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
Progress in Global Multicompartmental Modelling of DDT
Stemmler, I.; Lammel, G.
2009-04-01
Dichlorophenyltrichloroethane, DDT, and its major metabolite dichlorophenyldichloroethylene, DDE, are long-lived in the environment (persistent) and circulate since the 1950s. They accumulate along food chains, cause detrimental effects in marine and terrestrial wild life, and pose a hazard for human health. DDT was widely used as an insecticide in the past and is still in use in a number of tropical countries to combat vector borne diseases like malaria and typhus. It is a multicompartmental substance with only a small mass fraction residing in air. A global multicompartment chemistry transport model (MPI-MCTM; Semeena et al., 2006) is used to study the environmental distribution and fate of dichlorodiphenyltrichloroethane (DDT). For the first time a horizontally and vertically resolved global model was used to perform a long-term simulation of DDT and DDE. The model is based on general circulation models for the ocean (MPIOM; Marsland et al., 2003) and atmosphere (ECHAM5). In addition, an oceanic biogeochemistry model (HAMOCC5.1; Maier-Reimer et al., 2005 ) and a microphysical aerosol model (HAM; Stier et al., 2005 ) are included. Multicompartmental substances are cycling in atmosphere (3 phases), ocean (3 phases), top soil (3 phases), and vegetation surfaces. The model was run for 40 years forced with historical agricultural application data of 1950-1990. The model results show that the global environmental contamination started to decrease in air, soil and vegetation after the applications peaked in 1965-70. In some regions, however, the DDT mass had not yet reached a maximum in 1990 and was still accumulating mass until the end of the simulation. Modelled DDT and DDE concentrations in atmosphere, ocean and soil are evaluated by comparison with observational data. The evaluation of the model results indicate that degradation of DDE in air was underestimated. Also for DDT, the discrepancies between model results and observations are related to uncertainties of
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.
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.
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.
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.
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.
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.
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.
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
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.
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.
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.
Brookings, Ted; Goeritz, Marie L; Marder, Eve
2014-11-01
We describe a new technique to fit conductance-based neuron models to intracellular voltage traces from isolated biological neurons. The biological neurons are recorded in current-clamp with pink (1/f) noise injected to perturb the activity of the neuron. The new algorithm finds a set of parameters that allows a multicompartmental model neuron to match the recorded voltage trace. Attempting to match a recorded voltage trace directly has a well-known problem: mismatch in the timing of action potentials between biological and model neuron is inevitable and results in poor phenomenological match between the model and data. Our approach avoids this by applying a weak control adjustment to the model to promote alignment during the fitting procedure. This approach is closely related to the control theoretic concept of a Luenberger observer. We tested this approach on synthetic data and on data recorded from an anterior gastric receptor neuron from the stomatogastric ganglion of the crab Cancer borealis. To test the flexibility of this approach, the synthetic data were constructed with conductance models that were different from the ones used in the fitting model. For both synthetic and biological data, the resultant models had good spike-timing accuracy. Copyright © 2014 the American Physiological Society.
Copper metabolism: a multicompartmental model of copper kinetics in the rat
International Nuclear Information System (INIS)
Dunn, M.A.
1985-01-01
A qualitative multicompartmental model was developed that describes the whole-body kinetics of copper metabolism in the adult rat. The model was developed from radiocopper percent dose vs. time data measured over a three day period in plasma, liver, skin, skeletal muscle, bile and feces after the intravenous injection of 10 μg copper labeled with 64 Cu. Plasma radiocopper was separated into ceruloplasmin (Cp) and nonceruloplasmin (NCp) fractions. Liver cytosolic radiocopper was fractionated into void volume superoxide dismutase (SOD) containing and metallothionein fractions by gel filtration. Liver particulate fractions were isolated by differential centrifugation. The SAAM and CONSAM modeling programs were used to develop the model. The sizes of compartments, fractional rate constants and mass transfer rates between compartments were evaluated. The intracellular metabolism of copper was similar in hepatic and extrahepatic tissues being comprised of a faster turning over compartment (FTC) exchanging copper with NCp and a slower turning over compartment (STC) with input from Cp. Output from the STC was into the FTC. In the liver the STC was postulated to represent SOD copper which unlike the extrahepatic tissues received much of its input from the FTC. A small amount of biliary copper (9%) was postulated to return to plasma NCp by enterohepatic recycling. The model developed was contrasted and compared with two previous models of copper metabolism
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.
Traveling Wave Solutions of Reaction-Diffusion Equations Arising in Atherosclerosis Models
Directory of Open Access Journals (Sweden)
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.
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...
Energy Technology Data Exchange (ETDEWEB)
Hays, M.T.; Broome, M.R.; Turrel, J.M.
1988-06-01
A comprehensive multicompartmental kinetic model was developed to account for the distribution and metabolism of simultaneously injected radioactive iodide (iodide*), T3 (T3*), and T4 (T4*) in six normal and seven spontaneously hyperthyroid cats. Data from plasma samples (analyzed by HPLC), urine, feces, and thyroid accumulation were incorporated into the model. The submodels for iodide*, T3*, and T4* all included both a fast and a slow exchange compartment connecting with the plasma compartment. The best-fit iodide* model also included a delay compartment, presumed to be pooling of gastrosalivary secretions. This delay was 62% longer in the hyperthyroid cats than in the euthyroid cats. Unexpectedly, all of the exchange parameters for both T4 and T3 were significantly slowed in hyperthyroidism, possibly because the hyperthyroid cats were older. None of the plasma equivalent volumes of the exchange compartments of iodide*, T3*, or T4* was significantly different in the hyperthyroid cats, although the plasma equivalent volume of the fast T4 exchange compartments were reduced. Secretion of recycled T4* from the thyroid into the plasma T4* compartment was essential to model fit, but its quantity could not be uniquely identified in the absence of multiple thyroid data points. Thyroid secretion of T3* was not detectable. Comparing the fast and slow compartments, there was a shift of T4* deiodination into the fast exchange compartment in hyperthyroidism. Total body mean residence times (MRTs) of iodide* and T3* were not affected by hyperthyroidism, but mean T4* MRT was decreased 23%. Total fractional T4 to T3 conversion was unchanged in hyperthyroidism, although the amount of T3 produced by this route was increased nearly 5-fold because of higher concentrations of donor stable T4.
International Nuclear Information System (INIS)
Hays, M.T.; Broome, M.R.; Turrel, J.M.
1988-01-01
A comprehensive multicompartmental kinetic model was developed to account for the distribution and metabolism of simultaneously injected radioactive iodide (iodide*), T3 (T3*), and T4 (T4*) in six normal and seven spontaneously hyperthyroid cats. Data from plasma samples (analyzed by HPLC), urine, feces, and thyroid accumulation were incorporated into the model. The submodels for iodide*, T3*, and T4* all included both a fast and a slow exchange compartment connecting with the plasma compartment. The best-fit iodide* model also included a delay compartment, presumed to be pooling of gastrosalivary secretions. This delay was 62% longer in the hyperthyroid cats than in the euthyroid cats. Unexpectedly, all of the exchange parameters for both T4 and T3 were significantly slowed in hyperthyroidism, possibly because the hyperthyroid cats were older. None of the plasma equivalent volumes of the exchange compartments of iodide*, T3*, or T4* was significantly different in the hyperthyroid cats, although the plasma equivalent volume of the fast T4 exchange compartments were reduced. Secretion of recycled T4* from the thyroid into the plasma T4* compartment was essential to model fit, but its quantity could not be uniquely identified in the absence of multiple thyroid data points. Thyroid secretion of T3* was not detectable. Comparing the fast and slow compartments, there was a shift of T4* deiodination into the fast exchange compartment in hyperthyroidism. Total body mean residence times (MRTs) of iodide* and T3* were not affected by hyperthyroidism, but mean T4* MRT was decreased 23%. Total fractional T4 to T3 conversion was unchanged in hyperthyroidism, although the amount of T3 produced by this route was increased nearly 5-fold because of higher concentrations of donor stable T4
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.
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.
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.
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
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.
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.
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.
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.
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.
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.
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).
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.
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 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.
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
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
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.
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)
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)
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.
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.
Bannink, A.; Dijkstra, J.; Koopmans, S.J.; Mroz, Z.
2006-01-01
A rationale is given for a modelling approach to identify the mechanisms involved in the functioning and metabolic activity of tissues in the wall of the gastrointestinal tract. Maintenance and productive functions are discussed and related to the distinct compartments of the gastrointestinal tract
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.
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
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
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.
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
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
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
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...
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
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
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)
Yamamoto, Yumi; Valitalo, Pyry A.; van den Berg, Dirk-Jan; Hartman, Robin; van den Brink, Willem; Wong, Yin Cheong; Huntjens, Dymphy R.; Proost, Johannes H.; Vermeulen, An; Krauwinkel, Walter; Bakshi, Suruchi; Aranzana-Climent, Vincent; Marchand, Sandrine; Dahyot-Fizelier, Claire; Couet, William; Danhof, Meindert; van Hasselt, Johan G. C.; de lange, Elizabeth C. M.
Purpose Predicting target site drug concentration in the brain is of key importance for the successful development of drugs acting on the central nervous system. We propose a generic mathematical model to describe the pharmacokinetics in brain compartments, and apply this model to predict human
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.
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)
John C Vardakis
Full Text Available This study proposes the implementation of a Multiple-Network Poroelastic Theory (MPET model coupled with finite-volume computational fluid dynamics for the purpose of studying, in detail, the effects of obstructing CSF transport within an anatomically accurate cerebral environment. The MPET representation allows the investigation of fluid transport between CSF, brain parenchyma and cerebral blood, in an integral and comprehensive manner. A key novelty in the model is the amalgamation of anatomically accurate choroid plexuses with their feeding arteries and a simple relationship relaxing the constraint of a unique permeability for the CSF compartment. This was done in order to account for the Aquaporin-4-mediated swelling characteristics. The aim of this varying permeability compartment was to bring to light a feedback mechanism that could counteract the effects of ventricular dilation and subsequent elevations of CSF pressure through the efflux of excess CSF into the blood system. This model is used to demonstrate the impact of aqueductal stenosis and fourth ventricle outlet obstruction (FVOO. The implications of treating such a clinical condition with the aid of endoscopic third (ETV and endoscopic fourth (EFV ventriculostomy are considered. We observed peak CSF velocities in the aqueduct of the order of 15.6 cm/s in the healthy case, 45.4 cm/s and 72.8 cm/s for the mild and severe cases respectively. The application of ETV reduced the aqueductal velocity to levels around 16-17 cm/s. Ventricular displacement, CSF pressure, wall shear stress (WSS and pressure difference between lateral and fourth ventricles (ΔP increased with applied stenosis, and subsequently dropped to nominal levels with the application of ETV. The greatest reversal of the effects of atresia come by opting for ETV rather than the more complicated procedure of EFV.
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.
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 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.
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.
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)
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.
Maximum Principles for Discrete and Semidiscrete Reaction-Diffusion Equation
Directory of Open Access Journals (Sweden)
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.
Havenaar, R.; Jong, A. de; Koenen, M.E.; Bilsen, J. van; Janssen, A.M.; Labij, E.; Westerbeek, H.J.M.
2013-01-01
Aim of this study was to investigate the digestion of transglutaminase cross-linked caseinate (XLC) versus native caseinate (NC) in solution and in cheese spread under digestive conditions for adults and children mimicked in a gastrointestinal model. Samples were collected for gel electrophoresis
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
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...
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.
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
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.
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
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.
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...
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.
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
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
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.
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.
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.
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.
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,...
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.
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
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.
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.
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
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
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.
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.
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.
In vivo kinematics of a robot-assisted uni- and multi-compartmental knee arthroplasty.
Watanabe, Toshifumi; Abbasi, Ali Z; Conditt, Michael A; Christopher, Jennifer; Kreuzer, Stefan; Otto, Jason K; Banks, Scott A
2014-07-01
There is great interest in providing reliable and durable treatments for one- and two-compartment arthritic degeneration of the cruciate-ligament intact knee. One approach is to resurface only the diseased compartments with discrete unicompartmental components, retaining the undamaged compartment(s). However, placing multiple small implants into the knee presents a greater surgical challenge than total knee arthroplasty, so it is not certain that the natural knee mechanics can be maintained or restored. The goal of this study was to determine whether near-normal knee kinematics can be obtained with a robot-assisted multi-compartmental knee arthroplasty. Thirteen patients with 15 multi-compartmental knee arthroplasties using haptic robotic-assisted bone preparation were involved in this study. Nine subjects received a medial unicompartmental knee arthroplasty (UKA), three subjects received a medial UKA and patellofemoral (PF) arthroplasty, and three subjects received medial and lateral bi-unicondylar arthroplasty. Knee motions were recorded using video-fluoroscopy an average of 13 months (6-29 months) after surgery during stair and kneeling activities. The three-dimensional position and orientation of the implant components were determined using model-image registration techniques. Knee kinematics during maximum flexion kneeling showed femoral external rotation and posterior lateral condylar translation. All knees showed femoral external rotation and posterior condylar translation with flexion during the step activity. Knees with medial UKA and PF arthroplasty showed the most femoral external rotation and posterior translation, and knees with bicondylar UKA showed the least. Knees with accurately placed uni- or bi-compartmental arthroplasty exhibited stable knee kinematics consistent with intact and functioning cruciate ligaments. The patterns of tibiofemoral motion were more similar to natural knees than commonly has been observed in knees with total knee
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.
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.
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.
An analytic algorithm for the space-time fractional reaction-diffusion equation
Directory of Open Access Journals (Sweden)
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.
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
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
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.
Numerical Solutions of Singularly Perturbed Reaction Diffusion Equation with Sobolev Gradients
Directory of Open Access Journals (Sweden)
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.
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.
Multicompartmental analysis of the kinetics of monoclonal antibody in cancer patients
International Nuclear Information System (INIS)
Koizumi, K.; De Nardo, G.L.; De Nardo, S.J.; Peng, J.S.; Macey, D.J.; Hisada, K.; Tonami, N.
1985-01-01
Multicompartmental models were applied for analysis of kinetics of iodide labeled monoclonal antibody in cancer patients. About 14 compartments such as intravascular antibody pool, interstitial antibody pool, antibody processors, tumor antigen site, intravascular immune complex pool, intravascular iodide pool, and urine iodide pool were assumed. This model accounts for three molecular species, the antibody, and antibody complex, and free iodide or iodinated peptides. Patients were injected with I-123-Lym-1 IgG2a (anti B cell lymphoma antibody). After injection, blood and urine samples were sequentially collected. Plasma and urine were separated by HPLC into fractions of intact antibody, immune complex, and free iodide. This information was used for input data in the theoretical model. SAAM computer program was used to solve these compartmental models. Published linear rate constants for human serum albumin and human non-immune IgG were initially used. However, data calculated from the model differed from observed curves in several respects. The kinetics of mouse monoclonal antibody, a foreign protein in a patient, were significantly different from those reported for human IgG. When a nonlinear, saturable hepatic processor was incorporated in the model, calculated data fit the observed data better. This kinetic model provides a basis for calculating radiation doses for radioiodinated antibodies
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.
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
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
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.
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.
Attractor of reaction-diffusion equations in Banach spaces
Directory of Open Access Journals (Sweden)
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
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.
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
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.
On the solutions of fractional reaction-diffusion equations
Directory of Open Access Journals (Sweden)
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.)
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
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
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.
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.
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.
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.
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
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/.
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.
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.
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.
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.
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
Evolution of density profiles for reaction-diffusion processes
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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)
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.
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
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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)
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.
A Reaction-Diffusion-Based Coding Rate Control Mechanism for Camera Sensor Networks
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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.
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.
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.
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).
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.
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.
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.
Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources
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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.
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.
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
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.
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.
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
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.
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
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.
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.
Existence of global solutions to reaction-diffusion systems via a Lyapunov functional
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Said Kouachi
2001-10-01
Full Text Available The purpose of this paper is to construct polynomial functionals (according to solutions of the coupled reaction-diffusion equations which give $L^{p}$-bounds for solutions. When the reaction terms are sufficiently regular, using the well known regularizing effect, we deduce the existence of global solutions. These functionals are obtained independently of work done by Malham and Xin [11].
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
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.
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
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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)
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.
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.
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.
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
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.
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.
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
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.
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.
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
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.
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.
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.
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.
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.
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.
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 \
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.
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.
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.
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.
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.
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)
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.
DEFF Research Database (Denmark)
Ingerslev, Anne Krog; Karaman, İbrahim; Bağcıoğlu, Murat
2015-01-01
The effects of increased intake of dietary fiber as either arabinoxylan (AX) or resistant starch (RS) compared to a typical low dietary fiber Western-style diet (WSD) on the metabolomics responses was studied in gastrointestinal content and tissue, peripheral plasma and urine using a multicompart...... of multicompartmental metabolomics offers information about the correlations between the compartments of the digestive system, providing additional insight into effects of increased whole grain intake.......The effects of increased intake of dietary fiber as either arabinoxylan (AX) or resistant starch (RS) compared to a typical low dietary fiber Western-style diet (WSD) on the metabolomics responses was studied in gastrointestinal content and tissue, peripheral plasma and urine using......, and a low dietary fiber intake were detected using multi block analysis. This study provides insight into microbial fermentation products in the gastrointestinal tract, and suggests a potential role in sulfate conjugation of metabolites on the bioavailability of ingested nutrients. In addition, the use...
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
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
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.
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
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
Directory of Open Access Journals (Sweden)
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.
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
Directory of Open Access Journals (Sweden)
Marcos Mônico-Neto
2015-01-01
Full Text Available Objective. Describe multicompartmental changes in the fat and various muscle fiber types, as well as the hormonal profile and metabolic rate induced by SD in rats. Methods. Twenty adult male Wistar rats were equally distributed into two groups: experimental group (EG and control group (CG. The EG was submitted to SD for 96 h. Blood levels of corticosterone (CORT, total testosterone (TESTO, insulin like growth factor-1 (IGF-1, and thyroid hormones (T3 and T4 were used to assess the catabolic environment. Muscle trophism was measured using a cross-sectional area of various muscles (glycolytic, mixed, and oxidative, and lipolysis was inferred by the weight of fat depots from various locations, such as subcutaneous, retroperitoneal, and epididymal. The metabolic rate was measured using oxygen consumption (V˙O2 measurement. Results. SD increased CORT levels and decreased TESTO, IGF-1, and T4. All fat depots were reduced in weight after SD. Glycolytic and mixed muscles showed atrophy, whereas atrophy was not observed in oxidative muscle. Conclusion. Our data suggest that glycolytic muscle fibers are more sensitive to atrophy than oxidative fibers during SD and that fat depots are reduced regardless of their location.
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.
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
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.
The kinetics of multi-compartmentalized systems, studied by radioactive tracers
International Nuclear Information System (INIS)
Gouveia, A.S. de.
1978-01-01
The use of compartmental models to investigate kinetic problems is presented. This use is restricted, however, to linear models. As an application of different methods, the kinetic behaviour of haemaccel labelled with iodine 131 is studied, the interval of the physically viable solutions being established. The existence of a class of solutions is explained as a result of lack of knowledge of a complete data set. The possibility of obtaining a single solution is also discussed. The formalism of the program SAAM (Simulation, Analysis and modelling) now judged very important for the study of multi-compartimental analysis is presented. (I.C.R) [pt
The VANAM experiments M1 and M2 - test results and multi-compartmental analysis
International Nuclear Information System (INIS)
Kanzleiter, T.; Fischer, K.O.; Allelein, H.J.; Schwarz, S.; Weber, G.
1991-01-01
To model the phenomena occurring in a reactor containment during a severe accident, a new generation of computer codes has been developed which enable simultaneous analysis of thermal hydraulics and aerosol behaviour in a multicompartment geometry. The VANAM experiments in the 630-m 3 Battelle model containment are being performed to verify these codes, in particular the (FIPLOC-M) code. The experimental results obtained so far reveal distinct multicompartment effects like inhomogeneous steam-air-aerosol distribution and enhanced local aerosol depletion by volume condensation. Analyses with the FIPLOC-M code show the possibilities of adequately modeling those effects. (author)
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
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.
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.
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
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.
DEFF Research Database (Denmark)
Nørskov, Natalja; Hedemann, Mette Skou; Lærke, Helle Nygaard
2013-01-01
A multicompartmental nontargeted LC–MS metabolomics approach was used to study the metabolic responses on plasma and urine of hypercholesterolemic pigs after consumption of diets with contrasting dietary fiber composition (whole grain rye with added rye bran versus refined wheat). To study...... the metabolic responses, we performed a supervised multivariate data analyses used for pattern recognition, which revealed marked effects of the diets on both plasma and urine metabolic profiles. Diverse pools of metabolites were responsible for the discrimination between the diets. Elevated levels of phenolic...... compounds and dicarboxylic acids were detected in urine of pigs after rye consumption compared to refined wheat. Furthermore, consumption of rye was characterized by lower levels of linoleic acid derived oxylipins and cholesterol in the plasma metabolic profiles. These results indicate that higher...
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
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)
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.
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.
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.
Hallock, Michael J; Stone, John E; Roberts, Elijah; Fry, Corey; Luthey-Schulten, Zaida
2014-05-01
Simulation of in vivo cellular processes with the reaction-diffusion master equation (RDME) is a computationally expensive task. Our previous software enabled simulation of inhomogeneous biochemical systems for small bacteria over long time scales using the MPD-RDME method on a single GPU. Simulations of larger eukaryotic systems exceed the on-board memory capacity of individual GPUs, and long time simulations of modest-sized cells such as yeast are impractical on a single GPU. We present a new multi-GPU parallel implementation of the MPD-RDME method based on a spatial decomposition approach that supports dynamic load balancing for workstations containing GPUs of varying performance and memory capacity. We take advantage of high-performance features of CUDA for peer-to-peer GPU memory transfers and evaluate the performance of our algorithms on state-of-the-art GPU devices. We present parallel e ciency and performance results for simulations using multiple GPUs as system size, particle counts, and number of reactions grow. We also demonstrate multi-GPU performance in simulations of the Min protein system in E. coli . Moreover, our multi-GPU decomposition and load balancing approach can be generalized to other lattice-based problems.
Directory of Open Access Journals (Sweden)
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.
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
Energy Technology Data Exchange (ETDEWEB)
Frost, J.J.; Douglass, K.H.; Mayberg, H.S.; Dannals, R.F.; Links, J.M.; Wilson, A.A.; Ravert, H.T.; Crozier, W.C.; Wagner, H.N. Jr.
1989-06-01
(11C)-Carfentanil is a high affinity opiate agonist that can be used to localize mu opiate receptors in humans by positron emission tomography (PET). A four-compartment model was used to obtain quantitative estimates of rate constants for receptor association and dissociation. PET studies were performed in five normal subjects in the absence and presence of 1 mg/kg naloxone. Arterial plasma concentration of (11C)-carfentanil and its labeled metabolites were determined during each PET study. The value of k3/k4 = Bmax/kD was determined for each subject in the presence and absence of naloxone. There was a significant reduction in the value of k3/k4 from 3.4 +/- 0.92 to 0.26 +/- 0.13 in the thalamus (p less than 0.01) and from 1.8 +/- 0.33 to 0.16 +/- 0.065 in the frontal cortex (p less than 0.001). Mean values of frontal cortex/occipital cortex and thalamus/occipital cortex ratios were determined for the interval 35-70 min after injection when receptor binding is high relative to nonspecific binding. The relationship between the measured region/occipital cortex values and the corresponding values of k3/k4 in the presence and absence of naloxone was: regions/occipital cortex = 0.95 + 0.74 (k3/k4) with r = 0.98 (n = 20). Simulation studies also demonstrated a linear relationship between the thalamus/occipital cortex or frontal cortex/occipital cortex ratio and k3/k4 for less than twofold increases or decreases in k3/k4. Simulation studies in which thalamic blood flow was varied demonstrated no significant effect on the region/occipital cortex ratio at 35-70 min for a twofold increase or fourfold decrease in blood flow. Therefore, the region/occipital cortex ratio can be used to quantitate changes in k3/k4 when tracer kinetic modeling is not feasible.
International Nuclear Information System (INIS)
Frost, J.J.; Douglass, K.H.; Mayberg, H.S.; Dannals, R.F.; Links, J.M.; Wilson, A.A.; Ravert, H.T.; Crozier, W.C.; Wagner, H.N. Jr.
1989-01-01
[11C]-Carfentanil is a high affinity opiate agonist that can be used to localize mu opiate receptors in humans by positron emission tomography (PET). A four-compartment model was used to obtain quantitative estimates of rate constants for receptor association and dissociation. PET studies were performed in five normal subjects in the absence and presence of 1 mg/kg naloxone. Arterial plasma concentration of [11C]-carfentanil and its labeled metabolites were determined during each PET study. The value of k3/k4 = Bmax/kD was determined for each subject in the presence and absence of naloxone. There was a significant reduction in the value of k3/k4 from 3.4 +/- 0.92 to 0.26 +/- 0.13 in the thalamus (p less than 0.01) and from 1.8 +/- 0.33 to 0.16 +/- 0.065 in the frontal cortex (p less than 0.001). Mean values of frontal cortex/occipital cortex and thalamus/occipital cortex ratios were determined for the interval 35-70 min after injection when receptor binding is high relative to nonspecific binding. The relationship between the measured region/occipital cortex values and the corresponding values of k3/k4 in the presence and absence of naloxone was: regions/occipital cortex = 0.95 + 0.74 (k3/k4) with r = 0.98 (n = 20). Simulation studies also demonstrated a linear relationship between the thalamus/occipital cortex or frontal cortex/occipital cortex ratio and k3/k4 for less than twofold increases or decreases in k3/k4. Simulation studies in which thalamic blood flow was varied demonstrated no significant effect on the region/occipital cortex ratio at 35-70 min for a twofold increase or fourfold decrease in blood flow. Therefore, the region/occipital cortex ratio can be used to quantitate changes in k3/k4 when tracer kinetic modeling is not feasible
International Nuclear Information System (INIS)
Biver, F.; Goldman, S.; Luxen, A.; Monclus, M.; Forestini, M.; Mendlewicz, J.; Lotstra, F.
1994-01-01
Serotoninergic type 2 (5HT 2 ) receptors have been implicated in the regulation of many brain functions in humans and may play a role in several neurological and psychiatric diseases. Fluorine-18 altanserin has been proposed as a new radiotracer for the study of 5HT 2 receptors by PET because of its high affinity for 5HT 2 receptors (Ki: 0.13 nM) and its good specificity in in vitro studies. Dynamic PET studies were carried out in 12 healthy volunteers after intravenous injection of 0.1 mCi/kg [ 18 F] altanserin. Ninety minutes after injection, we observed mainly cortical binding. Basal ganglia and cerebellum showed very low uptake and the frontal cortex to cerebellum ratio was about 3. To evaluate the quantitative distribution of this ligand in the brain, we used two different methods of data analysis: a four-compartment model was used to achieve quantitative evaluation of rate constants (K 1 and k 2 through k 6 ) by non-linear regression, and a multiple-time graphical analysis technique for reversible binding was employed for the measurement of k 1 /k 2 and k 3 /k 4 ratios. Using both methods, we found significant differences in binding capacity (estimated by k 3 /k 4 = B max /K d ) between regions, the values increasing as follows: occipital, limbic, parietal, frontal and temporal cortex. After correction of values obtained by the graphical method for the existence of non-specific binding, results generated by the two methods were consistent. (orig.)
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)
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)
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.
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.
International Nuclear Information System (INIS)
Kershaw, P.J.; Pentreath, R.J.; Gurbutt, P.A.; Woodhead, D.S.; Durance, J.A.; Camplin, W.C.
1988-01-01
A multi-compartmental box model of the Irish Sea has been developed to predict the distribution and radiological consequences of radionuclides discharged from the Sellafield reprocessing plant. The box structure was based on observations of radionuclide distributions in the sea bed and the water circulation was generated from extensive time-series data on 137 Cs concentrations in seawater. Measurements of naturally-occurring nuclides provided both data on the extent and rate of these processes and a means to validate the model assumptions. The model structure is briefly outlined, comparisons are made between model predictions and field observation, and some of the difficulties in making such comparisons are discussed. (author)
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.
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.
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.
Evaluation of samarium-153 and holmium-166-EDTMP in the normal baboon model
Energy Technology Data Exchange (ETDEWEB)
Louw, W.K.A.; Dormehl, I.C.; Rensburg, A.J. van; Hugo, N.; Alberts, A.S.; Forsyth, O.E.; Beverley, G.; Sweetlove, M.A.; Marais, J.; Loetter, M.G.; Aswegen, A. van
1996-11-01
Bone-seeking radiopharmaceuticals such as ethylenediaminetetramethylene phosphonate (EDTMP) complexes of samarium-153 and holmium-166 are receiving considerable attention for therapeutic treatment of bone metastases. In this study, using the baboon experimental model, multicompartmental analysis revealed that with regard to pharmacokinetics, biodistribution, and skeletal localisation, {sup 166}Ho-EDTMP was significantly inferior to {sup 153}Sm-EDTMP and {sup 99m}Tc-MDP. A more suitable {sup 166}Ho-bone-seeking agent should thus be sought for closer similarity to {sup 153}Sm-EDTMP to exploit fully the therapeutic potential of its shorter half-life and more energetic beta radiation.
