integer, and the initial data $u_0$, $v_0$ are bounded uniformly continuous and nonnegative. It is known that by a simple comparison if $b=0$, $a=1$, $dleq 1$ and $h(v=v^m$ with $min mathbb{N}^*$, the solutions are uniformly bounded in time. When $d>a=1$, $b=0$, $h(v=v^m$ with $min mathbb{N}^*$, Collet and Xin [2] proved the existence of global classical solutions and showed that the $L^infty $ norm of $v$ can not grow faster than $O(loglog t$ for any space dimension. In our case, no comparison principle seems to apply. Nevertheless using techniques form [2], we essentially prove the existence of global classical solutions if $a
Reaction-Diffusion Automata Phenomenology, Localisations, Computation
Adamatzky, Andrew
2013-01-01
Reaction-diffusion and excitable media are amongst most intriguing substrates. Despite apparent simplicity of the physical processes involved the media exhibit a wide range of amazing patterns: from target and spiral waves to travelling localisations and stationary breathing patterns. These media are at the heart of most natural processes, including morphogenesis of living beings, geological formations, nervous and muscular activity, and socio-economic developments. This book explores a minimalist paradigm of studying reaction-diffusion and excitable media using locally-connected networks of finite-state machines: cellular automata and automata on proximity graphs. Cellular automata are marvellous objects per se because they show us how to generate and manage complexity using very simple rules of dynamical transitions. When combined with the reaction-diffusion paradigm the cellular automata become an essential user-friendly tool for modelling natural systems and designing future and emergent computing arch...
Speed ot travelling waves in reaction-diffusion equations
International Nuclear Information System (INIS)
Benguria, R.D.; Depassier, M.C.; Mendez, V.
2002-01-01
Reaction diffusion equations arise in several problems of population dynamics, flame propagation and others. In one dimensional cases the systems may evolve into travelling fronts. Here we concentrate on a reaction diffusion equation which arises as a simple model for chemotaxis and present results for the speed of the travelling fronts. (Author)
Directory of Open Access Journals (Sweden)
Margaret E. Johnson
2014-09-01
Full Text Available We present a new algorithm for simulating reaction-diffusion equations at single-particle resolution. Our algorithm is designed to be both accurate and simple to implement, and to be applicable to large and heterogeneous systems, including those arising in systems biology applications. We combine the use of the exact Green’s function for a pair of reacting particles with the approximate free-diffusion propagator for position updates to particles. Trajectory reweighting in our free-propagator reweighting (FPR method recovers the exact association rates for a pair of interacting particles at all times. FPR simulations of many-body systems accurately reproduce the theoretically known dynamic behavior for a variety of different reaction types. FPR does not suffer from the loss of efficiency common to other path-reweighting schemes, first, because corrections apply only in the immediate vicinity of reacting particles and, second, because by construction the average weight factor equals one upon leaving this reaction zone. FPR applications include the modeling of pathways and networks of protein-driven processes where reaction rates can vary widely and thousands of proteins may participate in the formation of large assemblies. With a limited amount of bookkeeping necessary to ensure proper association rates for each reactant pair, FPR can account for changes to reaction rates or diffusion constants as a result of reaction events. Importantly, FPR can also be extended to physical descriptions of protein interactions with long-range forces, as we demonstrate here for Coulombic interactions.
Directory of Open Access Journals (Sweden)
Marco A. Velasco
2016-10-01
Full Text Available Scaffolds are essential in bone tissue engineering, as they provide support to cells and growth factors necessary to regenerate tissue. In addition, they meet the mechanical function of the bone while it regenerates. Currently, the multiple methods for designing and manufacturing scaffolds are based on regular structures from a unit cell that repeats in a given domain. However, these methods do not resemble the actual structure of the trabecular bone which may work against osseous tissue regeneration. To explore the design of porous structures with similar mechanical properties to native bone, a geometric generation scheme from a reaction-diffusion model and its manufacturing via a material jetting system is proposed. This article presents the methodology used, the geometric characteristics and the modulus of elasticity of the scaffolds designed and manufactured. The method proposed shows its potential to generate structures that allow to control the basic scaffold properties for bone tissue engineering such as the width of the channels and porosity. The mechanical properties of our scaffolds are similar to trabecular tissue present in vertebrae and tibia bones. Tests on the manufactured scaffolds show that it is necessary to consider the orientation of the object relative to the printing system because the channel geometry, mechanical properties and roughness are heavily influenced by the position of the surface analyzed with respect to the printing axis. A possible line for future work may be the establishment of a set of guidelines to consider the effects of manufacturing processes in designing stages.
Azimi, Mohammad; Jamali, Yousef; Mofrad, Mohammad R K
2011-01-01
Diffusion plays a key role in many biochemical reaction systems seen in nature. Scenarios where diffusion behavior is critical can be seen in the cell and subcellular compartments where molecular crowding limits the interaction between particles. We investigate the application of a computational method for modeling the diffusion of molecules and macromolecules in three-dimensional solutions using agent based modeling. This method allows for realistic modeling of a system of particles with different properties such as size, diffusion coefficients, and affinity as well as the environment properties such as viscosity and geometry. Simulations using these movement probabilities yield behavior that mimics natural diffusion. Using this modeling framework, we simulate the effects of molecular crowding on effective diffusion and have validated the results of our model using Langevin dynamics simulations and note that they are in good agreement with previous experimental data. Furthermore, we investigate an extension of this framework where single discrete cells can contain multiple particles of varying size in an effort to highlight errors that can arise from discretization that lead to the unnatural behavior of particles undergoing diffusion. Subsequently, we explore various algorithms that differ in how they handle the movement of multiple particles per cell and suggest an algorithm that properly accommodates multiple particles of various sizes per cell that can replicate the natural behavior of these particles diffusing. Finally, we use the present modeling framework to investigate the effect of structural geometry on the directionality of diffusion in the cell cytoskeleton with the observation that parallel orientation in the structural geometry of actin filaments of filopodia and the branched structure of lamellipodia can give directionality to diffusion at the filopodia-lamellipodia interface.
Directory of Open Access Journals (Sweden)
Kalannagari Viswanath
2015-01-01
Full Text Available Ultrasound imaging is one of the available imaging techniques used for diagnosis of kidney abnormalities, which may be like change in shape and position and swelling of limb; there are also other Kidney abnormalities such as formation of stones, cysts, blockage of urine, congenital anomalies, and cancerous cells. During surgical processes it is vital to recognize the true and precise location of kidney stone. The detection of kidney stones using ultrasound imaging is a highly challenging task as they are of low contrast and contain speckle noise. This challenge is overcome by employing suitable image processing techniques. The ultrasound image is first preprocessed to get rid of speckle noise using the image restoration process. The restored image is smoothened using Gabor filter and the subsequent image is enhanced by histogram equalization. The preprocessed image is achieved with level set segmentation to detect the stone region. Segmentation process is employed twice for getting better results; first to segment kidney portion and then to segment the stone portion, respectively. In this work, the level set segmentation uses two terms, namely, momentum and resilient propagation (Rprop to detect the stone portion. After segmentation, the extracted region of the kidney stone is given to Symlets, Biorthogonal (bio3.7, bio3.9, and bio4.4, and Daubechies lifting scheme wavelet subbands to extract energy levels. These energy levels provide evidence about presence of stone, by comparing them with that of the normal energy levels. They are trained by multilayer perceptron (MLP and back propagation (BP ANN to classify and its type of stone with an accuracy of 98.8%. The prosed work is designed and real time is implemented on both Filed Programmable Gate Array Vertex-2Pro FPGA using Xilinx System Generator (XSG Verilog and Matlab 2012a.
Circumnutation modeled by reaction-diffusion equations
Energy Technology Data Exchange (ETDEWEB)
Lubkin, S.R.
1992-01-01
In studies of biological oscillators, plants are only rarely examined. The authors study a common sub-diurnal oscillation of plants, called circumnutation. Based on experimental evidence that the oscillations consist of a turgor wave traveling around a growing plant part, circumnutation is modeled by a nonlinear reaction-diffusion system with cylindrical geometry. Because of its simplicity, and because biological oscillations are so common, an oscillatory [lambda]-[omega] reaction-diffusion system is chosen for the model. The authors study behavior of traveling waves in [lambda]-[omega] systems. The authors show the existence of Hopf bifurcations and the stability of the limit cycles born at the Hopf bifurcation for some parameter values. Using a Lindstedt-type perturbation scheme, the authors construct periodic solutions of the [lambda]-[omega] system near a Hopf bifurcation and show that the periodic solutions superimposed on the original traveling wave have the effect of altering its overall frequency and amplitude. Circumnutating plants generally display a strong directional preference to their oscillations, which is species-dependent. Circumnutation is modeled by a [lambda]-[omega] system on an annulus of variable width, which does not possess reflection symmetry about any axis. The annulus represents a region of high potassium concentration in the cross-section of the stem. The asymmetry of the annulus represents the anatomical asymmetry of the plant. Traveling waves are constructed on this variable-width annulus by a perturbation scheme, and perturbing the width of the annulus alters the amplitude and frequency of traveling waves on the domain by a small (order [epsilon][sup 2]) amount. The speed, frequency, and stability are unaffected by the direction of travel of the wave on the annulus. This indicates that the [lambda]-[omega] system on a variable-width domain cannot account for directional preferences of traveling waves in biological systems.
Diffusive instabilities in hyperbolic reaction-diffusion equations
Zemskov, Evgeny P.; Horsthemke, Werner
2016-03-01
We investigate two-variable reaction-diffusion systems of the hyperbolic type. A linear stability analysis is performed, and the conditions for diffusion-driven instabilities are derived. Two basic types of eigenvalues, real and complex, are described. Dispersion curves for both types of eigenvalues are plotted and their behavior is analyzed. The real case is related to the Turing instability, and the complex one corresponds to the wave instability. We emphasize the interesting feature that the wave instability in the hyperbolic equations occurs in two-variable systems, whereas in the parabolic case one needs three reaction-diffusion equations.
International Nuclear Information System (INIS)
Garcia Velarde, M.
1977-01-01
Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs
International Nuclear Information System (INIS)
Garcia Velarde, M.
1977-01-01
Thermoconvective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Benard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (author) [es
Energy Technology Data Exchange (ETDEWEB)
Garcia Velarde, M.
1977-07-01
Thermo convective instabilities in horizontal fluid layers are discussed with emphasis on the Rayleigh-Bernard model problem. Steady solutions and time-dependent phenomena (relaxation oscillations and transition to turbulence) are studied within the nonlinear Boussinesq-Oberbeck approximation. Homogeneous steady solutions, limit cycles, and inhomogeneous (ordered) spatial structures are also studied in simple reaction-diffusion systems. Lastly, the non-periodic attractor that appears at large Rayleigh numbers in the truncated Boussinesq-Oberbeck model of Lorenz, is constructed, and a discussion of turbulent behavior is given. (Author) 105 refs.
Laser spot detection based on reaction diffusion
Czech Academy of Sciences Publication Activity Database
Vázquez-Otero, Alejandro; Khikhlukha, Danila; Solano-Altamirano, J. M.; Dormido, R.; Duro, N.
2016-01-01
Roč. 16, č. 3 (2016), s. 1-11, č. článku 315. ISSN 1424-8220 R&D Projects: GA MŠk EF15_008/0000162 Grant - others:ELI Beamlines(XE) CZ.02.1.01/0.0/0.0/15_008/0000162 Institutional support: RVO:68378271 Keywords : laser spot detection * laser beam detection * reaction diffusion models * Fitzhugh-Nagumo model * reaction diffusion computation * Turing patterns Subject RIV: BL - Plasma and Gas Discharge Physics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 2.677, year: 2016
Cohabitation reaction-diffusion model for virus focal infections
Amor, Daniel R.; Fort, Joaquim
2014-12-01
The propagation of virus infection fronts has been typically modeled using a set of classical (noncohabitation) reaction-diffusion equations for interacting species. However, for some single-species systems it has been recently shown that noncohabitation reaction-diffusion equations may lead to unrealistic descriptions. We argue that previous virus infection models also have this limitation, because they assume that a virion can simultaneously reproduce inside a cell and diffuse away from it. For this reason, we build a several-species cohabitation model that does not have this limitation. Furthermore, we perform a sensitivity analysis for the most relevant parameters of the model, and we compare the predicted infection speed with observed data for two different strains of the T7 virus.
Reaction diffusion equations with boundary degeneracy
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Huashui Zhan
2016-03-01
Full Text Available In this article, we consider the reaction diffusion equation $$ \\frac{\\partial u}{\\partial t} = \\Delta A(u,\\quad (x,t\\in \\Omega \\times (0,T, $$ with the homogeneous boundary condition. Inspired by the Fichera-Oleinik theory, if the equation is not only strongly degenerate in the interior of $\\Omega$, but also degenerate on the boundary, we show that the solution of the equation is free from any limitation of the boundary condition.
Programming reaction-diffusion: From theory to micro- and nanofabrication
Campbell, Christopher James
Nature often uses reaction-diffusion(RD) as a means of making structures and materials of unique properties or morphologies on scales from macro- (e.g., stripes in zebras, tigers, and seashells, and formations in trees, agates, and rocks) to microscopic (e.g., cellular growth, chemotaxis and biological waves). However, reaction-diffusion phenomena have not yet been applied in modern materials science and micro-/nanotechnology. In this context, RD systems are particularly promising for micropatterning of surfaces. Unlike conventional micropatterning techniques that modify the properties of the substrate only at the locations to which a modifying agent - be it a chemical or radiation - is delivered, RD can, in principle, evolve chemicals delivered onto a surface into structures of characteristic dimensions significantly smaller than those of the original pattern. In this Dissertation, I describe how reaction-diffusions are programmed and executed via a new micropatterning technique called Wet Stamping to (i) transform microscopic patterns of chemicals delivered onto thin films of dry gelatin into regular arrays of lines of submicrometer thicknesses, multicolor arrays on the micrometer scale, or three-dimensional microstructured surfaces; (ii) modify the properties of a surface by precisely delivering an oxidant to change hydrophilicity or deliver silanes or thiols to build a self-assembling monolayer; or (iii) cut into a metal, glass, or crystal surface by delivery of an etchant to form binary and curvilinear three-dimensional microstructures. This technique has allowed for a fundamental understanding and control of reaction-diffusion processes down to the nanoscale. In addition, this platform has allowed for the development of a range of applications on the micro- and nanoscale, including microlenses, microfluidic devices, and templates for studying cell motility and cancer metastasis.
Reaction rates for a generalized reaction-diffusion master equation.
Hellander, Stefan; Petzold, Linda
2016-01-01
It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach, in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is of the order of the reaction radius of a reacting pair of molecules.
Glider-based computing in reaction-diffusion hexagonal cellular automata
International Nuclear Information System (INIS)
Adamatzky, Andrew; Wuensche, Andrew; De Lacy Costello, Benjamin
2006-01-01
A three-state hexagonal cellular automaton, discovered in [Wuensche A. Glider dynamics in 3-value hexagonal cellular automata: the beehive rule. Int J Unconvention Comput, in press], presents a conceptual discrete model of a reaction-diffusion system with inhibitor and activator reagents. The automaton model of reaction-diffusion exhibits mobile localized patterns (gliders) in its space-time dynamics. We show how to implement the basic computational operations with these mobile localizations, and thus demonstrate collision-based logical universality of the hexagonal reaction-diffusion cellular automaton
Hierarchical Stereo Matching in Two-Scale Space for Cyber-Physical System
Directory of Open Access Journals (Sweden)
Eunah Choi
2017-07-01
Full Text Available Dense disparity map estimation from a high-resolution stereo image is a very difficult problem in terms of both matching accuracy and computation efficiency. Thus, an exhaustive disparity search at full resolution is required. In general, examining more pixels in the stereo view results in more ambiguous correspondences. When a high-resolution image is down-sampled, the high-frequency components of the fine-scaled image are at risk of disappearing in the coarse-resolution image. Furthermore, if erroneous disparity estimates caused by missing high-frequency components are propagated across scale space, ultimately, false disparity estimates are obtained. To solve these problems, we introduce an efficient hierarchical stereo matching method in two-scale space. This method applies disparity estimation to the reduced-resolution image, and the disparity result is then up-sampled to the original resolution. The disparity estimation values of the high-frequency (or edge component regions of the full-resolution image are combined with the up-sampled disparity results. In this study, we extracted the high-frequency areas from the scale-space representation by using difference of Gaussian (DoG or found edge components, using a Canny operator. Then, edge-aware disparity propagation was used to refine the disparity map. The experimental results show that the proposed algorithm outperforms previous methods.
Hierarchical Stereo Matching in Two-Scale Space for Cyber-Physical System.
Choi, Eunah; Lee, Sangyoon; Hong, Hyunki
2017-07-21
Dense disparity map estimation from a high-resolution stereo image is a very difficult problem in terms of both matching accuracy and computation efficiency. Thus, an exhaustive disparity search at full resolution is required. In general, examining more pixels in the stereo view results in more ambiguous correspondences. When a high-resolution image is down-sampled, the high-frequency components of the fine-scaled image are at risk of disappearing in the coarse-resolution image. Furthermore, if erroneous disparity estimates caused by missing high-frequency components are propagated across scale space, ultimately, false disparity estimates are obtained. To solve these problems, we introduce an efficient hierarchical stereo matching method in two-scale space. This method applies disparity estimation to the reduced-resolution image, and the disparity result is then up-sampled to the original resolution. The disparity estimation values of the high-frequency (or edge component) regions of the full-resolution image are combined with the up-sampled disparity results. In this study, we extracted the high-frequency areas from the scale-space representation by using difference of Gaussian (DoG) or found edge components, using a Canny operator. Then, edge-aware disparity propagation was used to refine the disparity map. The experimental results show that the proposed algorithm outperforms previous methods.
Reaction diffusion and solid state chemical kinetics handbook
Dybkov, V I
2010-01-01
This monograph deals with a physico-chemical approach to the problem of the solid-state growth of chemical compound layers and reaction-diffusion in binary heterogeneous systems formed by two solids; as well as a solid with a liquid or a gas. It is explained why the number of compound layers growing at the interface between the original phases is usually much lower than the number of chemical compounds in the phase diagram of a given binary system. For example, of the eight intermetallic compounds which exist in the aluminium-zirconium binary system, only ZrAl3 was found to grow as a separate
Reaction-diffusion pulses: a combustion model
International Nuclear Information System (INIS)
Campos, Daniel; Llebot, Josep Enric; Fort, Joaquim
2004-01-01
We focus on a reaction-diffusion approach proposed recently for experiments on combustion processes, where the heat released by combustion follows first-order reaction kinetics. This case allows us to perform an exhaustive analytical study. Specifically, we obtain the exact expressions for the speed of the thermal pulses, their maximum temperature and the condition of self-sustenance. Finally, we propose two generalizations of the model, namely, the case of several reactants burning together, and that of time-delayed heat conduction. We find an excellent agreement between our analytical results and simulations
Reaction diffusion equations and quadratic convergence
Directory of Open Access Journals (Sweden)
A. S. Vatsala
1997-01-01
Full Text Available In this paper, the method of generalized quasilinearization has been extended to reaction diffusion equations. The extension includes earlier known results as special cases. The earlier results developed are when (i the right-hand side function is the sum of a convex and concave function, and (ii the right-hand function can be made convex by adding a convex function. In our present result, if the monotone iterates are mildly nonlinear, we establish the quadratic convergence as in the quasilinearization method. If the iterates are totally linear then the iterates converge semi-quadratically.
Parametric pattern selection in a reaction-diffusion model.
Directory of Open Access Journals (Sweden)
Michael Stich
Full Text Available We compare spot patterns generated by Turing mechanisms with those generated by replication cascades, in a model one-dimensional reaction-diffusion system. We determine the stability region of spot solutions in parameter space as a function of a natural control parameter (feed-rate where degenerate patterns with different numbers of spots coexist for a fixed feed-rate. While it is possible to generate identical patterns via both mechanisms, we show that replication cascades lead to a wider choice of pattern profiles that can be selected through a tuning of the feed-rate, exploiting hysteresis and directionality effects of the different pattern pathways.
Domainal cleavage as an Anisotropic Reaction-diffusion Process
Mulchrone, Kieran; Meere, Patrick
2017-04-01
Domainal cleavage comprises zones dominated by quartz and feldspar (QF-domains) and zones dominated by Mica (M-domains) which form at low metamorphic grades. The protolith is typically fairly homogeneous mudstone, siltstone, sandstone or limestone. Wet diffusion or pressure solution along grain boundaries is a key mechanism in the development of domanial cleavage. However, this does not explain why M-domains become sub-regularly spaced, visually evident in coarser-grained rocks, and take on an anastomising morphology. The ratio of M to QF-domains by volume can range from 1 to 0.1 and lower i.e. in extreme cases M-domains are intermittent but regularly spaced. It is suggested here that an anisotropic reaction-diffusion process model can explain these features. The imposed stress field instantaneously leads to anisotropy of diffusion by narrowing intergranular channels perpendicular to the principal stress. This leads to a preferred diffusion of chemicals parallel to the principal stress direction and lower diffusion rates in the normal direction. Combining this with the chemical reaction of pressure solution produces an anisotropic reaction-diffusion system. Both isotropic and anistropic reaction diffusion systems lead to pattern formation as discovered by Alan Turing on the 1950's as an explanation for patterns found in animal skins such as spots and stripes. Thus domanial cleavage is a striped pattern induced by diffusion anisotropy combined with a chemical reaction. Furthermore, rates of chemical reaction in intergranular fluids is likely to be many orders of magnitude greater that rates of deformation. Therefore we expect domanial cleavage to form relatively rapidly. As deformation progresses the M-domains behave less competently and may be the site of enhanced shearing. An example from Co. Cork, Ireland demonstrates shear folding in low-grade metasedimentary rocks with reverse shear along M-domains at a high angle to the maximum compressive stress.
Reaction-diffusion with stochastic decay rates.
Lapeyre, G John; Dentz, Marco
2017-07-26
Understanding anomalous transport and reaction kinetics due to microscopic physical and chemical disorder is a long-standing goal in many fields including geophysics, biology, and engineering. We consider reaction-diffusion characterized by fluctuations in both transport times and decay rates. We introduce and analyze a model framework that explicitly connects microscopic fluctuations with the mescoscopic description. For broad distributions of transport and reaction time scales we compute the particle density and derive the equations governing its evolution, finding power-law decay of the survival probability, and spatially varying decay that leads to subdiffusion and an asymptotically stationary surviving-particle density. These anomalies are clearly attributable to non-Markovian effects that couple transport and chemical properties in both reaction and diffusion terms.
Reaction rates for mesoscopic reaction-diffusion kinetics.
Hellander, Stefan; Hellander, Andreas; Petzold, Linda
2015-02-01
The mesoscopic reaction-diffusion master equation (RDME) is a popular modeling framework frequently applied to stochastic reaction-diffusion kinetics in systems biology. The RDME is derived from assumptions about the underlying physical properties of the system, and it may produce unphysical results for models where those assumptions fail. In that case, other more comprehensive models are better suited, such as hard-sphere Brownian dynamics (BD). Although the RDME is a model in its own right, and not inferred from any specific microscale model, it proves useful to attempt to approximate a microscale model by a specific choice of mesoscopic reaction rates. In this paper we derive mesoscopic scale-dependent reaction rates by matching certain statistics of the RDME solution to statistics of the solution of a widely used microscopic BD model: the Smoluchowski model with a Robin boundary condition at the reaction radius of two molecules. We also establish fundamental limits on the range of mesh resolutions for which this approach yields accurate results and show both theoretically and in numerical examples that as we approach the lower fundamental limit, the mesoscopic dynamics approach the microscopic dynamics. We show that for mesh sizes below the fundamental lower limit, results are less accurate. Thus, the lower limit determines the mesh size for which we obtain the most accurate results.
Reaction rates for reaction-diffusion kinetics on unstructured meshes.
Hellander, Stefan; Petzold, Linda
2017-02-14
The reaction-diffusion master equation is a stochastic model often utilized in the study of biochemical reaction networks in living cells. It is applied when the spatial distribution of molecules is important to the dynamics of the system. A viable approach to resolve the complex geometry of cells accurately is to discretize space with an unstructured mesh. Diffusion is modeled as discrete jumps between nodes on the mesh, and the diffusion jump rates can be obtained through a discretization of the diffusion equation on the mesh. Reactions can occur when molecules occupy the same voxel. In this paper, we develop a method for computing accurate reaction rates between molecules occupying the same voxel in an unstructured mesh. For large voxels, these rates are known to be well approximated by the reaction rates derived by Collins and Kimball, but as the mesh is refined, no analytical expression for the rates exists. We reduce the problem of computing accurate reaction rates to a pure preprocessing step, depending only on the mesh and not on the model parameters, and we devise an efficient numerical scheme to estimate them to high accuracy. We show in several numerical examples that as we refine the mesh, the results obtained with the reaction-diffusion master equation approach those of a more fine-grained Smoluchowski particle-tracking model.
Chemical computing with reaction-diffusion processes.
Gorecki, J; Gizynski, K; Guzowski, J; Gorecka, J N; Garstecki, P; Gruenert, G; Dittrich, P
2015-07-28
Chemical reactions are responsible for information processing in living organisms. It is believed that the basic features of biological computing activity are reflected by a reaction-diffusion medium. We illustrate the ideas of chemical information processing considering the Belousov-Zhabotinsky (BZ) reaction and its photosensitive variant. The computational universality of information processing is demonstrated. For different methods of information coding constructions of the simplest signal processing devices are described. The function performed by a particular device is determined by the geometrical structure of oscillatory (or of excitable) and non-excitable regions of the medium. In a living organism, the brain is created as a self-grown structure of interacting nonlinear elements and reaches its functionality as the result of learning. We discuss whether such a strategy can be adopted for generation of chemical information processing devices. Recent studies have shown that lipid-covered droplets containing solution of reagents of BZ reaction can be transported by a flowing oil. Therefore, structures of droplets can be spontaneously formed at specific non-equilibrium conditions, for example forced by flows in a microfluidic reactor. We describe how to introduce information to a droplet structure, track the information flow inside it and optimize medium evolution to achieve the maximum reliability. Applications of droplet structures for classification tasks are discussed. © 2015 The Author(s) Published by the Royal Society. All rights reserved.
Domain decomposition multigrid methods for nonlinear reaction-diffusion problems
Arrarás, A.; Gaspar, F. J.; Portero, L.; Rodrigo, C.
2015-03-01
In this work, we propose efficient discretizations for nonlinear evolutionary reaction-diffusion problems on general two-dimensional domains. The spatial domain is discretized through an unstructured coarse triangulation, which is subsequently refined via regular triangular grids. Following the method of lines approach, we first consider a finite element spatial discretization, and then use a linearly implicit splitting time integrator related to a suitable decomposition of the triangulation nodes. Such a procedure provides a linear system per internal stage. The equations corresponding to those nodes lying strictly inside the elements of the coarse triangulation can be decoupled and solved in parallel using geometric multigrid techniques. The method is unconditionally stable and computationally efficient, since it avoids the need for Schwarz-type iteration procedures. In addition, it is formulated for triangular elements, thus yielding much flexibility in the discretization of complex geometries. To illustrate its practical utility, the algorithm is shown to reproduce the pattern-forming dynamics of the Schnakenberg model.
Reaction-diffusion modeling of hydrogen in beryllium
Energy Technology Data Exchange (ETDEWEB)
Wensing, Mirko; Matveev, Dmitry; Linsmeier, Christian [Forschungszentrum Juelich GmbH, Institut fuer Energie- und Klimaforschung - Plasmaphysik (Germany)
2016-07-01
Beryllium will be used as first-wall material for the future fusion reactor ITER as well as in the breeding blanket of DEMO. In both cases it is important to understand the mechanisms of hydrogen retention in beryllium. In earlier experiments with beryllium low-energy binding states of hydrogen were observed by thermal desorption spectroscopy (TDS) which are not yet well understood. Two candidates for these states are considered: beryllium-hydride phases within the bulk and surface effects. The retention of deuterium in beryllium is studied by a reaction rate approach using a coupled reaction diffusion system (CRDS)-model relying on ab initio data from density functional theory calculations (DFT). In this contribution we try to assess the influence of surface recombination.
A Series Solution of the Cauchy Problem for Turing Reaction-diffusion Model
Directory of Open Access Journals (Sweden)
L. Päivärinta
2011-12-01
Full Text Available In this paper, the series pattern solution of the Cauchy problem for Turing reaction-diffusion model is obtained by using the homotopy analysis method (HAM. Turing reaction-diffusion model is nonlinear reaction-diffusion system which usually has power-law nonlinearities or may be rewritten in the form of power-law nonlinearities. Using the HAM, it is possible to find the exact solution or an approximate solution of the problem. This technique provides a series of functions which converges rapidly to the exact solution of the problem. The efficiency of the approach will be shown by applying the procedure on two problems. Furthermore, the so-called homotopy-Pade technique (HPT is applied to enlarge the convergence region and rate of solution series given by the HAM.
International Nuclear Information System (INIS)
Song Qiankun; Cao Jinde
2005-01-01
Both exponential stability and periodic solutions are considered for a class of bi-directional associative memory (BAM) neural networks with delays and reaction-diffusion terms by constructing suitable Lyapunov functional and some analysis techniques. The general sufficient conditions are given ensuring the global exponential stability and existence of periodic solutions of BAM neural networks with delays and reaction-diffusion terms. These presented conditions are in terms of system parameters and have important leading significance in the design and applications of globally exponentially stable and periodic oscillatory neural circuits for BAM with delays and reaction-diffusion terms
International Nuclear Information System (INIS)
Li Zuoan; Li Kelin
2009-01-01
In this paper, we investigate a class of impulsive fuzzy cellular neural networks with distributed delays and reaction-diffusion terms. By employing the delay differential inequality with impulsive initial conditions and M-matrix theory, we find some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive fuzzy cellular neural networks with distributed delays and reaction-diffusion terms. In particular, the estimate of the exponential converging index is also provided, which depends on the system parameters. An example is given to show the effectiveness of the results obtained here.
Field theory of propagating reaction-diffusion fronts
International Nuclear Information System (INIS)
Escudero, C.
2004-01-01
The problem of velocity selection of reaction-diffusion fronts has been widely investigated. While the mean-field limit results are well known theoretically, there is a lack of analytic progress in those cases in which fluctuations are to be taken into account. Here, we construct an analytic theory connecting the first principles of the reaction-diffusion process to an effective equation of motion via field-theoretic arguments, and we arrive at results already confirmed by numerical simulations
Study of ODE limit problems for reaction-diffusion equations
Directory of Open Access Journals (Sweden)
Jacson Simsen
2018-01-01
Full Text Available In this work we study ODE limit problems for reaction-diffusion equations for large diffusion and we study the sensitivity of nonlinear ODEs with respect to initial conditions and exponent parameters. Moreover, we prove continuity of the flow and weak upper semicontinuity of a family of global attractors for reaction-diffusion equations with spatially variable exponents when the exponents go to 2 in \\(L^{\\infty}(\\Omega\\ and the diffusion coefficients go to infinity.
Zubarev nonequilibrium statistical operator method in Renyi statistics. Reaction-diffusion processes
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P. Kostrobij
2014-09-01
Full Text Available The Zubarev nonequilibrium statistical operator (NSO method in Renyi statistics is discussed. The solution of q-parametrized Liouville equation within the NSO method is obtained. A statistical approach for a consistent description of reaction-diffusion processes in "gas-adsorbate-metal" system is proposed using the NSO method in Renyi statistics.
Reaction-diffusion model of hair-bundle morphogenesis.
Jacobo, Adrian; Hudspeth, A J
2014-10-28
The hair bundle, an apical specialization of the hair cell composed of several rows of regularly organized stereocilia and a kinocilium, is essential for mechanotransduction in the ear. Its precise organization allows the hair bundle to convert mechanical stimuli to electrical signals; mutations that alter the bundle's morphology often cause deafness. However, little is known about the proteins involved in the process of morphogenesis and how the structure of the bundle arises through interactions between these molecules. We present a mathematical model based on simple reaction-diffusion mechanisms that can reproduce the shape and organization of the hair bundle. This model suggests that the boundary of the cell and the kinocilium act as signaling centers that establish the bundle's shape. The interaction of two proteins forms a hexagonal Turing pattern--a periodic modulation of the concentrations of the morphogens, sustained by local activation and long-range inhibition of the reactants--that sets a blueprint for the location of the stereocilia. Finally we use this model to predict how different alterations to the system might impact the shape and organization of the hair bundle.
Reaction Diffusion Voronoi Diagrams: From Sensors Data to Computing
Directory of Open Access Journals (Sweden)
Alejandro Vázquez-Otero
2015-05-01
Full Text Available In this paper, a new method to solve computational problems using reaction diffusion (RD systems is presented. The novelty relies on the use of a model configuration that tailors its spatiotemporal dynamics to develop Voronoi diagrams (VD as a part of the system’s natural evolution. The proposed framework is deployed in a solution of related robotic problems, where the generalized VD are used to identify topological places in a grid map of the environment that is created from sensor measurements. The ability of the RD-based computation to integrate external information, like a grid map representing the environment in the model computational grid, permits a direct integration of sensor data into the model dynamics. The experimental results indicate that this method exhibits significantly less sensitivity to noisy data than the standard algorithms for determining VD in a grid. In addition, previous drawbacks of the computational algorithms based on RD models, like the generation of volatile solutions by means of excitable waves, are now overcome by final stable states.
Reaction-diffusion problems in the physics of hot plasmas
Wilhelmsson, H
2000-01-01
The physics of hot plasmas is of great importance for describing many phenomena in the universe and is fundamental for the prospect of future fusion energy production on Earth. Nontrivial results of nonlinear electromagnetic effects in plasmas include the self-organization and self-formation in the plasma of structures compact in time and space. These are the consequences of competing processes of nonlinear interactions and can be best described using reaction-diffusion equations. Reaction-Diffusion Problems in the Physics of Hot Plasmas is focused on paradigmatic problems of a reaction-diffusion type met in many branches of science, concerning in particular the nonlinear interaction of electromagnetic fields with plasmas.
Reaction Diffusion and Chemotaxis for Decentralized Gathering on FPGAs
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Bernard Girau
2009-01-01
and rapid simulations of the complex dynamics of this reaction-diffusion model. Then we describe the FPGA implementation of the environment together with the agents, to study the major challenges that must be solved when designing a fast embedded implementation of the decentralized gathering model. We analyze the results according to the different goals of these hardware implementations.
Traveling Wave Solutions in a Reaction-Diffusion Epidemic Model
Wang, Sheng; Liu, Wenbin; Guo, Zhengguang; Wang, Weiming
2013-01-01
We investigate the traveling wave solutions in a reaction-diffusion epidemic model. The existence of the wave solutions is derived through monotone iteration of a pair of classical upper and lower solutions. The traveling wave solutions are shown to be unique and strictly monotonic. Furthermore, we determine the critical minimal wave speed.
Evans functions and bifurcations of nonlinear waves of some nonlinear reaction diffusion equations
Zhang, Linghai
2017-10-01
The main purposes of this paper are to accomplish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear system of reaction diffusion equations ut =uxx + α [ βH (u - θ) - u ] - w, wt = ε (u - γw) and to establish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ], under different conditions on the model constants. To establish the bifurcation for the system, we will study the existence and instability of a standing pulse solution if 0 1; the existence and instability of two standing wave fronts if 2 (1 + αγ) θ = αβγ and 0 0 is a positive constant, if 0 mathematical neuroscience.
Random Attractors for Stochastic Retarded Reaction-Diffusion Equations on Unbounded Domains
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Xiaoquan Ding
2013-01-01
Full Text Available This paper is devoted to a stochastic retarded reaction-diffusion equation on all d-dimensional space with additive white noise. We first show that the stochastic retarded reaction-diffusion equation generates a random dynamical system by transforming this stochastic equation into a random one through a tempered stationary random homeomorphism. Then, we establish the existence of a random attractor for the random equation. And the existence of a random attractor for the stochastic equation follows from the conjugation relation between two random dynamical systems. The pullback asymptotic compactness is proved by uniform estimates on solutions for large space and time variables. These estimates are obtained by a cut-off technique.
Traveling Wave Solutions of Reaction-Diffusion Equations Arising in Atherosclerosis Models
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Narcisa Apreutesei
2014-05-01
Full Text Available In this short review article, two atherosclerosis models are presented, one as a scalar equation and the other one as a system of two equations. They are given in terms of reaction-diffusion equations in an infinite strip with nonlinear boundary conditions. The existence of traveling wave solutions is studied for these models. The monostable and bistable cases are introduced and analyzed.
Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds
Desvillettes, Laurent
2008-01-01
In the continuation of [Desvillettes, L., Fellner, K.: Exponential Decay toward Equilibrium via Entropy Methods for Reaction-Diffusion Equations. J. Math. Anal. Appl. 319 (2006), no. 1, 157-176], we study reversible reaction-diffusion equations via entropy methods (based on the free energy functional) for a 1D system of four species. We improve the existing theory by getting 1) almost exponential convergence in L1 to the steady state via a precise entropy-entropy dissipation estimate, 2) an explicit global L∞ bound via interpolation of a polynomially growing H1 bound with the almost exponential L1 convergence, and 3), finally, explicit exponential convergence to the steady state in all Sobolev norms.
Event-triggered synchronization for reaction-diffusion complex networks via random sampling
Dong, Tao; Wang, Aijuan; Zhu, Huiyun; Liao, Xiaofeng
2018-04-01
In this paper, the synchronization problem of the reaction-diffusion complex networks (RDCNs) with Dirichlet boundary conditions is considered, where the data is sampled randomly. An event-triggered controller based on the sampled data is proposed, which can reduce the number of controller and the communication load. Under this strategy, the synchronization problem of the diffusion complex network is equivalently converted to the stability of a of reaction-diffusion complex dynamical systems with time delay. By using the matrix inequality technique and Lyapunov method, the synchronization conditions of the RDCNs are derived, which are dependent on the diffusion term. Moreover, it is found the proposed control strategy can get rid of the Zeno behavior naturally. Finally, a numerical example is given to verify the obtained results.
Maximum Principles for Discrete and Semidiscrete Reaction-Diffusion Equation
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Petr Stehlík
2015-01-01
Full Text Available We study reaction-diffusion equations with a general reaction function f on one-dimensional lattices with continuous or discrete time ux′ (or Δtux=k(ux-1-2ux+ux+1+f(ux, x∈Z. We prove weak and strong maximum and minimum principles for corresponding initial-boundary value problems. Whereas the maximum principles in the semidiscrete case (continuous time exhibit similar features to those of fully continuous reaction-diffusion model, in the discrete case the weak maximum principle holds for a smaller class of functions and the strong maximum principle is valid in a weaker sense. We describe in detail how the validity of maximum principles depends on the nonlinearity and the time step. We illustrate our results on the Nagumo equation with the bistable nonlinearity.
Numerical solution of a reaction-diffusion equation
International Nuclear Information System (INIS)
Moyano, Edgardo A.; Scarpettini, Alberto F.
2000-01-01
The purpose of the present work to continue the observations and the numerical experiences on a reaction-diffusion model, that is a simplified form of the neutronic flux equation. The model is parabolic, nonlinear, with Dirichlet boundary conditions. The purpose is to approximate non trivial solutions, asymptotically stables for t → ∞, that is solutions that tend to the elliptic problem, in the Lyapunov sense. It belongs to the so-called reaction-diffusion equations of semi linear kind, that is, linear equations in the heat operator and they have a nonlinear reaction function, in this case f (u, a, b) = u (a - b u), being u concentration, a and b parameters. The study of the incidence of these parameters take an interest to the neutronic flux physics. So that we search non trivial, positive and bounded solutions. The used algorithm is based on the concept of monotone and ordered sequences, and on the existence theorem of Amann and Sattinger. (author)
Reaction diffusion voronoi diagrams: from sensors data to computing
Czech Academy of Sciences Publication Activity Database
Vázquez-Otero, Alejandro (ed.); Faigl, J.; Dormido, R.; Duro, N.
2015-01-01
Roč. 15, č. 6 (2015), s. 12736-12764 ISSN 1424-8220 R&D Projects: GA MŠk ED1.1.00/02.0061 Grant - others:ELI Beamlines(XE) CZ.1.05/1.1.00/02.0061 Institutional support: RVO:68378271 Keywords : reaction diffusion * FitzHugh–Nagumo * path planning * navigation * exploration Subject RIV: BD - Theory of Information Impact factor: 2.033, year: 2015
Multiple Scale Reaction-Diffusion-Advection Problems with Moving Fronts
Nefedov, Nikolay
2016-06-01
In this work we discuss the further development of the general scheme of the asymptotic method of differential inequalities to investigate stability and motion of sharp internal layers (fronts) for nonlinear singularly perturbed parabolic equations, which are called in applications reaction-diffusion-advection equations. Our approach is illustrated for some new important cases of initial boundary value problems. We present results on stability and on the motion of the fronts.
Traveling waves in a nonlocal, piecewise linear reaction-diffusion population model
Autry, E. A.; Bayliss, A.; Volpert, V. A.
2017-08-01
We consider an analytically tractable switching model that is a simplification of a nonlocal, nonlinear reaction-diffusion model of population growth where we take the source term to be piecewise linear. The form of this source term allows us to consider both the monostable and bistable versions of the problem. By transforming to a traveling frame and choosing specific kernel functions, we are able to reduce the problem to a system of algebraic equations. We construct solutions and examine the propagation speed and monotonicity of the resulting waves.
