Parametric spatiotemporal oscillation in reaction-diffusion systems.

Science.gov (United States)

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.

Decay to Equilibrium for Energy-Reaction-Diffusion Systems

KAUST Repository

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

KAUST Repository

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.

Delay-induced wave instabilities in single-species reaction-diffusion systems

Science.gov (United States)

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.

Long-Time Dynamic Response and Stochastic Resonance of Subdiffusive Overdamped Bistable Fractional Fokker-Planck Systems

International Nuclear Information System (INIS)

Yan-Mei, Kang; Yao-Lin, Jiang

2008-01-01

To explore the influence of anomalous diffusion on stochastic resonance (SR) more deeply and effectively, the method of moments is extended to subdiffusive overdamped bistable fractional Fokker-Planck systems for calculating the long-time linear dynamic response. It is found that the method of moments attains high accuracy with the truncation order N = 10, and in normal diffusion such obtained spectral amplification factor (SAF) of the first-order harmonic is also confirmed by stochastic simulation. Observing the SAF of the odd-order harmonics we find some interesting results, i.e. for smaller driving frequency the decrease of sub diffusion exponent inhibits the stochastic resonance (SR), while for larger driving frequency the decrease of sub diffusion exponent enhances the second SR peak, but the first one vanishes and a double SR is induced in the third-order harmonic at the same time. These observations suggest that the anomalous diffusion has important influence on the bistable dynamics

Splitting Schemes & Segregation In Reaction-(Cross-)Diffusion Systems

OpenAIRE

Carrillo, José A.; Fagioli, Simone; Santambrogio, Filippo; Schmidtchen, Markus

2017-01-01

One of the most fascinating phenomena observed in reaction-diffusion systems is the emergence of segregated solutions, i.e. population densities with disjoint supports. We analyse such a reaction cross-diffusion system. In order to prove existence of weak solutions for a wide class of initial data without restriction about their supports or their positivity, we propose a variational splitting scheme combining ODEs with methods from optimal transport. In addition, this approach allows us to pr...

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...

Bifurcation of positive solutions to scalar reaction-diffusion equations with nonlinear boundary condition

Science.gov (United States)

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.

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.

Nonlinear reaction-diffusion systems conditional symmetry, exact solutions and their applications in biology

CERN Document Server

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,...

Temporal cross-correlation asymmetry and departure from equilibrium in a bistable chemical system.

Science.gov (United States)

Bianca, C; Lemarchand, A

2014-06-14

This paper aims at determining sustained reaction fluxes in a nonlinear chemical system driven in a nonequilibrium steady state. The method relies on the computation of cross-correlation functions for the internal fluctuations of chemical species concentrations. By employing Langevin-type equations, we derive approximate analytical formulas for the cross-correlation functions associated with nonlinear dynamics. Kinetic Monte Carlo simulations of the chemical master equation are performed in order to check the validity of the Langevin equations for a bistable chemical system. The two approaches are found in excellent agreement, except for critical parameter values where the bifurcation between monostability and bistability occurs. From the theoretical point of view, the results imply that the behavior of cross-correlation functions cannot be exploited to measure sustained reaction fluxes in a specific nonlinear system without the prior knowledge of the associated chemical mechanism and the rate constants.

Reaction-diffusion systems in intracellular molecular transport and control.

Science.gov (United States)

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.

Estimation and prediction of convection-diffusion-reaction systems from point measurement

NARCIS (Netherlands)

Vries, D.

2008-01-01

Different procedures with respect to estimation and prediction of systems characterized by convection, diffusion and reactions on the basis of point measurement data, have been studied. Two applications of these convection-diffusion-reaction (CDR) systems have been used as a case study of the

Pacemaker-driven stochastic resonance on diffusive and complex networks of bistable oscillators

Energy Technology Data Exchange (ETDEWEB)

Perc, Matjaz; Gosak, Marko [Department of Physics, Faculty of Natural Sciences and Mathematics, University of Maribor, Koroska cesta 160, SI-2000 Maribor (Slovenia)], E-mail: matjaz.perc@uni-mb.si

2008-05-15

We study the phenomenon of stochastic resonance on diffusive, small-world and scale-free networks consisting of bistable overdamped oscillators. Important thereby is the fact that the external subthreshold periodic forcing is introduced only to a single oscillator of the network. Hence, the forcing acts as a pacemaker trying to impose its rhythm on the whole network through the unit to which it is introduced. Without the addition of additive spatiotemporal noise, however, the whole network, including the unit that is directly exposed to the pacemaker, remains trapped forever in one of the two stable steady states of the local dynamics. We show that the correlation between the frequency of subthreshold pacemaker activity and the response of the network is resonantly dependent on the intensity of additive noise. The reported pacemaker-driven stochastic resonance depends most significantly on the coupling strength and the underlying network structure. Namely, the outreach of the pacemaker obeys the classic diffusion law in the case of nearest-neighbor interactions, thus being proportional to the square root of the coupling strength, whereas it becomes superdiffusive by an appropriate small-world or scale-free topology of the interaction network. In particular, the scale-free topology is identified as being optimal for the dissemination of localized rhythmic activity across the whole network. Also, we show that the ratio between the clustering coefficient and the characteristic path length is the crucial quantity defining the ability of a small-world network to facilitate the outreach of the pacemaker-emitted subthreshold rhythm. We additionally confirm these findings by using the FitzHugh-Nagumo excitable system as an alternative to the bistable overdamped oscillator.

Pacemaker-driven stochastic resonance on diffusive and complex networks of bistable oscillators

International Nuclear Information System (INIS)

Perc, Matjaz; Gosak, Marko

2008-01-01

We study the phenomenon of stochastic resonance on diffusive, small-world and scale-free networks consisting of bistable overdamped oscillators. Important thereby is the fact that the external subthreshold periodic forcing is introduced only to a single oscillator of the network. Hence, the forcing acts as a pacemaker trying to impose its rhythm on the whole network through the unit to which it is introduced. Without the addition of additive spatiotemporal noise, however, the whole network, including the unit that is directly exposed to the pacemaker, remains trapped forever in one of the two stable steady states of the local dynamics. We show that the correlation between the frequency of subthreshold pacemaker activity and the response of the network is resonantly dependent on the intensity of additive noise. The reported pacemaker-driven stochastic resonance depends most significantly on the coupling strength and the underlying network structure. Namely, the outreach of the pacemaker obeys the classic diffusion law in the case of nearest-neighbor interactions, thus being proportional to the square root of the coupling strength, whereas it becomes superdiffusive by an appropriate small-world or scale-free topology of the interaction network. In particular, the scale-free topology is identified as being optimal for the dissemination of localized rhythmic activity across the whole network. Also, we show that the ratio between the clustering coefficient and the characteristic path length is the crucial quantity defining the ability of a small-world network to facilitate the outreach of the pacemaker-emitted subthreshold rhythm. We additionally confirm these findings by using the FitzHugh-Nagumo excitable system as an alternative to the bistable overdamped oscillator

Chaos in a new bistable rotating electromechanical system

International Nuclear Information System (INIS)

Tsapla Fotsa, R.; Woafo, P.

2016-01-01

Highlights: • A new electromechanical system with rotating arm and bistable potential energy is studied. • The bistability is generated by the interaction of three permanent magnets, one fixed at the end of the arm and two other fixed at equal distance relative to the central position of the arm. • It exhibits dissipative and Hamiltonian chaos. • Such a bistable electromechanical system can be used as the actuation part of chaotic sieves and mixers. - Abstract: A device consisting of an induction motor activating a rotating rigid arm is designed and comprises a bistable potential due to the presence of three permanent magnets. Its mathematical equations are established and the numerical results both in the absence and in the presence of magnets are compared. The generation of chaotic behavior is achieved using two different external excitations: sinewave and square wave. In the presence of magnets, the system presents periodic and dissipative chaotic dynamics. Approximating the global potential energy to a bistable quartic potential, the Melnikov method is used to derive the conditions for the appearance of Hamiltonian chaos. Such a device can be used for industrial and domestic applications for mixing and sieving activities.

The entropy dissipation method for spatially inhomogeneous reaction-diffusion-type systems

KAUST Repository

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.

Bistable microvalve and microcatheter system

Science.gov (United States)

Seward, Kirk Patrick

2003-05-20

A bistable microvalve of shape memory material is operatively connected to a microcatheter. The bistable microvalve includes a tip that can be closed off until it is in the desired position. Once it is in position it can opened and closed. The system uses heat and pressure to open and close the microvalve. The shape memory material will change stiffness and shape when heated above a transition temperature. The shape memory material is adapted to move from a first shape to a second shape, either open or closed, where it can perform a desired function.

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.

Bifurcation of transition paths induced by coupled bistable systems.

Science.gov (United States)

Tian, Chengzhe; Mitarai, Namiko

2016-06-07

We discuss the transition paths in a coupled bistable system consisting of interacting multiple identical bistable motifs. We propose a simple model of coupled bistable gene circuits as an example and show that its transition paths are bifurcating. We then derive a criterion to predict the bifurcation of transition paths in a generalized coupled bistable system. We confirm the validity of the theory for the example system by numerical simulation. We also demonstrate in the example system that, if the steady states of individual gene circuits are not changed by the coupling, the bifurcation pattern is not dependent on the number of gene circuits. We further show that the transition rate exponentially decreases with the number of gene circuits when the transition path does not bifurcate, while a bifurcation facilitates the transition by lowering the quasi-potential energy barrier.

An incomplete assembly with thresholding algorithm for systems of reaction-diffusion equations in three space dimensions IAT for reaction-diffusion systems

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

Turing Patterns in a Reaction-Diffusion System

International Nuclear Information System (INIS)

Wu Yanning; Wang Pingjian; Hou Chunju; Liu Changsong; Zhu Zhengang

2006-01-01

We have further investigated Turing patterns in a reaction-diffusion system by theoretical analysis and numerical simulations. Simple Turing patterns and complex superlattice structures are observed. We find that the shape and type of Turing patterns depend on dynamical parameters and external periodic forcing, and is independent of effective diffusivity rate σ in the Lengyel-Epstein model. Our numerical results provide additional insight into understanding the mechanism of development of Turing patterns and predicting new pattern formations.

A bistable switch in dynamic thiodepsipeptide folding and template-directed ligation.

Science.gov (United States)

Mukherjee, Rakesh; Cohen-Luria, Rivka; Wagner, Nathaniel; Ashkenasy, Gonen

2015-10-12

Bistable reaction networks provide living cells with chemically controlled mechanisms for long-term memory storage. Such networks are also often switchable and can be flipped from one state to the other. We target here a major challenge in systems chemistry research, namely developing synthetic, non-enzymatic, networks that mimic such a complex function. Therefore, we describe a dynamic network that depending on initial thiodepsipeptide concentrations leads to one of two distinct steady states. This bistable system is readily switched by applying the appropriate stimuli. The relationship between the reaction network topology and its capacity to invoke bistability is then analyzed by control experiments and theory. We suggest that demonstrating bistable behavior using synthetic networks further highlights their possible role in early evolution, and may shine light on potential utility for novel applications, such as chemical memories. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Evaluation of bistable systems versus matched filters in detecting bipolar pulse signals

OpenAIRE

Duan, Fabing; Abbott, Derek; Gao, Qisheng

2004-01-01

This paper presents a thorough evaluation of a bistable system versus a matched filter in detecting bipolar pulse signals. The detectability of the bistable system can be optimized by adding noise, i.e. the stochastic resonance (SR) phenomenon. This SR effect is also demonstrated by approximate statistical detection theory of the bistable system and corresponding numerical simulations. Furthermore, the performance comparison results between the bistable system and the matched filter show that...

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

Rethinking pattern formation in reaction-diffusion systems

Science.gov (United States)

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.

Diffusive instabilities in hyperbolic reaction-diffusion equations

Science.gov (United States)

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.

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

Stochastic modeling and simulation of reaction-diffusion system with Hill function dynamics.

Science.gov (United States)

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.

Distribution in flowing reaction-diffusion systems

KAUST Repository

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

KAUST Repository

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.

The entropy dissipation method for spatially inhomogeneous reaction-diffusion-type systems

KAUST Repository

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

Control of transversal instabilities in reaction-diffusion systems

Science.gov (United States)

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.

A minimal model of burst-noise induced bistability.

Directory of Open Access Journals (Sweden)

Johannes Falk

Full Text Available We investigate the influence of intrinsic noise on stable states of a one-dimensional dynamical system that shows in its deterministic version a saddle-node bifurcation between monostable and bistable behaviour. The system is a modified version of the Schlögl model, which is a chemical reaction system with only one type of molecule. The strength of the intrinsic noise is varied without changing the deterministic description by introducing bursts in the autocatalytic production step. We study the transitions between monostable and bistable behavior in this system by evaluating the number of maxima of the stationary probability distribution. We find that changing the size of bursts can destroy and even induce saddle-node bifurcations. This means that a bursty production of molecules can qualitatively change the dynamics of a chemical reaction system even when the deterministic description remains unchanged.

Bistable dynamics of a levitated nanoparticle (Presentation Recording)

Science.gov (United States)

Ricci, Francesco; Spasenovic, M.; Rica, Raúl A.; Novotny, Lukas; Quidant, Romain

2015-08-01

Bistable systems are ubiquitous in nature. Classical examples in chemistry and biology include relaxation kinetics in chemical reactions [1] and stochastic resonance processes such as neuron firing [2,3]. Likewise, bistable systems play a key role in signal processing and information handling at the nanoscale, giving rise to intriguing applications such as optical switches [4], coherent signal amplification [5,6] and weak forces detection [5]. The interest and applicability of bistable systems are intimately connected with the complexity of their dynamics, typically due to the presence of a large number of parameters and nonlinearities. Appropriate modeling is therefore challenging. Alternatively, the possibility to experimentally recreate bistable systems in a clean and controlled way has recently become very appealing, but elusive and complicated. With this aim, we combined optical tweezers with a novel active feedback-cooling scheme to develop a well-defined opto-mechanical platform reaching unprecedented performances in terms of Q-factor, frequency stability and force sensitivity [7,8]. Our experimental system consists of a single nanoparticle levitated in high vacuum with optical tweezers, which behaves as a non-linear (Duffing) oscillator under appropriate conditions. Here, we prove it to be an ideal tool for a deep study of bistability. We demonstrate bistability of the nanoparticle by noise activated switching between two oscillation states, discussing our results in terms of a double-well potential model. We also show the flexibility of our system in shaping the potential at will, in order to meet the conditions prescribed by any bistable system that could therefore then be simulated with our setup. References [1] T. Amemiya, T. Ohmori, M. Nakaiwa, T. Yamamoto, and T. Yamaguchi, "Modeling of Nonlinear Chemical Reaction Systems and Two-Parameter Stochastic Resonance," J. Biol. Phys. 25 (1999) 73 [2] F. Moss, L. M. Ward, and W. G. Sannita, "Stochastic

Analytic descriptions of stochastic bistable systems under force ramp.

Science.gov (United States)

Friddle, Raymond W

2016-05-01

Solving the two-state master equation with time-dependent rates, the ubiquitous driven bistable system, is a long-standing problem that does not permit a complete solution for all driving rates. Here we show an accurate approximation to this problem by considering the system in the control parameter regime. The results are immediately applicable to a diverse range of bistable systems including single-molecule mechanics.

Diffusion-controlled reaction. V. Effect of concentration-dependent diffusion coefficient on reaction rate in graft polymerization

International Nuclear Information System (INIS)

Imre, K.; Odian, G.

1979-01-01

The effect of diffusion on radiation-initiated graft polymerization has been studied with emphasis on the single- and two-penetrant cases. When the physical properties of the penetrants are similar, the two-penetrant problems can be reduced to the single-penetrant problem by redefining the characteristic parameters of the system. The diffusion-free graft polymerization rate is assumed to be proportional to the upsilon power of the monomer concentration respectively, and, in which the proportionality constant a = k/sub p/R/sub i//sup w//k/sub t//sup z/, where k/sub p/ and k/sub t/ are the propagation and termination rate constants, respectively, and R/sub i/ is the initiation rate. The values of upsilon, w, and z depend on the particular reaction system. The results of earlier work were generalized by allowing a non-Fickian diffusion rate which predicts an essentially exponential dependence on the monomer concentration of the diffusion coefficient, D = D 0 [exp(deltaC/M)], where M is the saturation concentration. A reaction system is characterized by the three dimensionless parameters, upsilon, delta, and A = (L/2)[aM/sup (upsilon--1)//D 0 ]/sup 1/2/, where L is the polymer film thickness. Graft polymerization tends to become diffusion controlled as A increases. Larger values of delta and ν cause a reaction system to behave closer to the diffusion-free regime. Transition from diffusion-free to diffusion-controlled reaction involves changes in the dependence of the reaction rate on film thickness, initiation rate, and monomer concentration. Although the diffusion-free rate is w order in initiation rate, upsilon order in monomer, and independent of film thickness, the diffusion-controlled rate is w/2 order in initiator rate and inverse first-order in film thickness. Dependence of the diffusion-controlled rate on monomer is dependent in a complex manner on the diffusional characteristics of the reaction system. 11 figures, 4 tables

Analysis of diffusivity of the oscillating reaction components in a microreactor system

Directory of Open Access Journals (Sweden)

Martina Šafranko

2017-01-01

Full Text Available When performing oscillating reactions, periodical changes in the concentrations of reactants, intermediaries, and products take place. Due to the mentioned periodical changes of the concentrations, the information about the diffusivity of the components included into oscillating reactions is very important for the control of the oscillating reactions. Non-linear dynamics makes oscillating reactions very interesting for analysis in different reactor systems. In this paper, the analysis of diffusivity of the oscillating reaction components was performed in a microreactor, with the aim of identifying the limiting component. The geometry of the microreactor microchannel and a well defined flow profile ensure optimal conditions for the diffusion phenomena analysis, because diffusion profiles in a microreactor depend only on the residence time. In this paper, the analysis of diffusivity of the oscillating reaction components was performed in a microreactor equipped with 2 Y-shape inlets and 2 Y-shape outlets, with active volume of V = 4 μL at different residence times.

The role of fluctuations in bistability and oscillations during the H{sub 2} + O{sub 2} reaction on nanosized rhodium crystals

Energy Technology Data Exchange (ETDEWEB)

Grosfils, P.; Gaspard, P. [Center for Nonlinear Phenomena and Complex Systems (CENOLI), Université libre de Bruxelles (ULB), Campus Plaine Code Postal 231, B-1050 Brussels (Belgium); Visart de Bocarmé, T. [Center for Nonlinear Phenomena and Complex Systems (CENOLI) and Chemical Physics of Materials—Catalysis and Tribology, Université libre de Bruxelles (ULB), Campus Plaine Code Postal 243, B-1050 Brussels (Belgium)

2015-08-14

A combined experimental and theoretical study is presented of fluctuations observed by field ion microscopy in the catalytic reaction of water production on a rhodium tip. A stochastic approach is developed to provide a comprehensive understanding of the different phenomena observed in the experiment, including burst noise manifesting itself in a bistability regime, noisy oscillations, and nanopatterns with a cross-like oxidized zone separating the surface into four quadrants centered on the (111) facets. The study is based on a stochastic model numerically simulating the processes of adsorption, desorption, reaction, and transport. The surface diffusion of hydrogen is described as a percolation process dominated by large clusters corresponding to the four quadrants. The model reproduces the observed phenomena in the ranges of temperature, pressures, and electric field of the experiment.

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

Optimization of Bistable Viscoelastic Systems

DEFF Research Database (Denmark)

Jensen, Kristian Ejlebjærg; Szabo, Peter; Okkels, Fridolin

2014-01-01

driving pressure corresponding to the point of bistability, such that the effect is enhanced. The point of bistability is, however, not explicitly contained in the solution, so we opt for a heuristic approach based on the dissipation ratio between the asymmetric and unstable symmetric flow solutions. We...... find a design that significantly reduces the driving pressure required for bistability, and furthermore is in agreement with the approach followed by experimental researchers. Furthermore, by comparing the two asymmetric solutions, we succesfully apply the same approach to a problem with two fluids...

Asymmetric Effects on Escape Rates of Bistable System

International Nuclear Information System (INIS)

Wang Canjun; Mei Dongcheng; Dai Zucheng

2011-01-01

The asymmetric effects on the escape rates from the stable states x ± in the bistable system are analyzed. The results indicate that the multiplicative noise and the additive noise always enhance the particle escape from stable states x ± of bistable. However, the asymmetric parameter r enhances the particle escape from stable state x + , and holds back the particle escape from stable state x - . (general)

Controllable optical bistability in a three-mode optomechanical system with atom-cavity-mirror couplings

Science.gov (United States)

Chen, Bin; Wang, Xiao-Fang; Yan, Jia-Kai; Zhu, Xiao-Fei; Jiang, Cheng

2018-01-01

We theoretically investigate the optical bistable behavior in a three-mode optomechanical system with atom-cavity-mirror couplings. The effects of the cavity-pump detuning and the pump power on the bistable behavior are discussed detailedly, the impacts of the atom-pump detuning and the atom-cavity coupling strength on the bistability of the system are also explored, and the influences of the cavity-resonator coupling strength and the cavity decay rate are also taken into consideration. The numerical results demonstrate that by tuning these parameters the bistable behavior of the system can be freely switched on or off, and the threshold of the pump power for the bistability as well as the bistable region width can also be effectively controlled. These results can find potential applications in optical bistable switch in the quantum information processing.

Distributed order reaction-diffusion systems associated with Caputo derivatives

Science.gov (United States)

Saxena, R. K.; Mathai, A. M.; Haubold, H. J.

2014-08-01

This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation of distributed order associated with the Caputo derivatives as the time-derivative and Riesz-Feller fractional derivative as the space-derivative. The solution is derived by the application of the joint Laplace and Fourier transforms in compact and closed form in terms of the H-function. The results derived are of general nature and include the results investigated earlier by other authors, notably by Mainardi et al. ["The fundamental solution of the space-time fractional diffusion equation," Fractional Calculus Appl. Anal. 4, 153-202 (2001); Mainardi et al. "Fox H-functions in fractional diffusion," J. Comput. Appl. Math. 178, 321-331 (2005)] for the fundamental solution of the space-time fractional equation, including Haubold et al. ["Solutions of reaction-diffusion equations in terms of the H-function," Bull. Astron. Soc. India 35, 681-689 (2007)] and Saxena et al. ["Fractional reaction-diffusion equations," Astrophys. Space Sci. 305, 289-296 (2006a)] for fractional reaction-diffusion equations. The advantage of using the Riesz-Feller derivative lies in the fact that the solution of the fractional reaction-diffusion equation, containing this derivative, includes the fundamental solution for space-time fractional diffusion, which itself is a generalization of fractional diffusion, space-time fraction diffusion, and time-fractional diffusion, see Schneider and Wyss ["Fractional diffusion and wave equations," J. Math. Phys. 30, 134-144 (1989)]. These specialized types of diffusion can be interpreted as spatial probability density functions evolving in time and are expressible in terms of the H-function in compact forms. The convergence conditions for the double series occurring in the solutions are investigated. It is interesting to observe that the double series comes out to be a special case of the Srivastava-Daoust hypergeometric function of two variables

Pattern dynamics of the reaction-diffusion immune system.

Science.gov (United States)

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.

Dichotomous-noise-induced pattern formation in a reaction-diffusion system

Science.gov (United States)

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.

Optical bistability controlling light with light

CERN Document Server

Gibbs, Hyatt

1985-01-01

Optical Bistability: Controlling Light with Light focuses on optical bistability in nonlinear optical systems. Emphasis is on passive (non-laser) systems that exhibit reversible bistability with input intensity as the hysteresis variable, along with the physics and the potential applications of such systems for nonlinear optical signal processing. This book consists of seven chapters and begins with a historical overview of optical bistability in lasers and passive systems. The next chapter describes steady-state theories of optical bistability, including the Bonifacio-Lugiato model, as we

Anomalous dimension in a two-species reaction-diffusion system

Science.gov (United States)

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 \

Large-time behavior of solutions to a reaction-diffusion system with distributed microstructure

NARCIS (Netherlands)

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

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.

Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains

KAUST Repository

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

KAUST Repository

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.

Externally controlled anisotropy in pattern-forming reaction-diffusion systems.

Science.gov (United States)

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.

Bistable Microvalve For Use With Microcatheter System

Science.gov (United States)

Seward, Kirk Patrick

2003-12-16

A bistable microvalve of shape memory material is operatively connected to a microcatheter. The bistable microvalve includes a tip that can be closed off until it is in the desired position. Once it is in position it can be opened and closed. The system uses heat and pressure to open and close the microvalve. The shape memory material will change stiffness and shape when heated above a transition temperature. The shape memory material is adapted to move from a first shape to a second shape, either open or closed, where it can perform a desired function.

Controlling bistability by linear augmentation

International Nuclear Information System (INIS)

Sharma, Pooja Rani; Shrimali, Manish Dev; Prasad, Awadhesh; Feudel, Ulrike

2013-01-01

In many bistable oscillating systems only one of the attractors is desired to possessing certain system performance. We present a method to drive a bistable system to a desired target attractor by annihilating the other one. This shift from bistability to monostability is achieved by augmentation of the nonlinear oscillator with a linear control system. For a proper choice of the control function one of the attractors disappears at a critical coupling strength in an control-induced boundary crisis. This transition from bistability to monostability is demonstrated with two paradigmatic examples, the autonomous Chua oscillator and a neuronal system with a periodic input signal.

Nonlinear variational models for reaction and diffusion systems

International Nuclear Information System (INIS)

Tanyi, G.E.

1983-08-01

There exists a natural metric w.r.t. which the density dependent diffusion operator is harmonic in the sense of Eells and Sampson. A physical corollary of this statement is the property that any two regular points on the orbit of a reaction or diffusion operator can be connected by a path along which the reaction rate is constant. (author)

A discrete model to study reaction-diffusion-mechanics systems.

Science.gov (United States)

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.

Controlling the optical bistability and multistability in a two-level pumped-probe system

International Nuclear Information System (INIS)

Mahmoudi, Mohammad; Sahrai, Mostafa; Masoumeh Mousavi, Seyede

2010-01-01

We study the behavior of the optical bistability (OB) and multistability (OM) in a two-level pumped-probe atomic system by means of a unidirectional ring cavity. We show that the optical bistability in a two-level atomic system can be controlled by adjusting the intensity of the pump field and the detuning between two fields. We find that applying the pumping field decreases the threshold of the optical bistability.

Coupling-induced oscillations in nonhomogeneous, overdamped, bistable systems

International Nuclear Information System (INIS)

Hernandez, Mayra; In, Visarath; Longhini, Patrick; Palacios, Antonio; Bulsara, Adi; Kho, Andy

2008-01-01

Coupling-induced oscillations in a homogeneous network of overdamped bistable systems have been previously studied both theoretically and experimentally for a system of N (odd) elements, unidirectionally coupled in a ring topology. In this work, we extend the analysis of this system to include a network of nonhomogeneous elements with respect to the parameter that controls the topology of the potential function and the bistability of each element. In particular, we quantify the effects of the nonhomogeneity on the onset of oscillations and the response of the network to external (assumed to be constant and very small) perturbations, using our (recently developed) coupled core fluxgate magnetometer as a representative system. The potential applications of this work include signal detection and characterization for a large class of sensor systems

Coupling-induced oscillations in nonhomogeneous, overdamped, bistable systems

Energy Technology Data Exchange (ETDEWEB)

Hernandez, Mayra [Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182 (United States)], E-mail: mayra.alina@yahoo.com; In, Visarath [Space and Naval Warfare Systems Center, Code 71730, 53560 Hull Street, San Diego, CA 92152-5001 (United States)], E-mail: visarath.in@navy.mil; Longhini, Patrick [Space and Naval Warfare Systems Center, Code 71730, 53560 Hull Street, San Diego, CA 92152-5001 (United States)], E-mail: longhini@navy.mil; Palacios, Antonio [Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182 (United States)], E-mail: palacios@euler.sdsu.edu; Bulsara, Adi [Space and Naval Warfare Systems Center, Code 71730, 53560 Hull Street, San Diego, CA 92152-5001 (United States)], E-mail: bulsara@spawar.navy.mil; Kho, Andy [Space and Naval Warfare Systems Center, Code 71730, 53560 Hull Street, San Diego, CA 92152-5001 (United States)], E-mail: kho@spawar.navy.mil

2008-06-09

Coupling-induced oscillations in a homogeneous network of overdamped bistable systems have been previously studied both theoretically and experimentally for a system of N (odd) elements, unidirectionally coupled in a ring topology. In this work, we extend the analysis of this system to include a network of nonhomogeneous elements with respect to the parameter that controls the topology of the potential function and the bistability of each element. In particular, we quantify the effects of the nonhomogeneity on the onset of oscillations and the response of the network to external (assumed to be constant and very small) perturbations, using our (recently developed) coupled core fluxgate magnetometer as a representative system. The potential applications of this work include signal detection and characterization for a large class of sensor systems.

Modeling of the interplay between single-file diffusion and conversion reaction in mesoporous systems

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.

Emergent structures in reaction-advection-diffusion systems on a sphere

Science.gov (United States)

Krause, Andrew L.; Burton, Abigail M.; Fadai, Nabil T.; Van Gorder, Robert A.

2018-04-01

We demonstrate unusual effects due to the addition of advection into a two-species reaction-diffusion system on the sphere. We find that advection introduces emergent behavior due to an interplay of the traditional Turing patterning mechanisms with the compact geometry of the sphere. Unidirectional advection within the Turing space of the reaction-diffusion system causes patterns to be generated at one point of the sphere, and transported to the antipodal point where they are destroyed. We illustrate these effects numerically and deduce conditions for Turing instabilities on local projections to understand the mechanisms behind these behaviors. We compare this behavior to planar advection which is shown to only transport patterns across the domain. Analogous transport results seem to hold for the sphere under azimuthal transport or away from the antipodal points in unidirectional flow regimes.

Bubbling and bistability in two parameter discrete systems

Indian Academy of Sciences (India)

The birth of X *. · is concurrent with the ... for bistability viz. a½, and the higher order bistability points a¾, etc. are marked. The quadrilateral marked as ... The characteristics of 2 parameter 1-d maps that exhibit bubbling/bistability related to their ...

Remodelling of cellular excitation (reaction) and intercellular coupling (diffusion) by chronic atrial fibrillation represented by a reaction-diffusion system

Science.gov (United States)

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.

Experimental chaotic quantification in bistable vortex induced vibration systems

Science.gov (United States)

Huynh, B. H.; Tjahjowidodo, T.

2017-02-01

The study of energy harvesting by means of vortex induced vibration systems has been initiated a few years ago and it is considered to be potential as a low water current energy source. The energy harvester is realized by exposing an elastically supported blunt structure under water flow. However, it is realized that the system will only perform at a limited operating range (water flow) that is attributed to the resonance phenomenon that occurs only at a frequency that corresponds to the fluid flow. An introduction of nonlinear elements seems to be a prominent solution to overcome the problem. Among many nonlinear elements, a bistable spring is known to be able to improve the harvested power by a vortex induced vibrations (VIV) based energy converter at the low velocity water flows. However, it is also observed that chaotic vibrations will occur at different operating ranges that will erratically diminish the harvested power and cause a difficulty in controlling the system that is due to the unpredictability in motions of the VIV structure. In order to design a bistable VIV energy converter with improved harvested power and minimum negative effect of chaotic vibrations, the bifurcation map of the system for varying governing parameters is highly on demand. In this study, chaotic vibrations of a VIV energy converter enhanced by a bistable stiffness element are quantified in a wide range of the governing parameters, i.e. damping and bistable gap. Chaotic vibrations of the bistable VIV energy converter are simulated by utilization of a wake oscillator model and quantified based on the calculation of the Lyapunov exponent. Ultimately, a series of experiments of the system in a water tunnel, facilitated by a computer-based force-feedback testing platform, is carried out to validate the existence of chaotic responses. The main challenge in dealing with experimental data is in distinguishing chaotic response from noise-contaminated periodic responses as noise will smear

A numerical study of one-dimensional replicating patterns in reaction-diffusion systems with non-linear diffusion coefficients

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

Concentration fluctuations in non-isothermal reaction-diffusion systems. II. The nonlinear case

NARCIS (Netherlands)

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

Simulations of pattern dynamics for reaction-diffusion systems via SIMULINK.

Science.gov (United States)

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

Exact substitute processes for diffusion-reaction systems with local complete exclusion rules

International Nuclear Information System (INIS)

Schulz, Michael; Reineker, Peter

2005-01-01

Lattice systems with one species diffusion-reaction processes under local complete exclusion rules are studied analytically starting from the usual master equations with discrete variables and their corresponding representation in a Fock space. On this basis, a formulation of the transition probability as a Grassmann path integral is derived in a straightforward manner. It will be demonstrated that this Grassmann path integral is equivalent to a set of Ito stochastic differential equations. Averages of arbitrary variables and correlation functions of the underlying diffusion-reaction system can be expressed as weighted averages over all solutions of the system of stochastic differential equations. Furthermore, these differential equations are equivalent to a Fokker-Planck equation describing the probability distribution of the actual Ito solutions. This probability distribution depends on continuous variables in contrast to the original master equation, and their stochastic dynamics may be interpreted as a substitute process which is completely equivalent to the original lattice dynamics. Especially, averages and correlation functions of the continuous variables are connected to the corresponding lattice quantities by simple relations. Although the substitute process for diffusion-reaction systems with exclusion rules has some similarities to the well-known substitute process for the same system without exclusion rules, there exists a set of remarkable differences. The given approach is not only valid for the discussed single-species processes. We give sufficient arguments to show that arbitrary combinations of unimolecular and bimolecular lattice reactions under complete local exclusions may be described in terms of our approach

Travelling wave and convergence in stage-structured reaction-diffusion competitive models with nonlocal delays

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

A bistable mechanism for directional sensing

International Nuclear Information System (INIS)

Beta, C; Amselem, G; Bodenschatz, E

2008-01-01

We present a generic mechanism for directional sensing in eukaryotic cells that is based on bistable dynamics. As the key feature of this modeling approach, the velocity of trigger waves in the bistable sensing system changes its sign across cells that are exposed to an external chemoattractant gradient. This is achieved by combining a two-component activator/inhibitor system with a bistable switch that induces an identical symmetry breaking for arbitrary gradient input signals. A simple kinetic example is designed to illustrate the dynamics of a bistable directional sensing mechanism in numerical simulations

Entire solutions for bistable lattice differential equations with obstacles

CERN Document Server

Hoffman, Aaron; Vleck, E S Van

2018-01-01

The authors consider scalar lattice differential equations posed on square lattices in two space dimensions. Under certain natural conditions they show that wave-like solutions exist when obstacles (characterized by "holes") are present in the lattice. Their work generalizes to the discrete spatial setting the results obtained in Berestycki, Hamel, and Matuno (2009) for the propagation of waves around obstacles in continuous spatial domains. The analysis hinges upon the development of sub and super-solutions for a class of discrete bistable reaction-diffusion problems and on a generalization of a classical result due to Aronson and Weinberger that concerns the spreading of localized disturbances.

Noticeable positive Doppler effect on optical bistability in an N-type active Raman gain atomic system

International Nuclear Information System (INIS)

Chang Zeng-Guang; Zhang Jing-Tao; Niu Yue-Ping; Gong Shang-Qing

2012-01-01

We theoretically investigate the Doppler effect on optical bistability in an N-type active Raman gain atomic system inside an optical ring cavity. It is shown that the Doppler effect can greatly enhance the dispersion and thus create the bistable behaviour or greatly increase the bistable region, which has been known as the positive Doppler effect on optical bistability. In addition, we find that a positive Doppler effect can change optical bistability from the hybrid dispersion-gain type to a dispersive type

Mathematical analysis and numerical simulation of patterns in fractional and classical reaction-diffusion systems

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.