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
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.
Hopf bifurcations in a fractional reaction–diffusion model for the ...
African Journals Online (AJOL)
The phenomenon of hopf bifurcation has been well-studied and applied to many physical situations to explain behaviour of solutions resulting from differential and partial differential equations. This phenomenon is applied to a fractional reaction diffusion model for tumor invasion and development. The result suggests that ...
Analysis of mathematical modelling on potentiometric biosensors.
Mehala, N; Rajendran, L
2014-01-01
A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories.
Temperature bounds in a model of laminar flames
International Nuclear Information System (INIS)
Kirane, M.; Badraoui, S.
1994-06-01
We consider reaction-diffusion equations coupling temperature and mass fraction in one-step-reaction model of combustion in R N . Uniform temperature bounds are derived when the Lewis number is less than one. This result completes the case of Lewis number greater than one studied by J.D. Avrin and M. Kirane ''Temperature growth and temperature bounds in special cases of combustion models'' (to appear in Applicable Analysis). (author). 5 refs
Modeling the system dynamics for nutrient removal in an innovative septic tank media filter.
Xuan, Zhemin; Chang, Ni-Bin; Wanielista, Martin
2012-05-01
A next generation septic tank media filter to replace or enhance the current on-site wastewater treatment drainfields was proposed in this study. Unit operation with known treatment efficiencies, flow pattern identification, and system dynamics modeling was cohesively concatenated in order to prove the concept of a newly developed media filter. A multicompartmental model addressing system dynamics and feedbacks based on our assumed microbiological processes accounting for aerobic, anoxic, and anaerobic conditions in the media filter was constructed and calibrated with the aid of in situ measurements and the understanding of the flow patterns. Such a calibrated system dynamics model was then applied for a sensitivity analysis under changing inflow conditions based on the rates of nitrification and denitrification characterized through the field-scale testing. This advancement may contribute to design such a drainfield media filter in household septic tank systems in the future.
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
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...
International Nuclear Information System (INIS)
Wen, Zijuan; Fu, Shengmao
2016-01-01
This paper deals with a strongly coupled reaction-diffusion system modeling a competitor-competitor-mutualist three-species model with diffusion, self-diffusion and nonlinear cross-diffusion and subject to Neumann boundary conditions. First, we establish the persistence of a corresponding reaction-diffusion system without self- and cross-diffusion. Second, the global asymptotic stability of the unique positive equilibrium for weakly coupled PDE system is established by using a comparison method. Moreover, under certain conditions about the intra- and inter-species effects, we prove that the uniform positive steady state is linearly unstable for the cross-diffusion system when one of the cross-diffusions is large enough. The results indicate that Turing instability can be driven solely from strong diffusion effect of the first species (or the second species or the third species) due to the pressure of the second species (or the first species).
Wickman, J.; Diehl, S.; Blasius, B.; Klausmeier, C.; Ryabov, A.; Brännström, Å.
2017-01-01
Spatial structure can decisively influence the way evolutionary processes unfold. Several methods have thus far been used to study evolution in spatial systems, including population genetics, quantitative genetics, momentclosure approximations, and individual-based models. Here we extend the study of spatial evolutionary dynamics to eco-evolutionary models based on reaction-diffusion equations and adaptive dynamics. Specifically, we derive expressions for the strength of directional and stabi...
Dynamics of a Diffusive Predator-Prey Model with Allee Effect on Predator
Directory of Open Access Journals (Sweden)
Xiaoqin Wang
2013-01-01
Full Text Available The reaction-diffusion Holling-Tanner prey-predator model considering the Allee effect on predator, under zero-flux boundary conditions, is discussed. Some properties of the solutions, such as dissipation and persistence, are obtained. Local and global stability of the positive equilibrium and Turing instability are studied. With the help of the numerical simulations, the rich Turing patterns, including holes, stripes, and spots patterns, are obtained.
Stochastic Modeling and Deterministic Limit of Catalytic Surface Processes
DEFF Research Database (Denmark)
Starke, Jens; Reichert, Christian; Eiswirth, Markus
2007-01-01
Three levels of modeling, microscopic, mesoscopic and macroscopic are discussed for the CO oxidation on low-index platinum single crystal surfaces. The introduced models on the microscopic and mesoscopic level are stochastic while the model on the macroscopic level is deterministic. It can......, such that in contrast to the microscopic model the spatial resolution is reduced. The derivation of deterministic limit equations is in correspondence with the successful description of experiments under low-pressure conditions by deterministic reaction-diffusion equations while for intermediate pressures phenomena...
Particle in the Brusselator Model with Flow
DEFF Research Database (Denmark)
Kuptsov, P.V.; Kuznetsov, S.P.; Mosekilde, Erik
2002-01-01
We consider the interaction of a small moving particle with a stationary space-periodic pattern in a chemical reaction-diffusion system with a flow. The pattern is produced by a one-dimensional Brusselator model that is perturbed by a constant displacement from the equilibrium state at the inlet....... By partially blocking the flow, the particle gives rise to a local increment of the flow rate. For certain parameter values a response with intermittent Hopf and Turing type structures is observed. In other regimes a wave of substitution of missing peaks runs across the pattern....
Mathematical Modeling the Geometric Regularity in Proteus Mirabilis Colonies
Zhang, Bin; Jiang, Yi; Minsu Kim Collaboration
Proteus Mirabilis colony exhibits striking spatiotemporal regularity, with concentric ring patterns with alternative high and low bacteria density in space, and periodicity for repetition process of growth and swarm in time. We present a simple mathematical model to explain the spatiotemporal regularity of P. Mirabilis colonies. We study a one-dimensional system. Using a reaction-diffusion model with thresholds in cell density and nutrient concentration, we recreated periodic growth and spread patterns, suggesting that the nutrient constraint and cell density regulation might be sufficient to explain the spatiotemporal periodicity in P. Mirabilis colonies. We further verify this result using a cell based model.
Ordering phase transition in the one-dimensional Axelrod model
Vilone, D.; Vespignani, A.; Castellano, C.
2002-12-01
We study the one-dimensional behavior of a cellular automaton aimed at the description of the formation and evolution of cultural domains. The model exhibits a non-equilibrium transition between a phase with all the system sharing the same culture and a disordered phase of coexisting regions with different cultural features. Depending on the initial distribution of the disorder the transition occurs at different values of the model parameters. This phenomenology is qualitatively captured by a mean-field approach, which maps the dynamics into a multi-species reaction-diffusion problem.
Computational models of airway branching morphogenesis.
Varner, Victor D; Nelson, Celeste M
2017-07-01
The bronchial network of the mammalian lung consists of millions of dichotomous branches arranged in a highly complex, space-filling tree. Recent computational models of branching morphogenesis in the lung have helped uncover the biological mechanisms that construct this ramified architecture. In this review, we focus on three different theoretical approaches - geometric modeling, reaction-diffusion modeling, and continuum mechanical modeling - and discuss how, taken together, these models have identified the geometric principles necessary to build an efficient bronchial network, as well as the patterning mechanisms that specify airway geometry in the developing embryo. We emphasize models that are integrated with biological experiments and suggest how recent progress in computational modeling has advanced our understanding of airway branching morphogenesis. Copyright © 2016 Elsevier Ltd. All rights reserved.
Modeling and analyzing stripe patterns in fish skin
Zheng, Yibo; Zhang, Lei; Wang, Yuan; Liang, Ping; Kang, Junjian
2009-11-01
The formation mechanism of stripe patterns in the skin of tropical fishes has been investigated by a coupled two variable reaction diffusion model. Two types of spatial inhomogeneities have been introduced into a homogenous system. Several Turing modes pumped by the Turing instability give rise to a simple stripe pattern. It is found that the Turing mechanism can only determine the wavelength of stripe pattern. The orientation of stripe pattern is determined by the spatial inhomogeneity. Our numerical results suggest that it may be the most possible mechanism for the forming process of fish skin patterns.
A Time-Delayed Mathematical Model for Tumor Growth with the Effect of a Periodic Therapy.
Xu, Shihe; Wei, Xiangqing; Zhang, Fangwei
2016-01-01
A time-delayed mathematical model for tumor growth with the effect of periodic therapy is studied. The establishment of the model is based on the reaction-diffusion dynamics and mass conservation law and is considered with a time delay in cell proliferation process. Sufficient conditions for the global stability of tumor free equilibrium are given. We also prove that if external concentration of nutrients is large the tumor will not disappear and the conditions under which there exist periodic solutions to the model are also determined. Results are illustrated by computer simulations.
A Time-Delayed Mathematical Model for Tumor Growth with the Effect of a Periodic Therapy
Directory of Open Access Journals (Sweden)
Shihe Xu
2016-01-01
Full Text Available A time-delayed mathematical model for tumor growth with the effect of periodic therapy is studied. The establishment of the model is based on the reaction-diffusion dynamics and mass conservation law and is considered with a time delay in cell proliferation process. Sufficient conditions for the global stability of tumor free equilibrium are given. We also prove that if external concentration of nutrients is large the tumor will not disappear and the conditions under which there exist periodic solutions to the model are also determined. Results are illustrated by computer simulations.
Global solution for a chemotactic haptotactic model of cancer invasion
Tao, Youshan; Wang, Mingjun
2008-10-01
This paper deals with a mathematical model of cancer invasion of tissue recently proposed by Chaplain and Lolas. The model consists of a reaction-diffusion-taxis partial differential equation (PDE) describing the evolution of tumour cell density, a reaction-diffusion PDE governing the evolution of the proteolytic enzyme concentration and an ordinary differential equation modelling the proteolysis of the extracellular matrix (ECM). In addition to random motion, the tumour cells are directed not only by haptotaxis (cellular locomotion directed in response to a concentration gradient of adhesive molecules along the ECM) but also by chemotaxis (cellular locomotion directed in response to a concentration gradient of the diffusible proteolytic enzyme). In one space dimension, the global existence and uniqueness of a classical solution to this combined chemotactic-haptotactic model is proved for any chemotactic coefficient χ > 0. In two and three space dimensions, the global existence is proved for small χ/μ (where μ is the logistic growth rate of the tumour cells). The fundamental point of proof is to raise the regularity of a solution from L1 to Lp (p > 1). Furthermore, the existence of blow-up solutions to a sub-model in two space dimensions for large χ shows, to some extent, that the condition that χ/μ is small is necessary for the global existence of a solution to the full model.
Bayesian model selection validates a biokinetic model for zirconium processing in humans
2012-01-01
Background In radiation protection, biokinetic models for zirconium processing are of crucial importance in dose estimation and further risk analysis for humans exposed to this radioactive substance. They provide limiting values of detrimental effects and build the basis for applications in internal dosimetry, the prediction for radioactive zirconium retention in various organs as well as retrospective dosimetry. Multi-compartmental models are the tool of choice for simulating the processing of zirconium. Although easily interpretable, determining the exact compartment structure and interaction mechanisms is generally daunting. In the context of observing the dynamics of multiple compartments, Bayesian methods provide efficient tools for model inference and selection. Results We are the first to apply a Markov chain Monte Carlo approach to compute Bayes factors for the evaluation of two competing models for zirconium processing in the human body after ingestion. Based on in vivo measurements of human plasma and urine levels we were able to show that a recently published model is superior to the standard model of the International Commission on Radiological Protection. The Bayes factors were estimated by means of the numerically stable thermodynamic integration in combination with a recently developed copula-based Metropolis-Hastings sampler. Conclusions In contrast to the standard model the novel model predicts lower accretion of zirconium in bones. This results in lower levels of noxious doses for exposed individuals. Moreover, the Bayesian approach allows for retrospective dose assessment, including credible intervals for the initially ingested zirconium, in a significantly more reliable fashion than previously possible. All methods presented here are readily applicable to many modeling tasks in systems biology. PMID:22863152
SpikingLab: modelling agents controlled by Spiking Neural Networks in Netlogo.
Jimenez-Romero, Cristian; Johnson, Jeffrey
2017-01-01
The scientific interest attracted by Spiking Neural Networks (SNN) has lead to the development of tools for the simulation and study of neuronal dynamics ranging from phenomenological models to the more sophisticated and biologically accurate Hodgkin-and-Huxley-based and multi-compartmental models. However, despite the multiple features offered by neural modelling tools, their integration with environments for the simulation of robots and agents can be challenging and time consuming. The implementation of artificial neural circuits to control robots generally involves the following tasks: (1) understanding the simulation tools, (2) creating the neural circuit in the neural simulator, (3) linking the simulated neural circuit with the environment of the agent and (4) programming the appropriate interface in the robot or agent to use the neural controller. The accomplishment of the above-mentioned tasks can be challenging, especially for undergraduate students or novice researchers. This paper presents an alternative tool which facilitates the simulation of simple SNN circuits using the multi-agent simulation and the programming environment Netlogo (educational software that simplifies the study and experimentation of complex systems). The engine proposed and implemented in Netlogo for the simulation of a functional model of SNN is a simplification of integrate and fire (I&F) models. The characteristics of the engine (including neuronal dynamics, STDP learning and synaptic delay) are demonstrated through the implementation of an agent representing an artificial insect controlled by a simple neural circuit. The setup of the experiment and its outcomes are described in this work.
Neurofitter: a parameter tuning package for a wide range of electrophysiological neuron models
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Werner Van Geit
2007-11-01
Full Text Available The increase in available computational power and the higher quality of experimental recordings have turned the tuning of neuron model parameters into a problem that can be solved by automatic global optimization algorithms. Neurofitter is a software tool that interfaces existing neural simulation software and sophisticated optimization algorithms with a new way to compute the error measure. This error measure represents how well a given parameter set is able to reproduce the experimental data. It is based on the phase-plane trajectory density method, which is insensitive to small phase differences between model and data. Neurofitter enables the effortless combination of many different time-dependent data traces into the error measure, allowing the neuroscientist to focus on what are the seminal properties of the model. We show results obtained by applying Neurofitter to a simple single compartmental model and a complex multi-compartmental Purkinje cell (PC model. These examples show that the method is able to solve a variety of tuning problems and demonstrate details of its practical application.
A compartmental model of the cAMP/PKA/MAPK pathway in Bio-PEPA
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Federica Ciocchetta
2009-11-01
Full Text Available The vast majority of biochemical systems involve the exchange of information between different compartments, either in the form of transportation or via the intervention of membrane proteins which are able to transmit stimuli between bordering compartments. The correct quantitative handling of compartments is, therefore, extremely important when modelling real biochemical systems. The Bio-PEPA process algebra is equipped with the capability of explicitly defining quantitative information such as compartment volumes and membrane surface areas. Furthermore, the recent development of the Bio-PEPA Eclipse Plug-in allows us to perform a correct stochastic simulation of multi-compartmental models. Here we present a Bio-PEPA compartmental model of the cAMP/PKA/MAPK pathway. We analyse the system using the Bio-PEPA Eclipse Plug-in and we show the correctness of our model by comparison with an existing ODE model. Furthermore, we perform computational experiments in order to investigate certain properties of the pathway. Specifically, we focus on the system response to the inhibition and strengthening of feedback loops and to the variation in the activity of key pathway reactions and we observe how these modifications affect the behaviour of the pathway. These experiments are useful to understand the control and regulatory mechanisms of the system.
Gas and grain chemical composition in cold cores as predicted by the Nautilus three-phase model
Ruaud, Maxime; Wakelam, Valentine; Hersant, Franck
2016-07-01
We present an extended version of the two-phase gas-grain code NAUTILUS to the three-phase modelling of gas and grain chemistry of cold cores. In this model, both the mantle and the surface are considered as chemically active. We also take into account the competition among reaction, diffusion and evaporation. The model predictions are confronted to ice observations in the envelope of low-mass and massive young stellar objects as well as towards background stars. Modelled gas-phase abundances are compared to species observed towards TMC-1 (CP) and L134N dark clouds. We find that our model successfully reproduces the observed ice species. It is found that the reaction-diffusion competition strongly enhances reactions with barriers and more specifically reactions with H2, which is abundant on grains. This finding highlights the importance having a good approach to determine the abundance of H2 on grains. Consequently, it is found that the major N-bearing species on grains go from NH3 to N2 and HCN when the reaction-diffusion competition is taken into account. In the gas phase and before a few 105 yr, we find that the three-phase model does not have a strong impact on the observed species compared to the two-phase model. After this time, the computed abundances dramatically decrease due to the strong accretion on dust, which is not counterbalanced by the desorption less efficient than in the two-phase model. This strongly constrains the chemical age of cold cores to be of the order of few 105 yr.
Xu, Shihe; Bai, Meng; Zhang, Fangwei
2017-12-01
In this paper, the existence, uniqueness and exponential stability of almost periodic solutions for a mathematical model of tumour growth are studied. The establishment of the model is based on the reaction-diffusion dynamics and mass conservation law and is considered with a delay in the cell proliferation process. Using a fixed-point theorem in cones, the existence and uniqueness of almost periodic solutions for different parameter values of the model is proved. Moreover, by the Gronwall inequality, sufficient conditions are established for the exponential stability of the unique almost periodic solution. Results are illustrated by computer simulations.
Computational modeling predicts the ionic mechanism of late-onset responses in Unipolar Brush Cells
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Sathyaa eSubramaniyam
2014-08-01
Full Text Available Unipolar Brush Cells (UBCs have been suggested to have a strong impact on cerebellar granular layer functioning, yet the corresponding cellular mechanisms remain poorly understood. UBCs have recently been reported to generate, in addition to early-onset glutamatergic synaptic responses, a late-onset response (LOR composed of a slow depolarizing ramp followed by a spike burst (Locatelli et al., 2013. The LOR activates as a consequence of synaptic activity and involves an intracellular cascade modulating H- and TRP-current gating. In order to assess the LOR mechanisms, we have developed a UBC multi-compartmental model (including soma, dendrite, initial segment and axon incorporating biologically realistic representations of ionic currents and a generic coupling mechanism regulating TRP and H channel gating. The model finely reproduced UBC responses to current injection, including a low-threshold spike sustained by CaLVA currents, a persistent discharge sustained by CaHVA currents, and a rebound burst following hyperpolarization sustained by H- and CaLVA-currents. Moreover, the model predicted that H- and TRP-current regulation was necessary and sufficient to generate the LOR and its dependence on the intensity and duration of mossy fiber activity. Therefore, the model showed that, using a basic set of ionic channels, UBCs generate a rich repertoire of delayed bursts, which could take part to the formation of tunable delay-lines in the local microcircuit.
Computational modeling predicts the ionic mechanism of late-onset responses in unipolar brush cells.
Subramaniyam, Sathyaa; Solinas, Sergio; Perin, Paola; Locatelli, Francesca; Masetto, Sergio; D'Angelo, Egidio
2014-01-01
Unipolar Brush Cells (UBCs) have been suggested to play a critical role in cerebellar functioning, yet the corresponding cellular mechanisms remain poorly understood. UBCs have recently been reported to generate, in addition to early-onset glutamate receptor-dependent synaptic responses, a late-onset response (LOR) composed of a slow depolarizing ramp followed by a spike burst (Locatelli et al., 2013). The LOR activates as a consequence of synaptic activity and involves an intracellular cascade modulating H- and TRP-current gating. In order to assess the LOR mechanisms, we have developed a UBC multi-compartmental model (including soma, dendrite, initial segment, and axon) incorporating biologically realistic representations of ionic currents and a cytoplasmic coupling mechanism regulating TRP and H channel gating. The model finely reproduced UBC responses to current injection, including a burst triggered by a low-threshold spike (LTS) sustained by CaLVA currents, a persistent discharge sustained by CaHVA currents, and a rebound burst following hyperpolarization sustained by H- and CaLVA-currents. Moreover, the model predicted that H- and TRP-current regulation was necessary and sufficient to generate the LOR and its dependence on the intensity and duration of mossy fiber activity. Therefore, the model showed that, using a basic set of ionic channels, UBCs generate a rich repertoire of bursts, which could effectively implement tunable delay-lines in the local microcircuit.
Crystal plasticity modeling of irradiation growth in Zircaloy-2
Patra, Anirban; Tomé, Carlos N.; Golubov, Stanislav I.
2017-08-01
A physically based reaction-diffusion model is implemented in the visco-plastic self-consistent (VPSC) crystal plasticity framework to simulate irradiation growth in hcp Zr and its alloys. The reaction-diffusion model accounts for the defects produced by the cascade of displaced atoms, their diffusion to lattice sinks and the contribution to crystallographic strain at the level of single crystals. The VPSC framework accounts for intergranular interactions and irradiation creep, and calculates the strain in the polycrystalline ensemble. A novel scheme is proposed to model the simultaneous evolution of both, number density and radius, of irradiation-induced dislocation loops directly from experimental data of dislocation density evolution during irradiation. This framework is used to predict the irradiation growth behaviour of cold-worked Zircaloy-2 and trends compared to available experimental data. The role of internal stresses in inducing irradiation creep is discussed. Effects of grain size, texture and external stress on the coupled irradiation growth and creep behaviour are also studied and compared with available experimental data.
Stochastic modeling of catalytic processes in nanoporous materials: Beyond mean-field approach
Energy Technology Data Exchange (ETDEWEB)
Garcia, Andres [Iowa State Univ., Ames, IA (United States)
2017-08-05
Transport and reaction in zeolites and other porous materials, such as mesoporous silica particles, has been a focus of interest in recent years. This is in part due to the possibility of anomalous transport effects (e.g. single-file diffusion) and its impact in the reaction yield in catalytic processes. Computational simulations are often used to study these complex nonequilibrium systems. Computer simulations using Molecular Dynamics (MD) techniques are prohibitive, so instead coarse grained one-dimensional models with the aid of Kinetic Monte Carlo (KMC) simulations are used. Both techniques can be computationally expensive, both time and resource wise. These coarse-grained systems can be exactly described by a set of coupled stochastic master equations, that describe the reaction-diffusion kinetics of the system. The equations can be written exactly, however, coupling between the equations and terms within the equations make it impossible to solve them exactly; approximations must be made. One of the most common methods to obtain approximate solutions is to use Mean Field (MF) theory. MF treatments yield reasonable results at high ratios of reaction rate k to hop rate h of the particles, but fail completely at low k=h due to the over-estimation of fluxes of particles within the pore. We develop a method to estimate fluxes and intrapore diffusivity in simple one- dimensional reaction-diffusion models at high and low k=h, where the pores are coupled to an equilibrated three-dimensional fluid. We thus successfully describe analytically these simple reaction-diffusion one-dimensional systems. Extensions to models considering behavior with long range steric interactions and wider pores require determination of multiple boundary conditions. We give a prescription to estimate the required parameters for these simulations. For one dimensional systems, if single-file diffusion is relaxed, additional parameters to describe particle exchange have to be introduced. We use
A nonlocal spatial model for Lyme disease
Yu, Xiao; Zhao, Xiao-Qiang
2016-07-01
This paper is devoted to the study of a nonlocal and time-delayed reaction-diffusion model for Lyme disease with a spatially heterogeneous structure. In the case of a bounded domain, we first prove the existence of the positive steady state and a threshold type result for the disease-free system, and then establish the global dynamics for the model system in terms of the basic reproduction number. In the case of an unbound domain, we obtain the existence of the disease spreading speed and its coincidence with the minimal wave speed. At last, we use numerical simulations to verify our analytic results and investigate the influence of model parameters and spatial heterogeneity on the disease infection risk.
Traveling waves in a diffusive predator-prey model with holling type-III functional response
International Nuclear Information System (INIS)
Li Wantong; Wu Shiliang
2008-01-01
We establish the existence of traveling wave solutions and small amplitude traveling wave train solutions for a reaction-diffusion system based on a predator-prey model with Holling type-III functional response. The analysis is in the three-dimensional phase space of the nonlinear ordinary differential equation system given by the diffusive predator-prey system in the traveling wave variable. The methods used to prove the results are the shooting argument, invariant manifold theory and the Hopf bifurcation theorem
Quantum mechanical analogy for solving a competitive coexistence model in ecology
International Nuclear Information System (INIS)
Wio, H.S.; Kuperman, M.N.; Haeften, B. von
1994-07-01
We have studied an ecological system of three species: a strong and a weak one, competing for a single food resource, modelled as a reaction-diffusion process. An exact analytical solution has been found through a quantum mechanical analogy. Such solution indicates that in certain situations the classical results on extinction and coexistence of Lotka-Volterra type equations are no longer valid, essentially, as a consequence of the weak species mobility. A stability analysis of this solution against changes in different parameters has been carried out. (author). 19 refs, 5 figs
Impact of delay on disease outbreak in a spatial epidemic model
Zhao, Xia-Xia; Wang, Jian-Zhong
2015-04-01
One of the central issues in studying epidemic spreading is the mechanism on disease outbreak. In this paper, we investigate the effects of time delay on disease outbreak in spatial epidemics based on a reaction-diffusion model. By mathematical analysis and numerical simulations, we show that when time delay is more than a critical value, the disease outbreaks. The obtained results show that the time delay is an important factor in the spread of the disease, which may provide new insights on disease control.
Modelling of Amperometric Biosensor Used for Synergistic Substrates Determination
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Dainius Simelevicius
2012-04-01
Full Text Available In this paper the operation of an amperometric biosensor producing a chemically amplified signal is modelled numerically. The chemical amplification is achieved by using synergistic substrates. The model is based on non-stationary reaction-diffusion equations. The model involves three layers (compartments: a layer of enzyme solution entrapped on the electrode surface, a dialysis membrane covering the enzyme layer and an outer diffusion layer which is modelled by the Nernst approach. The equation system is solved numerically by using the finite difference technique. The biosensor response and sensitivity are investigated by altering the model parameters influencing the enzyme kinetics as well as the mass transport by diffusion. The biosensor action was analyzed with a special emphasis to the effect of the chemical amplification. The simulation results qualitatively explain and confirm the experimentally observed effect of the synergistic substrates conversion on the biosensor response.
Directory of Open Access Journals (Sweden)
Koshy Santosh
2008-01-01
Full Text Available Juvenile nasopharyngeal angiofibroma (JNA is a rare vascular neoplasm occurring almost exclusively in adolescent males. Although benign, it is often locally aggressive and can erode into surrounding tissues and structures resulting in significant morbidity and mortality. In 20% of cases, there is intracranial extension. In this paper, we report on the total excision of a large, recurrent JNA with intracranial extension into the middle cranial fossa encroaching into the cavernous sinus, by right temporal craniotomy and extended osteoplastic maxillotomy.
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.
Zukowska, Barbara; Pacyna, Jozef; Namiesnik, Jacek
2005-02-01
The ELOISE EU EuroCat project integrated natural and social sciences to link the impacts affecting the coastal sea to the human activities developed along the catchments. In EuroCat project river catchments' changes and their impact on the inflow area were analysed. The information was linked with environmental models. The part of the EU ELOISE EuroCat project focusing on the Vistula River catchment and the Baltic Sea costal zone was named VisCat. Within the framework of the EU ELOISE EuroCat - VisCat project, CoZMo-POP (Coastal Zone Model for Persistent Organic Pollutants), a non-steady-state multicompartmental mass balance model of long-term chemical fate in the coastal environment or the drainage basin of a large lake environment was used. The model is parameterised and tested herein to simulate the long-term fate and distribution of selected HCHs (hexachlorocyclohexanes) and PCBs (polychlorinated biphenyls) in the Gulf of Gdansk and the Vistula River drainage basin environment. The model can also be used in the future to predict future concentrations in relation to various emission scenarios and in management of economic development and regulations of substance-emission to this environment. However, this would require more extensive efforts in the future on model parameterisation and validation in order to increase the confidence in current model outputs.
A model for hydrolytic degradation and erosion of biodegradable polymers.
Sevim, Kevser; Pan, Jingzhe
2018-01-15
For aliphatic polyesters such as PLAs and PGAs, there is a strong interplay between the hydrolytic degradation and erosion - degradation leads to a critically low molecular weight at which erosion starts. This paper considers the underlying physical and chemical processes of hydrolytic degradation and erosion. Several kinetic mechanisms are incorporated into a mathematical model in an attempt to explain different behaviours of mass loss observed in experiments. In the combined model, autocatalytic hydrolysis, oligomer production and their diffusion are considered together with surface and interior erosion using a set of differential equations and Monte Carlo technique. Oligomer and drug diffusion are modelled using Fick's law with the diffusion coefficients dependent on porosity. The porosity is due to the formation of cavities which are a result of polymer erosion. The model can follow mass loss and drug release up to 100%, which cannot be explained using a simple reaction-diffusion. The model is applied to two case studies from the literature to demonstrate its validity. The case studies show that a critical molecular weight for the onset of polymer erosion and an incubation period for the polymer dissolution are two critical factors that need to be considered when predicting mass loss and drug release. In order to design bioresorbable implants, it is important to have a mathematical model to predict polymer degradation and corresponding drug release. However, very different behaviours of polymer degradation have been observed and there is no single model that can capture all these behaviours. For the first time, the model presented in this paper is capable of capture all these observed behaviours by switching on and off different underlying mechanisms. Unlike the existing reaction-diffusion models, the model presented here can follow the degradation and drug release all the way to the full disappearance of an implant. Crown Copyright © 2017. Published by
Pattern formation in superdiffusion Oregonator model
Feng, Fan; Yan, Jia; Liu, Fu-Cheng; He, Ya-Feng
2016-10-01
Pattern formations in an Oregonator model with superdiffusion are studied in two-dimensional (2D) numerical simulations. Stability analyses are performed by applying Fourier and Laplace transforms to the space fractional reaction-diffusion systems. Antispiral, stable turing patterns, and travelling patterns are observed by changing the diffusion index of the activator. Analyses of Floquet multipliers show that the limit cycle solution loses stability at the wave number of the primitive vector of the travelling hexagonal pattern. We also observed a transition between antispiral and spiral by changing the diffusion index of the inhibitor. Project supported by the National Natural Science Foundation of China (Grant Nos. 11205044 and 11405042), the Research Foundation of Education Bureau of Hebei Province, China (Grant Nos. Y2012009 and ZD2015025), the Program for Young Principal Investigators of Hebei Province, China, and the Midwest Universities Comprehensive Strength Promotion Project.