Lacitignola, Deborah; Bozzini, Benedetto; Frittelli, Massimo; Sgura, Ivonne
2017-07-01
The present paper deals with the pattern formation properties of a specific morpho-electrochemical reaction-diffusion model on a sphere. The physico-chemical background to this study is the morphological control of material electrodeposited onto spherical particles. The particular experimental case of interest refers to the optimization of novel metal-air flow batteries and addresses the electrodeposition of zinc onto inert spherical supports. Morphological control in this step of the high-energy battery operation is crucial to the energetic efficiency of the recharge process and to the durability of the whole energy-storage device. To rationalise this technological challenge within a mathematical modeling perspective, we consider the reaction-diffusion system for metal electrodeposition introduced in [Bozzini et al., J. Solid State Electr.17, 467-479 (2013)] and extend its study to spherical domains. Conditions are derived for the occurrence of the Turing instability phenomenon and the steady patterns emerging at the onset of Turing instability are investigated. The reaction-diffusion system on spherical domains is solved numerically by means of the Lumped Surface Finite Element Method (LSFEM) in space combined with the IMEX Euler method in time. The effect on pattern formation of variations in the domain size is investigated both qualitatively, by means of systematic numerical simulations, and quantitatively by introducing suitable indicators that allow to assign each pattern to a given morphological class. An experimental validation of the obtained results is finally presented for the case of zinc electrodeposition from alkaline zincate solutions onto copper spheres.
Breakdown of the reaction-diffusion master equation with nonelementary rates.
Smith, Stephen; Grima, Ramon
2016-05-01
The chemical master equation (CME) is the exact mathematical formulation of chemical reactions occurring in a dilute and well-mixed volume. The reaction-diffusion master equation (RDME) is a stochastic description of reaction-diffusion processes on a spatial lattice, assuming well mixing only on the length scale of the lattice. It is clear that, for the sake of consistency, the solution of the RDME of a chemical system should converge to the solution of the CME of the same system in the limit of fast diffusion: Indeed, this has been tacitly assumed in most literature concerning the RDME. We show that, in the limit of fast diffusion, the RDME indeed converges to a master equation but not necessarily the CME. We introduce a class of propensity functions, such that if the RDME has propensities exclusively of this class, then the RDME converges to the CME of the same system, whereas if the RDME has propensities not in this class, then convergence is not guaranteed. These are revealed to be elementary and nonelementary propensities, respectively. We also show that independent of the type of propensity, the RDME converges to the CME in the simultaneous limit of fast diffusion and large volumes. We illustrate our results with some simple example systems and argue that the RDME cannot generally be an accurate description of systems with nonelementary rates.
Simpson, Matthew J; Sharp, Jesse A; Morrow, Liam C; Baker, Ruth E
2015-01-01
Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction-diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction-diffusion equation on a growing domain, 0 reaction-diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially-confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially-confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.
Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations
Indekeu, Joseph O.; Smets, Ruben
2017-08-01
Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.
Multiscale Reaction-Diffusion Algorithms: PDE-Assisted Brownian Dynamics
Franz, Benjamin
2013-06-19
Two algorithms that combine Brownian dynami cs (BD) simulations with mean-field partial differential equations (PDEs) are presented. This PDE-assisted Brownian dynamics (PBD) methodology provides exact particle tracking data in parts of the domain, whilst making use of a mean-field reaction-diffusion PDE description elsewhere. The first PBD algorithm couples BD simulations with PDEs by randomly creating new particles close to the interface, which partitions the domain, and by reincorporating particles into the continuum PDE-description when they cross the interface. The second PBD algorithm introduces an overlap region, where both descriptions exist in parallel. It is shown that the overlap region is required to accurately compute variances using PBD simulations. Advantages of both PBD approaches are discussed and illustrative numerical examples are presented. © 2013 Society for Industrial and Applied Mathematics.
Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations
Alzahrani, Hasnaa H.
2016-07-26
A tailored integration scheme is developed to treat stiff reaction-diffusion prob- lems. The construction adapts a stiff solver, namely VODE, to treat reaction im- plicitly together with explicit treatment of diffusion. The second-order Runge-Kutta- Chebyshev (RKC) scheme is adjusted to integrate diffusion. Spatial operator is de- scretised by second-order finite differences on a uniform grid. The overall solution is advanced over S fractional stiff integrations, where S corresponds to the number of RKC stages. The behavior of the scheme is analyzed by applying it to three simple problems. The results show that it achieves second-order accuracy, thus, preserving the formal accuracy of the original RKC. The presented development sets the stage for future extensions, particularly, to multidimensional reacting flows with detailed chemistry.
Poznanski, R R
2010-09-01
A reaction-diffusion model is presented to encapsulate calcium-induced calcium release (CICR) as a potential mechanism for somatofugal bias of dendritic calcium movement in starburst amacrine cells. Calcium dynamics involves a simple calcium extrusion (pump) and a buffering mechanism of calcium binding proteins homogeneously distributed over the plasma membrane of the endoplasmic reticulum within starburst amacrine cells. The system of reaction-diffusion equations in the excess buffer (or low calcium concentration) approximation are reformulated as a nonlinear Volterra integral equation which is solved analytically via a regular perturbation series expansion in response to calcium feedback from a continuously and uniformly distributed calcium sources. Calculation of luminal calcium diffusion in the absence of buffering enables a wave to travel at distances of 120 μm from the soma to distal tips of a starburst amacrine cell dendrite in 100 msec, yet in the presence of discretely distributed calcium-binding proteins it is unknown whether the propagating calcium wave-front in the somatofugal direction is further impeded by endogenous buffers. If so, this would indicate CICR to be an unlikely mechanism of retinal direction selectivity in starburst amacrine cells.
International Nuclear Information System (INIS)
Moyano, Edgardo A.; Scarpettini, Alberto F.
2003-01-01
A semi linear model of weakly coupled parabolic p.d.e. with reaction-diffusion is investigated. The system describes fission gas transfer from grain interior of UO 2 to grain boundaries. The problem is studied in a bounded domain. Using the upper-lower solutions method, two monotone sequences for the finite differences equations are constructed. Reasons are mentioned that allow to affirm that in the proposed functional sector the algorithm converges to the unique solution of the differential system. (author)
A fractional reaction-diffusion description of supply and demand
Benzaquen, Michael; Bouchaud, Jean-Philippe
2018-02-01
We suggest that the broad distribution of time scales in financial markets could be a crucial ingredient to reproduce realistic price dynamics in stylised Agent-Based Models. We propose a fractional reaction-diffusion model for the dynamics of latent liquidity in financial markets, where agents are very heterogeneous in terms of their characteristic frequencies. Several features of our model are amenable to an exact analytical treatment. We find in particular that the impact is a concave function of the transacted volume (aka the "square-root impact law"), as in the normal diffusion limit. However, the impact kernel decays as t-β with β = 1/2 in the diffusive case, which is inconsistent with market efficiency. In the sub-diffusive case the decay exponent β takes any value in [0, 1/2], and can be tuned to match the empirical value β ≈ 1/4. Numerical simulations confirm our theoretical results. Several extensions of the model are suggested. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
Evolution of density profiles for reaction-diffusion processes
International Nuclear Information System (INIS)
Ondarza-Rovira, R.
1990-01-01
The purpose of this work is to study the reaction diffusion equations for the concentration of one species in one spatial dimension. Nonlinear diffusion equations paly an important role in several fields: Physics, Kinetic Chemistry, Poblational Biology, Neurophysics, etc. The study of the behavior of solutions, with nonlinear diffusion coefficient, and monomial creation and annihilation terms, is considered. It is found, that when the exponent of the annihilation term is smaller than the one of the creation term, unstable equilibrium solutions may exist, for which solutions above it explode in finite time, but solutions below it decay exponentially. By means of the reduction to quadratures technique, it is found that is possible to obtain travelling wave solution in those cases when the annihilation term is greater than the creation term. This method of solution always permits to know the propagation velocity of the front, even if the concentration cannot be written in closed form. The portraits of the solutions in phase space show the existence of solutions which velocities may be smaller or greater than the ones found analytically. Linear and nonlinear diffusion equations, differ significantly in that the former are of change of solutions are considered. This is reminiscent of the fact that linear diffusion yields infinite propagation speed, even though the speed of the front is finite. When the strength of the annihilation term increases, as compared with that of the creation term, arbitrary initial conditions (studied numerically) relax to stable platforms that move indefinitly with constant speed. (Author)
Setting initial conditions for inflation with reaction-diffusion equation
Bagchi, Partha; Das, Arpan; Dave, Shreyansh S.; Sengupta, Srikumar; Srivastava, Ajit M.
2018-03-01
We discuss the issue of setting appropriate initial conditions for inflation. Specifically, we consider natural inflation model and discuss the fine tuning required for setting almost homogeneous initial conditions over a region of order several times the Hubble size which is orders of magnitude larger than any relevant correlation length for field fluctuations. We then propose to use the special propagating front solutions of reaction-diffusion equations for localized field domains of smaller sizes. Due to very small velocities of these propagating fronts we find that the inflaton field in such a field domain changes very slowly, contrary to naive expectation of rapid roll down to the true vacuum. Continued expansion leads to the energy density in the Hubble region being dominated by the vacuum energy, thereby beginning the inflationary phase. Our results show that inflation can occur even with a single localized field domain of size smaller than the Hubble size. We discuss possible extensions of our results for different inflationary models, as well as various limitations of our analysis (e.g. neglecting self gravity of the localized field domain).
A reaction-diffusion model of cholinergic retinal waves.
Directory of Open Access Journals (Sweden)
Benjamin Lansdell
2014-12-01
Full Text Available Prior to receiving visual stimuli, spontaneous, correlated activity in the retina, called retinal waves, drives activity-dependent developmental programs. Early-stage waves mediated by acetylcholine (ACh manifest as slow, spreading bursts of action potentials. They are believed to be initiated by the spontaneous firing of Starburst Amacrine Cells (SACs, whose dense, recurrent connectivity then propagates this activity laterally. Their inter-wave interval and shifting wave boundaries are the result of the slow after-hyperpolarization of the SACs creating an evolving mosaic of recruitable and refractory cells, which can and cannot participate in waves, respectively. Recent evidence suggests that cholinergic waves may be modulated by the extracellular concentration of ACh. Here, we construct a simplified, biophysically consistent, reaction-diffusion model of cholinergic retinal waves capable of recapitulating wave dynamics observed in mice retina recordings. The dense, recurrent connectivity of SACs is modeled through local, excitatory coupling occurring via the volume release and diffusion of ACh. In addition to simulation, we are thus able to use non-linear wave theory to connect wave features to underlying physiological parameters, making the model useful in determining appropriate pharmacological manipulations to experimentally produce waves of a prescribed spatiotemporal character. The model is used to determine how ACh mediated connectivity may modulate wave activity, and how parameters such as the spontaneous activation rate and sAHP refractory period contribute to critical wave size variability.
Nucleation of reaction-diffusion waves on curved surfaces
International Nuclear Information System (INIS)
Kneer, Frederike; Schöll, Eckehard; Dahlem, Markus A
2014-01-01
We study reaction-diffusion waves on curved two-dimensional surfaces, and determine the influence of curvature upon the nucleation and propagation of spatially localized waves in an excitable medium modelled by the generic FitzHugh–Nagumo model. We show that the stability of propagating wave segments depends crucially on the curvature of the surface. As they propagate, they may shrink to the uniform steady state, or expand, depending on whether they are smaller or larger, respectively, than a critical nucleus. This critical nucleus for wave propagation is modified by the curvature acting like an effective space-dependent local spatial coupling, similar to diffuson, thus extending the regime of propagating excitation waves beyond the excitation threshold of flat surfaces. In particular, a negative gradient of Gaussian curvature Γ, as on the outside of a torus surface (positive Γ), when the wave segment symmetrically extends into the inside (negative Γ), allows for stable propagation of localized wave segments remaining unchanged in size and shape, or oscillating periodically in size. (paper)
Propagation Phenomena in a Bistable Reaction Diffusion System.
1981-05-01
Differential Equations 23 (1977), 335-367. 3. Casten, R. H., H. Cohen, and P. Lagerstrom, Perturbation analysis of an approximation to Hodgkin - Huxley theory...in several applications, e.g. see [18]. Here, we extend consideration to parameter ranges, e.g. y large enough, for which the v - w dynamics are...ones. A global picture (Figure 6) is provided for e, y -parameter regimes in which the various waves exist. Finally, in Section 4, we present numerical
Periodic pulse solutions to slowly nonlinear reaction-diffusion systems
Rijk, de B.
2016-01-01
The presence of a small parameter can reduce the complexity of the stability analysis of pattern solutions. This reduction manifests itself through the complex-analytic Evans function, which vanishes on the spectrum of the linearization about the pattern. For certain 'slowly linear' prototype models
Hybrid approaches for multiple-species stochastic reaction-diffusion models
Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K.; Byrne, Helen
2015-10-01
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.
Hybrid approaches for multiple-species stochastic reaction-diffusion models.
Spill, Fabian
2015-10-01
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.
Scalable implicit methods for reaction-diffusion equations in two and three space dimensions
Energy Technology Data Exchange (ETDEWEB)
Veronese, S.V.; Othmer, H.G. [Univ. of Utah, Salt Lake City, UT (United States)
1996-12-31
This paper describes the implementation of a solver for systems of semi-linear parabolic partial differential equations in two and three space dimensions. The solver is based on a parallel implementation of a non-linear Alternating Direction Implicit (ADI) scheme which uses a Cartesian grid in space and an implicit time-stepping algorithm. Various reordering strategies for the linearized equations are used to reduce the stride and improve the overall effectiveness of the parallel implementation. We have successfully used this solver for large-scale reaction-diffusion problems in computational biology and medicine in which the desired solution is a traveling wave that may contain rapid transitions. A number of examples that illustrate the efficiency and accuracy of the method are given here; the theoretical analysis will be presented.
An adaptive algorithm for simulation of stochastic reaction-diffusion processes
International Nuclear Information System (INIS)
Ferm, Lars; Hellander, Andreas; Loetstedt, Per
2010-01-01
We propose an adaptive hybrid method suitable for stochastic simulation of diffusion dominated reaction-diffusion processes. For such systems, simulation of the diffusion requires the predominant part of the computing time. In order to reduce the computational work, the diffusion in parts of the domain is treated macroscopically, in other parts with the tau-leap method and in the remaining parts with Gillespie's stochastic simulation algorithm (SSA) as implemented in the next subvolume method (NSM). The chemical reactions are handled by SSA everywhere in the computational domain. A trajectory of the process is advanced in time by an operator splitting technique and the timesteps are chosen adaptively. The spatial adaptation is based on estimates of the errors in the tau-leap method and the macroscopic diffusion. The accuracy and efficiency of the method are demonstrated in examples from molecular biology where the domain is discretized by unstructured meshes.
Reprint of Domain decomposition multigrid methods for nonlinear reaction-diffusion problems
Arrarás, A.; Gaspar, F. J.; Portero, L.; Rodrigo, C.
2015-04-01
In this work, we propose efficient discretizations for nonlinear evolutionary reaction-diffusion problems on general two-dimensional domains. The spatial domain is discretized through an unstructured coarse triangulation, which is subsequently refined via regular triangular grids. Following the method of lines approach, we first consider a finite element spatial discretization, and then use a linearly implicit splitting time integrator related to a suitable decomposition of the triangulation nodes. Such a procedure provides a linear system per internal stage. The equations corresponding to those nodes lying strictly inside the elements of the coarse triangulation can be decoupled and solved in parallel using geometric multigrid techniques. The method is unconditionally stable and computationally efficient, since it avoids the need for Schwarz-type iteration procedures. In addition, it is formulated for triangular elements, thus yielding much flexibility in the discretization of complex geometries. To illustrate its practical utility, the algorithm is shown to reproduce the pattern-forming dynamics of the Schnakenberg model.
Global dynamics of a nonlocal delayed reaction-diffusion equation on a half plane
Hu, Wenjie; Duan, Yueliang
2018-04-01
We consider a delayed reaction-diffusion equation with spatial nonlocality on a half plane that describes population dynamics of a two-stage species living in a semi-infinite environment. A Neumann boundary condition is imposed accounting for an isolated domain. To describe the global dynamics, we first establish some a priori estimate for nontrivial solutions after investigating asymptotic properties of the nonlocal delayed effect and the diffusion operator, which enables us to show the permanence of the equation with respect to the compact open topology. We then employ standard dynamical system arguments to establish the global attractivity of the nontrivial equilibrium. The main results are illustrated by the diffusive Nicholson's blowfly equation and the diffusive Mackey-Glass equation.
International Nuclear Information System (INIS)
Xu Rui; Chaplain, M.A.J.; Davidson, F.A.
2006-01-01
In this paper, we first investigate a stage-structured competitive model with time delays, harvesting, and nonlocal spatial effect. By using an iterative technique recently developed by Wu and Zou (Wu J, Zou X. Travelling wave fronts of reaction-diffusion systems with delay. J Dynam Differen Equat 2001;13:651-87), sufficient conditions are established for the existence of travelling front solution connecting the two boundary equilibria in the case when there is no positive equilibrium. The travelling wave front corresponds to an invasion by a stronger species which drives the weaker species to extinction. Secondly, we consider a stage-structured competitive model with time delays and nonlocal spatial effect when the domain is finite. We prove the global stability of each of the nonnegative equilibria and demonstrate that the more complex model studied here admits three possible long term behaviors: coexistence, bistability and dominance as is the case for the standard Lotka-Voltera competitive model
Wang, Xiaohu; Lu, Kening; Wang, Bixiang
2018-01-01
In this paper, we study the Wong-Zakai approximations given by a stationary process via the Wiener shift and their associated long term behavior of the stochastic reaction-diffusion equation driven by a white noise. We first prove the existence and uniqueness of tempered pullback attractors for the Wong-Zakai approximations of stochastic reaction-diffusion equation. Then, we show that the attractors of Wong-Zakai approximations converges to the attractor of the stochastic reaction-diffusion equation for both additive and multiplicative noise.
Study on monostable and bistable reaction-diffusion equations by iteration of travelling wave maps
Yi, Taishan; Chen, Yuming
2017-12-01
In this paper, based on the iterative properties of travelling wave maps, we develop a new method to obtain spreading speeds and asymptotic propagation for monostable and bistable reaction-diffusion equations. Precisely, for Dirichlet problems of monostable reaction-diffusion equations on the half line, by making links between travelling wave maps and integral operators associated with the Dirichlet diffusion kernel (the latter is NOT invariant under translation), we obtain some iteration properties of the Dirichlet diffusion and some a priori estimates on nontrivial solutions of Dirichlet problems under travelling wave transformation. We then provide the asymptotic behavior of nontrivial solutions in the space-time region for Dirichlet problems. These enable us to develop a unified method to obtain results on heterogeneous steady states, travelling waves, spreading speeds, and asymptotic spreading behavior for Dirichlet problem of monostable reaction-diffusion equations on R+ as well as of monostable/bistable reaction-diffusion equations on R.
On positive solutions of reaction-diffusion equation with Caratheodory nonlinear term
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O. V. Kapustyan
2009-09-01
Full Text Available In the paper for reaction-diffusion equation with Caratheodory nonlinear term under conditions, which do not guarantee uniqueness of Cauchy problem solution, we prove the global resolvability in the class of nonnegative integrable functions.
International Nuclear Information System (INIS)
Liang Jinling; Cao Jinde
2003-01-01
Employing general Halanay inequality, we analyze the global exponential stability of a class of reaction-diffusion recurrent neural networks with time-varying delays. Several new sufficient conditions are obtained to ensure existence, uniqueness and global exponential stability of the equilibrium point of delayed reaction-diffusion recurrent neural networks. The results extend and improve the earlier publications. In addition, an example is given to show the effectiveness of the obtained result
Richter, Otto; Moenickes, Sylvia; Suhling, Frank
2012-02-01
The spatial dynamics of range expansion is studied in dependence of temperature. The main elements population dynamics, competition and dispersal are combined in a coherent approach based on a system of coupled partial differential equations of the reaction-diffusion type. The nonlinear reaction terms comprise population dynamic models with temperature dependent reproduction rates subject to an Allee effect and mutual competition. The effect of temperature on travelling wave solutions is investigated for a one dimensional model version. One main result is the importance of the Allee effect for the crossing of regions with unsuitable habitats. The nonlinearities of the interaction terms give rise to a richness of spatio-temporal dynamic patterns. In two dimensions, the resulting non-linear initial boundary value problems are solved over geometries of heterogeneous landscapes. Geo referenced model parameters such as mean temperature and elevation are imported into the finite element tool COMSOL Multiphysics from a geographical information system. The model is applied to the range expansion of species at the scale of middle Europe. Copyright © 2011 Elsevier Inc. All rights reserved.
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Lionel Roques
Full Text Available We propose and develop a general approach based on reaction-diffusion equations for modelling a species dynamics in a realistic two-dimensional (2D landscape crossed by linear one-dimensional (1D corridors, such as roads, hedgerows or rivers. Our approach is based on a hybrid "2D/1D model", i.e, a system of 2D and 1D reaction-diffusion equations with homogeneous coefficients, in which each equation describes the population dynamics in a given 2D or 1D element of the landscape. Using the example of the range expansion of the tiger mosquito Aedes albopictus in France and its main highways as 1D corridors, we show that the model can be fitted to realistic observation data. We develop a mechanistic-statistical approach, based on the coupling between a model of population dynamics and a probabilistic model of the observation process. This allows us to bridge the gap between the data (3 levels of infestation, at the scale of a French department and the output of the model (population densities at each point of the landscape, and to estimate the model parameter values using a maximum-likelihood approach. Using classical model comparison criteria, we obtain a better fit and a better predictive power with the 2D/1D model than with a standard homogeneous reaction-diffusion model. This shows the potential importance of taking into account the effect of the corridors (highways in the present case on species dynamics. With regard to the particular case of A. albopictus, the conclusion that highways played an important role in species range expansion in mainland France is consistent with recent findings from the literature.
2016-01-01
We propose and develop a general approach based on reaction-diffusion equations for modelling a species dynamics in a realistic two-dimensional (2D) landscape crossed by linear one-dimensional (1D) corridors, such as roads, hedgerows or rivers. Our approach is based on a hybrid “2D/1D model”, i.e, a system of 2D and 1D reaction-diffusion equations with homogeneous coefficients, in which each equation describes the population dynamics in a given 2D or 1D element of the landscape. Using the example of the range expansion of the tiger mosquito Aedes albopictus in France and its main highways as 1D corridors, we show that the model can be fitted to realistic observation data. We develop a mechanistic-statistical approach, based on the coupling between a model of population dynamics and a probabilistic model of the observation process. This allows us to bridge the gap between the data (3 levels of infestation, at the scale of a French department) and the output of the model (population densities at each point of the landscape), and to estimate the model parameter values using a maximum-likelihood approach. Using classical model comparison criteria, we obtain a better fit and a better predictive power with the 2D/1D model than with a standard homogeneous reaction-diffusion model. This shows the potential importance of taking into account the effect of the corridors (highways in the present case) on species dynamics. With regard to the particular case of A. albopictus, the conclusion that highways played an important role in species range expansion in mainland France is consistent with recent findings from the literature. PMID:26986201
Roques, Lionel; Bonnefon, Olivier
2016-01-01
We propose and develop a general approach based on reaction-diffusion equations for modelling a species dynamics in a realistic two-dimensional (2D) landscape crossed by linear one-dimensional (1D) corridors, such as roads, hedgerows or rivers. Our approach is based on a hybrid "2D/1D model", i.e, a system of 2D and 1D reaction-diffusion equations with homogeneous coefficients, in which each equation describes the population dynamics in a given 2D or 1D element of the landscape. Using the example of the range expansion of the tiger mosquito Aedes albopictus in France and its main highways as 1D corridors, we show that the model can be fitted to realistic observation data. We develop a mechanistic-statistical approach, based on the coupling between a model of population dynamics and a probabilistic model of the observation process. This allows us to bridge the gap between the data (3 levels of infestation, at the scale of a French department) and the output of the model (population densities at each point of the landscape), and to estimate the model parameter values using a maximum-likelihood approach. Using classical model comparison criteria, we obtain a better fit and a better predictive power with the 2D/1D model than with a standard homogeneous reaction-diffusion model. This shows the potential importance of taking into account the effect of the corridors (highways in the present case) on species dynamics. With regard to the particular case of A. albopictus, the conclusion that highways played an important role in species range expansion in mainland France is consistent with recent findings from the literature.
Dissipation and displacement of hotspots in reaction-diffusion models of crime.
Short, Martin B; Brantingham, P Jeffrey; Bertozzi, Andrea L; Tita, George E
2010-03-02
The mechanisms driving the nucleation, spread, and dissipation of crime hotspots are poorly understood. As a consequence, the ability of law enforcement agencies to use mapped crime patterns to design crime prevention strategies is severely hampered. We also lack robust expectations about how different policing interventions should impact crime. Here we present a mathematical framework based on reaction-diffusion partial differential equations for studying the dynamics of crime hotspots. The system of equations is based on empirical evidence for how offenders move and mix with potential victims or targets. Analysis shows that crime hotspots form when the enhanced risk of repeat crimes diffuses locally, but not so far as to bind distant crime together. Crime hotspots may form as either supercritical or subcritical bifurcations, the latter the result of large spikes in crime that override linearly stable, uniform crime distributions. Our mathematical methods show that subcritical crime hotspots may be permanently eradicated with police suppression, whereas supercritical hotspots are displaced following a characteristic spatial pattern. Our results thus provide a mechanistic explanation for recent failures to observe crime displacement in experimental field tests of hotspot policing.
Fourier spectral methods for fractional-in-space reaction-diffusion equations
Bueno-Orovio, Alfonso
2014-04-01
© 2014, Springer Science+Business Media Dordrecht. Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains of ℝ. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.
Hurdal, Monica K.; Striegel, Deborah A.
2011-11-01
Modeling and understanding cortical folding pattern formation is important for quantifying cortical development. We present a biomathematical model for cortical folding pattern formation in the human brain and apply this model to study diseases involving cortical pattern malformations associated with neural migration disorders. Polymicrogyria is a cortical malformation disease resulting in an excessive number of small gyri. Our mathematical model uses a Turing reaction-diffusion system to model cortical folding. The lateral ventricle (LV) and ventricular zone (VZ) of the brain are critical components in the formation of cortical patterning. In early cortical development the shape of the LV can be modeled with a prolate spheroid and the VZ with a prolate spheroid surface. We use our model to study how global cortex characteristics, such as size and shape of the LV, affect cortical pattern formation. We demonstrate increasing domain scale can increase the number of gyri and sulci formed. Changes in LV shape can account for sulcus directionality. By incorporating LV size and shape, our model is able to elucidate which parameters can lead to excessive cortical folding.
The two-regime method for optimizing stochastic reaction-diffusion simulations
Flegg, M. B.
2011-10-19
Spatial organization and noise play an important role in molecular systems biology. In recent years, a number of software packages have been developed for stochastic spatio-temporal simulation, ranging from detailed molecular-based approaches to less detailed compartment-based simulations. Compartment-based approaches yield quick and accurate mesoscopic results, but lack the level of detail that is characteristic of the computationally intensive molecular-based models. Often microscopic detail is only required in a small region (e.g. close to the cell membrane). Currently, the best way to achieve microscopic detail is to use a resource-intensive simulation over the whole domain. We develop the two-regime method (TRM) in which a molecular-based algorithm is used where desired and a compartment-based approach is used elsewhere. We present easy-to-implement coupling conditions which ensure that the TRM results have the same accuracy as a detailed molecular-based model in the whole simulation domain. Therefore, the TRM combines strengths of previously developed stochastic reaction-diffusion software to efficiently explore the behaviour of biological models. Illustrative examples and the mathematical justification of the TRM are also presented.
WNT and DKK Determine Hair Follicle Spacing Through a Reaction-Diffusion Mechanism
Sick, Stefanie; Reinker, Stefan; Timmer, Jens; Schlake, Thomas
2006-12-01
Mathematical reaction-diffusion models have been suggested to describe formation of animal pigmentation patterns and distribution of epidermal appendages. However, the crucial signals and in vivo mechanisms are still elusive. Here we identify WNT and its inhibitor DKK as primary determinants of murine hair follicle spacing, using a combined experimental and computational modeling approach. Transgenic DKK overexpression reduces overall appendage density. Moderate suppression of endogenous WNT signaling forces follicles to form clusters during an otherwise normal morphogenetic program. These results confirm predictions of a WNT/DKK-specific mathematical model and provide in vivo corroboration of the reaction-diffusion mechanism for epidermal appendage formation.
International Nuclear Information System (INIS)
Wang Jian; Lu Junguo
2008-01-01
In this paper, we study the global exponential stability of fuzzy cellular neural networks with delays and reaction-diffusion terms. By constructing a suitable Lyapunov functional and utilizing some inequality techniques, we obtain a sufficient condition for the uniqueness and global exponential stability of the equilibrium solution for a class of fuzzy cellular neural networks with delays and reaction-diffusion terms. The result imposes constraint conditions on the network parameters independently of the delay parameter. The result is also easy to check and plays an important role in the design and application of globally exponentially stable fuzzy neural circuits
Hopf bifurcation in a delayed reaction-diffusion-advection population model
Chen, Shanshan; Lou, Yuan; Wei, Junjie
2018-04-01
In this paper, we investigate a reaction-diffusion-advection model with time delay effect. The stability/instability of the spatially nonhomogeneous positive steady state and the associated Hopf bifurcation are investigated when the given parameter of the model is near the principle eigenvalue of an elliptic operator. Our results imply that time delay can make the spatially nonhomogeneous positive steady state unstable for a reaction-diffusion-advection model, and the model can exhibit oscillatory pattern through Hopf bifurcation. The effect of advection on Hopf bifurcation values is also considered, and our results suggest that Hopf bifurcation is more likely to occur when the advection rate increases.
Polyanin, A. D.; Sorokin, V. G.
2017-12-01
The paper deals with nonlinear reaction-diffusion equations with one or several delays. We formulate theorems that allow constructing exact solutions for some classes of these equations, which depend on several arbitrary functions. Examples of application of these theorems for obtaining new exact solutions in elementary functions are provided. We state basic principles of construction, selection, and use of test problems for nonlinear partial differential equations with delay. Some test problems which can be suitable for estimating accuracy of approximate analytical and numerical methods of solving reaction-diffusion equations with delay are presented. Some examples of numerical solutions of nonlinear test problems with delay are considered.
Time-independent reaction-diffusion equation with a discontinuous reactive term
Levashova, N. T.; Nefedov, N. N.; Orlov, A. O.
2017-05-01
A two-dimensional singularly perturbed elliptic equation referred to in applications as the reaction-diffusion equation is considered. The nonlinearity describing the reaction is assumed to be discontinuous on a certain closed curve. On the basis of the generalized asymptotic comparison principle, the existence of smooth solution is proven and the accuracy of the asymptotic approximation is estimated.
Dynamical Behaviors of Stochastic Reaction-Diffusion Cohen-Grossberg Neural Networks with Delays
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Li Wan
2012-01-01
Full Text Available This paper investigates dynamical behaviors of stochastic Cohen-Grossberg neural network with delays and reaction diffusion. By employing Lyapunov method, Poincaré inequality and matrix technique, some sufficient criteria on ultimate boundedness, weak attractor, and asymptotic stability are obtained. Finally, a numerical example is given to illustrate the correctness and effectiveness of our theoretical results.
Bifurcation Analysis of Gene Propagation Model Governed by Reaction-Diffusion Equations
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Guichen Lu
2016-01-01
Full Text Available We present a theoretical analysis of the attractor bifurcation for gene propagation model governed by reaction-diffusion equations. We investigate the dynamical transition problems of the model under the homogeneous boundary conditions. By using the dynamical transition theory, we give a complete characterization of the bifurcated objects in terms of the biological parameters of the problem.
Patterns in a nonlocal time-delayed reaction-diffusion equation
Guo, Shangjiang
2018-02-01
In this paper, the existence, stability, and multiplicity of nontrivial (spatially homogeneous or nonhomogeneous) steady-state solution and periodic solutions for a reaction-diffusion model with nonlocal delay effect and Dirichlet/Neumann boundary condition are investigated by using Lyapunov-Schmidt reduction. Moreover, we illustrate our general results by applications to population models with one-dimensional spatial domain.
Brandt-Pollmann, U; Lebiedz, D; Diehl, M; Sager, S; Schlöder, J
2005-09-01
Theoretical and experimental studies related to manipulation of pattern formation in self-organizing reaction-diffusion processes by appropriate control stimuli become increasingly important both in chemical engineering and cellular biochemistry. In a model study, we demonstrate here exemplarily the application of an efficient nonlinear model predictive control (NMPC) algorithm to real-time optimal feedback control of pattern formation in a bacterial chemotaxis system modeled by nonlinear partial differential equations. The corresponding drift-diffusion model type is representative for many (bio)chemical systems involving nonlinear reaction dynamics and nonlinear diffusion. We show how the computed optimal feedback control strategy exploits the system inherent physical property of wave propagation to achieve desired control aims. We discuss various applications of our approach to optimal control of spatiotemporal dynamics.
A reaction-diffusion model of CO2 influx into an oocyte
Somersalo, Erkki; Occhipinti, Rossana; Boron, Walter F.; Calvetti, Daniela
2012-01-01
We have developed and implemented a novel mathematical model for simulating transients in surface pH (pHS) and intracellular pH (pHi) caused by the influx of carbon dioxide (CO2) into a Xenopus oocyte. These transients are important tools for studying gas channels. We assume that the oocyte is a sphere surrounded by a thin layer of unstirred fluid, the extracellular unconvected fluid (EUF), which is in turn surrounded by the well-stirred bulk extracellular fluid (BECF) that represents an infinite reservoir for all solutes. Here, we assume that the oocyte plasma membrane is permeable only to CO2. In both the EUF and intracellular space, solute concentrations can change because of diffusion and reactions. The reactions are the slow equilibration of the CO2 hydration-dehydration reactions and competing equilibria among carbonic acid (H2CO3)/bicarbonate ( HCO3-) and a multitude of non-CO2/HCO3- buffers. Mathematically, the model is described by a coupled system of reaction-diffusion equations that—assuming spherical radial symmetry—we solved using the method of lines with appropriate stiff solvers. In agreement with experimental data (Musa-Aziz et al, PNAS 2009, 106:5406–5411), the model predicts that exposing the cell to extracellular 1.5% CO2/10 mM HCO3- (pH 7.50) causes pHi to fall and pHS to rise rapidly to a peak and then decay. Moreover, the model provides insights into the competition between diffusion and reaction processes when we change the width of the EUF, membrane permeability to CO2, native extra-and intracellular carbonic anhydrase-like activities, the non-CO2/HCO3- (intrinsic) intracellular buffering power, or mobility of intrinsic intracellular buffers. PMID:22728674
International Nuclear Information System (INIS)
Wang Linshan; Zhang Yan; Zhang Zhe; Wang Yangfan
2009-01-01
Global exponential robust stability is considered for a class of reaction-diffusion uncertain neural networks with time-varying delays. The purpose of the problem addressed is to establish some easy-to-test criteria for global exponential robust stability for the uncertain systems by means of a new Lyapunov-Krasovskii functional and a linear matrix inequality (LMI). A numerical example is exploited to show the usefulness of the derived LMI-based stability conditions.
Stamova, Ivanka; Stamov, Gani
2017-12-01
In this paper, we propose a fractional-order neural network system with time-varying delays and reaction-diffusion terms. We first develop a new Mittag-Leffler synchronization strategy for the controlled nodes via impulsive controllers. Using the fractional Lyapunov method sufficient conditions are given. We also study the global Mittag-Leffler synchronization of two identical fractional impulsive reaction-diffusion neural networks using linear controllers, which was an open problem even for integer-order models. Since the Mittag-Leffler stability notion is a generalization of the exponential stability concept for fractional-order systems, our results extend and improve the exponential impulsive control theory of neural network system with time-varying delays and reaction-diffusion terms to the fractional-order case. The fractional-order derivatives allow us to model the long-term memory in the neural networks, and thus the present research provides with a conceptually straightforward mathematical representation of rather complex processes. Illustrative examples are presented to show the validity of the obtained results. We show that by means of appropriate impulsive controllers we can realize the stability goal and to control the qualitative behavior of the states. An image encryption scheme is extended using fractional derivatives. Copyright © 2017 Elsevier Ltd. All rights reserved.
Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Torres, L.; Escobar-Jiménez, R. F.
2018-02-01
A reaction-diffusion system can be represented by the Gray-Scott model. The reaction-diffusion dynamic is described by a pair of time and space dependent Partial Differential Equations (PDEs). In this paper, a generalization of the Gray-Scott model by using variable-order fractional differential equations is proposed. The variable-orders were set as smooth functions bounded in (0 , 1 ] and, specifically, the Liouville-Caputo and the Atangana-Baleanu-Caputo fractional derivatives were used to express the time differentiation. In order to find a numerical solution of the proposed model, the finite difference method together with the Adams method were applied. The simulations results showed the chaotic behavior of the proposed model when different variable-orders are applied.
Synthesis and materialization of a reaction-diffusion French flag pattern
Zadorin, Anton S.; Rondelez, Yannick; Gines, Guillaume; Dilhas, Vadim; Urtel, Georg; Zambrano, Adrian; Galas, Jean-Christophe; Estevez-Torres, André
2017-10-01
During embryo development, patterns of protein concentration appear in response to morphogen gradients. These patterns provide spatial and chemical information that directs the fate of the underlying cells. Here, we emulate this process within non-living matter and demonstrate the autonomous structuration of a synthetic material. First, we use DNA-based reaction networks to synthesize a French flag, an archetypal pattern composed of three chemically distinct zones with sharp borders whose synthetic analogue has remained elusive. A bistable network within a shallow concentration gradient creates an immobile, sharp and long-lasting concentration front through a reaction-diffusion mechanism. The combination of two bistable circuits generates a French flag pattern whose 'phenotype' can be reprogrammed by network mutation. Second, these concentration patterns control the macroscopic organization of DNA-decorated particles, inducing a French flag pattern of colloidal aggregation. This experimental framework could be used to test reaction-diffusion models and fabricate soft materials following an autonomous developmental programme.
Heat kernel regularization of the effective action for stochastic reaction-diffusion equations.
Hochberg, D; Molina-París, C; Visser, M
2001-03-01
The presence of fluctuations and nonlinear interactions can lead to scale dependence in the parameters appearing in stochastic differential equations. Stochastic dynamics can be formulated in terms of functional integrals. In this paper we apply the heat kernel method to study the short distance renormalizability of a stochastic (polynomial) reaction-diffusion equation with real additive noise. We calculate the one-loop effective action and its ultraviolet scale dependent divergences. We show that for white noise a polynomial reaction-diffusion equation is one-loop finite in d=0 and d=1, and is one-loop renormalizable in d=2 and d=3 space dimensions. We obtain the one-loop renormalization group equations and find they run with scale only in d=2.
An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations
Burrage, Kevin
2012-01-01
Fractional differential equations are becoming increasingly used as a modelling tool for processes associated with anomalous diffusion or spatial heterogeneity. However, the presence of a fractional differential operator causes memory (time fractional) or nonlocality (space fractional) issues that impose a number of computational constraints. In this paper we develop efficient, scalable techniques for solving fractional-in-space reaction diffusion equations using the finite element method on both structured and unstructured grids via robust techniques for computing the fractional power of a matrix times a vector. Our approach is show-cased by solving the fractional Fisher and fractional Allen-Cahn reaction-diffusion equations in two and three spatial dimensions, and analyzing the speed of the traveling wave and size of the interface in terms of the fractional power of the underlying Laplacian operator. © 2012 Society for Industrial and Applied Mathematics.
Liu, Bingchen; Dong, Mengzhen; Li, Fengjie
2018-04-01
This paper deals with a reaction-diffusion problem with coupled nonlinear inner sources and nonlocal boundary flux. Firstly, we propose the critical exponents on nonsimultaneous blow-up under some conditions on the initial data. Secondly, we combine the scaling technique and the Green's identity method to determine four kinds of simultaneous blow-up rates. Thirdly, the lower and the upper bounds of blow-up time are derived by using Sobolev-type differential inequalities.
Liu, Ping; Shi, Junping
2018-01-01
The bifurcation of non-trivial steady state solutions of a scalar reaction-diffusion equation with nonlinear boundary conditions is considered using several new abstract bifurcation theorems. The existence and stability of positive steady state solutions are proved using a unified approach. The general results are applied to a Laplace equation with nonlinear boundary condition and bistable nonlinearity, and an elliptic equation with superlinear nonlinearity and sublinear boundary conditions.
An analytic algorithm for the space-time fractional reaction-diffusion equation
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M. G. Brikaa
2015-11-01
Full Text Available In this paper, we solve the space-time fractional reaction-diffusion equation by the fractional homotopy analysis method. Solutions of different examples of the reaction term will be computed and investigated. The approximation solutions of the studied models will be put in the form of convergent series to be easily computed and simulated. Comparison with the approximation solution of the classical case of the studied modeled with their approximation errors will also be studied.
Compact-like kink in a real electrical reaction-diffusion chain
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Comte, J.C. [Laboratoire de Physiopathologie des Reseaux Neuronaux du Cycle Veille-Sommeil, CNRS UMR 5167, Faculte de Medecine Laennec 7, Rue Guillaume Paradin, 69372 Lyon Cedex 08 (France)]. E-mail: comtejc@sommeil.univ-lyon1.fr; Marquie, P. [Laboratoire d' Electronique, Informatique et Image (LE2i) UMR CNRS 5158, Aile des Sciences de l' Ingenieur, BP 47870, 21078 Dijon Cedex (France)
2006-07-15
We demonstrate experimentally the compact-like kinks existence in a real electrical reaction-diffusion chain. Our measures show that such entities are strictly localized and consequently present a finite spatial extent. We show equally that the kink velocity is threshold-dependent. A theoretical quantification of the critical coupling under which propagation fails is also achieved and reveals that nonlinear coupling leads to a propagation failure reduction.
Czech Academy of Sciences Publication Activity Database
Ainsworth, M.; Vejchodský, Tomáš
2011-01-01
Roč. 119, č. 2 (2011), s. 219-243 ISSN 0029-599X R&D Projects: GA AV ČR IAA100760702; GA ČR(CZ) GA102/07/0496 Institutional research plan: CEZ:AV0Z10190503 Keywords : a posteriori error estimates * singularly perturbed problems * reaction-diffusion Subject RIV: BA - General Mathematics Impact factor: 1.321, year: 2011 http://www.springerlink.com/content/d384608709584278/
International Nuclear Information System (INIS)
Lou, X.; Cui, B.
