Study on monostable and bistable reaction-diffusion equations by iteration of travelling wave maps
Yi, Taishan; Chen, Yuming
2017-12-01
In this paper, based on the iterative properties of travelling wave maps, we develop a new method to obtain spreading speeds and asymptotic propagation for monostable and bistable reaction-diffusion equations. Precisely, for Dirichlet problems of monostable reaction-diffusion equations on the half line, by making links between travelling wave maps and integral operators associated with the Dirichlet diffusion kernel (the latter is NOT invariant under translation), we obtain some iteration properties of the Dirichlet diffusion and some a priori estimates on nontrivial solutions of Dirichlet problems under travelling wave transformation. We then provide the asymptotic behavior of nontrivial solutions in the space-time region for Dirichlet problems. These enable us to develop a unified method to obtain results on heterogeneous steady states, travelling waves, spreading speeds, and asymptotic spreading behavior for Dirichlet problem of monostable reaction-diffusion equations on R+ as well as of monostable/bistable reaction-diffusion equations on R.
Maximum Principles for Discrete and Semidiscrete Reaction-Diffusion Equation
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Petr Stehlík
2015-01-01
Full Text Available We study reaction-diffusion equations with a general reaction function f on one-dimensional lattices with continuous or discrete time ux′ (or Δtux=k(ux-1-2ux+ux+1+f(ux, x∈Z. We prove weak and strong maximum and minimum principles for corresponding initial-boundary value problems. Whereas the maximum principles in the semidiscrete case (continuous time exhibit similar features to those of fully continuous reaction-diffusion model, in the discrete case the weak maximum principle holds for a smaller class of functions and the strong maximum principle is valid in a weaker sense. We describe in detail how the validity of maximum principles depends on the nonlinearity and the time step. We illustrate our results on the Nagumo equation with the bistable nonlinearity.
Reaction diffusion equations with boundary degeneracy
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Huashui Zhan
2016-03-01
Full Text Available In this article, we consider the reaction diffusion equation $$ \\frac{\\partial u}{\\partial t} = \\Delta A(u,\\quad (x,t\\in \\Omega \\times (0,T, $$ with the homogeneous boundary condition. Inspired by the Fichera-Oleinik theory, if the equation is not only strongly degenerate in the interior of $\\Omega$, but also degenerate on the boundary, we show that the solution of the equation is free from any limitation of the boundary condition.
Dynamics of interface in three-dimensional anisotropic bistable reaction-diffusion system
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He Zhizhu; Liu, Jing
2010-01-01
This paper presents a theoretical investigation of dynamics of interface (wave front) in three-dimensional (3D) reaction-diffusion (RD) system for bistable media with anisotropy constructed by means of anisotropic surface tension. An equation of motion for the wave front is derived to carry out stability analysis of transverse perturbations, which discloses mechanism of pattern formation such as labyrinthine in 3D bistable media. Particularly, the effects of anisotropy on wave propagation are studied. It was found that, sufficiently strong anisotropy can induce dynamical instabilities and lead to breakup of the wave front. With the fast-inhibitor limit, the bistable system can further be described by a variational dynamics so that the boundary integral method is adopted to study the dynamics of wave fronts.
Reaction diffusion equations and quadratic convergence
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A. S. Vatsala
1997-01-01
Full Text Available In this paper, the method of generalized quasilinearization has been extended to reaction diffusion equations. The extension includes earlier known results as special cases. The earlier results developed are when (i the right-hand side function is the sum of a convex and concave function, and (ii the right-hand function can be made convex by adding a convex function. In our present result, if the monotone iterates are mildly nonlinear, we establish the quadratic convergence as in the quasilinearization method. If the iterates are totally linear then the iterates converge semi-quadratically.
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Wu Shiliang; Li Wantong
2009-01-01
This paper deals with the global asymptotic stability and uniqueness (up to translation) of bistable traveling fronts in a class of reaction-diffusion systems. The known results do not apply in solving these problems because the reaction terms do not satisfy the required monotone condition. To overcome the difficulty, a weak monotone condition is proposed for the reaction terms, which is called interval monotone condition. Under such a weak monotone condition, the existence and comparison theorem of solutions is first established for reaction-diffusion systems on R by appealing to the theory of abstract differential equations. The global asymptotic stability and uniqueness (up to translation) of bistable traveling fronts are then proved by the elementary super- and sub-solution comparison and squeezing methods for nonlinear evolution equations. Finally, these abstract results are applied to a two species competition-diffusion model and a system modeling man-environment-man epidemics.
Traveling Wave Solutions of Reaction-Diffusion Equations Arising in Atherosclerosis Models
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Narcisa Apreutesei
2014-05-01
Full Text Available In this short review article, two atherosclerosis models are presented, one as a scalar equation and the other one as a system of two equations. They are given in terms of reaction-diffusion equations in an infinite strip with nonlinear boundary conditions. The existence of traveling wave solutions is studied for these models. The monostable and bistable cases are introduced and analyzed.
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.
Speed ot travelling waves in reaction-diffusion equations
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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)
Nonlinear analysis of a reaction-diffusion system: Amplitude equations
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Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)
2012-10-15
A reaction-diffusion system with a nonlinear diffusion term is considered. Based on nonlinear analysis, the amplitude equations are obtained in the cases of the Hopf and Turing instabilities in the system. Turing pattern-forming regions in the parameter space are determined for supercritical and subcritical instabilities in a two-component reaction-diffusion system.
Study of ODE limit problems for reaction-diffusion equations
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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.
Circumnutation modeled by reaction-diffusion equations
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Lubkin, S.R.
1992-01-01
In studies of biological oscillators, plants are only rarely examined. The authors study a common sub-diurnal oscillation of plants, called circumnutation. Based on experimental evidence that the oscillations consist of a turgor wave traveling around a growing plant part, circumnutation is modeled by a nonlinear reaction-diffusion system with cylindrical geometry. Because of its simplicity, and because biological oscillations are so common, an oscillatory [lambda]-[omega] reaction-diffusion system is chosen for the model. The authors study behavior of traveling waves in [lambda]-[omega] systems. The authors show the existence of Hopf bifurcations and the stability of the limit cycles born at the Hopf bifurcation for some parameter values. Using a Lindstedt-type perturbation scheme, the authors construct periodic solutions of the [lambda]-[omega] system near a Hopf bifurcation and show that the periodic solutions superimposed on the original traveling wave have the effect of altering its overall frequency and amplitude. Circumnutating plants generally display a strong directional preference to their oscillations, which is species-dependent. Circumnutation is modeled by a [lambda]-[omega] system on an annulus of variable width, which does not possess reflection symmetry about any axis. The annulus represents a region of high potassium concentration in the cross-section of the stem. The asymmetry of the annulus represents the anatomical asymmetry of the plant. Traveling waves are constructed on this variable-width annulus by a perturbation scheme, and perturbing the width of the annulus alters the amplitude and frequency of traveling waves on the domain by a small (order [epsilon][sup 2]) amount. The speed, frequency, and stability are unaffected by the direction of travel of the wave on the annulus. This indicates that the [lambda]-[omega] system on a variable-width domain cannot account for directional preferences of traveling waves in biological systems.
Propagation Phenomena in a Bistable Reaction Diffusion System.
1981-05-01
Differential Equations 23 (1977), 335-367. 3. Casten, R. H., H. Cohen, and P. Lagerstrom, Perturbation analysis of an approximation to Hodgkin - Huxley theory...in several applications, e.g. see [18]. Here, we extend consideration to parameter ranges, e.g. y large enough, for which the v - w dynamics are...ones. A global picture (Figure 6) is provided for e, y -parameter regimes in which the various waves exist. Finally, in Section 4, we present numerical
Explosive instabilities of reaction-diffusion equations
Wilhelmsson, H.
1987-07-01
Explicit solutions are obtained for evolution equations for explosively unstable situations. These solutions include the effects of diffusion with linear or quadratic density dependence of the diffusion coefficient. As a result of balance between the diffusion and nonlinear terms, explosive growth in time can occur with a preservation in shape of certain spatial distributions. The solutions are generalized to cases of two interacting populations.
Diffusive instabilities in hyperbolic reaction-diffusion equations
Zemskov, Evgeny P.; Horsthemke, Werner
2016-03-01
We investigate two-variable reaction-diffusion systems of the hyperbolic type. A linear stability analysis is performed, and the conditions for diffusion-driven instabilities are derived. Two basic types of eigenvalues, real and complex, are described. Dispersion curves for both types of eigenvalues are plotted and their behavior is analyzed. The real case is related to the Turing instability, and the complex one corresponds to the wave instability. We emphasize the interesting feature that the wave instability in the hyperbolic equations occurs in two-variable systems, whereas in the parabolic case one needs three reaction-diffusion equations.
Oscillatory pulses and wave trains in a bistable reaction-diffusion system with cross diffusion.
Zemskov, Evgeny P; Tsyganov, Mikhail A; Horsthemke, Werner
2017-01-01
We study waves with exponentially decaying oscillatory tails in a reaction-diffusion system with linear cross diffusion. To be specific, we consider a piecewise linear approximation of the FitzHugh-Nagumo model, also known as the Bonhoeffer-van der Pol model. We focus on two types of traveling waves, namely solitary pulses that correspond to a homoclinic solution, and sequences of pulses or wave trains, i.e., a periodic solution. The effect of cross diffusion on wave profiles and speed of propagation is analyzed. We find the intriguing result that both pulses and wave trains occur in the bistable cross-diffusive FitzHugh-Nagumo system, whereas only fronts exist in the standard bistable system without cross diffusion.
Numerical solution of a reaction-diffusion equation
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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)
Traveling and Pinned Fronts in Bistable Reaction-Diffusion Systems on Networks
Kouvaris, Nikos E.; Kori, Hiroshi; Mikhailov, Alexander S.
2012-01-01
Traveling fronts and stationary localized patterns in bistable reaction-diffusion systems have been broadly studied for classical continuous media and regular lattices. Analogs of such non-equilibrium patterns are also possible in networks. Here, we consider traveling and stationary patterns in bistable one-component systems on random Erdös-Rényi, scale-free and hierarchical tree networks. As revealed through numerical simulations, traveling fronts exist in network-organized systems. They represent waves of transition from one stable state into another, spreading over the entire network. The fronts can furthermore be pinned, thus forming stationary structures. While pinning of fronts has previously been considered for chains of diffusively coupled bistable elements, the network architecture brings about significant differences. An important role is played by the degree (the number of connections) of a node. For regular trees with a fixed branching factor, the pinning conditions are analytically determined. For large Erdös-Rényi and scale-free networks, the mean-field theory for stationary patterns is constructed. PMID:23028746
Reaction rates for a generalized reaction-diffusion master equation.
Hellander, Stefan; Petzold, Linda
2016-01-01
It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach, in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is of the order of the reaction radius of a reacting pair of molecules.
Periodic solutions to systems of reaction-diffusion equations
Rosen, G.
1976-01-01
Necessary and sufficient conditions are derived for the existence of temporally periodic 'dissipative structure' solutions in weak diffusion with the reaction rate terms dominant in a generic system of reaction-diffusion differential equations. The enumerator index i of the equations denotes the density or concentration of the ith participating molecular or biological species, and D sub i is the diffusivity constant for the ith species while Q sub i (c), an algebraic function of the n-tuple c, expresses the local rate of production of the ith species due to chemical reactions or biological interactions.
Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations
Indekeu, Joseph O.; Smets, Ruben
2017-08-01
Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.
Setting initial conditions for inflation with reaction-diffusion equation
Bagchi, Partha; Das, Arpan; Dave, Shreyansh S.; Sengupta, Srikumar; Srivastava, Ajit M.
2018-03-01
We discuss the issue of setting appropriate initial conditions for inflation. Specifically, we consider natural inflation model and discuss the fine tuning required for setting almost homogeneous initial conditions over a region of order several times the Hubble size which is orders of magnitude larger than any relevant correlation length for field fluctuations. We then propose to use the special propagating front solutions of reaction-diffusion equations for localized field domains of smaller sizes. Due to very small velocities of these propagating fronts we find that the inflaton field in such a field domain changes very slowly, contrary to naive expectation of rapid roll down to the true vacuum. Continued expansion leads to the energy density in the Hubble region being dominated by the vacuum energy, thereby beginning the inflationary phase. Our results show that inflation can occur even with a single localized field domain of size smaller than the Hubble size. We discuss possible extensions of our results for different inflationary models, as well as various limitations of our analysis (e.g. neglecting self gravity of the localized field domain).
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.
On positive solutions of reaction-diffusion equation with Caratheodory nonlinear term
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O. V. Kapustyan
2009-09-01
Full Text Available In the paper for reaction-diffusion equation with Caratheodory nonlinear term under conditions, which do not guarantee uniqueness of Cauchy problem solution, we prove the global resolvability in the class of nonnegative integrable functions.
Entire solutions for bistable lattice differential equations with obstacles
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.
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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.
Mixed, Nonsplit, Extended Stability, Stiff Integration of Reaction Diffusion Equations
Alzahrani, Hasnaa H.
2016-07-26
A tailored integration scheme is developed to treat stiff reaction-diffusion prob- lems. The construction adapts a stiff solver, namely VODE, to treat reaction im- plicitly together with explicit treatment of diffusion. The second-order Runge-Kutta- Chebyshev (RKC) scheme is adjusted to integrate diffusion. Spatial operator is de- scretised by second-order finite differences on a uniform grid. The overall solution is advanced over S fractional stiff integrations, where S corresponds to the number of RKC stages. The behavior of the scheme is analyzed by applying it to three simple problems. The results show that it achieves second-order accuracy, thus, preserving the formal accuracy of the original RKC. The presented development sets the stage for future extensions, particularly, to multidimensional reacting flows with detailed chemistry.
Polyanin, A. D.; Sorokin, V. G.
2017-12-01
The paper deals with nonlinear reaction-diffusion equations with one or several delays. We formulate theorems that allow constructing exact solutions for some classes of these equations, which depend on several arbitrary functions. Examples of application of these theorems for obtaining new exact solutions in elementary functions are provided. We state basic principles of construction, selection, and use of test problems for nonlinear partial differential equations with delay. Some test problems which can be suitable for estimating accuracy of approximate analytical and numerical methods of solving reaction-diffusion equations with delay are presented. Some examples of numerical solutions of nonlinear test problems with delay are considered.
Spherically Symmetric Waves of a Reaction-Diffusion Equation.
1980-02-01
travelling pulses of the Fitzhugh- Nagumo and Hodgkin - Huxley equations, travelling fronts in some scalar equations such as the Fisher equation and...appropriate function space. A semiflow on a space Y is a func- + + tion S : Y x R - Y (whose domain may not be all of Y x IR , but must be an open subset...which satisfies (1) S(S( y ,t),s) = S( y ,t+s) and (2) S is continuous on its domain. S is said to be a local semiflow if for each y E Y , a set of the form ( y
Time-independent reaction-diffusion equation with a discontinuous reactive term
Levashova, N. T.; Nefedov, N. N.; Orlov, A. O.
2017-05-01
A two-dimensional singularly perturbed elliptic equation referred to in applications as the reaction-diffusion equation is considered. The nonlinearity describing the reaction is assumed to be discontinuous on a certain closed curve. On the basis of the generalized asymptotic comparison principle, the existence of smooth solution is proven and the accuracy of the asymptotic approximation is estimated.
Bifurcation Analysis of Gene Propagation Model Governed by Reaction-Diffusion Equations
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Guichen Lu
2016-01-01
Full Text Available We present a theoretical analysis of the attractor bifurcation for gene propagation model governed by reaction-diffusion equations. We investigate the dynamical transition problems of the model under the homogeneous boundary conditions. By using the dynamical transition theory, we give a complete characterization of the bifurcated objects in terms of the biological parameters of the problem.
Random Attractors for Stochastic Retarded Reaction-Diffusion Equations on Unbounded Domains
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Xiaoquan Ding
2013-01-01
Full Text Available This paper is devoted to a stochastic retarded reaction-diffusion equation on all d-dimensional space with additive white noise. We first show that the stochastic retarded reaction-diffusion equation generates a random dynamical system by transforming this stochastic equation into a random one through a tempered stationary random homeomorphism. Then, we establish the existence of a random attractor for the random equation. And the existence of a random attractor for the stochastic equation follows from the conjugation relation between two random dynamical systems. The pullback asymptotic compactness is proved by uniform estimates on solutions for large space and time variables. These estimates are obtained by a cut-off technique.
Heat kernel regularization of the effective action for stochastic reaction-diffusion equations.
Hochberg, D; Molina-París, C; Visser, M
2001-03-01
The presence of fluctuations and nonlinear interactions can lead to scale dependence in the parameters appearing in stochastic differential equations. Stochastic dynamics can be formulated in terms of functional integrals. In this paper we apply the heat kernel method to study the short distance renormalizability of a stochastic (polynomial) reaction-diffusion equation with real additive noise. We calculate the one-loop effective action and its ultraviolet scale dependent divergences. We show that for white noise a polynomial reaction-diffusion equation is one-loop finite in d=0 and d=1, and is one-loop renormalizable in d=2 and d=3 space dimensions. We obtain the one-loop renormalization group equations and find they run with scale only in d=2.
An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations
Burrage, Kevin
2012-01-01
Fractional differential equations are becoming increasingly used as a modelling tool for processes associated with anomalous diffusion or spatial heterogeneity. However, the presence of a fractional differential operator causes memory (time fractional) or nonlocality (space fractional) issues that impose a number of computational constraints. In this paper we develop efficient, scalable techniques for solving fractional-in-space reaction diffusion equations using the finite element method on both structured and unstructured grids via robust techniques for computing the fractional power of a matrix times a vector. Our approach is show-cased by solving the fractional Fisher and fractional Allen-Cahn reaction-diffusion equations in two and three spatial dimensions, and analyzing the speed of the traveling wave and size of the interface in terms of the fractional power of the underlying Laplacian operator. © 2012 Society for Industrial and Applied Mathematics.
Non-Fickian delay reaction-diffusion equations: theoretical and numerical study
Ferreira, J. A.; Branco, J. R.; Silva, P. da
2007-01-01
The Fisher’s equation is established combining the Fick’s law for the flux and the mass conservation law. Assuming that the reaction term depends on the solution at some past time, a delay parameter is introduced and the delay Fisher’s equation is obtained. Modifying the Fick’s law for the flux considering a temporal memory term, integro-differential equations of Volterra type were introduced in the literature. In these paper we study reaction-diffusion equations obtained co...
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.
Evans functions and bifurcations of nonlinear waves of some nonlinear reaction diffusion equations
Zhang, Linghai
2017-10-01
The main purposes of this paper are to accomplish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear system of reaction diffusion equations ut =uxx + α [ βH (u - θ) - u ] - w, wt = ε (u - γw) and to establish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ], under different conditions on the model constants. To establish the bifurcation for the system, we will study the existence and instability of a standing pulse solution if 0 1; the existence and instability of two standing wave fronts if 2 (1 + αγ) θ = αβγ and 0 0 is a positive constant, if 0 mathematical neuroscience.
Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds
Desvillettes, Laurent
2008-01-01
In the continuation of [Desvillettes, L., Fellner, K.: Exponential Decay toward Equilibrium via Entropy Methods for Reaction-Diffusion Equations. J. Math. Anal. Appl. 319 (2006), no. 1, 157-176], we study reversible reaction-diffusion equations via entropy methods (based on the free energy functional) for a 1D system of four species. We improve the existing theory by getting 1) almost exponential convergence in L1 to the steady state via a precise entropy-entropy dissipation estimate, 2) an explicit global L∞ bound via interpolation of a polynomially growing H1 bound with the almost exponential L1 convergence, and 3), finally, explicit exponential convergence to the steady state in all Sobolev norms.
An analytic algorithm for the space-time fractional reaction-diffusion equation
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M. G. Brikaa
2015-11-01
Full Text Available In this paper, we solve the space-time fractional reaction-diffusion equation by the fractional homotopy analysis method. Solutions of different examples of the reaction term will be computed and investigated. The approximation solutions of the studied models will be put in the form of convergent series to be easily computed and simulated. Comparison with the approximation solution of the classical case of the studied modeled with their approximation errors will also be studied.
On the uniform boundedness of the solutions of systems of reaction-diffusion equations
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L. Melkemi
2005-12-01
Full Text Available We consider a system of reaction-diffusion equations for which the uniform boundedness of the solutions can not be derived by existing methods. The system may represent, in particular, an epidemic model describing the spread of an infection disease within a population. We present an $L^{p}$ argument allowing to establish the global existence and the uniform boundedness of the solutions of the considered system.
Simpson, Matthew J; Sharp, Jesse A; Morrow, Liam C; Baker, Ruth E
2015-01-01
Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction-diffusion equations on growing domains that have been primarily studied using approximate numerical solutions. Recently, we have shown how to obtain an exact solution to a single, uncoupled, linear reaction-diffusion equation on a growing domain, 0 reaction-diffusion equations on a growing domain. This system of equations can be used to study the spatial and temporal distributions of different generations of cells within a population that diffuses and proliferates within a growing tissue. The exact solution is obtained by applying an uncoupling transformation, and the uncoupled equations are solved separately before applying the inverse uncoupling transformation to give the coupled solution. We present several example calculations to illustrate different types of behaviour. The first example calculation corresponds to a situation where the initially-confined population diffuses sufficiently slowly that it is unable to reach the moving boundary at x = L(t). In contrast, the second example calculation corresponds to a situation where the initially-confined population is able to overcome the domain growth and reach the moving boundary at x = L(t). In its basic format, the uncoupling transformation at first appears to be restricted to deal only with the case where each generation of cells has a distinct proliferation rate. However, we also demonstrate how the uncoupling transformation can be used when each generation has the same proliferation rate by evaluating the exact solutions as an appropriate limit.
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
Global dynamics of a nonlocal delayed reaction-diffusion equation on a half plane
Hu, Wenjie; Duan, Yueliang
2018-04-01
We consider a delayed reaction-diffusion equation with spatial nonlocality on a half plane that describes population dynamics of a two-stage species living in a semi-infinite environment. A Neumann boundary condition is imposed accounting for an isolated domain. To describe the global dynamics, we first establish some a priori estimate for nontrivial solutions after investigating asymptotic properties of the nonlocal delayed effect and the diffusion operator, which enables us to show the permanence of the equation with respect to the compact open topology. We then employ standard dynamical system arguments to establish the global attractivity of the nontrivial equilibrium. The main results are illustrated by the diffusive Nicholson's blowfly equation and the diffusive Mackey-Glass equation.
Breakdown of the reaction-diffusion master equation with nonelementary rates.
Smith, Stephen; Grima, Ramon
2016-05-01
The chemical master equation (CME) is the exact mathematical formulation of chemical reactions occurring in a dilute and well-mixed volume. The reaction-diffusion master equation (RDME) is a stochastic description of reaction-diffusion processes on a spatial lattice, assuming well mixing only on the length scale of the lattice. It is clear that, for the sake of consistency, the solution of the RDME of a chemical system should converge to the solution of the CME of the same system in the limit of fast diffusion: Indeed, this has been tacitly assumed in most literature concerning the RDME. We show that, in the limit of fast diffusion, the RDME indeed converges to a master equation but not necessarily the CME. We introduce a class of propensity functions, such that if the RDME has propensities exclusively of this class, then the RDME converges to the CME of the same system, whereas if the RDME has propensities not in this class, then convergence is not guaranteed. These are revealed to be elementary and nonelementary propensities, respectively. We also show that independent of the type of propensity, the RDME converges to the CME in the simultaneous limit of fast diffusion and large volumes. We illustrate our results with some simple example systems and argue that the RDME cannot generally be an accurate description of systems with nonelementary rates.
Zhou, Shengfan
2017-11-01
In this paper, we first improve the existing conditions for the existence of a random exponential attractor for a continuous cocycle on a separable Banach space. Then we consider the existence of a random exponential attractor for stochastic non-autonomous reaction-diffusion equation with multiplicative noise defined in R3, which implies the existence of a random attractor with finite fractal dimension. The essential difficulty here is the continuity of the spectrum of the linear part of the equation, which can be overcome by the "tail" estimation of solutions of equation and carefully decomposing the solution into a sum of three parts, of whose, one part is finite-dimensional and other two parts are "quickly decay" in mean sense.
Poznanski, R R
2010-09-01
A reaction-diffusion model is presented to encapsulate calcium-induced calcium release (CICR) as a potential mechanism for somatofugal bias of dendritic calcium movement in starburst amacrine cells. Calcium dynamics involves a simple calcium extrusion (pump) and a buffering mechanism of calcium binding proteins homogeneously distributed over the plasma membrane of the endoplasmic reticulum within starburst amacrine cells. The system of reaction-diffusion equations in the excess buffer (or low calcium concentration) approximation are reformulated as a nonlinear Volterra integral equation which is solved analytically via a regular perturbation series expansion in response to calcium feedback from a continuously and uniformly distributed calcium sources. Calculation of luminal calcium diffusion in the absence of buffering enables a wave to travel at distances of 120 μm from the soma to distal tips of a starburst amacrine cell dendrite in 100 msec, yet in the presence of discretely distributed calcium-binding proteins it is unknown whether the propagating calcium wave-front in the somatofugal direction is further impeded by endogenous buffers. If so, this would indicate CICR to be an unlikely mechanism of retinal direction selectivity in starburst amacrine cells.
Scalable implicit methods for reaction-diffusion equations in two and three space dimensions
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Veronese, S.V.; Othmer, H.G. [Univ. of Utah, Salt Lake City, UT (United States)
1996-12-31
This paper describes the implementation of a solver for systems of semi-linear parabolic partial differential equations in two and three space dimensions. The solver is based on a parallel implementation of a non-linear Alternating Direction Implicit (ADI) scheme which uses a Cartesian grid in space and an implicit time-stepping algorithm. Various reordering strategies for the linearized equations are used to reduce the stride and improve the overall effectiveness of the parallel implementation. We have successfully used this solver for large-scale reaction-diffusion problems in computational biology and medicine in which the desired solution is a traveling wave that may contain rapid transitions. A number of examples that illustrate the efficiency and accuracy of the method are given here; the theoretical analysis will be presented.
Automatic simplification of systems of reaction-diffusion equations by a posteriori analysis.
Maybank, Philip J; Whiteley, Jonathan P
2014-02-01
Many mathematical models in biology and physiology are represented by systems of nonlinear differential equations. In recent years these models have become increasingly complex in order to explain the enormous volume of data now available. A key role of modellers is to determine which components of the model have the greatest effect on a given observed behaviour. An approach for automatically fulfilling this role, based on a posteriori analysis, has recently been developed for nonlinear initial value ordinary differential equations [J.P. Whiteley, Model reduction using a posteriori analysis, Math. Biosci. 225 (2010) 44-52]. In this paper we extend this model reduction technique for application to both steady-state and time-dependent nonlinear reaction-diffusion systems. Exemplar problems drawn from biology are used to demonstrate the applicability of the technique. Copyright © 2014 Elsevier Inc. All rights reserved.
Numerical methods for one-dimensional reaction-diffusion equations arising in combustion theory
Ramos, J. I.
1987-01-01
A review of numerical methods for one-dimensional reaction-diffusion equations arising in combustion theory is presented. The methods reviewed include explicit, implicit, quasi-linearization, time linearization, operator-splitting, random walk and finite-element techniques and methods of lines. Adaptive and nonadaptive procedures are also reviewed. These techniques are applied first to solve two model problems which have exact traveling wave solutions with which the numerical results can be compared. This comparison is performed in terms of both the wave profile and computed wave speed. It is shown that the computed wave speed is not a good indicator of the accuracy of a particular method. A fourth-order time-linearized, Hermitian compact operator technique is found to be the most accurate method for a variety of time and space sizes.
Saxena, R. K.; Mathai, A. M.; Haubold, H. J.
2015-10-01
This paper deals with the investigation of the computational solutions of an unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the generalized fractional time-derivative defined by Hilfer (2000), the space derivative of second order by the Riesz-Feller fractional derivative and adding the function ϕ (x, t) which is a nonlinear function governing reaction. The solution is derived by the application of the Laplace and Fourier transforms in a compact and closed form in terms of the H-function. The main result obtained in this paper provides an elegant extension of the fundamental solution for the space-time fractional diffusion equation obtained earlier by Mainardi et al. (2001, 2005) and a result very recently given by Tomovski et al. (2011). Computational representation of the fundamental solution is also obtained explicitly. Fractional order moments of the distribution are deduced. At the end, mild extensions of the derived results associated with a finite number of Riesz-Feller space fractional derivatives are also discussed.
Harko, Tiberiu; Mak, Man Kwong
2015-02-01
We consider quasi-stationary (travelling wave type) solutions to a nonlinear reaction-diffusion equation with arbitrary, autonomous coefficients, describing the evolution of glioblastomas, aggressive primary brain tumors that are characterized by extensive infiltration into the brain and are highly resistant to treatment. The second order nonlinear equation describing the glioblastoma growth through travelling waves can be reduced to a first order Abel type equation. By using the integrability conditions for the Abel equation several classes of exact travelling wave solutions of the general reaction-diffusion equation that describes glioblastoma growth are obtained, corresponding to different forms of the product of the diffusion and reaction functions. The solutions are obtained by using the Chiellini lemma and the Lemke transformation, respectively, and the corresponding equations represent generalizations of the classical Fisher-Kolmogorov equation. The biological implications of two classes of solutions are also investigated by using both numerical and semi-analytical methods for realistic values of the biological parameters.
Fourier spectral methods for fractional-in-space reaction-diffusion equations
Bueno-Orovio, Alfonso
2014-04-01
© 2014, Springer Science+Business Media Dordrecht. Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains of ℝ. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.
Cooper, Crystal Diane
A computer program was modified to model the dynamics of morphogen concentrations in a developing eye of a Xenopus laevis frog. The dynamics were modelled because it is believed that the behavior of the morphogen concentrations determine how the developing eye maps to the brain. The eye in the xenophus grows as a series of rings, and thus this is the model used. The basis for the simulation are experiments done by Sullivan et al. Following the experiment, aIl eye ring is 'split' in half, inverted, and then 'pasted' onto a donor half. The purpose of the program is to replicate and analyze the results that were found experimentally: a graft made on a north to south axis (dorsal to ventral) produces a change in vision along the east to west axis (anterior to posterior). Four modified Gierer-Meinhardt reaction- diffusion equations are used to simulate the operation. In the second part of the research, the program was further modified and a time series analysis was done on the results. It was found that the modified Gierer- Meinhardt equations demonstrated chaotic behavior under certain conditions. The dynamics included fixed points, limit cycles, transient chaos, intermittent chaos, and strange attractors. The creation and destruction of fractal torii was found.
Richter, Otto; Moenickes, Sylvia; Suhling, Frank
2012-02-01
The spatial dynamics of range expansion is studied in dependence of temperature. The main elements population dynamics, competition and dispersal are combined in a coherent approach based on a system of coupled partial differential equations of the reaction-diffusion type. The nonlinear reaction terms comprise population dynamic models with temperature dependent reproduction rates subject to an Allee effect and mutual competition. The effect of temperature on travelling wave solutions is investigated for a one dimensional model version. One main result is the importance of the Allee effect for the crossing of regions with unsuitable habitats. The nonlinearities of the interaction terms give rise to a richness of spatio-temporal dynamic patterns. In two dimensions, the resulting non-linear initial boundary value problems are solved over geometries of heterogeneous landscapes. Geo referenced model parameters such as mean temperature and elevation are imported into the finite element tool COMSOL Multiphysics from a geographical information system. The model is applied to the range expansion of species at the scale of middle Europe. Copyright © 2011 Elsevier Inc. All rights reserved.
Global existence of solutions for some coupled systems of reaction-diffusion equations
Salem, Abdelmalek; Amar, Youkana
2010-01-01
The aim of this work is to study the global existence of solutions for some coupled systems of reaction diffusion which describe the spread within a population of infectious disease. We consider a triangular matrix diffusion and we show that we can prove global existence of classical solutions for the nonlinearities of weakly exponential growth.
Patterns in a nonlocal time-delayed reaction-diffusion equation
Guo, Shangjiang
2018-02-01
In this paper, the existence, stability, and multiplicity of nontrivial (spatially homogeneous or nonhomogeneous) steady-state solution and periodic solutions for a reaction-diffusion model with nonlocal delay effect and Dirichlet/Neumann boundary condition are investigated by using Lyapunov-Schmidt reduction. Moreover, we illustrate our general results by applications to population models with one-dimensional spatial domain.
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Moyano, Edgardo A.; Scarpettini, Alberto F.
2003-01-01
A semi linear model of weakly coupled parabolic p.d.e. with reaction-diffusion is investigated. The system describes fission gas transfer from grain interior of UO 2 to grain boundaries. The problem is studied in a bounded domain. Using the upper-lower solutions method, two monotone sequences for the finite differences equations are constructed. Reasons are mentioned that allow to affirm that in the proposed functional sector the algorithm converges to the unique solution of the differential system. (author)
Directory of Open Access Journals (Sweden)
M.H. Tiwana
2017-04-01
Full Text Available This work investigates the fractional non linear reaction diffusion (FNRD system of Lotka-Volterra type. The system of equations together with the boundary conditions are solved by Homotopy perturbation transform method (HPTM. The series solutions are obtained for the two cases (homogeneous and non-homogeneous of FNRD system. The effect of fractional parameter on the mass concentration of two species are shown and discussed with the help of 3D graphs.
Nefedov, N. N.; Nikulin, E. I.
2018-01-01
A singularly perturbed periodic in time problem for a parabolic reaction-diffusion equation in a two-dimensional domain is studied. The case of existence of an internal transition layer under the conditions of balanced and unbalanced rapid reaction is considered. An asymptotic expansion of a solution is constructed. To justify the asymptotic expansion thus constructed, the asymptotic method of differential inequalities is used. The Lyapunov asymptotic stability of a periodic solution is investigated.
Liu, Bingchen; Dong, Mengzhen; Li, Fengjie
2018-04-01
This paper deals with a reaction-diffusion problem with coupled nonlinear inner sources and nonlocal boundary flux. Firstly, we propose the critical exponents on nonsimultaneous blow-up under some conditions on the initial data. Secondly, we combine the scaling technique and the Green's identity method to determine four kinds of simultaneous blow-up rates. Thirdly, the lower and the upper bounds of blow-up time are derived by using Sobolev-type differential inequalities.
On one model problem for the reaction-diffusion-advection equation
Davydova, M. A.; Zakharova, S. A.; Levashova, N. T.
2017-09-01
The asymptotic behavior of the solution with boundary layers in the time-independent mathematical model of reaction-diffusion-advection arising when describing the distribution of greenhouse gases in the surface atmospheric layer is studied. On the basis of the asymptotic method of differential inequalities, the existence of a boundary-layer solution and its asymptotic Lyapunov stability as a steady-state solution of the corresponding parabolic problem is proven. One of the results of this work is the determination of the local domain of the attraction of a boundary-layer solution.
Monostable traveling waves for a time-periodic and delayed nonlocal reaction-diffusion equation
Li, Panxiao; Wu, Shi-Liang
2018-04-01
This paper is concerned with a time-periodic and delayed nonlocal reaction-diffusion population model with monostable nonlinearity. Under quasi-monotone or non-quasi-monotone assumptions, it is known that there exists a critical wave speed c_*>0 such that a periodic traveling wave exists if and only if the wave speed is above c_*. In this paper, we first prove the uniqueness of non-critical periodic traveling waves regardless of whether the model is quasi-monotone or not. Further, in the quasi-monotone case, we establish the exponential stability of non-critical periodic traveling fronts. Finally, we illustrate the main results by discussing two types of death and birth functions arising from population biology.
Shankar, Varun; Wright, Grady B; Kirby, Robert M; Fogelson, Aaron L
2016-06-01
In this paper, we present a method based on Radial Basis Function (RBF)-generated Finite Differences (FD) for numerically solving diffusion and reaction-diffusion equations (PDEs) on closed surfaces embedded in ℝ d . Our method uses a method-of-lines formulation, in which surface derivatives that appear in the PDEs are approximated locally using RBF interpolation. The method requires only scattered nodes representing the surface and normal vectors at those scattered nodes. All computations use only extrinsic coordinates, thereby avoiding coordinate distortions and singularities. We also present an optimization procedure that allows for the stabilization of the discrete differential operators generated by our RBF-FD method by selecting shape parameters for each stencil that correspond to a global target condition number. We show the convergence of our method on two surfaces for different stencil sizes, and present applications to nonlinear PDEs simulated both on implicit/parametric surfaces and more general surfaces represented by point clouds.
Adam, A. M. A.; Bashier, E. B. M.; Hashim, M. H. A.; Patidar, K. C.