Towards mathematical model of grain sub-division and rim structure formation
International Nuclear Information System (INIS)
Kinoshita, Mikiyasu; Kitajima, Shoichi; Sonoda, Ken
1999-01-01
The high burnup LWR UO 2 fuels show a notable micro-structural change around pellet outer zone and it called rim structure. It is observed at temperature as low as 400degC so that fission track and cascade mixing could be the key mechanism. SEM observation revealed that the structure primarily appear on free surfaces of UO 2 , indicating strong sink for point defects may have a big role. And as generic observations, increase of lattice parameter indicates extensive amount of vacancies are stored in high burnup fuel, which may induce the restructuring interacting with dislocations of high density at high burnup. Considering these observations a model of reaction-diffusion process of defects with irradiation induced transport is proposed. The equations are investigated numerically. The model indicates that an instability starts when dislocation network starts intensive interaction with vacancy flux which is modified by interstitial diffusion between spatial segments. It appeared to be similar to the Turing type instability which indicates that the rim structure formation is one kind of the self-organizing processes of open reaction-diffusion systems. (author)
Denis, S; Sayd, T; Georges, A; Chambon, C; Chalancon, S; Santé-Lhoutellier, V; Blanquet-Diot, S
2016-06-15
In humans, meat ensures the supply of proteins with high nutritional value and indispensable amino acids. The main goal of the present study was to compare the degradation of meat proteins in adult and elderly digestive conditions. Cooked meat was subjected to in vitro digestion in the dynamic multi-compartmental TIM (TNO gastroIntestinal Model) system. Digestibility and bioaccessibility were determined using nitrogen balance and digestion products were identified using mass spectrometry. The TIM model was adapted according to in vivo data to mimic the specific digestive conditions of elderly people. Meat protein digestibility and bioaccessibility were around 96 and 60% respectively and were not influenced by age (P > 0.05). As much as 800 peptides were identified in the duodenal and jejunal compartments issued from 50 meat proteins with a percentage of coverage varying from 13 to 69%. Six proteins, mainly from the cytosol, were differentially hydrolyzed under the adult and elderly digestive conditions. Pyruvate kinase was the only protein clearly showing a delay in its degradation under elderly digestive conditions. This study provides significant insights into the understanding of meat protein dynamic digestion. Such data will be helpful to design in vivo studies aiming to evaluate dietary strategies that can attenuate muscle mass loss and more generally maintain a better quality of life in the elderly population.
Human physiologically based pharmacokinetic model for propofol
Directory of Open Access Journals (Sweden)
Schnider Thomas W
2005-04-01
Full Text Available Abstract Background Propofol is widely used for both short-term anesthesia and long-term sedation. It has unusual pharmacokinetics because of its high lipid solubility. The standard approach to describing the pharmacokinetics is by a multi-compartmental model. This paper presents the first detailed human physiologically based pharmacokinetic (PBPK model for propofol. Methods PKQuest, a freely distributed software routine http://www.pkquest.com, was used for all the calculations. The "standard human" PBPK parameters developed in previous applications is used. It is assumed that the blood and tissue binding is determined by simple partition into the tissue lipid, which is characterized by two previously determined set of parameters: 1 the value of the propofol oil/water partition coefficient; 2 the lipid fraction in the blood and tissues. The model was fit to the individual experimental data of Schnider et. al., Anesthesiology, 1998; 88:1170 in which an initial bolus dose was followed 60 minutes later by a one hour constant infusion. Results The PBPK model provides a good description of the experimental data over a large range of input dosage, subject age and fat fraction. Only one adjustable parameter (the liver clearance is required to describe the constant infusion phase for each individual subject. In order to fit the bolus injection phase, for 10 or the 24 subjects it was necessary to assume that a fraction of the bolus dose was sequestered and then slowly released from the lungs (characterized by two additional parameters. The average weighted residual error (WRE of the PBPK model fit to the both the bolus and infusion phases was 15%; similar to the WRE for just the constant infusion phase obtained by Schnider et. al. using a 6-parameter NONMEM compartmental model. Conclusion A PBPK model using standard human parameters and a simple description of tissue binding provides a good description of human propofol kinetics. The major advantage of a
Wickman, Jonas; Diehl, Sebastian; Blasius, Bernd; Klausmeier, Christopher A; Ryabov, Alexey B; Brännström, Åke
2017-04-01
Spatial structure can decisively influence the way evolutionary processes unfold. To date, several methods have been used to study evolution in spatial systems, including population genetics, quantitative genetics, moment-closure approximations, and individual-based models. Here we extend the study of spatial evolutionary dynamics to eco-evolutionary models based on reaction-diffusion equations and adaptive dynamics. Specifically, we derive expressions for the strength of directional and stabilizing/disruptive selection that apply both in continuous space and to metacommunities with symmetrical dispersal between patches. For directional selection on a quantitative trait, this yields a way to integrate local directional selection across space and determine whether the trait value will increase or decrease. The robustness of this prediction is validated against quantitative genetics. For stabilizing/disruptive selection, we show that spatial heterogeneity always contributes to disruptive selection and hence always promotes evolutionary branching. The expression for directional selection is numerically very efficient and hence lends itself to simulation studies of evolutionary community assembly. We illustrate the application and utility of the expressions for this purpose with two examples of the evolution of resource utilization. Finally, we outline the domain of applicability of reaction-diffusion equations as a modeling framework and discuss their limitations.
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.
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.
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.
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...
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.
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
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)
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
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.
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
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)
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....
Modeling the neuroanatomic propagation of ALS in the spinal cord
Drawert, Brian; Thakore, Nimish; Mitchell, Brian; Pioro, Erik; Ravits, John; Petzold, Linda R.
2017-07-01
Recent hypotheses of amyotrophic lateral sclerosis (ALS) progression have posited a point-source origin of motor neuron death with neuroanatomic propagation either contiguously to adjacent regions, or along networks via axonal and synaptic connections. Although the molecular mechanisms of propagation are unknown, one leading hypothesis is a "prion-like" spread of misfolded and aggregated proteins, including SOD1 and TDP-43. We have developed a mathematical model representing cellular and molecular spread of ALS in the human spinal cord. Our model is based on the stochastic reaction-diffusion master equation approach using a tetrahedral discretized space to capture the complex geometry of the spinal cord. Domain dimension and shape was obtained by reconstructing human spinal cord from high-resolution magnetic resonance (MR) images and known gross and histological neuroanatomy. Our preliminary results qualitatively recapitulate the clinically observed pattern of spread of ALS thorough the spinal cord.
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.
Directory of Open Access Journals (Sweden)
Li Hua-Rong
2014-01-01
Full Text Available Two improved multigrain models (MGMs for preparing homopolypropylene and long chain branched polypropylene via propylene polymerization using silica-supported metallocene or dual function metallocene as catalysts are presented in this paper. The presented models are used to predict the intraparticle flow fields involved in the polymerizations. The simulation results show that the flow field distributions involve dare basically identical. The results also show that both the two polymerization processes have an initiation stage and the controlling step for them is reaction-diffusion-reaction with the polymerization proceeding. Furthermore, the simulation results show that the intra particle mass transfer resistance has significant effect on the polymerization but the heat transfer resistance can be ignored.
Directory of Open Access Journals (Sweden)
Peter J Siekmeier
Full Text Available A large number of cellular level abnormalities have been identified in the hippocampus of schizophrenic subjects. Nonetheless, it remains uncertain how these pathologies interact at a system level to create clinical symptoms, and this has hindered the development of more effective antipsychotic medications. Using a 72-processor supercomputer, we created a tissue level hippocampal simulation, featuring multicompartmental neuron models with multiple ion channel subtypes and synaptic channels with realistic temporal dynamics. As an index of the schizophrenic phenotype, we used the specific inability of the model to attune to 40 Hz (gamma band stimulation, a well-characterized abnormality in schizophrenia. We examined several possible combinations of putatively schizophrenogenic cellular lesions by systematically varying model parameters representing NMDA channel function, dendritic spine density, and GABA system integrity, conducting 910 trials in total. Two discrete "clusters" of neuropathological changes were identified. The most robust was characterized by co-occurring modest reductions in NMDA system function (-30% and dendritic spine density (-30%. Another set of lesions had greater NMDA hypofunction along with low level GABA system dysregulation. To the schizophrenic model, we applied the effects of 1,500 virtual medications, which were implemented by varying five model parameters, independently, in a graded manner; the effects of known drugs were also applied. The simulation accurately distinguished agents that are known to lack clinical efficacy, and identified novel mechanisms (e.g., decrease in AMPA conductance decay time constant, increase in projection strength of calretinin-positive interneurons and combinations of mechanisms that could re-equilibrate model behavior. These findings shed light on the mechanistic links between schizophrenic neuropathology and the gamma band oscillatory abnormalities observed in the illness. As such, they
A Model for Selection of Eyespots on Butterfly Wings.
Sekimura, Toshio; Venkataraman, Chandrasekhar; Madzvamuse, Anotida
2015-01-01
The development of eyespots on the wing surface of butterflies of the family Nympalidae is one of the most studied examples of biological pattern formation.However, little is known about the mechanism that determines the number and precise locations of eyespots on the wing. Eyespots develop around signaling centers, called foci, that are located equidistant from wing veins along the midline of a wing cell (an area bounded by veins). A fundamental question that remains unsolved is, why a certain wing cell develops an eyespot, while other wing cells do not. We illustrate that the key to understanding focus point selection may be in the venation system of the wing disc. Our main hypothesis is that changes in morphogen concentration along the proximal boundary veins of wing cells govern focus point selection. Based on previous studies, we focus on a spatially two-dimensional reaction-diffusion system model posed in the interior of each wing cell that describes the formation of focus points. Using finite element based numerical simulations, we demonstrate that variation in the proximal boundary condition is sufficient to robustly select whether an eyespot focus point forms in otherwise identical wing cells. We also illustrate that this behavior is robust to small perturbations in the parameters and geometry and moderate levels of noise. Hence, we suggest that an anterior-posterior pattern of morphogen concentration along the proximal vein may be the main determinant of the distribution of focus points on the wing surface. In order to complete our model, we propose a two stage reaction-diffusion system model, in which an one-dimensional surface reaction-diffusion system, posed on the proximal vein, generates the morphogen concentrations that act as non-homogeneous Dirichlet (i.e., fixed) boundary conditions for the two-dimensional reaction-diffusion model posed in the wing cells. The two-stage model appears capable of generating focus point distributions observed in
A Model for Selection of Eyespots on Butterfly Wings.
Directory of Open Access Journals (Sweden)
Toshio Sekimura
Full Text Available The development of eyespots on the wing surface of butterflies of the family Nympalidae is one of the most studied examples of biological pattern formation.However, little is known about the mechanism that determines the number and precise locations of eyespots on the wing. Eyespots develop around signaling centers, called foci, that are located equidistant from wing veins along the midline of a wing cell (an area bounded by veins. A fundamental question that remains unsolved is, why a certain wing cell develops an eyespot, while other wing cells do not.We illustrate that the key to understanding focus point selection may be in the venation system of the wing disc. Our main hypothesis is that changes in morphogen concentration along the proximal boundary veins of wing cells govern focus point selection. Based on previous studies, we focus on a spatially two-dimensional reaction-diffusion system model posed in the interior of each wing cell that describes the formation of focus points. Using finite element based numerical simulations, we demonstrate that variation in the proximal boundary condition is sufficient to robustly select whether an eyespot focus point forms in otherwise identical wing cells. We also illustrate that this behavior is robust to small perturbations in the parameters and geometry and moderate levels of noise. Hence, we suggest that an anterior-posterior pattern of morphogen concentration along the proximal vein may be the main determinant of the distribution of focus points on the wing surface. In order to complete our model, we propose a two stage reaction-diffusion system model, in which an one-dimensional surface reaction-diffusion system, posed on the proximal vein, generates the morphogen concentrations that act as non-homogeneous Dirichlet (i.e., fixed boundary conditions for the two-dimensional reaction-diffusion model posed in the wing cells. The two-stage model appears capable of generating focus point distributions
Stochastic lattice model of synaptic membrane protein domains.
Li, Yiwei; Kahraman, Osman; Haselwandter, Christoph A
2017-05-01
Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and characteristic size of synaptic domains observed in experiments. We show that our stochastic lattice model yields quantitative agreement with mean-field models of nonlinear diffusion in crowded membranes. Through a combination of analytic and numerical solutions of the master equation governing the reaction dynamics at synaptic domains, together with kinetic Monte Carlo simulations, we find substantial discrepancies between mean-field and stochastic models for the reaction dynamics at synaptic domains. Based on the reaction and diffusion properties of synaptic receptors and scaffolds suggested by previous experiments and mean-field calculations, we show that the stochastic reaction-diffusion dynamics of synaptic receptors and scaffolds provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the observed single-molecule trajectories, and spatial heterogeneity in the effective rates at which receptors and scaffolds are recycled at the cell membrane. Our work sheds light on the physical mechanisms and principles linking the collective properties of membrane protein domains to the stochastic dynamics that rule their molecular components.
Preterm labor--modeling the uterine electrical activity from cellular level to surface recording.
Rihana, S; Marque, C
2008-01-01
Uterine electrical activity is correlated to the appearance of uterine contractions. forceful contractions appear at the end of term. Therefore, understanding the genesis and the propagation of uterine electrical activity may provide an efficient tool to diagnose preterm labor. Moreover, the control of uterine excitability seems to have important consequences in the control of preterm labor. Modeling the electrical activity in uterine tissue is thus an important step in understanding physiological uterine contractile mechanisms and to permit uterine EMG simulation. Our model presented in this paper, incorporates ion channel models at the cell level, the reaction diffusion equations at the tissue level and the spatiotemporal integration at the uterine EMG reconstructed level. This model validates some key physiological observation hypotheses concerning uterine excitability and propagation.
Localized structures and front propagation in the Lengyel-Epstein model
DEFF Research Database (Denmark)
Jensen, O.; Pannbacker, Viggo Ole; Mosekilde, Erik
1994-01-01
Pattern selection, localized structure formation, and front propagation are analyzed within the framework of a model for the chlorine dioxide-iodine-malonic acid reaction that represents a key to understanding recently obtained Turing structures. This model is distinguished from previously studied......, simple reaction-diffusion models by producing a strongly subcritical transition to stripes. The wave number for the modes of maximum linear gain is calculated and compared with the dominant wave number for the finally selected, stationary structures grown from the homogeneous steady state or developed...... bifurcation. In the subcritical regime there is an interval where the front velocity vanishes as a result of a pinning of the front to the underlying structure. In 2D, two different nucleation mechanisms for hexagonal structures are illustrated on the Lengyel-Epstein and the Brusselator model. Finally...
Computing the Local Field Potential (LFP) from Integrate-and-Fire Network Models
Cuntz, Hermann; Lansner, Anders; Panzeri, Stefano; Einevoll, Gaute T.
2015-01-01
Leaky integrate-and-fire (LIF) network models are commonly used to study how the spiking dynamics of neural networks changes with stimuli, tasks or dynamic network states. However, neurophysiological studies in vivo often rather measure the mass activity of neuronal microcircuits with the local field potential (LFP). Given that LFPs are generated by spatially separated currents across the neuronal membrane, they cannot be computed directly from quantities defined in models of point-like LIF neurons. Here, we explore the best approximation for predicting the LFP based on standard output from point-neuron LIF networks. To search for this best “LFP proxy”, we compared LFP predictions from candidate proxies based on LIF network output (e.g, firing rates, membrane potentials, synaptic currents) with “ground-truth” LFP obtained when the LIF network synaptic input currents were injected into an analogous three-dimensional (3D) network model of multi-compartmental neurons with realistic morphology, spatial distributions of somata and synapses. We found that a specific fixed linear combination of the LIF synaptic currents provided an accurate LFP proxy, accounting for most of the variance of the LFP time course observed in the 3D network for all recording locations. This proxy performed well over a broad set of conditions, including substantial variations of the neuronal morphologies. Our results provide a simple formula for estimating the time course of the LFP from LIF network simulations in cases where a single pyramidal population dominates the LFP generation, and thereby facilitate quantitative comparison between computational models and experimental LFP recordings in vivo. PMID:26657024
Computing the Local Field Potential (LFP from Integrate-and-Fire Network Models.
Directory of Open Access Journals (Sweden)
Alberto Mazzoni
2015-12-01
Full Text Available Leaky integrate-and-fire (LIF network models are commonly used to study how the spiking dynamics of neural networks changes with stimuli, tasks or dynamic network states. However, neurophysiological studies in vivo often rather measure the mass activity of neuronal microcircuits with the local field potential (LFP. Given that LFPs are generated by spatially separated currents across the neuronal membrane, they cannot be computed directly from quantities defined in models of point-like LIF neurons. Here, we explore the best approximation for predicting the LFP based on standard output from point-neuron LIF networks. To search for this best "LFP proxy", we compared LFP predictions from candidate proxies based on LIF network output (e.g, firing rates, membrane potentials, synaptic currents with "ground-truth" LFP obtained when the LIF network synaptic input currents were injected into an analogous three-dimensional (3D network model of multi-compartmental neurons with realistic morphology, spatial distributions of somata and synapses. We found that a specific fixed linear combination of the LIF synaptic currents provided an accurate LFP proxy, accounting for most of the variance of the LFP time course observed in the 3D network for all recording locations. This proxy performed well over a broad set of conditions, including substantial variations of the neuronal morphologies. Our results provide a simple formula for estimating the time course of the LFP from LIF network simulations in cases where a single pyramidal population dominates the LFP generation, and thereby facilitate quantitative comparison between computational models and experimental LFP recordings in vivo.
de la Cruz, Roberto; Guerrero, Pilar; Calvo, Juan; Alarcón, Tomás
2017-12-01
The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction-diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction-diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge of
Diffusive spatio-temporal noise in a first-passage time model for intracellular calcium release
Flegg, Mark B.
2013-01-01
The intracellular release of calcium from the endoplasmic reticulum is controlled by ion channels. The resulting calcium signals exhibit a rich spatio-temporal signature, which originates at least partly from microscopic fluctuations. While stochasticity in the gating transition of ion channels has been incorporated into many models, the distribution of calcium is usually described by deterministic reaction-diffusion equations. Here we test the validity of the latter modeling approach by using two different models to calculate the frequency of localized calcium signals (calcium puffs) from clustered IP3 receptor channels. The complexity of the full calcium system is here limited to the basic opening mechanism of the ion channels and, in the mathematical reduction simplifies to the calculation of a first passage time. Two models are then studied: (i) a hybrid model, where channel gating is treated stochastically, while calcium concentration is deterministic and (ii) a fully stochastic model with noisy channel gating and Brownian calcium ion motion. The second model utilises the recently developed two-regime method [M. B. Flegg, S. J. Chapman, and R. Erban, "The two-regime method for optimizing stochastic reaction-diffusion simulations," J. R. Soc., Interface 9, 859-868 (2012)] in order to simulate a large domain with precision required only near the Ca2+ absorbing channels. The expected time for a first channel opening that results in a calcium puff event is calculated. It is found that for a large diffusion constant, predictions of the interpuff time are significantly overestimated using the model (i) with a deterministic non-spatial calcium variable. It is thus demonstrated that the presence of diffusive noise in local concentrations of intracellular Ca2+ ions can substantially influence the occurrence of calcium signals. The presented approach and results may also be relevant for other cell-physiological first-passage time problems with small ligand concentration
3D Spatial Modeling Plan for Biospice
National Research Council Canada - National Science Library
Adalsteinsson, David; Colella, Phil
2008-01-01
.... The principal accomplishments include the development of a new class of methods for simulating reaction-diffusion processes in cells, and of an end-to-end methodology for obtaining discretization...
Garzón-Alvarado, Diego A
2013-01-21
This article develops a model of the appearance and location of the primary centers of ossification in the calvaria. The model uses a system of reaction-diffusion equations of two molecules (BMP and Noggin) whose behavior is of type activator-substrate and its solution produces Turing patterns, which represents the primary ossification centers. Additionally, the model includes the level of cell maturation as a function of the location of mesenchymal cells. Thus the mature cells can become osteoblasts due to the action of BMP2. Therefore, with this model, we can have two frontal primary centers, two parietal, and one, two or more occipital centers. The location of these centers in the simplified computational model is highly consistent with those centers found at an embryonic level. Copyright © 2012 Elsevier Ltd. All rights reserved.
Pharmacokinetic modeling of a gel-delivered dapivirine microbicide in humans.
Halwes, Michael E; Steinbach-Rankins, Jill M; Frieboes, Hermann B
2016-10-10
Although a number of drugs have been developed for the treatment and prevention of human immunodeficiency virus (HIV) infection, it has proven difficult to optimize the drug and dosage parameters. The vaginal tissue, comprised of epithelial, stromal and blood compartments presents a complex system which challenges evaluation of drug kinetics solely through empirical effort. To provide insight into the underlying processes, mathematical modeling and computational simulation have been applied to the study of retroviral microbicide pharmacokinetics. Building upon previous pioneering work that modeled the delivery of Tenofovir (TFV) via topical delivery to the vaginal environment, here we computationally evaluate the performance of the retroviral inhibitor dapivirine released from a microbicide gel. We adapt the TFV model to simulate the multicompartmental diffusion and uptake of dapivirine into the blood plasma and vaginal compartments. The results show that dapivirine is expected to accumulate at the interface between the gel and epithelium compartments due to its hydrophobic characteristics. Hydrophobicity also results in decreased diffusivity, which may impact distribution by up to 2 orders of magnitude compared to TFV. Maximum concentrations of dapivirine in the epithelium, stroma, and blood were 9.9e7, 2.45e6, and 119pg/mL, respectively. This suggests that greater initial doses or longer time frames are required to obtain higher drug concentrations in the epithelium. These observations may have important ramifications if a specific time frame is required for efficacy, or if a minimum/maximum concentration is needed in the mucus, epithelium, or stroma based on combined efficacy and safety data. Copyright © 2016 Elsevier B.V. All rights reserved.
Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology.
Schaff, James C; Gao, Fei; Li, Ye; Novak, Igor L; Slepchenko, Boris M
2016-12-01
Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity. However, general-purpose hybrid solvers for spatially resolved simulations of reaction-diffusion systems are not widely available. Here we describe fundamentals of a general-purpose spatial hybrid method. The method generates realizations of a spatially inhomogeneous hybrid system by appropriately integrating capabilities of a deterministic partial differential equation solver with a popular particle-based stochastic simulator, Smoldyn. Rigorous validation of the algorithm is detailed, using a simple model of calcium 'sparks' as a testbed. The solver is then applied to a deterministic-stochastic model of spontaneous emergence of cell polarity. The approach is general enough to be implemented within biologist-friendly software frameworks such as Virtual Cell.
Rate turnover in mechano-catalytic coupling: A model and its microscopic origin
Energy Technology Data Exchange (ETDEWEB)
Roy, Mahua; Grazioli, Gianmarc; Andricioaei, Ioan, E-mail: andricio@uci.edu [Department of Chemistry, University of California, Irvine, California 92697 (United States)
2015-07-28
A novel aspect in the area of mechano-chemistry concerns the effect of external forces on enzyme activity, i.e., the existence of mechano-catalytic coupling. Recent experiments on enzyme-catalyzed disulphide bond reduction in proteins under the effect of a force applied on the termini of the protein substrate reveal an unexpected biphasic force dependence for the bond cleavage rate. Here, using atomistic molecular dynamics simulations combined with Smoluchowski theory, we propose a model for this behavior. For a broad range of forces and systems, the model reproduces the experimentally observed rates by solving a reaction-diffusion equation for a “protein coordinate” diffusing in a force-dependent effective potential. The atomistic simulations are used to compute, from first principles, the parameters of the model via a quasiharmonic analysis. Additionally, the simulations are also used to provide details about the microscopic degrees of freedom that are important for the underlying mechano-catalysis.
Rate turnover in mechano-catalytic coupling: A model and its microscopic origin
International Nuclear Information System (INIS)
Roy, Mahua; Grazioli, Gianmarc; Andricioaei, Ioan
2015-01-01
A novel aspect in the area of mechano-chemistry concerns the effect of external forces on enzyme activity, i.e., the existence of mechano-catalytic coupling. Recent experiments on enzyme-catalyzed disulphide bond reduction in proteins under the effect of a force applied on the termini of the protein substrate reveal an unexpected biphasic force dependence for the bond cleavage rate. Here, using atomistic molecular dynamics simulations combined with Smoluchowski theory, we propose a model for this behavior. For a broad range of forces and systems, the model reproduces the experimentally observed rates by solving a reaction-diffusion equation for a “protein coordinate” diffusing in a force-dependent effective potential. The atomistic simulations are used to compute, from first principles, the parameters of the model via a quasiharmonic analysis. Additionally, the simulations are also used to provide details about the microscopic degrees of freedom that are important for the underlying mechano-catalysis
The conceptual basis of mathematics in cardiology IV: statistics and model fitting.
Bates, Jason H T; Sobel, Burton E
2003-06-01
This is the fourth in a series of four articles developed for the readers of Coronary Artery Disease. Without language ideas cannot be articulated. What may not be so immediately obvious is that they cannot be formulated either. One of the essential languages of cardiology is mathematics. Unfortunately, medical education does not emphasize, and in fact, often neglects empowering physicians to think mathematically. Reference to statistics, conditional probability, multicompartmental modeling, algebra, calculus and transforms is common but often without provision of genuine conceptual understanding. At the University of Vermont College of Medicine, Professor Bates developed a course designed to address these deficiencies. The course covered mathematical principles pertinent to clinical cardiovascular and pulmonary medicine and research. It focused on fundamental concepts to facilitate formulation and grasp of ideas. This series of four articles was developed to make the material available for a wider audience. The articles will be published sequentially in Coronary Artery Disease. Beginning with fundamental axioms and basic algebraic manipulations they address algebra, function and graph theory, real and complex numbers, calculus and differential equations, mathematical modeling, linear system theory and integral transforms and statistical theory. The principles and concepts they address provide the foundation needed for in-depth study of any of these topics. Perhaps of even more importance, they should empower cardiologists and cardiovascular researchers to utilize the language of mathematics in assessing the phenomena of immediate pertinence to diagnosis, pathophysiology and therapeutics. The presentations are interposed with queries (by Coronary Artery Disease abbreviated as CAD) simulating the nature of interactions that occurred during the course itself. Each article concludes with one or more examples illustrating application of the concepts covered to
Diffusive flux in a model of stochastically gated oxygen transport in insect respiration
Energy Technology Data Exchange (ETDEWEB)
Berezhkovskii, Alexander M. [Mathematical and Statistical Computing Laboratory, Division of Computational Bioscience, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892 (United States); Shvartsman, Stanislav Y. [Department of Chemical and Biological Engineering and Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, New Jersey 08544 (United States)
2016-05-28
Oxygen delivery to insect tissues is controlled by transport through a branched tubular network that is connected to the atmosphere by valve-like gates, known as spiracles. In certain physiological regimes, the spiracles appear to be randomly switching between open and closed states. Quantitative analysis of this regime leads a reaction-diffusion problem with stochastically switching boundary condition. We derive an expression for the diffusive flux at long times in this problem. Our approach starts with the derivation of the passage probability for a single particle that diffuses between a stochastically gated boundary, which models the opening and closing spiracle, and the perfectly absorbing boundary, which models oxygen absorption by the tissue. This passage probability is then used to derive an expression giving the diffusive flux as a function of the geometric parameters of the tube and characteristic time scales of diffusion and gate dynamics.
The role of advection in a two-species competition model
Averill, Isabel; Lou, Yuan
2017-01-01
The effects of weak and strong advection on the dynamics of reaction-diffusion models have long been studied. In contrast, the role of intermediate advection remains poorly understood. For example, concentration phenomena can occur when advection is strong, providing a mechanism for the coexistence of multiple populations, in contrast with the situation of weak advection where coexistence may not be possible. The transition of the dynamics from weak to strong advection is generally difficult to determine. In this work the authors consider a mathematical model of two competing populations in a spatially varying but temporally constant environment, where both species have the same population dynamics but different dispersal strategies: one species adopts random dispersal, while the dispersal strategy for the other species is a combination of random dispersal and advection upward along the resource gradient. For any given diffusion rates the authors consider the bifurcation diagram of positive steady states by u...