Experimental Analysis of a Coupled Energy Harvesting System with Monostable and Bistable Configuration

International Nuclear Information System (INIS)

Hoffmann, D; Folkmer, B; Manoli, Y

2014-01-01

In this paper we present experimental results from an energy harvesting system with two coupled energy harvesters. The energy conversion mechanism of the two coupled energy harvesters is based on the electromagnetic principle. The coupling is generated by two magnets in a repulsive arrangement. In this manner a bistable configuration can be obtained if the gap between the magnets is sufficiently small. We demonstrate that the total power output can be increased in comparison to a linear reference system, if specific conditions are fulfilled. In this respect, the highest power output occurs in the nonlinear region of a monostable system configuration, mostly near the transition to a bistable configuration. On the other hand, the results also indicate, that a bistable operating mode does not necessarily enhance the power output of the coupled system

Non-Archimedean reaction-ultradiffusion equations and complex hierarchic systems

Science.gov (United States)

Zúñiga-Galindo, W. A.

2018-06-01

We initiate the study of non-Archimedean reaction-ultradiffusion equations and their connections with models of complex hierarchic systems. From a mathematical perspective, the equations studied here are the p-adic counterpart of the integro-differential models for phase separation introduced by Bates and Chmaj. Our equations are also generalizations of the ultradiffusion equations on trees studied in the 1980s by Ogielski, Stein, Bachas, Huberman, among others, and also generalizations of the master equations of the Avetisov et al models, which describe certain complex hierarchic systems. From a physical perspective, our equations are gradient flows of non-Archimedean free energy functionals and their solutions describe the macroscopic density profile of a bistable material whose space of states has an ultrametric structure. Some of our results are p-adic analogs of some well-known results in the Archimedean setting, however, the mechanism of diffusion is completely different due to the fact that it occurs in an ultrametric space.

Multi-scale simulation of reaction-diffusion systems

NARCIS (Netherlands)

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

A review of the recent research on vibration energy harvesting via bistable systems

International Nuclear Information System (INIS)

Harne, R L; Wang, K W

2013-01-01

The investigation of the conversion of vibrational energy into electrical power has become a major field of research. In recent years, bistable energy harvesting devices have attracted significant attention due to some of their unique features. Through a snap-through action, bistable systems transition from one stable state to the other, which could cause large amplitude motion and dramatically increase power generation. Due to their nonlinear characteristics, such devices may be effective across a broad-frequency bandwidth. Consequently, a rapid engagement of research has been undertaken to understand bistable electromechanical dynamics and to utilize the insight for the development of improved designs. This paper reviews, consolidates, and reports on the major efforts and findings documented in the literature. A common analytical framework for bistable electromechanical dynamics is presented, the principal results are provided, the wide variety of bistable energy harvesters are described, and some remaining challenges and proposed solutions are summarized. (topical review)

Heat dissipation and information flow for delayed bistable Langevin systems near coherence resonance.

Science.gov (United States)

Xiao, Tiejun

2016-11-01

In this paper, stochastic thermodynamics of delayed bistable Langevin systems near coherence resonance is discussed. We calculate the heat dissipation rate and the information flow of a delayed bistable Langevin system under various noise intensities. Both the heat dissipation rate and the information flow are found to be bell-shaped functions of the noise intensity, which implies that coherence resonance manifests itself in the thermodynamic properties.

Plasmon-modulated bistable four-wave mixing signals from a metal nanoparticle-monolayer MoS2 nanoresonator hybrid system.

Science.gov (United States)

Li, Jian-Bo; Tan, Xiao-Long; Ma, Jin-Hong; Xu, Si-Qin; Kuang, Zhi-Wei; Liang, Shan; Xiao, Si; He, Meng-Dong; Kim, Nam-Chol; Luo, Jian-Hua; Chen, Li-Qun

2018-06-22

We present a study for the impact of exciton-phonon and exciton-plasmon interactions on bistable four-wave mixing (FWM) signals in a metal nanoparticle (MNP)-monolayer MoS 2 nanoresonator hybrid system. Via tracing the FWM response we predict that, depending on the excitation conditions and the system parameters, such a system exhibits 'U-shaped' bistable FWM signals. We also map out bistability phase diagrams within the system's parameter space. Especially, we show that compared with the exciton-phonon interaction, a strong exciton-plasmon interaction plays a dominant role in the generation of optical bistability, and the bistable region will be greatly broadened by shortening the distance between the MNP and the monolayer MoS 2 nanoresonator. In the weak exciton-plasmon coupling regime, the impact of exciton-phonon interaction on optical bistability will become obvious. The scheme proposed may be used for building optical switches and logic-gate devices for optical computing and quantum information processing.

Bistable Mechanisms for Space Applications.

Science.gov (United States)

Zirbel, Shannon A; Tolman, Kyler A; Trease, Brian P; Howell, Larry L

2016-01-01

Compliant bistable mechanisms are monolithic devices with two stable equilibrium positions separated by an unstable equilibrium position. They show promise in space applications as nonexplosive release mechanisms in deployment systems, thereby eliminating friction and improving the reliability and precision of those mechanical devices. This paper presents both analytical and numerical models that are used to predict bistable behavior and can be used to create bistable mechanisms in materials not previously feasible for compliant mechanisms. Materials compatible with space applications are evaluated for use as bistable mechanisms and prototypes are fabricated in three different materials. Pin-puller and cutter release mechanisms are proposed as potential space applications.

Exact analytical solutions for nonlinear reaction-diffusion equations

International Nuclear Information System (INIS)

Liu Chunping

2003-01-01

By using a direct method via the computer algebraic system of Mathematica, some exact analytical solutions to a class of nonlinear reaction-diffusion equations are presented in closed form. Subsequently, the hyperbolic function solutions and the triangular function solutions of the coupled nonlinear reaction-diffusion equations are obtained in a unified way

Speed ot travelling waves in reaction-diffusion equations

International Nuclear Information System (INIS)

Benguria, R.D.; Depassier, M.C.; Mendez, V.

2002-01-01

Reaction diffusion equations arise in several problems of population dynamics, flame propagation and others. In one dimensional cases the systems may evolve into travelling fronts. Here we concentrate on a reaction diffusion equation which arises as a simple model for chemotaxis and present results for the speed of the travelling fronts. (Author)

Feynman-Kac equations for reaction and diffusion processes

Science.gov (United States)

Hou, Ru; Deng, Weihua

2018-04-01

This paper provides a theoretical framework for deriving the forward and backward Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing both diffusion and reaction processes. Once given the diffusion type and reaction rate, a specific forward or backward Feynman-Kac equation can be obtained. The results in this paper include those for normal/anomalous diffusions and reactions with linear/nonlinear rates. Using the derived equations, we apply our findings to compute some physical (experimentally measurable) statistics, including the occupation time in half-space, the first passage time, and the occupation time in half-interval with an absorbing or reflecting boundary, for the physical system with anomalous diffusion and spontaneous evanescence.

Transcriptional delay stabilizes bistable gene networks.

Science.gov (United States)

Gupta, Chinmaya; López, José Manuel; Ott, William; Josić, Krešimir; Bennett, Matthew R

2013-08-02

Transcriptional delay can significantly impact the dynamics of gene networks. Here we examine how such delay affects bistable systems. We investigate several stochastic models of bistable gene networks and find that increasing delay dramatically increases the mean residence times near stable states. To explain this, we introduce a non-Markovian, analytically tractable reduced model. The model shows that stabilization is the consequence of an increased number of failed transitions between stable states. Each of the bistable systems that we simulate behaves in this manner.

Plasmon-modulated bistable four-wave mixing signals from a metal nanoparticle-monolayer MoS2 nanoresonator hybrid system

Science.gov (United States)

Li, Jian-Bo; Tan, Xiao-Long; Ma, Jin-Hong; Xu, Si-Qin; Kuang, Zhi-Wei; Liang, Shan; Xiao, Si; He, Meng-Dong; Kim, Nam-Chol; Luo, Jian-Hua; Chen, Li-Qun

2018-06-01

We present a study for the impact of exciton-phonon and exciton-plasmon interactions on bistable four-wave mixing (FWM) signals in a metal nanoparticle (MNP)-monolayer MoS2 nanoresonator hybrid system. Via tracing the FWM response we predict that, depending on the excitation conditions and the system parameters, such a system exhibits ‘U-shaped’ bistable FWM signals. We also map out bistability phase diagrams within the system’s parameter space. Especially, we show that compared with the exciton-phonon interaction, a strong exciton-plasmon interaction plays a dominant role in the generation of optical bistability, and the bistable region will be greatly broadened by shortening the distance between the MNP and the monolayer MoS2 nanoresonator. In the weak exciton-plasmon coupling regime, the impact of exciton-phonon interaction on optical bistability will become obvious. The scheme proposed may be used for building optical switches and logic-gate devices for optical computing and quantum information processing.

Reaction-Diffusion Automata Phenomenology, Localisations, Computation

CERN Document Server

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...

Propagating gene expression fronts in a one-dimensional coupled system of artificial cells

Science.gov (United States)

Tayar, Alexandra M.; Karzbrun, Eyal; Noireaux, Vincent; Bar-Ziv, Roy H.

2015-12-01

Living systems employ front propagation and spatiotemporal patterns encoded in biochemical reactions for communication, self-organization and computation. Emulating such dynamics in minimal systems is important for understanding physical principles in living cells and in vitro. Here, we report a one-dimensional array of DNA compartments in a silicon chip as a coupled system of artificial cells, offering the means to implement reaction-diffusion dynamics by integrated genetic circuits and chip geometry. Using a bistable circuit we programmed a front of protein synthesis propagating in the array as a cascade of signal amplification and short-range diffusion. The front velocity is maximal at a saddle-node bifurcation from a bistable regime with travelling fronts to a monostable regime that is spatially homogeneous. Near the bifurcation the system exhibits large variability between compartments, providing a possible mechanism for population diversity. This demonstrates that on-chip integrated gene circuits are dynamical systems driving spatiotemporal patterns, cellular variability and symmetry breaking.

Numerical simulation of reaction-diffusion systems by modified cubic B-spline differential quadrature method

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.

Critical behavior in reaction-diffusion systems exhibiting absorbing phase transition

CERN Document Server

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.

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

Optical bistability without the rotating wave approximation

Energy Technology Data Exchange (ETDEWEB)

Sharaby, Yasser A., E-mail: Yasser_Sharaby@hotmail.co [Physics Department, Faculty of Applied Sciences, Suez Canal University, Suez (Egypt); Joshi, Amitabh, E-mail: ajoshi@eiu.ed [Department of Physics, Eastern Illinois University, Charleston, IL 61920 (United States); Hassan, Shoukry S., E-mail: Shoukryhassan@hotmail.co [Mathematics Department, College of Science, University of Bahrain, P.O. Box 32038 (Bahrain)

2010-04-26

Optical bistability for two-level atomic system in a ring cavity is investigated outside the rotating wave approximation (RWA) using non-autonomous Maxwell-Bloch equations with Fourier decomposition up to first harmonic. The first harmonic output field component exhibits reversed or closed loop bistability simultaneously with the usual (anti-clockwise) bistability in the fundamental field component.

Optical bistability without the rotating wave approximation

International Nuclear Information System (INIS)

Sharaby, Yasser A.; Joshi, Amitabh; Hassan, Shoukry S.

2010-01-01

Optical bistability for two-level atomic system in a ring cavity is investigated outside the rotating wave approximation (RWA) using non-autonomous Maxwell-Bloch equations with Fourier decomposition up to first harmonic. The first harmonic output field component exhibits reversed or closed loop bistability simultaneously with the usual (anti-clockwise) bistability in the fundamental field component.

Bubbling and bistability in two parameter discrete systems

OpenAIRE

Ambika, G.; Sujatha, N. V.

2000-01-01

We present a graphical analysis of the mechanisms underlying the occurrences of bubbling sequences and bistability regions in the bifurcation scenario of a special class of one dimensional two parameter maps. The main result of the analysis is that whether it is bubbling or bistability is decided by the sign of the third derivative at the inflection point of the map function.

Synchronous parallel kinetic Monte Carlo for continuum diffusion-reaction systems

International Nuclear Information System (INIS)

Martinez, E.; Marian, J.; Kalos, M.H.; Perlado, J.M.

2008-01-01

A novel parallel kinetic Monte Carlo (kMC) algorithm formulated on the basis of perfect time synchronicity is presented. The algorithm is intended as a generalization of the standard n-fold kMC method, and is trivially implemented in parallel architectures. In its present form, the algorithm is not rigorous in the sense that boundary conflicts are ignored. We demonstrate, however, that, in their absence, or if they were correctly accounted for, our algorithm solves the same master equation as the serial method. We test the validity and parallel performance of the method by solving several pure diffusion problems (i.e. with no particle interactions) with known analytical solution. We also study diffusion-reaction systems with known asymptotic behavior and find that, for large systems with interaction radii smaller than the typical diffusion length, boundary conflicts are negligible and do not affect the global kinetic evolution, which is seen to agree with the expected analytical behavior. Our method is a controlled approximation in the sense that the error incurred by ignoring boundary conflicts can be quantified intrinsically, during the course of a simulation, and decreased arbitrarily (controlled) by modifying a few problem-dependent simulation parameters

Synchronized stability in a reaction–diffusion neural network model

Energy Technology Data Exchange (ETDEWEB)

Wang, Ling; Zhao, Hongyong, E-mail: hongyongz@126.com

2014-11-14

The reaction–diffusion neural network consisting of a pair of identical tri-neuron loops is considered. We present detailed discussions about the synchronized stability and Hopf bifurcation, deducing the non-trivial role that delay plays in different locations. The corresponding numerical simulations are used to illustrate the effectiveness of the obtained results. In addition, the numerical results about the effects of diffusion reveal that diffusion may speed up the tendency to synchronization and induce the synchronized equilibrium point to be stable. Furthermore, if the parameters are located in appropriate regions, multiple unstability and bistability or unstability and bistability may coexist. - Highlights: • Point to non-trivial role that τ plays in different positions. • Diffusion speeds up the tendency to synchronization. • Diffusion induces the synchronized equilibrium point to be stable. • The coexistence of multiple unstability and bistability or unstability and bistability.

Synchronized stability in a reaction–diffusion neural network model

International Nuclear Information System (INIS)

Wang, Ling; Zhao, Hongyong

2014-01-01

The reaction–diffusion neural network consisting of a pair of identical tri-neuron loops is considered. We present detailed discussions about the synchronized stability and Hopf bifurcation, deducing the non-trivial role that delay plays in different locations. The corresponding numerical simulations are used to illustrate the effectiveness of the obtained results. In addition, the numerical results about the effects of diffusion reveal that diffusion may speed up the tendency to synchronization and induce the synchronized equilibrium point to be stable. Furthermore, if the parameters are located in appropriate regions, multiple unstability and bistability or unstability and bistability may coexist. - Highlights: • Point to non-trivial role that τ plays in different positions. • Diffusion speeds up the tendency to synchronization. • Diffusion induces the synchronized equilibrium point to be stable. • The coexistence of multiple unstability and bistability or unstability and bistability

Spatiotemporal chaos of self-replicating spots in reaction-diffusion systems.

Science.gov (United States)

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.

Nonequilibrium transition and pattern formation in a linear reaction-diffusion system with self-regulated kinetics

Science.gov (United States)

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.

Cell individuality: the bistable gene expression of the type III secretion system in Dickeya dadantii 3937.

Science.gov (United States)

Zeng, Quan; Laiosa, Michael D; Steeber, Douglas A; Biddle, Eulandria M; Peng, Quan; Yang, Ching-Hong

2012-01-01

Dickeya dadantii 3937 is a gram-negative phytopathogenic bacterium that expresses genes encoding a type III secretion system (T3SS) in a bistable pattern when cultured in a homogeneous minimal media. In this work, we further characterized the bistable gene expression of T3SS at the single-cell level. We demonstrated that bistable expression of the HrpL-regulon genes, such as hrpA and hrpN, is controlled by the same regulatory mechanism. We also showed that the expression level of the T3SS master regulatory gene hrpL plays an important role in the development of the bistable expression of hrpA. A high expression level of hrpL is required but unable to guarantee the high-state expression of hrpA in a cell. In addition, bistable expression patterns of T3SS genes in other gram-negative pathogens of the Enterobacteriaceae and Pseudomonadaceae families were also described in this study. This suggests that the T3SS bistability might be a conserved population behavior in several gram-negative bacterial pathogens.

Conditional symmetries for systems of PDEs: new definitions and their application for reaction-diffusion systems

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.

Mode-locking in advection-reaction-diffusion systems: An invariant manifold perspective

Science.gov (United States)

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.

A genetic bistable switch utilizing nonlinear protein degradation.

Science.gov (United States)

Huang, Daniel; Holtz, William J; Maharbiz, Michel M

2012-07-09

Bistability is a fundamental property in engineered and natural systems, conferring the ability to switch and retain states. Synthetic bistable switches in prokaryotes have mainly utilized transcriptional components in their construction. Using both transcriptional and enzymatic components, creating a hybrid system, allows for wider bistable parameter ranges in a circuit. In this paper, we demonstrate a tunable family of hybrid bistable switches in E. coli using both transcriptional components and an enzymatic component. The design contains two linked positive feedback loops. The first loop utilizes the lambda repressor, CI, and the second positive feedback loop incorporates the Lon protease found in Mesoplasma florum (mf-Lon). We experimentally tested for bistable behavior in exponential growth phase, and found that our hybrid bistable switch was able to retain its state in the absence of an input signal throughout 40 cycles of cell division. We also tested the transient behavior of our switch and found that switching speeds can be tuned by changing the expression rate of mf-Lon. To our knowledge, this work demonstrates the first use of dynamic expression of an orthogonal and heterologous protease to tune a nonlinear protein degradation circuit. The hybrid switch is potentially a more robust and tunable topology for use in prokaryotic systems.

Degree, instability and bifurcation of reaction-diffusion systems with obstacles near certain hyperbolas

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

Effective reaction rates in diffusion-limited phosphorylation-dephosphorylation cycles

Science.gov (United States)

Szymańska, Paulina; Kochańczyk, Marek; Miekisz, Jacek; Lipniacki, Tomasz

2015-02-01

We investigate the kinetics of the ubiquitous phosphorylation-dephosphorylation cycle on biological membranes by means of kinetic Monte Carlo simulations on the triangular lattice. We establish the dependence of effective macroscopic reaction rate coefficients as well as the steady-state phosphorylated substrate fraction on the diffusion coefficient and concentrations of opposing enzymes: kinases and phosphatases. In the limits of zero and infinite diffusion, the numerical results agree with analytical predictions; these two limits give the lower and the upper bound for the macroscopic rate coefficients, respectively. In the zero-diffusion limit, which is important in the analysis of dense systems, phosphorylation and dephosphorylation reactions can convert only these substrates which remain in contact with opposing enzymes. In the most studied regime of nonzero but small diffusion, a contribution linearly proportional to the diffusion coefficient appears in the reaction rate. In this regime, the presence of opposing enzymes creates inhomogeneities in the (de)phosphorylated substrate distributions: The spatial correlation function shows that enzymes are surrounded by clouds of converted substrates. This effect becomes important at low enzyme concentrations, substantially lowering effective reaction rates. Effective reaction rates decrease with decreasing diffusion and this dependence is more pronounced for the less-abundant enzyme. Consequently, the steady-state fraction of phosphorylated substrates can increase or decrease with diffusion, depending on relative concentrations of both enzymes. Additionally, steady states are controlled by molecular crowders which, mostly by lowering the effective diffusion of reactants, favor the more abundant enzyme.

Bistability of Cavity Magnon Polaritons

Science.gov (United States)

Wang, Yi-Pu; Zhang, Guo-Qiang; Zhang, Dengke; Li, Tie-Fu; Hu, C.-M.; You, J. Q.

2018-01-01

We report the first observation of the magnon-polariton bistability in a cavity magnonics system consisting of cavity photons strongly interacting with the magnons in a small yttrium iron garnet (YIG) sphere. The bistable behaviors emerged as sharp frequency switchings of the cavity magnon polaritons (CMPs) and related to the transition between states with large and small numbers of polaritons. In our experiment, we align, respectively, the [100] and [110] crystallographic axes of the YIG sphere parallel to the static magnetic field and find very different bistable behaviors (e.g., clockwise and counter-clockwise hysteresis loops) in these two cases. The experimental results are well fitted and explained as being due to the Kerr nonlinearity with either a positive or negative coefficient. Moreover, when the magnetic field is tuned away from the anticrossing point of CMPs, we observe simultaneous bistability of both magnons and cavity photons by applying a drive field on the lower branch.

Optically levitated nanoparticle as a model system for stochastic bistable dynamics.

Science.gov (United States)

Ricci, F; Rica, R A; Spasenović, M; Gieseler, J; Rondin, L; Novotny, L; Quidant, R

2017-05-09

Nano-mechanical resonators have gained an increasing importance in nanotechnology owing to their contributions to both fundamental and applied science. Yet, their small dimensions and mass raises some challenges as their dynamics gets dominated by nonlinearities that degrade their performance, for instance in sensing applications. Here, we report on the precise control of the nonlinear and stochastic bistable dynamics of a levitated nanoparticle in high vacuum. We demonstrate how it can lead to efficient signal amplification schemes, including stochastic resonance. This work contributes to showing the use of levitated nanoparticles as a model system for stochastic bistable dynamics, with applications to a wide variety of fields.

Control of stochastic resonance in bistable systems by using periodic signals

International Nuclear Information System (INIS)

Min, Lin; Li-Min, Fang; Yong-Jun, Zheng

2009-01-01

According to the characteristic structure of double wells in bistable systems, this paper analyses stochastic fluctuations in the single potential well and probability transitions between the two potential wells and proposes a method of controlling stochastic resonance by using a periodic signal. Results of theoretical analysis and numerical simulation show that the phenomenon of stochastic resonance happens when the time scales of the periodic signal and the noise-induced probability transitions between the two potential wells achieve stochastic synchronization. By adding a bistable system with a controllable periodic signal, fluctuations in the single potential well can be effectively controlled, thus affecting the probability transitions between the two potential wells. In this way, an effective control can be achieved which allows one to either enhance or realize stochastic resonance

The mechanism of Turing pattern formation in a positive feedback system with cross diffusion

International Nuclear Information System (INIS)

Yang, Xiyan; Liu, Tuoqi; Zhang, Jiajun; Zhou, Tianshou

2014-01-01

In this paper, we analyze a reaction–diffusion (R–D) system with a double negative feedback loop and find cases where self diffusion alone cannot lead to Turing pattern formation but cross diffusion can. Specifically, we first derive a set of sufficient conditions for Turing instability by performing linear stability analysis, then plot two bifurcation diagrams that specifically identify Turing regions in the parameter phase plane, and finally numerically demonstrate representative Turing patterns according to the theoretical predictions. Our analysis combined with previous studies actually implies an interesting fact that Turing patterns can be generated not only in a class of monostable R–D systems where cross diffusion is not necessary but also in a class of bistable R–D systems where cross diffusion is necessary. In addition, our model would be a good candidate for experimentally testing Turing pattern formation from the viewpoint of synthetic biology. (paper)

Solid state reaction studies in Fe3O4–TiO2 system by diffusion couple method

International Nuclear Information System (INIS)

Ren, Zhongshan; Hu, Xiaojun; Xue, Xiangxin; Chou, Kuochih

2013-01-01

Highlights: •The solid state reactions of Fe2O3-TiO2 system was studied by the diffusion couple method. •Different products were formed by diffusion, and the FeTiO3 was more stable phase. •The inter-diffusion coefficients and diffusion activation energy were estimated. -- Abstract: The solid state reactions in Fe 3 O 4 –TiO 2 system has been studied by diffusion couple experiments at 1323–1473 K, in which the oxygen partial pressure was controlled by the CO–CO 2 gas mixture. The XRD analysis was used to confirm the phases of the inter-compound, and the concentration profiles were determined by electron probe microanalysis (EPMA). Based on the concentration profile of Ti, the inter-diffusion coefficients in Fe 3 O 4 phase, which were both temperature and concentration of Ti ions dependent, were calculated by the modified Boltzmann–Matano method. According to the relation between the thickness of diffusion layer and temperature, the diffusion coefficient of the Fe 3 O 4 –TiO 2 system was obtained. According to the Arrhenius equation, the estimated diffusion activation energy was about 282.1 ± 18.8 kJ mol −1

External boundary effects on simultaneous diffusion and reaction processes

International Nuclear Information System (INIS)

Le Roux, M.N.; Wilhelmsson, H.

1989-01-01

External boundaries influence the spatial and temporal structure of evolution of dynamic systems governed by reaction-diffusion equations. Critical limits, i.e. thresholds for explosive growth or onset of diffusion dominated decay, are found to be caused by the presence of the boundary and to depend on: the position of the boundary, where the density is assumed to be zero at any instant of time: the mutual weights (coefficients) and powers of the nonlinear reaction and diffusion processes; and the initial spatial distribution. However, for particular relations between the nonlinear powers of the reaction and diffusion terms the critical limits do not depend on the initial conditions. The results are obtained by simulation experiment for one, two and three dimensions. Trends in the dynamic evolution of the system with an external boundary imposed are compared with the corresponding analytic results obtained for free boundary. Interesting applications are found in various areas, e.g. in the field of high temperature fusion plasma where the evolution of the temperature profile for the so-called H-mode (constant plasma density) is described

Design and experiment of controlled bistable vortex induced vibration energy harvesting systems operating in chaotic regions

Science.gov (United States)

Huynh, B. H.; Tjahjowidodo, T.; Zhong, Z.-W.; Wang, Y.; Srikanth, N.

2018-01-01

Vortex induced vibration based energy harvesting systems have gained interests in these recent years due to its potential as a low water current energy source. However, the effectiveness of the system is limited only at a certain water current due to the resonance principle that governs the concept. In order to extend the working range, a bistable spring to support the structure is introduced on the system. The improvement on the performance is essentially dependent on the bistable gap as one of the main parameters of the nonlinear spring. A sufficiently large bistable gap will result in a significant performance improvement. Unfortunately, a large bistable gap might also increase a chance of chaotic responses, which in turn will result in diminutive harvested power. To mitigate the problem, an appropriate control structure is required to stabilize the chaotic vibrations of a VIV energy converter with the bistable supporting structure. Based on the nature of the double-well potential energy in a bistable spring, the ideal control structure will attempt to drive the responses to inter-well periodic vibrations in order to maximize the harvested power. In this paper, the OGY control algorithm is designed and implemented to the system. The control strategy is selected since it requires only a small perturbation in a structural parameter to execute the control effort, thus, minimum power is needed to drive the control input. Facilitated by a wake oscillator model, the bistable VIV system is modelled as a 4-dimensional autonomous continuous-time dynamical system. To implement the controller strategy, the system is discretized at a period estimated from the subspace hyperplane intersecting to the chaotic trajectory, whereas the fixed points that correspond to the desired periodic orbits are estimated by the recurrence method. Simultaneously, the Jacobian and sensitivity matrices are estimated by the least square regression method. Based on the defined fixed point and the

Optical bistability using quantum interference in V-type atoms

International Nuclear Information System (INIS)

Anton, M A; Calderon, Oscar G

2002-01-01

The behaviour of a V-type three-level atomic system in a ring cavity driven by a coherent field is studied. We consider a V configuration under conditions such that interference between decay channels is important. We find that when quantum interference is taken into account, optical bistability can be realized with a considerable decrease in the threshold intensity and the cooperative parameter. On the other hand, we also include the finite bandwidth of the driving field and study its role in the optical bistable response. It is found that at certain linewidths of the driving field optical bistability is obtained even if the system satisfies the trapping condition and the threshold intensity can be controlled. Furthermore, a change from the optical bistability due to quantum interference to the usual bistable behaviour based on saturation occurs as the driving field linewidth increases

Bistable behaviour of biexciton population in a dense exciton-biexciton system in semiconductors

International Nuclear Information System (INIS)

Nguyen Ba An.

1986-05-01

The steady state bistable behaviour of biexciton population in a dense exciton-biexciton semiconductor is considered. The intrinsic optical feedback is provided by the recombination mechanism. The exciton-biexciton and biexciton-biexciton interactions play the role of non-linearity responsible for biexciton bistability to occur. The conditions leading to the effect of bistability are obtained and two-parameter phase transition diagrams are drawn for both intensity and frequency bistable phenomena. (author)

Similarity solutions of reaction–diffusion equation with space- and time-dependent diffusion and reaction terms

Energy Technology Data Exchange (ETDEWEB)

Ho, C.-L. [Department of Physics, Tamkang University, Tamsui 25137, Taiwan (China); Lee, C.-C., E-mail: chieh.no27@gmail.com [Center of General Education, Aletheia University, Tamsui 25103, Taiwan (China)

2016-01-15

We consider solvability of the generalized reaction–diffusion equation with both space- and time-dependent diffusion and reaction terms by means of the similarity method. By introducing the similarity variable, the reaction–diffusion equation is reduced to an ordinary differential equation. Matching the resulting ordinary differential equation with known exactly solvable equations, one can obtain corresponding exactly solvable reaction–diffusion systems. Several representative examples of exactly solvable reaction–diffusion equations are presented.

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

Nonlinear waves in reaction-diffusion systems: The effect of transport memory

Science.gov (United States)

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.

Controlling the optical bistability beyond the multi-photon resonance condition in a three-level closed-loop atomic system

International Nuclear Information System (INIS)

Mahmoudi, Mohammad; Nozari, Narges; Vafafard, Azar; Sahrai, Mostafa

2012-01-01

We investigate the optical bistability behavior of a three-level closed-loop atomic system beyond the multi-photon resonance condition. Using the Floquet decomposition, we solve the time-dependent equations of motion, beyond the multi-photon resonance condition. By identifying the different scattering processes contributing to the medium response, it is shown that in general the optical bistability behavior of the system is not phase-dependent. The phase dependence is due to the scattering of the driving and coupling fields into the probe field at a frequency, which, in general, differs from the probe field frequency. - Highlights: → We investigate optical bistability of a three-level closed-loop atomic system, beyond the multi-photon resonance condition. → By applying Floquet decomposition to the equation of motion, the different scattering processes contributing to the medium response are determined. → It is shown that the phase dependence of optical bistability arises from the scattering of the driving and coupling fields into the probe field frequency.

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.

Non-resonant energy harvesting via an adaptive bistable potential

International Nuclear Information System (INIS)

Hosseinloo, Ashkan Haji; Turitsyn, Konstantin

2016-01-01

Narrow bandwidth and easy detuning, inefficiency in broadband and non-stationary excitations, and difficulties in matching a linear harvester’s resonance frequency to low-frequency excitations at small scales, have convinced researchers to investigate nonlinear, and in particular bistable, energy harvesters in recent years. However, bistable harvesters suffer from co-existing low and high energy orbits, and sensitivity to initial conditions, and have recently been proven inefficient when subjected to many real-world random and non-stationary excitations. Here, we propose a novel non-resonant buy-low-sell-high strategy that can significantly improve the harvester’s effectiveness at low frequencies in a much more robust fashion. This strategy could be realized by a passive adaptive bistable system. Simulation results confirm the high effectiveness of the adaptive bistable system following a buy-low-sell-high logic when subjected to harmonic and random non-stationary walking excitations compared to its conventional bistable and linear counterparts. (paper)

Bistable energy harvesting enhancement with an auxiliary linear oscillator

Science.gov (United States)

Harne, R. L.; Thota, M.; Wang, K. W.

2013-12-01

Recent work has indicated that linear vibrational energy harvesters with an appended degree-of-freedom (DOF) may be advantageous for introducing new dynamic forms to extend the operational bandwidth. Given the additional interest in bistable harvester designs, which exhibit a propitious snap through effect from one stable state to the other, it is a logical extension to explore the influence of an added DOF to a bistable system. However, bistable snap through is not a resonant phenomenon, which tempers the presumption that the dynamics induced by an additional DOF on bistable designs would inherently be beneficial as for linear systems. This paper presents two analytical formulations to assess the fundamental and superharmonic steady-state dynamics of an excited bistable energy harvester to which is attached an auxiliary linear oscillator. From an energy harvesting perspective, the model predicts that the additional linear DOF uniformly amplifies the bistable harvester response magnitude and generated power for excitation frequencies less than the attachment’s resonance while improved power density spans a bandwidth below this frequency. Analyses predict bandwidths having co-existent responses composed of a unique proportion of fundamental and superharmonic dynamics. Experiments validate key analytical predictions and observe the ability for the coupled system to develop an advantageous multi-harmonic interwell response when the initial conditions are insufficient for continuous high-energy orbit at the excitation frequency. Overall, the addition of an auxiliary linear oscillator to a bistable harvester is found to be an effective means of enhancing the energy harvesting performance and robustness.

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.

Optical bistability and multistability in a three-level Δ-type atomic system under the nonresonant condition

International Nuclear Information System (INIS)

Ai-Xi, Chen; Zhi-Ping, Wang; De-Hai, Chen; Yan-Qiu, Xu

2009-01-01

Under a nonresonant condition, we theoretically investigate hybrid absorptive-dispersive optical bistability and multistability behaviours in a three-level Δ-type system by using a microwave field to drive a hyperfine transition between two upper excited states inside a unidirectional ring cavity. We find that the optical bistability and multistability behaviours can be controlled by adjusting the intensity of the microwave field or the intensity of the coherent coupling field. Furthermore, our studies show an interesting phenomenon of the transition from the optical bistability to the optical multistability only by changing the negative detuning of the coupling field into the positive detuning of the coupling field. (classical areas of phenomenology)

Phase dependence of optical bistability and multistability in a four-level quantum system near a plasmonic nanostructure

International Nuclear Information System (INIS)

Asadpour, Seyyed Hossein; Rahimpour Soleimani, H.

2016-01-01

The optical bistability and multistability properties of a four-level quantum system near a plasmonic nanostructure embedded in a unidirectional ring cavity are studied theoretically. Two orthogonal circularly polarized laser fields with the same frequency, different phases and electric fields amplitude are interacted by four-level quantum system. It is found that in the presence of the plasmonic nanostructure, the bistable behaviors related to one of the laser fields propagating through the unidirectional ring cavity can be modified by relative phase and amplitude control of another laser fields. Our obtained results show that the optical bistability can be converted into the optical multistability by varying the value of distance between the quantum system and the surface of the plasmonic nanostructure. Moreover, it is shown that under specific condition related to the distance, the lasing without population inversion can be obtained

Phase dependence of optical bistability and multistability in a four-level quantum system near a plasmonic nanostructure

Energy Technology Data Exchange (ETDEWEB)

Asadpour, Seyyed Hossein; Rahimpour Soleimani, H., E-mail: Rahimpour@guilan.ac.ir [Computational Nanophysics Laboratory (CNL), Department of Physics, University of Guilan, Rasht (Iran, Islamic Republic of)

2016-01-14

The optical bistability and multistability properties of a four-level quantum system near a plasmonic nanostructure embedded in a unidirectional ring cavity are studied theoretically. Two orthogonal circularly polarized laser fields with the same frequency, different phases and electric fields amplitude are interacted by four-level quantum system. It is found that in the presence of the plasmonic nanostructure, the bistable behaviors related to one of the laser fields propagating through the unidirectional ring cavity can be modified by relative phase and amplitude control of another laser fields. Our obtained results show that the optical bistability can be converted into the optical multistability by varying the value of distance between the quantum system and the surface of the plasmonic nanostructure. Moreover, it is shown that under specific condition related to the distance, the lasing without population inversion can be obtained.

Controlling the optical bistability via quantum interference in a four-level N-type atomic system

International Nuclear Information System (INIS)

Sahrai, M.; Asadpour, S.H.; Mahrami, H.; Sadighi-Bonabi, R.

2011-01-01

We investigate the optical bistability (OB) and optical multi-stability (OM) in a four-level N-type atomic system. The effect of spontaneously generated coherence (SGC) on OB and OM is then discussed. It is found that SGC makes the medium phase dependent, so the optical bistability and multi-stability threshold can be controlled via relative phase between applied fields. We realize that the frequency detuning of probe and coupling fields with the corresponding atomic transition plays an important role in creation OB and OM. Moreover, the effect of laser coupling fields and an incoherent pumping field on reduction of OB and OM threshold is then discussed. - Highlights: → We modulate the optical bistability (OB) in a four-level N-type atomic system. The effect of spontaneously generated coherence on OB is discussed. → Spontaneously generated coherence makes the medium phase dependent. → The frequency of coupling field can reduce OB threshold. → We discuss the effect of an incoherent pumping field on reduction of OB threshold.