2017-07-01
In this work, we design and analyze a fitted numerical method to solve a reaction-diffusion model with time delay, namely, a delayed version of a population model which is an extension of the logistic growth (LG) equation for a food-limited population proposed by Smith [F.E. Smith, Population dynamics in Daphnia magna and a new model for population growth, Ecology 44 (1963) 651-663]. Seeing that the analytical solution (in closed form) is hard to obtain, we seek for a robust numerical method. The method consists of a Fourier-pseudospectral semi-discretization in space and a fitted operator implicit-explicit scheme in temporal direction. The proposed method is analyzed for convergence and we found that it is unconditionally stable. Illustrative numerical results will be presented at the conference.
Identifiability for the pointwise source detection in Fisher’s reaction-diffusion equation
Ben Belgacem, Faker
2012-06-01
We are interested in the detection of a pointwise source in a class of semi-linear advection-diffusion-reaction equations of Fisher type. The source is determined by its location, which may be steady or unsteady, and its time-dependent intensity. Observations recorded at a couple of points are the available data. One observing station is located upstream of the source and the other downstream. This is a severely ill-posed nonlinear inverse problem. In this paper, we pursue an identifiability result. The process we follow has been developed earlier for the linear model and may be sharpened to operate for the semi-linear equation. It is based on the uniqueness for a parabolic (semi-linear) sideways problem, which is obtained by a suitable unique continuation theorem. We state a maximum principle that turns out to be necessary for our proof. The identifiability is finally obtained for a stationary or a moving source. Many applications may be found in biology, chemical physiology or environmental science. The problem we deal with is the detection of pointwise organic pollution sources in rivers and channels. The basic equation to consider is the one-dimensional biochemical oxygen demand equation, with a nonlinear power growth inhibitor and/or the Michaelis-Menten reaction coefficient.
Bistable dark solitons of a cubic-quintic Helmholtz equation
International Nuclear Information System (INIS)
Christian, J. M.; McDonald, G. S.; Chamorro-Posada, P.
2010-01-01
We provide a report on exact analytical bistable dark spatial solitons of a nonlinear Helmholtz equation with a cubic-quintic refractive-index model. Our analysis begins with an investigation of the modulational instability characteristics of Helmholtz plane waves. We then derive a dark soliton by mapping the desired asymptotic form onto a uniform background field and obtain a more general solution by deploying rotational invariance laws in the laboratory frame. The geometry of the new soliton is explored in detail, and a range of new physical predictions is uncovered. Particular attention is paid to the unified phenomena of arbitrary-angle off-axis propagation and nondegenerate bistability. Crucially, the corresponding solution of paraxial theory emerges in a simultaneous multiple limit. We conclude with a set of computer simulations that examine the role of Helmholtz dark solitons as robust attractors.
Pontes, J.; Walgraef, D.; Christov, C. I.
2010-11-01
Strain localization and dislocation pattern formation are typical features of plastic deformation in metals and alloys. Glide and climb dislocation motion along with accompanying production/annihilation processes of dislocations lead to the occurrence of instabilities of initially uniform dislocation distributions. These instabilities result into the development of various types of dislocation micro-structures, such as dislocation cells, slip and kink bands, persistent slip bands, labyrinth structures, etc., depending on the externally applied loading and the intrinsic lattice constraints. The Walgraef-Aifantis (WA) (Walgraef and Aifanits, J. Appl. Phys., 58, 668, 1985) model is an example of a reaction-diffusion model of coupled nonlinear equations which describe 0 formation of forest (immobile) and gliding (mobile) dislocation densities in the presence of cyclic loading. This paper discuss two versions of the WA model and focus on a finite difference, second order in time 1-Nicolson semi-implicit scheme, with internal iterations at each time step and a spatial splitting using the Stabilizing, Correction (Christov and Pontes, Mathematical and Computer Modelling, 35, 87, 2002) for solving the model evolution equations in two dimensions. The results of two simulations are presented. More complete results will appear in a forthcoming paper.
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.
Directory of Open Access Journals (Sweden)
Octavio Batta
2016-10-01
Full Text Available We present a derivative-free algorithm for solving bound constrained systems of nonlinear monotone equations. The algorithm generates feasible iterates using in a systematic way the residual as search direction and a suitable step-length closely related to the Barzilai-Borwein choice. A convergence analysis is described. We also present one application in solving problems related with the study of reaction-diffusion processes that can be described by nonlinear partial differential equations of elliptic type. Numerical experiences are included to highlight the efficacy of proposed algorithm.
Bistability in the chemical master equation for dual phosphorylation cycles
Bazzani, Armando; Castellani, Gastone C.; Giampieri, Enrico; Remondini, Daniel; Cooper, Leon N.
2012-06-01
Dual phospho/dephosphorylation cycles, as well as covalent enzymatic-catalyzed modifications of substrates are widely diffused within cellular systems and are crucial for the control of complex responses such as learning, memory, and cellular fate determination. Despite the large body of deterministic studies and the increasing work aimed at elucidating the effect of noise in such systems, some aspects remain unclear. Here we study the stationary distribution provided by the two-dimensional chemical master equation for a well-known model of a two step phospho/dephosphorylation cycle using the quasi-steady state approximation of enzymatic kinetics. Our aim is to analyze the role of fluctuations and the molecules distribution properties in the transition to a bistable regime. When detailed balance conditions are satisfied it is possible to compute equilibrium distributions in a closed and explicit form. When detailed balance is not satisfied, the stationary non-equilibrium state is strongly influenced by the chemical fluxes. In the last case, we show how the external field derived from the generation and recombination transition rates, can be decomposed by the Helmholtz theorem, into a conservative and a rotational (irreversible) part. Moreover, this decomposition allows to compute the stationary distribution via a perturbative approach. For a finite number of molecules there exists diffusion dynamics in a macroscopic region of the state space where a relevant transition rate between the two critical points is observed. Further, the stationary distribution function can be approximated by the solution of a Fokker-Planck equation. We illustrate the theoretical results using several numerical simulations.
MacDonald, G; Mackenzie, J A; Nolan, M; Insall, R H
2016-03-15
In this paper, we devise a moving mesh finite element method for the approximate solution of coupled bulk-surface reaction-diffusion equations on an evolving two dimensional domain. Fundamental to the success of the method is the robust generation of bulk and surface meshes. For this purpose, we use a novel moving mesh partial differential equation (MMPDE) approach. The developed method is applied to model problems with known analytical solutions; these experiments indicate second-order spatial and temporal accuracy. Coupled bulk-surface problems occur frequently in many areas; in particular, in the modelling of eukaryotic cell migration and chemotaxis. We apply the method to a model of the two-way interaction of a migrating cell in a chemotactic field, where the bulk region corresponds to the extracellular region and the surface to the cell membrane.
International Nuclear Information System (INIS)
Hormuth II, David A; Weis, Jared A; Barnes, Stephanie L; Miga, Michael I; Yankeelov, Thomas E; Rericha, Erin C; Quaranta, Vito
2015-01-01
Reaction–diffusion models have been widely used to model glioma growth. However, it has not been shown how accurately this model can predict future tumor status using model parameters (i.e., tumor cell diffusion and proliferation) estimated from quantitative in vivo imaging data. To this end, we used in silico studies to develop the methods needed to accurately estimate tumor specific reaction–diffusion model parameters, and then tested the accuracy with which these parameters can predict future growth. The analogous study was then performed in a murine model of glioma growth. The parameter estimation approach was tested using an in silico tumor ‘grown’ for ten days as dictated by the reaction–diffusion equation. Parameters were estimated from early time points and used to predict subsequent growth. Prediction accuracy was assessed at global (total volume and Dice value) and local (concordance correlation coefficient, CCC) levels. Guided by the in silico study, rats (n = 9) with C6 gliomas, imaged with diffusion weighted magnetic resonance imaging, were used to evaluate the model’s accuracy for predicting in vivo tumor growth. The in silico study resulted in low global (tumor volume error <8.8%, Dice >0.92) and local (CCC values >0.80) level errors for predictions up to six days into the future. The in vivo study showed higher global (tumor volume error >11.7%, Dice <0.81) and higher local (CCC <0.33) level errors over the same time period. The in silico study shows that model parameters can be accurately estimated and used to accurately predict future tumor growth at both the global and local scale. However, the poor predictive accuracy in the experimental study suggests the reaction–diffusion equation is an incomplete description of in vivo C6 glioma biology and may require further modeling of intra-tumor interactions including segmentation of (for example) proliferative and necrotic regions. (paper)
Traveling waves in a nonlocal, piecewise linear reaction-diffusion population model
Autry, E. A.; Bayliss, A.; Volpert, V. A.
2017-08-01
We consider an analytically tractable switching model that is a simplification of a nonlocal, nonlinear reaction-diffusion model of population growth where we take the source term to be piecewise linear. The form of this source term allows us to consider both the monostable and bistable versions of the problem. By transforming to a traveling frame and choosing specific kernel functions, we are able to reduce the problem to a system of algebraic equations. We construct solutions and examine the propagation speed and monotonicity of the resulting waves.
reaction-diffusion system with fractional derivatives
Directory of Open Access Journals (Sweden)
Kamel Haouam
2006-01-01
Full Text Available We give some necessary conditions for local and global existence of a solution to reaction-diffusion system of type (FDS with temporal and spacial fractional derivatives. As in the case of single equation of type (STFE studied by M. Kirane et al. (2005, we prove that these conditions depend on the behavior of initial conditions for large |x|.
Second-order differential-delay equation to describe a hybrid bistable device
Vallee, R.; Dubois, P.; Cote, M.; Delisle, C.
1987-08-01
The problem of a dynamical system with delayed feedback, a hybrid bistable device, characterized by n response times and described by an nth-order differential-delay equation (DDE) is discussed. Starting from a linear-stability analysis of the DDE, the effects of the second-order differential terms on the position of the first bifurcation and on the frequency of the resulting self-oscillation are shown. The effects of the third-order differential terms on the first bifurcation are also considered. Experimental results are shown to support the linear analysis.
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
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
Crosta, M.
2011-12-05
We characterize the full family of soliton solutions sitting over a background plane wave and ruled by the cubic-quintic nonlinear Schrödinger equation in the regime where a quintic focusing term represents a saturation of the cubic defocusing nonlinearity. We discuss the existence and properties of solitons in terms of catastrophe theory and fully characterize bistability and instabilities of the dark-antidark pairs, revealing mechanisms of decay of antidark solitons into dispersive shock waves.
Parand, K.; Nikarya, M.
2017-11-01
In this paper a novel method will be introduced to solve a nonlinear partial differential equation (PDE). In the proposed method, we use the spectral collocation method based on Bessel functions of the first kind and the Jacobian free Newton-generalized minimum residual (JFNGMRes) method with adaptive preconditioner. In this work a nonlinear PDE has been converted to a nonlinear system of algebraic equations using the collocation method based on Bessel functions without any linearization, discretization or getting the help of any other methods. Finally, by using JFNGMRes, the solution of the nonlinear algebraic system is achieved. To illustrate the reliability and efficiency of the proposed method, we solve some examples of the famous Fisher equation. We compare our results with other methods.
Reaction-diffusion with stochastic decay rates.
Lapeyre, G John; Dentz, Marco
2017-07-26
Understanding anomalous transport and reaction kinetics due to microscopic physical and chemical disorder is a long-standing goal in many fields including geophysics, biology, and engineering. We consider reaction-diffusion characterized by fluctuations in both transport times and decay rates. We introduce and analyze a model framework that explicitly connects microscopic fluctuations with the mescoscopic description. For broad distributions of transport and reaction time scales we compute the particle density and derive the equations governing its evolution, finding power-law decay of the survival probability, and spatially varying decay that leads to subdiffusion and an asymptotically stationary surviving-particle density. These anomalies are clearly attributable to non-Markovian effects that couple transport and chemical properties in both reaction and diffusion terms.
Reaction-diffusion problems in the physics of hot plasmas
Wilhelmsson, H
2000-01-01
The physics of hot plasmas is of great importance for describing many phenomena in the universe and is fundamental for the prospect of future fusion energy production on Earth. Nontrivial results of nonlinear electromagnetic effects in plasmas include the self-organization and self-formation in the plasma of structures compact in time and space. These are the consequences of competing processes of nonlinear interactions and can be best described using reaction-diffusion equations. Reaction-Diffusion Problems in the Physics of Hot Plasmas is focused on paradigmatic problems of a reaction-diffusion type met in many branches of science, concerning in particular the nonlinear interaction of electromagnetic fields with plasmas.
Distributed order reaction-diffusion systems associated with Caputo derivatives
Saxena, R. K.; Mathai, A. M.; Haubold, H. J.
2014-08-01
This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation of distributed order associated with the Caputo derivatives as the time-derivative and Riesz-Feller fractional derivative as the space-derivative. The solution is derived by the application of the joint Laplace and Fourier transforms in compact and closed form in terms of the H-function. The results derived are of general nature and include the results investigated earlier by other authors, notably by Mainardi et al. ["The fundamental solution of the space-time fractional diffusion equation," Fractional Calculus Appl. Anal. 4, 153-202 (2001); Mainardi et al. "Fox H-functions in fractional diffusion," J. Comput. Appl. Math. 178, 321-331 (2005)] for the fundamental solution of the space-time fractional equation, including Haubold et al. ["Solutions of reaction-diffusion equations in terms of the H-function," Bull. Astron. Soc. India 35, 681-689 (2007)] and Saxena et al. ["Fractional reaction-diffusion equations," Astrophys. Space Sci. 305, 289-296 (2006a)] for fractional reaction-diffusion equations. The advantage of using the Riesz-Feller derivative lies in the fact that the solution of the fractional reaction-diffusion equation, containing this derivative, includes the fundamental solution for space-time fractional diffusion, which itself is a generalization of fractional diffusion, space-time fraction diffusion, and time-fractional diffusion, see Schneider and Wyss ["Fractional diffusion and wave equations," J. Math. Phys. 30, 134-144 (1989)]. These specialized types of diffusion can be interpreted as spatial probability density functions evolving in time and are expressible in terms of the H-function in compact forms. The convergence conditions for the double series occurring in the solutions are investigated. It is interesting to observe that the double series comes out to be a special case of the Srivastava-Daoust hypergeometric function of two variables
Multiple Scale Reaction-Diffusion-Advection Problems with Moving Fronts
Nefedov, Nikolay
2016-06-01
In this work we discuss the further development of the general scheme of the asymptotic method of differential inequalities to investigate stability and motion of sharp internal layers (fronts) for nonlinear singularly perturbed parabolic equations, which are called in applications reaction-diffusion-advection equations. Our approach is illustrated for some new important cases of initial boundary value problems. We present results on stability and on the motion of the fronts.
Synthesis and materialization of a reaction-diffusion French flag pattern
Zadorin, Anton S.; Rondelez, Yannick; Gines, Guillaume; Dilhas, Vadim; Urtel, Georg; Zambrano, Adrian; Galas, Jean-Christophe; Estevez-Torres, André
2017-10-01
During embryo development, patterns of protein concentration appear in response to morphogen gradients. These patterns provide spatial and chemical information that directs the fate of the underlying cells. Here, we emulate this process within non-living matter and demonstrate the autonomous structuration of a synthetic material. First, we use DNA-based reaction networks to synthesize a French flag, an archetypal pattern composed of three chemically distinct zones with sharp borders whose synthetic analogue has remained elusive. A bistable network within a shallow concentration gradient creates an immobile, sharp and long-lasting concentration front through a reaction-diffusion mechanism. The combination of two bistable circuits generates a French flag pattern whose 'phenotype' can be reprogrammed by network mutation. Second, these concentration patterns control the macroscopic organization of DNA-decorated particles, inducing a French flag pattern of colloidal aggregation. This experimental framework could be used to test reaction-diffusion models and fabricate soft materials following an autonomous developmental programme.
Cohabitation reaction-diffusion model for virus focal infections
Amor, Daniel R.; Fort, Joaquim
2014-12-01
The propagation of virus infection fronts has been typically modeled using a set of classical (noncohabitation) reaction-diffusion equations for interacting species. However, for some single-species systems it has been recently shown that noncohabitation reaction-diffusion equations may lead to unrealistic descriptions. We argue that previous virus infection models also have this limitation, because they assume that a virion can simultaneously reproduce inside a cell and diffuse away from it. For this reason, we build a several-species cohabitation model that does not have this limitation. Furthermore, we perform a sensitivity analysis for the most relevant parameters of the model, and we compare the predicted infection speed with observed data for two different strains of the T7 virus.
Reaction-Diffusion Automata Phenomenology, Localisations, Computation
Adamatzky, Andrew
2013-01-01
Reaction-diffusion and excitable media are amongst most intriguing substrates. Despite apparent simplicity of the physical processes involved the media exhibit a wide range of amazing patterns: from target and spiral waves to travelling localisations and stationary breathing patterns. These media are at the heart of most natural processes, including morphogenesis of living beings, geological formations, nervous and muscular activity, and socio-economic developments. This book explores a minimalist paradigm of studying reaction-diffusion and excitable media using locally-connected networks of finite-state machines: cellular automata and automata on proximity graphs. Cellular automata are marvellous objects per se because they show us how to generate and manage complexity using very simple rules of dynamical transitions. When combined with the reaction-diffusion paradigm the cellular automata become an essential user-friendly tool for modelling natural systems and designing future and emergent computing arch...
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
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.
Reaction rates for reaction-diffusion kinetics on unstructured meshes.
Hellander, Stefan; Petzold, Linda
2017-02-14
The reaction-diffusion master equation is a stochastic model often utilized in the study of biochemical reaction networks in living cells. It is applied when the spatial distribution of molecules is important to the dynamics of the system. A viable approach to resolve the complex geometry of cells accurately is to discretize space with an unstructured mesh. Diffusion is modeled as discrete jumps between nodes on the mesh, and the diffusion jump rates can be obtained through a discretization of the diffusion equation on the mesh. Reactions can occur when molecules occupy the same voxel. In this paper, we develop a method for computing accurate reaction rates between molecules occupying the same voxel in an unstructured mesh. For large voxels, these rates are known to be well approximated by the reaction rates derived by Collins and Kimball, but as the mesh is refined, no analytical expression for the rates exists. We reduce the problem of computing accurate reaction rates to a pure preprocessing step, depending only on the mesh and not on the model parameters, and we devise an efficient numerical scheme to estimate them to high accuracy. We show in several numerical examples that as we refine the mesh, the results obtained with the reaction-diffusion master equation approach those of a more fine-grained Smoluchowski particle-tracking model.
Simulating mesoscopic reaction-diffusion systems using the Gillespie algorithm
Energy Technology Data Exchange (ETDEWEB)
Bernstein, David
2004-12-12
We examine an application of the Gillespie algorithm to simulating spatially inhomogeneous reaction-diffusion systems in mesoscopic volumes such as cells and microchambers. The method involves discretizing the chamber into elements and modeling the diffusion of chemical species by the movement of molecules between neighboring elements. These transitions are expressed in the form of a set of reactions which are added to the chemical system. The derivation of the rates of these diffusion reactions is by comparison with a finite volume discretization of the heat equation on an unevenly spaced grid. The diffusion coefficient of each species is allowed to be inhomogeneous in space, including discontinuities. The resulting system is solved by the Gillespie algorithm using the fast direct method. We show that in an appropriate limit the method reproduces exact solutions of the heat equation for a purely diffusive system and the nonlinear reaction-rate equation describing the cubic autocatalytic reaction.
A discrete model to study reaction-diffusion-mechanics systems.
Weise, Louis D; Nash, Martyn P; Panfilov, Alexander V
2011-01-01
This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.
A discrete model to study reaction-diffusion-mechanics systems.
Directory of Open Access Journals (Sweden)
Louis D Weise
Full Text Available This article introduces a discrete reaction-diffusion-mechanics (dRDM model to study the effects of deformation on reaction-diffusion (RD processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material. Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.
Reaction-diffusion 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
Pattern formation in the bistable Gray-Scott model
DEFF Research Database (Denmark)
Mazin, W.; Rasmussen, K.E.; Mosekilde, Erik
1996-01-01
The paper presents a computer simulation study of a variety of far-from-equilibrium phenomena that can arise in a bistable chemical reaction-diffusion system which also displays Turing and Hopf instabilities. The Turing bifurcation curve and the wave number for the patterns of maximum linear grow...
Reaction rates for mesoscopic reaction-diffusion kinetics.
Hellander, Stefan; Hellander, Andreas; Petzold, Linda
2015-02-01
The mesoscopic reaction-diffusion master equation (RDME) is a popular modeling framework frequently applied to stochastic reaction-diffusion kinetics in systems biology. The RDME is derived from assumptions about the underlying physical properties of the system, and it may produce unphysical results for models where those assumptions fail. In that case, other more comprehensive models are better suited, such as hard-sphere Brownian dynamics (BD). Although the RDME is a model in its own right, and not inferred from any specific microscale model, it proves useful to attempt to approximate a microscale model by a specific choice of mesoscopic reaction rates. In this paper we derive mesoscopic scale-dependent reaction rates by matching certain statistics of the RDME solution to statistics of the solution of a widely used microscopic BD model: the Smoluchowski model with a Robin boundary condition at the reaction radius of two molecules. We also establish fundamental limits on the range of mesh resolutions for which this approach yields accurate results and show both theoretically and in numerical examples that as we approach the lower fundamental limit, the mesoscopic dynamics approach the microscopic dynamics. We show that for mesh sizes below the fundamental lower limit, results are less accurate. Thus, the lower limit determines the mesh size for which we obtain the most accurate results.
Domain decomposition multigrid methods for nonlinear reaction-diffusion problems
Arrarás, A.; Gaspar, F. J.; Portero, L.; Rodrigo, C.
2015-03-01
In this work, we propose efficient discretizations for nonlinear evolutionary reaction-diffusion problems on general two-dimensional domains. The spatial domain is discretized through an unstructured coarse triangulation, which is subsequently refined via regular triangular grids. Following the method of lines approach, we first consider a finite element spatial discretization, and then use a linearly implicit splitting time integrator related to a suitable decomposition of the triangulation nodes. Such a procedure provides a linear system per internal stage. The equations corresponding to those nodes lying strictly inside the elements of the coarse triangulation can be decoupled and solved in parallel using geometric multigrid techniques. The method is unconditionally stable and computationally efficient, since it avoids the need for Schwarz-type iteration procedures. In addition, it is formulated for triangular elements, thus yielding much flexibility in the discretization of complex geometries. To illustrate its practical utility, the algorithm is shown to reproduce the pattern-forming dynamics of the Schnakenberg model.
Multiscale Reaction-Diffusion Algorithms: PDE-Assisted Brownian Dynamics
Franz, Benjamin
2013-06-19
Two algorithms that combine Brownian dynami cs (BD) simulations with mean-field partial differential equations (PDEs) are presented. This PDE-assisted Brownian dynamics (PBD) methodology provides exact particle tracking data in parts of the domain, whilst making use of a mean-field reaction-diffusion PDE description elsewhere. The first PBD algorithm couples BD simulations with PDEs by randomly creating new particles close to the interface, which partitions the domain, and by reincorporating particles into the continuum PDE-description when they cross the interface. The second PBD algorithm introduces an overlap region, where both descriptions exist in parallel. It is shown that the overlap region is required to accurately compute variances using PBD simulations. Advantages of both PBD approaches are discussed and illustrative numerical examples are presented. © 2013 Society for Industrial and Applied Mathematics.
Zubarev nonequilibrium statistical operator method in Renyi statistics. Reaction-diffusion processes
Directory of Open Access Journals (Sweden)
P. Kostrobij
2014-09-01
Full Text Available The Zubarev nonequilibrium statistical operator (NSO method in Renyi statistics is discussed. The solution of q-parametrized Liouville equation within the NSO method is obtained. A statistical approach for a consistent description of reaction-diffusion processes in "gas-adsorbate-metal" system is proposed using the NSO method in Renyi statistics.
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].
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,...
Stochastic modeling and simulation of reaction-diffusion system with Hill function dynamics.
Chen, Minghan; Li, Fei; Wang, Shuo; Cao, Young
2017-03-14
Stochastic simulation of reaction-diffusion systems presents great challenges for spatiotemporal biological modeling and simulation. One widely used framework for stochastic simulation of reaction-diffusion systems is reaction diffusion master equation (RDME). Previous studies have discovered that for the RDME, when discretization size approaches zero, reaction time for bimolecular reactions in high dimensional domains tends to infinity. In this paper, we demonstrate that in the 1D domain, highly nonlinear reaction dynamics given by Hill function may also have dramatic change when discretization size is smaller than a critical value. Moreover, we discuss methods to avoid this problem: smoothing over space, fixed length smoothing over space and a hybrid method. Our analysis reveals that the switch-like Hill dynamics reduces to a linear function of discretization size when the discretization size is small enough. The three proposed methods could correctly (under certain precision) simulate Hill function dynamics in the microscopic RDME system.
Kimizuka, M; Munakata, T; Rosinberg, M L
2010-10-01
We consider a network of N noisy bistable elements with global time-delayed couplings. In a two-state description, where elements are represented by Ising spins, the collective dynamics is described by an infinite hierarchy of coupled master equations which was solved at the mean-field level in the thermodynamic limit. When the number of elements is finite, as is the case in actual laser networks, an analytical description was deemed so far intractable and numerical studies seemed to be necessary. In this paper we consider the case of two interacting elements and show that a partial analytical description of the stationary state is possible if the stochastic process is time symmetric. This requires some relationship between the transition rates to be satisfied.
Evolution of density profiles for reaction-diffusion processes
International Nuclear Information System (INIS)
Ondarza-Rovira, R.
1990-01-01
The purpose of this work is to study the reaction diffusion equations for the concentration of one species in one spatial dimension. Nonlinear diffusion equations paly an important role in several fields: Physics, Kinetic Chemistry, Poblational Biology, Neurophysics, etc. The study of the behavior of solutions, with nonlinear diffusion coefficient, and monomial creation and annihilation terms, is considered. It is found, that when the exponent of the annihilation term is smaller than the one of the creation term, unstable equilibrium solutions may exist, for which solutions above it explode in finite time, but solutions below it decay exponentially. By means of the reduction to quadratures technique, it is found that is possible to obtain travelling wave solution in those cases when the annihilation term is greater than the creation term. This method of solution always permits to know the propagation velocity of the front, even if the concentration cannot be written in closed form. The portraits of the solutions in phase space show the existence of solutions which velocities may be smaller or greater than the ones found analytically. Linear and nonlinear diffusion equations, differ significantly in that the former are of change of solutions are considered. This is reminiscent of the fact that linear diffusion yields infinite propagation speed, even though the speed of the front is finite. When the strength of the annihilation term increases, as compared with that of the creation term, arbitrary initial conditions (studied numerically) relax to stable platforms that move indefinitly with constant speed. (Author)
Chemical computing with reaction-diffusion processes.
Gorecki, J; Gizynski, K; Guzowski, J; Gorecka, J N; Garstecki, P; Gruenert, G; Dittrich, P
2015-07-28
Chemical reactions are responsible for information processing in living organisms. It is believed that the basic features of biological computing activity are reflected by a reaction-diffusion medium. We illustrate the ideas of chemical information processing considering the Belousov-Zhabotinsky (BZ) reaction and its photosensitive variant. The computational universality of information processing is demonstrated. For different methods of information coding constructions of the simplest signal processing devices are described. The function performed by a particular device is determined by the geometrical structure of oscillatory (or of excitable) and non-excitable regions of the medium. In a living organism, the brain is created as a self-grown structure of interacting nonlinear elements and reaches its functionality as the result of learning. We discuss whether such a strategy can be adopted for generation of chemical information processing devices. Recent studies have shown that lipid-covered droplets containing solution of reagents of BZ reaction can be transported by a flowing oil. Therefore, structures of droplets can be spontaneously formed at specific non-equilibrium conditions, for example forced by flows in a microfluidic reactor. We describe how to introduce information to a droplet structure, track the information flow inside it and optimize medium evolution to achieve the maximum reliability. Applications of droplet structures for classification tasks are discussed. © 2015 The Author(s) Published by the Royal Society. All rights reserved.
Reaction-diffusion mechanisms and quantum spin systems
Schütz, Gunter M.
We present a brief tutorial introduction into the quantum Hamiltonian formalism for stochastic many-body systems defined in terms of a master equation for their time evolution. These models describe interacting classical particle systems where particles hop on a lattice and may undergo reactions such as A+A→0. The quantum Hamiltonian formalism for the master equation provides a convenient general framework for the treatment of such models which, by various mappings, are capable of describing a wide variety of phenomena in non-equilibrium physics and in random media. The formalism is particularly useful if the quantum Hamiltonian has continuous global symmetries or if it is integrable, i.e. has an infinite set of conservation laws. This is demonstrated in the case of the exclusion process and for a toy model of tumor growth. Experimental applications of other integrable reaction-diffusion models in various areas of polymer physics (gel electrophoresis of DNA, exciton dynamics on polymers and the kinetics of biopolymerization on RNA) are pointed out.
Decay to Equilibrium for Energy-Reaction-Diffusion Systems
Haskovec, Jan
2018-02-06
We derive thermodynamically consistent models of reaction-diffusion equations coupled to a heat equation. While the total energy is conserved, the total entropy serves as a driving functional such that the full coupled system is a gradient flow. The novelty of the approach is the Onsager structure, which is the dual form of a gradient system, and the formulation in terms of the densities and the internal energy. In these variables it is possible to assume that the entropy density is strictly concave such that there is a unique maximizer (thermodynamical equilibrium) given linear constraints on the total energy and suitable density constraints. We consider two particular systems of this type, namely, a diffusion-reaction bipolar energy transport system, and a drift-diffusion-reaction energy transport system with confining potential. We prove corresponding entropy-entropy production inequalities with explicitly calculable constants and establish the convergence to thermodynamical equilibrium, first in entropy and later in L norm using Cziszár–Kullback–Pinsker type inequalities.
Nonexplosion of solutions to stochastic reaction-diffusion equations
Czech Academy of Sciences Publication Activity Database
Dozzi, M.; Maslowski, Bohdan
2002-01-01
Roč. 82, - (2002), s. 745-751 ISSN 0044-2267 Institutional research plan: CEZ:AV0Z1019905 Keywords : stochastic parabolic PDEďs%nonexplosion Subject RIV: ba - General Mathematics Impact factor: 0.085, year: 2002
Pulses in singularly perturbed reaction-diffusion systems
Veerman, Frederik Willem Johan
2013-01-01
In this thesis, the existence and stability of pulse solutions in two-component, singularly perturbed reaction-diffusion systems is analysed using dynamical systems techniques. New phenomena in very general types of systems emerge when geometrical techniques are applied.
The smallest chemical reaction system with bistability
Directory of Open Access Journals (Sweden)
Wilhelm Thomas
2009-09-01
Full Text Available Abstract Background Bistability underlies basic biological phenomena, such as cell division, differentiation, cancer onset, and apoptosis. So far biologists identified two necessary conditions for bistability: positive feedback and ultrasensitivity. Results Biological systems are based upon elementary mono- and bimolecular chemical reactions. In order to definitely clarify all necessary conditions for bistability we here present the corresponding minimal system. According to our definition, it contains the minimal number of (i reactants, (ii reactions, and (iii terms in the corresponding ordinary differential equations (decreasing importance from i-iii. The minimal bistable system contains two reactants and four irreversible reactions (three bimolecular, one monomolecular. We discuss the roles of the reactions with respect to the necessary conditions for bistability: two reactions comprise the positive feedback loop, a third reaction filters out small stimuli thus enabling a stable 'off' state, and the fourth reaction prevents explosions. We argue that prevention of explosion is a third general necessary condition for bistability, which is so far lacking discussion in the literature. Moreover, in addition to proving that in two-component systems three steady states are necessary for bistability (five for tristability, etc., we also present a simple general method to design such systems: one just needs one production and three different degradation mechanisms (one production, five degradations for tristability, etc.. This helps modelling multistable systems and it is important for corresponding synthetic biology projects. Conclusion The presented minimal bistable system finally clarifies the often discussed question for the necessary conditions for bistability. The three necessary conditions are: positive feedback, a mechanism to filter out small stimuli and a mechanism to prevent explosions. This is important for modelling bistability with
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.
Nefedov, Nikolay
2017-02-01
This is an extended variant of the paper presented at MURPHYS-HSFS 2016 conference in Barcelona. We discuss further development of the asymptotic method of differential inequalities to investigate existence and stability of sharp internal layers (fronts) for nonlinear singularly perturbed periodic parabolic problems and initial boundary value problems with blow-up of fronts for reaction-diffusion-advection equations. In particular, we consider periodic solutions with internal layer in the case of balanced reaction. For the initial boundary value problems we prove the existence of fronts and give their asymptotic approximation including the new case of blowing-up fronts. This case we illustrate by the generalised Burgers equation.
Simulations of pattern dynamics for reaction-diffusion systems via SIMULINK.
Wang, Kaier; Steyn-Ross, Moira L; Steyn-Ross, D Alistair; Wilson, Marcus T; Sleigh, Jamie W; Shiraishi, Yoichi
2014-04-11
Investigation of the nonlinear pattern dynamics of a reaction-diffusion system almost always requires numerical solution of the system's set of defining differential equations. Traditionally, this would be done by selecting an appropriate differential equation solver from a library of such solvers, then writing computer codes (in a programming language such as C or Matlab) to access the selected solver and display the integrated results as a function of space and time. This "code-based" approach is flexible and powerful, but requires a certain level of programming sophistication. A modern alternative is to use a graphical programming interface such as Simulink to construct a data-flow diagram by assembling and linking appropriate code blocks drawn from a library. The result is a visual representation of the inter-relationships between the state variables whose output can be made completely equivalent to the code-based solution. As a tutorial introduction, we first demonstrate application of the Simulink data-flow technique to the classical van der Pol nonlinear oscillator, and compare Matlab and Simulink coding approaches to solving the van der Pol ordinary differential equations. We then show how to introduce space (in one and two dimensions) by solving numerically the partial differential equations for two different reaction-diffusion systems: the well-known Brusselator chemical reactor, and a continuum model for a two-dimensional sheet of human cortex whose neurons are linked by both chemical and electrical (diffusive) synapses. We compare the relative performances of the Matlab and Simulink implementations. The pattern simulations by Simulink are in good agreement with theoretical predictions. Compared with traditional coding approaches, the Simulink block-diagram paradigm reduces the time and programming burden required to implement a solution for reaction-diffusion systems of equations. Construction of the block-diagram does not require high-level programming
Gelens, Lendert; Matías, Manuel A; Gomila, Damià; Dorissen, Tom; Colet, Pere
2014-01-01
We study the influence of a linear nonlocal spatial coupling on the interaction of fronts connecting two equivalent stable states in the prototypical 1-dimensional real Ginzburg-Landau equation. While for local coupling the fronts are always monotonic and therefore the dynamical behavior leads to coarsening and the annihilation of pairs of fronts, nonlocal terms can induce spatial oscillations in the front, allowing for the creation of localized structures, emerging from pinning between two fronts. We show this for three different nonlocal influence kernels. The first two, mod-exponential and Gaussian, are positive definite and decay exponentially or faster, while the third one, a Mexican-hat kernel, is not positive definite.
Elliptic partial differential equations
Volpert, Vitaly
If we had to formulate in one sentence what this book is about it might be "How partial differential equations can help to understand heat explosion, tumor growth or evolution of biological species". These and many other applications are described by reaction-diffusion equations. The theory of reaction-diffusion equations appeared in the first half of the last century. In the present time, it is widely used in population dynamics, chemical physics, biomedical modelling. The purpose of this book is to present the mathematical theory of reaction-diffusion equations in the context of their numerous applications. We will go from the general mathematical theory to specific equations and then to their applications. Mathematical anaylsis of reaction-diffusion equations will be based on the theory of Fredholm operators presented in the first volume. Existence, stability and bifurcations of solutions will be studied for bounded domains and in the case of travelling waves. The classical theory of reaction-diffusion equ...
Reaction Diffusion and Chemotaxis for Decentralized Gathering on FPGAs
Directory of Open Access Journals (Sweden)
Bernard Girau
2009-01-01
and rapid simulations of the complex dynamics of this reaction-diffusion model. Then we describe the FPGA implementation of the environment together with the agents, to study the major challenges that must be solved when designing a fast embedded implementation of the decentralized gathering model. We analyze the results according to the different goals of these hardware implementations.
Analytically solvable models of reaction-diffusion systems
Energy Technology Data Exchange (ETDEWEB)
Zemskov, E P; Kassner, K [Institut fuer Theoretische Physik, Otto-von-Guericke-Universitaet, Universitaetsplatz 2, 39106 Magdeburg (Germany)
2004-05-01
We consider a class of analytically solvable models of reaction-diffusion systems. An analytical treatment is possible because the nonlinear reaction term is approximated by a piecewise linear function. As particular examples we choose front and pulse solutions to illustrate the matching procedure in the one-dimensional case.