Stability Analysis of a Model of Atherogenesis: An Energy Estimate Approach II
Ibragimov, A. I.; McNeal, C. J.; Ritter, L. R.; Walton, J. R.
2010-01-01
This paper considers modelling atherogenesis, the initiation of atherosclerosis, as an inflammatory instability. Motivated by the disease paradigm articulated by Russell Ross, atherogenesis is viewed as an inflammatory spiral with positive feedback loop involving key cellular and chemical species interacting and reacting within the intimal layer of muscular arteries. The inflammation is modelled through a system of non-linear reaction-diffusion-convection partial differential equations. 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 conditions on system parameters leading to instability. Among the questions addressed in the analysis is the possible mitigating effect of anti-oxidants upon transition to the inflammatory spiral. © 2010 Taylor & Francis.
International Nuclear Information System (INIS)
Besser, Achim; Schwarz, Ulrich S
2007-01-01
Biochemistry and mechanics are closely coupled in cell adhesion. At sites of cell-matrix adhesion, mechanical force triggers signaling through the Rho-pathway, which leads to structural reinforcement and increased contractility in the actin cytoskeleton. The resulting force acts back to the sites of adhesion, resulting in a positive feedback loop for mature adhesion. Here, we model this biochemical-mechanical feedback loop for the special case when the actin cytoskeleton is organized in stress fibers, which are contractile bundles of actin filaments. Activation of myosin II molecular motors through the Rho-pathway is described by a system of reaction-diffusion equations, which are coupled into a viscoelastic model for a contractile actin bundle. We find strong spatial gradients in the activation of contractility and in the corresponding deformation pattern of the stress fiber, in good agreement with experimental findings
Malaga, Karlo A.; Schroeder, Karen E.; Patel, Paras R.; Irwin, Zachary T.; Thompson, David E.; Bentley, J. Nicole; Lempka, Scott F.; Chestek, Cynthia A.; Patil, Parag G.
2016-02-01
Objective. We characterized electrode stability over twelve weeks of impedance and neural recording data from four chronically-implanted Utah arrays in two rhesus macaques, and investigated the effects of glial scarring and interface interactions at the electrode recording site on signal quality using a computational model. Approach. A finite-element model of a Utah array microelectrode in neural tissue was coupled with a multi-compartmental model of a neuron to quantify the effects of encapsulation thickness, encapsulation resistivity, and interface resistivity on electrode impedance and waveform amplitude. The coupled model was then reconciled with the in vivo data. Histology was obtained seventeen weeks post-implantation to measure gliosis. Main results. From week 1-3, mean impedance and amplitude increased at rates of 115.8 kΩ/week and 23.1 μV/week, respectively. This initial ramp up in impedance and amplitude was observed across all arrays, and is consistent with biofouling (increasing interface resistivity) and edema clearing (increasing tissue resistivity), respectively, in the model. Beyond week 3, the trends leveled out. Histology showed that thin scars formed around the electrodes. In the model, scarring could not match the in vivo data. However, a thin interface layer at the electrode tip could. Despite having a large effect on impedance, interface resistivity did not have a noticeable effect on amplitude. Significance. This study suggests that scarring does not cause an electrical problem with regard to signal quality since it does not appear to be the main contributor to increasing impedance or significantly affect amplitude unless it displaces neurons. This, in turn, suggests that neural signals can be obtained reliably despite scarring as long as the recording site has sufficiently low impedance after accumulating a thin layer of biofouling. Therefore, advancements in microelectrode technology may be expedited by focusing on improvements to the
Kaplan, Bernhard A.; Lansner, Anders
2014-01-01
Olfactory sensory information passes through several processing stages before an odor percept emerges. The question how the olfactory system learns to create odor representations linking those different levels and how it learns to connect and discriminate between them is largely unresolved. We present a large-scale network model with single and multi-compartmental Hodgkin–Huxley type model neurons representing olfactory receptor neurons (ORNs) in the epithelium, periglomerular cells, mitral/tufted cells and granule cells in the olfactory bulb (OB), and three types of cortical cells in the piriform cortex (PC). Odor patterns are calculated based on affinities between ORNs and odor stimuli derived from physico-chemical descriptors of behaviorally relevant real-world odorants. The properties of ORNs were tuned to show saturated response curves with increasing concentration as seen in experiments. On the level of the OB we explored the possibility of using a fuzzy concentration interval code, which was implemented through dendro-dendritic inhibition leading to winner-take-all like dynamics between mitral/tufted cells belonging to the same glomerulus. The connectivity from mitral/tufted cells to PC neurons was self-organized from a mutual information measure and by using a competitive Hebbian–Bayesian learning algorithm based on the response patterns of mitral/tufted cells to different odors yielding a distributed feed-forward projection to the PC. The PC was implemented as a modular attractor network with a recurrent connectivity that was likewise organized through Hebbian–Bayesian learning. We demonstrate the functionality of the model in a one-sniff-learning and recognition task on a set of 50 odorants. Furthermore, we study its robustness against noise on the receptor level and its ability to perform concentration invariant odor recognition. Moreover, we investigate the pattern completion capabilities of the system and rivalry dynamics for odor mixtures. PMID
Directory of Open Access Journals (Sweden)
Arne Vladimir Blackman
2014-07-01
Full Text Available Accurate 3D reconstruction of neurons is vital for applications linking anatomy and physiology. Reconstructions are typically created using Neurolucida after biocytin histology (BH. An alternative inexpensive and fast method is to use freeware such as Neuromantic to reconstruct from fluorescence imaging (FI stacks acquired using 2-photon laser-scanning microscopy during physiological recording. We compare these two methods with respect to morphometry, cell classification, and multicompartmental modeling in the NEURON simulation environment. Quantitative morphological analysis of the same cells reconstructed using both methods reveals that whilst biocytin reconstructions facilitate tracing of more distal collaterals, both methods are comparable in representing the overall morphology: automated clustering of reconstructions from both methods successfully separates neocortical basket cells from pyramidal cells but not BH from FI reconstructions. BH reconstructions suffer more from tissue shrinkage and compression artifacts than FI reconstructions do. FI reconstructions, on the other hand, consistently have larger process diameters. Consequently, significant differences in NEURON modeling of excitatory post-synaptic potential (EPSP forward propagation are seen between the two methods, with FI reconstructions exhibiting smaller depolarizations. Simulated action potential backpropagation (bAP, however, is indistinguishable between reconstructions obtained with the two methods. In our hands, BH reconstructions are necessary for NEURON modeling and detailed morphological tracing, and thus remain state of the art, although they are more labor intensive, more expensive, and suffer from a higher failure rate. However, for a subset of anatomical applications such as cell type identification, FI reconstructions are superior, because of indistinguishable classification performance with greater ease of use, essentially 100% success rate, and lower cost.
Spreading Speed, Traveling Waves, and Minimal Domain Size in Impulsive Reaction–Diffusion Models
Lewis, Mark A.
2012-08-15
How growth, mortality, and dispersal in a species affect the species\\' spread and persistence constitutes a central problem in spatial ecology. We propose impulsive reaction-diffusion equation models for species with distinct reproductive and dispersal stages. These models can describe a seasonal birth pulse plus nonlinear mortality and dispersal throughout the year. Alternatively, they can describe seasonal harvesting, plus nonlinear birth and mortality as well as dispersal throughout the year. The population dynamics in the seasonal pulse is described by a discrete map that gives the density of the population at the end of a pulse as a possibly nonmonotone function of the density of the population at the beginning of the pulse. The dynamics in the dispersal stage is governed by a nonlinear reaction-diffusion equation in a bounded or unbounded domain. We develop a spatially explicit theoretical framework that links species vital rates (mortality or fecundity) and dispersal characteristics with species\\' spreading speeds, traveling wave speeds, as well as minimal domain size for species persistence. We provide an explicit formula for the spreading speed in terms of model parameters, and show that the spreading speed can be characterized as the slowest speed of a class of traveling wave solutions. We also give an explicit formula for the minimal domain size using model parameters. Our results show how the diffusion coefficient, and the combination of discrete- and continuous-time growth and mortality determine the spread and persistence dynamics of the population in a wide variety of ecological scenarios. Numerical simulations are presented to demonstrate the theoretical results. © 2012 Society for Mathematical Biology.
Cardiac Electromechanical Models: From Cell to Organ
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Natalia A Trayanova
2011-08-01
Full Text Available The heart is a multiphysics and multiscale system that has driven the development of the most sophisticated mathematical models at the frontiers of computation physiology and medicine. This review focuses on electromechanical (EM models of the heart from the molecular level of myofilaments to anatomical models of the organ. Because of the coupling in terms of function and emergent behaviors at each level of biological hierarchy, separation of behaviors at a given scale is difficult. Here, a separation is drawn at the cell level so that the first half addresses subcellular/single cell models and the second half addresses organ models. At the subcelluar level, myofilament models represent actin-myosin interaction and Ca-based activation. Myofilament models and their refinements represent an overview of the development in the field. The discussion of specific models emphasizes the roles of cooperative mechanisms and sarcomere length dependence of contraction force, considered the cellular basis of the Frank-Starling law. A model of electrophysiology and Ca handling can be coupled to a myofilament model to produce an EM cell model, and representative examples are summarized to provide an overview of the progression of field. The second half of the review covers organ-level models that require solution of the electrical component as a reaction-diffusion system and the mechanical component, in which active tension generated by the myocytes produces deformation of the organ as described by the equations of continuum mechanics. As outlined in the review, different organ-level models have chosen to use different ionic and myofilament models depending on the specific application; this choice has been largely dictated by compromises between model complexity and computational tractability. The review also addresses application areas of EM models such as cardiac resynchronization therapy and the role of mechano-electric coupling in arrhythmias and
Marcotte, Christopher D; Grigoriev, Roman O
2016-09-01
This paper introduces a numerical method for computing the spectrum of adjoint (left) eigenfunctions of spiral wave solutions to reaction-diffusion systems in arbitrary geometries. The method is illustrated by computing over a hundred eigenfunctions associated with an unstable time-periodic single-spiral solution of the Karma model on a square domain. We show that all leading adjoint eigenfunctions are exponentially localized in the vicinity of the spiral tip, although the marginal modes (response functions) demonstrate the strongest localization. We also discuss the implications of the localization for the dynamics and control of unstable spiral waves. In particular, the interaction with no-flux boundaries leads to a drift of spiral waves which can be understood with the help of the response functions.
Global dynamics of a PDE model for aedes aegypti mosquitoe incorporating female sexual preference
Parshad, Rana
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 technique. The model incorporates female mosquitoes sexual preference for wild males over sterile males. We show global existence of strong solution for the system. We then derive uniform estimates to prove the existence of a global attractor in L-2(Omega), for the system. The attractor is shown to be L-infinity(Omega) regular and posess state of extinction, if the injection of sterile males is large enough. We also provide upper bounds on the Hausdorff and fractal dimensions of the attractor.
International Nuclear Information System (INIS)
Medvinskii, Aleksandr B; Tikhonova, Irina A; Tikhonov, D A; Ivanitskii, Genrikh R; Petrovskii, Sergei V; Li, B.-L.; Venturino, E; Malchow, H
2002-01-01
The current turn-of-the-century period witnesses the intensive use of the bioproducts of the World Ocean while at the same time calling for precautions to preserve its ecological stability. This requires that biophysical processes in aquatic systems be comprehensively explored and new methods for monitoring their dynamics be developed. While aquatic and terrestrial ecosystems have much in common in terms of their mathematical description, there are essential differences between them. For example, the mobility of oceanic plankton is mainly controlled by diffusion processes, whereas terrestrial organisms naturally enough obey totally different laws. This paper is focused on the processes underlying the dynamics of spatially inhomogeneous plankton communities. We demonstrate that conceptual reaction-diffusion mathematical models are an appropriate tool for investigating both complex spatio-temporal plankton dynamics and the fractal properties of planktivorous fish school walks. (reviews of topical problems)
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Athanasakis, I E; Papadopoulou, E P; Saridakis, Y G
2014-01-01
Fisher's equation has been widely used to model the biological invasion of single-species communities in homogeneous one dimensional habitats. In this study we develop high order numerical methods to accurately capture the spatiotemporal dynamics of the generalized Fisher equation, a nonlinear reaction-diffusion equation characterized by density dependent non-linear diffusion. Working towards this direction we consider strong stability preserving Runge-Kutta (RK) temporal discretization schemes coupled with the Hermite cubic Collocation (HC) spatial discretization method. We investigate their convergence and stability properties to reveal efficient HC-RK pairs for the numerical treatment of the generalized Fisher equation. The Hadamard product is used to characterize the collocation discretized non linear equation terms as a first step for the treatment of generalized systems of relevant equations. Numerical experimentation is included to demonstrate the performance of the methods
Selection, calibration, and validation of models of tumor growth.
Lima, E A B F; Oden, J T; Hormuth, D A; Yankeelov, T E; Almeida, R C
2016-11-01
This paper presents general approaches for addressing some of the most important issues in predictive computational oncology concerned with developing classes of predictive models of tumor growth. First, the process of developing mathematical models of vascular tumors evolving in the complex, heterogeneous, macroenvironment of living tissue; second, the selection of the most plausible models among these classes, given relevant observational data; third, the statistical calibration and validation of models in these classes, and finally, the prediction of key Quantities of Interest (QOIs) relevant to patient survival and the effect of various therapies. The most challenging aspects of this endeavor is that all of these issues often involve confounding uncertainties: in observational data, in model parameters, in model selection, and in the features targeted in the prediction. Our approach can be referred to as "model agnostic" in that no single model is advocated; rather, a general approach that explores powerful mixture-theory representations of tissue behavior while accounting for a range of relevant biological factors is presented, which leads to many potentially predictive models. Then representative classes are identified which provide a starting point for the implementation of OPAL, the Occam Plausibility Algorithm (OPAL) which enables the modeler to select the most plausible models (for given data) and to determine if the model is a valid tool for predicting tumor growth and morphology ( in vivo ). All of these approaches account for uncertainties in the model, the observational data, the model parameters, and the target QOI. We demonstrate these processes by comparing a list of models for tumor growth, including reaction-diffusion models, phase-fields models, and models with and without mechanical deformation effects, for glioma growth measured in murine experiments. Examples are provided that exhibit quite acceptable predictions of tumor growth in laboratory
Numerical approaches to model perturbation fire in turing pattern formations
Campagna, R.; Brancaccio, M.; Cuomo, S.; Mazzoleni, S.; Russo, L.; Siettos, K.; Giannino, F.
2017-11-01
Turing patterns were observed in chemical, physical and biological systems described by coupled reaction-diffusion equations. Several models have been formulated proposing the water as the causal mechanism of vegetation pattern formation, but this isn't an exhaustive hypothesis in some natural environments. An alternative explanation has been related to the plant-soil negative feedback. In Marasco et al. [1] the authors explored the hypothesis that both mechanisms contribute in the formation of regular and irregular vegetation patterns. The mathematical model consists in three partial differential equations (PDEs) that take into account for a dynamic balance between biomass, water and toxic compounds. A numerical approach is mandatory also to investigate on the predictions of this kind of models. In this paper we start from the mathematical model described in [1], set the model parameters such that the biomass reaches a stable spatial pattern (spots) and present preliminary studies about the occurrence of perturbing events, such as wildfire, that can affect the regularity of the biomass configuration.
One-dimensional model for QCD at high energy
International Nuclear Information System (INIS)
Iancu, E.; Santana Amaral, J.T. de; Soyez, G.; Triantafyllopoulos, D.N.
2007-01-01
We propose a stochastic particle model in (1+1) dimensions, with one dimension corresponding to rapidity and the other one to the transverse size of a dipole in QCD, which mimics high-energy evolution and scattering in QCD in the presence of both saturation and particle-number fluctuations, and hence of pomeron loops. The model evolves via non-linear particle splitting, with a non-local splitting rate which is constrained by boost-invariance and multiple scattering. The splitting rate saturates at high density, so like the gluon emission rate in the JIMWLK evolution. In the mean field approximation obtained by ignoring fluctuations, the model exhibits the hallmarks of the BK equation, namely a BFKL-like evolution at low density, the formation of a traveling wave, and geometric scaling. In the full evolution including fluctuations, the geometric scaling is washed out at high energy and replaced by diffusive scaling. It is likely that the model belongs to the universality class of the reaction-diffusion process. The analysis of the model sheds new light on the pomeron loops equations in QCD and their possible improvements
Spädtke, P
2013-01-01
Modeling of technical machines became a standard technique since computer became powerful enough to handle the amount of data relevant to the specific system. Simulation of an existing physical device requires the knowledge of all relevant quantities. Electric fields given by the surrounding boundary as well as magnetic fields caused by coils or permanent magnets have to be known. Internal sources for both fields are sometimes taken into account, such as space charge forces or the internal magnetic field of a moving bunch of charged particles. Used solver routines are briefly described and some bench-marking is shown to estimate necessary computing times for different problems. Different types of charged particle sources will be shown together with a suitable model to describe the physical model. Electron guns are covered as well as different ion sources (volume ion sources, laser ion sources, Penning ion sources, electron resonance ion sources, and H$^-$-sources) together with some remarks on beam transport.
A passive physical model for DnaK chaperoning
Uhl, Lionel; Dumont, Audrey; Dukan, Sam
2018-03-01
Almost all living organisms use protein chaperones with a view to preventing proteins from misfolding or aggregation either spontaneously or during cellular stress. This work uses a reaction-diffusion stochastic model to describe the dynamic localization of the Hsp70 chaperone DnaK in Escherichia coli cells during transient proteotoxic collapse characterized by the accumulation of insoluble proteins. In the model, misfolded (‘abnormal’) proteins are produced during alcoholic stress and have the propensity to aggregate with a polymerization-like kinetics. When aggregates diffuse more slowly they grow larger. According to Michaelis-Menten-type kinetics, DnaK has the propensity to bind with misfolded proteins or aggregates in order to catalyse refolding. To match experimental fluorescence microscopy data showing clusters of DnaK-GFP localized in multiple foci, the model includes spatial zones with local reduced diffusion rates to generate spontaneous assemblies of DnaK called ‘foci’. Numerical simulations of our model succeed in reproducing the kinetics of DnaK localization experimentally observed. DnaK starts from foci, moves to large aggregates during acute stress, resolves those aggregates during recovery and finally returns to its initial punctate localization pattern. Finally, we compare real biological events with hypothetical repartitions of the protein aggregates or DnaK. We then notice that DnaK action is more efficient on protein aggregates than on protein homogeneously distributed.
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
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
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
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
Neic, Aurel; Campos, Fernando O; Prassl, Anton J; Niederer, Steven A; Bishop, Martin J; Vigmond, Edward J; Plank, Gernot
2017-10-01
Anatomically accurate and biophysically detailed bidomain models of the human heart have proven a powerful tool for gaining quantitative insight into the links between electrical sources in the myocardium and the concomitant current flow in the surrounding medium as they represent their relationship mechanistically based on first principles. Such models are increasingly considered as a clinical research tool with the perspective of being used, ultimately, as a complementary diagnostic modality. An important prerequisite in many clinical modeling applications is the ability of models to faithfully replicate potential maps and electrograms recorded from a given patient. However, while the personalization of electrophysiology models based on the gold standard bidomain formulation is in principle feasible, the associated computational expenses are significant, rendering their use incompatible with clinical time frames. In this study we report on the development of a novel computationally efficient reaction-eikonal (R-E) model for modeling extracellular potential maps and electrograms. Using a biventricular human electrophysiology model, which incorporates a topologically realistic His-Purkinje system (HPS), we demonstrate by comparing against a high-resolution reaction-diffusion (R-D) bidomain model that the R-E model predicts extracellular potential fields, electrograms as well as ECGs at the body surface with high fidelity and offers vast computational savings greater than three orders of magnitude. Due to their efficiency R-E models are ideally suitable for forward simulations in clinical modeling studies which attempt to personalize electrophysiological model features.
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
Modeling cooperating micro-organisms in antibiotic environment.
Book, Gilad; Ingham, Colin; Ariel, Gil
2017-01-01
Recent experiments with the bacteria Paenibacillus vortex reveal a remarkable strategy enabling it to cope with antibiotics by cooperating with a different bacterium-Escherichia coli. While P. vortex is a highly effective swarmer, it is sensitive to the antibiotic ampicillin. On the other hand, E. coli can degrade ampicillin but is non-motile when grown on high agar percentages. The two bacterial species form a shared colony in which E. coli is transported by P. vortex and E. coli detoxifies the ampicillin. The paper presents a simplified model, consisting of coupled reaction-diffusion equations, describing the development of ring patterns in the shared colony. Our results demonstrate some of the possible cooperative movement strategies bacteria utilize in order to survive harsh conditions. In addition, we explore the behavior of mixed colonies under new conditions such as antibiotic gradients, synchronization between colonies and possible dynamics of a 3-species system including P. vortex, E. coli and a carbon producing algae that provides nutrients under illuminated, nutrient poor conditions. The derived model was able to simulate an asymmetric relationship between two or three micro-organisms where cooperation is required for survival. Computationally, in order to avoid numerical artifacts due to symmetries within the discretizing grid, the model was solved using a second order Vectorizable Random Lattices method, which is developed as a finite volume scheme on a random grid.
Modeling cooperating micro-organisms in antibiotic environment.
Directory of Open Access Journals (Sweden)
Gilad Book
Full Text Available Recent experiments with the bacteria Paenibacillus vortex reveal a remarkable strategy enabling it to cope with antibiotics by cooperating with a different bacterium-Escherichia coli. While P. vortex is a highly effective swarmer, it is sensitive to the antibiotic ampicillin. On the other hand, E. coli can degrade ampicillin but is non-motile when grown on high agar percentages. The two bacterial species form a shared colony in which E. coli is transported by P. vortex and E. coli detoxifies the ampicillin. The paper presents a simplified model, consisting of coupled reaction-diffusion equations, describing the development of ring patterns in the shared colony. Our results demonstrate some of the possible cooperative movement strategies bacteria utilize in order to survive harsh conditions. In addition, we explore the behavior of mixed colonies under new conditions such as antibiotic gradients, synchronization between colonies and possible dynamics of a 3-species system including P. vortex, E. coli and a carbon producing algae that provides nutrients under illuminated, nutrient poor conditions. The derived model was able to simulate an asymmetric relationship between two or three micro-organisms where cooperation is required for survival. Computationally, in order to avoid numerical artifacts due to symmetries within the discretizing grid, the model was solved using a second order Vectorizable Random Lattices method, which is developed as a finite volume scheme on a random grid.
Mathematical modeling of acid-base physiology.
Occhipinti, Rossana; Boron, Walter F
2015-01-01
pH is one of the most important parameters in life, influencing virtually every biological process at the cellular, tissue, and whole-body level. Thus, for cells, it is critical to regulate intracellular pH (pHi) and, for multicellular organisms, to regulate extracellular pH (pHo). pHi regulation depends on the opposing actions of plasma-membrane transporters that tend to increase pHi, and others that tend to decrease pHi. In addition, passive fluxes of uncharged species (e.g., CO2, NH3) and charged species (e.g., HCO3(-), [Formula: see text] ) perturb pHi. These movements not only influence one another, but also perturb the equilibria of a multitude of intracellular and extracellular buffers. Thus, even at the level of a single cell, perturbations in acid-base reactions, diffusion, and transport are so complex that it is impossible to understand them without a quantitative model. Here we summarize some mathematical models developed to shed light onto the complex interconnected events triggered by acids-base movements. We then describe a mathematical model of a spherical cells-which to our knowledge is the first one capable of handling a multitude of buffer reactions-that our team has recently developed to simulate changes in pHi and pHo caused by movements of acid-base equivalents across the plasma membrane of a Xenopus oocyte. Finally, we extend our work to a consideration of the effects of simultaneous CO2 and HCO3(-) influx into a cell, and envision how future models might extend to other cell types (e.g., erythrocytes) or tissues (e.g., renal proximal-tubule epithelium) important for whole-body pH homeostasis. Copyright © 2015 Elsevier Ltd. All rights reserved.
From equilibrium spin models to probabilistic cellular automata
International Nuclear Information System (INIS)
Georges, A.; Le Doussal, P.
1989-01-01
The general equivalence between D-dimensional probabilistic cellular automata (PCA) and (D + 1)-dimensional equilibrium spin models satisfying a disorder condition is first described in a pedagogical way and then used to analyze the phase diagrams, the critical behavior, and the universality classes of some automato. Diagrammatic representations of time-dependent correlation functions PCA are introduced. Two important classes of PCA are singled out for which these correlation functions simplify: (1) Quasi-Hamiltonian automata, which have a current-carrying steady state, and for which some correlation functions are those of a D-dimensional static model PCA satisfying the detailed balance condition appear as a particular case of these rules for which the current vanishes. (2) Linear (and more generally affine) PCA for which the diagrammatics reduces to a random walk problem closely related to (D + 1)-dimensional directed SAWs: both problems display a critical behavior with mean-field exponents in any dimension. The correlation length and effective velocity of propagation of excitations can be calculated for affine PCA, as is shown on an explicit D = 1 example. The authors conclude with some remarks on nonlinear PCA, for which the diagrammatics is related to reaction-diffusion processes, and which belong in some cases to the universality class of Reggeon field theory
Path integral formulation and Feynman rules for phylogenetic branching models
Energy Technology Data Exchange (ETDEWEB)
Jarvis, P D; Bashford, J D; Sumner, J G [School of Mathematics and Physics, University of Tasmania, GPO Box 252C, 7001 Hobart, TAS (Australia)
2005-11-04
A dynamical picture of phylogenetic evolution is given in terms of Markov models on a state space, comprising joint probability distributions for character types of taxonomic classes. Phylogenetic branching is a process which augments the number of taxa under consideration, and hence the rank of the underlying joint probability state tensor. We point out the combinatorial necessity for a second-quantized, or Fock space setting, incorporating discrete counting labels for taxa and character types, to allow for a description in the number basis. Rate operators describing both time evolution without branching, and also phylogenetic branching events, are identified. A detailed development of these ideas is given, using standard transcriptions from the microscopic formulation of non-equilibrium reaction-diffusion or birth-death processes. These give the relations between stochastic rate matrices, the matrix elements of the corresponding evolution operators representing them, and the integral kernels needed to implement these as path integrals. The 'free' theory (without branching) is solved, and the correct trilinear 'interaction' terms (representing branching events) are presented. The full model is developed in perturbation theory via the derivation of explicit Feynman rules which establish that the probabilities (pattern frequencies of leaf colourations) arising as matrix elements of the time evolution operator are identical with those computed via the standard analysis. Simple examples (phylogenetic trees with two or three leaves), are discussed in detail. Further implications for the work are briefly considered including the role of time reparametrization covariance.
Path integral formulation and Feynman rules for phylogenetic branching models
International Nuclear Information System (INIS)
Jarvis, P D; Bashford, J D; Sumner, J G
2005-01-01
A dynamical picture of phylogenetic evolution is given in terms of Markov models on a state space, comprising joint probability distributions for character types of taxonomic classes. Phylogenetic branching is a process which augments the number of taxa under consideration, and hence the rank of the underlying joint probability state tensor. We point out the combinatorial necessity for a second-quantized, or Fock space setting, incorporating discrete counting labels for taxa and character types, to allow for a description in the number basis. Rate operators describing both time evolution without branching, and also phylogenetic branching events, are identified. A detailed development of these ideas is given, using standard transcriptions from the microscopic formulation of non-equilibrium reaction-diffusion or birth-death processes. These give the relations between stochastic rate matrices, the matrix elements of the corresponding evolution operators representing them, and the integral kernels needed to implement these as path integrals. The 'free' theory (without branching) is solved, and the correct trilinear 'interaction' terms (representing branching events) are presented. The full model is developed in perturbation theory via the derivation of explicit Feynman rules which establish that the probabilities (pattern frequencies of leaf colourations) arising as matrix elements of the time evolution operator are identical with those computed via the standard analysis. Simple examples (phylogenetic trees with two or three leaves), are discussed in detail. Further implications for the work are briefly considered including the role of time reparametrization covariance
Yates, Christian A; Flegg, Mark B
2015-05-06
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs), which assumes there are sufficient densities of particles that a continuum approximation is valid. However, owing to recent advances in computational power, the simulation and therefore postulation, of computationally intensive individual-based models has become a popular way to investigate the effects of noise in reaction-diffusion systems in which regions of low copy numbers exist. The specific stochastic models with which we shall be concerned in this manuscript are referred to as 'compartment-based' or 'on-lattice'. These models are characterized by a discretization of the computational domain into a grid/lattice of 'compartments'. Within each compartment, particles are assumed to be well mixed and are permitted to react with other particles within their compartment or to transfer between neighbouring compartments. Stochastic models provide accuracy, but at the cost of significant computational resources. For models that have regions of both low and high concentrations, it is often desirable, for reasons of efficiency, to employ coupled multi-scale modelling paradigms. In this work, we develop two hybrid algorithms in which a PDE in one region of the domain is coupled to a compartment-based model in the other. Rather than attempting to balance average fluxes, our algorithms answer a more fundamental question: 'how are individual particles transported between the vastly different model descriptions?' First, we present an algorithm derived by carefully redefining the continuous PDE concentration as a probability distribution. While this first algorithm shows very strong convergence to analytical solutions of test problems, it can be cumbersome to simulate. Our second algorithm is a simplified and more efficient implementation of
Kemper, A; Nishino, T; Schadschneider, A; Zittartz, J
2003-01-01
We develop a new variant of the recently introduced stochastic transfer matrix DMRG which we call stochastic light-cone corner-transfer-matrix DMRG (LCTMRG). It is a numerical method to compute dynamic properties of one-dimensional stochastic processes. As suggested by its name, the LCTMRG is a modification of the corner-transfer-matrix DMRG, adjusted by an additional causality argument. As an example, two reaction-diffusion models, the diffusion-annihilation process and the branch-fusion process are studied and compared with exact data and Monte Carlo simulations to estimate the capability and accuracy of the new method. The number of possible Trotter steps of more than 10 sup 5 shows a considerable improvement on the old stochastic TMRG algorithm.