Genes contribute to the switching dynamics of bistable perception.

Science.gov (United States)

Shannon, Robert W; Patrick, Christopher J; Jiang, Yi; Bernat, Edward; He, Sheng

2011-03-09

Ordinarily, the visual system provides an unambiguous representation of the world. However, at times alternative plausible interpretations of a given stimulus arise, resulting in a dynamic perceptual alternation of the differing interpretations, commonly referred to as bistable or rivalrous perception. Recent research suggests that common neural mechanisms may be involved in the dynamics of very different types of bistable phenomena. Further, evidence has emerged that genetic factors may be involved in determining the rate of switch for at least one form of bistable perception, known as binocular rivalry. The current study evaluated whether genetic factors contribute to the switching dynamics for distinctly different variants of bistable perception in the same participant sample. Switching rates were recorded for MZ and DZ twin participants in two different bistable perception tasks, binocular rivalry and the Necker Cube. Strong concordance in switching rates across both tasks was evident for MZ but not DZ twins, indicating that genetic factors indeed contribute to the dynamics of multiple forms of bistable perception.

Convergence to a pulsating travelling wave for an epidemic reaction-diffusion system with non-diffusive susceptible population.

Science.gov (United States)

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.

Phase-dependent optical bistability and multistability in a semiconductor quantum well system

International Nuclear Information System (INIS)

Wang Zhiping; Fan Hongyi

2010-01-01

We theoretically investigate the hybrid absorptive-dispersive optical bistability and multistability in a four-level inverted-Y quantum well system inside a unidirectional ring cavity. We find that the coupling field, the pumping field as well as the cycling field can affect the optical bistability and multistability dramatically, which can be used to manipulate efficiently the threshold intensity and the hysteresis loop. The effects of the relative phase and the electronic cooperation parameter on the OB and OM are also studied. Our study is much more practical than its atomic counterpart due to its flexible design and the wide adjustable parameters. Thus, it may provide some new possibilities for technological applications in optoelectronics and solid-state quantum information science.

RKC time-stepping for advection-diffusion-reaction problems

International Nuclear Information System (INIS)

Verwer, J.G.; Sommeijer, B.P.; Hundsdorfer, W.

2004-01-01

The original explicit Runge-Kutta-Chebyshev (RKC) method is a stabilized second-order integration method for pure diffusion problems. Recently, it has been extended in an implicit-explicit manner to also incorporate highly stiff reaction terms. This implicit-explicit RKC method thus treats diffusion terms explicitly and the highly stiff reaction terms implicitly. The current paper deals with the incorporation of advection terms for the explicit method, thus aiming at the implicit-explicit RKC integration of advection-diffusion-reaction equations in a manner that advection and diffusion terms are treated simultaneously and explicitly and the highly stiff reaction terms implicitly

Optical bistability via quantum interference from incoherent pumping and spontaneous emission

International Nuclear Information System (INIS)

Sahrai, M.; Asadpour, S.H.; Sadighi-Bonabi, R.

2011-01-01

We theoretically investigate the optical bistability (OB) in a V-type three-level atomic system confined in a unidirectional ring cavity via incoherent pumping field. It is shown that the threshold of optical bistability can be controlled by the rate of an incoherent pumping field and by interference mechanism arising from the spontaneous emission and incoherent pumping field. We demonstrate that the optical bistability converts to optical multi-stability (OM) by the quantum interference mechanism. - Highlights: → We modulate the optical bistability (OB) in a four-level N-type atomic system. → The threshold of optical bistability can be controlled by the quantum interferences. → OB converts to optical multi-stability (OM) by the quantum interferences. → We discuss the effect of an incoherent pumping field on reduction of OB threshold.

Controllable optical bistability in photonic-crystal one-atom laser

International Nuclear Information System (INIS)

Guo Xiaoyong; Lue Shuchen

2009-01-01

We investigate the property of optical bistability in a photonic-crystal one-atom laser when nonlinear microcavity is present. The physical system consists of a coherently driven two-level light emitter strongly coupled to a high-quality microcavity which is embedded within a photonic crystal and another coherent probing field which has incident into the microcavity. In our case, the microcavity is fabricated by nonlinear material and placed as an impurity in photonic crystal. This study reveals that such a system can exhibit optical bistability. The dependence of threshold value and hysteresis loop on the photonic band gap of the photonic crystal, driving field Rabi frequency and dephasing processes, are studied. Our results clearly illustrate the ability to control optical bistability through suitable photonic-crystal architectures and external coherent driving field, and this study suggests that in a photonic-crystal nonlinear microcavity, the one-atom laser acts as an effective controllable bistable device in the design of all-light digital computing systems in the near future.

Reaction-diffusion controlled growth of complex structures

Science.gov (United States)

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

Existence and exponential stability of traveling waves for delayed reaction-diffusion systems

Science.gov (United States)

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.

Asymptotic behavior of equilibrium states of reaction-diffusion systems with mass conservation

Science.gov (United States)

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.

Effect on the mean first passage time in symmetrical bistable systems by cross-correlation between noises

International Nuclear Information System (INIS)

Wang, J.; Cao, L.; Wu, D.J.

2003-01-01

We present an analytic investigation of the mean first passage time in two opposite directions (from the left well to the right well and from right to left) by studying symmetrical bistable systems driven by correlated Gaussian white noises, and prove that the mean first passage time in two opposite directions is not symmetrical any more when noises are correlated. As examples, the mean first passage time in the quartic bistable model and the sawtooth bistable model are calculated, respectively. From the analytic results of the mean first passage time, we testify further the relation T(from x - to x + ,λ)≠T(from x + to x - ,λ) in the same area of the parameter plan. Moreover, it is found that the dependences of T + (i.e., T(from x - to x + ,λ)) and T - (i.e., T(from x + to x - ,λ)) upon the multiplicative noise intensity Q and the additive noise intensity D exhibit entirely different properties. For same areas of the parameter plan: in the quartic bistable system, when the T + vs. Q curve exhibits a maximum, while the T - vs. Q curve is monotonous; when the T + vs. D curve is monotonous, while the T - vs. D curve experiences a phase transition from decreasing monotonously to possessing one minimum. Increasing Q, when the T + vs. D curve experiences a phase transition from decreasing monotonously to possessing one maximum, while the T - vs. D curve only increases monotonously. Similar behaviours also exist in the sawtooth bistable model

Inertial effects in diffusion-limited reactions

International Nuclear Information System (INIS)

Dorsaz, N; Foffi, G; De Michele, C; Piazza, F

2010-01-01

Diffusion-limited reactions are commonly found in biochemical processes such as enzyme catalysis, colloid and protein aggregation and binding between different macromolecules in cells. Usually, such reactions are modeled within the Smoluchowski framework by considering purely diffusive boundary problems. However, inertial effects are not always negligible in real biological or physical media on typical observation time frames. This is all the more so for non-bulk phenomena involving physical boundaries, that introduce additional time and space constraints. In this paper, we present and test a novel numerical scheme, based on event-driven Brownian dynamics, that allows us to explore a wide range of velocity relaxation times, from the purely diffusive case to the underdamped regime. We show that our algorithm perfectly reproduces the solution of the Fokker-Planck problem with absorbing boundary conditions in all the regimes considered and is thus a good tool for studying diffusion-guided reactions in complex biological environments.

Numerical analysis of intrinsic bistability and chromatic switching in Tm3+ single-doped systems under photon avalanche pumping scheme

International Nuclear Information System (INIS)

Li Li; Zhang Xinlu; Chen Lixue

2008-01-01

In this paper, we predict and numerically demonstrate the intrinsic intensity bistability, spectra bistability and chromatic switching of visible-infrared emission in Tm 3+ single-doped systems that are pumped by the photon avalanche scheme at 648 nm. Based on the coupled rate equation theory, the evolutions of the populations at various Tm 3+ energy levels, emission spectra and fluorescence intensity versus pump excitation are numerically investigated in detail. The results show that intrinsic optical bistability (IOB) associated with emission spectra and luminescence intensity takes place in the vicinity of the avalanche threshold (∼10 kW cm -2 ). When the pump excitation rises above the switching threshold (∼17.5 kW cm -2 ), the chromatic switching between the infrared (1716 nm) and the visible blue (452/469 nm) spectra can be performed. Moreover, the influences of system parameters on IOB and the origin of chromatic switching are discussed. These unique characteristics of Tm 3+ -doped systems would lead to the new possibility of the development of pump-controlled all-solid-state luminescence switches and optical bistability switches.

Convergence to Equilibrium in Energy-Reaction-Diffusion Systems Using Vector-Valued Functional Inequalities

Science.gov (United States)

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.

On square-wave-driven stochastic resonance for energy harvesting in a bistable system

Energy Technology Data Exchange (ETDEWEB)

Su, Dongxu, E-mail: sudx@iis.u-tokyo.ac.jp [Graduate School of Engineering, The University of Tokyo, Tokyo 1538505 (Japan); Zheng, Rencheng; Nakano, Kimihiko [Institute of Industrial Science, The University of Tokyo, Tokyo 1538505 (Japan); Cartmell, Matthew P [Department of Mechanical Engineering, University of Sheffield, Sheffield S1 3JD (United Kingdom)

2014-11-15

Stochastic resonance is a physical phenomenon through which the throughput of energy within an oscillator excited by a stochastic source can be boosted by adding a small modulating excitation. This study investigates the feasibility of implementing square-wave-driven stochastic resonance to enhance energy harvesting. The motivating hypothesis was that such stochastic resonance can be efficiently realized in a bistable mechanism. However, the condition for the occurrence of stochastic resonance is conventionally defined by the Kramers rate. This definition is inadequate because of the necessity and difficulty in estimating white noise density. A bistable mechanism has been designed using an explicit analytical model which implies a new approach for achieving stochastic resonance in the paper. Experimental tests confirm that the addition of a small-scale force to the bistable system excited by a random signal apparently leads to a corresponding amplification of the response that we now term square-wave-driven stochastic resonance. The study therefore indicates that this approach may be a promising way to improve the performance of an energy harvester under certain forms of random excitation.

On square-wave-driven stochastic resonance for energy harvesting in a bistable system

International Nuclear Information System (INIS)

Su, Dongxu; Zheng, Rencheng; Nakano, Kimihiko; Cartmell, Matthew P

2014-01-01

Stochastic resonance is a physical phenomenon through which the throughput of energy within an oscillator excited by a stochastic source can be boosted by adding a small modulating excitation. This study investigates the feasibility of implementing square-wave-driven stochastic resonance to enhance energy harvesting. The motivating hypothesis was that such stochastic resonance can be efficiently realized in a bistable mechanism. However, the condition for the occurrence of stochastic resonance is conventionally defined by the Kramers rate. This definition is inadequate because of the necessity and difficulty in estimating white noise density. A bistable mechanism has been designed using an explicit analytical model which implies a new approach for achieving stochastic resonance in the paper. Experimental tests confirm that the addition of a small-scale force to the bistable system excited by a random signal apparently leads to a corresponding amplification of the response that we now term square-wave-driven stochastic resonance. The study therefore indicates that this approach may be a promising way to improve the performance of an energy harvester under certain forms of random excitation

A Miniature Coupled Bistable Vibration Energy Harvester

International Nuclear Information System (INIS)

Zhu, D; Arthur, D C; Beeby, S P

2014-01-01

This paper reports the design and test of a miniature coupled bistable vibration energy harvester. Operation of a bistable structure largely depends on vibration amplitude rather than frequency, which makes it very promising for wideband vibration energy harvesting applications. A coupled bistable structure consists of a pair of mobile magnets that create two potential wells and thus the bistable phenomenon. It requires lower excitation to trigger bistable operation compared to conventional bistable structures. Based on previous research, this work focused on miniaturisation of the coupled bistable structure for energy harvesting application. The proposed bistable energy harvester is a combination of a Duffing's nonlinear structure and a linear assisting resonator. Experimental results show that the output spectrum of the miniature coupled bistable vibration energy harvester was the superposition of several spectra. It had a higher maximum output power and a much greater bandwidth compared to simply the Duffing's structure without the assisting resonator

Permanganate diffusion and reaction in sedimentary rocks.

Science.gov (United States)

Huang, Qiuyuan; Dong, Hailiang; Towne, Rachael M; Fischer, Timothy B; Schaefer, Charles E

2014-04-01

In situ chemical oxidation using permanganate has frequently been used to treat chlorinated solvents in fractured bedrock aquifers. However, in systems where matrix back-diffusion is an important process, the ability of the oxidant to migrate and treat target contaminants within the rock matrix will likely determine the overall effectiveness of this remedial approach. In this study, a series of diffusion experiments were performed to measure the permanganate diffusion and reaction in four different types of sedimentary rocks (dark gray mudstone, light gray mudstone, red sandstone, and tan sandstone). Results showed that, within the experimental time frame (~2 months), oxidant migration into the rock was limited to distances less than 500 μm. The observed diffusivities for permanganate into the rock matrices ranged from 5.3 × 10(-13) to 1.3 × 10(-11) cm(2)/s. These values were reasonably predicted by accounting for both the rock oxidant demand and the effective diffusivity of the rock. Various Mn minerals formed as surface coatings from reduction of permanganate coupled with oxidation of total organic carbon (TOC), and the nature of the formed Mn minerals was dependent upon the rock type. Post-treatment tracer testing showed that these Mn mineral coatings had a negligible impact on diffusion through the rock. Overall, our results showed that the extent of permanganate diffusion and reaction depended on rock properties, including porosity, mineralogy, and organic carbon. These results have important implications for our understanding of long-term organic contaminant remediation in sedimentary rocks using permanganate. Copyright © 2014 Elsevier B.V. All rights reserved.

Stochastic dynamics of a delayed bistable system with multiplicative noise

Energy Technology Data Exchange (ETDEWEB)

Dung, Nguyen Tien, E-mail: dung-nguyentien10@yahoo.com, E-mail: dungnt@fpt.edu.vn [Department of Mathematics, FPT University, No 8 Ton That Thuyet, My Dinh, Tu Liem, Hanoi (Viet Nam)

2014-05-15

In this paper we investigate the properties of a delayed bistable system under the effect of multiplicative noise. We first prove the existence and uniqueness of the positive solution and show that its moments are uniformly bounded. Then, we study stochastic dynamics of the solution in long time, the lower and upper bounds for the paths and an estimate for the average value are provided.

Traveling waves in the discrete fast buffered bistable system.

Science.gov (United States)

Tsai, Je-Chiang; Sneyd, James

2007-11-01

We study the existence and uniqueness of traveling wave solutions of the discrete buffered bistable equation. Buffered excitable systems are used to model, among other things, the propagation of waves of increased calcium concentration, and discrete models are often used to describe the propagation of such waves across multiple cells. We derive necessary conditions for the existence of waves, and, under some restrictive technical assumptions, we derive sufficient conditions. When the wave exists it is unique and stable.

Geometric and potential dynamics interpretation of the optic ring resonator bistability

Science.gov (United States)

Chiangga, S.; Chittha, T.; Frank, T. D.

2015-07-01

The optical bistability is a fundamental nonlinear feature of the ring resonator. A geometric and potential dynamics interpretation of the bistability is given. Accordingly, the bistability of the nonlinear system is shown to be a consequence of geometric laws of vector calculus describing the resonator ring. In contrast, the so-called transcendental relations that have been obtained in the literature in order to describe the optical wave are interpreted in terms of potential dynamical systems. The proposed novel interpretation provides new insights into the nature of the ring resonator optical bistability. The fundamental work by Rukhlenko, Premaratne and Agrawal (2010) as well as a more recent study by Chiangga, Pitakwongsaporn, Frank and Yupapin (2013) are considered.

Fundamental role of bistability in optimal homeostatic control

Science.gov (United States)

Wang, Guanyu

2013-03-01

Bistability is a fundamental phenomenon in nature and has a number of fine properties. However, these properties are consequences of bistability at the physiological level, which do not explain why it had to emerge during evolution. Using optimal homeostasis as the first principle and Pontryagin's Maximum Principle as the optimization approach, I find that bistability emerges as an indispensable control mechanism. Because the mathematical model is general and the result is independent of parameters, it is likely that most biological systems use bistability to control homeostasis. Glucose homeostasis represents a good example. It turns out that bistability is the only solution to a dilemma in glucose homeostasis: high insulin efficiency is required for rapid plasma glucose clearance, whereas an insulin sparing state is required to guarantee the brain's safety during fasting. This new perspective can illuminate studies on the twin epidemics of obesity and diabetes and the corresponding intervening strategies. For example, overnutrition and sedentary lifestyle may represent sudden environmental changes that cause the lose of optimality, which may contribute to the marked rise of obesity and diabetes in our generation.

Curved fronts in the Belousov-Zhabotinskii reaction-diffusion systems in R2

Science.gov (United States)

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.

Effects of error feedback on a nonlinear bistable system with stochastic resonance

International Nuclear Information System (INIS)

Li Jian-Long; Zhou Hui

2012-01-01

In this paper, we discuss the effects of error feedback on the output of a nonlinear bistable system with stochastic resonance. The bit error rate is employed to quantify the performance of the system. The theoretical analysis and the numerical simulation are presented. By investigating the performances of the nonlinear systems with different strengths of error feedback, we argue that the presented system may provide guidance for practical nonlinear signal processing

Solid state reaction studies in Fe{sub 3}O{sub 4}–TiO{sub 2} system by diffusion couple method

Energy Technology Data Exchange (ETDEWEB)

Ren, Zhongshan [State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 100083 (China); School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083 (China); Hu, Xiaojun, E-mail: huxiaojun@ustb.edu.cn [State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 100083 (China); School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083 (China); Xue, Xiangxin [School of Materials and Metallurgy, Northeastern University, Shenyang 110006 (China); Chou, Kuochih [State Key Laboratory of Advanced Metallurgy, University of Science and Technology Beijing, Beijing 100083 (China); School of Metallurgical and Ecological Engineering, University of Science and Technology Beijing, Beijing 100083 (China)

2013-12-15

Highlights: •The solid state reactions of Fe2O3-TiO2 system was studied by the diffusion couple method. •Different products were formed by diffusion, and the FeTiO3 was more stable phase. •The inter-diffusion coefficients and diffusion activation energy were estimated. -- Abstract: The solid state reactions in Fe{sub 3}O{sub 4}–TiO{sub 2} system has been studied by diffusion couple experiments at 1323–1473 K, in which the oxygen partial pressure was controlled by the CO–CO{sub 2} gas mixture. The XRD analysis was used to confirm the phases of the inter-compound, and the concentration profiles were determined by electron probe microanalysis (EPMA). Based on the concentration profile of Ti, the inter-diffusion coefficients in Fe{sub 3}O{sub 4} phase, which were both temperature and concentration of Ti ions dependent, were calculated by the modified Boltzmann–Matano method. According to the relation between the thickness of diffusion layer and temperature, the diffusion coefficient of the Fe{sub 3}O{sub 4}–TiO{sub 2} system was obtained. According to the Arrhenius equation, the estimated diffusion activation energy was about 282.1 ± 18.8 kJ mol{sup −1}.

Flow-Injection Responses of Diffusion Processes and Chemical Reactions

DEFF Research Database (Denmark)

Andersen, Jens Enevold Thaulov

2000-01-01

tool of automated analytical chemistry. The need for an even lower consumption of chemicals and for computer analysis has motivated a study of the FIA peak itself, that is, a theoretical model was developed, that provides detailed knowledge of the FIA profile. It was shown that the flow in a FIA...... manifold may be characterised by a diffusion coefficient that depends on flow rate, denoted as the kinematic diffusion coefficient. The description was applied to systems involving species of chromium, both in the case of simple diffusion and in the case of chemical reactions. It is suggested that it may...... be used in the resolution of FIA profiles to obtain information about the content of interference’s, in the study of chemical reaction kinetics and to measure absolute concentrations within the FIA-detector cell....

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.

Asymptotic stability of a coupled advection-diffusion-reaction system arising in bioreactor processes

Directory of Open Access Journals (Sweden)

Maria Crespo

2017-08-01

Full Text Available In this work, we present an asymptotic analysis of a coupled system of two advection-diffusion-reaction equations with Danckwerts boundary conditions, which models the interaction between a microbial population (e.g., bacteria, called biomass, and a diluted organic contaminant (e.g., nitrates, called substrate, in a continuous flow bioreactor. This system exhibits, under suitable conditions, two stable equilibrium states: one steady state in which the biomass becomes extinct and no reaction is produced, called washout, and another steady state, which corresponds to the partial elimination of the substrate. We use the linearization method to give sufficient conditions for the linear asymptotic stability of the two stable equilibrium configurations. Finally, we compare our asymptotic analysis with the usual asymptotic analysis associated to the continuous bioreactor when it is modeled with ordinary differential equations.

Optical bistability and multistability in polaritonic materials doped with nanoparticles

International Nuclear Information System (INIS)

Wang, Zhiping; Yu, Benli

2014-01-01

We investigate the optical bistability and multistability in polaritonic materials doped with nanoparticles inside an optical ring cavity. It is found that the optical bistability and multistability can be easily controlled by adjusting the corresponding parameters of the system properly. The effect of the dipole–dipole interaction has also been included in the formulation, which leads to interesting phenomena. Our scheme opens up the possibility of controling the optical bistability and multistability in polaritonic materials doped with nanoparticles. (letter)

A novel bistable energy harvesting concept

International Nuclear Information System (INIS)

Scarselli, G; Nicassio, F; Pinto, F; Ciampa, F; Iervolino, O; Meo, M

2016-01-01

Bistable energy harvesting has become a major field of research due to some unique features for converting mechanical energy into electrical power. When properly loaded, bistable structures snap-through from one stable configuration to another, causing large strains and consequently power generation. Moreover, bistable structures can harvest energy across a broad-frequency bandwidth due to their nonlinear characteristics. Despite the fact that snap-through may be triggered regardless of the form or frequency of exciting vibration, the external force must reach a specific snap-through activation threshold value to trigger the transition from one stable state to another. This aspect is a limiting factor for realistic vibration energy harvesting application with bistable devices. This paper presents a novel power harvesting concept for bistable composites based on a ‘lever effect’ aimed at minimising the activation force to cause the snap through by choosing properly the bistable structures’ constraints. The concept was demonstrated with the help of numerical simulation and experimental testing. The results showed that the actuation force is one order of magnitude smaller (3%–6%) than the activation force of conventionally constrained bistable devices. In addition, it was shown that the output voltage was higher than the conventional configuration, leading to a significant increase in power generation. This novel concept could lead to a new generation of more efficient bistable energy harvesters for realistic vibration environments. (paper)

Vorticity field, helicity integral and persistence of entanglement in reaction-diffusion systems

International Nuclear Information System (INIS)

Trueba, J L; Arrayas, M

2009-01-01

We show that a global description of the stability of entangled structures in reaction-diffusion systems can be made by means of a helicity integral. A vorticity vector field is defined for these systems, as in electromagnetism or fluid dynamics. We have found under which conditions the helicity is conserved or lost through the boundaries of the medium, so the entanglement of structures observed is preserved or disappears during time evolution. We illustrate the theory with an example of knotted entanglement in a FitzHugh-Nagumo model. For this model, we introduce new non-trivial initial conditions using the Hopf fibration and follow the time evolution of the entanglement. (fast track communication)

Vorticity field, helicity integral and persistence of entanglement in reaction-diffusion systems

Energy Technology Data Exchange (ETDEWEB)

Trueba, J L; Arrayas, M [Area de Electromagnetismo, Universidad Rey Juan Carlos, Camino del Molino s/n, 28943 Fuenlabrada, Madrid (Spain)

2009-07-17

We show that a global description of the stability of entangled structures in reaction-diffusion systems can be made by means of a helicity integral. A vorticity vector field is defined for these systems, as in electromagnetism or fluid dynamics. We have found under which conditions the helicity is conserved or lost through the boundaries of the medium, so the entanglement of structures observed is preserved or disappears during time evolution. We illustrate the theory with an example of knotted entanglement in a FitzHugh-Nagumo model. For this model, we introduce new non-trivial initial conditions using the Hopf fibration and follow the time evolution of the entanglement. (fast track communication)

What is refractive optical bistability

International Nuclear Information System (INIS)

Dzhehov, Tomislav

1993-01-01

The basic elements of the theory of refractive optical bistability, assuming mediums with linear absorption are given. Special attention is paid to bistable etalons of semiconductor materials an oxide glasses, since some of them are considered as promising components for optical bistability applications. The design optimization of such devices for minimum switching intensity is analyzed. Computer simulation of the transfer characteristic recording for two InSb etalons is presented. (author)

Noise-induced coherence in bistable systems with multiple time delays

International Nuclear Information System (INIS)

Jiang Yu; Dong, Shi-Hai; Lozada-Cassou, M.

2004-01-01

We study the correlation properties of noise-driven bistable systems with multiple time-delay feedbacks. For small noisy perturbation and feedback magnitude, we derive the autocorrelation function and the power spectrum based on the two-state model with transition rates depending on the earlier states of the system. A comparison between the single and double time delays reveals that the auto correlation functions exhibit exponential decay with small undulation for the double time delays, in contrast with the remarkable oscillatory behavior at small time lags for the single time delay

Numerical and experimental study of bistable plates for morphing structures

Science.gov (United States)

Nicassio, F.; Scarselli, G.; Avanzini, G.; Del Core, G.

2017-04-01

This study is concerned with the activation energy threshold of bistable composite plates in order to tailor a bistable system for specific aeronautical applications. The aim is to explore potential configurations of the bistable plates and their dynamic behavior for designing novel morphing structure suitable for aerodynamic surfaces and, as a possible further application, for power harvesters. Bistable laminates have two stable mechanical shapes that can withstand aerodynamic loads without additional constraint forces or locking mechanisms. This kind of structures, when properly loaded, snap-through from one stable configuration to another, causing large strains that can also be used for power harvesting scopes. The transition between the stable states of the composite laminate can be triggered, in principle, simply by aerodynamic loads (pilot, disturbance or passive inputs) without the need of servo-activated control systems. Both numerical simulations based on Finite Element models and experimental testing based on different activating forcing spectra are used to validate this concept. The results show that dynamic activation of bistable plates depend on different parameters that need to be carefully managed for their use as aircraft passive wing flaps.

Event-triggered synchronization for reaction-diffusion complex networks via random sampling

Science.gov (United States)

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.

Hybrid optoelectronic device with multiple bistable outputs

Energy Technology Data Exchange (ETDEWEB)

Costazo-Caso, Pablo A; Jin Yiye; Gelh, Michael; Granieri, Sergio; Siahmakoun, Azad, E-mail: pcostanzo@ing.unlp.edu.are, E-mail: granieri@rose-hulma.edu, E-mail: siahmako@rose-hulma.edu [Department of Physics and Optical Engineering, Rose-Hulman Institute of Technology, 5500 Wabash Avenue, Terre Haute, IN 47803 (United States)

2011-01-01

Optoelectronic circuits which exhibit optical and electrical bistability with hysteresis behavior are proposed and experimentally demonstrated. The systems are based on semiconductor optical amplifiers (SOA), bipolar junction transistors (BJT), PIN photodiodes (PD) and laser diodes externally modulated with integrated electro-absorption modulators (LD-EAM). The device operates based on two independent phenomena leading to both electrical bistability and optical bistability. The electrical bistability is due to the series connection of two p-i-n structures (SOA, BJT, PD or LD) in reverse bias. The optical bistability is consequence of the quantum confined Stark effect (QCSE) in the multi-quantum well (MQW) structure in the intrinsic region of the device. This effect produces the optical modulation of the transmitted light through the SOA (or reflected from the PD). Finally, because the optical transmission of the SOA (in reverse bias) and the reflected light from the PD are so small, a LD-EAM modulated by the voltage across these devices are employed to obtain a higher output optical power. Experiments show that the maximum switching frequency is in MHz range and the rise/fall times lower than 1 us. The temporal response is mainly limited by the electrical capacitance of the devices and the parasitic inductances of the connecting wires. The effects of these components can be reduced in current integration technologies.

Bistable minimum energy structures (BiMES) for binary robotics

International Nuclear Information System (INIS)

Follador, M; Conn, A T; Rossiter, J

2015-01-01

Bistable minimum energy structures (BiMES) are devices derived from the union of the concepts of dielectric elastomer minimum energy structures and bistable systems. This article presents this novel approach to active, elastic and bistable structures. BiMES are based on dielectric elastomer actuators (DEAs), which act as antagonists and provide the actuation for switching between the two equilibrium positions. A central elastic beam is the backbone of the structure and is buckled into the minimum energy configurations by the action of the two DEAs. The theory and the model of the device are presented, and also its fabrication process. BiMES are considered as fundamental units for more complex structures, which are presented and fabricated as proof of concept. Two different ways of combining the multiple units are proposed: a parallel configuration, to make a simple gripper, and a serial configuration, to generate a binary device. The possibility of using the bistable system as a continuous bender actuator, by modulating the actuation voltage of the two DEAs, was also investigated. (paper)

The effects of intrinsic noise on the behaviour of bistable cell regulatory systems under quasi-steady state conditions.

Science.gov (United States)

de la Cruz, Roberto; Guerrero, Pilar; Spill, Fabian; Alarcón, Tomás

2015-08-21

We analyse the effect of intrinsic fluctuations on the properties of bistable stochastic systems with time scale separation operating under quasi-steady state conditions. We first formulate a stochastic generalisation of the quasi-steady state approximation based on the semi-classical approximation of the partial differential equation for the generating function associated with the chemical master equation. Such approximation proceeds by optimising an action functional whose associated set of Euler-Lagrange (Hamilton) equations provides the most likely fluctuation path. We show that, under appropriate conditions granting time scale separation, the Hamiltonian can be re-scaled so that the set of Hamilton equations splits up into slow and fast variables, whereby the quasi-steady state approximation can be applied. We analyse two particular examples of systems whose mean-field limit has been shown to exhibit bi-stability: an enzyme-catalysed system of two mutually inhibitory proteins and a gene regulatory circuit with self-activation. Our theory establishes that the number of molecules of the conserved species is order parameters whose variation regulates bistable behaviour in the associated systems beyond the predictions of the mean-field theory. This prediction is fully confirmed by direct numerical simulations using the stochastic simulation algorithm. This result allows us to propose strategies whereby, by varying the number of molecules of the three conserved chemical species, cell properties associated to bistable behaviour (phenotype, cell-cycle status, etc.) can be controlled.

The effects of intrinsic noise on the behaviour of bistable cell regulatory systems under quasi-steady state conditions

Energy Technology Data Exchange (ETDEWEB)

Cruz, Roberto; Alarcón, Tomás de la [Centre de Recerca Matemàtica. Edifici C, Campus de Bellaterra, 08193 Bellaterra (Barcelona) (Spain); Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona) (Spain); Guerrero, Pilar [Department of Mathematics, University College London, Gower Street, London WC1E 6BT (United Kingdom); Spill, Fabian [Department of Biomedical Engineering, Boston University, 44 Cummington Street, Boston, Massachusetts 02215 (United States); Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139 (United States)

2015-08-21

We analyse the effect of intrinsic fluctuations on the properties of bistable stochastic systems with time scale separation operating under quasi-steady state conditions. We first formulate a stochastic generalisation of the quasi-steady state approximation based on the semi-classical approximation of the partial differential equation for the generating function associated with the chemical master equation. Such approximation proceeds by optimising an action functional whose associated set of Euler-Lagrange (Hamilton) equations provides the most likely fluctuation path. We show that, under appropriate conditions granting time scale separation, the Hamiltonian can be re-scaled so that the set of Hamilton equations splits up into slow and fast variables, whereby the quasi-steady state approximation can be applied. We analyse two particular examples of systems whose mean-field limit has been shown to exhibit bi-stability: an enzyme-catalysed system of two mutually inhibitory proteins and a gene regulatory circuit with self-activation. Our theory establishes that the number of molecules of the conserved species is order parameters whose variation regulates bistable behaviour in the associated systems beyond the predictions of the mean-field theory. This prediction is fully confirmed by direct numerical simulations using the stochastic simulation algorithm. This result allows us to propose strategies whereby, by varying the number of molecules of the three conserved chemical species, cell properties associated to bistable behaviour (phenotype, cell-cycle status, etc.) can be controlled.

Existence of global solutions to reaction-diffusion systems via a Lyapunov functional

Directory of Open Access Journals (Sweden)

Said Kouachi

2001-10-01

Full Text Available The purpose of this paper is to construct polynomial functionals (according to solutions of the coupled reaction-diffusion equations which give $L^{p}$-bounds for solutions. When the reaction terms are sufficiently regular, using the well known regularizing effect, we deduce the existence of global solutions. These functionals are obtained independently of work done by Malham and Xin [11].

Bistable responses in bacterial genetic networks: Designs and dynamical consequences

Science.gov (United States)

Tiwari, Abhinav; Ray, J. Christian J.; Narula, Jatin; Igoshin, Oleg A.

2011-01-01

A key property of living cells is their ability to react to stimuli with specific biochemical responses. These responses can be understood through the dynamics of underlying biochemical and genetic networks. Evolutionary design principles have been well studied in networks that display graded responses, with a continuous relationship between input signal and system output. Alternatively, biochemical networks can exhibit bistable responses so that over a range of signals the network possesses two stable steady states. In this review, we discuss several conceptual examples illustrating network designs that can result in a bistable response of the biochemical network. Next, we examine manifestations of these designs in bacterial master-regulatory genetic circuits. In particular, we discuss mechanisms and dynamic consequences of bistability in three circuits: two-component systems, sigma-factor networks, and a multistep phosphorelay. Analyzing these examples allows us to expand our knowledge of evolutionary design principles for networks with bistable responses. PMID:21385588

Bistable scattering in graphene-coated dielectric nanowires.

Science.gov (United States)

Li, Rujiang; Wang, Huaping; Zheng, Bin; Dehdashti, Shahram; Li, Erping; Chen, Hongsheng

2017-06-22

In nonlinear plasmonics, the switching threshold of optical bistability is limited by the weak nonlinear responses from the conventional Kerr dielectric media. Considering the giant nonlinear susceptibility of graphene, here we develop a nonlinear scattering model under the mean field approximation and study the bistable scattering in graphene-coated dielectric nanowires based on the semi-analytical solutions. We find that the switching intensities of bistable scattering can be smaller than 1 MW cm -2 at the working frequency. To further decrease the switching intensities, we show that the most important factor that restricts the bistable scattering is the relaxation time of graphene. Our work not only reveals some general characteristics of graphene-based bistable scattering, but also provides a guidance to further applications of optical bistability in the high speed all-optical signal processing.

Unidirectional Transition Waves in Bistable Lattices.

Science.gov (United States)

Nadkarni, Neel; Arrieta, Andres F; Chong, Christopher; Kochmann, Dennis M; Daraio, Chiara

2016-06-17

We present a model system for strongly nonlinear transition waves generated in a periodic lattice of bistable members connected by magnetic links. The asymmetry of the on-site energy wells created by the bistable members produces a mechanical diode that supports only unidirectional transition wave propagation with constant wave velocity. We theoretically justify the cause of the unidirectionality of the transition wave and confirm these predictions by experiments and simulations. We further identify how the wave velocity and profile are uniquely linked to the double-well energy landscape, which serves as a blueprint for transition wave control.

Stochastic reaction-diffusion algorithms for macromolecular crowding

Science.gov (United States)

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.

Interlinked bistable mechanisms generate robust mitotic transitions.