Turing instability in reaction-diffusion systems with nonlinear diffusion
Energy Technology Data Exchange (ETDEWEB)
Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)
2013-10-15
The Turing instability is studied in two-component reaction-diffusion systems with nonlinear diffusion terms, and the regions in parametric space where Turing patterns can form are determined. The boundaries between super- and subcritical bifurcations are found. Calculations are performed for one-dimensional brusselator and oregonator models.
Traveling Wave Solutions in a Reaction-Diffusion Epidemic Model
Wang, Sheng; Liu, Wenbin; Guo, Zhengguang; Wang, Weiming
2013-01-01
We investigate the traveling wave solutions in a reaction-diffusion epidemic model. The existence of the wave solutions is derived through monotone iteration of a pair of classical upper and lower solutions. The traveling wave solutions are shown to be unique and strictly monotonic. Furthermore, we determine the critical minimal wave speed.
Fatima, T Tasnim; Muntean, A Adrian; Aiki, T
2012-01-01
This paper treats the solvability of a semilinear reaction-diffusion system, which incorporates transport (diffusion) and reaction effects emerging from two separated spatial scales: $x$ - macro and $y$ - micro. The system's origin connects to the modeling of concrete corrosion in sewer concrete pipes. It consists of three partial differential equations which are mass-balances of concentrations, as well as, one ordinary differential equation tracking the damage-by-corrosion. The system is sem...
Sheng, Yin; Zeng, Zhigang
2017-09-01
In this paper, synchronization of stochastic reaction-diffusion neural networks with Dirichlet boundary conditions and unbounded discrete time-varying delays is investigated. By virtue of theories of partial differential equations, inequality methods, and stochastic analysis techniques, pth moment exponential synchronization and almost sure exponential synchronization of the underlying neural networks are developed. The obtained results in this study enhance and generalize some earlier ones. The effectiveness and merits of the theoretical criteria are substantiated by two numerical simulations. Copyright © 2017 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Luisa Malaguti
2011-01-01
Full Text Available The paper deals with a degenerate reaction-diffusion equation, including aggregative movements and convective terms. The model also incorporates a real parameter causing the change from a purely diffusive to a diffusive-aggregative and to a purely aggregative regime. Existence and qualitative properties of traveling wave solutions are investigated, and estimates of their threshold speeds are furnished. Further, the continuous dependence of the threshold wave speed and of the wave profiles on a real parameter is studied, both when the process maintains its diffusion-aggregation nature and when it switches from it to another regime.
Parametric spatiotemporal oscillation in reaction-diffusion systems.
Ghosh, Shyamolina; Ray, Deb Shankar
2016-03-01
We consider a reaction-diffusion system in a homogeneous stable steady state. On perturbation by a time-dependent sinusoidal forcing of a suitable scaling parameter the system exhibits parametric spatiotemporal instability beyond a critical threshold frequency. We have formulated a general scheme to calculate the threshold condition for oscillation and the range of unstable spatial modes lying within a V-shaped region reminiscent of Arnold's tongue. Full numerical simulations show that depending on the specificity of nonlinearity of the models, the instability may result in time-periodic stationary patterns in the form of standing clusters or spatially localized breathing patterns with characteristic wavelengths. Our theoretical analysis of the parametric oscillation in reaction-diffusion system is corroborated by full numerical simulation of two well-known chemical dynamical models: chlorite-iodine-malonic acid and Briggs-Rauscher reactions.
Reaction diffusion voronoi diagrams: from sensors data to computing
Czech Academy of Sciences Publication Activity Database
Vázquez-Otero, Alejandro (ed.); Faigl, J.; Dormido, R.; Duro, N.
2015-01-01
Roč. 15, č. 6 (2015), s. 12736-12764 ISSN 1424-8220 R&D Projects: GA MŠk ED1.1.00/02.0061 Grant - others:ELI Beamlines(XE) CZ.1.05/1.1.00/02.0061 Institutional support: RVO:68378271 Keywords : reaction diffusion * FitzHugh–Nagumo * path planning * navigation * exploration Subject RIV: BD - Theory of Information Impact factor: 2.033, year: 2015
Existence of Solutions for a Quasilinear Reaction Diffusion System
Tian, Canrong
2012-01-01
The degenerate reaction diffusion system has been applied to a variety of physical and engineering problems. This paper is extended the existence of solutions from the quasimonotone reaction functions (e.g., inhibitor-inhibitor mechanism) to the mixed quasimonotone reaction functions (e.g., activator-inhibitor mechanism). By Schauder fixed point theorem, it is shown that the system admits at least one positive solution if there exist a coupled of upper and lower solutions. This result is appl...
Nonlinear dynamics of reaction-diffusion systems: Analysis and computations
International Nuclear Information System (INIS)
Wilhelmsson, H.
1991-01-01
Equilibria and dynamics of reaction-diffusion systems are studied by means of analysis and computations based on a central expansions method for radially symmetric as well as angularly asymmetric distributions. Effects of boundary conditions are included. The interplay between the different processes in the evolution of the system is considered. The investigation provides a unified description in one, two and three dimensions. A particular application concerns the time evolution of temperature profiles in a fusion reactor plasma. (au)
Programming reaction-diffusion: From theory to micro- and nanofabrication
Campbell, Christopher James
Nature often uses reaction-diffusion(RD) as a means of making structures and materials of unique properties or morphologies on scales from macro- (e.g., stripes in zebras, tigers, and seashells, and formations in trees, agates, and rocks) to microscopic (e.g., cellular growth, chemotaxis and biological waves). However, reaction-diffusion phenomena have not yet been applied in modern materials science and micro-/nanotechnology. In this context, RD systems are particularly promising for micropatterning of surfaces. Unlike conventional micropatterning techniques that modify the properties of the substrate only at the locations to which a modifying agent - be it a chemical or radiation - is delivered, RD can, in principle, evolve chemicals delivered onto a surface into structures of characteristic dimensions significantly smaller than those of the original pattern. In this Dissertation, I describe how reaction-diffusions are programmed and executed via a new micropatterning technique called Wet Stamping to (i) transform microscopic patterns of chemicals delivered onto thin films of dry gelatin into regular arrays of lines of submicrometer thicknesses, multicolor arrays on the micrometer scale, or three-dimensional microstructured surfaces; (ii) modify the properties of a surface by precisely delivering an oxidant to change hydrophilicity or deliver silanes or thiols to build a self-assembling monolayer; or (iii) cut into a metal, glass, or crystal surface by delivery of an etchant to form binary and curvilinear three-dimensional microstructures. This technique has allowed for a fundamental understanding and control of reaction-diffusion processes down to the nanoscale. In addition, this platform has allowed for the development of a range of applications on the micro- and nanoscale, including microlenses, microfluidic devices, and templates for studying cell motility and cancer metastasis.
Global Bifurcation for a Reaction-Diffusion System with Inclusions
Czech Academy of Sciences Publication Activity Database
Eisner, Jan; Kučera, Milan; Väth, M.
2009-01-01
Roč. 28, č. 4 (2009), s. 373-409 ISSN 0232-2064 R&D Projects: GA AV ČR IAA100190506 Institutional research plan: CEZ:AV0Z10190503 Keywords : global bifurcation * degree * stationary solutions * reaction-diffusion system * Laplace operator Subject RIV: BA - General Mathematics Impact factor: 0.371, year: 2009 http://www.ems-ph.org/journals/show_abstract.php?issn=0232-2064&vol=28&iss=4&rank=1
Control of transversal instabilities in reaction-diffusion systems
Molnos, Sonja; Löber, Jakob; Totz, Jan Frederik; Engel, Harald
2015-01-01
In two-dimensional reaction-diffusion systems, local curvature perturbations in the shape of traveling waves are typically damped out and disappear in the course of time. If, however, the inhibitor diffuses much faster than the activator, transversal instabilities can arise, leading from flat to folded, spatio-temporally modulated wave shapes and to spreading spiral turbulence. For experimentally relevant parameter values, the photosensitive Belousov-Zhabotinsky reaction (PBZR) does not exhib...
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...
The entropy dissipation method for spatially inhomogeneous reaction-diffusion-type systems
Di Francesco, M.
2008-12-08
We study the long-time asymptotics of reaction-diffusion-type systems that feature a monotone decaying entropy (Lyapunov, free energy) functional. We consider both bounded domains and confining potentials on the whole space for arbitrary space dimensions. Our aim is to derive quantitative expressions for (or estimates of) the rates of convergence towards an (entropy minimizing) equilibrium state in terms of the constants of diffusion and reaction and with respect to conserved quantities. Our method, the so-called entropy approach, seeks to quantify convergence to equilibrium by using functional inequalities, which relate quantitatively the entropy and its dissipation in time. The entropy approach is well suited to nonlinear problems and known to be quite robust with respect to model variations. It has already been widely applied to scalar diffusion-convection equations, and the main goal of this paper is to study its generalization to systems of partial differential equations that contain diffusion and reaction terms and admit fewer conservation laws than the size of the system. In particular, we successfully apply the entropy approach to general linear systems and to a nonlinear example of a reaction-diffusion-convection system arising in solid-state physics as a paradigm for general nonlinear systems. © 2008 The Royal Society.
Dinesh Kumar, S.; Nageshwar Rao, R.; Pramod Chakravarthy, P.
2017-11-01
In this paper, we consider a boundary value problem for a singularly perturbed delay differential equation of reaction-diffusion type. We construct an exponentially fitted numerical method using Numerov finite difference scheme, which resolves not only the boundary layers but also the interior layers arising from the delay term. An extensive amount of computational work has been carried out to demonstrate the applicability of the proposed method.
Stability and Hopf Bifurcation of a Reaction-Diffusion Neutral Neuron System with Time Delay
Dong, Tao; Xia, Linmao
2017-12-01
In this paper, a type of reaction-diffusion neutral neuron system with time delay under homogeneous Neumann boundary conditions is considered. By constructing a basis of phase space based on the eigenvectors of the corresponding Laplace operator, the characteristic equation of this system is obtained. Then, by selecting time delay and self-feedback strength as the bifurcating parameters respectively, the dynamic behaviors including local stability and Hopf bifurcation near the zero equilibrium point are investigated when the time delay and self-feedback strength vary. Furthermore, the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are obtained by using the normal form and the center manifold theorem for the corresponding partial differential equation. Finally, two simulation examples are given to verify the theory.
Domainal cleavage as an Anisotropic Reaction-diffusion Process
Mulchrone, Kieran; Meere, Patrick
2017-04-01
Domainal cleavage comprises zones dominated by quartz and feldspar (QF-domains) and zones dominated by Mica (M-domains) which form at low metamorphic grades. The protolith is typically fairly homogeneous mudstone, siltstone, sandstone or limestone. Wet diffusion or pressure solution along grain boundaries is a key mechanism in the development of domanial cleavage. However, this does not explain why M-domains become sub-regularly spaced, visually evident in coarser-grained rocks, and take on an anastomising morphology. The ratio of M to QF-domains by volume can range from 1 to 0.1 and lower i.e. in extreme cases M-domains are intermittent but regularly spaced. It is suggested here that an anisotropic reaction-diffusion process model can explain these features. The imposed stress field instantaneously leads to anisotropy of diffusion by narrowing intergranular channels perpendicular to the principal stress. This leads to a preferred diffusion of chemicals parallel to the principal stress direction and lower diffusion rates in the normal direction. Combining this with the chemical reaction of pressure solution produces an anisotropic reaction-diffusion system. Both isotropic and anistropic reaction diffusion systems lead to pattern formation as discovered by Alan Turing on the 1950's as an explanation for patterns found in animal skins such as spots and stripes. Thus domanial cleavage is a striped pattern induced by diffusion anisotropy combined with a chemical reaction. Furthermore, rates of chemical reaction in intergranular fluids is likely to be many orders of magnitude greater that rates of deformation. Therefore we expect domanial cleavage to form relatively rapidly. As deformation progresses the M-domains behave less competently and may be the site of enhanced shearing. An example from Co. Cork, Ireland demonstrates shear folding in low-grade metasedimentary rocks with reverse shear along M-domains at a high angle to the maximum compressive stress.
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.
Parametric pattern selection in a reaction-diffusion model.
Directory of Open Access Journals (Sweden)
Michael Stich
Full Text Available We compare spot patterns generated by Turing mechanisms with those generated by replication cascades, in a model one-dimensional reaction-diffusion system. We determine the stability region of spot solutions in parameter space as a function of a natural control parameter (feed-rate where degenerate patterns with different numbers of spots coexist for a fixed feed-rate. While it is possible to generate identical patterns via both mechanisms, we show that replication cascades lead to a wider choice of pattern profiles that can be selected through a tuning of the feed-rate, exploiting hysteresis and directionality effects of the different pattern pathways.
Reaction diffusion and solid state chemical kinetics handbook
Dybkov, V I
2010-01-01
This monograph deals with a physico-chemical approach to the problem of the solid-state growth of chemical compound layers and reaction-diffusion in binary heterogeneous systems formed by two solids; as well as a solid with a liquid or a gas. It is explained why the number of compound layers growing at the interface between the original phases is usually much lower than the number of chemical compounds in the phase diagram of a given binary system. For example, of the eight intermetallic compounds which exist in the aluminium-zirconium binary system, only ZrAl3 was found to grow as a separate
Reprint of Domain decomposition multigrid methods for nonlinear reaction-diffusion problems
Arrarás, A.; Gaspar, F. J.; Portero, L.; Rodrigo, C.
2015-04-01
In this work, we propose efficient discretizations for nonlinear evolutionary reaction-diffusion problems on general two-dimensional domains. The spatial domain is discretized through an unstructured coarse triangulation, which is subsequently refined via regular triangular grids. Following the method of lines approach, we first consider a finite element spatial discretization, and then use a linearly implicit splitting time integrator related to a suitable decomposition of the triangulation nodes. Such a procedure provides a linear system per internal stage. The equations corresponding to those nodes lying strictly inside the elements of the coarse triangulation can be decoupled and solved in parallel using geometric multigrid techniques. The method is unconditionally stable and computationally efficient, since it avoids the need for Schwarz-type iteration procedures. In addition, it is formulated for triangular elements, thus yielding much flexibility in the discretization of complex geometries. To illustrate its practical utility, the algorithm is shown to reproduce the pattern-forming dynamics of the Schnakenberg model.
An observer for an occluded reaction-diffusion system with spatially varying parameters
Kramer, Sean; Bollt, Erik M.
2017-03-01
Spatially dependent parameters of a two-component chaotic reaction-diffusion partial differential equation (PDE) model describing ocean ecology are observed by sampling a single species. We estimate the model parameters and the other species in the system by autosynchronization, where quantities of interest are evolved according to misfit between model and observations, to only partially observed data. Our motivating example comes from oceanic ecology as viewed by remote sensing data, but where noisy occluded data are realized in the form of cloud cover. We demonstrate a method to learn a large-scale coupled synchronizing system that represents the spatio-temporal dynamics and apply a network approach to analyze manifold stability.
Critical behavior in reaction-diffusion systems exhibiting absorbing phase transition
Ódor, G
2003-01-01
Phase transitions of reaction-diffusion systems with site occupation restriction and with particle creation that requires n>1 parents and where explicit diffusion of single particles (A) exists are reviewed. Arguments based on mean-field approximation and simulations are given which support novel kind of non-equilibrium criticality. These are in contradiction with the implications of a suggested phenomenological, multiplicative noise Langevin equation approach and with some of recent numerical analysis. Simulation results for the one and two dimensional binary spreading 2A -> 4A, 4A -> 2A model display a new type of mean-field criticality characterized by alpha=1/3 and beta=1/2 critical exponents suggested in cond-mat/0210615.
Numerical solution and asymptotic behavior for a nonlocal reaction-diffusion coupled systems
Chin, Pius W. M.
2017-07-01
This paper is considered on a class of nonlocal systems of reaction-diffusion equations with coefficients which are Lipschitz-continuous positive functions. In this model, we are concerned with designing a coupling technique consisting of the non-standard finite difference(NSFD) and finite element method(FEM) both in time and space respectively. We prove theoretically that the schemes designed by the above technique converges optimally in some specified norms for given conditions. Furthermore, we show that the numerical solutions of the said schemes replicates the decaying properties of the exact solutions. Numerical experiments are presented to justify the above theory and some practical studies are carried out for the asymptotic behavior of the schemes under consideration.
Grytskyy, Dmytro; Diesmann, Markus; Helias, Moritz
2016-06-01
Self-organized structures in networks with spike-timing dependent synaptic plasticity (STDP) are likely to play a central role for information processing in the brain. In the present study we derive a reaction-diffusion-like formalism for plastic feed-forward networks of nonlinear rate-based model neurons with a correlation sensitive learning rule inspired by and being qualitatively similar to STDP. After obtaining equations that describe the change of the spatial shape of the signal from layer to layer, we derive a criterion for the nonlinearity necessary to obtain stable dynamics for arbitrary input. We classify the possible scenarios of signal evolution and find that close to the transition to the unstable regime metastable solutions appear. The form of these dissipative solitons is determined analytically and the evolution and interaction of several such coexistent objects is investigated.
Asymptotic behavior of equilibrium states of reaction-diffusion systems with mass conservation
Chern, Jann-Long; Morita, Yoshihisa; Shieh, Tien-Tsan
2018-01-01
We deal with a stationary problem of a reaction-diffusion system with a conservation law under the Neumann boundary condition. It is shown that the stationary problem turns to be the Euler-Lagrange equation of an energy functional with a mass constraint. When the domain is the finite interval (0 , 1), we investigate the asymptotic profile of a strictly monotone minimizer of the energy as d, the ratio of the diffusion coefficient of the system, tends to zero. In view of a logarithmic function in the leading term of the potential, we get to a scaling parameter κ satisfying the relation ε : =√{ d } =√{ log κ } /κ2. The main result shows that a sequence of minimizers converges to a Dirac mass multiplied by the total mass and that by a scaling with κ the asymptotic profile exhibits a parabola in the nonvanishing region. We also prove the existence of an unstable monotone solution when the mass is small.
Hopping transport in hostile reaction-diffusion systems
Missel, Andrew R.; Dahmen, Karin A.
2009-02-01
We investigate transport in a disordered reaction-diffusion model consisting of particles which are allowed to diffuse, compete with one another (2A→A) , give birth in small areas called “oases” (A→2A) , and die in the “desert” outside the oases (A→0) . This model has previously been used to study bacterial populations in the laboratory and is related to a model of plankton populations in the oceans. We first consider the nature of transport between two oases: In the limit of high growth rate, this is effectively a first passage process, and we are able to determine the first passage time probability density function in the limit of large oasis separation. This result is then used along with the theory of hopping conduction in doped semiconductors to estimate the time taken by a population to cross a large system.
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.
Attractor for a Reaction-Diffusion System Modeling Cancer Network
Directory of Open Access Journals (Sweden)
Xueyong Chen
2014-01-01
Full Text Available A reaction-diffusion cancer network regulated by microRNA is considered in this paper. We study the asymptotic behavior of solution and show the existence of global uniformly bounded solution to the system in a bounded domain Ω⊂Rn. Some estimates and asymptotic compactness of the solutions are proved. As a result, we establish the existence of the global attractor in L2(Ω×L2(Ω and prove that the solution converges to stable steady states. These results can help to understand the dynamical character of cancer network and propose a new insight to study the mechanism of cancer. In the end, the numerical simulation shows that the analytical results agree with numerical simulation.
Stochastic partial differential equations
Chow, Pao-Liu
2014-01-01
Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Itô Type Lévy Processes and Stochastic IntegralsStochastic Differential Equations of Lévy Type Comments Scalar Equations of First Order Introduction Generalized Itô's Formula Linear Stochastic Equations Quasilinear Equations General Remarks Stochastic Parabolic Equations Introduction Preliminaries Solution of Stochastic Heat EquationLinear Equations with Additive Noise Some Regularity Properties Stochastic Reaction-Diffusion Equations Parabolic Equations with Grad
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
Directory of Open Access Journals (Sweden)
Matthew J Simpson
Full Text Available Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0
Simpson, Matthew J
2015-01-01
Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction-diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such models have mainly involved solving the PDEs numerically. Here, we present a framework for calculating the exact solution of a linear reaction-diffusion PDE on a growing domain. We derive an exact solution for a general class of one-dimensional linear reaction-diffusion process on 0solutions with numerical approximations confirms the veracity of the method. Furthermore, our examples illustrate a delicate interplay between: (i) the rate at which the domain elongates, (ii) the diffusivity associated with the spreading density profile, (iii) the reaction rate, and (iv) the initial condition. Altering the balance between these four features leads to different outcomes in terms of whether an initial profile, located near x = 0, eventually overcomes the domain growth and colonizes the entire length of the domain by reaching the boundary where x = L(t).
Analytic descriptions of stochastic bistable systems under force ramp.
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.
Hybrid approaches for multiple-species stochastic reaction-diffusion models
Spill, Fabian; Guerrero, Pilar; Alarcon, Tomas; Maini, Philip K.; Byrne, Helen
2015-10-01
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.
Hybrid approaches for multiple-species stochastic reaction-diffusion models.
Spill, Fabian
2015-10-01
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. In this way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.
Reaction-diffusion model of hair-bundle morphogenesis.
Jacobo, Adrian; Hudspeth, A J
2014-10-28
The hair bundle, an apical specialization of the hair cell composed of several rows of regularly organized stereocilia and a kinocilium, is essential for mechanotransduction in the ear. Its precise organization allows the hair bundle to convert mechanical stimuli to electrical signals; mutations that alter the bundle's morphology often cause deafness. However, little is known about the proteins involved in the process of morphogenesis and how the structure of the bundle arises through interactions between these molecules. We present a mathematical model based on simple reaction-diffusion mechanisms that can reproduce the shape and organization of the hair bundle. This model suggests that the boundary of the cell and the kinocilium act as signaling centers that establish the bundle's shape. The interaction of two proteins forms a hexagonal Turing pattern--a periodic modulation of the concentrations of the morphogens, sustained by local activation and long-range inhibition of the reactants--that sets a blueprint for the location of the stereocilia. Finally we use this model to predict how different alterations to the system might impact the shape and organization of the hair bundle.
A fractional reaction-diffusion description of supply and demand
Benzaquen, Michael; Bouchaud, Jean-Philippe
2018-02-01
We suggest that the broad distribution of time scales in financial markets could be a crucial ingredient to reproduce realistic price dynamics in stylised Agent-Based Models. We propose a fractional reaction-diffusion model for the dynamics of latent liquidity in financial markets, where agents are very heterogeneous in terms of their characteristic frequencies. Several features of our model are amenable to an exact analytical treatment. We find in particular that the impact is a concave function of the transacted volume (aka the "square-root impact law"), as in the normal diffusion limit. However, the impact kernel decays as t-β with β = 1/2 in the diffusive case, which is inconsistent with market efficiency. In the sub-diffusive case the decay exponent β takes any value in [0, 1/2], and can be tuned to match the empirical value β ≈ 1/4. Numerical simulations confirm our theoretical results. Several extensions of the model are suggested. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.
Reaction Diffusion Voronoi Diagrams: From Sensors Data to Computing
Directory of Open Access Journals (Sweden)
Alejandro Vázquez-Otero
2015-05-01
Full Text Available In this paper, a new method to solve computational problems using reaction diffusion (RD systems is presented. The novelty relies on the use of a model configuration that tailors its spatiotemporal dynamics to develop Voronoi diagrams (VD as a part of the system’s natural evolution. The proposed framework is deployed in a solution of related robotic problems, where the generalized VD are used to identify topological places in a grid map of the environment that is created from sensor measurements. The ability of the RD-based computation to integrate external information, like a grid map representing the environment in the model computational grid, permits a direct integration of sensor data into the model dynamics. The experimental results indicate that this method exhibits significantly less sensitivity to noisy data than the standard algorithms for determining VD in a grid. In addition, previous drawbacks of the computational algorithms based on RD models, like the generation of volatile solutions by means of excitable waves, are now overcome by final stable states.
A reaction-diffusion model of cholinergic retinal waves.
Directory of Open Access Journals (Sweden)
Benjamin Lansdell
2014-12-01
Full Text Available Prior to receiving visual stimuli, spontaneous, correlated activity in the retina, called retinal waves, drives activity-dependent developmental programs. Early-stage waves mediated by acetylcholine (ACh manifest as slow, spreading bursts of action potentials. They are believed to be initiated by the spontaneous firing of Starburst Amacrine Cells (SACs, whose dense, recurrent connectivity then propagates this activity laterally. Their inter-wave interval and shifting wave boundaries are the result of the slow after-hyperpolarization of the SACs creating an evolving mosaic of recruitable and refractory cells, which can and cannot participate in waves, respectively. Recent evidence suggests that cholinergic waves may be modulated by the extracellular concentration of ACh. Here, we construct a simplified, biophysically consistent, reaction-diffusion model of cholinergic retinal waves capable of recapitulating wave dynamics observed in mice retina recordings. The dense, recurrent connectivity of SACs is modeled through local, excitatory coupling occurring via the volume release and diffusion of ACh. In addition to simulation, we are thus able to use non-linear wave theory to connect wave features to underlying physiological parameters, making the model useful in determining appropriate pharmacological manipulations to experimentally produce waves of a prescribed spatiotemporal character. The model is used to determine how ACh mediated connectivity may modulate wave activity, and how parameters such as the spontaneous activation rate and sAHP refractory period contribute to critical wave size variability.
Nucleation of reaction-diffusion waves on curved surfaces
International Nuclear Information System (INIS)
Kneer, Frederike; Schöll, Eckehard; Dahlem, Markus A
2014-01-01
We study reaction-diffusion waves on curved two-dimensional surfaces, and determine the influence of curvature upon the nucleation and propagation of spatially localized waves in an excitable medium modelled by the generic FitzHugh–Nagumo model. We show that the stability of propagating wave segments depends crucially on the curvature of the surface. As they propagate, they may shrink to the uniform steady state, or expand, depending on whether they are smaller or larger, respectively, than a critical nucleus. This critical nucleus for wave propagation is modified by the curvature acting like an effective space-dependent local spatial coupling, similar to diffuson, thus extending the regime of propagating excitation waves beyond the excitation threshold of flat surfaces. In particular, a negative gradient of Gaussian curvature Γ, as on the outside of a torus surface (positive Γ), when the wave segment symmetrically extends into the inside (negative Γ), allows for stable propagation of localized wave segments remaining unchanged in size and shape, or oscillating periodically in size. (paper)
Directory of Open Access Journals (Sweden)
Lionel Roques
Full Text Available We propose and develop a general approach based on reaction-diffusion equations for modelling a species dynamics in a realistic two-dimensional (2D landscape crossed by linear one-dimensional (1D corridors, such as roads, hedgerows or rivers. Our approach is based on a hybrid "2D/1D model", i.e, a system of 2D and 1D reaction-diffusion equations with homogeneous coefficients, in which each equation describes the population dynamics in a given 2D or 1D element of the landscape. Using the example of the range expansion of the tiger mosquito Aedes albopictus in France and its main highways as 1D corridors, we show that the model can be fitted to realistic observation data. We develop a mechanistic-statistical approach, based on the coupling between a model of population dynamics and a probabilistic model of the observation process. This allows us to bridge the gap between the data (3 levels of infestation, at the scale of a French department and the output of the model (population densities at each point of the landscape, and to estimate the model parameter values using a maximum-likelihood approach. Using classical model comparison criteria, we obtain a better fit and a better predictive power with the 2D/1D model than with a standard homogeneous reaction-diffusion model. This shows the potential importance of taking into account the effect of the corridors (highways in the present case on species dynamics. With regard to the particular case of A. albopictus, the conclusion that highways played an important role in species range expansion in mainland France is consistent with recent findings from the literature.
2016-01-01
We propose and develop a general approach based on reaction-diffusion equations for modelling a species dynamics in a realistic two-dimensional (2D) landscape crossed by linear one-dimensional (1D) corridors, such as roads, hedgerows or rivers. Our approach is based on a hybrid “2D/1D model”, i.e, a system of 2D and 1D reaction-diffusion equations with homogeneous coefficients, in which each equation describes the population dynamics in a given 2D or 1D element of the landscape. Using the example of the range expansion of the tiger mosquito Aedes albopictus in France and its main highways as 1D corridors, we show that the model can be fitted to realistic observation data. We develop a mechanistic-statistical approach, based on the coupling between a model of population dynamics and a probabilistic model of the observation process. This allows us to bridge the gap between the data (3 levels of infestation, at the scale of a French department) and the output of the model (population densities at each point of the landscape), and to estimate the model parameter values using a maximum-likelihood approach. Using classical model comparison criteria, we obtain a better fit and a better predictive power with the 2D/1D model than with a standard homogeneous reaction-diffusion model. This shows the potential importance of taking into account the effect of the corridors (highways in the present case) on species dynamics. With regard to the particular case of A. albopictus, the conclusion that highways played an important role in species range expansion in mainland France is consistent with recent findings from the literature. PMID:26986201
Roques, Lionel; Bonnefon, Olivier
2016-01-01
We propose and develop a general approach based on reaction-diffusion equations for modelling a species dynamics in a realistic two-dimensional (2D) landscape crossed by linear one-dimensional (1D) corridors, such as roads, hedgerows or rivers. Our approach is based on a hybrid "2D/1D model", i.e, a system of 2D and 1D reaction-diffusion equations with homogeneous coefficients, in which each equation describes the population dynamics in a given 2D or 1D element of the landscape. Using the example of the range expansion of the tiger mosquito Aedes albopictus in France and its main highways as 1D corridors, we show that the model can be fitted to realistic observation data. We develop a mechanistic-statistical approach, based on the coupling between a model of population dynamics and a probabilistic model of the observation process. This allows us to bridge the gap between the data (3 levels of infestation, at the scale of a French department) and the output of the model (population densities at each point of the landscape), and to estimate the model parameter values using a maximum-likelihood approach. Using classical model comparison criteria, we obtain a better fit and a better predictive power with the 2D/1D model than with a standard homogeneous reaction-diffusion model. This shows the potential importance of taking into account the effect of the corridors (highways in the present case) on species dynamics. With regard to the particular case of A. albopictus, the conclusion that highways played an important role in species range expansion in mainland France is consistent with recent findings from the literature.
Directory of Open Access Journals (Sweden)
Felicia Shirly Peace
2014-01-01
Full Text Available A mathematical model of the dynamics of the self-ignition of a reaction-diffusion system is studied in this paper. An approximate analytical method (modified Adomian decomposition method is used to solve nonlinear differential equations under steady-state condition. Analytical expressions for concentrations of the gas reactant and the temperature have been derived for Lewis number (Le and parameters β, γ, and ϕ2. Furthermore, in this work, the numerical simulation of the problem is also reported using MATLAB program. An agreement between analytical and numerical results is noted.
A priori L∞ estimates for solutions of a class of reaction-diffusion systems.
Du, Zengji; Peng, Rui
2016-05-01
In this short paper, we establish a priori L∞-norm estimates for solutions of a class of reaction-diffusion systems which can be used to model the spread of infectious disease. The developed technique may find applications in other reaction-diffusion systems.
Pattern formation in reaction-diffusion and ferrofluid systems
Ytreberg, Frederick Martin
2000-11-01
The study of pattern forming systems has been of growing interest to biologists, chemists and physicists in recent years. Generally, these pattern forming systems involve competing interactions that lead to instabilities, driving the system to form a pattern. In this project, we look at two such pattern forming systems. The first is a reaction-diffusion system, where the competition is between the activator and the inhibitor, and the second is a thin layer of ferrofluid which exhibits pattern formation due to a competition between magnetic and surface energies. Numerical simulation of the Gierer-Meinhardt model for reaction and diffusion is used to study the sequence of transitions from islands of high activator concentration to stripes of high activator concentration to wells of depleted activator. This sequence can occur by activator saturation or by inhibitor depletion. Four quantitative measures are introduced which display different trends depending upon whether the transition is driven by activator saturation or inhibitor depletion. These four measures characterize the transitions, and enhance understanding of the system. A model for the Helmholtz free energy is derived to predict aggregate spacing in thin layers of ferrofluid. When a drop of ferrofluid is confined between two glass plates and subjected to an external magnetic field, the particles in the ferrofluid aggregate, forming a hexagonal array. This theoretical model, once fully developed, is used to predict aggregate spacing for this hexagonal pattern as a function of external magnetic field, the ramping rate of the external magnetic field, and plate separation. The results of this model are then compared to experimental data, demonstrating excellent agreement.
Dissipation and displacement of hotspots in reaction-diffusion models of crime.
Short, Martin B; Brantingham, P Jeffrey; Bertozzi, Andrea L; Tita, George E
2010-03-02
The mechanisms driving the nucleation, spread, and dissipation of crime hotspots are poorly understood. As a consequence, the ability of law enforcement agencies to use mapped crime patterns to design crime prevention strategies is severely hampered. We also lack robust expectations about how different policing interventions should impact crime. Here we present a mathematical framework based on reaction-diffusion partial differential equations for studying the dynamics of crime hotspots. The system of equations is based on empirical evidence for how offenders move and mix with potential victims or targets. Analysis shows that crime hotspots form when the enhanced risk of repeat crimes diffuses locally, but not so far as to bind distant crime together. Crime hotspots may form as either supercritical or subcritical bifurcations, the latter the result of large spikes in crime that override linearly stable, uniform crime distributions. Our mathematical methods show that subcritical crime hotspots may be permanently eradicated with police suppression, whereas supercritical hotspots are displaced following a characteristic spatial pattern. Our results thus provide a mechanistic explanation for recent failures to observe crime displacement in experimental field tests of hotspot policing.
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
Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Torres, L.; Escobar-Jiménez, R. F.
2018-02-01
A reaction-diffusion system can be represented by the Gray-Scott model. The reaction-diffusion dynamic is described by a pair of time and space dependent Partial Differential Equations (PDEs). In this paper, a generalization of the Gray-Scott model by using variable-order fractional differential equations is proposed. The variable-orders were set as smooth functions bounded in (0 , 1 ] and, specifically, the Liouville-Caputo and the Atangana-Baleanu-Caputo fractional derivatives were used to express the time differentiation. In order to find a numerical solution of the proposed model, the finite difference method together with the Adams method were applied. The simulations results showed the chaotic behavior of the proposed model when different variable-orders are applied.
The unsaturated bistable stochastic resonance system.
Zhao, Wenli; Wang, Juan; Wang, Linze
2013-09-01
We investigated the characteristics of the output saturation of the classical continuous bistable system (saturation bistable system) and its impact on stochastic resonance (SR). We further proposed a piecewise bistable SR system (unsaturated bistable system) and developed the expression of signal-to-noise ratio (SNR) using the adiabatic approximation theory. Compared with the saturation bistable system, the SNR is significantly improved in our unsaturated bistable SR system. The numerical simulation showed that the unsaturated bistable system performed better in extracting weak signals from strong background noise than the saturation bistable system.
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)
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.
Bistable Mechanisms for Space Applications.
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.
Bistable Mechanisms for Space Applications
Zirbel, Shannon A.; Tolman, Kyler A.; Trease, Brian P.
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. PMID:28030588
A nonlocal and periodic reaction-diffusion-advection model of a single phytoplankton species.
Peng, Rui; Zhao, Xiao-Qiang
2016-02-01
In this article, we are concerned with a nonlocal reaction-diffusion-advection model which describes the evolution of a single phytoplankton species in a eutrophic vertical water column where the species relies solely on light for its metabolism. The new feature of our modeling equation lies in that the incident light intensity and the death rate are assumed to be time periodic with a common period. We first establish a threshold type result on the global dynamics of this model in terms of the basic reproduction number R0. Then we derive various characterizations of R0 with respect to the vertical turbulent diffusion rate, the sinking or buoyant rate and the water column depth, respectively, which in turn give rather precise conditions to determine whether the phytoplankton persist or become extinct. Our theoretical results not only extend the existing ones for the time-independent case, but also reveal new interesting effects of the modeling parameters and the time-periodic heterogeneous environment on persistence and extinction of the phytoplankton species, and thereby suggest important implications for phytoplankton growth control.
Bistable microelectromechanical actuator
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.
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
Computation of effectiveness factor for a reaction-diffusion process ...
African Journals Online (AJOL)
An isothermal and steady state continuity equation for a key component in a catalyst particle was developed and applied to lactose hydrolysis in a fixed bed reactor containing an immobilized enzyme of β-galactosidase on spherical chitosan beads, where lactose (substrate) was taken as the key component. The differential ...
Distributed processing in bistable perception
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
Determinants of bistability in induction of the Escherichia coli lac operon.