Smeets-Peeters, M.; Watson, T.; Minekus, M.; Havenaar, R.
1998-01-01
Food and nutrition studies in animals and human beings often meet with technical difficulties and sometimes with ethical questions. An alternative to research in living animals is the dynamic multicompartmental in vitro model for the gastrointestinal tract described by Minekus et al. (1995) and
Spiral waves are stable in discrete element models of two-dimensional homogeneous excitable media
Feldman, A. B.; Chernyak, Y. B.; Cohen, R. J.
1998-01-01
The spontaneous breakup of a single spiral wave of excitation into a turbulent wave pattern has been observed in both discrete element models and continuous reaction-diffusion models of spatially homogeneous 2D excitable media. These results have attracted considerable interest, since spiral breakup is thought to be an important mechanism of transition from the heart rhythm disturbance ventricular tachycardia to the fatal arrhythmia ventricular fibrillation. It is not known whether this process can occur in the absence of disease-induced spatial heterogeneity of the electrical properties of the ventricular tissue. Candidate mechanisms for spiral breakup in uniform 2D media have emerged, but the physical validity of the mechanisms and their applicability to myocardium require further scrutiny. In this letter, we examine the computer simulation results obtained in two discrete element models and show that the instability of each spiral is an artifact resulting from an unphysical dependence of wave speed on wave front curvature in the medium. We conclude that spiral breakup does not occur in these two models at the specified parameter values and that great care must be exercised in the representation of a continuous excitable medium via discrete elements.
Directory of Open Access Journals (Sweden)
F.C.F. Lopes
2003-12-01
treatments: 1- resting period of 30 days without concentrate, 2- resting period of 30 days with concentrate and 3- resting period of 45 days with concentrate. In the dry season cows grazed elephantgrass during the night and were fed on chopped sugarcane plus 1% ammonium sulphate:urea (9:1 between milkings. The rate of passage was estimated by using chromium complexed to the cellular wall of elephantgrass extrusas collected during the first, second and third grazing days of each treatment. In the second trial carried out during the rainy season 12 lactating crossbred cows (four rumen fistulated were used. The treatments were resting periods of 30 or 45 days without supplementation. Parameters of particulate passage kinectics were estimated by two models (age-independent double-compartmental and age-dependent multicompartmental which provided similar results of ruminal passage rates values. However, larger values of post-ruminal passage rates were generally obtained with the age-dependent multicompartmental model. In the dry season, the ruminal and post-ruminal passage rates were, respectively, 0.042 and 0.087/h (age-independent double-compartmental model and 0.041 and 0.109/h (age-dependent multicompartmental model. In the rainy season, values of 0.035 and 0.056/h, and 0.029 and 0.090/h, were observed, respectively.
A continuous flow microfluidic calorimeter: 3-D numerical modeling with aqueous reactants
Energy Technology Data Exchange (ETDEWEB)
Sen, Mehmet A., E-mail: mehmet.sen@mathworks.com [Northeastern University, Department of Mechanical and Industrial Engineering, 360 Hungtington Avenue, 334 Snell Engineering Center, Boston, MA 02115 (United States); Kowalski, Gregory J., E-mail: gkowal@coe.neu.edu [Northeastern University, Department of Mechanical and Industrial Engineering, 360 Hungtington Avenue, 334 Snell Engineering Center, Boston, MA 02115 (United States); Fiering, Jason, E-mail: jfiering@draper.com [Charles Stark Draper Laboratory, 555 Technology Square, Cambridge, MA 02139 (United States); Larson, Dale, E-mail: dlarson@draper.com [Charles Stark Draper Laboratory, 555 Technology Square, Cambridge, MA 02139 (United States)
2015-03-10
Highlights: • A co-flow microreactor is modeled in flow, reaction/diffusion, and thermal domains. • Analysis shows how arrayed temperature sensors can provide enthalpy of reaction. • Optical plasmonic temperature sensors could be arrayed suitably for calorimetry. • The reactor studied has a volume of 25 nL. - Abstract: A computational analysis of the reacting flow field, species diffusion and heat transfer processes with thermal boundary layer effects in a microchannel reactor with a coflow configuration was performed. Two parallel adjacent streams of aqueous reactants flow along a wide, shallow, enclosed channel in contact with a substrate, which is affixed to a temperature controlled plate. The Fluent computational fluid dynamics package solved the Navier–Stokes, mass transport and energy equations. The energy model, including the enthalpy of reaction as a nonuniform heat source, was validated by calculating the energy balance at several control volumes in the microchannel. Analysis reveals that the temperature is nearly uniform across the channel thickness, in the direction normal to the substrate surface; hence, measurements made by sensors at or near the surface are representative of the average temperature. Additionally, modeling the channel with a glass substrate and a silicone cover shows that heat transfer is predominantly due to the glass substrate. Finally, using the numerical results, we suggest that a microcalorimeter could be based on this configuration, and that temperature sensors such as optical nanohole array sensors could have sufficient spatial resolution to determine enthalpy of reaction.
A computational model of amoeboid cell swimming in unbounded medium and through obstacles
Campbell, Eric; Bagchi, Prosenjit
2017-11-01
Pseudopod-driven motility is commonly observed in eukaryotic cells. Pseudopodia are actin-rich protrusions of the cellular membrane which extend, bifurcate, and retract in cycles resulting in amoeboid locomotion. While actin-myosin interactions are responsible for pseudopod generation, cell deformability is crucial concerning pseudopod dynamics. Because pseudopodia are highly dynamic, cells are capable of deforming into complex shapes over time. Pseudopod-driven motility represents a multiscale and complex process, coupling cell deformation, protein biochemistry, and cytoplasmic and extracellular fluid motion. In this work, we present a 3D computational model of amoeboid cell swimming in an extracellular medium (ECM). The ECM is represented as a fluid medium with or without obstacles. The model integrates full cell deformation, a coarse-grain reaction-diffusion system for protein dynamics, and fluid interaction. Our model generates pseudopodia which bifurcate and retract, showing remarkable similarity to experimental observations. Influence of cell deformation, protein diffusivity and cytoplasmic viscosity on the swimming speed is analyzed in terms of altered pseudopod dynamics. Insights into the role of matrix porosity and obstacle size on cell motility are also provided. Funded by NSF CBET 1438255.
A Stefan model for mass transfer in a rotating disk reaction vessel
BOHUN, C. S.
2015-05-04
Copyright © Cambridge University Press 2015. In this paper, we focus on the process of mass transfer in the rotating disk apparatus formulated as a Stefan problem with consideration given to both the hydrodynamics of the process and the specific chemical reactions occurring in the bulk. The wide range in the reaction rates of the underlying chemistry allows for a natural decoupling of the problem into a simplified set of weakly coupled convective-reaction-diffusion equations for the slowly reacting chemical species and a set of algebraic relations for the species that react rapidly. An analysis of the chemical equilibrium conditions identifies an expansion parameter and a reduced model that remains valid for arbitrarily large times. Numerical solutions of the model are compared to an asymptotic analysis revealing three distinct time scales and chemical diffusion boundary layer that lies completely inside the hydrodynamic layer. Formulated as a Stefan problem, the model generalizes the work of Levich (Levich and Spalding (1962) Physicochemical hydrodynamics, vol. 689, Prentice-Hall Englewood Cliffs, NJ) and will help better understand the natural limitations of the rotating disk reaction vessel when consideration is made for the reacting chemical species.
A lattice-model representation of continuous-time random walks
International Nuclear Information System (INIS)
Campos, Daniel; Mendez, Vicenc
2008-01-01
We report some ideas for constructing lattice models (LMs) as a discrete approach to the reaction-dispersal (RD) or reaction-random walks (RRW) models. The analysis of a rather general class of Markovian and non-Markovian processes, from the point of view of their wavefront solutions, let us show that in some regimes their macroscopic dynamics (front speed) turns out to be different from that by classical reaction-diffusion equations, which are often used as a mean-field approximation to the problem. So, the convenience of a more general framework as that given by the continuous-time random walks (CTRW) is claimed. Here we use LMs as a numerical approach in order to support that idea, while in previous works our discussion was restricted to analytical models. For the two specific cases studied here, we derive and analyze the mean-field expressions for our LMs. As a result, we are able to provide some links between the numerical and analytical approaches studied
A lattice-model representation of continuous-time random walks
Energy Technology Data Exchange (ETDEWEB)
Campos, Daniel [School of Mathematics, Department of Applied Mathematics, University of Manchester, Manchester M60 1QD (United Kingdom); Mendez, Vicenc [Grup de Fisica Estadistica, Departament de Fisica, Universitat Autonoma de Barcelona, 08193 Bellaterra (Barcelona) (Spain)], E-mail: daniel.campos@uab.es, E-mail: vicenc.mendez@uab.es
2008-02-29
We report some ideas for constructing lattice models (LMs) as a discrete approach to the reaction-dispersal (RD) or reaction-random walks (RRW) models. The analysis of a rather general class of Markovian and non-Markovian processes, from the point of view of their wavefront solutions, let us show that in some regimes their macroscopic dynamics (front speed) turns out to be different from that by classical reaction-diffusion equations, which are often used as a mean-field approximation to the problem. So, the convenience of a more general framework as that given by the continuous-time random walks (CTRW) is claimed. Here we use LMs as a numerical approach in order to support that idea, while in previous works our discussion was restricted to analytical models. For the two specific cases studied here, we derive and analyze the mean-field expressions for our LMs. As a result, we are able to provide some links between the numerical and analytical approaches studied.
Modelling the development and arrangement of the primary vascular structure in plants.
Cartenì, Fabrizio; Giannino, Francesco; Schweingruber, Fritz Hans; Mazzoleni, Stefano
2014-09-01
The process of vascular development in plants results in the formation of a specific array of bundles that run throughout the plant in a characteristic spatial arrangement. Although much is known about the genes involved in the specification of procambium, phloem and xylem, the dynamic processes and interactions that define the development of the radial arrangement of such tissues remain elusive. This study presents a spatially explicit reaction-diffusion model defining a set of logical and functional rules to simulate the differentiation of procambium, phloem and xylem and their spatial patterns, starting from a homogeneous group of undifferentiated cells. Simulation results showed that the model is capable of reproducing most vascular patterns observed in plants, from primitive and simple structures made up of a single strand of vascular bundles (protostele), to more complex and evolved structures, with separated vascular bundles arranged in an ordered pattern within the plant section (e.g. eustele). The results presented demonstrate, as a proof of concept, that a common genetic-molecular machinery can be the basis of different spatial patterns of plant vascular development. Moreover, the model has the potential to become a useful tool to test different hypotheses of genetic and molecular interactions involved in the specification of vascular tissues.
A continuous flow microfluidic calorimeter: 3-D numerical modeling with aqueous reactants
International Nuclear Information System (INIS)
Sen, Mehmet A.; Kowalski, Gregory J.; Fiering, Jason; Larson, Dale
2015-01-01
Highlights: • A co-flow microreactor is modeled in flow, reaction/diffusion, and thermal domains. • Analysis shows how arrayed temperature sensors can provide enthalpy of reaction. • Optical plasmonic temperature sensors could be arrayed suitably for calorimetry. • The reactor studied has a volume of 25 nL. - Abstract: A computational analysis of the reacting flow field, species diffusion and heat transfer processes with thermal boundary layer effects in a microchannel reactor with a coflow configuration was performed. Two parallel adjacent streams of aqueous reactants flow along a wide, shallow, enclosed channel in contact with a substrate, which is affixed to a temperature controlled plate. The Fluent computational fluid dynamics package solved the Navier–Stokes, mass transport and energy equations. The energy model, including the enthalpy of reaction as a nonuniform heat source, was validated by calculating the energy balance at several control volumes in the microchannel. Analysis reveals that the temperature is nearly uniform across the channel thickness, in the direction normal to the substrate surface; hence, measurements made by sensors at or near the surface are representative of the average temperature. Additionally, modeling the channel with a glass substrate and a silicone cover shows that heat transfer is predominantly due to the glass substrate. Finally, using the numerical results, we suggest that a microcalorimeter could be based on this configuration, and that temperature sensors such as optical nanohole array sensors could have sufficient spatial resolution to determine enthalpy of reaction
Schenz, Daniel; Shima, Yasuaki; Kuroda, Shigeru; Nakagaki, Toshiyuki; Ueda, Kei-Ichi
2017-11-01
Exploring free space (scouting) efficiently is a non-trivial task for organisms of limited perception, such as the amoeboid Physarum polycephalum. However, the strategy behind its exploratory behaviour has not yet been characterised. In this organism, as the extension of the frontal part into free space is directly supported by the transport of body mass from behind, the formation of transport channels (routing) plays the main role in that strategy. Here, we study the organism’s exploration by letting it expand through a corridor of constant width. When turning at a corner of the corridor, the organism constructed a main transport vein tracing a centre-in-centre line. We argue that this is efficient for mass transport due to its short length, and check this intuition with a new algorithm that can predict the main vein’s position from the frontal tip’s progression. We then present a numerical model that incorporates reaction-diffusion dynamics for the behaviour of the organism’s growth front and current reinforcement dynamics for the formation of the vein network in its wake, as well as interactions between the two. The accuracy of the model is tested against the behaviour of the real organism and the importance of the interaction between growth tip dynamics and vein network development is analysed by studying variants of the model. We conclude by offering a biological interpretation of the well-known current reinforcement rule in the context of the natural exploratory behaviour of Physarum polycephalum.
Unusual spiral wave dynamics in the Kessler-Levine model of an excitable medium.
Oikawa, N; Bodenschatz, E; Zykov, V S
2015-05-01
The Kessler-Levine model is a two-component reaction-diffusion system that describes spatiotemporal dynamics of the messenger molecules in a cell-to-cell signaling process during the aggregation of social amoeba cells. An excitation wave arising in the model has a phase wave at the wave back, which simply follows the wave front after a fixed time interval with the same propagation velocity. Generally speaking, the medium excitability and the refractoriness are two important factors which determine the spiral wave dynamics in any excitable media. The model allows us to separate these two factors relatively easily since the medium refractoriness can be changed independently of the medium excitability. For rigidly rotating waves, the universal relationship has been established by using a modified free-boundary approach, which assumes that the front and the back of a propagating wave are thin in comparison to the wave plateau. By taking a finite thickness of the domain boundary into consideration, the validity of the proposed excitability measure has been essentially improved. A novel method of numerical simulation to suppress the spiral wave instabilities is introduced. The trajectories of the spiral tip observed for a long refractory period have been investigated under a systematic variation of the medium refractoriness.
The effects of noise on binocular rivalry waves: a stochastic neural field model
Webber, Matthew A
2013-03-12
We analyze the effects of extrinsic noise on traveling waves of visual perception in a competitive neural field model of binocular rivalry. The model consists of two one-dimensional excitatory neural fields, whose activity variables represent the responses to left-eye and right-eye stimuli, respectively. The two networks mutually inhibit each other, and slow adaptation is incorporated into the model by taking the network connections to exhibit synaptic depression. We first show how, in the absence of any noise, the system supports a propagating composite wave consisting of an invading activity front in one network co-moving with a retreating front in the other network. Using a separation of time scales and perturbation methods previously developed for stochastic reaction-diffusion equations, we then show how extrinsic noise in the activity variables leads to a diffusive-like displacement (wandering) of the composite wave from its uniformly translating position at long time scales, and fluctuations in the wave profile around its instantaneous position at short time scales. We use our analysis to calculate the first-passage-time distribution for a stochastic rivalry wave to travel a fixed distance, which we find to be given by an inverse Gaussian. Finally, we investigate the effects of noise in the depression variables, which under an adiabatic approximation lead to quenched disorder in the neural fields during propagation of a wave. © 2013 IOP Publishing Ltd and SISSA Medialab srl.
Multiphase modelling of vascular tumour growth in two spatial dimensions
Hubbard, M.E.
2013-01-01
In this paper we present a continuum mathematical model of vascular tumour growth which is based on a multiphase framework in which the tissue is decomposed into four distinct phases and the principles of conservation of mass and momentum are applied to the normal/healthy cells, tumour cells, blood vessels and extracellular material. The inclusion of a diffusible nutrient, supplied by the blood vessels, allows the vasculature to have a nonlocal influence on the other phases. Two-dimensional computational simulations are carried out on unstructured, triangular meshes to allow a natural treatment of irregular geometries, and the tumour boundary is captured as a diffuse interface on this mesh, thereby obviating the need to explicitly track the (potentially highly irregular and ill-defined) tumour boundary. A hybrid finite volume/finite element algorithm is used to discretise the continuum model: the application of a conservative, upwind, finite volume scheme to the hyperbolic mass balance equations and a finite element scheme with a stable element pair to the generalised Stokes equations derived from momentum balance, leads to a robust algorithm which does not use any form of artificial stabilisation. The use of a matrix-free Newton iteration with a finite element scheme for the nutrient reaction-diffusion equations allows full nonlinearity in the source terms of the mathematical model.Numerical simulations reveal that this four-phase model reproduces the characteristic pattern of tumour growth in which a necrotic core forms behind an expanding rim of well-vascularised proliferating tumour cells. The simulations consistently predict linear tumour growth rates. The dependence of both the speed with which the tumour grows and the irregularity of the invading tumour front on the model parameters is investigated. © 2012 Elsevier Ltd.
Directory of Open Access Journals (Sweden)
Bomi Framroze
2014-05-01
Full Text Available Background: The TIM-1 system is a computer-controlled multi-compartmental dynamic model that closely simulates in vivo gastrointestinal tract digestion in humans. During digestion, the compounds released from meal matrix by gastric and intestinal secretions (enzymes are progressively absorbed through semipermeable membranes depending on their molecular weight. These absorbed (dialysed compounds are considered as bioaccessible, which means that they can be theoretically absorbed by the small intestine in the body. Methods: Salmon protein hydrolysate (SPH, whey protein hydrolysates extensively (WPHHigh or weakly (WPH-Low hydrolysed, non-hydrolysed whey protein isolate (WPI and mixtures of WPI:SPH (90:10, 80:20 were digested in TIM-1 using the conditions for a fast gastrointestinal transit that simulate the digestion of a liquid meal in human adults. During digestion (2 hours, samples were collected in intestinal compartments (duodenum, jejunum, and ileum and in both jejunal and ileal dialysates to determine their nitrogen content. All the products were compared in terms of kinetics of nitrogen absorption through the semipermeable membranes (bioaccessible nitrogen and nitrogen distribution throughout the intestinal compartments at the end of the 2 hour digestion. Results: After a 2 h-digestion in TIM-1, SPH was the protein substrate from which the highest amount of nitrogen (67.0% becomes available for the small intestine absorption. WPH-High had the second highest amount (56.0% of bioaccessible nitrogen while this amount decreased to 38.5–42.2% for the other protein substrates. The high nitrogen bioaccessibility of SPH is consistent with its richness in low molecular weight peptides (50% < 1000 Da. Conclusions: The results of this study indicate that SPH provides a higher proportion of bioaccessible nitrogen to a healthy adult compared to all forms of whey proteins, including extensively hydrolysed whey protein hydrolysate. The substitution of
Directory of Open Access Journals (Sweden)
Thomas Heiberg
2016-05-01
Full Text Available Despite its prominent placement between the retina and primary visual cortex in the early visual pathway, the role of the dorsal lateral geniculate nucleus (dLGN in molding and regulating the visual signals entering the brain is still poorly understood. A striking feature of the dLGN circuit is that relay cells (RCs and interneurons (INs form so-called triadic synapses, where an IN dendritic terminal can be simultaneously postsynaptic to a retinal ganglion cell (GC input and presynaptic to an RC dendrite, allowing for so-called triadic inhibition. Taking advantage of a recently developed biophysically detailed multicompartmental model for an IN, we here investigate putative effects of these different inhibitory actions of INs, i.e., triadic inhibition and standard axonal inhibition, on the response properties of RCs. We compute and investigate so-called area-response curves, that is, trial-averaged visual spike responses vs. spot size, for circular flashing spots in a network of RCs and INs. The model parameters are grossly tuned to give results in qualitative accordance with previous in vivo data of responses to such stimuli for cat GCs and RCs. We particularly investigate how the model ingredients affect salient response properties such as the receptive-field center size of RCs and INs, maximal responses and center-surround antagonisms. For example, while triadic inhibition not involving firing of IN action potentials was found to provide only a non-linear gain control of the conversion of input spikes to output spikes by RCs, axonal inhibition was in contrast found to substantially affect the receptive-field center size: the larger the inhibition, the more the RC center size shrinks compared to the GC providing the feedforward excitation. Thus, a possible role of the different inhibitory actions from INs to RCs in the dLGN circuit is to provide separate mechanisms for overall gain control (direct triadic inhibition and regulation of spatial
Heiberg, Thomas; Hagen, Espen; Halnes, Geir; Einevoll, Gaute T
2016-05-01
Despite its prominent placement between the retina and primary visual cortex in the early visual pathway, the role of the dorsal lateral geniculate nucleus (dLGN) in molding and regulating the visual signals entering the brain is still poorly understood. A striking feature of the dLGN circuit is that relay cells (RCs) and interneurons (INs) form so-called triadic synapses, where an IN dendritic terminal can be simultaneously postsynaptic to a retinal ganglion cell (GC) input and presynaptic to an RC dendrite, allowing for so-called triadic inhibition. Taking advantage of a recently developed biophysically detailed multicompartmental model for an IN, we here investigate putative effects of these different inhibitory actions of INs, i.e., triadic inhibition and standard axonal inhibition, on the response properties of RCs. We compute and investigate so-called area-response curves, that is, trial-averaged visual spike responses vs. spot size, for circular flashing spots in a network of RCs and INs. The model parameters are grossly tuned to give results in qualitative accordance with previous in vivo data of responses to such stimuli for cat GCs and RCs. We particularly investigate how the model ingredients affect salient response properties such as the receptive-field center size of RCs and INs, maximal responses and center-surround antagonisms. For example, while triadic inhibition not involving firing of IN action potentials was found to provide only a non-linear gain control of the conversion of input spikes to output spikes by RCs, axonal inhibition was in contrast found to substantially affect the receptive-field center size: the larger the inhibition, the more the RC center size shrinks compared to the GC providing the feedforward excitation. Thus, a possible role of the different inhibitory actions from INs to RCs in the dLGN circuit is to provide separate mechanisms for overall gain control (direct triadic inhibition) and regulation of spatial resolution
A computational model for BMP movement in sea urchin embryos.
van Heijster, Peter; Hardway, Heather; Kaper, Tasso J; Bradham, Cynthia A
2014-12-21
Bone morphogen proteins (BMPs) are distributed along a dorsal-ventral (DV) gradient in many developing embryos. The spatial distribution of this signaling ligand is critical for correct DV axis specification. In various species, BMP expression is spatially localized, and BMP gradient formation relies on BMP transport, which in turn requires interactions with the extracellular proteins Short gastrulation/Chordin (Chd) and Twisted gastrulation (Tsg). These binding interactions promote BMP movement and concomitantly inhibit BMP signaling. The protease Tolloid (Tld) cleaves Chd, which releases BMP from the complex and permits it to bind the BMP receptor and signal. In sea urchin embryos, BMP is produced in the ventral ectoderm, but signals in the dorsal ectoderm. The transport of BMP from the ventral ectoderm to the dorsal ectoderm in sea urchin embryos is not understood. Therefore, using information from a series of experiments, we adapt the mathematical model of Mizutani et al. (2005) and embed it as the reaction part of a one-dimensional reaction-diffusion model. We use it to study aspects of this transport process in sea urchin embryos. We demonstrate that the receptor-bound BMP concentration exhibits dorsally centered peaks of the same type as those observed experimentally when the ternary transport complex (Chd-Tsg-BMP) forms relatively quickly and BMP receptor binding is relatively slow. Similarly, dorsally centered peaks are created when the diffusivities of BMP, Chd, and Chd-Tsg are relatively low and that of Chd-Tsg-BMP is relatively high, and the model dynamics also suggest that Tld is a principal regulator of the system. At the end of this paper, we briefly compare the observed dynamics in the sea urchin model to a version that applies to the fly embryo, and we find that the same conditions can account for BMP transport in the two types of embryos only if Tld levels are reduced in sea urchin compared to fly. Copyright © 2014 Elsevier Ltd. All rights
Growth of the flat bones of the membranous neurocranium: a computational model.
Garzón-Alvarado, Diego A; González, Andres; Gutiérrez, Maria Lucia
2013-12-01
This article assumes two stages in the formation of the bones in the calvaria, the first one takes into account the formation of the primary centers of ossification. This step counts on the differentiation from mesenchymal cells into osteoblasts. A molecular mechanism is used based on a system of reaction-diffusion between two antagonistic molecules, which are BMP2 and Noggin. To this effect we used equations whose behavior allows finding Turing patterns that determine the location of the primary centers. In the second step of the model we used a molecule that is expressed by osteoblasts, called Dxl5 and that is expressed from the osteoblasts of each flat bone. This molecule allows bone growth through its borders through cell differentiation adjacent to each bone of the skull. The model has been implemented numerically using the finite element method. The results allow us to observe a good approximation of the formation of flat bones of the membranous skull as well as the formation of fontanelles and sutures. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.
Spike solutions in Gierer#x2013;Meinhardt model with a time dependent anomaly exponent
Nec, Yana
2018-01-01
Experimental evidence of complex dispersion regimes in natural systems, where the growth of the mean square displacement in time cannot be characterised by a single power, has been accruing for the past two decades. In such processes the exponent γ(t) in ⟨r2⟩ ∼ tγ(t) at times might be approximated by a piecewise constant function, or it can be a continuous function. Variable order differential equations are an emerging mathematical tool with a strong potential to model these systems. However, variable order differential equations are not tractable by the classic differential equations theory. This contribution illustrates how a classic method can be adapted to gain insight into a system of this type. Herein a variable order Gierer-Meinhardt model is posed, a generic reaction- diffusion system of a chemical origin. With a fixed order this system possesses a solution in the form of a constellation of arbitrarily situated localised pulses, when the components' diffusivity ratio is asymptotically small. The pattern was shown to exist subject to multiple step-like transitions between normal diffusion and sub-diffusion, as well as between distinct sub-diffusive regimes. The analytical approximation obtained permits qualitative analysis of the impact thereof. Numerical solution for typical cross-over scenarios revealed such features as earlier equilibration and non-monotonic excursions before attainment of equilibrium. The method is general and allows for an approximate numerical solution with any reasonably behaved γ(t).
Mönnich, David; Troost, Esther G. C.; Kaanders, Johannes H. A. M.; Oyen, Wim J. G.; Alber, Markus; Thorwarth, Daniela
2011-04-01
Hypoxia can be assessed non-invasively by positron emission tomography (PET) using radiotracers such as [18F]fluoromisonidazole (Fmiso) accumulating in poorly oxygenated cells. Typical features of dynamic Fmiso PET data are high signal variability in the first hour after tracer administration and slow formation of a consistent contrast. The purpose of this study is to investigate whether these characteristics can be explained by the current conception of the underlying microscopic processes and to identify fundamental effects. This is achieved by modelling and simulating tissue oxygenation and tracer dynamics on the microscopic scale. In simulations, vessel structures on histology-derived maps act as sources and sinks for oxygen as well as tracer molecules. Molecular distributions in the extravascular space are determined by reaction-diffusion equations, which are solved numerically using a two-dimensional finite element method. Simulated Fmiso time activity curves (TACs), though not directly comparable to PET TACs, reproduce major characteristics of clinical curves, indicating that the microscopic model and the parameter values are adequate. Evidence for dependence of the early PET signal on the vascular fraction is found. Further, possible effects leading to late contrast formation and potential implications on the quantification of Fmiso PET data are discussed.