Science.gov (United States)

Hutter, Lukas H; Rata, Scott; Hochegger, Helfrid; Novák, Béla

2017-10-18

The transitions between phases of the cell cycle have evolved to be robust and switch-like, which ensures temporal separation of DNA replication, sister chromatid separation, and cell division. Mathematical models describing the biochemical interaction networks of cell cycle regulators attribute these properties to underlying bistable switches, which inherently generate robust, switch-like, and irreversible transitions between states. We have recently presented new mathematical models for two control systems that regulate crucial transitions in the cell cycle: mitotic entry and exit, 1 and the mitotic checkpoint. 2 Each of the two control systems is characterized by two interlinked bistable switches. In the case of mitotic checkpoint control, these switches are mutually activating, whereas in the case of the mitotic entry/exit network, the switches are mutually inhibiting. In this Perspective we describe the qualitative features of these regulatory motifs and show that having two interlinked bistable mechanisms further enhances robustness and irreversibility. We speculate that these network motifs also underlie other cell cycle transitions and cellular transitions between distinct biochemical states.

Harnessing the bistable composite shells to design a tunable phononic band gap structure

Science.gov (United States)

Li, Yi; Xu, Yanlong

2018-02-01

By proposing a system composed of an array of bistable composite shells immersed in air, we develop a new class of periodic structure to control the propagation of sound. Through numerical investigation, we find that the acoustic band gap of this system can be switched on and off by triggering the snap through deformation of the bistable composite shells. The shape of cross section and filling fraction of unit cell can be altered by different number of bistable composite shells, and they have strong impact on the position and width of the band gap. The proposed concept paves the way of using the bistable structures to design a new class of metamaterials that can be enable to manipulate sound.

Linear population allocation by bistable switches in response to transient stimulation.

Science.gov (United States)

Srimani, Jaydeep K; Yao, Guang; Neu, John; Tanouchi, Yu; Lee, Tae Jun; You, Lingchong

2014-01-01

Many cellular decision processes, including proliferation, differentiation, and phenotypic switching, are controlled by bistable signaling networks. In response to transient or intermediate input signals, these networks allocate a population fraction to each of two distinct states (e.g. OFF and ON). While extensive studies have been carried out to analyze various bistable networks, they are primarily focused on responses of bistable networks to sustained input signals. In this work, we investigate the response characteristics of bistable networks to transient signals, using both theoretical analysis and numerical simulation. We find that bistable systems exhibit a common property: for input signals with short durations, the fraction of switching cells increases linearly with the signal duration, allowing the population to integrate transient signals to tune its response. We propose that this allocation algorithm can be an optimal response strategy for certain cellular decisions in which excessive switching results in lower population fitness.

A broadband electromagnetic energy harvester with a coupled bistable structure

International Nuclear Information System (INIS)

Zhu, D; Beeby, S P

2013-01-01

This paper investigates a broadband electromagnetic energy harvester with a coupled bistable structure. Both analytical model and experimental results showed that the coupled bistable structure requires lower excitation force to trigger bistable operation than conventional bistable structures. A compact electromagnetic vibration energy harvester with a coupled bistable structure was implemented and tested. It was excited under white noise vibrations. Experimental results showed that the coupled bistable energy harvester can achieve bistable operation with lower excitation amplitude and generate more output power than both conventional bistable and linear energy harvesters under white noise excitation

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...

Divergence of relative difference in Gaussian distribution function and stochastic resonance in a bistable system with frictionless state transition

Science.gov (United States)

Kasai, Seiya; Ichiki, Akihisa; Tadokoro, Yukihiro

2018-03-01

A bistable system efficiently detects a weak signal by adding noise, which is referred to as stochastic resonance. A previous theory deals with friction in state transition; however, this hypothesis is inadequate when friction force is negligible such as in nano- and molecular-scale systems. We show that, when the transition occurs without friction, the sensitivity of the bistable system to a Gaussian-noise-imposed weak signal becomes significantly high. The sensitivity is determined by the relative difference in noise distribution function. We find that the relative difference in Gaussian distribution function diverges in its tail edge, resulting in a high sensitivity in the present system.

Effects of intrinsic stochasticity on delayed reaction-diffusion patterning systems

KAUST Repository

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

KAUST Repository

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.

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.

Bistable luminescence of trivalent rare-earth ions in crystals

International Nuclear Information System (INIS)

Sole, Jose Garcia; Ramirez O, Maria de la; Rodenas, Airan; Jaque, Daniel; Bausa, Luisa; Bettinelli, Marco; Speghini, Adolfo; Cavalli, Enrico; Ivleva, Lioudmila

2006-01-01

In this work, we have examined three new bistable systems based on the luminescence of three different crystals activated with trivalent rare earth ions. We have focussed our attention on Yb 3+ ions activators, for which the most relevant results are obtained. The first crystal, Sr 0.6 Ba 0.4 Nb 2 O 6 , is a ferroelectric material with a relatively low phase transition temperature (∼370 K), which provides bistability in the luminescence of Yb 3+ ions due to the thermal hysteresis associated with phase transition. The second crystal, LiNbO 3 , provides an intrinsic bistability in the luminescence of Yb 3+ ions, which is driven by changes in the excitation intensity. In the third crystal, NdPO 4 , a new mechanism of excitation intensity driven bistability is obtained when activated with Yb 3+ ions, due to a interplay between the Nd 3+ ↔Yb 3+ energy transfer and back transfer processes

A variational approach to bifurcation points of a reaction-diffusion system with obstacles and neumann boundary conditions

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

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

Diversity and functional properties of bistable pigments.

Science.gov (United States)

Tsukamoto, Hisao; Terakita, Akihisa

2010-11-01

Rhodopsin and related opsin-based pigments, which are photosensitive membrane proteins, have been extensively studied using a wide variety of techniques, with rhodopsin being the most understood G protein-coupled receptor (GPCR). Animals use various opsin-based pigments for vision and a wide variety of non-visual functions. Many functionally varied pigments are roughly divided into two kinds, based on their photoreaction: bistable and monostable pigments. Bistable pigments are thermally stable before and after photo-activation, but monostable pigments are stable only before activation. Here, we review the diversity of bistable pigments and their molecular characteristics. We also discuss the mechanisms underlying different molecular characteristics of bistable and monostable pigments. In addition, the potential of bistable pigments as a GPCR model is proposed.

Dynamics of one- and two-dimensional fronts in a bistable equation with time-delayed global feedback: Propagation failure and control mechanisms

International Nuclear Information System (INIS)

Boubendir, Yassine; Mendez, Vicenc; Rotstein, Horacio G.

2010-01-01

We study the evolution of fronts in a bistable equation with time-delayed global feedback in the fast reaction and slow diffusion regime. This equation generalizes the Hodgkin-Grafstein and Allen-Cahn equations. We derive a nonlinear equation governing the motion of fronts, which includes a term with delay. In the one-dimensional case this equation is linear. We study the motion of one- and two-dimensional fronts, finding a much richer dynamics than for the previously studied cases (without time-delayed global feedback). We explain the mechanism by which localized fronts created by inhibitory global coupling loose stability in a Hopf bifurcation as the delay time increases. We show that for certain delay times, the prevailing phase is different from that corresponding to the system in the absence of global coupling. Numerical simulations of the partial differential equation are in agreement with the analytical predictions.

Characterizing multistationarity regimes in biochemical reaction networks.

Directory of Open Access Journals (Sweden)

Irene Otero-Muras

Full Text Available Switch like responses appear as common strategies in the regulation of cellular systems. Here we present a method to characterize bistable regimes in biochemical reaction networks that can be of use to both direct and reverse engineering of biological switches. In the design of a synthetic biological switch, it is important to study the capability for bistability of the underlying biochemical network structure. Chemical Reaction Network Theory (CRNT may help at this level to decide whether a given network has the capacity for multiple positive equilibria, based on their structural properties. However, in order to build a working switch, we also need to ensure that the bistability property is robust, by studying the conditions leading to the existence of two different steady states. In the reverse engineering of biological switches, knowledge collected about the bistable regimes of the underlying potential model structures can contribute at the model identification stage to a drastic reduction of the feasible region in the parameter space of search. In this work, we make use and extend previous results of the CRNT, aiming not only to discriminate whether a biochemical reaction network can exhibit multiple steady states, but also to determine the regions within the whole space of parameters capable of producing multistationarity. To that purpose we present and justify a condition on the parameters of biochemical networks for the appearance of multistationarity, and propose an efficient and reliable computational method to check its satisfaction through the parameter space.

Distributed processing in bistable perception

NARCIS (Netherlands)

Knapen, T.H.J.

2007-01-01

A very incisive way of studying visual awareness and the mechanisms that underlie it, it to use bistable perception. In bistable perception, an observer's perceptual state alternates between one interpretation and its mutually exclusive counterpart while the stimulus remains the same. This gives us

Diffusion limited reactions in crystalline solids

International Nuclear Information System (INIS)

Fastenau, R.

1982-01-01

Diffusion limited reactions in crystal lattices are studied with diffusion and random walk theory. First the random walk on a crystal lattice is studied. These results are used in a formal study of diffusion limited reactions in which the following simplified traps are discussed: planes, cylinders, spheres, disks and rings. The traps are either present at the start of the process (annealing) or fed into the crystal at a constant rate (continuous production). For the study of trapping processes occurring in real crystals it was necessary to investigate the interaction of the reacting species on the atomic level. Using lattice relaxation calculations, several reactions were studied. These calculations result in a model for the potential energy of the crystal versus the separation of the reaction partners. This model is used in Monte Carlo simulations of the trapping process, which are made at a high trap density, since the extrapolation to the low density regime can be made using the formal part of this work. The following reactions were studied: the trapping of interstitial helium atoms by vacancies, self interstitial vacancy recombination, the trapping of vacancies by immobile, helium filled, vacancies and the capture of self interstitials and vacancies by dislocations. A part of these results is used in two models for the low temperature nucleation and growth of bubbles due to helium bombardment. The models described give the right bubble density versus helium dose, but differ widely in the fraction of helium present in the bubbles found. A mechanism of blistering based on a percolation effect is also discussed. (Auth.)

Heterogeneity induces spatiotemporal oscillations in reaction-diffusion systems

Science.gov (United States)

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.

Evans functions and bifurcations of nonlinear waves of some nonlinear reaction diffusion equations

Science.gov (United States)

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.

Automatic simplification of systems of reaction-diffusion equations by a posteriori analysis.

Science.gov (United States)

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.

Reaction-Transport Systems Mesoscopic Foundations, Fronts, and Spatial Instabilities

CERN Document Server

Horsthemke, Werner; Mendez, Vicenc

2010-01-01

This book is an introduction to the dynamics of reaction-diffusion systems, with a focus on fronts and stationary spatial patterns. Emphasis is on systems that are non-standard in the sense that either the transport is not simply classical diffusion (Brownian motion) or the system is not homogeneous. A important feature is the derivation of the basic phenomenological equations from the mesoscopic system properties. Topics addressed include transport with inertia, described by persistent random walks and hyperbolic reaction-transport equations and transport by anomalous diffusion, in particular subdiffusion, where the mean square displacement grows sublinearly with time. In particular reaction-diffusion systems are studied where the medium is in turn either spatially inhomogeneous, compositionally heterogeneous or spatially discrete. Applications span a vast range of interdisciplinary fields and the systems considered can be as different as human or animal groups migrating under external influences, population...

Stochastic resonance in bistable systems driven by harmonic noise

International Nuclear Information System (INIS)

Neiman, A.; Schimansky-Geier, L.

1994-01-01

We study stochastic resonance in a bistable system which is excited simultaneously by white and harmonic noise which we understand as the signal. In our case the spectral line of the signal has a finite width as it occurs in many real situations. Using techniques of cumulant analysis as well as computer simulations we find that the effect of stochastic resonance is preserved in the case of harmonic noise excitation. Moreover we show that the width of the spectral line of the signal at the output can be decreased via stochastic resonance. The last could be of importance in the practical using of the stochastic resonance

Laser Spot Detection Based on Reaction Diffusion

OpenAIRE

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...

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

Bistable near field and bistable transmittance in 2D composite slab consisting of nonlocal core-Kerr shell inclusions.

Science.gov (United States)

Huang, Yang; Wu, Ya Min; Gao, Lei

2017-01-23

We carry out a theoretical study on optical bistability of near field intensity and transmittance in two-dimensional nonlinear composite slab. This kind of 2D composite is composed of nonlocal metal/Kerr-type dielectric core-shell inclusions randomly embedded in the host medium, and we derivate the nonlinear relation between the field intensity in the shell of inclusions and the incident field intensity with self-consistent mean field approximation. Numerical demonstration has been performed to show the viable parameter space for the bistable near field. We show that nonlocality can provide broader region in geometric parameter space for bistable near field as well as bistable transmittance of the nonlocal composite slab compared to local case. Furthermore, we investigate the bistable transmittance in wavelength spectrum, and find that besides the input intensity, the wavelength operation could as well make the transmittance jump from a high value to a low one. This kind of self-tunable nano-composite slab might have potential application in optical switching devices.

Reaction time for trimolecular reactions in compartment-based reaction-diffusion models

Science.gov (United States)

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.

Bistable microelectromechanical actuator

Science.gov (United States)

Fleming, James G.

1999-01-01

A bistable microelectromechanical (MEM) actuator is formed on a substrate and includes a stressed membrane of generally rectangular shape that upon release assumes a curvilinear cross-sectional shape due to attachment at a midpoint to a resilient member and at opposing edges to a pair of elongate supports. The stressed membrane can be electrostatically switched between a pair of mechanical states having mirror-image symmetry, with the MEM actuator remaining in a quiescent state after a programming voltage is removed. The bistable MEM actuator according to various embodiments of the present invention can be used to form a nonvolatile memory element, an optical modulator (with a pair of mirrors supported above the membrane and moving in synchronism as the membrane is switched), a switchable mirror (with a single mirror supported above the membrane at the midpoint thereof) and a latching relay (with a pair of contacts that open and close as the membrane is switched). Arrays of bistable MEM actuators can be formed for applications including nonvolatile memories, optical displays and optical computing.

Statistical approach to bistable behaviour of a nonlinear system in a stationary field

International Nuclear Information System (INIS)

Luks, A.; Perina, J.; Perinova, V.; Bertolotti, M.; Sibilia, C.

1984-01-01

The quantum statistical properties of an elastic scattering process are investigated comprising crossed light beams which are in interaction with a particle (electron) beam treated as ''two-step'' system. Using the master equation and the generalized Fokker-Planck equation techniques, the integrated intensities are characterized by their probability distributions and it is demonstrated that single modes exhibit two-peak bistable behaviour. (author)

Controlling steady-state and dynamical properties of atomic optical bistability

CERN Document Server

Joshi, Amitabh

2012-01-01

This book provides a comprehensive introduction to the theoretical and experimental studies of atomic optical bistability and multistability, and their dynamical properties in systems with two- and three-level inhomogeneously-broadened atoms inside an optical cavity. By making use of the modified linear absorption and dispersion, as well as the greatly enhanced nonlinearity in the three-level electromagnetically induced transparency system, the optical bistablity and efficient all-optical switching can be achieved at relatively low laser powers, which can be well controlled and manipulated. Un

Stochastic resonance in an asymmetric bistable system driven by multiplicative colored noise and additive white noise

International Nuclear Information System (INIS)

Zhou Bingchang; Xu Wei

2008-01-01

The phenomenon of stochastic resonance (SR) in a bistable system driven by multiplicative colored and additive white noises and a periodic rectangular signal with a constant component is studied by using the unified colored noise approximation and the theory of signal-to-noise (SNR) in the adiabatic limit. The analytic expression of the SNR is obtained for arbitrary signal amplitude without being restricted to small amplitudes. The SNR is a non-monotonic function of intensities of multiplicative colored and additive white noises and correlation time of multiplicative colored noise, so SR exhibits in the bistable system. The effects of potential asymmetry r and correlation time τ of multiplicative colored noise on SNR are opposite. Moreover, It is more sensitive to control SR through adjusting the additive white noise intensity D than adjusting the multiplicative colored noise intensity Q

Meredys, a multi-compartment reaction-diffusion simulator using multistate realistic molecular complexes

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/.

Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations

KAUST Repository

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

Dynamic phase transition in diffusion-limited reactions

International Nuclear Information System (INIS)

Tauber, U.C.

2002-01-01

Many non-equilibrium systems display dynamic phase transitions from active to absorbing states, where fluctuations cease entirely. Based on a field theory representation of the master equation, the critical behavior can be analyzed by means of the renormalization group. The resulting universality classes for single-species systems are reviewed here. Generically, the critical exponents are those of directed percolation (Reggeon field theory), with critical dimension d c = 4. Yet local particle number parity conservation in even-offspring branching and annihilating random walks implies an inactive phase (emerging below d c = 4/3) that is characterized by the power laws of the pair annihilation reaction, and leads to different critical exponents at the transition. For local processes without memory, the pair contact process with diffusion represents the only other non-trivial universality class. The consistent treatment of restricted site occupations and quenched random reaction rates are important open issues (Author)

Bistable amphoteric centers in semiconductors

International Nuclear Information System (INIS)

Nikitina, A. G.; Zuev, V. V.

2008-01-01

It is shown that, at thermodynamic equilibrium, the release of charge carriers from the localized states of bistable amphoteric centers into quasi-free states depends on the degree of compensation. This brings about different functional dependences of the concentration of free charge carriers on temperature. It is found that, in uncompensated semiconductors, the concentration of free charge carriers follows the same dependence in the case of bistable amphoteric centers and bistable amphoteric U - centers, although the distributions of charge carriers over the charge states and configurations are different for these types of centers. The results can be used for interpreting various experimental data insufficiently explained in the context of the traditional approach

A broadband electromagnetic energy harvester with a coupled bistable structure

OpenAIRE

Zhu, Dibin; Beeby, Steve

2013-01-01

This paper investigates a broadband electromagnetic energy harvester with a coupled bistable structure. Both analytical model and experimental results showed that the coupled bistable structure requires lower excitation force to trigger bistable operation than conventional bistable structures. A compact electromagnetic vibration energy harvester with a coupled bistable structure was implemented and tested. It was excited under white noise vibrations. Experimental results showed that the coupl...

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.

Restrictive liquid-phase diffusion and reaction in bidispersed catalysts

International Nuclear Information System (INIS)

Lee, S.Y.; Seader, J.D.; Tsai, C.H.; Massoth, F.E.

1991-01-01

In this paper, the effect of bidispersed pore-size distribution on liquid-phase diffusion and reaction in NiMo/Al 2 O 3 catalysts is investigated by applying two bidispersed-pore-structure models, the random-pore model and a globular-structure model, to extensive experimental data, which were obtained from sorptive diffusion measurements at ambient conditions and catalytic reaction rate measurements on nitrogen-containing compounds. Transport of the molecules in the catalysts was found to be controlled by micropore diffusion, in accordance with the random-pore model, rather than macropore diffusion as predicted by the globular-structure model. A qualitative criterion for micropore-diffusion control is proposed: relatively small macroporosity and high catalyst pellet density. Since most hydrotreating catalysts have high density, diffusion in these types of catalysts may be controlled by micropore diffusion. Accordingly, it is believed in this case that increasing the size of micropores may be more effective to reduce intraparticle diffusion resistance than incorporating macropores alone

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

Bistability in self-activating genes regulated by non-coding RNAs

International Nuclear Information System (INIS)

Miro-Bueno, Jesus

2015-01-01

Non-coding RNA molecules are able to regulate gene expression and play an essential role in cells. On the other hand, bistability is an important behaviour of genetic networks. Here, we propose and study an ODE model in order to show how non-coding RNA can produce bistability in a simple way. The model comprises a single gene with positive feedback that is repressed by non-coding RNA molecules. We show how the values of all the reaction rates involved in the model are able to control the transitions between the high and low states. This new model can be interesting to clarify the role of non-coding RNA molecules in genetic networks. As well, these results can be interesting in synthetic biology for developing new genetic memories and biomolecular devices based on non-coding RNAs

GABA shapes the dynamics of bistable perception.

Science.gov (United States)

van Loon, Anouk M; Knapen, Tomas; Scholte, H Steven; St John-Saaltink, Elexa; Donner, Tobias H; Lamme, Victor A F

2013-05-06

Sometimes, perception fluctuates spontaneously between two distinct interpretations of a constant sensory input. These bistable perceptual phenomena provide a unique window into the neural mechanisms that create the contents of conscious perception. Models of bistable perception posit that mutual inhibition between stimulus-selective neural populations in visual cortex plays a key role in these spontaneous perceptual fluctuations. However, a direct link between neural inhibition and bistable perception has not yet been established experimentally. Here, we link perceptual dynamics in three distinct bistable visual illusions (binocular rivalry, motion-induced blindness, and structure from motion) to measurements of gamma-aminobutyric acid (GABA) concentrations in human visual cortex (as measured with magnetic resonance spectroscopy) and to pharmacological stimulation of the GABAA receptor by means of lorazepam. As predicted by a model of neural interactions underlying bistability, both higher GABA concentrations in visual cortex and lorazepam administration induced slower perceptual dynamics, as reflected in a reduced number of perceptual switches and a lengthening of percept durations. Thus, we show that GABA, the main inhibitory neurotransmitter, shapes the dynamics of bistable perception. These results pave the way for future studies into the competitive neural interactions across the visual cortical hierarchy that elicit conscious perception. Copyright © 2013 Elsevier Ltd. All rights reserved.

Coupled diffusion systems with localized nonlinear reactions

DEFF Research Database (Denmark)

Pedersen, M.; Lin, Zhigui

2001-01-01

This paper deals with the blowup rate and profile near the blowup time for the system of diffusion equations uit - δui = ui+1Pi(x0, t), (i = 1,...,k, uk+1 := uu) in Ω × (0, T) with boundary conditions ui = 0 on ∂Ω × [0, T). We show that the solution has a global blowup. The exact rate...

The derivation of a bistable criterion for double V-beam mechanisms

International Nuclear Information System (INIS)

Wu, Cho-Chun; Chen, Rongshun; Lin, Meng-Ju

2013-01-01

This study presents the theoretical derivation of the discriminant D as a structural and material criterion for determining whether bistability can occur in micromechanically bistable mechanisms. When D < 0, the mechanism displays bistable behavior if an appropriate force is applied to push the bistable mechanism, whereas when D > 0, bistable behavior cannot occur. The proposed V-beam bistable mechanism was successfully fabricated with various beam lengths and tilted angles. The experiments conducted in this study validated the theoretical study of bistability. A comparison of the theoretical solutions and experimental results shows good agreement. Results further show that to design a bistable V-beam mechanism, the tilted angle should be larger for the same beam length, whereas the beam length should be longer for the same tilted angle. The developed discriminant D can be used to predict if a bistable mechanism can achieve bistable behavior based on structural sizes and material properties. Consequently, researchers can reduce trial-and-error experiments when designing a bistable mechanism. A V-beam with a larger tilted angle of up to 5° was successfully fabricated to act as a bistable mechanism, compared to a 3.5° tilted angle in existing studies. Consequently, the proposed method has the advantages of shorter beam lengths and smaller device areas. (paper)

Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds

KAUST Repository

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.

Balancing bistable perception during self-motion.

Science.gov (United States)

van Elk, Michiel; Blanke, Olaf

2012-10-01

In two experiments we investigated whether bistable visual perception is influenced by passive own body displacements due to vestibular stimulation. For this we passively rotated our participants around the vertical (yaw) axis while observing different rotating bistable stimuli (bodily or non-bodily) with different ambiguous motion directions. Based on previous work on multimodal effects on bistable perception, we hypothesized that vestibular stimulation should alter bistable perception and that the effects should differ for bodily versus non-bodily stimuli. In the first experiment, it was found that the rotation bias (i.e., the difference between the percentage of time that a CW or CCW rotation was perceived) was selectively modulated by vestibular stimulation: the perceived duration of the bodily stimuli was longer for the rotation direction congruent with the subject's own body rotation, whereas the opposite was true for the non-bodily stimulus (Necker cube). The results found in the second experiment extend the findings from the first experiment and show that these vestibular effects on bistable perception only occur when the axis of rotation of the bodily stimulus matches the axis of passive own body rotation. These findings indicate that the effect of vestibular stimulation on the rotation bias depends on the stimulus that is presented and the rotation axis of the stimulus. Although most studies on vestibular processing have traditionally focused on multisensory signal integration for posture, balance, and heading direction, the present data show that vestibular self-motion influences the perception of bistable bodily stimuli revealing the importance of vestibular mechanisms for visual consciousness.

Catalytic conversion reactions mediated by single-file diffusion in linear nanopores: hydrodynamic versus stochastic behavior.

Science.gov (United States)

Ackerman, David M; Wang, Jing; Wendel, Joseph H; Liu, Da-Jiang; Pruski, Marek; Evans, James W

2011-03-21

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. Diffusion within the pores is subject to a strict single-file (no passing) constraint. 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 in this multispecies system. The h-RDE successfully describe nontrivial aspects of transient behavior, in contrast to the mf-RDE, and also correctly capture unreactive steady-state behavior in the pore interior. However, steady-state reactivity, which is localized near the pore ends when those regions are catalytic, is controlled by fluctuations not incorporated into the hydrodynamic treatment. The mf-RDE partly capture these fluctuation effects, but cannot describe scaling behavior of the reactivity.

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.

Organic bistable light-emitting devices

Science.gov (United States)

Ma, Liping; Liu, Jie; Pyo, Seungmoon; Yang, Yang

2002-01-01

An organic bistable device, with a unique trilayer structure consisting of organic/metal/organic sandwiched between two outmost metal electrodes, has been invented. [Y. Yang, L. P. Ma, and J. Liu, U.S. Patent Pending, U.S. 01/17206 (2001)]. When the device is biased with voltages beyond a critical value (for example 3 V), the device suddenly switches from a high-impedance state to a low-impedance state, with a difference in injection current of more than 6 orders of magnitude. When the device is switched to the low-impedance state, it remains in that state even when the power is off. (This is called "nonvolatile" phenomenon in memory devices.) The high-impedance state can be recovered by applying a reverse bias; therefore, this bistable device is ideal for memory applications. In order to increase the data read-out rate of this type of memory device, a regular polymer light-emitting diode has been integrated with the organic bistable device, such that it can be read out optically. These features make the organic bistable light-emitting device a promising candidate for several applications, such as digital memories, opto-electronic books, and recordable papers.

Design of a bistable switch to control cellular uptake.

Science.gov (United States)

Oyarzún, Diego A; Chaves, Madalena

2015-12-06

Bistable switches are widely used in synthetic biology to trigger cellular functions in response to environmental signals. All bistable switches developed so far, however, control the expression of target genes without access to other layers of the cellular machinery. Here, we propose a bistable switch to control the rate at which cells take up a metabolite from the environment. An uptake switch provides a new interface to command metabolic activity from the extracellular space and has great potential as a building block in more complex circuits that coordinate pathway activity across cell cultures, allocate metabolic tasks among different strains or require cell-to-cell communication with metabolic signals. Inspired by uptake systems found in nature, we propose to couple metabolite import and utilization with a genetic circuit under feedback regulation. Using mathematical models and analysis, we determined the circuit architectures that produce bistability and obtained their design space for bistability in terms of experimentally tuneable parameters. We found an activation-repression architecture to be the most robust switch because it displays bistability for the largest range of design parameters and requires little fine-tuning of the promoters' response curves. Our analytic results are based on on-off approximations of promoter activity and are in excellent qualitative agreement with simulations of more realistic models. With further analysis and simulation, we established conditions to maximize the parameter design space and to produce bimodal phenotypes via hysteresis and cell-to-cell variability. Our results highlight how mathematical analysis can drive the discovery of new circuits for synthetic biology, as the proposed circuit has all the hallmarks of a toggle switch and stands as a promising design to control metabolic phenotypes across cell cultures. © 2015 The Author(s).

Space charge effects and electronic bistability

International Nuclear Information System (INIS)

Ruffini, A.; Strumia, F.; Tommasi, O.

1996-01-01

The excitation of metastable states in an atomic beam apparatus by means of electron collision is a widespread technique. The authors have observed a large bistable behaviour in apparatus designed to provide an intense and collimated beam of metastable helium by excitation with orthogonally impinging electrons. This bistable behaviour largely affects the efficiency of the apparatus and is therefore worth of being carefully investigated. The apparatus has an electrode configuration equivalent to that of a tetrode valve with large intergrid distances. The bistability consists in a hysteresis cycle in the curve of the anode current vs. grid voltage. Experimental measurements, supported by a simple theoretical model and by numerical simulation, stress out the crucial role played by space charge effects for the onset of bistability. A comparison with previous observations of this phenomenon is given. Spontaneous current oscillations with various shapes have been recorded in one of the two curves of the hysteresis cycle

Amplification without inversion, fast light and optical bistability in a duplicated two-level system

International Nuclear Information System (INIS)

Ebrahimi Zohravi, Lida; Vafafard, Azar; Mahmoudi, Mohammad

2014-01-01

The optical properties of a weak probe field in a duplicated two-level system are investigated in multi-photon resonance (MPR) condition and beyond it. It is shown that by changing the relative phase of applied fields, the absorption switches to the amplification without inversion in MPR condition. By applying the Floquet decomposition to the equations of motion beyond MPR condition, it is shown that the phase-dependent behavior is valid only in MPR condition. Moreover, it is demonstrated that the group velocity of light pulse can be controlled by the intensity of the applied fields and the gain-assisted superluminal light propagation (fast light) is obtained in this system. In addition, the optical bistability (OB) behavior of the system is studied beyond MPR condition. We apply an indirect incoherent pumping field to the system and it is found that the group velocity and OB behavior of the system can be controlled by the incoherent pumping rate. - Highlights: • We studied the optical properties of DTL system under MPR condition and beyond it. • By changing the relative phase, the absorption switches to the amplification without inversion in MPR condition. • The gain-assisted superluminal light propagation (fast light) is obtained in this system. • The optical bistability (OB) behavior of the system is studied beyond MPR condition. • The incoherent pumping rate has a major role in controlling the group velocity and OB behavior of the system

The Induced Dimension Reduction method applied to convection-diffusion-reaction problems

NARCIS (Netherlands)

Astudillo, R.; Van Gijzen, M.B.

2016-01-01

Discretization of (linearized) convection-diffusion-reaction problems yields a large and sparse non symmetric linear system of equations, Ax = b. (1) In this work, we compare the computational behavior of the Induced Dimension Reduction method (IDR(s)) [10], with other short-recurrences Krylov

Stability and Hopf Bifurcation of a Reaction-Diffusion Neutral Neuron System with Time Delay

Science.gov (United States)

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.

Chaos control and synchronization in Bragg acousto-optic bistable systems driven by a separate chaotic system.

Science.gov (United States)

Wang, Rong; Gao, Jin-Yue

2005-09-01

In this paper we propose a new scheme to achieve chaos control and synchronization in Bragg acousto-optic bistable systems. In the scheme, we use the output of one system to drive two identical chaotic systems. Using the maximal conditional Lyapunov exponent (MCLE) as the criterion, we analyze the conditions for realizing chaos synchronization. Numerical calculation shows that the two identical systems in chaos with negative MCLEs and driven by a chaotic system can go into chaotic synchronization whether or not they were in chaos initially. The two systems can go into different periodic states from chaos following an inverse period-doubling bifurcation route as well when driven by a periodic system.

Bistability in a laser with injected signal

International Nuclear Information System (INIS)

Dorobantu, I.A.; Vlad, V.I.; Ursu, I.

1987-04-01

A unified description of bistability is given in free running lasers, optical bistable devices, ring lasers and lasers with an injected signal (LIS). A general review of laser instabilities is also presented in the frame of the theory of elementary catastrophes, emphasizing the apparence of higher order catastrophes in the case of a LIS suggesting thus a possibility to devise from first principles the whole hierarchy of laser instabilities. Experimental results on the bistability in the polarisation of LIS are also discussed. (authors)

Modelling non-homogeneous stochastic reaction-diffusion systems: the case study of gemcitabine-treated non-small cell lung cancer growth.

Science.gov (United States)

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

Bistable behavior of the lac operon in E. coli when induced with a mixture of lactose and TMG

Directory of Open Access Journals (Sweden)

Orlando Díaz-Hernández

2010-07-01

Full Text Available In this work we investigate multistability in the lac operon of Escherichia coli when it is induced by a mixture of lactose and the non-metabolizable thiomethyl galactoside (TMG. In accordance with previously published experimental results and computer simulations, our simulations predict that: (1 when the system is induced by TMG, the system shows a discernible bistable behavior while, (2 when the system is induced by lactose, bistability does not disappear but excessively high concentrations of lactose would be required to observe it. Finally, our simulation results predict that when a mixture of lactose and TMG is used, the bistability region in the extracellular glucose concentration vs. extracellular lactose concentration parameter space changes in such a way that the model predictions regarding bistability could be tested experimentally. These experiments could help to solve a recent controversy regarding the existence of bistability in the lac operon under natural conditions.

Bistable behavior of the lac operon in E. coli when induced with a mixture of lactose and TMG.

Science.gov (United States)

Díaz-Hernández, Orlando; Santillán, Moisés

2010-01-01

In this work we investigate multistability in the lac operon of Escherichia coli when it is induced by a mixture of lactose and the non-metabolizable thiomethyl galactoside (TMG). In accordance with previously published experimental results and computer simulations, our simulations predict that: (1) when the system is induced by TMG, the system shows a discernible bistable behavior while, (2) when the system is induced by lactose, bistability does not disappear but excessively high concentrations of lactose would be required to observe it. Finally, our simulation results predict that when a mixture of lactose and TMG is used, the bistability region in the extracellular glucose concentration vs. extracellular lactose concentration parameter space changes in such a way that the model predictions regarding bistability could be tested experimentally. These experiments could help to solve a recent controversy regarding the existence of bistability in the lac operon under natural conditions.

Reaction diffusion and solid state chemical kinetics handbook

CERN Document Server

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

Chaotic advection, diffusion, and reactions in open flows

International Nuclear Information System (INIS)

Tel, Tamas; Karolyi, Gyoergy; Pentek, Aron; Scheuring, Istvan; Toroczkai, Zoltan; Grebogi, Celso; Kadtke, James

2000-01-01

We review and generalize recent results on advection of particles in open time-periodic hydrodynamical flows. First, the problem of passive advection is considered, and its fractal and chaotic nature is pointed out. Next, we study the effect of weak molecular diffusion or randomness of the flow. Finally, we investigate the influence of passive advection on chemical or biological activity superimposed on open flows. The nondiffusive approach is shown to carry some features of a weak diffusion, due to the finiteness of the reaction range or reaction velocity. (c) 2000 American Institute of Physics

Does visual attention drive the dynamics of bistable perception?

Science.gov (United States)

Dieter, Kevin C; Brascamp, Jan; Tadin, Duje; Blake, Randolph

2016-10-01

How does attention interact with incoming sensory information to determine what we perceive? One domain in which this question has received serious consideration is that of bistable perception: a captivating class of phenomena that involves fluctuating visual experience in the face of physically unchanging sensory input. Here, some investigations have yielded support for the idea that attention alone determines what is seen, while others have implicated entirely attention-independent processes in driving alternations during bistable perception. We review the body of literature addressing this divide and conclude that in fact both sides are correct-depending on the form of bistable perception being considered. Converging evidence suggests that visual attention is required for alternations in the type of bistable perception called binocular rivalry, while alternations during other types of bistable perception appear to continue without requiring attention. We discuss some implications of this differential effect of attention for our understanding of the mechanisms underlying bistable perception, and examine how these mechanisms operate during our everyday visual experiences.

Two Bistable Switches Govern M Phase Entry.

Science.gov (United States)

Mochida, Satoru; Rata, Scott; Hino, Hirotsugu; Nagai, Takeharu; Novák, Béla

2016-12-19

The abrupt and irreversible transition from interphase to M phase is essential to separate DNA replication from chromosome segregation. This transition requires the switch-like phosphorylation of hundreds of proteins by the cyclin-dependent kinase 1 (Cdk1):cyclin B (CycB) complex. Previous studies have ascribed these switch-like phosphorylations to the auto-activation of Cdk1:CycB through the removal of inhibitory phosphorylations on Cdk1-Tyr15 [1, 2]. The positive feedback in Cdk1 activation creates a bistable switch that makes mitotic commitment irreversible [2-4]. Here, we surprisingly find that Cdk1 auto-activation is dispensable for irreversible, switch-like mitotic entry due to a second mechanism, whereby Cdk1:CycB inhibits its counteracting phosphatase (PP2A:B55). We show that the PP2A:B55-inhibiting Greatwall (Gwl)-endosulfine (ENSA) pathway is both necessary and sufficient for switch-like phosphorylations of mitotic substrates. Using purified components of the Gwl-ENSA pathway in a reconstituted system, we found a sharp Cdk1 threshold for phosphorylation of a luminescent mitotic substrate. The Cdk1 threshold to induce mitotic phosphorylation is distinctly higher than the Cdk1 threshold required to maintain these phosphorylations-evidence for bistability. A combination of mathematical modeling and biochemical reconstitution show that the bistable behavior of the Gwl-ENSA pathway emerges from its mutual antagonism with PP2A:B55. Our results demonstrate that two interlinked bistable mechanisms provide a robust solution for irreversible and switch-like mitotic entry. Copyright © 2016 Elsevier Ltd. All rights reserved.

