Resilience in reaction-diffusion systems
NASA Astrophysics Data System (ADS)
van Vuuren, J. H.
1999-10-01
Reaction-diffusion systems with zero-flux Neumann boundaries are widely used to model various kinds of interaction in, for example, the scientific fields of ecology, biology, chemistry, medicine and industry. The physical systems within these fields are often known to be (conditionally or unconditionally) resilient with respect to shocks, disturbances or catastrophies in the immediate environment. In order to be good mathematical models of such situations the reaction-diffusion systems must have the same resilient or asymptotic behaviour as that of the physical situation. Three fundamentally different kinds of reaction terms are usually distinguished according to the entry signs of the reaction Jacobian: mutualism, mixed (predator-prey) interaction and competition. The asymptotic stability (in the Poincare sense) of mutualistic systems has already been studied extensively, but the results cannot be generalized (globally) to the other two fundamental types, which are not order-preserving. A partial (local) generalization is, however given here for these two types, involving simple Jacobian inequalities and knowledge (often prompted by the underlying physical situation) of invariant sets in solution space. The return time of resilient systems and the approach rate of asymptotically stable solutions are also estimated. Key words: reaction-diffusion system; competition; resilience; asymptotic stability.
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.
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. PMID:27078346
Wave Phenomena in Reaction-Diffusion Systems
NASA Astrophysics Data System (ADS)
Steinbock, Oliver; Engel, Harald
2013-12-01
Pattern formation in excitable and oscillatory reaction-diffusion systems provides intriguing examples for the emergence of macroscopic order from molecular reaction events and Brownian motion. Here we review recent results on several aspects of excitation waves including anomalous dispersion, vortex pinning, and three-dimensional scroll waves. Anomalies in the speed-wavelength dependence of pulse trains include nonmonotonic behavior, bistability, and velocity gaps. We further report on the hysteresis effects during the pinning-depinning transition of twodimensional spiral waves. The pinning of three-dimensional scroll waves shows even richer dynamic complexity, partly due to the possibility of geometric and topological mismatches between the unexcitable, pinning heterogeneities and the one-dimensional rotation backbone of the vortex. As examples we present results on the pinning of scroll rings to spherical, C-shaped, and genus-2-type heterogeneities. We also review the main results of several experimental studies employing the Belousov-Zhabotinsky reaction and briefly discuss the biomedical relevance of this research especially in the context of cardiology.
NASA Astrophysics Data System (ADS)
Gaskins, Delora K.; Pruc, Emily E.; Epstein, Irving R.; Dolnik, Milos
2016-07-01
Turing patterns in the chlorine dioxide-iodine-malonic acid reaction were modified through additions of sodium halide salt solutions. The range of wavelengths obtained is several times larger than in the previously reported literature. Pattern wavelength was observed to significantly increase with sodium bromide or sodium chloride. A transition to a uniform state was found at high halide concentrations. The observed experimental results are qualitatively well reproduced in numerical simulations with the Lengyel-Epstein model with an additional chemically realistic kinetic term to account for the added halide and an adjustment of the activator diffusion rate to allow for interhalogen formation.
Gaskins, Delora K; Pruc, Emily E; Epstein, Irving R; Dolnik, Milos
2016-07-29
Turing patterns in the chlorine dioxide-iodine-malonic acid reaction were modified through additions of sodium halide salt solutions. The range of wavelengths obtained is several times larger than in the previously reported literature. Pattern wavelength was observed to significantly increase with sodium bromide or sodium chloride. A transition to a uniform state was found at high halide concentrations. The observed experimental results are qualitatively well reproduced in numerical simulations with the Lengyel-Epstein model with an additional chemically realistic kinetic term to account for the added halide and an adjustment of the activator diffusion rate to allow for interhalogen formation. PMID:27517779
Network representation of reaction--diffusion systems far from equilibrium.
Wyatt, J L
1978-09-01
This paper develops the network theory of chemical reaction systems from first principles. The network approach is then used to derive a canonical set of differential equations for reaction--diffusion systems, and an analysis of the Brusselator is presented as an example. PMID:755597
Turing instability in reaction-diffusion systems with nonlinear diffusion
NASA Astrophysics Data System (ADS)
Zemskov, E. P.
2013-10-01
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.
Turing instability in reaction-diffusion systems with nonlinear diffusion
Zemskov, E. P.
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.
Bifurcation characteristics of fractional reaction-diffusion systems
NASA Astrophysics Data System (ADS)
Datsko, Bohdan; Gafiychuk, Vasyl; Luchko, Yuri
2012-11-01
Anomalous behavior of many complex heterogeneous systems is known to be adequate modeled with the fractional differential equations and in particular with the fractional reaction-diffusion systems (FRDS). In this article, a generalized reaction-diffusion model in form of a system of nonlinear fractional partial differential equations is considered. It is shown that orders of the fractional derivatives contained in the FRDS are new bifurcation parameters that can change stability both of the spatially-homogeneous and of the spatially-nonhomogeneous stationary solutions. A general principle of linear stability for FRDS is formulated. The results of linear stability analysis are confirmed by computer simulations of some basic FRDS with classical nonlinearities. It is shown that stability of steady state solutions of FRDS and their evolution are mainly determined by the orders of the fractional derivatives and the eigenvalue spectrum of the linearized systems. Moreover, new types of spatiotemporal solutions and new mechanisms of pattern formation can be observed in FRDS because of new bifurcation types. Characteristic plots of evolution of steady state solutions for basic time-fractional reaction-diffusion systems are presented.
Resonant Phase Patterns in a Reaction-Diffusion System
Lin, Anna L.; Bertram, Matthias; Martinez, Karl; Swinney, Harry L.; Ardelea, Alexandre; Carey, Graham F.
2000-05-01
Resonance regions similar to the Arnol'd tongues found in single oscillator frequency locking are observed in experiments using a spatially extended periodically forced Belousov-Zhabotinsky system. We identify six distinct 2:1 subharmonic resonant patterns and describe them in terms of the position-dependent phase and magnitude of the oscillations. Some experimentally observed features are also found in numerical studies of a forced Brusselator reaction-diffusion model. (c) 2000 The American Physical Society.
Resonant phase patterns in a reaction-diffusion system
Lin; Bertram; Martinez; Swinney; Ardelea; Carey
2000-05-01
Resonance regions similar to the Arnol'd tongues found in single oscillator frequency locking are observed in experiments using a spatially extended periodically forced Belousov-Zhabotinsky system. We identify six distinct 2:1 subharmonic resonant patterns and describe them in terms of the position-dependent phase and magnitude of the oscillations. Some experimentally observed features are also found in numerical studies of a forced Brusselator reaction-diffusion model. PMID:10990655
Parametric Instabilities in Brusselator Reaction-Diffusion Systems
NASA Astrophysics Data System (ADS)
Geislinger, Brian; Purnell, Moriel; Kawai, Ryoichi
2002-10-01
We investigate the effects of a time-periodic parametric perturbation to a reaction diffusion system based on the Brusselator. The system becomes unstable when the pertubation frequency satisfies usual parametric resonance condition, and remains stable when the perturbation is out of resonance. When the perturbation is randomly inhomogenous, instabilites at these resonance frequencies form spatial patterns in parameter regions where the unperturbed system would be stable. However, these same patterns can be destroyed if the perturbation is homogeneous. These numerical results can be explained by two competing types of synchronizations - synchronization between neighbors (mutual synchronization) and synchronization to the perturbation (modulation synchronization).
Hybrid stochastic simulations of intracellular reaction-diffusion systems
Kalantzis, Georgios
2009-01-01
With the observation that stochasticity is important in biological systems, chemical kinetics have begun to receive wider interest. While the use of Monte Carlo discrete event simulations most accurately capture the variability of molecular species, they become computationally costly for complex reaction-diffusion systems with large populations of molecules. On the other hand, continuous time models are computationally efficient but they fail to capture any variability in the molecular species. In this study a novel hybrid stochastic approach is introduced for simulating reaction-diffusion systems. We developed a dynamic partitioning strategy using fractional propensities. In that way processes with high frequency are simulated mostly with deterministic rate-based equations, and those with low frequency mostly with the exact stochastic algorithm of Gillespie. In this way we preserve the stochastic behavior of cellular pathways while being able to apply it to large populations of molecules. In this article we describe this hybrid algorithmic approach, and we demonstrate its accuracy and efficiency compared with the Gillespie algorithm for two different systems. First, a model of intracellular viral kinetics with two steady states and second, a compartmental model of the postsynaptic spine head for studying the dynamics of Ca+2 and NMDA receptors. PMID:19414282
Analysis of reaction-diffusion systems with anomalous subdiffusion.
Haugh, Jason M
2009-07-22
Reaction-diffusion equations are the cornerstone of modeling biochemical systems with spatial gradients, which are relevant to biological processes such as signal transduction. Implicit in the formulation of these equations is the assumption of Fick's law, which states that the local diffusive flux of species i is proportional to its concentration gradient; however, in the context of complex fluids such as cytoplasm and cell membranes, the use of Fick's law is based on empiricism, whereas evidence has been mounting that such media foster anomalous subdiffusion (with mean-squared displacement increasing less than linearly with time) over certain length scales. Particularly when modeling diffusion-controlled reactions and other systems where the spatial domain is considered semi-infinite, assuming Fickian diffusion might not be appropriate. In this article, two simple, conceptually extreme models of anomalous subdiffusion are used in the framework of Green's functions to demonstrate the solution of four reaction-diffusion problems that are well known in the biophysical context of signal transduction: fluorescence recovery after photobleaching, the Smolochowski limit for diffusion-controlled reactions in solution, the spatial range of a diffusing molecule with finite lifetime, and the collision coupling mechanism of diffusion-controlled reactions in two dimensions. In each case, there are only subtle differences between the two subdiffusion models, suggesting how measurements of mean-squared displacement versus time might generally inform models of reactive systems with partial diffusion control.
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. PMID:21804911
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.
On the continuum time limit of reaction-diffusion systems
NASA Astrophysics Data System (ADS)
Grassberger, Peter
2013-09-01
The parity-conserving branching-annihilating random walk (pc-BARW) model is a reaction-diffusion system on a lattice where particles can branch into m offsprings with even m and hop to neighboring sites. If two or more particles land on the same site, they immediately annihilate pairwise. In this way the number of particles is preserved modulo two. It is well known that the pc-BARW with m = 2 in 1 spatial dimension has no phase transition (it is always subcritical), if the hopping is described by a continuous time random walk. In contrast, the m = 2 1-d pc-BARW has a phase transition when formulated in discrete time, but we show that the continuous time limit is non-trivial: When the time step \\delta t\\to 0 , the branching and hopping probabilities at the critical point scale with different powers of \\delta t . These powers are different for different microscopic realizations. Although this phenomenon is not observed in some other reaction-diffusion systems like, e.g., the contact process, we argue that it should be generic and not restricted to the 1-d pc-BARW model.
Simulating mesoscopic reaction-diffusion systems using the Gillespie algorithm
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.
Segmented waves in a reaction-diffusion-convection system.
Rossi, Federico; Budroni, Marcello A; Marchettini, Nadia; Carballido-Landeira, Jorge
2012-09-01
The interaction of traveling waves, with both Marangoni and buoyancy driven flows, can generate an extraordinary rich array of patterns ranging from stationary structures to chaotic waves. However, the inherent complexity of reaction-diffusion-convection (RDC) systems makes the explanation of the patterning mechanisms very difficult, both numerically and experimentally. In this paper, we describe the appearance of segmented waves in a shallow layer of an excitable Belousov-Zhabotinsky solution. The segmentation process was found to be dependent both on the depth of the solution and on the excitability of the reaction. We caught the essential features of the system through a RDC model, where the chemical waves were coupled both with surface and bulk fluid motions and we found that by varying the excitability of the reaction, and in turn the wavelength of the chemical fronts, it is possible to create a sort of hydrodynamic resonance structures (corridors), which are responsible for the segmentation process.
Amplitude equations for reaction-diffusion systems with cross diffusion
NASA Astrophysics Data System (ADS)
Zemskov, Evgeny P.; Vanag, Vladimir K.; Epstein, Irving R.
2011-09-01
Using Taylor series expansion, multiscaling, and further expansion in powers of a small parameter, we develop general amplitude equations for two-variable reaction-diffusion systems with cross-diffusion terms in the cases of Hopf and Turing instabilities. We apply this analysis to the Oregonator and Brusselator models and find that inhibitor cross diffusion induced by the activator and activator cross diffusion induced by the inhibitor have opposite effects in the two models as a result of the different structure of their community matrices. Our analysis facilitates finding regions of supercritical and subcritical bifurcations, as well as wave and antiwave domains and domains of turbulent waves in the case of Hopf instability.
Amplitude equations for reaction-diffusion systems with cross diffusion.
Zemskov, Evgeny P; Vanag, Vladimir K; Epstein, Irving R
2011-09-01
Using Taylor series expansion, multiscaling, and further expansion in powers of a small parameter, we develop general amplitude equations for two-variable reaction-diffusion systems with cross-diffusion terms in the cases of Hopf and Turing instabilities. We apply this analysis to the Oregonator and Brusselator models and find that inhibitor cross diffusion induced by the activator and activator cross diffusion induced by the inhibitor have opposite effects in the two models as a result of the different structure of their community matrices. Our analysis facilitates finding regions of supercritical and subcritical bifurcations, as well as wave and antiwave domains and domains of turbulent waves in the case of Hopf instability. PMID:22060484
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.
Hopping transport in hostile reaction-diffusion systems
NASA Astrophysics Data System (ADS)
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.