2008-01-01
In this paper we consider the problem of exponential stability for recurrent neural networks with multiple time varying delays and reaction-diffusion terms. The activation functions are supposed to be bounded and globally Lipschitz continuous. By means of Lyapunov functional, sufficient conditions are derived, which guarantee global exponential stability of the delayed neural network. Finally, a numerical example is given to show the correctness of our analysis. (author)
Owolabi, Kolade M.
2018-03-01
In this work, we are concerned with the solution of non-integer space-fractional reaction-diffusion equations with the Riemann-Liouville space-fractional derivative in high dimensions. We approximate the Riemann-Liouville derivative with the Fourier transform method and advance the resulting system in time with any time-stepping solver. In the numerical experiments, we expect the travelling wave to arise from the given initial condition on the computational domain (-∞, ∞), which we terminate in the numerical experiments with a large but truncated value of L. It is necessary to choose L large enough to allow the waves to have enough space to distribute. Experimental results in high dimensions on the space-fractional reaction-diffusion models with applications to biological models (Fisher and Allen-Cahn equations) are considered. Simulation results reveal that fractional reaction-diffusion equations can give rise to a range of physical phenomena when compared to non-integer-order cases. As a result, most meaningful and practical situations are found to be modelled with the concept of fractional calculus.
Dharani, S; Rakkiyappan, R; Cao, Jinde; Alsaedi, Ahmed
2017-08-01
This paper explores the problem of synchronization of a class of generalized reaction-diffusion neural networks with mixed time-varying delays. The mixed time-varying delays under consideration comprise of both discrete and distributed delays. Due to the development and merits of digital controllers, sampled-data control is a natural choice to establish synchronization in continuous-time systems. Using a newly introduced integral inequality, less conservative synchronization criteria that assure the global asymptotic synchronization of the considered generalized reaction-diffusion neural network and mixed delays are established in terms of linear matrix inequalities (LMIs). The obtained easy-to-test LMI-based synchronization criteria depends on the delay bounds in addition to the reaction-diffusion terms, which is more practicable. Upon solving these LMIs by using Matlab LMI control toolbox, a desired sampled-data controller gain can be acuqired without any difficulty. Finally, numerical examples are exploited to express the validity of the derived LMI-based synchronization criteria.
Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue
2018-01-01
This paper deals with the existence and stability of traveling wave solutions for a degenerate reaction-diffusion equation with time delay. The degeneracy of spatial diffusion together with the effect of time delay causes us the essential difficulty for the existence of the traveling waves and their stabilities. In order to treat this case, we first show the existence of smooth- and sharp-type traveling wave solutions in the case of c≥c^* for the degenerate reaction-diffusion equation without delay, where c^*>0 is the critical wave speed of smooth traveling waves. Then, as a small perturbation, we obtain the existence of the smooth non-critical traveling waves for the degenerate diffusion equation with small time delay τ >0 . Furthermore, we prove the global existence and uniqueness of C^{α ,β } -solution to the time-delayed degenerate reaction-diffusion equation via compactness analysis. Finally, by the weighted energy method, we prove that the smooth non-critical traveling wave is globally stable in the weighted L^1 -space. The exponential convergence rate is also derived.
A reaction-diffusion model of ROS-induced ROS release in a mitochondrial network.
Directory of Open Access Journals (Sweden)
Lufang Zhou
2010-01-01
Full Text Available Loss of mitochondrial function is a fundamental determinant of cell injury and death. In heart cells under metabolic stress, we have previously described how the abrupt collapse or oscillation of the mitochondrial energy state is synchronized across the mitochondrial network by local interactions dependent upon reactive oxygen species (ROS. Here, we develop a mathematical model of ROS-induced ROS release (RIRR based on reaction-diffusion (RD-RIRR in one- and two-dimensional mitochondrial networks. The nodes of the RD-RIRR network are comprised of models of individual mitochondria that include a mechanism of ROS-dependent oscillation based on the interplay between ROS production, transport, and scavenging; and incorporating the tricarboxylic acid (TCA cycle, oxidative phosphorylation, and Ca(2+ handling. Local mitochondrial interaction is mediated by superoxide (O2.- diffusion and the O2.(--dependent activation of an inner membrane anion channel (IMAC. In a 2D network composed of 500 mitochondria, model simulations reveal DeltaPsi(m depolarization waves similar to those observed when isolated guinea pig cardiomyocytes are subjected to a localized laser-flash or antioxidant depletion. The sensitivity of the propagation rate of the depolarization wave to O(2.- diffusion, production, and scavenging in the reaction-diffusion model is similar to that observed experimentally. In addition, we present novel experimental evidence, obtained in permeabilized cardiomyocytes, confirming that DeltaPsi(m depolarization is mediated specifically by O2.-. The present work demonstrates that the observed emergent macroscopic properties of the mitochondrial network can be reproduced in a reaction-diffusion model of RIRR. Moreover, the findings have uncovered a novel aspect of the synchronization mechanism, which is that clusters of mitochondria that are oscillating can entrain mitochondria that would otherwise display stable dynamics. The work identifies the
Sheng, Yin; Zeng, Zhigang
2017-09-01
In this paper, synchronization of stochastic reaction-diffusion neural networks with Dirichlet boundary conditions and unbounded discrete time-varying delays is investigated. By virtue of theories of partial differential equations, inequality methods, and stochastic analysis techniques, pth moment exponential synchronization and almost sure exponential synchronization of the underlying neural networks are developed. The obtained results in this study enhance and generalize some earlier ones. The effectiveness and merits of the theoretical criteria are substantiated by two numerical simulations. Copyright © 2017 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Wang Linshan; Zhang Zhe; Wang Yangfan
2008-01-01
Some criteria for the global stochastic exponential stability of the delayed reaction-diffusion recurrent neural networks with Markovian jumping parameters are presented. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, which are governed by a Markov process with discrete and finite state space. By employing a new Lyapunov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish some easy-to-test criteria of global exponential stability in the mean square for the stochastic neural networks. The criteria are computationally efficient, since they are in the forms of some linear matrix inequalities
Directory of Open Access Journals (Sweden)
Luisa Malaguti
2011-01-01
Full Text Available The paper deals with a degenerate reaction-diffusion equation, including aggregative movements and convective terms. The model also incorporates a real parameter causing the change from a purely diffusive to a diffusive-aggregative and to a purely aggregative regime. Existence and qualitative properties of traveling wave solutions are investigated, and estimates of their threshold speeds are furnished. Further, the continuous dependence of the threshold wave speed and of the wave profiles on a real parameter is studied, both when the process maintains its diffusion-aggregation nature and when it switches from it to another regime.
On one model problem for the reaction-diffusion-advection equation
Davydova, M. A.; Zakharova, S. A.; Levashova, N. T.
2017-09-01
The asymptotic behavior of the solution with boundary layers in the time-independent mathematical model of reaction-diffusion-advection arising when describing the distribution of greenhouse gases in the surface atmospheric layer is studied. On the basis of the asymptotic method of differential inequalities, the existence of a boundary-layer solution and its asymptotic Lyapunov stability as a steady-state solution of the corresponding parabolic problem is proven. One of the results of this work is the determination of the local domain of the attraction of a boundary-layer solution.
Nefedov, Nikolay
2017-02-01
This is an extended variant of the paper presented at MURPHYS-HSFS 2016 conference in Barcelona. We discuss further development of the asymptotic method of differential inequalities to investigate existence and stability of sharp internal layers (fronts) for nonlinear singularly perturbed periodic parabolic problems and initial boundary value problems with blow-up of fronts for reaction-diffusion-advection equations. In particular, we consider periodic solutions with internal layer in the case of balanced reaction. For the initial boundary value problems we prove the existence of fronts and give their asymptotic approximation including the new case of blowing-up fronts. This case we illustrate by the generalised Burgers equation.
Energy Technology Data Exchange (ETDEWEB)
Wang, Chi-Jen [Iowa State Univ., Ames, IA (United States)
2013-01-01
In this thesis, we analyze both the spatiotemporal behavior of: (A) non-linear “reaction” models utilizing (discrete) reaction-diffusion equations; and (B) spatial transport problems on surfaces and in nanopores utilizing the relevant (continuum) diffusion or Fokker-Planck equations. Thus, there are some common themes in these studies, as they all involve partial differential equations or their discrete analogues which incorporate a description of diffusion-type processes. However, there are also some qualitative differences, as shall be discussed below.
Adaptive exponential synchronization of delayed neural networks with reaction-diffusion terms
International Nuclear Information System (INIS)
Sheng Li; Yang Huizhong; Lou Xuyang
2009-01-01
This paper presents an exponential synchronization scheme for a class of neural networks with time-varying and distributed delays and reaction-diffusion terms. An adaptive synchronization controller is derived to achieve the exponential synchronization of the drive-response structure of neural networks by using the Lyapunov stability theory. At the same time, the update laws of parameters are proposed to guarantee the synchronization of delayed neural networks with all parameters unknown. It is shown that the approaches developed here extend and improve the ideas presented in recent literatures.
Non-Fickian delay reaction-diffusion equations: theoretical and numerical study
Ferreira, J. A.; Branco, J. R.; Silva, P. da
2007-01-01
The Fisher’s equation is established combining the Fick’s law for the flux and the mass conservation law. Assuming that the reaction term depends on the solution at some past time, a delay parameter is introduced and the delay Fisher’s equation is obtained. Modifying the Fick’s law for the flux considering a temporal memory term, integro-differential equations of Volterra type were introduced in the literature. In these paper we study reaction-diffusion equations obtained co...
Hallock, Michael J; Stone, John E; Roberts, Elijah; Fry, Corey; Luthey-Schulten, Zaida
2014-05-01
Simulation of in vivo cellular processes with the reaction-diffusion master equation (RDME) is a computationally expensive task. Our previous software enabled simulation of inhomogeneous biochemical systems for small bacteria over long time scales using the MPD-RDME method on a single GPU. Simulations of larger eukaryotic systems exceed the on-board memory capacity of individual GPUs, and long time simulations of modest-sized cells such as yeast are impractical on a single GPU. We present a new multi-GPU parallel implementation of the MPD-RDME method based on a spatial decomposition approach that supports dynamic load balancing for workstations containing GPUs of varying performance and memory capacity. We take advantage of high-performance features of CUDA for peer-to-peer GPU memory transfers and evaluate the performance of our algorithms on state-of-the-art GPU devices. We present parallel e ciency and performance results for simulations using multiple GPUs as system size, particle counts, and number of reactions grow. We also demonstrate multi-GPU performance in simulations of the Min protein system in E. coli . Moreover, our multi-GPU decomposition and load balancing approach can be generalized to other lattice-based problems.
Directory of Open Access Journals (Sweden)
Octavio Batta
2016-10-01
Full Text Available We present a derivative-free algorithm for solving bound constrained systems of nonlinear monotone equations. The algorithm generates feasible iterates using in a systematic way the residual as search direction and a suitable step-length closely related to the Barzilai-Borwein choice. A convergence analysis is described. We also present one application in solving problems related with the study of reaction-diffusion processes that can be described by nonlinear partial differential equations of elliptic type. Numerical experiences are included to highlight the efficacy of proposed algorithm.
International Nuclear Information System (INIS)
Lu Junguo
2008-01-01
In this paper, the global exponential stability and periodicity for a class of reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions are addressed by constructing suitable Lyapunov functionals and utilizing some inequality techniques. We first prove global exponential converge to 0 of the difference between any two solutions of the original reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions, the existence and uniqueness of equilibrium is the direct results of this procedure. This approach is different from the usually used one where the existence, uniqueness of equilibrium and stability are proved in two separate steps. Furthermore, we prove periodicity of the reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions. Sufficient conditions ensuring the global exponential stability and the existence of periodic oscillatory solutions for the reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions are given. These conditions are easy to check and have important leading significance in the design and application of reaction-diffusion recurrent neural networks with delays. Finally, two numerical examples are given to show the effectiveness of the obtained results
Yuvan, Steven; Bier, Martin
2018-02-01
Two decades ago Bak et al. (1997) [3] proposed a reaction-diffusion model to describe market fluctuations. In the model buyers and sellers diffuse from opposite ends of a 1D interval that represents a price range. Trades occur when buyers and sellers meet. We show analytically and numerically that the model well reproduces the square-root relation between traded volumes and price changes that is observed in real-life markets. The result is remarkable as this relation has commonly been explained in terms of more elaborate trader strategies. We furthermore explain why the square-root relation is robust under model modifications and we show how real-life bond market data exhibit the square-root relation.
Critical regimes driven by recurrent mobility patterns of reaction-diffusion processes in networks
Gómez-Gardeñes, J.; Soriano-Paños, D.; Arenas, A.
2018-04-01
Reaction-diffusion processes1 have been widely used to study dynamical processes in epidemics2-4 and ecology5 in networked metapopulations. In the context of epidemics6, reaction processes are understood as contagions within each subpopulation (patch), while diffusion represents the mobility of individuals between patches. Recently, the characteristics of human mobility7, such as its recurrent nature, have been proven crucial to understand the phase transition to endemic epidemic states8,9. Here, by developing a framework able to cope with the elementary epidemic processes, the spatial distribution of populations and the commuting mobility patterns, we discover three different critical regimes of the epidemic incidence as a function of these parameters. Interestingly, we reveal a regime of the reaction-diffussion process in which, counter-intuitively, mobility is detrimental to the spread of disease. We analytically determine the precise conditions for the emergence of any of the three possible critical regimes in real and synthetic networks.
Zhou, Shengfan
2017-11-01
In this paper, we first improve the existing conditions for the existence of a random exponential attractor for a continuous cocycle on a separable Banach space. Then we consider the existence of a random exponential attractor for stochastic non-autonomous reaction-diffusion equation with multiplicative noise defined in R3, which implies the existence of a random attractor with finite fractal dimension. The essential difficulty here is the continuity of the spectrum of the linear part of the equation, which can be overcome by the "tail" estimation of solutions of equation and carefully decomposing the solution into a sum of three parts, of whose, one part is finite-dimensional and other two parts are "quickly decay" in mean sense.
Numerical methods for one-dimensional reaction-diffusion equations arising in combustion theory
Ramos, J. I.
1987-01-01
A review of numerical methods for one-dimensional reaction-diffusion equations arising in combustion theory is presented. The methods reviewed include explicit, implicit, quasi-linearization, time linearization, operator-splitting, random walk and finite-element techniques and methods of lines. Adaptive and nonadaptive procedures are also reviewed. These techniques are applied first to solve two model problems which have exact traveling wave solutions with which the numerical results can be compared. This comparison is performed in terms of both the wave profile and computed wave speed. It is shown that the computed wave speed is not a good indicator of the accuracy of a particular method. A fourth-order time-linearized, Hermitian compact operator technique is found to be the most accurate method for a variety of time and space sizes.
Grytskyy, Dmytro; Diesmann, Markus; Helias, Moritz
2016-06-01
Self-organized structures in networks with spike-timing dependent synaptic plasticity (STDP) are likely to play a central role for information processing in the brain. In the present study we derive a reaction-diffusion-like formalism for plastic feed-forward networks of nonlinear rate-based model neurons with a correlation sensitive learning rule inspired by and being qualitatively similar to STDP. After obtaining equations that describe the change of the spatial shape of the signal from layer to layer, we derive a criterion for the nonlinearity necessary to obtain stable dynamics for arbitrary input. We classify the possible scenarios of signal evolution and find that close to the transition to the unstable regime metastable solutions appear. The form of these dissipative solitons is determined analytically and the evolution and interaction of several such coexistent objects is investigated.
International Nuclear Information System (INIS)
Hepburn, I.; De Schutter, E.; Chen, W.
2016-01-01
Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either in a discrete time or discrete space framework, which has led to the development of parallel methods that can take advantage of the power of modern supercomputers in recent years. We systematically test suggested components of stochastic reaction-diffusion operator splitting in the literature and discuss their effects on accuracy. We introduce an operator splitting implementation for irregular meshes that enhances accuracy with minimal performance cost. We test a range of models in small-scale MPI simulations from simple diffusion models to realistic biological models and find that multi-dimensional geometry partitioning is an important consideration for optimum performance. We demonstrate performance gains of 1-3 orders of magnitude in the parallel implementation, with peak performance strongly dependent on model specification.
Monostable traveling waves for a time-periodic and delayed nonlocal reaction-diffusion equation
Li, Panxiao; Wu, Shi-Liang
2018-04-01
This paper is concerned with a time-periodic and delayed nonlocal reaction-diffusion population model with monostable nonlinearity. Under quasi-monotone or non-quasi-monotone assumptions, it is known that there exists a critical wave speed c_*>0 such that a periodic traveling wave exists if and only if the wave speed is above c_*. In this paper, we first prove the uniqueness of non-critical periodic traveling waves regardless of whether the model is quasi-monotone or not. Further, in the quasi-monotone case, we establish the exponential stability of non-critical periodic traveling fronts. Finally, we illustrate the main results by discussing two types of death and birth functions arising from population biology.
Ford Versypt, Ashlee N; Arendt, Paul D; Pack, Daniel W; Braatz, Richard D
2015-01-01
A mathematical reaction-diffusion model is defined to describe the gradual decomposition of polymer microspheres composed of poly(D,L-lactic-co-glycolic acid) (PLGA) that are used for pharmaceutical drug delivery over extended periods of time. The partial differential equation (PDE) model treats simultaneous first-order generation due to chemical reaction and diffusion of reaction products in spherical geometry to capture the microsphere-size-dependent effects of autocatalysis on PLGA erosion that occurs when the microspheres are exposed to aqueous media such as biological fluids. The model is solved analytically for the concentration of the autocatalytic carboxylic acid end groups of the polymer chains that comprise the microspheres as a function of radial position and time. The analytical solution for the reaction and transport of the autocatalytic chemical species is useful for predicting the conditions under which drug release from PLGA microspheres transitions from diffusion-controlled to erosion-controlled release, for understanding the dynamic coupling between the PLGA degradation and erosion mechanisms, and for designing drug release particles. The model is the first to provide an analytical prediction for the dynamics and spatial heterogeneities of PLGA degradation and erosion within a spherical particle. The analytical solution is applicable to other spherical systems with simultaneous diffusive transport and first-order generation by reaction.
International Nuclear Information System (INIS)
Wang Xiaohu; Xu Daoyi
2009-01-01
In this paper, the global exponential stability of impulsive fuzzy cellular neural networks with mixed delays and reaction-diffusion terms is considered. By establishing an integro-differential inequality with impulsive initial condition and using the properties of M-cone and eigenspace of the spectral radius of nonnegative matrices, several new sufficient conditions are obtained to ensure the global exponential stability of the equilibrium point for fuzzy cellular neural networks with delays and reaction-diffusion terms. These results extend and improve the earlier publications. Two examples are given to illustrate the efficiency of the obtained results.
Evidences for two scales in hadrons
International Nuclear Information System (INIS)
Kopeliovich, B. Z.; Potashnikova, I. K.; Schmidt, Ivan; Povh, B.
2007-01-01
Some unusual features observed in hadronic collisions at high energies can be understood assuming that gluons in hadrons are located within small spots occupying only about 10% of the hadrons' area. Such a conjecture about the presence of two scales in hadrons helps to explain the following: why diffractive gluon radiation is so suppressed; why the triple-Pomeron coupling shows no t dependence; why total hadronic cross sections rise so slowly with energy; why diffraction cones shrink so slowly, and why α P ' R ' ; why the transition from hard to soft regimes in the structure functions occurs at rather large Q 2 ; why the observed Cronin effect at collider energies is so weak; why hard reactions sensitive to primordial parton motion (direct photon, Drell-Yan dileptons, heavy flavors, back-to-back dihadrons, seagull effect, etc.) demand such a large transverse momenta of the projectile partons, which is not explained by next-to-leading order calculations; why the onset of nuclear shadowing for gluons is so delayed compared to quarks; and why shadowing is so weak
Czech Academy of Sciences Publication Activity Database
Klika, Václav; Baker, R. E.; Headon, D.; Gaffney, E. A.
2012-01-01
Roč. 74, č. 4 (2012), s. 935-957 ISSN 0092-8240 Institutional research plan: CEZ:AV0Z20760514 Keywords : reaction-diffusion * receptor-mediated patterning * turing models Subject RIV: BO - Biophysics Impact factor: 2.023, year: 2012 http://www.springerlink.com/content/9713544x6871w4n6/?MUD=MP
International Nuclear Information System (INIS)
Adamatzky, Andrew; Lacy Costello, Benjamin de
2003-01-01
A reaction-diffusion chemical computer in this context is a planar uniform chemical reactor, where data and results of a computation are represented by concentration profiles of reactants and the computation itself is implemented via the spreading and interaction of diffusive and phase waves. This class of chemical computers are efficient at solving problems with a 'natural' parallelism where data sets are decomposable onto a large number of geographically neighboring domains which are then processed in parallel. Typical problems of this type include image processing, geometrical transformations and optimisation. When chemical based devices are used to solve such problems questions regarding their reproducible, efficiency and the accuracy of their computations arise. In addition to these questions what are the limitations of reaction-diffusion chemical processors--what type of problems cannot currently and are unlikely ever to be solved? To answer the questions we study how a Voronoi diagram is constructed and how it is inverted in a planar chemical processor. We demonstrate that a Voronoi diagram is computed only partially in the chemical processor. We also prove that given a specific Voronoi diagram it is impossible to reconstruct the planar set (from which diagram was computed) in the reaction-diffusion chemical processor. In the Letter we open the first ever line of enquiry into the computational inability of reaction-diffusion chemical computers
Saxena, R. K.; Mathai, A. M.; Haubold, H. J.
2015-10-01
This paper deals with the investigation of the computational solutions of an unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the generalized fractional time-derivative defined by Hilfer (2000), the space derivative of second order by the Riesz-Feller fractional derivative and adding the function ϕ (x, t) which is a nonlinear function governing reaction. The solution is derived by the application of the Laplace and Fourier transforms in a compact and closed form in terms of the H-function. The main result obtained in this paper provides an elegant extension of the fundamental solution for the space-time fractional diffusion equation obtained earlier by Mainardi et al. (2001, 2005) and a result very recently given by Tomovski et al. (2011). Computational representation of the fundamental solution is also obtained explicitly. Fractional order moments of the distribution are deduced. At the end, mild extensions of the derived results associated with a finite number of Riesz-Feller space fractional derivatives are also discussed.
Cooper, Crystal Diane
A computer program was modified to model the dynamics of morphogen concentrations in a developing eye of a Xenopus laevis frog. The dynamics were modelled because it is believed that the behavior of the morphogen concentrations determine how the developing eye maps to the brain. The eye in the xenophus grows as a series of rings, and thus this is the model used. The basis for the simulation are experiments done by Sullivan et al. Following the experiment, aIl eye ring is 'split' in half, inverted, and then 'pasted' onto a donor half. The purpose of the program is to replicate and analyze the results that were found experimentally: a graft made on a north to south axis (dorsal to ventral) produces a change in vision along the east to west axis (anterior to posterior). Four modified Gierer-Meinhardt reaction- diffusion equations are used to simulate the operation. In the second part of the research, the program was further modified and a time series analysis was done on the results. It was found that the modified Gierer- Meinhardt equations demonstrated chaotic behavior under certain conditions. The dynamics included fixed points, limit cycles, transient chaos, intermittent chaos, and strange attractors. The creation and destruction of fractal torii was found.
Image-Based Measurement of H2O2 Reaction-Diffusion in Wounded Zebrafish Larvae.
Jelcic, Mark; Enyedi, Balázs; Xavier, João B; Niethammer, Philipp
2017-05-09
Epithelial injury induces rapid recruitment of antimicrobial leukocytes to the wound site. In zebrafish larvae, activation of the epithelial NADPH oxidase Duox at the wound margin is required early during this response. Before injury, leukocytes are near the vascular region, that is, ∼100-300 μm away from the injury site. How Duox establishes long-range signaling to leukocytes is unclear. We conceived that extracellular hydrogen peroxide (H 2 O 2 ) generated by Duox diffuses through the tissue to directly regulate chemotactic signaling in these cells. But before it can oxidize cellular proteins, H 2 O 2 must get past the antioxidant barriers that protect the cellular proteome. To test whether, or on which length scales this occurs during physiological wound signaling, we developed a computational method based on reaction-diffusion principles that infers H 2 O 2 degradation rates from intravital H 2 O 2 -biosensor imaging data. Our results indicate that at high tissue H 2 O 2 levels the peroxiredoxin-thioredoxin antioxidant chain becomes overwhelmed, and H 2 O 2 degradation stalls or ceases. Although the wound H 2 O 2 gradient reaches deep into the tissue, it likely overcomes antioxidant barriers only within ∼30 μm of the wound margin. Thus, Duox-mediated long-range signaling may require other spatial relay mechanisms besides extracellular H 2 O 2 diffusion. Copyright © 2017 Biophysical Society. Published by Elsevier Inc. All rights reserved.
A nonlocal and periodic reaction-diffusion-advection model of a single phytoplankton species.
Peng, Rui; Zhao, Xiao-Qiang
2016-02-01
In this article, we are concerned with a nonlocal reaction-diffusion-advection model which describes the evolution of a single phytoplankton species in a eutrophic vertical water column where the species relies solely on light for its metabolism. The new feature of our modeling equation lies in that the incident light intensity and the death rate are assumed to be time periodic with a common period. We first establish a threshold type result on the global dynamics of this model in terms of the basic reproduction number R0. Then we derive various characterizations of R0 with respect to the vertical turbulent diffusion rate, the sinking or buoyant rate and the water column depth, respectively, which in turn give rather precise conditions to determine whether the phytoplankton persist or become extinct. Our theoretical results not only extend the existing ones for the time-independent case, but also reveal new interesting effects of the modeling parameters and the time-periodic heterogeneous environment on persistence and extinction of the phytoplankton species, and thereby suggest important implications for phytoplankton growth control.
Chirality Controls Reaction-Diffusion of Nanoparticles for Inhibiting Cancer Cells.
Du, Xuewen; Zhou, Jie; Wang, Jiaqing; Zhou, Rong; Xu, Bing
2017-01-01
Reaction-diffusion (RD) is the most important inherent feature of living organism, but it has yet to be used for developing biofunctional nanoparticles (NPs). Here we show the use of chirality to control the RD of NPs for selectively inhibiting cancer cells. We observe that L-phosphotyrosine (L-pY) decorated NPs (NP@L-pYs) are innocuous to cells, but D-pY decorated ones (NP@D-pYs) selectively inhibit cancer cells. Our study shows that alkaline phosphatases (ALP), presented in the culture and overexpressed on the cancer cells, dephosphorylates NP@L-pYs much faster than NP@D-pYs. Such a rate difference allows the NP@D-pYs to be mainly dephosphorylated on cell surface, thus adhering selectively on the cancer cells to result in poly(ADP-ribose)polymerase (PARP) hyperactivation mediated cell death. Without phosphate groups or being prematurely dephosphorylated before reaching cancer cells (as the case of NP@L-pYs), the NPs are innocuous to cells. Moreover, NP@D-pYs even exhibit more potent activity than cisplatin for inhibiting platinum-resistant ovarian cancer cells (e.g., A2780-cis). As the first example of chirality controlling RD process of NPs for inhibiting cancer cells, this work illustrates a fundamentally new way for developing nanomedicine based on RD processes and nanoparticles.
Harko, Tiberiu; Mak, Man Kwong
2015-02-01
We consider quasi-stationary (travelling wave type) solutions to a nonlinear reaction-diffusion equation with arbitrary, autonomous coefficients, describing the evolution of glioblastomas, aggressive primary brain tumors that are characterized by extensive infiltration into the brain and are highly resistant to treatment. The second order nonlinear equation describing the glioblastoma growth through travelling waves can be reduced to a first order Abel type equation. By using the integrability conditions for the Abel equation several classes of exact travelling wave solutions of the general reaction-diffusion equation that describes glioblastoma growth are obtained, corresponding to different forms of the product of the diffusion and reaction functions. The solutions are obtained by using the Chiellini lemma and the Lemke transformation, respectively, and the corresponding equations represent generalizations of the classical Fisher-Kolmogorov equation. The biological implications of two classes of solutions are also investigated by using both numerical and semi-analytical methods for realistic values of the biological parameters.
Nefedov, N. N.; Nikulin, E. I.
2018-01-01
A singularly perturbed periodic in time problem for a parabolic reaction-diffusion equation in a two-dimensional domain is studied. The case of existence of an internal transition layer under the conditions of balanced and unbalanced rapid reaction is considered. An asymptotic expansion of a solution is constructed. To justify the asymptotic expansion thus constructed, the asymptotic method of differential inequalities is used. The Lyapunov asymptotic stability of a periodic solution is investigated.
Dinesh Kumar, S.; Nageshwar Rao, R.; Pramod Chakravarthy, P.
2017-11-01
In this paper, we consider a boundary value problem for a singularly perturbed delay differential equation of reaction-diffusion type. We construct an exponentially fitted numerical method using Numerov finite difference scheme, which resolves not only the boundary layers but also the interior layers arising from the delay term. An extensive amount of computational work has been carried out to demonstrate the applicability of the proposed method.
Li, Zhe; Xu, Rui
2012-04-01
In this paper, a class of stochastic reaction-diffusion neural networks with time delays in the leakage terms is investigated. By using the Lyapunov functional method and linear matrix inequality (LMI) approach, sufficient conditions are derived to ensure the global asymptotic stability of an equilibrium point of the networks in the mean square. The results can be easily solved by MATLAB LMI toolbox. Finally, a numerical example is given to demonstrate the effectiveness and conservativeness of our theoretical results.
Directory of Open Access Journals (Sweden)
Matthew J Simpson
Full Text Available Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0
Simpson, Matthew J
2015-01-01
Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0solutions with numerical approximations confirms the veracity of the method. Furthermore, our examples illustrate a delicate interplay between: (i) the rate at which the domain elongates, (ii) the diffusivity associated with the spreading density profile, (iii) the reaction rate, and (iv) the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t).
Reaction-diffusion systems in natural sciences and new technology transfer
Keller, André A.
2012-12-01
Diffusion mechanisms in natural sciences and innovation management involve partial differential equations (PDEs). This is due to their spatio-temporal dimensions. Functional semi-discretized PDEs (with lattice spatial structures or time delays) may be even more adapted to real world problems. In the modeling process, PDEs can also formalize behaviors, such as the logistic growth of populations with migration, and the adopters’ dynamics of new products in innovation models. In biology, these events are related to variations in the environment, population densities and overcrowding, migration and spreading of humans, animals, plants and other cells and organisms. In chemical reactions, molecules of different species interact locally and diffuse. In the management of new technologies, the diffusion processes of innovations in the marketplace (e.g., the mobile phone) are a major subject. These innovation diffusion models refer mainly to epidemic models. This contribution introduces that modeling process by using PDEs and reviews the essential features of the dynamics and control in biological, chemical and new technology transfer. This paper is essentially user-oriented with basic nonlinear evolution equations, delay PDEs, several analytical and numerical methods for solving, different solutions, and with the use of mathematical packages, notebooks and codes. The computations are carried out by using the software Wolfram Mathematica®7, and C++ codes.
Signal Transmission of Biological Reaction-Diffusion System by Using Synchronization
Directory of Open Access Journals (Sweden)
Lingli Zhou
2017-10-01
Full Text Available Molecular signal transmission in cell is very crucial for information exchange. How to understand its transmission mechanism has attracted many researchers. In this paper, we prove that signal transmission problem between neural tumor molecules and drug molecules can be achieved by synchronous control. To achieve our purpose, we derive the Fokker-Plank equation by using the Langevin equation and theory of random walk, this is a model which can express the concentration change of neural tumor molecules. Second, according to the biological character that vesicles in cell can be combined with cell membrane to release the cargo which plays a role of signal transmission, we preliminarily analyzed the mechanism of tumor-drug molecular interaction. Third, we propose the view of synchronous control which means the process of vesicle docking with their target membrane is a synchronization process, and we can achieve the precise treatment of disease by using synchronous control. We believe this synchronous control mechanism is reasonable and two examples are given to illustrate the correctness of our results obtained in this paper.
A free boundary problem for a reaction-diffusion system with nonlinear memory
DEFF Research Database (Denmark)
Lin, Zhigui; Ling, Zhi; Pedersen, Michael
2013-01-01
We consider a integro-partial differential equation with a free boundary which appears in the theory of the nuclear dynamics. First, local existence and uniqueness are obtained by using the contraction mapping theorem. Then, the behavior of the free boundary and the blow-up criteria are obtained...
Bifurcation for a reaction-diffusion system with unilateral and Neumann boundary conditions
Czech Academy of Sciences Publication Activity Database
Kučera, Milan; Väth, Martin
2012-01-01
Roč. 252, č. 4 (2012), s. 2951-2982 ISSN 0022-0396 R&D Projects: GA AV ČR IAA100190805 Institutional research plan: CEZ:AV0Z10190503 Keywords : global bifurcation * degree * stationary solutions Subject RIV: BA - General Mathematics Impact factor: 1.480, year: 2012 http://www.sciencedirect.com/science/article/pii/S0022039611004530
Czech Academy of Sciences Publication Activity Database
Väth, Martin
2011-01-01
Roč. 12, č. 2 (2011), s. 817-836 ISSN 1468-1218 R&D Projects: GA AV ČR IAA100190805 Institutional research plan: CEZ:AV0Z10190503 Keywords : global bifurcation * degree * stationary solutions Subject RIV: BA - General Mathematics Impact factor: 2.043, year: 2011 http://www.sciencedirect.com/science/article/pii/S1468121810001951
On the Existence of a Free Boundary for a Class of Reaction-Diffusion Systems.
1982-02-01
I. Diaz. " Soluciones con soporte compacto para alguno. problemas semilineales". Collect. Math. 30 (1979), 141-179. -26- [121 J. I. Diaz. Tecnica de...supersoluciones locales para problemas estacionarios no lineales: applicacion al estudio de flujoe subsonicos. Memory of the Real Academia de Ciencias
Optimal control of an invasive species using a reaction-diffusion model and linear programming
Bonneau, Mathieu; Johnson, Fred A.; Smith, Brian J.; Romagosa, Christina M.; Martin, Julien; Mazzotti, Frank J.
2017-01-01
Managing an invasive species is particularly challenging as little is generally known about the species’ biological characteristics in its new habitat. In practice, removal of individuals often starts before the species is studied to provide the information that will later improve control. Therefore, the locations and the amount of control have to be determined in the face of great uncertainty about the species characteristics and with a limited amount of resources. We propose framing spatial control as a linear programming optimization problem. This formulation, paired with a discrete reaction-diffusion model, permits calculation of an optimal control strategy that minimizes the remaining number of invaders for a fixed cost or that minimizes the control cost for containment or protecting specific areas from invasion. We propose computing the optimal strategy for a range of possible model parameters, representing current uncertainty on the possible invasion scenarios. Then, a best strategy can be identified depending on the risk attitude of the decision-maker. We use this framework to study the spatial control of the Argentine black and white tegus (Salvator merianae) in South Florida. There is uncertainty about tegu demography and we considered several combinations of model parameters, exhibiting various dynamics of invasion. For a fixed one-year budget, we show that the risk-averse strategy, which optimizes the worst-case scenario of tegus’ dynamics, and the risk-neutral strategy, which optimizes the expected scenario, both concentrated control close to the point of introduction. A risk-seeking strategy, which optimizes the best-case scenario, focuses more on models where eradication of the species in a cell is possible and consists of spreading control as much as possible. For the establishment of a containment area, assuming an exponential growth we show that with current control methods it might not be possible to implement such a strategy for some of the
Seirin Lee, S.
2010-03-23
Turing\\'s pattern formation mechanism exhibits sensitivity to the details of the initial conditions suggesting that, in isolation, it cannot robustly generate pattern within noisy biological environments. Nonetheless, secondary aspects of developmental self-organisation, such as a growing domain, have been shown to ameliorate this aberrant model behaviour. Furthermore, while in-situ hybridisation reveals the presence of gene expression in developmental processes, the influence of such dynamics on Turing\\'s model has received limited attention. Here, we novelly focus on the Gierer-Meinhardt reaction diffusion system considering delays due the time taken for gene expression, while incorporating a number of different domain growth profiles to further explore the influence and interplay of domain growth and gene expression on Turing\\'s mechanism. We find extensive pathological model behaviour, exhibiting one or more of the following: temporal oscillations with no spatial structure, a failure of the Turing instability and an extreme sensitivity to the initial conditions, the growth profile and the duration of gene expression. This deviant behaviour is even more severe than observed in previous studies of Schnakenberg kinetics on exponentially growing domains in the presence of gene expression (Gaffney and Monk in Bull. Math. Biol. 68:99-130, 2006). Our results emphasise that gene expression dynamics induce unrealistic behaviour in Turing\\'s model for multiple choices of kinetics and thus such aberrant modelling predictions are likely to be generic. They also highlight that domain growth can no longer ameliorate the excessive sensitivity of Turing\\'s mechanism in the presence of gene expression time delays. The above, extensive, pathologies suggest that, in the presence of gene expression, Turing\\'s mechanism would generally require a novel and extensive secondary mechanism to control reaction diffusion patterning. © 2010 Society for Mathematical Biology.
Directory of Open Access Journals (Sweden)
Herman N C Berghuijs
Full Text Available The rate of photosynthesis depends on the CO2 partial pressure near Rubisco, Cc, which is commonly calculated by models using the overall mesophyll resistance. Such models do not explain the difference between the CO2 level in the intercellular air space and Cc mechanistically. This problem can be overcome by reaction-diffusion models for CO2 transport, production and fixation in leaves. However, most reaction-diffusion models are complex and unattractive for procedures that require a large number of runs, like parameter optimisation. This study provides a simpler reaction-diffusion model. It is parameterized by both leaf physiological and leaf anatomical data. The anatomical data consisted of the thickness of the cell wall, cytosol and stroma, and the area ratios of mesophyll exposed to the intercellular air space to leaf surfaces and exposed chloroplast to exposed mesophyll surfaces. The model was used directly to estimate photosynthetic parameters from a subset of the measured light and CO2 response curves; the remaining data were used for validation. The model predicted light and CO2 response curves reasonably well for 15 days old tomato (cv. Admiro leaves, if (photorespiratory CO2 release was assumed to take place in the inner cytosol or in the gaps between the chloroplasts. The model was also used to calculate the fraction of CO2 produced by (photorespiration that is re-assimilated in the stroma, and this fraction ranged from 56 to 76%. In future research, the model should be further validated to better understand how the re-assimilation of (photorespired CO2 is affected by environmental conditions and physiological parameters.
Flow through a Two-Scale Porosity Material
Directory of Open Access Journals (Sweden)
A. G. Andersson
2009-01-01
Full Text Available Flow through a two-scale porous medium is here investigated by a unique comparison between simulations performed with computational fluid dynamics and the boundary element method with microparticle image velocimetry in model geometries.
ReaDDy--a software for particle-based reaction-diffusion dynamics in crowded cellular environments.
Directory of Open Access Journals (Sweden)
Johannes Schöneberg
Full Text Available We introduce the software package ReaDDy for simulation of detailed spatiotemporal mechanisms of dynamical processes in the cell, based on reaction-diffusion dynamics with particle resolution. In contrast to other particle-based reaction kinetics programs, ReaDDy supports particle interaction potentials. This permits effects such as space exclusion, molecular crowding and aggregation to be modeled. The biomolecules simulated can be represented as a sphere, or as a more complex geometry such as a domain structure or polymer chain. ReaDDy bridges the gap between small-scale but highly detailed molecular dynamics or Brownian dynamics simulations and large-scale but little-detailed reaction kinetics simulations. ReaDDy has a modular design that enables the exchange of the computing core by efficient platform-specific implementations or dynamical models that are different from Brownian dynamics.
Shankar, Varun; Wright, Grady B; Kirby, Robert M; Fogelson, Aaron L
2016-06-01
In this paper, we present a method based on Radial Basis Function (RBF)-generated Finite Differences (FD) for numerically solving diffusion and reaction-diffusion equations (PDEs) on closed surfaces embedded in ℝ d . Our method uses a method-of-lines formulation, in which surface derivatives that appear in the PDEs are approximated locally using RBF interpolation. The method requires only scattered nodes representing the surface and normal vectors at those scattered nodes. All computations use only extrinsic coordinates, thereby avoiding coordinate distortions and singularities. We also present an optimization procedure that allows for the stabilization of the discrete differential operators generated by our RBF-FD method by selecting shape parameters for each stencil that correspond to a global target condition number. We show the convergence of our method on two surfaces for different stencil sizes, and present applications to nonlinear PDEs simulated both on implicit/parametric surfaces and more general surfaces represented by point clouds.
Adam, A. M. A.; Bashier, E. B. M.; Hashim, M. H. A.; Patidar, K. C.
2017-07-01
In this work, we design and analyze a fitted numerical method to solve a reaction-diffusion model with time delay, namely, a delayed version of a population model which is an extension of the logistic growth (LG) equation for a food-limited population proposed by Smith [F.E. Smith, Population dynamics in Daphnia magna and a new model for population growth, Ecology 44 (1963) 651-663]. Seeing that the analytical solution (in closed form) is hard to obtain, we seek for a robust numerical method. The method consists of a Fourier-pseudospectral semi-discretization in space and a fitted operator implicit-explicit scheme in temporal direction. The proposed method is analyzed for convergence and we found that it is unconditionally stable. Illustrative numerical results will be presented at the conference.
ReaDDy - A Software for Particle-Based Reaction-Diffusion Dynamics in Crowded Cellular Environments
Schöneberg, Johannes; Noé, Frank
2013-01-01
We introduce the software package ReaDDy for simulation of detailed spatiotemporal mechanisms of dynamical processes in the cell, based on reaction-diffusion dynamics with particle resolution. In contrast to other particle-based reaction kinetics programs, ReaDDy supports particle interaction potentials. This permits effects such as space exclusion, molecular crowding and aggregation to be modeled. The biomolecules simulated can be represented as a sphere, or as a more complex geometry such as a domain structure or polymer chain. ReaDDy bridges the gap between small-scale but highly detailed molecular dynamics or Brownian dynamics simulations and large-scale but little-detailed reaction kinetics simulations. ReaDDy has a modular design that enables the exchange of the computing core by efficient platform-specific implementations or dynamical models that are different from Brownian dynamics. PMID:24040218
Two-scale modelling for hydro-mechanical damage
International Nuclear Information System (INIS)
Frey, J.; Chambon, R.; Dascalu, C.