Pattern formation in three-dimensional reaction-diffusion systems

Science.gov (United States)

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.

Excitonic optical bistability in n-type doped semiconductors

International Nuclear Information System (INIS)

Nguyen Ba An; Le Thi Cat Tuong

1991-07-01

A resonant monochromatic pump laser generates coherent excitons in an n-type doped semiconductor. Both exciton-exciton and exciton-donor interactions come into play. The former interaction can give rise to the appearance of optical bistability which is heavily influenced by the latter one. When optical bistability occurs at a fixed laser frequency both its holding intensity and hysteresis loop size are shown to decrease with increasing donor concentration. Two possibilities are suggested for experimentally determining one of the two parameters of the system - the exciton-donor coupling constant and the donor concentration, if the other parameter is known beforehand. (author). 36 refs, 2 figs

Synchronization criteria for generalized reaction-diffusion neural networks via periodically intermittent control.

Science.gov (United States)

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.

Solutes and cells - aspects of advection-diffusion-reaction phenomena in biochips

DEFF Research Database (Denmark)

Vedel, Søren

2012-01-01

the dependencies on density. This shows that the varied single-cell behavior including the overall modulations imposed by density arise as a natural consequence of pseudopod-driven motility in a social context. The final subproject concerns the combined effects of advection, diffusion and reaction of several......Cell’), and the overall title of the project is Solutes and cells — aspects of advection-diffusion-reaction phenomena in biochips. The work has consisted of several projects focusing on theory, and to some extend analysis of experimental data, with advection-diffusion-reaction phenomena of solutes as the recurring theme...... quantitatively interpret the proximal concentration of specific solutes, and integrate this to achieve biological functions. In three specific examples, the author and co-workers have investigated different aspects of the influence of advection, diffusion and reaction on solute distributions, as well...

Perceptual incongruence influences bistability and cortical activation

NARCIS (Netherlands)

Brouwer, G.J.; Tong, F.; Hagoort, P.; van Ee, R.

2009-01-01

We employed a parametric psychophysical design in combination with functional imaging to examine the influence of metric changes in perceptual incongruence on perceptual alternation rates and cortical responses. Subjects viewed a bistable stimulus defined by incongruent depth cues; bistability

GABA shapes the dynamics of bistable perception

NARCIS (Netherlands)

van Loon, A.M.; Knapen, T.; Scholte, H.S.; St. John-Saaltink, E.; Donner, T.H.; Lamme, V.A.F.

2013-01-01

Sometimes, perception fluctuates spontaneously between two distinct interpretations of a constant sensory input. These bistable perceptual phenomena provide a unique window into the neural mechanisms that create the contents of conscious perception. Models of bistable perception posit that mutual

1D to 3D diffusion-reaction kinetics of defects in crystals

DEFF Research Database (Denmark)

Trinkaus, H.; Heinisch, H.L.; Barashev, A.V.

2002-01-01

Microstructural features evolving in crystalline solids from diffusion-reaction kinetics of mobile components depend crucially on the dimension of the underlying diffusion process which is commonly assumed to be three-dimensional (3D). In metals, irradiation-induced displacement cascades produce...... clusters of self-interstitials performing 1D diffusion. Changes between equivalent 1D diffusion paths and transversal diffusion result in diffusion-reaction kinetics between one and three dimensions. An analytical approach suggests a single-variable function (master curve) interpolating between the 1D...

Bistability induces episodic spike communication by inhibitory neurons in neuronal networks.

Science.gov (United States)

Kazantsev, V B; Asatryan, S Yu

2011-09-01

Bistability is one of the important features of nonlinear dynamical systems. In neurodynamics, bistability has been found in basic Hodgkin-Huxley equations describing the cell membrane dynamics. When the neuron is clamped near its threshold, the stable rest potential may coexist with the stable limit cycle describing periodic spiking. However, this effect is often neglected in network computations where the neurons are typically reduced to threshold firing units (e.g., integrate-and-fire models). We found that the bistability may induce spike communication by inhibitory coupled neurons in the spiking network. The communication is realized in the form of episodic discharges with synchronous (correlated) spikes during the episodes. A spiking phase map is constructed to describe the synchronization and to estimate basic spike phase locking modes.

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.

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)

Revisiting bistability in the lysis/lysogeny circuit of bacteriophage lambda.

Directory of Open Access Journals (Sweden)

Michael Bednarz

Full Text Available The lysis/lysogeny switch of bacteriophage lambda serves as a paradigm for binary cell fate decision, long-term maintenance of cellular state and stimulus-triggered switching between states. In the literature, the system is often referred to as "bistable." However, it remains unclear whether this term provides an accurate description or is instead a misnomer. Here we address this question directly. We first quantify transcriptional regulation governing lysogenic maintenance using a single-cell fluorescence reporter. We then use the single-cell data to derive a stochastic theoretical model for the underlying regulatory network. We use the model to predict the steady states of the system and then validate these predictions experimentally. Specifically, a regime of bistability, and the resulting hysteretic behavior, are observed. Beyond the steady states, the theoretical model successfully predicts the kinetics of switching from lysogeny to lysis. Our results show how the physics-inspired concept of bistability can be reliably used to describe cellular phenotype, and how an experimentally-calibrated theoretical model can have accurate predictive power for cell-state switching.

Temporal nonlocality in bistable perception

Science.gov (United States)

Atmanspacher, Harald; Filk, Thomas

2012-12-01

A novel conceptual framework for theoretical psychology is presented and illustrated for the example of bistable perception. A basic formal feature of this framework is the non-commutativity of operations acting on mental states. A corresponding model for the bistable perception of ambiguous stimuli, the Necker-Zeno model, is sketched and some empirical evidence for it so far is described. It is discussed how a temporal nonlocality of mental states, predicted by the model, can be understood and tested.

Rigorous Multicomponent Reactive Separations Modelling: Complete Consideration of Reaction-Diffusion Phenomena

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-diffusion

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.

A Comparison of Deterministic and Stochastic Modeling Approaches for Biochemical Reaction Systems: On Fixed Points, Means, and Modes.

Science.gov (United States)

Hahl, Sayuri K; Kremling, Andreas

2016-01-01

In the mathematical modeling of biochemical reactions, a convenient standard approach is to use ordinary differential equations (ODEs) that follow the law of mass action. However, this deterministic ansatz is based on simplifications; in particular, it neglects noise, which is inherent to biological processes. In contrast, the stochasticity of reactions is captured in detail by the discrete chemical master equation (CME). Therefore, the CME is frequently applied to mesoscopic systems, where copy numbers of involved components are small and random fluctuations are thus significant. Here, we compare those two common modeling approaches, aiming at identifying parallels and discrepancies between deterministic variables and possible stochastic counterparts like the mean or modes of the state space probability distribution. To that end, a mathematically flexible reaction scheme of autoregulatory gene expression is translated into the corresponding ODE and CME formulations. We show that in the thermodynamic limit, deterministic stable fixed points usually correspond well to the modes in the stationary probability distribution. However, this connection might be disrupted in small systems. The discrepancies are characterized and systematically traced back to the magnitude of the stoichiometric coefficients and to the presence of nonlinear reactions. These factors are found to synergistically promote large and highly asymmetric fluctuations. As a consequence, bistable but unimodal, and monostable but bimodal systems can emerge. This clearly challenges the role of ODE modeling in the description of cellular signaling and regulation, where some of the involved components usually occur in low copy numbers. Nevertheless, systems whose bimodality originates from deterministic bistability are found to sustain a more robust separation of the two states compared to bimodal, but monostable systems. In regulatory circuits that require precise coordination, ODE modeling is thus still

A study on stochastic resonance of one-dimensional bistable system in the neighborhood of bifurcation point with the moment method

Energy Technology Data Exchange (ETDEWEB)

Zhang Guangjun [State Key Laboratory of Mechanical Structural Strength and Vibration, School of Architectural Engineering and Mechanics, Xi' an Jiaotong University, Xi' an, Shaanxi (China); Xu Jianxue [State Key Laboratory of Mechanical Structural Strength and Vibration, School of Architectural Engineering and Mechanics, Xi' an Jiaotong University, Xi' an, Shaanxi (China)] e-mail: jxxu@mail.xjtu.edu.cn

2006-02-01

This paper analyzes the stochastic resonance induced by a novel transition of one-dimensional bistable system in the neighborhood of bifurcation point with the method of moment, which refer to the transition of system motion among a potential well of stable fixed point before bifurcation of original system and double-well potential of two coexisting stable fixed points after original system bifurcation at the presence of internal noise. The results show: the semi-analytical result of stochastic resonance of one-dimensional bistable system in the neighborhood of bifurcation point may be obtained, and the semi-analytical result is in accord with the one of Monte Carlo simulation qualitatively, the occurrence of stochastic resonance is related to the bifurcation of noisy nonlinear dynamical system moment equations, which induce the transfer of energy of ensemble average (Ex) of system response in each frequency component and make the energy of ensemble average of system response concentrate on the frequency of input signal, stochastic resonance occurs.

A study on stochastic resonance of one-dimensional bistable system in the neighborhood of bifurcation point with the moment method

International Nuclear Information System (INIS)

Zhang Guangjun; Xu Jianxue

2006-01-01

This paper analyzes the stochastic resonance induced by a novel transition of one-dimensional bistable system in the neighborhood of bifurcation point with the method of moment, which refer to the transition of system motion among a potential well of stable fixed point before bifurcation of original system and double-well potential of two coexisting stable fixed points after original system bifurcation at the presence of internal noise. The results show: the semi-analytical result of stochastic resonance of one-dimensional bistable system in the neighborhood of bifurcation point may be obtained, and the semi-analytical result is in accord with the one of Monte Carlo simulation qualitatively, the occurrence of stochastic resonance is related to the bifurcation of noisy nonlinear dynamical system moment equations, which induce the transfer of energy of ensemble average (Ex) of system response in each frequency component and make the energy of ensemble average of system response concentrate on the frequency of input signal, stochastic resonance occurs

Laser Spot Detection Based on Reaction Diffusion.

Science.gov (United States)

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.

Real-time nonlinear feedback control of pattern formation in (bio)chemical reaction-diffusion processes: a model study.

Science.gov (United States)

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.

Bistable perception modeled as competing stochastic integrations at two levels.

Science.gov (United States)

Gigante, Guido; Mattia, Maurizio; Braun, Jochen; Del Giudice, Paolo

2009-07-01

We propose a novel explanation for bistable perception, namely, the collective dynamics of multiple neural populations that are individually meta-stable. Distributed representations of sensory input and of perceptual state build gradually through noise-driven transitions in these populations, until the competition between alternative representations is resolved by a threshold mechanism. The perpetual repetition of this collective race to threshold renders perception bistable. This collective dynamics - which is largely uncoupled from the time-scales that govern individual populations or neurons - explains many hitherto puzzling observations about bistable perception: the wide range of mean alternation rates exhibited by bistable phenomena, the consistent variability of successive dominance periods, and the stabilizing effect of past perceptual states. It also predicts a number of previously unsuspected relationships between observable quantities characterizing bistable perception. We conclude that bistable perception reflects the collective nature of neural decision making rather than properties of individual populations or neurons.

Diffusion characteristics in the Cu-Ti system

Energy Technology Data Exchange (ETDEWEB)

Laik, Arijit; Kale, Gajanan Balaji [Bhabha Atomic Reseach Centre, Mumbai (India). Materials Science Div.; Bhanumurthy, Karanam [Bhabha Atomic Reseach Centre, Mumbai (India). Scientific Information Resource Div.; Kashyap, Bhagwati Prasad [Indian Institute of Technology Bombay, Mumbai (India). Dept. of Metallurgical Engineering

2012-06-15

The formation and growth of intermetallic compounds by diffusion reaction of Cu and Ti were investigated in the temperature range 720 - 860 C using bulk diffusion couples. Only four, out of the seven stable intermediate compounds of the Cu-Ti system, were formed in the diffusion reaction zone in the sequence CuTi, Cu{sub 4}Ti, Cu{sub 4}Ti{sub 3} and CuTi{sub 2}. The activation energies required for the growth of these compounds were determined. The diffusion characteristics of Cu{sub 4}Ti, CuTi and Cu{sub 4}Ti{sub 3} and Cu(Ti) solid solution were evaluated. The activation energies for diffusion in these compounds were 192.2, 187.7 and 209.2 kJ mol{sup -1} respectively, while in Cu(Ti), the activation energy increased linearly from 201.0 kJ mol{sup -1} to 247.5 kJ mol{sup -1} with increasing concentration of Ti, in the range 0.5 - 4.0 at.%. The impurity diffusion coefficient of Ti in Cu and its temperature dependence were also estimated. A correlation between the impurity diffusion parameters for several elements in Cu matrix has been established. (orig.)

Bistable firing properties of soleus motor units in unrestrained rats

DEFF Research Database (Denmark)

EKEN, T.; KIEHN, O.

1989-01-01

of the motoneuron pool by stimulation of la afferents, or inhibition by stimulation of skin afferents. The shifts were not related to gross limb movements. This phenomenon is referred to as a bistable firing pattern. Bistable firing also occurred spontaneously during quiet standing. Typically the firing frequency...... was unchanged or only phasically influenced. These results demonstrate for the first time a bistable firing pattern during postural activity in the intact animal. The firing pattern closely resembles the bistable behaviour described in spinal motoneurons in reduced preparations, where it is due to the presence...... of a plateau potential. This suggests that the bistable firing is unexplained by plateau potentials also in the intact animal....

The interplay of multiple feedback loops with post-translational kinetics results in bistability of mycobacterial stress response

International Nuclear Information System (INIS)

Tiwari, Abhinav; Igoshin, Oleg A; Balázsi, Gábor; Gennaro, Maria Laura

2010-01-01

Bacterial persistence is the phenomenon in which a genetically identical fraction of a bacterial population can survive exposure to stress by reduction or cessation of growth. Persistence in mycobacteria has been recently linked to a stress-response network, consisting of the MprA/MprB two-component system and alternative sigma factor σ E . This network contains multiple positive transcriptional feedback loops which may give rise to bistability, making it a good candidate for controlling the mycobacterial persistence switch. To analyze the possibility of bistability, we develop a method that involves decoupling of the network into transcriptional and post-translational interaction modules. As a result we reduce the dimensionality of the dynamical system and independently analyze input–output relations in the two modules to formulate a necessary condition for bistability in terms of their logarithmic gains. We show that neither the positive autoregulation in the MprA/MprB network nor the σ E -mediated transcriptional feedback is sufficient to induce bistability in a biochemically realistic parameter range. Nonetheless, inclusion of the post-translational regulation of σ E by RseA increases the effective cooperativity of the system, resulting in bistability that is robust to parameter variation. We predict that overexpression or deletion of RseA, the key element controlling the ultrasensitive response, can eliminate bistability

Triggered Snap-Through of Bistable Shells

Science.gov (United States)

Cai, Yijie; Huang, Shicheng; Trase, Ian; Hu, Nan; Chen, Zi

Elastic bistable shells are common structures in nature and engineering, such as the lobes of the Venus flytrap or the surface of a toy jumping poppers. Despite their ubiquity, the parameters that control the bistability of such structures are not well understood. In this study, we explore how the geometrical features of radially symmetric elastic shells affect the shape and potential energy of a shell's stable states, and how to tune certain parameters in order to generate a snap-through transition from a convex semi-stable state to concave stable state. We fabricated a series of elastic shells with varying geometric parameters out of silicone rubber and measured the resulting potential energy in the semi-stable state. Finite element simulations were also conducted in order to determine the deformation and stress in the shells during snap-through. It was found that the energy of the semi-stable state is controlled by only two geometric parameters and a dimensionless ratio. We also noted two distinct transitions during snap-through, one between monostability and semi-bistability (the state a popper toy is in before it snaps-through and jumps), and a second transition between semi-bistability and true bistability. This work shows that it is possible to use a set of simple parameters to tailor the energy landscape of an elastic shell in order to generate complex trigger motions for their potential use in smart applications. Z.C. acknowledge support from Society in Science-Branco Weiss Fellowship, administered by ETH Zurich.

Topical Meeting on Optical Bistability Held at Rochester, New York on 15-17 June 1983.

Science.gov (United States)

1983-01-01

ThB16-1 SELF-BEATING INSTABILITIES IN BISTABLE DEVICES J.A. MARTIN-PEREDA .. M.A. MURIEL DEPARTAMENTO DE ELECTRONICA CUANTICA E.T.S. ING...OPTICAL BISTABLL SYSTEMS J.A. MARTIN PEREDA M.A. MURIEL ; DEPARTAMENIO DE ELECTRONICA CUANTICA E.T.S. ING. TELLCOMUNICACION UNIVERSIDAD POLITECNICA DE

On Medium Chemical Reaction in Diffusion-Based Molecular Communication: a Two-Way Relaying Example

OpenAIRE

Farahnak-Ghazani, Maryam; Aminian, Gholamali; Mirmohseni, Mahtab; Gohari, Amin; Nasiri-Kenari, Masoumeh

2016-01-01

Chemical reactions are a prominent feature of molecular communication (MC) systems, with no direct parallels in wireless communications. While chemical reactions may be used inside the transmitter nodes, receiver nodes or the communication medium, we focus on its utility in the medium in this paper. Such chemical reactions can be used to perform computation over the medium as molecules diffuse and react with each other (physical-layer computation). We propose the use of chemical reactions for...

Study of dynamics of glucose-glucose oxidase-ferricyanide reaction

Science.gov (United States)

Nováková, A.; Schreiberová, L.; Schreiber, I.

2011-12-01

This work is focused on dynamics of the glucose-glucose oxidase-ferricyanide enzymatic reaction with or without sodium hydroxide in a continuous-flow stirred tank reactor (CSTR) and in a batch reactor. This reaction exhibits pH-variations having autocatalytic character and is reported to provide nonlinear dynamic behavior (bistability, excitability). The dynamical behavior of the reaction was examined within a wide range of inlet parameters. The main inlet parameters were the ratio of concentrations of sodium hydroxide and ferricyanide and the flow rate. In a batch reactor we observed an autocatalytic drop of pH from slightly basic to medium acidic values. In a CSTR our aim was to find bistability in the presence of sodium hydroxide. However, only a basic steady state was found. In order to reach an acidic steady state, we investigated the system in the absence of sodium hydroxide. Under these conditions the transition from the basic to the acidic steady state was observed when inlet glucose concentration was increased.

Longitudinal magnetic bistability of electroplated wires

International Nuclear Information System (INIS)

Kurlyandskaya, G.V.; Garcia-Miquel, H.; Vazquez, M.; Svalov, A.V.; Vas'kovskiy, V.O.

2002-01-01

Fe 20 Ni 74 Co 6 and Fe 20 Ni 64 Co 16 1 μm thick magnetic tubes electroplated onto Cu 98 Be 2 conductive wire have been investigated in as-deposited state, after heat treatment under longitudinal magnetic field for 1 h at 330 deg. C, and after rf-sputtering deposition of the additional 2 μm Fe 19 Ni 81 layer. Heat treatments and an additional layer deposition modify the shape of hysteresis loops. Magnetically bistable behaviour, observed after the field annealing at a temperature of 330 deg. C, is studied as a function of the length of the samples. This is the first report by our knowledge on the bistable behaviour of the electroplated wires. The bistability of these wires is promising for applications such as tagging or pulse generator applications

Internal Diffusion-Controlled Enzyme Reaction: The Acetylcholinesterase Kinetics.

Science.gov (United States)

Lee, Sangyun; Kim, Ji-Hyun; Lee, Sangyoub

2012-02-14

Acetylcholinesterase is an enzyme with a very high turnover rate; it quenches the neurotransmitter, acetylcholine, at the synapse. We have investigated the kinetics of the enzyme reaction by calculating the diffusion rate of the substrate molecule along an active site channel inside the enzyme from atomic-level molecular dynamics simulations. In contrast to the previous works, we have found that the internal substrate diffusion is the determinant of the acetylcholinesterase kinetics in the low substrate concentration limit. Our estimate of the overall bimolecular reaction rate constant for the enzyme is in good agreement with the experimental data. In addition, the present calculation provides a reasonable explanation for the effects of the ionic strength of solution and the mutation of surface residues of the enzyme. The study suggests that internal diffusion of the substrate could be a key factor in understanding the kinetics of enzymes of similar characteristics.

Diffuse Urticarial Reaction Associated with Titanium Dioxide Following Laser Tattoo Removal Treatments.

Science.gov (United States)

Willardson, Hal Bret; Kobayashi, Todd T; Arnold, Jason G; Hivnor, Chad M; Bowen, Casey D

2017-03-01

Local and generalized allergic reactions following laser tattoo removal have been documented, but are rare. To our knowledge, this is the fourth documented case of widespread urticarial eruptions following laser tattoo removal treatment. Unlike previously documented cases, this patient's reaction was found to be associated with titanium dioxide within the tattoo and her symptoms were recalcitrant to medical therapy. A 46-year-old female experienced diffuse urticarial plaques, erythema, and pruritis following multiple laser tattoo removal treatments with an Nd:YAG laser. The systemic allergic reaction was recalcitrant to increasing doses of antihistamines and corticosteroids. The tattoo was finally surgically excised. The excised tissue was analyzed by scanning electron microscopy and energy-dispersive X-ray analysis and contained high levels of titanium dioxide. Two weeks following the excision, and without the use of medical therapy, the patient had complete resolution of her generalized urticaria. Ours is the first documented case of a diffuse urticarial reaction following laser tattoo removal treatments that shows a strong association to titanium dioxide within the tattoo pigment. Herein, we describe a novel surgical approach to treat recalcitrant generalized allergic reaction to tattoo pigment.

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.

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.

Excitonic bistabilities, instabilities and chaos in laser-pumped semiconductor

International Nuclear Information System (INIS)

Nguyen Ba An; Nguyen Trung Dan; Hoang Xuan Nguyen

1992-07-01

The Hurwitz criteria are used for a stability analysis of the steady state excitonic optical bistability curves in a semiconductor pumped by an external laser resonant with the exciton level. Besides the middle branch of the bistability curves which is unstable in the sense of the linear stability theory, we have found other domains of instability in the upper and lower branches of the steady state curves. Numerical results show that a possible route to chaos in the photon-exciton system is period-doubling self-oscillation process. The influence of the presence of free carriers that coexist with the excitons is also discussed. (author). 16 refs, 6 figs

Bistable flow spectral analysis. Repercussions on jet pumps

International Nuclear Information System (INIS)

Gavilan Moreno, C.J.

2011-01-01

Highlights: → The most important thing in this paper, is the spectral characterization of the bistable flow in a Nuclear Power Plant. → This paper goes deeper in the effect of the bistable flow over the jet pump and the induced vibrations. → The jet pump frequencies are very close to natural jet pump frequencies, in the 3rd and 6th mode. - Abstract: There have been many attempts at characterizing and predicting bistable flow in boiling water reactors (BWRs). Nevertheless, in most cases the results have only managed to develop models that analytically reproduce the phenomenon (). Modeling has been forensic in all cases, while the capacity of the model focus on determining the exclusion areas on the recirculation flow map. The bistability process is known by its effects given there is no clear definition of its causal process. In the 1980s, Hitachi technicians () managed to reproduce bistable flow in the laboratory by means of pipe geometry, similar to that which is found in recirculation loops. The result was that the low flow pattern is formed by the appearance of a quasi stationary, helicoidal vortex in the recirculation collector's branches. This vortex creates greater frictional losses than regions without vortices, at the same discharge pressure. Neither the behavior nor the dynamics of these vortices were characterized in this paper. The aim of this paper is to characterize these vortices in such a way as to enable them to provide their own frequencies and their later effect on the jet pumps. The methodology used in this study is similar to the one used previously when analyzing the bistable flow in tube arrays with cross flow (). The method employed makes use of the power spectral density function. What differs is the field of application. We will analyze a Loop B with a bistable flow and compare the high and low flow situations. The same analysis will also be carried out on the loop that has not developed the bistable flow (Loop A) at the same moments

Basins of attraction of the bistable region of time-delayed cutting dynamics

Science.gov (United States)

Yan, Yao; Xu, Jian; Wiercigroch, Marian

2017-09-01

This paper investigates the effects of bistability in a nonsmooth time-delayed dynamical system, which is often manifested in science and engineering. Previous studies on cutting dynamics have demonstrated persistent coexistence of chatter and chatter-free responses in a bistable region located in the linearly stable zone. As there is no widely accepted definition of basins of attraction for time-delayed systems, bistable regions are coined as unsafe zones (UZs). Hence, we have attempted to define the basins of attraction and stability basins for a typical delayed system to get insight into the bistability in systems with time delays. Special attention was paid to the influences of delayed initial conditions, starting points, and states at time zero on the long-term dynamics of time-delayed systems. By using this concept, it has been confirmed that the chatter is prone to occur when the waviness frequency in the workpiece surface coincides with the effective natural frequency of the cutting process. Further investigations unveil a thin "boundary layer" inside the UZ in the immediate vicinity of the stability boundary, in which we observe an extremely fast growth of the chatter basin stability. The results reveal that the system is more stable when the initial cutting depth is smaller. The physics of the tool deflection at the instant of the tool-workpiece engagement is used to evaluate the cutting safety, and the safe level could be zero when the geometry of tool engagement is unfavorable. Finally, the basins of attraction are used to quench the chatter by a single strike, where the resultant "islands" offer an opportunity to suppress the chatter even when the cutting is very close to the stability boundary.

Basins of attraction of the bistable region of time-delayed cutting dynamics.

Science.gov (United States)

Yan, Yao; Xu, Jian; Wiercigroch, Marian

2017-09-01

This paper investigates the effects of bistability in a nonsmooth time-delayed dynamical system, which is often manifested in science and engineering. Previous studies on cutting dynamics have demonstrated persistent coexistence of chatter and chatter-free responses in a bistable region located in the linearly stable zone. As there is no widely accepted definition of basins of attraction for time-delayed systems, bistable regions are coined as unsafe zones (UZs). Hence, we have attempted to define the basins of attraction and stability basins for a typical delayed system to get insight into the bistability in systems with time delays. Special attention was paid to the influences of delayed initial conditions, starting points, and states at time zero on the long-term dynamics of time-delayed systems. By using this concept, it has been confirmed that the chatter is prone to occur when the waviness frequency in the workpiece surface coincides with the effective natural frequency of the cutting process. Further investigations unveil a thin "boundary layer" inside the UZ in the immediate vicinity of the stability boundary, in which we observe an extremely fast growth of the chatter basin stability. The results reveal that the system is more stable when the initial cutting depth is smaller. The physics of the tool deflection at the instant of the tool-workpiece engagement is used to evaluate the cutting safety, and the safe level could be zero when the geometry of tool engagement is unfavorable. Finally, the basins of attraction are used to quench the chatter by a single strike, where the resultant "islands" offer an opportunity to suppress the chatter even when the cutting is very close to the stability boundary.

Controllable optical bistability and multistability in a graphene monolayer system

Energy Technology Data Exchange (ETDEWEB)

Zhang, Duo, E-mail: zhangduo10@126.com [School of Electrical and Electronic Engineering, Wuhan Polytechnic University, Wuhan 430023 (China); Sun, Zhaoyu [School of Electrical and Electronic Engineering, Wuhan Polytechnic University, Wuhan 430023 (China); Ding, Chunling [School of Physics and Electronics, Henan University, Kaifeng 475004 (China); Yu, Rong [School of Science, Hubei Province Key Laboratory of Intelligent Robot, Wuhan Institute of Technology, Wuhan 430073 (China); Yang, Xiaoxue [Wuhan National Laboratory for Optoelectronics and School of Physics, Huazhong University of Science and Technology, Wuhan 430074 (China)

2016-02-15

We theoretically investigate the behavior of optical bistability (OB) and optical multistability (OM) in a graphene monolayer system driven by an elliptically polarized control field and a right-hand circularly polarized probe field. Our numerical results show that it is easy to realize the transition from OB to OM or vice versa by adjusting the frequency detunings of the probe field and the control field, as well as the polarization-dependent phase difference between the two components of the control laser field. The influences of the intensity of the control field and the cooperation parameter on the OB behavior are also discussed in detail. These results may provide some new possibilities for technological applications in optoelectronics and solid-state quantum information science.

Exact modelling of the optical bistability in ferroelectics via two-wave mixing: A system with full nonlinearity

Science.gov (United States)

Khushaini, Muhammad Asif A.; Ibrahim, Abdel-Baset M. A.; Choudhury, P. K.

2018-05-01

In this paper, we provide a complete mathematical model of the phenomenon of optical bistability (OB) resulting from the degenerate two-wave mixing (TWM) process of laser beams interacting with a single nonlinear layer of ferroelectric material. Starting with the electromagnetic wave equation for optical wave propagating in nonlinear media, a nonlinear coupled wave (CW) system with both self-phase modulation (SPM) and cross-phase modulation (XPM) sources of nonlinearity are derived. The complete CW system with full nonlinearity is solved numerically and a comparison between both the cases of with and without SPM at various combinations of design parameters is given. Furthermore, to provide a reliable theoretical model for the OB via TWM process, the results obtained theoretically are compared with the available experimental data. We found that the nonlinear system without SPM fails to predict the bistable response at lower combinations of the input parameters. However, at relatively higher values, the solution without SPM shows a reduction in the switching contrast and period in the OB response. A comparison with the experimental results shows better agreement with the system with full nonlinearity.

Frontoparietal cortex mediates perceptual transitions in bistable perception.

Science.gov (United States)

Weilnhammer, Veith A; Ludwig, Karin; Hesselmann, Guido; Sterzer, Philipp

2013-10-02

During bistable vision, perception oscillates between two mutually exclusive percepts despite constant sensory input. Greater BOLD responses in frontoparietal cortex have been shown to be associated with endogenous perceptual transitions compared with "replay" transitions designed to closely match bistability in both perceptual quality and timing. It has remained controversial, however, whether this enhanced activity reflects causal influences of these regions on processing at the sensory level or, alternatively, an effect of stimulus differences that result in, for example, longer durations of perceptual transitions in bistable perception compared with replay conditions. Using a rotating Lissajous figure in an fMRI experiment on 15 human participants, we controlled for potential confounds of differences in transition duration and confirmed previous findings of greater activity in frontoparietal areas for transitions during bistable perception. In addition, we applied dynamic causal modeling to identify the neural model that best explains the observed BOLD signals in terms of effective connectivity. We found that enhanced activity for perceptual transitions is associated with a modulation of top-down connectivity from frontal to visual cortex, thus arguing for a crucial role of frontoparietal cortex in perceptual transitions during bistable perception.

A bistable mechanism for chord extension morphing rotors

Science.gov (United States)

Johnson, Terrence; Frecker, Mary; Gandhi, Farhan

2009-03-01

Research efforts have shown that helicopter rotor blade morphing is an effective means to improve flight performance. Previous example of rotor blade morphing include using smart-materials for trailing deflection and rotor blade twist and tip twist, the development of a comfortable airfoil using compliant mechanisms, the use of a Gurney flap for air-flow deflection and centrifugal force actuated device to increase the span of the blade. In this paper we explore the use of a bistable mechanism for rotor morphing, specifically, blade chord extension using a bistable arc. Increasing the chord of the rotor blade is expected to generate more lift-load and improve helicopter performance. Bistable or "snap through" mechanisms have multiple stable equilibrium states and are a novel way to achieve large actuation output stroke. Bistable mechanisms do not require energy input to maintain a stable equilibrium state as both states do not require locking. In this work, we introduce a methodology for the design of bistable arcs for chord morphing using the finite element analysis and pseudo-rigid body model, to study the effect of different arc types, applied loads and rigidity on arc performance.

Liquid Film Diffusion on Reaction Rate in Submerged Biofilters

DEFF Research Database (Denmark)

Christiansen, Pia; Hollesen, Line; Harremoës, Poul

1995-01-01

Experiments were carried out in order to investigate the influence of liquid film diffusion on reaction rate in a submerged biofilter with denitrification and in order to compare with a theoretical study of the mass transfer coefficient. The experiments were carried out with varied flow, identified...... by the empty bed velocity of inflow and recirculation, respectively 1.3, 2.8, 5.6 and 10.9 m/h. The filter material consisted of 3 mm biostyren spheres. The results indicate that the influence of liquid film diffusion on reaction rate can be ignored....

Model-based design of bistable cell factories for metabolic engineering.

Science.gov (United States)

Srinivasan, Shyam; Cluett, William R; Mahadevan, Radhakrishnan

2018-04-15

Metabolism can exhibit dynamic phenomena like bistability due to the presence of regulatory motifs like the positive feedback loop. As cell factories, microorganisms with bistable metabolism can have a high and a low product flux at the two stable steady states, respectively. The exclusion of metabolic regulation and network dynamics limits the ability of pseudo-steady state stoichiometric models to detect the presence of bistability, and reliably assess the outcomes of design perturbations to metabolic networks. Using kinetic models of metabolism, we assess the change in the bistable characteristics of the network, and suggest designs based on perturbations to the positive feedback loop to enable the network to produce at its theoretical maximum rate. We show that the most optimal production design in parameter space, for a small bistable metabolic network, may exist at the boundary of the bistable region separating it from the monostable region of low product fluxes. The results of our analysis can be broadly applied to other bistable metabolic networks with similar positive feedback network topologies. This can complement existing model-based design strategies by providing a smaller number of feasible designs that need to be tested in vivo. http://lmse.biozone.utoronto.ca/downloads/. krishna.mahadevan@utoronto.ca. Supplementary data are available at Bioinformatics online.

Decision making in noisy bistable systems with time-dependent asymmetry

Science.gov (United States)

Nené, Nuno R.; Zaikin, Alexey

2013-01-01

Our work draws special attention to the importance of the effects of time-dependent parameters on decision making in bistable systems. Here, we extend previous studies of the mechanism known as speed-dependent cellular decision making in genetic circuits by performing an analytical treatment of the canonical supercritical pitchfork bifurcation problem with an additional time-dependent asymmetry and control parameter. This model has an analogous behavior to the genetic switch. In the presence of transient asymmetries and fluctuations, slow passage through the critical region in both systems increases substantially the probability of specific decision outcomes. We also study the relevance for attractor selection of reaching maximum values for the external asymmetry before and after the critical region. Overall, maximum asymmetries should be reached at an instant where the position of the critical point allows for compensation of the detrimental effects of noise in retaining memory of the transient asymmetries.

Stability analysis of impulsive fuzzy cellular neural networks with distributed delays and reaction-diffusion terms

International Nuclear Information System (INIS)

Li Zuoan; Li Kelin

2009-01-01

In this paper, we investigate a class of impulsive fuzzy cellular neural networks with distributed delays and reaction-diffusion terms. By employing the delay differential inequality with impulsive initial conditions and M-matrix theory, we find some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive fuzzy cellular neural networks with distributed delays and reaction-diffusion terms. In particular, the estimate of the exponential converging index is also provided, which depends on the system parameters. An example is given to show the effectiveness of the results obtained here.

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.

Multi-scale modeling of diffusion-controlled reactions in polymers: renormalisation of reactivity parameters.