International Nuclear Information System (INIS)
Gaerdenaes, Annemieke; Eckersten, Henrik; Reinlert, Andre; Gustafsson, David; Jansson, Per-Erik; Ekstroem, Per-Anders; Avila, Rodolfo; Greger, Maria
2009-10-01
We developed a general trace element model called Tracey to simulate dynamically the possible accumulation of radionuclides as a result of an long-term radioactive contamination of groundwater in terrestrial ecosystems. The overall objectives of the study are to: 1) Develop and evaluate a multi-compartmental model that dynamically simulates the transport and accumulation of a radionuclide in the soil-plant system at a time scale relevant for risk assessment of nuclear fuel waste; and 2) Asses the possible accumulation of radionuclide in terrestrial ecosystems due to an eventual long-term continuous radioactive groundwater contamination. Specific objectives were to assess: - The proportion of the contamination accumulated and where it is stored in the ecosystem. - The importance of the plant uptake approach for accumulation of radionuclides. - The most important radionuclide properties and ecosystem characteristics for accumulation and losses. - The proportion of the contamination lost and how is it lost. - The circumstances which stimulated export of radionuclides to other ecosystems. The model presented here, called Tracey, is a stand-alone version to allow for long simulation periods relevant for the time scale of risk assessment of nuclear waste (i.e. several thousand years) with time steps as short as one day. Tracey is a multi-compartmental model in which fluxes and storage of radionuclide are described for different plant parts and for several soil layers. Each layer includes pools of slowly and quickly decomposing litter, humus, solved and absorbed trace element. The trace element fluxes are assumed to be proportional to either water or carbon fluxes, these fluxes are simulated using the dynamic model CoupModel for fluxes of water, carbon, nitrogen and carbon in terrestrial ecosystems. Two different model approaches were used to describe plant uptake of radionuclides. The one called passive uptake approach is driven by water uptake and the one called active
Directory of Open Access Journals (Sweden)
Cecilia Suarez
Full Text Available Gliomas are the most common primary brain tumors and yet almost incurable due mainly to their great invasion capability. This represents a challenge to present clinical oncology. Here, we introduce a mathematical model aiming to improve tumor spreading capability definition. The model consists in a time dependent reaction-diffusion equation in a three-dimensional spatial domain that distinguishes between different brain topological structures. The model uses a series of digitized images from brain slices covering the whole human brain. The Talairach atlas included in the model describes brain structures at different levels. Also, the inclusion of the Brodmann areas allows prediction of the brain functions affected during tumor evolution and the estimation of correlated symptoms. The model is solved numerically using patient-specific parametrization and finite differences. Simulations consider an initial state with cellular proliferation alone (benign tumor, and an advanced state when infiltration starts (malign tumor. Survival time is estimated on the basis of tumor size and location. The model is used to predict tumor evolution in two clinical cases. In the first case, predictions show that real infiltrative areas are underestimated by current diagnostic imaging. In the second case, tumor spreading predictions were shown to be more accurate than those derived from previous models in the literature. Our results suggest that the inclusion of differential migration in glioma growth models constitutes another step towards a better prediction of tumor infiltration at the moment of surgical or radiosurgical target definition. Also, the addition of physiological/psychological considerations to classical anatomical models will provide a better and integral understanding of the patient disease at the moment of deciding therapeutic options, taking into account not only survival but also life quality.
Bandyopadhyay, Promode R; Hellum, Aren M
2014-10-23
Many slow-moving biological systems like seashells and zebrafish that do not contend with wall turbulence have somewhat organized pigmentation patterns flush with their outer surfaces that are formed by underlying autonomous reaction-diffusion (RD) mechanisms. In contrast, sharks and dolphins contend with wall turbulence, are fast swimmers, and have more organized skin patterns that are proud and sometimes vibrate. A nonlinear spatiotemporal analytical model is not available that explains the mechanism underlying control of flow with such proud patterns, despite the fact that shark and dolphin skins are major targets of reverse engineering mechanisms of drag and noise reduction. Comparable to RD, a minimal self-regulation model is given for wall turbulence regeneration in the transitional regime--laterally coupled, diffusively--which, although restricted to pre-breakdown durations and to a plane close and parallel to the wall, correctly reproduces many experimentally observed spatiotemporal organizations of vorticity in both laminar-to-turbulence transitioning and very low Reynolds number but turbulent regions. We further show that the onset of vorticity disorganization is delayed if the skin organization is treated as a spatiotemporal template of olivo-cerebellar phase reset mechanism. The model shows that the adaptation mechanisms of sharks and dolphins to their fluid environment have much in common.
Multiscale Modeling of Microbial Communities
Blanchard, Andrew
Although bacteria are single-celled organisms, they exist in nature primarily in the form of complex communities, participating in a vast array of social interactions through regulatory gene networks. The social interactions between individual cells drive the emergence of community structures, resulting in an intricate relationship across multiple spatiotemporal scales. Here, I present my work towards developing and applying the tools necessary to model the complex dynamics of bacterial communities. In Chapter 2, I utilize a reaction-diffusion model to determine the population dynamics for a population with two species. One species (CDI+) utilizes contact dependent inhibition to kill the other sensitive species (CDI-). The competition can produce diverse patterns, including extinction, coexistence, and localized aggregation. The emergence, relative abundance, and characteristic features of these patterns are collectively determined by the competitive benefit of CDI and its growth disadvantage for a given rate of population diffusion. The results provide a systematic and statistical view of CDI-based bacterial population competition, expanding the spectrum of our knowledge about CDI systems and possibly facilitating new experimental tests for a deeper understanding of bacterial interactions. In the following chapter, I present a systematic computational survey on the relationship between social interaction types and population structures for two-species communities by developing and utilizing a hybrid computational framework that combines discrete element techniques with reaction-diffusion equations. The impact of deleterious and beneficial interactions on the community are quantified. Deleterious interactions generate an increased variance in relative abundance, a drastic decrease in surviving lineages, and a rough expanding front. In contrast, beneficial interactions contribute to a reduced variance in relative abundance, an enhancement in lineage number, and a
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...
Mooranian, Armin; Negrulj, Rebecca; Arfuso, Frank; Al-Salami, Hani
2016-11-01
We have shown that the primary bile acid, cholic acid (CA), has anti-diabetic effects in vivo. Probucol (PB) is a lipophilic drug with potential applications in type 2 diabetes (T2D). This study aimed to encapsulate CA with PB and examine the formulation and surface characteristics of the microcapsules. We also tested the microcapsules' biological effects on pancreatic β-cells. Using the polymer, sodium alginate (SA), two formulations were prepared: PB-SA (control), and PB-CA-SA (test). Complete characterizations of the morphology, shape, size, chemical, thermal, and rheological properties, swelling and mechanical strength, cross-sectional imaging (Micro CT), stability, Zeta-potential, drug contents, and PB release profile were carried out, at different temperature and pH values. The microcapsules were applied to a NIT-1 cell culture and the supernatant was analyzed for insulin and TNF-α concentrations. CA incorporation optimized the PB microcapsules, which exhibited pseudoplastic-thixotropic rheological characteristics. The size of the microcapsules remained similar after CA addition, and the microcapsules showed even drug distribution and no chemical alterations of the excipients. Micro-CT imaging, differential scanning calorimetry, Fourier transform infrared spectroscopy, scanning electron microscopy, and energy-dispersive X-ray spectroscopy showed consistent microcapsules with uniform shape and morphology. PB-CA-SA microcapsules enhanced NIT-1 cell viability under hyperglycemic states and resulted in improved insulin release as well as reduced cytokine production at the physiological glucose levels. The addition of the primary bile acid, CA, improved the physical properties of the microcapsules and enhanced their pharmacological activity in vitro, suggesting potential applications in diabetes treatment.
A multiphase interfacial model for the dissolution of spent nuclear fuel
Jerden, James L.; Frey, Kurt; Ebert, William
2015-07-01
The Fuel Matrix Dissolution Model (FMDM) is an electrochemical reaction/diffusion model for the dissolution of spent uranium oxide fuel. The model was developed to provide radionuclide source terms for use in performance assessment calculations for various types of geologic repositories. It is based on mixed potential theory and consists of a two-phase fuel surface made up of UO2 and a noble metal bearing fission product phase in contact with groundwater. The corrosion potential at the surface of the dissolving fuel is calculated by balancing cathodic and anodic reactions occurring at the solution interfaces with UO2 and NMP surfaces. Dissolved oxygen and hydrogen peroxide generated by radiolysis of the groundwater are the major oxidizing agents that promote fuel dissolution. Several reactions occurring on noble metal alloy surfaces are electrically coupled to the UO2 and can catalyze or inhibit oxidative dissolution of the fuel. The most important of these is the oxidation of hydrogen, which counteracts the effects of oxidants (primarily H2O2 and O2). Inclusion of this reaction greatly decreases the oxidation of U(IV) and slows fuel dissolution significantly. In addition to radiolytic hydrogen, large quantities of hydrogen can be produced by the anoxic corrosion of steel structures within and near the fuel waste package. The model accurately predicts key experimental trends seen in literature data, the most important being the dramatic depression of the fuel dissolution rate by the presence of dissolved hydrogen at even relatively low concentrations (e.g., less than 1 mM). This hydrogen effect counteracts oxidation reactions and can limit fuel degradation to chemical dissolution, which results in radionuclide source term values that are four or five orders of magnitude lower than when oxidative dissolution processes are operative. This paper presents the scientific basis of the model, the approach for modeling used fuel in a disposal system, and preliminary
Directory of Open Access Journals (Sweden)
Georgios S Stamatakos
2017-01-01
Full Text Available A novel explicit triscale reaction-diffusion numerical model of glioblastoma multiforme tumor growth is presented. The model incorporates the handling of Neumann boundary conditions imposed by the cranium and takes into account both the inhomogeneous nature of human brain and the complexity of the skull geometry. The finite-difference time-domain method is adopted. To demonstrate the workflow of a possible clinical validation procedure, a clinical case/scenario is addressed. A good agreement of the in silico calculated value of the doubling time (ie, the time for tumor volume to double with the value of the same quantity based on tomographic imaging data has been observed. A theoretical exploration suggests that a rough but still quite informative value of the doubling time may be calculated based on a homogeneous brain model. The model could serve as the main component of a continuous mathematics-based glioblastoma oncosimulator aiming at supporting the clinician in the optimal patient-individualized design of treatment using the patient’s multiscale data and experimenting in silico (ie, on the computer.
Energy Technology Data Exchange (ETDEWEB)
Gaerdenaes, Annemieke (Dept. of Soil and Environment, Swedish Univ. of Agricultural Sciences, Uppsala (Sweden)); Eckersten, Henrik (Dept. of Ecology and Crop Production, Swedish Univ. of Agricultural Sciences, Uppsala (Sweden)); Reinlert, Andre (Dept. of Physical Geography and Ecosystems Analysis, Lund Univ., Lund (Sweden)); Gustafsson, David; Jansson, Per-Erik (Dept. Land and WaterResources, Royal Inst. of Technology, Stockholm (Sweden)); Ekstroem, Per-Anders; Avila, Rodolfo (Facilia AB, Bromma (Sweden)); Greger, Maria (Dept. of Botany, Stockholm Univ., Stockholm (Sweden))
2009-10-15
We developed a general trace element model called Tracey to simulate dynamically the possible accumulation of radionuclides as a result of an long-term radioactive contamination of groundwater in terrestrial ecosystems. The overall objectives of the study are to: 1) Develop and evaluate a multi-compartmental model that dynamically simulates the transport and accumulation of a radionuclide in the soil-plant system at a time scale relevant for risk assessment of nuclear fuel waste; and 2) Asses the possible accumulation of radionuclide in terrestrial ecosystems due to an eventual long-term continuous radioactive groundwater contamination. Specific objectives were to assess: - The proportion of the contamination accumulated and where it is stored in the ecosystem. - The importance of the plant uptake approach for accumulation of radionuclides. - The most important radionuclide properties and ecosystem characteristics for accumulation and losses. - The proportion of the contamination lost and how is it lost. - The circumstances which stimulated export of radionuclides to other ecosystems. The model presented here, called Tracey, is a stand-alone version to allow for long simulation periods relevant for the time scale of risk assessment of nuclear waste (i.e. several thousand years) with time steps as short as one day. Tracey is a multi-compartmental model in which fluxes and storage of radionuclide are described for different plant parts and for several soil layers. Each layer includes pools of slowly and quickly decomposing litter, humus, solved and absorbed trace element. The trace element fluxes are assumed to be proportional to either water or carbon fluxes, these fluxes are simulated using the dynamic model CoupModel for fluxes of water, carbon, nitrogen and carbon in terrestrial ecosystems. Two different model approaches were used to describe plant uptake of radionuclides. The one called passive uptake approach is driven by water uptake and the one called active
On the phase space structure of IP3 induced Ca2+ signalling and concepts for predictive modeling
Falcke, Martin; Moein, Mahsa; TilÅ«naitÄ--, Agne; Thul, Rüdiger; Skupin, Alexander
2018-04-01
The correspondence between mathematical structures and experimental systems is the basis of the generalizability of results found with specific systems and is the basis of the predictive power of theoretical physics. While physicists have confidence in this correspondence, it is less recognized in cellular biophysics. On the one hand, the complex organization of cellular dynamics involving a plethora of interacting molecules and the basic observation of cell variability seem to question its possibility. The practical difficulties of deriving the equations describing cellular behaviour from first principles support these doubts. On the other hand, ignoring such a correspondence would severely limit the possibility of predictive quantitative theory in biophysics. Additionally, the existence of functional modules (like pathways) across cell types suggests also the existence of mathematical structures with comparable universality. Only a few cellular systems have been sufficiently investigated in a variety of cell types to follow up these basic questions. IP3 induced Ca2+signalling is one of them, and the mathematical structure corresponding to it is subject of ongoing discussion. We review the system's general properties observed in a variety of cell types. They are captured by a reaction diffusion system. We discuss the phase space structure of its local dynamics. The spiking regime corresponds to noisy excitability. Models focussing on different aspects can be derived starting from this phase space structure. We discuss how the initial assumptions on the set of stochastic variables and phase space structure shape the predictions of parameter dependencies of the mathematical models resulting from the derivation.
Launois, Thomas; Ogée, Jérôme; Commane, Roisin; Wehr, Rchard; Meredith, Laura; Munger, Bill; Nelson, David; Saleska, Scott; Wofsy, Steve; Zahniser, Mark; Wingate, Lisa
2016-04-01
The exchange of CO2 between the terrestrial biosphere and the atmosphere is driven by photosynthetic uptake and respiratory loss, two fluxes currently estimated with considerable uncertainty at large scales. Model predictions indicate that these biosphere fluxes will be modified in the future as CO2 concentrations and temperatures increase; however, it still unclear to what extent. To address this challenge there is a need for better constraints on land surface model parameterisations. Additional atmospheric tracers of large-scale CO2 fluxes have been identified as potential candidates for this task. In particular carbonyl sulphide (OCS) has been proposed as a complementary tracer of gross photosynthesis over land, since OCS uptake by plants is dominated by carbonic anhydrase (CA) activity, an enzyme abundant in leaves that catalyses CO2 hydration during photosynthesis. However, although the mass budget at the ecosystem is dominated by the flux of OCS into leaves, some OCS is also exchanged between the atmosphere and the soil and this component of the budget requires constraining. In this study, we adapted the process-based isotope-enabled model MuSICA (Multi-layer Simulator of the Interactions between a vegetation Canopy and the Atmosphere) to include the transport, reaction, diffusion and production of OCS within a forested ecosystem. This model was combined with 3 years (2011-2013) of in situ measurements of OCS atmospheric concentration profiles and fluxes at the Harvard Forest (Massachussets, USA) to test hypotheses on the mechanisms responsible for CA-driven uptake by leaves and soils as well as possible OCS emissions during litter decomposition. Model simulations over the three years captured well the impact of diurnally and seasonally varying environmental conditions on the net ecosystem OCS flux. A sensitivity analysis on soil CA activity and soil OCS emission rates was also performed to quantify their impact on the vertical profiles of OCS inside the
Pham, Kara
2012-01-01
Gliomas are very aggressive brain tumours, in which tumour cells gain the ability to penetrate the surrounding normal tissue. The invasion mechanisms of this type of tumour remain to be elucidated. Our work is motivated by the migration/proliferation dichotomy (go-or-grow) hypothesis, i.e. the antagonistic migratory and proliferating cellular behaviours in a cell population, which may play a central role in these tumours. In this paper, we formulate a simple go-or-grow model to investigate the dynamics of a population of glioma cells for which the switch from a migratory to a proliferating phenotype (and vice versa) depends on the local cell density. The model consists of two reaction-diffusion equations describing cell migration, proliferation and a phenotypic switch. We use a combination of numerical and analytical techniques to characterize the development of spatio-temporal instabilities and travelling wave solutions generated by our model. We demonstrate that the density-dependent go-or-grow mechanism can produce complex dynamics similar to those associated with tumour heterogeneity and invasion.
STEPS: efficient simulation of stochastic reaction–diffusion models in realistic morphologies
Directory of Open Access Journals (Sweden)
Hepburn Iain
2012-05-01
Full Text Available Abstract Background Models of cellular molecular systems are built from components such as biochemical reactions (including interactions between ligands and membrane-bound proteins, conformational changes and active and passive transport. A discrete, stochastic description of the kinetics is often essential to capture the behavior of the system accurately. Where spatial effects play a prominent role the complex morphology of cells may have to be represented, along with aspects such as chemical localization and diffusion. This high level of detail makes efficiency a particularly important consideration for software that is designed to simulate such systems. Results We describe STEPS, a stochastic reaction–diffusion simulator developed with an emphasis on simulating biochemical signaling pathways accurately and efficiently. STEPS supports all the above-mentioned features, and well-validated support for SBML allows many existing biochemical models to be imported reliably. Complex boundaries can be represented accurately in externally generated 3D tetrahedral meshes imported by STEPS. The powerful Python interface facilitates model construction and simulation control. STEPS implements the composition and rejection method, a variation of the Gillespie SSA, supporting diffusion between tetrahedral elements within an efficient search and update engine. Additional support for well-mixed conditions and for deterministic model solution is implemented. Solver accuracy is confirmed with an original and extensive validation set consisting of isolated reaction, diffusion and reaction–diffusion systems. Accuracy imposes upper and lower limits on tetrahedron sizes, which are described in detail. By comparing to Smoldyn, we show how the voxel-based approach in STEPS is often faster than particle-based methods, with increasing advantage in larger systems, and by comparing to MesoRD we show the efficiency of the STEPS implementation. Conclusion STEPS simulates
Biogenic silica dissolution in diatom aggregates: insights from reactive transport modelling
Moriceau, B
2014-12-15
© Inter-Research 2014. Diatom aggregates contribute significantly to the vertical sinking flux of particulate matter in the ocean. These fragile structures form a specific microhabitat for the aggregated cells, but their internal chemical and physical characteristics remain largely unknown. Studies on the impact of aggregation on the Si cycle led to apparent inconsistency. Despite a lower biogenic silica (bSiO2) dissolution rate and diffusion of the silicic acid (dSi) being similar in aggregates and in sea-water, dSi surprisingly accumulates in aggregates. A reaction-diffusion model helps to clarify this incoherence by reconstructing dSi accumulation measured during batch experiments with aggregated and non-aggregated Skeletonema marinoi and Chaetoceros decipiens. The model calculates the effective bSiO2 dissolution rate as opposed to the experimental apparent bSiO2 dissolution rate, which is the results of the effective dissolution of bSiO2 and transport of dSi out of the aggregate. In the model, dSi transport out of the aggregate is modulated by alternatively considering retention (decrease of the dSi diffusion constant) and adsorption (reversible chemical bonds between dSi and the aggregate matrix) processes. Modelled bSiO2 dissolution is modulated by the impact of dSi concentration inside aggregates and diatom viability, as enhanced persistence of metabolically active diatoms has been observed in aggregates. Adsorption better explains dSi accumulation within and outside aggregates, raising the possible importance of dSi travelling within aggregates to the deep sea (potentially representing 20% of the total silica flux). The model indicates that bSiO2 dissolution is effectively decreased in aggregates mainly due to higher diatom viability but also to other parameters discussed herein.
An extended five-stream model for diffusion of ion-implanted dopants in monocrystalline silicon
International Nuclear Information System (INIS)
Khina, B.B.
2007-01-01
Low-energy high-dose ion implantation of different dopants (P, Sb, As, B and others) into monocrystalline silicon with subsequent thermal annealing is used for the formation of ultra-shallow p-n junctions in modern VLSI circuit technology. During annealing, dopant activation and diffusion in silicon takes place. The experimentally observed phenomenon of transient enhanced diffusion (TED), which is typically ascribed to the interaction of diffusing species with non-equilibrium point defects accumulated in silicon due to ion damage, and formation of small clusters and extended defects, hinders further down scaling of p-n junctions in VLSI circuits. TED is currently a subject of extensive experimental and theoretical investigation in many binary and multicomponent systems. However, the state-of-the-art mathematical models of dopant diffusion, which are based on the so-called 'five-stream' approach, and modern TCAD software packages such as SUPREM-4 (by Silvaco Data Systems, Ltd.) that implement these models encounter severe difficulties in describing TED. Solving the intricate problem of TED suppression and development of novel regimes of ion implantation and rapid thermal annealing is impossible without elaboration of new mathematical models and computer simulation of this complex phenomenon. In this work, an extended five-stream model for diffusion in silicon is developed which takes into account all possible charge states of point defects (vacancies and silicon self-interstitials) and diffusing pairs 'dopant atom-vacancy' and 'dopant atom-silicon self-interstitial'. The model includes the drift terms for differently charged point defects and pairs in the internal electric field and the kinetics of interaction between unlike 'species' (generation and annihilation of pairs and annihilation of point defects). Expressions for diffusion coefficients and numerous sink/source terms that appear in the non-linear, non-steady-state reaction-diffusion equations are derived
Energy Technology Data Exchange (ETDEWEB)
Gaerdenaes, Annemieke I. [Dept. of Soil and Environment, Swedish University of Agricultural Sciences (SLU), P.O. Box 7001, 750 07 Uppsala (Sweden); Eckersten, Henrik [Dept. of Ecology and Crop Production, SLU, P.O. Box 7042, 750 07 Uppsala (Sweden); Reinlert, Andre [Dept. of Physical Geography and Ecosystems Analysis, Lund University, 223 62 Lund (Sweden); MMT, Sven Kaellfelts Gata 11 SE 426 71 Vaestra Froelunda (Sweden); Gustafsson, David; Jansson, Per-Erik [Dept. Land and Water Resources, KTH, SE 100 44, Stockholm (Sweden); Ekstroem, Per-Anders [Facilia AB, Gustavlundsvaegen 151A, 167 51 Bromma (Sweden); Greger, Maria [Dept. of Ecology, Environment and Plant Sciences, Stockholm University, 106 91 Stockholm (Sweden)
2014-07-01
This study was conducted as part of the risk assessment of final deposits of nuclear fuel waste. The overall objective is to assess the possible accumulation of radionuclides in terrestrial ecosystems after an eventual long-term groundwater contamination. The specific objectives are to assess: i) What proportion of the contamination will accumulate in the soil-plant-system? ii) Where in the soil-plant- system will it accumulate? iii) Which ecosystem characteristics and radionuclides properties are important for the accumulation? and iv) Under which circumstances do losses from the ecosystems occur? We developed the dynamic model Tracey (Gaerdenaes et al. 2009) describing cycling of radionuclides in terrestrial ecosystems with high temporal resolution (1 day). The model is a multi-compartmental model in which fluxes and storage of radionuclides are described for different plant parts and soil pools in each of the 10 soil layers. The radionuclide fluxes are driven either by water or carbon fluxes. The water and the carbon fluxes are simulated with the dynamic, bio-geophysical Coup Model (Jansson and Karlberg, 2004). Tracey includes two root uptake approaches of radionuclides; (i) passive uptake driven by root water uptake and (ii) active uptake driven by plant growth. A linear approach describes the adsorption of radionuclides to soil particles and organic matter. Tracey was applied on two ecosystems with contrasting hydrology, the mixed Pinus-Picea forests found in the dry, elevated areas and the Alnus forests found in the wet, low-land areas of Uppland in central east Sweden. Different varieties of the two forest types were created by varying the root depth and radiation use efficiency. The climate was cold-temperate and based on 30-year daily weather data from Uppsala. The assumed groundwater contamination was close to 1 mg of an unspecified radionuclide per m2 and year. This load corresponds to 1 Bq per m{sup 2} and year of {sup 238}U, a common long
International Nuclear Information System (INIS)
Gago-Arias, Araceli; Espinoza, Ignacio; Sánchez-Nieto, Beatriz; Aguiar, Pablo; Pardo-Montero, Juan
2016-01-01
The resistance of hypoxic cells to radiation, due to the oxygen dependence of radiosensitivity, is well known and must be taken into account to accurately calculate the radiation induced cell death. A proper modelling of the response of tumours to radiation requires deriving the distribution of oxygen at a microscopic scale. This usually involves solving the reaction-diffusion equation in tumour voxels using a vascularization distribution model. Moreover, re-oxygenation arises during the course of radiotherapy, one reason being the increase of available oxygen caused by cell killing, which can turn hypoxic tumours into oxic. In this work we study the effect of cell death kinetics in tumour oxygenation modelling, analysing how it affects the timing of re-oxygenation, surviving fraction and tumour control. Two models of cell death are compared, an instantaneous cell killing, mimicking early apoptosis, and a delayed cell death scenario in which cells can die shortly after being damaged, as well as long after irradiation. For each of these scenarios, the decrease in oxygen consumption due to cell death can be computed globally (macroscopic voxel average) or locally (microscopic). A re-oxygenation model already used in the literature, the so called full re-oxygenation, is also considered. The impact of cell death kinetics and re-oxygenation on tumour responses is illustrated for two radiotherapy fractionation schemes: a conventional schedule, and a hypofractionated treatment. The results show large differences in the doses needed to achieve 50% tumour control for the investigated cell death models. Moreover, the models affect the tumour responses differently depending on the treatment schedule. This corroborates the complex nature of re-oxygenation, showing the need to take into account the kinetics of cell death in radiation response models. (paper)
Yun, Jian; Shang, Song-Chao; Wei, Xiao-Dan; Liu, Shuang; Li, Zhi-Jie
2016-01-01
Language is characterized by both ecological properties and social properties, and competition is the basic form of language evolution. The rise and decline of one language is a result of competition between languages. Moreover, this rise and decline directly influences the diversity of human culture. Mathematics and computer modeling for language competition has been a popular topic in the fields of linguistics, mathematics, computer science, ecology, and other disciplines. Currently, there are several problems in the research on language competition modeling. First, comprehensive mathematical analysis is absent in most studies of language competition models. Next, most language competition models are based on the assumption that one language in the model is stronger than the other. These studies tend to ignore cases where there is a balance of power in the competition. The competition between two well-matched languages is more practical, because it can facilitate the co-development of two languages. A third issue with current studies is that many studies have an evolution result where the weaker language inevitably goes extinct. From the integrated point of view of ecology and sociology, this paper improves the Lotka-Volterra model and basic reaction-diffusion model to propose an "ecology-society" computational model for describing language competition. Furthermore, a strict and comprehensive mathematical analysis was made for the stability of the equilibria. Two languages in competition may be either well-matched or greatly different in strength, which was reflected in the experimental design. The results revealed that language coexistence, and even co-development, are likely to occur during language competition.
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.
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.