Dreisigmeyer, D W; Stajic, J; Nemenman, I; Hlavacek, W S; Wall, M E
2008-09-01
The authors have developed a mathematical model of regulation of expression of the Escherichia coli lac operon, and have investigated bistability in its steady-state induction behaviour in the absence of external glucose. Numerical analysis of equations describing regulation by artificial inducers revealed two natural bistability parameters that can be used to control the range of inducer concentrations over which the model exhibits bistability. By tuning these bistability parameters, the authors found a family of biophysically reasonable systems that are consistent with an experimentally determined bistable region for induction by thio-methylgalactoside (TMG) (in Ozbudak et al. Nature, 2004, 427; p. 737). To model regulation by lactose, the authors developed similar equations in which allolactose, a metabolic intermediate in lactose metabolism and a natural inducer of lac, is the inducer. For biophysically reasonable parameter values, these equations yield no bistability in response to induction by lactose - only systems with an unphysically small permease-dependent export effect can exhibit small amounts of bistability for limited ranges of parameter values. These results cast doubt on the relevance of bistability in the lac operon within the natural context of E. coli, and help shed light on the controversy among existing theoretical studies that address this issue. The results also motivate a deeper experimental characterisation of permease-independent transport of lac inducers, and suggest an experimental approach to address the relevance of bistability in the lac operon within the natural context of E. coli. The sensitivity of lac bistability to the type of inducer emphasises the importance of metabolism in determining the functions of genetic regulatory networks.
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
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.
New mechanism of spiral wave initiation in a reaction-diffusion-mechanics system.
Directory of Open Access Journals (Sweden)
Louis D Weise
Full Text Available Spiral wave initiation in the heart muscle is a mechanism for the onset of dangerous cardiac arrhythmias. A standard protocol for spiral wave initiation is the application of a stimulus in the refractory tail of a propagating excitation wave, a region that we call the "classical vulnerable zone." Previous studies of vulnerability to spiral wave initiation did not take the influence of deformation into account, which has been shown to have a substantial effect on the excitation process of cardiomyocytes via the mechano-electrical feedback phenomenon. In this work we study the effect of deformation on the vulnerability of excitable media in a discrete reaction-diffusion-mechanics (dRDM model. The dRDM model combines FitzHugh-Nagumo type equations for cardiac excitation with a discrete mechanical description of a finite-elastic isotropic material (Seth material to model cardiac excitation-contraction coupling and stretch activated depolarizing current. We show that deformation alters the "classical," and forms a new vulnerable zone at longer coupling intervals. This mechanically caused vulnerable zone results in a new mechanism of spiral wave initiation, where unidirectional conduction block and rotation directions of the consequently initiated spiral waves are opposite compared to the mechanism of spiral wave initiation due to the "classical vulnerable zone." We show that this new mechanism of spiral wave initiation can naturally occur in situations that involve wave fronts with curvature, and discuss its relation to supernormal excitability of cardiac tissue. The concept of mechanically induced vulnerability may lead to a better understanding about the onset of dangerous heart arrhythmias via mechano-electrical feedback.
A reaction-diffusion model of CO2 influx into an oocyte
Somersalo, Erkki; Occhipinti, Rossana; Boron, Walter F.; Calvetti, Daniela
2012-01-01
We have developed and implemented a novel mathematical model for simulating transients in surface pH (pHS) and intracellular pH (pHi) caused by the influx of carbon dioxide (CO2) into a Xenopus oocyte. These transients are important tools for studying gas channels. We assume that the oocyte is a sphere surrounded by a thin layer of unstirred fluid, the extracellular unconvected fluid (EUF), which is in turn surrounded by the well-stirred bulk extracellular fluid (BECF) that represents an infinite reservoir for all solutes. Here, we assume that the oocyte plasma membrane is permeable only to CO2. In both the EUF and intracellular space, solute concentrations can change because of diffusion and reactions. The reactions are the slow equilibration of the CO2 hydration-dehydration reactions and competing equilibria among carbonic acid (H2CO3)/bicarbonate ( HCO3-) and a multitude of non-CO2/HCO3- buffers. Mathematically, the model is described by a coupled system of reaction-diffusion equations that—assuming spherical radial symmetry—we solved using the method of lines with appropriate stiff solvers. In agreement with experimental data (Musa-Aziz et al, PNAS 2009, 106:5406–5411), the model predicts that exposing the cell to extracellular 1.5% CO2/10 mM HCO3- (pH 7.50) causes pHi to fall and pHS to rise rapidly to a peak and then decay. Moreover, the model provides insights into the competition between diffusion and reaction processes when we change the width of the EUF, membrane permeability to CO2, native extra-and intracellular carbonic anhydrase-like activities, the non-CO2/HCO3- (intrinsic) intracellular buffering power, or mobility of intrinsic intracellular buffers. PMID:22728674
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.
Reversibly Bistable Flexible Electronics
Alfaraj, Nasir
2015-05-01
Introducing the notion of transformational silicon electronics has paved the way for integrating various applications with silicon-based, modern, high-performance electronic circuits that are mechanically flexible and optically semitransparent. While maintaining large-scale production and prototyping rapidity, this flexible and translucent scheme demonstrates the potential to transform conventionally stiff electronic devices into thin and foldable ones without compromising long-term performance and reliability. In this work, we report on the fabrication and characterization of reversibly bistable flexible electronic switches that utilize flexible n-channel metal-oxide-semiconductor field-effect transistors. The transistors are fabricated initially on rigid (100) silicon substrates before they are peeled off. They can be used to control flexible batches of light-emitting diodes, demonstrating both the relative ease of scaling at minimum cost and maximum reliability and the feasibility of integration. The peeled-off silicon fabric is about 25 µm thick. The fabricated devices are transferred to a reversibly bistable flexible platform through which, for example, a flexible smartphone can be wrapped around a user’s wrist and can also be set back to its original mechanical position. Buckling and cyclic bending of such host platforms brings a completely new dimension to the development of flexible electronics, especially rollable displays.
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...
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 Series Solution of the Cauchy Problem for Turing Reaction-diffusion Model
Directory of Open Access Journals (Sweden)
L. Päivärinta
2011-12-01
Full Text Available In this paper, the series pattern solution of the Cauchy problem for Turing reaction-diffusion model is obtained by using the homotopy analysis method (HAM. Turing reaction-diffusion model is nonlinear reaction-diffusion system which usually has power-law nonlinearities or may be rewritten in the form of power-law nonlinearities. Using the HAM, it is possible to find the exact solution or an approximate solution of the problem. This technique provides a series of functions which converges rapidly to the exact solution of the problem. The efficiency of the approach will be shown by applying the procedure on two problems. Furthermore, the so-called homotopy-Pade technique (HPT is applied to enlarge the convergence region and rate of solution series given by the HAM.
Dynamic Analysis of a Reaction-Diffusion Rumor Propagation Model
Zhao, Hongyong; Zhu, Linhe
2016-06-01
The rapid development of the Internet, especially the emergence of the social networks, leads rumor propagation into a new media era. Rumor propagation in social networks has brought new challenges to network security and social stability. This paper, based on partial differential equations (PDEs), proposes a new SIS rumor propagation model by considering the effect of the communication between the different rumor infected users on rumor propagation. The stabilities of a nonrumor equilibrium point and a rumor-spreading equilibrium point are discussed by linearization technique and the upper and lower solutions method, and the existence of a traveling wave solution is established by the cross-iteration scheme accompanied by the technique of upper and lower solutions and Schauder’s fixed point theorem. Furthermore, we add the time delay to rumor propagation and deduce the conditions of Hopf bifurcation and stability switches for the rumor-spreading equilibrium point by taking the time delay as the bifurcation parameter. Finally, numerical simulations are performed to illustrate the theoretical results.
A reaction-diffusion model of cytosolic hydrogen peroxide.
Lim, Joseph B; Langford, Troy F; Huang, Beijing K; Deen, William M; Sikes, Hadley D
2016-01-01
As a signaling molecule in mammalian cells, hydrogen peroxide (H2O2) determines the thiol/disulfide oxidation state of several key proteins in the cytosol. Localization is a key concept in redox signaling; the concentrations of signaling molecules within the cell are expected to vary in time and in space in manner that is essential for function. However, as a simplification, all theoretical studies of intracellular hydrogen peroxide and many experimental studies to date have treated the cytosol as a well-mixed compartment. In this work, we incorporate our previously reported reduced kinetic model of the network of reactions that metabolize hydrogen peroxide in the cytosol into a model that explicitly treats diffusion along with reaction. We modeled a bolus addition experiment, solved the model analytically, and used the resulting equations to quantify the spatiotemporal variations in intracellular H2O2 that result from this kind of perturbation to the extracellular H2O2 concentration. We predict that micromolar bolus additions of H2O2 to suspensions of HeLa cells (0.8 × 10(9)cells/l) result in increases in the intracellular concentration that are localized near the membrane. These findings challenge the assumption that intracellular concentrations of H2O2 are increased uniformly throughout the cell during bolus addition experiments and provide a theoretical basis for differing phenotypic responses of cells to intracellular versus extracellular perturbations to H2O2 levels. Copyright © 2015 Elsevier Inc. All rights reserved.
Existence of global solutions for systems of reaction-diffusion equations on unbounded domains
Directory of Open Access Journals (Sweden)
Salah Badraoui
2002-08-01
Full Text Available We consider, an initial-value problem for the thermal-diffusive combustion system $$displaylines{ u_t=aDelta u-uh(v cr v_t=bDelta u+dDelta v+uh(v, }$$ where $a>0$, $d>0$, $beq 0$, $xin mathbb{R}^n$, $ngeq 1$, with $h(v=v^m$, $m$ is an even nonnegative integer, and the initial data $u_0$, $v_0$ are bounded uniformly continuous and nonnegative. It is known that by a simple comparison if $b=0$, $a=1$, $dleq 1$ and $h(v=v^m$ with $min mathbb{N}^*$, the solutions are uniformly bounded in time. When $d>a=1$, $b=0$, $h(v=v^m$ with $min mathbb{N}^*$, Collet and Xin [2] proved the existence of global classical solutions and showed that the $L^infty $ norm of $v$ can not grow faster than $O(loglog t$ for any space dimension. In our case, no comparison principle seems to apply. Nevertheless using techniques form [2], we essentially prove the existence of global classical solutions if $a
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
WNT and DKK Determine Hair Follicle Spacing Through a Reaction-Diffusion Mechanism
Sick, Stefanie; Reinker, Stefan; Timmer, Jens; Schlake, Thomas
2006-12-01
Mathematical reaction-diffusion models have been suggested to describe formation of animal pigmentation patterns and distribution of epidermal appendages. However, the crucial signals and in vivo mechanisms are still elusive. Here we identify WNT and its inhibitor DKK as primary determinants of murine hair follicle spacing, using a combined experimental and computational modeling approach. Transgenic DKK overexpression reduces overall appendage density. Moderate suppression of endogenous WNT signaling forces follicles to form clusters during an otherwise normal morphogenetic program. These results confirm predictions of a WNT/DKK-specific mathematical model and provide in vivo corroboration of the reaction-diffusion mechanism for epidermal appendage formation.
International Nuclear Information System (INIS)
Li Zuoan; Li Kelin
2009-01-01
In this paper, we investigate a class of impulsive fuzzy cellular neural networks with distributed delays and reaction-diffusion terms. By employing the delay differential inequality with impulsive initial conditions and M-matrix theory, we find some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive fuzzy cellular neural networks with distributed delays and reaction-diffusion terms. In particular, the estimate of the exponential converging index is also provided, which depends on the system parameters. An example is given to show the effectiveness of the results obtained here.
International Nuclear Information System (INIS)
Wang Jian; Lu Junguo
2008-01-01
In this paper, we study the global exponential stability of fuzzy cellular neural networks with delays and reaction-diffusion terms. By constructing a suitable Lyapunov functional and utilizing some inequality techniques, we obtain a sufficient condition for the uniqueness and global exponential stability of the equilibrium solution for a class of fuzzy cellular neural networks with delays and reaction-diffusion terms. The result imposes constraint conditions on the network parameters independently of the delay parameter. The result is also easy to check and plays an important role in the design and application of globally exponentially stable fuzzy neural circuits
Hopf bifurcation in a delayed reaction-diffusion-advection population model
Chen, Shanshan; Lou, Yuan; Wei, Junjie
2018-04-01
In this paper, we investigate a reaction-diffusion-advection model with time delay effect. The stability/instability of the spatially nonhomogeneous positive steady state and the associated Hopf bifurcation are investigated when the given parameter of the model is near the principle eigenvalue of an elliptic operator. Our results imply that time delay can make the spatially nonhomogeneous positive steady state unstable for a reaction-diffusion-advection model, and the model can exhibit oscillatory pattern through Hopf bifurcation. The effect of advection on Hopf bifurcation values is also considered, and our results suggest that Hopf bifurcation is more likely to occur when the advection rate increases.
Bistability of Cavity Magnon Polaritons
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.
Bistability of Cavity Magnon Polaritons.
Wang, Yi-Pu; Zhang, Guo-Qiang; Zhang, Dengke; Li, Tie-Fu; Hu, C-M; You, J Q
2018-02-02
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.
Temporal nonlocality in bistable perception
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.
Phase-Reduction Approach to Synchronization of Spatiotemporal Rhythms in Reaction-Diffusion Systems
Nakao, Hiroya; Yanagita, Tatsuo; Kawamura, Yoji
2014-04-01
Reaction-diffusion systems can describe a wide class of rhythmic spatiotemporal patterns observed in chemical and biological systems, such as circulating pulses on a ring, oscillating spots, target waves, and rotating spirals. These rhythmic dynamics can be considered limit cycles of reaction-diffusion systems. However, the conventional phase-reduction theory, which provides a simple unified framework for analyzing synchronization properties of limit-cycle oscillators subjected to weak forcing, has mostly been restricted to low-dimensional dynamical systems. Here, we develop a phase-reduction theory for stable limit-cycle solutions of reaction-diffusion systems with infinite-dimensional state space. By generalizing the notion of isochrons to functional space, the phase-sensitivity function—a fundamental quantity for phase reduction—is derived. For illustration, several rhythmic dynamics of the FitzHugh-Nagumo model of excitable media are considered. Nontrivial phase-response properties and synchronization dynamics are revealed, reflecting their complex spatiotemporal organization. Our theory will provide a general basis for the analysis and control of spatiotemporal rhythms in various reaction-diffusion systems.
Czech Academy of Sciences Publication Activity Database
Eisner, J.; Väth, Martin
2016-01-01
Roč. 135, April (2016), s. 158-193 ISSN 0362-546X Institutional support: RVO:67985840 Keywords : reaction-diffusion system * turing instability * global bifurcation Subject RIV: BA - General Mathematics Impact factor: 1.192, year: 2016 http://www.sciencedirect.com/science/article/pii/S0362546X16000146
Dynamical Behaviors of Stochastic Reaction-Diffusion Cohen-Grossberg Neural Networks with Delays
Directory of Open Access Journals (Sweden)
Li Wan
2012-01-01
Full Text Available This paper investigates dynamical behaviors of stochastic Cohen-Grossberg neural network with delays and reaction diffusion. By employing Lyapunov method, Poincaré inequality and matrix technique, some sufficient criteria on ultimate boundedness, weak attractor, and asymptotic stability are obtained. Finally, a numerical example is given to illustrate the correctness and effectiveness of our theoretical results.
Stochastic reaction-diffusion systems with H\\"older continuous multiplicative noise
Kunze, Markus C.
2012-01-01
We prove pathwise uniqueness and strong existence of solutions for stochastic reaction-diffusion systems with locally Lipschitz continuous reaction term of polynomial growth and H\\"older continuous multiplicative noise. Under additional assumptions on the coefficients, we also prove positivity of the solutions.
Czech Academy of Sciences Publication Activity Database
Eisner, J.; Väth, Martin
2016-01-01
Roč. 135, April (2016), s. 158-193 ISSN 0362-546X Institutional support: RVO:67985840 Keywords : reaction -diffusion system * turing instability * global bifurcation Subject RIV: BA - General Mathematics Impact factor: 1.192, year: 2016 http://www.sciencedirect.com/science/article/pii/S0362546X16000146
Stability results for a reaction-diffusion system with a single measurement
Energy Technology Data Exchange (ETDEWEB)
Ramoul, Hichem [Centre universitaire de Khenchela, Route de Batna, BP 1252, Liberte, 40004 Khenchela (Algeria); Gaitan, Patricia [Laboratoire d' analyse, topologie, probabilites CNRS UMR 6632, Marseille (France) and Universite Aix-Marseille II (France); Cristofol, Michel [Laboratoire d' analyse, topologie, probabilites CNRS UMR 6632, Marseille, France and Universite Aix-Marseille III (France)
2007-06-15
For a two by two reaction-diffusion system on a bounded domain we give a simultaneous stability result for one coefficient and for the initial conditions. The key ingredient is a global Carleman-type estimate with a single observation acting on a subdomain.
Trend to equilibrium for a reaction-diffusion system modelling reversible enzyme reaction
Elias, Jan
2016-01-01
20 pages; A spatio-temporal evolution of chemicals appearing in a reversible enzyme reaction and modelled by a four component reaction-diffusion system with the reaction terms obtained by the law of mass action is considered. The large time behaviour of the system is studied by means of entropy methods.
Trend to Equilibrium for a Reaction-Diffusion System Modelling Reversible Enzyme Reaction.
Eliaš, Ján
2018-01-01
A spatio-temporal evolution of chemicals appearing in a reversible enzyme reaction and modelled by a four-component reaction-diffusion system with the reaction terms obtained by the law of mass action is considered. The large time behaviour of the system is studied by means of entropy methods.
Perceptual incongruence influences bistability and cortical activation
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
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
Spatial bistability generates hunchback expression sharpness in the Drosophila embryo.
Directory of Open Access Journals (Sweden)
Francisco J P Lopes
2008-09-01
Full Text Available During embryonic development, the positional information provided by concentration gradients of maternal factors directs pattern formation by providing spatially dependent cues for gene expression. In the fruit fly, Drosophila melanogaster, a classic example of this is the sharp on-off activation of the hunchback (hb gene at midembryo, in response to local concentrations of the smooth anterior-posterior Bicoid (Bcd gradient. The regulatory region for hb contains multiple binding sites for the Bcd protein as well as multiple binding sites for the Hb protein. Some previous studies have suggested that Bcd is sufficient for properly sharpened Hb expression, yet other evidence suggests a need for additional regulation. We experimentally quantified the dynamics of hb gene expression in flies that were wild-type, were mutant for hb self-regulation or Bcd binding, or contained an artificial promoter construct consisting of six Bcd and two Hb sites. In addition to these experiments, we developed a reaction-diffusion model of hb transcription, with Bcd cooperative binding and hb self-regulation, and used Zero Eigenvalue Analysis to look for multiple stationary states in the reaction network. Our model reproduces the hb developmental dynamics and correctly predicts the mutant patterns. Analysis of our model indicates that the Hb sharpness can be produced by spatial bistability, in which hb self-regulation produces two stable levels of expression. In the absence of self-regulation, the bistable behavior vanishes and Hb sharpness is disrupted. Bcd cooperative binding affects the position where bistability occurs but is not itself sufficient for a sharp Hb pattern. Our results show that the control of Hb sharpness and positioning, by hb self-regulation and Bcd cooperativity, respectively, are separate processes that can be altered independently. Our model, which matches the changes in Hb position and sharpness observed in different experiments, provides a
On the bistable zone of milling processes.
Dombovari, Zoltan; Stepan, Gabor
2015-09-28
A modal-based model of milling machine tools subjected to time-periodic nonlinear cutting forces is introduced. The model describes the phenomenon of bistability for certain cutting parameters. In engineering, these parameter domains are referred to as unsafe zones, where steady-state milling may switch to chatter for certain perturbations. In mathematical terms, these are the parameter domains where the periodic solution of the corresponding nonlinear, time-periodic delay differential equation is linearly stable, but its domain of attraction is limited due to the existence of an unstable quasi-periodic solution emerging from a secondary Hopf bifurcation. A semi-numerical method is presented to identify the borders of these bistable zones by tracking the motion of the milling tool edges as they might leave the surface of the workpiece during the cutting operation. This requires the tracking of unstable quasi-periodic solutions and the checking of their grazing to a time-periodic switching surface in the infinite-dimensional phase space. As the parameters of the linear structural behaviour of the tool/machine tool system can be obtained by means of standard modal testing, the developed numerical algorithm provides efficient support for the design of milling processes with quick estimates of those parameter domains where chatter can still appear in spite of setting the parameters into linearly stable domains. © 2015 The Authors.
Interface dynamics and domain growth in thermally bistable fluids
International Nuclear Information System (INIS)
Shaviv, N.J.; Regev, O.
1994-01-01
Domain growth kinetics in a thermally bistable fluid with heat diffusion is studied. The time evolution of interfaces between the stable phases is calculated numerically in two dimensions and compared to some general results derived analytically. The qualitative behavior is found to be similar to the previously studied cases where fluid dynamics was neglected. There are, however, several important differences such as the value of the dynamical exponent, which determines the power law of the system's correlation length growth. The introduction of fluid motion into the model introduces additional properties, unfamiliar to previously studied systems, like the change of the pressure or the size of the system. This behavior is due to the advection of mass. The present model may have general relevance to any system modeled by a real Ginzburg-Landau-type equation coupled to fluid dynamical conservation equations. In particular, it is a step forward on the way to a faithful modeling of thermally bistable cloudy astrophysical media
Functionally rigid bistable [2]rotaxanes
DEFF Research Database (Denmark)
Nygaard, Sune; Leung, Ken C-F; Aprahamian, Ivan
2007-01-01
was investigated as a means to simplify both molecular structure and switching function previously observed in related bistable [2]rotaxanes with flexible spacers between their stations and incorporating a cyclobis(paraquat-p-phenylene) (CBPQT4+) ring. The nondegenerate MPTTF-NP switch was isolated as near isomer......-free bistable [2]rotaxane. Utilization of MPTTF removes the cis/trans isomerization that characterizes the tetrathiafulvalene (TTF) parent core structure. Furthermore, only one translational isomer is observed (> 95 ... component resides, to all intents and purposes, predominantly on the MPTTF unit in the ground state. As a consequence of these two effects, the assignment of NMR and UV-vis data is more simplified as compared to previous donor-acceptor bistable [2]rotaxanes. This development has not only allowed for much...
Optical bistability controlling light with light
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
Flow-induced symmetry reduction in two-dimensional reaction-diffusion system
Hu, Hai Xiang; Li, Xiao Chun; Li, Qian Shu
2009-03-01
The influence of uniform flow on the pattern formation is investigated in a two-dimensional reaction-diffusion system. It is found that the convective flow plays a key role on pattern modulation. Both traveling and stationary periodic patterns are obtained. At moderate flow rates, the perfect hexagon, phase-shifted hexagon and stable square, which are essentially unstable in unperturbed reaction-diffusion systems, are obtained. These patterns move downstream. If the flow rate is increased further, the stationary flow-oriented stripes develop and compete with the spots. If the flow rate exceeds some critical value, the system is convectively unstable and the stationary stripes prevail against the traveling spots. The above patterns all have the same critical wavenumber associated with Turing bifurcation, which indicates that Turing instability produces the patterns while the flow induces the symmetry reduction, i.e., from six-fold symmetry to four-fold one, and to two-fold one ultimately.
Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains
Madzvamuse, Anotida
2009-08-29
By using asymptotic theory, we generalise the Turing diffusively-driven instability conditions for reaction-diffusion systems with slow, isotropic domain growth. There are two fundamental biological differences between the Turing conditions on fixed and growing domains, namely: (i) we need not enforce cross nor pure kinetic conditions and (ii) the restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Our theoretical findings are confirmed and reinforced by numerical simulations for the special cases of isotropic linear, exponential and logistic growth profiles. In particular we illustrate an example of a reaction-diffusion system which cannot exhibit a diffusively-driven instability on a fixed domain but is unstable in the presence of slow growth. © Springer-Verlag 2009.
Event-triggered synchronization for reaction-diffusion complex networks via random sampling
Dong, Tao; Wang, Aijuan; Zhu, Huiyun; Liao, Xiaofeng
2018-04-01
In this paper, the synchronization problem of the reaction-diffusion complex networks (RDCNs) with Dirichlet boundary conditions is considered, where the data is sampled randomly. An event-triggered controller based on the sampled data is proposed, which can reduce the number of controller and the communication load. Under this strategy, the synchronization problem of the diffusion complex network is equivalently converted to the stability of a of reaction-diffusion complex dynamical systems with time delay. By using the matrix inequality technique and Lyapunov method, the synchronization conditions of the RDCNs are derived, which are dependent on the diffusion term. Moreover, it is found the proposed control strategy can get rid of the Zeno behavior naturally. Finally, a numerical example is given to verify the obtained results.
Bistable microvalve and microcatheter system
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.
Compact-like kink in a real electrical reaction-diffusion chain
Energy Technology Data Exchange (ETDEWEB)
Comte, J.C. [Laboratoire de Physiopathologie des Reseaux Neuronaux du Cycle Veille-Sommeil, CNRS UMR 5167, Faculte de Medecine Laennec 7, Rue Guillaume Paradin, 69372 Lyon Cedex 08 (France)]. E-mail: comtejc@sommeil.univ-lyon1.fr; Marquie, P. [Laboratoire d' Electronique, Informatique et Image (LE2i) UMR CNRS 5158, Aile des Sciences de l' Ingenieur, BP 47870, 21078 Dijon Cedex (France)
2006-07-15
We demonstrate experimentally the compact-like kinks existence in a real electrical reaction-diffusion chain. Our measures show that such entities are strictly localized and consequently present a finite spatial extent. We show equally that the kink velocity is threshold-dependent. A theoretical quantification of the critical coupling under which propagation fails is also achieved and reveals that nonlinear coupling leads to a propagation failure reduction.
Czech Academy of Sciences Publication Activity Database
Ainsworth, M.; Vejchodský, Tomáš
2011-01-01
Roč. 119, č. 2 (2011), s. 219-243 ISSN 0029-599X R&D Projects: GA AV ČR IAA100760702; GA ČR(CZ) GA102/07/0496 Institutional research plan: CEZ:AV0Z10190503 Keywords : a posteriori error estimates * singularly perturbed problems * reaction-diffusion Subject RIV: BA - General Mathematics Impact factor: 1.321, year: 2011 http://www.springerlink.com/content/d384608709584278/
STEPS: Modeling and Simulating Complex Reaction-Diffusion Systems with Python
Wils, Stefan; Schutter, Erik De
2009-01-01
We describe how the use of the Python language improved the user interface of the program STEPS. STEPS is a simulation platform for modeling and stochastic simulation of coupled reaction-diffusion systems with complex 3-dimensional boundary conditions. Setting up such models is a complicated process that consists of many phases. Initial versions of STEPS relied on a static input format that did not cleanly separate these phases, limiting modelers in how they could control the simulation and b...
Czech Academy of Sciences Publication Activity Database
Baltaev, J.I.; Kučera, Milan; Väth, Martin
2012-01-01
Roč. 57, č. 2 (2012), s. 143-165 ISSN 0862-7940 R&D Projects: GA AV ČR IAA100190805 Institutional research plan: CEZ:AV0Z10190503 Keywords : reaction -diffusion system * unilateral condition * variational inequality Subject RIV: BA - General Mathematics Impact factor: 0.222, year: 2012 http://www.springerlink.com/content/e1km86727356pl88/
Bifurcation points for a reaction-diffusion system with two inequalities
Czech Academy of Sciences Publication Activity Database
Eisner, J.; Kučera, Milan; Väth, M.
2010-01-01
Roč. 365, č. 1 (2010), s. 176-194 ISSN 0022-247X R&D Projects: GA AV ČR IAA100190805 Institutional research plan: CEZ:AV0Z10190503 Keywords : global bifurcation * degree * stationary solutions * reaction -diffusion system * variational inequality * Signorini boundary condition * Laplace operator Subject RIV: BA - General Mathematics Impact factor: 1.174, year: 2010 http://www.sciencedirect.com/science/article/pii/S0022247X09008579
Location of bifurcation points for a reaction-diffusion system with Neumann-Signorini conditions
Czech Academy of Sciences Publication Activity Database
Eisner, J.; Väth, Martin
2011-01-01
Roč. 11, č. 4 (2011), s. 809-836 ISSN 1536-1365 R&D Projects: GA AV ČR IAA100190805 Institutional research plan: CEZ:AV0Z10190503 Keywords : global bifurcation * stationary solutions * reaction -diffusion system Subject RIV: BA - General Mathematics Impact factor: 0.644, year: 2011 http://www.advancednonlinearstudies.com/Archive/V11N4/ANLS_V11N4_pg809-836.pdf
International Nuclear Information System (INIS)
Lou, X.; Cui, B.
2008-01-01
In this paper we consider the problem of exponential stability for recurrent neural networks with multiple time varying delays and reaction-diffusion terms. The activation functions are supposed to be bounded and globally Lipschitz continuous. By means of Lyapunov functional, sufficient conditions are derived, which guarantee global exponential stability of the delayed neural network. Finally, a numerical example is given to show the correctness of our analysis. (author)
Kouvaris, Nikos E; Sebek, Michael; Iribarne, Albert; Díaz-Guilera, Albert; Kiss, István Z
2017-04-01
We present theoretical and experimental studies on pattern formation with bistable dynamical units coupled in a star network configuration. By applying a localized perturbation to the central or the peripheral elements, we demonstrate the subsequent spreading, pinning, or retraction of the activations; such analysis enables the characterization of the formation of stationary patterns of localized activity. The results are interpreted with a theoretical analysis of a simplified bistable reaction-diffusion model. Weak coupling results in trivial pinned states where the activation cannot propagate. At strong coupling, a uniform state is expected with active or inactive elements at small or large degree networks, respectively. A nontrivial stationary spatial pattern, corresponding to an activation pinning, is predicted to occur at an intermediate number of peripheral elements and at intermediate coupling strengths, where the central activation of the network is pinned, but the peripheral activation propagates toward the center. The results are confirmed in experiments with star networks of bistable electrochemical reactions. The experiments confirm the existence of the stationary spatial patterns and the dependence of coupling strength on the number of peripheral elements for transitions between pinned and retreating or spreading fronts in forced network configurations (where the central or periphery elements are forced to maintain their states).
International Nuclear Information System (INIS)
Song Qiankun; Cao Jinde
2005-01-01
Both exponential stability and periodic solutions are considered for a class of bi-directional associative memory (BAM) neural networks with delays and reaction-diffusion terms by constructing suitable Lyapunov functional and some analysis techniques. The general sufficient conditions are given ensuring the global exponential stability and existence of periodic solutions of BAM neural networks with delays and reaction-diffusion terms. These presented conditions are in terms of system parameters and have important leading significance in the design and applications of globally exponentially stable and periodic oscillatory neural circuits for BAM with delays and reaction-diffusion terms
Flexible Bistable Cholesteric Reflective Displays
Yang, Deng-Ke
2006-03-01
Cholesteric liquid crystals (ChLCs) exhibit two stable states at zero field condition-the reflecting planar state and the nonreflecting focal conic state. ChLCs are an excellent candidate for inexpensive and rugged electronic books and papers. This paper will review the display cell structure,materials and drive schemes for flexible bistable cholesteric (Ch) reflective displays.
Ford Versypt, Ashlee N; Arendt, Paul D; Pack, Daniel W; Braatz, Richard D
2015-01-01
A mathematical reaction-diffusion model is defined to describe the gradual decomposition of polymer microspheres composed of poly(D,L-lactic-co-glycolic acid) (PLGA) that are used for pharmaceutical drug delivery over extended periods of time. The partial differential equation (PDE) model treats simultaneous first-order generation due to chemical reaction and diffusion of reaction products in spherical geometry to capture the microsphere-size-dependent effects of autocatalysis on PLGA erosion that occurs when the microspheres are exposed to aqueous media such as biological fluids. The model is solved analytically for the concentration of the autocatalytic carboxylic acid end groups of the polymer chains that comprise the microspheres as a function of radial position and time. The analytical solution for the reaction and transport of the autocatalytic chemical species is useful for predicting the conditions under which drug release from PLGA microspheres transitions from diffusion-controlled to erosion-controlled release, for understanding the dynamic coupling between the PLGA degradation and erosion mechanisms, and for designing drug release particles. The model is the first to provide an analytical prediction for the dynamics and spatial heterogeneities of PLGA degradation and erosion within a spherical particle. The analytical solution is applicable to other spherical systems with simultaneous diffusive transport and first-order generation by reaction.
Hallock, Michael J; Stone, John E; Roberts, Elijah; Fry, Corey; Luthey-Schulten, Zaida
2014-05-01
Simulation of in vivo cellular processes with the reaction-diffusion master equation (RDME) is a computationally expensive task. Our previous software enabled simulation of inhomogeneous biochemical systems for small bacteria over long time scales using the MPD-RDME method on a single GPU. Simulations of larger eukaryotic systems exceed the on-board memory capacity of individual GPUs, and long time simulations of modest-sized cells such as yeast are impractical on a single GPU. We present a new multi-GPU parallel implementation of the MPD-RDME method based on a spatial decomposition approach that supports dynamic load balancing for workstations containing GPUs of varying performance and memory capacity. We take advantage of high-performance features of CUDA for peer-to-peer GPU memory transfers and evaluate the performance of our algorithms on state-of-the-art GPU devices. We present parallel e ciency and performance results for simulations using multiple GPUs as system size, particle counts, and number of reactions grow. We also demonstrate multi-GPU performance in simulations of the Min protein system in E. coli . Moreover, our multi-GPU decomposition and load balancing approach can be generalized to other lattice-based problems.
DEFF Research Database (Denmark)
Sönmez, Ümit; Tutum, Cem Celal
2008-01-01
In this work, a new compliant bistable mechanism design is introduced. The combined use of pseudo-rigid-body model (PRBM) and the Elastica buckling theory is presented for the first time to analyze the new design. This mechanism consists of the large deflecting straight beams, buckling beams......, and a slider. The kinematic analysis of this new mechanism is studied, using nonlinear Elastica buckling beam theory, the PRBM of a large deflecting cantilever beam, the vector loop closure equations, and numerically solving nonlinear algebraic equations. A design method of the bistable mechanism...
Avcu, N; Alyürük, H; Demir, G K; Pekergin, F; Cavas, L; Güzeliş, C
2015-06-01
This paper employs the root locus method to conduct a detailed investigation of the parameter regions that ensure bistability in a well-studied gene regulatory network namely, lac operon of Escherichia coli (E. coli). In contrast to previous works, the parametric bistability conditions observed in this study constitute a complete set of necessary and sufficient conditions. These conditions were derived by applying the root locus method to the polynomial equilibrium equation of the lac operon model to determine the parameter values yielding the multiple real roots necessary for bistability. The lac operon model used was defined as an ordinary differential equation system in a state equation form with a rational right hand side, and it was compatible with the Hill and Michaelis-Menten approaches of enzyme kinetics used to describe biochemical reactions that govern lactose metabolism. The developed root locus method can be used to study the steady-state behavior of any type of convergent biological system model based on mass action kinetics. This method provides a solution to the problem of analyzing gene regulatory networks under parameter uncertainties because the root locus method considers the model parameters as variable, rather than fixed. The obtained bistability ranges for the lac operon model parameters have the potential to elucidate the appearance of bistability for E. coli cells in in vivo experiments, and they could also be used to design robust hysteretic switches in synthetic biology. Copyright © 2015 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Nguyen Van Phu; Dinh Van Hoang
2005-01-01
In this paper is presented the transformation of characteristics of optical bistability effect and of generated pulses in operation of a DFB laser with two sections. By solving the rate equations describing the operation of this laser the appearance of optical bistability effect in stationary regime and of short pulses in transient regime is obtained. With the variation of dynamical laser parameter we can evaluate the transformation indicated above. The method of examination used here is simple for determining the influence of any dynamical laser parameter on characteristics of optical bistability effect and generated pulses. (author)
Lacitignola, Deborah; Bozzini, Benedetto; Frittelli, Massimo; Sgura, Ivonne
2017-07-01
The present paper deals with the pattern formation properties of a specific morpho-electrochemical reaction-diffusion model on a sphere. The physico-chemical background to this study is the morphological control of material electrodeposited onto spherical particles. The particular experimental case of interest refers to the optimization of novel metal-air flow batteries and addresses the electrodeposition of zinc onto inert spherical supports. Morphological control in this step of the high-energy battery operation is crucial to the energetic efficiency of the recharge process and to the durability of the whole energy-storage device. To rationalise this technological challenge within a mathematical modeling perspective, we consider the reaction-diffusion system for metal electrodeposition introduced in [Bozzini et al., J. Solid State Electr.17, 467-479 (2013)] and extend its study to spherical domains. Conditions are derived for the occurrence of the Turing instability phenomenon and the steady patterns emerging at the onset of Turing instability are investigated. The reaction-diffusion system on spherical domains is solved numerically by means of the Lumped Surface Finite Element Method (LSFEM) in space combined with the IMEX Euler method in time. The effect on pattern formation of variations in the domain size is investigated both qualitatively, by means of systematic numerical simulations, and quantitatively by introducing suitable indicators that allow to assign each pattern to a given morphological class. An experimental validation of the obtained results is finally presented for the case of zinc electrodeposition from alkaline zincate solutions onto copper spheres.