Science.gov (United States)

Everaers, Ralf; Rosa, Angelo

2012-01-07

The quantitative description of polymeric systems requires hierarchical modeling schemes, which bridge the gap between the atomic scale, relevant to chemical or biomolecular reactions, and the macromolecular scale, where the longest relaxation modes occur. Here, we use the formalism for diffusion-controlled reactions in polymers developed by Wilemski, Fixman, and Doi to discuss the renormalisation of the reactivity parameters in polymer models with varying spatial resolution. In particular, we show that the adjustments are independent of chain length. As a consequence, it is possible to match reactions times between descriptions with different resolution for relatively short reference chains and to use the coarse-grained model to make quantitative predictions for longer chains. We illustrate our results by a detailed discussion of the classical problem of chain cyclization in the Rouse model, which offers the simplest example of a multi-scale descriptions, if we consider differently discretized Rouse models for the same physical system. Moreover, we are able to explore different combinations of compact and non-compact diffusion in the local and large-scale dynamics by varying the embedding dimension.

Bistable Reflective Etalon (BRET)

National Research Council Canada - National Science Library

Shellenbarger, Zane

2003-01-01

This project designed, fabricated, and characterized normal-incidence etalon structures at 1550 nm wavelength operation for application, as bistable elements, to photonic analog-to-digital conversion...

Multistability in Bistable Ferroelectric Materials toward Adaptive Applications

NARCIS (Netherlands)

Ghosh, Anirban; Koster, Gertjan; Rijnders, Augustinus J.H.M.

2016-01-01

Traditionally thermodynamically bistable ferroic materials are used for nonvolatile operations based on logic gates (e.g., in the form of field effect transistors). But, this inherent bistability in these class of materials limits their applicability for adaptive operations. Emulating biological

Propagating fronts in reaction-transport systems with memory

Energy Technology Data Exchange (ETDEWEB)

Yadav, A. [Department of Chemistry, Southern Methodist University, Dallas, TX 75275-0314 (United States)], E-mail: ayadav1@lsu.edu; Fedotov, Sergei [School of Mathematics, University of Manchester, Manchester M60 1DQ (United Kingdom)], E-mail: sergei.fedotov@manchester.ac.uk; Mendez, Vicenc [Grup de Fisica Estadistica, Departament de Fisica, Universitat Autonoma de Barcelona, E-08193 Bellaterra (Spain)], E-mail: vicenc.mendez@uab.es; Horsthemke, Werner [Department of Chemistry, Southern Methodist University, Dallas, TX 75275-0314 (United States)], E-mail: whorsthe@smu.edu

2007-11-26

In reaction-transport systems with non-standard diffusion, the memory of the transport causes a coupling of reactions and transport. We investigate the effect of this coupling for systems with Fisher-type kinetics and obtain a general analytical expression for the front speed. We apply our results to the specific case of subdiffusion.

A minimally-resolved immersed boundary model for reaction-diffusion problems

OpenAIRE

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...

Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport

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.

Global dynamics of a nonlocal delayed reaction-diffusion equation on a half plane

Science.gov (United States)

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.

Emergent Chemical Behavior in Variable-Volume Protocells

Directory of Open Access Journals (Sweden)

Ben Shirt-Ediss

2015-01-01

Full Text Available Artificial protocellular compartments and lipid vesicles have been used as model systems to understand the origins and requirements for early cells, as well as to design encapsulated reactors for biotechnology. One prominent feature of vesicles is the semi-permeable nature of their membranes, able to support passive diffusion of individual solute species into/out of the compartment, in addition to an osmotic water flow in the opposite direction to the net solute concentration gradient. Crucially, this water flow affects the internal aqueous volume of the vesicle in response to osmotic imbalances, in particular those created by ongoing reactions within the system. In this theoretical study, we pay attention to this often overlooked aspect and show, via the use of a simple semi-spatial vesicle reactor model, that a changing solvent volume introduces interesting non-linearities into an encapsulated chemistry. Focusing on bistability, we demonstrate how a changing volume compartment can degenerate existing bistable reactions, but also promote emergent bistability from very simple reactions, which are not bistable in bulk conditions. One particularly remarkable effect is that two or more chemically-independent reactions, with mutually exclusive reaction kinetics, are able to couple their dynamics through the variation of solvent volume inside the vesicle. Our results suggest that other chemical innovations should be expected when more realistic and active properties of protocellular compartments are taken into account.

A reaction-diffusion model of CO2 influx into an oocyte

Science.gov (United States)

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

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.

Diffusion coefficients of tracers in glassy polymer systems prepared by gamma radiolysis

International Nuclear Information System (INIS)

Tonge, M.P.; Gilbert, R.G.

1996-01-01

Diffusion-controlled reactions are common in free radical polymerisation reactions, especially in glassy polymer matrices. Such reactions commonly have an important influence on the polymerisation process and final polymer properties. For example, the dominant growth-stopping event (bimolecular termination) is generally diffusion-controlled. In glassy polymer systems, where molecular mobility is very low, the chain growth mechanism (propagation) may become diffusion-controlled. At present, the mechanism for propagation in glassy polymers is poorly understood, but it is expected by the Smoluchowski expression applied to propagation to depend strongly on the diffusion coefficient of monomer. The objective of this study is to measure reliable diffusion coefficients of small tracer molecules in glassy polymers, and compare these with propagation rate coefficients in similar systems, by the prediction above. Samples were initially prepared in a sealed sampled cell containing monomer, inert diluent, and tracer dye. After irradiation for several days, complete conversion of monomer to polymer can be obtained. The diffusion coefficients for two tracer dyes have been measured as a function of weight fraction polymer glassy poly(methyl methacrylate) samples

Electrical bistabilities and memory stabilities of nonvolatile bistable devices fabricated utilizing C60 molecules embedded in a polymethyl methacrylate layer

International Nuclear Information System (INIS)

Cho, Sung Hwan; Lee, Dong Ik; Jung, Jae Hun; Kim, Tae Whan

2009-01-01

Current-voltage (I-V) measurements on Al/fullerene (C 60 ) molecules embedded in polymethyl methacrylate/Al devices at 300 K showed a current bistability due to the existence of the C 60 molecules. The on/off ratio of the current bistability for the memory devices was as large as 10 3 . The retention time of the devices was above 2.5 x 10 4 s at room temperature, and cycling endurance tests on these devices indicated that the ON and OFF currents showed no degradation until 50 000 cycles. Carrier transport mechanisms for the nonvolatile bistable devices are described on the basis of the I-V experimental and fitting results.

Oscillations in the bistable regime of neuronal networks.

Science.gov (United States)

Roxin, Alex; Compte, Albert

2016-07-01

Bistability between attracting fixed points in neuronal networks has been hypothesized to underlie persistent activity observed in several cortical areas during working memory tasks. In network models this kind of bistability arises due to strong recurrent excitation, sufficient to generate a state of high activity created in a saddle-node (SN) bifurcation. On the other hand, canonical network models of excitatory and inhibitory neurons (E-I networks) robustly produce oscillatory states via a Hopf (H) bifurcation due to the E-I loop. This mechanism for generating oscillations has been invoked to explain the emergence of brain rhythms in the β to γ bands. Although both bistability and oscillatory activity have been intensively studied in network models, there has not been much focus on the coincidence of the two. Here we show that when oscillations emerge in E-I networks in the bistable regime, their phenomenology can be explained to a large extent by considering coincident SN and H bifurcations, known as a codimension two Takens-Bogdanov bifurcation. In particular, we find that such oscillations are not composed of a stable limit cycle, but rather are due to noise-driven oscillatory fluctuations. Furthermore, oscillations in the bistable regime can, in principle, have arbitrarily low frequency.

Hopf bifurcation in a reaction-diffusive two-species model with nonlocal delay effect and general functional response

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.

Unstable Modes and Order Parameters of Bistable Signaling Pathways at Saddle-Node Bifurcations: A Theoretical Study Based on Synergetics

Directory of Open Access Journals (Sweden)

Till D. Frank

2016-01-01

Full Text Available Mathematical modeling has become an indispensable part of systems biology which is a discipline that has become increasingly popular in recent years. In this context, our understanding of bistable signaling pathways in terms of mathematical modeling is of particular importance because such bistable components perform crucial functions in living cells. Bistable signaling pathways can act as switches or memory functions and can determine cell fate. In the present study, properties of mathematical models of bistable signaling pathways are examined from the perspective of synergetics, a theory of self-organization and pattern formation founded by Hermann Haken. At the heart of synergetics is the concept of so-called unstable modes or order parameters that determine the behavior of systems as a whole close to bifurcation points. How to determine these order parameters for bistable signaling pathways at saddle-node bifurcation points is shown. The procedure is outlined in general and an explicit example is worked out in detail.

Propensity for Bistability of Bursting and Silence in the Leech Heart Interneuron

Directory of Open Access Journals (Sweden)

Tatiana Dashevskiy

2018-02-01

Full Text Available The coexistence of neuronal activity regimes has been reported under normal and pathological conditions. Such multistability could enhance the flexibility of the nervous system and has many implications for motor control, memory, and decision making. Multistability is commonly promoted by neuromodulation targeting specific membrane ionic currents. Here, we investigated how modulation of different ionic currents could affect the neuronal propensity for bistability. We considered a leech heart interneuron model. It exhibits bistability of bursting and silence in a narrow range of the leak current parameters, conductance (gleak and reversal potential (Eleak. We assessed the propensity for bistability of the model by using bifurcation diagrams. On the diagram (gleak, Eleak, we mapped bursting and silent regimes. For the canonical value of Eleak we determined the range of gleak which supported the bistability. We use this range as an index of propensity for bistability. We investigated how this index was affected by alterations of ionic currents. We systematically changed their conductances, one at a time, and built corresponding bifurcation diagrams in parameter planes of the maximal conductance of a given current and the leak conductance. We found that conductance of only one current substantially affected the index of propensity; the increase of the maximal conductance of the hyperpolarization-activated cationic current increased the propensity index. The second conductance with the strongest effect was the conductance of the low-threshold fast Ca2+ current; its reduction increased the propensity index although the effect was about two times smaller in magnitude. Analyzing the model with both changes applied simultaneously, we found that the diagram (gleak, Eleak showed a progressively expanded area of bistability of bursting and silence.

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

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.

Modeling of Reaction Processes Controlled by Diffusion

International Nuclear Information System (INIS)

Revelli, Jorge

2003-01-01

Stochastic modeling is quite powerful in science and technology.The technics derived from this process have been used with great success in laser theory, biological systems and chemical reactions.Besides, they provide a theoretical framework for the analysis of experimental results on the field of particle's diffusion in ordered and disordered materials.In this work we analyze transport processes in one-dimensional fluctuating media, which are media that change their state in time.This fact induces changes in the movements of the particles giving rise to different phenomena and dynamics that will be described and analyzed in this work.We present some random walk models to describe these fluctuating media.These models include state transitions governed by different dynamical processes.We also analyze the trapping problem in a lattice by means of a simple model which predicts a resonance-like phenomenon.Also we study effective diffusion processes over surfaces due to random walks in the bulk.We consider different boundary conditions and transitions movements.We derive expressions that describe diffusion behaviors constrained to bulk restrictions and the dynamic of the particles.Finally it is important to mention that the theoretical results obtained from the models proposed in this work are compared with Monte Carlo simulations.We find, in general, excellent agreements between the theory and the simulations

Bistable soliton states and switching in doubly inhomogeneously ...

Indian Academy of Sciences (India)

Dec. 2001 physics pp. 969–979. Bistable soliton states and switching in doubly inhomogeneously doped fiber couplers. AJIT KUMAR. Department of Physics, Indian Institute of Technology, Hauz Khas, New Delhi 110 016, India. Abstract. Switching between the bistable soliton states in a doubly and inhomogeneously doped.

Wong-Zakai approximations and attractors for stochastic reaction-diffusion equations on unbounded domains

Science.gov (United States)

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.

A gradient structure for reaction–diffusion systems and for energy-drift-diffusion systems

International Nuclear Information System (INIS)

Mielke, Alexander

2011-01-01

In recent years the theory of the Wasserstein metric has opened up new treatments of diffusion equations as gradient systems, where the free energy or entropy take the role of the driving functional and where the space is equipped with the Wasserstein metric. We show on the formal level that this gradient structure can be generalized to reaction–diffusion systems with reversible mass-action kinetic. The metric is constructed using the dual dissipation potential, which is a quadratic functional of all chemical potentials including the mobilities as well as the reaction kinetics. The metric structure is obtained by Legendre transform from the dual dissipation potential. The same ideas extend to systems including electrostatic interactions or a correct energy balance via coupling to the heat equation. We show this by treating the semiconductor equations involving the electron and hole densities, the electrostatic potential, and the temperature. Thus, the models in Albinus et al (2002 Nonlinearity 15 367–83), which stimulated this work, have a gradient structure

Brain mechanisms for simple perception and bistable perception.

Science.gov (United States)

Wang, Megan; Arteaga, Daniel; He, Biyu J

2013-08-27

When faced with ambiguous sensory inputs, subjective perception alternates between the different interpretations in a stochastic manner. Such multistable perception phenomena have intrigued scientists and laymen alike for over a century. Despite rigorous investigations, the underlying mechanisms of multistable perception remain elusive. Recent studies using multivariate pattern analysis revealed that activity patterns in posterior visual areas correlate with fluctuating percepts. However, increasing evidence suggests that vision--and perception at large--is an active inferential process involving hierarchical brain systems. We applied searchlight multivariate pattern analysis to functional magnetic resonance imaging signals across the human brain to decode perceptual content during bistable perception and simple unambiguous perception. Although perceptually reflective activity patterns during simple perception localized predominantly to posterior visual regions, bistable perception involved additionally many higher-order frontoparietal and temporal regions. Moreover, compared with simple perception, both top-down and bottom-up influences were dramatically enhanced during bistable perception. We further studied the intermittent presentation of ambiguous images--a condition that is known to elicit perceptual memory. Compared with continuous presentation, intermittent presentation recruited even more higher-order regions and was accompanied by further strengthened top-down influences but relatively weakened bottom-up influences. Taken together, these results strongly support an active top-down inferential process in perception.

Hybrid approaches for multiple-species stochastic reaction-diffusion models

Science.gov (United States)

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.

KAUST Repository

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.

Hybrid approaches for multiple-species stochastic reaction-diffusion models.

KAUST Repository

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.

Soft tissue deformation modelling through neural dynamics-based reaction-diffusion mechanics.

Science.gov (United States)

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.

Bistable (latching) solenoid actuated propellant isolation valve

Science.gov (United States)

Wichmann, H.; Deboi, H. H.

1979-01-01

The design, fabrication, assembly and test of a development configuration bistable (latching) solenoid actuated propellant isolation valve suitable for the control hydrazine and liquid fluorine to an 800 pound thrust rocket engine is described. The valve features a balanced poppet, utilizing metal bellows, a hard poppet/seat interface and a flexure support system for the internal moving components. This support system eliminates sliding surfaces, thereby rendering the valve free of self generated particles.

Controlling the optical bistability and transmission coefficient in a four-level atomic medium

International Nuclear Information System (INIS)

Asadpour, Seyyed Hossein; Eslami-Majd, Abdullah

2012-01-01

A novel four level atomic configuration is proposed for controlling the optical bistability and transmission coefficient with application on all-optical switching. Two circularly polarized components from a weak linearly-polarized probe beam are interacted separately by two transitions of this medium. A coherent coupling field has derived another atomic transition. It is demonstrated that the transmission coefficient of two orthogonally polarized beams at different frequencies can be achieved by adjusting the magnitude of the external magnetic field. It is found that the threshold of the optical bistability can be controlled by magnitude of the external magnetic field. Also, it is shown that optical bistability can be converted to optical multistability by switching the two orthogonally polarized beams. - Highlights: ► An inverted Y-type four level atomic system is proposed. ► Transmission coefficient can be controlled by a novel interesting parameter. ► Optical bistability and multistability can be achieved via external magnetic field. ► It is shown that our proposed model is suitable for all optical switching application.

Modeling convection-diffusion-reaction systems for microfluidic molecular communications with surface-based receivers in Internet of Bio-Nano Things.

Directory of Open Access Journals (Sweden)

Murat Kuscu

Full Text Available We consider a microfluidic molecular communication (MC system, where the concentration-encoded molecular messages are transported via fluid flow-induced convection and diffusion, and detected by a surface-based MC receiver with ligand receptors placed at the bottom of the microfluidic channel. The overall system is a convection-diffusion-reaction system that can only be solved by numerical methods, e.g., finite element analysis (FEA. However, analytical models are key for the information and communication technology (ICT, as they enable an optimisation framework to develop advanced communication techniques, such as optimum detection methods and reliable transmission schemes. In this direction, we develop an analytical model to approximate the expected time course of bound receptor concentration, i.e., the received signal used to decode the transmitted messages. The model obviates the need for computationally expensive numerical methods by capturing the nonlinearities caused by laminar flow resulting in parabolic velocity profile, and finite number of ligand receptors leading to receiver saturation. The model also captures the effects of reactive surface depletion layer resulting from the mass transport limitations and moving reaction boundary originated from the passage of finite-duration molecular concentration pulse over the receiver surface. Based on the proposed model, we derive closed form analytical expressions that approximate the received pulse width, pulse delay and pulse amplitude, which can be used to optimize the system from an ICT perspective. We evaluate the accuracy of the proposed model by comparing model-based analytical results to the numerical results obtained by solving the exact system model with COMSOL Multiphysics.

Modeling convection-diffusion-reaction systems for microfluidic molecular communications with surface-based receivers in Internet of Bio-Nano Things.

Science.gov (United States)

Kuscu, Murat; Akan, Ozgur B

2018-01-01

We consider a microfluidic molecular communication (MC) system, where the concentration-encoded molecular messages are transported via fluid flow-induced convection and diffusion, and detected by a surface-based MC receiver with ligand receptors placed at the bottom of the microfluidic channel. The overall system is a convection-diffusion-reaction system that can only be solved by numerical methods, e.g., finite element analysis (FEA). However, analytical models are key for the information and communication technology (ICT), as they enable an optimisation framework to develop advanced communication techniques, such as optimum detection methods and reliable transmission schemes. In this direction, we develop an analytical model to approximate the expected time course of bound receptor concentration, i.e., the received signal used to decode the transmitted messages. The model obviates the need for computationally expensive numerical methods by capturing the nonlinearities caused by laminar flow resulting in parabolic velocity profile, and finite number of ligand receptors leading to receiver saturation. The model also captures the effects of reactive surface depletion layer resulting from the mass transport limitations and moving reaction boundary originated from the passage of finite-duration molecular concentration pulse over the receiver surface. Based on the proposed model, we derive closed form analytical expressions that approximate the received pulse width, pulse delay and pulse amplitude, which can be used to optimize the system from an ICT perspective. We evaluate the accuracy of the proposed model by comparing model-based analytical results to the numerical results obtained by solving the exact system model with COMSOL Multiphysics.

Dynamics and bistability in a reduced model of the lac operon

Science.gov (United States)

Yildirim, Necmettin; Santillán, Moisés; Horike, Daisuke; Mackey, Michael C.

2004-06-01

It is known that the lac operon regulatory pathway is capable of showing bistable behavior. This is an important complex feature, arising from the nonlinearity of the involved mechanisms, which is essential to understand the dynamic behavior of this molecular regulatory system. To find which of the mechanisms involved in the regulation of the lac operon is the origin of bistability, we take a previously published model which accounts for the dynamics of mRNA, lactose, allolactose, permease and β-galactosidase involvement and simplify it by ignoring permease dynamics (assuming a constant permease concentration). To test the behavior of the reduced model, three existing sets of data on β-galactosidase levels as a function of time are simulated and we obtain a reasonable agreement between the data and the model predictions. The steady states of the reduced model were numerically and analytically analyzed and it was shown that it may indeed display bistability, depending on the extracellular lactose concentration and growth rate.

Parabolic equations in biology growth, reaction, movement and diffusion

CERN Document Server

Perthame, Benoît

2015-01-01

This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents these aspects from a mathematical perspective, with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so, it uncovers the mechanisms at work behind Turing instability, pattern formation and invasion waves. This involves several mathematical tools, such as stability and instability analysis, blow-up in finite time, asymptotic methods and relative entropy properties. Given the content presented, the book is well suited as a textbook for master-level coursework.

Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations

KAUST Repository

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.

Magnetic-field induced bistability in a quasi-one-dimensional semiconductor microcavity

International Nuclear Information System (INIS)

Zhang, Chuanyi; Zhang, Weifeng

2015-01-01

We theoretically study the magnetic-field induced bistability in a quasi-one-dimensional semiconductor microcavity. A critical magnetic field is obtained, and the bistability appears if a magnetic field is greater than the critical value. For a positive energy detuning of the pump from the bare exciton polaritons, one bistability loop first emerges, then it divides into two loops, and finally one of them vanishes with the increasing magnetic field. This phenomenon originates from the magnetic-field modulated interactions for opposite spins. In the variational process, there are two important effects: one is a logic gate with a small variation of the excitation laser, and the other is a spin texture like skyrmion and this texture is periodic if the energy detuning varies periodically in real space, which is useful for designing the spin-dependent optoelectronic devices. - Highlights: • We study the bistability induced by a magnetic field in a microcavity. • One bistability loop can divide into two, and then the two loops return to one. • A spin texture like skyrmion and logic gate arise in the variation of bistability loop

Ground-state thermodynamics of bistable redox-active donor-acceptor mechanically interlocked molecules.

Science.gov (United States)

Fahrenbach, Albert C; Bruns, Carson J; Cao, Dennis; Stoddart, J Fraser

2012-09-18

Fashioned through billions of years of evolution, biological molecular machines, such as ATP synthase, myosin, and kinesin, use the intricate relative motions of their components to drive some of life's most essential processes. Having control over the motions in molecules is imperative for life to function, and many chemists have designed, synthesized, and investigated artificial molecular systems that also express controllable motions within molecules. Using bistable mechanically interlocked molecules (MIMs), based on donor-acceptor recognition motifs, we have sought to imitate the sophisticated nanoscale machines present in living systems. In this Account, we analyze the thermodynamic characteristics of a series of redox-switchable [2]rotaxanes and [2]catenanes. Control and understanding of the relative intramolecular movements of components in MIMs have been vital in the development of a variety of applications of these compounds ranging from molecular electronic devices to drug delivery systems. These bistable donor-acceptor MIMs undergo redox-activated switching between two isomeric states. Under ambient conditions, the dominant translational isomer, the ground-state coconformation (GSCC), is in equilibrium with the less favored translational isomer, the metastable-state coconformation (MSCC). By manipulating the redox state of the recognition site associated with the GSCC, we can stimulate the relative movements of the components in these bistable MIMs. The thermodynamic parameters of model host-guest complexes provide a good starting point to rationalize the ratio of GSCC to MSCC at equilibrium. The bistable [2]rotaxanes show a strong correlation between the relative free energies of model complexes and the ground-state distribution constants (K(GS)). This relationship does not always hold for bistable [2]catenanes, most likely because of the additional steric and electronic constraints present when the two rings are mechanically interlocked with each other

Proof of existence of global solutions for m-component reaction-diffusion systems with mixed boundary conditions via the Lyapunov functional method

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)

Stochastic resonance and MFPT in an asymmetric bistable system driven by correlated multiplicative colored noise and additive white noise

Science.gov (United States)

Shi, Pei-Ming; Li, Qun; Han, Dong-Ying

2017-06-01

This paper investigates a new asymmetric bistable model driven by correlated multiplicative colored noise and additive white noise. The mean first-passage time (MFPT) and the signal-to-noise ratio (SNR) as the indexes of evaluating the model are researched. Based on the two-state theory and the adiabatic approximation theory, the expressions of MFPT and SNR have been obtained for the asymmetric bistable system driven by a periodic signal, correlated multiplicative colored noise and additive noise. Simulation results show that it is easier to generate stochastic resonance (SR) to adjust the intensity of correlation strength λ. Meanwhile, the decrease of asymmetric coefficient r2 and the increase of noise intensity are beneficial to realize the transition between the two steady states in the system. At the same time, the twice SR phenomena can be observed by adjusting additive white noise and correlation strength. The influence of asymmetry of potential function on the MFPTs in two different directions is different.

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

An experimental design method leading to chemical Turing patterns.

Science.gov (United States)

Horváth, Judit; Szalai, István; De Kepper, Patrick

2009-05-08

Chemical reaction-diffusion patterns often serve as prototypes for pattern formation in living systems, but only two isothermal single-phase reaction systems have produced sustained stationary reaction-diffusion patterns so far. We designed an experimental method to search for additional systems on the basis of three steps: (i) generate spatial bistability by operating autoactivated reactions in open spatial reactors; (ii) use an independent negative-feedback species to produce spatiotemporal oscillations; and (iii) induce a space-scale separation of the activatory and inhibitory processes with a low-mobility complexing agent. We successfully applied this method to a hydrogen-ion autoactivated reaction, the thiourea-iodate-sulfite (TuIS) reaction, and noticeably produced stationary hexagonal arrays of spots and parallel stripes of pH patterns attributed to a Turing bifurcation. This method could be extended to biochemical reactions.

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.

Two optical bistability domains in composites of metal nanoparticles with nonlinear dielectric core

Energy Technology Data Exchange (ETDEWEB)

Shewamare, Sisay, E-mail: sisayshewa20@yahoo.com [Department of Physics, Addis Ababa University, P.O. Box 1176, Addis Ababa (Ethiopia); Mal' nev, V.N., E-mail: vadimnmalnev@yahoo.com [Department of Physics, Addis Ababa University, P.O. Box 1176, Addis Ababa (Ethiopia)

2012-12-15

It is shown that the local field in metal spherical particles with a dielectric core in an external varying electric field has two maxima at two different frequencies. The second maximum becomes more important with an increment in the metal fraction. Due to the nonlinear dielectric function of the core, the composite of these inclusions may have two optically induced bistability domains at different frequencies. At rather high metal fraction, two bistability domains merge and form one entire bistability domain. The parameters of these domains are studied numerically. The paper focuses on the second bistability domain, which has not been discussed in the literature so far. This domain exists in a comparatively narrow frequency range and its onset fields are lower than those of the first bistability domain. The lowest bistability onset fields are obtained in the entire domain. This peculiarity of the optical induced bistability in the metal composite with small dielectric cores can be attractive for possible applications.

Two optical bistability domains in composites of metal nanoparticles with nonlinear dielectric core

International Nuclear Information System (INIS)

Shewamare, Sisay; Mal'nev, V.N.

2012-01-01

It is shown that the local field in metal spherical particles with a dielectric core in an external varying electric field has two maxima at two different frequencies. The second maximum becomes more important with an increment in the metal fraction. Due to the nonlinear dielectric function of the core, the composite of these inclusions may have two optically induced bistability domains at different frequencies. At rather high metal fraction, two bistability domains merge and form one entire bistability domain. The parameters of these domains are studied numerically. The paper focuses on the second bistability domain, which has not been discussed in the literature so far. This domain exists in a comparatively narrow frequency range and its onset fields are lower than those of the first bistability domain. The lowest bistability onset fields are obtained in the entire domain. This peculiarity of the optical induced bistability in the metal composite with small dielectric cores can be attractive for possible applications.

Dynamic and energetic characteristics of a bistable piezoelectric vibration energy harvester with an elastic magnifier

Science.gov (United States)

Wang, Guangqing; Liao, Wei-Hsin; Yang, Binqiang; Wang, Xuebao; Xu, Wentan; Li, Xiuling

2018-05-01

Bistable piezoelectric energy harvesters are being increasingly seen as an alternative to batteries in low-power devices. However, their energy harvesting characteristics are limited. To enhance these, we use a configuration including an elastic magnifier to amplify base excitation and provide sufficient kinetic energy to overcome potential well barriers, thus leading to large-amplitude bistable motion. We derive the distributed parameter mathematical model of this configuration by using Hamilton's principle. We then investigate the nonlinear dynamic behaviors and energetic characteristics and analyze the bifurcation for the equilibrium solution of the model. The simulations and experiments show high electromechanical responses and energy generation characteristics of the proposed system over a broad frequency band. The results suggest that, compared with a typical bistable piezoelectric energy harvester, the proposed energy harvester system with an elastic magnifier can provide higher output over a broader frequency band at lower excitation levels by adjusting the system's mass and stiffness ratios.

Stability Analysis of a Reaction-Diffusion System Modeling Atherogenesis

KAUST Repository

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

Optical bistability induced by quantum coherence in a negative index atomic medium

International Nuclear Information System (INIS)

Zhang Hong-Jun; Sun Hui; Li Jin-Ping; Yin Bao-Yin; Guo Hong-Ju

2013-01-01

Bistability behaviors in an optical ring cavity filled with a dense V-type four-level atomic medium are theoretically investigated. It is found that the optical bistability can appear in the negative refraction frequency band, while both the bistability and multi-stability can occur in the positive refraction frequency bands. Therefore, optical bistability can be realized from conventional material to negative index material due to quantum coherence in our scheme. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Bistability of heat transfer of a viscous liquid under conditions of flow channel

International Nuclear Information System (INIS)

Melkikh, A.V.; Seleznev, V.D.

2001-01-01

The heat exchange model for a viscous liquid flowing under the pressure drop effect in a tube, surrounded by the medium with a lower temperature, is considered. It is shown that the system bistable behavior is possible by availability of the liquid viscosity exponential dependence on the temperature and by negligible dissipative heat release. The transitions between cold and hot flows in this case should proceed by a jump. The liquid and channel parameters, whereby the bistability may be observed, are determined [ru

Passing to the limit in a Wasserstein gradient flow : from diffusion to reaction

NARCIS (Netherlands)

Arnrich, S.; Mielke, A.; Peletier, M.A.; Savaré, G.; Veneroni, M.

2012-01-01

We study a singular-limit problem arising in the modelling of chemical reactions. At finite e > 0, the system is described by a Fokker-Planck convection-diffusion equation with a double-well convection potential. This potential is scaled by 1 / e and in the limit e --> 0, the solution concentrates

Competitive autocatalytic reactions in chaotic flows with diffusion: Prediction using finite-time Lyapunov exponents

International Nuclear Information System (INIS)

Schlick, Conor P.; Umbanhowar, Paul B.; Ottino, Julio M.; Lueptow, Richard M.

2014-01-01

We investigate chaotic advection and diffusion in autocatalytic reactions for time-periodic sine flow computationally using a mapping method with operator splitting. We specifically consider three different autocatalytic reaction schemes: a single autocatalytic reaction, competitive autocatalytic reactions, which can provide insight into problems of chiral symmetry breaking and homochirality, and competitive autocatalytic reactions with recycling. In competitive autocatalytic reactions, species B and C both undergo an autocatalytic reaction with species A such that A+B→2B and A+C→2C. Small amounts of initially spatially localized B and C and a large amount of spatially homogeneous A are advected by the velocity field, diffuse, and react until A is completely consumed and only B and C remain. We find that local finite-time Lyapunov exponents (FTLEs) can accurately predict the final average concentrations of B and C after the reaction completes. The species that starts in the region with the larger FTLE has, with high probability, the larger average concentration at the end of the reaction. If B and C start in regions with similar FTLEs, their average concentrations at the end of the reaction will also be similar. When a recycling reaction is added, the system evolves towards a single species state, with the FTLE often being useful in predicting which species fills the entire domain and which is depleted. The FTLE approach is also demonstrated for competitive autocatalytic reactions in journal bearing flow, an experimentally realizable flow that generates chaotic dynamics

Reaction effects in diffusive shock acceleration

International Nuclear Information System (INIS)

Drury, L.Oc.

1984-01-01

The effects of the reaction of accelerated particles back on the shock wave in the diffusive-shock-acceleration model of cosmic-ray generation are investigated theoretically. Effects examined include changes in the shock structure, modifications of the input and output spectra, scattering effects, and possible instabilities in the small-scale structure. It is pointed out that the latter two effects are applicable to any spatially localized acceleration mechanism. 14 references

Ca++ dependent bistability induced by serotonin in spinal motoneurons

DEFF Research Database (Denmark)

Hounsgaard, J.; Kiehn, O.

1985-01-01

The plateau potential, responsible for the bistable state of spinal motoneurons, recently described in the decerebrate cat, was suggested to depend on serotonin (Hounsgaard et al. 1984). In an in vitro preparation of the spinal cord of the turtle we now show that serotonin, applied directly...... to the bath, transforms the intrinsic response properties of motoneurons, uncovering a plateau potential and voltage sensitive bistability. The changes induced by serotonin were blocked by Mn++, while the plateau potential and the bistability remained after application of tetrodotoxin. We conclude...... that serotonin controls the expression of a Ca++ dependent plateau potential in motoneurons....

Dynamic control of a bistable wing under aerodynamic loading

International Nuclear Information System (INIS)

Bilgen, Onur; Arrieta, Andres F; Friswell, Michael I; Hagedorn, Peter

2013-01-01

The aerodynamic evaluation of a dynamic control technique applied to a bistable unsymmetrical cross-ply composite plate with surface bonded piezoelectric actuators is presented. The plate is clamped on one end to form a low-aspect-ratio wing. A previously proposed dynamic control method, utilizing bending resonance in different stable equilibrium positions, is used to induce snap-through between the two equilibrium states. Compared to quasi-static actuation, driving the bistable plate near resonance using surface bonded piezoelectric materials requires, theoretically, a lower peak excitation voltage to achieve snap-through. First, a set of extensive wind tunnel experiments are conducted on the passive bistable wing to understand the change in the dynamic behavior under various aerodynamic conditions. The passive wing demonstrated sufficient bending stiffness to sustain its shape under aerodynamic loading while preserving the desired bistable behavior. Next, by the use of the resonant control technique, the plate is turned into an effectively monostable structure, or alternatively, both stable equilibrium positions can be reached actively from the other stable equilibrium. Dynamic forward and reverse snap-through is demonstrated in the wind tunnel which shows both the effectiveness of the piezoelectric actuation as well as the load carrying capability of both states of the bistable wing. (paper)

Bistable four-wave mixing response in a semiconductor quantum dot coupled to a photonic crystal nanocavity.

Science.gov (United States)

Li, Jian-Bo; Xiao, Si; Liang, Shan; He, Meng-Dong; Luo, Jian-Hua; Kim, Nam-Chol; Chen, Li-Qun

2017-10-16

We perform a theoretical study of the bistable four-wave mixing (FWM) response in a coupled system comprised of a semiconductor quantum dot (SQD) and a photonic crystal (PC) nanocavity in which the SQD is embedded. It is shown that the shape of the FWM spectrum can switch among single-peaked, double-peaked, triple-peaked, and four-peaked arising from the vacuum Rabi splitting and the exciton-nanocavity coupling. Especially, we map out bistability phase diagrams within a parameter subspace of the system, and find that it is easy to turn on or off the bistable FWM response by only adjusting the excitation frequency or the pumping intensity. Our results offer a feasible means for measuring the SQD-PC nanocavity coupling strength and open a new avenue to design optical switches and memories.

Investigation of a bistable dual-stage vibration isolator under harmonic excitation

International Nuclear Information System (INIS)

Yang, Kai; Huang, Hai; Harne, R L; Wang, K W

2014-01-01

This study explores the steady-state performance of a dual-stage vibration isolator, which is configured by a bistable oscillator and a linear oscillator. The potential force of the bistable stage comprises negative linear and positive cubic nonlinear stiffnesses such that the two restoring force contributions may counterbalance to minimize dynamic force transmission. By applying a first-order harmonic balance, it is predicted that the bistable dual-stage isolator may significantly outperform an equivalent pure linear dual-stage isolator. This conclusion is verified through a series of numerical investigations. Following a parametric study, design guidelines are detailed to achieve performance improvements. Then, the ‘valley’ response, which is the special phenomenon of the bistable dual-stage isolator due to the counterbalance of the negative linear and positive nonlinear potential forces, is revealed and quantitatively explained. Numerical studies demonstrate the role of initial conditions, and it is shown that the likelihood of beneficial single periodic valley and intra-well responses for isolation purposes can be increased by greater bistable stage damping. Finally, a bistable dual-stage isolator prototype is developed and tested, and the numerical and experimental results verify the theoretical predictions. (paper)

On the Green's function of the partially diffusion-controlled reversible ABCD reaction for radiation chemistry codes

Energy Technology Data Exchange (ETDEWEB)

Plante, Ianik, E-mail: ianik.plante-1@nasa.gov [Wyle Science, Technology & Engineering, 1290 Hercules, Houston, TX 77058 (United States); Devroye, Luc, E-mail: lucdevroye@gmail.com [School of Computer Science, McGill University, 3480 University Street, Montreal H3A 0E9 (Canada)

2015-09-15

Several computer codes simulating chemical reactions in particles systems are based on the Green's functions of the diffusion equation (GFDE). Indeed, many types of chemical systems have been simulated using the exact GFDE, which has also become the gold standard for validating other theoretical models. In this work, a simulation algorithm is presented to sample the interparticle distance for partially diffusion-controlled reversible ABCD reaction. This algorithm is considered exact for 2-particles systems, is faster than conventional look-up tables and uses only a few kilobytes of memory. The simulation results obtained with this method are compared with those obtained with the independent reaction times (IRT) method. This work is part of our effort in developing models to understand the role of chemical reactions in the radiation effects on cells and tissues and may eventually be included in event-based models of space radiation risks. However, as many reactions are of this type in biological systems, this algorithm might play a pivotal role in future simulation programs not only in radiation chemistry, but also in the simulation of biochemical networks in time and space as well.

