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.
Distribution in flowing reaction-diffusion systems
Kamimura, Atsushi; Herrmann, Hans J.; Ito, Nobuyasu
2009-01-01
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.
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.
Pattern formation in reaction diffusion systems with finite geometry
International Nuclear Information System (INIS)
Borzi, C.; Wio, H.
1990-04-01
We analyze the one-component, one-dimensional, reaction-diffusion equation through a simple inverse method. We confine the system and fix the boundary conditions as to induce pattern formation. We analyze the stability of those patterns. Our goal is to get information about the reaction term out of the preknowledgment of the pattern. (author). 5 refs
Analytically solvable models of reaction-diffusion systems
Energy Technology Data Exchange (ETDEWEB)
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.
Reaction-diffusion systems in intracellular molecular transport and control.
Soh, Siowling; Byrska, Marta; Kandere-Grzybowska, Kristiana; Grzybowski, Bartosz A
2010-06-07
Chemical reactions make cells work only if the participating chemicals are delivered to desired locations in a timely and precise fashion. Most research to date has focused on active-transport mechanisms, although passive diffusion is often equally rapid and energetically less costly. Capitalizing on these advantages, cells have developed sophisticated reaction-diffusion (RD) systems that control a wide range of cellular functions-from chemotaxis and cell division, through signaling cascades and oscillations, to cell motility. These apparently diverse systems share many common features and are "wired" according to "generic" motifs such as nonlinear kinetics, autocatalysis, and feedback loops. Understanding the operation of these complex (bio)chemical systems requires the analysis of pertinent transport-kinetic equations or, at least on a qualitative level, of the characteristic times of the constituent subprocesses. Therefore, in reviewing the manifestations of cellular RD, we also describe basic theory of reaction-diffusion phenomena.
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.
Turing Patterns in a Reaction-Diffusion System
International Nuclear Information System (INIS)
Wu Yanning; Wang Pingjian; Hou Chunju; Liu Changsong; Zhu Zhengang
2006-01-01
We have further investigated Turing patterns in a reaction-diffusion system by theoretical analysis and numerical simulations. Simple Turing patterns and complex superlattice structures are observed. We find that the shape and type of Turing patterns depend on dynamical parameters and external periodic forcing, and is independent of effective diffusivity rate σ in the Lengyel-Epstein model. Our numerical results provide additional insight into understanding the mechanism of development of Turing patterns and predicting new pattern formations.
A Weak Comparison Principle for Reaction-Diffusion Systems
Directory of Open Access Journals (Sweden)
José Valero
2012-01-01
Full Text Available We prove a weak comparison principle for a reaction-diffusion system without uniqueness of solutions. We apply the abstract results to the Lotka-Volterra system with diffusion, a generalized logistic equation, and to a model of fractional-order chemical autocatalysis with decay. Moreover, in the case of the Lotka-Volterra system a weak maximum principle is given, and a suitable estimate in the space of essentially bounded functions L∞ is proved for at least one solution of the problem.
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.
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.
Pattern dynamics of the reaction-diffusion immune system.
Zheng, Qianqian; Shen, Jianwei; Wang, Zhijie
2018-01-01
In this paper, we will investigate the effect of diffusion, which is ubiquitous in nature, on the immune system using a reaction-diffusion model in order to understand the dynamical behavior of complex patterns and control the dynamics of different patterns. Through control theory and linear stability analysis of local equilibrium, we obtain the optimal condition under which the system loses stability and a Turing pattern occurs. By combining mathematical analysis and numerical simulation, we show the possible patterns and how these patterns evolve. In addition, we establish a bridge between the complex patterns and the biological mechanism using the results from a previous study in Nature Cell Biology. The results in this paper can help us better understand the biological significance of the immune system.
Control of transversal instabilities in reaction-diffusion systems
Totz, Sonja; Löber, Jakob; Totz, Jan Frederik; Engel, Harald
2018-05-01
In two-dimensional reaction-diffusion systems, local curvature perturbations on traveling waves are typically damped out and vanish. However, if the inhibitor diffuses much faster than the activator, transversal instabilities can arise, leading from flat to folded, spatio-temporally modulated waves and to spreading spiral turbulence. Here, we propose a scheme to induce or inhibit these instabilities via a spatio-temporal feedback loop. In a piecewise-linear version of the FitzHugh–Nagumo model, transversal instabilities and spiral turbulence in the uncontrolled system are shown to be suppressed in the presence of control, thereby stabilizing plane wave propagation. Conversely, in numerical simulations with the modified Oregonator model for the photosensitive Belousov–Zhabotinsky reaction, which does not exhibit transversal instabilities on its own, we demonstrate the feasibility of inducing transversal instabilities and study the emerging wave patterns in a well-controlled manner.
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.
Decay to Equilibrium for Energy-Reaction-Diffusion Systems
Haskovec, Jan; Hittmeir, Sabine; Markowich, Peter A.; Mielke, Alexander
2018-01-01
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.
Rethinking pattern formation in reaction-diffusion systems
Halatek, J.; Frey, E.
2018-05-01
The present theoretical framework for the analysis of pattern formation in complex systems is mostly limited to the vicinity of fixed (global) equilibria. Here we present a new theoretical approach to characterize dynamical states arbitrarily far from (global) equilibrium. We show that reaction-diffusion systems that are driven by locally mass-conserving interactions can be understood in terms of local equilibria of diffusively coupled compartments. Diffusive coupling generically induces lateral redistribution of the globally conserved quantities, and the variable local amounts of these quantities determine the local equilibria in each compartment. We find that, even far from global equilibrium, the system is well characterized by its moving local equilibria. We apply this framework to in vitro Min protein pattern formation, a paradigmatic model for biological pattern formation. Within our framework we can predict and explain transitions between chemical turbulence and order arbitrarily far from global equilibrium. Our results reveal conceptually new principles of self-organized pattern formation that may well govern diverse dynamical systems.
Heterogeneity induces spatiotemporal oscillations in reaction-diffusion systems
Krause, Andrew L.; Klika, Václav; Woolley, Thomas E.; Gaffney, Eamonn A.
2018-05-01
We report on an instability arising in activator-inhibitor reaction-diffusion (RD) systems with a simple spatial heterogeneity. This instability gives rise to periodic creation, translation, and destruction of spike solutions that are commonly formed due to Turing instabilities. While this behavior is oscillatory in nature, it occurs purely within the Turing space such that no region of the domain would give rise to a Hopf bifurcation for the homogeneous equilibrium. We use the shadow limit of the Gierer-Meinhardt system to show that the speed of spike movement can be predicted from well-known asymptotic theory, but that this theory is unable to explain the emergence of these spatiotemporal oscillations. Instead, we numerically explore this system and show that the oscillatory behavior is caused by the destabilization of a steady spike pattern due to the creation of a new spike arising from endogeneous activator production. We demonstrate that on the edge of this instability, the period of the oscillations goes to infinity, although it does not fit the profile of any well-known bifurcation of a limit cycle. We show that nearby stationary states are either Turing unstable or undergo saddle-node bifurcations near the onset of the oscillatory instability, suggesting that the periodic motion does not emerge from a local equilibrium. We demonstrate the robustness of this spatiotemporal oscillation by exploring small localized heterogeneity and showing that this behavior also occurs in the Schnakenberg RD model. Our results suggest that this phenomenon is ubiquitous in spatially heterogeneous RD systems, but that current tools, such as stability of spike solutions and shadow-limit asymptotics, do not elucidate understanding. This opens several avenues for further mathematical analysis and highlights difficulties in explaining how robust patterning emerges from Turing's mechanism in the presence of even small spatial heterogeneity.
Multi-scale simulation of reaction-diffusion systems
Vijaykumar, A.
2017-01-01
In many reaction-diffusion processes, ranging from biochemical networks, catalysis, to complex self-assembly, the spatial distribution of the reactants and the stochastic character of their interactions are crucial for the macroscopic behavior. The recently developed mesoscopic Green’s Function
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
Pattern formation in three-dimensional reaction-diffusion systems
Callahan, T. K.; Knobloch, E.
1999-08-01
Existing group theoretic analysis of pattern formation in three dimensions [T.K. Callahan, E. Knobloch, Symmetry-breaking bifurcations on cubic lattices, Nonlinearity 10 (1997) 1179-1216] is used to make specific predictions about the formation of three-dimensional patterns in two models of the Turing instability, the Brusselator model and the Lengyel-Epstein model. Spatially periodic patterns having the periodicity of the simple cubic (SC), face-centered cubic (FCC) or body-centered cubic (BCC) lattices are considered. An efficient center manifold reduction is described and used to identify parameter regimes permitting stable lamellæ, SC, FCC, double-diamond, hexagonal prism, BCC and BCCI states. Both models possess a special wavenumber k* at which the normal form coefficients take on fixed model-independent ratios and both are described by identical bifurcation diagrams. This property is generic for two-species chemical reaction-diffusion models with a single activator and inhibitor.
Reaction diffusion in chromium-zircaloy-2 system
International Nuclear Information System (INIS)
Xiang Wenxin; Ying Shihao
2001-01-01
Reaction diffusion in the chromium-zircaloy-2 diffusion couples is investigated in the temperature range of 1023 - 1123 K. Scanning electron microscope (SEM) and energy dispersive spectrum (EDS) were used to measure the thickness of the reaction layer and to determine the Zr, Fe and Cr concentration penetrate profile in reaction layer, respectively. The growth kinetics of reaction layer has been studied and the results show that the growth of intermetallic compound is controlled by the process of volume diffusion as the layer growth approximately obeys the parabolic law. Interdiffusion coefficients were calculated using Boltzmann-Matano-Heumann model. Calculated interdiffusion coefficients were compared with those obtained on the condition that Cr dissolves in Zr and merely forms dilute solid solution. The comparison indicates that Cr diffuses in dilute solid solution is five orders of magnitude faster than in Zr(Fe, Cr) 2 intermetallic compound
Amplitude equations for a sub-diffusive reaction-diffusion system
International Nuclear Information System (INIS)
Nec, Y; Nepomnyashchy, A A
2008-01-01
A sub-diffusive reaction-diffusion system with a positive definite memory operator and a nonlinear reaction term is analysed. Amplitude equations (Ginzburg-Landau type) are derived for short wave (Turing) and long wave (Hopf) bifurcation points
Cross-diffusional effect in a telegraph reaction diffusion Lotka-Volterra two competitive system
International Nuclear Information System (INIS)
Abdusalam, H.A; Fahmy, E.S.
2003-01-01
It is known now that, telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion in several branches of sciences. Telegraph reaction diffusion Lotka-Volterra two competitive system is considered. We observed that this system can give rise to diffusive instability only in the presence of cross-diffusion. Local and global stability analysis in the cross-diffusional effect are studied by considering suitable Lyapunov functional
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.
International Nuclear Information System (INIS)
Cherniha, Roman
2010-01-01
New definitions of Q-conditional symmetry for systems of PDEs are presented, which generalize the standard notation of non-classical (conditional) symmetry. It is shown that different types of Q-conditional symmetry of a system generate a hierarchy of conditional symmetry operators. A class of two-component nonlinear reaction-diffusion systems is examined to demonstrate the applicability of the definitions proposed and it is shown when different definitions of Q-conditional symmetry lead to the same operators.
The entropy dissipation method for spatially inhomogeneous reaction-diffusion-type systems
Di Francesco, M.; Fellner, K.; Markowich, P. A
2008-01-01
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
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...
Stability Analysis of a Reaction-Diffusion System Modeling Atherogenesis
Ibragimov, Akif; Ritter, Laura; Walton, Jay R.
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
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
Large-time behavior of solutions to a reaction-diffusion system with distributed microstructure
Muntean, A.
2009-01-01
Abstract We study the large-time behavior of a class of reaction-diffusion systems with constant distributed microstructure arising when modeling diffusion and reaction in structured porous media. The main result of this Note is the following: As t ¿ 8 the macroscopic concentration vanishes, while
Concentration fluctuations in non-isothermal reaction-diffusion systems. II. The nonlinear case
Bedeaux, D.; Ortiz de Zárate, J.M.; Pagonabarraga, I.; Sengers, J.V.; Kjelstrup, S.
2011-01-01
In this paper, we consider a simple reaction-diffusion system, namely, a binary fluid mixture with an association-dissociation reaction between two species. We study fluctuations at hydrodynamic spatiotemporal scales when this mixture is driven out of equilibrium by the presence of a temperature
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.
Delay-induced wave instabilities in single-species reaction-diffusion systems
Otto, Andereas; Wang, Jian; Radons, Günter
2017-11-01
The Turing (wave) instability is only possible in reaction-diffusion systems with more than one (two) components. Motivated by the fact that a time delay increases the dimension of a system, we investigate the presence of diffusion-driven instabilities in single-species reaction-diffusion systems with delay. The stability of arbitrary one-component systems with a single discrete delay, with distributed delay, or with a variable delay is systematically analyzed. We show that a wave instability can appear from an equilibrium of single-species reaction-diffusion systems with fluctuating or distributed delay, which is not possible in similar systems with constant discrete delay or without delay. More precisely, we show by basic analytic arguments and by numerical simulations that fast asymmetric delay fluctuations or asymmetrically distributed delays can lead to wave instabilities in these systems. Examples, for the resulting traveling waves are shown for a Fisher-KPP equation with distributed delay in the reaction term. In addition, we have studied diffusion-induced instabilities from homogeneous periodic orbits in the same systems with variable delay, where the homogeneous periodic orbits are attracting resonant periodic solutions of the system without diffusion, i.e., periodic orbits of the Hutchinson equation with time-varying delay. If diffusion is introduced, standing waves can emerge whose temporal period is equal to the period of the variable delay.
Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains
Madzvamuse, Anotida; Gaffney, Eamonn A.; Maini, Philip K.
2009-01-01
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.
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.
Dichotomous-noise-induced pattern formation in a reaction-diffusion system
Das, Debojyoti; Ray, Deb Shankar
2013-06-01
We consider a generic reaction-diffusion system in which one of the parameters is subjected to dichotomous noise by controlling the flow of one of the reacting species in a continuous-flow-stirred-tank reactor (CSTR) -membrane reactor. The linear stability analysis in an extended phase space is carried out by invoking Furutzu-Novikov procedure for exponentially correlated multiplicative noise to derive the instability condition in the plane of the noise parameters (correlation time and strength of the noise). We demonstrate that depending on the correlation time an optimal strength of noise governs the self-organization. Our theoretical analysis is corroborated by numerical simulations on pattern formation in a chlorine-dioxide-iodine-malonic acid reaction-diffusion system.
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.
Nonlinear waves in reaction-diffusion systems: The effect of transport memory
International Nuclear Information System (INIS)
Manne, K. K.; Hurd, A. J.; Kenkre, V. M.
2000-01-01
Motivated by the problem of determining stress distributions in granular materials, we study the effect of finite transport correlation times on the propagation of nonlinear wave fronts in reaction-diffusion systems. We obtain results such as the possibility of spatial oscillations in the wave-front shape for certain values of the system parameters and high enough wave-front speeds. We also generalize earlier known results concerning the minimum wave-front speed and shape-speed relationships stemming from the finiteness of the correlation times. Analytic investigations are made possible by a piecewise linear representation of the nonlinearity. (c) 2000 The American Physical Society
Spatiotemporal chaos of self-replicating spots in reaction-diffusion systems.
Wang, Hongli; Ouyang, Qi
2007-11-23
The statistical properties of self-replicating spots in the reaction-diffusion Gray-Scott model are analyzed. In the chaotic regime of the system, the spots that dominate the spatiotemporal chaos grow and divide in two or decay into the background randomly and continuously. The rates at which the spots are created and decay are observed to be linearly dependent on the number of spots in the system. We derive a probabilistic description of the spot dynamics based on the statistical independence of spots and thus propose a characterization of the spatiotemporal chaos dominated by replicating spots.
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.
Nonlinear waves in reaction-diffusion systems: The effect of transport memory
Manne, K. K.; Hurd, A. J.; Kenkre, V. M.
2000-04-01
Motivated by the problem of determining stress distributions in granular materials, we study the effect of finite transport correlation times on the propagation of nonlinear wave fronts in reaction-diffusion systems. We obtain results such as the possibility of spatial oscillations in the wave-front shape for certain values of the system parameters and high enough wave-front speeds. We also generalize earlier known results concerning the minimum wave-front speed and shape-speed relationships stemming from the finiteness of the correlation times. Analytic investigations are made possible by a piecewise linear representation of the nonlinearity.
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.
Square Turing patterns in reaction-diffusion systems with coupled layers
Energy Technology Data Exchange (ETDEWEB)
Li, Jing [State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Beijing 100871 (China); Wang, Hongli, E-mail: hlwang@pku.edu.cn, E-mail: qi@pku.edu.cn [State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Beijing 100871 (China); Center for Quantitative Biology, Peking University, Beijing 100871 (China); Ouyang, Qi, E-mail: hlwang@pku.edu.cn, E-mail: qi@pku.edu.cn [State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Beijing 100871 (China); Center for Quantitative Biology, Peking University, Beijing 100871 (China); The Peking-Tsinghua Center for Life Sciences, Beijing 100871 (China)
2014-06-15
Square Turing patterns are usually unstable in reaction-diffusion systems and are rarely observed in corresponding experiments and simulations. We report here an example of spontaneous formation of square Turing patterns with the Lengyel-Epstein model of two coupled layers. The squares are found to be a result of the resonance between two supercritical Turing modes with an appropriate ratio. Besides, the spatiotemporal resonance of Turing modes resembles to the mode-locking phenomenon. Analysis of the general amplitude equations for square patterns reveals that the fixed point corresponding to square Turing patterns is stationary when the parameters adopt appropriate values.
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.
Vorticity field, helicity integral and persistence of entanglement in reaction-diffusion systems
International Nuclear Information System (INIS)
Trueba, J L; Arrayas, M
2009-01-01
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)
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.
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.
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.
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.
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.
Anomalous dimension in a two-species reaction-diffusion system
Vollmayr-Lee, Benjamin; Hanson, Jack; McIsaac, R. Scott; Hellerick, Joshua D.
2018-01-01
We study a two-species reaction-diffusion system with the reactions A+A\\to (0, A) and A+B\\to A , with general diffusion constants D A and D B . Previous studies showed that for dimensions d≤slant 2 the B particle density decays with a nontrivial, universal exponent that includes an anomalous dimension resulting from field renormalization. We demonstrate via renormalization group methods that the scaled B particle correlation function has a distinct anomalous dimension resulting in the asymptotic scaling \\tilde CBB(r, t) ˜ tφf(r/\\sqrt{t}) , where the exponent ϕ results from the renormalization of the square of the field associated with the B particles. We compute this exponent to first order in \
Mode-locking in advection-reaction-diffusion systems: An invariant manifold perspective
Locke, Rory A.; Mahoney, John R.; Mitchell, Kevin A.
2018-01-01
Fronts propagating in two-dimensional advection-reaction-diffusion systems exhibit a rich topological structure. When the underlying fluid flow is periodic in space and time, the reaction front can lock to the driving frequency. We explain this mode-locking phenomenon using the so-called burning invariant manifolds (BIMs). In fact, the mode-locked profile is delineated by a BIM attached to a relative periodic orbit (RPO) of the front element dynamics. Changes in the type (and loss) of mode-locking can be understood in terms of local and global bifurcations of the RPOs and their BIMs. We illustrate these concepts numerically using a chain of alternating vortices in a channel geometry.
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
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
Directory of Open Access Journals (Sweden)
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].
Boundedness for a system of reaction-diffusion equations with more general Arrhenius term. Pt. 1
International Nuclear Information System (INIS)
Okoya, S.S.
1992-11-01
In this paper, we consider an extended model of a coupled nonlinear reaction-diffusion equation with Neumann-Neumann boundary conditions. We obtain upper linear growth bound for one of the components. We also find the corresponding bound for the case of Dirichlet-Dirichlet boundary conditions. (author). 12 refs
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.
International Nuclear Information System (INIS)
Ferreri, J. C.; Carmen, A. del
1998-01-01
A numerical study of the dynamics of pattern evolution in reaction-diffusion systems is performed, although limited to one spatial dimension. The diffusion coefficients are nonlinear, based on powers of the scalar variables. The system keeps the dynamics of previous studies in the literature, but the presence of nonlinear diffusion generates a field of strong nonlinear interactions due to the presence of receding travelling waves. This field is limited by the plane of symmetry of the space domain and the last born outgoing travelling wave. These effects are discussed. (author). 10 refs., 7 figs
Cluster geometry and survival probability in systems driven by reaction-diffusion dynamics
International Nuclear Information System (INIS)
Windus, Alastair; Jensen, Henrik J
2008-01-01
We consider a reaction-diffusion model incorporating the reactions A→φ, A→2A and 2A→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.
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.
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.
New mechanism of spiral wave initiation in a reaction-diffusion-mechanics system.
Weise, Louis D; Panfilov, Alexander V
2011-01-01
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.; Baker, Ruth E.; Gaffney, Eamonn A.; Maini, Philip K.; Seirin-Lee, Sungrim
2012-01-01
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.
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.