A reaction-diffusion model of ROS-induced ROS release in a mitochondrial network.
Directory of Open Access Journals (Sweden)
Lufang Zhou
2010-01-01
Full Text Available Loss of mitochondrial function is a fundamental determinant of cell injury and death. In heart cells under metabolic stress, we have previously described how the abrupt collapse or oscillation of the mitochondrial energy state is synchronized across the mitochondrial network by local interactions dependent upon reactive oxygen species (ROS. Here, we develop a mathematical model of ROS-induced ROS release (RIRR based on reaction-diffusion (RD-RIRR in one- and two-dimensional mitochondrial networks. The nodes of the RD-RIRR network are comprised of models of individual mitochondria that include a mechanism of ROS-dependent oscillation based on the interplay between ROS production, transport, and scavenging; and incorporating the tricarboxylic acid (TCA cycle, oxidative phosphorylation, and Ca(2+ handling. Local mitochondrial interaction is mediated by superoxide (O2.- diffusion and the O2.(--dependent activation of an inner membrane anion channel (IMAC. In a 2D network composed of 500 mitochondria, model simulations reveal DeltaPsi(m depolarization waves similar to those observed when isolated guinea pig cardiomyocytes are subjected to a localized laser-flash or antioxidant depletion. The sensitivity of the propagation rate of the depolarization wave to O(2.- diffusion, production, and scavenging in the reaction-diffusion model is similar to that observed experimentally. In addition, we present novel experimental evidence, obtained in permeabilized cardiomyocytes, confirming that DeltaPsi(m depolarization is mediated specifically by O2.-. The present work demonstrates that the observed emergent macroscopic properties of the mitochondrial network can be reproduced in a reaction-diffusion model of RIRR. Moreover, the findings have uncovered a novel aspect of the synchronization mechanism, which is that clusters of mitochondria that are oscillating can entrain mitochondria that would otherwise display stable dynamics. The work identifies the
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.
Existence and exponential stability of traveling waves for delayed reaction-diffusion systems
Hsu, Cheng-Hsiung; Yang, Tzi-Sheng; Yu, Zhixian
2018-03-01
The purpose of this work is to investigate the existence and exponential stability of traveling wave solutions for general delayed multi-component reaction-diffusion systems. Following the monotone iteration scheme via an explicit construction of a pair of upper and lower solutions, we first obtain the existence of monostable traveling wave solutions connecting two different equilibria. Then, applying the techniques of weighted energy method and comparison principle, we show that all solutions of the Cauchy problem for the considered systems converge exponentially to traveling wave solutions provided that the initial perturbations around the traveling wave fronts belong to a suitable weighted Sobolev space.
International Nuclear Information System (INIS)
Wang Linshan; Zhang Zhe; Wang Yangfan
2008-01-01
Some criteria for the global stochastic exponential stability of the delayed reaction-diffusion recurrent neural networks with Markovian jumping parameters are presented. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, which are governed by a Markov process with discrete and finite state space. By employing a new Lyapunov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish some easy-to-test criteria of global exponential stability in the mean square for the stochastic neural networks. The criteria are computationally efficient, since they are in the forms of some linear matrix inequalities
Global existence and blowup for free boundary problems of coupled reaction-diffusion systems
Directory of Open Access Journals (Sweden)
Jianping Sun
2014-05-01
Full Text Available This article concerns a free boundary problem for a reaction-diffusion system modeling the cooperative interaction of two diffusion biological species in one space dimension. First we show the existence and uniqueness of a local classical solution, then we study the asymptotic behavior of the free boundary problem. Our results show that the free boundary problem admits a global solution if the inter-specific competitions are strong, while, if the inter-specific competitions are weak, there exist the blowup solution and a global fast solution.
Mahara, Hitoshi; Okada, Koichi; Nomura, Atsushi; Miike, Hidetoshi; Sakurai, Tatsunari
2009-07-01
We found a rotating global structure induced by the dynamical force of local chemical activity in a thin solution layer of excitable Belousov-Zhabotinsky reaction coupled with diffusion. The surface flow and deformation associated with chemical spiral waves (wavelength about 1 mm) represents a global unidirectional structure and a global tilt in the entire Petri dish (100 mm in diameter), respectively. For these observations, we scanned the condition of hierarchal pattern selection. From this result, the bromomalonic acid has an important role to induce the rotating global structure. An interaction between a reaction-diffusion process and a surface-tension-driven effect leads to such hierarchal pattern with different scales.
Basin of Attraction of Solutions with Pattern Formation in Slow-Fast Reaction-Diffusion Systems.
Ambrosio, B; Aziz-Alaoui, M A
2016-12-01
This article is devoted to the characterization of the basin of attraction of pattern solutions for some slow-fast reaction-diffusion systems with a symmetric property and an underlying oscillatory reaction part. We characterize some subsets of initial conditions that prevent the dynamical system to evolve asymptotically toward solutions which are homogeneous in space. We also perform numerical simulations that illustrate theoretical results and give rise to symmetric and non-symmetric pattern solutions. We obtain these last solutions by choosing particular random initial conditions.
Adaptive exponential synchronization of delayed neural networks with reaction-diffusion terms
International Nuclear Information System (INIS)
Sheng Li; Yang Huizhong; Lou Xuyang
2009-01-01
This paper presents an exponential synchronization scheme for a class of neural networks with time-varying and distributed delays and reaction-diffusion terms. An adaptive synchronization controller is derived to achieve the exponential synchronization of the drive-response structure of neural networks by using the Lyapunov stability theory. At the same time, the update laws of parameters are proposed to guarantee the synchronization of delayed neural networks with all parameters unknown. It is shown that the approaches developed here extend and improve the ideas presented in recent literatures.
Externally controlled anisotropy in pattern-forming reaction-diffusion systems.
Escala, Dario M; Guiu-Souto, Jacobo; Muñuzuri, Alberto P
2015-06-01
The effect of centrifugal forces is analyzed in a pattern-forming reaction-diffusion system. Numerical simulations conducted on the appropriate extension of the Oregonator model for the Belousov-Zhabotinsky reaction show a great variety of dynamical behaviors in such a system. In general, the system exhibits an anisotropy that results in new types of patterns or in a global displacement of the previous one. We consider the effect of both constant and periodically modulated centrifugal forces on the different types of patterns that the system may exhibit. A detailed analysis of the patterns and behaviors observed for the different parameter values considered is presented here.
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
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)
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
International Nuclear Information System (INIS)
Li, Li; Li-Xue, Chen; Xin-Lu, Zhang
2009-01-01
We present theoretically a novel intrinsic optical bistability (IOB) in the Tm 3+ /Yb 3+ codoped system with a photon avalanche mechanism. Numerical simulations based on the rate equation model demonstrate distinct IOB hysteresis and critical slowing dynamics around the avalanche thresholds. Such an IOB characteristic in Tm 3+ /Yb 3+ codoped crystal has potential applications in solid-state bistable optical displays and luminescence switchers in visible-infrared spectra. (fundamental areas of phenomenology (including applications))
Bistable diverter valve in microfluidics
Czech Academy of Sciences Publication Activity Database
Tesař, Václav; Bandulasena, H.C.H.
2011-01-01
Roč. 50, č. 5 (2011), s. 1225-1233 ISSN 0723-4864 R&D Projects: GA ČR GA101/07/1499; GA AV ČR IAA200760705 Institutional research plan: CEZ:AV0Z20760514 Keywords : fluidics * bistable diverter valves * pressure-driven microfluidics Subject RIV: BK - Fluid Dynamics Impact factor: 1.735, year: 2011 http://www.springerlink.com/content/x4907p1908151522/
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.
Bistability in biochemical signaling models.
Sobie, Eric A
2011-09-20
This Teaching Resource provides lecture notes, slides, and a student assignment for a two-part lecture on the principles underlying bistability in biochemical signaling networks, which are illustrated with examples from the literature. The lectures cover analog, or graded, versus digital, all-or-none, responses in cells, with examples from different types of biological processes requiring each. Rate-balance plots are introduced as a method for determining whether generic one-variable systems exhibit one or several stable steady states. Bifurcation diagrams are presented as a more general method for detecting the presence of bistability in biochemical signaling networks. The examples include an artificial toggle switch, the lac operon in bacteria, and the mitogen-activated protein kinase cascade in both Xenopus oocytes and mammalian cells. The second part of the lecture links the concepts of bistability more closely to the mathematical tools provided by dynamical systems analysis. The examples from the first part of the lecture are analyzed with phase-plane techniques and bifurcation analysis, using the scientific programming language MATLAB. Using these programs as a template, the assignment requires the students to implement a model from the literature and analyze the stability of this model's steady states.
Brain networks underlying bistable perception.
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.
International Nuclear Information System (INIS)
Wang Guang-Qing; Liao Wei-Hsin
2015-01-01
This work focuses on how to maintain a high-energy orbit motion of a bistable oscillator when subjected to a low level excitation. An elastic magnifier (EM) positioned between the base and the bistable oscillator is used to magnify the base vibration displacement to significantly enhance the output characteristics of the bistable oscillator. The dimensionless electromechanical equations of the bistable oscillator with an EM are derived, and the effects of the mass and stiffness ratios between the EM and the bistable oscillator on the output displacement are studied. It is shown that the jump phenomenon occurs at a lower excitation level with increasing the mass and stiffness ratios. With the comparison of the displacement trajectories and the phase portraits obtained from experiments, it is validated that the bistable oscillator with an EM can effectively oscillate in a high-energy orbit and can generate a superior output vibration at a low excitation level as compared with the bistable oscillator without an EM. (paper)
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)
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
Diversity and functional properties of bistable pigments.
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.
Switching between bistable states in a discrete nonlinear model with long-range dispersion
DEFF Research Database (Denmark)
Johansson, Magnus; Gaididei, Yuri B.; Christiansen, Peter Leth
1998-01-01
In the framework of a discrete nonlinear Schrodinger equation with long-range dispersion, we propose a general mechanism for obtaining a controlled switching between bistable localized excitations. We show that the application of a spatially symmetric kick leads to the excitation of an internal...
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.
Yuvan, Steven; Bier, Martin
2018-02-01
Two decades ago Bak et al. (1997) [3] proposed a reaction-diffusion model to describe market fluctuations. In the model buyers and sellers diffuse from opposite ends of a 1D interval that represents a price range. Trades occur when buyers and sellers meet. We show analytically and numerically that the model well reproduces the square-root relation between traded volumes and price changes that is observed in real-life markets. The result is remarkable as this relation has commonly been explained in terms of more elaborate trader strategies. We furthermore explain why the square-root relation is robust under model modifications and we show how real-life bond market data exhibit the square-root relation.
Critical regimes driven by recurrent mobility patterns of reaction-diffusion processes in networks
Gómez-Gardeñes, J.; Soriano-Paños, D.; Arenas, A.
2018-04-01
Reaction-diffusion processes1 have been widely used to study dynamical processes in epidemics2-4 and ecology5 in networked metapopulations. In the context of epidemics6, reaction processes are understood as contagions within each subpopulation (patch), while diffusion represents the mobility of individuals between patches. Recently, the characteristics of human mobility7, such as its recurrent nature, have been proven crucial to understand the phase transition to endemic epidemic states8,9. Here, by developing a framework able to cope with the elementary epidemic processes, the spatial distribution of populations and the commuting mobility patterns, we discover three different critical regimes of the epidemic incidence as a function of these parameters. Interestingly, we reveal a regime of the reaction-diffussion process in which, counter-intuitively, mobility is detrimental to the spread of disease. We analytically determine the precise conditions for the emergence of any of the three possible critical regimes in real and synthetic networks.
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.
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)
International Nuclear Information System (INIS)
Hepburn, I.; De Schutter, E.; Chen, W.
2016-01-01
Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either in a discrete time or discrete space framework, which has led to the development of parallel methods that can take advantage of the power of modern supercomputers in recent years. We systematically test suggested components of stochastic reaction-diffusion operator splitting in the literature and discuss their effects on accuracy. We introduce an operator splitting implementation for irregular meshes that enhances accuracy with minimal performance cost. We test a range of models in small-scale MPI simulations from simple diffusion models to realistic biological models and find that multi-dimensional geometry partitioning is an important consideration for optimum performance. We demonstrate performance gains of 1-3 orders of magnitude in the parallel implementation, with peak performance strongly dependent on model specification.
Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources
Directory of Open Access Journals (Sweden)
Ida de Bonis
2017-09-01
Full Text Available We discuss the existence of a class of weak solutions to a nonlinear parabolic system of reaction-diffusion type endowed with singular production terms by reaction. The singularity is due to a potential occurrence of quenching localized to the domain boundary. The kind of quenching we have in mind is due to a twofold contribution: (i the choice of boundary conditions, modeling in our case the contact with an infinite reservoir filled with ready-to-react chemicals and (ii the use of a particular nonlinear, non-Lipschitz structure of the reaction kinetics. Our working techniques use fine energy estimates for approximating non-singular problems and uniform control on the set where singularities are localizing.
STEPS: modeling and simulating complex reaction-diffusion systems with Python
Directory of Open Access Journals (Sweden)
Stefan Wils
2009-06-01
Full Text Available We describe how the use of the Python language improved the user interface of the program STEPS. STEPS is a simulation platform for modeling and stochastic simulation of coupled reaction-diffusion systems with complex 3-dimensional boundary conditions. Setting up such models is a complicated process that consists of many phases. Initial versions of STEPS relied on a static input format that did not cleanly separate these phases, limiting modelers in how they could control the simulation and becoming increasingly complex as new features and new simulation algorithms were added. We solved all of these problems by tightly integrating STEPS with Python, using SWIG to expose our existing simulation code.
Ge, Hao; Qian, Hong
2009-10-02
We show that the thermodynamic limit of a bistable phosphorylation-dephosphorylation cycle has a selection rule for the "more stable" macroscopic steady state. The analysis is akin to the Maxwell construction. Based on the chemical master equation approach, it is shown that, except at a critical point, bistability disappears in the stochastic model when fluctuation is sufficiently low but unneglectable. Onsager's Gaussian fluctuation theory applies to the unique macroscopic steady state. With an initial state in the basin of attraction of the "less stable" steady state, the deterministic dynamics obtained by the law of mass action is a metastable phenomenon. Stability and robustness in cell biology are emergent stochastic concepts.
A broadband electromagnetic energy harvester with a coupled bistable structure
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...
Application of the Asymptotic Taylor Expansion Method to Bistable Potentials
Directory of Open Access Journals (Sweden)
Okan Ozer
2013-01-01
Full Text Available A recent method called asymptotic Taylor expansion (ATEM is applied to determine the analytical expression for eigenfunctions and numerical results for eigenvalues of the Schrödinger equation for the bistable potentials. Optimal truncation of the Taylor series gives a best possible analytical expression for eigenfunctions and numerical results for eigenvalues. It is shown that the results are obtained by a simple algorithm constructed for a computer system using symbolic or numerical calculation. It is observed that ATEM produces excellent results consistent with the existing literature.
Bistable Helmholtz solitons in cubic-quintic materials
International Nuclear Information System (INIS)
Christian, J. M.; McDonald, G. S.; Chamorro-Posada, P.
2007-01-01
We propose a nonlinear Helmholtz equation for modeling the evolution of broad optical beams in media with a cubic-quintic intensity-dependent refractive index. This type of nonlinearity is appropriate for some semiconductor materials, glasses, and polymers. Exact analytical soliton solutions are presented that describe self-trapped nonparaxial beams propagating at any angle with respect to the reference direction. These spatially symmetric solutions are, to the best of our knowledge, the first bistable Helmholtz solitons to be derived. Accompanying conservation laws (both integral and particular forms) are also reported. Numerical simulations investigate the stability of the solitons, which appear to be remarkably robust against perturbations
Optical bistability of graphene in the terahertz range
DEFF Research Database (Denmark)
Peres, N. M. R.; Bludov, Yu V.; Santos, Jaime E.
2014-01-01
We use an exact solution of the relaxation-time Boltzmann equation in a uniform ac electric field to describe the nonlinear optical response of graphene in the terahertz (THz) range. The cases of monolayer, bilayer, and ABA-stacked trilayer graphene are considered, and the monolayer species...... is shown to be the most appropriate one to exploit the nonlinear free electron response. We find that a single layer of graphene shows optical bistability in the THz range, within the electromagnetic power range attainable in practice. The current associated with the third harmonic generation is also...
International Nuclear Information System (INIS)
Wang Xiaohu; Xu Daoyi
2009-01-01
In this paper, the global exponential stability of impulsive fuzzy cellular neural networks with mixed delays and reaction-diffusion terms is considered. By establishing an integro-differential inequality with impulsive initial condition and using the properties of M-cone and eigenspace of the spectral radius of nonnegative matrices, several new sufficient conditions are obtained to ensure the global exponential stability of the equilibrium point for fuzzy cellular neural networks with delays and reaction-diffusion terms. These results extend and improve the earlier publications. Two examples are given to illustrate the efficiency of the obtained results.
Effect of second-order coupling on optical bistability in a hybrid optomechanical system
Asghari Nejad, Ali; Baghshahi, Hamid R.; Askari, Hassan R.
2017-11-01
We theoretically investigate an optomechanical system consisting of two coupled cavities, a bare optomechanical cavity and a traditional one. An optical parametric amplifier (OPA) is placed inside the traditional cavity. Optomechanical cavity has an oscillating mirror and a fixed one. In addition to the first order coupling between mechanical resonator of the system and the radiation pressure of optomechanical cavity, we consider a second order interaction between them. The evaluation of the system's behavior shows bistability in the mean photon number of optomechanical cavity. Our results show that, the second order coupling leads to degenerate solutions for the equation of mean photon number of optomechanical cavity. We see that the strength of SOC can change the domain of bistability region of optomechanical cavity. Also, properties of the field driving OPA have remarkable effects on the stability of optomechanical cavity. Moreover, we show that the domain of bistability region can be modified by changing of optical properties of the system.
Transcriptional delay stabilizes bistable gene networks.
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.
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
Czech Academy of Sciences Publication Activity Database
Klika, Václav; Baker, R. E.; Headon, D.; Gaffney, E. A.
2012-01-01
Roč. 74, č. 4 (2012), s. 935-957 ISSN 0092-8240 Institutional research plan: CEZ:AV0Z20760514 Keywords : reaction-diffusion * receptor-mediated patterning * turing models Subject RIV: BO - Biophysics Impact factor: 2.023, year: 2012 http://www.springerlink.com/content/9713544x6871w4n6/?MUD=MP
International Nuclear Information System (INIS)
Adamatzky, Andrew; Lacy Costello, Benjamin de
2003-01-01
A reaction-diffusion chemical computer in this context is a planar uniform chemical reactor, where data and results of a computation are represented by concentration profiles of reactants and the computation itself is implemented via the spreading and interaction of diffusive and phase waves. This class of chemical computers are efficient at solving problems with a 'natural' parallelism where data sets are decomposable onto a large number of geographically neighboring domains which are then processed in parallel. Typical problems of this type include image processing, geometrical transformations and optimisation. When chemical based devices are used to solve such problems questions regarding their reproducible, efficiency and the accuracy of their computations arise. In addition to these questions what are the limitations of reaction-diffusion chemical processors--what type of problems cannot currently and are unlikely ever to be solved? To answer the questions we study how a Voronoi diagram is constructed and how it is inverted in a planar chemical processor. We demonstrate that a Voronoi diagram is computed only partially in the chemical processor. We also prove that given a specific Voronoi diagram it is impossible to reconstruct the planar set (from which diagram was computed) in the reaction-diffusion chemical processor. In the Letter we open the first ever line of enquiry into the computational inability of reaction-diffusion chemical computers
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
Bistable fluidic valve is electrically switched
Fiet, O.; Salvinski, R. J.
1970-01-01
Bistable control valve is selectively switched by direct application of an electrical field to divert fluid from one output channel to another. Valve is inexpensive, has no moving parts, and operates on fluids which are relatively poor electrical conductors.
Hurdal, Monica K.; Striegel, Deborah A.
2011-11-01
Modeling and understanding cortical folding pattern formation is important for quantifying cortical development. We present a biomathematical model for cortical folding pattern formation in the human brain and apply this model to study diseases involving cortical pattern malformations associated with neural migration disorders. Polymicrogyria is a cortical malformation disease resulting in an excessive number of small gyri. Our mathematical model uses a Turing reaction-diffusion system to model cortical folding. The lateral ventricle (LV) and ventricular zone (VZ) of the brain are critical components in the formation of cortical patterning. In early cortical development the shape of the LV can be modeled with a prolate spheroid and the VZ with a prolate spheroid surface. We use our model to study how global cortex characteristics, such as size and shape of the LV, affect cortical pattern formation. We demonstrate increasing domain scale can increase the number of gyri and sulci formed. Changes in LV shape can account for sulcus directionality. By incorporating LV size and shape, our model is able to elucidate which parameters can lead to excessive cortical folding.
Bursting regimes in a reaction-diffusion system with action potential-dependent equilibrium.
Directory of Open Access Journals (Sweden)
Stephen R Meier
Full Text Available The equilibrium Nernst potential plays a critical role in neural cell dynamics. A common approximation used in studying electrical dynamics of excitable cells is that the ionic concentrations inside and outside the cell membranes act as charge reservoirs and remain effectively constant during excitation events. Research into brain electrical activity suggests that relaxing this assumption may provide a better understanding of normal and pathophysiological functioning of the brain. In this paper we explore time-dependent ionic concentrations by allowing the ion-specific Nernst potentials to vary with developing transmembrane potential. As a specific implementation, we incorporate the potential-dependent Nernst shift into a one-dimensional Morris-Lecar reaction-diffusion model. Our main findings result from a region in parameter space where self-sustaining oscillations occur without external forcing. Studying the system close to the bifurcation boundary, we explore the vulnerability of the system with respect to external stimulations which disrupt these oscillations and send the system to a stable equilibrium. We also present results for an extended, one-dimensional cable of excitable tissue tuned to this parameter regime and stimulated, giving rise to complex spatiotemporal pattern formation. Potential applications to the emergence of neuronal bursting in similar two-variable systems and to pathophysiological seizure-like activity are discussed.
Image-Based Measurement of H2O2 Reaction-Diffusion in Wounded Zebrafish Larvae.
Jelcic, Mark; Enyedi, Balázs; Xavier, João B; Niethammer, Philipp
2017-05-09
Epithelial injury induces rapid recruitment of antimicrobial leukocytes to the wound site. In zebrafish larvae, activation of the epithelial NADPH oxidase Duox at the wound margin is required early during this response. Before injury, leukocytes are near the vascular region, that is, ∼100-300 μm away from the injury site. How Duox establishes long-range signaling to leukocytes is unclear. We conceived that extracellular hydrogen peroxide (H 2 O 2 ) generated by Duox diffuses through the tissue to directly regulate chemotactic signaling in these cells. But before it can oxidize cellular proteins, H 2 O 2 must get past the antioxidant barriers that protect the cellular proteome. To test whether, or on which length scales this occurs during physiological wound signaling, we developed a computational method based on reaction-diffusion principles that infers H 2 O 2 degradation rates from intravital H 2 O 2 -biosensor imaging data. Our results indicate that at high tissue H 2 O 2 levels the peroxiredoxin-thioredoxin antioxidant chain becomes overwhelmed, and H 2 O 2 degradation stalls or ceases. Although the wound H 2 O 2 gradient reaches deep into the tissue, it likely overcomes antioxidant barriers only within ∼30 μm of the wound margin. Thus, Duox-mediated long-range signaling may require other spatial relay mechanisms besides extracellular H 2 O 2 diffusion. Copyright © 2017 Biophysical Society. Published by Elsevier Inc. All rights reserved.
The two-regime method for optimizing stochastic reaction-diffusion simulations
Flegg, M. B.
2011-10-19
Spatial organization and noise play an important role in molecular systems biology. In recent years, a number of software packages have been developed for stochastic spatio-temporal simulation, ranging from detailed molecular-based approaches to less detailed compartment-based simulations. Compartment-based approaches yield quick and accurate mesoscopic results, but lack the level of detail that is characteristic of the computationally intensive molecular-based models. Often microscopic detail is only required in a small region (e.g. close to the cell membrane). Currently, the best way to achieve microscopic detail is to use a resource-intensive simulation over the whole domain. We develop the two-regime method (TRM) in which a molecular-based algorithm is used where desired and a compartment-based approach is used elsewhere. We present easy-to-implement coupling conditions which ensure that the TRM results have the same accuracy as a detailed molecular-based model in the whole simulation domain. Therefore, the TRM combines strengths of previously developed stochastic reaction-diffusion software to efficiently explore the behaviour of biological models. Illustrative examples and the mathematical justification of the TRM are also presented.
Parallel Solutions for Voxel-Based Simulations of Reaction-Diffusion Systems
Directory of Open Access Journals (Sweden)
Daniele D’Agostino
2014-01-01
Full Text Available There is an increasing awareness of the pivotal role of noise in biochemical processes and of the effect of molecular crowding on the dynamics of biochemical systems. This necessity has given rise to a strong need for suitable and sophisticated algorithms for the simulation of biological phenomena taking into account both spatial effects and noise. However, the high computational effort characterizing simulation approaches, coupled with the necessity to simulate the models several times to achieve statistically relevant information on the model behaviours, makes such kind of algorithms very time-consuming for studying real systems. So far, different parallelization approaches have been deployed to reduce the computational time required to simulate the temporal dynamics of biochemical systems using stochastic algorithms. In this work we discuss these aspects for the spatial TAU-leaping in crowded compartments (STAUCC simulator, a voxel-based method for the stochastic simulation of reaction-diffusion processes which relies on the Sτ-DPP algorithm. In particular we present how the characteristics of the algorithm can be exploited for an effective parallelization on the present heterogeneous HPC architectures.
Chirality Controls Reaction-Diffusion of Nanoparticles for Inhibiting Cancer Cells.
Du, Xuewen; Zhou, Jie; Wang, Jiaqing; Zhou, Rong; Xu, Bing
2017-01-01
Reaction-diffusion (RD) is the most important inherent feature of living organism, but it has yet to be used for developing biofunctional nanoparticles (NPs). Here we show the use of chirality to control the RD of NPs for selectively inhibiting cancer cells. We observe that L-phosphotyrosine (L-pY) decorated NPs (NP@L-pYs) are innocuous to cells, but D-pY decorated ones (NP@D-pYs) selectively inhibit cancer cells. Our study shows that alkaline phosphatases (ALP), presented in the culture and overexpressed on the cancer cells, dephosphorylates NP@L-pYs much faster than NP@D-pYs. Such a rate difference allows the NP@D-pYs to be mainly dephosphorylated on cell surface, thus adhering selectively on the cancer cells to result in poly(ADP-ribose)polymerase (PARP) hyperactivation mediated cell death. Without phosphate groups or being prematurely dephosphorylated before reaching cancer cells (as the case of NP@L-pYs), the NPs are innocuous to cells. Moreover, NP@D-pYs even exhibit more potent activity than cisplatin for inhibiting platinum-resistant ovarian cancer cells (e.g., A2780-cis). As the first example of chirality controlling RD process of NPs for inhibiting cancer cells, this work illustrates a fundamentally new way for developing nanomedicine based on RD processes and nanoparticles.
GABA shapes the dynamics of bistable perception.
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.
Temporal cross-correlation asymmetry and departure from equilibrium in a bistable chemical system.
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.
Coupled chaotic attractors and driving-induced bistability: A brief ...
Indian Academy of Sciences (India)
2015-02-04
breaking interactions in a drive–response system with the driving-induced bistability. The basins of attraction on the initial conditions plane are observed for the driving-induced bistability. The basins are dependent on the interaction ...
The geodynamo as a bistable oscillator
Hoyng, P.; Ossendrijver, M. A. J. H.; Schmitt, D.
2001-07-01
Our intent is to provide a simple and quantitative understanding of the variability of the axial dipole component of the geomagnetic field on both short and long time scales. To this end we study the statistical properties of a prototype nonlinear mean field model. An azimuthal average is employed, so that (1) we address only the axisymmetric component of the field, and (2) the dynamo parameters have a random component that fluctuates on the (fast) eddy turnover time scale. Numerical solutions with a rapidly fluctuating alpha reproduce several features of the geomagnetic field: (1) a variable, dominantly dipolar field with additional fine structure due to excited overtones, and sudden reversals during which the field becomes almost quadrupolar, (2) aborted reversals and excursions, (3) intervals between reversals having a Poisson distribution. These properties are robust, and appear regardless of the type of nonlinearity and the model parameters. A technique is presented for analysing the statistical properties of dynamo models of this type. The Fokker-Planck equation for the amplitude a of the fundamental dipole mode shows that a behaves as the position of a heavily damped particle in a bistable potential ~(1-a^2)^2, subject to random forcing. The dipole amplitude oscillates near the bottom of one well and makes occasional jumps to the other. These reversals are induced solely by the overtones. Theoretical expressions are derived for the statistical distribution of the dipole amplitude, the variance of the dipole amplitude between reversals, and the mean reversal rate. The model explains why the reversal rate increases with increasing secular variation, as observed. Moreover, the present reversal rate of the geodynamo, once per (2-3)x10^5years, is shown to imply a secular variation of the dipole moment of ~15% (about the current value). The theoretical dipole amplitude distribution agrees well with the Sint-800 data.
Bistable soliton states and switching in doubly inhomogeneously ...
Indian Academy of Sciences (India)
there has been a considerable interest in bistable solitons in glass fibers (with non-Kerr properties), in connection with optical bistability and other possible applications leading to switching and logic-gate devices. In literature one distinguishes between two kinds of bistable solitons: one for which the nonlinear propagation ...
Bistable dynamics of an insect–pathogen model
Indian Academy of Sciences (India)
Here, we were able to construct an insect–pathogen model which has bistable dynamics. This simple model may be helpful to identify the universal mechanisms which lead to bistability in a biological system. The control of bistable system is very difficult because the dynamics has sensitivity to initial conditions. Therefore, to ...
Simultaneous and non-simultaneous blow-up and uniform blow-up profiles for reaction-diffusion system
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Zhengqiu Ling
2012-11-01
Full Text Available This article concerns the blow-up solutions of a reaction-diffusion system with nonlocal sources, subject to the homogeneous Dirichlet boundary conditions. The criteria used to identify simultaneous and non-simultaneous blow-up of solutions by using the parameters p and q in the model are proposed. Also, the uniform blow-up profiles in the interior domain are established.
Li, Zhe; Xu, Rui
2012-04-01
In this paper, a class of stochastic reaction-diffusion neural networks with time delays in the leakage terms is investigated. By using the Lyapunov functional method and linear matrix inequality (LMI) approach, sufficient conditions are derived to ensure the global asymptotic stability of an equilibrium point of the networks in the mean square. The results can be easily solved by MATLAB LMI toolbox. Finally, a numerical example is given to demonstrate the effectiveness and conservativeness of our theoretical results.
Origin of bistability in the lac Operon.
Santillán, M; Mackey, M C; Zeron, E S
2007-06-01
Multistability is an emergent dynamic property that has been invoked to explain multiple coexisting biological states. In this work, we investigate the origin of bistability in the lac operon. To do this, we develop a mathematical model for the regulatory pathway in this system and compare the model predictions with other experimental results in which a nonmetabolizable inducer was employed. We investigate the effect of lactose metabolism using this model, and show that it greatly modifies the bistable region in the external lactose (Le) versus external glucose (Ge) parameter space. The model also predicts that lactose metabolism can cause bistability to disappear for very low Ge. We have also carried out stochastic numerical simulations of the model for several values of Ge and Le. Our results indicate that bistability can help guarantee that Escherichia coli consumes glucose and lactose in the most efficient possible way. Namely, the lac operon is induced only when there is almost no glucose in the growing medium, but if Le is high, the operon induction level increases abruptly when the levels of glucose in the environment decrease to very low values. We demonstrate that this behavior could not be obtained without bistability if the stability of the induced and uninduced states is to be preserved. Finally, we point out that the present methods and results may be useful to study the emergence of multistability in biological systems other than the lac operon.
Hybrid optoelectronic device with multiple bistable outputs
Costazo-Caso, Pablo A.; Jin, Yiye; Gelh, Michael; Granieri, Sergio; Siahmakoun, Azad
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.
Optimal control of an invasive species using a reaction-diffusion model and linear programming
Bonneau, Mathieu; Johnson, Fred A.; Smith, Brian J.; Romagosa, Christina M.; Martin, Julien; Mazzotti, Frank J.
2017-01-01
Managing an invasive species is particularly challenging as little is generally known about the species’ biological characteristics in its new habitat. In practice, removal of individuals often starts before the species is studied to provide the information that will later improve control. Therefore, the locations and the amount of control have to be determined in the face of great uncertainty about the species characteristics and with a limited amount of resources. We propose framing spatial control as a linear programming optimization problem. This formulation, paired with a discrete reaction-diffusion model, permits calculation of an optimal control strategy that minimizes the remaining number of invaders for a fixed cost or that minimizes the control cost for containment or protecting specific areas from invasion. We propose computing the optimal strategy for a range of possible model parameters, representing current uncertainty on the possible invasion scenarios. Then, a best strategy can be identified depending on the risk attitude of the decision-maker. We use this framework to study the spatial control of the Argentine black and white tegus (Salvator merianae) in South Florida. There is uncertainty about tegu demography and we considered several combinations of model parameters, exhibiting various dynamics of invasion. For a fixed one-year budget, we show that the risk-averse strategy, which optimizes the worst-case scenario of tegus’ dynamics, and the risk-neutral strategy, which optimizes the expected scenario, both concentrated control close to the point of introduction. A risk-seeking strategy, which optimizes the best-case scenario, focuses more on models where eradication of the species in a cell is possible and consists of spreading control as much as possible. For the establishment of a containment area, assuming an exponential growth we show that with current control methods it might not be possible to implement such a strategy for some of the
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.
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.
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.
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....
Balancing bistable perception during self-motion.
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.
Bistable Microvalve For Use With Microcatheter System
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.
Unidirectional Transition Waves in Bistable Lattices.
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.
Bistable Topological Insulator with Exciton-Polaritons
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.
Neuromechanistic Model of Auditory Bistability.
Directory of Open Access Journals (Sweden)
James Rankin
2015-11-01
Full Text Available Sequences of higher frequency A and lower frequency B tones repeating in an ABA- triplet pattern are widely used to study auditory streaming. One may experience either an integrated percept, a single ABA-ABA- stream, or a segregated percept, separate but simultaneous streams A-A-A-A- and -B---B--. During minutes-long presentations, subjects may report irregular alternations between these interpretations. We combine neuromechanistic modeling and psychoacoustic experiments to study these persistent alternations and to characterize the effects of manipulating stimulus parameters. Unlike many phenomenological models with abstract, percept-specific competition and fixed inputs, our network model comprises neuronal units with sensory feature dependent inputs that mimic the pulsatile-like A1 responses to tones in the ABA- triplets. It embodies a neuronal computation for percept competition thought to occur beyond primary auditory cortex (A1. Mutual inhibition, adaptation and noise are implemented. We include slow NDMA recurrent excitation for local temporal memory that enables linkage across sound gaps from one triplet to the next. Percepts in our model are identified in the firing patterns of the neuronal units. We predict with the model that manipulations of the frequency difference between tones A and B should affect the dominance durations of the stronger percept, the one dominant a larger fraction of time, more than those of the weaker percept-a property that has been previously established and generalized across several visual bistable paradigms. We confirm the qualitative prediction with our psychoacoustic experiments and use the behavioral data to further constrain and improve the model, achieving quantitative agreement between experimental and modeling results. Our work and model provide a platform that can be extended to consider other stimulus conditions, including the effects of context and volition.
Theoretical Investigation of the Bistability Effect in Non-Self-Sustained Discharges in Kr and Ar
International Nuclear Information System (INIS)
Dyatko, N.A.; Napartovich, A.P.