2010-01-01
solid conservation is achieved following the skeleton during the movement and finally the balance equation of the fluid is achieved at the microstructure scale. The non-linear problem is solved using a Newton- Raphson iteration process, in order to compute the resulting linearized system, all the needed quantities, namely the stress of the mixture, the density, the fluid mass flow, the fluid mass variation and linearization of those, are resulting from the microstructure analysis. At the microscopic scale, fluid and solid phase are described explicitly. Granular geometry is used for the R.E.V. Grains are modelled using large strain (hyper) elastic law, separated by micro-cracks filled by fluid. The fracture process of these cracks, at the interfaces between each grain, is modelled by a cohesive law. To perform the analysis on the microstructure, boundaries conditions, resulting from the macroscopic level, are applied on the R.E.V.: - Linear or periodic displacement are computed using a macroscopic gradient of deformation. - Linear or periodic boundary pressures are computed using both a macroscopic gradient of pressure and an average pressure. This two-scale method gives us a numerical law to describe complex hydro-mechanic damage process at the microstructure scale. Complex morphologies, like quartz inclusion in the argillite matrix, are considered. The reciprocal influence damage-permeability is studied numerically. (authors)
International Nuclear Information System (INIS)
Ahmadi, A.; Meyer, M.; Rouzineau, D.; Prevost, M.; Alix, P.; Laloue, N.
2010-01-01
This paper gives the first step of the development of a rigorous multicomponent reactive separation model. Such a model is highly essential to further the optimization of acid gases removal plants (CO 2 capture, gas treating, etc.) in terms of size and energy consumption, since chemical solvents are conventionally used. Firstly, two main modelling approaches are presented: the equilibrium-based and the rate-based approaches. Secondly, an extended rate-based model with rigorous modelling methodology for diffusion-reaction phenomena is proposed. The film theory and the generalized Maxwell-Stefan equations are used in order to characterize multicomponent interactions. The complete chain of chemical reactions is taken into account. The reactions can be kinetically controlled or at chemical equilibrium, and they are considered for both liquid film and liquid bulk. Thirdly, the method of numerical resolution is described. Coupling the generalized Maxwell-Stefan equations with chemical equilibrium equations leads to a highly non-linear Differential-Algebraic Equations system known as DAE index 3. The set of equations is discretized with finite-differences as its integration by Gear method is complex. The resulting algebraic system is resolved by the Newton- Raphson method. Finally, the present model and the associated methods of numerical resolution are validated for the example of esterification of methanol. This archetype non-electrolytic system permits an interesting analysis of reaction impact on mass transfer, especially near the phase interface. The numerical resolution of the model by Newton-Raphson method gives good results in terms of calculation time and convergence. The simulations show that the impact of reactions at chemical equilibrium and that of kinetically controlled reactions with high kinetics on mass transfer is relatively similar. Moreover, the Fick's law is less adapted for multicomponent mixtures where some abnormalities such as counter
Two-scale approach to oscillatory singularly perturbed transport equations
Frénod, Emmanuel
2017-01-01
This book presents the classical results of the two-scale convergence theory and explains – using several figures – why it works. It then shows how to use this theory to homogenize ordinary differential equations with oscillating coefficients as well as oscillatory singularly perturbed ordinary differential equations. In addition, it explores the homogenization of hyperbolic partial differential equations with oscillating coefficients and linear oscillatory singularly perturbed hyperbolic partial differential equations. Further, it introduces readers to the two-scale numerical methods that can be built from the previous approaches to solve oscillatory singularly perturbed transport equations (ODE and hyperbolic PDE) and demonstrates how they can be used efficiently. This book appeals to master’s and PhD students interested in homogenization and numerics, as well as to the Iter community.
Reaction-diffusion on the fully-connected lattice: A+A\\rightarrow A
Turban, Loïc; Fortin, Jean-Yves
2018-04-01
Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong fluctuations in low dimensions. In this work we study this problem on the fully-connected lattice, an infinite-dimensional system in the thermodynamic limit, for which mean-field behaviour is expected. Exact expressions for the particle density distribution at a given time and survival time distribution for a given number of particles are obtained. In particular, we show that the time needed to reach a finite number of surviving particles (vanishing density in the scaling limit) displays strong fluctuations and extreme value statistics, characterized by a universal class of non-Gaussian distributions with singular behaviour.
Pontes, J.; Walgraef, D.; Christov, C. I.
2010-11-01
Strain localization and dislocation pattern formation are typical features of plastic deformation in metals and alloys. Glide and climb dislocation motion along with accompanying production/annihilation processes of dislocations lead to the occurrence of instabilities of initially uniform dislocation distributions. These instabilities result into the development of various types of dislocation micro-structures, such as dislocation cells, slip and kink bands, persistent slip bands, labyrinth structures, etc., depending on the externally applied loading and the intrinsic lattice constraints. The Walgraef-Aifantis (WA) (Walgraef and Aifanits, J. Appl. Phys., 58, 668, 1985) model is an example of a reaction-diffusion model of coupled nonlinear equations which describe 0 formation of forest (immobile) and gliding (mobile) dislocation densities in the presence of cyclic loading. This paper discuss two versions of the WA model and focus on a finite difference, second order in time 1-Nicolson semi-implicit scheme, with internal iterations at each time step and a spatial splitting using the Stabilizing, Correction (Christov and Pontes, Mathematical and Computer Modelling, 35, 87, 2002) for solving the model evolution equations in two dimensions. The results of two simulations are presented. More complete results will appear in a forthcoming paper.
Tewary, Mukul; Ostblom, Joel; Prochazka, Laura; Zulueta-Coarasa, Teresa; Shakiba, Nika; Fernandez-Gonzalez, Rodrigo; Zandstra, Peter W
2017-12-01
How position-dependent cell fate acquisition occurs during embryogenesis is a central question in developmental biology. To study this process, we developed a defined, high-throughput assay to induce peri-gastrulation-associated patterning in geometrically confined human pluripotent stem cell (hPSC) colonies. We observed that, upon BMP4 treatment, phosphorylated SMAD1 (pSMAD1) activity in the colonies organized into a radial gradient. We developed a reaction-diffusion (RD)-based computational model and observed that the self-organization of pSMAD1 signaling was consistent with the RD principle. Consequent fate acquisition occurred as a function of both pSMAD1 signaling strength and duration of induction, consistent with the positional-information (PI) paradigm. We propose that the self-organized peri-gastrulation-like fate patterning in BMP4-treated geometrically confined hPSC colonies arises via a stepwise model of RD followed by PI. This two-step model predicted experimental responses to perturbations of key parameters such as colony size and BMP4 dose. Furthermore, it also predicted experimental conditions that resulted in RD-like periodic patterning in large hPSC colonies, and rescued peri-gastrulation-like patterning in colony sizes previously thought to be reticent to this behavior. © 2017. Published by The Company of Biologists Ltd.
Tcaciuc, A Patricia; Borrelli, Raffaella; Zaninetta, Luciano M; Gschwend, Philip M
2018-01-24
Passive sampling is becoming a widely used tool for assessing freely dissolved concentrations of hydrophobic organic contaminants in environmental media. For certain media and target analytes, the time to reach equilibrium exceeds the deployment time, and in such cases, the loss of performance reference compounds (PRCs), loaded in the sampler before deployment, is one of the common ways used to assess the fractional equilibration of target analytes. The key assumption behind the use of PRCs is that their release is solely diffusion driven. But in this work, we show that PRC transformations in the sediment can have a measurable impact on the PRC releases and even allow estimation of that compound's transformation rate in the environment of interest. We found that in both field and lab incubations, the loss of the 13 C 2,4'-DDT PRC from a polyethylene (PE) passive sampler deployed at the sediment-water interface was accelerated compared to the loss of other PRCs ( 13 C-labeled PCBs, 13 C-labeled DDE and DDD). The DDT PRC loss was also accompanied by accumulation in the PE of its degradation product, 13 C 2,4'-DDD. Using a 1D reaction-diffusion model, we deduced the in situ degradation rates of DDT from the measured PRC loss. The in situ degradation rates increased with depth into the sediment bed (0.14 d -1 at 0-10 cm and 1.4 d -1 at 30-40 cm) and although they could not be independently validated, these rates compared favorably with literature values. This work shows that passive sampling users should be cautious when choosing PRCs, as degradation processes can affect some PRC's releases from the passive sampler. More importantly, this work opens up the opportunity for novel applications of passive samplers, particularly with regard to investigating in situ degradation rates, pathways, and products for both legacy and emerging contaminants. However, further work is needed to confirm that the rates deduced from model fitting of PRC loss are a true reflection of DDT
Czech Academy of Sciences Publication Activity Database
Kučera, Milan; Navrátil, J.
2018-01-01
Roč. 166, January (2018), s. 154-180 ISSN 0362-546X Institutional support: RVO:67985840 Keywords : global bifurcation * maximal eigenvalue * positively homogeneous operators Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.192, year: 2016 http://www.sciencedirect.com/science/ article /pii/S0362546X17302559?via%3Dihub
Czech Academy of Sciences Publication Activity Database
Kučera, Milan; Navrátil, J.
2018-01-01
Roč. 166, January (2018), s. 154-180 ISSN 0362-546X Institutional support: RVO:67985840 Keywords : global bifurcation * maximal eigenvalue * positively homogeneous operators Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.192, year: 2016 http://www. science direct.com/ science /article/pii/S0362546X17302559?via%3Dihub
MacDonald, G; Mackenzie, J A; Nolan, M; Insall, R H
2016-03-15
In this paper, we devise a moving mesh finite element method for the approximate solution of coupled bulk-surface reaction-diffusion equations on an evolving two dimensional domain. Fundamental to the success of the method is the robust generation of bulk and surface meshes. For this purpose, we use a novel moving mesh partial differential equation (MMPDE) approach. The developed method is applied to model problems with known analytical solutions; these experiments indicate second-order spatial and temporal accuracy. Coupled bulk-surface problems occur frequently in many areas; in particular, in the modelling of eukaryotic cell migration and chemotaxis. We apply the method to a model of the two-way interaction of a migrating cell in a chemotactic field, where the bulk region corresponds to the extracellular region and the surface to the cell membrane.
An Efficient Two-Scale Hybrid Embedded Fracture Model for Shale Gas Simulation
Amir, Sahar Z.
2016-12-27
Natural and hydraulic fractures existence and state differs on a reservoir-by-reservoir or even on a well-by-well basis leading to the necessity of exploring the flow regimes variations with respect to the diverse fracture-network shapes forged. Conventional Dual-Porosity Dual-Permeability (DPDP) schemes are not adequate to model such complex fracture-network systems. To overcome this difficulty, in this paper, an iterative Hybrid Embedded multiscale (two-scale) Fracture model (HEF) is applied on a derived fit-for-purpose shale gas model. The HEF model involves splitting the fracture computations into two scales: 1) fine-scale solves for the flux exchange parameter within each grid cell; 2) coarse-scale solves for the pressure applied to the domain grid cells using the flux exchange parameter computed at each grid cell from the fine-scale. After that, the D dimensions matrix pressure and the (D-1) lower dimensional fracture pressure are solved as a system to apply the matrix-fracture coupling. HEF model combines the DPDP overlapping continua concept, the DFN lower dimensional fractures concept, the HFN hierarchical fracture concept, and the CCFD model simplicity. As for the fit-for-purpose shale gas model, various fit-for-purpose shale gas models can be derived using any set of selected properties plugged in one of the most popularly used proposed literature models as shown in the appendix. Also, this paper shows that shale extreme low permeability cause flow behavior to be dominated by the structure and magnitude of high permeability fractures.
Reaction-diffusion based co-synthesis of stable α- and β-cobalt hydroxide in bio-organic gels
Al-Ghoul, Mazen; El-Rassy, Houssam; Coradin, Thibaud; Mokalled, Tharwat
2010-03-01
We report the preparation, dynamics of formation and extensive characterization of a stable two-phase system of crystalline α- and β-Co(OH) 2. The method is based on the reaction and diffusion of hydroxide ions into a biopolymer gel (agar, gelatin) containing Co(II). The spatio-temporal dynamics leading to the formation and coexistence of two polymorphs exhibit a complicated and rich pattern whereby the system proceeds as a propagating Ostwald ripening front that continuously transforms blue/green α-Co(OH) 2 to crystalline β-Co(OH) 2. Depending on the nature of the gel, the system might further exhibit fascinating Liesegang bands. The coexisting polymorphs were characterized using XRD, FTIR, UV-vis, TGA, SEM and TEM, and EPR. The FTIR spectra reveal the intercalation of water molecules and chloride ions between the hydroxyl layers in the case of α-Co(OH) 2. X-ray diffraction and electronic microscopy investigations confirm the aforementioned Ostwald ripening process during the phase transformation whereby almost-amorphous α-Co(OH) 2 dissolves to form crystalline β-Co(OH) 2 5 μm in length. The UV-vis reflectance spectra reveal that the origin of the blue/green color in the α-polymorph is due to the tetrahedrally coordinated Co(II) ions existing within the octahedral Co(II) layers. The reorganization of these tetrahedral Co(II) ions in the α-polymorph to form octahedral Co(II) in the β-polymorph is shown to take place in seconds without induction time. α-Co(OH) 2 was found to be mesoporous while the β-polymorph is microporous with low nitrogen adsorption capacities. Due to dipole-dipole broadening, no EPR spectrum was obtained for the β-polymorphs even at low temperature. In contrast, the obtained EPR spectrum of the α-polymorph was consistent with that of Co(II) in various materials.
Klika, Václav
2011-11-10
Understanding the mechanisms governing and regulating self-organisation in the developing embryo is a key challenge that has puzzled and fascinated scientists for decades. Since its conception in 1952 the Turing model has been a paradigm for pattern formation, motivating numerous theoretical and experimental studies, though its verification at the molecular level in biological systems has remained elusive. In this work, we consider the influence of receptor-mediated dynamics within the framework of Turing models, showing how non-diffusing species impact the conditions for the emergence of self-organisation. We illustrate our results within the framework of hair follicle pre-patterning, showing how receptor interaction structures can be constrained by the requirement for patterning, without the need for detailed knowledge of the network dynamics. Finally, in the light of our results, we discuss the ability of such systems to pattern outside the classical limits of the Turing model, and the inherent dangers involved in model reduction. © 2011 Society for Mathematical Biology.
Well-posedness of a two-scale model for liquid phase epitaxy with elasticity
Kutter, Michael; Rohde, Christian; Sändig, Anna-Margarete
2017-07-01
Epitaxy, a special form of crystal growth, is a technically relevant process for the production of thin films and layers. It can generate microstructures of different morphologies, such as steps, spirals or pyramids. These microstructures are influenced by elastic effects in the epitaxial layer. There are different epitaxial techniques, one being liquid phase epitaxy. Thereby, single particles are deposited out of a supersaturated liquid solution on a substrate where they contribute to the growth process. This article studies a two-scale model including elasticity, introduced in Eck et al. (Eur Phys J Special Topics 177:5-21, 2009) and extended in Eck et al. (2006). It consists of a macroscopic Navier-Stokes system and a macroscopic convection-diffusion equation for the transport of matter in the liquid, and a microscopic problem that combines a phase field approximation of a Burton-Cabrera-Frank model for the evolution of the epitaxial layer, a Stokes system for the fluid flow near the layer and an elasticity system for the elastic deformation of the solid film. Suitable conditions couple the single parts of the model. As the main result, existence and uniqueness of a solution are proven in suitable function spaces. Furthermore, an iterative solving procedure is proposed, which reflects, on the one hand, the strategy of the proof of the main result via fixed point arguments and, on the other hand, can be the basis for a numerical algorithm.
A two-scale model for correlation between B cell VDJ usage in zebrafish
Pan, Keyao; Deem, Michael
2011-03-01
The zebrafish (Danio rerio) is one of the model animals for study of immunology. The dynamics of the adaptive immune system in zebrafish is similar to that in higher animals. In this work, we built a two-scale model to simulate the dynamics of B cells in primary and secondary immune reactions in zebrafish and to explain the reported correlation between VDJ usage of B cell repertoires in distinct zebrafish. The first scale of the model consists of a generalized NK model to simulate the B cell maturation process in the 10-day primary immune response. The second scale uses a delay ordinary differential equation system to model the immune responses in the 6-month lifespan of zebrafish. The generalized NK model shows that mature B cells specific to one antigen mostly possess a single VDJ recombination. The probability that mature B cells in two zebrafish have the same VDJ recombination increases with the B cell population size or the B cell selection intensity and decreases with the B cell hypermutation rate. The ODE model shows a distribution of correlation in the VDJ usage of the B cell repertoires in two six-month-old zebrafish that is highly similar to that from experiment. This work presents a simple theory to explain the experimentally observed correlation in VDJ usage of distinct zebrafish B cell repertoires after an immune response.
A Two-Scale Reduced Model for Darcy Flow in Fractured Porous Media
Chen, Huangxin
2016-06-01
In this paper, we develop a two-scale reduced model for simulating the Darcy flow in two-dimensional porous media with conductive fractures. We apply the approach motivated by the embedded fracture model (EFM) to simulate the flow on the coarse scale, and the effect of fractures on each coarse scale grid cell intersecting with fractures is represented by the discrete fracture model (DFM) on the fine scale. In the DFM used on the fine scale, the matrix-fracture system are resolved on unstructured grid which represents the fractures accurately, while in the EFM used on the coarse scale, the flux interaction between fractures and matrix are dealt with as a source term, and the matrix-fracture system can be resolved on structured grid. The Raviart-Thomas mixed finite element methods are used for the solution of the coupled flows in the matrix and the fractures on both fine and coarse scales. Numerical results are presented to demonstrate the efficiency of the proposed model for simulation of flow in fractured porous media.
Evaristo, J. A.; Willenbring, J.
2013-12-01
The time dependency of silicate mineral weathering has been explored in the literature in terms of processes and features that are intrinsic and extrinsic to the mineral [1]. However, although the advent of sophisticated reactive transport models has allowed for coupling increasingly complex reaction and transport processes [2,3], a simple and fundamental understanding of the temporal evolution of weathering is lacking. Here, we propose that a purely deterministic approach may not be sufficient given the inherent differences in reactivity over space and time. Therefore, we explore how a combined reaction-diffusion and random rate model - informed by a stochastic distribution of weathering rates K (T-1) - might be able to explain not only the temporal evolution but also the hydrodynamics of weathering during earthquakes; the latter being purportedly described by time-dependent property permeability (L2). Preliminary model results show that (1) an increase in dimensionless quantity βrp, where β is the diffusion length (L-1) and rp is the distance between pores (L), leads to a decrease in minimum reaction rate with time from the relation Kmin ∝ e-βrp/rp ; (2) at a given porosity, a time-dependent decrease in reactivity arises as permeability decreases due to decreasing pore size (and therefore increasing rp), which in turn may be related to the time-dependent feedback between dissolution and precipitation; (3) while permeability is lower in older soils, transient stresses as during earthquakes [4], may induce more efficient "declogging" of pores in these soils than in younger soils due to higher hydrodynamic viscous shear stress, thereby, resulting in a coseismic change in stream discharge Q; and (4) subsequent weathering beyond t~Kmin-1 exhibits a fall in rates, marking the cessation of logarithmic decay possibly due to dissolution-precipitation feedback. [1] White and Brantley (2003), Chem. Geol. 202, 479. [2] Lichtner P.C. (1996), Mineralogical Society of
A Two-Scale Approach to Numerically Predict the Strength and Degradation of Composites
Li, W.; Jia, Y. J.; Li, L. X.
2018-02-01
Regarding the composite structure firstly as a composite on the macro-scale and then as the fiber phase and matrix phase on the meso scale, a two-scale approach is proposed to numerically predict the strength of fiber-reinforced composites. As the first step, the stress field is calculated by combining the macro-scale and meso-scale analysis together. With the stress field, the strength index is defined and the initial strength is then predicted. As the second step, the damage is defined and the degradation strength is then predicted. The two-scale approach is validated by analyzing a woven fiber reinforced composite under compression after impact (CAI) loading. Compared with the conventional homogenization approach, the present two-scale approach can not only calculate the stress and the damage of constituent phases on the meso scale, but obtain well correlated CAI strengths with the experimental test.
Assessing Self-Efficacy in Infant Care: A Comparison of Two Scales
Directory of Open Access Journals (Sweden)
Tassanee Prasopkittikun, RN, PhD
2008-09-01
Conclusion: The findings suggest that correlations between SICS and two different response formats do not reach the criteria for use as alternatives to each other. However, further research is needed, with particular emphasis on the investigation of construct validity and comparisons between the two scales.
A two-scale finite element formulation for the dynamic analysis of heterogeneous materials
Energy Technology Data Exchange (ETDEWEB)
Ionita, Axinte [Los Alamos National Laboratory
2008-01-01
In the analysis of heterogeneous materials using a two-scale Finite Element Method (FEM) the usual assumption is that the Representative Volume Element (RVE) of the micro-scale is much smaller than the finite element discretization of the macro-scale. However there are situations in which the RVE becomes comparable with, or even bigger than the finite element. These situations are considered in this article from the perspective of a two-scale FEM dynamic analysis. Using the principle of virtual power, new equations for the fluctuating fields are developed in terms of velocities rather than displacements. To allow more flexibility in the analysis, a scaling deformation tensor is introduced together with a procedure for its determination. Numerical examples using the new approach are presented.
Second-order two-scale method for bending behaviors of composite plate with periodic configuration
International Nuclear Information System (INIS)
Zhu Guoqing; Cui Junzhi
2010-01-01
In this paper, the second-order two-scale analysis method for bending behaviors of the plate made from composites with 3-D periodic configuration is presented by means of construction way. It can capture the microscopic 3-D mechanics behaviors caused from 3-D micro-structures. First, directly starting from the 3-D elastic plate model of composite materials with 3-D periodic configuration, three cell models are defined, and correspondingly the three classes of cell functions only defined on 3 normalized cells are constructed. And then, the effective homogenization parameters of composites are calculated from those local functions, it leads to a 2-D homogenized laminar plate problem. Next, to solve it the homogenization solution is obtained. Finally, the second-order two-scale solution is constructed from the micro-cell functions and the homogenization solution.
A two-scale roughness model for the gloss of coated paper
Elton, N. J.
2008-08-01
A model for gloss is developed for surfaces with two-scale random roughness where one scale lies in the wavelength region (microroughness) and the other in the geometrical optics limit (macroroughness). A number of important industrial materials such as coated and printed paper and some paints exhibit such two-scale rough surfaces. Scalar Kirchhoff theory is used to describe scattering in the wavelength region and a facet model used for roughness features much greater than the wavelength. Simple analytical expressions are presented for the gloss of surfaces with Gaussian, modified and intermediate Lorentzian distributions of surface slopes, valid for gloss at high angle of incidence. In the model, gloss depends only on refractive index, rms microroughness amplitude and the FWHM of the surface slope distribution, all of which may be obtained experimentally. Model predictions are compared with experimental results for a range of coated papers and gloss standards, and found to be in fair agreement within model limitations.
Quasi-potential and Two-Scale Large Deviation Theory for Gillespie Dynamics
Li, Tiejun
2016-01-07
The construction of energy landscape for bio-dynamics is attracting more and more attention recent years. In this talk, I will introduce the strategy to construct the landscape from the connection to rare events, which relies on the large deviation theory for Gillespie-type jump dynamics. In the application to a typical genetic switching model, the two-scale large deviation theory is developed to take into account the fast switching of DNA states. The comparison with other proposals are also discussed. We demonstrate different diffusive limits arise when considering different regimes for genetic translation and switching processes.
Two-scale cost efficiency optimization of 5G wireless backhaul networks
Ge, Xiaohu; Tu, Song; Mao, Guoqiang; Lau, Vincent K. N.; Pan, Linghui
2016-01-01
To cater for the demands of future fifth generation (5G) ultra-dense small cell networks, the wireless backhaul network is an attractive solution for the urban deployment of 5G wireless networks. Optimization of 5G wireless backhaul networks is a key issue. In this paper we propose a two-scale optimization solution to maximize the cost efficiency of 5G wireless backhaul networks. Specifically, the number and positions of gateways are optimized in the long time scale of 5G wireless backhaul ne...
Two scale damage model and related numerical issues for thermo-mechanical high cycle fatigue
International Nuclear Information System (INIS)
Desmorat, R.; Kane, A.; Seyedi, M.; Sermage, J.P.
2007-01-01
On the idea that fatigue damage is localized at the microscopic scale, a scale smaller than the mesoscopic one of the Representative Volume Element (RVE), a three-dimensional two scale damage model has been proposed for High Cycle Fatigue applications. It is extended here to aniso-thermal cases and then to thermo-mechanical fatigue. The modeling consists in the micro-mechanics analysis of a weak micro-inclusion subjected to plasticity and damage embedded in an elastic meso-element (the RVE of continuum mechanics). The consideration of plasticity coupled with damage equations at micro-scale, altogether with Eshelby-Kroner localization law, allows to compute the value of microscopic damage up to failure for any kind of loading, 1D or 3D, cyclic or random, isothermal or aniso-thermal, mechanical, thermal or thermo-mechanical. A robust numerical scheme is proposed in order to make the computations fast. A post-processor for damage and fatigue (DAMAGE-2005) has been developed. It applies to complex thermo-mechanical loadings. Examples of the representation by the two scale damage model of physical phenomena related to High Cycle Fatigue are given such as the mean stress effect, the non-linear accumulation of damage. Examples of thermal and thermo-mechanical fatigue as well as complex applications on real size testing structure subjected to thermo-mechanical fatigue are detailed. (authors)
Rahbani, Janane
2012-01-01
We study the kinetics and mechanism of intercalation and de-intercalation of small anions during the formation of crystalline α-Co(OH) 2 and its transformation to β-Co(OH) 2 within a reaction-diffusion framework. We therein use fluorescence spectroscopy with Rhodamine 6G (Rh6G) as a probe as well as other spectroscopic and imaging techniques. The method is based on the reaction and diffusion of hydroxide ions into a gel matrix containing the Co(ii) ions, the conjugate anions to be intercalated and Rh6G. The advantage of this simple method is that it allows us to separate throughout space the various stages during the formation of α-Co(OH) 2 and its transformation to β-Co(OH) 2, thus enabling fluorescence measurements of the those stages by simply focusing on different areas of the tube. It also permits us to extract with ease the solids for characterization and image analysis. The macroscopic evolution of the system, which consists of a leading blue front designating the formation of α-Co(OH) 2 followed by a sharp blue/pink interface designating the transformation to the pink β-Co(OH) 2, exhibits different dynamics depending on the anion present in the gel. At a certain stage, the blue/pink interface stops its propagation and only the blue front continues. This represents clear evidence of the dependence of the kinetics of intercalation and de-intercalation on the nature of the anion. The coexisting polymorphs were collected and characterized using XRD, FTIR, Raman and UV-Vis. The fluorescence images of the α-Co(OH) 2 reveal clearly the presence of Rh6G between its layers, whereas images from the β polymorph indicate the opposite. Moreover, the fluorescence of Rh6G is monitored during the formation of α-Co(OH) 2 and its conversion to β-Co(OH) 2. During the formation, the fluorescence intensity and lifetime are significantly increased whereas the opposite happens during the transformation to the β phase. We are able to calculate the activation energies
A critique and comparison of two scales from fifteen years of studying compulsive buying.
Manolis, Chris; Roberts, James A; Kashyap, Vishal
2008-02-01
Compulsive buying is an important construct in marketing that has far-reaching personal and social implications. The profile of the adult compulsive buyer in the literature is based largely on the 1992 Faber and O'Guinn Compulsive Buying Scale. A second compulsive buying scale by Edwards has also been used but sparingly. Empirical research conducted over that past 15 years with these two scales shows that, although both scales were designed to measure compulsive buying, the two appear to be different operationalizations of the construct. The present review raises several psychometric issues about both scales. Their robustness is crucial to a clear understanding of the antecedents and consequences of compulsive buying. Directions for research are added.
Probing the two-scale-factor universality hypothesis by exact rotation symmetry-breaking mechanism
Energy Technology Data Exchange (ETDEWEB)
Neto, J.F.S.; Lima, K.A.L.; Carvalho, P.R.S. [Universidade Federal do Piaui, Departamento de Fisica, Teresina, PI (Brazil); Sena-Junior, M.I. [Universidade de Pernambuco, Escola Politecnica de Pernambuco, Recife, PE (Brazil); Universidade Federal de Alagoas, Instituto de Fisica, Maceio, AL (Brazil)
2017-12-15
We probe the two-scale-factor universality hypothesis by evaluating, firstly explicitly and analytically at the one-loop order, the loop quantum corrections to the amplitude ratios for O(N)λφ{sup 4} scalar field theories with rotation symmetry breaking in three distinct and independent methods in which the rotation symmetry-breaking mechanism is treated exactly. We show that the rotation symmetry-breaking amplitude ratios turn out to be identical in the three methods and equal to their respective rotation symmetry-breaking ones, although the amplitudes themselves, in general, depend on the method employed and on the rotation symmetry-breaking parameter. At the end, we show that all these results can be generalized, through an inductive process based on a general theorem emerging from the exact calculation, to any loop level and physically interpreted based on symmetry ideas. (orig.)
Daya Angkat dan Tarik Kapal Barang Menggunakan Turbosail Dengan Model Simulasi K-Omega Two Scale
Directory of Open Access Journals (Sweden)
Eka Sari Wijiaanti
2013-06-01
Full Text Available Seiring dengan ramainya arus keluar masuk penduduk dan pengiriman barang pribadi melalui paket-paket jasa pengiriman menambah ramainya arus transportasi darat dan laut. Namun, kondisi tersebut tidak dibarengi dengan pengelolaan sumber energi bahan bakar khususnya transportasi laut. Aerodinamis kapal laut harus didukung oleh kecepatan angin yang bertiup di sekitar kapal tersebut. Dengan mendesain sebuah turbosail pada kapal barang, kita dapat mengkolaborasikan sumber energi fosil dan energi angin. Desain Turbosail yang tepat untuk digunakan pada kapal barang.penelitian ini bertujuan untuk mengetahui bagaimana aliran turbulen di sekitar turbosail serta mendapatkan simulasi terbaik. Profil turbovoile dirancang dengan bentuk bulat telur untuk meningkatkan kinerja aerodinamis dengan mengurangi hambatan dengan mengamati koefisien lift dan drag yang dihasilkan dengan Model Simulasi K-Omega Two Scale. Dari hasil penelitian menunjukan bahwa nilai koefisien angkat dan tarik meningkat sesuai dengan kenaikan bilangan Reynolds.
Two-scale correlation and energy cascade in three-dimensional turbulent flows
International Nuclear Information System (INIS)
Huang, Y X; Schmitt, F G; Gagne, Y
2014-01-01
In this paper, we propose a high-order harmonic-free methodology, namely arbitrary-order Hilbert spectral analysis, to estimate the two-scale correlation (TSC). When applied to fully developed turbulent velocity, we find that the scale-dependent Hilbert energy satisfies a lognormal distribution on both the inertial and dissipation ranges. The maximum probability density function of the logarithm of the Hilbert energy obeys a power law with a scaling exponent γ ≃ 0.33 in the inertial range. For the measured TSC, we observe a logarithmic correlation law with an experimental exponent α ≃ 0.37 on both the inertial and dissipation ranges. The correlation itself is found to be self-similar with respect to the distance between the two considered scales and a central frequency ω c in the logarithm space. An empirical nonlinear and nonlocal triad-scale interaction formula is proposed to describe the observed TSC. This triadic interaction can be interpreted as experimental evidence of a small-scale nonlinear and nonlocal coupling inside the self-similarity of the Richardson–Kolmogorov phenomenological cascade picture. (paper)
Directory of Open Access Journals (Sweden)
Désirée Annabel Lie
2013-12-01
Full Text Available Rationale : The validated 19-item Readiness for Interprofessional Learning Scale (RIPLS is often used for assessing attitudes toward interprofessional education (IPE. The 12-item Interdisciplinary Education Perception Scale (IEPS, also used for this purpose, has not been validated among the professions of medicine, pharmacy, and physician assistants (PAs. The discriminatory ability of the two scales has not been directly compared. Comparison of the two will aid educators in selecting the optimal scale. Objective : To compare psychometric properties of the RIPLS and IEPS and to examine the ability of each scale to discriminate mean scores among student subgroups (gender, profession, seniority, and prior IPE exposure. Method : We conducted a cross-sectional (Qualtrics© survey (RIPLS and IEPS of junior and senior students in medicine (n=360, pharmacy (n=360, and the PA profession (n=106. Descriptive statistics were used to report aggregate mean scores of subgroups. The internal consistency of each scale was assessed using Cronbach's α. Concurrent validity was measured by Pearson's correlation coefficients. Independent-sample t-tests and analysis of variances (ANOVAs were performed to assess the discriminatory ability of each scale. Cohen's d effect sizes were calculated for all significant pair-wise comparisons. Results : Response rate was 82%. Cronbach's α was 0.85 (RIPLS and 0.91 (IEPS. The RIPLS discriminated scores by gender among junior students only, and scores by IPE exposure among all students. The IEPS distinguished score differences for the three professions among junior students and by prior IPE exposure for all three professions. Neither scale detected differences in mean scores by profession among all students or by level of training among the three professions. Conclusions : Neither the RIPLS nor the IEPS has greater discriminatory ability for detecting attitude differences among the student subgroups. Reason for differences may be
Lie, Désirée Annabel; Fung, Cha Chi; Trial, Janet; Lohenry, Kevin
2013-12-02
The validated 19-item Readiness for Interprofessional Learning Scale (RIPLS) is often used for assessing attitudes toward interprofessional education (IPE). The 12-item Interdisciplinary Education Perception Scale (IEPS), also used for this purpose, has not been validated among the professions of medicine, pharmacy, and physician assistants (PAs). The discriminatory ability of the two scales has not been directly compared. Comparison of the two will aid educators in selecting the optimal scale. To compare psychometric properties of the RIPLS and IEPS and to examine the ability of each scale to discriminate mean scores among student subgroups (gender, profession, seniority, and prior IPE exposure). We conducted a cross-sectional (Qualtrics(©)) survey (RIPLS and IEPS) of junior and senior students in medicine (n=360), pharmacy (n=360), and the PA profession (n=106). Descriptive statistics were used to report aggregate mean scores of subgroups. The internal consistency of each scale was assessed using Cronbach's α. Concurrent validity was measured by Pearson's correlation coefficients. Independent-sample t-tests and analysis of variances (ANOVAs) were performed to assess the discriminatory ability of each scale. Cohen's d effect sizes were calculated for all significant pair-wise comparisons. Response rate was 82%. Cronbach's α was 0.85 (RIPLS) and 0.91 (IEPS). The RIPLS discriminated scores by gender among junior students only, and scores by IPE exposure among all students. The IEPS distinguished score differences for the three professions among junior students and by prior IPE exposure for all three professions. Neither scale detected differences in mean scores by profession among all students or by level of training among the three professions. Neither the RIPLS nor the IEPS has greater discriminatory ability for detecting attitude differences among the student subgroups. Reason for differences may be explained by slightly different scale constructs. The RIPLS
Two-Scale 13C Metabolic Flux Analysis for Metabolic Engineering.
Ando, David; Garcia Martin, Hector
2018-01-01
Accelerating the Design-Build-Test-Learn (DBTL) cycle in synthetic biology is critical to achieving rapid and facile bioengineering of organisms for the production of, e.g., biofuels and other chemicals. The Learn phase involves using data obtained from the Test phase to inform the next Design phase. As part of the Learn phase, mathematical models of metabolic fluxes give a mechanistic level of comprehension to cellular metabolism, isolating the principle drivers of metabolic behavior from the peripheral ones, and directing future experimental designs and engineering methodologies. Furthermore, the measurement of intracellular metabolic fluxes is specifically noteworthy as providing a rapid and easy-to-understand picture of how carbon and energy flow throughout the cell. Here, we present a detailed guide to performing metabolic flux analysis in the Learn phase of the DBTL cycle, where we show how one can take the isotope labeling data from a 13 C labeling experiment and immediately turn it into a determination of cellular fluxes that points in the direction of genetic engineering strategies that will advance the metabolic engineering process.For our modeling purposes we use the Joint BioEnergy Institute (JBEI) Quantitative Metabolic Modeling (jQMM) library, which provides an open-source, python-based framework for modeling internal metabolic fluxes and making actionable predictions on how to modify cellular metabolism for specific bioengineering goals. It presents a complete toolbox for performing different types of flux analysis such as Flux Balance Analysis, 13 C Metabolic Flux Analysis, and it introduces the capability to use 13 C labeling experimental data to constrain comprehensive genome-scale models through a technique called two-scale 13 C Metabolic Flux Analysis (2S- 13 C MFA) [1]. In addition to several other capabilities, the jQMM is also able to predict the effects of knockouts using the MoMA and ROOM methodologies. The use of the jQMM library is
Parand, K.; Nikarya, M.
2017-11-01
In this paper a novel method will be introduced to solve a nonlinear partial differential equation (PDE). In the proposed method, we use the spectral collocation method based on Bessel functions of the first kind and the Jacobian free Newton-generalized minimum residual (JFNGMRes) method with adaptive preconditioner. In this work a nonlinear PDE has been converted to a nonlinear system of algebraic equations using the collocation method based on Bessel functions without any linearization, discretization or getting the help of any other methods. Finally, by using JFNGMRes, the solution of the nonlinear algebraic system is achieved. To illustrate the reliability and efficiency of the proposed method, we solve some examples of the famous Fisher equation. We compare our results with other methods.
Volpe, Robert J.; Briesch, Amy M.
2016-01-01
This study examines the dependability of two scaling approaches for using a five-item Direct Behavior Rating multi-item scale to assess student disruptive behavior. A series of generalizability theory studies were used to compare a traditional frequency-based scaling approach with an approach wherein the informant compares a target student's…
Explosive instabilities of reaction-diffusion equations
Wilhelmsson, H.
1987-07-01
Explicit solutions are obtained for evolution equations for explosively unstable situations. These solutions include the effects of diffusion with linear or quadratic density dependence of the diffusion coefficient. As a result of balance between the diffusion and nonlinear terms, explosive growth in time can occur with a preservation in shape of certain spatial distributions. The solutions are generalized to cases of two interacting populations.
Reaction-diffusion models of decontamination
DEFF Research Database (Denmark)
Hjorth, Poul G.
A contaminant, which also contains a polymer is in the form of droplets on a solid surface. It is to be removed by the action of a decontaminant, which is applied in aqueous solution. The contaminant is only sparingly soluble in water, so the reaction mechanism is that it slowly dissolves...... in the aqueous solution and then is oxidized by the decontaminant. The polymer is insoluble in water, and so builds up near the interface, where its presence can impede the transport of contaminant. In these circumstances, Dstl wish to have mathematical models that give an understanding of the process, and can...
Vigolo, Paolo; Buzzo, Ottavia; Buzzo, Maurizio; Mutinelli, Sabrina
2017-02-01
Plaque control is crucial for the prevention of inflammatory periodontal disease. Hand scaling instruments have been shown to be efficient for the removal of plaque; however, routine periodontal prophylactic procedures may modify the surface profile of restorative materials. The purpose of this study was to assess in vitro the changes in roughness of alumina, zirconia, and lithium disilicate surfaces treated by two hand scaling instruments. Forty-eight alumina specimens, 48 zirconia specimens, and 48 lithium disilicate specimens, were selected. All specimens were divided into three groups of 16 each; one group for each material was considered the control group and no scaling procedures were performed; the second group of each material was exposed to scaling with steel curettes simulating standard clinical conditions; the third group of each material was exposed to scaling with titanium curettes. After scaling, the surface roughness of the specimens was evaluated with a profilometer. First, a statistical test was carried out to evaluate the difference in surface roughness before the scaling procedure of the three materials was effected (Kruskal-Wallis test). Subsequently, the effect of curette material (steel and titanium) on roughness difference and roughness ratio was analyzed throughout the entire sample and within each material group, and a nonparametric test for dependent values was conducted (Wilcoxon signed-rank test). Finally, the roughness ratios of the three material groups were compared by means of a Kruskal-Wallis test and a Wilcoxon signed-rank test. Upon completion of profilometric evaluation, representative specimens from each group were prepared for SEM evaluation to evaluate the effects of the two scaling systems on the different surfaces qualitatively. After scaling procedure, the roughness profile value increased in all disks. Classifying the full sample according to curette used, the roughness of the disks treated with a steel curette reached a
Amir, Sahar Z.
2017-06-09
A Hybrid Embedded Fracture (HEF) model was developed to reduce various computational costs while maintaining physical accuracy (Amir and Sun, 2016). HEF splits the computations into fine scale and coarse scale. Fine scale solves analytically for the matrix-fracture flux exchange parameter. Coarse scale solves for the properties of the entire system. In literature, fractures were assumed to be either vertical or horizontal for simplification (Warren and Root, 1963). Matrix-fracture flux exchange parameter was given few equations built on that assumption (Kazemi, 1968; Lemonnier and Bourbiaux, 2010). However, such simplified cases do not apply directly for actual random fracture shapes, directions, orientations …etc. This paper shows that the HEF fine scale analytic solution (Amir and Sun, 2016) generates the flux exchange parameter found in literature for vertical and horizontal fracture cases. For other fracture cases, the flux exchange parameter changes according to the angle, slop, direction, … etc. This conclusion rises from the analysis of both: the Discrete Fracture Network (DFN) and the HEF schemes. The behavior of both schemes is analyzed with exactly similar fracture conditions and the results are shown and discussed. Then, a generalization is illustrated for any slightly compressible single-phase fluid within fractured porous media and its results are discussed.
A two scale modeling and computational framework for vibration-induced Raynaud syndrome.