Self-replication of mesa patterns in reaction diffusion systems
NASA Astrophysics Data System (ADS)
Kolokolnikov, T.; Ward, M. J.; Wei, J.
2007-12-01
Certain two-component reaction-diffusion systems on a finite interval are known to possess mesa (box-like) steady-state patterns in the singularly perturbed limit of small diffusivity for one of the two solution components. As the diffusivity D of the second component is decreased below some critical value Dc, with Dc=O(1), the existence of a steady-state mesa pattern is lost, triggering the onset of a mesa self-replication event that ultimately leads to the creation of additional mesas. The initiation of this phenomena is studied in detail for a particular scaling limit of the Brusselator model. Near the existence threshold Dc of a single steady-state mesa, it is shown that an internal layer forms in the centre of the mesa. The structure of the solution within this internal layer is shown to be governed by a certain core problem, comprised of a single nonautonomous second-order ODE. By analysing this core problem using rigorous and formal asymptotic methods, and by using the Singular Limit Eigenvalue Problem (SLEP) method to asymptotically calculate small eigenvalues, an analytical verification of the conditions of Nishiura and Ueyama [Y. Nishiura, D. Ueyama, A skeleton structure of self-replicating dynamics, Physica D 130 (1) (1999) 73-104], believed to be responsible for self-replication, is given. These conditions include: (1) The existence of a saddle-node threshold at which the steady-state mesa pattern disappears; (2) the dimple-shaped eigenfunction at the threshold, believed to be responsible for the initiation of the replication process; and (3) the stability of the mesa pattern above the existence threshold. Finally, we show that the core problem is universal in the sense that it pertains to a class of reaction-diffusion systems, including the Gierer-Meinhardt model with saturation, where mesa self-replication also occurs.
Stochastic operator-splitting method for reaction-diffusion systems
NASA Astrophysics Data System (ADS)
Choi, TaiJung; Maurya, Mano Ram; Tartakovsky, Daniel M.; Subramaniam, Shankar
2012-11-01
Many biochemical processes at the sub-cellular level involve a small number of molecules. The local numbers of these molecules vary in space and time, and exhibit random fluctuations that can only be captured with stochastic simulations. We present a novel stochastic operator-splitting algorithm to model such reaction-diffusion phenomena. The reaction and diffusion steps employ stochastic simulation algorithms and Brownian dynamics, respectively. Through theoretical analysis, we have developed an algorithm to identify if the system is reaction-controlled, diffusion-controlled or is in an intermediate regime. The time-step size is chosen accordingly at each step of the simulation. We have used three examples to demonstrate the accuracy and robustness of the proposed algorithm. The first example deals with diffusion of two chemical species undergoing an irreversible bimolecular reaction. It is used to validate our algorithm by comparing its results with the solution obtained from a corresponding deterministic partial differential equation at low and high number of molecules. In this example, we also compare the results from our method to those obtained using a Gillespie multi-particle (GMP) method. The second example, which models simplified RNA synthesis, is used to study the performance of our algorithm in reaction- and diffusion-controlled regimes and to investigate the effects of local inhomogeneity. The third example models reaction-diffusion of CheY molecules through the cytoplasm of Escherichia coli during chemotaxis. It is used to compare the algorithm's performance against the GMP method. Our analysis demonstrates that the proposed algorithm enables accurate simulation of the kinetics of complex and spatially heterogeneous systems. It is also computationally more efficient than commonly used alternatives, such as the GMP method.
Reaction -Diffusion Systems in Intracellular Molecular Transport and Control
Soh, Siowling; Byrska, Marta; Kandere-Grzybowska, Kristiana
2013-01-01
Chemical reactions make cells work only if the participating chemicals are delivered to desired locations in a timely and precise fashion. While most research to date has focused on the so-called active-transport mechanisms, “passive” diffusion is often equally rapid and is always energetically less costly. Capitalizing on these advantages, cells have developed sophisticated reaction-diffusion (RD) systems that control a wide range of cellular functions – from chemotaxis and cell division, through signaling cascades and oscillations, to cell motility. Despite their apparent diversity, these systems share many common features and are “wired” according to “generic” motifs involving non-linear kinetics, autocatalysis, and feedback loops. Understanding the operation of these complex (bio)chemical systems requires the analysis of pertinent transport-kinetic equations or, at least on a qualitative level, of the characteristic times describing constituent sub-processes. Therefore, in reviewing the manifestations of cellular RD, we also attempt to familiarize the reader with the basic theory of these processes. PMID:20518023
Dichotomous-noise-induced pattern formation in a reaction-diffusion system
NASA Astrophysics Data System (ADS)
Das, Debojyoti; Ray, Deb Shankar
2013-06-01
We consider a generic reaction-diffusion system in which one of the parameters is subjected to dichotomous noise by controlling the flow of one of the reacting species in a continuous-flow-stirred-tank reactor (CSTR) -membrane reactor. The linear stability analysis in an extended phase space is carried out by invoking Furutzu-Novikov procedure for exponentially correlated multiplicative noise to derive the instability condition in the plane of the noise parameters (correlation time and strength of the noise). We demonstrate that depending on the correlation time an optimal strength of noise governs the self-organization. Our theoretical analysis is corroborated by numerical simulations on pattern formation in a chlorine-dioxide-iodine-malonic acid reaction-diffusion system.
Reaction-diffusion mechanisms and quantum spin systems
NASA Astrophysics Data System (ADS)
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.
Note: From reaction-diffusion systems to confined Brownian motion
NASA Astrophysics Data System (ADS)
Martens, S.
2016-07-01
In this note, we demonstrated for the first time that one can derive an expression for the effective diffusion coefficient, equal to the Lifson-Jackson formula, using a subsequent homogenization of the 1D reaction-diffusion-advection equation. The latter has been derived by applying asymptotic perturbation analysis to the underlying 3D reaction-diffusion equation with spatially dependent no-flux boundary conditions and incorporates the effects of boundary interactions on the reactants via a boundary-induced advection term [S. Martens et al, Phys. Rev. E 91, 022902 (2015)].
Perturbations and dynamics of reaction-diffusion systems with mass conservation.
Kuwamura, Masataka; Morita, Yoshihisa
2015-07-01
In some reaction-diffusion systems where the total mass of their components is conserved, solutions with initial values near a homogeneous equilibrium converge to a simple localized pattern (spike) after exhibiting Turing-like patterns near the equilibrium for appropriate diffusion coefficients. In this study, we investigate the perturbed reaction-diffusion systems of such conserved systems. We show that a reaction-diffusion model with a globally stable homogeneous equilibrium can exhibit large amplitude Turing-like patterns in the transient dynamics. Moreover, we propose a three-component model, which exhibits an alternating repetition of spatially (almost) homogeneous oscillations and large amplitude Turing-like patterns.
A Simple Demonstration of Convective Effects on Reaction-Diffusion Systems: A Burning Cigarette.
ERIC Educational Resources Information Center
Pojman, John A.
1990-01-01
Described is a demonstration that provides an introduction to nonequilibrium reaction-diffusion systems and the coupling of hydrodynamics to chemical reactions. Experiments that demonstrate autocatalytic behavior that are effected by gravity and convection are included. (KR)
An Integration Factor Method for Stochastic and Stiff Reaction-Diffusion Systems
Ta, Catherine; Wang, Dongyong; Nie, Qing
2015-01-01
Stochastic effects are often present in the biochemical systems involving reactions and diffusions. When the reactions are stiff, existing numerical methods for stochastic reaction diffusion equations require either very small time steps for any explicit schemes or solving large nonlinear systems at each time step for the implicit schemes. Here we present a class of semi-implicit integration factor methods that treat the diffusion term exactly and reaction implicitly for a system of stochastic reaction-diffusion equations. Our linear stability analysis shows the advantage of such methods for both small and large amplitudes of noise. Direct use of the method to solving several linear and nonlinear stochastic reaction-diffusion equations demonstrates good accuracy, efficiency, and stability properties. This new class of methods, which are easy to implement, will have broader applications in solving stochastic reaction-diffusion equations arising from models in biology and physical sciences. PMID:25983341
An integration factor method for stochastic and stiff reaction-diffusion systems
NASA Astrophysics Data System (ADS)
Ta, Catherine; Wang, Dongyong; Nie, Qing
2015-08-01
Stochastic effects are often present in the biochemical systems involving reactions and diffusions. When the reactions are stiff, existing numerical methods for stochastic reaction diffusion equations require either very small time steps for any explicit schemes or solving large nonlinear systems at each time step for the implicit schemes. Here we present a class of semi-implicit integration factor methods that treat the diffusion term exactly and reaction implicitly for a system of stochastic reaction-diffusion equations. Our linear stability analysis shows the advantage of such methods for both small and large amplitudes of noise. Direct use of the method to solving several linear and nonlinear stochastic reaction-diffusion equations demonstrates good accuracy, efficiency, and stability properties. This new class of methods, which are easy to implement, will have broader applications in solving stochastic reaction-diffusion equations arising from models in biology and physical sciences.
Liu, Changchun; Sadik, Mohamed M.; Mauk, Michael G.; Edelstein, Paul H.; Bushman, Frederic D.; Gross, Robert; Bau, Haim H.
2014-01-01
Real-time amplification and quantification of specific nucleic acid sequences plays a major role in medical and biotechnological applications. In the case of infectious diseases, such as HIV, quantification of the pathogen-load in patient specimens is critical to assess disease progression and effectiveness of drug therapy. Typically, nucleic acid quantification requires expensive instruments, such as real-time PCR machines, which are not appropriate for on-site use and for low-resource settings. This paper describes a simple, low-cost, reaction-diffusion based method for end-point quantification of target nucleic acids undergoing enzymatic amplification. The number of target molecules is inferred from the position of the reaction-diffusion front, analogous to reading temperature in a mercury thermometer. The method was tested for HIV viral load monitoring and performed on par with conventional benchtop methods. The proposed method is suitable for nucleic acid quantification at point of care, compatible with multiplexing and high-throughput processing, and can function instrument-free. PMID:25477046
Solitary travelling auto-waves in fractional reaction-diffusion systems
NASA Astrophysics Data System (ADS)
Datsko, Bohdan; Gafiychuk, Vasyl; Podlubny, Igor
2015-06-01
In this article we study properties of solitary auto-waves in nonlinear fractional reaction-diffusion systems. As an example, the generalised FitzHugh-Nagumo model with time-fractional derivatives is considered. By a linear stability analysis and computer simulation it is shown that the order of the fractional derivative can substantially change the properties of solitary auto-waves and significantly enrich nonlinear system dynamics. The main properties of solitary travelling wave solutions, including the shape of the waves, the domain of their existence, as well as the parameters of their propagation in fractional reaction-diffusion systems, are investigated.
Resonant Chemical Oscillations: Pattern Formation in Reaction-Diffusion Systems
NASA Astrophysics Data System (ADS)
Lin, Anna L.
2003-03-01
Using the Belousov-Zhabotinsky (BZ) chemical system we explore the resonant response of spatially-extended oscillatory and excitable media to periodic perturbation. Resonance in excitable media is particularly relevant to biological systems, where excitable dynamics (threshold response to stimulus and refractoriness) are common. Methods to quantify spatio-temporal patterns will be discussed and the resonant patterns in excitable and oscillatory media will be compared. Experimental observations are compared to the results from numerical simulations of the Brusselator and FitzHugh-Nagumo models and from a forced complex Ginzburg-Landau amplitude equation.
Nonlinear stability in reaction-diffusion systems via optimal Lyapunov functions
NASA Astrophysics Data System (ADS)
Lombardo, S.; Mulone, G.; Trovato, M.
2008-06-01
We define optimal Lyapunov functions to study nonlinear stability of constant solutions to reaction-diffusion systems. A computable and finite radius of attraction for the initial data is obtained. Applications are given to the well-known Brusselator model and a three-species model for the spatial spread of rabies among foxes.
Modelling and simulating reaction-diffusion systems using coloured Petri nets.
Liu, Fei; Blätke, Mary-Ann; Heiner, Monika; Yang, Ming
2014-10-01
Reaction-diffusion systems often play an important role in systems biology when developmental processes are involved. Traditional methods of modelling and simulating such systems require substantial prior knowledge of mathematics and/or simulation algorithms. Such skills may impose a challenge for biologists, when they are not equally well-trained in mathematics and computer science. Coloured Petri nets as a high-level and graphical language offer an attractive alternative, which is easily approachable. In this paper, we investigate a coloured Petri net framework integrating deterministic, stochastic and hybrid modelling formalisms and corresponding simulation algorithms for the modelling and simulation of reaction-diffusion processes that may be closely coupled with signalling pathways, metabolic reactions and/or gene expression. Such systems often manifest multiscaleness in time, space and/or concentration. We introduce our approach by means of some basic diffusion scenarios, and test it against an established case study, the Brusselator model. PMID:25150626
NASA Astrophysics Data System (ADS)
Bau, Haim; Liu, Changchun; Killawala, Chitvan; Sadik, Mohamed; Mauk, Michael
2014-11-01
Real-time amplification and quantification of specific nucleic acid sequences plays a major role in many medical and biotechnological applications. In the case of infectious diseases, quantification of the pathogen-load in patient specimens is critical to assessing disease progression, effectiveness of drug therapy, and emergence of drug-resistance. Typically, nucleic acid quantification requires sophisticated and expensive instruments, such as real-time PCR machines, which are not appropriate for on-site use and for low resource settings. We describe a simple, low-cost, reactiondiffusion based method for end-point quantification of target nucleic acids undergoing enzymatic amplification. The number of target molecules is inferred from the position of the reaction-diffusion front, analogous to reading temperature in a mercury thermometer. We model the process with the Fisher Kolmogoroff Petrovskii Piscounoff (FKPP) Equation and compare theoretical predictions with experimental observations. The proposed method is suitable for nucleic acid quantification at the point of care, compatible with multiplexing and high-throughput processing, and can function instrument-free. C.L. was supported by NIH/NIAID K25AI099160; M.S. was supported by the Pennsylvania Ben Franklin Technology Development Authority; C.K. and H.B. were funded, in part, by NIH/NIAID 1R41AI104418-01A1.