2004-01-01
The electron energy distribution function and the related plasma parameters in non-self-sustained discharges in Kr and Ar are studied theoretically. The investigations are carried out by numerically solving the corresponding Boltzmann equation for the electron energy distribution function with allowance for electron-electron collisions. The electron energy distribution and electron density are calculated self-consistently as functions of the intensity q of the source of secondary electrons and the magnitude of the reduced electric field E/N. The main goal of the investigations was to determine the conditions under which the plasma exhibits bistable parameters. Calculations show that, for discharges in Kr, there is a certain range of q and E/N values in which the Boltzmann equation has two different stable solutions. For an Ar plasma, such a bistability effect was not found: over the parameter range under consideration, the Boltzmann equation has a unique solution. Various plasma parameters (such as the effective electron temperature, electron drift velocity, and electron current density) are calculated for different discharge conditions, including those corresponding to the bistability effect
Directory of Open Access Journals (Sweden)
Margaret E. Johnson
2014-09-01
Full Text Available We present a new algorithm for simulating reaction-diffusion equations at single-particle resolution. Our algorithm is designed to be both accurate and simple to implement, and to be applicable to large and heterogeneous systems, including those arising in systems biology applications. We combine the use of the exact Green’s function for a pair of reacting particles with the approximate free-diffusion propagator for position updates to particles. Trajectory reweighting in our free-propagator reweighting (FPR method recovers the exact association rates for a pair of interacting particles at all times. FPR simulations of many-body systems accurately reproduce the theoretically known dynamic behavior for a variety of different reaction types. FPR does not suffer from the loss of efficiency common to other path-reweighting schemes, first, because corrections apply only in the immediate vicinity of reacting particles and, second, because by construction the average weight factor equals one upon leaving this reaction zone. FPR applications include the modeling of pathways and networks of protein-driven processes where reaction rates can vary widely and thousands of proteins may participate in the formation of large assemblies. With a limited amount of bookkeeping necessary to ensure proper association rates for each reactant pair, FPR can account for changes to reaction rates or diffusion constants as a result of reaction events. Importantly, FPR can also be extended to physical descriptions of protein interactions with long-range forces, as we demonstrate here for Coulombic interactions.
A CW Gunn diode bistable switching element.
Hurtado, M.; Rosenbaum, F. J.
1972-01-01
Experiments with a current-controlled bistable switching element using a CW Gunn diode are reported. Switching rates of the order of 10 MHz have been obtained. Switching is initiated by current pulses of short duration (5-10 ns). Rise times of the order of several nanoseconds could be obtained.
Metastable and bistable defects in silicon
International Nuclear Information System (INIS)
Mukashev, Bulat N; Abdullin, Kh A; Gorelkinskii, Yurii V
2000-01-01
Existing data on the properties and structure of metastable and bistable defects in silicon are analyzed. Primary radiation-induced defects (vacancies, self-interstitial atoms, and Frenkel pairs), complexes of oxygen, carbon, hydrogen, and other impurity atoms and defects with negative correlation energy are considered. (reviews of topical problems)
Organic bistable light-emitting devices
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.
Dimensionality reduction of bistable biological systems.
Zakharova, A; Nikoloski, Z; Koseska, A
2013-03-01
Time hierarchies, arising as a result of interactions between system's components, represent a ubiquitous property of dynamical biological systems. In addition, biological systems have been attributed switch-like properties modulating the response to various stimuli across different organisms and environmental conditions. Therefore, establishing the interplay between these features of system dynamics renders itself a challenging question of practical interest in biology. Existing methods are suitable for systems with one stable steady state employed as a well-defined reference. In such systems, the characterization of the time hierarchies has already been used for determining the components that contribute to the dynamics of biological systems. However, the application of these methods to bistable nonlinear systems is impeded due to their inherent dependence on the reference state, which in this case is no longer unique. Here, we extend the applicability of the reference-state analysis by proposing, analyzing, and applying a novel method, which allows investigation of the time hierarchies in systems exhibiting bistability. The proposed method is in turn used in identifying the components, other than reactions, which determine the systemic dynamical properties. We demonstrate that in biological systems of varying levels of complexity and spanning different biological levels, the method can be effectively employed for model simplification while ensuring preservation of qualitative dynamical properties (i.e., bistability). Finally, by establishing a connection between techniques from nonlinear dynamics and multivariate statistics, the proposed approach provides the basis for extending reference-based analysis to bistable systems.
Directory of Open Access Journals (Sweden)
Herman N C Berghuijs
Full Text Available The rate of photosynthesis depends on the CO2 partial pressure near Rubisco, Cc, which is commonly calculated by models using the overall mesophyll resistance. Such models do not explain the difference between the CO2 level in the intercellular air space and Cc mechanistically. This problem can be overcome by reaction-diffusion models for CO2 transport, production and fixation in leaves. However, most reaction-diffusion models are complex and unattractive for procedures that require a large number of runs, like parameter optimisation. This study provides a simpler reaction-diffusion model. It is parameterized by both leaf physiological and leaf anatomical data. The anatomical data consisted of the thickness of the cell wall, cytosol and stroma, and the area ratios of mesophyll exposed to the intercellular air space to leaf surfaces and exposed chloroplast to exposed mesophyll surfaces. The model was used directly to estimate photosynthetic parameters from a subset of the measured light and CO2 response curves; the remaining data were used for validation. The model predicted light and CO2 response curves reasonably well for 15 days old tomato (cv. Admiro leaves, if (photorespiratory CO2 release was assumed to take place in the inner cytosol or in the gaps between the chloroplasts. The model was also used to calculate the fraction of CO2 produced by (photorespiration that is re-assimilated in the stroma, and this fraction ranged from 56 to 76%. In future research, the model should be further validated to better understand how the re-assimilation of (photorespired CO2 is affected by environmental conditions and physiological parameters.
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.
A free boundary problem for a reaction-diffusion system with nonlinear memory
DEFF Research Database (Denmark)
Lin, Zhigui; Ling, Zhi; Pedersen, Michael
2013-01-01
We consider a integro-partial differential equation with a free boundary which appears in the theory of the nuclear dynamics. First, local existence and uniqueness are obtained by using the contraction mapping theorem. Then, the behavior of the free boundary and the blow-up criteria are obtained...
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
Bistable scattering in graphene-coated dielectric nanowires.
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.
Bistable perception modeled as competing stochastic integrations at two levels.
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.
Fronts and waves of actin polymerization in a bistability-based mechanism of circular dorsal ruffles
Bernitt, Erik; Döbereiner, Hans-Günther; Gov, Nir S.; Yochelis, Arik
2017-06-01
During macropinocytosis, cells remodel their morphologies for the uptake of extracellular matter. This endocytotic mechanism relies on the collapse and closure of precursory structures, which are propagating actin-based, ring-shaped vertical undulations at the dorsal (top) cell membrane, a.k.a. circular dorsal ruffles (CDRs). As such, CDRs are essential to a range of vital and pathogenic processes alike. Here we show, based on both experimental data and theoretical analysis, that CDRs are propagating fronts of actin polymerization in a bistable system. The theory relies on a novel mass-conserving reaction-diffusion model, which associates the expansion and contraction of waves to distinct counter-propagating front solutions. Moreover, the model predicts that under a change in parameters (for example, biochemical conditions) CDRs may be pinned and fluctuate near the cell boundary or exhibit complex spiral wave dynamics due to a wave instability. We observe both phenomena also in our experiments indicating the conditions for which macropinocytosis is suppressed.
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)
Frequency selective bistable switching in metamaterial based photonic bandgap medium
Jose, Jolly
2014-10-01
We present frequency selective bistable response at the defect mode of the zero-nbar bandgap of a photonic bandgap (PBG) material made of negative and positive index media. The nonlinear (Kerr) layer acts as the defect layer in the periodic PBG material. Incorporating metamaterial based electromagnetically induced transparency (EIT) like resonance in the positive layer leads to unprecedented line narrowing of the defect mode which in turn facilitates narrow frequency selective bistable operation, wherein all the bistable characteristics can be effectively engineered. Thresholding the output intensity selects the narrow band of frequencies that exhibit bistability.
Durable bistable auxetics made of rigid solids
Shang, Xiao; Liu, Lu; Rafsanjani, Ahmad; Pasini, Damiano
2018-02-01
Bistable Auxetic Metamaterials (BAMs) are a class of monolithic perforated periodic structures with negative Poisson's ratio. Under tension, a BAM can expand and reach a second state of equilibrium through a globally large shape transformation that is ensured by the flexibility of its elastomeric base material. However, if made from a rigid polymer, or metal, BAM ceases to function due to the inevitable rupture of its ligaments. The goal of this work is to extend the unique functionality of the original kirigami architecture of BAM to a rigid solid base material. We use experiments and numerical simulations to assess performance, bistability and durability of rigid BAMs at 10,000 cycles. Geometric maps are presented to elucidate the role of the main descriptors of BAM architecture. The proposed design enables the realization of BAM from a large palette of materials, including elastic-perfectly plastic materials and potentially brittle materials.
Reaction-diffusion systems in natural sciences and new technology transfer
Keller, André A.
2012-12-01
Diffusion mechanisms in natural sciences and innovation management involve partial differential equations (PDEs). This is due to their spatio-temporal dimensions. Functional semi-discretized PDEs (with lattice spatial structures or time delays) may be even more adapted to real world problems. In the modeling process, PDEs can also formalize behaviors, such as the logistic growth of populations with migration, and the adopters’ dynamics of new products in innovation models. In biology, these events are related to variations in the environment, population densities and overcrowding, migration and spreading of humans, animals, plants and other cells and organisms. In chemical reactions, molecules of different species interact locally and diffuse. In the management of new technologies, the diffusion processes of innovations in the marketplace (e.g., the mobile phone) are a major subject. These innovation diffusion models refer mainly to epidemic models. This contribution introduces that modeling process by using PDEs and reviews the essential features of the dynamics and control in biological, chemical and new technology transfer. This paper is essentially user-oriented with basic nonlinear evolution equations, delay PDEs, several analytical and numerical methods for solving, different solutions, and with the use of mathematical packages, notebooks and codes. The computations are carried out by using the software Wolfram Mathematica®7, and C++ codes.
Signal Transmission of Biological Reaction-Diffusion System by Using Synchronization
Directory of Open Access Journals (Sweden)
Lingli Zhou
2017-10-01
Full Text Available Molecular signal transmission in cell is very crucial for information exchange. How to understand its transmission mechanism has attracted many researchers. In this paper, we prove that signal transmission problem between neural tumor molecules and drug molecules can be achieved by synchronous control. To achieve our purpose, we derive the Fokker-Plank equation by using the Langevin equation and theory of random walk, this is a model which can express the concentration change of neural tumor molecules. Second, according to the biological character that vesicles in cell can be combined with cell membrane to release the cargo which plays a role of signal transmission, we preliminarily analyzed the mechanism of tumor-drug molecular interaction. Third, we propose the view of synchronous control which means the process of vesicle docking with their target membrane is a synchronization process, and we can achieve the precise treatment of disease by using synchronous control. We believe this synchronous control mechanism is reasonable and two examples are given to illustrate the correctness of our results obtained in this paper.
Two Bistable Switches Govern M Phase Entry.
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.
Bistable (latching) solenoid actuated propellant isolation valve
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.
Interlinked bistable mechanisms generate robust mitotic transitions.
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.
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.
Bistable flows in precessing spheroids
Energy Technology Data Exchange (ETDEWEB)
Cébron, D, E-mail: david.cebron@ujf-grenoble.fr [Université Grenoble Alpes, CNRS, ISTerre, Grenoble (France)
2015-04-15
Precession driven flows are found in any rotating container filled with liquid, when the rotation axis itself rotates about a secondary axis that is fixed in an inertial frame of reference. Because of its relevance for planetary fluid layers, many works consider spheroidal containers, where the uniform vorticity component of the bulk flow is reliably given by the well-known equations obtained by Busse (1968 J. Fluid Mech. 33 739–51). So far however, no analytical result for the solutions is available. Moreover, the cases where multiple flows can coexist have not been investigated in detail since their discovery by Noir et al (2003 Geophys. J. Int. 154 407–16). In this work we aim at deriving analytical results for the solutions, aiming in particular at first estimating the ranges of parameters where multiple solutions exist, and second studying quantitatively their stability. Using the models recently proposed by Noir and Cébron (2013 J. Fluid Mech. 737 412–39), which are more generic in the inviscid limit than the equations of Busse, we analytically describe these solutions, their conditions of existence, and their stability in a systematic manner. We then successfully compare these analytical results with the theory of Busse (1968). Dynamical model equations are finally proposed to investigate the stability of the solutions, which describe the bifurcation of the unstable flow solution. We also report for the first time the possibility that time-dependent multiple flows can coexist in precessing triaxial ellipsoids. Numerical integrations of the algebraic and differential equations have been efficiently performed with the dedicated script FLIPPER (supplementary material). (paper)
Fahrenbach, Albert C; Bruns, Carson J; Cao, Dennis; Stoddart, J Fraser
2012-09-18
. Measuring the ground-state distribution constants of bistable MIMs presents its own set of challenges. While it is possible, in principle, to determine these constants using NMR and UV-vis spectroscopies, these methods lack the sensitivity to permit the determination of ratios of translational isomers greater than 10:1 with sufficient accuracy and precision. A simple application of the Nernst equation, in combination with variable scan-rate cyclic voltammetry, however, allows the direct measurement of ground-state distribution constants across a wide range (K(GS) = 10-10(4)) of values.
ReaDDy--a software for particle-based reaction-diffusion dynamics in crowded cellular environments.
Directory of Open Access Journals (Sweden)
Johannes Schöneberg
Full Text Available We introduce the software package ReaDDy for simulation of detailed spatiotemporal mechanisms of dynamical processes in the cell, based on reaction-diffusion dynamics with particle resolution. In contrast to other particle-based reaction kinetics programs, ReaDDy supports particle interaction potentials. This permits effects such as space exclusion, molecular crowding and aggregation to be modeled. The biomolecules simulated can be represented as a sphere, or as a more complex geometry such as a domain structure or polymer chain. ReaDDy bridges the gap between small-scale but highly detailed molecular dynamics or Brownian dynamics simulations and large-scale but little-detailed reaction kinetics simulations. ReaDDy has a modular design that enables the exchange of the computing core by efficient platform-specific implementations or dynamical models that are different from Brownian dynamics.
ReaDDy - A Software for Particle-Based Reaction-Diffusion Dynamics in Crowded Cellular Environments
Schöneberg, Johannes; Noé, Frank
2013-01-01
We introduce the software package ReaDDy for simulation of detailed spatiotemporal mechanisms of dynamical processes in the cell, based on reaction-diffusion dynamics with particle resolution. In contrast to other particle-based reaction kinetics programs, ReaDDy supports particle interaction potentials. This permits effects such as space exclusion, molecular crowding and aggregation to be modeled. The biomolecules simulated can be represented as a sphere, or as a more complex geometry such as a domain structure or polymer chain. ReaDDy bridges the gap between small-scale but highly detailed molecular dynamics or Brownian dynamics simulations and large-scale but little-detailed reaction kinetics simulations. ReaDDy has a modular design that enables the exchange of the computing core by efficient platform-specific implementations or dynamical models that are different from Brownian dynamics. PMID:24040218
Spatially explicit control of invasive species using a reaction-diffusion model
Bonneau, Mathieu; Johnson, Fred A.; Romagosa, Christina M.
2016-01-01
Invasive species, which can be responsible for severe economic and environmental damages, must often be managed over a wide area with limited resources, and the optimal allocation of effort in space and time can be challenging. If the spatial range of the invasive species is large, control actions might be applied only on some parcels of land, for example because of property type, accessibility, or limited human resources. Selecting the locations for control is critical and can significantly impact management efficiency. To help make decisions concerning the spatial allocation of control actions, we propose a simulation based approach, where the spatial distribution of the invader is approximated by a reaction–diffusion model. We extend the classic Fisher equation to incorporate the effect of control both in the diffusion and local growth of the invader. The modified reaction–diffusion model that we propose accounts for the effect of control, not only on the controlled locations, but on neighboring locations, which are based on the theoretical speed of the invasion front. Based on simulated examples, we show the superiority of our model compared to the state-of-the-art approach. We illustrate the use of this model for the management of Burmese pythons in the Everglades (Florida, USA). Thanks to the generality of the modified reaction–diffusion model, this framework is potentially suitable for a wide class of management problems and provides a tool for managers to predict the effects of different management strategies.
Bistability in a hybrid optomechanical system: effect of a gain medium
Asghari Nejad, A.; Baghshahi, H. R.; Askari, H. R.
2017-11-01
In this paper, we investigate the optical bistability of a hybrid optomechanical system consisting of two coupled cavities: a bare optomechanical cavity (with an oscillating mirror at one end) and a traditional one. The traditional cavity is filled with an optical parametric amplifier (OPA), and an input pump laser is applied to it. The Hamiltonian of the system is written in a rotating frame. The dynamics of the system is driven by the quantum Langevin equations of motion. We demonstrate that the presence of an OPA can dramatically affect the type of stability of the optomechanical cavity. We show that it is possible to create a proper optical bistability for the optomechanical cavity by changing the gain coefficient of the OPA. Also, it is shown that changing the phase of the field driving the OPA has two different effects on the bistability region of the optomechanical cavity. Moreover, we show that by choosing a proper value for the detuning of the traditional cavity it is possible to observe a tristable behavior in the optomechanical cavity.
Bistable soliton states and switching in doubly inhomogeneously ...
Indian Academy of Sciences (India)
Bistable soliton states and switching in doubly inhomogeneously doped ﬁber couplers. Ajit Kumar. Theoretical aspects of optical solitons Volume 57 Issue 5-6 November-December 2001 pp 969-979 ... Switching between the bistable soliton states in a doubly and inhomogeneously doped ﬁber system is studied numerically.
Bistable polarization switching in a continuous wave ruby laser
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.
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.
Multistability in Bistable Ferroelectric Materials toward Adaptive Applications
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
Harne, R. L.; Zhang, Chunlin; Li, Bing; Wang, K. W.
2016-07-01
Impulsive energies are abundant throughout the natural and built environments, for instance as stimulated by wind gusts, foot-steps, or vehicle-road interactions. In the interest of maximizing the sustainability of society's technological developments, one idea is to capture these high-amplitude and abrupt energies and convert them into usable electrical power such as for sensors which otherwise rely on less sustainable power supplies. In this spirit, the considerable sensitivity to impulse-type events previously uncovered for bistable oscillators has motivated recent experimental and numerical studies on the power generation performance of bistable vibration energy harvesters. To lead to an effective and efficient predictive tool and design guide, this research develops a new analytical approach to estimate the electroelastic response and power generation of a bistable energy harvester when excited by an impulse. Comparison with values determined by direct simulation of the governing equations shows that the analytically predicted net converted energies are very accurate for a wide range of impulse strengths. Extensive experimental investigations are undertaken to validate the analytical approach and it is seen that the predicted estimates of the impulsive energy conversion are in excellent agreement with the measurements, and the detailed structural dynamics are correctly reproduced. As a result, the analytical approach represents a significant leap forward in the understanding of how to effectively leverage bistable structures as energy harvesting devices and introduces new means to elucidate the transient and far-from-equilibrium dynamics of nonlinear systems more generally.
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.
Traveling wave behavior for a generalized fisher equation
International Nuclear Information System (INIS)
Feng Zhaosheng
2008-01-01
There is the widespread existence of wave phenomena in physics, chemistry and biology. This clearly necessitates a study of traveling waves in depth and of the modeling and analysis involved. In the present paper, we study a nonlinear reaction-diffusion equation, which can be regarded as a generalized Fisher equation. Applying the Cole-Hopf transformation and the first integral method, we obtain a class of traveling solitary wave solutions for this generalized Fisher equation
A hierarchical stochastic model for bistable perception.
Directory of Open Access Journals (Sweden)
Stefan Albert
2017-11-01
Full Text Available Viewing of ambiguous stimuli can lead to bistable perception alternating between the possible percepts. During continuous presentation of ambiguous stimuli, percept changes occur as single events, whereas during intermittent presentation of ambiguous stimuli, percept changes occur at more or less regular intervals either as single events or bursts. Response patterns can be highly variable and have been reported to show systematic differences between patients with schizophrenia and healthy controls. Existing models of bistable perception often use detailed assumptions and large parameter sets which make parameter estimation challenging. Here we propose a parsimonious stochastic model that provides a link between empirical data analysis of the observed response patterns and detailed models of underlying neuronal processes. Firstly, we use a Hidden Markov Model (HMM for the times between percept changes, which assumes one single state in continuous presentation and a stable and an unstable state in intermittent presentation. The HMM captures the observed differences between patients with schizophrenia and healthy controls, but remains descriptive. Therefore, we secondly propose a hierarchical Brownian model (HBM, which produces similar response patterns but also provides a relation to potential underlying mechanisms. The main idea is that neuronal activity is described as an activity difference between two competing neuronal populations reflected in Brownian motions with drift. This differential activity generates switching between the two conflicting percepts and between stable and unstable states with similar mechanisms on different neuronal levels. With only a small number of parameters, the HBM can be fitted closely to a high variety of response patterns and captures group differences between healthy controls and patients with schizophrenia. At the same time, it provides a link to mechanistic models of bistable perception, linking the group
A hierarchical stochastic model for bistable perception.
Albert, Stefan; Schmack, Katharina; Sterzer, Philipp; Schneider, Gaby
2017-11-01
Viewing of ambiguous stimuli can lead to bistable perception alternating between the possible percepts. During continuous presentation of ambiguous stimuli, percept changes occur as single events, whereas during intermittent presentation of ambiguous stimuli, percept changes occur at more or less regular intervals either as single events or bursts. Response patterns can be highly variable and have been reported to show systematic differences between patients with schizophrenia and healthy controls. Existing models of bistable perception often use detailed assumptions and large parameter sets which make parameter estimation challenging. Here we propose a parsimonious stochastic model that provides a link between empirical data analysis of the observed response patterns and detailed models of underlying neuronal processes. Firstly, we use a Hidden Markov Model (HMM) for the times between percept changes, which assumes one single state in continuous presentation and a stable and an unstable state in intermittent presentation. The HMM captures the observed differences between patients with schizophrenia and healthy controls, but remains descriptive. Therefore, we secondly propose a hierarchical Brownian model (HBM), which produces similar response patterns but also provides a relation to potential underlying mechanisms. The main idea is that neuronal activity is described as an activity difference between two competing neuronal populations reflected in Brownian motions with drift. This differential activity generates switching between the two conflicting percepts and between stable and unstable states with similar mechanisms on different neuronal levels. With only a small number of parameters, the HBM can be fitted closely to a high variety of response patterns and captures group differences between healthy controls and patients with schizophrenia. At the same time, it provides a link to mechanistic models of bistable perception, linking the group differences to
Bistability in Coupled Oscillators Exhibiting Synchronized Dynamics
Olusola, O. I.; Vincent, U. E.; Njah, A. N.; Olowofela, J. A.
2010-05-01
We report some new results associated with the synchronization behavior of two coupled double-well Duffing oscillators (DDOs). Some sufficient algebraic criteria for global chaos synchronization of the drive and response DDOs via linear state error feedback control are obtained by means of Lyapunov stability theory. The synchronization is achieved through a bistable state in which a periodic attractor co-exists with a chaotic attractor. Using the linear perturbation analysis, the prevalence of attractors in parameter space and the associated bifurcations are examined. Subcritical and supercritical Hopf bifurcations and abundance of Arnold tongues — a signature of mode locking phenomenon are found.
Bistability in mushroom-type metamaterials
Fernandes, David E.; Silveirinha, Mário G.
2017-07-01
Here, we study the electromagnetic response of asymmetric mushroom-type metamaterials loaded with nonlinear elements. It is shown that near a Fano resonance, these structures may have a strong tunable, bistable, and switchable response and enable giant nonlinear effects. By using an effective medium theory and full wave simulations, it is proven that the nonlinear elements may allow the reflection and transmission coefficients to follow hysteresis loops, and to switch the metamaterial between "go" and "no-go" states similar to an ideal electromagnetic switch.
Lattice stretching bistability and dynamic heterogeneity
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Savin, A. V.; Zolotaryuk, A. V.
2012-01-01
A simple one-dimensional lattice model is suggested to describe the experimentally observed plateau in force-stretching diagrams for some macromolecules. This chain model involves the nearest-neighbor interaction of a Morse-like potential (required to have a saturation branch) and a harmonic second......-neighbor coupling. Under an external stretching applied to the chain ends, the intersite Morse-like potential results in the appearance of a double-well potential within each chain monomer, whereas the interaction between the second neighbors provides a homogeneous bistable (degenerate) ground state, at least...
Stability and morphing characteristics of bistable composite laminates
Tawfik, Samer A.
The focus of the current research is to investigate the potential of using bistable unsymmetric cross-ply laminated composites as a means for achieving structures with morphed characteristics. To this end, an investigation of the design space for laminated composites exhibiting bistable behavior is undertaken and the key parameters controlling their behavior are identified. For this purpose a nonlinear Finite Element methodology using ABAQUS(TM) code is developed to predict both the cured shapes and the stability characteristics of unsymmetric cross-ply laminates. In addition, an experimental program is developed to validate the analytically predicted results through comparison with test data. A new method is proposed for attaching piezoelectric actuators to a bistable panel in order to preserve its favorable stability characteristics as well as optimizing the actuators performance. The developed nonlinear FE methodology is extended to predict the actuation requirements of bistable panels. Actuator requirements, predicted using the nonlinear FE analysis, are found to be in agreement with the test results. The current research also explores the potential for implementing bistable panels for Uninhabited Aerial Vehicle (UAV) wing configuration. To this end, a set of bistable panels is manufactured by combining symmetric and unsymmetric balanced and unbalanced stacking sequence and their stability characteristics are predicted. A preliminary analysis of the aerodynamic characteristics of the manufactured panels is carried out and the aerodynamic benefits of manufactured bistable panel are noted.
Development of FPGA-Based Bistable Unit
Energy Technology Data Exchange (ETDEWEB)
Lee, Yoon Hee; Jeong, See Chae; Ha, Jae Hong [Korea Power Engineering Company, Daejeon (Korea, Republic of)
2010-05-15
It is well known that existing nuclear power plant (NPP) control systems contain many components which are becoming obsolete at an increasing rate. Various studies have been conducted to address control system hardware obsolescence. Obsolete analog and digital control systems in non-nuclear power plants are commonly replaced with modern digital control systems, programmable logic controllers (PLC) and distributed control systems (DCS). Field Programmable Gate Arrays (FPGAs) are highlighted as an alternative means for obsolete control systems. FPGAs are advanced digital integrated circuits (ICs) that contain configurable (programmable) blocks of logic along with configurable interconnects between these blocks. Designers can configure (program) such devices to perform a tremendous variety of tasks. FPGAs have been evolved from the technology of Programmable Logic Device (PLD). Nowadays they can contain millions of logic gates by nanotechnology and so be used to implement extremely large and complex functions that previously could be realized only using Application-Specific Integrated Circuits (ASICs). This paper is to present the development of a bistable unit which executes protection functions realized in FPGAs. Functional test is performed to verify its function. An Actel ProASIC3 FPGA platform is implemented as the bistable unit for Plant Protection System (PPS).
Single coil bistable, bidirectional micromechanical actuator
Tabat, Ned; Guckel, Henry
1998-09-15
Micromechanical actuators capable of bidirectional and bistable operation can be formed on substrates using lithographic processing techniques. Bistable operation of the microactuator is obtained using a single coil and a magnetic core with a gap. A plunger having two magnetic heads is supported for back and forth linear movement with respect to the gap in the magnetic core, and is spring biased to a neutral position in which the two heads are on each side of the gap in the core. The single electrical coil is coupled to the core and is provided with electrical current to attract one of the heads toward the core by reluctance action to drive the plunger to a limit of travel in one direction. The current is then cut off and the plunger returns by spring action toward the gap, whereafter the current is reapplied to the coil to attract the other head of the plunger by reluctance action to drive the plunger to its other limit of travel. This process can be repeated at a time when switching of the actuator is required.
Tewary, Mukul; Ostblom, Joel; Prochazka, Laura; Zulueta-Coarasa, Teresa; Shakiba, Nika; Fernandez-Gonzalez, Rodrigo; Zandstra, Peter W
2017-12-01
How position-dependent cell fate acquisition occurs during embryogenesis is a central question in developmental biology. To study this process, we developed a defined, high-throughput assay to induce peri-gastrulation-associated patterning in geometrically confined human pluripotent stem cell (hPSC) colonies. We observed that, upon BMP4 treatment, phosphorylated SMAD1 (pSMAD1) activity in the colonies organized into a radial gradient. We developed a reaction-diffusion (RD)-based computational model and observed that the self-organization of pSMAD1 signaling was consistent with the RD principle. Consequent fate acquisition occurred as a function of both pSMAD1 signaling strength and duration of induction, consistent with the positional-information (PI) paradigm. We propose that the self-organized peri-gastrulation-like fate patterning in BMP4-treated geometrically confined hPSC colonies arises via a stepwise model of RD followed by PI. This two-step model predicted experimental responses to perturbations of key parameters such as colony size and BMP4 dose. Furthermore, it also predicted experimental conditions that resulted in RD-like periodic patterning in large hPSC colonies, and rescued peri-gastrulation-like patterning in colony sizes previously thought to be reticent to this behavior. © 2017. Published by The Company of Biologists Ltd.
Monotonous property of non-oscillations of the damped Duffing's equation
International Nuclear Information System (INIS)
Feng Zhaosheng
2006-01-01
In this paper, we give a qualitative study to the damped Duffing's equation by means of the qualitative theory of planar systems. Under certain parametric conditions, the monotonous property of the bounded non-oscillations is obtained. Explicit exact solutions are obtained by a direct method and application of this approach to a reaction-diffusion equation is presented
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...
On the Selection of Bistability in Genetic Regulatory Circuits
Ghim, Cheol-Min; Almaas, Eivind
2008-03-01
Bistability is a defining character of switching and memory devices. Many regulatory circuits observed in cellular reaction networks contain ``bistability motifs'' that endow a cell with efficient and reliable switching between different physiological modes of operation. One of the best characterized system, the lac operon in E. coli, has been shown to display a saddle-node bifurcation when induced by nonmetabolizable lactose analogue inducers, such as isopropylthio-β-D-galactoside (IPTG) and thio-methyl-galactoside (TMG). Motivated by the absence of bifurcation in the same system with its natural inducer, lactose, we studied the conditions for bistability and rationalized its fitness effects in the light of evolution. Stochastic simulations as well as mean-field approach confirm that history-dependent behavior as well as nongenetic inheritance, being realized by bistability motifs, may be beneficial in fluctuating environments.
Bistable responses in bacterial genetic networks: Designs and dynamical consequences
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 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
Bifurcation of transition paths induced by coupled bistable systems.
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.
Bistability, Epigenetics, and Bet-Hedging in Bacteria
Veening, Jan-Willem; Smits, Wiep Klaas; Kuipers, Oscar P.
2008-01-01
Clonal populations of microbial cells often show a high degree of phenotypic variability under homogeneous conditions. Stochastic fluctuations in the cellular components that determine cellular states can cause two distinct subpopulations, a property called bistability Phenotypic heterogeneity can
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)
The theory of stability, bistability, and instability in three-mode class-A lasers
International Nuclear Information System (INIS)
Jahanpanah, J; Rahdar, A A
2014-01-01
Instability is an inevitable and common problem in all different kinds of lasers when they are oscillating in both single-and multi-mode states. Here, the stability conditions are investigated for a three-mode class-A laser. A set of linear equations is derived for the stable oscillation of the cavity central mode together with its left and right adjacent longitudinal modes. The coefficient determinant of stability equations is Hermitian and equal to zero for the roots of two diagonal arrays. In other words, the novelty of our work is to expand the stability coefficient determinant in terms of main diagonal arrays rather than for one row or one column. These diagonal roots lead to two lower and upper boundary curves in the form of a bifurcation. The lower boundary curve mimics the single-mode laser and delimits the instability region (with no above-threshold oscillating mode) from the bistability region (with two above-threshold oscillating modes). The upper boundary curve mimics the two-mode laser and delimits the bistability region from the stability region, in which all three-longitudinal modes are simultaneously oscillating in the above-threshold state. (paper)
A genetic bistable switch utilizing nonlinear protein degradation.
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.
Does visual attention drive the dynamics of bistable perception?
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.
Genes contribute to the switching dynamics of bistable perception.
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.
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.
International Nuclear Information System (INIS)
Wang Linshan; Zhang Yan; Zhang Zhe; Wang Yangfan
2009-01-01
Global exponential robust stability is considered for a class of reaction-diffusion uncertain neural networks with time-varying delays. The purpose of the problem addressed is to establish some easy-to-test criteria for global exponential robust stability for the uncertain systems by means of a new Lyapunov-Krasovskii functional and a linear matrix inequality (LMI). A numerical example is exploited to show the usefulness of the derived LMI-based stability conditions.
Stamova, Ivanka; Stamov, Gani
2017-12-01
In this paper, we propose a fractional-order neural network system with time-varying delays and reaction-diffusion terms. We first develop a new Mittag-Leffler synchronization strategy for the controlled nodes via impulsive controllers. Using the fractional Lyapunov method sufficient conditions are given. We also study the global Mittag-Leffler synchronization of two identical fractional impulsive reaction-diffusion neural networks using linear controllers, which was an open problem even for integer-order models. Since the Mittag-Leffler stability notion is a generalization of the exponential stability concept for fractional-order systems, our results extend and improve the exponential impulsive control theory of neural network system with time-varying delays and reaction-diffusion terms to the fractional-order case. The fractional-order derivatives allow us to model the long-term memory in the neural networks, and thus the present research provides with a conceptually straightforward mathematical representation of rather complex processes. Illustrative examples are presented to show the validity of the obtained results. We show that by means of appropriate impulsive controllers we can realize the stability goal and to control the qualitative behavior of the states. An image encryption scheme is extended using fractional derivatives. Copyright © 2017 Elsevier Ltd. All rights reserved.
Dharani, S; Rakkiyappan, R; Cao, Jinde; Alsaedi, Ahmed
2017-08-01
This paper explores the problem of synchronization of a class of generalized reaction-diffusion neural networks with mixed time-varying delays. The mixed time-varying delays under consideration comprise of both discrete and distributed delays. Due to the development and merits of digital controllers, sampled-data control is a natural choice to establish synchronization in continuous-time systems. Using a newly introduced integral inequality, less conservative synchronization criteria that assure the global asymptotic synchronization of the considered generalized reaction-diffusion neural network and mixed delays are established in terms of linear matrix inequalities (LMIs). The obtained easy-to-test LMI-based synchronization criteria depends on the delay bounds in addition to the reaction-diffusion terms, which is more practicable. Upon solving these LMIs by using Matlab LMI control toolbox, a desired sampled-data controller gain can be acuqired without any difficulty. Finally, numerical examples are exploited to express the validity of the derived LMI-based synchronization criteria.
Tcaciuc, A Patricia; Borrelli, Raffaella; Zaninetta, Luciano M; Gschwend, Philip M
2018-01-24
Passive sampling is becoming a widely used tool for assessing freely dissolved concentrations of hydrophobic organic contaminants in environmental media. For certain media and target analytes, the time to reach equilibrium exceeds the deployment time, and in such cases, the loss of performance reference compounds (PRCs), loaded in the sampler before deployment, is one of the common ways used to assess the fractional equilibration of target analytes. The key assumption behind the use of PRCs is that their release is solely diffusion driven. But in this work, we show that PRC transformations in the sediment can have a measurable impact on the PRC releases and even allow estimation of that compound's transformation rate in the environment of interest. We found that in both field and lab incubations, the loss of the 13 C 2,4'-DDT PRC from a polyethylene (PE) passive sampler deployed at the sediment-water interface was accelerated compared to the loss of other PRCs ( 13 C-labeled PCBs, 13 C-labeled DDE and DDD). The DDT PRC loss was also accompanied by accumulation in the PE of its degradation product, 13 C 2,4'-DDD. Using a 1D reaction-diffusion model, we deduced the in situ degradation rates of DDT from the measured PRC loss. The in situ degradation rates increased with depth into the sediment bed (0.14 d -1 at 0-10 cm and 1.4 d -1 at 30-40 cm) and although they could not be independently validated, these rates compared favorably with literature values. This work shows that passive sampling users should be cautious when choosing PRCs, as degradation processes can affect some PRC's releases from the passive sampler. More importantly, this work opens up the opportunity for novel applications of passive samplers, particularly with regard to investigating in situ degradation rates, pathways, and products for both legacy and emerging contaminants. However, further work is needed to confirm that the rates deduced from model fitting of PRC loss are a true reflection of DDT
Flip-flop between soft-spring and hard-spring bistabilities in the ...
Indian Academy of Sciences (India)
freedom Toda oscillator that originally exhibits soft-spring bistability with counterclockwise hysteresis cycle. We observe that if the truncation is made third order, the harmonic bistability changes to hard-spring type with a clockwise hysteresis cycle.
In Silico Evolved lac Operons Exhibit Bistability for Artificial Inducers, but Not for Lactose
van Hoek, M. J. A.; Hogeweg, P.
2006-01-01
Bistability in the lac operon of Escherichia coli has been widely studied, both experimentally and theoretically. Experimentally, bistability has been observed when E. coli is induced by an artificial, nonmetabolizable, inducer. However, if the lac operon is induced with lactose, the natural inducer, bistability has not been demonstrated. We derive an analytical expression that can predict the occurrence of bistability both for artificial inducers and lactose. We find very different condition...