Jiang, Ting-Xin; Widelitz, Randall B; Shen, Wei-Min; Will, Peter; Wu, Da-Yu; Lin, Chih-Min; Jung, Han-Sung; Chuong, Cheng-Ming
2004-01-01
Pattern formation is a fundamental morphogenetic process. Models based on genetic and epigenetic control have been proposed but remain controversial. Here we use feather morphogenesis for further evaluation. Adhesion molecules and/or signaling molecules were first expressed homogenously in feather tracts (restrictive mode, appear earlier) or directly in bud or inter-bud regions ( de novo mode, appear later). They either activate or inhibit bud formation, but paradoxically colocalize in the bud. Using feather bud reconstitution, we showed that completely dissociated cells can reform periodic patterns without reference to previous positional codes. The patterning process has the characteristics of being self-organizing, dynamic and plastic. The final pattern is an equilibrium state reached by competition, and the number and size of buds can be altered based on cell number and activator/inhibitor ratio, respectively. We developed a Digital Hormone Model which consists of (1) competent cells without identity that move randomly in a space, (2) extracellular signaling hormones which diffuse by a reaction-diffusion mechanism and activate or inhibit cell adhesion, and (3) cells which respond with topological stochastic actions manifested as changes in cell adhesion. Based on probability, the results are cell clusters arranged in dots or stripes. Thus genetic control provides combinational molecular information which defines the properties of the cells but not the final pattern. Epigenetic control governs interactions among cells and their environment based on physical-chemical rules (such as those described in the Digital Hormone Model). Complex integument patterning is the sum of these two components of control and that is why integument patterns are usually similar but non-identical. These principles may be shared by other pattern formation processes such as barb ridge formation, fingerprints, pigmentation patterning, etc. The Digital Hormone Model can also be applied to
Guo, Muyi; Cai, Yan; Yao, Xinke; Li, Zhiyong
2018-08-07
Observational studies have identified angiogenesis from the adventitial vasa vasorum and intraplaque hemorrhage (IPH) as critical factors in atherosclerotic plaque progression and destabilization. Here we propose a mathematical model incorporating intraplaque neovascularization and hemodynamic calculation with plaque destabilization for the quantitative evaluation of the role of neoangiogenesis and IPH in the vulnerable atherosclerotic plaque formation. An angiogenic microvasculature is generated by two-dimensional nine-point discretization of endothelial cell proliferation and migration from the vasa vasorum. Three key cells (endothelial cells, smooth muscle cells and macrophages) and three key chemicals (vascular endothelial growth factors, extracellular matrix and matrix metalloproteinase) are involved in the plaque progression model, and described by the reaction-diffusion partial differential equations. The hemodynamic calculation of the microcirculation on the generated microvessel network is carried out by coupling the intravascular, interstitial and transvascular flow. The plasma concentration in the interstitial domain is defined as the description of IPH area according to the diffusion and convection with the interstitial fluid flow, as well as the extravascular movement across the leaky vessel wall. The simulation results demonstrate a series of pathophysiological phenomena during the vulnerable progression of an atherosclerotic plaque, including the expanding necrotic core, the exacerbated inflammation, the high microvessel density (MVD) region at the shoulder areas, the transvascular flow through the capillary wall and the IPH. The important role of IPH in the plaque destabilization is evidenced by simulations with varied model parameters. It is found that the IPH can significantly speed up the plaque vulnerability by increasing necrotic core and thinning fibrous cap. In addition, the decreased MVD and vessel permeability may slow down the process of
Laplanche, Christophe; Elger, Arnaud; Santoul, Frédéric; Thiede, Gary P.; Budy, Phaedra
2018-01-01
Management actions aimed at eradicating exotic fish species from riverine ecosystems can be better informed by forecasting abilities of mechanistic models. We illustrate this point with an example of the Logan River, Utah, originally populated with endemic cutthroat trout (Oncorhynchus clarkii utah), which compete with exotic brown trout (Salmo trutta). The coexistence equilibrium was disrupted by a large scale, experimental removal of the exotic species in 2009–2011 (on average, 8.2% of the stock each year), followed by an increase in the density of the native species. We built a spatially-explicit, reaction-diffusion model encompassing four key processes: population growth in heterogeneous habitat, competition, dispersal, and a management action. We calibrated the model with detailed long-term monitoring data (2001–2016) collected along the 35.4-km long river main channel. Our model, although simple, did a remarkable job reproducing the system steady state prior to the management action. Insights gained from the model independent predictions are consistent with available knowledge and indicate that the exotic species is more competitive; however, the native species still occupies more favorable habitat upstream. Dynamic runs of the model also recreated the observed increase of the native species following the management action. The model can simulate two possible distinct long-term outcomes: recovery or eradication of the exotic species. The processing of available knowledge using Bayesian methods allowed us to conclude that the chance for eradication of the invader was low at the beginning of the experimental removal (0.7% in 2009) and increased (20.5% in 2016) by using more recent monitoring data. We show that accessible mathematical and numerical tools can provide highly informative insights for managers (e.g., outcome of their conservation actions), identify knowledge gaps, and provide testable theory for researchers.
Brinkman, Daniel
2013-05-01
We present and discuss a mathematical model for the operation of bilayer organic photovoltaic devices. Our model couples drift-diffusion-recombination equations for the charge carriers (specifically, electrons and holes) with a reaction-diffusion equation for the excitons/polaron pairs and Poisson\\'s equation for the self-consistent electrostatic potential. The material difference (i.e. the HOMO/LUMO gap) of the two organic substrates forming the bilayer device is included as a work-function potential. Firstly, we perform an asymptotic analysis of the scaled one-dimensional stationary state system: (i) with focus on the dynamics on the interface and (ii) with the goal of simplifying the bulk dynamics away from the interface. Secondly, we present a two-dimensional hybrid discontinuous Galerkin finite element numerical scheme which is very well suited to resolve: (i) the material changes, (ii) the resulting strong variation over the interface, and (iii) the necessary upwinding in the discretization of drift-diffusion equations. Finally, we compare the numerical results with the approximating asymptotics. © 2013 World Scientific Publishing Company.
Dehghan, Mehdi; Mohammadi, Vahid
2017-03-01
As is said in [27], the tumor-growth model is the incorporation of nutrient within the mixture as opposed to being modeled with an auxiliary reaction-diffusion equation. The formulation involves systems of highly nonlinear partial differential equations of surface effects through diffuse-interface models [27]. Simulations of this practical model using numerical methods can be applied for evaluating it. The present paper investigates the solution of the tumor growth model with meshless techniques. Meshless methods are applied based on the collocation technique which employ multiquadrics (MQ) radial basis function (RBFs) and generalized moving least squares (GMLS) procedures. The main advantages of these choices come back to the natural behavior of meshless approaches. As well as, a method based on meshless approach can be applied easily for finding the solution of partial differential equations in high-dimension using any distributions of points on regular and irregular domains. The present paper involves a time-dependent system of partial differential equations that describes four-species tumor growth model. To overcome the time variable, two procedures will be used. One of them is a semi-implicit finite difference method based on Crank-Nicolson scheme and another one is based on explicit Runge-Kutta time integration. The first case gives a linear system of algebraic equations which will be solved at each time-step. The second case will be efficient but conditionally stable. The obtained numerical results are reported to confirm the ability of these techniques for solving the two and three-dimensional tumor-growth equations.
Energy Technology Data Exchange (ETDEWEB)
Becker, Stefan; Mang, Andreas; Toma, Alina; Buzug, Thorsten M. [University of Luebeck (Germany). Institute of Medical Engineering
2010-12-15
The present work introduces a novel method for approximating mass effect of primary brain tumors. The spatio-temporal dynamics of cancerous cells are modeled by means of a deterministic reaction-diffusion equation. Diffusion tensor information obtained from a probabilistic diffusion tensor imaging atlas is incorporated into the model to simulate anisotropic diffusion of cancerous cells. To account for the expansive nature of the tumor, the computed net cell density of malignant cells is linked to a parametric deformation model. This mass effect model is based on the so-called directly manipulated free form deformation. Spatial correspondence between two successive simulation steps is established by tracking landmarks, which are attached to the boundary of the gross tumor volume. The movement of these landmarks is used to compute the new configuration of the control points and, hence, determines the resulting deformation. To prevent a deformation of rigid structures (i.e. the skull), fixed shielding landmarks are introduced. In a refinement step, an adaptive landmark scheme ensures a dense sampling of the tumor isosurface, which in turn allows for an appropriate representation of the tumor shape. The influence of different parameters on the model is demonstrated by a set of simulations. Additionally, simulation results are qualitatively compared to an exemplary set of clinical magnetic resonance images of patients diagnosed with high-grade glioma. Careful visual inspection of the results demonstrates the potential of the implemented model and provides first evidence that the computed approximation of tumor mass effect is sensible. The shape of diffusive brain tumors (glioblastoma multiforme) can be recovered and approximately matches the observations in real clinical data. (orig.)
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.
A Stefan model for mass transfer in a rotating disk reaction vessel
BOHUN, C. S.
2015-01-01
chemical reactions occurring in the bulk. The wide range in the reaction rates of the underlying chemistry allows for a natural decoupling of the problem into a simplified set of weakly coupled convective-reaction-diffusion equations for the slowly reacting
Safety analysis of the Chernobyl accident origin decontamination waste burials in Belarus
International Nuclear Information System (INIS)
Skurat, V.V.; Shiryaeva, N.M.; Myshkina, N.K.; Gvozdev, A.A.; Serebryanyj, G.Z.; Golikova, N.B.
2002-01-01
Potential dangerous of the decontamination waste burials was estimated by means of the generalized multicompartmental model. Characteristics of 24 the most large and unfavorable decontamination waste burials are shown and an estimate of their safety is given. The burial effect zones were determined (100-300 m). A reliability of the forecasting estimate of potential dangerous radioactive contamination of ground waters near the burials was checked on example of the Dudichi decontamination waste burial
Nosikov, I. A.; Klimenko, M. V.; Bessarab, P. F.; Zhbankov, G. A.
2017-07-01
Point-to-point ray tracing is an important problem in many fields of science. While direct variational methods where some trajectory is transformed to an optimal one are routinely used in calculations of pathways of seismic waves, chemical reactions, diffusion processes, etc., this approach is not widely known in ionospheric point-to-point ray tracing. We apply the Nudged Elastic Band (NEB) method to a radio wave propagation problem. In the NEB method, a chain of points which gives a discrete representation of the radio wave ray is adjusted iteratively to an optimal configuration satisfying the Fermat's principle, while the endpoints of the trajectory are kept fixed according to the boundary conditions. Transverse displacements define the radio ray trajectory, while springs between the points control their distribution along the ray. The method is applied to a study of point-to-point ionospheric ray tracing, where the propagation medium is obtained with the International Reference Ionosphere model taking into account traveling ionospheric disturbances. A 2-dimensional representation of the optical path functional is developed and used to gain insight into the fundamental difference between high and low rays. We conclude that high and low rays are minima and saddle points of the optical path functional, respectively.
Optimal distributed control of a diffuse interface model of tumor growth
Colli, Pierluigi; Gilardi, Gianni; Rocca, Elisabetta; Sprekels, Jürgen
2017-06-01
In this paper, a distributed optimal control problem is studied for a diffuse interface model of tumor growth which was proposed by Hawkins-Daruud et al in Hawkins-Daruud et al (2011 Int. J. Numer. Math. Biomed. Eng. 28 3-24). The model consists of a Cahn-Hilliard equation for the tumor cell fraction φ coupled to a reaction-diffusion equation for a function σ representing the nutrient-rich extracellular water volume fraction. The distributed control u monitors as a right-hand side of the equation for σ and can be interpreted as a nutrient supply or a medication, while the cost function, which is of standard tracking type, is meant to keep the tumor cell fraction under control during the evolution. We show that the control-to-state operator is Fréchet differentiable between appropriate Banach spaces and derive the first-order necessary optimality conditions in terms of a variational inequality involving the adjoint state variables. The financial support of the FP7-IDEAS-ERC-StG #256872 (EntroPhase) and of the project Fondazione Cariplo-Regione Lombardia MEGAsTAR ‘Matematica d’Eccellenza in biologia ed ingegneria come accelleratore di una nuona strateGia per l’ATtRattività dell’ateneo pavese’ is gratefully acknowledged. The paper also benefited from the support of the MIUR-PRIN Grant 2015PA5MP7 ‘Calculus of Variations’ for PC and GG, and the GNAMPA (Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni) of INdAM (Istituto Nazionale di Alta Matematica) for PC, GG and ER.
Modeling Space-Time Dependent Helium Bubble Evolution in Tungsten Armor under IFE Conditions
International Nuclear Information System (INIS)
Qiyang Hu; Shahram Sharafat; Nasr Ghoniem
2006-01-01
The High Average Power Laser (HAPL) program is a coordinated effort to develop Laser Inertial Fusion Energy. The implosion of the D-T target produces a spectrum of neutrons, X-rays, and charged particles, which arrive at the first wall (FW) at different times within about 2.5 μs at a frequency of 5 to 10 Hz. Helium is one of several high-energy charged particle constituents impinging on the candidate tungsten armored low activation ferritic steel First Wall. The spread of the implanted debris and burn helium energies results in a unique space-time dependent implantation profile that spans about 10 μm in tungsten. Co-implantation of X-rays and other ions results in spatially dependent damage profiles and rapid space-time dependent temperature spikes and gradients. The rate of helium transport and helium bubble formation will vary significantly throughout the implanted region. Furthermore, helium will also be transported via the migration of helium bubbles and non-equilibrium helium-vacancy clusters. The HEROS code was developed at UCLA to model the spatial and time-dependent helium bubble nucleation, growth, coalescence, and migration under transient damage rates and transient temperature gradients. The HEROS code is based on kinetic rate theory, which includes clustering of helium and vacancies, helium mobility, helium-vacancy cluster stability, cavity nucleation and growth and other microstructural features such as interstitial loop evolution, grain boundaries, and precipitates. The HEROS code is based on space-time discretization of reaction-diffusion type equations to account for migration of mobile species between neighboring bins as single atoms, clusters, or bubbles. HAPL chamber FW implantation conditions are used to model helium bubble evolution in the implanted tungsten. Helium recycling rate predictions are compared with experimental results of helium ion implantation experiments. (author)
Energy Technology Data Exchange (ETDEWEB)
Dou Jianhong; Xia Ling; Zhang Yu; Shou Guofa [Department of Biomedical Engineering, Zhejiang University, Hangzhou 310027 (China); Wei Qing; Liu Feng; Crozier, Stuart [School of Information Technology and Electrical Engineering, University of Queensland, St Lucia, Brisbane, Queensland 4072 (Australia)], E-mail: xialing@zju.edu.cn
2009-01-21
Asynchronous electrical activation, induced by bundle branch block (BBB), can cause reduced ventricular function. However, the effects of BBB on the mechanical function of heart are difficult to assess experimentally. Many heart models have been developed to investigate cardiac properties during BBB but have mainly focused on the electrophysiological properties. To date, the mechanical function of BBB has not been well investigated. Based on a three-dimensional electromechanical canine heart model, the mechanical properties of complete left and right bundle branch block (LBBB and RBBB) were simulated. The anatomical model as well as the fiber orientations of a dog heart was reconstructed from magnetic resonance imaging (MRI) and diffusion tensor MRI (DT-MRI). Using the solutions of reaction-diffusion equations and with a strategy of parallel computation, the asynchronous excitation propagation and intraventricular conduction in BBB was simulated. The mechanics of myocardial tissues were computed with time-, sarcomere length-dependent uniaxial active stress initiated at the time of depolarization. The quantification of mechanical intra- and interventricular asynchrony of BBB was then investigated using the finite-element method with an eight-node isoparametric element. The simulation results show that (1) there exists inter- and intraventricular systolic dyssynchrony during BBB; (2) RBBB may have more mechanical synchrony and better systolic function of the left ventricle (LV) than LBBB; (3) the ventricles always move toward the early-activated ventricle; and (4) the septum experiences higher stress than left and right ventricular free walls in BBB. The simulation results validate clinical and experimental recordings of heart deformation and provide regional quantitative estimates of ventricular wall strain and stress. The present work suggests that an electromechanical heart model, incorporating real geometry and fiber orientations, may be helpful for better
Modeling Radiation Effectiveness for Inactivation of Bacillus Spores
2015-09-17
radiation . 3.6.1 Ionizing Radiation Damage. Some of the ROS’ discussed in Section 3.3 cause indirect damage to the spore’s DNA. They can produce... ionizing radiation damage has focused on the effects of charged particles in their tracks. The charged particles create radiation - induced products and...3.8.1 Reaction-Diffusion of ROS Within the Spore. A demonstrative scenario will be explored in order to simulate the indirect effects of ionizing
Simulations of Chemotaxis and Random Motility in Finite Domains
National Research Council Canada - National Science Library
Jabbarzadeh, Ehsan; Abrams, Cameron F
2005-01-01
.... The model couples fully time-dependent finite-difference solution of a reaction-diffusion equation for the concentration field of a generic chemoattractant to biased random walks representing individual moving cells...
Ogée, Jerome; Wehr, Richard; Commane, Roisin; Launois, Thomas; Meredith, Laura; Munger, Bill; Nelson, David; Saleska, Scott; Zahniser, Mark; Wofsy, Steve; Wingate, Lisa
2016-04-01
The net flux of carbon dioxide between the land surface and the atmosphere is dominated by photosynthesis and soil respiration, two of the largest gross CO2 fluxes in the carbon cycle. More robust estimates of these gross fluxes could be obtained from the atmospheric budgets of other valuable tracers, such as carbonyl sulfide (COS) or the carbon and oxygen isotope compositions (δ13C and δ18O) of atmospheric CO2. Over the past decades, the global atmospheric flask network has measured the inter-annual and intra-annual variations in the concentrations of these tracers. However, knowledge gaps and a lack of high-resolution multi-tracer ecosystem-scale measurements have hindered the development of process-based models that can simulate the behaviour of each tracer in response to environmental drivers. We present novel datasets of net ecosystem COS, 13CO2 and CO18O exchange and vertical profile data collected over 3 consecutive growing seasons (2011-2013) at the Harvard forest flux site. We then used the process-based model MuSICA (multi-layer Simulator of the Interactions between vegetation Canopy and the Atmosphere) to include the transport, reaction, diffusion and production of each tracer within the forest and exchanged with the atmosphere. Model simulations over the three years captured well the impact of diurnally and seasonally varying environmental conditions on the net ecosystem exchange of each tracer. The model also captured well the dynamic vertical features of tracer behaviour within the canopy. This unique dataset and model sensitivity analysis highlights the benefit in the collection of multi-tracer high-resolution field datasets and the developement of multi-tracer land surface models to provide valuable constraints on photosynthesis and respiration across scales in the near future.
Multiscale Simulation and Modeling of Multilayer Heteroepitactic Growth of C60 on Pentacene.
Acevedo, Yaset M; Cantrell, Rebecca A; Berard, Philip G; Koch, Donald L; Clancy, Paulette
2016-03-29
We apply multiscale methods to describe the strained growth of multiple layers of C60 on a thin film of pentacene. We study this growth in the presence of a monolayer pentacene step to compare our simulations to recent experimental studies by Breuer and Witte of submonolayer growth in the presence of monolayer steps. The molecular-level details of this organic semiconductor interface have ramifications on the macroscale structural and electronic behavior of this system and allow us to describe several unexplained experimental observations for this system. The growth of a C60 thin film on a pentacene surface is complicated by the differing crystal habits of the two component species, leading to heteroepitactical growth. In order to probe this growth, we use three computational methods that offer different approaches to coarse-graining the system and differing degrees of computational efficiency. We present a new, efficient reaction-diffusion continuum model for 2D systems whose results compare well with mesoscale kinetic Monte Carlo (KMC) results for submonolayer growth. KMC extends our ability to simulate multiple layers but requires a library of predefined rates for event transitions. Coarse-grained molecular dynamics (CGMD) circumvents KMC's need for predefined lattices, allowing defects and grain boundaries to provide a more realistic thin film morphology. For multilayer growth, in this particularly suitable candidate for coarse-graining, CGMD is a preferable approach to KMC. Combining the results from these three methods, we show that the lattice strain induced by heteroepitactical growth promotes 3D growth and the creation of defects in the first monolayer. The CGMD results are consistent with experimental results on the same system by Conrad et al. and by Breuer and Witte in which C60 aggregates change from a 2D structure at low temperature to 3D clusters along the pentacene step edges at higher temperatures.
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
A multiphase interfacial model for the dissolution of spent nuclear fuel
Energy Technology Data Exchange (ETDEWEB)
Jerden, James L., E-mail: jerden@anl.gov [Argonne National Laboratory, 9700 South Cass Ave., Argonne, IL 60439 (United States); Frey, Kurt [University of Notre Dame, Notre Dame, IN 46556 (United States); Ebert, William [Argonne National Laboratory, 9700 South Cass Ave., Argonne, IL 60439 (United States)
2015-07-15
Highlights: • This model accounts for chemistry, temperature, radiolysis, U(VI) minerals, and hydrogen effect. • The hydrogen effect dominates processes determining spent fuel dissolution rate. • The hydrogen effect protects uranium oxide spent fuel from oxidative dissolution. - Abstract: The Fuel Matrix Dissolution Model (FMDM) is an electrochemical reaction/diffusion model for the dissolution of spent uranium oxide fuel. The model was developed to provide radionuclide source terms for use in performance assessment calculations for various types of geologic repositories. It is based on mixed potential theory and consists of a two-phase fuel surface made up of UO{sub 2} and a noble metal bearing fission product phase in contact with groundwater. The corrosion potential at the surface of the dissolving fuel is calculated by balancing cathodic and anodic reactions occurring at the solution interfaces with UO{sub 2} and NMP surfaces. Dissolved oxygen and hydrogen peroxide generated by radiolysis of the groundwater are the major oxidizing agents that promote fuel dissolution. Several reactions occurring on noble metal alloy surfaces are electrically coupled to the UO{sub 2} and can catalyze or inhibit oxidative dissolution of the fuel. The most important of these is the oxidation of hydrogen, which counteracts the effects of oxidants (primarily H{sub 2}O{sub 2} and O{sub 2}). Inclusion of this reaction greatly decreases the oxidation of U(IV) and slows fuel dissolution significantly. In addition to radiolytic hydrogen, large quantities of hydrogen can be produced by the anoxic corrosion of steel structures within and near the fuel waste package. The model accurately predicts key experimental trends seen in literature data, the most important being the dramatic depression of the fuel dissolution rate by the presence of dissolved hydrogen at even relatively low concentrations (e.g., less than 1 mM). This hydrogen effect counteracts oxidation reactions and can limit
Directory of Open Access Journals (Sweden)
Mark P Little
2009-10-01
Full Text Available Atherosclerosis is the main cause of coronary heart disease and stroke, the two major causes of death in developed society. There is emerging evidence of excess risk of cardiovascular disease at low radiation doses in various occupationally exposed groups receiving small daily radiation doses. Assuming that they are causal, the mechanisms for effects of chronic fractionated radiation exposures on cardiovascular disease are unclear. We outline a spatial reaction-diffusion model for atherosclerosis and perform stability analysis, based wherever possible on human data. We show that a predicted consequence of multiple small radiation doses is to cause mean chemo-attractant (MCP-1 concentration to increase linearly with cumulative dose. The main driver for the increase in MCP-1 is monocyte death, and consequent reduction in MCP-1 degradation. The radiation-induced risks predicted by the model are quantitatively consistent with those observed in a number of occupationally-exposed groups. The changes in equilibrium MCP-1 concentrations with low density lipoprotein cholesterol concentration are also consistent with experimental and epidemiologic data. This proposed mechanism would be experimentally testable. If true, it also has substantive implications for radiological protection, which at present does not take cardiovascular disease into account. The Japanese A-bomb survivor data implies that cardiovascular disease and cancer mortality contribute similarly to radiogenic risk. The major uncertainty in assessing the low-dose risk of cardiovascular disease is the shape of the dose response relationship, which is unclear in the Japanese data. The analysis of the present paper suggests that linear extrapolation would be appropriate for this endpoint.
Andre, B. J.; Rajaram, H.; Silverstein, J.
2010-12-01
Acid mine drainage, AMD, results from the oxidation of metal sulfide minerals (e.g. pyrite), producing ferrous iron and sulfuric acid. Acidophilic autotrophic bacteria such as Acidithiobacillus ferrooxidans and Leptospirillum ferrooxidans obtain energy by oxidizing ferrous iron back to ferric iron, using oxygen as the electron acceptor. Most existing models of AMD do not account for microbial kinetics or iron geochemistry rigorously. Instead they assume that oxygen limitation controls pyrite oxidation and thus focus on oxygen transport. These models have been successfully used for simulating conditions where oxygen availability is a limiting factor (e.g. source prevention by capping), but have not been shown to effectively model acid generation and effluent chemistry under a wider range of conditions. The key reactions, oxidation of pyrite and oxidation of ferrous iron, are both slow kinetic processes. Despite being extensively studied for the last thirty years, there is still not a consensus in the literature about the basic mechanisms, limiting factors or rate expressions for microbially enhanced oxidation of metal sulfides. An indirect leaching mechanism (chemical oxidation of pyrite by ferric iron to produce ferrous iron, with regeneration of ferric iron by microbial oxidation of ferrous iron) is used as the foundation of a conceptual model for microbially enhanced oxidation of pyrite. Using literature data, a rate expression for microbial consumption of ferrous iron is developed that accounts for oxygen, ferrous iron and pH limitation. Reaction rate expressions for oxidation of pyrite and chemical oxidation of ferrous iron are selected from the literature. A completely mixed stirred tank reactor (CSTR) model is implemented coupling the kinetic rate expressions, speciation calculations and flow. The model simulates generation of AMD and effluent chemistry that qualitatively agrees with column reactor and single rock experiments. A one dimensional reaction
Computational Modeling of Fluctuations in Energy and Metabolic Pathways of Methanogenic Archaea
Energy Technology Data Exchange (ETDEWEB)
Luthey-Schulten, Zaida [Univ. of Illinois, Urbana-Champaign, IL (United States). Dept. of Chemistry; Carl R. Woese Inst. for Genomic Biology
2017-01-04
The methanogenic archaea, anaerobic microbes that convert CO2 and H2 and/or other small organic fermentation products into methane, play an unusually large role in the global carbon cycle. As they perform the final step in the anaerobic breakdown of biomass, methanogens are a biogenic source of an estimated one billion tons methane each year. Depending on the location, produced methane can be considered as either a greenhouse gas (agricultural byproduct), sequestered carbon storage (methane hydrate deposits), or a potential energy source (organic wastewater treatment). These microbes therefore represent an important target for biotechnology applications. Computational models of methanogens with predictive power are useful aids in the adaptation of methanogenic systems, but need to connect processes of wide-ranging time and length scales. In this project, we developed several computational methodologies for modeling the dynamic behavior of entire cells that connects stochastic reaction-diffusion dynamics of individual biochemical pathways with genome-scale modeling of metabolic networks. While each of these techniques were in the realm of well-defined computational methods, here we integrated them to develop several entirely new approaches to systems biology. The first scientific aim of the project was to model how noise in a biochemical pathway propagates into cellular phenotypes. Genetic circuits have been optimized by evolution to regulate molecular processes despite stochastic noise, but the effect of such noise on a cellular biochemical networks is currently unknown. An integrated stochastic/systems model of Escherichia coli species was created to analyze how noise in protein expression gives—and therefore noise in metabolic fluxes—gives rise to multiple cellular phenotype in isogenic population. After the initial work developing and validating methods that allow characterization of the heterogeneity in the model organism E. coli, the project shifted toward
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)
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.
International Nuclear Information System (INIS)
Cruz, Roberto de la; Guerrero, Pilar; Calvo, Juan; Alarcón, Tomás
2017-01-01
The development of hybrid methodologies is of current interest in both multi-scale modelling and stochastic reaction–diffusion systems regarding their applications to biology. We formulate a hybrid method for stochastic multi-scale models of cells populations that extends the remit of existing hybrid methods for reaction–diffusion systems. Such method is developed for a stochastic multi-scale model of tumour growth, i.e. population-dynamical models which account for the effects of intrinsic noise affecting both the number of cells and the intracellular dynamics. In order to formulate this method, we develop a coarse-grained approximation for both the full stochastic model and its mean-field limit. Such approximation involves averaging out the age-structure (which accounts for the multi-scale nature of the model) by assuming that the age distribution of the population settles onto equilibrium very fast. We then couple the coarse-grained mean-field model to the full stochastic multi-scale model. By doing so, within the mean-field region, we are neglecting noise in both cell numbers (population) and their birth rates (structure). This implies that, in addition to the issues that arise in stochastic-reaction diffusion systems, we need to account for the age-structure of the population when attempting to couple both descriptions. We exploit our coarse-graining model so that, within the mean-field region, the age-distribution is in equilibrium and we know its explicit form. This allows us to couple both domains consistently, as upon transference of cells from the mean-field to the stochastic region, we sample the equilibrium age distribution. Furthermore, our method allows us to investigate the effects of intracellular noise, i.e. fluctuations of the birth rate, on collective properties such as travelling wave velocity. We show that the combination of population and birth-rate noise gives rise to large fluctuations of the birth rate in the region at the leading edge
DEFF Research Database (Denmark)
Cameron, Ian; Gani, Rafiqul
2011-01-01
This chapter deals with the practicalities of building, testing, deploying and maintaining models. It gives specific advice for each phase of the modelling cycle. To do this, a modelling framework is introduced which covers: problem and model definition; model conceptualization; model data...... requirements; model construction; model solution; model verification; model validation and finally model deployment and maintenance. Within the adopted methodology, each step is discussedthrough the consideration of key issues and questions relevant to the modelling activity. Practical advice, based on many...
Freeman, Thomas J.