Spiral patterns near Turing instability in a discrete reaction diffusion system
International Nuclear Information System (INIS)
Li, Meifeng; Han, Bo; Xu, Li; Zhang, Guang
2013-01-01
In this paper, linear stability analysis is applied to an exponential discrete Lotka–Volterra system, which describes the competition between two identical species. Conditions for the Turing instability are obtained and the emergence of spiral patterns is demonstrated by means of numerical simulations in the vicinity of the bifurcation point. Moreover, the impact of crucial system parameters on the stability and coherence of spiral patterns is illustrated on several examples
Instability induced by cross-diffusion in reaction-diffusion systems
DEFF Research Database (Denmark)
Tian, Canrong; Lin, Zhigui; Pedersen, Michael
2010-01-01
In this paper the instability of the uniform equilibrium of a general strongly coupled reaction–diffusion is discussed. In unbounded domain and bounded domain the sufficient conditions for the instability are obtained respectively. The conclusion is applied to the ecosystem, it is shown that cros...... can induce the instability of an equilibrium which is stable for the kinetic system and for the self-diffusion–reaction system.......In this paper the instability of the uniform equilibrium of a general strongly coupled reaction–diffusion is discussed. In unbounded domain and bounded domain the sufficient conditions for the instability are obtained respectively. The conclusion is applied to the ecosystem, it is shown that cross-diffusion...
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.
Ducrot, Arnaud; Giletti, Thomas
2014-09-01
In this work we study the asymptotic behaviour of the Kermack-McKendrick reaction-diffusion system in a periodic environment with non-diffusive susceptible population. This problem was proposed by Kallen et al. as a model for the spatial spread for epidemics, where it can be reasonable to assume that the susceptible population is motionless. For arbitrary dimensional space we prove that large classes of solutions of such a system have an asymptotic spreading speed in large time, and that the infected population has some pulse-like asymptotic shape. The analysis of the one-dimensional problem is more developed, as we are able to uncover a much more accurate description of the profile of solutions. Indeed, we will see that, for some initially compactly supported infected population, the profile of the solution converges to some pulsating travelling wave with minimal speed, that is to some entire solution moving at a constant positive speed and whose profile's shape is periodic in time.
Curved fronts in the Belousov-Zhabotinskii reaction-diffusion systems in R2
Niu, Hong-Tao; Wang, Zhi-Cheng; Bu, Zhen-Hui
2018-05-01
In this paper we consider a diffusion system with the Belousov-Zhabotinskii (BZ for short) chemical reaction. Following Brazhnik and Tyson [4] and Pérez-Muñuzuri et al. [45], who predicted V-shaped fronts theoretically and discovered V-shaped fronts by experiments respectively, we give a rigorous mathematical proof of their results. We establish the existence of V-shaped traveling fronts in R2 by constructing a proper supersolution and a subsolution. Furthermore, we establish the stability of the V-shaped front in R2.
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.
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, ε. We also discover a short range of parameter values where random oscillations are observed. With an increase in the value of ε, 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, ε, and the substrate concentrations.
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...
Exact analytical solutions for nonlinear reaction-diffusion equations
International Nuclear Information System (INIS)
Liu Chunping
2003-01-01
By using a direct method via the computer algebraic system of Mathematica, some exact analytical solutions to a class of nonlinear reaction-diffusion equations are presented in closed form. Subsequently, the hyperbolic function solutions and the triangular function solutions of the coupled nonlinear reaction-diffusion equations are obtained in a unified way
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)
Lecca, Paola; Morpurgo, Daniele
2012-01-01
Reaction-diffusion based models have been widely used in the literature for modeling the growth of solid tumors. Many of the current models treat both diffusion/consumption of nutrients and cell proliferation. The majority of these models use classical transport/mass conservation equations for describing the distribution of molecular species in tumor spheroids, and the Fick's law for describing the flux of uncharged molecules (i.e oxygen, glucose). Commonly, the equations for the cell movement and proliferation are first order differential equations describing the rate of change of the velocity of the cells with respect to the spatial coordinates as a function of the nutrient's gradient. Several modifications of these equations have been developed in the last decade to explicitly indicate that the tumor includes cells, interstitial fluids and extracellular matrix: these variants provided a model of tumor as a multiphase material with these as the different phases. Most of the current reaction-diffusion tumor models are deterministic and do not model the diffusion as a local state-dependent process in a non-homogeneous medium at the micro- and meso-scale of the intra- and inter-cellular processes, respectively. Furthermore, a stochastic reaction-diffusion model in which diffusive transport of the molecular species of nutrients and chemotherapy drugs as well as the interactions of the tumor cells with these species is a novel approach. The application of this approach to he scase of non-small cell lung cancer treated with gemcitabine is also novel. We present a stochastic reaction-diffusion model of non-small cell lung cancer growth in the specification formalism of the tool Redi, we recently developed for simulating reaction-diffusion systems. We also describe how a spatial gradient of nutrients and oncological drugs affects the tumor progression. Our model is based on a generalization of the Fick's first diffusion law that allows to model diffusive transport in non
International Nuclear Information System (INIS)
Abdelmalek, Salem; Kouachi, Said
2007-01-01
To prove global existence for solutions of m-component reaction-diffusion systems presents fundamental difficulties in the case in which some components of the system satisfy Neumann boundary conditions while others satisfy nonhomogeneous Dirichlet boundary conditions and nonhomogeneous Robin boundary conditions. The purpose of this paper is to prove the existence of a global solution using a single inequality for the polynomial growth condition of the reaction terms. Our technique is based on the construction of polynomial functionals. This result generalizes those obtained recently by Kouachi et al (at press), Kouachi (2002 Electron. J. Diff. Eqns 2002 1), Kouachi (2001 Electron. J. Diff. Eqns 2001 1) and independently by Malham and Xin (1998 Commun. Math. Phys. 193 287)
Laser Spot Detection Based on Reaction Diffusion
Alejandro Vázquez-Otero; Danila Khikhlukha; J. M. Solano-Altamirano; Raquel Dormido; Natividad Duro
2016-01-01
Center-location of a laser spot is a problem of interest when the laser is used for processing and performing measurements. Measurement quality depends on correctly determining the location of the laser spot. Hence, improving and proposing algorithms for the correct location of the spots are fundamental issues in laser-based measurements. In this paper we introduce a Reaction Diffusion (RD) system as the main computational framework for robustly finding laser spot centers. The method presente...
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.
Zhang, Henggui; Garratt, Clifford J.; Kharche, Sanjay; Holden, Arun V.
2009-06-01
Human atrial tissue is an excitable system, in which myocytes are excitable elements, and cell-to-cell electrotonic interactions are via diffusive interactions of cell membrane potentials. We developed a family of excitable system models for human atrium at cellular, tissue and anatomical levels for both normal and chronic atrial fibrillation (AF) conditions. The effects of AF-induced remodelling of cell membrane ionic channels (reaction kinetics) and intercellular gap junctional coupling (diffusion) on atrial excitability, conduction of excitation waves and dynamics of re-entrant excitation waves are quantified. Both ionic channel and gap junctional coupling remodelling have rate dependent effects on atrial propagation. Membrane channel conductance remodelling allows the propagation of activity at higher rates than those sustained in normal tissue or in tissue with gap junctional remodelling alone. Membrane channel conductance remodelling is essential for the propagation of activity at rates higher than 300/min as seen in AF. Spatially heterogeneous gap junction coupling remodelling increased the risk of conduction block, an essential factor for the genesis of re-entry. In 2D and 3D anatomical models, the dynamical behaviours of re-entrant excitation waves are also altered by membrane channel modelling. This study provides insights to understand the pro-arrhythmic effects of AF-induced reaction and diffusion remodelling in atrial tissue.
International Nuclear Information System (INIS)
Ghorai, Santu; Poria, Swarup
2016-01-01
Spatiotemporal dynamics of a predator–prey system in presence of spatial diffusion is investigated in presence of additional food exists for predators. Conditions for stability of Hopf as well as Turing patterns in a spatial domain are determined by making use of the linear stability analysis. Impact of additional food is clear from these conditions. Numerical simulation results are presented in order to validate the analytical findings. Finally numerical simulations are carried out around the steady state under zero flux boundary conditions. With the help of numerical simulations, the different types of spatial patterns (including stationary spatial pattern, oscillatory pattern, and spatiotemporal chaos) are identified in this diffusive predator–prey system in presence of additional food, depending on the quantity, quality of the additional food and the spatial domain and other parameters of the model. The key observation is that spatiotemporal chaos can be controlled supplying suitable additional food to predator. These investigations may be useful to understand complex spatiotemporal dynamics of population dynamical models in presence of additional food.
Laser Spot Detection Based on Reaction Diffusion.
Vázquez-Otero, Alejandro; Khikhlukha, Danila; Solano-Altamirano, J M; Dormido, Raquel; Duro, Natividad
2016-03-01
Center-location of a laser spot is a problem of interest when the laser is used for processing and performing measurements. Measurement quality depends on correctly determining the location of the laser spot. Hence, improving and proposing algorithms for the correct location of the spots are fundamental issues in laser-based measurements. In this paper we introduce a Reaction Diffusion (RD) system as the main computational framework for robustly finding laser spot centers. The method presented is compared with a conventional approach for locating laser spots, and the experimental results indicate that RD-based computation generates reliable and precise solutions. These results confirm the flexibility of the new computational paradigm based on RD systems for addressing problems that can be reduced to a set of geometric operations.
Laser Spot Detection Based on Reaction Diffusion
Directory of Open Access Journals (Sweden)
Alejandro Vázquez-Otero
2016-03-01
Full Text Available Center-location of a laser spot is a problem of interest when the laser is used for processing and performing measurements. Measurement quality depends on correctly determining the location of the laser spot. Hence, improving and proposing algorithms for the correct location of the spots are fundamental issues in laser-based measurements. In this paper we introduce a Reaction Diffusion (RD system as the main computational framework for robustly finding laser spot centers. The method presented is compared with a conventional approach for locating laser spots, and the experimental results indicate that RD-based computation generates reliable and precise solutions. These results confirm the flexibility of the new computational paradigm based on RD systems for addressing problems that can be reduced to a set of geometric operations.
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.
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.
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
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
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
An Application of Equivalence Transformations to Reaction Diffusion Equations
Directory of Open Access Journals (Sweden)
Mariano Torrisi
2015-10-01
Full Text Available In this paper, we consider a quite general class of advection reaction diffusion systems. By using an equivalence generator, derived in a previous paper, the authors apply a projection theorem to determine some special forms of the constitutive functions that allow the extension by one of the two-dimensional principal Lie algebra. As an example, a special case is discussed at the end of the paper.
Reaction diffusion equations with boundary degeneracy
Directory of Open Access Journals (Sweden)
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.
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.
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
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 pulses: a combustion model
Energy Technology Data Exchange (ETDEWEB)
Campos, Daniel [Grup de FIsica EstadIstica, Dept. de FIsica, Universitat Autonoma de Barcelona, E-08193 Bellaterrra (Spain); Llebot, Josep Enric [Grup de FIsica EstadIstica, Dept. de FIsica, Universitat Autonoma de Barcelona, E-08193 Bellaterrra (Spain); Fort, Joaquim [Dept. de FIsica, Univ. de Girona, Campus de Montilivi, 17071 Girona, Catalonia (Spain)
2004-07-02
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 controlled growth of complex structures
Noorduin, Willem; Mahadevan, L.; Aizenberg, Joanna
2013-03-01
Understanding how the emergence of complex forms and shapes in biominerals came about is both of fundamental and practical interest. Although biomineralization processes and organization strategies to give higher order architectures have been studied extensively, synthetic approaches to mimic these self-assembled structures are highly complex and have been difficult to emulate, let alone replicate. The emergence of solution patterns has been found in reaction-diffusion systems such as Turing patterns and the BZ reaction. Intrigued by this spontaneous formation of complexity we explored if similar processes can lead to patterns in the solid state. We here identify a reaction-diffusion system in which the shape of the solidified products is a direct readout of the environmental conditions. Based on insights in the underlying mechanism, we developed a toolbox of engineering strategies to deterministically sculpt patterns and shapes, and combine different morphologies to create a landscape of hierarchical multi scale-complex tectonic architectures with unprecedented levels of complexity. These findings may hold profound implications for understanding, mimicking and ultimately expanding upon nature's morphogenesis strategies, allowing the synthesis of advanced highly complex microscale materials and devices. WLN acknowledges the Netherlands Organization for Scientific Research for financial support
Guiding brine shrimp through mazes by solving reaction diffusion equations
Singal, Krishma; Fenton, Flavio
Excitable systems driven by reaction diffusion equations have been shown to not only find solutions to mazes but to also to find the shortest path between the beginning and the end of the maze. In this talk we describe how we can use the Fitzhugh-Nagumo model, a generic model for excitable media, to solve a maze by varying the basin of attraction of its two fixed points. We demonstrate how two dimensional mazes are solved numerically using a Java Applet and then accelerated to run in real time by using graphic processors (GPUs). An application of this work is shown by guiding phototactic brine shrimp through a maze solved by the algorithm. Once the path is obtained, an Arduino directs the shrimp through the maze using lights from LEDs placed at the floor of the Maze. This method running in real time could be eventually used for guiding robots and cars through traffic.
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.
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.
Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations
Alzahrani, Hasnaa H.
2016-01-01
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
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.
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 traveling wave front as well as the existence and instability of a standing pulse solution if 0 traveling wave front as well as the existence and instability of an upside down standing pulse solution if 0 traveling wave back of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ] -w0, where w0 = α (β - 2 θ) > 0 is a positive constant, if 0 motivation to study the existence, stability, instability and bifurcations of the nonlinear waves is to study the existence and stability/instability of infinitely many fast/slow multiple traveling pulse solutions of the nonlinear system of reaction diffusion equations. The existence and stability of infinitely many fast multiple traveling pulse solutions are of great interests in mathematical neuroscience.
Stochastic flows, reaction-diffusion processes, and morphogenesis
International Nuclear Information System (INIS)
Kozak, J.J.; Hatlee, M.D.; Musho, M.K.; Politowicz, P.A.; Walsh, C.A.
1983-01-01
Recently, an exact procedure has been introduced [C. A. Walsh and J. J. Kozak, Phys. Rev. Lett.. 47: 1500 (1981)] for calculating the expected walk length for a walker undergoing random displacements on a finite or infinite (periodic) d-dimensional lattice with traps (reactive sites). The method (which is based on a classification of the symmetry of the sites surrounding the central deep trap and a coding of the fate of the random walker as it encounters a site of given symmetry) is applied here to several problems in lattice statistics for each of which exact results are presented. First, we assess the importance of lattice geometry in influencing the efficiency of reaction-diffusion processs in simple and multiple trap systems by reporting values of for square (cubic) versus hexagonal lattices in d = 2,3. We then show how the method may be applied to variable-step (distance-dependent) walks for a single walker on a given lattice and also demonstrate the calculation of the expected walk length for the case of multiple walkers. Finally, we make contact with recent discussions of ''mixing'' by showing that the degree of chaos associated with flows in certain lattice-systems can be calibrated by monitoring the lattice walks induced by the Poincare map of a certain parabolic function
Stochastic reaction-diffusion algorithms for macromolecular crowding
Sturrock, Marc
2016-06-01
Compartment-based (lattice-based) reaction-diffusion algorithms are often used for studying complex stochastic spatio-temporal processes inside cells. In this paper the influence of macromolecular crowding on stochastic reaction-diffusion simulations is investigated. Reaction-diffusion processes are considered on two different kinds of compartmental lattice, a cubic lattice and a hexagonal close packed lattice, and solved using two different algorithms, the stochastic simulation algorithm and the spatiocyte algorithm (Arjunan and Tomita 2010 Syst. Synth. Biol. 4, 35-53). Obstacles (modelling macromolecular crowding) are shown to have substantial effects on the mean squared displacement and average number of molecules in the domain but the nature of these effects is dependent on the choice of lattice, with the cubic lattice being more susceptible to the effects of the obstacles. Finally, improvements for both algorithms are presented.
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 and Chemotaxis for Decentralized Gathering on FPGAs
Directory of Open Access Journals (Sweden)
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 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.
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.
Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds
Desvillettes, Laurent; Fellner, Klemens
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.
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)
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.
Attractor of reaction-diffusion equations in Banach spaces
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José Valero
2001-04-01
Full Text Available In this paper we prove first some abstract theorems on existence of global attractors for differential inclusions generated by w-dissipative operators. Then these results are applied to reaction-diffusion equations in which the Babach space Lp is used as phase space. Finally, new results concerning the fractal dimension of the global attractor in the space L2 are obtained.
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.
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
Effects of two-scale transverse crack systems on the non-linear behaviour of a 2D SiC-SiC composite
Energy Technology Data Exchange (ETDEWEB)
Morvan, J.-M.; Baste, S. [Bordeaux-1 Univ., 33 - Talence (France). Lab. de Mecanique Physique
1998-07-31
By using both an ultrasonic device and an extensometer, it is possible to know which stiffness coefficients change during the damage process of a material and which part of the global strain is either elastic or inelastic. The influence of the two damage mechanisms is described for a woven 2D SiC-SiC composite. It appears that the two scales of this composite have a great influence on its behaviour. Two elementary mechanisms occur at both scales of the material: at the mesostructure level consisting of the bundles as well as of the inter-bundle matrix and at the microstructure level made from both the fibres and the intra-bundle matrix. The inelastic strains are sensitive to this two-scale effect: an increment of strain at constant stress that comes to saturation corresponding to the inter-bundle damage process and a strain which needs an increase in stress as cracking occurs at the fibres scale. With the help of a model that predicts the compliance changes caused by a crack system in a solid, it is possible to predict the crack density variation at both scales as well as the geometry of the various crack systems during monotonous loading. Furthermore, when the crack opening is taken into account, it appears that the inelastic strain is governed by the transverse crack density. (orig.) 12 refs.
Reaction-diffusion fronts with inhomogeneous initial conditions
Energy Technology Data Exchange (ETDEWEB)
Bena, I [Departement de Physique Theorique, Universite de Geneve, CH-1211 Geneva 4 (Switzerland); Droz, M [Departement de Physique Theorique, Universite de Geneve, CH-1211 Geneva 4 (Switzerland); Martens, K [Departement de Physique Theorique, Universite de Geneve, CH-1211 Geneva 4 (Switzerland); Racz, Z [Institute for Theoretical Physics, Eoetvoes University, 1117 Budapest (Hungary)
2007-02-14
Properties of reaction zones resulting from A+B {yields} C type reaction-diffusion processes are investigated by analytical and numerical methods. The reagents A and B are separated initially and, in addition, there is an initial macroscopic inhomogeneity in the distribution of the B species. For simple two-dimensional geometries, exact analytical results are presented for the time evolution of the geometric shape of the front. We also show using cellular automata simulations that the fluctuations can be neglected both in the shape and in the width of the front.
On the solutions of fractional reaction-diffusion equations
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Jagdev Singh
2013-05-01
Full Text Available In this paper, we obtain the solution of a fractional reaction-diffusion equation associated with the generalized Riemann-Liouville fractional derivative as the time derivative and Riesz-Feller fractional derivative as the space-derivative. The results are derived by the application of the Laplace and Fourier transforms in compact and elegant form in terms of Mittag-Leffler function and H-function. The results obtained here are of general nature and include the results investigated earlier by many authors.
Explosive instabilities of reaction-diffusion equations including pinch effects
International Nuclear Information System (INIS)
Wilhelmsson, H.
1992-01-01
Particular solutions of reaction-diffusion equations for temperature are obtained for explosively unstable situations. As a result of the interplay between inertial, diffusion, pinch and source processes certain 'bell-shaped' distributions may grow explosively in time with preserved shape of the spatial distribution. The effect of the pinch, which requires a density inhomogeneity, is found to diminish the effect of diffusion, or inversely to support the inertial and source processes in creating the explosion. The results may be described in terms of elliptic integrals or. more simply, by means of expansions in the spatial coordinate. An application is the temperature evolution of a burning fusion plasma. (au) (18 refs.)
Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations
International Nuclear Information System (INIS)
Indekeu, Joseph O; Smets, Ruben
2017-01-01
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. (paper)
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.
Directory of Open Access Journals (Sweden)
Le Novère Nicolas
2010-03-01
Full Text Available Abstract Background Most cellular signal transduction mechanisms depend on a few molecular partners whose roles depend on their position and movement in relation to the input signal. This movement can follow various rules and take place in different compartments. Additionally, the molecules can form transient complexes. Complexation and signal transduction depend on the specific states partners and complexes adopt. Several spatial simulator have been developed to date, but none are able to model reaction-diffusion of realistic multi-state transient complexes. Results Meredys allows for the simulation of multi-component, multi-feature state molecular species in two and three dimensions. Several compartments can be defined with different diffusion and boundary properties. The software employs a Brownian dynamics engine to simulate reaction-diffusion systems at the reactive particle level, based on compartment properties, complex structure, and hydro-dynamic radii. Zeroth-, first-, and second order reactions are supported. The molecular complexes have realistic geometries. Reactive species can contain user-defined feature states which can modify reaction rates and outcome. Models are defined in a versatile NeuroML input file. The simulation volume can be split in subvolumes to speed up run-time. Conclusions Meredys provides a powerful and versatile way to run accurate simulations of molecular and sub-cellular systems, that complement existing multi-agent simulation systems. Meredys is a Free Software and the source code is available at http://meredys.sourceforge.net/.
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)
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)
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.
International Nuclear Information System (INIS)
Han, Renji; Dai, Binxiang
2017-01-01
Highlights: • We model general two-dimensional reaction-diffusion with nonlocal delay. • The existence of unique positive steady state is studied. • The bilinear form for the proposed system is given. • The existence, direction of Hopf bifurcation are given by symmetry method. - Abstract: A nonlocal delayed reaction-diffusive two-species model with Dirichlet boundary condition and general functional response is investigated in this paper. Based on the Lyapunov–Schmidt reduction, the existence, bifurcation direction and stability of Hopf bifurcating periodic orbits near the positive spatially nonhomogeneous steady-state solution are obtained, where the time delay is taken as the bifurcation parameter. Moreover, the general results are applied to a diffusive Lotka–Volterra type food-limited population model with nonlocal delay effect, and it is found that diffusion and nonlocal delay can also affect the other dynamic behavior of the system by numerical experiments.