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)
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)
Evaluation of bistable systems versus matched filters in detecting bipolar pulse signals
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...
ERC Workshop on Geometric Partial Differential Equations
Novaga, Matteo; Valdinoci, Enrico
2013-01-01
This book is the outcome of a conference held at the Centro De Giorgi of the Scuola Normale of Pisa in September 2012. The aim of the conference was to discuss recent results on nonlinear partial differential equations, and more specifically geometric evolutions and reaction-diffusion equations. Particular attention was paid to self-similar solutions, such as solitons and travelling waves, asymptotic behaviour, formation of singularities and qualitative properties of solutions. These problems arise in many models from Physics, Biology, Image Processing and Applied Mathematics in general, and have attracted a lot of attention in recent years.
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)
Bistability of mangrove forests and competition with freshwater plants
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.
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)
Oscillations in the bistable regime of neuronal networks.
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.
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)
Frontoparietal cortex mediates perceptual transitions in bistable perception.
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.
Numerical and experimental study of bistable plates for morphing structures
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.
A bistable mechanism for chord extension morphing rotors
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.
Directory of Open Access Journals (Sweden)
Ali Izadi
2015-10-01
Full Text Available In this study, substrates concentration profile has been studied in a porous matrix containing immobilized amyloglucosidase for glucose production. This analysis has been performed by using of an analytical method called Least Square Method and results have been compared with numerical solution. Effects of effective diffusivity (, Michael's constant (, maximum reaction rate ( and initial substrate concentration ( are studied on Soluble Starch and Dextrin concentration in the spherical support. Outcomes reveal that Least Square Method has an excellent agreement with numerical solution and in the center of support, substrate concentration is minimum and increasing of effective diffusivity and Michael's constant reduce the Soluble Starch and Dextrin profile gradient.
Bistability and Asynchrony in a Boolean Model of the L-arabinose Operon in Escherichia coli.
Jenkins, Andy; Macauley, Matthew
2017-08-01
The lactose operon in Escherichia coli was the first known gene regulatory network, and it is frequently used as a prototype for new modeling paradigms. Historically, many of these modeling frameworks use differential equations. More recently, Stigler and Veliz-Cuba proposed a Boolean model that captures the bistability of the system and all of the biological steady states. In this paper, we model the well-known arabinose operon in E. coli with a Boolean network. This has several complex features not found in the lac operon, such as a protein that is both an activator and repressor, a DNA looping mechanism for gene repression, and the lack of inducer exclusion by glucose. For 11 out of 12 choices of initial conditions, we use computational algebra and Sage to verify that the state space contains a single fixed point that correctly matches the biology. The final initial condition, medium levels of arabinose and no glucose, successfully predicts the system's bistability. Finally, we compare the state space under synchronous and asynchronous update and see that the former has several artificial cycles that go away under a general asynchronous update.
Bistable direction switching in an off-axis pumped continuous wave ruby laser
Afzal, R. Sohrab; Lawandy, N. M.
1988-01-01
A report is presented of the observation of hysteretic bistable direction switching in a single-mode CW ruby laser system. This effect is only observed when the pump beam which is focused into the ruby rod is misaligned with respect to the rod end faces. At low pump powers, the ruby lases in a mode nearly collinear with the pump axis. At a higher pump power the ruby switches to a mode that is collinear with the rod end faces and preserves the original polarization. The effect is large enough to switch the beam by an angle equal to twice the diffraction angle. The observations show that under steady-state pumping, a CW ruby laser can exhibit bistable operation in its output direction and power. A calculation using the heat equation with two concentric cylinders with one as a heat source (pump laser) and the outer wall of the other held at 77 K, gives an increase in core temperature of about 0.01 K. Therefore, the increase in temperature is not large enough to change the index of refraction to account for such large macroscopic effects.
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.
Bistable cholesteric liquid crystal light shutter with multielectrode driving.
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.
A geometric theory for semilinear almost-periodic parabolic partial differential equations on RN
International Nuclear Information System (INIS)
Vuillermot, P.A.
1991-01-01
In this short expository article we review various applications of some geometric methods which have been recently devised to investigate the long time behaviour of classical solutions to certain semilinear almost-periodic reaction-diffusion equations on R N . As a consequence, we also show how to construct almost-periodic attractors for such equations and how to investigate their stability properties. The class of problems which we analyse here contains in particular well known equations of population genetics. (author). 17 refs
Design of a bistable switch to control cellular uptake.
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).
Optical bistability in nonlinear composites with coated ellipsoidal nanoparticles
Pinchuk, A
2003-01-01
Nonlinear composite structures show great promise for use in optical switching, signal processing, etc. We derive an effective nonlinear dielectric permittivity of composite structures where coated ellipsoidal nonlinear particles are imbedded in a linear host medium. The derived expression for the effective dielectric permittivity tensor follows the Clasius-Mossotti approximation. We observe conditions for the existence of the optical bistability effect in a coated ellipsoidal particle with a nonlinear core and a metallic shell. Our numerical results show stronger bistability effects in more dense suspensions of nonlinear heterogeneous ellipsoids.
An Optically Driven Bistable Janus Rotor with Patterned Metal Coatings.
Zong, Yiwu; Liu, Jing; Liu, Rui; Guo, Honglian; Yang, Mingcheng; Li, Zhiyuan; Chen, Ke
2015-11-24
Bistable rotation is realized for a gold-coated Janus colloidal particle in an infrared optical trap. The metal coating on the Janus particles are patterned by sputtering gold on a monolayer of closely packed polystyrene particles. The Janus particle is observed to stably rotate in an optical trap. Both the direction and the rate of rotation can be experimentally controlled. Numerical calculations reveal that the bistable rotation is the result of spontaneous symmetry breaking induced by the uneven curvature of the coating patterns on the Janus sphere. Our results thus provide a simple method to construct large quantities of fully functional rotary motors for nano- or microdevices.
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
The Necker-Zeno model for bistable perception.
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.
Bistable gradient networks. II. Storage capacity and behavior near saturation
McGraw, Patrick N.; Menzinger, Michael
2003-01-01
We examine numerically the storage capacity and the behavior near saturation of an attractor neural network consisting of bistable elements with an adjustable coupling strength, the bistable gradient network. For strong coupling, we find evidence of a first-order “memory blackout” phase transition, as in the Hopfield network. For weak coupling, on the other hand, there is no evidence of such a transition and memorized patterns can be stable even at high levels of loading. The enhanced storage capacity comes, however, at the cost of imperfect retrieval of the patterns from corrupted versions.
In silico evolved lac operons exhibit bistability for artificial inducers, but not for lactose.
van Hoek, M J A; Hogeweg, P
2006-10-15
Bistability in the lac operon of Escherichia coli has been widely studied, both experimentally and theoretically. Experimentally, bistability has been observed when E. coli is induced by an artificial, nonmetabolizable, inducer. However, if the lac operon is induced with lactose, the natural inducer, bistability has not been demonstrated. We derive an analytical expression that can predict the occurrence of bistability both for artificial inducers and lactose. We find very different conditions for bistability in the two cases. Indeed, for artificial inducers bistability is predicted, but for lactose the condition for bistability is much more difficult to satisfy. Moreover, we demonstrate that in silico evolution of the lac operon generates an operon that avoids bistability with respect to lactose, but does exhibit bistability with respect to artificial inducers. The activity of this evolved operon strikingly resembles the experimentally observed activity of the operon. Thus our computational experiments suggest that the wild-type lac operon, which regulates lactose metabolism, is not a bistable switch. Nevertheless, for engineering purposes, this operon can be used as a bistable switch with artificial inducers.
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.
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.
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.
THE DENSITY DISTRIBUTION IN TURBULENT BISTABLE FLOWS
International Nuclear Information System (INIS)
Gazol, Adriana; Kim, Jongsoo
2013-01-01
We numerically study the volume density probability distribution function (n-PDF) and the column density probability distribution function (Σ-PDF) resulting from thermally bistable turbulent flows. We analyze three-dimensional hydrodynamic models in periodic boxes of 100 pc by side, where turbulence is driven in the Fourier space at a wavenumber corresponding to 50 pc. At low densities (n ∼ –3 ), the n-PDF is well described by a lognormal distribution for an average local Mach number ranging from ∼0.2 to ∼5.5. As a consequence of the nonlinear development of thermal instability (TI), the logarithmic variance of the distribution of the diffuse gas increases with M faster than in the well-known isothermal case. The average local Mach number for the dense gas (n ∼> 7.1 cm –3 ) goes from ∼1.1 to ∼16.9 and the shape of the high-density zone of the n-PDF changes from a power law at low Mach numbers to a lognormal at high M values. In the latter case, the width of the distribution is smaller than in the isothermal case and grows slower with M. At high column densities, the Σ-PDF is well described by a lognormal for all of the Mach numbers we consider and, due to the presence of TI, the width of the distribution is systematically larger than in the isothermal case but follows a qualitatively similar behavior as M increases. Although a relationship between the width of the distribution and M can be found for each one of the cases mentioned above, these relations are different from those of the isothermal case.
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
Simulating the room-temperature dynamic motion of a ferromagnetic vortex in a bistable potential
Haber, E.; Badea, R.; Berezovsky, J.
2018-05-01
The ability to precisely and reliably control the dynamics of ferromagnetic (FM) vortices could lead to novel nonvolatile memory devices and logic gates. Intrinsic and fabricated defects in the FM material can pin vortices and complicate the dynamics. Here, we simulated switching a vortex between bistable pinning sites using magnetic field pulses. The dynamic motion was modeled with the Thiele equation for a massless, rigid vortex subject to room-temperature thermal noise. The dynamics were explored both when the system was at zero temperature and at room-temperature. The probability of switching for different pulses was calculated, and the major features are explained using the basins of attraction map of the two pinning sites.
Stochastic resonance in a time-delayed asymmetric bistable system with mixed periodic signal
International Nuclear Information System (INIS)
Yong-Feng, Guo; Wei, Xu; Liang, Wang
2010-01-01
This paper studies the phenomenon of stochastic resonance in an asymmetric bistable system with time-delayed feedback and mixed periodic signal by using the theory of signal-to-noise ratio in the adiabatic limit. A general approximate Fokker–Planck equation and the expression of the signal-to-noise ratio are derived through the small time delay approximation at both fundamental harmonics and mixed harmonics. The effects of the additive noise intensity Q, multiplicative noise intensity D, static asymmetry r and delay time τ on the signal-to-noise ratio are discussed. It is found that the higher mixed harmonics and the static asymmetry r can restrain stochastic resonance, and the delay time τ can enhance stochastic resonance. Moreover, the longer the delay time τ is, the larger the additive noise intensity Q and the multiplicative noise intensity D are, when the stochastic resonance appears. (general)
Bistable dynamics of an insect–pathogen model
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 85; Issue 1. Bistable dynamics of an ... Here we consider density-dependent models of transmission because we characterize diseases that spread through environmental propagules or through random contact among individuals. We consider the case where the ...
Dynamics of a bistable Miura-origami structure.
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.
Reversal Negativity and Bistable Stimuli: Attention, Awareness, or Something Else?
Intaite, Monika; Koivisto, Mika; Ruksenas, Osvaldas; Revonsuo, Antti
2010-01-01
Ambiguous (or bistable) figures are visual stimuli that have two mutually exclusive perceptual interpretations that spontaneously alternate with each other. Perceptual reversals, as compared with non-reversals, typically elicit a negative difference called reversal negativity (RN), peaking around 250 ms from stimulus onset. The cognitive…
Kerr nonlinearity and plasmonic bistability in graphene nanoribbons
DEFF Research Database (Denmark)
Christensen, Thomas; Yan, Wei; Jauho, Antti-Pekka
2015-01-01
due to field enhancement, and the total nonlinearity is significantly affected by the field inhomogeneity of the plasmonic excitation. Finally, we discuss the emergence of a plasmonic bistability which exists for energies red-shifted relative to the linear resonance. Our results offer insights...
Drag force actuated bistable microswitches for flow sensing
Kuipers, W.J.; van Baar, J.J.J.; Dijkstra, Marcel; Wiegerink, Remco J.; Lammerink, Theodorus S.J.; de Boer, J.H.; Krijnen, Gijsbertus J.M.
2006-01-01
This paper presents bistable microswitches with Au contacts with the aim to combine them with artificial hairs for flow sensing. The Au contacts are applied on both ends of a silicon nitride beam, suspended by a torsional bar at its center. The beam is provided with electrodes for electrostatic
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)
Phenomenological approach to bistable behavior of Josephson junctions
International Nuclear Information System (INIS)
Nishi, K.; Nara, S.; Hamanaka, K.
1985-01-01
The interaction of unbiased Josephson junction with external electromagnetic field in the presence of externally applied uniform magnetic field is theoretically examined by means of phenomenological treatment. It is proposed that an irradiated junction with suitably chosen parameters shows a bistable behavior of voltage across the junction as a function of the radiation intensity
The Missing Luminous Blue Variables and the Bistability Jump
Smith, N.; Vink, J.S.; de Koter, A.
2004-01-01
We discuss an interesting feature of the distribution of luminous blue variables (LBVs) on the H-R diagram, and we propose a connection with the bistability jump seen in the winds of early-type supergiants. There appears to be a deficiency of quiescent LBVs on the S Doradus instability strip at
Dynamics of a bistable Miura-origami structure
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.
Bistable dynamics of a levitated nanoparticle (Presentation Recording)
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
Resonant activation in bistable semiconductor lasers
International Nuclear Information System (INIS)
Lepri, Stefano; Giacomelli, Giovanni
2007-01-01
We theoretically investigate the possibility of observing resonant activation in the hopping dynamics of two-mode semiconductor lasers. We present a series of simulations of a rate-equation model under random and periodic modulation of the bias current. In both cases, for an optimal choice of the modulation time scale, the hopping times between the stable lasing modes attain a minimum. The simulation data are understood by means of an effective one-dimensional Langevin equation with multiplicative fluctuations. Our conclusions apply to both edge-emitting and vertical cavity lasers, thus opening the way to several experimental tests in such optical systems
Bistability of the naturally induced lactose utilization system of Escherichia coli
Stajic, Jelena; Wall, Michael
2006-03-01
In the absence of the preferred sugar glucose, lactose utilization machinery in the bacterium E. coli is activated. The genetic circuit responsible for this response, lac operon, has been observed to exhibit bistability when induced by an artificial inducer, TMG. Here we investigate conditions under which bistability might be observed in response to lactose. The aim of our study is to establish whether the natural system exhibits bistability, as is often assumed despite the lack of experimental support.
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.
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
Seirin Lee, S.
2010-03-23
Turing\\'s pattern formation mechanism exhibits sensitivity to the details of the initial conditions suggesting that, in isolation, it cannot robustly generate pattern within noisy biological environments. Nonetheless, secondary aspects of developmental self-organisation, such as a growing domain, have been shown to ameliorate this aberrant model behaviour. Furthermore, while in-situ hybridisation reveals the presence of gene expression in developmental processes, the influence of such dynamics on Turing\\'s model has received limited attention. Here, we novelly focus on the Gierer-Meinhardt reaction diffusion system considering delays due the time taken for gene expression, while incorporating a number of different domain growth profiles to further explore the influence and interplay of domain growth and gene expression on Turing\\'s mechanism. We find extensive pathological model behaviour, exhibiting one or more of the following: temporal oscillations with no spatial structure, a failure of the Turing instability and an extreme sensitivity to the initial conditions, the growth profile and the duration of gene expression. This deviant behaviour is even more severe than observed in previous studies of Schnakenberg kinetics on exponentially growing domains in the presence of gene expression (Gaffney and Monk in Bull. Math. Biol. 68:99-130, 2006). Our results emphasise that gene expression dynamics induce unrealistic behaviour in Turing\\'s model for multiple choices of kinetics and thus such aberrant modelling predictions are likely to be generic. They also highlight that domain growth can no longer ameliorate the excessive sensitivity of Turing\\'s mechanism in the presence of gene expression time delays. The above, extensive, pathologies suggest that, in the presence of gene expression, Turing\\'s mechanism would generally require a novel and extensive secondary mechanism to control reaction diffusion patterning. © 2010 Society for Mathematical Biology.
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.
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
A Redox-Active Bistable Molecular Switch Mounted inside a Metal-Organic Framework.
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.
Control of Bistability in a Delayed Duffing Oscillator
Directory of Open Access Journals (Sweden)
Mustapha Hamdi
2012-01-01
Full Text Available The effect of a high-frequency excitation on nontrivial solutions and bistability in a delayed Duffing oscillator with a delayed displacement feedback is investigated in this paper. We use the technique of direct partition of motion and the multiple scales method to obtain the slow dynamic of the system and its slow flow. The analysis of the slow flow provides approximations of the Hopf and secondary Hopf bifurcation curves. As a result, this study shows that increasing the delay gain, the system undergoes a secondary Hopf bifurcation. Further, it is indicated that as the frequency of the excitation is increased, the Hopf and secondary Hopf bifurcation curves overlap giving birth in the parameter space to small regions of bistability where a stable trivial steady state and a stable limit cycle coexist. Numerical simulations are carried out to validate the analytical finding.
Novel piezoelectric bistable oscillator architecture for wideband vibration energy harvesting
International Nuclear Information System (INIS)
Liu, W Q; Badel, A; Formosa, F; Wu, Y P; Agbossou, A
2013-01-01
Bistable vibration energy harvesters are attracting more and more interest because of their capability to scavenge energy over a large frequency band. The bistable effect is usually based on magnetic interaction or buckled beams. This paper presents a novel architecture based on amplified piezoelectric structures. This buckled spring–mass architecture allows the energy of the dynamic mass to be converted into electrical energy in the piezoelectric materials as efficiently as possible. Modeling and design are performed and a normalized expression of the harvester behavior is given. Chirp and band-limited noise excitations are used to evaluate the proposed harvester’s performances. Simulation and experimental results are in good agreement. A method of using a spectrum plot for investigating the interwell motion is presented. The effect of the electric load impedance matching strategy is also studied. Results and comparisons with the literature show that the proposed device combines a large bandwidth and a high power density. (paper)
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.
Modeling bistable behaviors in morphing structures through finite element simulations.
Guo, Qiaohang; Zheng, Huang; Chen, Wenzhe; Chen, Zi
2014-01-01
Bistable structures, exemplified by the Venus flytrap and slap bracelets, can transit between different configurations upon certain external stimulation. Here we study, through three-dimensional finite element simulations, the bistable behaviors in elastic plates in the absence of terminate loads, but with pre-strains in one (or both) of the two composite layers. Both the scenarios with and without a given geometric mis-orientation angle are investigated, the results of which are consistent with recent theoretical and experimental studies. This work can open ample venues for programmable designs of plant/shell structures with large deformations, with applications in designing bio-inspired robotics for biomedical research and morphing/deployable structures in aerospace engineering.
Waterbomb base: a symmetric single-vertex bistable origami mechanism
Hanna, Brandon H.; Lund, Jason M.; Lang, Robert J.; Magleby, Spencer P.; Howell, Larry L.
2014-09-01
The origami waterbomb base is a single-vertex bistable origami mechanism that has unique properties which may prove useful in a variety of applications. It also shows promise as a test bed for smart materials and actuation because of its straightforward geometry and multiple phases of motion, ranging from simple to more complex. This study develops a quantitative understanding of the symmetric waterbomb base's kinetic behavior. This is done by completing kinematic and potential energy analyses to understand and predict bistable behavior. A physical prototype is constructed and tested to validate the results of the analyses. Finite element and virtual work analyses based on the prototype are used to explore the locations of the stable equilibrium positions and the force-deflection response. The model results are verified through comparisons to measurements on a physical prototype. The resulting models describe waterbomb base behavior and provide an engineering tool for application development.
Mathematical modeling of Myosin induced bistability of Lamellipodial fragments.
Hirsch, S; Manhart, A; Schmeiser, C
2017-01-01
For various cell types and for lamellipodial fragments on flat surfaces, externally induced and spontaneous transitions between symmetric nonmoving states and polarized migration have been observed. This behavior is indicative of bistability of the cytoskeleton dynamics. In this work, the Filament Based Lamellipodium Model (FBLM), a two-dimensional, anisotropic, two-phase continuum model for the dynamics of the actin filament network in lamellipodia, is extended by a new description of actin-myosin interaction. For appropriately chosen parameter values, the resulting model has bistable dynamics with stable states showing the qualitative features observed in experiments. This is demonstrated by numerical simulations and by an analysis of a strongly simplified version of the FBLM with rigid filaments and planar lamellipodia at the cell front and rear.
Internal optical bistability of quasi-two-dimensional semiconductor nanoheterostructures
Derevyanchuk, Oleksandr V.; Kramar, Natalia K.; Kramar, Valeriy M.
2018-01-01
We represent the results of numerical computations of the frequency and temperature domains of possible realization of internal optical bistability in flat quasi-two-dimensional semiconductor nanoheterostructures with a single quantum well (i.e., nanofilms). Particular computations have been made for a nanofilm of layered semiconductor PbI2 embedded in dielectric medium, i.e. ethylene-methacrylic acid (E-MAA) copolymer. It is shown that an increase in the nanofilm's thickness leads to a long-wave shift of the frequency range of the manifestation the phenomenon of bistability, to increase the size of the hysteresis loop, as well as to the expansion of the temperature interval at which the realization of this phenomenon is possible.
Bistability threshold inside hysteresis loop of nonlinear fiber Bragg gratings.
Yosia, Yosia; Ping, Shum; Chao, Lu
2005-06-27
We show the Cross Phase Modulation (XPM) effect between CW probe that operates in bistability region and strong Gaussian pump in a Fiber Bragg Grating (FBG) by Implicit 4th Order Runge-Kutta Method. The XPM effect results in three unique nonlinear switching behaviors of the probe transmission depending on the pump peak intensity and its Full Width Half Maximum (FWHM) value. From this observation, we offer the FBG three potential nonlinear switching applications in all-optical signal processing domain as: a step-up all-optical switching, an all-optical inverter, and an all-optical limiter. The bistability threshold that determines the nonlinear switching behaviors of probe transmission after Gaussian pump injection is defined numerically and shown to be equivalent to the unstable state inside hysteresis loop.
Stochastic sensitivity of a bistable energy model for visual perception
Pisarchik, Alexander N.; Bashkirtseva, Irina; Ryashko, Lev
2017-01-01
Modern trends in physiology, psychology and cognitive neuroscience suggest that noise is an essential component of brain functionality and self-organization. With adequate noise the brain as a complex dynamical system can easily access different ordered states and improve signal detection for decision-making by preventing deadlocks. Using a stochastic sensitivity function approach, we analyze how sensitive equilibrium points are to Gaussian noise in a bistable energy model often used for qualitative description of visual perception. The probability distribution of noise-induced transitions between two coexisting percepts is calculated at different noise intensity and system stability. Stochastic squeezing of the hysteresis range and its transition from positive (bistable regime) to negative (intermittency regime) are demonstrated as the noise intensity increases. The hysteresis is more sensitive to noise in the system with higher stability.
Waterbomb base: a symmetric single-vertex bistable origami mechanism
International Nuclear Information System (INIS)
Hanna, Brandon H; Lund, Jason M; Magleby, Spencer P; Howell, Larry L; Lang, Robert J
2014-01-01
The origami waterbomb base is a single-vertex bistable origami mechanism that has unique properties which may prove useful in a variety of applications. It also shows promise as a test bed for smart materials and actuation because of its straightforward geometry and multiple phases of motion, ranging from simple to more complex. This study develops a quantitative understanding of the symmetric waterbomb base's kinetic behavior. This is done by completing kinematic and potential energy analyses to understand and predict bistable behavior. A physical prototype is constructed and tested to validate the results of the analyses. Finite element and virtual work analyses based on the prototype are used to explore the locations of the stable equilibrium positions and the force–deflection response. The model results are verified through comparisons to measurements on a physical prototype. The resulting models describe waterbomb base behavior and provide an engineering tool for application development. (paper)
Circular magnetic bistability in Co-rich amorphous microwires
International Nuclear Information System (INIS)
Chizhik, A; Gonzalez, J; Zhukov, A; Blanco, J M
2003-01-01
Circular magnetic bistability associated with a large Barkhausen jump between two states with opposite directions of circular magnetization have been observed by magneto-optical Kerr effect in nearly-zero magnetostrictive glass covered Co-rich amorphous microwire. The influence of external axial tensile stress on the circular switching field has been studied. Observed results have been related with a circular magneto-elastic anisotropy induced by a tensile stress in the outer transversally magnetized shell of the microwire
A Precise Temperature-Responsive Bistable Switch Controlling Yersinia Virulence.
Nuss, Aaron Mischa; Schuster, Franziska; Roselius, Louisa; Klein, Johannes; Bücker, René; Herbst, Katharina; Heroven, Ann Kathrin; Pisano, Fabio; Wittmann, Christoph; Münch, Richard; Müller, Johannes; Jahn, Dieter; Dersch, Petra
2016-12-01
Different biomolecules have been identified in bacterial pathogens that sense changes in temperature and trigger expression of virulence programs upon host entry. However, the dynamics and quantitative outcome of this response in individual cells of a population, and how this influences pathogenicity are unknown. Here, we address these questions using a thermosensing virulence regulator of an intestinal pathogen (RovA of Yersinia pseudotuberculosis) as a model. We reveal that this regulator is part of a novel thermoresponsive bistable switch, which leads to high- and low-invasive subpopulations within a narrow temperature range. The temperature range in which bistability is observed is defined by the degradation and synthesis rate of the regulator, and is further adjustable via a nutrient-responsive regulator. The thermoresponsive switch is also characterized by a hysteretic behavior in which activation and deactivation occurred on vastly different time scales. Mathematical modeling accurately mirrored the experimental behavior and predicted that the thermoresponsiveness of this sophisticated bistable switch is mainly determined by the thermo-triggered increase of RovA proteolysis. We further observed RovA ON and OFF subpopulations of Y. pseudotuberculosis in the Peyer's patches and caecum of infected mice, and that changes in the RovA ON/OFF cell ratio reduce tissue colonization and overall virulence. This points to a bet-hedging strategy in which the thermoresponsive bistable switch plays a key role in adapting the bacteria to the fluctuating conditions encountered as they pass through the host's intestinal epithelium and suggests novel strategies for the development of antimicrobial therapies.
A Precise Temperature-Responsive Bistable Switch Controlling Yersinia Virulence.
Directory of Open Access Journals (Sweden)
Aaron Mischa Nuss
2016-12-01
Full Text Available Different biomolecules have been identified in bacterial pathogens that sense changes in temperature and trigger expression of virulence programs upon host entry. However, the dynamics and quantitative outcome of this response in individual cells of a population, and how this influences pathogenicity are unknown. Here, we address these questions using a thermosensing virulence regulator of an intestinal pathogen (RovA of Yersinia pseudotuberculosis as a model. We reveal that this regulator is part of a novel thermoresponsive bistable switch, which leads to high- and low-invasive subpopulations within a narrow temperature range. The temperature range in which bistability is observed is defined by the degradation and synthesis rate of the regulator, and is further adjustable via a nutrient-responsive regulator. The thermoresponsive switch is also characterized by a hysteretic behavior in which activation and deactivation occurred on vastly different time scales. Mathematical modeling accurately mirrored the experimental behavior and predicted that the thermoresponsiveness of this sophisticated bistable switch is mainly determined by the thermo-triggered increase of RovA proteolysis. We further observed RovA ON and OFF subpopulations of Y. pseudotuberculosis in the Peyer's patches and caecum of infected mice, and that changes in the RovA ON/OFF cell ratio reduce tissue colonization and overall virulence. This points to a bet-hedging strategy in which the thermoresponsive bistable switch plays a key role in adapting the bacteria to the fluctuating conditions encountered as they pass through the host's intestinal epithelium and suggests novel strategies for the development of antimicrobial therapies.
Autocatalytic, bistable, oscillatory networks of biologically relevant organic reactions
Semenov, Sergey N.; Kraft, Lewis J.; Ainla, Alar; Zhao, Mengxia; Baghbanzadeh, Mostafa; Campbell, Victoria E.; Kang, Kyungtae; Fox, Jerome M.; Whitesides, George M.
2016-09-01
Networks of organic chemical reactions are important in life and probably played a central part in its origin. Network dynamics regulate cell division, circadian rhythms, nerve impulses and chemotaxis, and guide the development of organisms. Although out-of-equilibrium networks of chemical reactions have the potential to display emergent network dynamics such as spontaneous pattern formation, bistability and periodic oscillations, the principles that enable networks of organic reactions to develop complex behaviours are incompletely understood. Here we describe a network of biologically relevant organic reactions (amide formation, thiolate-thioester exchange, thiolate-disulfide interchange and conjugate addition) that displays bistability and oscillations in the concentrations of organic thiols and amides. Oscillations arise from the interaction between three subcomponents of the network: an autocatalytic cycle that generates thiols and amides from thioesters and dialkyl disulfides; a trigger that controls autocatalytic growth; and inhibitory processes that remove activating thiol species that are produced during the autocatalytic cycle. In contrast to previous studies that have demonstrated oscillations and bistability using highly evolved biomolecules (enzymes and DNA) or inorganic molecules of questionable biochemical relevance (for example, those used in Belousov-Zhabotinskii-type reactions), the organic molecules we use are relevant to metabolism and similar to those that might have existed on the early Earth. By using small organic molecules to build a network of organic reactions with autocatalytic, bistable and oscillatory behaviour, we identify principles that explain the ways in which dynamic networks relevant to life could have developed. Modifications of this network will clarify the influence of molecular structure on the dynamics of reaction networks, and may enable the design of biomimetic networks and of synthetic self-regulating and evolving
Bistable switches control memory and plasticity in cellular differentiation
Wang, Lei; Walker, Brandon L.; Iannaccone, Stephen; Bhatt, Devang; Kennedy, Patrick J.; Tse, William T.
2009-01-01
Development of stem and progenitor cells into specialized tissues in multicellular organisms involves a series of cell fate decisions. Cellular differentiation in higher organisms is generally considered irreversible, and the idea of developmental plasticity in postnatal tissues is controversial. Here, we show that inhibition of mitogen-activated protein kinase (MAPK) in a human bone marrow stromal cell-derived myogenic subclone suppresses their myogenic ability and converts them into satellite cell-like precursors that respond to osteogenic stimulation. Clonal analysis of the induced osteogenic response reveals ultrasensitivity and an “all-or-none” behavior, hallmarks of a bistable switch mechanism with stochastic noise. The response demonstrates cellular memory, which is contingent on the accumulation of an intracellular factor and can be erased by factor dilution through cell divisions or inhibition of protein synthesis. The effect of MAPK inhibition also exhibits memory and appears to be controlled by another bistable switch further upstream that determines cell fate. Once the memory associated with osteogenic differentiation is erased, the cells regain their myogenic ability. These results support a model of cell fate decision in which a network of bistable switches controls inducible production of lineage-specific differentiation factors. A competitive balance between these factors determines cell fate. Our work underscores the dynamic nature of cellular differentiation and explains mechanistically the dual properties of stability and plasticity associated with the process. PMID:19366677
Brain mechanisms for simple perception and bistable perception.
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.
Interplay of bistable kinetics of gene expression during cellular growth
International Nuclear Information System (INIS)
Zhdanov, Vladimir P
2009-01-01
In cells, the bistable kinetics of gene expression can be observed on the level of (i) one gene with positive feedback between protein and mRNA production, (ii) two genes with negative mutual feedback between protein and mRNA production, or (iii) in more complex cases. We analyse the interplay of two genes of type (ii) governed by a gene of type (i) during cellular growth. In particular, using kinetic Monte Carlo simulations, we show that in the case where gene 1, operating in the bistable regime, regulates mutually inhibiting genes 2 and 3, also operating in the bistable regime, the latter genes may eventually be trapped either to the state with high transcriptional activity of gene 2 and low activity of gene 3 or to the state with high transcriptional activity of gene 3 and low activity of gene 2. The probability to get to one of these states depends on the values of the model parameters. If genes 2 and 3 are kinetically equivalent, the probability is equal to 0.5. Thus, our model illustrates how different intracellular states can be chosen at random with predetermined probabilities. This type of kinetics of gene expression may be behind complex processes occurring in cells, e.g., behind the choice of the fate by stem cells
Optical Bistability For Optical Signal Processing And Computing
Peyghambarian, N.; Gibbs, H. M.
1985-02-01
In this paper we present the basic principles of optical bistability and summarize the current advances in semiconductor optical switching, with emphasis on recent results in GaAs, CuCI, InAs, InSb, CdS, ZnS, and ZnSe etalons. These devices have great potential for applications involving optical signal processing and computing. As an example, we discuss the use of arrays of bistable devices for parallel optical processing and for addressable spatial light modulators. The use of nonlinear etalons as optical gates is also illustrated. To date, GaAs devices have shown the most favorable characteristics for practical applications. They operate at room temperature with a few milliwatts of power using a laser diode as the only light source. Quasi-cw operation and optical fiber signal regeneration have also been demonstrated. A GaAs NOR gate operates in 1 ps with <3 pJ incident energy; this, of course, implies a 1 ps switch-on time for a bistable etalon.
Bistability in spinal motoneurons in vivo: systematic variations in rhythmic firing patterns.
Lee, R H; Heckman, C J
1998-08-01
In the presence of the monoamines serotonin and norepinephrine, spinal motoneurons can exhibit bistable behavior, in which a brief period of excitatory input evokes prolonged self-sustained firing. A brief inhibitory input returns the cell to the quiescent state. To determine whether motoneurons differ in their capacity for bistable behavior, intracellular recordings were obtained in the decerebrate cat preparation. To enhance the likelihood of encountering bistable behavior, the noradrenergic alpha1 agonist methoxamine was applied to the ventral surface of the cord. The capacity of the cells to produce bistable behavior was assessed from the duration of self-sustained firing evoked by a brief (1.5 s) excitatory synaptic input from muscle spindle Ia afferents. About 35% (17 of 49) of the cells produced steady self-sustained firing for >3 s and were considered fully bistable. The other 32 cells ( approximately 65%) were partially bistable, with self-sustained firing lasting zero current, so that the ascending current threshold was positive while the descending current threshold was negative. This negative offset meant that fully bistable cells could exhibit tonic firing without depolarizing injected current. Partially bistable cells exhibited very different F-I characteristics. Firing rate acceleration was just as large as in fully bistable cells but did not occur until well above the current level needed to initiate rhythmic firing. F-I gain after acceleration was negative, there was little to no hysteresis between the ascending and descending firing thresholds, and both thresholds were above the zero current level. These properties of partially bistable cells suggest their functional role is in tasks requiring relatively brief, high forces. The low thresholds of fully bistable cells mean they will be readily recruited in low force tasks like posture, where their prolonged self-sustained firing would be advantageous.
Trajectory attractors of equations of mathematical physics
International Nuclear Information System (INIS)
Vishik, Marko I; Chepyzhov, Vladimir V
2011-01-01
In this survey the method of trajectory dynamical systems and trajectory attractors is described, and is applied in the study of the limiting asymptotic behaviour of solutions of non-linear evolution equations. This method is especially useful in the study of dissipative equations of mathematical physics for which the corresponding Cauchy initial-value problem has a global (weak) solution with respect to the time but the uniqueness of this solution either has not been established or does not hold. An important example of such an equation is the 3D Navier-Stokes system in a bounded domain. In such a situation one cannot use directly the classical scheme of construction of a dynamical system in the phase space of initial conditions of the Cauchy problem of a given equation and find a global attractor of this dynamical system. Nevertheless, for such equations it is possible to construct a trajectory dynamical system and investigate a trajectory attractor of the corresponding translation semigroup. This universal method is applied for various types of equations arising in mathematical physics: for general dissipative reaction-diffusion systems, for the 3D Navier-Stokes system, for dissipative wave equations, for non-linear elliptic equations in cylindrical domains, and for other equations and systems. Special attention is given to using the method of trajectory attractors in approximation and perturbation problems arising in complicated models of mathematical physics. Bibliography: 96 titles.
Take it of leave it : Mechanisms underlying bacterial bistable regulatory networks
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
International Nuclear Information System (INIS)
Ivanyukovich, V.A.; Karas', V.I.; Lomako, V.M.