Differential diffusivity of Nodal and Lefty underlies a reaction-diffusion patterning system.
Müller, Patrick; Rogers, Katherine W; Jordan, Ben M; Lee, Joon S; Robson, Drew; Ramanathan, Sharad; Schier, Alexander F
2012-05-11
Biological systems involving short-range activators and long-range inhibitors can generate complex patterns. Reaction-diffusion models postulate that differences in signaling range are caused by differential diffusivity of inhibitor and activator. Other models suggest that differential clearance underlies different signaling ranges. To test these models, we measured the biophysical properties of the Nodal/Lefty activator/inhibitor system during zebrafish embryogenesis. Analysis of Nodal and Lefty gradients revealed that Nodals have a shorter range than Lefty proteins. Pulse-labeling analysis indicated that Nodals and Leftys have similar clearance kinetics, whereas fluorescence recovery assays revealed that Leftys have a higher effective diffusion coefficient than Nodals. These results indicate that differential diffusivity is the major determinant of the differences in Nodal/Lefty range and provide biophysical support for reaction-diffusion models of activator/inhibitor-mediated patterning.
Differential diffusivity of Nodal and Lefty underlies a reaction-diffusion patterning system
Müller, Patrick; Rogers, Katherine W.; Jordan, Ben M.; Lee, Joon S.; Robson, Drew; Ramanathan, Sharad; Schier, Alexander F.
2012-01-01
Biological systems involving short-range activators and long-range inhibitors can generate complex patterns. Reaction-diffusion models postulate that differences in signaling range are caused by differential diffusivity of inhibitor and activator. Other models suggest that differential clearance underlies different signaling ranges. To test these models, we measured the biophysical properties of the Nodal/Lefty activator/inhibitor system during zebrafish embryogenesis. Analysis of Nodal and Lefty gradients reveals that Nodals have a shorter range than Lefty proteins. Pulse-labelinganalysis indicates that Nodals and Leftys have similar clearance kinetics, whereas fluorescence recovery assays reveal that Leftys have a higher effective diffusion coefficient than Nodals. These results indicate that differential diffusivity is the major determinant of the differences in Nodal/Lefty range and provide biophysical support for reaction-diffusion models of activator/inhibitor-mediated patterning. PMID:22499809
Primal-mixed formulations for reaction-diffusion systems on deforming domains
NASA Astrophysics Data System (ADS)
Ruiz-Baier, Ricardo
2015-10-01
We propose a finite element formulation for a coupled elasticity-reaction-diffusion system written in a fully Lagrangian form and governing the spatio-temporal interaction of species inside an elastic, or hyper-elastic body. A primal weak formulation is the baseline model for the reaction-diffusion system written in the deformed domain, and a finite element method with piecewise linear approximations is employed for its spatial discretization. On the other hand, the strain is introduced as mixed variable in the equations of elastodynamics, which in turn acts as coupling field needed to update the diffusion tensor of the modified reaction-diffusion system written in a deformed domain. The discrete mechanical problem yields a mixed finite element scheme based on row-wise Raviart-Thomas elements for stresses, Brezzi-Douglas-Marini elements for displacements, and piecewise constant pressure approximations. The application of the present framework in the study of several coupled biological systems on deforming geometries in two and three spatial dimensions is discussed, and some illustrative examples are provided and extensively analyzed.
An adaptive tau-leaping method for stochastic simulations of reaction-diffusion systems
NASA Astrophysics Data System (ADS)
Padgett, Jill M. A.; Ilie, Silvana
2016-03-01
Stochastic modelling is critical for studying many biochemical processes in a cell, in particular when some reacting species have low population numbers. For many such cellular processes the spatial distribution of the molecular species plays a key role. The evolution of spatially heterogeneous biochemical systems with some species in low amounts is accurately described by the mesoscopic model of the Reaction-Diffusion Master Equation. The Inhomogeneous Stochastic Simulation Algorithm provides an exact strategy to numerically solve this model, but it is computationally very expensive on realistic applications. We propose a novel adaptive time-stepping scheme for the tau-leaping method for approximating the solution of the Reaction-Diffusion Master Equation. This technique combines effective strategies for variable time-stepping with path preservation to reduce the computational cost, while maintaining the desired accuracy. The numerical tests on various examples arising in applications show the improved efficiency achieved by the new adaptive method.
Zhao, Su; Ovadia, Jeremy; Liu, Xinfeng; Zhang, Yong-Tao; Nie, Qing
2011-01-01
For reaction-diffusion-advection equations, the stiffness from the reaction and diffusion terms often requires very restricted time step size, while the nonlinear advection term may lead to a sharp gradient in localized spatial regions. It is challenging to design numerical methods that can efficiently handle both difficulties. For reaction-diffusion systems with both stiff reaction and diffusion terms, implicit integration factor (IIF) method and its higher dimensional analog compact IIF (cIIF) serve as an efficient class of time-stepping methods, and their second order version is linearly unconditionally stable. For nonlinear hyperbolic equations, weighted essentially non-oscillatory (WENO) methods are a class of schemes with a uniformly high-order of accuracy in smooth regions of the solution, which can also resolve the sharp gradient in an accurate and essentially non-oscillatory fashion. In this paper, we couple IIF/cIIF with WENO methods using the operator splitting approach to solve reaction-diffusion-advection equations. In particular, we apply the IIF/cIIF method to the stiff reaction and diffusion terms and the WENO method to the advection term in two different splitting sequences. Calculation of local truncation error and direct numerical simulations for both splitting approaches show the second order accuracy of the splitting method, and linear stability analysis and direct comparison with other approaches reveals excellent efficiency and stability properties. Applications of the splitting approach to two biological systems demonstrate that the overall method is accurate and efficient, and the splitting sequence consisting of two reaction-diffusion steps is more desirable than the one consisting of two advection steps, because CWC exhibits better accuracy and stability. PMID:21666863
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.
Turing space in reaction-diffusion systems with density-dependent cross diffusion
NASA Astrophysics Data System (ADS)
Zemskov, E. P.; Kassner, K.; Hauser, M. J. B.; Horsthemke, W.
2013-03-01
Reaction-diffusion systems with cross-diffusion terms that depend linearly on density are studied via linear stability analysis and weakly nonlinear analysis. We obtain and analyze the conditions for the Turing instability and derive a universal form of these conditions. We discuss the features of the pattern-forming regions in parameter space for a cross activator-inhibitor system, the Brusselator model, and for a pure activator-inhibitor system, the two-variable Oregonator model. The supercritical or subcritical character of the Turing bifurcation for the Brusselator is determined by deriving an amplitude equation for patterns near the instability threshold.
Reaction-diffusion system with Brusselator kinetics: Control of a quasiperiodic route to chaos
NASA Astrophysics Data System (ADS)
Chakravarti, S.; Marek, M.; Ray, W. H.
1995-09-01
A methodology for controlling complex dynamics and chaos in distributed parameter systems is discussed. The reaction-diffusion system with Brusselator kinetics, where the torus-doubling route to chaos exists in a defined range of parameter values, is used as an example. Poincaré maps and singular value decomposition are used for characterization of quasiperiodic and chaotic attractors and for the identification of dominant modes. Tested modal feedback control schemes based on identified dominant spatial modes confirm the possibility of stabilization of simple quasiperiodic trajectories in the complex quasiperiodic or chaotic spatiotemporal patterns.
Nonlinear Waves in Reaction Diffusion Systems: The Effect of Transport Memory
HURD,ALAN J.; KENKRE,V.M.; MANNE,K.K.
1999-11-04
Motivated by the problem of determining stress distributions in granular materials, we study the effect of finite transport correlation times on the propagation of nonlinear wavefronts in reaction diffusion systems. We obtain new results such as the possibility of spatial oscillations in the wavefront shape for certain values of the system parameters and high enough wavefront speeds. We also generalize earlier known results concerning the minimum wavefront speed and shape-speed relationships stemming from the finiteness of the correlation times. Analytic investigations are made possible by a piece-wise linear representation of the nonlinearity.
Simulations of pattern dynamics for reaction-diffusion systems via SIMULINK
2014-01-01
Background 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. Results 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. Conclusions 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
George, Jacob; Varghese, George
2005-02-15
The mechanism of rhythmic pattern formation in reaction-diffusion systems is investigated theoretically by introducing a new concept. The boundary that separates the two reacting species virtually migrates as the diffusion proceeds into the gelatinous medium. Based on this boundary migration scenario, all the well-established relations on Liesegang patterns could be proved, in a rather modified way. The idea of formation of intermediate colloidal haze prior to patterning along with the moving boundary model proved to be efficient in predicting the concentration dependence of the width of the spatiotemporal patterns. The experimental observations support the width law relation developed.
Square Turing patterns in reaction-diffusion systems with coupled layers
Li, Jing; Wang, Hongli E-mail: qi@pku.edu.cn; Ouyang, Qi E-mail: qi@pku.edu.cn
2014-06-15
Square Turing patterns are usually unstable in reaction-diffusion systems and are rarely observed in corresponding experiments and simulations. We report here an example of spontaneous formation of square Turing patterns with the Lengyel-Epstein model of two coupled layers. The squares are found to be a result of the resonance between two supercritical Turing modes with an appropriate ratio. Besides, the spatiotemporal resonance of Turing modes resembles to the mode-locking phenomenon. Analysis of the general amplitude equations for square patterns reveals that the fixed point corresponding to square Turing patterns is stationary when the parameters adopt appropriate values.
Wave reflection in a reaction-diffusion system: breathing patterns and attenuation of the echo.
Tsyganov, M A; Ivanitsky, G R; Zemskov, E P
2014-05-01
Formation and interaction of the one-dimensional excitation waves in a reaction-diffusion system with the piecewise linear reaction functions of the Tonnelier-Gerstner type are studied. We show that there exists a parameter region where the established regime of wave propagation depends on initial conditions. Wave phenomena with a complex behavior are found: (i) the reflection of waves at a growing distance (the remote reflection) upon their collision with each other or with no-flux boundaries and (ii) the periodic transformation of waves with the jumping from one regime of wave propagation to another (the periodic trigger wave).
STEPS: Modeling and Simulating Complex Reaction-Diffusion Systems with Python.
Wils, Stefan; De Schutter, Erik
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 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. PMID:19623245
Cross-diffusion-driven instability for reaction-diffusion systems: analysis and simulations.
Madzvamuse, Anotida; Ndakwo, Hussaini S; Barreira, Raquel
2015-03-01
By introducing linear cross-diffusion for a two-component reaction-diffusion system with activator-depleted reaction kinetics (Gierer and Meinhardt, Kybernetik 12:30-39, 1972; Prigogine and Lefever, J Chem Phys 48:1695-1700, 1968; Schnakenberg, J Theor Biol 81:389-400, 1979), we derive cross-diffusion-driven instability conditions and show that they are a generalisation of the classical diffusion-driven instability conditions in the absence of cross-diffusion. Our most revealing result is that, in contrast to the classical reaction-diffusion systems without cross-diffusion, it is no longer necessary to enforce that one of the species diffuse much faster than the other. Furthermore, it is no longer necessary to have an activator-inhibitor mechanism as premises for pattern formation, activator-activator, inhibitor-inhibitor reaction kinetics as well as short-range inhibition and long-range activation all have the potential of giving rise to cross-diffusion-driven instability. To support our theoretical findings, we compute cross-diffusion induced parameter spaces and demonstrate similarities and differences to those obtained using standard reaction-diffusion theory. Finite element numerical simulations on planary square domains are presented to back-up theoretical predictions. For the numerical simulations presented, we choose parameter values from and outside the classical Turing diffusively-driven instability space; outside, these are chosen to belong to cross-diffusively-driven instability parameter spaces. Our numerical experiments validate our theoretical predictions that parameter spaces induced by cross-diffusion in both the [Formula: see text] and [Formula: see text] components of the reaction-diffusion system are substantially larger and different from those without cross-diffusion. Furthermore, the parameter spaces without cross-diffusion are sub-spaces of the cross-diffusion induced parameter spaces. Our results allow experimentalists to have a wider range
NASA Astrophysics Data System (ADS)
Wang, Hongli; Zhang, Ke; Ouyang, Qi
2006-09-01
We report frequency-locked resonant patterns induced by additive noise in periodically forced reaction-diffusion Brusselator model. In the regime of 2:1 frequency-locking and homogeneous oscillation, the introduction of additive noise, which is colored in time and white in space, generates and sustains resonant patterns of hexagons, stripes, and labyrinths which oscillate at half of the forcing frequency. Both the noise strength and the correlation time control the pattern formation. The system transits from homogeneous to hexagons, stripes, and to labyrinths successively as the noise strength is adjusted. Good frequency-locked patterns are only sustained by the colored noise and a finite time correlation is necessary. At the limit of white noise with zero temporal correlation, irregular patterns which are only nearly resonant come out as the noise strength is adjusted. The phenomenon induced by colored noise in the forced reaction-diffusion system is demonstrated to correspond to noise-induced Turing instability in the corresponding forced complex Ginzburg-Landau equation.