Semi-analytical solutions of the Schnakenberg model of a reaction-diffusion cell with feedback
Al Noufaey, K. S.
2018-06-01
This paper considers the application of a semi-analytical method to the Schnakenberg model of a reaction-diffusion cell. The semi-analytical method is based on the Galerkin method which approximates the original governing partial differential equations as a system of ordinary differential equations. Steady-state curves, bifurcation diagrams and the region of parameter space in which Hopf bifurcations occur are presented for semi-analytical solutions and the numerical solution. The effect of feedback control, via altering various concentrations in the boundary reservoirs in response to concentrations in the cell centre, is examined. It is shown that increasing the magnitude of feedback leads to destabilization of the system, whereas decreasing this parameter to negative values of large magnitude stabilizes the system. The semi-analytical solutions agree well with numerical solutions of the governing equations.
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.
Hybrid approaches for multiple-species stochastic reaction-diffusion models.
Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K; Byrne, Helen
2015-01-01
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.
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.
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
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.
Sheng, Yin; Zhang, Hao; Zeng, Zhigang
2017-10-01
This paper is concerned with synchronization for a class of reaction-diffusion neural networks with Dirichlet boundary conditions and infinite discrete time-varying delays. By utilizing theories of partial differential equations, Green's formula, inequality techniques, and the concept of comparison, algebraic criteria are presented to guarantee master-slave synchronization of the underlying reaction-diffusion neural networks via a designed controller. Additionally, sufficient conditions on exponential synchronization of reaction-diffusion neural networks with finite time-varying delays are established. The proposed criteria herein enhance and generalize some published ones. Three numerical examples are presented to substantiate the validity and merits of the obtained theoretical results.
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.
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
Directory of Open Access Journals (Sweden)
Qiankun Song
2007-06-01
Full Text Available Impulsive bidirectional associative memory neural network model with time-varying delays and reaction-diffusion terms is considered. Several sufficient conditions ensuring the existence, uniqueness, and global exponential stability of equilibrium point for the addressed neural network are derived by M-matrix theory, analytic methods, and inequality techniques. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The obtained results in this paper are less restrictive than previously known criteria. Two examples are given to show the effectiveness of the obtained results.
Directory of Open Access Journals (Sweden)
Cao Jinde
2007-01-01
Full Text Available Impulsive bidirectional associative memory neural network model with time-varying delays and reaction-diffusion terms is considered. Several sufficient conditions ensuring the existence, uniqueness, and global exponential stability of equilibrium point for the addressed neural network are derived by M-matrix theory, analytic methods, and inequality techniques. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. The obtained results in this paper are less restrictive than previously known criteria. Two examples are given to show the effectiveness of the obtained results.
Towards reaction-diffusion computing devices based on minority-carrier transport in semiconductors
International Nuclear Information System (INIS)
Asai, Tetsuya; Adamatzky, Andrew; Amemiya, Yoshihito
2004-01-01
Reaction-diffusion (RD) chemical systems are known to realize sensible computation when both data and results of the computation are encoded in concentration profiles of chemical species; the computation is implemented via spreading and interaction of either diffusive or phase waves. Thin-layer chemical systems are thought of therefore as massively-parallel locally-connected computing devices, where micro-volume of the medium is analogous to an elementary processor. Practical applications of the RD chemical systems are reduced however due to very low speed of traveling waves which makes real-time computation senseless. To overcome the speed-limitations while preserving unique features of RD computers we propose a semiconductor RD computing device where minority carriers diffuse as chemical species and reaction elements are represented by p-n-p-n diodes. We offer blue-prints of the RD semiconductor devices, and study in computer simulation propagation phenomena of the density wave of minority carriers. We then demonstrate what computational problems can be solved in RD semiconductor devices and evaluate space-time complexity of computation in the devices
Spatiotemporal Patterns in a Ratio-Dependent Food Chain Model with Reaction-Diffusion
Directory of Open Access Journals (Sweden)
Lei Zhang
2014-01-01
Full Text Available Predator-prey models describe biological phenomena of pursuit-evasion interaction. And this interaction exists widely in the world for the necessary energy supplement of species. In this paper, we have investigated a ratio-dependent spatially extended food chain model. Based on the bifurcation analysis (Hopf and Turing, we give the spatial pattern formation via numerical simulation, that is, the evolution process of the system near the coexistence equilibrium point (u2*,v2*,w2*, and find that the model dynamics exhibits complex pattern replication. For fixed parameters, on increasing the control parameter c1, the sequence “holes → holes-stripe mixtures → stripes → spots-stripe mixtures → spots” pattern is observed. And in the case of pure Hopf instability, the model exhibits chaotic wave pattern replication. Furthermore, we consider the pattern formation in the case of which the top predator is extinct, that is, the evolution process of the system near the equilibrium point (u1*,v1*,0, and find that the model dynamics exhibits stripes-spots pattern replication. Our results show that reaction-diffusion model is an appropriate tool for investigating fundamental mechanism of complex spatiotemporal dynamics. It will be useful for studying the dynamic complexity of ecosystems.
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Inci Cilingir Sungu
2015-01-01
Full Text Available A new application of the hybrid generalized differential transform and finite difference method is proposed by solving time fractional nonlinear reaction-diffusion equations. This method is a combination of the multi-time-stepping temporal generalized differential transform and the spatial finite difference methods. The procedure first converts the time-evolutionary equations into Poisson equations which are then solved using the central difference method. The temporal differential transform method as used in the paper takes care of stability and the finite difference method on the resulting equation results in a system of diagonally dominant linear algebraic equations. The Gauss-Seidel iterative procedure then used to solve the linear system thus has assured convergence. To have optimized convergence rate, numerical experiments were done by using a combination of factors involving multi-time-stepping, spatial step size, and degree of the polynomial fit in time. It is shown that the hybrid technique is reliable, accurate, and easy to apply.
Gan, Qintao; Lv, Tianshi; Fu, Zhenhua
2016-04-01
In this paper, the synchronization problem for a class of generalized neural networks with time-varying delays and reaction-diffusion terms is investigated concerning Neumann boundary conditions in terms of p-norm. The proposed generalized neural networks model includes reaction-diffusion local field neural networks and reaction-diffusion static neural networks as its special cases. By establishing a new inequality, some simple and useful conditions are obtained analytically to guarantee the global exponential synchronization of the addressed neural networks under the periodically intermittent control. According to the theoretical results, the influences of diffusion coefficients, diffusion space, and control rate on synchronization are analyzed. Finally, the feasibility and effectiveness of the proposed methods are shown by simulation examples, and by choosing different diffusion coefficients, diffusion spaces, and control rates, different controlled synchronization states can be obtained.
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.
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.
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.
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
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.
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.
Flexible single molecule simulation of reaction-diffusion processes
International Nuclear Information System (INIS)
Hellander, Stefan; Loetstedt, Per
2011-01-01
An algorithm is developed for simulation of the motion and reactions of single molecules at a microscopic level. The molecules diffuse in a solvent and react with each other or a polymer and molecules can dissociate. Such simulations are of interest e.g. in molecular biology. The algorithm is similar to the Green's function reaction dynamics (GFRD) algorithm by van Zon and ten Wolde where longer time steps can be taken by computing the probability density functions (PDFs) and then sample from the distribution functions. Our computation of the PDFs is much less complicated than GFRD and more flexible. The solution of the partial differential equation for the PDF is split into two steps to simplify the calculations. The sampling is without splitting error in two of the coordinate directions for a pair of molecules and a molecule-polymer interaction and is approximate in the third direction. The PDF is obtained either from an analytical solution or a numerical discretization. The errors due to the operator splitting, the partitioning of the system, and the numerical approximations are analyzed. The method is applied to three different systems involving up to four reactions. Comparisons with other mesoscopic and macroscopic models show excellent agreement.
Soft tissue deformation modelling through neural dynamics-based reaction-diffusion mechanics.
Zhang, Jinao; Zhong, Yongmin; Gu, Chengfan
2018-05-30
Soft tissue deformation modelling forms the basis of development of surgical simulation, surgical planning and robotic-assisted minimally invasive surgery. This paper presents a new methodology for modelling of soft tissue deformation based on reaction-diffusion mechanics via neural dynamics. The potential energy stored in soft tissues due to a mechanical load to deform tissues away from their rest state is treated as the equivalent transmembrane potential energy, and it is distributed in the tissue masses in the manner of reaction-diffusion propagation of nonlinear electrical waves. The reaction-diffusion propagation of mechanical potential energy and nonrigid mechanics of motion are combined to model soft tissue deformation and its dynamics, both of which are further formulated as the dynamics of cellular neural networks to achieve real-time computational performance. The proposed methodology is implemented with a haptic device for interactive soft tissue deformation with force feedback. Experimental results demonstrate that the proposed methodology exhibits nonlinear force-displacement relationship for nonlinear soft tissue deformation. Homogeneous, anisotropic and heterogeneous soft tissue material properties can be modelled through the inherent physical properties of mass points. Graphical abstract Soft tissue deformation modelling with haptic feedback via neural dynamics-based reaction-diffusion mechanics.
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.
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.
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
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.
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.
Delay-induced Turing-like waves for one-species reaction-diffusion model on a network
Petit, Julien; Carletti, Timoteo; Asllani, Malbor; Fanelli, Duccio
2015-09-01
A one-species time-delay reaction-diffusion system defined on a complex network is studied. Traveling waves are predicted to occur following a symmetry-breaking instability of a homogeneous stationary stable solution, subject to an external nonhomogeneous perturbation. These are generalized Turing-like waves that materialize in a single-species populations dynamics model, as the unexpected byproduct of the imposed delay in the diffusion part. Sufficient conditions for the onset of the instability are mathematically provided by performing a linear stability analysis adapted to time-delayed differential equations. The method here developed exploits the properties of the Lambert W-function. The prediction of the theory are confirmed by direct numerical simulation carried out for a modified version of the classical Fisher model, defined on a Watts-Strogatz network and with the inclusion of the delay.
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.
Reaction-diffusion processes in zero transverse dimensions as toy models for high-energy QCD
International Nuclear Information System (INIS)
Armesto, Nestor; Bondarenko, Sergey; Quiroga-Arias, Paloma; Milhano, Jose Guilherme
2008-01-01
We examine numerically different zero-dimensional reaction-diffusion processes as candidate toy models for high-energy QCD evolution. Of the models examined-Reggeon Field Theory, Directed Percolation and Reversible Processes-only the latter shows the behaviour commonly expected, namely an increase of the scattering amplitude with increasing rapidity. Further, we find that increasing recombination terms, quantum loops and the heuristic inclusion of a running of the couplings, generically slow down the evolution.
Numerical Solutions of Singularly Perturbed Reaction Diffusion Equation with Sobolev Gradients
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Nauman Raza
2013-01-01
Full Text Available Critical points related to the singular perturbed reaction diffusion models are calculated using weighted Sobolev gradient method in finite element setting. Performance of different Sobolev gradients has been discussed for varying diffusion coefficient values. A comparison is shown between the weighted and unweighted Sobolev gradients in two and three dimensions. The superiority of the method is also demonstrated by showing comparison with Newton's method.
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.
Passivity analysis for uncertain BAM neural networks with time delays and reaction-diffusions
Zhou, Jianping; Xu, Shengyuan; Shen, Hao; Zhang, Baoyong
2013-08-01
This article deals with the problem of passivity analysis for delayed reaction-diffusion bidirectional associative memory (BAM) neural networks with weight uncertainties. By using a new integral inequality, we first present a passivity condition for the nominal networks, and then extend the result to the case with linear fractional weight uncertainties. The proposed conditions are expressed in terms of linear matrix inequalities, and thus can be checked easily. Examples are provided to demonstrate the effectiveness of the proposed results.
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)
A minimally-resolved immersed boundary model for reaction-diffusion problems
Pal Singh Bhalla, A; Griffith, BE; Patankar, NA; Donev, A
2013-01-01
We develop an immersed boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a minimally-resolved "blob" using many fewer degrees of freedom per particle than standard discretization approaches. More complicated or more highly resolved particle shapes can be built out of a collection of reactive blobs. We demonstrate numerically that the blo...
Contribution to an effective design method for stationary reaction-diffusion patterns
Energy Technology Data Exchange (ETDEWEB)
Szalai, István; Horváth, Judit [Laboratory of Nonlinear Chemical Dynamics, Institute of Chemistry, Eötvös Loránd University, P.O. Box 32, H-1518 Budapest 112 (Hungary); De Kepper, Patrick [Centre de Recherche Paul Pascal, CNRS, University of Bordeaux, 115, Avenue Schweitzer, F-33600 Pessac (France)
2015-06-15
The British mathematician Alan Turing predicted, in his seminal 1952 publication, that stationary reaction-diffusion patterns could spontaneously develop in reacting chemical or biochemical solutions. The first two clear experimental demonstrations of such a phenomenon were not made before the early 1990s when the design of new chemical oscillatory reactions and appropriate open spatial chemical reactors had been invented. Yet, the number of pattern producing reactions had not grown until 2009 when we developed an operational design method, which takes into account the feeding conditions and other specificities of real open spatial reactors. Since then, on the basis of this method, five additional reactions were shown to produce stationary reaction-diffusion patterns. To gain a clearer view on where our methodical approach on the patterning capacity of a reaction stands, numerical studies in conditions that mimic true open spatial reactors were made. In these numerical experiments, we explored the patterning capacity of Rabai's model for pH driven Landolt type reactions as a function of experimentally attainable parameters that control the main time and length scales. Because of the straightforward reversible binding of protons to carboxylate carrying polymer chains, this class of reaction is at the base of the chemistry leading to most of the stationary reaction-diffusion patterns presently observed. We compare our model predictions with experimental observations and comment on agreements and differences.
Contribution to an effective design method for stationary reaction-diffusion patterns
International Nuclear Information System (INIS)
Szalai, István; Horváth, Judit; De Kepper, Patrick
2015-01-01
The British mathematician Alan Turing predicted, in his seminal 1952 publication, that stationary reaction-diffusion patterns could spontaneously develop in reacting chemical or biochemical solutions. The first two clear experimental demonstrations of such a phenomenon were not made before the early 1990s when the design of new chemical oscillatory reactions and appropriate open spatial chemical reactors had been invented. Yet, the number of pattern producing reactions had not grown until 2009 when we developed an operational design method, which takes into account the feeding conditions and other specificities of real open spatial reactors. Since then, on the basis of this method, five additional reactions were shown to produce stationary reaction-diffusion patterns. To gain a clearer view on where our methodical approach on the patterning capacity of a reaction stands, numerical studies in conditions that mimic true open spatial reactors were made. In these numerical experiments, we explored the patterning capacity of Rabai's model for pH driven Landolt type reactions as a function of experimentally attainable parameters that control the main time and length scales. Because of the straightforward reversible binding of protons to carboxylate carrying polymer chains, this class of reaction is at the base of the chemistry leading to most of the stationary reaction-diffusion patterns presently observed. We compare our model predictions with experimental observations and comment on agreements and differences
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.
Huang, Rui; Jin, Chunhua; Mei, Ming; Yin, Jingxue
2018-06-01
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.
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.
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
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.
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.
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.
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.
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
Reaction time for trimolecular reactions in compartment-based reaction-diffusion models
Li, Fei; Chen, Minghan; Erban, Radek; Cao, Yang
2018-05-01
Trimolecular reaction models are investigated in the compartment-based (lattice-based) framework for stochastic reaction-diffusion modeling. The formulae for the first collision time and the mean reaction time are derived for the case where three molecules are present in the solution under periodic boundary conditions. For the case of reflecting boundary conditions, similar formulae are obtained using a computer-assisted approach. The accuracy of these formulae is further verified through comparison with numerical results. The presented derivation is based on the first passage time analysis of Montroll [J. Math. Phys. 10, 753 (1969)]. Montroll's results for two-dimensional lattice-based random walks are adapted and applied to compartment-based models of trimolecular reactions, which are studied in one-dimensional or pseudo one-dimensional domains.
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.
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.
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.
Regularity of random attractors for fractional stochastic reaction-diffusion equations on Rn
Gu, Anhui; Li, Dingshi; Wang, Bixiang; Yang, Han
2018-06-01
We investigate the regularity of random attractors for the non-autonomous non-local fractional stochastic reaction-diffusion equations in Hs (Rn) with s ∈ (0 , 1). We prove the existence and uniqueness of the tempered random attractor that is compact in Hs (Rn) and attracts all tempered random subsets of L2 (Rn) with respect to the norm of Hs (Rn). The main difficulty is to show the pullback asymptotic compactness of solutions in Hs (Rn) due to the noncompactness of Sobolev embeddings on unbounded domains and the almost sure nondifferentiability of the sample paths of the Wiener process. We establish such compactness by the ideas of uniform tail-estimates and the spectral decomposition of solutions in bounded domains.
Schwarz, Karsten; Rieger, Heiko
2013-03-01
We present an efficient Monte Carlo method to simulate reaction-diffusion processes with spatially varying particle annihilation or transformation rates as it occurs for instance in the context of motor-driven intracellular transport. Like Green's function reaction dynamics and first-passage time methods, our algorithm avoids small diffusive hops by propagating sufficiently distant particles in large hops to the boundaries of protective domains. Since for spatially varying annihilation or transformation rates the single particle diffusion propagator is not known analytically, we present an algorithm that generates efficiently either particle displacements or annihilations with the correct statistics, as we prove rigorously. The numerical efficiency of the algorithm is demonstrated with an illustrative example.
A Reaction-Diffusion-Based Coding Rate Control Mechanism for Camera Sensor Networks
Directory of Open Access Journals (Sweden)
Naoki Wakamiya
2010-08-01
Full Text Available A wireless camera sensor network is useful for surveillance and monitoring for its visibility and easy deployment. However, it suffers from the limited capacity of wireless communication and a network is easily overflown with a considerable amount of video traffic. In this paper, we propose an autonomous video coding rate control mechanism where each camera sensor node can autonomously determine its coding rate in accordance with the location and velocity of target objects. For this purpose, we adopted a biological model, i.e., reaction-diffusion model, inspired by the similarity of biological spatial patterns and the spatial distribution of video coding rate. Through simulation and practical experiments, we verify the effectiveness of our proposal.
A reaction-diffusion-based coding rate control mechanism for camera sensor networks.
Yamamoto, Hiroshi; Hyodo, Katsuya; Wakamiya, Naoki; Murata, Masayuki
2010-01-01
A wireless camera sensor network is useful for surveillance and monitoring for its visibility and easy deployment. However, it suffers from the limited capacity of wireless communication and a network is easily overflown with a considerable amount of video traffic. In this paper, we propose an autonomous video coding rate control mechanism where each camera sensor node can autonomously determine its coding rate in accordance with the location and velocity of target objects. For this purpose, we adopted a biological model, i.e., reaction-diffusion model, inspired by the similarity of biological spatial patterns and the spatial distribution of video coding rate. Through simulation and practical experiments, we verify the effectiveness of our proposal.
Energy Technology Data Exchange (ETDEWEB)
Hepburn, I.; De Schutter, E., E-mail: erik@oist.jp [Computational Neuroscience Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904 0495 (Japan); Theoretical Neurobiology & Neuroengineering, University of Antwerp, Antwerp 2610 (Belgium); Chen, W. [Computational Neuroscience Unit, Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904 0495 (Japan)
2016-08-07
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.
Accurate numerical simulation of reaction-diffusion processes for heavy oil recovery
Energy Technology Data Exchange (ETDEWEB)
Govind, P.A.; Srinivasan, S. [Society of Petroleum Engineers, Richardson, TX (United States)]|[Texas Univ., Austin, TX (United States)
2008-10-15
This study evaluated a reaction-diffusion simulation tool designed to analyze the displacement of carbon dioxide (CO{sub 2}) in a simultaneous injection of carbon dioxide and elemental sodium in a heavy oil reservoir. Sodium was used due to the exothermic reaction of sodium with in situ that occurs when heat is used to reduce oil viscosity. The process also results in the formation of sodium hydroxide that reduces interfacial tension at the bitumen interface. A commercial simulation tool was used to model the sodium transport mechanism to the reaction interface through diffusion as well as the reaction zone's subsequent displacement. The aim of the study was to verify if the in situ reaction was able to generate sufficient heat to reduce oil viscosity and improve the displacement of the heavy oil. The study also assessed the accuracy of the reaction front simulation tool, in which an alternate method was used to model the propagation front as a moving heat source. The sensitivity of the simulation results were then evaluated in relation to the diffusion coefficient in order to understand the scaling characteristics of the reaction-diffusion zone. A pore-scale simulation was then up-scaled to grid blocks. Results of the study showed that when sodium suspended in liquid CO{sub 2} is injected into reservoirs, it diffuses through the carrier phase and interacts with water. A random walk diffusion algorithm with reactive dissipation was implemented to more accurately characterize reaction and diffusion processes. It was concluded that the algorithm modelled physical dispersion while neglecting the effect of numerical dispersion. 10 refs., 3 tabs., 24 figs.
Directory of Open Access Journals (Sweden)
Shahid Hasnain
2017-07-01
Full Text Available This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.
Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman
2017-07-01
This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.
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
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.
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
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
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.