Hua, Yue; Lemerle, Pierre; Ganghoffer, Jean-François
2017-07-01
Hand-Arm Vibration syndrome (HAVS), usually caused by long-term use of hand-held power tools, can in certain manifestations alter the peripheral blood circulation in the hand-arm region. HAVS typically occurs after exposure to cold, causing an abnormally strong vasoconstriction of blood vessels. A pathoanatomical mechanism suggests that a reduction of the lumen of the blood vessels in VWF (Vibration White Finger) subjects, due to either hypertrophy or thickening of the vessel wall, may be at the origin of the disease. However, the direct and indirect effects of the load of the hand-held tools on the structure of blood vessels remain controversial:.one hypothesis is the mechanical action of vibration on the local acral dysregulation and/or on the vessel histomorphological modifications. Another hypothesis is the participation of the sympathetic nervous system to this dysregulation. In this paper, we assume the modifications as mechanobiological growth and the load-effect relationship may be interpreted as directly or indirectly induced. This work is the first attempt to model the effect of vibration through soft tissues onto the distal capillaries, addressing the double paradigm of multi space-time scales, i.e. low period vibration versus high time constant of the growth phenomenon as well as vibrations propagating in the macroscopic tissue including the microscopic capillary structures subjected to a pathological microstructural evolution. The objective is to lay down the theoretical basis of growth modeling for the small distal artery, with the ability to predict the geometrical and structural changes of the arterial walls caused by vibration exposure. We adopt the key idea of splitting the problem into one global vibration problem at the macroscopic scale and one local growth problem at the micro level. The macroscopic hyperelastic viscous dynamic model of the fingertip cross-section is validated by fitting experimental data. It is then used in steady
Carr, E. J.; Perré, P.; Turner, I. W.
2016-12-01
Numerous problems involving gradient-driven transport processes-e.g., Fourier's and Darcy's law-in heterogeneous materials concern a physical domain that is much larger than the scale at which the coefficients vary spatially. To overcome the prohibitive computational cost associated with such problems, the well-established Distributed Microstructure Model (DMM) provides a two-scale description of the transport process that produces a computationally cheap approximation to the fine-scale solution. This is achieved via the introduction of sparsely distributed micro-cells that together resolve small patches of the fine-scale structure: a macroscopic equation with an effective coefficient describes the global transport and a microscopic equation governs the local transport within each micro-cell. In this paper, we propose a new formulation, the Extended Distributed Microstructure Model (EDMM), where the macroscopic flux is instead defined as the average of the microscopic fluxes within the micro-cells. This avoids the need for any effective parameters and more accurately accounts for a non-equilibrium field in the micro-cells. Another important contribution of the work is the presentation of a new and improved numerical scheme for performing the two-scale computations using control volume, Krylov subspace and parallel computing techniques. Numerical tests are carried out on two challenging test problems: heat conduction in a composite medium and unsaturated water flow in heterogeneous soils. The results indicate that while DMM is more efficient, EDMM is more accurate and is able to capture additional fine-scale features in the solution.
Directory of Open Access Journals (Sweden)
Łydżba Dariusz
2014-03-01
Full Text Available The needle probe test, as a thermal conductivity measurement method, has become very popular in recent years. In the present study, the efficiency of this methodology, for the case of composite materials, is investigated based on the numerical simulations. The material under study is a two-phase composite with periodic microstructure of “matrix-inclusion” type. Two-scale analysis, incorporating micromechanics approach, is performed. First, the effective thermal conductivity of the composite considered is found by the solution of the appropriate boundary value problem stated for the single unit cell. Next, numerical simulations of the needle probe test are carried out. In this case, two different locations of the measuring sensor are considered. It is shown that the “equivalent” conductivity, derived from the probe test, is strongly affected by the location of the sensor. Moreover, comparing the results obtained for different scales, one can notice that the “equivalent” conductivity cannot be interpreted as the effective one for the composites considered. Hence, a crude approximation of the effective property is proposed based on the volume fractions of constituents and the equivalent conductivities derived from different sensor locations.
Random attractors for stochastic lattice reversible Gray-Scott systems with additive noise
Directory of Open Access Journals (Sweden)
Hongyan Li
2015-10-01
Full Text Available In this article, we prove the existence of a random attractor of the stochastic three-component reversible Gray-Scott system on infinite lattice with additive noise. We use a transformation of addition involved with Ornstein-Uhlenbeck process, for proving the pullback absorbing property and the pullback asymptotic compactness of the reaction diffusion system with cubic nonlinearity.
Directory of Open Access Journals (Sweden)
Fabiana T. da Costa
2000-01-01
Full Text Available O objetivo deste estudo foi traduzir e adaptar duas escalas que avaliam as dimensões de responsividade e exigência parentais com adolescentes, as quais permitem a classificação de quatro estilos parentais. As escalas foram aplicadas a 378 adolescentes, tendo apresentado índices de consistência interna adequados (alpha entre 0,70 e 0,83. Análises de variância revelaram que a exigência materna percebida foi maior do que a paterna entre adolescentes de ambos os sexos, mas as garotas perceberam níveis de exigência (materna e paterna mais altos do que os garotos. A responsividade materna observada foi superior à paterna para ambos os sexos, porém as mulheres atribuíram escores de responsividade mais altos às suas mães do que os homens. Não houve diferenças entre os sexos quanto ao nível de responsividade paterna. A proporção de estilos parentais observada nesta amostra foi 13,3% (autoritário, 36,7% (autoritativo, 14,5% (indulgente e 35,5% (negligente, sugerindo que nossa cultura não é tão permissiva quanto se supõe usualmente.The aim of this study was to translate and adapt two scales of parental responsiveness and demandingness to Portuguese (Brazil. According to these scales levels, it is possible to categorize four parenting styles. The scales were administred to 378 adolescents of both sexes and showed satisfactory reliability coefficients (alpha between 0,70 and 0,83. Analysis of variance indicated that perceived mothers demandingness was greater than fathers for both sexes, but girls observed higher levels of parental demandingness than boys. Both males and females attributed higher scores of responsiveness to their mothers than to their fathers, but girls scored higher on mothers responsiveness than boys. No significant differences between sexes were found for fathers level of responsiveness. The frequency of parenting styles observed in this sample was 13,3% (authoritarian, 36,7% (authoritative, 14
A new fitted operator finite difference method to solve systems of ...
African Journals Online (AJOL)
In this paper, we design and analyze a robust FOFDM to solve a system of coupled singularly perturbed parabolic reaction-diffusion equations. We use the backward Euler method for the semi-discretization in time. An FOFDM is then developed to solve the resulting set of boundary value problems. The proposed method is ...
Qualitative analysis on a cubic predator-prey system with diffusion
Directory of Open Access Journals (Sweden)
Qunyi Bie
2011-04-01
Full Text Available In this paper, we study a cubic predator-prey model with diffusion. We first establish the global stability of the trivial and nontrivial constant steady states for the reaction diffusion system, and then prove the existence and non-existence results concerning non-constant positive stationary solutions by using topological argument and the energy method, respectively.
Global Solutions for an -Component System of Activator-Inhibitor Type
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S. Abdelmalek
2013-01-01
Full Text Available This paper deals with a reaction-diffusion system with fractional reactions modeling -substances into interaction following activator-inhibitor's scheme. The existence of global solutions is obtained via a judicious Lyapunov functional that generalizes the one introduced by Masuda and Takahashi.
Reaction-Transport Systems Mesoscopic Foundations, Fronts, and Spatial Instabilities
Horsthemke, Werner; Mendez, Vicenc
2010-01-01
This book is an introduction to the dynamics of reaction-diffusion systems, with a focus on fronts and stationary spatial patterns. Emphasis is on systems that are non-standard in the sense that either the transport is not simply classical diffusion (Brownian motion) or the system is not homogeneous. A important feature is the derivation of the basic phenomenological equations from the mesoscopic system properties. Topics addressed include transport with inertia, described by persistent random walks and hyperbolic reaction-transport equations and transport by anomalous diffusion, in particular subdiffusion, where the mean square displacement grows sublinearly with time. In particular reaction-diffusion systems are studied where the medium is in turn either spatially inhomogeneous, compositionally heterogeneous or spatially discrete. Applications span a vast range of interdisciplinary fields and the systems considered can be as different as human or animal groups migrating under external influences, population...
International Nuclear Information System (INIS)
Habibi, Z.
2011-01-01
We are interested in the homogenization of heat transfer in periodic porous media modelling the geometry of a gas cooled nuclear reactor. This geometry is made of a solid media perforated by several long thin parallel cylinders, the diameter of which is of the same order than the period. The heat is transported by conduction in the solid part of the domain and by conduction, convection and radiative transfer in the fluid part (the cylinders). A non-local boundary condition models the radiative heat transfer on the cylinder walls. It is a stationary analysis corresponding to a nominal performance of the reactor core, and also non-stationary corresponding to a normal shut-down of the core. To obtain the homogenized problem we first use a formal two-scale asymptotic expansion method. The mathematical justification of our results is based on the notion of two-scale convergence. One feature of this work in dimension 3 is that it combines homogenization with a 3D to 2D asymptotic analysis since the radiative transfer in the limit cell problem is purely two-dimensional. A second feature of this work is the study of this heat transfer when it contains an oscillating thermal source at the microscopic level and a thermal exchange with the perforations. In this context, our numerical analysis shows a non-negligible contribution of the second order corrector which helps us to model the gradients appearing between the source area and the perforations. (author) [fr
Directory of Open Access Journals (Sweden)
Wronski M.
2017-12-01
Full Text Available The goal of this work was theoretical and experimental study of micro- and macroscopic mechanical fields of 6061 aluminum alloy induced by the asymmetric rolling process. Two-scale constitutive law was used by implementing an elasto-plastic self-consistent scheme into the Finite Element code (ABAQUS/Explicit. The model was applied to study the asymmetric rolling. Such a deformation process induces heterogeneous mechanical fields that were reproduced by the model thanks to the crystallographic nature of constitutive law used. The studied material was processed, at room temperature, in one rolling pass to 36% reduction. The resulting material modifications were compared with predictions of the two-scale model. Namely, the calculated textures were compared with experimental ones determined by X-ray diffraction. Especially, detailed quantitative analysis of texture variation across the sample thickness was done. The influence of this texture variation on plastic anisotropy was studied. The advantages of asymmetric rolling process over symmetric one were identified. The main benefits are a nearly homogeneous crystallographic texture, reduced rolling normal forces and homogenization of plastic anisotropy through the sample thickness.
Malekan, Mohammad; Barros, Felício B.
2017-12-01
Generalized or extended finite element method (G/XFEM) models the crack by enriching functions of partition of unity type with discontinuous functions that represent well the physical behavior of the problem. However, this enrichment functions are not available for all problem types. Thus, one can use numerically-built (global-local) enrichment functions to have a better approximate procedure. This paper investigates the effects of micro-defects/inhomogeneities on a main crack behavior by modeling the micro-defects/inhomogeneities in the local problem using a two-scale G/XFEM. The global-local enrichment functions are influenced by the micro-defects/inhomogeneities from the local problem and thus change the approximate solution of the global problem with the main crack. This approach is presented in detail by solving three different linear elastic fracture mechanics problems for different cases: two plane stress and a Reissner-Mindlin plate problems. The numerical results obtained with the two-scale G/XFEM are compared with the reference solutions from the analytical, numerical solution using standard G/XFEM method and ABAQUS as well, and from the literature.
Computation of effectiveness factor for a reaction-diffusion process ...
African Journals Online (AJOL)
An isothermal and steady state continuity equation for a key component in a catalyst particle was developed and applied to lactose hydrolysis in a fixed bed reactor containing an immobilized enzyme of β-galactosidase on spherical chitosan beads, where lactose (substrate) was taken as the key component. The differential ...
Threshold sensing through a synthetic enzymatic reaction-diffusion network.
Semenov, Sergey N; Markvoort, Albert J; de Greef, Tom F A; Huck, Wilhelm T S
2014-07-28
A wet stamping method to precisely control concentrations of enzymes and inhibitors in place and time inside layered gels is reported. By combining enzymatic reactions such as autocatalysis and inhibition with spatial delivery of components through soft lithographic techniques, a biochemical reaction network capable of recognizing the spatial distribution of an enzyme was constructed. The experimental method can be used to assess fundamental principles of spatiotemporal order formation in chemical reaction networks. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Spherically Symmetric Waves of a Reaction-Diffusion Equation.
1980-02-01
travelling pulses of the Fitzhugh- Nagumo and Hodgkin - Huxley equations, travelling fronts in some scalar equations such as the Fisher equation and...appropriate function space. A semiflow on a space Y is a func- + + tion S : Y x R - Y (whose domain may not be all of Y x IR , but must be an open subset...which satisfies (1) S(S( y ,t),s) = S( y ,t+s) and (2) S is continuous on its domain. S is said to be a local semiflow if for each y E Y , a set of the form ( y
Dynamic Analysis of a Reaction-Diffusion Rumor Propagation Model
Zhao, Hongyong; Zhu, Linhe
2016-06-01
The rapid development of the Internet, especially the emergence of the social networks, leads rumor propagation into a new media era. Rumor propagation in social networks has brought new challenges to network security and social stability. This paper, based on partial differential equations (PDEs), proposes a new SIS rumor propagation model by considering the effect of the communication between the different rumor infected users on rumor propagation. The stabilities of a nonrumor equilibrium point and a rumor-spreading equilibrium point are discussed by linearization technique and the upper and lower solutions method, and the existence of a traveling wave solution is established by the cross-iteration scheme accompanied by the technique of upper and lower solutions and Schauder’s fixed point theorem. Furthermore, we add the time delay to rumor propagation and deduce the conditions of Hopf bifurcation and stability switches for the rumor-spreading equilibrium point by taking the time delay as the bifurcation parameter. Finally, numerical simulations are performed to illustrate the theoretical results.
A GPU Reaction Diffusion Soil-Microbial Model
Falconer, Ruth; Houston, Alasdair; Schmidt, Sonja; Otten, Wilfred
2014-05-01
Parallelised algorithms are frequent in bioinformatics as a consequence of the close link to informatics - however in the field of soil science and ecology they are less prevalent. A current challenge in soil ecology is to link habitat structure to microbial dynamics. Soil science is therefore entering the 'big data' paradigm as a consequence of integrating data pertinent to the physical soil environment obtained via imaging and theoretical models describing growth and development of microbial dynamics permitting accurate analyses of spatio-temporal properties of different soil microenvironments. The microenvironment is often captured by 3D imaging (CT tomography) which yields large datasets and when used in computational studies the physical sizes of the samples that are amenable to computation are less than 1 cm3. Today's commodity graphics cards are programmable and possess a data parallel architecture that in many cases is capable of out-performing the CPU in terms of computational rates. The programmable aspect is achieved via a low-level parallel programming language (CUDA, OpenCL and DirectX). We ported a Soil-Microbial Model onto the GPU using the DirectX Compute API. We noted a significant computational speed up as well as an increase in the physical size that can be simulated. Some of the drawbacks of such an approach were concerned with numerical precision and the steep learning curve associated with GPGPU technologies.
Nonexplosion of solutions to stochastic reaction-diffusion equations
Czech Academy of Sciences Publication Activity Database
Dozzi, M.; Maslowski, Bohdan
2002-01-01
Roč. 82, - (2002), s. 745-751 ISSN 0044-2267 Institutional research plan: CEZ:AV0Z1019905 Keywords : stochastic parabolic PDEďs%nonexplosion Subject RIV: ba - General Mathematics Impact factor: 0.085, year: 2002
A reaction-diffusion model of cytosolic hydrogen peroxide.
Lim, Joseph B; Langford, Troy F; Huang, Beijing K; Deen, William M; Sikes, Hadley D
2016-01-01
As a signaling molecule in mammalian cells, hydrogen peroxide (H2O2) determines the thiol/disulfide oxidation state of several key proteins in the cytosol. Localization is a key concept in redox signaling; the concentrations of signaling molecules within the cell are expected to vary in time and in space in manner that is essential for function. However, as a simplification, all theoretical studies of intracellular hydrogen peroxide and many experimental studies to date have treated the cytosol as a well-mixed compartment. In this work, we incorporate our previously reported reduced kinetic model of the network of reactions that metabolize hydrogen peroxide in the cytosol into a model that explicitly treats diffusion along with reaction. We modeled a bolus addition experiment, solved the model analytically, and used the resulting equations to quantify the spatiotemporal variations in intracellular H2O2 that result from this kind of perturbation to the extracellular H2O2 concentration. We predict that micromolar bolus additions of H2O2 to suspensions of HeLa cells (0.8 × 10(9)cells/l) result in increases in the intracellular concentration that are localized near the membrane. These findings challenge the assumption that intracellular concentrations of H2O2 are increased uniformly throughout the cell during bolus addition experiments and provide a theoretical basis for differing phenotypic responses of cells to intracellular versus extracellular perturbations to H2O2 levels. Copyright © 2015 Elsevier Inc. All rights reserved.
Directory of Open Access Journals (Sweden)
Shengmao Fu
2010-01-01
Full Text Available We study a cubic predator-prey system with stage structure for the prey. This system is a generalization of the two-species Lotka-Volterra predator-prey model. Firstly, we consider the asymptotical stability of equilibrium points to the system of ordinary differential equations type. Then, the global existence of solutions and the stability of equilibrium points to the system of weakly coupled reaction-diffusion type are discussed. Finally, the existence of nonnegative classical global solutions to the system of strongly coupled reaction-diffusion type is investigated when the space dimension is less than 6, and the global asymptotic stability of unique positive equilibrium point of the system is proved by constructing Lyapunov functions.
Emergent structures in reaction-advection-diffusion systems on a sphere
Krause, Andrew L.; Burton, Abigail M.; Fadai, Nabil T.; Van Gorder, Robert A.
2018-04-01
We demonstrate unusual effects due to the addition of advection into a two-species reaction-diffusion system on the sphere. We find that advection introduces emergent behavior due to an interplay of the traditional Turing patterning mechanisms with the compact geometry of the sphere. Unidirectional advection within the Turing space of the reaction-diffusion system causes patterns to be generated at one point of the sphere, and transported to the antipodal point where they are destroyed. We illustrate these effects numerically and deduce conditions for Turing instabilities on local projections to understand the mechanisms behind these behaviors. We compare this behavior to planar advection which is shown to only transport patterns across the domain. Analogous transport results seem to hold for the sphere under azimuthal transport or away from the antipodal points in unidirectional flow regimes.
Energy Technology Data Exchange (ETDEWEB)
Saide, Pablo (CGRER, Center for Global and Regional Environmental Research, Univ. of Iowa, Iowa City, IA (United States)), e-mail: pablo-saide@uiowa.edu; Bocquet, Marc (Universite Paris-Est, CEREA Joint Laboratory Ecole des Ponts ParisTech and EDF RandD, Champs-sur-Marne (France); INRIA, Paris Rocquencourt Research Center (France)); Osses, Axel (Departamento de Ingeniera Matematica, Universidad de Chile, Santiago (Chile); Centro de Modelamiento Matematico, UMI 2807/Universidad de Chile-CNRS, Santiago (Chile)); Gallardo, Laura (Centro de Modelamiento Matematico, UMI 2807/Universidad de Chile-CNRS, Santiago (Chile); Departamento de Geofisica, Universidad de Chile, Santiago (Chile))
2011-07-15
When constraining surface emissions of air pollutants using inverse modelling one often encounters spurious corrections to the inventory at places where emissions and observations are colocated, referred to here as the colocalization problem. Several approaches have been used to deal with this problem: coarsening the spatial resolution of emissions; adding spatial correlations to the covariance matrices; adding constraints on the spatial derivatives into the functional being minimized; and multiplying the emission error covariance matrix by weighting factors. Intercomparison of methods for a carbon monoxide inversion over a city shows that even though all methods diminish the colocalization problem and produce similar general patterns, detailed information can greatly change according to the method used ranging from smooth, isotropic and short range modifications to not so smooth, non-isotropic and long range modifications. Poisson (non-Gaussian) and Gaussian assumptions both show these patterns, but for the Poisson case the emissions are naturally restricted to be positive and changes are given by means of multiplicative correction factors, producing results closer to the true nature of emission errors. Finally, we propose and test a new two-step, two-scale, fully Bayesian approach that deals with the colocalization problem and can be implemented for any prior density distribution
A predator-prey system with stage-structure for predator and nonlocal delay
DEFF Research Database (Denmark)
Lin, Z.G.; Pedersen, Michael; Zhang, Lai
2010-01-01
This paper deals with the behavior of solutions to the reaction-diffusion system under homogeneous Neumann boundary condition, which describes a prey-predator model with nonlocal delay. Sufficient conditions for the global stability of each equilibrium are derived by the Lyapunov functional...... and the results show that the introduction of stage-structure into predator positively affects the coexistence of prey and predator. Numerical simulations are performed to illustrate the results....
Lie symmetries of the shigesada-Kawasaki-Teramoto system
Cherniha, Roman; Davydovych, Vasyl'; Muzyka, Liliia
2017-04-01
The Shigesada-Kawasaki-Teramoto system, which consists of two reaction-diffusion equations with variable cross-diffusion and quadratic nonlinearities, is considered. The system is the most important case of the biologically motivated model proposed by Shigesada et al. (J. Theor. Biol.79(1979) 83-99). A complete description of Lie symmetries for this system is derived. It is proved that the Shigesada-Kawasaki-Teramoto system admits a wide range of different Lie symmetries depending on coefficient values. In particular, the Lie symmetry operators with highly unusual structure are unveiled and applied for finding exact solutions of the relevant nonlinear system with cross-diffusion.
Mathematical aspects of pattern formation in biological systems
Wei, Juncheng
2013-01-01
This monograph is concerned with the mathematical analysis of patterns which are encountered in biological systems. It summarises, expands and relates results obtained in the field during the last fifteen years. It also links the results to biological applications and highlights their relevance to phenomena in nature. Of particular concern are large-amplitude patterns far from equilibrium in biologically relevant models.The approach adopted in the monograph is based on the following paradigms:â€¢ Examine the existence of spiky steady states in reaction-diffusion systems and select as observabl
Information Processing Capacity of Dynamical Systems
Dambre, Joni; Verstraeten, David; Schrauwen, Benjamin; Massar, Serge
2012-07-01
Many dynamical systems, both natural and artificial, are stimulated by time dependent external signals, somehow processing the information contained therein. We demonstrate how to quantify the different modes in which information can be processed by such systems and combine them to define the computational capacity of a dynamical system. This is bounded by the number of linearly independent state variables of the dynamical system, equaling it if the system obeys the fading memory condition. It can be interpreted as the total number of linearly independent functions of its stimuli the system can compute. Our theory combines concepts from machine learning (reservoir computing), system modeling, stochastic processes, and functional analysis. We illustrate our theory by numerical simulations for the logistic map, a recurrent neural network, and a two-dimensional reaction diffusion system, uncovering universal trade-offs between the non-linearity of the computation and the system's short-term memory.
Information Processing Capacity of Dynamical Systems
Dambre, Joni; Verstraeten, David; Schrauwen, Benjamin; Massar, Serge
2012-01-01
Many dynamical systems, both natural and artificial, are stimulated by time dependent external signals, somehow processing the information contained therein. We demonstrate how to quantify the different modes in which information can be processed by such systems and combine them to define the computational capacity of a dynamical system. This is bounded by the number of linearly independent state variables of the dynamical system, equaling it if the system obeys the fading memory condition. It can be interpreted as the total number of linearly independent functions of its stimuli the system can compute. Our theory combines concepts from machine learning (reservoir computing), system modeling, stochastic processes, and functional analysis. We illustrate our theory by numerical simulations for the logistic map, a recurrent neural network, and a two-dimensional reaction diffusion system, uncovering universal trade-offs between the non-linearity of the computation and the system's short-term memory. PMID:22816038
International Nuclear Information System (INIS)
Krumenacker, Laurent
2015-01-01
During the life's cycle of a hydraulic installation, the occurrence of cavitation can cause significant damages on the material's surface. The quantification of the cavitation intensity in different geometry can be useful to get better designs for new installations, but also to improve the operating and to optimize maintenance of existing equipments. The development of universal laws of similarity from experiments is difficult due to the large number of parameters governing cavitating flows. With the increase of computational performance, numerical simulations offer the opportunity to study this phenomenon in various geometries. The main difficulty of this approach is the scale's difference existing between the numerical simulations U-RANS used to calculate the cavitating flow and mechanisms of bubble's collapse held responsible for damages on the solid. The proposed method in this thesis is based on a post-treatment of the U-RANS simulations to characterize a distribution of bubbles and to simulate their behavior at lower spatial and temporal scales. Our first objective is to make explicit a system of equations corresponding to phenomena occurring locally in the two-phase flow. This work leads to the development of mixture variables taking into account the presence of non-condensable gases in the fluid. Assumptions are taken to make the system, after using the Reynolds averaging procedure, equivalent to those, using a homogeneous approach, implemented in the unsteady cavitating flows solvers previously developed in the laboratory. The characterization of bubbles made by this post-treatment takes into account both the surface tension and the presence of non-condensable gases. The development of a solver for the simulation of the dynamic of a bubble cloud is started. It aims to take into account both the interactions between bubbles and non-spherical deformations with a potential method. First results of these simulations are presented and small
Froger, J.-L.; Remy, D.; Bonvalot, S.; Legrand, D.
2007-03-01
Model of the area, we propose that the deep source have a magmatic origin while the shallow source is most likely related to hydrothermal fluids. In our interpretation, the on-going deformation processes observed at Lastarria-Cordon del Azufre volcanic complex could represent an evolving pre-caldera silicic system. Further field geological and geophysical investigations will be required to confirm these hypotheses and refine the proposed model, mostly based on satellite observations.
Two scale high gain adaptive control
Polderman, Jan W.; Mareels, I.M.Y.; Mareels, Iven
2004-01-01
Simple adaptive controllers based on high gain output feedback suffer a lack of robustness with respect to bounded disturbances. Existing modifications achieve boundedness of all solutions but introduce solutions that, even in the absence of disturbances, do not achieve regulation. In this paper a
Complex and adaptive dynamical systems a primer
Gros, Claudius
2015-01-01
This primer offers readers an introduction to the central concepts that form our modern understanding of complex and emergent behavior, together with detailed coverage of accompanying mathematical methods. All calculations are presented step by step and are easy to follow. This new fourth edition has been fully reorganized and includes new chapters, figures and exercises. The core aspects of modern complex system sciences are presented in the first chapters, covering network theory, dynamical systems, bifurcation and catastrophe theory, chaos and adaptive processes, together with the principle of self-organization in reaction-diffusion systems and social animals. Modern information theoretical principles are treated in further chapters, together with the concept of self-organized criticality, gene regulation networks, hypercycles and coevolutionary avalanches, synchronization phenomena, absorbing phase transitions and the cognitive system approach to the brain. Technical course prerequisites are the standard ...
Mathematical aspects of reacting and diffusing systems
Fife, Paul C
1979-01-01
Modeling and analyzing the dynamics of chemical mixtures by means of differ- tial equations is one of the prime concerns of chemical engineering theorists. These equations often take the form of systems of nonlinear parabolic partial d- ferential equations, or reaction-diffusion equations, when there is diffusion of chemical substances involved. A good overview of this endeavor can be had by re- ing the two volumes by R. Aris (1975), who himself was one of the main contributors to the theory. Enthusiasm for the models developed has been shared by parts of the mathematical community, and these models have, in fact, provided motivation for some beautiful mathematical results. There are analogies between chemical reactors and certain biological systems. One such analogy is rather obvious: a single living organism is a dynamic structure built of molecules and ions, many of which react and diffuse. Other analogies are less obvious; for example, the electric potential of a membrane can diffuse like a chemical, and ...
Di Francesco, Marco
2011-04-01
The dependence of tumor on essential nutrients is known to be crucial for its evolution and has become one of the targets for medical therapies. Based on this fact a reaction-diffusion system with chemotaxis term and nutrient-based growth of tumors is presented. The formulation of the model considers also an influence of tumor and pharmacological factors on nutrient concentration. In the paper, convergence of solutions to constant, stationary states in the one-dimensional case for small perturbation of the equilibria is investigated. The nonlinear stability results are obtained by means of the classical symmetrization method and energy Sobolev estimates. © 2010 Elsevier Ltd.
On a nonlocal system for vegetation in drylands.
Alfaro, Matthieu; Izuhara, Hirofumi; Mimura, Masayasu
2018-02-10
Several mathematical models are proposed to understand spatial patchy vegetation patterns arising in drylands. In this paper, we consider the system with nonlocal dispersal of plants (through a redistribution kernel for seeds) proposed by Pueyo et al. (Oikos 117:1522-1532, 2008) as a model for vegetation in water-limited ecosystems. It consists in two reaction diffusion equations for surface water and soil water, combined with an integro-differential equation for plants. For this system, under suitable assumptions, we prove well-posedness using the Schauder fixed point theorem. In addition, we consider the stationary problem from the viewpoint of vegetated pattern formation, and show a transition of vegetation patterns when parameter values (rainfall, seed dispersal range, seed germination rate) in the system vary. The influence of the shape of the redistribution kernel is also discussed.
Three-valued logic gates in reaction-diffusion excitable media
International Nuclear Information System (INIS)
Motoike, Ikuko N.; Adamatzky, Andrew
2005-01-01
It is well established now that excitable media are capable of implementing of a wide range of computational operations, from image processing to logical computation to navigation of robots. The findings published so far in the field of logical computation were concerned solely with realization of boolean logic. This imposed somewhat artificial limitations on a suitability of excitable media for logical reasoning and restricted a range of possible applications of these non-classical computational devices in the field of artificial intelligence. In the paper we go beyond binary logic and show how to implement three-valued logical operations in toy models of geometrically constrained excitable media. We realize several types of logical gates, including Lukasiewicz conjunction and disjunction, and Sobocinski conjunction in cellular automata and FitzHugh-Nagumo models of T-shaped excitable media
Reaction-diffusion path planning in a hybrid chemical and cellular-automaton processor
International Nuclear Information System (INIS)
Adamatzky, Andrew; Lacy Costello, Benjamin de
2003-01-01
To find the shortest collision-free path in a room containing obstacles we designed a chemical processor and coupled it with a cellular-automaton processor. In the chemical processor obstacles are represented by sites of high concentration of potassium iodide and a planar substrate is saturated with palladium chloride. Potassium iodide diffuses into the substrate and reacts with palladium chloride. A dark coloured precipitate of palladium iodide is formed almost everywhere except sites where two or more diffusion wavefronts collide. The less coloured sites are situated at the furthest distance from obstacles. Thus, the chemical processor develops a repulsive field, generated by obstacles. A snapshot of the chemical processor is inputted to a cellular automaton. The automaton behaves like a discrete excitable media; also, every cell of the automaton is supplied with a pointer that shows an origin of the cell's excitation. The excitation spreads along the cells corresponding to precipitate depleted sites of the chemical processor. When the destination-site is excited, waves travel on the lattice and update the orientations of the pointers. Thus, the automaton constructs a spanning tree, made of pointers, that guides a traveler towards the destination point. Thus, the automaton medium generates an attractive field and combination of this attractive field with the repulsive field, generated by the chemical processor, provides us with a solution of the collision-free path problem
Spatially explicit control of invasive species using a reaction-diffusion model
Bonneau, Mathieu; Johnson, Fred A.; Romagosa, Christina M.
2016-01-01
Invasive species, which can be responsible for severe economic and environmental damages, must often be managed over a wide area with limited resources, and the optimal allocation of effort in space and time can be challenging. If the spatial range of the invasive species is large, control actions might be applied only on some parcels of land, for example because of property type, accessibility, or limited human resources. Selecting the locations for control is critical and can significantly impact management efficiency. To help make decisions concerning the spatial allocation of control actions, we propose a simulation based approach, where the spatial distribution of the invader is approximated by a reaction–diffusion model. We extend the classic Fisher equation to incorporate the effect of control both in the diffusion and local growth of the invader. The modified reaction–diffusion model that we propose accounts for the effect of control, not only on the controlled locations, but on neighboring locations, which are based on the theoretical speed of the invasion front. Based on simulated examples, we show the superiority of our model compared to the state-of-the-art approach. We illustrate the use of this model for the management of Burmese pythons in the Everglades (Florida, USA). Thanks to the generality of the modified reaction–diffusion model, this framework is potentially suitable for a wide class of management problems and provides a tool for managers to predict the effects of different management strategies.
Numerical Methods for Reaction-Diffusion Problems with Non-Differentiable Kinetics.
1986-11-07
MATHENATIC . A K AZIZ ET AL. UNCLASSIFIED 67 NOV 86 UMBC-MRR-86-2 AFOSR-TR-B?-1636 F/G 12/1 N U. 2 5 1*1 2 AD-A185 405 . FILE REPORT DOCUMENTATION PAGE Is...us in computations . It is of interest to note that the solution Gh of (4.1) does not have a discrete dead core in the sense that ui,j 0 0 at any point...the origin. In this case, the error in the computations below can be measured exactly. In other cases, the true solution is replaced by an
Energy Technology Data Exchange (ETDEWEB)
De Oliveira Santos, F. [Grand Accelerateur National d' Ions Lourds, UMR 6415, 14 - Caen (France)
2007-07-01
Nuclear reactions can occur at low kinetic energy. Low-energy reactions are characterized by a strong dependence on the structure of the compound nucleus. It turns out that it is possible to study the nuclear structure by measuring these reactions. In this course, three types of reactions are treated: Resonant Elastic Scattering (such as N{sup 14}(p,p)N{sup 14}), Inelastic Scattering (such as N{sup 14}(p,p')N{sup 14*}) and Astrophysical reactions (such as N{sup 14}(p,{gamma})O{sup 15}). (author)
International Nuclear Information System (INIS)
Musho, M.K.; Kozak, J.J.
1984-01-01
A method is presented for calculating exactly the relative width (sigma 2 )/sup 1/2// , the skewness γ 1 , and the kurtosis γ 2 characterizing the probability distribution function for three random-walk models of diffusion-controlled processes. For processes in which a diffusing coreactant A reacts irreversibly with a target molecule B situated at a reaction center, three models are considered. The first is the traditional one of an unbiased, nearest-neighbor random walk on a d-dimensional periodic/confining lattice with traps; the second involves the consideration of unbiased, non-nearest-neigh bor (i.e., variable-step length) walks on the same d-dimensional lattice; and, the third deals with the case of a biased, nearest-neighbor walk on a d-dimensional lattice (wherein a walker experiences a potential centered at the deep trap site of the lattice). Our method, which has been described in detail elsewhere [P.A. Politowicz and J. J. Kozak, Phys. Rev. B 28, 5549 (1983)] is based on the use of group theoretic arguments within the framework of the theory of finite Markov processes
Hydrostatics and dynamical large deviations for a reaction-diffusion model
Landim, Claudio; Tsunoda, Kenkichi
2015-01-01
We consider the superposition of a symmetric simple exclusion dynamics, speeded-up in time, with a spin-flip dynamics in a one-dimensional interval with periodic boundary conditions. We prove the hydrostatics and the dynamical large deviation principle.
Reaction-Diffusion Degradation Model for Delayed Erosion of Cross-Linked Polyanhydride Biomaterials
Domanskyi, Sergii; Poetz, Katie L.; Shipp, Devon A.; Privman, Vladimir
2015-01-01
We develop a theoretical model to explain the long induction interval of water intake that precedes the onset of erosion due to degradation caused by hydrolysis in the recently synthesized and studied cross-linked polyanhydrides. Various kinetic mechanisms are incorporated in the model in an attempt to explain the experimental data for the mass loss profile. Our key finding is that the observed long induction interval is attributable to the nonlinear dependence of the degradation rate constan...
Identifiability for the pointwise source detection in Fisher’s reaction-diffusion equation
Ben Belgacem, Faker
2012-06-01
We are interested in the detection of a pointwise source in a class of semi-linear advection-diffusion-reaction equations of Fisher type. The source is determined by its location, which may be steady or unsteady, and its time-dependent intensity. Observations recorded at a couple of points are the available data. One observing station is located upstream of the source and the other downstream. This is a severely ill-posed nonlinear inverse problem. In this paper, we pursue an identifiability result. The process we follow has been developed earlier for the linear model and may be sharpened to operate for the semi-linear equation. It is based on the uniqueness for a parabolic (semi-linear) sideways problem, which is obtained by a suitable unique continuation theorem. We state a maximum principle that turns out to be necessary for our proof. The identifiability is finally obtained for a stationary or a moving source. Many applications may be found in biology, chemical physiology or environmental science. The problem we deal with is the detection of pointwise organic pollution sources in rivers and channels. The basic equation to consider is the one-dimensional biochemical oxygen demand equation, with a nonlinear power growth inhibitor and/or the Michaelis-Menten reaction coefficient.
Molecular finite-size effects in stochastic models of equilibrium chemical systems.
Cianci, Claudia; Smith, Stephen; Grima, Ramon
2016-02-28
The reaction-diffusion master equation (RDME) is a standard modelling approach for understanding stochastic and spatial chemical kinetics. An inherent assumption is that molecules are point-like. Here, we introduce the excluded volume reaction-diffusion master equation (vRDME) which takes into account volume exclusion effects on stochastic kinetics due to a finite molecular radius. We obtain an exact closed form solution of the RDME and of the vRDME for a general chemical system in equilibrium conditions. The difference between the two solutions increases with the ratio of molecular diameter to the compartment length scale. We show that an increase in the fraction of excluded space can (i) lead to deviations from the classical inverse square root law for the noise-strength, (ii) flip the skewness of the probability distribution from right to left-skewed, (iii) shift the equilibrium of bimolecular reactions so that more product molecules are formed, and (iv) strongly modulate the Fano factors and coefficients of variation. These volume exclusion effects are found to be particularly pronounced for chemical species not involved in chemical conservation laws. Finally, we show that statistics obtained using the vRDME are in good agreement with those obtained from Brownian dynamics with excluded volume interactions.
Uniform attractors for non-autonomous random dynamical systems
Cui, Hongyong; Langa, José A.
2017-07-01
This paper is devoted to establishing a (random) uniform attractor theory for non-autonomous random dynamical systems (NRDS). The uniform attractor is defined as the minimal compact uniformly pullback attracting random set. Nevertheless, the uniform pullback attraction in fact implies a uniform forward attraction in probability, and implies also an almost uniform pullback attraction for discrete time-sequences. Though no invariance is required by definition, the uniform attractor can have a negative semi-invariance under certain conditions. Several existence criteria for uniform attractors are given, and the relationship between uniform and cocycle attractors is carefully studied. To overcome the measurability difficulty, the symbol space is required to be Polish which is shown fulfilled by the hulls of Llocp (R ;Lr) functions, p , r > 1. Moreover, uniform attractors for continuous NRDS are shown determined by uniformly attracting deterministic compact sets. Finally, the uniform attractor for a stochastic reaction-diffusion equation with translation-bounded external forcing are studied as applications.
Barker, Blake; Jung, Soyeun; Zumbrun, Kevin
2018-03-01
Turing patterns on unbounded domains have been widely studied in systems of reaction-diffusion equations. However, up to now, they have not been studied for systems of conservation laws. Here, we (i) derive conditions for Turing instability in conservation laws and (ii) use these conditions to find families of periodic solutions bifurcating from uniform states, numerically continuing these families into the large-amplitude regime. For the examples studied, numerical stability analysis suggests that stable periodic waves can emerge either from supercritical Turing bifurcations or, via secondary bifurcation as amplitude is increased, from subcritical Turing bifurcations. This answers in the affirmative a question of Oh-Zumbrun whether stable periodic solutions of conservation laws can occur. Determination of a full small-amplitude stability diagram - specifically, determination of rigorous Eckhaus-type stability conditions - remains an interesting open problem.
Directory of Open Access Journals (Sweden)
Wenzhen Gan
2013-01-01
Full Text Available This paper is concerned with the asymptotical behavior of solutions to the reaction-diffusion system under homogeneous Neumann boundary condition. By taking food ingestion and species' moving into account, the model is further coupled with Michaelis-Menten type functional response and nonlocal delay. Sufficient conditions are derived for the global stability of the positive steady state and the semitrivial steady state of the proposed problem by using the Lyapunov functional. Our results show that intraspecific competition benefits the coexistence of prey and predator. Furthermore, the introduction of Michaelis-Menten type functional response positively affects the coexistence of prey and predator, and the nonlocal delay is harmless for stabilities of all nonnegative steady states of the system. Numerical simulations are carried out to illustrate the main results.
Origin of the two scales of wind ripples on Mars
Lapotre, M. G. A.; Ewing, R. C.; Lamb, M. P.; Fischer, W. W.; Grotzinger, J. P.; Rubin, D. M.; Lewis, K. W.; Ballard, M.; Day, M. D.; Gupta, S.; Banham, S.; Bridges, N.; Des Marais, D. J.; Fraeman, A. A.; Grant, J. A., III; Ming, D. W.; Mischna, M.; Rice, M. S.; Sumner, D. Y.; Vasavada, A. R.; Yingst, R. A.
2016-12-01
Earth's sandy deserts host two main types of bedforms - decimeter-scale ripples and larger dunes. Years of orbital observations on Mars also confirmed the existence of two modes of active eolian bedforms - meter-scale ripples, and dunes. By analogy to terrestrial ripples, which are thought to form from a grain mechanism, it was hypothesized that large martian ripples also formed from grain impacts, but spaced further apart due to elongated saltation trajectories from the lower martian gravity and different atmospheric properties. However, the Curiosity rover recently documented the coexistence of three scales of bedforms in Gale crater. Because a grain impact mechanism cannot readily explain two distinct and coeval ripple modes in similar sand sizes, a new mechanism seems to be required to explain one of the scales of ripples. Small ripples are most similar to Earth's impact ripples, with straight crests and subdued profiles. In contrast, large martian ripples are sinuous and asymmetric, with lee slopes dominated by grain flows and grainfall deposits. Thus, large martian ripples resemble current ripples formed underwater on Earth, suggesting that they may form from a fluid-drag mechanism. To test this hypothesis, we develop a scaling relation to predict the spacing of fluid-drag ripples from an extensive flume data compilation. The size of large martian ripples is predicted by our scaling relation when adjusted for martian atmospheric properties. Specifically, we propose that the wavelength of martian wind-drag ripples arises from the high kinematic viscosity of the low-density atmosphere. Because fluid density controls drag-ripple size, our scaling relation can help constrain paleoatmospheric density from wind-drag ripple stratification.