Wang, Hongli; Zhang, Ke; Ouyang, Qi
2006-09-01
We report frequency-locked resonant patterns induced by additive noise in periodically forced reaction-diffusion Brusselator model. In the regime of 2:1 frequency-locking and homogeneous oscillation, the introduction of additive noise, which is colored in time and white in space, generates and sustains resonant patterns of hexagons, stripes, and labyrinths which oscillate at half of the forcing frequency. Both the noise strength and the correlation time control the pattern formation. The system transits from homogeneous to hexagons, stripes, and to labyrinths successively as the noise strength is adjusted. Good frequency-locked patterns are only sustained by the colored noise and a finite time correlation is necessary. At the limit of white noise with zero temporal correlation, irregular patterns which are only nearly resonant come out as the noise strength is adjusted. The phenomenon induced by colored noise in the forced reaction-diffusion system is demonstrated to correspond to noise-induced Turing instability in the corresponding forced complex Ginzburg-Landau equation. PMID:17025732
Self-similar fast-reaction limits for reaction-diffusion systems on unbounded domains
NASA Astrophysics Data System (ADS)
Crooks, E. C. M.; Hilhorst, D.
2016-08-01
We present a unified approach to characterising fast-reaction limits of systems of either two reaction-diffusion equations, or one reaction-diffusion equation and one ordinary differential equation, on unbounded domains, motivated by models of fast chemical reactions where either one or both reactant(s) is/are mobile. For appropriate initial data, solutions of four classes of problems each converge in the fast-reaction limit k → ∞ to a self-similar limit profile that has one of four forms, depending on how many components diffuse and whether the spatial domain is a half or whole line. For fixed k, long-time convergence to these same self-similar profiles is also established, thanks to a scaling argument of Kamin. Our results generalise earlier work of Hilhorst, van der Hout and Peletier to a much wider class of problems, and provide a quantitative description of the penetration of one substance into another in both the fast-reaction and long-time regimes.
Spatiotemporal patterns in reaction-diffusion system and in a vibrated granular bed
Swinney, H.L.; Lee, K.J.; McCormick, W.D.
1995-12-31
Experiments on a quasi-two-dimensional reaction-diffusion system reveal transitions from a uniform state to stationary hexagonal, striped, and rhombic spatial patterns. For other reactor conditions lamellae and self-replicating spot patterns are observed. These patterns form in continuously fed thin gel reactors that can be maintained indefinitely in well-defined nonequilibrium states. Reaction-diffusion models with two chemical species yield patterns similar to those observed in the experiments. Pattern formation is also being examined in vertically oscillated thin granular layers (typically 3-30 particle diameters deep). For small acceleration amplitudes, a granular layer is flat, but above a well-defined critical acceleration amplitude, spatial patterns spontaneously form. Disordered time-dependent granular patterns are observed as well as regular patterns of squares, stripes, and hexagons. A one-dimensional model consisting of a completely inelastic ball colliding with a sinusoidally oscillating platform provides a semi-quantitative description of most of the observed bifurcations between the different spatiotemporal regimes.
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. PMID:19658764
Turing bifurcation in a reaction-diffusion system with density-dependent dispersal
NASA Astrophysics Data System (ADS)
Kumar, Niraj; Horsthemke, Werner
2010-05-01
Motivated by the recent finding [N. Kumar, G.M. Viswanathan, V.M. Kenkre, Physica A 388 (2009) 3687] that the dynamics of particles undergoing density-dependent nonlinear diffusion shows sub-diffusive behaviour, we study the Turing bifurcation in a two-variable system with this kind of dispersal. We perform a linear stability analysis of the uniform steady state to find the conditions for the Turing bifurcation and compare it with the standard Turing condition in a reaction-diffusion system, where dispersal is described by simple Fickian diffusion. While activator-inhibitor kinetics are a necessary condition for the Turing instability as in standard two-variable systems, the instability can occur even if the diffusion constant of the inhibitor is equal to or smaller than that of the activator. We apply these results to two model systems, the Brusselator and the Gierer-Meinhardt model.
Transition to Spatio-Temporal Chaos with Increasing Length in the Reaction-Diffusion System
NASA Astrophysics Data System (ADS)
Trail, Collin; Tomlin, Brett; Olsen, Thomas; Wiener, Richard J.
2003-11-01
Calculations based up the Reaction-Diffusion model (H. Riecke and H.-G. Paap, Europhys. Lett. 14), 1235 (1991).have proven to be suggestive for a wide variety of pattern forming systems, including Taylor-Couette flow with hourglass geometry(Richard J. Wiener et al), Phys. Rev. E 55, 5489 (1997).. Seeking insight to guide experimental investigations, we extend these calculations. Previous calculations indicated that in smaller systems, only temporal chaos, located in a small region, would be observed, while in longer systems instabilities would form over a wide region. Our simulations explore this transition from purely temporal chaos to spatio-temporal chaos as the length of the system is increased.
NASA Astrophysics Data System (ADS)
Mittal, R. C.; Jiwari, Ram
2011-01-01
In this paper, a rapid, convergent and accurate differential quadrature method (DQM) is employed for numerical study of a two-dimensional reaction-diffusion Brusselator system. In the Brusselator system the reaction terms arise from the mathematical modeling of chemical systems such as in enzymatic reactions, and in plasma and laser physics in multiple coupling between modes. By employing DQM, accurate results can be obtained using fewer grid points in spatial domain for a large value of T = 50. We also found that Chebyshev-Gauss-Lobatto grid points give excellent results in comparison to other grid points such as uniform grid points. Three examples are solved to illustrate the accuracy and efficiency of the DQM. Convergence and stability of the method is also examined.
Travelling waves in a reaction-diffusion system modelling fungal mycelia
NASA Astrophysics Data System (ADS)
Davidson, F. A.; Sleeman, B. D.; Crawford, J. W.
1997-06-01
We discuss travelling-wave solutions of a system of coupled reaction--diffusion equations used by the authors to describe the macroscopic behaviour of fungal mycelia. Such systems have been used in a multitude of applications; and, in particular, Merkin and Needham (1990, Proc. R. Soc. Lond. A 430, 315-45) have studied a certain formulation as a model for generic isothermal chemical reactions. We show that an alternative analysis provides more complete results in ascertaining the conditions under which travelling-wave solutions exist and that it allows a wider range of parameter values to be considered; this is essential to the application considered in the present case. Numerical investigations of travelling-wave solutions and the related initial-value problem are included to motivate and extend the analysis.
NASA Astrophysics Data System (ADS)
Fernandes, Ryan I.; Fairweather, Graeme
2012-08-01
An alternating direction implicit (ADI) orthogonal spline collocation (OSC) method is described for the approximate solution of a class of nonlinear reaction-diffusion systems. Its efficacy is demonstrated on the solution of well-known examples of such systems, specifically the Brusselator, Gray-Scott, Gierer-Meinhardt and Schnakenberg models, and comparisons are made with other numerical techniques considered in the literature. The new ADI method is based on an extrapolated Crank-Nicolson OSC method and is algebraically linear. It is efficient, requiring at each time level only O(N) operations where N is the number of unknowns. Moreover, it is shown to produce approximations which are of optimal global accuracy in various norms, and to possess superconvergence properties.
Hybrid stochastic simulation of reaction-diffusion systems with slow and fast dynamics
Strehl, Robert; Ilie, Silvana
2015-12-21
In this paper, we present a novel hybrid method to simulate discrete stochastic reaction-diffusion models arising in biochemical signaling pathways. We study moderately stiff systems, for which we can partition each reaction or diffusion channel into either a slow or fast subset, based on its propensity. Numerical approaches missing this distinction are often limited with respect to computational run time or approximation quality. We design an approximate scheme that remedies these pitfalls by using a new blending strategy of the well-established inhomogeneous stochastic simulation algorithm and the tau-leaping simulation method. The advantages of our hybrid simulation algorithm are demonstrated on three benchmarking systems, with special focus on approximation accuracy and efficiency.
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. PMID:24418010
Wave-Pinning and Cell Polarity from a Bistable Reaction-Diffusion System
Mori, Yoichiro; Jilkine, Alexandra; Edelstein-Keshet, Leah
2008-01-01
Motile eukaryotic cells polarize in response to external signals. Numerous mechanisms have been suggested to account for this symmetry breaking and for the ensuing robust polarization. Implicated in this process are various proteins that are recruited to the plasma membrane and segregate at an emergent front or back of the polarizing cell. Among these are PI3K, PTEN, and members of the Rho family GTPases such as Cdc42, Rac, and Rho. Many such proteins, including the Rho GTPases, cycle between active membrane-bound forms and inactive cytosolic forms. In previous work, we have shown that this property, together with appropriate crosstalk, endows a biochemical circuit (Cdc42, Rac, and Rho) with the property of inherent polarizability. Here we show that this property is present in an even simpler system comprised of a single active/inactive protein pair with positive feedback to its own activation. The simplicity of this minimal system also allows us to explain the mechanism using insights from mathematical analysis. The basic idea resides in a well-known property of reaction-diffusion systems with bistable kinetics, namely, propagation of fronts. However, it crucially depends on exchange between active and inactive forms of the chemicals with unequal rates of diffusion, and overall conservation to pin the waves into a stable polar distribution. We refer to these dynamics as wave-pinning and we show that this phenomenon is distinct from Turing-instability-generated pattern formation that occurs in reaction-diffusion systems that appear to be very similar. We explain the mathematical basis of the phenomenon, relate it to spatial segregation of Rho GTPases, and show how it can account for spatial amplification and maintenance of polarity, as well as sensitivity to new stimuli typical in polarization of eukaryotic cells. PMID:18212014
Spatiotemporal chaos in an electric current driven ionic reaction-diffusion system.
Hasal, P.; Munster, A. F.; Marek, M.
1994-09-01
Two types of transitions from the time-periodic spatiotemporal patterns to chaotic ones in the spatially one-dimensional ionic reaction-diffusion system forced either with direct or alternating electric field are described and analyzed by numerical techniques. An ionic version of the Brusselator kinetic scheme is considered. The Karhunen-Loeve decomposition technique is shown to be a possible tool for the global representation of dynamic behavior, but fails as a tool in the identification of the route of transition to chaos in the case of direct current forcing. Higher dimensional chaos with two positive Lyapunov exponents has been identified for the case of alternating current forcing. Results of the Karhunen-Loeve analysis are compared to results of classical analysis of local time series (attractor dimensions, Lyapunov exponents). PMID:12780130
Spatiotemporal chaos in an electric current driven ionic reaction-diffusion system
NASA Astrophysics Data System (ADS)
Hasal, P.; Münster, A. F.; Marek, M.
1994-09-01
Two types of transitions from the time-periodic spatiotemporal patterns to chaotic ones in the spatially one-dimensional ionic reaction-diffusion system forced either with direct or alternating electric field are described and analyzed by numerical techniques. An ionic version of the Brusselator kinetic scheme is considered. The Karhunen-Loève decomposition technique is shown to be a possible tool for the global representation of dynamic behavior, but fails as a tool in the identification of the route of transition to chaos in the case of direct current forcing. Higher dimensional chaos with two positive Lyapunov exponents has been identified for the case of alternating current forcing. Results of the Karhunen-Loève analysis are compared to results of classical analysis of local time series (attractor dimensions, Lyapunov exponents).
Spatial propagation for a two component reaction-diffusion system arising in population dynamics
NASA Astrophysics Data System (ADS)
Ducrot, Arnaud
2016-06-01
In this work a two component epidemic reaction-diffusion system posed on the whole space RN is considered. Uniform boundedness of the solutions is proved using suitable local Lp-estimates. The spatial invasion of a localized introduced amount of infective is studied yielding to the derivation of the asymptotic speed of spread for the infection. This part is achieved using uniform persistence ideas. The state of the population after the epidemic is further investigated using different Lyapunov like arguments. The solution is shown to converge the endemic equilibrium point behind the front in the equi-diffusional case. For general diffusion coefficient unique ergodicity of the tail of invasion is obtained by constructing a suitable sub-harmonic map.
Signaling gradients in cascades of two-state reaction-diffusion systems.
Berezhkovskii, Alexander M; Coppey, Mathieu; Shvartsman, Stanislav Y
2009-01-27
Biological networks frequently use cascades, generally defined as chain-like arrangements of similar modules. Spatially lumped cascades can serve as noise filters, time-delay, or thresholding elements. The operation and functional capabilities of spatially distributed cascades are much less understood. Motivated by studies of pattern formation in the early Drosophila embryo, we analyze cascades of 2-state reaction-diffusion systems. At each stage within such as a cascade, a diffusible particle is reversibly bound by immobile traps and can be annihilated in both mobile and immobile states. When trapped, these particles drive the next stage by converting mobile particles of a different type from a passive to active form. The cascade initiated by injection of mobile particles into the first stage. We derive analytical expressions for the steady-state concentration profiles of mobile and immobile particles and analyze how the output of a cascade is controlled by properties of the constituent stages. PMID:19147842
A Robust and Efficient Method for Steady State Patterns in Reaction-Diffusion Systems
Lo, Wing-Cheong; Chen, Long; Wang, Ming; Nie, Qing
2012-01-01
An inhomogeneous steady state pattern of nonlinear reaction-diffusion equations with no-flux boundary conditions is usually computed by solving the corresponding time-dependent reaction-diffusion equations using temporal schemes. Nonlinear solvers (e.g., Newton’s method) take less CPU time in direct computation for the steady state; however, their convergence is sensitive to the initial guess, often leading to divergence or convergence to spatially homogeneous solution. Systematically numerical exploration of spatial patterns of reaction-diffusion equations under different parameter regimes requires that the numerical method be efficient and robust to initial condition or initial guess, with better likelihood of convergence to an inhomogeneous pattern. Here, a new approach that combines the advantages of temporal schemes in robustness and Newton’s method in fast convergence in solving steady states of reaction-diffusion equations is proposed. In particular, an adaptive implicit Euler with inexact solver (AIIE) method is found to be much more efficient than temporal schemes and more robust in convergence than typical nonlinear solvers (e.g., Newton’s method) in finding the inhomogeneous pattern. Application of this new approach to two reaction-diffusion equations in one, two, and three spatial dimensions, along with direct comparisons to several other existing methods, demonstrates that AIIE is a more desirable method for searching inhomogeneous spatial patterns of reaction-diffusion equations in a large parameter space. PMID:22773849
The dynamics of localized spot patterns for reaction-diffusion systems on the sphere
NASA Astrophysics Data System (ADS)
Trinh, Philippe H.; Ward, Michael J.