Quantitative modeling of the reaction/diffusion kinetics of two-chemistry photopolymers
Kowalski, Benjamin Andrew
Optically driven diffusion in photopolymers is an appealing material platform for a broad range of applications, in which the recorded refractive index patterns serve either as images (e.g. data storage, display holography) or as optical elements (e.g. custom GRIN components, integrated optical devices). A quantitative understanding of the reaction/diffusion kinetics is difficult to obtain directly, but is nevertheless necessary in order to fully exploit the wide array of design freedoms in these materials. A general strategy for characterizing these kinetics is proposed, in which key processes are decoupled and independently measured. This strategy enables prediction of a material's potential refractive index change, solely on the basis of its chemical components. The degree to which a material does not reach this potential reveals the fraction of monomer that has participated in unwanted reactions, reducing spatial resolution and dynamic range. This approach is demonstrated for a model material similar to commercial media, achieving quantitative predictions of index response over three orders of exposure dose (~1 to ~103 mJ cm-2) and three orders of feature size (0.35 to 500 microns). The resulting insights enable guided, rational design of new material formulations with demonstrated performance improvement.
Bifurcation analysis of a delay reaction-diffusion malware propagation model with feedback control
Zhu, Linhe; Zhao, Hongyong; Wang, Xiaoming
2015-05-01
With the rapid development of network information technology, information networks security has become a very critical issue in our work and daily life. This paper attempts to develop a delay reaction-diffusion model with a state feedback controller to describe the process of malware propagation in mobile wireless sensor networks (MWSNs). By analyzing the stability and Hopf bifurcation, we show that the state feedback method can successfully be used to control unstable steady states or periodic oscillations. Moreover, formulas for determining the properties of the bifurcating periodic oscillations are derived by applying the normal form method and center manifold theorem. Finally, we conduct extensive simulations on large-scale MWSNs to evaluate the proposed model. Numerical evidences show that the linear term of the controller is enough to delay the onset of the Hopf bifurcation and the properties of the bifurcation can be regulated to achieve some desirable behaviors by choosing the appropriate higher terms of the controller. Furthermore, we obtain that the spatial-temporal dynamic characteristics of malware propagation are closely related to the rate constant for nodes leaving the infective class for recovered class and the mobile behavior of nodes.
A reaction-diffusion model for radiation-induced bystander effects.
Olobatuyi, Oluwole; de Vries, Gerda; Hillen, Thomas
2017-08-01
We develop and analyze a reaction-diffusion model to investigate the dynamics of the lifespan of a bystander signal emitted when cells are exposed to radiation. Experimental studies by Mothersill and Seymour 1997, using malignant epithelial cell lines, found that an emitted bystander signal can still cause bystander effects in cells even 60 h after its emission. Several other experiments have also shown that the signal can persist for months and even years. Also, bystander effects have been hypothesized as one of the factors responsible for the phenomenon of low-dose hyper-radiosensitivity and increased radioresistance (HRS/IRR). Here, we confirm this hypothesis with a mathematical model, which we fit to Joiner's data on HRS/IRR in a T98G glioma cell line. Furthermore, we use phase plane analysis to understand the full dynamics of the signal's lifespan. We find that both single and multiple radiation exposure can lead to bystander signals that either persist temporarily or permanently. We also found that, in an heterogeneous environment, the size of the domain exposed to radiation and the number of radiation exposures can determine whether a signal will persist temporarily or permanently. Finally, we use sensitivity analysis to identify those cell parameters that affect the signal's lifespan and the signal-induced cell death the most.
Dóka, Éva; Lente, Gábor
2017-04-13
This work presents a rigorous mathematical study of the effect of unavoidable inhomogeneities in laser flash photolysis experiments. There are two different kinds of inhomegenities: the first arises from diffusion, whereas the second one has geometric origins (the shapes of the excitation and detection light beams). Both of these are taken into account in our reported model, which gives rise to a set of reaction-diffusion type partial differential equations. These equations are solved by a specially developed finite volume method. As an example, the aqueous reaction between the sulfate ion radical and iodide ion is used, for which sufficiently detailed experimental data are available from an earlier publication. The results showed that diffusion itself is in general too slow to influence the kinetic curves on the usual time scales of laser flash photolysis experiments. However, the use of the absorbances measured (e.g., to calculate the molar absorption coefficients of transient species) requires very detailed mathematical consideration and full knowledge of the geometrical shapes of the excitation laser beam and the separate detection light beam. It is also noted that the usual pseudo-first-order approach to evaluating the kinetic traces can be used successfully even if the usual large excess condition is not rigorously met in the reaction cell locally.
A Reaction-Diffusion Model for Synapse Growth and Long-Term Memory
Liu, Kang; Lisman, John; Hagan, Michael
Memory storage involves strengthening of synaptic transmission known as long-term potentiation (LTP). The late phase of LTP is associated with structural processes that enlarge the synapse. Yet, synapses must be stable, despite continual subunit turnover, over the lifetime of an encoded memory. These considerations suggest that synapses are variable-size stable structure (VSSS), meaning they can switch between multiple metastable structures with different sizes. The mechanisms underlying VSSS are poorly understood. While experiments and theory have suggested that the interplay between diffusion and receptor-scaffold interactions can lead to a preferred stable size for synaptic domains, such a mechanism cannot explain how synapses adopt widely different sizes. Here we develop a minimal reaction-diffusion model of VSSS for synapse growth, incorporating the recent observation from super-resolution microscopy that neural activity can build compositional heterogeneities within synaptic domains. We find that introducing such heterogeneities can change the stable domain size in a controlled manner. We discuss a potential connection between this model and experimental data on synapse sizes, and how it provides a possible mechanism to structurally encode graded long-term memory. We acknowledge the support from NSF INSPIRE Award number IOS-1526941 (KL, MFH, JL) and the Brandeis Center for Bioinspired Soft Materials, an NSF MRSEC, DMR- 1420382 (MFH).
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.
A reaction-diffusion model to capture disparity selectivity in primary visual cortex.
Directory of Open Access Journals (Sweden)
Mohammed Sultan Mohiuddin Siddiqui
Full Text Available Decades of experimental studies are available on disparity selective cells in visual cortex of macaque and cat. Recently, local disparity map for iso-orientation sites for near-vertical edge preference is reported in area 18 of cat visual cortex. No experiment is yet reported on complete disparity map in V1. Disparity map for layer IV in V1 can provide insight into how disparity selective complex cell receptive field is organized from simple cell subunits. Though substantial amounts of experimental data on disparity selective cells is available, no model on receptive field development of such cells or disparity map development exists in literature. We model disparity selectivity in layer IV of cat V1 using a reaction-diffusion two-eye paradigm. In this model, the wiring between LGN and cortical layer IV is determined by resource an LGN cell has for supporting connections to cortical cells and competition for target space in layer IV. While competing for target space, the same type of LGN cells, irrespective of whether it belongs to left-eye-specific or right-eye-specific LGN layer, cooperate with each other while trying to push off the other type. Our model captures realistic 2D disparity selective simple cell receptive fields, their response properties and disparity map along with orientation and ocular dominance maps. There is lack of correlation between ocular dominance and disparity selectivity at the cell population level. At the map level, disparity selectivity topography is not random but weakly clustered for similar preferred disparities. This is similar to the experimental result reported for macaque. The details of weakly clustered disparity selectivity map in V1 indicate two types of complex cell receptive field organization.
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.
Chen, Wu-Hua; Luo, Shixian; Zheng, Wei Xing
2016-12-01
This paper presents a new impulsive synchronization criterion of two identical reaction-diffusion neural networks with discrete and unbounded distributed delays. The new criterion is established by applying an impulse-time-dependent Lyapunov functional combined with the use of a new type of integral inequality for treating the reaction-diffusion terms. The impulse-time-dependent feature of the proposed Lyapunov functional can capture more hybrid dynamical behaviors of the impulsive reaction-diffusion neural networks than the conventional impulse-time-independent Lyapunov functions/functionals, while the new integral inequality, which is derived from Wirtinger's inequality, overcomes the conservatism introduced by the integral inequality used in the previous results. Numerical examples demonstrate the effectiveness of the proposed method. Later, the developed impulsive synchronization method is applied to build a spatiotemporal chaotic cryptosystem that can transmit an encrypted image. The experimental results verify that the proposed image-encrypting cryptosystem has the advantages of large key space and high security against some traditional attacks.
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 0exact solutions 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).
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...nonlinearity, nonlinear boundary conditions, dead core set, chemical reactions Work Unit Number I - Applied Analysis (1) Seccion de Matematicas
Alternans and Spiral Breakup in an Excitable Reaction-Diffusion System: A Simulation Study.
Gani, M Osman; Ogawa, Toshiyuki
2014-01-01
The determination of the mechanisms of spiral breakup in excitable media is still an open problem for researchers. In the context of cardiac electrophysiological activities, spiral breakup exhibits complex spatiotemporal pattern known as ventricular fibrillation. The latter is the major cause of sudden cardiac deaths all over the world. In this paper, we numerically study the instability of periodic planar traveling wave solution in two dimensions. The emergence of stable spiral pattern is observed in the considered model. This pattern occurs when the heart is malfunctioning (i.e., ventricular tachycardia). We show that the spiral wave breakup is a consequence of the transverse instability of the planar traveling wave solutions. The alternans, that is, the oscillation of pulse widths, is observed in our simulation results. Moreover, we calculate the widths of spiral pulses numerically and observe that the stable spiral pattern bifurcates to an oscillatory wave pattern in a one-parameter family of solutions. The spiral breakup occurs far below the bifurcation when the maximum and the minimum excited states become more distinct, and hence the alternans becomes more pronounced.
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........ Finally, we examine the long-time behavior of the global solution. We show that the solution is global and fast if the initial data are small....
Dynamics of embedded curves by doubly-nonlocal reaction-diffusion systems
von Brecht, James H.; Blair, Ryan
2017-11-01
We study a class of nonlocal, energy-driven dynamical models that govern the motion of closed, embedded curves from both an energetic and dynamical perspective. Our energetic results provide a variety of ways to understand physically motivated energetic models in terms of more classical, combinatorial measures of complexity for embedded curves. This line of investigation culminates in a family of complexity bounds that relate a rather broad class of models to a generalized, or weighted, variant of the crossing number. Our dynamic results include global well-posedness of the associated partial differential equations, regularity of equilibria for these flows as well as a more detailed investigation of dynamics near such equilibria. Finally, we explore a few global dynamical properties of these models numerically.
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
On Two-Scale Modelling of Heat and Mass Transfer
International Nuclear Information System (INIS)
Vala, J.; Stastnik, S.
2008-01-01
Modelling of macroscopic behaviour of materials, consisting of several layers or components, whose microscopic (at least stochastic) analysis is available, as well as (more general) simulation of non-local phenomena, complicated coupled processes, etc., requires both deeper understanding of physical principles and development of mathematical theories and software algorithms. Starting from the (relatively simple) example of phase transformation in substitutional alloys, this paper sketches the general formulation of a nonlinear system of partial differential equations of evolution for the heat and mass transfer (useful in mechanical and civil engineering, etc.), corresponding to conservation principles of thermodynamics, both at the micro- and at the macroscopic level, and suggests an algorithm for scale-bridging, based on the robust finite element techniques. Some existence and convergence questions, namely those based on the construction of sequences of Rothe and on the mathematical theory of two-scale convergence, are discussed together with references to useful generalizations, required by new technologies.
On Two-Scale Modelling of Heat and Mass Transfer
Vala, J.; Št'astník, S.
2008-09-01
Modelling of macroscopic behaviour of materials, consisting of several layers or components, whose microscopic (at least stochastic) analysis is available, as well as (more general) simulation of non-local phenomena, complicated coupled processes, etc., requires both deeper understanding of physical principles and development of mathematical theories and software algorithms. Starting from the (relatively simple) example of phase transformation in substitutional alloys, this paper sketches the general formulation of a nonlinear system of partial differential equations of evolution for the heat and mass transfer (useful in mechanical and civil engineering, etc.), corresponding to conservation principles of thermodynamics, both at the micro- and at the macroscopic level, and suggests an algorithm for scale-bridging, based on the robust finite element techniques. Some existence and convergence questions, namely those based on the construction of sequences of Rothe and on the mathematical theory of two-scale convergence, are discussed together with references to useful generalizations, required by new technologies.
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.
International Nuclear Information System (INIS)
Lu Junguo; Lu Linji
2009-01-01
In this paper, global exponential stability and periodicity of a class of reaction-diffusion recurrent neural networks with distributed delays and Dirichlet boundary conditions are studied by constructing suitable Lyapunov functionals and utilizing some inequality techniques. We first prove global exponential convergence to 0 of the difference between any two solutions of the original neural networks, 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. Secondly, we prove periodicity. Sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the equilibrium and periodic solution are given. These conditions are easy to verify and our results play an important role in the design and application of globally exponentially stable neural circuits and periodic oscillatory neural circuits.
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.
D'Ambrosio, Raffaele; Moccaldi, Martina; Paternoster, Beatrice
2018-05-01
In this paper, an adapted numerical scheme for reaction-diffusion problems generating periodic wavefronts is introduced. Adapted numerical methods for such evolutionary problems are specially tuned to follow prescribed qualitative behaviors of the solutions, making the numerical scheme more accurate and efficient as compared with traditional schemes already known in the literature. Adaptation through the so-called exponential fitting technique leads to methods whose coefficients depend on unknown parameters related to the dynamics and aimed to be numerically computed. Here we propose a strategy for a cheap and accurate estimation of such parameters, which consists essentially in minimizing the leading term of the local truncation error whose expression is provided in a rigorous accuracy analysis. In particular, the presented estimation technique has been applied to a numerical scheme based on combining an adapted finite difference discretization in space with an implicit-explicit time discretization. Numerical experiments confirming the effectiveness of the approach are also provided.
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.
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)
Annihilation or Creation of Particles: An Autonomous Reaction-Diffusion Process
International Nuclear Information System (INIS)
Roshani, Farinaz
2010-12-01
Annihilation or creation of particles on a D-dimensional region with boundaries is considered. Particles can be injected or extracted at the boundary as well. Two general behaviours of this system are investigated. The stationary behaviour of this system, and the dominant way of the relaxation of the system towards its stationary state. Based on the first behaviour, static phase transitions (discontinuous changes in the stationary profiles of the system) are investigated. Based on the second behaviour, dynamical phase transitions (discontinuous changes in the relaxation-times of the system) are studied. The investigation is specialized to systems in which the evolution equation of one-point functions are closed (the autonomous system). (author)
The two-regime method for optimizing stochastic reaction-diffusion simulations
Flegg, M. B.; Chapman, S. J.; Erban, R.
2011-01-01
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
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.
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
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.
Zhu, Xiaolu; Yang, Hao
2017-12-01
The recently emerged four-dimensional (4D) biofabrication technique aims to create dynamic three-dimensional (3D) biological structures that can transform their shapes or functionalities with time when an external stimulus is imposed or when cell postprinting self-assembly occurs. The evolution of 3D pattern of branching geometry via self-assembly of cells is critical for 4D biofabrication of artificial organs or tissues with branched geometry. However, it is still unclear that how the formation and evolution of these branching pattern are biologically encoded. We study the 4D fabrication of lung branching structures utilizing a simulation model on the reaction-diffusion mechanism, which is established using partial differential equations of four variables, describing the reaction and diffusion process of morphogens with time during the development process of lung branching. The simulation results present the forming process of 3D branching pattern, and also interpret the behaviors of side branching and tip splitting as the stalk growing, through 3D visualization of numerical simulation.
Saliba, Daniel; Al-Ghoul, Mazen
2016-11-01
We report the synthesis of magnesium-aluminium layered double hydroxide (LDH) using a reaction-diffusion framework (RDF) that exploits the multiscale coupling of molecular diffusion with chemical reactions, nucleation and growth of crystals. In an RDF, the hydroxide anions are allowed to diffuse into an organic gel matrix containing the salt mixture needed for the precipitation of the LDH. The chemical structure and composition of the synthesized magnesium-aluminium LDHs are determined using powder X-ray diffraction (PXRD), thermo-gravimetric analysis, differential scanning calorimetry, solid-state nuclear magnetic resonance (SSNMR), Fourier transform infrared and energy dispersive X-ray spectroscopy. This novel technique also allows the investigation of the mechanism of intercalation of some fluorescent probes, such as the neutral three-dimensional rhodamine B (RhB) and the negatively charged two-dimensional 8-hydroxypyrene-1,3,6-trisulfonic acid (HPTS), using in situ steady-state fluorescence spectroscopy. The incorporation of these organic dyes inside the interlayer region of the LDH is confirmed via fluorescence microscopy, solid-state lifetime, SSNMR and PXRD. The activation energies of intercalation of the corresponding molecules (RhB and HPTS) are computed and exhibit dependence on the geometry of the involved probe (two or three dimensions), the charge of the fluorescent molecule (anionic, cationic or neutral) and the cationic ratio of the corresponding LDH. This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.
Directory of Open Access Journals (Sweden)
Dmitry V. Lukyanenko
2017-01-01
Full Text Available This work develops a theory of the asymptotic-numerical investigation of the moving fronts in reaction-diffusion-advection models. By considering the numerical solution of the singularly perturbed Burgers’s equation we discuss a method of dynamically adapted mesh construction that is able to significantly improve the numerical solution of this type of equations. For the construction we use a priori information that is based on the asymptotic analysis of the problem. In particular, we take into account the information about the speed of the transition layer, its width and structure. Our algorithms are able to reduce significantly complexity and enhance stability of the numerical calculations in comparison with classical approaches for solving this class of problems. The numerical experiment is presented to demonstrate the effectiveness of the proposed method.The article is published in the authors’ wording.
Directory of Open Access Journals (Sweden)
Roman Cherniha
2018-04-01
Full Text Available This review is devoted to search for Lie and Q-conditional (nonclassical symmetries and exact solutions of a class of reaction-diffusion-convection equations with exponential nonlinearities. A complete Lie symmetry classification of the class is derived via two different algorithms in order to show that the result depends essentially on the type of equivalence transformations used for the classification. Moreover, a complete description of Q-conditional symmetries for PDEs from the class in question is also presented. It is shown that all the well-known results for reaction-diffusion equations with exponential nonlinearities follow as particular cases from the results derived for this class of reaction-diffusion-convection equations. The symmetries obtained for constructing exact solutions of the relevant equations are successfully applied. The exact solutions are compared with those found by means of different techniques. Finally, an application of the exact solutions for solving boundary-value problems arising in population dynamics is presented.
Mean Field Limits for Interacting Diffusions in a Two-Scale Potential
Gomes, S. N.; Pavliotis, G. A.
2018-06-01
In this paper, we study the combined mean field and homogenization limits for a system of weakly interacting diffusions moving in a two-scale, locally periodic confining potential, of the form considered in Duncan et al. (Brownian motion in an N-scale periodic potential, arXiv:1605.05854, 2016b). We show that, although the mean field and homogenization limits commute for finite times, they do not, in general, commute in the long time limit. In particular, the bifurcation diagrams for the stationary states can be different depending on the order with which we take the two limits. Furthermore, we construct the bifurcation diagram for the stationary McKean-Vlasov equation in a two-scale potential, before passing to the homogenization limit, and we analyze the effect of the multiple local minima in the confining potential on the number and the stability of stationary solutions.
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. science direct.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.sciencedirect.com/science/article/pii/S0362546X17302559?via%3Dihub
Weise, L.D.
2012-01-01
Heart failure due to cardiac arrhythmias is a major cause of death in the industrialized world. Cardiac arrhythmia is often caused by spi- ral waves of electrical activity in the cardiac muscle. Therefore, it is a major task in cardiology to understand the mechanisms of spiral wave initiation in the
Two-scale large deviations for chemical reaction kinetics through second quantization path integral
International Nuclear Information System (INIS)
Li, Tiejun; Lin, Feng
2016-01-01
Motivated by the study of rare events for a typical genetic switching model in systems biology, in this paper we aim to establish the general two-scale large deviations for chemical reaction systems. We build a formal approach to explicitly obtain the large deviation rate functionals for the considered two-scale processes based upon the second quantization path integral technique. We get three important types of large deviation results when the underlying two timescales are in three different regimes. This is realized by singular perturbation analysis to the rate functionals obtained by the path integral. We find that the three regimes possess the same deterministic mean-field limit but completely different chemical Langevin approximations. The obtained results are natural extensions of the classical large volume limit for chemical reactions. We also discuss its implication on the single-molecule Michaelis–Menten kinetics. Our framework and results can be applied to understand general multi-scale systems including diffusion processes. (paper)
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.