Two-scale analysis of intermittency in fully developed turbulence
Energy Technology Data Exchange (ETDEWEB)
Badii, R.; Talkner, P. [Paul Scherrer Inst. (PSI), Villigen (Switzerland)
1999-08-01
A self-affinity test for turbulent time series is applied to experimental data for the estimation of intermittency exponents. The method employs exact relations satisfied by joint expectations of observables computed across two different length scales. One of these constitutes a verification tool for the existence and the extent of the inertial range. (author) 2 figs., 13 refs.
Numerical modeling of aluminium foam on two scales
Czech Academy of Sciences Publication Activity Database
Němeček, J.; Denk, F.; Zlámal, Petr
2015-01-01
Roč. 267, September (2015), s. 506-516 ISSN 0096-3003 R&D Projects: GA ČR(CZ) GAP105/12/0824 Institutional support: RVO:68378297 Keywords : closed-cell aluminium foam * Alporas * multiscale modeling * homogenization * FFT * finite element modeling Subject RIV: JI - Composite Materials Impact factor: 1.345, year: 2015 http://www.sciencedirect.com/science/article/pii/S0096300315001162
Conformal invariance in conditioned stochastic particle systems
Schütz, Gunter M.
2017-08-01
We consider space-time correlations in generic one-dimensional stochastic interacting particle systems with short-range interactions that undergo a fluctuation with an atypically activity of particle jumps or reactions or spin flips. We briefly review the approach in the framework of the quantum Hamiltonian formalism and present examples where the dynamics during such large fluctuations is governed not by the typical stationary dynamics, but by ballistic universality classes with dynamical exponent z=1 that are described unitary conformally invariant field theories with central charge c. For reaction-diffusion and spin flip dynamics we identify critical points (a) in the Ising universality class with c=1/2 , and (b) in the universality class of the three-states Potts model with c=4/5 . For the Ising universality class we obtain a universal scaling form for the generating function of cumulants of the jump activity. For repulsive driven diffusive systems with one conservation law the regime of an atypically high current or hopping activity is generically conformally invariant with central charge c=1 .
Drawert, Brian; Trogdon, Michael; Toor, Salman; Petzold, Linda; Hellander, Andreas
2017-01-01
Computational experiments using spatial stochastic simulations have led to important new biological insights, but they require specialized tools and a complex software stack, as well as large and scalable compute and data analysis resources due to the large computational cost associated with Monte Carlo computational workflows. The complexity of setting up and managing a large-scale distributed computation environment to support productive and reproducible modeling can be prohibitive for practitioners in systems biology. This results in a barrier to the adoption of spatial stochastic simulation tools, effectively limiting the type of biological questions addressed by quantitative modeling. In this paper, we present PyURDME, a new, user-friendly spatial modeling and simulation package, and MOLNs, a cloud computing appliance for distributed simulation of stochastic reaction-diffusion models. MOLNs is based on IPython and provides an interactive programming platform for development of sharable and reproducible distributed parallel computational experiments. PMID:28190948
International Nuclear Information System (INIS)
Anon.
1980-01-01
Papers in this session describe the concept of mined geologic disposal system and methods for ensuring that the system, when developed, will meet all technical requirements. Also presented in the session are analyses of system parameters, such as cost and nuclear criticality potential, as well as a technical analysis of a requirement that the system permit retrieval of the waste for some period of time. The final paper discusses studies under way to investigate technical alternatives or complements to the mined geologic disposal system. Titles of the presented papers are: (1) Waste Isolation System; (2) Waste Isolation Economics; (3) BWIP Technical Baseline; (4) Criticality Considerations in Geologic Disposal of High-Level Waste; (5) Retrieving Nuclear Wastes from Repository; (6) NWTS Programs for the Evaluation of Technical Alternatives or Complements to Mined Geologic Repositories - Purpose and Objectives
Directory of Open Access Journals (Sweden)
Alexander Leonessa
2000-01-01
Full Text Available A nonlinear robust control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving nominal system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear robust control strategy is developed that robustly stabilizes a given nonlinear system over a prescribed range of system uncertainty by robustly stabilizing a collection of nonlinear controlled uncertain subsystems. The robust switching nonlinear controller architecture is designed based on a generalized (lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized nominal system equilibria. The proposed framework robustly stabilizes a compact positively invariant set of a given nonlinear uncertain dynamical system with structured parametric uncertainty. Finally, the efficacy of the proposed approach is demonstrated on a jet engine propulsion control problem with uncertain pressure-flow map data.
A review and guidance for pattern selection in spatiotemporal system
Wang, Chunni; Ma, Jun
2018-03-01
Pattern estimation and selection in media can give important clues to understand the collective response to external stimulus by detecting the observable variables. Both reaction-diffusion systems (RDs) and neuronal networks can be treated as multi-agent systems from molecular level, intrinsic cooperation, competition. An external stimulus or attack can cause collapse of spatial order and distribution, while appropriate noise can enhance the consensus in the spatiotemporal systems. Pattern formation and synchronization stability can bridge isolated oscillators and the network by coupling these nodes with appropriate connection types. As a result, the dynamical behaviors can be detected and discussed by developing different spatial patterns and realizing network synchronization. Indeed, the collective response of network and multi-agent system depends on the local kinetics of nodes and cells. It is better to know the standard bifurcation analysis and stability control schemes before dealing with network problems. In this review, dynamics discussion and synchronization control on low-dimensional systems, pattern formation and synchronization stability on network, wave stability in RDs and neuronal network are summarized. Finally, possible guidance is presented when some physical effects such as polarization field and electromagnetic induction are considered.
International Nuclear Information System (INIS)
Hormuth II, David A; Weis, Jared A; Barnes, Stephanie L; Miga, Michael I; Yankeelov, Thomas E; Rericha, Erin C; Quaranta, Vito
2015-01-01
Reaction–diffusion models have been widely used to model glioma growth. However, it has not been shown how accurately this model can predict future tumor status using model parameters (i.e., tumor cell diffusion and proliferation) estimated from quantitative in vivo imaging data. To this end, we used in silico studies to develop the methods needed to accurately estimate tumor specific reaction–diffusion model parameters, and then tested the accuracy with which these parameters can predict future growth. The analogous study was then performed in a murine model of glioma growth. The parameter estimation approach was tested using an in silico tumor ‘grown’ for ten days as dictated by the reaction–diffusion equation. Parameters were estimated from early time points and used to predict subsequent growth. Prediction accuracy was assessed at global (total volume and Dice value) and local (concordance correlation coefficient, CCC) levels. Guided by the in silico study, rats (n = 9) with C6 gliomas, imaged with diffusion weighted magnetic resonance imaging, were used to evaluate the model’s accuracy for predicting in vivo tumor growth. The in silico study resulted in low global (tumor volume error <8.8%, Dice >0.92) and local (CCC values >0.80) level errors for predictions up to six days into the future. The in vivo study showed higher global (tumor volume error >11.7%, Dice <0.81) and higher local (CCC <0.33) level errors over the same time period. The in silico study shows that model parameters can be accurately estimated and used to accurately predict future tumor growth at both the global and local scale. However, the poor predictive accuracy in the experimental study suggests the reaction–diffusion equation is an incomplete description of in vivo C6 glioma biology and may require further modeling of intra-tumor interactions including segmentation of (for example) proliferative and necrotic regions. (paper)
Khan, Easir A.
2010-12-15
Core-shell micromembrane reactors are a novel class of materials where a catalyst and a shape-selective membrane are synergistically housed in a single particle. In this work, we report the synthesis of micrometer -sized core-shell particles containing a catalyst core and a thin permselective zeolite shell and their application as a micromembrane reactor for the selective hydrogenation of the 1-hexene and 3,3-dimethyl-1-butene isomers. The bare catalyst, which is made from porous silica loaded with catalytically active nickel, showed no reactant selectivity between hexene isomers, but the core-shell particles showed high selectivities up to 300 for a 1-hexene conversion of 90%. © 2010 American Chemical Society.
Directory of Open Access Journals (Sweden)
Stefan Kindermann
2015-01-01
Full Text Available Fluorescence recovery after photobleaching (FRAP is a widely used measurement technique to determine the mobility of fluorescent molecules within living cells. While the experimental setup and protocol for FRAP experiments are usually fixed, data (preprocessing represents an important issue. The aim of this paper is twofold. First, we formulate and solve the problem of relevant FRAP data selection. The theoretical findings are illustrated by the comparison of the results of parameter identification when the full data set was used and the case when the irrelevant data set (data with negligible impact on the confidence interval of the estimated parameters was removed from the data space. Second, we analyze and compare two approaches of FRAP data processing. Our proposition, surprisingly for the FRAP community, claims that the data set represented by the FRAP recovery curves in form of a time series (integrated data approach commonly used by the FRAP community leads to a larger confidence interval compared to the full (spatiotemporal data approach.
How to build master equations for complex systems
Breuer, Heinz-Peter; Petruccione, Francesco
1995-12-01
Typical complex systems, e. g., complex chemical reactions, reaction-diffusion systems, and turbulent fluids are described on a macroscopic level, that is, neglecting fluctuations, with the help of deterministic equations for corresponding variables. In this article it is shown on a phenomenological level, that these systems can be described in terms of integer- or real-valued Markov processes as well, which are governed by master equations. The latter are constructed such that the macroscopic law and the fluctuations around it are reproduced correctly. Stochastic processes defined through master equations can easily be simulated. The efficiency, the stability and the parallelization of the algorithms for stochastic simulations are discussed for some examples. In the last part of the paper it is shown that the same phenomenological approach can be successfully applied to open quantum systems. The wave function is assumed to be a complex valued stochastic process in Hilbert space and the quantum master equation for the statistical operator is regarded as the equation of motion for the two-point correlation function.
Nonlinear Dynamics, Chaotic and Complex Systems
Infeld, E.; Zelazny, R.; Galkowski, A.
2011-04-01
Part I. Dynamic Systems Bifurcation Theory and Chaos: 1. Chaos in random dynamical systems V. M. Gunldach; 2. Controlling chaos using embedded unstable periodic orbits: the problem of optimal periodic orbits B. R. Hunt and E. Ott; 3. Chaotic tracer dynamics in open hydrodynamical flows G. Karolyi, A. Pentek, T. Tel and Z. Toroczkai; 4. Homoclinic chaos L. P. Shilnikov; Part II. Spatially Extended Systems: 5. Hydrodynamics of relativistic probability flows I. Bialynicki-Birula; 6. Waves in ionic reaction-diffusion-migration systems P. Hasal, V. Nevoral, I. Schreiber, H. Sevcikova, D. Snita, and M. Marek; 7. Anomalous scaling in turbulence: a field theoretical approach V. Lvov and I. Procaccia; 8. Abelian sandpile cellular automata M. Markosova; 9. Transport in an incompletely chaotic magnetic field F. Spineanu; Part III. Dynamical Chaos Quantum Physics and Foundations Of Statistical Mechanics: 10. Non-equilibrium statistical mechanics and ergodic theory L. A. Bunimovich; 11. Pseudochaos in statistical physics B. Chirikov; 12. Foundations of non-equilibrium statistical mechanics J. P. Dougherty; 13. Thermomechanical particle simulations W. G. Hoover, H. A. Posch, C. H. Dellago, O. Kum, C. G. Hoover, A. J. De Groot and B. L. Holian; 14. Quantum dynamics on a Markov background and irreversibility B. Pavlov; 15. Time chaos and the laws of nature I. Prigogine and D. J. Driebe; 16. Evolutionary Q and cognitive systems: dynamic entropies and predictability of evolutionary processes W. Ebeling; 17. Spatiotemporal chaos information processing in neural networks H. Szu; 18. Phase transitions and learning in neural networks C. Van den Broeck; 19. Synthesis of chaos A. Vanecek and S. Celikovsky; 20. Computational complexity of continuous problems H. Wozniakowski; Part IV. Complex Systems As An Interface Between Natural Sciences and Environmental Social and Economic Sciences: 21. Stochastic differential geometry in finance studies V. G. Makhankov; Part V. Conference Banquet
Directory of Open Access Journals (Sweden)
Patrick L. Brockett
1978-01-01
Full Text Available Suppose S={{Xnj, j=1,2,…,kn}} is an infinitesimal system of random variables whose centered sums converge in law to a (necessarily infinitely divisible distribution with Levy representation determined by the triple (γ,σ2,M. If {Yj, j=1,2,…} are independent indentically distributed random variables independent of S, then the system S′={{YjXnj,j=1,2,…,kn}} is obtained by randomizing the scale parameters in S according to the distribution of Y1. We give sufficient conditions on the distribution of Y in terms of an index of convergence of S, to insure that centered sums from S′ be convergent. If such sums converge to a distribution determined by (γ′,(σ′2,Λ, then the exact relationship between (γ,σ2,M and (γ′,(σ′2,Λ is established. Also investigated is when limit distributions from S and S′ are of the same type, and conditions insuring products of random variables belong to the domain of attraction of a stable law.
Directory of Open Access Journals (Sweden)
K. Swarnalatha
2013-01-01
Full Text Available Risk analysis of urban aquatic systems due to heavy metals turns significant due to their peculiar properties viz. persis tence, non-degradab ility, toxicity, and accumulation. Akkulam Veli (AV, an urba n tropical lake in south India is subjected to various environmental stresses due to multiple waste discharge, sand mining, developmental activities, tour ism related activitie s etc. Hence, a comprehensive approach is adopted for risk assessment using modified degree of contamination factor, toxicity units based on numerical sediment quality guidelines (SQGs, and potentialecological risk indices. The study revealed the presence of toxic metals such as Cr, C d, Pb and As and the lake is rated under ‘low ecological risk’ category.
Computational study of patterns in simple nonequilibrium systems
International Nuclear Information System (INIS)
Barach, J.P.
1997-01-01
We present computational studies of a two component reaction diffusion system of the Grey and Scott type. The calculation involves a discrete treatment of the diffusion equation and some details of that problem are explained. As the simulation calculation runs over a 200x200 square spatial field ridge like patterns develop if one diffusion coefficient is about twice the size of the other and if the rate parameters are in a narrow range. Pattern development is faster when the reaction rates are larger, within this range. It is shown that for an advancing wave, the lead component has a wider front than the other although in steady state the two components obey a ridge/valley or valley/ridge equilibrium. We investigate ways in which a more complex time dependence could be introduced to the system and display one example of such a possible expansion of the study. A correlation coefficient study shows a modest but distinct difference between our pattern development and a random field. copyright 1997 American Institute of Physics
Reversible and irreversible reaction fronts in two competing reactions system
International Nuclear Information System (INIS)
Sinder, M.; Taitelbaum, H.; Pelleg, J.
2002-01-01
A modeling of the non-equilibrium diffusion phenomena of the impurities in the semiconductors is based on the reaction-diffusion equations for local concentrations of the components. Through this approach a new feature, a reaction front, may be caused by reaction in diffusion profiles of the components. The asymptotic long-time properties of the reaction fronts in the system with initially separated components and two competing reactions: reversible A 1 +B↔C 1 and irreversible A 2 +B→C 2 are studied in this work. It is assumed that the backward constant of the reaction A 1 +B↔C 1 is small. The dynamics of the system is described as a cross-over between the 'irreversible' regime for small times and the 'reversible' regime for large times. It is shown that the 'irreversible' regime is characterized by single reaction zone, in which both reactions occur. The two reaction fronts, reversible A 1 +B↔C 1 and irreversible A 2 +C 1 →A 1 +C 2 appear in the 'reversible' regime. Numerical computing of the mean-field kinetics equations confirms these asymptotic results. The experimental tests of the theoretical predictions relating to the diffusion phenomena in semiconductors are discussed
International Nuclear Information System (INIS)
Kozak, J.J.; Lenoir, P.M.; Musho, M.K.; Tembe, B.L.
1984-01-01
We study in this paper the dynamics induced by models for photochemical water cleavage systems, focusing on the spatial and temporal factors influencing electron transfer and charge separation processes in such systems. The reaction-diffusion theory is formulated in full generality and the consequences explored in a number of spatio-temporal regimes, viz. the spatially homogeneous system in the long-time limit (i.e. the steady state for a well-stirred system), the spatially homogeneous system in evolution, and the spatially inhomogeneous system in evolution (where, in the latter study, we consider electron transfer at the cluster surface to be governed by a rate constant that reflects the localized nature of such processes). The results of numerical simulations are presented for all three cases and used to highlight the importance of heterogeneous environments in enhancing the cage escape yield of charge separated species, and to demonstrate the dependence of the hydrogen yield on the localization of electron-transfer processes in the vicinity of the microcatalyst surface
A Fluid Membrane-Based Soluble Ligand Display System for Live CellAssays
Energy Technology Data Exchange (ETDEWEB)
Nam, Jwa-Min; Nair, Pradeep N.; Neve, Richard M.; Gray, Joe W.; Groves, Jay T.
2005-10-14
Cell communication modulates numerous biological processes including proliferation, apoptosis, motility, invasion and differentiation. Correspondingly, there has been significant interest in the development of surface display strategies for the presentation of signaling molecules to living cells. This effort has primarily focused on naturally surface-bound ligands, such as extracellular matrix components and cell membranes. Soluble ligands (e.g. growth factors and cytokines) play an important role in intercellular communications, and their display in a surface-bound format would be of great utility in the design of array-based live cell assays. Recently, several cell microarray systems that display cDNA, RNAi, or small molecules in a surface array format were proven to be useful in accelerating high-throughput functional genetic studies and screening therapeutic agents. These surface display methods provide a flexible platform for the systematic, combinatorial investigation of genes and small molecules affecting cellular processes and phenotypes of interest. In an analogous sense, it would be an important advance if one could display soluble signaling ligands in a surface assay format that allows for systematic, patterned presentation of soluble ligands to live cells. Such a technique would make it possible to examine cellular phenotypes of interest in a parallel format with soluble signaling ligands as one of the display parameters. Herein we report a ligand-modified fluid supported lipid bilayer (SLB) assay system that can be used to functionally display soluble ligands to cells in situ (Figure 1A). By displaying soluble ligands on a SLB surface, both solution behavior (the ability to become locally enriched by reaction-diffusion processes) and solid behavior (the ability to control the spatial location of the ligands in an open system) could be combined. The method reported herein benefits from the naturally fluid state of the supported membrane, which allows
Hydra, a fruitful model system for 270 years.
Galliot, Brigitte
2012-01-01
The discovery of Hydra regeneration by Abraham Trembley in 1744 promoted much scientific curiosity thanks to his clever design of experimental strategies away from the natural environment. Since then, this little freshwater cnidarian polyp flourished as a potent and fruitful model system. Here, we review some general biological questions that benefitted from Hydra research, such as the nature of embryogenesis, neurogenesis, induction by organizers, sex reversal, symbiosis, aging, feeding behavior, light regulation, multipotency of somatic stem cells, temperature-induced cell death, neuronal transdifferentiation, to cite only a few. To understand how phenotypes arise, theoricists also chose Hydra to model patterning and morphogenetic events, providing helpful concepts such as reaction-diffusion, positional information, and autocatalysis combined with lateral inhibition. Indeed, throughout these past 270 years, scientists used transplantation and grafting experiments, together with tissue, cell and molecular labelings, as well as biochemical procedures, in order to establish the solid foundations of cell and developmental biology. Nowadays, thanks to transgenic, genomic and proteomic tools, Hydra remains a promising model for these fields, but also for addressing novel questions such as evolutionary mechanisms, maintenance of dynamic homeostasis, regulation of stemness, functions of autophagy, cell death, stress response, innate immunity, bioactive compounds in ecosystems, ecotoxicant sensing and science communication.
On the dynamics of a non-local parabolic equation arising from the Gierer-Meinhardt system
Kavallaris, Nikos I.; Suzuki, Takashi
2017-05-01
The purpose of the current paper is to contribute to the comprehension of the dynamics of the shadow system of an activator-inhibitor system known as a Gierer-Meinhardt model. Shadow systems are intended to work as an intermediate step between single equations and reaction-diffusion systems. In the case where the inhibitor’s response to the activator’s growth is rather weak, then the shadow system of the Gierer-Meinhardt model is reduced to a single though non-local equation whose dynamics will be investigated. We mainly focus on the derivation of blow-up results for this non-local equation which can be seen as instability patterns of the shadow system. In particular, a diffusion driven instability (DDI), or Turing instability, in the neighbourhood of a constant stationary solution, which it is destabilised via diffusion-driven blow-up, is obtained. The latter actually indicates the formation of some unstable patterns, whilst some stability results of global-in-time solutions towards non-constant steady states guarantee the occurrence of some stable patterns.
Stochastic Dynamics in Spatially Extended Physical and Biological Systems
Jafarpour, Farshid
In this thesis, I discuss three different problems of stochastic nature in spatially extended systems: (1) a noise induced mechanism for the emergence of biological homochirality in early life self-replicators, (2) the amplification effect of nonnormality on stochastic Turing patterns in reaction diffusion systems, and (3) the velocity statistics of edge dislocations in plastic deformation of crystalline material. In Part I, I present a new model for the origin of homochirality, the observed single-handedness of biological amino acids and sugars, in prebiotic self-replicator. Homochirality has long been attributed to autocatalysis, a frequently assumed precursor for self-replication. However, the stability of homochiral states in deterministic autocatalytic systems relies on cross inhibition of the two chiral states, an unlikely scenario for early life self-replicators. Here, I present a theory for a stochastic individual-level model of autocatalysis due to early life self-replicators. Without chiral inhibition, the racemic state is the global attractor of the deterministic dynamics, but intrinsic multiplicative noise stabilizes the homochiral states, in both well-mixed and spatially-extended systems. I conclude that autocatalysis is a viable mechanism for homochirality, without imposing additional nonlinearities such as chiral inhibition. In Part II, I study the amplification effect of nonnormality on the steady state amplitude of fluctuation-induced Turing patterns. The phenomenon occurs generally in Turing-like pattern forming systems such as reaction-diffusion systems, does not require a large separation of diffusion constant, and yields pattern whose amplitude can be orders of magnitude larger than the fluctuations that cause the patterns. The analytical treatment shows that patterns are amplified due to an interplay between noise, non-orthogonality of eigenvectors of the linear stability matrix, and a separation of time scales, all built-in feature of
Cross-diffusion-induced subharmonic spatial resonances in a predator-prey system
Gambino, G.; Lombardo, M. C.; Sammartino, M.
2018-01-01
In this paper we investigate the complex dynamics originated by a cross-diffusion-induced subharmonic destabilization of the fundamental subcritical Turing mode in a predator-prey reaction-diffusion system. The model we consider consists of a two-species Lotka-Volterra system with linear diffusion and a nonlinear cross-diffusion term in the predator equation. The taxis term in the search strategy of the predator is responsible for the onset of complex dynamics. In fact, our model does not exhibit any Hopf or wave instability, and on the basis of the linear analysis one should only expect stationary patterns; nevertheless, the presence of the nonlinear cross-diffusion term is able to induce a secondary instability: due to a subharmonic spatial resonance, the stationary primary branch bifurcates to an out-of-phase oscillating solution. Noticeably, the strong resonance between the harmonic and the subharmonic is able to generate the oscillating pattern albeit the subharmonic is below criticality. We show that, as the control parameter is varied, the oscillating solution (sub T mode) can undergo a sequence of secondary instabilities, generating a transition toward chaotic dynamics. Finally, we investigate the emergence of sub T -mode solutions on two-dimensional domains: when the fundamental mode describes a square pattern, subharmonic resonance originates oscillating square patterns. In the case of subcritical Turing hexagon solutions, the internal interactions with a subharmonic mode are able to generate the so-called "twinkling-eyes" pattern.
Directory of Open Access Journals (Sweden)
Francesco Rundo
2018-01-01
Full Text Available Physiological signals are widely used to perform medical assessment for monitoring an extensive range of pathologies, usually related to cardio-vascular diseases. Among these, both PhotoPlethysmoGraphy (PPG and Electrocardiography (ECG signals are those more employed. PPG signals are an emerging non-invasive measurement technique used to study blood volume pulsations through the detection and analysis of the back-scattered optical radiation coming from the skin. ECG is the process of recording the electrical activity of the heart over a period of time using electrodes placed on the skin. In the present paper we propose a physiological ECG/PPG “combo” pipeline using an innovative bio-inspired nonlinear system based on a reaction-diffusion mathematical model, implemented by means of the Cellular Neural Network (CNN methodology, to filter PPG signal by assigning a recognition score to the waveforms in the time series. The resulting “clean” PPG signal exempts from distortion and artifacts is used to validate for diagnostic purpose an EGC signal simultaneously detected for a same patient. The multisite combo PPG-ECG system proposed in this work overpasses the limitations of the state of the art in this field providing a reliable system for assessing the above-mentioned physiological parameters and their monitoring over time for robust medical assessment. The proposed system has been validated and the results confirmed the robustness of the proposed approach.
Systems of branching, annihilating, and coalescing particles
Czech Academy of Sciences Publication Activity Database
Athreya, S. R.; Swart, Jan M.
2012-01-01
Roč. 17, č. 80 (2012), s. 1-32 ISSN 1083-6489 R&D Projects: GA ČR GAP201/10/0752 Institutional support: RVO:67985556 Keywords : reaction-diffusion process * branching * coalescence * annihilation * thinning * Poissonization Subject RIV: BA - General Mathematics Impact factor: 0.785, year: 2012 http://library.utia.cas.cz/separaty/2012/SI/swart-0381108.pdf
Energy Technology Data Exchange (ETDEWEB)
Ginting, Victor
2014-03-15
it was demonstrated that a posteriori analyses in general and in particular one that uses adjoint methods can accurately and efficiently compute numerical error estimates and sensitivity for critical Quantities of Interest (QoIs) that depend on a large number of parameters. Activities include: analysis and implementation of several time integration techniques for solving system of ODEs as typically obtained from spatial discretization of PDE systems; multirate integration methods for ordinary differential equations; formulation and analysis of an iterative multi-discretization Galerkin finite element method for multi-scale reaction-diffusion equations; investigation of an inexpensive postprocessing technique to estimate the error of finite element solution of the second-order quasi-linear elliptic problems measured in some global metrics; investigation of an application of the residual-based a posteriori error estimates to symmetric interior penalty discontinuous Galerkin method for solving a class of second order quasi-linear elliptic problems; a posteriori analysis of explicit time integrations for system of linear ordinary differential equations; derivation of accurate a posteriori goal oriented error estimates for a user-defined quantity of interest for two classes of first and second order IMEX schemes for advection-diffusion-reaction problems; Postprocessing finite element solution; and A Bayesian Framework for Uncertain Quantification of Porous Media Flows.
Classical and Quantum Nonlinear Integrable Systems: Theory and Application
International Nuclear Information System (INIS)
Brzezinski, Tomasz
2003-01-01
This is a very interesting collection of introductory and review articles on the theory and applications of classical and quantum integrable systems. The book reviews several integrable systems such as the KdV equation, vertex models, RSOS and IRF models, spin chains, integrable differential equations, discrete systems, Ising, Potts and other lattice models and reaction--diffusion processes, as well as outlining major methods of solving integrable systems. These include Lax pairs, Baecklund and Miura transformations, the inverse scattering method, various types of the Bethe Ansatz, Painleve methods, the dbar method and fusion methods to mention just a few. The book is divided into two parts, each containing five chapters. The first part is devoted to classical integrable systems and introduces the subject through the KdV equation, and then proceeds through Painleve analysis, discrete systems and two-dimensional integrable partial differential equations, to culminate in the review of solvable lattice models in statistical physics, solved through the coordinate and algebraic Bethe Ansatz methods. The second part deals with quantum integrable systems, and begins with an outline of unifying approaches to quantum, statistical, ultralocal and non-ultralocal systems. The theory and methods of solving quantum integrable spin chains are then described. Recent developments in applying Bethe Ansatz methods in condensed matter physics, including superconductivity and nanoscale physics, are reviewed. The book concludes with an introduction to diffusion-reaction processes. Every chapter is devoted to a different subject and is self-contained, and thus can be read separately. A reader interesting in classical methods of solitons, such as the methods of solving the KdV equation, can start from Chapter 1, while a reader interested in the Bethe Ansatz method can immediately proceed to Chapter 5, and so on. Thus the book should appeal and be useful to a wide range of theoretical
Revisiting the Stability of Spatially Heterogeneous Predator-Prey Systems Under Eutrophication.
Farkas, J Z; Morozov, A Yu; Arashkevich, E G; Nikishina, A
2015-10-01
We employ partial integro-differential equations to model trophic interaction in a spatially extended heterogeneous environment. Compared to classical reaction-diffusion models, this framework allows us to more realistically describe the situation where movement of individuals occurs on a faster time scale than on the demographic (population) time scale, and we cannot determine population growth based on local density. However, most of the results reported so far for such systems have only been verified numerically and for a particular choice of model functions, which obviously casts doubts about these findings. In this paper, we analyse a class of integro-differential predator-prey models with a highly mobile predator in a heterogeneous environment, and we reveal the main factors stabilizing such systems. In particular, we explore an ecologically relevant case of interactions in a highly eutrophic environment, where the prey carrying capacity can be formally set to 'infinity'. We investigate two main scenarios: (1) the spatial gradient of the growth rate is due to abiotic factors only, and (2) the local growth rate depends on the global density distribution across the environment (e.g. due to non-local self-shading). For an arbitrary spatial gradient of the prey growth rate, we analytically investigate the possibility of the predator-prey equilibrium in such systems and we explore the conditions of stability of this equilibrium. In particular, we demonstrate that for a Holling type I (linear) functional response, the predator can stabilize the system at low prey density even for an 'unlimited' carrying capacity. We conclude that the interplay between spatial heterogeneity in the prey growth and fast displacement of the predator across the habitat works as an efficient stabilizing mechanism. These results highlight the generality of the stabilization mechanisms we find in spatially structured predator-prey ecological systems in a heterogeneous environment.
Directory of Open Access Journals (Sweden)
Ali Izadi
2015-10-01
Full Text Available In this study, substrates concentration profile has been studied in a porous matrix containing immobilized amyloglucosidase for glucose production. This analysis has been performed by using of an analytical method called Least Square Method and results have been compared with numerical solution. Effects of effective diffusivity (, Michael's constant (, maximum reaction rate ( and initial substrate concentration ( are studied on Soluble Starch and Dextrin concentration in the spherical support. Outcomes reveal that Least Square Method has an excellent agreement with numerical solution and in the center of support, substrate concentration is minimum and increasing of effective diffusivity and Michael's constant reduce the Soluble Starch and Dextrin profile gradient.
Czech Academy of Sciences Publication Activity Database
Ainsworth, M.; Vejchodský, Tomáš
2014-01-01
Roč. 281, November 2014 (2014), s. 184-199 ISSN 0045-7825 Grant - others:European Commission(XE) StochDetBioModel(328008) Program:FP7 Institutional support: RVO:67985840 Keywords : finite element analysis * a posteriori error estimate * singularly perturbed problems Subject RIV: BA - General Mathematics Impact factor: 2.959, year: 2014 http://www.sciencedirect.com/science/article/pii/S0045782514002746
Chaudhury, Srabanti; Cherayil, Binny J.
2007-09-01
Single-molecule equations for the Michaelis-Menten [Biochem. Z. 49, 333 (1913)] mechanism of enzyme action are analyzed within the Wilemski-Fixman [J. Chem. Phys. 58, 4009 (1973); 60, 866 (1974)] approximation after the effects of dynamic disorder—modeled by the anomalous diffusion of a particle in a harmonic well—are incorporated into the catalytic step of the reaction. The solution of the Michaelis-Menten equations is used to calculate the distribution of waiting times between successive catalytic turnovers in the enzyme β-galactosidase. The calculated distribution is found to agree qualitatively with experimental results on this enzyme obtained at four different substrate concentrations. The calculations are also consistent with measurements of correlations in the fluctuations of the fluorescent light emitted during the course of catalysis, and with measurements of the concentration dependence of the randomness parameter.
Technical Report --Final Work Accomplishment
Energy Technology Data Exchange (ETDEWEB)
Kim, Eun Heui
2007-11-19
The main goal of this project was to understand the solution structure of nonlinear boundary value problems arising in self-similar solutions of nonlinear systems of multidimensional conservation laws. This project further extended to study on biocomplex systems including Morphogen gradients systems (reaction-diffusion systems) and tumor growth and its treatment model problems (free boundary, conservation of mass and reaction-diffusion systems). The list of publications and the summary of those publications are listed.
Pulse dynamics in a three-component system: Stability and bifurcations
van Heijster, P.; Doelman, A.; Kaper, T.J.
2008-01-01
In this article, we analyze the stability and the associated bifurcations of several types of pulse solutions in a singularly perturbed three-component reaction-diffusion equation that has its origin as a model for gas discharge dynamics. Due to the richness and complexity of the dynamics generated
Wu, Wei; Wang, Jin
2013-09-28
We established a potential and flux field landscape theory to quantify the global stability and dynamics of general spatially dependent non-equilibrium deterministic and stochastic systems. We extended our potential and flux landscape theory for spatially independent non-equilibrium stochastic systems described by Fokker-Planck equations to spatially dependent stochastic systems governed by general functional Fokker-Planck equations as well as functional Kramers-Moyal equations derived from master equations. Our general theory is applied to reaction-diffusion systems. For equilibrium spatially dependent systems with detailed balance, the potential field landscape alone, defined in terms of the steady state probability distribution functional, determines the global stability and dynamics of the system. The global stability of the system is closely related to the topography of the potential field landscape in terms of the basins of attraction and barrier heights in the field configuration state space. The effective driving force of the system is generated by the functional gradient of the potential field alone. For non-equilibrium spatially dependent systems, the curl probability flux field is indispensable in breaking detailed balance and creating non-equilibrium condition for the system. A complete characterization of the non-equilibrium dynamics of the spatially dependent system requires both the potential field and the curl probability flux field. While the non-equilibrium potential field landscape attracts the system down along the functional gradient similar to an electron moving in an electric field, the non-equilibrium flux field drives the system in a curly way similar to an electron moving in a magnetic field. In the small fluctuation limit, the intrinsic potential field as the small fluctuation limit of the potential field for spatially dependent non-equilibrium systems, which is closely related to the steady state probability distribution functional, is
Depressive symptoms and cognitive decline in older african americans: two scales and their factors.
Turner, Arlener D; Capuano, Ana W; Wilson, Robert S; Barnes, Lisa L
2015-06-01
Depressive symptoms are common in older adults, and researchers have explored the possibility of a link between depressive symptoms and cognitive decline, with mixed results. Most studies use total score of the Center for Epidemiological Studies Depression Scale (CES-D) with predominately non-Hispanic white participants. We sought to examine the relationship between the four factors of the CES-D and cognitive decline in older African Americans. Generalizability was determined using the Geriatric Depression Scale (GDS) and its factors. Participants without dementia from the Minority Aging Research Study (N = 298, mean age: 74 ± 5.68) underwent annual clinical evaluations (mean years: 5 ± 1.9), including depression assessment and cognitive testing, from which global and specific measures were derived. Cognitive decline was examined with linear mixed models adjusted for demographic variables and indicators of vascular risk. Total CES-D score was not related to baseline cognition or change over time, whereas total GDS score was related to decline in semantic and working memory. In examining CES-D factors, lack of positive affect (e.g., anhedonia) was related to decline in global cognition, episodic memory, and perceptual speed. Similarly for the GDS, anhedonia was associated with decline in semantic memory, and increased negative affect was associated with decline in global cognition and episodic, semantic, and working memory. Results suggest that depressive symptoms, particularly anhedonia and negative affect, are related to cognitive decline in older African Americans. Published by Elsevier Inc.
Directory of Open Access Journals (Sweden)
Byeong-Hee Mihn
2017-03-01
Full Text Available This study examines the scale unique instruments used for astronomical observation during the Joseon dynasty. The Small Simplified Armillary Sphere (小簡儀, So-ganui and the Sun-and-Stars Time-Determining Instrument (日星定時儀, Ilseong-jeongsi-ui are minimized astronomical instruments, which can be characterized, respectively, as an observational instrument and a clock, and were influenced by the Simplified Armilla (簡儀, Jianyi of the Yuan dynasty. These two instruments were equipped with several rings, and the rings of one were similar both in size and in scale to those of the other. Using the classic method of drawing the scale on the circumference of a ring, we analyze the scales of the Small Simplified Armillary Sphere and the Sun-and-Stars Time-Determining Instrument. Like the scale feature of the Simplified Armilla, we find that these two instruments selected the specific circumference which can be drawn by two kinds of scales. If Joseon’s astronomical instruments is applied by the dual scale drawing on one circumference, we suggest that 3.14 was used as the ratio of the circumference of circle, not 3 like China, when the ring’s size was calculated in that time. From the size of Hundred-interval disk of the extant Simplified Sundial in Korea, we make a conclusion that the three rings’ diameter of the Sun-and-Stars Time-Determining Instrument described in the Sejiong Sillok (世宗實錄, Veritable Records of the King Sejong refers to that of the middle circle of every ring, not the outer circle. As analyzing the degree of 28 lunar lodges (lunar mansions in the equator written by Chiljeongsan-naepyeon (七政算內篇, the Inner Volume of Calculation of the Motions of the Seven Celestial Determinants, we also obtain the result that the scale of the Celestial-circumference-degree in the Small Simplified Armillary Sphere was made with a scale error about 0.1 du in root mean square (RMS.
The cultural validation of two scales to assess social stigma in leprosy.
Peters, Ruth M H; Dadun; Van Brakel, Wim H; Zweekhorst, Marjolein B M; Damayanti, Rita; Bunders, Joske F G; Irwanto
2014-01-01
Stigma plays in an important role in the lives of persons affected by neglected tropical diseases, and assessment of stigma is important to document this. The aim of this study is to test the cross-cultural validity of the Community Stigma Scale (EMIC-CSS) and the Social Distance Scale (SDS) in the field of leprosy in Cirebon District, Indonesia. Cultural equivalence was tested by assessing the conceptual, item, semantic, operational and measurement equivalence of these instruments. A qualitative exploratory study was conducted to increase our understanding of the concept of stigma in Cirebon District. A process of translation, discussions, trainings and a pilot study followed. A sample of 259 community members was selected through convenience sampling and 67 repeated measures were obtained to assess the psychometric measurement properties. The aspects and items in the SDS and EMIC-CSS seem equally relevant and important in the target culture. The response scales were adapted to ensure that meaning is transferred accurately and no changes to the scale format (e.g. lay out, statements or questions) of both scales were made. A positive correlation was found between the EMIC-CSS and the SDS total scores (r=0.41). Cronbach's alphas of 0.83 and 0.87 were found for the EMIC-CSS and SDS. The exploratory factor analysis indicated for both scales an adequate fit as unidimensional scale. A standard error of measurement of 2.38 was found in the EMIC-CSS and of 1.78 in the SDS. The test-retest reliability coefficient was respectively, 0.84 and 0.75. No floor or ceiling effects were found. According to current international standards, our findings indicate that the EMIC-CSS and the SDS have adequate cultural validity to assess social stigma in leprosy in the Bahasa Indonesia-speaking population of Cirebon District. We believe the scales can be further improved, for instance, by adding, changing and rephrasing certain items. Finally, we provide suggestions for use with other neglected tropical diseases.
On the Measurement of Procrastination: Comparing Two Scales in Six European Countries.
Svartdal, Frode; Pfuhl, Gerit; Nordby, Kent; Foschi, Gioel; Klingsieck, Katrin B; Rozental, Alexander; Carlbring, Per; Lindblom-Ylänne, Sari; Rębkowska, Kaja
2016-01-01
Procrastination is a common problem, but defining and measuring it has been subject to some debate. This paper summarizes results from students and employees (N = 2893) in Finland, Germany, Italy, Norway, Poland, and Sweden using the Pure Procrastination Scale (PPS) and the Irrational Procrastination Scale (IPS; Steel, 2010), both assumed to measure unidimensional and closely related constructs. Confirmatory factor analyses indicated inadequate configural fit for the suggested one-factor model for PPS; however, acceptable fit was observed for a three-factor model corresponding to the three different scales the PPS is based on. Testing measurement invariance over countries and students-employees revealed configural but not strong or strict invariance, indicating that both instruments are somewhat sensitive to cultural differences. We conclude that the PPS and IPS are valid measures of procrastination, and that the PPS may be particularly useful in assessing cultural differences in unnecessary delay.
SCOPA-sleep and PDSS: two scales for assessment of sleep disorder in Parkinson's disease
Martinez-Martin, Pablo; Visser, Martine; Rodriguez-Blazquez, Carmen; Marinus, Johan; Chaudhuri, K. Ray; van Hilten, Jacobus J.; Cubo-Delgado, E.; Aguilar-Barberá, M.; Escalante, S.; Rojo, A.; Campdelacreu, J.; Bergareche, A.; Frades, B.; Arroyo, S.
2008-01-01
This study evaluated the comparative validity and usefulness of the Parkinson's Disease Sleep Scale (PDSS) and the Scales for Outcomes in PD-Sleep Scale (SCOPA-S), two disease-specific rating scales for assessing sleep disorders in Parkinson's disease (PD). Hoehn and Yahr staging (HY), SCOPA-Motor,
Heating of field-reversed plasma rings estimated with two scaling models
Energy Technology Data Exchange (ETDEWEB)
Shearer, J.W.
1978-05-18
Scaling calculations are presented of the one temperature heating of a field-reversed plasma ring. Two sharp-boundary models of the ring are considered: the long thin approximation and a pinch model. Isobaric, adiabatic, and isovolumetric cases are considered, corresponding to various ways of heating the plasma in a real experiment by using neutral beams, or by raising the magnetic field. It is found that the shape of the plasma changes markedly with heating. The least sensitive shape change (as a function of temperature) is found for the isovolumetric heating case, which can be achieved by combining neutral beam heating with compression. The complications introduced by this heating problem suggest that it is desirable, if possible, to create a field reversed ring which is already quite hot, rather than cold.