On the Green's function of the partially diffusion-controlled reversible ABCD reaction for radiation chemistry codes

International Nuclear Information System (INIS)

Plante, Ianik; Devroye, Luc

2015-01-01

Several computer codes simulating chemical reactions in particles systems are based on the Green's functions of the diffusion equation (GFDE). Indeed, many types of chemical systems have been simulated using the exact GFDE, which has also become the gold standard for validating other theoretical models. In this work, a simulation algorithm is presented to sample the interparticle distance for partially diffusion-controlled reversible ABCD reaction. This algorithm is considered exact for 2-particles systems, is faster than conventional look-up tables and uses only a few kilobytes of memory. The simulation results obtained with this method are compared with those obtained with the independent reaction times (IRT) method. This work is part of our effort in developing models to understand the role of chemical reactions in the radiation effects on cells and tissues and may eventually be included in event-based models of space radiation risks. However, as many reactions are of this type in biological systems, this algorithm might play a pivotal role in future simulation programs not only in radiation chemistry, but also in the simulation of biochemical networks in time and space as well

Exact solutions of certain nonlinear chemotaxis diffusion reaction ...

Indian Academy of Sciences (India)

constructed coupled differential equations. The results obtained ... Nonlinear diffusion reaction equation; chemotaxis; auxiliary equation method; solitary wave solutions. ..... fact limits the scope of applications of the derived results. ... Research Fellowship and AP acknowledges DU and DST for PURSE grant for financial.

Optical Bistability in Graded Core-Shell Granular Composites

International Nuclear Information System (INIS)

Wu Ya-Min; Chen Guo-Qing; Xue Si-Zhong; Zhu Zhuo-Wei; Ma Chao-Qun

2012-01-01

The intrinsic optical bistability (OB) of graded core-shell granular composites is investigated. The coated particles are made of cores with gradient dielectric function in c (r) = A(r/a) k and nonlinear shells. In view of the exponential distribution of the core dielectric constant, the potential functions of each region are obtained by solving the Maxwell equations, and the mathematical expressions of electric field in the shells and cores are determined. Numerical study reveals that the optical bistable threshold and the threshold width of the composite medium are dependent on the shell thickness, core dielectric exponent, and power function coefficient. The optical bistable width increases with the decreasing shell thickness and the power exponent and with the increasing power function coefficient

Bistable output from a coupled-resonator vertical-cavity laser diode

International Nuclear Information System (INIS)

Fischer, A. J.; Choquette, K. D.; Chow, W. W.; Allerman, A. A.; Geib, K.

2000-01-01

We report a monolithic coupled-resonator vertical-cavity laser with an ion-implanted top cavity and a selectively oxidized bottom cavity which exhibits bistable behavior in the light output versus injection current. Large bistability regions over current ranges as wide as 18 mA have been observed with on/off contrast ratios of greater than 20 dB. The position and width of the bistability region can be varied by changing the bias to the top cavity. Switching between on and off states can be accomplished with changes as small as 250 μW to the electrical power applied to the top cavity. The bistable behavior is the response of the nonlinear susceptibility in the top cavity to the changes in the bottom intracavity laser intensity as the bottom cavity reaches the thermal rollover point

Coupling between feedback loops in autoregulatory networks affects bistability range, open-loop gain and switching times

International Nuclear Information System (INIS)

Tiwari, Abhinav; Igoshin, Oleg A

2012-01-01

Biochemical regulatory networks governing diverse cellular processes such as stress-response, differentiation and cell cycle often contain coupled feedback loops. We aim at understanding how features of feedback architecture, such as the number of loops, the sign of the loops and the type of their coupling, affect network dynamical performance. Specifically, we investigate how bistability range, maximum open-loop gain and switching times of a network with transcriptional positive feedback are affected by additive or multiplicative coupling with another positive- or negative-feedback loop. We show that a network's bistability range is positively correlated with its maximum open-loop gain and that both quantities depend on the sign of the feedback loops and the type of feedback coupling. Moreover, we find that the addition of positive feedback could decrease the bistability range if we control the basal level in the signal-response curves of the two systems. Furthermore, the addition of negative feedback has the capacity to increase the bistability range if its dissociation constant is much lower than that of the positive feedback. We also find that the addition of a positive feedback to a bistable network increases the robustness of its bistability range, whereas the addition of a negative feedback decreases it. Finally, we show that the switching time for a transition from a high to a low steady state increases with the effective fold change in gene regulation. In summary, we show that the effect of coupled feedback loops on the bistability range and switching times depends on the underlying mechanistic details. (paper)

Mathematical aspects of reacting and diffusing systems

CERN Document Server

Fife, Paul C

1979-01-01

Modeling and analyzing the dynamics of chemical mixtures by means of differ- tial equations is one of the prime concerns of chemical engineering theorists. These equations often take the form of systems of nonlinear parabolic partial d- ferential equations, or reaction-diffusion equations, when there is diffusion of chemical substances involved. A good overview of this endeavor can be had by re- ing the two volumes by R. Aris (1975), who himself was one of the main contributors to the theory. Enthusiasm for the models developed has been shared by parts of the mathematical community, and these models have, in fact, provided motivation for some beautiful mathematical results. There are analogies between chemical reactors and certain biological systems. One such analogy is rather obvious: a single living organism is a dynamic structure built of molecules and ions, many of which react and diffuse. Other analogies are less obvious; for example, the electric potential of a membrane can diffuse like a chemical, and ...

A Redox-Active Bistable Molecular Switch Mounted inside a Metal-Organic Framework.

Science.gov (United States)

Chen, Qishui; Sun, Junling; Li, Peng; Hod, Idan; Moghadam, Peyman Z; Kean, Zachary S; Snurr, Randall Q; Hupp, Joseph T; Farha, Omar K; Stoddart, J Fraser

2016-11-02

We describe the incorporation of a bistable mechanically interlocked molecule (MIM) into a robust Zr-based metal-organic framework (MOF), NU-1000, by employing a post-synthetic functionalization protocol. On average, close to two bistable [2]catenanes can be incorporated per repeating unit of the hexagonal channels of NU-1000. The reversible redox-switching of the bistable [2]catenanes is retained inside the MOF, as evidenced by solid-state UV-vis-NIR reflectance spectroscopy and cyclic voltammetry. This research demonstrates that bistable MIMs are capable of exhibiting robust dynamics inside the nanopores of a MOF.

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.

Homogenization of a thermo-diffusion system with Smoluchowski interactions

NARCIS (Netherlands)

Krehel, O.; Aiki, T.; Muntean, A.

2014-01-01

We study the solvability and homogenization of a thermal-diffusion reaction problem posed in a periodically perforated domain. The system describes the motion of populations of hot colloidal particles interacting together via Smoluchowski production terms. The upscaled system, obtained via two-scale

Synchronization of Reaction-Diffusion Neural Networks With Dirichlet Boundary Conditions and Infinite Delays.

Science.gov (United States)

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.

Bistability and self-oscillations effects in a polariton-laser semiconductor microcavity

International Nuclear Information System (INIS)

Cotta, E A; Matinaga, F M

2007-01-01

We report an experimental observation of polaritonic optical bistability of the laser emission in a planar semiconductor microcavity with a 100 0 A GaAs single quantum well in the strong-coupling regime. The bistability curves show crossings that indicate a competition between a Kerr-like effect induced by the polariton population and thermal effects. Associated with the bistability, laser-like emission occurs at the bare cavity mode

Thermally activated reaction–diffusion-controlled chemical bulk reactions of gases and solids

Directory of Open Access Journals (Sweden)

S. Möller

2015-01-01

Full Text Available The chemical kinetics of the reaction of thin films with reactive gases is investigated. The removal of thin films using thermally activated solid–gas to gas reactions is a method to in-situ control deposition inventory in vacuum and plasma vessels. Significant scatter of experimental deposit removal rates at apparently similar conditions was observed in the past, highlighting the need for understanding the underlying processes. A model based on the presence of reactive gas in the films bulk and chemical kinetics is presented. The model describes the diffusion of reactive gas into the film and its chemical interaction with film constituents in the bulk using a stationary reaction–diffusion equation. This yields the reactive gas concentration and reaction rates. Diffusion and reaction rate limitations are depicted in parameter studies. Comparison with literature data on tokamak co-deposit removal results in good agreement of removal rates as a function of pressure, film thickness and temperature.

Investigation of bistable perception with the "silhouette spinner": sit still, spin the dancer with your will.

Science.gov (United States)

Liu, Chao-Hsuan; Tzeng, Ovid J L; Hung, Daisy L; Tseng, Philip; Juan, Chi-Hung

2012-05-01

Many studies have used static and non-biologically related stimuli to investigate bistable perception and found that the percept is usually dominated by their intrinsic nature with some influence of voluntary control from the viewer. Here we used a dynamic stimulus of a rotating human body, the silhouette spinner illusion, to investigate how the viewers' intentions may affect their percepts. In two experiments, we manipulated observer intention (active or passive), fixation position (body or feet), and spinning velocity (fast, medium, or slow). Our results showed that the normalized alternating rate between two bistable percepts was greater when (1) participants actively attempted to switch percepts, (2) when participants fixated at the spinner's feet rather than the body, inducing as many as 25 switches of the bistable percepts within 1 min, and (3) when they watched the spinner at high velocity. These results suggest that a dynamic biologically-bistable percept can be quickly alternated by the viewers' intention. Furthermore, the higher alternating rate in the feet condition compared to the body condition suggests a role for biological meaningfulness in determining bistable percepts, where 'biologically plausible' interpretations are favored by the visual system. Copyright © 2012 Elsevier Ltd. All rights reserved.

Bistable polarization switching in a continuous wave ruby laser

Science.gov (United States)

Lawandy, N. M.; Afzal, R. Sohrab

1988-01-01

Bistability in the output power, polarization state, and mode volume of an argon-ion laser pumped single mode ruby laser at 6943 A has been observed. The laser operates in a radially confined mode which exhibits hysteresis and bistability only when the pump polarization is parallel to the c-axis.

Reaction phases and diffusion paths in SiC/metal systems

Energy Technology Data Exchange (ETDEWEB)

Naka, M.; Fukai, T. [Osaka Univ., Osaka (Japan); Schuster, J.C. [Vienna Univ., Vienna (Austria)

2004-07-01

The interface structures between SiC and metal are reviewed at SiC/metal systems. Metal groups are divided to carbide forming metals and non-carbide forming metals. Carbide forming metals form metal carbide granular or zone at metal side, and metal silicide zone at SiC side. The further diffusion of Si and C from SiC causes the formation of T ternary phase depending metal. Non-carbide forming metals form silicide zone containing graphite or the layered structure of metal silicide and metal silicide containing graphite. The diffusion path between SiC and metal are formed along tie-lines connecting SiC and metal on the corresponding ternary Si-C-M system. The reactivity of metals is dominated by the forming ability of carbide or silicide. Te reactivity tendency of elements are discussed on the periodical table of elements, and Ti among elements shows the highest reactivity among carbide forming metals. For non-carbide forming metals the reactivity sequence of metals is Fe>Ni>Co. (orig.)

Stochastic resonance in a stochastic bistable system with additive noises and square–wave signal

International Nuclear Information System (INIS)

Feng, Guo; Xiang-Dong, Luo; Shao-Fu, Li; Yu-Rong, Zhou

2010-01-01

This paper considers the stochastic resonance in a stochastic bistable system driven by a periodic square-wave signal and a static force as well as by additive white noise and dichotomous noise from the viewpoint of signal-to-noise ratio. It finds that the signal-to-noise ratio appears as stochastic resonance behaviour when it is plotted as a function of the noise strength of the white noise and dichotomous noise, as a function of the system parameters, or as a function of the static force. Moreover, the influence of the strength of the stochastic potential force and the correlation rate of the dichotomous noise on the signal-to-noise ratio is investigated. (general)

Perceptual incongruence influences bistability and cortical activation.

Directory of Open Access Journals (Sweden)

Gijs Joost Brouwer

Full Text Available We employed a parametric psychophysical design in combination with functional imaging to examine the influence of metric changes in perceptual incongruence on perceptual alternation rates and cortical responses. Subjects viewed a bistable stimulus defined by incongruent depth cues; bistability resulted from incongruence between binocular disparity and monocular perspective cues that specify different slants (slant rivalry. Psychophysical results revealed that perceptual alternation rates were positively correlated with the degree of perceived incongruence. Functional imaging revealed systematic increases in activity that paralleled the psychophysical results within anterior intraparietal sulcus, prior to the onset of perceptual alternations. We suggest that this cortical activity predicts the frequency of subsequent alternations, implying a putative causal role for these areas in initiating bistable perception. In contrast, areas implicated in form and depth processing (LOC and V3A were sensitive to the degree of slant, but failed to show increases in activity when these cues were in conflict.

Variational methods applied to problems of diffusion and reaction

CERN Document Server

Strieder, William

1973-01-01

This monograph is an account of some problems involving diffusion or diffusion with simultaneous reaction that can be illuminated by the use of variational principles. It was written during a period that included sabbatical leaves of one of us (W. S. ) at the University of Minnesota and the other (R. A. ) at the University of Cambridge and we are grateful to the Petroleum Research Fund for helping to support the former and the Guggenheim Foundation for making possible the latter. We would also like to thank Stephen Prager for getting us together in the first place and for showing how interesting and useful these methods can be. We have also benefitted from correspondence with Dr. A. M. Arthurs of the University of York and from the counsel of Dr. B. D. Coleman the general editor of this series. Table of Contents Chapter 1. Introduction and Preliminaries . 1. 1. General Survey 1 1. 2. Phenomenological Descriptions of Diffusion and Reaction 2 1. 3. Correlation Functions for Random Suspensions 4 1. 4. Mean Free ...

Hopf bifurcation in a delayed reaction-diffusion-advection population model

Science.gov (United States)

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.

The Necker-Zeno model for bistable perception.

Science.gov (United States)

Atmanspacher, Harald; Filk, Thomas

2013-10-01

A novel conceptual framework for theoretical psychology is presented and illustrated for the example of bistable perception. A basic formal feature of this framework is the non-commutativity of operations acting on mental states. A corresponding model for the bistable perception of ambiguous stimuli, the Necker-Zeno model, is sketched and some empirical evidence for it so far is described. It is discussed how a temporal non-locality of mental states, predicted by the model, can be understood and tested. © 2013 Cognitive Science Society, Inc.

Solitary wave solutions of selective nonlinear diffusion-reaction ...

Indian Academy of Sciences (India)

An auto-Bäcklund transformation derived in the homogeneous balance method is employed to obtain several new exact solutions of certain kinds of nonlin- ear diffusion-reaction (D-R) equations. These equations arise in a variety of problems in physical, chemical, biological, social and ecological sciences. Keywords.

Computer-assisted design for scaling up systems based on DNA reaction networks.

Science.gov (United States)

Aubert, Nathanaël; Mosca, Clément; Fujii, Teruo; Hagiya, Masami; Rondelez, Yannick

2014-04-06

In the past few years, there have been many exciting advances in the field of molecular programming, reaching a point where implementation of non-trivial systems, such as neural networks or switchable bistable networks, is a reality. Such systems require nonlinearity, be it through signal amplification, digitalization or the generation of autonomous dynamics such as oscillations. The biochemistry of DNA systems provides such mechanisms, but assembling them in a constructive manner is still a difficult and sometimes counterintuitive process. Moreover, realistic prediction of the actual evolution of concentrations over time requires a number of side reactions, such as leaks, cross-talks or competitive interactions, to be taken into account. In this case, the design of a system targeting a given function takes much trial and error before the correct architecture can be found. To speed up this process, we have created DNA Artificial Circuits Computer-Assisted Design (DACCAD), a computer-assisted design software that supports the construction of systems for the DNA toolbox. DACCAD is ultimately aimed to design actual in vitro implementations, which is made possible by building on the experimental knowledge available on the DNA toolbox. We illustrate its effectiveness by designing various systems, from Montagne et al.'s Oligator or Padirac et al.'s bistable system to new and complex networks, including a two-bit counter or a frequency divider as well as an example of very large system encoding the game Mastermind. In the process, we highlight a variety of behaviours, such as enzymatic saturation and load effect, which would be hard to handle or even predict with a simpler model. We also show that those mechanisms, while generally seen as detrimental, can be used in a positive way, as functional part of a design. Additionally, the number of parameters included in these simulations can be large, especially in the case of complex systems. For this reason, we included the

Optical wall dynamics induced by coexistence of monostable and bistable spatial regions.

Science.gov (United States)

Odent, V; Louvergneaux, E; Clerc, M G; Andrade-Silva, I

2016-11-01

When nonequilibrium extended homogeneous systems exhibit multistability, it leads to the presence of domain walls between the existing equilibria. Depending on the stability of the steady states, the dynamics differs. Here, we consider the interface dynamics in the case of a spatially inhomogeneous system, namely, an optical system where the control parameter is spatially Gaussian. Then interfaces connect the monostable and the bistable nonuniform states that are associated with two distinct spatial regions. The coexistence of these two regions of different stability induces relaxation dynamics and the propagation of a wall with a time-dependent speed. We emphasize analytically these two dynamical behaviors using a generic bistable model. Experimentally, an inhomogeneous Gaussian light beam traveling through either a dye-doped liquid crystal cell or a Kerr cavity depicts these behaviors, in agreement with the theoretical predictions.

Qualitative analysis on a cubic predator-prey system with diffusion

Directory of Open Access Journals (Sweden)

Qunyi Bie

2011-04-01

Full Text Available In this paper, we study a cubic predator-prey model with diffusion. We first establish the global stability of the trivial and nontrivial constant steady states for the reaction diffusion system, and then prove the existence and non-existence results concerning non-constant positive stationary solutions by using topological argument and the energy method, respectively.

Bistable cholesteric liquid crystal light shutter with multielectrode driving.

Science.gov (United States)

Li, Cheng-Chang; Tseng, Heng-Yi; Pai, Tsung-Wei; Wu, Yu-Ching; Hsu, Wen-Hao; Jau, Hung-Chang; Chen, Chun-Wei; Lin, Tsung-Hsien

2014-08-01

An electrically activated bistable light shutter that exploits polymer-stabilized cholesteric liquid crystal film was developed. Under double-sided three-terminal electrode driving, the device can be bistable and switched between focal conic and homeotropic textures with a uniform in-plane and vertical electrical field. The transparent state with a transmittance of 80% and the opaque/scattering state with a transmittance of 13% can be realized without any optical compensation film, and each can be simply switched to the other by applying a pulse voltage. Also, gray-scale selection can be performed by varying the applied voltage. The designed energy-saving bistable light shutter can be utilized to preserve privacy and control illumination and the flow of energy.

Bistable Topological Insulator with Exciton-Polaritons

Science.gov (United States)

Kartashov, Yaroslav V.; Skryabin, Dmitry V.

2017-12-01

The functionality of many nonlinear and quantum optical devices relies on the effect of optical bistability. Using microcavity exciton-polaritons in a honeycomb arrangement of microcavity pillars, we report the resonance response and bistability of topological edge states. A balance between the pump, loss, and nonlinearity ensures a broad range of dynamical stability and controls the distribution of power between counterpropagating states on the opposite edges of the honeycomb lattice stripe. Tuning energy and polarization of the pump photons, while keeping their momentum constant, we demonstrate control of the propagation direction of the dominant edge state. Our results facilitate the development of practical applications of topological photonics.

Dynamics of a bistable Miura-origami structure

Science.gov (United States)

Fang, Hongbin; Li, Suyi; Ji, Huimin; Wang, K. W.

2017-05-01

Origami-inspired structures and materials have shown extraordinary properties and performances originating from the intricate geometries of folding. However, current state of the art studies have mostly focused on static and quasistatic characteristics. This research performs a comprehensive experimental and analytical study on the dynamics of origami folding through investigating a stacked Miura-Ori (SMO) structure with intrinsic bistability. We fabricate and experimentally investigated a bistable SMO prototype with rigid facets and flexible crease lines. Under harmonic base excitation, the SMO exhibits both intrawell and interwell oscillations. Spectrum analyses reveal that the dominant nonlinearities of SMO are quadratic and cubic, which generate rich dynamics including subharmonic and chaotic oscillations. The identified nonlinearities indicate that a third-order polynomial can be employed to approximate the measured force-displacement relationship. Such an approximation is validated via numerical study by qualitatively reproducing the phenomena observed in the experiments. The dynamic characteristics of the bistable SMO resemble those of a Helmholtz-Duffing oscillator (HDO); this suggests the possibility of applying the established tools and insights of HDO to predict origami dynamics. We also show that the bistability of SMO can be programmed within a large design space via tailoring the crease stiffness and initial stress-free configurations. The results of this research offer a wealth of fundamental insights into the dynamics of origami folding, and provide a solid foundation for developing foldable and deployable structures and materials with embedded dynamic functionalities.

Dynamics of a bistable Miura-origami structure.

Science.gov (United States)

Fang, Hongbin; Li, Suyi; Ji, Huimin; Wang, K W

2017-05-01

Origami-inspired structures and materials have shown extraordinary properties and performances originating from the intricate geometries of folding. However, current state of the art studies have mostly focused on static and quasistatic characteristics. This research performs a comprehensive experimental and analytical study on the dynamics of origami folding through investigating a stacked Miura-Ori (SMO) structure with intrinsic bistability. We fabricate and experimentally investigated a bistable SMO prototype with rigid facets and flexible crease lines. Under harmonic base excitation, the SMO exhibits both intrawell and interwell oscillations. Spectrum analyses reveal that the dominant nonlinearities of SMO are quadratic and cubic, which generate rich dynamics including subharmonic and chaotic oscillations. The identified nonlinearities indicate that a third-order polynomial can be employed to approximate the measured force-displacement relationship. Such an approximation is validated via numerical study by qualitatively reproducing the phenomena observed in the experiments. The dynamic characteristics of the bistable SMO resemble those of a Helmholtz-Duffing oscillator (HDO); this suggests the possibility of applying the established tools and insights of HDO to predict origami dynamics. We also show that the bistability of SMO can be programmed within a large design space via tailoring the crease stiffness and initial stress-free configurations. The results of this research offer a wealth of fundamental insights into the dynamics of origami folding, and provide a solid foundation for developing foldable and deployable structures and materials with embedded dynamic functionalities.

A quintuple quantum dot system for electrical and optical control of multi/bistability in a telecommunication window

International Nuclear Information System (INIS)

Mehmannavaz, Mohammad Reza; Sattari, Hamed

2015-01-01

We propose a model for a quintuple coupled quantum dot system based on a GaAs/AlGaAs heterostructure. Then, we analyze the optical bistability (OB) and optical multistability (OM) behaviours and transition between the regimes at a wavelength of λ=1.550 μm. We take the benefit of consecutive and parallel interdot tunnelling and an incoherent pumping field for electrical and even optical control of the processes. It is shown that OB, OM and transition between them can be accomplished and controlled by adjusting the rate of the inter-dot tunnellings (electrical bias), probe wavelength detuning and rate of the optical incoherent pumping field. By proper choice of the controlling parameters, the bistable hysteresis loop becomes narrower, which makes it easier for the cavity field to reach saturation. We interpret the OB and OM behaviours by discussing the absorption of the active medium. We also investigate switching time between the two stable states when the output field jumps from a lower branch to an upper branch. Such a controllable OB/OM and transition between them in multiple QD molecules at a wavelength of 1.550 μm, may provide some new possibilities for technological applications in optoelectronics, solid-state quantum information science and systems dealing with signal processing. (letter)

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.)

Cellular automata for spatiotemporal pattern formation from reaction–diffusion partial differential equations

International Nuclear Information System (INIS)

Ohmori, Shousuke; Yamazaki, Yoshihiro

2016-01-01

Ultradiscrete equations are derived from a set of reaction–diffusion partial differential equations, and cellular automaton rules are obtained on the basis of the ultradiscrete equations. Some rules reproduce the dynamical properties of the original reaction–diffusion equations, namely, bistability and pulse annihilation. Furthermore, other rules bring about soliton-like preservation and periodic pulse generation with a pacemaker, which are not obtained from the original reaction–diffusion equations. (author)

Bistability of mangrove forests and competition with freshwater plants

Science.gov (United States)

Jiang, Jiang; Fuller, Douglas O; Teh, Su Yean; Zhai, Lu; Koh, Hock Lye; DeAngelis, Donald L.; Sternberg, L.D.S.L.

2015-01-01

Halophytic communities such as mangrove forests and buttonwood hammocks tend to border freshwater plant communities as sharp ecotones. Most studies attribute this purely to underlying physical templates, such as groundwater salinity gradients caused by tidal flux and topography. However, a few recent studies hypothesize that self-reinforcing feedback between vegetation and vadose zone salinity are also involved and create a bistable situation in which either halophytic dominated habitat or freshwater plant communities may dominate as alternative stable states. Here, we revisit the bistability hypothesis and demonstrate the mechanisms that result in bistability. We demonstrate with remote sensing imagery the sharp boundaries between freshwater hardwood hammock communities in southern Florida and halophytic communities such as buttonwood hammocks and mangroves. We further document from the literature how transpiration of mangroves and freshwater plants respond differently to vadose zone salinity, thus altering the salinity through feedback. Using mathematical models, we show how the self-reinforcing feedback, together with physical template, controls the ecotones between halophytic and freshwater communities. Regions of bistability along environmental gradients of salinity have the potential for large-scale vegetation shifts following pulse disturbances such as hurricane tidal surges in Florida, or tsunamis in other regions. The size of the region of bistability can be large for low-lying coastal habitat due to the saline water table, which extends inland due to salinity intrusion. We suggest coupling ecological and hydrologic processes as a framework for future studies.

On Uniform Decay of the Entropy for Reaction–Diffusion Systems

KAUST Repository

Mielke, Alexander

2014-09-10

This work provides entropy decay estimates for classes of nonlinear reaction–diffusion systems modeling reversible chemical reactions under the detailed-balance condition. We obtain explicit bounds for the exponential decay of the relative logarithmic entropy, being based essentially on the application of the Log-Sobolev estimate and a convexification argument only, making it quite robust to model variations. An important feature of our analysis is the interaction of the two different dissipative mechanisms: pure diffusion, forcing the system asymptotically to the homogeneous state, and pure reaction, forcing the solution to the (possibly inhomogeneous) chemical equilibrium. Only the interaction of both mechanisms provides the convergence to the homogeneous equilibrium. Moreover, we introduce two generalizations of the main result: (i) vanishing diffusion constants in some chemical components and (ii) usage of different entropy functionals. We provide a few examples to highlight the usability of our approach and shortly discuss possible further applications and open questions.

Effects on nuclear fusion reaction on diffusion and thermal conduction in a magnetoplasma

International Nuclear Information System (INIS)

Sakai, Kazuo; Aono, Osamu.

1976-12-01

In spite of the well spread belief in the field of irreversible thermodynamics, vectorial phenomena couple thermodynamically with the scalar phenomena. Transport coefficients concerning the diffusion and the thermal conduction across a strong magnetic field are calculated in the presence of the deuteron-triton fusion reaction on the basis of the gas kinetic theory. When the reaction takes place, the diffusion increases and the thermal conduction decreases. Effects of the reaction exceed those of the Coulomb collision as the temperature is high enough. (auth.)

Exact solutions of some coupled nonlinear diffusion-reaction ...

Indian Academy of Sciences (India)

certain coupled diffusion-reaction (D-R) equations of very general nature. In recent years, various direct methods have been proposed to find the exact solu- tions not only of nonlinear partial differential equations but also of their coupled versions. These methods include unified ansatz approach [3], extended hyperbolic func ...

Diffusion and phase growth in heterophase systems. 1

International Nuclear Information System (INIS)

Mchedlov-Petrosyan, P.O.

1989-01-01

The present paper gives the view of theoretical study of diffusion processes in ternary and more component solid-state systems, caused by chemical reactions and phase growth. Internal oxidation of alloys, nitridation, borating etc. are the well-known and widely investigated processes of such type. Self-consistent theoretical model of such processes must take into account both the effect of concentration macroscopic districutions on new phase precipitation growth and precipitation reaction on concentration distribution; heterophase must be explicitly allowed for. As for binary system, diffusion theory, running into the phase growth, is well developed and completely presented in monographs, the carried out theoretical investigations of ternary systems are explicitly deficient. The first part of the review presents analysis of available theoretical studies approximately up to 1980. Ratios between various analytically solved models are discussed in detail. It is shown that they don't satisfy to full extent the above-given requirements. More consistent, both numerically and analytically solvable models developed for the last years, are considered in the review second part. 119 refs

Bi-stable optical actuator

Science.gov (United States)

Holdener, Fred R.; Boyd, Robert D.

2000-01-01

The present invention is a bi-stable optical actuator device that is depowered in both stable positions. A bearing is used to transfer motion and smoothly transition from one state to another. The optical actuator device may be maintained in a stable position either by gravity or a restraining device.

Heat Diffusion in Gases, Including Effects of Chemical Reaction

Science.gov (United States)

Hansen, C. Frederick

1960-01-01

The diffusion of heat through gases is treated where the coefficients of thermal conductivity and diffusivity are functions of temperature. The diffusivity is taken proportional to the integral of thermal conductivity, where the gas is ideal, and is considered constant over the temperature interval in which a chemical reaction occurs. The heat diffusion equation is then solved numerically for a semi-infinite gas medium with constant initial and boundary conditions. These solutions are in a dimensionless form applicable to gases in general, and they are used, along with measured shock velocity and heat flux through a shock reflecting surface, to evaluate the integral of thermal conductivity for air up to 5000 degrees Kelvin. This integral has the properties of a heat flux potential and replaces temperature as the dependent variable for problems of heat diffusion in media with variable coefficients. Examples are given in which the heat flux at the stagnation region of blunt hypersonic bodies is expressed in terms of this potential.

Painlevé analysis and exact solutions for the Belousov–Zhabotinskii reaction–diffusion system

International Nuclear Information System (INIS)

Kudryashov, Nikolay A.; Zakharchenko, Anastasia S.

2014-01-01

A system of equations for description of the Belousov–Zhabotinskii chemical reaction is considered. The Painlevé analysis of this reaction–diffusion system is studied. Exact traveling wave solutions of the system for the Belousov–Zhabotinskii reaction are found. Periodic solutions expressed in terms of the Weierstrass elliptic function are also given

Brain networks underlying bistable perception.

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Baker, Daniel H; Karapanagiotidis, Theodoros; Coggan, David D; Wailes-Newson, Kirstie; Smallwood, Jonathan

2015-10-01

Bistable stimuli, such as the Necker Cube, demonstrate that experience can change in the absence of changes in the environment. Such phenomena can be used to assess stimulus-independent aspects of conscious experience. The current study used resting state functional magnetic resonance imaging (rs-fMRI) to index stimulus-independent changes in neural activity to understand the neural architecture that determines dominance durations during bistable perception (using binocular rivalry and Necker cube stimuli). Anterior regions of the Superior Parietal Lobule (SPL) exhibited robust connectivity with regions of primary sensorimotor cortex. The strength of this region's connectivity with the striatum predicted shorter dominance durations during binocular rivalry, whereas its connectivity to pre-motor cortex predicted longer dominance durations for the Necker Cube. Posterior regions of the SPL, on the other hand, were coupled to associative cortex in the temporal and frontal lobes. The posterior SPL's connectivity to the temporal lobe predicted longer dominance during binocular rivalry. In conjunction with prior work, these data suggest that the anterior SPL contributes to perceptual rivalry through the inhibition of incongruent bottom up information, whereas the posterior SPL influences rivalry by supporting the current interpretation of a bistable stimulus. Our data suggests that the functional connectivity of the SPL with regions of sensory, motor, and associative cortex allows it to regulate the interpretation of the environment that forms the focus of conscious attention at a specific moment in time. Copyright © 2015. Published by Elsevier Inc.

Lake Restoration in Terms of Ecological Resilience: a Numerical Study of Biomanipulations under Bistable Conditions

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Takashi Amemiya

2005-12-01

Full Text Available An abstract version of the comprehensive aquatic simulation model (CASM is found to exhibit bistability under intermediate loading of nutrient input, supporting the alternative-stable-states theory and field observations for shallow lakes. Our simulations of biomanipulations under the bistable conditions reveal that a reduction in the abundance of zooplanktivorous fish cannot switch the system from a turbid to a clear state. Rather, a direct reduction of phytoplankton and detritus was found to be most effective to make this switch in the present model. These results imply that multiple manipulations may be effective for practical restorations of lakes. We discuss the present results of biomanipulations in terms of ecological resilience in multivariable systems or natural systems.

Stochastic amplification and signaling in enzymatic futile cycles through noise-induced bistability with oscillations

Science.gov (United States)

Samoilov, Michael; Plyasunov, Sergey; Arkin, Adam P.

2005-02-01

Stochastic effects in biomolecular systems have now been recognized as a major physiologically and evolutionarily important factor in the development and function of many living organisms. Nevertheless, they are often thought of as providing only moderate refinements to the behaviors otherwise predicted by the classical deterministic system description. In this work we show by using both analytical and numerical investigation that at least in one ubiquitous class of (bio)chemical-reaction mechanisms, enzymatic futile cycles, the external noise may induce a bistable oscillatory (dynamic switching) behavior that is both quantitatively and qualitatively different from what is predicted or possible deterministically. We further demonstrate that the noise required to produce these distinct properties can itself be caused by a set of auxiliary chemical reactions, making it feasible for biological systems of sufficient complexity to generate such behavior internally. This new stochastic dynamics then serves to confer additional functional modalities on the enzymatic futile cycle mechanism that include stochastic amplification and signaling, the characteristics of which could be controlled by both the type and parameters of the driving noise. Hence, such noise-induced phenomena may, among other roles, potentially offer a novel type of control mechanism in pathways that contain these cycles and the like units. In particular, observations of endogenous or externally driven noise-induced dynamics in regulatory networks may thus provide additional insight into their topology, structure, and kinetics. network motif | signal transduction | chemical reaction | synthetic biology | systems biology

On Uniform Decay of the Entropy for Reaction–Diffusion Systems

KAUST Repository

Mielke, Alexander; Haskovec, Jan; Markowich, Peter A.

2014-01-01

This work provides entropy decay estimates for classes of nonlinear reaction–diffusion systems modeling reversible chemical reactions under the detailed-balance condition. We obtain explicit bounds for the exponential decay of the relative

Multiple Bistability in Quinonoid-Bridged Diiron(II) Complexes: Influence of Bridge Symmetry on Bistable Properties.