Arjunan, Satya Nanda Vel; Tomita, Masaru
2010-03-01
Many important cellular processes are regulated by reaction-diffusion (RD) of molecules that takes place both in the cytoplasm and on the membrane. To model and analyze such multicompartmental processes, we developed a lattice-based Monte Carlo method, Spatiocyte that supports RD in volume and surface compartments at single molecule resolution. Stochasticity in RD and the excluded volume effect brought by intracellular molecular crowding, both of which can significantly affect RD and thus, cellular processes, are also supported. We verified the method by comparing simulation results of diffusion, irreversible and reversible reactions with the predicted analytical and best available numerical solutions. Moreover, to directly compare the localization patterns of molecules in fluorescence microscopy images with simulation, we devised a visualization method that mimics the microphotography process by showing the trajectory of simulated molecules averaged according to the camera exposure time. In the rod-shaped bacterium Escherichia coli, the division site is suppressed at the cell poles by periodic pole-to-pole oscillations of the Min proteins (MinC, MinD and MinE) arising from carefully orchestrated RD in both cytoplasm and membrane compartments. Using Spatiocyte we could model and reproduce the in vivo MinDE localization dynamics by accounting for the previously reported properties of MinE. Our results suggest that the MinE ring, which is essential in preventing polar septation, is largely composed of MinE that is transiently attached to the membrane independently after recruited by MinD. Overall, Spatiocyte allows simulation and visualization of complex spatial and reaction-diffusion mediated cellular processes in volumes and surfaces. As we showed, it can potentially provide mechanistic insights otherwise difficult to obtain experimentally. The online version of this article (doi:10.1007/s11693-009-9047-2) contains supplementary material, which is available to
Shi, Kuangyu; Bayer, Christine; Gaertner, Florian C; Astner, Sabrina T; Wilkens, Jan J; Nüsslin, Fridtjof; Vaupel, Peter; Ziegler, Sibylle I
2017-02-01
Positron-emission tomography (PET) with hypoxia specific tracers provides a noninvasive method to assess the tumor oxygenation status. Reaction-diffusion models have advantages in revealing the quantitative relation between in vivo imaging and the tumor microenvironment. However, there is no quantitative comparison of the simulation results with the real PET measurements yet. The lack of experimental support hampers further applications of computational simulation models. This study aims to compare the simulation results with a preclinical [ 18 F]FMISO PET study and to optimize the reaction-diffusion model accordingly. Nude mice with xenografted human squamous cell carcinomas (CAL33) were investigated with a 2 h dynamic [ 18 F]FMISO PET followed by immunofluorescence staining using the hypoxia marker pimonidazole and the endothelium marker CD 31. A large data pool of tumor time-activity curves (TAC) was simulated for each mouse by feeding the arterial input function (AIF) extracted from experiments into the model with different configurations of the tumor microenvironment. A measured TAC was considered to match a simulated TAC when the difference metric was below a certain, noise-dependent threshold. As an extension to the well-established Kelly model, a flow-limited oxygen-dependent (FLOD) model was developed to improve the matching between measurements and simulations. The matching rate between the simulated TACs of the Kelly model and the mouse PET data ranged from 0 to 28.1% (on average 9.8%). By modifying the Kelly model to an FLOD model, the matching rate between the simulation and the PET measurements could be improved to 41.2-84.8% (on average 64.4%). Using a simulation data pool and a matching strategy, we were able to compare the simulated temporal course of dynamic PET with in vivo measurements. By modifying the Kelly model to a FLOD model, the computational simulation was able to approach the dynamic [ 18 F]FMISO measurements in the investigated
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.
An Efficient Two-Scale Hybrid Embedded Fracture Model for Shale Gas Simulation
Amir, Sahar Z.; Sun, Shuyu
2016-01-01
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.
Characterization of two-scale gradient Young measures and application to homogenization
Babadjian, Jean-Francois; Baia, Margarida; Santos, Pedro M.
2006-01-01
This work is devoted to the study of two-scale gradient Young measures naturally arising in nonlinear elasticity homogenization problems. Precisely, a characterization of this class of measures is derived and an integral representation formula for homogenized energies, whose integrands satisfy very weak regularity assumptions, is obtained in terms of two-scale gradient Young measures.
Klika, Vá clav; Baker, Ruth E.; Headon, Denis; Gaffney, Eamonn A.
2011-01-01
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
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.
On an extension of the method of two-scale convergence and its applications
International Nuclear Information System (INIS)
Zhikov, V V
2000-01-01
The concept of two-scale convergence associated with a fixed periodic Borel measure μ is introduced. In the case when dμ=dx is Lebesgue measure on the torus convergence in the sense of Nguetseng-Allaire is obtained. The main properties of two-scale convergence are revealed by the simultaneous consideration of a sequence of functions and a sequence of their gradients. An application of two-scale convergence to the homogenization of some problems in the theory of porous media (the double-porosity model) is presented. A mathematical notion of 'softly or weakly coupled parallel flows' is worked out. A homogenized operator is constructed and the convergence result itself is interpreted as a 'strong two-scale resolvent convergence'. Problems concerning the behaviour of the spectrum under homogenization are touched upon in this connection
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.
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.
Directory of Open Access Journals (Sweden)
Demongeot Jacques
2004-06-01
Full Text Available Abstract Background The transport of intra-cellular particles by microtubules is a major biological function. Under appropriate in vitro conditions, microtubule preparations behave as a 'complex' system and show 'emergent' phenomena. In particular, they form dissipative structures that self-organise over macroscopic distances by a combination of reaction and diffusion. Results Here, we show that self-organisation also gives rise to a collective transport of colloidal particles along a specific direction. Particles, such as polystyrene beads, chromosomes, nuclei, and vesicles are carried at speeds of several microns per minute. The process also results in the macroscopic self-organisation of these particles. After self-organisation is completed, they show the same pattern of organisation as the microtubules. Numerical simulations of a population of growing and shrinking microtubules, incorporating experimentally realistic reaction dynamics, predict self-organisation. They forecast that during self-organisation, macroscopic parallel arrays of oriented microtubules form which cross the reaction space in successive waves. Such travelling waves are capable of transporting colloidal particles. The fact that in the simulations, the aligned arrays move along the same direction and at the same speed as the particles move, suggest that this process forms the underlying mechanism for the observed transport properties. Conclusions This process constitutes a novel physical chemical mechanism by which chemical energy is converted into collective transport of colloidal particles along a given direction. Self-organisation of this type provides a new mechanism by which intra cellular particles such as chromosomes and vesicles can be displaced and simultaneously organised by microtubules. It is plausible that processes of this type occur in vivo.
Glade, Nicolas; Demongeot, Jacques; Tabony, James
2004-01-01
Background The transport of intra-cellular particles by microtubules is a major biological function. Under appropriate in vitro conditions, microtubule preparations behave as a 'complex' system and show 'emergent' phenomena. In particular, they form dissipative structures that self-organise over macroscopic distances by a combination of reaction and diffusion. Results Here, we show that self-organisation also gives rise to a collective transport of colloidal particles along a specific direction. Particles, such as polystyrene beads, chromosomes, nuclei, and vesicles are carried at speeds of several microns per minute. The process also results in the macroscopic self-organisation of these particles. After self-organisation is completed, they show the same pattern of organisation as the microtubules. Numerical simulations of a population of growing and shrinking microtubules, incorporating experimentally realistic reaction dynamics, predict self-organisation. They forecast that during self-organisation, macroscopic parallel arrays of oriented microtubules form which cross the reaction space in successive waves. Such travelling waves are capable of transporting colloidal particles. The fact that in the simulations, the aligned arrays move along the same direction and at the same speed as the particles move, suggest that this process forms the underlying mechanism for the observed transport properties. Conclusions This process constitutes a novel physical chemical mechanism by which chemical energy is converted into collective transport of colloidal particles along a given direction. Self-organisation of this type provides a new mechanism by which intra cellular particles such as chromosomes and vesicles can be displaced and simultaneously organised by microtubules. It is plausible that processes of this type occur in vivo. PMID:15176973
One-dimensional conduction through supporting electrolytes: two-scale cathodic Debye layer.
Almog, Yaniv; Yariv, Ehud
2011-10-01
Supporting-electrolyte solutions comprise chemically inert cations and anions, produced by salt dissolution, together with a reactive ionic species that may be consumed and generated on bounding ion-selective surfaces (e.g., electrodes or membranes). Upon application of an external voltage, a Faraday current is thereby established. It is natural to analyze this ternary-system process through a one-dimensional transport problem, employing the thin Debye-layer limit. Using a simple model of ideal ion-selective membranes, we have recently addressed this problem for moderate voltages [Yariv and Almog, Phys. Rev. Lett. 105, 176101 (2010)], predicting currents that scale as a fractional power of Debye thickness. We address herein the complementary problem of moderate currents. We employ matched asymptotic expansions, separately analyzing the two inner thin Debye layers adjacent to the ion-selective surfaces and the outer electroneutral region outside them. A straightforward calculation following comparable singular-perturbation analyses of binary systems is frustrated by the prediction of negative ionic concentrations near the cathode. Accompanying numerical simulations, performed for small values of Debye thickness, indicate a number unconventional features occurring at that region, such as inert-cation concentration amplification and electric-field intensification. The current-voltage correlation data of the electrochemical cell, obtained from compilation of these simulations, does not approach a limit as the Debye thickness vanishes. Resolution of these puzzles reveals a transformation of the asymptotic structure of the cathodic Debye layer. This reflects the emergence of an internal boundary layer, adjacent to the cathode, wherein field and concentration scaling differs from those of the Gouy-Chapman theory. The two-scale feature of the cathodic Debye layer is manifested through a logarithmic voltage scaling with Debye thickness. Accounting for this scaling, the
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.
Quasi-potential and Two-Scale Large Deviation Theory for Gillespie Dynamics
Li, Tiejun; Li, Fangting; Li, Xianggang; Lu, Cheng
2016-01-01
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
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.
The Backscattering Phase Function for a Sphere with a Two-Scale Relief of Rough Surface
Klass, E. V.
2017-12-01
The backscattering of light from spherical surfaces characterized by one and two-scale roughness reliefs has been investigated. The analysis is performed using the three-dimensional Monte-Carlo program POKS-RG (geometrical-optics approximation), which makes it possible to take into account the roughness of objects under study by introducing local geometries of different levels. The geometric module of the program is aimed at describing objects by equations of second-order surfaces. One-scale roughness is set as an ensemble of geometric figures (convex or concave halves of ellipsoids or cones). The two-scale roughness is modeled by convex halves of ellipsoids, with surface containing ellipsoidal pores. It is shown that a spherical surface with one-scale convex inhomogeneities has a flatter backscattering phase function than a surface with concave inhomogeneities (pores). For a sphere with two-scale roughness, the dependence of the backscattering intensity is found to be determined mostly by the lower-level inhomogeneities. The influence of roughness on the dependence of the backscattering from different spatial regions of spherical surface is analyzed.
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 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)
[The development and validation of two scales on retribution practices: PRG-13 and PRE-21].
Boada-Grau, Joan; Costa-Solé, Jordi; Gil-Ripoll, Carme; Vigil-Colet, Andreu
2012-01-01
The present study outlines the development process of two scales that measure general and specific retribution practices in organisations. Historically, retribution has been the subject of research of other social sciences such as Sociology and Business Administration. In Psychology, and more specifically in Work and Organisational Psychology, there are hardly any studies or inventories designed to evaluate retribution practices. In order to accomplish the objectives, a sample of 237 employees was selected, 42.6% of whom were women and 57.4% were men. We performed and exploratory factorial analysis using principal axis factoring as extraction method and an oblique rotation (oblimin) to analyse the two scales. The former is made up of four factors and the latter is a two-factor scale. The reliability coefficients of the six subscales we obtained ranged between .72 and .89. External validity was analysed using the correlations obtained between the two inventories and the Balanced Scorecard. The two tools were found to be two potentially useful scales to evaluate retribution practices.
Two-scale characterization of deformation-induced anisotropy of polycrystalline metals
International Nuclear Information System (INIS)
Watanabe, Ikumu; Terada, Kenjiro
2004-01-01
The anisotropic macro-scale mechanical behavior of polycrystalline metals is characterized by incorporating the micro-scale constitutive model of single crystal plasticity into the two-scale modeling based on the mathematical homogenization theory. The two-scale simulations are conducted to analyze the macro-scale anisotropy induced by micro-scale plastic deformation of the polycrystalline aggregate. In the simulations, the micro-scale representative volume element (RVE) of a polycrystalline aggregate is uniformly loaded in one direction, unloaded to macroscopically zero stress in a certain stage of deformation and then re-loaded in the different directions. The last re-loading calculations provide different macro-scale responses of the RVE, which can be the appearance of material anisotropy. We then try to examine the effects of the intergranular and intragranular behaviors on the anisotropy by means of various illustrations of plastic deformation process in stead of the use of pole figures for the change of crystallographic orientations
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.)
Rahbani, Janane; Khashab, Niveen M.; Patra, Digambara; Al-Ghoul, Mazen
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
Martinez, William; Etchegaray, Jason M; Thomas, Eric J; Hickson, Gerald B; Lehmann, Lisa Soleymani; Schleyer, Anneliese M; Best, Jennifer A; Shelburne, Julia T; May, Natalie B; Bell, Sigall K
2015-11-01
To develop and test the psychometric properties of two new survey scales aiming to measure the extent to which the clinical environment supports speaking up about (a) patient safety concerns and (b) unprofessional behaviour. Residents from six large US academic medical centres completed an anonymous, electronic survey containing questions regarding safety culture and speaking up about safety and professionalism concerns. Confirmatory factor analysis supported two separate, one-factor speaking up climates (SUCs) among residents; one focused on patient safety concerns (SUC-Safe scale) and the other focused on unprofessional behaviour (SUC-Prof scale). Both scales had good internal consistency (Cronbach's α>0.70) and were unique from validated safety and teamwork climate measures (rspeaking up behaviour about safety and professionalism concerns (r=0.21, pspeaking up behaviour among residents. These two scales may fill an existing gap in residency and safety culture assessments by measuring the openness of communication about safety and professionalism concerns, two important aspects of safety culture that are under-represented in existing metrics. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://group.bmj.com/group/rights-licensing/permissions.
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)
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.
2010-09-01
Influences of microstructure and properties of an aluminium alloy on resistance to dynamic perforation are predicted using a decoupled multiscale ... simulated performance. Library parameters typical for aluminium alloys (Kohn, 1969) are used for the macroscopic equation of state of Al 2139, details of...Two-Scale Modelling of Effects of Microstructure and Thermomechanical Properties on Dynamic Performance of an Aluminium Alloy by J. D
A Two-Scale Reduced Model for Darcy Flow in Fractured Porous Media
Chen, Huangxin; Sun, Shuyu
2016-01-01
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
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...
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.
Amir, Sahar Z.; Chen, Huangxin; Sun, Shuyu
2017-01-01
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.
Jarrett, Angela M.; Hormuth, David A.; Barnes, Stephanie L.; Feng, Xinzeng; Huang, Wei; Yankeelov, Thomas E.
2018-05-01
Clinical methods for assessing tumor response to therapy are largely rudimentary, monitoring only temporal changes in tumor size. Our goal is to predict the response of breast tumors to therapy using a mathematical model that utilizes magnetic resonance imaging (MRI) data obtained non-invasively from individual patients. We extended a previously established, mechanically coupled, reaction-diffusion model for predicting tumor response initialized with patient-specific diffusion weighted MRI (DW-MRI) data by including the effects of chemotherapy drug delivery, which is estimated using dynamic contrast-enhanced (DCE-) MRI data. The extended, drug incorporated, model is initialized using patient-specific DW-MRI and DCE-MRI data. Data sets from five breast cancer patients were used—obtained before, after one cycle, and at mid-point of neoadjuvant chemotherapy. The DCE-MRI data was used to estimate spatiotemporal variations in tumor perfusion with the extended Kety–Tofts model. The physiological parameters derived from DCE-MRI were used to model changes in delivery of therapy drugs within the tumor for incorporation in the extended model. We simulated the original model and the extended model in both 2D and 3D and compare the results for this five-patient cohort. Preliminary results show reductions in the error of model predicted tumor cellularity and size compared to the experimentally-measured results for the third MRI scan when therapy was incorporated. Comparing the two models for agreement between the predicted total cellularity and the calculated total cellularity (from the DW-MRI data) reveals an increased concordance correlation coefficient from 0.81 to 0.98 for the 2D analysis and 0.85 to 0.99 for the 3D analysis (p < 0.01 for each) when the extended model was used in place of the original model. This study demonstrates the plausibility of using DCE-MRI data as a means to estimate drug delivery on a patient-specific basis in predictive models and
Chung, Eva Yin-Han; Lam, Gigi
2018-05-29
The World Health Organization has asserted the importance of enhancing participation of people with disabilities within the International Classification of Functioning, Disability and Health framework. Participation is regarded as a vital outcome in community-based rehabilitation. The actualization of the right to participate is limited by social stigma and discrimination. To date, there is no validated instrument for use in Chinese communities to measure participation restriction or self-perceived stigma. This study aimed to translate and validate the Participation Scale and the Explanatory Model Interview Catalogue (EMIC) Stigma Scale for use in Chinese communities with people with physical disabilities. The Chinese versions of the Participation Scale and the EMIC stigma scale were administered to 264 adults with physical disabilities. The two scales were examined separately. The reliability analysis was studied in conjunction with the construct validity. Reliability analysis was conducted to assess the internal consistency and item-total correlation. Exploratory factor analysis was conducted to investigate the latent patterns of relationships among variables. A Rasch model analysis was conducted to test the dimensionality, internal validity, item hierarchy, and scoring category structure of the two scales. Both the Participation Scale and the EMIC stigma scale were confirmed to have good internal consistency and high item-total correlation. Exploratory factor analysis revealed the factor structure of the two scales, which demonstrated the fitting of a pattern of variables within the studied construct. The Participation Scale was found to be multidimensional, whereas the EMIC stigma scale was confirmed to be unidimensional. The item hierarchies of the Participation Scale and the EMIC stigma scale were discussed and were regarded as compatible with the cultural characteristics of Chinese communities. The Chinese versions of the Participation Scale and the EMIC
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.
Systematic front distortion and presence of consecutive fronts in a precipitation system
Volford, A.; Izsak, F.; Ripszam, M.; Lagzi, I.
2006-01-01
A new simple reaction-diffusion system is presented focusing on pattern formation phenomena as consecutive precipitation fronts and distortion of the precipitation front.The chemical system investigated here is based on the amphoteric property of aluminum hydroxide and exhibits two unique phenomena.
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
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.
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...
Splitting Schemes & Segregation In Reaction-(Cross-)Diffusion Systems
Carrillo, José A.; Fagioli, Simone; Santambrogio, Filippo; Schmidtchen, Markus
2017-01-01
One of the most fascinating phenomena observed in reaction-diffusion systems is the emergence of segregated solutions, i.e. population densities with disjoint supports. We analyse such a reaction cross-diffusion system. In order to prove existence of weak solutions for a wide class of initial data without restriction about their supports or their positivity, we propose a variational splitting scheme combining ODEs with methods from optimal transport. In addition, this approach allows us to pr...
Di Martino, Gerardo; Iodice, Antonio; Natale, Antonio; Riccio, Daniele; Ruello, Giuseppe
2015-04-01
The recently proposed polarimetric two-scale two- component model (PTSTCM) in principle allows us obtaining a reasonable estimation of the soil moisture even in moderately vegetated areas, where the volumetric scattering contribution is non-negligible, provided that the surface component is dominant and the double-bounce component is negligible. Here we test the PTSTCM validity range by applying it to polarimetric SAR data acquired on areas for which, at the same times of SAR acquisitions, ground measurements of soil moisture were performed. In particular, we employ the AGRISAR'06 database, which includes data from several fields covering a period that spans all the phases of vegetation growth.
Kochmann, Julian; Wulfinghoff, Stephan; Ehle, Lisa; Mayer, Joachim; Svendsen, Bob; Reese, Stefanie
2017-09-01
Recently, two-scale FE-FFT-based methods (e.g., Spahn et al. in Comput Methods Appl Mech Eng 268:871-883, 2014; Kochmann et al. in Comput Methods Appl Mech Eng 305:89-110, 2016) have been proposed to predict the microscopic and overall mechanical behavior of heterogeneous materials. The purpose of this work is the extension to elasto-viscoplastic polycrystals, efficient and robust Fourier solvers and the prediction of micromechanical fields during macroscopic deformation processes. Assuming scale separation, the macroscopic problem is solved using the finite element method. The solution of the microscopic problem, which is embedded as a periodic unit cell (UC) in each macroscopic integration point, is found by employing fast Fourier transforms, fixed-point and Newton-Krylov methods. The overall material behavior is defined by the mean UC response. In order to ensure spatially converged micromechanical fields as well as feasible overall CPU times, an efficient but simple solution strategy for two-scale simulations is proposed. As an example, the constitutive behavior of 42CrMo4 steel is predicted during macroscopic three-point bending tests.
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.
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
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 ...
Waste dissolution with chemical reaction, diffusion and advection
International Nuclear Information System (INIS)
Chambre, P.L.; Kang, C.H.; Lee, W.W.L.; Pigford, T.H.
1987-06-01
This paper extends the mass-transfer analysis to include the effect of advective transport in predicting the steady-state dissolution rate, with a chemical-reaction-rate boundary condition at the surface of a waste form of arbitrary shape. This new theory provides an analytic means of predicting the ground-water velocities at which dissolution rate in a geologic environment will be governed entirely to the chemical reaction rate. As an illustration, we consider the steady-state potential flow of ground water in porous rock surrounding a spherical waste solid. 3 refs., 2 figs
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.
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
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.
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....
Phase diagrams of the Fe-rich part of the Fe-W system under high pressure
International Nuclear Information System (INIS)
Yamane, T.; Kang, Y.S.; Minamino, Y.; Araki, H.; Hiraki, A.; Miyamoto, Y.
1995-01-01
Phase diagrams of the Fe-rich part of the Fe-W system under high pressure (1.2 and 2.2 GPa) were established by a reaction-diffusion method and calculated with thermodynamic and volumetric data. When high pressure is applied, the γ region extends and the α region contracts. As a result of increasing pressure, eutectoid and peritectoid reactions appear. (orig.)
Transient bimodality in interacting particle systems
International Nuclear Information System (INIS)
Calderoni, P.; Pellegrinotti, A.; Presutti, E.; Vares, M.E.