On the measurement of procrastination: Comparing two scales in six European countries
Directory of Open Access Journals (Sweden)
Frode Svartdal
2016-08-01
Full Text Available Procrastination is a common problem, but defining and measuring it has been subject to some debate. This paper summarizes results from students and employees (N = 2893 in Finland, Germany, Italy, Norway, Poland and Sweden using the Pure Procrastination Scale (PPS and the Irrational Procrastination Scale (IPS (Steel, 2010, both assumed to measure unidimensional and closely related constructs. Confirmatory factor analyses (CFA indicated inadequate configural fit for the suggested one-factor model for PPS; however, acceptable fit was observed for a three-factor model corresponding to the three different scales the PPS is based on. Testing measurement invariance over countries and students-employees revealed configural but not strong or strict invariance, indicating that both instruments are somewhat sensitive to cultural differences. We conclude that the PPS and IPS are valid measures of procrastination, and that the PPS may be particularly useful in assessing cultural differences in unnecessary delay.
Comparison of two scales for evaluation of smile and dental attractiveness
Directory of Open Access Journals (Sweden)
Pedro Lima Emmerich Oliveira
2015-04-01
Full Text Available OBJECTIVE: To compare the visual analogue scale (VAS and the simplified Q-sort method used to investigate the highest level of agreement among dentists, orthodontists and laypeople when assessing smile and dental attractiveness. MATERIAL AND METHODS: An album containing 258 photos of 86 individuals with their lips at rest, a slight and broad smile, was assessed by 25 dentists (general clinicians and various specialties, 23 orthodontists and 27 laypeople with regard to smile and dental attractiveness. To this end, both VAS and simplified Q-sort method were used. Agreements were calculated by intraclass correlation coefficient (ICC. RESULTS: For the single measurement between the VAS method and the simplified Q-sort method, all simplified Q-sort rates were higher in all groups. The simplified Q-sort method results ranged between 0.42 and 0.49 while those of the VAS method varied between 0.37 and 0.42. The simplified Q-sort method also presented higher mean measurement values (0.95 and 0.96 in comparison to VAS (0.94 and 0.95. CONCLUSIONS: Both scales may be considered reliable for evaluating smile and dental attractiveness; however, the simplified Q-Sort method presented slightly higher values than the VAS method.
Heating of field-reversed plasma rings estimated with two scaling models
International Nuclear Information System (INIS)
Shearer, J.W.
1978-01-01
Scaling calculations are presented of the one temperature heating of a field-reversed plasma ring. Two sharp-boundary models of the ring are considered: the long thin approximation and a pinch model. Isobaric, adiabatic, and isovolumetric cases are considered, corresponding to various ways of heating the plasma in a real experiment by using neutral beams, or by raising the magnetic field. It is found that the shape of the plasma changes markedly with heating. The least sensitive shape change (as a function of temperature) is found for the isovolumetric heating case, which can be achieved by combining neutral beam heating with compression. The complications introduced by this heating problem suggest that it is desirable, if possible, to create a field reversed ring which is already quite hot, rather than cold
Measuring pregnancy planning: A psychometric evaluation and comparison of two scales.
Drevin, Jennifer; Kristiansson, Per; Stern, Jenny; Rosenblad, Andreas
2017-11-01
To psychometrically test the London Measure of Unplanned Pregnancy and compare it with the Swedish Pregnancy Planning Scale. The incidence of unplanned pregnancies is an important indicator of reproductive health. The London Measure of Unplanned Pregnancy measures pregnancy planning by taking contraceptive use, timing, intention to become pregnant, desire for pregnancy, partner agreement, and pre-conceptual preparations into account. It has, however, previously not been psychometrically evaluated using confirmatory factor analysis. The Likert-scored single-item Swedish Pregnancy Planning Scale has been developed to measure the woman's own view of pregnancy planning level. Cross-sectional design. In 2012-2013, 5493 pregnant women living in Sweden were invited to participate in the Swedish Pregnancy Planning study, of whom 3327 (61%) agreed to participate and answered a questionnaire. A test-retest pilot study was conducted in 2011-2012. Thirty-two participants responded to the questionnaire on two occasions 14 days apart. Data were analysed using confirmatory factor analysis, Cohen's weighted kappa and Spearman's correlation. All items of the London Measure of Unplanned Pregnancy contributed to measuring pregnancy planning, but four items had low item-reliability. The London Measure of Unplanned Pregnancy and Swedish Pregnancy Planning Scale corresponded reasonably well with each other and both showed good test-retest reliability. The London Measure of Unplanned Pregnancy may benefit from item reduction and its usefulness may be questioned. The Swedish Pregnancy Planning Scale is time-efficient and shows acceptable reliability and construct validity, which makes it more useful for measuring pregnancy planning. © 2017 John Wiley & Sons Ltd.
Two-scale approach to dynamic localization failure of AISI 316H stainless steel sheets
Directory of Open Access Journals (Sweden)
Gambin W.
2008-01-01
Full Text Available Dynamic localization failure of a thin sheet made of AISI 316H steel is considered on the macroscopic and mesoscopic level for proportional and nonproportional stress paths. On the macroscopic level, we propose: (1 the replacement of time as independent variable by a function of plastic dissipation and (2 dependence of the initial equivalent yield stress on stress rate. On the mesoscopic level - the regularized Schmid model for description of the single grain behavior is used and the polycrystalline yield surface generated by the texture development enables to improve the Forming Limit Diagrams for the sheet element.
Batigün, Ayşegül Durak; Sahin, Nesrin H
2006-01-01
The purpose of the present study is to investigate the psychometric properties of two instruments developed to measure Type-A behaviors and job satisfaction, two important variables mentioned in the stress literature. The data were collected from two different samples, one composed of 426 bank personnel, the other composed of 94 adults working in a private company. The findings are presented separately under the titles Study I and Study II. In both of the studies the assessment instruments used were: Stress Audit (Symptoms), Stress Audit (Vulnerability), Stress Coping Behaviors, Job Satisfaction Scale, and Type-A Behaviors Inventory. For both of the instruments, the studies were based on factor analyses. For Type-A Behaviors Inventory the analyses revealed 4 factors, while for Job Satisfaction Scale they revealed 6 factors. The factor subscales developed from these factors were found to have satisfactory Cronbach's alphas. For Type-A Behaviors Inventory they ranged between .40 and .90; whereas for Job Satisfaction Inventory these values were between .53 and .94. Both studies also included correlational analyses to specify the criterion validity values of the two instruments. The findings revealed that both of the instruments had satisfactory psychometric values, indicating that they can be reliably used in health psychology and job stress studies.
Two Scales, Hybrid Model for Soils, Involving Artificial Neural Network and Finite Element Procedure
Directory of Open Access Journals (Sweden)
Krasiński Marcin
2015-02-01
Full Text Available A hybrid ANN-FE solution is presented as a result of two level analysis of soils: a level of a laboratory sample and a level of engineering geotechnical problem. Engineering properties of soils (sands are represented directly in the form of ANN (this is in contrast with our former paper where ANN approximated constitutive relationships. Initially the ANN is trained with Duncan formula (Duncan and Chang [2], then it is re-trained (calibrated with some available experimental data, specific for the soil considered. The obtained approximation of the constitutive parameters is used directly in finite element method at the level of a single element at the scale of the laboratory sample to check the correct representation of the laboratory test. Then, the finite element that was successfully tested at the level of laboratory sample is used at the macro level to solve engineering problems involving the soil for which it was calibrated.
The cultural validation of two scales to assess social stigma in leprosy
Peters, R.M.H.; van Brakel, W.H.; Zweekhorst, M.B.M.; Bunders-Aelen, J.G.F.; Irwanto, I
2014-01-01
Cultural equivalence was tested by assessing the conceptual, item, semantic, operational and measurement equivalence of these instruments. A qualitative exploratory study was conducted to increase our understanding of the concept of stigma in Cirebon District. A process of translation, discussions,
Uranium and radon in private bedrock well water in Maine: geospatial analysis at two scales
Yang, Qiang; Smitherman, Paul; Hess, C.T.; Culbertson, Charles W.; Marvinney, Robert G.; Zheng, Yan
2014-01-01
In greater Augusta of central Maine, 53 out of 1093 (4.8%) private bedrock well water samples from 1534 km2 contained [U] >30 μg/L, the U.S. Environmental Protection Agency’s (EPA) Maximum Contaminant Level (MCL) for drinking water; and 226 out of 786 (29%) samples from 1135 km2 showed [Rn] >4,000 pCi/L (148 Bq/L), the U.S. EPA’s Alternative MCL. Groundwater pH, calcite dissolution and redox condition are factors controlling the distribution of groundwater U but not Rn due to their divergent chemical and hydrological properties. Groundwater U is associated with incompatible elements (S, As, Mo, F, and Cs) in water samples within granitic intrusions. Elevated [U] and [Rn] are located within 5–10 km distance of granitic intrusions but do not show correlations with metamorphism at intermediate scales (100−101 km). This spatial association is confirmed by a high-density sampling (n = 331, 5–40 samples per km2) at local scales (≤10–1 km) and the statewide sampling (n = 5857, 1 sample per 16 km2) at regional scales (102–103 km). Wells located within 5 km of granitic intrusions are at risk of containing high levels of [U] and [Rn]. Approximately 48 800–63 900 and 324 000 people in Maine are estimated at risk of exposure to U (>30 μg/L) and Rn (>4000 pCi/L) in well water, respectively.
Uranium and radon in private bedrock well water in Maine: geospatial analysis at two scales.
Yang, Qiang; Smitherman, Paul; Hess, C T; Culbertson, Charles W; Marvinney, Robert G; Smith, Andrew E; Zheng, Yan
2014-04-15
In greater Augusta of central Maine, 53 out of 1093 (4.8%) private bedrock well water samples from 1534 km(2) contained [U] >30 μg/L, the U.S. Environmental Protection Agency's (EPA) Maximum Contaminant Level (MCL) for drinking water; and 226 out of 786 (29%) samples from 1135 km(2) showed [Rn] >4,000 pCi/L (148 Bq/L), the U.S. EPA's Alternative MCL. Groundwater pH, calcite dissolution and redox condition are factors controlling the distribution of groundwater U but not Rn due to their divergent chemical and hydrological properties. Groundwater U is associated with incompatible elements (S, As, Mo, F, and Cs) in water samples within granitic intrusions. Elevated [U] and [Rn] are located within 5-10 km distance of granitic intrusions but do not show correlations with metamorphism at intermediate scales (10(0)-10(1) km). This spatial association is confirmed by a high-density sampling (n = 331, 5-40 samples per km(2)) at local scales (≤10(-1) km) and the statewide sampling (n = 5857, 1 sample per 16 km(2)) at regional scales (10(2)-10(3) km). Wells located within 5 km of granitic intrusions are at risk of containing high levels of [U] and [Rn]. Approximately 48 800-63 900 and 324 000 people in Maine are estimated at risk of exposure to U (>30 μg/L) and Rn (>4000 pCi/L) in well water, respectively.
The Cultural Validation of Two Scales to Assess Social Stigma in Leprosy
Peters, Ruth M. H.; Dadun; Van Brakel, Wim H.; Zweekhorst, Marjolein B. M.; Damayanti, Rita; Bunders, Joske F. G.; Irwanto
2014-01-01
Background Stigma plays in an important role in the lives of persons affected by neglected tropical diseases, and assessment of stigma is important to document this. The aim of this study is to test the cross-cultural validity of the Community Stigma Scale (EMIC-CSS) and the Social Distance Scale (SDS) in the field of leprosy in Cirebon District, Indonesia. Methodology/principle findings Cultural equivalence was tested by assessing the conceptual, item, semantic, operational and measurement equivalence of these instruments. A qualitative exploratory study was conducted to increase our understanding of the concept of stigma in Cirebon District. A process of translation, discussions, trainings and a pilot study followed. A sample of 259 community members was selected through convenience sampling and 67 repeated measures were obtained to assess the psychometric measurement properties. The aspects and items in the SDS and EMIC-CSS seem equally relevant and important in the target culture. The response scales were adapted to ensure that meaning is transferred accurately and no changes to the scale format (e.g. lay out, statements or questions) of both scales were made. A positive correlation was found between the EMIC-CSS and the SDS total scores (r = 0.41). Cronbach's alphas of 0.83 and 0.87 were found for the EMIC-CSS and SDS. The exploratory factor analysis indicated for both scales an adequate fit as unidimensional scale. A standard error of measurement of 2.38 was found in the EMIC-CSS and of 1.78 in the SDS. The test-retest reliability coefficient was respectively, 0.84 and 0.75. No floor or ceiling effects were found. Conclusions/significance According to current international standards, our findings indicate that the EMIC-CSS and the SDS have adequate cultural validity to assess social stigma in leprosy in the Bahasa Indonesia-speaking population of Cirebon District. We believe the scales can be further improved, for instance, by adding, changing and rephrasing certain items. Finally, we provide suggestions for use with other neglected tropical diseases. PMID:25376007
Energy Technology Data Exchange (ETDEWEB)
Wang, Jing [Iowa State Univ., Ames, IA (United States)
2013-01-11
We analyze the spatiotemporal behavior of species concentrations in a diffusion-mediated conversion reaction which occurs at catalytic sites within linear pores of nanometer diameter. A strict single-file (no passing) constraint occurs in the diffusion within such narrow pores. Both transient and steady-state behavior is precisely characterized by kinetic Monte Carlo simulations of a spatially discrete lattice–gas model for this reaction–diffusion process considering various distributions of catalytic sites. Exact hierarchical master equations can also be developed for this model. Their analysis, after application of mean-field type truncation approximations, produces discrete reaction–diffusion type equations (mf-RDE). For slowly varying concentrations, we further develop coarse-grained continuum hydrodynamic reaction–diffusion equations (h-RDE) incorporating a precise treatment of single-file diffusion (SFD) in this multispecies system. Noting the shortcomings of mf-RDE and h-RDE, we then develop a generalized hydrodynamic (GH) formulation of appropriate gh-RDE which incorporates an unconventional description of chemical diffusion in mixed-component quasi-single-file systems based on a refined picture of tracer diffusion for finite-length pores. The gh-RDE elucidate the non-exponential decay of the steady-state reactant concentration into the pore and the non-mean-field scaling of the reactant penetration depth. Then an extended model of a catalytic conversion reaction within a functionalized nanoporous material is developed to assess the effect of varying the reaction product – pore interior interaction from attractive to repulsive. The analysis is performed utilizing the generalized hydrodynamic formulation of the reaction-diffusion equations which can reliably capture the complex interplay between reaction and restricted transport for both irreversible and reversible reactions.
Global existence and asymptotic behaviour for a degenerate diffusive SEIR model
Directory of Open Access Journals (Sweden)
T. Aliziane
2005-02-01
Full Text Available In this paper we analyze the global existence and asymptotic behavior of a reaction diffusion system with degenerate diffusion arising in modeling the spatial spread of an epidemic disease.
Global existence and asymptotic behavior for a nonlinear degenerate SIS model
Directory of Open Access Journals (Sweden)
Tarik Ali Ziane
2013-01-01
Full Text Available In this paper we investigate the global existence and asymptotic behavior of a reaction diffusion system with degenerate diffusion arising in the modeling and the spatial spread of an epidemic disease.
Pattern formation at interfaces
Maier, Giulio; Nepomnyashchy, Alexander
2010-01-01
Applying modern nonlinear stability theory to problems of continuous media mechanics in the presence of interfaces, this text is relevant to materials science, chemical engineering, and heat transfer technologies, as well as to reaction-diffusion systems.
Dynamic instabilities in the kinetics of growth and disassembly of microtubules
Katrukha, Eugene
2016-01-01
Dynamic instability of microtubules is considered using frameworks of non-linear thermodynamics and non-equilibrium reaction-diffusion systems. Stochastic assembly/disassembly phases in the polymerization dynamics of microtubules are treated as a result of collective clusterization of microdefects (holes in structure). The model explains experimentally observed power law dependence of catastrophe frequency from the microtubule growth rate. Additional reaction-diffusion-precipitation model is ...
Synergetic aspects of gas-discharge: lateral patterns in dc systems with a high ohmic barrier
Purwins, H.-G.; Stollenwerk, L.
2014-12-01
article. A short review of possible theoretical approaches reveals that a theoretical description of the experimentally observed patterns is far from being satisfactory. Bearing this in mind, a qualitative model of the reaction-diffusion type is considered. Surprisingly enough, this model allows for a qualitative description of almost all fundamental patterns that have been observed experimentally. Also, so far the predictive power of this model is unmatched.
Synergetic aspects of gas-discharge: lateral patterns in dc systems with a high ohmic barrier
International Nuclear Information System (INIS)
Purwins, H-G; Stollenwerk, L
2014-01-01
article. A short review of possible theoretical approaches reveals that a theoretical description of the experimentally observed patterns is far from being satisfactory. Bearing this in mind, a qualitative model of the reaction-diffusion type is considered. Surprisingly enough, this model allows for a qualitative description of almost all fundamental patterns that have been observed experimentally. Also, so far the predictive power of this model is unmatched. (topical review)
Energy Technology Data Exchange (ETDEWEB)
Brunel, V
1999-06-29
This thesis presents three studies that are respectively the spin-1 disordered chain, the non magnetic impurities in the spin-1/2 chain and the reaction-diffusion process. The spin-1 chain of weak disorder is performed by the Abelian bosonization and the renormalization group. This allows to take into account the competition between the disorder and the interactions and predicts the effects of various spin-1 anisotropy chain phases under many different disorders. A second work uses the non magnetic impurities as local probes of the correlations in the spin-1/2 chain. When the impurities are connected to the chain boundary, the author predicts a temperature dependence of the relaxation rate (1/T) of the nuclear spin impurities, different from the case of these impurities connected to the whole chain. The last work deals with one dimensional reaction-diffusion problem. The Jordan-Wigner transformation allows to consider a fermionic field theory that critical exponents follow from the renormalization group. (A.L.B.)
Strategies and Rubrics for Teaching Complex Systems Theory to Novices (Invited)
Fichter, L. S.
2010-12-01
algorithms, etc.) leading to 19 learning outcomes that encompass most of the universality properties that characterize complex systems. They are developed in a specific order to achieve specific ends of understanding. We use these models in various depths and formats in courses ranging from gened courses, to evolutionary systems and environmental systems, to upper level geology courses. Depending on the goals of a course, the learning outcomes can be applied to understanding many other complex systems; e.g. oscillating chemical reactions (reaction-diffusion and activator-inhibitor systems), autocatalytic networks, hysteresis (bistable) systems, networks, and the rise/collapse of complex societies. We use these and other complex systems concepts in various classes to talk about the origin of life, ecosystem organization, game theory, extinction events, and environmental system behaviors. The applications are almost endless. The complete learning progression with models, computer programs, experiments, and learning outcomes is available at: www.jmu.edu/geology/ComplexEvolutionarySystems/
DEFF Research Database (Denmark)
Jeppesen, Palle
1996-01-01
The lecture note is aimed at introducing system budgets for optical communication systems. It treats optical fiber communication systems (six generations), system design, bandwidth effects, other system impairments and optical amplifiers.......The lecture note is aimed at introducing system budgets for optical communication systems. It treats optical fiber communication systems (six generations), system design, bandwidth effects, other system impairments and optical amplifiers....
The Episodic Nature of Experience: A Dynamical Systems Analysis.
Sreekumar, Vishnu; Dennis, Simon; Doxas, Isidoros
2017-07-01
Context is an important construct in many domains of cognition, including learning, memory, and emotion. We used dynamical systems methods to demonstrate the episodic nature of experience by showing a natural separation between the scales over which within-context and between-context relationships operate. To do this, we represented an individual's emails extending over about 5 years in a high-dimensional semantic space and computed the dimensionalities of the subspaces occupied by these emails. Personal discourse has a two-scaled geometry with smaller within-context dimensionalities than between-context dimensionalities. Prior studies have shown that reading experience (Doxas, Dennis, & Oliver, 2010) and visual experience (Sreekumar, Dennis, Doxas, Zhuang, & Belkin, 2014) have a similar two-scaled structure. Furthermore, the recurrence plot of the emails revealed that experience is predictable and hierarchical, supporting the constructs of some influential theories of memory. The results demonstrate that experience is not scale-free and provide an important target for accounts of how experience shapes cognition. Copyright © 2016 Cognitive Science Society, Inc.
Liquid-liquid phase transition and glass transition in a monoatomic model system.
Xu, Limei; Buldyrev, Sergey V; Giovambattista, Nicolas; Stanley, H Eugene
2010-01-01
We review our recent study on the polyamorphism of the liquid and glass states in a monatomic system, a two-scale spherical-symmetric Jagla model with both attractive and repulsive interactions. This potential with a parametrization for which crystallization can be avoided and both the glass transition and the liquid-liquid phase transition are clearly separated, displays water-like anomalies as well as polyamorphism in both liquid and glassy states, providing a unique opportunity to study the interplay between the liquid-liquid phase transition and the glass transition. Our study on a simple model may be useful in understanding recent studies of polyamorphism in metallic glasses.
International Nuclear Information System (INIS)
Gossler
1980-01-01
The present paper deals with - controlled area ventilation systems - ventilation systems for switchgear-building and control-room - other ventilation systems for safety equipments - service systems for ventilation systems. (orig./RW)
2010-09-01
direction X1, TD denoting the transverse direction X2 and ND denoting the normal direction X3. In addition to the ensemble of 300 randomly oriented...variables such as plastic deformation or damage (Voyiadjis and Abu Al- Rub , 2006). Several mesh densities were considered, with only half of the full...G.Z. and Abu Al- Rub , R.K. (2006) ‘A finite strain plastic-damage model for high velocity impacts using combined viscosity and gradient localization
International Nuclear Information System (INIS)
Divinski, S.V.; Hisker, F.; Kang, Y.-S.; Lee, J.-S.; Herzig, Chr.
2004-01-01
Solute diffusion of Ag in nanocrystalline γ-Fe - 40wt%Ni alloy was studied by means of the radiotracer technique in an extended temperature interval (489-1200 K). The powder metallurgical method was applied to produce nanomaterial which consisted of micrometer-large clusters (agglomerates) of nanometer sized grains. Two types of internal interfaces contributed as short-circuit paths for diffusion: the nanocrystalline grain boundaries (GB) and the inter-agglomerate interfaces (subscript a). Combining the recent results on Ag GB diffusion in coarse-grained γ-Fe - 40wt%Ni alloy and the present diffusion data in the nanocrystalline alloy the Ag segregation was determined as function of temperature. Ag segregates strongly at GBs in the γ-Fe - 40wt%Ni alloy with a segregation enthalpy of H s =-47 kJ/mol. Knowing the segregation factor, the experimental data on Ag diffusion along both nanocrystalline and inter-agglomerate interfaces in the nanomaterial were systematically analyzed in dependence on the different kinetic regimes. The sensitive radiotracer experiments and the subsequent diffusion profile analysis resulted in a consistent set of diffusion data in the whole investigated temperature range with Arrhenius behavior for both the Ag nano-GB diffusion (D 0 gb =4.7x10 -4 m 2 /s, H gb =173 kJ/mol) as well as for the much faster inter-agglomerate interface diffusion (D 0 a =8.1x10 -5 m 2 /s, H a =91 kJ/mol)
Energy Technology Data Exchange (ETDEWEB)
Rosas Paleta, M. G. Araceli [Benemerita Universidad Autonoma de Puebla, Puebla, Puebla (Mexico); Bautista Rodriguez, C. Moises [Alter-Energias Puebla, Puebla (Mexico)] email: celso.bautista@thyssenkrupp.com; Rivera Marquez, J. Antonio; Tepale Ochoa, Nancy [Benemerita Universidad Autonoma de Puebla, Puebla, Puebla (Mexico)
2009-09-15
The efficiency of a PEMFC fuel battery is limited due to a variety of mass transport-related phenomena that take place while it is operating. The electromotive force of the PEM fuel battery is related to the generation of concentration gradients resulting from the distribution of the reactants on the active sites of the electrode. The reactant gases supplied to the PEMFC are distributed over the diffusion layer of the electrodes through the channels of the polar plates. They then spread toward the active layer where the semi-reactions take place. Another important aspect is the presence of water molecules, a product of the reaction. When they accumulate, they cover the porosity of the electrodes, involving the reduction in the flow of reactants, even at high current density values and, combined with the diffusion phenomena involved, cause the PEMFC to complete cease functioning. The critical parameters for the transport phenomena are porosity, the diameter of the pore in the diffusion layer and the characteristics of the distribution of the reactants. The present works includes an experimental design of two distribution media and two diffusion media of the reactant gases in a PEMFC, involving three case studies. The results show significantly notable interactions between the diameter of the pore, the type of diffusion layer applied and the type of distributor applied. The combination in the second case significantly reduces the ohmic resistance and moderately reduces the diffusion resistances. While the combination in case three notably increases the ohmic resistance, diffusion resistance is significantly reduced. [Spanish] La eficiencia de una pila a combustible tipo PEMFC es limitada por diversos fenomenos de transporte de masa presentes durante su funcionamiento. La fuerza electromotriz de la pila a combustible tipo PEM esta relacionada con la generacion de gradientes de concentracion los cuales se dan como resultado de la distribucion de los reactivos sobre los sitios activos del electrodo. Los gases reactivos suministrados a una PEMFC se distribuyen sobre la capa de difusion de los electrodos por medio de los canales de las placas polares, posteriormente difunden hacia la capa activa donde se llevan a cabo las semi-reacciones. Otro aspecto importante es la presencia de las moleculas de agua, producto de la reaccion, que al acumularse cubren la porosidad de los electrodos implicando la reduccion del flujo de los reactivos, incluso a altos valores de densidad de corriente se combina con los fenomenos de difusion involucrados, ocasionando; el cese total en el funcionamiento de la PEMFC. Los parametros criticos para los fenomenos de transporte son la porosidad, el diametro del poro en la capa de difusion y las caracteristicas de distribucion de reactivos. El presente trabajo comprende un diseno experimental entre dos medios de distribucion y dos medios de difusion de gases reactivos en una PEMFC, implicando tres casos de estudio. Los resultados obtenidos muestran interacciones notablemente significativas entre el diametro de poro, el tipo de capa de difusion aplicada y el tipo de distribuidor aplicado. La combinacion en el segundo caso reduce significativamente las resistencias ohmicas y moderadamente las resistencias por difusion mientras la combinacion del caso tres incrementa notablemente las resistencias ohmicas sin embargo reducen las resistencias por difusion de forma importante.
Thermal systems; Systemes thermiques
Energy Technology Data Exchange (ETDEWEB)
Lalot, S. [Valenciennes Univ. et du Hainaut Cambresis, LME, 59 (France); Lecoeuche, S. [Ecole des Mines de Douai, Dept. GIP, 59 - Douai (France)]|[Lille Univ. des Sciences et Technologies, 59 - Villeneuve d' Ascq (France); Ahmad, M.; Sallee, H.; Quenard, D. [CSTB, 38 - Saint Martin d' Heres (France); Bontemps, A. [Universite Joseph Fourier, LEGI/GRETh, 38 - Grenoble (France); Gascoin, N.; Gillard, P.; Bernard, S. [Laboratoire d' Energetique, Explosion, Structure, 18 - Bourges (France); Gascoin, N.; Toure, Y. [Laboratoire Vision et Robotique, 18 - Bourges (France); Daniau, E.; Bouchez, M. [MBDA, 18 - Bourges (France); Dobrovicescu, A.; Stanciu, D. [Bucarest Univ. Polytechnique, Faculte de Genie Mecanique (Romania); Stoian, M. [Reims Univ. Champagne Ardenne, Faculte des Sciences, UTAP/LTM, 51 (France); Bruch, A.; Fourmigue, J.F.; Colasson, S. [CEA Grenoble, Lab. Greth, 38 (France); Bontemps, A. [Universite Joseph Fourier, LEGI/GRETh, 38 - Grenoble (France); Voicu, I.; Mare, T.; Miriel, J. [Institut National des Sciences Appliquees (INSA), LGCGM, IUT, 35 - Rennes (France); Galanis, N. [Sherbrooke Univ., Genie Mecanique, QC (Canada); Nemer, M.; Clodic, D. [Ecole des Mines de Paris, Centre Energetique et Procedes, 75 (France); Lasbet, Y.; Auvity, B.; Castelain, C.; Peerhossaini, H. [Nantes Univ., Ecole Polytechnique, Lab. de Thermocinetiquede Nantes, UMR-CNRS 6607, 44 (France)
2005-07-01
This session about thermal systems gathers 26 articles dealing with: neural model of a compact heat exchanger; experimental study and numerical simulation of the thermal behaviour of test-cells with walls made of a combination of phase change materials and super-insulating materials; hydraulic and thermal modeling of a supercritical fluid with pyrolysis inside a heated channel: pre-dimensioning of an experimental study; energy analysis of the heat recovery devices of a cryogenic system; numerical simulation of the thermo-hydraulic behaviour of a supercritical CO{sub 2} flow inside a vertical tube; mixed convection inside dual-tube exchangers; development of a nodal approach with homogenization for the simulation of the brazing cycle of a heat exchanger; chaotic exchanger for the cooling of low temperature fuel cells; structural optimization of the internal fins of a cylindrical generator; a new experimental approach for the study of the local boiling inside the channels of exchangers with plates and fins; experimental study of the flow regimes of boiling hydrocarbons on a bundle of staggered tubes; energy study of heat recovery exchangers used in Claude-type refrigerating systems; general model of Carnot engine submitted to various operating constraints; the free pistons Stirling cogeneration system; natural gas supplied cogeneration system with polymer membrane fuel cell; influence of the CRN coating on the heat flux inside the tool during the wood unrolling process; transport and mixture of a passive scalar injected inside the wake of a Ahmed body; control of a laser welding-brazing process by infrared thermography; 2D self-adaptative method for contours detection: application to the images of an aniso-thermal jet; exergy and exergy-economical study of an 'Ericsson' engine-based micro-cogeneration system; simplified air-conditioning of telephone switching equipments; parametric study of the 'low-energy' individual dwelling; brief synthesis of
Energy Technology Data Exchange (ETDEWEB)
Sternberg, K.
2007-02-08
Molten carbonate fuel cells (MCFCs) allow an efficient and environmentally friendly energy production by converting the chemical energy contained in the fuel gas in virtue of electro-chemical reactions. In order to predict the effect of the electro-chemical reactions and to control the dynamical behavior of the fuel cell a mathematical model has to be found. The molten carbonate fuel cell (MCFC) can indeed be described by a highly complex,large scale, semi-linear system of partial differential algebraic equations. This system includes a reaction-diffusion-equation of parabolic type, several reaction-transport-equations of hyperbolic type, several ordinary differential equations and finally a system of integro-differential algebraic equations which describes the nonlinear non-standard boundary conditions for the entire partial differential algebraic equation system (PDAE-system). The existence of an analytical or the computability of a numerical solution for this high-dimensional PDAE-system depends on the kind of the differential equations and their special characteristics. Apart from theoretical investigations, the real process has to be controlled, more precisely optimally controlled. Hence, on the basis of the PDAE-system an optimal control problem is set up, whose analytical and numerical solvability is closely linked to the solvability of the PDAE-system. Moreover the solution of that optimal control problem is made more difficult by inaccuracies in the underlying database, which does not supply sufficiently accurate values for the model parameters. Therefore the optimal control problem must also be investigated with respect to small disturbances of model parameters. The aim of this work is to analyze the relevant dynamic behavior of MCFCs and to develop concepts for their optimal process control. Therefore this work is concerned with the simulation, the optimal control and the sensitivity analysis of a mathematical model for MCDCs, which can be characterized
Data Systems vs. Information Systems
Amatayakul, Margret K.
1982-01-01
This paper examines the current status of “hospital information systems” with respect to the distinction between data systems and information systems. It is proposed that the systems currently existing are incomplete data dystems resulting in ineffective information systems.
Georgiana Marin; Mihai Catalin Andrei
2011-01-01
In recent decades IT and computer systems have evolved rapidly in economic informatics field. The goal is to create user friendly information systems that respond promptly and accurately to requests. Informatics systems evolved into decision assisted systems, and such systems are converted, based on gained experience, in expert systems for creative problem solving that an organization is facing. Expert systems are aimed at rebuilding human reasoning on the expertise obtained from experts, sto...
DEFF Research Database (Denmark)
Wagner, Falko Jens
1999-01-01
Multibody Systems is one area, in which methods for solving DAEs are of special interst. This chapter is about multibody systems, why they result in DAE systems and what kind of problems that can arise when dealing with multibody systems and formulating their corresponding DAE system....
International Nuclear Information System (INIS)
Kube, L.J.
1978-01-01
This invention relates generally to gas-cooled nuclear reactor systems and, more particularly, to an improved closure system for a pressure vessel in such a system wherein a penetration is provided for accommodating a heat exchanger. (author)
Lymphatic system ... neck, under the arms, and groin. The lymph system includes the: Tonsils Adenoids Spleen Thymus ... JE, Flynn JA, Solomon BS, Stewart RW. Lymphatic system. In: Ball JW, Dains JE, Flynn JA, Solomon ...
International Nuclear Information System (INIS)
Sokalski, A.
1982-01-01
History, organizational structure and operation principles of INIS system are presented. The preparation of input, checking and data processing as well as output production, computer forms of files and information retrieval systems are described in detail. The active participation of Poland in the system is emphasized. The possible ways of system development are presented. (author)
Energy Technology Data Exchange (ETDEWEB)
John Ross
2003-04-30
The Final Technical Report summarizes research accomplishments and Publications in the period of 5/1/99 to 4/30/03 done on the grant. Extensive progress was made in the period covered by this report in the areas of chemical kinetics of non-linear systems; spatial structures, reaction - diffusion systems, and thermodynamic and stochastic theory of electrochemical and general systems.
Physically-based Surface Texture Synthesis Using a Coupled Finite Element System.
Bajaj, Chandrajit; Zhang, Yongjie; Xu, Guoliang
2008-01-01
This paper describes a stable and robust finite element solver for physically-based texture synthesis over arbitrary manifold surfaces. Our approach solves the reaction-diffusion equation coupled with an anisotropic diffusion equation over surfaces, using a Galerkin based finite element method (FEM). This method avoids distortions and discontinuities often caused by traditional texture mapping techniques, especially for arbitrary manifold surfaces. Several varieties of textures are obtained by selecting different values of control parameters in the governing differential equations, and furthermore enhanced quality textures are generated by fairing out noise in input surface meshes.
Habayeb, A R
1987-01-01
Highlights three principal applications of system effectiveness: hardware system evaluation, organizational development and evaluation, and conflict analysis. The text emphasizes the commonality of the system effectiveness discipline. The first part of the work presents a framework for system effectiveness, partitioning and hierarchy of hardware systems. The second part covers the structure, hierarchy, states, functions and activities of organizations. Contains an extended Appendix on mathematical concepts and also several project suggestions.
DEFF Research Database (Denmark)
Aceto, Luca; Ingolfsdottir, Anna; Larsen, Kim Guldstrand
A reactive system comprises networks of computing components, achieving their goals through interaction among themselves and their environment. Thus even relatively small systems may exhibit unexpectedly complex behaviours. As moreover reactive systems are often used in safety critical systems......, the need for mathematically based formal methodology is increasingly important. There are many books that look at particular methodologies for such systems. This book offers a more balanced introduction for graduate students and describes the various approaches, their strengths and weaknesses, and when...
Simple computation of reaction–diffusion processes on point clouds
Macdonald, Colin B.
2013-05-20
The study of reaction-diffusion processes is much more complicated on general curved surfaces than on standard Cartesian coordinate spaces. Here we show how to formulate and solve systems of reaction-diffusion equations on surfaces in an extremely simple way, using only the standard Cartesian form of differential operators, and a discrete unorganized point set to represent the surface. Our method decouples surface geometry from the underlying differential operators. As a consequence, it becomes possible to formulate and solve rather general reaction-diffusion equations on general surfaces without having to consider the complexities of differential geometry or sophisticated numerical analysis. To illustrate the generality of the method, computations for surface diffusion, pattern formation, excitable media, and bulk-surface coupling are provided for a variety of complex point cloud surfaces.
Directory of Open Access Journals (Sweden)
Jan Lánský
2017-06-01
Full Text Available Cryptocurrency systems are purely digital and decentralized systems that use cryptographic principles to confirm transactions. Bitcoin is the first and also the most widespread cryptocurrency. The aim of this article is to introduce Bitcoin system using a language understandable also to readers without computer science education. This article captures the Bitcoin system from three perspectives: internal structure, network and users. Emphasis is placed on brief and clear definitions (system components and their mutual relationships. A new system view of the stated terms constitutes author’s own contribution.
National Aeronautics and Space Administration — The autonomous systems (AS) project, led by NASA Ames, is developing software for system operation automation. AS technology will help astronauts make more decisions...
Schomaker, Verner; Lingafelter, E. C.
1985-01-01
Discusses characteristics of crystal systems, comparing (in table format) crystal systems with lattice types, number of restrictions, nature of the restrictions, and other lattices that can accidently show the same metrical symmetry. (JN)
International Nuclear Information System (INIS)
Vanin, V.R.
1990-01-01
The multidetector systems for high resolution gamma spectroscopy are presented. The observable parameters for identifying nuclides produced simultaneously in the reaction are analysed discussing the efficiency of filter systems. (M.C.K.)
... and symptoms may result from the tear drainage system becoming obstructed at any point from the puncta ... specializes in the eyelids, orbit, and tear drain system. It’s also important that he or she is ...
The biliary system creates, moves, stores, and releases bile into the duodenum . This helps the body digest food. It also assists ... from the liver to the duodenum. The biliary system includes: The gallbladder Bile ducts and certain cells ...
International Nuclear Information System (INIS)
Haldy, P.A.
1988-01-01
The definitions of the terms 'artificial intelligence' and 'expert systems', the methodology, areas of employment and limits of expert systems are discussed. The operation of an expert system is described, especially the presentation and organization of knowledge as well as interference and control. Methods and tools for expert system development are presented and their application in nuclear energy are briefly addressed. 7 figs., 2 tabs., 6 refs
DEFF Research Database (Denmark)
Madsen, Tanja Kidholm Osmann; Bahnsen, Chris Holmberg; Jensen, Morten Bornø
This deliverable is part of WP4. Overall WP4 is motivated by the need for automatic systems that can ease the task of annotating massive amounts of traffic data. Concretely this deliverable is related to WP4.2 - the watchdog system. The idea with the watchdog is to develop a system that can remov...
Indian Academy of Sciences (India)
system programmers should take into consideration all possi- bilities and write programs that do not fail. Responsiveness: Embedded systems should respond to events as soon as possible. For example, a patient monitoring system should process the patient'S heart signals quickly and immedi- ately notify if any abnormality ...
Pellerano, Fernando
2015-01-01
This short course provides information on what systems engineering is and how the systems engineer guides requirements, interfaces with the discipline leads, and resolves technical issues. There are many system-wide issues that either impact or are impacted by the thermal subsystem. This course will introduce these issues and illustrate them with real life examples.
DEFF Research Database (Denmark)
Manelius, Anne-Mette; Beim, Anne
2007-01-01
Opsamling af diskussioner på konferencen og udstillingen Creative Systems i september/oktober 2007. Konferencen og Udstillingen Creative Systems sætter fokus på systemer som en positiv drivkraft i den kreative skabelsesproces. CINARK inviterede fire internationale kapaciteter, som indenfor hver...
Indian Academy of Sciences (India)
IAS Admin
Systems biology seeks to study biological systems as a whole, contrary to the reductionist approach that has dominated biology. Such a view of biological systems emanating from strong foundations of molecular level understanding of the individual components in terms of their form, function and interactions is promising to ...
... Staying Safe Videos for Educators Search English Español Digestive System KidsHealth / For Parents / Digestive System What's in this ... the body can absorb and use. About the Digestive System Almost all animals have a tube-type digestive ...
Indian Academy of Sciences (India)
sumer electronic systems, they are cost sensitive. Thus their cost must be low. Robustness: Embedded systems should be robust since they operate in a harsh environment. They should endure vibrations, power supply fluctuations and excessive heat. Due to limited power supply in an embedded system, the power ...
Globalization technique for projected Newton–Krylov methods
Chen, Jinhai; Vuik, C.
2017-01-01
Large-scale systems of nonlinear equations appear in many applications. In various applications, the solution of the nonlinear equations should also be in a certain interval. A typical application is a discretized system of reaction diffusion equations. It is well known that chemical species should
Tsichritzis, Dionysios C; Rheinboldt, Werner
1974-01-01
Operating Systems deals with the fundamental concepts and principles that govern the behavior of operating systems. Many issues regarding the structure of operating systems, including the problems of managing processes, processors, and memory, are examined. Various aspects of operating systems are also discussed, from input-output and files to security, protection, reliability, design methods, performance evaluation, and implementation methods.Comprised of 10 chapters, this volume begins with an overview of what constitutes an operating system, followed by a discussion on the definition and pr
International Nuclear Information System (INIS)
Wauthier, J.; Fiori, R.
1990-01-01
The development, the characteristics and the applications of a multifunction system are presented. The system is used on the RBES laboratory pipes, at Marcoule. The system was developed in order to allow, without time loss, the modification of the circuit function by replacing only one component. The following elements form the multifunction system: a fixed base, which is part of the tube, a removable piece, which is inserted into the base, a cover plate and its locking system. The material, chosen among commercial trade marks, required small modifications in order to be used in the circuit [fr
DEFF Research Database (Denmark)
The tutorial will discuss the definition of cognitive systems as the possibilities to extend the current systems engineering paradigm in order to perceive, learn, reason and interact robustly in open-ended changing environments. I will also address cognitive systems in a historical perspective an...... in cognitive systems include e.g. personalized information systems, sensor network systems, social dynamics system and Web2.0, and cognitive components analysis. I will use example from our own research and link to other research activities.......The tutorial will discuss the definition of cognitive systems as the possibilities to extend the current systems engineering paradigm in order to perceive, learn, reason and interact robustly in open-ended changing environments. I will also address cognitive systems in a historical perspective...... to be modeled within a limited set of predefined specifications. There will inevitably be a need for robust decisions and behaviors in novel situations that include handling of conflicts and ambiguities based on the capability and knowledge of the artificial cognitive system. Further, there is a need...