1989-01-01
A new radiation configurational-bistable defect diffring from the known similar defects by the fact that it possessestemperature inversion of states is detected in gallium arsenide. Configurational-bistable rearrangements are shown to be considered as phase transitions of the second type
Nugroho, Bintoro; Iskandar, Alexander; Malyshev, V.A.; Knoester, Jasper
2013-01-01
We conduct a theoretical study of the bistable optical response of a nanoparticle heterodimer comprised of a closely spaced semiconductor quantum dot and a metal nanoparticle. The bistable nature of the response results from the interplay between the quantum dot's optical nonlinearity and its
Bistable traveling waves for a competitive-cooperative system with nonlocal delays
Tian, Yanling; Zhao, Xiao-Qiang
2018-04-01
This paper is devoted to the study of bistable traveling waves for a competitive-cooperative reaction and diffusion system with nonlocal time delays. The existence of bistable waves is established by appealing to the theory of monotone semiflows and the finite-delay approximations. Then the global stability of such traveling waves is obtained via a squeezing technique and a dynamical systems approach.
International Nuclear Information System (INIS)
Ivanyukovich, V.A.; Karas', V.I.; Lomako, V.M.
1989-01-01
A new radiation defect with a bistable configuration was discovered in gallium arsenide. It differed from similar known defects by an inversion of states caused by variation of temperature. It is shown that configuration-bistable modifications of the structure can be regarded as second-order phase transitions
Topical Meeting on Optical Bistability Held at Rochester, New York on 15-17 June 1983.
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
Bistable traveling wave solutions in a competitive recursion system with Ricker nonlinearity
Directory of Open Access Journals (Sweden)
Shuxia Pan
2014-03-01
Full Text Available Using an abstract scheme of monotone semiflows, the existence of bistable traveling wave solutions of a competitive recursion system is established. From the viewpoint of population dynamics, the bistable traveling wave solutions describe the strong inter-specific actions between two competitive species.
Linear population allocation by bistable switches in response to transient stimulation.
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.
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.
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)
Energy Technology Data Exchange (ETDEWEB)
Chevriaux, D
2007-06-15
We study wave scattering in different nonlinear media possessing a natural forbidden band gap. In particular, we show the existence of a bistable behavior in media governed by the sine-Gordon equation (short pendular chain, Josephson junction array, quantum Hall bilayer), or the nonlinear Schroedinger equation (Kerr and Bragg media), in discrete and continuous models. These different media are submitted to periodic boundary conditions with a frequency in the forbidden band gap and an amplitude that determines their stability states. Indeed, for a sufficient amplitude (supra-transmission), the medium switches from reflector to transmitter, hence allowing the output signal to jump from evanescent to large values. We give a complete analytical description of the bistability that allows to understand the different stationary states observed and to predict the switch of one state to the other. (author)
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
Directory of Open Access Journals (Sweden)
Marco A. Velasco
2016-10-01
Full Text Available Scaffolds are essential in bone tissue engineering, as they provide support to cells and growth factors necessary to regenerate tissue. In addition, they meet the mechanical function of the bone while it regenerates. Currently, the multiple methods for designing and manufacturing scaffolds are based on regular structures from a unit cell that repeats in a given domain. However, these methods do not resemble the actual structure of the trabecular bone which may work against osseous tissue regeneration. To explore the design of porous structures with similar mechanical properties to native bone, a geometric generation scheme from a reaction-diffusion model and its manufacturing via a material jetting system is proposed. This article presents the methodology used, the geometric characteristics and the modulus of elasticity of the scaffolds designed and manufactured. The method proposed shows its potential to generate structures that allow to control the basic scaffold properties for bone tissue engineering such as the width of the channels and porosity. The mechanical properties of our scaffolds are similar to trabecular tissue present in vertebrae and tibia bones. Tests on the manufactured scaffolds show that it is necessary to consider the orientation of the object relative to the printing system because the channel geometry, mechanical properties and roughness are heavily influenced by the position of the surface analyzed with respect to the printing axis. A possible line for future work may be the establishment of a set of guidelines to consider the effects of manufacturing processes in designing stages.
Owolabi, Kolade M.
2017-03-01
In this paper, some nonlinear space-fractional order reaction-diffusion equations (SFORDE) on a finite but large spatial domain x ∈ [0, L], x = x(x , y , z) and t ∈ [0, T] are considered. Also in this work, the standard reaction-diffusion system with boundary conditions is generalized by replacing the second-order spatial derivatives with Riemann-Liouville space-fractional derivatives of order α, for 0 Fourier spectral method is introduced as a better alternative to existing low order schemes for the integration of fractional in space reaction-diffusion problems in conjunction with an adaptive exponential time differencing method, and solve a range of one-, two- and three-components SFORDE numerically to obtain patterns in one- and two-dimensions with a straight forward extension to three spatial dimensions in a sub-diffusive (0 reaction-diffusion case. With application to models in biology and physics, different spatiotemporal dynamics are observed and displayed.
The tunable bistable and multistable memory effect in polymer nanowires
International Nuclear Information System (INIS)
Rahman, Atikur; Sanyal, Milan K
2008-01-01
Tunable bistable and multistable resistance switching in conducting polymer nanowires has been reported. These wires show reproducible switching transition under several READ-WRITE-ERASE cycles. The switching is observed at low temperature and the ON/OFF resistance ratio for the voltage biased switching transition was found to be more than 10 3 . Current biased measurements show lower ON/OFF ratio and some of the nanowires exhibit a multistable switching transition in current biased measurements. The threshold voltage for switching and the ON/OFF resistance ratio can be tuned by changing doping concentration of the nanowires
Electron transfer dynamics of bistable single-molecule junctions
DEFF Research Database (Denmark)
Danilov, A.V; Kubatkin, S.; Kafanov, S. G.
2006-01-01
We present transport measurements of single-molecule junctions bridged by a molecule with three benzene rings connected by two double bonds and with thiol end-groups that allow chemical binding to gold electrodes. The I-V curves show switching behavior between two distinct states. By statistical ...... analysis of the switching events, we show that a 300 meV mode mediates the transition between the two states. We propose that breaking and reformation of a S-H bond in the contact zone between molecule and electrode explains the observed bistability....
Intercellular calcium waves in glial cells with bistable dynamics
Wei, Fang; Shuai, Jianwei
2011-04-01
A two-dimensional model is proposed for intercellular calcium (Ca2 +) waves with Ca2 +-induced IP3 regeneration and the diffusion of IP3 through gap junctions. Many experimental observations in glial cells, i.e. responding to local mechanical stimulation, glutamate application, mechanical stimulation followed by ACh application, and glutamate followed by mechanical stimulation, are reproduced and classified by the model. We show that a glial cell model with bistable dynamics, i.e. a Ca2 + oscillation state coexisting with a fixed point, can cause a prolonged plateau of Ca2 + signals in the cells nearby the stimulated cell when the cell network responds to the local mechanical stimulation.
Voltage-driven beam bistability in a reorientational uniaxial dielectric
Directory of Open Access Journals (Sweden)
Armando Piccardi
2016-04-01
Full Text Available We report on voltage controlled bistability of optical beams propagating in a nonlocal reorientational uniaxial dielectric, namely, nematic liquid crystals. In the nonlinear regime where spatial solitons can be generated, two stable states are accessible to a beam of given power in a finite interval of applied voltages, one state corresponding to linear diffraction and the other to self-confinement. We observe such a first-order transition and the associated hysteresis in a configuration when both the beam and the voltage reorientate the molecules beyond a threshold.
A faster switching regime for zenithal bistable nematic displays
International Nuclear Information System (INIS)
Rudin, J.
1997-01-01
A simpler and faster switching regime for Zenithal Bistable Nematic displays is reported. A cell, based on homeotropic alignment of nematic liquid crystal over a continuous blazed monograting on one surface, can be switched using bipolar pulses an order of magnitude faster than monopolar pulses of the same voltage. We propose that this regime relies on simple dielectric coupling to drive the cell into a higher energy state with a long pulse time, and the relaxation into a lower energy state after the creation of surface defects from a shorter applied pulse. Although flexoelectric effects are observed, they do not form the basis of state selection as was proposed for the monopolar pulses
Optical bistability in electrically coupled SOA-BJT devices
Costanzo-Caso, Pablo A.; Jin, Yiye; Gehl, Michael; Granieri, Sergio; Siahmakoun, Azad
2010-06-01
A novel optical bistable device based on an electrically coupled semiconductor optical amplifier (SOA) and a bipolar juncture transistor (BJT) is proposed and experimentally demonstrated. The measured switching time is about 0.9-1.0 us, mainly limited by the electrical capacitance of the SOA and the parasitic inductance of the electrical connections. However, the effects of parasitic components can be reduced employing current electronic-photonic integration circuits (EPIC). Numerical simulations confirm that for capacitance values in tens of femtofarads switching speed can reach tens of GHz.
Bistability in a complementary metal oxide semiconductor inverter circuit.
Carroll, Thomas L
2005-09-01
Radiofrequency signals can disrupt the operation of low frequency circuits. A digital inverter circuit would seem to be immune to such disruption, because its output state usually jumps abruptly between 0 and 5 V. Nevertheless, when driven with a high frequency signal, the inverter can have two coexisting stable states (which are not at 0 and 5 V). Slow switching between these states (by changing the rf signal) will produce a low frequency signal. I demonstrate the bistability in a circuit experiment and in a simple model of the circuit.
Optical bistabilities of higher harmonics: Inhomogeneous and transverse effects
Energy Technology Data Exchange (ETDEWEB)
Hassan, S.S., E-mail: Shoukryhassan@hotmail.com [Department of Mathematics, College of Science, University of Bahrain, P.O. Box 32038 (Bahrain); Manchester Metropolitan University, Dept. of Computing, Maths. and Digital Technology, Manchester M1 5GD (United Kingdom); Sharaby, Y.A., E-mail: Yasser_Sharaby@hotmail.com [Department of Physics, Faculty of Science, Suez Canal University, Suez (Egypt); Ali, M.F.M., E-mail: dr.mona.fathy@hotmail.com [Department of Mathematics: Faculty of Science, Ain Shams University, Cairo (Egypt); Joshi, A., E-mail: ajoshi@eiu.edu [Department of Physics, Eastern Illinois University, Charleston, IL 61920 (United States)
2012-10-15
The steady state behavior of optical bistable system in a ring cavity with transverse field variations and inhomogeneousely broadened two-level atoms is investigated outside the rotating wave approximation (RWA). Analytical and numerical investigation is presented for different cases of transverse field variations with Lorentzian or Gaussian line widths. When both (transverse and inhomogeneous) features taken into account, the first harmonic output field component outside the RWA exhibits a one-way switching down processes (butterfly OB) or reversed (clockwise) OB behavior, depending on the atomic linewidth shape.
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.
Model-based design of bistable cell factories for metabolic engineering.
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.
Control and characterization of a bistable laminate generated with piezoelectricity
Lee, Andrew J.; Moosavian, Amin; Inman, Daniel J.
2017-08-01
Extensive research has been conducted on utilizing smart materials such as piezoelectric and shape memory alloy actuators to induce snap through of bistable structures for morphing applications. However, there has only been limited success in initiating snap through from both stable states due to the lack of actuation authority. A novel solution in the form of a piezoelectrically generated bistable laminate consisting of only macro fiber composites (MFC), allowing complete configuration control without any external assistance, is explored in detail here. Specifically, this paper presents the full analytical, computational, and experimental results of the laminate’s design, geometry, bifurcation behavior, and snap through capability. By bonding two actuated MFCs in a [0MFC/90MFC]T layup and releasing the voltage post cure, piezoelectric strain anisotropy and the resulting in-plane residual stresses yield two statically stable states that are cylindrically shaped. The analytical model uses the Rayleigh-Ritz minimization of total potential energy and finite element analysis is implemented in MSC Nastran. The [0MFC/90MFC]T laminate is then manufactured and experimentally characterized for model validation. This paper demonstrates the adaptive laminate’s unassisted forward and reverse snap through capability enabled by the efficiencies gained from simultaneously being the actuator and the primary structure.
Magnetic actuation and transition shapes of a bistable spherical cap
Directory of Open Access Journals (Sweden)
E.G. Loukaides
2014-10-01
Full Text Available Multistable shells have been proposed for a variety of applications; however, their actuation is almost exclusively addressed through embedded piezoelectric patches. Additional actuation techniques are needed for applications requiring high strains or where remote actuation is desirable. Part of the reason for the lack of research in this area is the absence of appropriate models describing the detailed deformation and energetics of such shells. This work presents a bistable spherical cap made of iron carbonyl-infused polydimethylsiloxane. The magnetizable structure can be actuated remotely through permanent magnets while the transition is recorded with a high-speed camera. Moreover, the experiment is reproduced in a finite element (FE dynamic model for comparison with the physical observations. High-speed footage of the physical cap inversion together with the FE modeling gives valuable insight on preferable intermediate geometries. Both methods return similar values for the magnetic field strength required for the snap-through. High-strain multistable spherical cap transformation is demonstrated, based on informed material selection. We discover that non-axisymmetric transition shapes are preferred in intermediate geometries by bistable spherical caps. We develop the methods for design and analysis of such actuators, including the feasibility of remote actuation methods for multistable shells.
Boolean models can explain bistability in the lac operon.
Veliz-Cuba, Alan; Stigler, Brandilyn
2011-06-01
The lac operon in Escherichia coli has been studied extensively and is one of the earliest gene systems found to undergo both positive and negative control. The lac operon is known to exhibit bistability, in the sense that the operon is either induced or uninduced. Many dynamical models have been proposed to capture this phenomenon. While most are based on complex mathematical formulations, it has been suggested that for other gene systems network topology is sufficient to produce the desired dynamical behavior. We present a Boolean network as a discrete model for the lac operon. Our model includes the two main glucose control mechanisms of catabolite repression and inducer exclusion. We show that this Boolean model is capable of predicting the ON and OFF steady states and bistability. Further, we present a reduced model which shows that lac mRNA and lactose form the core of the lac operon, and that this reduced model exhibits the same dynamics. This work suggests that the key to model qualitative dynamics of gene systems is the topology of the network and Boolean models are well suited for this purpose.
Designing a stochastic genetic switch by coupling chaos and bistability
Energy Technology Data Exchange (ETDEWEB)
Zhao, Xiang [State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Beijing 100871 (China); Ouyang, Qi [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); Wang, Hongli, E-mail: hlwang@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)
2015-11-15
In stem cell differentiation, a pluripotent stem cell becomes progressively specialized and generates specific cell types through a series of epigenetic processes. How cells can precisely determine their fate in a fluctuating environment is a currently unsolved problem. In this paper, we suggest an abstract gene regulatory network to describe mathematically the differentiation phenomenon featuring stochasticity, divergent cell fates, and robustness. The network consists of three functional motifs: an upstream chaotic motif, a buffering motif of incoherent feed forward loop capable of generating a pulse, and a downstream motif which is bistable. The dynamic behavior is typically a transient chaos with fractal basin boundaries. The trajectories take transiently chaotic journeys before divergently settling down to the bistable states. The ratio of the probability that the high state is achieved to the probability that the low state is reached can maintain a constant in a population of cells with varied molecular fluctuations. The ratio can be turned up or down when proper parameters are adjusted. The model suggests a possible mechanism for the robustness against fluctuations that is prominently featured in pluripotent cell differentiations and developmental phenomena.
A new concept for active bistable twisting structures
Schultz, Marc R.
2005-05-01
A novel type of morphing structure capable of a large change in shape with a small energy input is discussed in this paper. The considered structures consist of two curved shells that are joined in a specific manner to form a bistable airfoil-like structure. The two stable shapes have a difference in axial twist, and the structure may be transformed between the stable shapes by a simple snap-through action. The benefit of a bistable structure of this type is that, if the stable shapes are operational shapes, power is needed only to transform the structure from one shape to another. The discussed structures could be used in aerodynamic applications such as morphing wings, or as aerodynamic control surfaces. The investigation discussed in this paper considers both experiment and finite-element analysis. Several graphite-epoxy composite and one steel device were created as proof-of-concept models. To demonstrate active control of these structures, piezocomposite actuators were applied to one of the composite structures and used to transform the structure between stable shapes. The analysis was used to compare the predicted shapes with the experimental shapes, and to study how changes to the geometric input values affected the shape and operational characteristics of the structures. The predicted shapes showed excellent agreement with the experimental shapes, and the results of the parametric study suggest that the shapes and the snap-through characteristics can be easily tailored to meet specific needs.
Optical bi-stable shutter development/improvement
Lizon, J. L.; Haddad, N.; Castillo, R.
2012-09-01
Two of the VLT instruments (Giraffe and VIMOS) are using the large magnetic E/150 from Prontor (with an aperture diameter of 150 mm). As we were facing an unacceptable number of failures with this component some improvement plan was discussed already in 2004. The final decision for starting this program was conditioned by the decision from the constructor to stop the production. The opportunity was taken to improve the design building a fully bi-stable mechanism in order to reduce the thermal dissipation. The project was developed in collaboration between the two main ESO sites doing the best use of the manpower and of the technical capability available at the two centers. The project took advantage of the laser Mask Manufacturing Unit and the invar sheets used to prepare the VIMOS MOS mask to fabricate the shutter petals. Our paper describes the development including the intensive and long optimization period. To conclude this optimization we proceed with a long life test on two units. These units have demonstrate a very high level of reliability (up to 100 000 cycles without failure which can be estimated to an equivalent 6 years of operation of the instrument) A new bi-stable shutter driver and controller have also been developed. Some of the highlights of this unit are the fully configurable coil driving parameters, usage of braking strategy to dump mechanical vibration and reduce mechanical wearing, configurable usage of OPEN and CLOSE sensors, non volatile storage of parameters, user friendly front panel interface.
Evaristo, J. A.; Willenbring, J.
2013-12-01
The time dependency of silicate mineral weathering has been explored in the literature in terms of processes and features that are intrinsic and extrinsic to the mineral [1]. However, although the advent of sophisticated reactive transport models has allowed for coupling increasingly complex reaction and transport processes [2,3], a simple and fundamental understanding of the temporal evolution of weathering is lacking. Here, we propose that a purely deterministic approach may not be sufficient given the inherent differences in reactivity over space and time. Therefore, we explore how a combined reaction-diffusion and random rate model - informed by a stochastic distribution of weathering rates K (T-1) - might be able to explain not only the temporal evolution but also the hydrodynamics of weathering during earthquakes; the latter being purportedly described by time-dependent property permeability (L2). Preliminary model results show that (1) an increase in dimensionless quantity βrp, where β is the diffusion length (L-1) and rp is the distance between pores (L), leads to a decrease in minimum reaction rate with time from the relation Kmin ∝ e-βrp/rp ; (2) at a given porosity, a time-dependent decrease in reactivity arises as permeability decreases due to decreasing pore size (and therefore increasing rp), which in turn may be related to the time-dependent feedback between dissolution and precipitation; (3) while permeability is lower in older soils, transient stresses as during earthquakes [4], may induce more efficient "declogging" of pores in these soils than in younger soils due to higher hydrodynamic viscous shear stress, thereby, resulting in a coseismic change in stream discharge Q; and (4) subsequent weathering beyond t~Kmin-1 exhibits a fall in rates, marking the cessation of logarithmic decay possibly due to dissolution-precipitation feedback. [1] White and Brantley (2003), Chem. Geol. 202, 479. [2] Lichtner P.C. (1996), Mineralogical Society of
Blowup Analysis for a Nonlocal Diffusion Equation with Reaction and Absorption
Directory of Open Access Journals (Sweden)
Yulan Wang
2012-01-01
Full Text Available We investigate a nonlocal reaction diffusion equation with absorption under Neumann boundary. We obtain optimal conditions on the exponents of the reaction and absorption terms for the existence of solutions blowing up in finite time, or for the global existence and boundedness of all solutions. For the blowup solutions, we also study the blowup rate estimates and the localization of blowup set. Moreover, we show some numerical experiments which illustrate our results.
Optical nonlinearity and bistability in the bound exciton energy range of CdS
International Nuclear Information System (INIS)
Hoenig, T.; Gutowski, J.
1988-01-01
Under high excitation conditions thick CdS samples show pronounced broad-band nonlinear transmission in the bound exciton region and up to a wavelength of about 515 nm at cryo-temperatures. This behavior is only explainable in a model based on impurity neutralization and bound exciton creation. The suitability of these nonlinearities to yield optical bistability will be shown. Bistable operation is investigated in dependence of crystal thickness, impurity concentration, excitation density, wavelength, and temperature. A strong correlation to acceptor-bound exciton generation is obtained, and the explanation of this bistable operation fits well with that of the above mentioned transmission behavior. (author)
Bistability Analysis of Excitatory-Inhibitory Neural Networks in Limited-Sustained-Activity Regime
International Nuclear Information System (INIS)
Ni Yun; Wu Liang; Wu Dan; Zhu Shiqun
2011-01-01
Bistable behavior of neuronal complex networks is investigated in the limited-sustained-activity regime when the network is composed of excitatory and inhibitory neurons. The standard stability analysis is performed on the two metastable states separately. Both theoretical analysis and numerical simulations show consistently that the difference between time scales of excitatory and inhibitory populations can influence the dynamical behaviors of the neuronal networks dramatically, leading to the transition from bistable behaviors with memory effects to the collapse of bistable behaviors. These results may suggest one possible neuronal information processing by only tuning time scales. (interdisciplinary physics and related areas of science and technology)
Bistability and hysteresis in the emergence of pulses in microstrip Gunn-diode circuits
Energy Technology Data Exchange (ETDEWEB)
Yurchenko, V. B., E-mail: v.yurchenko@nuim.ie [O. Ya. Usikov Institute for Radiophysics and Electronics, National Academy of Sciences of Ukraine, 12 Proskura St., Kharkiv 61085 (Ukraine); Electrical and Electronic Engineering Department, Gazi University, Celal Bayar Bulvari, Ankara 06570 (Turkey); Yurchenko, L. V. [O. Ya. Usikov Institute for Radiophysics and Electronics, National Academy of Sciences of Ukraine, 12 Proskura St., Kharkiv 61085 (Ukraine)
2014-12-15
We develop time-domain simulations of microwave and THz radiation sources built as arrays of active devices when the radiation wavelength is small as compared to spacing between electronic components. We pursue an approach when the system is represented by equations with time-delay feedback that could generate chaos and other forms of complicated dynamics. The approach simplifies simulations of ultra-wideband effects and exceeds capabilities of frequency-domain methods. As a model case, we simulated a microstrip circuit with Gunn diode and a remote resonator emitting the radiation towards infinity. We observed the emergence of either the continuous waves or the trains of high-frequency pulses depending on the bias conditions. We found bistability and hysteresis in the onset of different oscillation modes that depends on the way of driving the bias voltage into the domain of instability of the given system. The results would allow one to improve the design of THz radiation sources with time-delay coupling between components.
The rate dependent response of a bistable chain at finite temperature
Benichou, Itamar; Zhang, Yaojun; Dudko, Olga K.; Givli, Sefi
2016-10-01
We study the rate dependent response of a bistable chain subjected to thermal fluctuations. The study is motivated by the fact that the behavior of this model system is prototypical to a wide range of nonlinear processes in materials physics, biology and chemistry. To account for the stochastic nature of the system response, we formulate a set of governing equations for the evolution of the probability density of meta-stable configurations. Based on this approach, we calculate the behavior for a wide range of parametric values, such as rate, temperature, overall stiffness, and number of elements in the chain. Our results suggest that fundamental characteristics of the response, such as average transition stress and hysteresis, can be captured by a simple law which folds the influence of all these factors into a single non-dimensional quantity. We also show that the applicability of analytical results previously obtained for single-well systems can be extended to systems having multiple wells by proper definition of rate and of the transition stress.
Bistability and hysteresis in the emergence of pulses in microstrip Gunn-diode circuits
Directory of Open Access Journals (Sweden)
V. B. Yurchenko
2014-12-01
Full Text Available We develop time-domain simulations of microwave and THz radiation sources built as arrays of active devices when the radiation wavelength is small as compared to spacing between electronic components. We pursue an approach when the system is represented by equations with time-delay feedback that could generate chaos and other forms of complicated dynamics. The approach simplifies simulations of ultra-wideband effects and exceeds capabilities of frequency-domain methods. As a model case, we simulated a microstrip circuit with Gunn diode and a remote resonator emitting the radiation towards infinity. We observed the emergence of either the continuous waves or the trains of high-frequency pulses depending on the bias conditions. We found bistability and hysteresis in the onset of different oscillation modes that depends on the way of driving the bias voltage into the domain of instability of the given system. The results would allow one to improve the design of THz radiation sources with time-delay coupling between components.
Yuan, Xu-Jin
2012-09-01
In comparison with the phenomenon of negative index refraction observed in artificial meta-materials, it is interesting to ask if this type of behavior also exists or not in reaction-diffusion systems that support nonlinear chemical waves. Previous studies indicate that the negative index refraction could occur on a interface between a medium of a normal wave and a medium that supports anti-waves. Here we investigate the phenomenon in the complex Ginzburg—Landau equation (CGLE) in a close relationship with the quantitative model for the chloriteiodide-malonic acid (CIMA) reaction. The amplitude equation CGLE is deduced from the CIMA reaction, and simulations with mapped parameters from the reaction-diffusion equation reveal that the competition between normal waves and anti-waves on the interface determines whether the negative index refraction occurs or not.
Iterative solution of the semiconductor device equations
Energy Technology Data Exchange (ETDEWEB)
Bova, S.W.; Carey, G.F. [Univ. of Texas, Austin, TX (United States)
1996-12-31
Most semiconductor device models can be described by a nonlinear Poisson equation for the electrostatic potential coupled to a system of convection-reaction-diffusion equations for the transport of charge and energy. These equations are typically solved in a decoupled fashion and e.g. Newton`s method is used to obtain the resulting sequences of linear systems. The Poisson problem leads to a symmetric, positive definite system which we solve iteratively using conjugate gradient. The transport equations lead to nonsymmetric, indefinite systems, thereby complicating the selection of an appropriate iterative method. Moreover, their solutions exhibit steep layers and are subject to numerical oscillations and instabilities if standard Galerkin-type discretization strategies are used. In the present study, we use an upwind finite element technique for the transport equations. We also evaluate the performance of different iterative methods for the transport equations and investigate various preconditioners for a few generalized gradient methods. Numerical examples are given for a representative two-dimensional depletion MOSFET.
International Nuclear Information System (INIS)
Vysotskyi, Bogdan; Parrain, Fabien; Lefeuvre, Elie; Aubry, Denis; Gaucher, Philippe
2016-01-01
The purpose of the presented work is to introduce the novel design of electrostatic energy harvester using bistable mechanism with compensational springs in gravity field capable of providing the output of several μW under the excitation of extremely small amplitude (up to 0.2g) and low frequency (10-100Hz). Presented energy harvester uses the bistable hysteresis modification to achieve low-frequency low-amplitude sensibility. It was demonstrated with finite element modelling (FEM) that hysteresis width produced by bistability is changing with a constant linear coefficient as a function of a compensational spring stiffness and thus a device sensitivity could be adjusted to the minimum point for the amplitude of external excitation. Further, highly non-linear bistable double curved beam mechanism assures the high sensitivity in frequencial domain due to the non-defined bandwidth. The equivalent circuit technique is used for simulating the device performance. (paper)
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
Harnessing the bistable composite shells to design a tunable phononic band gap structure
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.
International Nuclear Information System (INIS)
Uche, C; Elston, S J; Parry-Jones, L A
2005-01-01
Nematic liquid crystals have been shown to exhibit zenithal electro-optic bistability in devices containing sinusoidal and deformed sinusoidal gratings. Recently it has been shown that zenithal bistable states can also be supported at isolated edges of square gratings. In this paper, we present microscopic observations of bistability in cells containing sinusoidal gratings and long-pitch square gratings. We have also investigated a novel display based on square wells. High frame-rate video microscopy was used to obtain time-sequenced images when the devices were switched with monopolar pulses. These show that zenithal bistable switching can occur by two different processes: (i) domain growth (observed in cells containing sinusoidal gratings) and (ii) homogenous switching (observed in cells containing isolated edges
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)
A bistable switch in dynamic thiodepsipeptide folding and template-directed ligation.
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.
Bistable Output from a Coupled-Resonator Vertical-Cavity Laser Diode
Energy Technology Data Exchange (ETDEWEB)
FISCHER,ARTHUR J.; CHOQUETTE,KENT D.; CHOW,WENG W.; ALLERMAN,ANDREW A.; GEIB,KENT M.
2000-07-20
The authors 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 {micro}W to the electrical power applied to the top cavity. Theoretical analysis suggests that 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.
Optical bistability of a thin film of resonant atoms in a phase-sensitive thermostate
International Nuclear Information System (INIS)
Basharov, A.M.
1995-01-01
It is shown theoretically that when a thin film of two-level atoms interacting with a resonant coherent electromagnetic wave is additionally illuminated with a squeezed field, a bistable transmission/reflection regime for coherent waves is obtained. This regime depends strongly on the phase difference between the coherent and the squeezed fields. New regimes, including a bistable regime, for the interaction of a coherent field with a film of resonant atoms are predicted based on this phenomenon. 14 refs., 5 figs
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
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.
Bistable laser device with multiple coupled active vertical-cavity resonators
Fischer, Arthur J.; Choquette, Kent D.; Chow, Weng W.
2003-08-19
A new class of bistable coupled-resonator vertical-cavity semiconductor laser devices has been developed. These bistable laser devices can be switched, either electrically or optically, between lasing and non-lasing states. A switching signal with a power of a fraction of a milliwatt can change the laser output of such a device by a factor of a hundred, thereby enabling a range of optical switching and data encoding applications.
A predictive coding account of bistable perception - a model-based fMRI study.
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
DEFF Research Database (Denmark)
Tuz, Vladimir R.; Novitsky, Denis V.; Prosvirnin, Sergey L.
2014-01-01
, while light reflected from the other side has its polarization unchanged. Using the nonlinear transfer matrix calculations in the frequency domain, it is demonstrated that defect resonances in the nonlinear reflection spectra undergo bending, resulting in polarization bistability of reflected light....... This bistability is shown to result in abrupt switching between linear polarization of the output reflected light when the input intensity is varied. This switching is confirmed in finite-difference time-domain simulations, and its hysteresis character is established....
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
Stable patterns for fourth-order parabolic equations
van den Berg, J. B.; Vandervorst, R. C.
2002-01-01
We consider fourth-order parabolic equations of gradient type. For the sake of simplicity, the analysis is carried out for the specific equation $u\\sb t=-\\gamma\\ u\\sb {xxxx}+\\beta u\\sb {xx}-F\\sp \\prime(u)$ with $(t,x)\\in (0,\\infty)\\times(0, L)$ and $\\gamma,\\beta>0$ and where $F(u)$ is a bistable potential. We study its stable equilibria as a function of the ratio $\\gamma/beta\\sp 2$. As the ratio $\\gamma/beta\\sp 2$ crosses an explicit threshold value, the number of stable ...
Cramps: a sign of motoneurone 'bistability' in a human patient.
Baldissera, F; Cavallari, P; Dworzak, F
1991-12-09
In a patient suffering from severe long-lasting cramps, cramps were triggered in the triceps surae by volleys in homonymous Ia afferents (elicited by electrical stimulation or by tendon taps) and were interrupted by antidromic invasion and Renshaw inhibition of triceps surae motoneurones (evoked by a single maximal stimulation of motor axons). This result suggests that the mechanisms which generate the cramps are intrinsic to alpha-motoneurone somata. A similar on-off switching of a self-sustained motor discharge has been observed in the decerebrate cat and recognized to depend on 'bistability' of the motoneuronal membrane. We propose that the same mechanism may be at the origin of the cramp discharge.
Angular dependence of the exchange bias for the bistable state
Energy Technology Data Exchange (ETDEWEB)
Bai, Yuhao [College of Physics and Electronic Information, Shanxi Normal University, Linfen 041004 (China); Research College of materials science, Shanxi Normal University, Linfen 041004 (China); Xu, Xiaohong, E-mail: xuxh@dns.sxnu.edu.cn [Research College of materials science, Shanxi Normal University, Linfen 041004 (China); Key Laboratory of Magnetic Molecules and Magnetic Information Materials, Ministry of Education, Shanxi Normal University, Linfen 041004 (China)
2017-06-15
The angular dependence of the exchange bias (ADEB) has been investigated in detail when the exchange-coupled ferromagnetic (FM)/antiferromagnetic (AFM) bilayer is in the bistable state. Complete and incomplete jump phenomena were found at the intrinsic easy and hard axes, when they pass through two special positions making the angular deviation of 58.2826° and 121.7174° from the easy axis of the uniaxial anisotropy, respectively. The combination of these different types of the jump phenomena at the intrinsic easy and hard axes yields five distinct types of the ADEB. The physical condition for each type of ADEB is established. Additionally, the extreme value problem of the exchange bias field and coercivity are also discussed, which is an important technological issue in the design of the magnetoresistive and spintronic devices. These results enable us to make a comprehensive understanding of the experimental ADEB curves.
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.
Bistability of flight states for heavy falling plates
Lau, Edwin; Huang, Wei-Xi
2017-11-01
Interactions of falling flat plates in two-dimensional flows is presented through direct numerical simulation and immersed boundary method. The transition from steady falling to tumbling flight for heavy plates is presented. At steep angles of release, the plates undergo a period of amplitude increasing fluttering motion before developing to tumble. For the same fluid-solid system of Reynolds number Re and moment of inertia I*, shallow angles of release develop to a state of steady falling after a period of diminishing fluttering amplitude. Simulations further construct a mapping of this bistable region. Relationships among Re, I*, and the critical angles of release separating the two flight states are also provided. The inclusion of this finding on the mapping of flight states suggests fluttering motion as a transitional state before the onset of tumble. National Natural Science Foundation of China or NSFC (Grant No. 11322221).
Synaptic Bistability Due to Nucleation and Evaporation of Receptor Clusters
Burlakov, V. M.
2012-01-10
We introduce a bistability mechanism for long-term synaptic plasticity based on switching between two metastable states that contain significantly different numbers of synaptic receptors. One state is characterized by a two-dimensional gas of mobile interacting receptors and is stabilized against clustering by a high nucleation barrier. The other state contains a receptor gas in equilibrium with a large cluster of immobile receptors, which is stabilized by the turnover rate of receptors into and out of the synapse. Transitions between the two states can be initiated by either an increase (potentiation) or a decrease (depotentiation) of the net receptor flux into the synapse. This changes the saturation level of the receptor gas and triggers nucleation or evaporation of receptor clusters. © 2012 American Physical Society.
Laurent, M; Charvin, G; Guespin-Michel, J
2005-12-14
Bistability is the capacity of a system to switch in an "all-or-none" manner between alternative steady states. This powerful concept originates from the analysis of non-linear equations driving open systems. It is one of the various patterns of regulation associated with a particular class of dynamic structures that Glansdorff and Prigogine baptised "dissipative structures". The idea of discontinuous transitions between alternative states was first formulated much earlier, by Delbrück, in 1949. Cohn and Horibata and Novick and Weiner confirmed that such transitions occur in experiments on the lactose operon carried out ten years later. Modelling with non-linear differential equations made it possible to simulate the dynamic behaviour of the lac operon, and modelling by asynchronous logical analysis elucidated the determinant role played by positive feedback circuits in the emergence of multistationarity. Nevertheless, these studies were largely ignored until the recent demonstration of the hysteretic nature of the bistable transition between alternative states of the lac operon. As originally suggested by Delbrück, the pattern of lactose consumption adopted by the bacterium is controlled epigenetically rather than genetically: the true key determinant is the direction of change of an environmental variable with respect to the structural components of the operon.
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.
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)
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
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.
Melanopsin bistability: a fly's eye technology in the human retina.
Directory of Open Access Journals (Sweden)
Ludovic S Mure
Full Text Available In addition to rods and cones, the human retina contains light-sensitive ganglion cells that express melanopsin, a photopigment with signal transduction mechanisms similar to that of invertebrate rhabdomeric photopigments (IRP. Like fly rhodopsins, melanopsin acts as a dual-state photosensitive flip-flop in which light drives both phototransduction responses and chromophore photoregeneration that bestows independence from the retinoid cycle required by rods and cones to regenerate photoresponsiveness following bleaching by light. To explore the hypothesis that melanopsin in humans expresses the properties of a bistable photopigment in vivo we used the pupillary light reflex (PLR as a tool but with methods designed to study invertebrate photoreceptors. We show that the pupil only attains a fully stabilized state of constriction after several minutes of light exposure, a feature that is consistent with typical IRP photoequilibrium spectra. We further demonstrate that previous exposure to long wavelength light increases, while short wavelength light decreases the amplitude of pupil constriction, a fundamental property of IRP difference spectra. Modelling these responses to invertebrate photopigment templates yields two putative spectra for the underlying R and M photopigment states with peaks at 481 nm and 587 nm respectively. Furthermore, this bistable mechanism may confer a novel form of "photic memory" since information of prior light conditions is retained and shapes subsequent responses to light. These results suggest that the human retina exploits fly-like photoreceptive mechanisms that are potentially important for the modulation of non-visual responses to light and highlights the ubiquitous nature of photoswitchable photosensors across living organisms.