This paper discusses six different models of organizational structure and leadership, including the scalar chain or pyramid model, the continuum model, the grid model, the linking pin model, the contingency model, and the circle or democratic model. Each model is examined in a separate section that describes the model and its development, lists…
Pop, Mihaela; Sermesant, Maxime; Liu, Garry; Relan, Jatin; Mansi, Tommaso; Soong, Alan; Peyrat, Jean-Marc; Truong, Michael V; Fefer, Paul; McVeigh, Elliot R; Delingette, Herve; Dick, Alexander J; Ayache, Nicholas; Wright, Graham A
2012-02-01
Cardiac computer models can help us understand and predict the propagation of excitation waves (i.e., action potential, AP) in healthy and pathologic hearts. Our broad aim is to develop accurate 3D MR image-based computer models of electrophysiology in large hearts (translatable to clinical applications) and to validate them experimentally. The specific goals of this paper were to match models with maps of the propagation of optical AP on the epicardial surface using large porcine hearts with scars, estimating several parameters relevant to macroscopic reaction-diffusion electrophysiological models. We used voltage-sensitive dyes to image AP in large porcine hearts with scars (three specimens had chronic myocardial infarct, and three had radiofrequency RF acute scars). We first analyzed the main AP waves' characteristics: duration (APD) and propagation under controlled pacing locations and frequencies as recorded from 2D optical images. We further built 3D MR image-based computer models that have information derived from the optical measures, as well as morphologic MRI data (i.e., myocardial anatomy, fiber directions and scar definition). The scar morphology from MR images was validated against corresponding whole-mount histology. We also compared the measured 3D isochronal maps of depolarization to simulated isochrones (the latter replicating precisely the experimental conditions), performing model customization and 3D volumetric adjustments of the local conductivity. Our results demonstrated that mean APD in the border zone (BZ) of the infarct scars was reduced by ~13% (compared to ~318 ms measured in normal zone, NZ), but APD did not change significantly in the thin BZ of the ablation scars. A generic value for velocity ratio (1:2.7) in healthy myocardial tissue was derived from measured values of transverse and longitudinal conduction velocities relative to fibers direction (22 cm/s and 60 cm/s, respectively). The model customization and 3D volumetric
ten Cate, Jacob M
2015-01-01
Developing experimental models to understand dental caries has been the theme in our research group. Our first, the pH-cycling model, was developed to investigate the chemical reactions in enamel or dentine, which lead to dental caries. It aimed to leverage our understanding of the fluoride mode of action and was also utilized for the formulation of oral care products. In addition, we made use of intra-oral (in situ) models to study other features of the oral environment that drive the de/remineralization balance in individual patients. This model addressed basic questions, such as how enamel and dentine are affected by challenges in the oral cavity, as well as practical issues related to fluoride toothpaste efficacy. The observation that perhaps fluoride is not sufficiently potent to reduce dental caries in the present-day society triggered us to expand our knowledge in the bacterial aetiology of dental caries. For this we developed the Amsterdam Active Attachment biofilm model. Different from studies on planktonic ('single') bacteria, this biofilm model captures bacteria in a habitat similar to dental plaque. With data from the combination of these models, it should be possible to study separate processes which together may lead to dental caries. Also products and novel agents could be evaluated that interfere with either of the processes. Having these separate models in place, a suggestion is made to design computer models to encompass the available information. Models but also role models are of the utmost importance in bringing and guiding research and researchers. 2015 S. Karger AG, Basel
DEFF Research Database (Denmark)
Carlson, Kerstin
The International Criminal Tribunal for the former Yugoslavia (ICTY) was the first and most celebrated of a wave of international criminal tribunals (ICTs) built in the 1990s designed to advance liberalism through international criminal law. Model(ing) Justice examines the case law of the ICTY...
ten Cate, J.M.
2015-01-01
Developing experimental models to understand dental caries has been the theme in our research group. Our first, the pH-cycling model, was developed to investigate the chemical reactions in enamel or dentine, which lead to dental caries. It aimed to leverage our understanding of the fluoride mode of
Modelling SDL, Modelling Languages
Directory of Open Access Journals (Sweden)
Michael Piefel
2007-02-01
Full Text Available Today's software systems are too complex to implement them and model them using only one language. As a result, modern software engineering uses different languages for different levels of abstraction and different system aspects. Thus to handle an increasing number of related or integrated languages is the most challenging task in the development of tools. We use object oriented metamodelling to describe languages. Object orientation allows us to derive abstract reusable concept definitions (concept classes from existing languages. This language definition technique concentrates on semantic abstractions rather than syntactical peculiarities. We present a set of common concept classes that describe structure, behaviour, and data aspects of high-level modelling languages. Our models contain syntax modelling using the OMG MOF as well as static semantic constraints written in OMG OCL. We derive metamodels for subsets of SDL and UML from these common concepts, and we show for parts of these languages that they can be modelled and related to each other through the same abstract concepts.
Directory of Open Access Journals (Sweden)
Shirmohammadi Adel
2006-10-01
binding rate parameters from FRAP data, we propose conducting two FRAP experiments on the same class of macromolecule and cell. One experiment should be used to measure the molecular diffusion coefficient independently of binding in an effective diffusion regime and the other should be conducted in a reaction dominant or reaction-diffusion regime to quantify binding rate parameters. The method described in this paper is likely to be widely used to estimate in-vivo biomolecule mass transport and binding rate parameters.
Anaïs Schaeffer
2012-01-01
By analysing the production of mesons in the forward region of LHC proton-proton collisions, the LHCf collaboration has provided key information needed to calibrate extremely high-energy cosmic ray models. Average transverse momentum (pT) as a function of rapidity loss ∆y. Black dots represent LHCf data and the red diamonds represent SPS experiment UA7 results. The predictions of hadronic interaction models are shown by open boxes (sibyll 2.1), open circles (qgsjet II-03) and open triangles (epos 1.99). Among these models, epos 1.99 shows the best overall agreement with the LHCf data. LHCf is dedicated to the measurement of neutral particles emitted at extremely small angles in the very forward region of LHC collisions. Two imaging calorimeters – Arm1 and Arm2 – take data 140 m either side of the ATLAS interaction point. “The physics goal of this type of analysis is to provide data for calibrating the hadron interaction models – the well-known &...
Association of apolipoprotein M with high-density lipoprotein kinetics in overweight-obese men
DEFF Research Database (Denmark)
Ooi, Esther M M; Watts, Gerald F; Chan, Dick C
2009-01-01
cholesterol and HDL cholesterol (ptriglyceride, NEFA, insulin, glucose, HOMA score or adiponectin concentrations. Plasma apoM was positively associated with both apoA-I and apoA-II concentrations (r=0.406, p...%). The kinetics of HDL apoA-I and apoA-II were measured using intravenous administration of D(3)-leucine, gas chromatography-mass spectrometry and multi-compartmental modeling. RESULTS: Plasma apoM was inversely associated with body mass index and positively associated with plasma total cholesterol, LDL...... apoM and triglycerides were significant, independent predictors of HDL apoA-I FCR (adjusted R(2)=16%, p
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.
Hansen, Maximilian; Scholz, Denis; Froeschmann, Marie-Louise; Schöne, Bernd R.; Spötl, Christoph
2017-08-01
Speleothem stable carbon isotope (δ13C) records provide important paleoclimate and paleo-environmental information. However, the interpretation of these records in terms of past climate or environmental change remains challenging because of various processes affecting the δ13C signals. A process that has only been sparsely discussed so far is carbon isotope exchange between the gaseous CO2 of the cave atmosphere and the dissolved inorganic carbon (DIC) contained in the thin solution film on the speleothem, which may be particularly important for strongly ventilated caves. Here we present a novel, complete reaction diffusion model describing carbon isotope exchange between gaseous CO2 and the DIC in thin solution films. The model considers all parameters affecting carbon isotope exchange, such as diffusion into, out of and within the film, the chemical reactions occurring within the film as well as the dependence of diffusion and the reaction rates on isotopic mass and temperature. To verify the model, we conducted laboratory experiments under completely controlled, cave-analogue conditions at three different temperatures (10, 20, 30 °C). We exposed thin (≈0.1 mm) films of a NaHCO3 solution with four different concentrations (1, 2, 5 and 10 mmol/l, respectively) to a nitrogen atmosphere containing a specific amount of CO2 (1000 and 3000 ppmV). The experimentally observed temporal evolution of the pH and δ13C values of the DIC is in good agreement with the model predictions. The carbon isotope exchange times in our experiments range from ca. 200 to ca. 16,000 s and strongly depend on temperature, film thickness, atmospheric pCO2 and the concentration of DIC. For low pCO2 (between 500 and 1000 ppmV, as for strongly ventilated caves), our time constants are substantially lower than those derived in a previous study, suggesting a potentially stronger influence of carbon isotope exchange on speleothem δ13C values. However, this process should only have an
DEFF Research Database (Denmark)
Larsen, Lars Bjørn; Vesterager, Johan
This report provides an overview of the existing models of global manufacturing, describes the required modelling views and associated methods and identifies tools, which can provide support for this modelling activity.The model adopted for global manufacturing is that of an extended enterprise s...
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)
A.A. Malykh
2017-08-01
Full Text Available In this paper, the concept of locally simple models is considered. Locally simple models are arbitrarily complex models built from relatively simple components. A lot of practically important domains of discourse can be described as locally simple models, for example, business models of enterprises and companies. Up to now, research in human reasoning automation has been mainly concentrated around the most intellectually intensive activities, such as automated theorem proving. On the other hand, the retailer business model is formed from ”jobs”, and each ”job” can be modelled and automated more or less easily. At the same time, the whole retailer model as an integrated system is extremely complex. In this paper, we offer a variant of the mathematical definition of a locally simple model. This definition is intended for modelling a wide range of domains. Therefore, we also must take into account the perceptual and psychological issues. Logic is elitist, and if we want to attract to our models as many people as possible, we need to hide this elitism behind some metaphor, to which ’ordinary’ people are accustomed. As such a metaphor, we use the concept of a document, so our locally simple models are called document models. Document models are built in the paradigm of semantic programming. This allows us to achieve another important goal - to make the documentary models executable. Executable models are models that can act as practical information systems in the described domain of discourse. Thus, if our model is executable, then programming becomes redundant. The direct use of a model, instead of its programming coding, brings important advantages, for example, a drastic cost reduction for development and maintenance. Moreover, since the model is well and sound, and not dissolved within programming modules, we can directly apply AI tools, in particular, machine learning. This significantly expands the possibilities for automation and
Chang, CC
2012-01-01
Model theory deals with a branch of mathematical logic showing connections between a formal language and its interpretations or models. This is the first and most successful textbook in logical model theory. Extensively updated and corrected in 1990 to accommodate developments in model theoretic methods - including classification theory and nonstandard analysis - the third edition added entirely new sections, exercises, and references. Each chapter introduces an individual method and discusses specific applications. Basic methods of constructing models include constants, elementary chains, Sko
Healy, Richard W.; Scanlon, Bridget R.
2010-01-01
Simulation models are widely used in all types of hydrologic studies, and many of these models can be used to estimate recharge. Models can provide important insight into the functioning of hydrologic systems by identifying factors that influence recharge. The predictive capability of models can be used to evaluate how changes in climate, water use, land use, and other factors may affect recharge rates. Most hydrological simulation models, including watershed models and groundwater-flow models, are based on some form of water-budget equation, so the material in this chapter is closely linked to that in Chapter 2. Empirical models that are not based on a water-budget equation have also been used for estimating recharge; these models generally take the form of simple estimation equations that define annual recharge as a function of precipitation and possibly other climatic data or watershed characteristics.Model complexity varies greatly. Some models are simple accounting models; others attempt to accurately represent the physics of water movement through each compartment of the hydrologic system. Some models provide estimates of recharge explicitly; for example, a model based on the Richards equation can simulate water movement from the soil surface through the unsaturated zone to the water table. Recharge estimates can be obtained indirectly from other models. For example, recharge is a parameter in groundwater-flow models that solve for hydraulic head (i.e. groundwater level). Recharge estimates can be obtained through a model calibration process in which recharge and other model parameter values are adjusted so that simulated water levels agree with measured water levels. The simulation that provides the closest agreement is called the best fit, and the recharge value used in that simulation is the model-generated estimate of recharge.
International Nuclear Information System (INIS)
Buchler, J.R.; Gottesman, S.T.; Hunter, J.H. Jr.
1990-01-01
Various papers on galactic models are presented. Individual topics addressed include: observations relating to galactic mass distributions; the structure of the Galaxy; mass distribution in spiral galaxies; rotation curves of spiral galaxies in clusters; grand design, multiple arm, and flocculent spiral galaxies; observations of barred spirals; ringed galaxies; elliptical galaxies; the modal approach to models of galaxies; self-consistent models of spiral galaxies; dynamical models of spiral galaxies; N-body models. Also discussed are: two-component models of galaxies; simulations of cloudy, gaseous galactic disks; numerical experiments on the stability of hot stellar systems; instabilities of slowly rotating galaxies; spiral structure as a recurrent instability; model gas flows in selected barred spiral galaxies; bar shapes and orbital stochasticity; three-dimensional models; polar ring galaxies; dynamical models of polar rings
Model-model Perencanaan Strategik
Amirin, Tatang M
2005-01-01
The process of strategic planning, used to be called as long-term planning, consists of several components, including strategic analysis, setting strategic direction (covering of mission, vision, and values), and action planning. Many writers develop models representing the steps of the strategic planning process, i.e. basic planning model, problem-based planning model, scenario model, and organic or self-organizing model.
DEFF Research Database (Denmark)
Bækgaard, Lars
2001-01-01
The purpose of this chapter is to discuss conceptual event modeling within a context of information modeling. Traditionally, information modeling has been concerned with the modeling of a universe of discourse in terms of information structures. However, most interesting universes of discourse...... are dynamic and we present a modeling approach that can be used to model such dynamics.We characterize events as both information objects and change agents (Bækgaard 1997). When viewed as information objects events are phenomena that can be observed and described. For example, borrow events in a library can...
Stability in a diffusive food chain model with Michaelis-Menten functional response
DEFF Research Database (Denmark)
Lin, Zhigui; Pedersen, Michael
2004-01-01
This paper deals with the behavior of positive solutions to a reaction-diffusion system with homogeneous Neumann boundary conditions describing a three species food chain. A sufficient condition for the local asymptotical stability is given by linearization and also a sufficient condition...... for the global asymptotical stability is given by a Lyapunov function. Our result shows that the equilibrium solution is globally asymptotically stable if the net birth rate of the first species is big enough and the net death rate of the third species is neither too big nor too small. (C) 2004 Elsevier Ltd. All...
Martin, Francois-Pierre J; Wang, Yulan; Sprenger, Norbert; Yap, Ivan K S; Lundstedt, Torbjörn; Lek, Per; Rezzi, Serge; Ramadan, Ziad; van Bladeren, Peter; Fay, Laurent B; Kochhar, Sunil; Lindon, John C; Holmes, Elaine; Nicholson, Jeremy K
2008-01-01
The transgenomic metabolic effects of exposure to either Lactobacillus paracasei or Lactobacillus rhamnosus probiotics have been measured and mapped in humanized extended genome mice (germ-free mice colonized with human baby flora). Statistical analysis of the compartmental fluctuations in diverse metabolic compartments, including biofluids, tissue and cecal short-chain fatty acids (SCFAs) in relation to microbial population modulation generated a novel top-down systems biology view of the host response to probiotic intervention. Probiotic exposure exerted microbiome modification and resulted in altered hepatic lipid metabolism coupled with lowered plasma lipoprotein levels and apparent stimulated glycolysis. Probiotic treatments also altered a diverse range of pathways outcomes, including amino-acid metabolism, methylamines and SCFAs. The novel application of hierarchical-principal component analysis allowed visualization of multicompartmental transgenomic metabolic interactions that could also be resolved at the compartment and pathway level. These integrated system investigations demonstrate the potential of metabolic profiling as a top-down systems biology driver for investigating the mechanistic basis of probiotic action and the therapeutic surveillance of the gut microbial activity related to dietary supplementation of probiotics. PMID:18197175
DEFF Research Database (Denmark)
Ashauer, Roman; Albert, Carlo; Augustine, Starrlight
2016-01-01
The General Unified Threshold model for Survival (GUTS) integrates previously published toxicokinetic-toxicodynamic models and estimates survival with explicitly defined assumptions. Importantly, GUTS accounts for time-variable exposure to the stressor. We performed three studies to test...
DEFF Research Database (Denmark)
Sales-Cruz, Mauricio; Piccolo, Chiara; Heitzig, Martina
2011-01-01
covered, illustrating several models such as the Wilson equation and NRTL equation, along with their solution strategies. A section shows how to use experimental data to regress the property model parameters using a least squares approach. A full model analysis is applied in each example that discusses...... the degrees of freedom, dependent and independent variables and solution strategy. Vapour-liquid and solid-liquid equilibrium is covered, and applications to droplet evaporation and kinetic models are given....
DEFF Research Database (Denmark)
Ravn, Anders P.; Staunstrup, Jørgen
1994-01-01
This paper proposes a model for specifying interfaces between concurrently executing modules of a computing system. The model does not prescribe a particular type of communication protocol and is aimed at describing interfaces between both software and hardware modules or a combination of the two....... The model describes both functional and timing properties of an interface...
Hydrological models are mediating models
Babel, L. V.; Karssenberg, D.
2013-08-01
Despite the increasing role of models in hydrological research and decision-making processes, only few accounts of the nature and function of models exist in hydrology. Earlier considerations have traditionally been conducted while making a clear distinction between physically-based and conceptual models. A new philosophical account, primarily based on the fields of physics and economics, transcends classes of models and scientific disciplines by considering models as "mediators" between theory and observations. The core of this approach lies in identifying models as (1) being only partially dependent on theory and observations, (2) integrating non-deductive elements in their construction, and (3) carrying the role of instruments of scientific enquiry about both theory and the world. The applicability of this approach to hydrology is evaluated in the present article. Three widely used hydrological models, each showing a different degree of apparent physicality, are confronted to the main characteristics of the "mediating models" concept. We argue that irrespective of their kind, hydrological models depend on both theory and observations, rather than merely on one of these two domains. Their construction is additionally involving a large number of miscellaneous, external ingredients, such as past experiences, model objectives, knowledge and preferences of the modeller, as well as hardware and software resources. We show that hydrological models convey the role of instruments in scientific practice by mediating between theory and the world. It results from these considerations that the traditional distinction between physically-based and conceptual models is necessarily too simplistic and refers at best to the stage at which theory and observations are steering model construction. The large variety of ingredients involved in model construction would deserve closer attention, for being rarely explicitly presented in peer-reviewed literature. We believe that devoting
International Nuclear Information System (INIS)
Phillips, C.K.
1985-12-01
This lecture provides a survey of the methods used to model fast magnetosonic wave coupling, propagation, and absorption in tokamaks. The validity and limitations of three distinct types of modelling codes, which will be contrasted, include discrete models which utilize ray tracing techniques, approximate continuous field models based on a parabolic approximation of the wave equation, and full field models derived using finite difference techniques. Inclusion of mode conversion effects in these models and modification of the minority distribution function will also be discussed. The lecture will conclude with a presentation of time-dependent global transport simulations of ICRF-heated tokamak discharges obtained in conjunction with the ICRF modelling codes. 52 refs., 15 figs
Modelling in Business Model design
Simonse, W.L.
2013-01-01
It appears that business model design might not always produce a design or model as the expected result. However when designers are involved, a visual model or artefact is produced. To assist strategic managers in thinking about how they can act, the designers challenge is to combine strategy and
DEWIT, R; VANDENENDE, FP; VANGEMERDEN, H
A deterministic one-dimensional reaction diffusion model was constructed to simulate benthic stratification patterns and population dynamics of cyanobacteria, purple and colorless sulfur bacteria as found in marine microbial mats. The model involves the major biogeochemical processes of the sulfur
Finite Element Methods On Very Large, Dynamic Tubular Grid Encoded Implicit Surfaces
DEFF Research Database (Denmark)
Nemitz, Oliver; Nielsen, Michael Bang; Rumpf, Martin
2009-01-01
dynamic tubular grid encoding format for a narrow band. A reaction diffusion model on a fixed surface and surface evolution driven by a nonlinear geometric diffusion approach, by isotropic or truly anisotropic curvature motion, are investigated as characteristic model problems. The proposed methods...
International Nuclear Information System (INIS)
Michel, F.C.
1989-01-01
Three existing eclipse models for the PSR 1957 + 20 pulsar are discussed in terms of their requirements and the information they yield about the pulsar wind: the interacting wind from a companion model, the magnetosphere model, and the occulting disk model. It is shown out that the wind model requires an MHD wind from the pulsar, with enough particles that the Poynting flux of the wind can be thermalized; in this model, a large flux of energetic radiation from the pulsar is required to accompany the wind and drive the wind off the companion. The magnetosphere model requires an EM wind, which is Poynting flux dominated; the advantage of this model over the wind model is that the plasma density inside the magnetosphere can be orders of magnitude larger than in a magnetospheric tail blown back by wind interaction. The occulting disk model also requires an EM wind so that the interaction would be pushed down onto the companion surface, minimizing direct interaction of the wind with the orbiting macroscopic particles
International Nuclear Information System (INIS)
Yang, H.
1999-01-01
The purpose of this analysis and model report (AMR) for the Ventilation Model is to analyze the effects of pre-closure continuous ventilation in the Engineered Barrier System (EBS) emplacement drifts and provide heat removal data to support EBS design. It will also provide input data (initial conditions, and time varying boundary conditions) for the EBS post-closure performance assessment and the EBS Water Distribution and Removal Process Model. The objective of the analysis is to develop, describe, and apply calculation methods and models that can be used to predict thermal conditions within emplacement drifts under forced ventilation during the pre-closure period. The scope of this analysis includes: (1) Provide a general description of effects and heat transfer process of emplacement drift ventilation. (2) Develop a modeling approach to simulate the impacts of pre-closure ventilation on the thermal conditions in emplacement drifts. (3) Identify and document inputs to be used for modeling emplacement ventilation. (4) Perform calculations of temperatures and heat removal in the emplacement drift. (5) Address general considerations of the effect of water/moisture removal by ventilation on the repository thermal conditions. The numerical modeling in this document will be limited to heat-only modeling and calculations. Only a preliminary assessment of the heat/moisture ventilation effects and modeling method will be performed in this revision. Modeling of moisture effects on heat removal and emplacement drift temperature may be performed in the future
DEFF Research Database (Denmark)
Blomhøj, Morten
2004-01-01
Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical...... roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical...... modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive...
2016-01-01
This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.
Bottle, Neil
2013-01-01
The Model : making exhibition was curated by Brian Kennedy in collaboration with Allies & Morrison in September 2013. For the London Design Festival, the Model : making exhibition looked at the increased use of new technologies by both craft-makers and architectural model makers. In both practices traditional ways of making by hand are increasingly being combined with the latest technologies of digital imaging, laser cutting, CNC machining and 3D printing. This exhibition focussed on ...
International Nuclear Information System (INIS)
Frampton, Paul H.
1998-01-01
In this talk I begin with some general discussion of model building in particle theory, emphasizing the need for motivation and testability. Three illustrative examples are then described. The first is the Left-Right model which provides an explanation for the chirality of quarks and leptons. The second is the 331-model which offers a first step to understanding the three generations of quarks and leptons. Third and last is the SU(15) model which can accommodate the light leptoquarks possibly seen at HERA
International Nuclear Information System (INIS)
Frampton, P.H.
1998-01-01
In this talk I begin with some general discussion of model building in particle theory, emphasizing the need for motivation and testability. Three illustrative examples are then described. The first is the Left-Right model which provides an explanation for the chirality of quarks and leptons. The second is the 331-model which offers a first step to understanding the three generations of quarks and leptons. Third and last is the SU(15) model which can accommodate the light leptoquarks possibly seen at HERA. copyright 1998 American Institute of Physics
Modeling Documents with Event Model
Directory of Open Access Journals (Sweden)
Longhui Wang
2015-08-01
Full Text Available Currently deep learning has made great breakthroughs in visual and speech processing, mainly because it draws lessons from the hierarchical mode that brain deals with images and speech. In the field of NLP, a topic model is one of the important ways for modeling documents. Topic models are built on a generative model that clearly does not match the way humans write. In this paper, we propose Event Model, which is unsupervised and based on the language processing mechanism of neurolinguistics, to model documents. In Event Model, documents are descriptions of concrete or abstract events seen, heard, or sensed by people and words are objects in the events. Event Model has two stages: word learning and dimensionality reduction. Word learning is to learn semantics of words based on deep learning. Dimensionality reduction is the process that representing a document as a low dimensional vector by a linear mode that is completely different from topic models. Event Model achieves state-of-the-art results on document retrieval tasks.
DEFF Research Database (Denmark)
Gøtze, Jens Peter; Krentz, Andrew
2014-01-01
In this issue of Cardiovascular Endocrinology, we are proud to present a broad and dedicated spectrum of reviews on animal models in cardiovascular disease. The reviews cover most aspects of animal models in science from basic differences and similarities between small animals and the human...
Jongerden, M.R.; Haverkort, Boudewijn R.H.M.
2008-01-01
The use of mobile devices is often limited by the capacity of the employed batteries. The battery lifetime determines how long one can use a device. Battery modeling can help to predict, and possibly extend this lifetime. Many different battery models have been developed over the years. However,
DEFF Research Database (Denmark)
Højgaard, Tomas; Hansen, Rune
The purpose of this paper is to introduce Didactical Modelling as a research methodology in mathematics education. We compare the methodology with other approaches and argue that Didactical Modelling has its own specificity. We discuss the methodological “why” and explain why we find it useful...
Kempen, van A.; Kok, H.; Wagter, H.
1992-01-01
In Computer Aided Drafting three groups of three-dimensional geometric modelling can be recognized: wire frame, surface and solid modelling. One of the methods to describe a solid is by using a boundary based representation. The topology of the surface of a solid is the adjacency information between
Poortman, Sybilla; Sloep, Peter
2006-01-01
Educational models describes a case study on a complex learning object. Possibilities are investigated for using this learning object, which is based on a particular educational model, outside of its original context. Furthermore, this study provides advice that might lead to an increase in
International Nuclear Information System (INIS)
V. Chipman
2002-01-01
The purpose of the Ventilation Model is to simulate the heat transfer processes in and around waste emplacement drifts during periods of forced ventilation. The model evaluates the effects of emplacement drift ventilation on the thermal conditions in the emplacement drifts and surrounding rock mass, and calculates the heat removal by ventilation as a measure of the viability of ventilation to delay the onset of peak repository temperature and reduce its magnitude. The heat removal by ventilation is temporally and spatially dependent, and is expressed as the fraction of heat carried away by the ventilation air compared to the fraction of heat produced by radionuclide decay. One minus the heat removal is called the wall heat fraction, or the remaining amount of heat that is transferred via conduction to the surrounding rock mass. Downstream models, such as the ''Multiscale Thermohydrologic Model'' (BSC 2001), use the wall heat fractions as outputted from the Ventilation Model to initialize their postclosure analyses
DEFF Research Database (Denmark)
Kindler, Ekkart
2009-01-01
, these notations have been extended in order to increase expressiveness and to be more competitive. This resulted in an increasing number of notations and formalisms for modelling business processes and in an increase of the different modelling constructs provided by modelling notations, which makes it difficult......There are many different notations and formalisms for modelling business processes and workflows. These notations and formalisms have been introduced with different purposes and objectives. Later, influenced by other notations, comparisons with other tools, or by standardization efforts...... to compare modelling notations and to make transformations between them. One of the reasons is that, in each notation, the new concepts are introduced in a different way by extending the already existing constructs. In this chapter, we go the opposite direction: We show that it is possible to add most...
Directory of Open Access Journals (Sweden)
P. Grimaldi
2012-07-01
Full Text Available These mandatory guidelines are provided for preparation of papers accepted for publication in the series of Volumes of The The stereometric modelling means modelling achieved with : – the use of a pair of virtual cameras, with parallel axes and positioned at a mutual distance average of 1/10 of the distance camera-object (in practice the realization and use of a stereometric camera in the modeling program; – the shot visualization in two distinct windows – the stereoscopic viewing of the shot while modelling. Since the definition of "3D vision" is inaccurately referred to as the simple perspective of an object, it is required to add the word stereo so that "3D stereo vision " shall stand for "three-dimensional view" and ,therefore, measure the width, height and depth of the surveyed image. Thanks to the development of a stereo metric model , either real or virtual, through the "materialization", either real or virtual, of the optical-stereo metric model made visible with a stereoscope. It is feasible a continuous on line updating of the cultural heritage with the help of photogrammetry and stereometric modelling. The catalogue of the Architectonic Photogrammetry Laboratory of Politecnico di Bari is available on line at: http://rappresentazione.stereofot.it:591/StereoFot/FMPro?-db=StereoFot.fp5&-lay=Scheda&-format=cerca.htm&-view
Modeling complexes of modeled proteins.
Anishchenko, Ivan; Kundrotas, Petras J; Vakser, Ilya A
2017-03-01
Structural characterization of proteins is essential for understanding life processes at the molecular level. However, only a fraction of known proteins have experimentally determined structures. This fraction is even smaller for protein-protein complexes. Thus, structural modeling of protein-protein interactions (docking) primarily has to rely on modeled structures of the individual proteins, which typically are less accurate than the experimentally determined ones. Such "double" modeling is the Grand Challenge of structural reconstruction of the interactome. Yet it remains so far largely untested in a systematic way. We present a comprehensive validation of template-based and free docking on a set of 165 complexes, where each protein model has six levels of structural accuracy, from 1 to 6 Å C α RMSD. Many template-based docking predictions fall into acceptable quality category, according to the CAPRI criteria, even for highly inaccurate proteins (5-6 Å RMSD), although the number of such models (and, consequently, the docking success rate) drops significantly for models with RMSD > 4 Å. The results show that the existing docking methodologies can be successfully applied to protein models with a broad range of structural accuracy, and the template-based docking is much less sensitive to inaccuracies of protein models than the free docking. Proteins 2017; 85:470-478. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.
DEFF Research Database (Denmark)
Kreiner, Svend; Christensen, Karl Bang
Rasch models; Partial Credit models; Rating Scale models; Item bias; Differential item functioning; Local independence; Graphical models......Rasch models; Partial Credit models; Rating Scale models; Item bias; Differential item functioning; Local independence; Graphical models...