2016-03-01
In the singularly perturbed limit corresponding to a large diffusivity ratio between two components in a reaction-diffusion (RD) system, quasi-equilibrium spot patterns are often admitted, producing a solution that concentrates at a discrete set of points in the domain. In this paper, we derive and study the differential algebraic equation (DAE) that characterizes the slow dynamics for such spot patterns for the Brusselator RD model on the surface of a sphere. Asymptotic and numerical solutions are presented for the system governing the spot strengths, and we describe the complex bifurcation structure and demonstrate the occurrence of imperfection sensitivity due to higher order effects. Localized spot patterns can undergo a fast time instability and we derive the conditions for this phenomena, which depend on the spatial configuration of the spots and the parameters in the system. In the absence of these instabilities, our numerical solutions of the DAE system for N = 2 to N = 8 spots suggest a large basin of attraction to a small set of possible steady-state configurations. We discuss the connections between our results and the study of point vortices on the sphere, as well as the problem of determining a set of elliptic Fekete points, which correspond to globally minimizing the discrete logarithmic energy for N points on the sphere.
Pattern formation in reaction-diffusion systems: From spiral waves to turbulence
NASA Astrophysics Data System (ADS)
Davidsen, Joern
2009-05-01
Almost all systems we encounter in nature possess some sort of form or structure. In many cases, the structures arise from an initially unstructured state without the action of an agent that predetermines the pattern. Such self-organized structures emerge from cooperative interactions among the constituents of the system and often exhibit properties that are distinct from those of their constituent elements or molecules. For example, chemical waves in reaction-diffusion systems are at the core of a huge variety of physical, chemical, and biological processes. In (quasi) two-dimensional situations, spiral wave patterns are especially prevalent and determine the characteristics of processes such as surface catalytic oxidation reactions, contraction of the heart muscle, and various signaling mechanisms in biological systems. In this talk, I will review and discuss recent theoretical and experimental results regarding the dynamics, properties and stability of spiral waves and their three-dimensional analog (scroll waves). Special emphasis will be given to synchronization defect lines which generically arise in complex-oscillatory media, and the phenomenon of defect-mediated turbulence or filament turbulence where the dynamics of a pattern is dominated by the rapid motion, nucleation, and annihilation of spirals or scroll waves, respectively. The latter is of direct relevance in the context of ventricular fibrillation - a turbulent electrical wave activity that destroys the coherent contraction of the ventricular muscle and its main pumping function leading to sudden cardiac death.
Dynamics of a reaction-diffusion system with Brusselator kinetics under feedback control
NASA Astrophysics Data System (ADS)
Karafyllis, Iasson; Christofides, Panagiotis D.; Daoutidis, Prodromos
1999-01-01
This paper studies the dynamics of the reaction-diffusion Brusselator model with Neumann and Dirichlet boundary conditions, under linear and nonlinear modal feedback control. The bifurcation parameters are for the Neumann problem the concentration of one of the reactants and for the Dirichlet problem the diffusion coefficient of one of the reactants. The study of the dynamics of the system is based on methods of bifurcation theory and the application of Poincaré maps. A direct comparison of the dynamics of the open-loop and closed-loop systems establishes that the use of feedback control significantly suppresses the rich open-loop dynamics. In addition, the superiority of the nonlinear controller over a linear controller, in attenuating the effect of bifurcations on the output of the closed-loop system, and the ability of the nonlinear controller to stabilize the system states at the spatially uniform solution provided the number of manipulated inputs is sufficiently large are shown for both the Neumann and Dirichlet problems.
Hopping Conduction and Bacteria: Transport Properties of Disordered Reaction-Diffusion Systems
NASA Astrophysics Data System (ADS)
Missel, Andrew; Dahmen, Karin
2008-03-01
Reaction-diffusion (RD) systems are used to model everything from the formation of animal coat patterns to the spread of genes in a population to the seasonal variation of plankton density in the ocean. In all of these problems, disorder plays a large role, but determining its effects on transport properties in RD systems has been a challenge. We present here both analytical and numerical studies of a particular disordered RD system consisting of particles which are allowed to diffuse and compete for resources (2A->A) with spatially homogeneous rates, reproduce (A->2A) in certain areas (``oases''), and die (A->0) everywhere else (the ``desert''). In the low oasis density regime, transport is mediated through rare ``hopping events'' in which a small number of particles diffuse through the desert from one oasis to another; the situation is mathematically analogous to hopping conduction in doped semiconductors, and this analogy, along with some ideas from first passage percolation theory, allows us to make some quantitative predictions about the transport properties of the system on a large scale.
Parallel Solutions for Voxel-Based Simulations of Reaction-Diffusion Systems
D'Agostino, Daniele; Pasquale, Giulia; Clematis, Andrea; Maj, Carlo; Mosca, Ettore; Milanesi, Luciano; Merelli, Ivan
2014-01-01
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. PMID:25045716
Szalai, István; Cuiñas, Daniel; Takács, Nándor; Horváth, Judit; De Kepper, Patrick
2012-08-01
In his seminal 1952 paper, Alan Turing predicted that diffusion could spontaneously drive an initially uniform solution of reacting chemicals to develop stable spatially periodic concentration patterns. It took nearly 40 years before the first two unquestionable experimental demonstrations of such reaction-diffusion patterns could be made in isothermal single phase reaction systems. The number of these examples stagnated for nearly 20 years. We recently proposed a design method that made their number increase to six in less than 3 years. In this report, we formally justify our original semi-empirical method and support the approach with numerical simulations based on a simple but realistic kinetic model. To retain a number of basic properties of real spatial reactors but keep calculations to a minimal complexity, we introduce a new way to collapse the confined spatial direction of these reactors. Contrary to similar reduced descriptions, we take into account the effect of the geometric size in the confinement direction and the influence of the differences in the diffusion coefficient on exchange rates of species with their feed environment. We experimentally support the method by the observation of stationary patterns in red-ox reactions not based on oxihalogen chemistry. Emphasis is also brought on how one of these new systems can process different initial conditions and memorize them in the form of localized patterns of different geometries.
Szalai, István; Cuiñas, Daniel; Takács, Nándor; Horváth, Judit; De Kepper, Patrick
2012-08-01
In his seminal 1952 paper, Alan Turing predicted that diffusion could spontaneously drive an initially uniform solution of reacting chemicals to develop stable spatially periodic concentration patterns. It took nearly 40 years before the first two unquestionable experimental demonstrations of such reaction-diffusion patterns could be made in isothermal single phase reaction systems. The number of these examples stagnated for nearly 20 years. We recently proposed a design method that made their number increase to six in less than 3 years. In this report, we formally justify our original semi-empirical method and support the approach with numerical simulations based on a simple but realistic kinetic model. To retain a number of basic properties of real spatial reactors but keep calculations to a minimal complexity, we introduce a new way to collapse the confined spatial direction of these reactors. Contrary to similar reduced descriptions, we take into account the effect of the geometric size in the confinement direction and the influence of the differences in the diffusion coefficient on exchange rates of species with their feed environment. We experimentally support the method by the observation of stationary patterns in red-ox reactions not based on oxihalogen chemistry. Emphasis is also brought on how one of these new systems can process different initial conditions and memorize them in the form of localized patterns of different geometries. PMID:23919126
NASA Astrophysics Data System (ADS)
Li, Xin-Zheng; Bai, Zhan-Guo; Li, Yan; Zhao, Kun
2016-03-01
In this paper, various kinds of spontaneous dynamic patterns are investigated based on a two-layer nonlinearly coupled Brusselator model. It is found that, when the Hopf mode or supercritical Turing mode respectively plays major role in the short or long wavelength mode layer, the dynamic patterns appear under the action of nonlinearly coupling interactions in the reaction-diffusion system. The stripe pattern can change its symmetrical structure and form other graphics when influenced by small perturbations sourced from other modes. If two supercritical Turing modes are nonlinearly coupled together, the transition from Turing instability to Hopf instability may appear in the short wavelength mode layer, and the twinkling-eye square pattern, traveling and rotating pattern will be obtained in the two subsystems. If Turing mode and subharmonic Turing mode satisfy the three-mode resonance relation, twinkling-eye patterns are generated, and oscillating spots are arranged as square lattice in the two-dimensional space. When the subharmonic Turing mode satisfies the spatio-temporal phase matching condition, the traveling patterns, including the rhombus, hexagon and square patterns are obtained, which presents different moving velocities. It is found that the wave intensity plays an important role in pattern formation and pattern selection.
A transition in the spatially integrated reaction rate of bimolecular reaction-diffusion systems
NASA Astrophysics Data System (ADS)
Arshadi, Masoud; Rajaram, Harihar
2015-09-01
Numerical simulations of diffusion with bimolecular reaction demonstrate a transition in the spatially integrated reaction rate—increasing with time initially, and transitioning to a decrease with time. In previous work, this reaction-diffusion problem has been analyzed as a Stefan problem involving a distinct moving boundary (reaction front), leading to predictions that front motion scales as √t, and correspondingly the spatially integrated reaction rate decreases as the square root of time 1/√t. We present a general nondimensionalization of the problem and a perturbation analysis to show that there is an early time regime where the spatially integrated reaction rate scales as √t rather than 1/√t. The duration of this early time regime (where the spatially integrated reaction rate is kinetically rather than diffusion controlled) is shown to depend on the kinetic rate parameters, diffusion coefficients, and initial concentrations of the two species. Numerical simulation results confirm the theoretical estimates of the transition time. We present illustrative calculations in the context of in situ chemical oxidation for remediation of fractured rock systems where contaminants are largely dissolved in the rock matrix. We consider different contaminants of concern (COCs), including TCE, PCE, MTBE, and RDX. While the early time regime is very short lived for TCE, it can persist over months to years for MTBE and RDX, due to slow oxidation kinetics.
Exclusive traveling waves for competitive reaction-diffusion systems and their stabilities
NASA Astrophysics Data System (ADS)
Leung, Anthony W.; Hou, Xiaojie; Li, Yi
2008-02-01
We study the existence, uniqueness and asymptotic behavior, as well as the stability of a special kind of traveling wave solutions for competitive PDE systems involving intrinsic growth, competition, crowding effects and diffusion. The traveling waves are exclusive in the sense that as the variable goes to positive or negative infinity, different species are close to extinction or carrying capacity. We perform an appropriate affine transformation of the traveling wave equations into monotone form and construct appropriate upper and lower solutions. By this means, we reduce the existence proof to application of well-known theory about monotone traveling wave systems (cf. [A. Leung, Systems of Nonlinear Partial Differential Equations: Applications to Biology and Engineering, MIA, Kluwer, Boston, 1989; J. Wu, X. Zou, Traveling wave fronts of reaction-diffusion systems with delay, J. Dynam. Differential Equations 13 (2001) 651-687] and [I. Volpert, V. Volpert, VE Volpert, Traveling Wave Solutions of Parabolic Systems, Transl. Math. Monogr., vol. 140, Amer. Math. Soc., Providence, RI, 1994]). Then, by using spectral analysis of the linearization over the profile, we prove the orbital stability of the traveling wave in some Banach spaces with exponentially weighted norm. Furthermore, we show that the introduction of some weight is necessary in the sense that, in general, traveling wave solutions with initial perturbations in the (unweighted) space C0 are unstable (cf. [I. Volpert, V. Volpert, V. Volpert, Traveling Wave Solutions of Parabolic Systems, Transl. Math. Monogr., vol. 140, Amer. Math. Soc., Providence, RI, 1994] and [D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math., vol. 840, Springer-Verlag, New York, 1981]).
NASA Astrophysics Data System (ADS)
Ropp, David L.; Shadid, John N.
2005-03-01
In this paper numerical results are reviewed [D.L. Ropp, J.N. Shadid, C.C. Ober, Studies of the accuracy of time integration methods for reaction-diffusion equations, J. Comput. Phys. 194 (2) (2004) 544-574] that demonstrate that common second-order operator-splitting methods can exhibit instabilities when integrating the Brusselator equations out to moderate times of about seven periods of oscillation. These instabilities are manifested as high wave number spatial errors. In this paper, we further analyze this problem, and present a theorem for stability of operator-splitting methods applied to linear reaction-diffusion equations with indefinite reaction terms which controls both low and high wave number instabilities. A corollary shows that if L-stable methods are used for the diffusion term the high wave number instability will be controlled more easily. In the absence of L-stability, an additional time step condition that suppresses the high wave number modes appears to guarantee convergence at the asymptotic order for the operator-splitting method. Numerical results for a model problem confirm this theory, and results for the Brusselator problem agree as well.