1989-01-01
The authors consider a system of spins which have values ± 1 and evolve according to a jump Markov process whose generator is the sum of two generators, one describing a spin-flip Glauber process, the other a Kawasaki (stirring) evolution. It was proven elsewhere that if the Kawasaki dynamics is speeded up by a factor var-epsilon -2 , then, in the limit var-epsilon → 0 (continuum limit), propagation of chaos holds and the local magnetization solves a reaction-diffusion equation. They choose the parameters of the Glauber interaction so that the potential of the reaction term in the reaction-diffusion equation is a double-well potential with quartic maximum at the origin. They assume further that for each var-epsilon the system is in a finite interval of Z with var-epsilon -1 sites and periodic boundary conditions. They specify the initial measure as the product measure with 0 spin average, thus obtaining, in the continuum limit, a constant magnetic profile equal to 0, which is a stationary unstable solution to the reaction-diffusion equation. They prove that at times of the order var-epsilon -1/2 propagation of chaos does not hold any more and, in the limit as var-epsilon → 0, the state becomes a nontrivial superposition of Bernoulli measures with parameters corresponding to the minima of the reaction potential. The coefficients of such a superposition depend on time (on the scale var-epsilon -1/2 ) and at large times (on this scale) the coefficient of the term corresponding to the initial magnetization vanishes (transient bimodality). This differs from what was observed by De Masi, Presutti, and Vares, who considered a reaction potential with quadratic maximum and no bimodal effect was seen, as predicted by Broggi, Lugiato, and Colombo
Inoue, Yasushi; Katayama, Arata
2011-09-15
A two-scale evaluation concept of remediation technologies for a contaminated site was expanded by introducing life cycle costing (LCC) and economic input-output life cycle assessment (EIO-LCA). The expanded evaluation index, the rescue number for soil (RN(SOIL)) with LCC and EIO-LCA, comprises two scales, such as risk-cost, risk-energy consumption or risk-CO(2) emission of a remediation. The effectiveness of RN(SOIL) with LCC and EIO-LCA was examined in a typical contamination and remediation scenario in which dieldrin contaminated an agricultural field. Remediation was simulated using four technologies: disposal, high temperature thermal desorption, biopile and landfarming. Energy consumption and CO(2) emission were determined from a life cycle inventory analysis using monetary-based intensity based on an input-output table. The values of RN(SOIL) based on risk-cost, risk-energy consumption and risk-CO(2) emission were calculated, and then rankings of the candidates were compiled according to RN(SOIL) values. A comparison between three rankings showed the different ranking orders. The existence of differences in ranking order indicates that the scales would not have reciprocal compatibility for two-scale evaluation and that each scale should be used independently. The RN(SOIL) with LCA will be helpful in selecting a technology, provided an appropriate scale is determined. Copyright © 2011 Elsevier B.V. All rights reserved.
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
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 ...
Fellner, Klemens; Tang, Bao Quoc
2018-06-01
The convergence to equilibrium for renormalised solutions to nonlinear reaction-diffusion systems is studied. The considered reaction-diffusion systems arise from chemical reaction networks with mass action kinetics and satisfy the complex balanced condition. By applying the so-called entropy method, we show that if the system does not have boundary equilibria, i.e. equilibrium states lying on the boundary of R_+^N, then any renormalised solution converges exponentially to the complex balanced equilibrium with a rate, which can be computed explicitly up to a finite-dimensional inequality. This inequality is proven via a contradiction argument and thus not explicitly. An explicit method of proof, however, is provided for a specific application modelling a reversible enzyme reaction by exploiting the specific structure of the conservation laws. Our approach is also useful to study the trend to equilibrium for systems possessing boundary equilibria. More precisely, to show the convergence to equilibrium for systems with boundary equilibria, we establish a sufficient condition in terms of a modified finite-dimensional inequality along trajectories of the system. By assuming this condition, which roughly means that the system produces too much entropy to stay close to a boundary equilibrium for infinite time, the entropy method shows exponential convergence to equilibrium for renormalised solutions to complex balanced systems with boundary equilibria.
Phase transition universality classes of classical, nonequilibrium systems
Ódor, G
2004-01-01
In the first chapter I summarize the most important critical exponents and relations used in this work. In the second chapter I briefly address the question of scaling behavior at first order phase transitions.In chapter three I review dynamical extensions of basic static classes, show the effect of mixing dynamics and percolation behavior. The main body of this work is given in chapter four where genuine, dynamical universality classes specific to nonequilibrium systems are introduced. In chapter five I continue overviewing such nonequilibrium classes but in coupled, multi-component systems. Most of known transitions in low dimensional systems are between active and absorbing states of reaction-diffusion type systems, but I briefly introduce related classes that appear in interface growth models in chapter six. Some of them are related to critical behavior of coupled, multi-component systems. Finally in chapter seven I summarize families of absorbing state system classes, mean-field classes and the most freq...
International Nuclear Information System (INIS)
Upadhyay, Ranjit Kumar; Kumari, Nitu; Rai, Vikas
2009-01-01
In this paper, dynamical complexities in two reaction-diffusion (RD) model systems are explored. A spatial heterogeneity in the form of linear spatial gradient in the reproductive growth rate of the phytoplankton is incorporated in both the model systems. Extra mortality of the zooplankton due to toxin production by the phytoplankton is included in the second reaction diffusion model system. Effect of toxin production and spatial heterogeneity in the model systems are studied. Toxin production does not seem to have an appreciable effect on the asymptotic dynamics of the model systems. On the other hand, spatial heterogeneity does influence the dynamics. In particular, it increases the frequency of occurrence of chaos as evident from two dimensional parameter scans. Both these model systems display short term recurrent chaos [Rai V. Chaos in natural populations: edge or wedge? Ecol Complex 2004;1: 127-38] as they reside on 'edges of chaos' (EOC) [Rai V, Upadhyay RK. Evolving to the edge of chaos: chance or necessity? Chaos, Solitons and Fractals 2006;30:1074-87]. This suggests that the ecological systems have a tendency to evolve to EOC. The study corroborates the inferences drawn from an earlier study by Rai and Upadhyay [Rai V, Upadhyay RK. Evolving to the edge of chaos: chance or necessity? Chaos, Solitons and Fractals 2006;30:1074-87]. The system's dynamics is largely unpredictable and admits bursts of short-term predictability.
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.
Di Francesco, Marco; Twarogowska, Monika
2011-01-01
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.
Dynamical System Approach for Edge Detection Using Coupled FitzHugh-Nagumo Neurons.
Li, Shaobai; Dasmahapatra, Srinandan; Maharatna, Koushik
2015-12-01
The prospect of emulating the impressive computational capabilities of biological systems has led to considerable interest in the design of analog circuits that are potentially implementable in very large scale integration CMOS technology and are guided by biologically motivated models. For example, simple image processing tasks, such as the detection of edges in binary and grayscale images, have been performed by networks of FitzHugh-Nagumo-type neurons using the reaction-diffusion models. However, in these studies, the one-to-one mapping of image pixels to component neurons makes the size of the network a critical factor in any such implementation. In this paper, we develop a simplified version of the employed reaction-diffusion model in three steps. In the first step, we perform a detailed study to locate this threshold using continuous Lyapunov exponents from dynamical system theory. Furthermore, we render the diffusion in the system to be anisotropic, with the degree of anisotropy being set by the gradients of grayscale values in each image. The final step involves a simplification of the model that is achieved by eliminating the terms that couple the membrane potentials of adjacent neurons. We apply our technique to detect edges in data sets of artificially generated and real images, and we demonstrate that the performance is as good if not better than that of the previous methods without increasing the size of the network.
Control of complex dynamics and chaos in distributed parameter systems
Energy Technology Data Exchange (ETDEWEB)
Chakravarti, S.; Marek, M.; Ray, W.H. [Univ. of Wisconsin, Madison, WI (United States)
1995-12-31
This paper discusses a methodology for controlling complex dynamics and chaos in distributed parameter systems. The reaction-diffusion system with Brusselator kinetics, where the torus-doubling or quasi-periodic (two characteristic incommensurate frequencies) route to chaos exists in a defined range of parameter values, is used as an example. Poincare maps are used for characterization of quasi-periodic and chaotic attractors. The dominant modes or topos, which are inherent properties of the system, are identified by means of the Singular Value Decomposition. Tested modal feedback control schemas based on identified dominant spatial modes confirm the possibility of stabilization of simple quasi-periodic trajectories in the complex quasi-periodic or chaotic spatiotemporal patterns.
Nano-sized Adsorbate Structure Formation in Anisotropic Multilayer System
Kharchenko, Vasyl O.; Kharchenko, Dmitrii O.; Yanovsky, Vladimir V.
2017-05-01
In this article, we study dynamics of adsorbate island formation in a model plasma-condensate system numerically. We derive the generalized reaction-diffusion model for adsorptive multilayer system by taking into account anisotropy in transfer of adatoms between neighbor layers induced by electric field. It will be found that with an increase in the electric field strength, a structural transformation from nano-holes inside adsorbate matrix toward separated nano-sized adsorbate islands on a substrate is realized. Dynamics of adsorbate island sizes and corresponding distributions are analyzed in detail. This study provides an insight into details of self-organization of adatoms into nano-sized adsorbate islands in anisotropic multilayer plasma-condensate systems.
Effect of noise on defect chaos in a reaction-diffusion model.
Wang, Hongli; Ouyang, Qi
2005-06-01
The influence of noise on defect chaos due to breakup of spiral waves through Doppler and Eckhaus instabilities is investigated numerically with a modified Fitzhugh-Nagumo model. By numerical simulations we show that the noise can drastically enhance the creation and annihilation rates of topological defects. The noise-free probability distribution function for defects in this model is found not to fit with the previously reported squared-Poisson distribution. Under the influence of noise, the distributions are flattened, and can fit with the squared-Poisson or the modified-Poisson distribution. The defect lifetime and diffusive property of defects under the influence of noise are also checked in this model.
On the solution of reaction-diffusion equations with double diffusivity
Directory of Open Access Journals (Sweden)
B. D. Aggarwala
1987-01-01
Full Text Available In this paper, solution of a pair of Coupled Partial Differential equations is derived. These equations arise in the solution of problems of flow of homogeneous liquids in fissured rocks and heat conduction involving two temperatures. These equations have been considered by Hill and Aifantis, but the technique we use appears to be simpler and more direct, and some new results are derived. Also, discussion about the propagation of initial discontinuities is given and illustrated with graphs of some special cases.
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
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
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
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)
Crossover properties of a one-dimensional reaction-diffusion process with a transport current
International Nuclear Information System (INIS)
Fortin, Jean-Yves
2014-01-01
1D non-equilibrium models of particles subjected to a coagulation-diffusion process are important in understanding non-equilibrium dynamics, and fluctuation-dissipation relations. We consider in this paper transport properties in finite and semi-infinite one-dimensional chains. A set of particles freely hop between nearest-neighbor sites, with the additional condition that, when two particles meet, they merge instantaneously into one particle. A localized source of particle-current is imposed at the origin as well as a non-symmetric hopping rate between the left and right directions (particle drift). This model was previously studied with exact results for the particle density by Hinrichsen et al [1] in the long-time limit. We are interested here in the crossover process between a scaling regime and long-time behavior, starting with a chain filled with particles. As in the previous reference [1], we employ the empty-interval-particle method, where the probability of finding an empty interval between two given sites is considered. However a different method is developed here to treat the boundary conditions by imposing the continuity and differentiability of the interval probability, which allows for a closed and unique solution, especially for any given initial particle configuration. In the finite size case, we find a crossover between the scaling regime and two different exponential decays for the particle density as a function of the input current. Precise asymptotic expressions for the particle density and coagulation rate are given. (paper)
A strongly nonlinear reaction-diffusion model for a deterministic diffusive epidemic
International Nuclear Information System (INIS)
Kirane, M.; Kouachi, S.
1992-10-01
In the present paper the mathematical validity of a model on the spread of an infectious disease is proved. This model was proposed by Bailey. The mathematical validity is proved by means of a positivity, uniqueness and existence theorem. In spite of the apparent simplicity of the problem, the solution requires a delicate set of techniques. It seems very difficult to extend these techniques to a model in more than one dimension without imposing conditions on the diffusivities. (author). 7 refs
A strongly nonlinear reaction diffusion model for a deterministic diffusive epidemic
International Nuclear Information System (INIS)
Kirane, M.; Kouachi, S.
1993-04-01
In the present paper the mathematical validity of a model on the spread of an infectious disease is proved. This model was proposed by Bailey. The mathematical validity is proved by means of a positivity, uniqueness and existence theorem. Moreover the large time behaviour of the global solutions is analyzed. In spite of the apparent simplicity of the problem, the solution requires a delicate set of techniques. It seems very difficult to extend these techniques to a model in more than one dimension without imposing conditions on the data. (author). 9 refs
Fourier spectral methods for fractional-in-space reaction-diffusion equations
Bueno-Orovio, Alfonso; Kay, David; Burrage, Kevin
2014-01-01
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
An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations
Burrage, Kevin; Hale, Nicholas; Kay, David
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
International Nuclear Information System (INIS)
Swinney, H.L.
1988-09-01
Dynamical systems methods are being developed and used to characterize nonequilibrium processes and to address outstanding unresolved questions regarding bifurcations and chaos, especially in reaction-diffusion systems. An information-theoretic property, the mutual information, is being examined as a means for detecting and quantifying spatiotemporal chaos. A recent analysis has shown that information on dynamics deduced from noisy data can be used to reduce the noise in those data. These tools from dynamical systems and information theory are being applied to data obtained in laboratory experiments on homogeneous systems and on extended systems. A novel unstirred chemical reactor has been designed for studies of the development and evolution of chemical spatial patterns, and experiments with this reactor have yielded the first sustained chemical spatial patterns in a controlled laboratory environment. These laboratory experiments and numerical and analytic studies of models should provide general insights into spatiotemporal patterns in nonequilibrium systems. 14 refs
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.
Pattern Transitions in Bacterial Oscillating System under Nanofluidic Confinement
Shen, Jie-Pan; Chou, Chia-Fu
2011-03-01
Successful binary fission in E. coli relies on remarkable oscillatory behavior of the MinCDE protein system to determine the exact division site. The most favorable models to explain this fascinating spatiotemporal regulation on dynamic MinDE pattern formation in cells are based on reaction-diffusion scenario. Although not fully understood, geometric factors caused by bacterial morphology play a crucial role in MinDE dynamics. In the present study, bacteria were cultured, confined and reshaped in various micro/nanofluidic devices, to mimic either curvature changes of cell peripherals. Fluorescence imaging was utilized to detail the mode transitions in multiple MinDE patterns. The understanding of the physics in multiple pattern formations is further complemented via in silico modeling. The study synergizes the join merits of in vivo, in vitro and in silico approaches, to grasp the insight of stochastic dynamics inherited from the noisy mesoscopic biophysics. We acknowledge support from the Foresight Project, Academia Sinica.
The problem of birth of autowaves in parabolic systems with small diffusion
International Nuclear Information System (INIS)
Kolesov, A Yu; Rozov, N Kh; Sadovnichii, V A
2007-01-01
A parabolic reaction-diffusion system with zero Neumann boundary conditions at the end-points of a finite interval is considered under the following basic assumptions. First, the matrix diffusion coefficient in the system is proportional to a small parameter ε>0, and the system itself possesses a spatially homogeneous cycle (independent of the space variable) of amplitude of order √ε born by a zero equilibrium at an Andronov-Hopf bifurcation. Second, it is assumed that the matrix diffusion depends on an additional small parameter μ≥0, and for μ=0 there occurs in the stability problem for the homogeneous cycle the critical case of characteristic multiplier 1 of multiplicity 2 without Jordan block. Under these constraints and for independently varied parameters ε and μ the problem of the existence and the stability of spatially inhomogeneous auto-oscillations branching from the homogeneous cycle is analysed. Bibliography: 16 titles.
Bolhuis, Peter
Important reaction-diffusion processes, such as biochemical networks in living cells, or self-assembling soft matter, span many orders in length and time scales. In these systems, the reactants' spatial dynamics at mesoscopic length and time scales of microns and seconds is coupled to the reactions between the molecules at microscopic length and time scales of nanometers and milliseconds. This wide range of length and time scales makes these systems notoriously difficult to simulate. While mean-field rate equations cannot describe such processes, the mesoscopic Green's Function Reaction Dynamics (GFRD) method enables efficient simulation at the particle level provided the microscopic dynamics can be integrated out. Yet, many processes exhibit non-trivial microscopic dynamics that can qualitatively change the macroscopic behavior, calling for an atomistic, microscopic description. The recently developed multiscale Molecular Dynamics Green's Function Reaction Dynamics (MD-GFRD) approach combines GFRD for simulating the system at the mesocopic scale where particles are far apart, with microscopic Molecular (or Brownian) Dynamics, for simulating the system at the microscopic scale where reactants are in close proximity. The association and dissociation of particles are treated with rare event path sampling techniques. I will illustrate the efficiency of this method for patchy particle systems. Replacing the microscopic regime with a Markov State Model avoids the microscopic regime completely. The MSM is then pre-computed using advanced path-sampling techniques such as multistate transition interface sampling. I illustrate this approach on patchy particle systems that show multiple modes of binding. MD-GFRD is generic, and can be used to efficiently simulate reaction-diffusion systems at the particle level, including the orientational dynamics, opening up the possibility for large-scale simulations of e.g. protein signaling networks.
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.
Numerical modeling of aluminium foam on two scales
Czech Academy of Sciences Publication Activity Database
Němeček, J.; Denk, F.; Zlámal, Petr
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
Low-energy limit of two-scale field theories
International Nuclear Information System (INIS)
Leon, J.; Perez-Mercader, J.; Sanchez, M.F.
1991-01-01
We present a full and self-contained discussion of the decoupling theorem applied to several general models in four-dimensional field theory. We compute in each case the low-energy effective action and show the explicit one-loop expressions for each of the effective parameters. We find that for suitable conditions one can always build an effective low-energy theory where the conditions of the decoupling theorem are satisfied
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.
Drawert, Brian; Trogdon, Michael; Toor, Salman; Petzold, Linda; Hellander, Andreas
2016-01-01
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.
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 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.; Rajendran, Arvind; Lai, Zhiping
2010-01-01
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.
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.
Time behaviour of the reaction front in the catalytic A + B → B + C reaction-diffusion processes
International Nuclear Information System (INIS)
Nicolini, F.G.; Rodriguez, M.A.; Wio, H.S.
1994-07-01
The problem of the time evolution of the position and width of a reaction front between initially separated reactants for the catalytic reaction A + B → B + C (C inert) is treated within a recently introduced Galanin-like scheme. (author). 6 refs
Homogenization of a thermo-diffusion system with Smoluchowski interactions
Krehel, O.; Aiki, T.; Muntean, A.
2014-01-01
We study the solvability and homogenization of a thermal-diffusion reaction problem posed in a periodically perforated domain. The system describes the motion of populations of hot colloidal particles interacting together via Smoluchowski production terms. The upscaled system, obtained via two-scale
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
Strong disorder RG approach of random systems
International Nuclear Information System (INIS)
Igloi, Ferenc; Monthus, Cecile
2005-01-01
There is a large variety of quantum and classical systems in which the quenched disorder plays a dominant ro-circumflex le over quantum, thermal, or stochastic fluctuations: these systems display strong spatial heterogeneities, and many averaged observables are actually governed by rare regions. A unifying approach to treat the dynamical and/or static singularities of these systems has emerged recently, following the pioneering RG idea by Ma and Dasgupta and the detailed analysis by Fisher who showed that the Ma-Dasgupta RG rules yield asymptotic exact results if the broadness of the disorder grows indefinitely at large scales. Here we report these new developments by starting with an introduction of the main ingredients of the strong disorder RG method. We describe the basic properties of infinite disorder fixed points, which are realized at critical points, and of strong disorder fixed points, which control the singular behaviors in the Griffiths-phases. We then review in detail applications of the RG method to various disordered models, either (i) quantum models, such as random spin chains, ladders and higher dimensional spin systems, or (ii) classical models, such as diffusion in a random potential, equilibrium at low temperature and coarsening dynamics of classical random spin chains, trap models, delocalization transition of a random polymer from an interface, driven lattice gases and reaction diffusion models in the presence of quenched disorder. For several one-dimensional systems, the Ma-Dasgupta RG rules yields very detailed analytical results, whereas for other, mainly higher dimensional problems, the RG rules have to be implemented numerically. If available, the strong disorder RG results are compared with another, exact or numerical calculations
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
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
Propagating gene expression fronts in a one-dimensional coupled system of artificial cells
Tayar, Alexandra M.; Karzbrun, Eyal; Noireaux, Vincent; Bar-Ziv, Roy H.
2015-12-01
Living systems employ front propagation and spatiotemporal patterns encoded in biochemical reactions for communication, self-organization and computation. Emulating such dynamics in minimal systems is important for understanding physical principles in living cells and in vitro. Here, we report a one-dimensional array of DNA compartments in a silicon chip as a coupled system of artificial cells, offering the means to implement reaction-diffusion dynamics by integrated genetic circuits and chip geometry. Using a bistable circuit we programmed a front of protein synthesis propagating in the array as a cascade of signal amplification and short-range diffusion. The front velocity is maximal at a saddle-node bifurcation from a bistable regime with travelling fronts to a monostable regime that is spatially homogeneous. Near the bifurcation the system exhibits large variability between compartments, providing a possible mechanism for population diversity. This demonstrates that on-chip integrated gene circuits are dynamical systems driving spatiotemporal patterns, cellular variability and symmetry breaking.