DEFF Research Database (Denmark)
Hildebrandt, Thomas Troels; Cattani, Gian Luca
2016-01-01
An expert system is a computer system for inferring knowledge from a knowledge base, typically by using a set of inference rules. When the concept of expert systems was introduced at Stanford University in the early 1970s, the knowledge base was an unstructured set of facts. Today the knowledge...... base of expert systems is often given in terms of an ontology, extracted and built from various data sources by employing natural language-processing and statistics. To emphasize such capabilities, the term “expert” is now often replaced by “cognitive,” “knowledge,” “knowledge-based,” or “intelligent......” system. With very few exceptions, general-purpose expert systems have failed to emerge so far. However, expert systems are applied in specialized domains, particularly in healthcare. The increasing availability of large quantities of data to organizations today provides a valuable opportunity...
International Nuclear Information System (INIS)
Kagan, D.N.; Hubberstey, P.; Barker, M.G.
1985-01-01
The paper reviews the experimental and theoretical studies carried out on multicomponent alkali metal systems. Solid-liquid phase equilibria studies are mainly concerned with the systems Na-K-Rb and Na-K-Cs, and data on the liquidus temperatures in these systems are presented. The thermodynamic properties of the ternary Na-K-Cs eutectic system have been determined experimentally, and the enthalpy, heat capacity and excess functions of the alloy are given. An analysis of calculational methods used in determining thermodynamic functions of ternary liquid metals systems is described. Finally, data are tabulated for the density, compressibility, saturated vapour pressure, viscosity and thermal conductivity of the ternary Na-K-Cs eutectic system. (UK)
DEFF Research Database (Denmark)
Jensen, Mads Brath; Mortensen, Henrik Rubæk; Mullins, Michael
2009-01-01
This paper describes and reflects upon the results of an investigative project which explores the setting up of a material system - a parametric and generative assembly consisting of and taking into consideration material properties, manufacturing constraints and geometric behavior. The project...... approaches the subject through the construction of a logic-driven system aiming to explore the possibilities of a material system that fulfills spatial, structural and performative requirements concurrently and how these are negotiated in situations where they might be conflicting....
Kembellec, Gérald; Saleh, Imad
2014-01-01
Acclaimed by various content platforms (books, music, movies) and auction sites online, recommendation systems are key elements of digital strategies. If development was originally intended for the performance of information systems, the issues are now massively moved on logical optimization of the customer relationship, with the main objective to maximize potential sales. On the transdisciplinary approach, engines and recommender systems brings together contributions linking information science and communications, marketing, sociology, mathematics and computing. It deals with the understan
Federal Laboratory Consortium — The Energetic Systems Division provides full-spectrum energetic engineering services (project management, design, analysis, production support, in-service support,...
Irwin, J David
2011-01-01
Technology has now progressed to the point that intelligent systems are replacing humans in the decision making processes as well as aiding in the solution of very complex problems. In many cases intelligent systems are already outperforming human activities. Artificial neural networks are not only capable of learning how to classify patterns, such images or sequence of events, but they can also effectively model complex nonlinear systems. Their ability to classify sequences of events is probably more popular in industrial applications where there is an inherent need to model nonlinear system
DEFF Research Database (Denmark)
Aceto, Luca; Ingolfsdottir, Anna; Larsen, Kim Guldstrand
A reactive system comprises networks of computing components, achieving their goals through interaction among themselves and their environment. Thus even relatively small systems may exhibit unexpectedly complex behaviours. As moreover reactive systems are often used in safety critical systems...... they are best used. Milner's CCS and its operational semantics are introduced, together with the notions of behavioural equivalences based on bisimulation techniques and with recursive extensions of Hennessy-Milner logic. In the second part of the book, the presented theories are extended to take timing issues...
Anticipatory systems as linguistic systems
Ekdahl, Bertil
2000-05-01
The idea of system is well established although not well defined. What makes up a system depends on the observer. Thinking in terms of systems is only a convenient way to conceptualize organizations, natural or artificial, that show coherent properties. Among all properties, which can be ascribed to systems, one property seems to be more outstanding than others, namely that of being anticipatory. In nature, anticipatory properties are found only in living organizations. In this way it can be said to separate non-living systems from living because there is no indication that any natural phenomenon occurring in systems where there is no indication of life is anticipatory. The characteristic of living systems is that they are exposed to the evolution contrary to causal systems that do not undergo changes due to the influence of the environment. Causal systems are related to the past in such a way that subsequent situations can be calculated from knowledge of past situations. In causal systems the past is the cause of the present and there is no reference to the future as a determining agent, contrary to anticipatory systems where expectations are the cause of the present action. Since anticipatory properties are characteristic of living systems, this property, as all other properties in living systems, is a result of the evolution and can be found in plants as well as in animals. Thus, it is not only tied to consciousness but is found at a more basic level, i.e., in the interplay between genotype and phenotype. Anticipation is part of the genetic language in such a way that appropriate actions, for events in the anticipatory systems environment, are inscribed in the genes. Anticipatory behavior, as a result of the interpretation of the genetic language, has been selected by the evolution. In this paper anticipatory systems are regarded as linguistic systems and I argue that as such anticipation cannot be fragmented but must be holistically studied. This has the
Gröbner, Oswald
2006-01-01
The vacuum system of a particle accelerator must provide the necessary conditions for the high energy beam to avoid loss of particles and deterioration of the beam quality. In this talk we will review basic design concepts, vacuum components and procedures required for an accelerator vacuum system.
... jobs to do: B lymphocytes are like the body's military intelligence system, seeking out their targets and sending defenses ... like the soldiers, destroying the invaders that the intelligence system has ... that invades the body is called an antigen (pronounced: AN-tih-jun). ...
DEFF Research Database (Denmark)
Rose, Jørgen
1997-01-01
This report gives an overview of the different retrofitting possibilities that are available today. The report looks at both external and internal systems for external wall constructions, roof constructions, floor constructions and foundations. All systems are described in detail in respect to use...
International Nuclear Information System (INIS)
Ohyama, Takuya; Saegusa, Hiromitsu
2009-03-01
As a part of the research and development regarding characterisation of deep geological environment, the GEOMASS (GEOLOGICAL MODELLING ANALYSIS AND SIMULATION SOFTWARE) system has been developed by the Japan Atomic Energy Agency in order to carry out geological and hydrogeological modelling and groundwater flow simulation and so on. The GEOMASS system integrates a commercial geological interpretation system (EarthVision), which is used for geological modelling and visualisation, with a proprietary code for groundwater flow (FracAffinity). This integrated system allows users to make rapid improvement of models as data increases. Also, it is possible to perform more realistic groundwater flow simulation due to the capability of modelling the rock mass as a continuum with discrete hydro-structural features in the rock mass. This paper consists of 'Overview of GEOMASS system', FracAffinity Theoretical Background' and 'FracAffinity User Guide' and is edited as a GEOMASS system manual. 'Overview of GEOMASS system' describes the outline of this system. 'FracAffinity Theoretical Background' describes the information of technical background of FracAffinity software. FracAffinity User Guide' describes the structure of the FracAffinity input files, the usage of FracAffinity Interface and flow-solver. Updating of the FracAffinity has been continued as needed and FracAffinity version3.3 is the latest version at present (July 2008). (author)
Indian Academy of Sciences (India)
M Suresh Babu is currently a fourth year undergraduate student in the Department of. Computer Science and. Engineering, Narayana. Engineering College,. Nellore, Andhra Pradesh. He would like to work in operating systems, computer networks and also in Internet security concepts. Keywords. Operating systems, file sys-.
Indian Academy of Sciences (India)
The process concept and concurrency are at the heart of modern operating systems (OS). A process is the unit of work in a computer system. A process must be in main memory during execution. To improve the utilization of central processing unit. (CPU) as well as the speed of its response to its users, the computer must ...
Hoff, Karla
2016-01-01
In standard economics, individuals are rational actors and economic forces undermine institutions that impose large inefficiencies. The persistence of the caste system is evidence of the need for psychologically more realistic models of decision-making in economics. The caste system divides South Asian society into hereditary groups whose lowest ranks are represented as innately polluted. ...
Energy Technology Data Exchange (ETDEWEB)
Kaya, Yoichi
1987-01-10
In the wake of the oil shock in 1973, the need for developing more effective energy systems has been mounting. The dominant views and topics for power generation systems in terms of scale merit shifted from the advocacy of centralization/scaling-up of facilities to the soft energy path theory insisting on the efficiency of dispersed small-scale plants, followed by the recent holonic path theory which maintains that large and small scale plants should be centralized or dispersed in an optimum manner. At the same time, an autonomous-type system concept has emerged which points out that the energy systems can be operated efficiently through mutual coordination and cooperation between the suppliers and users to find a balance point that meets the market principle, while abolishing the conventional suppliers-governed system. As a result, the load management system based on time-of-use pricing or adaptive pricing is expected to be adopted widely in near future. All these new theories are aimed at developing flexible and reasonable system structures that can be adapted to the changing circumstances. (4 figs, 17 refs)
International Nuclear Information System (INIS)
Froggatt, R.J.
1981-01-01
The invention provides a two dimensional imaging system in which a pattern of radiation falling on the system is detected to give electrical signals for each of a plurality of strips across the pattern. The detection is repeated for different orientations of the strips and the whole processed by compensated back projection. For a shadow x-ray system a plurality of strip x-ray detectors are rotated on a turntable. For lower frequencies the pattern may be rotated with a Dove prism and the strips condensed to suit smaller detectors with a cylindrical lens. (author)
Sternberg, Shlomo
2010-01-01
Celebrated mathematician Shlomo Sternberg, a pioneer in the field of dynamical systems, created this modern one-semester introduction to the subject for his classes at Harvard University. Its wide-ranging treatment covers one-dimensional dynamics, differential equations, random walks, iterated function systems, symbolic dynamics, and Markov chains. Supplementary materials offer a variety of online components, including PowerPoint lecture slides for professors and MATLAB exercises.""Even though there are many dynamical systems books on the market, this book is bound to become a classic. The the
Directory of Open Access Journals (Sweden)
Oset E.
2012-12-01
Full Text Available I make a short review of the situation of the kaonic systems, with novel information supporting the two Λ(1405 states from the K-d → nπΣ reaction. A review is made of the K¯$ar K$NN system with recent calculations converging to smaller bindings and larger widths. Novel systems involving two kaons and one nucleon or three kaons are also reported and finally a short discussion is made of the analogous state DNN for which recent studies find a large binding and a small width.
U Rehman, Habib; McKee, Nida A; McKee, Michael L
2016-01-15
Several ring systems (Saturn systems) have been studied using DFT methods that include dispersion effects. Comparison with X-ray structures are made with three systems, and the agreement is quite good. Binding enthalpies and binding free energies in dichloromethane and toluene have been computed. The effect of an encapsulated lithium cation is accessed by comparing C60 @(C6 H4 )10 and [Li@C60 @(C6 H4 )10 ](+). The [Li@C60 ](+) cation is a much better acceptor than C60 which leads to greater donor-acceptor interactions and larger charge transfer from the ring to [Li@C60 ](+). © 2015 Wiley Periodicals, Inc.
Monotonous property of non-oscillations of the damped Duffing's equation
International Nuclear Information System (INIS)
Feng Zhaosheng
2006-01-01
In this paper, we give a qualitative study to the damped Duffing's equation by means of the qualitative theory of planar systems. Under certain parametric conditions, the monotonous property of the bounded non-oscillations is obtained. Explicit exact solutions are obtained by a direct method and application of this approach to a reaction-diffusion equation is presented
Pinwheel-like structures resulting from interaction of plane pulses of excitation.
Sielewiesiuk, Jakub; Górecki, Jerzy
2002-12-01
We demonstrate that complex spatiotemporal structures may appear in an excitable system as the result of interaction between two plane pulses. Such behavior has been obtained for FitzHugh-Nagumo type of dynamics by numerical integration of reaction-diffusion equations.
Pattern formation in the bistable Gray-Scott model
DEFF Research Database (Denmark)
Mazin, W.; Rasmussen, K.E.; Mosekilde, Erik
1996-01-01
The paper presents a computer simulation study of a variety of far-from-equilibrium phenomena that can arise in a bistable chemical reaction-diffusion system which also displays Turing and Hopf instabilities. The Turing bifurcation curve and the wave number for the patterns of maximum linear grow...
Stability in a diffusive food chain model with Michaelis-Menten functional response
DEFF Research Database (Denmark)
Lin, Zhigui; Pedersen, Michael
2004-01-01
This paper deals with the behavior of positive solutions to a reaction-diffusion system with homogeneous Neumann boundary conditions describing a three species food chain. A sufficient condition for the local asymptotical stability is given by linearization and also a sufficient condition...
Re-Entrant Hexagons and Locked Turing-Hopf Fronts in the CIMA Reaction
DEFF Research Database (Denmark)
Mosekilde, Erik; Larsen, F.; Dewel, G.
1998-01-01
Aspects of the mode-interaction and pattern-selection processes in far-from-equilibrium chemical reaction-diffusion systems are studied through numerical simulation of the Lengyel-Epstein Model. The competition between Hopf oscillations and Turing stripes is investigated by following the propagat...
Avdeev, Alexander A
2016-01-01
This monograph presents a systematic analysis of bubble system mathematics, using the mechanics of two-phase systems in non-equilibrium as the scope of analysis. The author introduces the thermodynamic foundations of bubble systems, ranging from the fundamental starting points to current research challenges. This book addresses a range of topics, including description methods of multi-phase systems, boundary and initial conditions as well as coupling requirements at the phase boundary. Moreover, it presents a detailed study of the basic problems of bubble dynamics in a liquid mass: growth (dynamically and thermally controlled), collapse, bubble pulsations, bubble rise and breakup. Special emphasis is placed on bubble dynamics in turbulent flows. The analysis results are used to write integral equations governing the rate of vapor generation (condensation) in non-equilibrium flows, thus creating a basis for solving a number of practical problems. This book is the first to present a comprehensive theory of boil...
African Journals Online (AJOL)
1,3,2-DIAZABORACYCLOALKANE. RING SYSTEM. Negussie Retta" and Robert H. Neilson. 'Department of Chemistry, Addis Ababa University, P.O. Box 1176, Addis Ababa, Ethiopia. Department of Chemistry, Texas Christian University.
Bartlett, R. G., Jr.
1973-01-01
The general anatomy and function of the human respiratory system is summarized. Breathing movements, control of breathing, lung volumes and capacities, mechanical relations, and factors relevant to respiratory support and equipment design are discussed.
CSIR Research Space (South Africa)
Wessels, Konrad J
2006-01-01
Full Text Available This chapter describes the current condition of dryland systems with respect to the services they provide and the drivers that determine trends in their provision. Within the context of the mounting global concern caused by land degradation...
Directory of Open Access Journals (Sweden)
Lixin Dong
2008-11-01
Full Text Available Two strategies towards the realization of nanotechnology have been presented, i.e., top-down and bottom up. The former one is mainly based on nanofabrication and includes technologies such as nano-lithography, nano-imprint, and etching. Presently, they are still 2D fabrication processes with low resolution. The later one is an assembly-based technique. At present, it includes such items as self-assembly, dip-pen lithography, and directed self-assembly. These techniques can generate regular nano patterns in large scales. To fabricate 3D complex nano devices there are still no effective ways by so far. Here we show our effort on the development of a nano laboratory, a prototype nanomanufacturing system, based on nanorobotic manipulations. In which, we take a hybrid strategy as shown in Fig. 1. In this system, nano fabrication and nano assembly can be performed in an arbitrary order to construct nano building blocks and finally nano devices. The most important feature in this system is that the products can be fed back into the system to shrink the system part by part leading to nanorobots. Property characterization can be performed in each intermediate process. Due to the nanorobotic manipulation system, dynamic measurement can be performed rather than conventional static observations.
Directory of Open Access Journals (Sweden)
Hermann Kopetz
2013-11-01
Full Text Available The global availability of communication services makes it possible to interconnect independently developed systems, called constituent systems, to provide new synergistic services and more efficient economic processes. The characteristics of these new Systems-of-Systems are qualitatively different from the classic monolithic systems. In the first part of this presentation we elaborate on these differences, particularly with respect to the autonomy of the constituent systems, to dependability, continuous evolution, and emergence. In the second part we look at a SoS from the point of view of cognitive complexity. Cognitive complexity is seen as a relation between a model of an SoS and the observer. In order to understand the behavior of a large SoS we have to generate models of adequate simplicity, i.e, of a cognitive complexity that can be handled by the limited capabilities of the human mind. We will discuss the importance of properly specifying and placing the relied-upon message interfaces between the constituent systems that form an open SoS and discuss simplification strategies that help to reduce the cognitive complexity.
Liquid-Liquid Phase Transition and Glass Transition in a Monoatomic Model System
Directory of Open Access Journals (Sweden)
Nicolas Giovambattista
2010-12-01
Full Text Available We review our recent study on the polyamorphism of the liquid and glass states in a monatomic system, a two-scale spherical-symmetric Jagla model with both attractive and repulsive interactions. This potential with a parametrization for which crystallization can be avoided and both the glass transition and the liquid-liquid phase transition are clearly separated, displays water-like anomalies as well as polyamorphism in both liquid and glassy states, providing a unique opportunity to study the interplay between the liquid-liquid phase transition and the glass transition. Our study on a simple model may be useful in understanding recent studies of polyamorphism in metallic glasses.
Energy Technology Data Exchange (ETDEWEB)
Graham, R.L.
1998-03-17
The Systems Studies Activity had two objectives: (1) to investigate nontechnical barriers to the deployment of biomass production and supply systems and (2) to enhance and extend existing systems models of bioenergy supply and use. For the first objective, the Activity focused on existing bioenergy markets. Four projects were undertaken: a comparative analysis of bioenergy in Sweden and Austria; a one-day workshop on nontechnical barriers jointly supported by the Production Systems Activity; the development and testing of a framework for analyzing barriers and drivers to bioenergy markets; and surveys of wood pellet users in Sweden, Austria and the US. For the second objective, two projects were undertaken. First, the Activity worked with the Integrated BioEnergy Systems (TBS) Activity of TEA Bioenergy Task XIII to enhance the BioEnergy Assessment Model (BEAM). This model is documented in the final report of the IBS Activity. The Systems Studies Activity contributed to enhancing the feedstock portion of the model by developing a coherent set of willow, poplar, and switchgrass production modules relevant to both the US and the UK. The Activity also developed a pretreatment module for switchgrass. Second, the Activity sponsored a three-day workshop on modeling bioenergy systems with the objectives of providing an overview of the types of models used to evaluate bioenergy and promoting communication among bioenergy modelers. There were nine guest speakers addressing different types of models used to evaluate different aspects of bioenergy, ranging from technoeconomic models based on the ASPEN software to linear programming models to develop feedstock supply curves for the US. The papers from this workshop have been submitted to Biomass and Bioenergy and are under editorial review.
Fiscal system analysis - contractual systems
International Nuclear Information System (INIS)
Kaiser, M.J.
2006-01-01
Production sharing contracts are one of the most popular forms of contractual system used in petroleum agreements around the world, but the manner in which the fiscal terms and contract parameters impact system measures is complicated and not well understood. The purpose of this paper is to quantify the influence of private and market uncertainty in contractual fiscal systems. A meta-modelling approach is employed that couples the results of a simulation model with regression analysis to construct numerical functionals that quantify the fiscal regime. Relationships are derived that specify how the present value, rate of return, and take statistics vary as a function of the system parameters. The deepwater Girassol field development in Angola is taken as a case study. (author)
On-line tuning of a fuzzy-logic power system stabilizer
International Nuclear Information System (INIS)
Hossein-Zadeh, N.; Kalam, A.
2002-01-01
A scheme for on-line tuning of a fuzzy-logic power system stabilizer is presented. firstly, a fuzzy-logic power system stabilizer is developed using speed deviation and accelerating power as the controller input variables. The inference mechanism of fuzzy-logic controller is represented by a decision table, constructed of linguistic IF-THEN rules. The Linguistic rules are available from experts and the design procedure is based on these rules. It assumed that an exact model of the plant is not available and it is difficult to extract the exact parameters of the power plant. Thus, the design procedure can not be based on an exact model. This is an advantage of fuzzy logic that makes the design of a controller possible without knowing the exact model of the plant. Secondly, two scaling parameters are introduced to tune the fuzzy-logic power system stabilizer. These scaling parameters are the outputs of another fuzzy-logic system, which gets the operating conditions of power system as inputs. These mechanism of tuning the fuzzy-logic power system stabilizer makes the fuzzy-logic power system stabilizer adaptive to changes in the operating conditions. Therefore, the degradation of the system response, under a wide range of operating conditions, is less compared to the system response with a fixed-parameter fuzzy-logic power system stabilizer and a conventional (linear) power system stabilizer. The tuned stabilizer has been tested by performing nonlinear simulations using a synchronous machine-infinite bus model. The responses are compared with a fixed parameters fuzzy-logic power system stabilizer and a conventional (linear) power system stabilizer. It is shown that the tuned fuzzy-logic power system stabilizer is superior to both of them
Olsen, Lola
1992-01-01
In addition to the discussions, Ocean Climate Data Workshop hosts gave participants an opportunity to hear about, see, and test for themselves some of the latest computer tools now available for those studying climate change and the oceans. Six speakers described computer systems and their functions. The introductory talks were followed by demonstrations to small groups of participants and some opportunities for participants to get hands-on experience. After this familiarization period, attendees were invited to return during the course of the Workshop and have one-on-one discussions and further hands-on experience with these systems. Brief summaries or abstracts of introductory presentations are addressed.
1992-01-01
Technology originating in a NASA-sponsored study of the measurement of microbial growth in zero gravity led to the development of Biomerieux Vitek, Inc.'s VITEK system. VITEK provides a physician with accurate diagnostic information and identifies the most effective medication. Test cards are employed to identify organisms and determine susceptibility to antibiotics. A photo-optical scanner scans the card and monitors changes in the growth of cells contained within the card. There are two configurations - VITEK and VITEK JR as well as VIDAS, a companion system that detects bacteria, viruses, etc. from patient specimens. The company was originally created by McDonnell Douglas, the NASA contractor.
DEFF Research Database (Denmark)
Schürmann, Carsten; Poswolsky, Adam
2009-01-01
Delphin is a functional programming language [Adam Poswolsky and Carsten Schürmann. Practical programming with higher-order encodings and dependent types. In European Symposium on Programming (ESOP), 2008] utilizing dependent higher-order datatypes. Delphin's two-level type-system cleanly separates...... data from computation, allowing for decidable type checking. The data level is LF [Robert Harper, Furio Honsell, and Gordon Plotkin. A framework for defining logics. Journal of the Association for Computing Machinery, 40(1):143-184, January 1993], which allows for the specification of deductive systems...
Van Steen, Maarten
2017-01-01
For this third edition of "Distributed Systems," the material has been thoroughly revised and extended, integrating principles and paradigms into nine chapters: 1. Introduction 2. Architectures 3. Processes 4. Communication 5. Naming 6. Coordination 7. Replication 8. Fault tolerance 9. Security A separation has been made between basic material and more specific subjects. The latter have been organized into boxed sections, which may be skipped on first reading. To assist in understanding the more algorithmic parts, example programs in Python have been included. The examples in the book leave out many details for readability, but the complete code is available through the book's Website, hosted at www.distributed-systems.net.
Energy Technology Data Exchange (ETDEWEB)
Wiley, H S.
2006-06-01
The biology revolution over the last 50 years has been driven by the ascendancy of molecular biology. This was enthusiastically embraced by most biologists because it took us into increasingly familiar territory. It took mysterious processes, such as the replication of genetic material and assigned them parts that could be readily understood by the human mind. When we think of ''molecular machines'' as being the underlying basis of life, we are using a paradigm derived from everyday experience. However, the price that we paid was a relentless drive towards reductionism and the attendant balkanization of biology. Now along comes ''systems biology'' that promises us a solution to the problem of ''knowing more and more about less and less''. Unlike molecular biology, systems biology appears to be taking us into unfamiliar intellectual territory, such as statistics, mathematics and computer modeling. Not surprisingly, systems biology has met with widespread skepticism and resistance. Why do we need systems biology anyway and how does this new area of research promise to change the face of biology in the next couple of decades?
Indian Academy of Sciences (India)
areas in which this type is useful are multimedia, virtual reality, and advanced scientific projects such as undersea exploration and planetary rovers. Because of the expanded uses for soft real-time functionality, it is finding its way into most current operating systems, including major versions of Unix and Windows NT OS.
Bell, Samantha
2018-01-01
"Using the new Next Generation Science Standards (NGSS), the My World of Science series provides the earliest readers with background on key STEM concepts. Solar System explores basic planetary astronomy in a simple, engaging way that will help readers develop word recognition and reading skills. Includes a glossary and index."-- Provided by publisher.
Christakis, Alexander; Hammond, Debora; Jackson, Michael; Laszlo, Alexander; Mitroff, Ian; Snowden, Dave; Troncale, Len; Carr-Chellman, Alison; Spector, J. Michael; Wilson, Brent
2013-01-01
Scholars representing the field of systems science were asked to identify what they considered to be the most exciting and imaginative work currently being done in their field, as well as how that work might change our understanding. The scholars included Alexander Christakis, Debora Hammond, Michael Jackson, Alexander Laszlo, Ian Mitroff, Dave…
International Nuclear Information System (INIS)
Mitchell, C.P.
1997-01-01
The objective of this paper is to demonstrate that a bioenergy system has to be considered as an integrated process in which each stage or step interacts with other steps in the overall process. There are a number of stages in the supply and conversion of woody biomass for energy. Each step in the chain has implications for the next step and for overall system efficiency. The resource can take many forms and will have varying physical and chemical characteristics which will influence the efficiency and cost of conversion. The point in the supply chain at which size and moisture content is reduced and the manner in which it is done is influential in determining feedstock delivered cost and overall system costs. To illustrate the interactions within the overall system, the influence of the nature, size and moisture content of delivered feedstocks on costs of generating electricity via thermal conversion processes is examined using a model developed to investigate the inter-relationships between the stages in the supply chain. (author)
Drenth, K.F.
1999-01-01
The transport system comprises at least one road surface (2) and at least one vehicle (4) on wheels (6). The road surface (2) has a substantially bowl-shaped cross section and the vehicle (4) is designed so that the wheels (6) run directly on the road surface (2) while the road surface (2) acts as a
Heteren, S. van
2015-01-01
Barrier-system dynamics are a function of antecedent topography and substrate lithology, Relative sea-level (RSL) changes, sediment availability and type, climate, vegetation type and cover, and various aero- and hydrodynamic processes during fair-weather conditions and extreme events. Global change
A properly functioning immune system is essential to good health. It defends the body against infectious agents and in some cases tumor cells. Individuals with immune deficiencies resulting from genetic defects, diseases (e.g., AIDS, leukemia), or drug therapies are more suscepti...
Aschbacher, Michael; Oliver, Bob
2016-01-01
This is a survey article on the theory of fusion systems, a relatively new area of mathematics with connections to local finite group theory, algebraic topology, and modular representation theory. We first describe the general theory and then look separately at these connections.
DEFF Research Database (Denmark)
Benveniste, Helene; Nedergaard, Maiken
2016-01-01
a so-called glymphatic pathway which comprise the peri-vascular space and acuaporin-4 water channels on astroglial endfeet. As such the glymphatic pathway can be perceived as a hitherto overlooked compartment of the extracellular space of the central nervous system which is involved in clearance...
We need theoretical physics approaches to study living systems
Blagoev, Krastan B.; Shukla, Kamal; affil="3" >Herbert Levine,
2013-08-01
, nor collect data on the kinetics of the many complex reactions. Instead, the focus was on formulating two- or three-component reaction-diffusion equations (e.g. the Oregonator), which could explain such generic features as the existence of rotating spiral waves (and their instability), the transition to chaos, the control of the reaction by light etc. By stressing mechanism instead of meticulous detail, one could understand the system even if there were still components and interactions waiting to be cataloged and quantified. In living systems, this way of thinking is even more crucial. A leading biologist once remarked to one of us that a calculation of in vivo cytoskeletal dynamics that did not take into account the fact that the particular cell in question had more than ten isoforms of actin could not possibly be correct. We need to counter that any calculation which takes into account all these isoforms is overwhelmingly likely to be vastly under-constrained and ultimately not useful. Adding more details can often bring us further from reality. Of course, the challenge for models is then falsification, i.e., finding robust predictions which can be directly tested experimentally. The most severe criticism, to quote Pauli, remains that 'your model is not even wrong.' Is this approach proving successful? In many cases it is too early to tell, but simple models have already proved useful in understanding protein folding, directed cell motility, gene expression variability and even laboratory-scale Darwinian evolution. One could argue as well that the extremely influential Hodgkin-Huxley approach to the action potential in neurons is a vastly oversimplified description and that is why it is tractable and compelling. There are other cases, however, where the model was too simple—the simple Turing instability does not account for Drosophila segment formation [2] and the binary state relaxational dynamics of the Hopfield model may prove incapable of explaining memory
DEFF Research Database (Denmark)
At first glance, this book may appear eclectic. It contains writings from architectural practice in a language and structure based on subjective views and experiences, combined with research contributions based on systematic design investigations of discrete computational systems. Discussions range...... from an undulating masonry wall at the University of Virginia erected by then-U.S. President Thomas Jefferson to agile robotic manufacturing processes and computational solver strategies based on graph networks. Conversely, the focus of this anthology is expressed directly in the title: bricks...... and systems. The basis for this theme is the work conducted at the Utzon(x) Research Group at Aalborg University, in combination with the rich tradition and implementation of masonry work in Denmark, which has attracted increasing attention from architectural practitioners and researchers alike. How should...
International Nuclear Information System (INIS)
Barbosa, H.J.C.; Guerreiro, J.N.C.; Toledo, E.M.
1980-01-01
Proceedings recently incorporated to TUBO system like the seismic analysis and the stress verification acccording to ASME-Boiler Rule and Pressure Vessel Code-section III are presented. The seismic analysis comprehend the consideration of uniform motion of the support, its multiple excitation, and the attainment of the spectral response for both cases. The module for stress verification uses stresses resulting fromthe combination of the loads specified by the user, in the automatic verification of permissible stresses for the pipings class 1 and 2, based on criteria NB-3650 and NC-3650 of ASME. The implementation of these proceedings in the TUBO system are discussed and a numerical example that covers the different phases of a stress analysis in a piping is presented [pt
DEFF Research Database (Denmark)
Poletto, Marco; Pasquero, Claudia
This is a manual investigating the subject of urban ecology and systemic development from the perspective of architectural design. It sets out to explore two main goals: to discuss the contemporary relevance of a systemic practice to architectural design, and to share a toolbox of informational...... design protocols developed to describe the city as a territory of self-organization. Collecting together nearly a decade of design experiments by the authors and their practice, ecoLogicStudio, the book discusses key disciplinary definitions such as ecologic urbanism, algorithmic architecture, bottom......-up or tactical design, behavioural space and the boundary of the natural and the artificial realms within the city and architecture. A new kind of "real-time world-city" is illustrated in the form of an operational design manual for the assemblage of proto-architectures, the incubation of proto...
Bilateral system. The ABACC system
International Nuclear Information System (INIS)
Nicolas, Ruben O.
2001-01-01
After relating the antecedents of the creation of the Brazilian-Argentine Agency for the Accounting and Control of Nuclear Materials (ABACC), the paper describes the common system of accounting and control set up by Argentina and Brazil. The organization of ABACC is also outlined
Physical system requirements: Overall system
International Nuclear Information System (INIS)
1992-01-01
The Nuclear Waste Policy Act (NWPA) of 1982 assigned to the Department of Energy (DOE) the responsibility for managing the disposal of spent nuclear fuel and high-level radioactive waste and established the Office of Civilian Radioactive Waste Management (OCRWM) for that purpose. The Secretary of Energy, in his November 1989 report to Congress (DOE/RW-0247), announced three new initiatives for conduct of the Civilian Radioactive Waste Management (CRWM) program. One of these initiatives was to establish improved management structure and procedures. In response, OCRWM performed a management study and the Direct subsequently issued the Management Systems Improvement Strategy (MSIS) on August 10, 1990, calling for a rigorous implementation of systems engineering principles with a special emphasis on functional analysis. This approach establishes a framework for integrating the program management efforts with the technical requirements analysis into a single, unified, and consistent program. The functional analysis approach recognizes that just the facilities and equipment comprising the physical waste management system must perform certain functions, so must certain programmatic and management functions be performed within the program in order to successfully bring the physical system into being
International Nuclear Information System (INIS)
Soulen, R.L.; Grosh, J.
1984-01-01
Invasive cardiovascular diagnostic procedures involve a finite risk and therefore can be recommended only when the benefit appears to exceed the risk by a substantial margin. The risk/benefit ratio varies not only with the procedure concerned but with the status of the vascular system, concomitant diseases, and the risks of both the suspected illness and its treatment. The risks inherent in the procedures per se are detailed in the sections to follow
Baumann, Mark J.; Kuca, Michal; Aragon, Mona L.
2016-02-02
A security system includes a structure having a structural surface. The structure is sized to contain an asset therein and configured to provide a forceful breaching delay. The structure has an opening formed therein to permit predetermined access to the asset contained within the structure. The structure includes intrusion detection features within or associated with the structure that are activated in response to at least a partial breach of the structure.
2015-07-31
early lifecycle phases will have intended quality outcomes. Requirements and Quality Validation Develop requirements elicitation and management...gradients within a system. That is, there are attack surfaces at internal APIs and service interfaces. The complexity also arises from particular features...interoperation (compatibility and support for with SoS APIs and practices), as well as a diverse range of ilities (evolvability/extensibility
Shannon, R.H.; Williamson, H.E.
1962-10-30
A boiling water type nuclear reactor power system having improved means of control is described. These means include provisions for either heating the coolant-moderator prior to entry into the reactor or shunting the coolantmoderator around the heating means in response to the demand from the heat engine. These provisions are in addition to means for withdrawing the control rods from the reactor. (AEC)
Directory of Open Access Journals (Sweden)
Yi Zhao
2012-01-01
Full Text Available Quantum instanton (QI approximation is recently proposed for the evaluations of the chemical reaction rate constants with use of full dimensional potential energy surfaces. Its strategy is to use the instanton mechanism and to approximate time-dependent quantum dynamics to the imaginary time propagation of the quantities of partition function. It thus incorporates the properties of the instanton idea and the quantum effect of partition function and can be applied to chemical reactions of complex systems. In this paper, we present the QI approach and its applications to several complex systems mainly done by us. The concrete systems include, (1 the reaction of H+CH4→H2+CH3, (2 the reaction of H+SiH4→H2+SiH3, (3 H diffusion on Ni(100 surface; and (4 surface-subsurface transport and interior migration for H/Ni. Available experimental and other theoretical data are also presented for the purpose of comparison.
Owolabi, Kolade M.
2017-03-01
In this paper, some nonlinear space-fractional order reaction-diffusion equations (SFORDE) on a finite but large spatial domain x ∈ [0, L], x = x(x , y , z) and t ∈ [0, T] are considered. Also in this work, the standard reaction-diffusion system with boundary conditions is generalized by replacing the second-order spatial derivatives with Riemann-Liouville space-fractional derivatives of order α, for 0 Fourier spectral method is introduced as a better alternative to existing low order schemes for the integration of fractional in space reaction-diffusion problems in conjunction with an adaptive exponential time differencing method, and solve a range of one-, two- and three-components SFORDE numerically to obtain patterns in one- and two-dimensions with a straight forward extension to three spatial dimensions in a sub-diffusive (0 reaction-diffusion case. With application to models in biology and physics, different spatiotemporal dynamics are observed and displayed.
Birkhoff, George D
1927-01-01
His research in dynamics constitutes the middle period of Birkhoff's scientific career, that of maturity and greatest power. -Yearbook of the American Philosophical Society The author's great book€¦is well known to all, and the diverse active modern developments in mathematics which have been inspired by this volume bear the most eloquent testimony to its quality and influence. -Zentralblatt MATH In 1927, G. D. Birkhoff wrote a remarkable treatise on the theory of dynamical systems that would inspire many later mathematicians to do great work. To a large extent, Birkhoff was writing about his o
Knoll, Peter
Videosensoren spielen für Fahrerassistenz systeme eine zentrale Rolle, da sie die Interpretation visueller Informationen (Objektklassifikation) gezielt unterstützen. Im Heckbereich kann die Video sensorik in der einfachsten Variante die ultraschallbasierte Einparkhilfe bei Einpark- und Rangiervorgängen unterstützen. Beim Nachtsichtsystem NightVision wird das mit Infrarotlicht angestrahlte Umfeld vor dem Fahrzeug mit einer Frontkamera aufgenommen und im Fahrzeugcockpit auf einem Display dem Fahrer angezeigt (s. Nachtsichtsysteme). Andere Fahrerassistenzsysteme verarbeiten die Videosignale und generieren daraus gezielt Informationen, die für eigenständige Funktionen (z. B. Spurverlassenswarner) oder aber als Zusatzinformation für andere Funktionen ausgewertet werden (Sensordatenfusion).
Bourlès, Henri
2013-01-01
Linear systems have all the necessary elements (modeling, identification, analysis and control), from an educational point of view, to help us understand the discipline of automation and apply it efficiently. This book is progressive and organized in such a way that different levels of readership are possible. It is addressed both to beginners and those with a good understanding of automation wishing to enhance their knowledge on the subject. The theory is rigorously developed and illustrated by numerous examples which can be reproduced with the help of appropriate computation software. 60 exe
Todreas, Neil E
2011-01-01
Principal Characteristics of Power ReactorsIntroductionPower CyclesPrimary Coolant SystemsReactor CoresFuel AssembliesAdvanced Water- and Gas-Cooled Reactors (Generation III And III+)Advanced Thermal and Fast Neutron Spectrum Reactors (Generation IV)ReferencesProblemsThermal Design Principles and ApplicationIntroductionOverall Plant Characteristics Influenced by Thermal Hydraulic ConsiderationsEnergy Production and Transfer ParametersThermal Design LimitsThermal Design MarginFigures of Merit for Core Thermal PerformanceThe Inverted Fuel ArrayThe Equivalent Annulus ApproximationReferencesProble
1990-01-01
Cox Sterile Products, Inc.'s Rapid Heat Transfer Sterilizer employs a heat exchange process that induces rapid air movement; the air becomes the heat transfer medium, maintaining a uniform temperature of 375 degrees Fahrenheit. It features pushbutton controls for three timing cycles for different instrument loads, a six-minute cycle for standard unpackaged instruments, eight minutes for certain specialized dental/medical instruments and 12 minutes for packaged instruments which can then be stored in a drawer in sterile condition. System will stay at 375 degrees all day. Continuous operation is not expensive because of the sterilizer's very low power requirements.
Kapich, Davorin D.
1987-01-01
A bearing system includes backup bearings for supporting a rotating shaft upon failure of primary bearings. In the preferred embodiment, the backup bearings are rolling element bearings having their rolling elements disposed out of contact with their associated respective inner races during normal functioning of the primary bearings. Displacement detection sensors are provided for detecting displacement of the shaft upon failure of the primary bearings. Upon detection of the failure of the primary bearings, the rolling elements and inner races of the backup bearings are brought into mutual contact by axial displacement of the shaft.
Expert Systems: What Is an Expert System?
Duval, Beverly K.; Main, Linda
1994-01-01
Describes expert systems and discusses their use in libraries. Highlights include parts of an expert system; expert system shells; an example of how to build an expert system; a bibliography of 34 sources of information on expert systems in libraries; and a list of 10 expert system shells used in libraries. (Contains five references.) (LRW)
Jersák, Jan
2007-01-01
Cílem studie je definovat možné směry dalšího vývoje nové aplikace pro potřeby cestovního ruchu, online rezervačního systému Booking System. Tohoto cíle je dosaženo jednak zkoumáním dosavadního vývoje aplikace a zásadních inovací, které přináší, a dále analýzou socioekonomického prostředí a konkurenčních služeb.
International Nuclear Information System (INIS)
Hackney, S.
1983-01-01
A system for posting hazardous materials into and out of an enclosure, such as a glovebox, through a port in a wall of the enclosure. The port is normally closed by a door which cooperates with a removable end closure, on a container or the like when the latter is presented to and secured at the port. The container is secured in position at the port by means of a rotatable coupling ring. A single interlock ensures that the door cannot be opened in the absence of a container at the port and also that the container cannot be removed from the port when the door is open. In place of the container, a glove secured to a rigid sleeve may be used to enable the operator to perform a work function within the glovebox. (author)
DEFF Research Database (Denmark)
Leleur, Steen
This book presents principles and methodology for planning in a complex world. It sets out a so-called systemic approach to planning, among other things, by applying “hard” and “soft” methodologies and methods in combination. The book is written for Ph.D and graduate students in engineering......, business and other fields, and it is useful for all professionals, across a wide range of employment areas, who share an interest in renewing planning practice. Such an endeavour is seen as both important and timely, recognising that many complex planning tasks necessitate organisations – be they public...... or private – to engage in planning to prepare proactive decision-making....
Palmero, Faustino; Lemos, M; Sánchez-Rey, Bernardo; Casado-Pascual, Jesús
2018-01-01
This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction a...
International Nuclear Information System (INIS)
Jones, E.L.
1983-01-01
A posting system for the movement of equipment, such as a manipulator, into and out of an enclosure e.g. a cell or glovebox, for toxic or radioactive materials has the manipulator arranged within a collapsible bellows-like container with an end of the container cooperating with a port entry to the enclosure. The collapsible container isolates the manipulator from the environment outside the enclosure and allows the manipulator to enter and leave the contaminated enclosure without breach of the containment. A particular construction of cell for use with radioactive material is described, having a thick wall of shielding material such as concrete provided with a door normally closed by a Pb shutter and having a cylindrical gamma shield block located over the shutter on the exterior of the wall. (author)