NASA Astrophysics Data System (ADS)
Li, Xin-Zheng; Bai, Zhan-Guo; Li, Yan; He, Ya-Feng; Zhao, Kun
2015-04-01
The resonance interaction between two modes is investigated using a two-layer coupled Brusselator model. When two different wavelength modes satisfy resonance conditions, new modes will appear, and a variety of superlattice patterns can be obtained in a short wavelength mode subsystem. We find that even though the wavenumbers of two Turing modes are fixed, the parameter changes have influences on wave intensity and pattern selection. When a hexagon pattern occurs in the short wavelength mode layer and a stripe pattern appears in the long wavelength mode layer, the Hopf instability may happen in a nonlinearly coupled model, and twinkling-eye hexagon and travelling hexagon patterns will be obtained. The symmetries of patterns resulting from the coupled modes may be different from those of their parents, such as the cluster hexagon pattern and square pattern. With the increase of perturbation and coupling intensity, the nonlinear system will convert between a static pattern and a dynamic pattern when the Turing instability and Hopf instability happen in the nonlinear system. Besides the wavenumber ratio and intensity ratio of the two different wavelength Turing modes, perturbation and coupling intensity play an important role in the pattern formation and selection. According to the simulation results, we find that two modes with different symmetries can also be in the spatial resonance under certain conditions, and complex patterns appear in the two-layer coupled reaction diffusion systems. Project supported by the National Natural Science Foundation of China (Grant No. 11247242), the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 51201057), and the Natural Science Foundation of Hebei Province, China (Grant No. A2014208171).
Effects of intrinsic noise on a cubic autocatalytic reaction-diffusion system.
Cooper, Fred; Ghoshal, Gourab; Pérez-Mercader, Juan
2014-06-01
Starting from our recent chemical master equation derivation of the model of an autocatalytic reaction-diffusion chemical system with reactions U+2V→[over λ_{0}]3V and V→[over μ]P, U→[over ν]Q, we determine the effects of intrinsic noise on the momentum-space behavior of its kinetic parameters and chemical concentrations. We demonstrate that the intrinsic noise induces n→n molecular interaction processes with n≥4, where n is the number of participating molecules of type U or V. The momentum dependences of the reaction rates are driven by the fact that the autocatalytic reaction (inelastic scattering) is renormalized through the existence of an arbitrary number of intermediate elastic scatterings, which can also be interpreted as the creation and subsequent decay of a three body composite state σ=ϕ_{u}ϕ_{v}^{2}, where ϕ_{i} corresponds to the fields representing the densities of U and V. Finally, we discuss the difference between representing σ as a composite or an elementary particle (molecule) with its own kinetic parameters. In one dimension, we find that while they show markedly different behavior in the short spatiotemporal scale, high-momentum (UV) limit, they are formally equivalent in the large spatiotemporal scale, low momentum (IR) regime. On the other hand, in two dimensions and greater, due to the effects of fluctuations, there is no way to experimentally distinguish between a fundamental and composite σ. Thus, in this regime, σ behaves as an entity unto itself, suggesting that it can be effectively treated as an independent chemical species.
Interface proliferation and the growth of labyrinths in a reaction-diffusion system
NASA Astrophysics Data System (ADS)
Goldstein, Raymond E.; Muraki, David J.; Petrich, Dean M.
1996-04-01
In the bistable regime of the FitzHugh-Nagumo model of reaction-diffusion systems, spatially homogeneous patterns may be nonlinearly unstable to the formation of compact "localized states." The formation of space-filling patterns from instabilities of such structures is studied in the context of a nonlocal contour dynamics model for the evolution of boundaries between high and low concentrations of the activator. An earlier heuristic derivation [D. M. Petrich and R. E. Goldstein,
Interface proliferation and the growth of labyrinths in a reaction-diffusion system
Goldstein, R.E.; Muraki, D.J.; Petrich, D.M. |
1996-04-01
In the bistable regime of the FitzHugh-Nagumo model of reaction-diffusion systems, spatially homogeneous patterns may be nonlinearly unstable to the formation of compact {open_quote}{open_quote}localized states.{close_quote}{close_quote} The formation of space-filling patterns from instabilities of such structures in the context of a nonlocal contour dynamics model for the evolution of boundaries between high and low concentrations of the activator. An earlier heuristic derivation [D. M. Petrich and R. E. Goldstein, Phys. Rev. Lett. {bold 72}, 1120 (1994)] is made more systematic by an asymptotic analysis appropriate to the limits of fast inhibition, sharp activator interfaces, and small asymmetry in the bistable minima. The resulting contour dynamics is temporally local, with the normal component of the velocity involving a local contribution linear in the interface curvature and a nonlocal component having the form of a screened Biot-Savart interaction. The amplitude of the nonlocal interaction is set by the activator-inhibitor coupling and controls the {open_quote}{open_quote}lateral inhibition{close_quote}{close_quote} responsible for the destabilization of localized structures such as spots and stripes, and the repulsion of nearby interfaces in the later stages of those instabilities. The phenomenology of pattern formation exhibited by the contour dynamics is consistent with that seen by Lee, McCormick, Ouyang, and Swinney in experiments on the iodide-ferrocyanide-sulfite reaction in a gel reactor. Extensive numerical studies of the underlying partial differential equations are presented and compared in detail with the contour dynamics. The similarity of these phenomena (and their mathematical description) with those observed in amphiphilic monolayers, type I superconductors in the intermediate state, and magnetic fluids in Hele-Shaw geometry are emphasized. {copyright} {ital 1996 The American Physical Society.}
NASA Astrophysics Data System (ADS)
Liang, Xing; Jiang, Jifa
The asymptotic behavior of discrete type-K monotone dynamical systems and reaction-diffusion equations is investigated. The studying content includes the index theory for fixed points, permanence, global stability, convergence everywhere and coexistence. It is shown that the system has a globally asymptotically stable fixed point if every fixed point is locally asymptotically stable with respect to the face it belongs to and at this point the principal eigenvalue of the diagonal partial derivative about any component not belonging to the face is not one. A nice result presented is the sufficient and necessary conditions for the system to have a globally asymptotically stable positive fixed point. It can be used to establish the sufficient conditions for the system to persist uniformly and the convergent result for all orbits. Applications are made to time-periodic Lotka-Volterra systems with diffusion, and sufficient conditions for such systems to have a unique positive periodic solution attracting all positive initial value functions are given. For more general time-periodic type-K monotone reaction-diffusion systems with spatial homogeneity, a simple condition is given to guarantee the convergence of all positive solutions.
Clustering and optimal arrangement of enzymes in reaction-diffusion systems.
Buchner, Alexander; Tostevin, Filipe; Gerland, Ulrich
2013-05-17
Enzymes within biochemical pathways are often colocalized, yet the consequences of specific spatial enzyme arrangements remain poorly understood. We study the impact of enzyme arrangement on reaction efficiency within a reaction-diffusion model. The optimal arrangement transitions from a cluster to a distributed profile as a single parameter, which controls the probability of reaction versus diffusive loss of pathway intermediates, is varied. We introduce the concept of enzyme exposure to explain how this transition arises from the stochastic nature of molecular reactions and diffusion.
Cluster geometry and survival probability in systems driven by reaction diffusion dynamics
NASA Astrophysics Data System (ADS)
Windus, Alastair; Jensen, Henrik J.
2008-11-01
We consider a reaction-diffusion model incorporating the reactions A→phi, A→2A and 2A→3A. Depending on the relative rates for sexual and asexual reproduction of the quantity A, the model exhibits either a continuous or first-order absorbing phase transition to an extinct state. A tricritical point separates the two phase lines. While we comment on this critical behaviour, the main focus of the paper is on the geometry of the population clusters that form. We observe the different cluster structures that arise at criticality for the three different types of critical behaviour and show that there exists a linear relationship for the survival probability against initial cluster size at the tricritical point only.
NASA Astrophysics Data System (ADS)
Huang, Wenzhang
2016-02-01
In this paper we further extend a recently developed method to investigate the existence of traveling waves solutions and their minimum wave speed for non-monotone reaction-diffusion systems. Our approach consists of two steps. First we develop a geometrical shooting argument, with the aid of the theorem of homotopy invariance on the fundamental group, to obtain the positive semi-traveling wave solutions for a large class of reaction-diffusion systems, including the models of predator-prey interaction (for both predator-independent/dependent functional responses), the models of combustion, Belousov-Zhabotinskii reaction, SI-type of disease transmission, and the model of biological flow reactor in chemostat. Next, we apply the results obtained from the first step to some models, such as the Beddinton-DeAngelis model and the model of biolocal flow reactor, to show the convergence of these semi-traveling wave solutions to an interior equilibrium point by the construction of a Lyapunov-type function, or the convergence of semi-traveling waves to another boundary equilibrium point by the further analysis of the asymptotical behavior of semi-traveling wave solutions.
Reaction-diffusion waves in biology.
Volpert, V; Petrovskii, S
2009-12-01
The theory of reaction-diffusion waves begins in the 1930s with the works in population dynamics, combustion theory and chemical kinetics. At the present time, it is a well developed area of research which includes qualitative properties of travelling waves for the scalar reaction-diffusion equation and for system of equations, complex nonlinear dynamics, numerous applications in physics, chemistry, biology, medicine. This paper reviews biological applications of reaction-diffusion waves. PMID:20416847
Budroni, M A; De Wit, A
2016-06-01
When two solutions containing separate reactants A and B of an oscillating reaction are put in contact in a gel, localized spatiotemporal patterns can develop around the contact zone thanks to the interplay of reaction and diffusion processes. Using the Brusselator model, we explore analytically the deployment in space and time of the bifurcation diagram of such an A+B→ oscillator system. We provide a parametric classification of possible instabilities as a function of the ratio of the initial reactant concentrations and of the reaction intermediate species diffusion coefficients. Related one-dimensional reaction-diffusion dynamics are studied numerically. We find that the system can spatially localize waves and Turing patterns as well as induce more complex dynamics such as zigzag spatiotemporal waves when Hopf and Turing modes interact. PMID:27415255
Budroni, M A; De Wit, A
2016-06-01
When two solutions containing separate reactants A and B of an oscillating reaction are put in contact in a gel, localized spatiotemporal patterns can develop around the contact zone thanks to the interplay of reaction and diffusion processes. Using the Brusselator model, we explore analytically the deployment in space and time of the bifurcation diagram of such an A+B→ oscillator system. We provide a parametric classification of possible instabilities as a function of the ratio of the initial reactant concentrations and of the reaction intermediate species diffusion coefficients. Related one-dimensional reaction-diffusion dynamics are studied numerically. We find that the system can spatially localize waves and Turing patterns as well as induce more complex dynamics such as zigzag spatiotemporal waves when Hopf and Turing modes interact.
Pattern formation in a two-component reaction-diffusion system with delayed processes on a network
NASA Astrophysics Data System (ADS)
Petit, Julien; Asllani, Malbor; Fanelli, Duccio; Lauwens, Ben; Carletti, Timoteo
2016-11-01
Reaction-diffusion systems with time-delay defined on complex networks have been studied in the framework of the emergence of Turing instabilities. The use of the Lambert W-function allowed us to get explicit analytic conditions for the onset of patterns as a function of the main involved parameters, the time-delay, the network topology and the diffusion coefficients. Depending on these parameters, the analysis predicts whether the system will evolve towards a stationary Turing pattern or rather to a wave pattern associated to a Hopf bifurcation. The possible outcomes of the linear analysis overcome the respective limitations of the single-species case with delay, and that of the classical activator-inhibitor variant without delay. Numerical results gained from the Mimura-Murray model support the theoretical approach.
NASA Astrophysics Data System (ADS)
Budroni, M. A.; De Wit, A.
2016-06-01
When two solutions containing separate reactants A and B of an oscillating reaction are put in contact in a gel, localized spatiotemporal patterns can develop around the contact zone thanks to the interplay of reaction and diffusion processes. Using the Brusselator model, we explore analytically the deployment in space and time of the bifurcation diagram of such an A +B → oscillator system. We provide a parametric classification of possible instabilities as a function of the ratio of the initial reactant concentrations and of the reaction intermediate species diffusion coefficients. Related one-dimensional reaction-diffusion dynamics are studied numerically. We find that the system can spatially localize waves and Turing patterns as well as induce more complex dynamics such as zigzag spatiotemporal waves when Hopf and Turing modes interact.
NASA Astrophysics Data System (ADS)
Olsen, Thomas; Hou, Yu; Trail, Collin; Wiener, Richard
2004-11-01
The Reaction-Diffusion model (H. Riecke and H.-G. Paap, Europhys. Lett. 14), 1235 (1991).has been applied to a wide variety of pattern forming systems. It correctly predicted a period doubling cascade to chaos in Taylor-Couette flow with hourglass geometry(Richard J. Wiener et al), Phys. Rev. E 55, 5489 (1997).. We have conducted a series of such simulations, varying the length of the system. This has enabled us to study the transition from a purely temporal chaos of the formation of new pairs of Taylor Vortices at a single location, to a spatio-temporal chaos of formation across a range of locations. Application to anticipated experiments will be discussed.