Directory of Open Access Journals (Sweden)
Francisco Simões
2011-12-01
Full Text Available O objetivo do presente trabalho é proceder à adaptação e validação de duas escalas breves de avaliação da motivação na aprendizagem: a Escala de Escolha Percebida na Aprendizagem e a Escala de Competência Percebida na Aprendizagem. O estudo abrangeu 510 participantes, com idades compreendidas entre os 9 e os 16 anos. Após a análise exploratória de dados, o trabalho envolveu a avaliação da consistência interna, sucedida de uma análise fatorial exploratória de ambas as escalas. Foram estudadas, também, a sua validade convergente, bem como a sua estabilidade temporal. Foi ainda realizada uma análise diferencial dos resultados quanto às variáveis gênero e ano de escolaridade. Os instrumentos revelam valores moderados a elevados no nível da consistência interna e estruturas unidimensionais à semelhança das versões originais em língua inglesa. Confirmam-se, também, várias das hipóteses colocadas quanto à sua validade convergente. Estudos adicionais relativamente à estabilidade temporal desses instrumentos parecem ser pertinentes.The aim of this study was to adapt and validate two brief scales in order to assess the subjective motivation for learning: the Perceived Choice for Learning Scale and the Perceived Competence for Learning Scale. The study involved 510 participants, ages 9-16 years old. After an exploratory data analysis, the study involved the assessment of internal consistency, followed by an exploratory factor analysis of both scales. Convergent validity and temporal stability of the two scales were also tested, along with a differential analysis regarding gender and school level of the participants. The instruments showed moderate to high levels of internal consistency and one-dimensional structures similar to their original versions in English. Several hypotheses concerning convergent validity were also supported by the study. Additional research seems to be recommendable to address temporal stability
A thermo-diffusion system with Smoluchowski interactions : well-posedness and homogenization
Krehel, O.; Aiki, T.; Muntean, A.
2014-01-01
We study the solvability and homogenization of a thermal-diffusion reaction problem posed in a periodically perforated domain. The system describes the motion of populations of hot colloidal particles interacting together via Smoluchowski production terms. The upscaled system, obtained via two-scale
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.
Second-order splitting schemes for a class of reactive systems
International Nuclear Information System (INIS)
Ren Zhuyin; Pope, Stephen B.
2008-01-01
We consider the numerical time integration of a class of reaction-transport systems that are described by a set of ordinary differential equations for primary variables. In the governing equations, the terms involved may require the knowledge of secondary variables, which are functions of the primary variables. Specifically, we consider the case where, given the primary variables, the evaluation of the secondary variables is computationally expensive. To solve this class of reaction-transport equations, we develop and demonstrate several computationally efficient splitting schemes, wherein the portions of the governing equations containing chemical reaction terms are separated from those parts containing the transport terms. A computationally efficient solution to the transport sub-step is achieved through the use of linearization or predictor-corrector methods. The splitting schemes are applied to the reactive flow in a continuously stirred tank reactor (CSTR) with the Davis-Skodjie reaction model, to the CO+H 2 oxidation in a CSTR with detailed chemical kinetics, and to a reaction-diffusion system with an extension of the Oregonator model of the Belousov-Zhabotinsky reaction. As demonstrated in the test problems, the proposed splitting schemes, which yield efficient solutions to the transport sub-step, achieve second-order accuracy in time
Rundo, Francesco; Conoci, Sabrina; Ortis, Alessandro; Battiato, Sebastiano
2018-01-30
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.
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
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.
Seirin Lee, S.; Gaffney, E. A.
2010-01-01
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
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.
Global dynamics of a PDE model for aedes aegypti mosquitoe incorporating female sexual preference
Parshad, Rana; Agusto, Folashade B.
2011-01-01
In this paper we study the long time dynamics of a reaction diffusion system, describing the spread of Aedes aegypti mosquitoes, which are the primary cause of dengue infection. The system incorporates a control attempt via the sterile insect
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.
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,
Two-scale homogenization to determine effective parameters of thin metallic-structured films
Marigo, Jean-Jacques
2016-01-01
We present a homogenization method based on matched asymptotic expansion technique to derive effective transmission conditions of thin structured films. The method leads unambiguously to effective parameters of the interface which define jump conditions or boundary conditions at an equivalent zero thickness interface. The homogenized interface model is presented in the context of electromagnetic waves for metallic inclusions associated with Neumann or Dirichlet boundary conditions for transverse electric or transverse magnetic wave polarization. By comparison with full-wave simulations, the model is shown to be valid for thin interfaces up to thicknesses close to the wavelength. We also compare our effective conditions with the two-sided impedance conditions obtained in transmission line theory and to the so-called generalized sheet transition conditions. PMID:27616916
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.
Mihn, Byeong-Hee; Choi, Goeun; Lee, Yong Sam
2017-03-01
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.
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.
More reasons to be straightforward: findings and norms for two scales relevant to social anxiety.
Rodebaugh, Thomas L; Heimberg, Richard G; Brown, Patrick J; Fernandez, Katya C; Blanco, Carlos; Schneier, Franklin R; Liebowitz, Michael R
2011-06-01
The validity of both the Social Interaction Anxiety Scale and Brief Fear of Negative Evaluation scale has been well-supported, yet the scales have a small number of reverse-scored items that may detract from the validity of their total scores. The current study investigates two characteristics of participants that may be associated with compromised validity of these items: higher age and lower levels of education. In community and clinical samples, the validity of each scale's reverse-scored items was moderated by age, years of education, or both. The straightforward items did not show this pattern. To encourage the use of the straightforward items of these scales, we provide normative data from the same samples as well as two large student samples. We contend that although response bias can be a substantial problem, the reverse-scored questions of these scales do not solve that problem and instead decrease overall validity. Copyright © 2011 Elsevier Ltd. All rights reserved.
Plochg, Thomas; Arah, Onyebuchi A; Botje, Daan; Thompson, Caroline A; Klazinga, Niek S; Wagner, Cordula; Mannion, Russell; Lombarts, Kiki
2014-04-01
Clinical management is hypothesized to be critical for hospital management and hospital performance. The aims of this study were to develop and validate professional involvement scales for measuring the level of clinical management by physicians and nurses in European hospitals. Testing of validity and reliability of scales derived from a questionnaire of 21 items was developed on the basis of a previous study and expert opinion and administered in a cross-sectional seven-country research project 'Deepening our Understanding of Quality improvement in Europe' (DUQuE). A sample of 3386 leading physicians and nurses working in 188 hospitals located in Czech Republic, France, Germany, Poland, Portugal, Spain and Turkey. Validity and reliability of professional involvement scales and subscales. Psychometric analysis yielded four subscales for leading physicians: (i) Administration and budgeting, (ii) Managing medical practice, (iii) Strategic management and (iv) Managing nursing practice. Only the first three factors applied well to the nurses. Cronbach's alpha for internal consistency ranged from 0.74 to 0.86 for the physicians, and from 0.61 to 0.81 for the nurses. Except for the 0.74 correlation between 'Administration and budgeting' and 'Managing medical practice' among physicians, all inter-scale correlations were measurement instrument can be used for international research on clinical management.
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.
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.
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.
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
International Nuclear Information System (INIS)
Adamson, S; Astapenko, V; Chernysheva, I; Chorkov, V; Deminsky, M; Demchenko, G; Demura, A; Demyanov, A; Dyatko, N; Eletzkii, A; Knizhnik, A; Kochetov, I; Napartovich, A; Rykova, E; Sukhanov, L; Umanskii, S; Vetchinkin, A; Zaitsevskii, A; Potapkin, B
2007-01-01
Present-day computational techniques provide a possibility of evaluating properties of macrosystems using ab initio quantum chemistry and theories of elementary processes. Physical and chemical phenomena on very different timescales have to be taken into account (excitation, emission, chemical reactions, diffusion) at different levels of refining. This refining covers a very wide region of parameters starting from the structure of species up to the macro chemical mechanism of their conversion. This multilevel approach is described in detail in the paper and includes interaction and data transfer between different levels of phenomena description. In the framework of the approach, unknown properties of molecules, ions and atoms (structure, potential energy curves, transition dipole moments) are calculated based on quantum-chemical methods. The calculation results are used to evaluate rate characteristics of physical and chemical processes. The developed kinetic state-to-state scheme is then used to calculate the macro properties of the system under investigation. As an example of the multilevel approach, the emission properties of the Ar-GaI 3 positive column discharge plasma were calculated using the Chemical Work Bench computational environment. The calculations yield the electron energy balance and emission efficiency as functions of plasma parameters
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
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.
Directory of Open Access Journals (Sweden)
Jayson Gutiérrez
2009-09-01
Full Text Available The way in which the information contained in genotypes is translated into complex phenotypic traits (i.e. embryonic expression patterns depends on its decoding by a multilayered hierarchy of biomolecular systems (regulatory networks. Each layer of this hierarchy displays its own regulatory schemes (i.e. operational rules such as +/- feedback and associated control parameters, resulting in characteristic variational constraints. This process can be conceptualized as a mapping issue, and in the context of highly-dimensional genotype-phenotype mappings (GPMs epistatic events have been shown to be ubiquitous, manifested in non-linear correspondences between changes in the genotype and their phenotypic effects. In this study I concentrate on epistatic phenomena pervading levels of biological organization above the genetic material, more specifically the realm of molecular networks. At this level, systems approaches to studying GPMs are specially suitable to shed light on the mechanistic basis of epistatic phenomena. To this aim, I constructed and analyzed ensembles of highly-modular (fully interconnected networks with distinctive topologies, each displaying dynamic behaviors that were categorized as either arbitrary or functional according to early patterning processes in the Drosophila embryo. Spatio-temporal expression trajectories in virtual syncytial embryos were simulated via reaction-diffusion models. My in silico mutational experiments show that: 1 the average fitness decay tendency to successively accumulated mutations in ensembles of functional networks indicates the prevalence of positive epistasis, whereas in ensembles of arbitrary networks negative epistasis is the dominant tendency; and 2 the evaluation of epistatic coefficients of diverse interaction orders indicates that, both positive and negative epistasis are more prevalent in functional networks than in arbitrary ones. Overall, I conclude that the phenotypic and fitness effects of
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.
Periodic and solitary wave solutions of cubic–quintic nonlinear ...
Indian Academy of Sciences (India)
Hence, most of the real nonlinear physical equations possess variable ... evolution of the system with time and second term represents the convective flux term. The ... Travelling wave solutions of nonlinear reaction-diffusion equations are.
Field theory of absorbing phase transitions with a non-diffusive conserved field
International Nuclear Information System (INIS)
Pastor-Satorras, R.; Vespignani, A.
2000-04-01
We investigate the critical behavior of a reaction-diffusion system exhibiting a continuous absorbing-state phase transition. The reaction-diffusion system strictly conserves the total density of particles, represented as a non-diffusive conserved field, and allows an infinite number of absorbing configurations. Numerical results show that it belongs to a wide universality class that also includes stochastic sandpile models. We derive microscopically the field theory representing this universality class. (author)
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/
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.
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....
Hernansaiz-Garrido, Helena; Alonso-Tapia, Jesús
2017-01-01
Internalized stigma and disclosure concerns are key elements for the study of mental health in people living with HIV. Since no measures of these constructs were available for Spanish population, this study sought to develop such instruments, to analyze their reliability and validity and to provide a short version. A heterogeneous sample of 458 adults from different Spanish-speaking countries completed the HIV-Internalized Stigma Scale and the HIV-Disclosure Concerns Scale, along with the Hospital Anxiety and Depression Scale, Rosenberg's Self-esteem Scale and other socio-demographic variables. Reliability and correlation analyses, exploratory factor analyses, path analyses with latent variables, and ANOVAs were conducted to test the scales' psychometric properties. The scales showed good reliability in terms of internal consistency and temporal stability, as well as good sensitivity and factorial and criterion validity. The HIV-Internalized Stigma Scale and the HIV-Disclosure Concerns Scale are reliable and valid means to assess these variables in several contexts.
Waite, Ian R.
2013-01-01
Research was conducted at 28-30 sites within eight study areas across the United States along a gradient of nutrient enrichment/agricultural land use between 2003 and 2007. Objectives were to test the application of an agricultural intensity index (AG-Index) and compare among various invertebrate and algal metrics to determine indicators of nutrient enrichment nationally and within three regions. The agricultural index was based on total nitrogen and phosphorus input to the watershed, percent watershed agriculture, and percent riparian agriculture. Among data sources, agriculture within riparian zone showed significant differences among values generated from remote sensing or from higher resolution orthophotography; median values dropped significantly when estimated by orthophotography. Percent agriculture in the watershed consistently had lower correlations to invertebrate and algal metrics than the developed AG-Index across all regions. Percent agriculture showed fewer pairwise comparisons that were significant than the same comparisons using the AG-Index. Highest correlations to the AG-Index regionally were −0.75 for Ephemeroptera, Plecoptera, and Trichoptera richness (EPTR) and −0.70 for algae Observed/Expected (O/E), nationally the highest was −0.43 for EPTR vs. total nitrogen and −0.62 for algae O/E vs. AG-Index. Results suggest that analysis of metrics at national scale can often detect large differences in disturbance, but more detail and specificity is obtained by analyzing data at regional scales.
Carvin, Rebecca; Good, Laura W.; Fitzpatrick, Faith A.; Diehl, Curt; Songer, Katherine; Meyer, Kimberly J.; Panuska, John C.; Richter, Steve; Whalley, Kyle
2018-01-01
This study tested a focused strategy for reducing phosphorus (P) and sediment loads in agricultural streams. The strategy involved selecting small watersheds identified as likely to respond relatively quickly, and then focusing conservation practices on high-contributing fields within those watersheds. Two 5,000 ha (12,360 ac) watersheds in the Driftless Area of south central Wisconsin, previously ranked in the top 6% of similarly sized Wisconsin watersheds for expected responsiveness to conservation efforts to reduce high P and sediment loads, were chosen for the study. The stream outlets from both watersheds were monitored from October of 2006 through September of 2016 for streamflow and concentrations of sediment, total P, and, beginning in October of 2009, total dissolved P. Fields and pastures having the highest potential P delivery to the streams in each watershed were identified using the Wisconsin P Index (Good et al. 2012). After three years of baseline monitoring (2006 to 2009), farmers implemented both field- and farm-based conservation practices in one watershed (treatment) as a means to reduce sediment and P inputs to the stream from the highest contributing areas, whereas there were no out-of-the-ordinary conservation efforts in the second watershed (control). Implementation occurred primarily in 2011 and 2012. In the four years following implementation of conservation practices (2013 through 2016), there was a statistically significant reduction in storm-event suspended sediment loads in the treatment watershed compared to the control watershed when the ground was not frozen (p = 0.047). While there was an apparent reduction in year-round suspended sediment event loads, it was not statistically significant at the 95% confidence level (p = 0.15). Total P loads were significantly reduced for runoff events (p < 0.01) with a median reduction of 50%. Total P and total dissolved P concentrations for low-flow conditions were also significantly reduced (p < 0.01) compared to the control watershed. This study demonstrated that a strategy that first identifies watersheds likely to respond to conservation efforts and then focuses implementation on relatively high-contributing fields within those watersheds can be successful in reducing stream P concentrations and loads.
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)
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)
Quantum one dimensional spin systems. Disorder and impurities
International Nuclear Information System (INIS)
Brunel, V.
1999-01-01
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.)
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.
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
Indian Academy of Sciences (India)
Embedded system, micro-con- troller ... Embedded systems differ from general purpose computers in many ... Low cost: As embedded systems are extensively used in con- .... operating systems for the desktop computers where scheduling.
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
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...
An electromechanical based deformable model for soft tissue simulation.
Zhong, Yongmin; Shirinzadeh, Bijan; Smith, Julian; Gu, Chengfan
2009-11-01
Soft tissue deformation is of great importance to surgery simulation. Although a significant amount of research efforts have been dedicated to simulating the behaviours of soft tissues, modelling of soft tissue deformation is still a challenging problem. This paper presents a new deformable model for simulation of soft tissue deformation from the electromechanical viewpoint of soft tissues. Soft tissue deformation is formulated as a reaction-diffusion process coupled with a mechanical load. The mechanical load applied to a soft tissue to cause a deformation is incorporated into the reaction-diffusion system, and consequently distributed among mass points of the soft tissue. Reaction-diffusion of mechanical load and non-rigid mechanics of motion are combined to govern the simulation dynamics of soft tissue deformation. An improved reaction-diffusion model is developed to describe the distribution of the mechanical load in soft tissues. A three-layer artificial cellular neural network is constructed to solve the reaction-diffusion model for real-time simulation of soft tissue deformation. A gradient based method is established to derive internal forces from the distribution of the mechanical load. Integration with a haptic device has also been achieved to simulate soft tissue deformation with haptic feedback. The proposed methodology does not only predict the typical behaviours of living tissues, but it also accepts both local and large-range deformations. It also accommodates isotropic, anisotropic and inhomogeneous deformations by simple modification of diffusion coefficients.
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)
Kim, Do Hun; Mun, Tae Hun; Kim, Dong Hwan
1999-02-01
This book introduces systems thinking and conceptual tool and modeling tool of dynamics system such as tragedy of single thinking, accessible way of system dynamics, feedback structure and causal loop diagram analysis, basic of system dynamics modeling, causal loop diagram and system dynamics modeling, information delay modeling, discovery and application for policy, modeling of crisis of agricultural and stock breeding products, dynamic model and lesson in ecosystem, development and decadence of cites and innovation of education forward system thinking.
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.
Simple computation of reaction–diffusion processes on point clouds
Macdonald, Colin B.; Merriman, Barry; Ruuth, Steven J.
2013-01-01
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.
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.
Coupling component systems towards systems of systems
Autran , Frédéric; Auzelle , Jean-Philippe; Cattan , Denise; Garnier , Jean-Luc; Luzeaux , Dominique; Mayer , Frédérique; Peyrichon , Marc; Ruault , Jean-René
2008-01-01
International audience; Systems of systems (SoS) are a hot topic in our "fully connected global world". Our aim is not to provide another definition of what SoS are, but rather to focus on the adequacy of reusing standard system architecting techniques within this approach in order to improve performance, fault detection and safety issues in large-scale coupled systems that definitely qualify as SoS, whatever the definition is. A key issue will be to secure the availability of the services pr...
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.
International Nuclear Information System (INIS)
Meyer, P.J.
1981-01-01
Systems included under the heading ''Reactor Auxillary Systems'' are those immediately involved with the reactor operation. These include the systems for dosing and letdown of reactor coolant, as well as for the chemical dosing, purification and treatment of the reactor coolant and the cooling system in the controlled area. The ancillary systems are mainly responsible for liquid and gaseous treatment and the waste treatment for final storage. (orig.)
Tzou, J. C.; Ward, M. J.
2018-06-01
Spot patterns, whereby the activator field becomes spatially localized near certain dynamically-evolving discrete spatial locations in a bounded multi-dimensional domain, is a common occurrence for two-component reaction-diffusion (RD) systems in the singular limit of a large diffusivity ratio. In previous studies of 2-D localized spot patterns for various specific well-known RD systems, the domain boundary was assumed to be impermeable to both the activator and inhibitor, and the reaction-kinetics were assumed to be spatially uniform. As an extension of this previous theory, we use formal asymptotic methods to study the existence, stability, and slow dynamics of localized spot patterns for the singularly perturbed 2-D Brusselator RD model when the domain boundary is only partially impermeable, as modeled by an inhomogeneous Robin boundary condition, or when there is an influx of inhibitor across the domain boundary. In our analysis, we will also allow for the effect of a spatially variable bulk feed term in the reaction kinetics. By applying our extended theory to the special case of one-spot patterns and ring patterns of spots inside the unit disk, we provide a detailed analysis of the effect on spot patterns of these three different sources of heterogeneity. In particular, when there is an influx of inhibitor across the boundary of the unit disk, a ring pattern of spots can become pinned to a ring-radius closer to the domain boundary. Under a Robin condition, a quasi-equilibrium ring pattern of spots is shown to exhibit a novel saddle-node bifurcation behavior in terms of either the inhibitor diffusivity, the Robin constant, or the ambient background concentration. A spatially variable bulk feed term, with a concentrated source of "fuel" inside the domain, is shown to yield a saddle-node bifurcation structure of spot equilibria, which leads to qualitatively new spot-pinning behavior. Results from our asymptotic theory are validated from full numerical
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.
Nash equilibria in noncooperative predator-prey games
Czech Academy of Sciences Publication Activity Database
Ramos, A. M.; Roubíček, Tomáš
2007-01-01
Roč. 56, č. 2 (2007), s. 211-241 ISSN 0095-4616 Grant - others:GA ČR(CZ) GA201/03/0934 Institutional research plan: CEZ:AV0Z10750506 Keywords : Reaction-diffusion system * Lotka-Voltera system * Nash equilibrium Subject RIV: BA - General Mathematics Impact factor: 0.873, year: 2007
Homogenization and dimension reduction of filtration combustion in heterogeneous thin layers
Fatima, T.; Ijioma, E.R.; Ogawa, T.; Muntean, A.
2014-01-01
We study the homogenization of a reaction-diffusion-convection system posed in an e-periodic d-thin layer made of a two-component (solid-air) composite material. The microscopic system includes heat flow, diffusion and convection coupled with a nonlinear surface chemical reaction. We treat two
Filamentary structures of the cosmic web and the nonlinear Schroedinger type equation
International Nuclear Information System (INIS)
Tigrak, E; Weygaert, R van de; Jones, B J T
2011-01-01
We show that the filamentary type structures of the cosmic web can be modeled as solitonic waves by solving the reaction diffusion system which is the hydrodynamical analogous of the nonlinear Schroedinger type equation. We find the analytical solution of this system by applying the Hirota direct method which produces the dissipative soliton solutions to formulate the dynamical evolution of the nonlinear structure formation.
Stochastic many-body problems in ecology, evolution, neuroscience, and systems biology
Butler, Thomas C.