Science.gov (United States)

van der Meer, Margarethe; Rechkemmer, Yvonne; Breitgoff, Frauke D; Marx, Raphael; Neugebauer, Petr; Frank, Uta; van Slageren, Joris; Sarkar, Biprajit

2016-11-21

Quinonoid bridges are well-suited for generating dinuclear assemblies that might display various bistable properties. In this contribution we present two diiron(II) complexes where the iron(II) centers are either bridged by the doubly deprotonated form of a symmetrically substituted quinonoid bridge, 2,5-bis[4-(isopropyl)anilino]-1,4-benzoquinone (H 2 L2') with a [O,N,O,N] donor set, or with the doubly deprotonated form of an unsymmetrically substituted quinonoid bridge, 2-[4-(isopropyl)anilino]-5-hydroxy-1,4-benzoquinone (H 2 L5') with a [O,O,O,N] donor set. Both complexes display temperature-induced spin crossover (SCO). The nature of the SCO is strongly dependent on the bridging ligand, with only the complex with the [O,O,O,N] donor set displaying a prominent hysteresis loop of about 55 K. Importantly, only the latter complex also shows a pronounced light-induced spin state change. Furthermore, both complexes can be oxidized to the mixed-valent iron(II)-iron(III) form, and the nature of the bridge determines the Robin and Day classification of these forms. Both complexes have been probed by a battery of electrochemical, spectroscopic, and magnetic methods, and this combined approach is used to shed light on the electronic structures of the complexes and on bistability. The results presented here thus show the potential of using the relatively new class of unsymmetrically substituted bridging quinonoid ligands for generating intriguing bistable properties and for performing site-specific magnetic switching.

Global exponential stability of reaction-diffusion recurrent neural networks with time-varying delays

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

Efficient numerical simulation of non-integer-order space-fractional reaction-diffusion equation via the Riemann-Liouville operator

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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.

Global exponential stability and periodicity of reaction-diffusion delayed recurrent neural networks with Dirichlet boundary conditions

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

Controllable optical bistability and multistability in asymmetric double quantum wells via spontaneously generated coherence

Energy Technology Data Exchange (ETDEWEB)

Chen, Yuan; Deng, Li [Department of Applied Physics, East China Jiaotong University, Nanchang, 330013 (China); Chen, Aixi, E-mail: aixichen@ecjtu.jx.cn [Department of Applied Physics, East China Jiaotong University, Nanchang, 330013 (China); Institute for Quantum Computing, University of Waterloo, Ontario N2L 3G1 (Canada)

2015-02-15

We investigate the nonlinear optical phenomena of the optical bistability and multistability via spontaneously generated coherence in an asymmetric double quantum well structure coupled by a weak probe field and a controlling field. It is shown that the threshold and hysteresis cycle of the optical bistability can be conveniently controlled only by adjusting the intensity of the SGC or the controlling field. Moreover, switching between optical bistability and multistability can be achieved. These studies may have practical significance for the preparation of optical bistable switching device.

Controllable optical bistability and multistability in asymmetric double quantum wells via spontaneously generated coherence

International Nuclear Information System (INIS)

Chen, Yuan; Deng, Li; Chen, Aixi

2015-01-01

We investigate the nonlinear optical phenomena of the optical bistability and multistability via spontaneously generated coherence in an asymmetric double quantum well structure coupled by a weak probe field and a controlling field. It is shown that the threshold and hysteresis cycle of the optical bistability can be conveniently controlled only by adjusting the intensity of the SGC or the controlling field. Moreover, switching between optical bistability and multistability can be achieved. These studies may have practical significance for the preparation of optical bistable switching device

Numerical and Experimental Studies on Nonlinear Dynamics and Performance of a Bistable Piezoelectric Cantilever Generator

Directory of Open Access Journals (Sweden)

Kangkang Guo

2015-01-01

Full Text Available A piezo-magneto-elastically coupled distributed-parameter model of a bistable piezoelectric cantilever generator is developed by using the generalized Hamilton principle. The influence of the spacing between two adjacent magnets on the static bifurcation characteristics of the system is studied and the range of magnet spacing corresponding to the bistable states is obtained. Numerical and experimental studies are carried out to analyze the bifurcation, response characteristics, and their impact on the electrical output performance under varying external excitations. Results indicate that interwell limit cycle motion of the beam around the two centers corresponds to optimum power output; interwell chaotic motion and multiperiodic motion including intrawell oscillations are less effective. At a given frequency, the phenomena of symmetric-breaking and amplitude-phase modulation are observed with increase of base excitation. Both period-doubling bifurcation and intermittency routes to chaotic motion in the bistable system are found. It can be observed that the power output is not proportional to the excitation level because of the bifurcation behaviours.

Input-Independent Energy Harvesting in Bistable Lattices from Transition Waves.

Science.gov (United States)

Hwang, Myungwon; Arrieta, Andres F

2018-02-26

We demonstrate the utilisation of transition waves for realising input-invariant, frequency-independent energy harvesting in 1D lattices of bistable elements. We propose a metamaterial-inspired design with an integrated electromechanical transduction mechanism to the unit cell, rendering the power conversion capability an intrinsic property of the lattice. Moreover, focusing of transmitted energy to desired locations is demonstrated numerically and experimentally by introducing engineered defects in the form of perturbation in mass or inter-element forcing. We achieve further localisation of energy and numerically observe a breather-like mode for the first time in this type of lattice, improving the harvesting performance by an order of magnitude. Our approach considers generic bistable unit cells and thus provides a universal mechanism to harvest energy and realise metamaterials effectively behaving as a capacitor and power delivery system.

Evidence for distinct mechanisms underlying attentional priming and sensory memory for bistable perception.

Science.gov (United States)

Brinkhuis, M A B; Kristjánsson, Á; Brascamp, J W

2015-08-01

Attentional selection in visual search paradigms and perceptual selection in bistable perception paradigms show functional similarities. For example, both are sensitive to trial history: They are biased toward previously selected targets or interpretations. We investigated whether priming by target selection in visual search and sensory memory for bistable perception are related. We did this by presenting two trial types to observers. We presented either ambiguous spheres that rotated over a central axis and could be perceived as rotating in one of two directions, or search displays in which the unambiguously rotating target and distractor spheres closely resembled the two possible interpretations of the ambiguous stimulus. We interleaved both trial types within experiments, to see whether priming by target selection during search trials would affect the perceptual outcome of bistable perception and, conversely, whether sensory memory during bistable perception would affect target selection times during search. Whereas we found intertrial repetition effects among consecutive search trials and among consecutive bistable trials, we did not find cross-paradigm effects. Thus, even though we could ascertain that our experiments robustly elicited processes of both search priming and sensory memory for bistable perception, these same experiments revealed no interaction between the two.

The Independent and Shared Mechanisms of Intrinsic Brain Dynamics: Insights From Bistable Perception

Directory of Open Access Journals (Sweden)

Teng Cao

2018-04-01

Full Text Available In bistable perception, constant input leads to alternating perception. The dynamics of the changing perception reflects the intrinsic dynamic properties of the “unconscious inferential” process in the brain. Under the same condition, individuals differ in how fast they experience the perceptual alternation. In this study, testing many forms of bistable perception in a large number of observers, we investigated the key question of whether there is a general and common mechanism or multiple and independent mechanisms that control the dynamics of the inferential brain. Bistable phenomena tested include binocular rivalry, vase-face, Necker cube, moving plaid, motion induced blindness, biological motion, spinning dancer, rotating cylinder, Lissajous-figure, rolling wheel, and translating diamond. Switching dynamics for each bistable percept was measured in 100 observers. Results show that the switching rates of subsets of bistable percept are highly correlated. The clustering of dynamic properties of some bistable phenomena but not an overall general control of switching dynamics implies that the brain’s inferential processes are both shared and independent – faster in constructing 3D structure from motion does not mean faster in integrating components into an objects.

Take it of leave it : Mechanisms underlying bacterial bistable regulatory networks

NARCIS (Netherlands)

Siebring, Jeroen; Sorg, Robin; Herber, Martijn; Kuipers, Oscar; Filloux, Alain A.M.

2012-01-01

Bistable switches occur in regulatory networks that can exist in two distinct stable states. Such networks allow distinct switching of individual cells. In bacteria these switches coexist with regulatory networks that respond gradually to environmental input. Bistable switches play key roles in high

Bistability and displacement fluctuations in a quantum nanomechanical oscillator

Science.gov (United States)

Avriller, R.; Murr, B.; Pistolesi, F.

2018-04-01

Remarkable features have been predicted for the mechanical fluctuations at the bistability transition of a classical oscillator coupled capacitively to a quantum dot [Micchi et al., Phys. Rev. Lett. 115, 206802 (2015), 10.1103/PhysRevLett.115.206802]. These results have been obtained in the regime ℏ ω0≪kBT ≪ℏ Γ , where ω0, T , and Γ are the mechanical resonating frequency, the temperature, and the tunneling rate, respectively. A similar behavior could be expected in the quantum regime of ℏ Γ ≪kBT ≪ℏ ω0 . We thus calculate the energy- and displacement-fluctuation spectra and study their behavior as a function of the electromechanical coupling constant when the system enters the Frank-Condon regime. We find that in analogy with the classical case, the energy-fluctuation spectrum and the displacement spectrum widths show a maximum for values of the coupling constant at which a mechanical bistability is established.

A Reliable Bistable Board Implementation through I/O Redundancy

International Nuclear Information System (INIS)

Kim, Min Gyu; Chung, Tae Hyok; Lee, Youn Sang; Kim, Tae Hee; Song, Seung Hwan

2010-01-01

Nuclear power plant safety systems and related equipment used in the design, including an accident in all driving conditions that must be proven In addition, the safety-related equipment that is derived according to the digitization of the safety equipment is the most important factors. Therefore, it is necessary to prove that the device was satisfied the requirements for a given performance for safety-related digital equipment for the life of the installation. These proven is done through the process, design verification of the equipment, production management, such as installation and maintenance. Among other things, it is most important to implement of the performance and reliability features the safety-related equipment in the design phase. In this paper, Bistable Board implemented to generate a ESF sign-on signal throughout the signal processing of input signal from sensors. Also, for the reliable signal input and output, I/O Module that implements the redundancy increases the reliability of the Bistable Board , to verify the performance of safety-related equipment

Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

Science.gov (United States)

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.

Existence and Stability of Traveling Waves for Degenerate Reaction-Diffusion Equation with Time Delay

Science.gov (United States)

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.

Convergence to equilibrium of renormalised solutions to nonlinear chemical reaction–diffusion systems

Science.gov (United States)

Fellner, Klemens; Tang, Bao Quoc

2018-06-01

The convergence to equilibrium for renormalised solutions to nonlinear reaction-diffusion systems is studied. The considered reaction-diffusion systems arise from chemical reaction networks with mass action kinetics and satisfy the complex balanced condition. By applying the so-called entropy method, we show that if the system does not have boundary equilibria, i.e. equilibrium states lying on the boundary of R_+^N, then any renormalised solution converges exponentially to the complex balanced equilibrium with a rate, which can be computed explicitly up to a finite-dimensional inequality. This inequality is proven via a contradiction argument and thus not explicitly. An explicit method of proof, however, is provided for a specific application modelling a reversible enzyme reaction by exploiting the specific structure of the conservation laws. Our approach is also useful to study the trend to equilibrium for systems possessing boundary equilibria. More precisely, to show the convergence to equilibrium for systems with boundary equilibria, we establish a sufficient condition in terms of a modified finite-dimensional inequality along trajectories of the system. By assuming this condition, which roughly means that the system produces too much entropy to stay close to a boundary equilibrium for infinite time, the entropy method shows exponential convergence to equilibrium for renormalised solutions to complex balanced systems with boundary equilibria.

Revisiting the Lissajous figure as a tool to study bistable perception.

Science.gov (United States)

Weilnhammer, V A; Ludwig, K; Sterzer, P; Hesselmann, G

2014-05-01

During bistable vision perception spontaneously "switches" between two mutually exclusive percepts despite constant sensory input. The endogenous nature of these perceptual transitions has motivated extensive research aimed at the underlying mechanisms, since spontaneous perceptual transitions of bistable stimuli should in principle allow for a dissociation of processes related to sensory stimulation from those related to conscious perception. However, transitions from one conscious percept to another are often not instantaneous, and participants usually report a considerable amount of mixed or unclear percepts. This feature of bistable vision makes it difficult to isolate transition-related visual processes. Here, we revisited an ambiguous depth-from-motion stimulus which was first introduced to experimental psychology more than 80 years ago. This rotating Lissajous figure might prove useful in complementing other bistable stimuli, since its perceptual transitions only occur at critical stimulus configurations and are virtually instantaneous, thus facilitating the construction of a perceptually equivalent replay condition. We found that three parameters of the Lissajous figure - complexity, line width, and rotational speed - differentially modulated its perceptual dominance durations and transition probabilities, thus providing experimenters with a versatile tool to study the perceptual dynamics of bistable vision. Copyright © 2014 Elsevier B.V. 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

Atom-loss-induced quantum optical bi-stability switch

International Nuclear Information System (INIS)

Wu Bao-Jun; Cui Fu-Cheng

2012-01-01

We investigate the nonlinear dynamics of a system composed of a cigar-shaped Bose—Einstein condensate and an optical cavity with the two sides coupled dispersively. By adopting discrete-mode approximation for the condensate, taking atom loss as a necessary part of the model to analyze the evolution of the system, while using trial and error method to find out steady states of the system as a reference, numerical simulation demonstrates that with a constant pump, atom loss will trigger a quantum optical bi-stability switch, which predicts a new interesting phenomenon for experiments to verify

Dynamics of unidirectionally coupled bistable Henon maps

International Nuclear Information System (INIS)

Sausedo-Solorio, J.M.; Pisarchik, A.N.

2011-01-01

We study dynamics of two bistable Henon maps coupled in a master-slave configuration. In the case of coexistence of two periodic orbits, the slave map evolves into the master map state after transients, which duration determines synchronization time and obeys a -1/2 power law with respect to the coupling strength. This scaling law is almost independent of the map parameter. In the case of coexistence of chaotic and periodic attractors, very complex dynamics is observed, including the emergence of new attractors as the coupling strength is increased. The attractor of the master map always exists in the slave map independently of the coupling strength. For a high coupling strength, complete synchronization can be achieved only for the attractor similar to that of the master map. -- Highlights: → We study dynamics of two bistable Henon maps coupled in a master-slave configuration. → Synchronization time for periodic orbits obeys a -1/2 power law with respect to coupling. → For a high coupling strength, the slave map remains bistable. → Complete synchronization can be achieved only when both maps stay at the same attractor.

Thiol-modified MoS2 nanosheets as a functional layer for electrical bistable devices

Science.gov (United States)

Li, Guan; Tan, Fenxue; Lv, Bokun; Wu, Mengying; Wang, Ruiqi; Lu, Yue; Li, Xu; Li, Zhiqiang; Teng, Feng

2018-01-01

Molybdenum disulfide nanosheets have been synthesized by one-pot method using 1-ODT as sulfur source and surfactant. The structure, morphology and optical properties of samples were investigated by XRD, FTIR, Abs spectrum and TEM patterns. The XRD pattern indicated that the as-obtained MoS2 belong to hexagonal system. The as-obtained MoS2 nanosheets blending with PVK could be used to fabricate an electrically bistable devices through a simple spin-coating method and the device exhibited an obvious electrical bistability properties. The charge transport mechanism of the device was discussed based on the filamentary switching models.

A predictive coding account of bistable perception - a model-based fMRI study.

Science.gov (United States)

Weilnhammer, Veith; Stuke, Heiner; Hesselmann, Guido; Sterzer, Philipp; Schmack, Katharina

2017-05-01

In bistable vision, subjective perception wavers between two interpretations of a constant ambiguous stimulus. This dissociation between conscious perception and sensory stimulation has motivated various empirical studies on the neural correlates of bistable perception, but the neurocomputational mechanism behind endogenous perceptual transitions has remained elusive. Here, we recurred to a generic Bayesian framework of predictive coding and devised a model that casts endogenous perceptual transitions as a consequence of prediction errors emerging from residual evidence for the suppressed percept. Data simulations revealed close similarities between the model's predictions and key temporal characteristics of perceptual bistability, indicating that the model was able to reproduce bistable perception. Fitting the predictive coding model to behavioural data from an fMRI-experiment on bistable perception, we found a correlation across participants between the model parameter encoding perceptual stabilization and the behaviourally measured frequency of perceptual transitions, corroborating that the model successfully accounted for participants' perception. Formal model comparison with established models of bistable perception based on mutual inhibition and adaptation, noise or a combination of adaptation and noise was used for the validation of the predictive coding model against the established models. Most importantly, model-based analyses of the fMRI data revealed that prediction error time-courses derived from the predictive coding model correlated with neural signal time-courses in bilateral inferior frontal gyri and anterior insulae. Voxel-wise model selection indicated a superiority of the predictive coding model over conventional analysis approaches in explaining neural activity in these frontal areas, suggesting that frontal cortex encodes prediction errors that mediate endogenous perceptual transitions in bistable perception. Taken together, our current work

A predictive coding account of bistable perception - a model-based fMRI study.

Directory of Open Access Journals (Sweden)

Veith Weilnhammer

2017-05-01

Full Text Available In bistable vision, subjective perception wavers between two interpretations of a constant ambiguous stimulus. This dissociation between conscious perception and sensory stimulation has motivated various empirical studies on the neural correlates of bistable perception, but the neurocomputational mechanism behind endogenous perceptual transitions has remained elusive. Here, we recurred to a generic Bayesian framework of predictive coding and devised a model that casts endogenous perceptual transitions as a consequence of prediction errors emerging from residual evidence for the suppressed percept. Data simulations revealed close similarities between the model's predictions and key temporal characteristics of perceptual bistability, indicating that the model was able to reproduce bistable perception. Fitting the predictive coding model to behavioural data from an fMRI-experiment on bistable perception, we found a correlation across participants between the model parameter encoding perceptual stabilization and the behaviourally measured frequency of perceptual transitions, corroborating that the model successfully accounted for participants' perception. Formal model comparison with established models of bistable perception based on mutual inhibition and adaptation, noise or a combination of adaptation and noise was used for the validation of the predictive coding model against the established models. Most importantly, model-based analyses of the fMRI data revealed that prediction error time-courses derived from the predictive coding model correlated with neural signal time-courses in bilateral inferior frontal gyri and anterior insulae. Voxel-wise model selection indicated a superiority of the predictive coding model over conventional analysis approaches in explaining neural activity in these frontal areas, suggesting that frontal cortex encodes prediction errors that mediate endogenous perceptual transitions in bistable perception. Taken together

Energy landscape and dynamics of brain activity during human bistable perception.

Science.gov (United States)

Watanabe, Takamitsu; Masuda, Naoki; Megumi, Fukuda; Kanai, Ryota; Rees, Geraint

2014-08-28

Individual differences in the structure of parietal and prefrontal cortex predict the stability of bistable visual perception. However, the mechanisms linking such individual differences in brain structures to behaviour remain elusive. Here we demonstrate a systematic relationship between the dynamics of brain activity, cortical structure and behaviour underpinning bistable perception. Using fMRI in humans, we find that the activity dynamics during bistable perception are well described as fluctuating between three spatially distributed energy minimums: visual-area-dominant, frontal-area-dominant and intermediate states. Transitions between these energy minimums predicted behaviour, with participants whose brain activity tend to reflect the visual-area-dominant state exhibiting more stable perception and those whose activity transits to frontal-area-dominant states reporting more frequent perceptual switches. Critically, these brain activity dynamics are correlated with individual differences in grey matter volume of the corresponding brain areas. Thus, individual differences in the large-scale dynamics of brain activity link focal brain structure with bistable perception.

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.

Optical bistability in the oscillation of an inhomogeneously broadened quasi-three-level laser

International Nuclear Information System (INIS)

Liu, Junhai; Tian, Xueping

2013-01-01

A theoretical modeling analysis is presented to study the optical bistability exhibited in the oscillation of an inhomogeneously broadened quasi-three-level laser. All the major characteristics of optical bistability depend on two normalized parameters, f and x a , which are defined by f = I sat,a /I sat,m and x a = 2α a0 p a /δ and are related to measurable properties of the laser medium. In comparison with the case of a homogeneously broadened laser, the essential condition for the occurrence of such bistability, f a /(x a + 1), turns out to be the same, whereas the intensities at the up- and down-thresholds are substantially increased and the bistability range is reduced. (paper)

Selective scanning tunnelling microscope electron-induced reactions of single biphenyl molecules on a Si(100) surface.

Science.gov (United States)

Riedel, Damien; Bocquet, Marie-Laure; Lesnard, Hervé; Lastapis, Mathieu; Lorente, Nicolas; Sonnet, Philippe; Dujardin, Gérald

2009-06-03

Selective electron-induced reactions of individual biphenyl molecules adsorbed in their weakly chemisorbed configuration on a Si(100) surface are investigated by using the tip of a low-temperature (5 K) scanning tunnelling microscope (STM) as an atomic size source of electrons. Selected types of molecular reactions are produced, depending on the polarity of the surface voltage during STM excitation. At negative surface voltages, the biphenyl molecule diffuses across the surface in its weakly chemisorbed configuration. At positive surface voltages, different types of molecular reactions are activated, which involve the change of adsorption configuration from the weakly chemisorbed to the strongly chemisorbed bistable and quadristable configurations. Calculated reaction pathways of the molecular reactions on the silicon surface, using the nudge elastic band method, provide evidence that the observed selectivity as a function of the surface voltage polarity cannot be ascribed to different activation energies. These results, together with the measured threshold surface voltages and the calculated molecular electronic structures via density functional theory, suggest that the electron-induced molecular reactions are driven by selective electron detachment (oxidation) or attachment (reduction) processes.

Mix and Inject: Reaction Initiation by Diffusion for Time-Resolved Macromolecular Crystallography

Directory of Open Access Journals (Sweden)

Marius Schmidt

2013-01-01

Full Text Available Time-resolved macromolecular crystallography unifies structure determination with chemical kinetics, since the structures of transient states and chemical and kinetic mechanisms can be determined simultaneously from the same data. To start a reaction in an enzyme, typically, an initially inactive substrate present in the crystal is activated. This has particular disadvantages that are circumvented when active substrate is directly provided by diffusion. However, then it is prohibitive to use macroscopic crystals because diffusion times become too long. With small micro- and nanocrystals diffusion times are adequately short for most enzymes and the reaction can be swiftly initiated. We demonstrate here that a time-resolved crystallographic experiment becomes feasible by mixing substrate with enzyme nanocrystals which are subsequently injected into the X-ray beam of a pulsed X-ray source.

Signatures of a quantum diffusion limited hydrogen atom tunneling reaction.

Science.gov (United States)

Balabanoff, Morgan E; Ruzi, Mahmut; Anderson, David T

2017-12-20

We are studying the details of hydrogen atom (H atom) quantum diffusion in highly enriched parahydrogen (pH 2 ) quantum solids doped with chemical species in an effort to better understand H atom transport and reactivity under these conditions. In this work we present kinetic studies of the 193 nm photo-induced chemistry of methanol (CH 3 OH) isolated in solid pH 2 . Short-term irradiation of CH 3 OH at 1.8 K readily produces CH 2 O and CO which we detect using FTIR spectroscopy. The in situ photochemistry also produces CH 3 O and H atoms which we can infer from the post-photolysis reaction kinetics that display significant CH 2 OH growth. The CH 2 OH growth kinetics indicate at least three separate tunneling reactions contribute; (i) reactions of photoproduced CH 3 O with the pH 2 host, (ii) H atom reactions with the CH 2 O photofragment, and (iii) long-range migration of H atoms and reaction with CH 3 OH. We assign the rapid CH 2 OH growth to the following CH 3 O + H 2 → CH 3 OH + H → CH 2 OH + H 2 two-step sequential tunneling mechanism by conducting analogous kinetic measurements using deuterated methanol (CD 3 OD). By performing photolysis experiments at 1.8 and 4.3 K, we show the post-photolysis reaction kinetics change qualitatively over this small temperature range. We use this qualitative change in the reaction kinetics with temperature to identify reactions that are quantum diffusion limited. While these results are specific to the conditions that exist in pH 2 quantum solids, they have direct implications on the analogous low temperature H atom tunneling reactions that occur on metal surfaces and on interstellar grains.

A thermo-diffusion system with Smoluchowski interactions : well-posedness and homogenization

NARCIS (Netherlands)

Krehel, O.; Aiki, T.; Muntean, A.

2014-01-01

We study the solvability and homogenization of a thermal-diffusion reaction problem posed in a periodically perforated domain. The system describes the motion of populations of hot colloidal particles interacting together via Smoluchowski production terms. The upscaled system, obtained via two-scale

First-passage time in a bistable potential with colored noise

International Nuclear Information System (INIS)

Ramirez-Piscina, L.; Maria Sancho, J.; Javier de la Rubia, F.; Lindenberg, K.; Tsironis, G.P.

1989-01-01

A precise digital simulation of a bistable system under the effect of colored noise is carried out. A set of data for the mean first-passage time is obtained. The results are interpreted and compared with presently available theories, which are revisited following a new insight. Discrepancies that have been discussed in the literature are understood within our framework

Chimera states in an ensemble of linearly locally coupled bistable oscillators

Science.gov (United States)

Shchapin, D. S.; Dmitrichev, A. S.; Nekorkin, V. I.

2017-11-01

Chimera states in a system with linear local connections have been studied. The system is a ring ensemble of analog bistable self-excited oscillators with a resistive coupling. It has been shown that the existence of chimera states is not due to the nonidentity of oscillators and noise, which is always present in real experiments, but is due to the nonlinear dynamics of the system on invariant tori with various dimensions.

Modeling the Influence of Diffusion-Controlled Reactions and Residual Termination and Deactivation on the Rate and Control of Bulk ATRP at High Conversions

Directory of Open Access Journals (Sweden)

Ali Mohammad Rabea

2015-04-01

Full Text Available In high-conversion atom transfer radical polymerization (ATRP, all the reactions, such as radical termination, radical deactivation, dormant chain activation, monomer propagation, etc. could become diffusion controlled sooner or later, depending on relative diffusivities of the involved reacting species. These diffusion-controlled reactions directly affect the rate of polymerization and the control of polymer molecular weight. A model is developed to investigate the influence of diffusion-controlled reactions on the high conversion ATRP kinetics. Model simulation reveals that diffusion-controlled termination slightly increases the rate, but it is the diffusion-controlled deactivation that causes auto-acceleration in the rate (“gel effect” and loss of control. At high conversions, radical chains are “trapped” because of high molecular weight. However, radical centers can still migrate through (1 radical deactivation–activation cycles and (2 monomer propagation, which introduce “residual termination” reactions. It is found that the “residual termination” does not have much influence on the polymerization kinetics. The migration of radical centers through propagation can however facilitate catalytic deactivation of radicals, which improves the control of polymer molecular weight to some extent. Dormant chain activation and monomer propagation also become diffusion controlled and finally stop the polymerization when the system approaches its glass state.

Reaction and diffusion in turbulent combustion

Energy Technology Data Exchange (ETDEWEB)

Pope, S.B. [Mechanical and Aerospace Engineering, Ithaca, NY (United States)

1993-12-01

The motivation for this project is the need to obtain a better quantitative understanding of the technologically-important phenomenon of turbulent combustion. In nearly all applications in which fuel is burned-for example, fossil-fuel power plants, furnaces, gas-turbines and internal-combustion engines-the combustion takes place in a turbulent flow. Designers continually demand more quantitative information about this phenomenon-in the form of turbulent combustion models-so that they can design equipment with increased efficiency and decreased environmental impact. For some time the PI has been developing a class of turbulent combustion models known as PDF methods. These methods have the important virtue that both convection and reaction can be treated without turbulence-modelling assumptions. However, a mixing model is required to account for the effects of molecular diffusion. Currently, the available mixing models are known to have some significant defects. The major motivation of the project is to seek a better understanding of molecular diffusion in turbulent reactive flows, and hence to develop a better mixing model.

Unified path integral approach to theories of diffusion-influenced reactions

Science.gov (United States)

Prüstel, Thorsten; Meier-Schellersheim, Martin

2017-08-01

Building on mathematical similarities between quantum mechanics and theories of diffusion-influenced reactions, we develop a general approach for computational modeling of diffusion-influenced reactions that is capable of capturing not only the classical Smoluchowski picture but also alternative theories, as is here exemplified by a volume reactivity model. In particular, we prove the path decomposition expansion of various Green's functions describing the irreversible and reversible reaction of an isolated pair of molecules. To this end, we exploit a connection between boundary value and interaction potential problems with δ - and δ'-function perturbation. We employ a known path-integral-based summation of a perturbation series to derive a number of exact identities relating propagators and survival probabilities satisfying different boundary conditions in a unified and systematic manner. Furthermore, we show how the path decomposition expansion represents the propagator as a product of three factors in the Laplace domain that correspond to quantities figuring prominently in stochastic spatially resolved simulation algorithms. This analysis will thus be useful for the interpretation of current and the design of future algorithms. Finally, we discuss the relation between the general approach and the theory of Brownian functionals and calculate the mean residence time for the case of irreversible and reversible reactions.

Diffusion-controlled reactions modeling in Geant4-DNA

Energy Technology Data Exchange (ETDEWEB)

Karamitros, M., E-mail: matkara@gmail.com [CNRS, IN2P3, CENBG, UMR 5797, F-33170 Gradignan (France); CNRS, INCIA, UMR 5287, F-33400 Talence (France); Luan, S. [University of New Mexico, Department of Computer Science, Albuquerque, NM (United States); Bernal, M.A. [Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, SP (Brazil); Allison, J. [Geant4 Associates International Ltd (United Kingdom); Baldacchino, G. [CEA Saclay, IRAMIS, LIDYL, Radiation Physical Chemistry Group, F-91191 Gif sur Yvette Cedex (France); CNRS, UMR3299, SIS2M, F-91191 Gif sur Yvette Cedex (France); Davidkova, M. [Nuclear Physics Institute of the ASCR, Prague (Czech Republic); Francis, Z. [Saint Joseph University, Faculty of Sciences, Department of Physics, Mkalles, Beirut (Lebanon); Friedland, W. [Helmholtz Zentrum München, German Research Center for Environmental Health, Institute of Radiation Protection, Ingolstädter Landstr. 1, 85764 Neuherberg (Germany); Ivantchenko, V. [Ecoanalytica, 119899 Moscow (Russian Federation); Geant4 Associates International Ltd (United Kingdom); Ivantchenko, A. [Geant4 Associates International Ltd (United Kingdom); Mantero, A. [SwHaRD s.r.l., via Buccari 9, 16153 Genova (Italy); Nieminem, P.; Santin, G. [ESA-ESTEC, 2200 AG Noordwijk (Netherlands); Tran, H.N. [Division of Nuclear Physics and Faculty of Applied Sciences, Ton Duc Thang University, Tan Phong Ward, District 7, Ho Chi Minh City (Viet Nam); Stepan, V. [CNRS, IN2P3, CENBG, UMR 5797, F-33170 Gradignan (France); Nuclear Physics Institute of the ASCR, Prague (Czech Republic); Incerti, S., E-mail: incerti@cenbg.in2p3.fr [CNRS, IN2P3, CENBG, UMR 5797, F-33170 Gradignan (France)

2014-10-01

Context Under irradiation, a biological system undergoes a cascade of chemical reactions that can lead to an alteration of its normal operation. There are different types of radiation and many competing reactions. As a result the kinetics of chemical species is extremely complex. The simulation becomes then a powerful tool which, by describing the basic principles of chemical reactions, can reveal the dynamics of the macroscopic system. To understand the dynamics of biological systems under radiation, since the 80s there have been on-going efforts carried out by several research groups to establish a mechanistic model that consists in describing all the physical, chemical and biological phenomena following the irradiation of single cells. This approach is generally divided into a succession of stages that follow each other in time: (1) the physical stage, where the ionizing particles interact directly with the biological material; (2) the physico-chemical stage, where the targeted molecules release their energy by dissociating, creating new chemical species; (3) the chemical stage, where the new chemical species interact with each other or with the biomolecules; (4) the biological stage, where the repairing mechanisms of the cell come into play. This article focuses on the modeling of the chemical stage. Method This article presents a general method of speeding-up chemical reaction simulations in fluids based on the Smoluchowski equation and Monte-Carlo methods, where all molecules are explicitly simulated and the solvent is treated as a continuum. The model describes diffusion-controlled reactions. This method has been implemented in Geant4-DNA. The keys to the new algorithm include: (1) the combination of a method to compute time steps dynamically with a Brownian bridge process to account for chemical reactions, which avoids costly fixed time step simulations; (2) a k–d tree data structure for quickly locating, for a given molecule, its closest reactants. The

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.

WNT and DKK Determine Hair Follicle Spacing Through a Reaction-Diffusion Mechanism

Science.gov (United States)

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.

Reverse bistable effect in ferroelectric liquid crystal devices with ultra-fast switching at low driving voltage.

Science.gov (United States)

Guo, Qi; Zhao, Xiaojin; Zhao, Huijie; Chigrinov, V G

2015-05-15

In this Letter, reverse bistable effect with deep-sub-millisecond switching time is first reported in ferroelectric liquid crystal (FLC) devices using a homogeneous photo-alignment technique. It is indicated by our experimental results that both the anchoring energy and the dielectric property of the FLC's alignment layer is critical for the existence of the reverse bistable effect. In addition, with the derived criteria of the reverse bistable effect, we quantitatively analyze the switching dynamics of the reverse bistable FLC and the transition condition between the traditional bistability and our presented reverse bistability. Moreover, the fabricated FLC device exhibits an ultra-fast switching of ∼160  μs and a high contrast ratio of 1000:1, both of which were measured at a low driving voltage of 11 V. The featured deep-sub-millisecond switching time is really advantageous for our presented reverse bistable FLC devices, which enables a significant quality improvement of the existing optical devices, as well as a wide range of new applications in photonics and display areas.

Mean first-passage time of an asymmetric bistable system driven by colour-correlated noise

Institute of Scientific and Technical Information of China (English)

Zhang Xiao-Yan; Xu Wei

2007-01-01

In this paper, the effect of every parameter (including p, q,r, λ,τ) on the mean first-passage time (MFPT) is investigated in an asymmetric bistable system driven by colour-correlated noise. The expression of MFPT has been obtained by applying the steepest-descent approximation. Numerical results show that (1) the intensity of multiplicative noise p and the intensity of additive noise q play different roles in the MFPT of the system, (2) suppression appears on the curve of the MFPT with small λ (e.g. λ＜ 0.5) but there is a peak on the curve of the MFPT when λ is big (e.g.λ＞ 0.5), and (3) with different values of r (e.g. r = 0.1, 0.5, 1.5), the effort of τ on the MFPT is diverse.

Mittag-Leffler synchronization of fractional neural networks with time-varying delays and reaction-diffusion terms using impulsive and linear controllers.

Science.gov (United States)

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.

Exact solutions of linear reaction-diffusion processes on a uniformly growing domain: criteria for successful colonization.

Science.gov (United States)

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).

Non-symmetric bi-stable flow around the Ahmed body

International Nuclear Information System (INIS)

Meile, W.; Ladinek, T.; Brenn, G.; Reppenhagen, A.; Fuchs, A.

2016-01-01

Highlights: • The non-symmetric bi-stable flow around the Ahmed body is investigated experimentally. • Bi-stability, described for symmetric flow by Cadot and co-workers, was found in nonsymmetric flow also. • The flow field randomly switches between two states. • The flow is subject to a spanwise instability identified by Cadot and co-workers for symmetric flow. • Aerodynamic forces fluctuate strongly due to the bi-stability. - Abstract: The flow around the Ahmed body at varying Reynolds numbers under yawing conditions is investigated experimentally. The body geometry belongs to a regime subject to spanwise flow instability identified in symmetric flow by Cadot and co-workers (Grandemange et al., 2013b). Our experiments cover the two slant angles 25° and 35° and Reynolds numbers up to 2.784 × 10"6. Special emphasis lies on the aerodynamics under side wind influence. For the 35° slant angle, forces and moments change significantly with the yawing angle in the range 10° ≤ |β| ≤ 15°. The lift and the pitching moment exhibit strong fluctuations due to bi-stable flow around a critical angle β of ±12.5°, where the pitching moment changes sign. Time series of the forces and moments are studied and explained by PIV measurements in the flow field near the rear of the body.

An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations

KAUST Repository

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.