NASA Astrophysics Data System (ADS)
Halmstad, Andrew; Olsen, Thomas; Wiener, Richard
2006-11-01
Previously, we have observed a period-doubling cascade to chaos in Modified Taylor-Couette Flow with Hourglass Geometry. Such behavior had been predicted by The Reaction-Diffusion model simulations. The chaotic formation of Taylor-Vortex pair formation was restricted to a very narrow band about the waist of the hourglass. It was suggested that with increasing lengths of systems, the chaotic region would expand. We present a battery of simulations to determine the variation of the size of the chaotic region with length, seeking the transition to spatio- temporal chaos. Richard J. Wiener et al, Phys. Rev. E 55, 5489 (1997). H. Riecke and H.-G. Paap, Europhys. Lett. 14, 1235 (1991).
The network method for solutions of oscillating reaction-diffusion systems
Horno, J.; Hayas, A.; Gonzalez-Fernandez, C.F.
1995-05-01
The network approach is a method whereby physicochemical systems are replaced by electrical networks, which are simulated by using a digital computer program such as PSPICE. The network method solves problems of great mathematical complexity in a versatile and efficient way. This method has been applied to a system involving coupled chemical reactions and diffusion (Brusselator system) as a prototype of an oscillating reaction system. 10 refs., 7 figs., 1 tab.
Patterns and Oscillations in Reaction-Diffusion Systems with Intrinsic Fluctuations
NASA Astrophysics Data System (ADS)
Giver, Michael; Goldstein, Daniel; Chakraborty, Bulbul
2013-03-01
Intrinsic or demographic noise has been shown to play an important role in the dynamics of a variety of systems including predator-prey populations, biochemical reactions within cells, and oscillatory chemical reaction systems, and is known to give rise to oscillations and pattern formation well outside the parameter range predicted by standard mean-field analysis. Initially motivated by an experimental model of cells and tissues where the cells are represented by chemical reagents isolated in emulsion droplets, we study the stochastic Brusselator, a simple activator-inhibitor chemical reaction model. Our work extends the results of recent studies on the zero and one dimensional systems with the ultimate goals of understanding the role of noise in spatially structured systems and engineering novel patterns and attractors induced by fluctuations. In the zero dimensional system, we observe a noise induced switching between small and large amplitude oscillations when a separation of time scales is present, while the spatially extended system displays a similar switching between a stationary Turing pattern and uniform oscillations.
Spatial structures in a reaction-diffusion system--detailed analysis of the "Brusselator".
Kubícek, M; Rýzler, V; Marek, M
1978-07-01
Continuous dependence of spatially nonuniform concentration profiles for the 'Brussellator" reaction mechanims on the characteristic length of the system is given both for zero flux and fixed boundary conditions. Branches of solutions arising through primary bifurcation form closed curves. Secondary bifurcations giving rise to spatially asymmetric solutions exist for fixed boundary conditions. Results of a stability analysis of individual solutions are discussed. A method of composing complex spatial profiles for higher lengths from elementary solutions for smaller lenghts is suggested and tested in the case of zero flux boundary conditions. Emergence of subsequently more complex stable patterns in dependence on increasing length of the system suggests many similarities to gradual build up of complex morphogenetic patterns. PMID:687769
Hexagonal Standing-Wave Patterns in Periodically Forced Reaction Diffusion Systems
NASA Astrophysics Data System (ADS)
Zhang, Ke; Wang, Hong-Li; Qiao, Chun; Ouyang, Qi
2006-06-01
The periodically forced spatially extended Brusselator is investigated in the oscillating regime. The temporal response and pattern formation within the 2:1 frequency-locking band where the system oscillates at one half of the forcing frequency are examined. An hexagonal standing-wave pattern and other resonant patterns are observed. The detailed phase diagram of resonance structure in the forcing frequency and forcing amplitude parameter space is calculated. The transitions between the resonant standing-wave patterns are of hysteresis when control parameters are varied, and the presence of multiplicity is demonstrated. Analysis in the framework of amplitude equation reveals that the spatial patterns of the standing waves come out as a result of Turing bifurcation in the amplitude equation.
Reaction diffusion in the NiCrAl and CoCrAl systems
NASA Technical Reports Server (NTRS)
Levine, S. R.
1978-01-01
The paper assesses the effect of overlay coating and substrate composition on the kinetics of coating depletion by interdiffusion. This is accomplished by examining the constitution, kinetics and activation energies for a series of diffusion couples primarily of the NiCrAl/Ni-10Cr or CoCrAl/Ni-10Cr type annealed at temperatures in the range 1000-1205 C for times up to 500 hr. A general procedure is developed for analyzing diffusion in multicomponent multiphase systems. It is shown that by introducing the concept of beta-source strength, which can be determined from appropriate phase diagrams, the Wagner solution for consumption of a second phase in a semiinfinite couple is successfully applied to the analysis of MCrAl couples. Thus, correlation of beta-recession rate constants with couple composition, total and diffusional activation energies, and interdiffusion coefficients are determined.
Sensitivity Analysis of Boundary Value Problems: Application to Nonlinear Reaction-Diffusion Systems
NASA Astrophysics Data System (ADS)
Reuven, Yakir; Smooke, Mitchell D.; Rabitz, Herschel
1986-05-01
A direct and very efficient approach for obtaining sensitivities of two-point boundary value problems solved by Newton's method is studied. The link between the solution method and the sensitivity equations is investigated together with matters of numerical accuracy and efficiency. This approach is employed in the analysis of a model three species, unimolecular, steady-state, premixed laminar flame. The numerical accuracy of the sensitivities is verified and their values are utilized for interpretation of the model results. It is found that parameters associated directly with the temperature play a dominant role. The system's Green's functions relating dependent variables are also controlled strongly by the temperature. In addition, flame speed sensitivities are calculated and shown to be a special class of derived sensitivity coefficients. Finally, some suggestions for the physical interpretation of sensitivities in model analysis are given.
NASA Astrophysics Data System (ADS)
Lenk, Claudia; Einax, Mario; Maass, Philipp
2013-04-01
Spatiotemporal excitation patterns in the FitzHugh-Nagumo model are studied, which result from the disturbance of a primary pacemaker by a secondary pacemaker. The primary and secondary pacemakers generate regular waves with frequencies fpace and fpert, respectively. The pacemakers are spatially separated, but waves emanating from them encounter each other via a small bridge. This leads to three different types I-III of irregular excitation patterns in disjunct domains of the fpace-fpert plane. Types I and II are caused by detachments of waves coming from the two pacemakers at corners of the bridge. Type III irregularities are confined to a boundary region of the system and originate from a partial penetration of the primary waves into a space, where circular wave fronts from the secondary pacemaker prevail. For this type, local frequencies can significantly exceed fpace and fpert. The degree of irregularity found for the three different types is quantified by the entropy of the local frequency distribution and an order parameter for phase coherence.
Siero, E; Doelman, A; Eppinga, M B; Rademacher, J D M; Rietkerk, M; Siteur, K
2015-03-01
For water-limited arid ecosystems, where water distribution and infiltration play a vital role, various models have been set up to explain vegetation patterning. On sloped terrains, vegetation aligned in bands has been observed ubiquitously. In this paper, we consider the appearance, stability, and bifurcations of 2D striped or banded patterns in an arid ecosystem model. We numerically show that the resilience of the vegetation bands is larger on steeper slopes by computing the stability regions (Busse balloons) of striped patterns with respect to 1D and transverse 2D perturbations. This is corroborated by numerical simulations with a slowly decreasing water input parameter. Here, long wavelength striped patterns are unstable against transverse perturbations, which we also rigorously prove on flat ground through an Evans function approach. In addition, we prove a "Squire theorem" for a class of two-component reaction-advection-diffusion systems that includes our model, showing that the onset of pattern formation in 2D is due to 1D instabilities in the direction of advection, which naturally leads to striped patterns. PMID:25833449
Siero, E; Doelman, A; Eppinga, M B; Rademacher, J D M; Rietkerk, M; Siteur, K
2015-03-01
For water-limited arid ecosystems, where water distribution and infiltration play a vital role, various models have been set up to explain vegetation patterning. On sloped terrains, vegetation aligned in bands has been observed ubiquitously. In this paper, we consider the appearance, stability, and bifurcations of 2D striped or banded patterns in an arid ecosystem model. We numerically show that the resilience of the vegetation bands is larger on steeper slopes by computing the stability regions (Busse balloons) of striped patterns with respect to 1D and transverse 2D perturbations. This is corroborated by numerical simulations with a slowly decreasing water input parameter. Here, long wavelength striped patterns are unstable against transverse perturbations, which we also rigorously prove on flat ground through an Evans function approach. In addition, we prove a "Squire theorem" for a class of two-component reaction-advection-diffusion systems that includes our model, showing that the onset of pattern formation in 2D is due to 1D instabilities in the direction of advection, which naturally leads to striped patterns.
NASA Astrophysics Data System (ADS)
Vanag, Vladimir K.
2004-09-01
Advances in nonequilibrium pattern formation in reaction-diffusion systems are reviewed. Special emphasis is placed on patterns found in the spatially extended Belousov-Zhabotinsky reaction dispersed in aerosol OT water-in-oil microemulsions (BZ-AOT system): Turing patterns, packet and standing waves, antispirals and segmented spirals, and accelerating waves and oscillons. All experimental results are explained theoretically and reproduced in computer simulations.
NASA Astrophysics Data System (ADS)
Lueptow, Richard M.; Schlick, Conor P.; Umbanhowar, Paul B.; Ottino, Julio M.
2013-11-01
We investigate chaotic advection and diffusion in competitive autocatalytic reactions. To study this subject, we use a computationally efficient method for solving advection-reaction-diffusion equations for periodic flows using a mapping method with operator splitting. In competitive autocatalytic reactions, there are two species, B and C, which both react autocatalytically with species A (A +B -->2B and A +C -->2C). If there is initially a small amount of spatially localized B and C and a large amount of A, all three species will be advected by the velocity field, diffuse, and react until A is completely consumed and only B and C remain. We find that the small scale interactions associated with the chaotic velocity field, specifically the local finite-time Lyapunov exponents (FTLEs), can accurately predict the final average concentrations of B and C after the reaction is complete. The species, B or C, that starts in the region with the larger FTLE has, with high probability, the larger average concentration at the end of the reaction. If species B and C start in regions having similar FTLEs, their average concentrations at the end of the reaction will also be similar. Funded by NSF Grant CMMI-1000469.
2012-01-01
Background Reaction-diffusion based models have been widely used in the literature for modeling the growth of solid tumors. Many of the current models treat both diffusion/consumption of nutrients and cell proliferation. The majority of these models use classical transport/mass conservation equations for describing the distribution of molecular species in tumor spheroids, and the Fick's law for describing the flux of uncharged molecules (i.e oxygen, glucose). Commonly, the equations for the cell movement and proliferation are first order differential equations describing the rate of change of the velocity of the cells with respect to the spatial coordinates as a function of the nutrient's gradient. Several modifications of these equations have been developed in the last decade to explicitly indicate that the tumor includes cells, interstitial fluids and extracellular matrix: these variants provided a model of tumor as a multiphase material with these as the different phases. Most of the current reaction-diffusion tumor models are deterministic and do not model the diffusion as a local state-dependent process in a non-homogeneous medium at the micro- and meso-scale of the intra- and inter-cellular processes, respectively. Furthermore, a stochastic reaction-diffusion model in which diffusive transport of the molecular species of nutrients and chemotherapy drugs as well as the interactions of the tumor cells with these species is a novel approach. The application of this approach to he scase of non-small cell lung cancer treated with gemcitabine is also novel. Methods We present a stochastic reaction-diffusion model of non-small cell lung cancer growth in the specification formalism of the tool Redi, we recently developed for simulating reaction-diffusion systems. We also describe how a spatial gradient of nutrients and oncological drugs affects the tumor progression. Our model is based on a generalization of the Fick's first diffusion law that allows to model
NASA Technical Reports Server (NTRS)
Hou, Jean W.; Sheen, Jeen S.
1987-01-01
The aim of this study is to find a reliable numerical algorithm to calculate thermal design sensitivities of a transient problem with discontinuous derivatives. The thermal system of interest is a transient heat conduction problem related to the curing process of a composite laminate. A logical function which can smoothly approximate the discontinuity is introduced to modify the system equation. Two commonly used methods, the adjoint variable method and the direct differentiation method, are then applied to find the design derivatives of the modified system. The comparisons of numerical results obtained by these two methods demonstrate that the direct differentiation method is a better choice to be used in calculating thermal design sensitivity.
NASA Astrophysics Data System (ADS)
Johnson, Margaret E.; Hummer, Gerhard
2014-07-01
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.
NASA Astrophysics Data System (ADS)
Zhang, Chunxia; Zhang, Hong; Ouyang, Qi; Hu, Bambi; Gunaratne, Gemunu H.
2003-09-01
The transition from spiral waves to defect-mediated turbulence was studied in a spatial open reactor using Belousov-Zhabotinsky reaction. The experimental results show a new mechanism of the transition from spirals to spatiotemporal chaos, in which the gradient effects in the three-dimensional system are essential. The transition scenario consists of two stages: first, the effects of gradients in the third dimension cause a splitting of the spiral tip and a deletion of certain wave segments, generating new wave sources; second, the waves sent by the new wave sources undergo a backfire instability, and the back waves are laterally unstable. As a result, defects are automatically generated and fill all over the system. The result of numerical simulation using the FitzHugh-Nagumo model essentially agrees with the experimental observation.
NASA Astrophysics Data System (ADS)
Zhang, Henggui; Garratt, Clifford J.; Kharche, Sanjay; Holden, Arun V.