Using the tools of many-body theory, I analyze problems in four different areas of biology dominated by strong fluctuations: The evolutionary history of the genetic code, spatiotemporal pattern formation in ecology, spatiotemporal pattern formation in neuroscience and the robustness of a model circadian rhythm circuit in systems biology. In the first two research chapters, I demonstrate that the genetic code is extremely optimal (in the sense that it manages the effects of point mutations or mistranslations efficiently), more than an order of magnitude beyond what was previously thought. I further show that the structure of the genetic code implies that early proteins were probably only loosely defined. Both the nature of early proteins and the extreme optimality of the genetic code are interpreted in light of recent theory [1] as evidence that the evolution of the genetic code was driven by evolutionary dynamics that were dominated by horizontal gene transfer. I then explore the optimality of a proposed precursor to the genetic code. The results show that the precursor code has only limited optimality, which is interpreted as evidence that the precursor emerged prior to translation, or else never existed. In the next part of the dissertation, I introduce a many-body formalism for reaction-diffusion systems described at the mesoscopic scale with master equations. I first apply this formalism to spatially-extended predator-prey ecosystems, resulting in the prediction that many-body correlations and fluctuations drive population cycles in time, called quasicycles. Most of these results were previously known, but were derived using the system size expansion [2, 3]. I next apply the analytical techniques developed in the study of quasi-cycles to a simple model of Turing patterns in a predator-prey ecosystem. This analysis shows that fluctuations drive the formation of a new kind of spatiotemporal pattern formation that I name "quasi-patterns." These quasi
International Nuclear Information System (INIS)
Honeck, H.C.
1975-04-01
A major computational system called JOSHUA has been under development at the Savannah River Laboratory since 1968. The JOSHUA System has two major parts: the Operating System and the Application System. The Operating System has been in production use since 1970 and provides data management, terminal, and job execution facilities. The Application System uses these facilities in solving problems in reactor physics and engineering. Features of the Application System are the two-dimensional lattice physics and three-dimensional transient reactor physics capabilities, which have been in use since 1971 and 1974, respectively. The capabilities of the JOSHUA System are summarized, and statistics on size, use, and development effort are provided. (U.S.)
Cabrera, Derek; Colosi, Laura; Lobdell, Claire
2008-08-01
Evaluation is one of many fields where "systems thinking" is popular and is said to hold great promise. However, there is disagreement about what constitutes systems thinking. Its meaning is ambiguous, and systems scholars have made diverse and divergent attempts to describe it. Alternative origins include: von Bertalanffy, Aristotle, Lao Tsu or multiple aperiodic "waves." Some scholars describe it as synonymous with systems sciences (i.e., nonlinear dynamics, complexity, chaos). Others view it as taxonomy-a laundry list of systems approaches. Within so much noise, it is often difficult for evaluators to find the systems thinking signal. Recent work in systems thinking describes it as an emergent property of four simple conceptual patterns (rules). For an evaluator to become a "systems thinker", he or she need not spend years learning many methods or nonlinear sciences. Instead, with some practice, one can learn to apply these four simple rules to existing evaluation knowledge with transformative results.
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...... 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...... 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....
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.)
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)
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 b...... for the application of expert systems, but also raises issues regarding privacy and legal liability....
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...... and methods, and the efficiency of the different systems are discussed....
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
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
Siemieniuch, C E; Sinclair, M A
2006-01-01
The paper presents a view of systems integration, from an ergonomics/human factors perspective, emphasising the process of systems integration as is carried out by humans. The first section discusses some of the fundamental issues in systems integration, such as the significance of systems boundaries, systems lifecycle and systems entropy, issues arising from complexity, the implications of systems immortality, and so on. The next section outlines various generic processes for executing systems integration, to act as guides for practitioners. These address both the design of the system to be integrated and the preparation of the wider system in which the integration will occur. Then the next section outlines some of the human-specific issues that would need to be addressed in such processes; for example, indeterminacy and incompleteness, the prediction of human reliability, workload issues, extended situation awareness, and knowledge lifecycle management. For all of these, suggestions and further readings are proposed. Finally, the conclusions section reiterates in condensed form the major issues arising from the above.
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)
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
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....
Vaughan, William W.
2016-01-01
The term “systems engineering” when entered into the Google search page, produces a significant number of results, evidence that systems engineering is recognized as being important for the success of essentially all products. Since most readers of this item will be rather well versed in documents concerning systems engineering, I have elected to share some of the points made on this subject in a document developed by the European Cooperation for Space Standardization (ECSS), a component of t...
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
Winther, Rasmus Grønfeldt
2008-08-19
Darwin's 19th century evolutionary theory of descent with modification through natural selection opened up a multidimensional and integrative conceptual space for biology. We explore three dimensions of this space: explanatory pattern, levels of selection, and degree of difference among units of the same type. Each dimension is defined by a respective pair of poles: law and narrative explanation, organismic and hierarchical selection, and variational and essentialist thinking. As a consequence of conceptual debates in the 20th century biological sciences, the poles of each pair came to be seen as mutually exclusive opposites. A significant amount of 21st century research focuses on systems (e.g., genomic, cellular, organismic, and ecological/global). Systemic Darwinism is emerging in this context. It follows a "compositional paradigm" according to which complex systems and their hierarchical networks of parts are the focus of biological investigation. Through the investigation of systems, Systemic Darwinism promises to reintegrate each dimension of Darwin's original logical space. Moreover, this ideally and potentially unified theory of biological ontology coordinates and integrates a plurality of mathematical biological theories (e.g., self-organization/structure, cladistics/history, and evolutionary genetics/function). Integrative Systemic Darwinism requires communal articulation from a plurality of perspectives. Although it is more general than these, it draws on previous advances in Systems Theory, Systems Biology, and Hierarchy Theory. Systemic Darwinism would greatly further bioengineering research and would provide a significantly deeper and more critical understanding of biological reality.
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. ...
Lu L.; Medo M.; Yeung C.H.; Zhang Y.-C.; Zhang Z.-K.; Zhou T.
2012-01-01
The ongoing rapid expansion of the Internet greatly increases the necessity of effective recommender systems for filtering the abundant information. Extensive research for recommender systems is conducted by a broad range of communities including social and computer scientists, physicists, and interdisciplinary researchers. Despite substantial theoretical and practical achievements, unification and comparison of different approaches are lacking, which impedes further advances. In this article...
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)
Systems integration (automation system). System integration (automation system)
Energy Technology Data Exchange (ETDEWEB)
Fujii, K; Komori, T; Fukuma, Y; Oikawa, M [Nippon Steal Corp., Tokyo (Japan)
1991-09-26
This paper introduces business activities on an automation systems integration (SI) started by a company in July,1988, and describes the SI concepts. The business activities include, with the CIM (unified production carried out on computers) and AMENITY (living environment) as the mainstays, a single responsibility construction ranging from consultation on structuring optimal systems for processing and assembling industries and intelligent buildings to system design, installation and after-sales services. With an SI standing on users {prime} position taken most importantly, the business starts from a planning and consultation under close coordination. On the conceptual basis of structuring optimal systems using the ompany {prime}s affluent know-hows and tools and adapting and applying with multi-vendors, open networks, centralized and distributed systems, the business is promoted with the accumulated technologies capable of realizing artificial intelligence and neural networks in its background, and supported with highly valuable business results in the past. 10 figs., 1 tab.
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...... deres felt har beskæftiget sig med udviklingen af systemer. Kieran Timberlake, markant amerikansk tegnestue; Mark West, Professor på University of Manitoba, Canada, og pioner indenfor anvendelse af tekstilforskalling til betonstøbninger; Matilda McQuaid, Arkitekturhistoriker og kurator på udstillingen...... om Extreme Textiles på amerikanske Cooper Hewit Design Museum, samt Professor Ludger Hovestadt, ved ETH, Zürich der fokuserer på udvikling og anvendelse af logaritmiske systemtilgange. Udstillingen diskuterede ud fra deres meget forskellige arbejder, det kreative potentiale i anvendelsen af systemer...
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...... 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...
Upgraded RECOVER system - CASDAC system
International Nuclear Information System (INIS)
Yamamoto, Yoichi; Koyama, Kinji
1992-03-01
The CASDAC (Containment And Surveillance Data Authenticated Communication) system has been developed by JAERI for nuclear safeguards and physical protection of nuclear material. This system was designed and constructed as an upgraded RECOVER system, design concept of which was based on the original RECOVER system and also the TRANSEAVER system. Both of them were developed several years ago as a remote monitoring system for continual verification of security and safeguards status of nuclear material. The system consists of two subsystems, one of them is a Grand Command Center (GCC) subsystem and the other is a facility subsystem. Communication between the two subsystems is controlled through the international telephone line network. Therefore all communication data are encrypted to prevent access by an unauthorized person who may intend to make a falsification, or tapping. The facility subsystem has an appropriate measure that ensure data security and reliable operation under unattended mode of operator. The software of this system is designed so as to be easily used in other different types of computers. This report describes the outline of the CASDAC system and the results of its performance test. This work has been carried out in the framework of Japan Support Programme for Agency Safeguards (JASPAS) as a project, JA-1. (author)
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
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...
A review on symmetries for certain Aedes aegypti models
Freire, Igor Leite; Torrisi, Mariano
2015-04-01
We summarize our results related with mathematical modeling of Aedes aegypti and its Lie symmetries. Moreover, some explicit, group-invariant solutions are also shown. Weak equivalence transformations of more general reaction diffusion systems are also considered. New classes of solutions are obtained.
African Journals Online (AJOL)
Items 1 - 50 of 821 ... Vol 24, No 4 (2001), A Category of L-Fuzzy Convergence Spaces, Abstract ... to solve systems of evolutionary reaction-diffusion equations, Abstract ... Vol 41, No 2 (2018), A new type of hermite matrix polynomial series ...
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.
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...... huge chunks of video data where no events/interactions of interest are occurring and hence let a user focus on manually annotation of only the interesting stuff....
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
International Nuclear Information System (INIS)
Riess, R.
1980-01-01
The present paper describes the coolant chemistry and its consequences for 1300 MWsub(e) KWU PWR plants. Some selected systems, i.e. primary heat transport system, steam water cycle and cooling water arrangements, are chosen for this description. Various aspects of coolant chemistry regarding general corrosion, selective types of corrosion and deposits on heat transfer surfaces have been discussed. The water supply systems necessary to fulfill the requirements of the coolant chemistry are discussed as well. It has been concluded that a good operating performance can only be achieved when - beside other factors - the water chemistry has been given sufficient consideration. (orig./RW)
International Nuclear Information System (INIS)
Riess, R.
1981-01-01
The present paper describes the coolant chemistry and its consequences for 1300 MWsub(e) KWU PWR plants. Some selected systems, i.e. primary heat transport system, steam water cycle and cooling water arrangements, are chosen for this description. Various aspects of coolant chemistry regarding general corrosion, selective types of corrosion and deposits on heat transfer surface have been discussed. The water supply systems necessary to fulfill the requirements of the coolant chemistry are discussed as well. It has been concluded that a good operating performance can only be achieved when - beside other factors - the water chemistry has been given sufficient consideration. (orig./RW)
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)
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.
The systems integration modeling system
International Nuclear Information System (INIS)
Danker, W.J.; Williams, J.R.
1990-01-01
This paper discusses the systems integration modeling system (SIMS), an analysis tool for the detailed evaluation of the structure and related performance of the Federal Waste Management System (FWMS) and its interface with waste generators. It's use for evaluations in support of system-level decisions as to FWMS configurations, the allocation, sizing, balancing and integration of functions among elements, and the establishment of system-preferred waste selection and sequencing methods and other operating strategies is presented. SIMS includes major analysis submodels which quantify the detailed characteristics of individual waste items, loaded casks and waste packages, simulate the detailed logistics of handling and processing discrete waste items and packages, and perform detailed cost evaluations
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.
The web site provides guidance and technical assistance for homeowners, government officials, industry professionals, and EPA partners about how to properly develop and manage individual onsite and community cluster systems that treat domestic wastewater.
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.
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...
Indian Academy of Sciences (India)
IAS Admin
study and understand the function of biological systems, particu- larly, the response of such .... understand the organisation and behaviour of prokaryotic sys- tems. ... relationship of the structure of a target molecule to its ability to bind a certain ...
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......, and it aims to illustrate and identify new modes of working in architecture, particularly with regards to brickwork and other complex systems of modular assemblies, whether physical or digital....
Lucas, P.J.F.
2005-01-01
Expert systems mimic the problem-solving activity of human experts in specialized domains by capturing and representing expert knowledge. Expert systems include a knowledge base, an inference engine that derives conclusions from the knowledge, and a user interface. Knowledge may be stored as if-then rules, orusing other formalisms such as frames and predicate logic. Uncertain knowledge may be represented using certainty factors, Bayesian networks, Dempster-Shafer belief functions, or fuzzy se...
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.
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
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)
International Nuclear Information System (INIS)
Miyano, Hiroshi; Narabayashi, Naoshi.
1990-01-01
The represent invention concerns a reactor system with improved water injection means to a pressure vessel of a BWR type reactor. A steam pump is connected to a heat removing system pipeline, a high pressure water injection system pipeline and a low pressure water injection system pipeline for injecting water into the pressure vessel. A pump actuation pipeline is disposed being branched from a main steam pump or a steam relieaf pipeline system, through which steams are supplied to actuate the steam pump and supply cooling water into the pressure vessel thereby cooling the reactor core. The steam pump converts the heat energy into the kinetic energy and elevates the pressure of water to a level higher than the pressure of the steams supplied by way of a pressure-elevating diffuser. Cooling water can be supplied to the pressure vessel by the pressure elevation. This can surely inject cooling water into the pressure vessel upon loss of coolant accident or in a case if reactor scram is necessary, without using an additional power source. (I.N.)
International Nuclear Information System (INIS)
Kelly, M.F.; Wyman, R.H.
1975-01-01
In spite of the remarkable safety record of the nuclear industry as a whole, recent public concern over the potential impact of the industry's accelerated growth has prompted ERDA to expand its emergency response procedures. The Atmospheric Release Advisory Capability, ARAC, is a computer communications system designed to enhance the existing emergency response capability of ERDA nuclear facilities. ARAC will add at least two new functions to this capability: centralized, real-time data acquisition and storage, and simulation of the long range atmospheric transport of hazardous materials. To perform these functions, ARAC employs four major sub-systems or facilities: the site facility, the central facility, the global weather center and the regional model. The system has been under development for the past two years at the Lawrence Livermore Laboratory of the University of California
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.
Caspers, W J
1989-01-01
This book is about spin systems as models for magnetic materials, especially antiferromagnetic lattices. Spin-systems are well-defined models, for which, in special cases, exact properties may be derived. These special cases are for the greater part, one- dimensional and restricted in their applicability, but they may give insight into general properties that also exist in higher dimension. This work pays special attention to qualitative differences between spin lattices of different dimensions. It also replaces the traditional picture of an (ordered) antiferromagnetic state of a Heisenberg sy
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.
... of the Immune System Print en español El sistema inmunitario Whether you're stomping through the showers ... of Use Notice of Nondiscrimination Visit the Nemours Web site. Note: All information on TeensHealth® is for ...
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.
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
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…
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
DEFF Research Database (Denmark)
Wattenhofer, Roger; Förster, Klaus-Tycho
2016-01-01
What happens if a single server is no longer powerful enough to service all your customers? The obvious choice is to add more servers and to use the majority approach (e.g. Paxos, Chapter 2) to guarantee consistency. However, even if you buy one million servers, a client still has to access more ...... study the theory behind overlapping sets, known as quorum systems....
Morecroft, John
System dynamics is an approach for thinking about and simulating situations and organisations of all kinds and sizes by visualising how the elements fit together, interact and change over time. This chapter, written by John Morecroft, describes modern system dynamics which retains the fundamentals developed in the 1950s by Jay W. Forrester of the MIT Sloan School of Management. It looks at feedback loops and time delays that affect system behaviour in a non-linear way, and illustrates how dynamic behaviour depends upon feedback loop structures. It also recognises improvements as part of the ongoing process of managing a situation in order to achieve goals. Significantly it recognises the importance of context, and practitioner skills. Feedback systems thinking views problems and solutions as being intertwined. The main concepts and tools: feedback structure and behaviour, causal loop diagrams, dynamics, are practically illustrated in a wide variety of contexts from a hot water shower through to a symphony orchestra and the practical application of the approach is described through several real examples of its use for strategic planning and evaluation.
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...
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...
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)
International Nuclear Information System (INIS)
Hamm, B.; Asbach, P.; Beyersdorff, D.; Hein, P.; Zaspel, U.
2007-01-01
The book is focussed on the radiological diagnostics of diseases in the urogential system. The description of the specific diseases, the identification by modern imaging techniques, the interpretation of examinatory results and therapeutic options are systematically treated in 4 chapters: kidney and adrenal glands, urinary tract, male genitals, female genitals
Fogassi, Leonardo; Ferrari, Pier Francesco
2011-01-01
Mirror neurons are a class of visuomotor neurons, discovered in the monkey premotor cortex and in an anatomically connected area of the inferior parietal lobule, that activate both during action execution and action observation. They constitute a circuit dedicated to match actions made by others with the internal motor representations of the observer. It has been proposed that this matching system enables individuals to understand others' behavior and motor intentions. Here we will describe the main features of mirror neurons in monkeys. Then we will present evidence of the presence of a mirror system in humans and of its involvement in several social-cognitive functions, such as imitation, intention, and emotion understanding. This system may have several implications at a cognitive level and could be linked to specific social deficits in humans such as autism. Recent investigations addressed the issue of the plasticity of the mirror neuron system in both monkeys and humans, suggesting also their possible use in rehabilitation. WIREs Cogn Sci 2011 2 22-38 DOI: 10.1002/wcs.89 For further resources related to this article, please visit the WIREs website. Copyright © 2010 John Wiley & Sons, Ltd.
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...
International Nuclear Information System (INIS)
Haefele, W.
1974-01-01
Up to the present the production, transmission and distribution of energy has been considered mostly as a fragmented problem; at best only subsystems have been considered. Today the scale of energy utilization is increasing rapidly, and correspondingly, the reliance of societies on energy. Such strong quantitative increases influence the qualitative nature of energy utilization in most of its aspects. Resources, reserves, reliability and environment are among the key words that may characterize the change in the nature of the energy utilization problem. Energy can no longer be considered an isolated technical and economical problem, rather it is embedded in the ecosphere and the society-technology complex. Restraints and boundary conditions have to be taken into account with the same degree of attention as in traditional technical problems, for example a steam turbine. This results in a strong degree of interweaving. Further, the purpose of providing energy becomes more visible, that is, to make survival possible in a civilized and highly populated world on a finite globe. Because of such interweaving and finiteness it is felt that energy should be considered as a system and therefore the term 'energy systems' is used. The production of energy is only one component of such a system; the handling of energy and the embedding of energy into the global and social complex in terms of ecology, economy, risks and resources are of similar importance. he systems approach to the energy problem needs more explanation. This paper is meant to give an outline of the underlying problems and it is hoped that by so doing the wide range of sometimes confusing voices about energy can be better understood. Such confusion starts already with the term 'energy crisis'. Is there an energy crisis or not? Much future work is required to tackle the problems of energy systems. This paper can only marginally help in that respect. But it is hoped that it will help understand the scope of the
Energy Technology Data Exchange (ETDEWEB)
Haefele, W [Nuclear Research Centre, Applied Systems Analysis and Reactor Physics, Karlsruhe (Germany); International Institute for Applied Systems Analysis, Laxenburg (Austria)
1974-07-01
Up to the present the production, transmission and distribution of energy has been considered mostly as a fragmented problem; at best only subsystems have been considered. Today the scale of energy utilization is increasing rapidly, and correspondingly, the reliance of societies on energy. Such strong quantitative increases influence the qualitative nature of energy utilization in most of its aspects. Resources, reserves, reliability and environment are among the key words that may characterize the change in the nature of the energy utilization problem. Energy can no longer be considered an isolated technical and economical problem, rather it is embedded in the ecosphere and the society-technology complex. Restraints and boundary conditions have to be taken into account with the same degree of attention as in traditional technical problems, for example a steam turbine. This results in a strong degree of interweaving. Further, the purpose of providing energy becomes more visible, that is, to make survival possible in a civilized and highly populated world on a finite globe. Because of such interweaving and finiteness it is felt that energy should be considered as a system and therefore the term 'energy systems' is used. The production of energy is only one component of such a system; the handling of energy and the embedding of energy into the global and social complex in terms of ecology, economy, risks and resources are of similar importance. he systems approach to the energy problem needs more explanation. This paper is meant to give an outline of the underlying problems and it is hoped that by so doing the wide range of sometimes confusing voices about energy can be better understood. Such confusion starts already with the term 'energy crisis'. Is there an energy crisis or not? Much future work is required to tackle the problems of energy systems. This paper can only marginally help in that respect. But it is hoped that it will help understand the scope of the
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
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
1979-01-01
The solar collectors shown are elements of domestic solar hot water systems produced by Solar One Ltd., Virginia Beach, Virginia. Design of these systems benefited from technical expertise provided Solar One by NASA's Langley Research Center. The company obtained a NASA technical support package describing the d e sign and operation of solar heating equipment in NASA's Tech House, a demonstration project in which aerospace and commercial building technology are combined in an energy- efficient home. Solar One received further assistance through personal contact with Langley solar experts. The company reports that the technical information provided by NASA influenced Solar One's panel design, its selection of a long-life panel coating which increases solar collection efficiency, and the method adopted for protecting solar collectors from freezing conditions.
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