2009-06-01
Human atrial tissue is an excitable system, in which myocytes are excitable elements, and cell-to-cell electrotonic interactions are via diffusive interactions of cell membrane potentials. We developed a family of excitable system models for human atrium at cellular, tissue and anatomical levels for both normal and chronic atrial fibrillation (AF) conditions. The effects of AF-induced remodelling of cell membrane ionic channels (reaction kinetics) and intercellular gap junctional coupling (diffusion) on atrial excitability, conduction of excitation waves and dynamics of re-entrant excitation waves are quantified. Both ionic channel and gap junctional coupling remodelling have rate dependent effects on atrial propagation. Membrane channel conductance remodelling allows the propagation of activity at higher rates than those sustained in normal tissue or in tissue with gap junctional remodelling alone. Membrane channel conductance remodelling is essential for the propagation of activity at rates higher than 300/min as seen in AF. Spatially heterogeneous gap junction coupling remodelling increased the risk of conduction block, an essential factor for the genesis of re-entry. In 2D and 3D anatomical models, the dynamical behaviours of re-entrant excitation waves are also altered by membrane channel modelling. This study provides insights to understand the pro-arrhythmic effects of AF-induced reaction and diffusion remodelling in atrial tissue.
Physarum machines: encapsulating reaction-diffusion to compute spanning tree
NASA Astrophysics Data System (ADS)
Adamatzky, Andrew
2007-12-01
The Physarum machine is a biological computing device, which employs plasmodium of Physarum polycephalum as an unconventional computing substrate. A reaction-diffusion computer is a chemical computing device that computes by propagating diffusive or excitation wave fronts. Reaction-diffusion computers, despite being computationally universal machines, are unable to construct certain classes of proximity graphs without the assistance of an external computing device. I demonstrate that the problem can be solved if the reaction-diffusion system is enclosed in a membrane with few ‘growth points’, sites guiding the pattern propagation. Experimental approximation of spanning trees by P. polycephalum slime mold demonstrates the feasibility of the approach. Findings provided advance theory of reaction-diffusion computation by enriching it with ideas of slime mold computation.
A Lattice Boltzmann Model for Oscillating Reaction-Diffusion
NASA Astrophysics Data System (ADS)
Rodríguez-Romo, Suemi; Ibañez-Orozco, Oscar; Sosa-Herrera, Antonio
2016-07-01
A computational algorithm based on the lattice Boltzmann method (LBM) is proposed to model reaction-diffusion systems. In this paper, we focus on how nonlinear chemical oscillators like Belousov-Zhabotinsky (BZ) and the chlorite-iodide-malonic acid (CIMA) reactions can be modeled by LBM and provide with new insight into the nature and applications of oscillating reactions. We use Gaussian pulse initial concentrations of sulfuric acid in different places of a bidimensional reactor and nondiffusive boundary walls. We clearly show how these systems evolve to a chaotic attractor and produce specific pattern images that are portrayed in the reactions trajectory to the corresponding chaotic attractor and can be used in robotic control.
Analysis of Coupled Reaction-Diffusion Equations for RNA Interactions
Hohn, Maryann E.; Li, Bo; Yang, Weihua
2015-01-01
We consider a system of coupled reaction-diffusion equations that models the interaction between multiple types of chemical species, particularly the interaction between one messenger RNA and different types of non-coding microRNAs in biological cells. We construct various modeling systems with different levels of complexity for the reaction, nonlinear diffusion, and coupled reaction and diffusion of the RNA interactions, respectively, with the most complex one being the full coupled reaction-diffusion equations. The simplest system consists of ordinary differential equations (ODE) modeling the chemical reaction. We present a derivation of this system using the chemical master equation and the mean-field approximation, and prove the existence, uniqueness, and linear stability of equilibrium solution of the ODE system. Next, we consider a single, nonlinear diffusion equation for one species that results from the slow diffusion of the others. Using variational techniques, we prove the existence and uniqueness of solution to a boundary-value problem of this nonlinear diffusion equation. Finally, we consider the full system of reaction-diffusion equations, both steady-state and time-dependent. We use the monotone method to construct iteratively upper and lower solutions and show that their respective limits are solutions to the reaction-diffusion system. For the time-dependent system of reaction-diffusion equations, we obtain the existence and uniqueness of global solutions. We also obtain some asymptotic properties of such solutions. PMID:25601722
Circumnutation modeled by reaction-diffusion equations
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.
Laser Spot Detection Based on Reaction Diffusion
Vázquez-Otero, Alejandro; Khikhlukha, Danila; Solano-Altamirano, J. M.; Dormido, Raquel; Duro, Natividad
2016-01-01
Center-location of a laser spot is a problem of interest when the laser is used for processing and performing measurements. Measurement quality depends on correctly determining the location of the laser spot. Hence, improving and proposing algorithms for the correct location of the spots are fundamental issues in laser-based measurements. In this paper we introduce a Reaction Diffusion (RD) system as the main computational framework for robustly finding laser spot centers. The method presented is compared with a conventional approach for locating laser spots, and the experimental results indicate that RD-based computation generates reliable and precise solutions. These results confirm the flexibility of the new computational paradigm based on RD systems for addressing problems that can be reduced to a set of geometric operations. PMID:26938537
Laser Spot Detection Based on Reaction Diffusion.
Vázquez-Otero, Alejandro; Khikhlukha, Danila; Solano-Altamirano, J M; Dormido, Raquel; Duro, Natividad
2016-03-01
Center-location of a laser spot is a problem of interest when the laser is used for processing and performing measurements. Measurement quality depends on correctly determining the location of the laser spot. Hence, improving and proposing algorithms for the correct location of the spots are fundamental issues in laser-based measurements. In this paper we introduce a Reaction Diffusion (RD) system as the main computational framework for robustly finding laser spot centers. The method presented is compared with a conventional approach for locating laser spots, and the experimental results indicate that RD-based computation generates reliable and precise solutions. These results confirm the flexibility of the new computational paradigm based on RD systems for addressing problems that can be reduced to a set of geometric operations.
Simple computation of reaction-diffusion processes on point clouds.
Macdonald, Colin B; Merriman, Barry; Ruuth, Steven J
2013-06-01
The study of reaction-diffusion processes is much more complicated on general curved surfaces than on standard Cartesian coordinate spaces. Here we show how to formulate and solve systems of reaction-diffusion equations on surfaces in an extremely simple way, using only the standard Cartesian form of differential operators, and a discrete unorganized point set to represent the surface. Our method decouples surface geometry from the underlying differential operators. As a consequence, it becomes possible to formulate and solve rather general reaction-diffusion equations on general surfaces without having to consider the complexities of differential geometry or sophisticated numerical analysis. To illustrate the generality of the method, computations for surface diffusion, pattern formation, excitable media, and bulk-surface coupling are provided for a variety of complex point cloud surfaces.
Langevin Equations for Reaction-Diffusion Processes.
Benitez, Federico; Duclut, Charlie; Chaté, Hugues; Delamotte, Bertrand; Dornic, Ivan; Muñoz, Miguel A
2016-09-01
For reaction-diffusion processes with at most bimolecular reactants, we derive well-behaved, numerically tractable, exact Langevin equations that govern a stochastic variable related to the response field in field theory. Using duality relations, we show how the particle number and other quantities of interest can be computed. Our work clarifies long-standing conceptual issues encountered in field-theoretical approaches and paves the way for systematic numerical and theoretical analyses of reaction-diffusion problems. PMID:27636462
Langevin Equations for Reaction-Diffusion Processes
NASA Astrophysics Data System (ADS)
Benitez, Federico; Duclut, Charlie; Chaté, Hugues; Delamotte, Bertrand; Dornic, Ivan; Muñoz, Miguel A.
2016-09-01
For reaction-diffusion processes with at most bimolecular reactants, we derive well-behaved, numerically tractable, exact Langevin equations that govern a stochastic variable related to the response field in field theory. Using duality relations, we show how the particle number and other quantities of interest can be computed. Our work clarifies long-standing conceptual issues encountered in field-theoretical approaches and paves the way for systematic numerical and theoretical analyses of reaction-diffusion problems.
Fluorescence Correlation Spectroscopy and Nonlinear Stochastic Reaction-Diffusion
Del Razo, Mauricio; Pan, Wenxiao; Qian, Hong; Lin, Guang
2014-05-30
The currently existing theory of fluorescence correlation spectroscopy (FCS) is based on the linear fluctuation theory originally developed by Einstein, Onsager, Lax, and others as a phenomenological approach to equilibrium fluctuations in bulk solutions. For mesoscopic reaction-diffusion systems with nonlinear chemical reactions among a small number of molecules, a situation often encountered in single-cell biochemistry, it is expected that FCS time correlation functions of a reaction-diffusion system can deviate from the classic results of Elson and Magde [Biopolymers (1974) 13:1-27]. We first discuss this nonlinear effect for reaction systems without diffusion. For nonlinear stochastic reaction-diffusion systems there are no closed solutions; therefore, stochastic Monte-Carlo simulations are carried out. We show that the deviation is small for a simple bimolecular reaction; the most significant deviations occur when the number of molecules is small and of the same order. Extending Delbrück-Gillespie’s theory for stochastic nonlinear reactions with rapidly stirring to reaction-diffusion systems provides a mesoscopic model for chemical and biochemical reactions at nanometric and mesoscopic level such as a single biological cell.
Konkoli, Zoran
2004-01-01
Theoretical methods for dealing with diffusion-controlled reactions inevitably rely on some kind of approximation, and to find the one that works on a particular problem is not always easy. Here the approximation used by Bogolyubov to study a weakly nonideal Bose gas, referred to as the weakly nonideal Bose gas approximation (WBGA), is applied in the analysis of three reaction-diffusion models: (i) A+A-->Ø, (ii) A+B-->Ø, and (iii) A+A,B+B,A+B-->Ø (the ABBA model). Two types of WBGA are considered, the simpler WBGA-I and the more complicated WBGA-II. All models are defined on the lattice to facilitate comparison with computer experiment (simulation). It is found that the WBGA describes the A+B reaction well, it reproduces the correct d/4 density decay exponent. However, it fails in the case of the A+A reaction and the ABBA model. (To cure the deficiency of WBGA in dealing with the A+A model, a hybrid of the WBGA and Kirkwood superposition approximations is suggested.) It is shown that the WBGA-I is identical to the dressed-tree calculation suggested by Lee [J. Phys. A 27, 2633 (1994)], and that the dressed-tree calculation does not lead to the d/2 density decay exponent when applied to the A+A reaction, as normally believed, but it predicts the d/4 decay exponent. Last, the usage of the small n(0) approximation suggested by Mattis and Glasser [Rev. Mod. Phys. 70, 979 (1998)] is questioned if used beyond the A+B reaction-diffusion model. PMID:14995603
Reaction-Diffusion Processes in Ultrathin Films of Photoresist
NASA Astrophysics Data System (ADS)
Perera, Ginusha; Stein, Gila
2011-03-01
Projection lithography is the primary technology used for patterning semiconductor devices. High-throughput manufacturing requires imaging materials (resists) that are highly sensitive to radiation, and this demand is satisfied through a process termed chemical amplification (CA). CA resists are comprised of a polymer resin (reactant) and photoacid generator (catalyst); a coupled reaction-diffusion mechanism drives image formation, where image resolution is limited by slow diffusion of the acid catalyst. There is evidence that thin film reaction rates deviate from the bulk behavior, and current models for image formation do not capture such effects. We demonstrate that X-Ray Diffraction can measure spatial extent-of-reaction in ultrathin films of a nanopatterned poly(4-hydroxystyrene-co-tertbutylacrylate) CA resist. The feedback acquired is used to construct predictive models for the coupled reaction-diffusion processes that incorporate the physics of confined polymers. Funded by NSF ECCS 0927147.
Reaction diffusion equation with spatio-temporal delay
NASA Astrophysics Data System (ADS)
Zhao, Zhihong; Rong, Erhua
2014-07-01
We investigate reaction-diffusion equation with spatio-temporal delays, the global existence, uniqueness and asymptotic behavior of solutions for which in relation to constant steady-state solution, included in the region of attraction of a stable steady solution. It is shown that if the delay reaction function satisfies some conditions and the system possesses a pair of upper and lower solutions then there exists a unique global solution. In terms of the maximal and minimal constant solutions of the corresponding steady-state problem, we get the asymptotic stability of reaction-diffusion equation with spatio-temporal delay. Applying this theory to Lotka-Volterra model with spatio-temporal delay, we get the global solution asymptotically tend to the steady-state problem's steady-state solution.
Cohabitation reaction-diffusion model for virus focal infections
NASA Astrophysics Data System (ADS)
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 processes at the nano- and microscales
NASA Astrophysics Data System (ADS)
Epstein, Irving R.; Xu, Bing
2016-04-01
The bottom-up fabrication of nano- and microscale structures from primary building blocks (molecules, colloidal particles) has made remarkable progress over the past two decades, but most research has focused on structural aspects, leaving our understanding of the dynamic and spatiotemporal aspects at a relatively primitive stage. In this Review, we draw inspiration from living cells to argue that it is now time to move beyond the generation of structures and explore dynamic processes at the nanoscale. We first introduce nanoscale self-assembly, self-organization and reaction-diffusion processes as essential features of cells. Then, we highlight recent progress towards designing and controlling these fundamental features of life in abiological systems. Specifically, we discuss examples of reaction-diffusion processes that lead to such outcomes as self-assembly, self-organization, unique nanostructures, chemical waves and dynamic order to illustrate their ubiquity within a unifying context of dynamic oscillations and energy dissipation. Finally, we suggest future directions for research on reaction-diffusion processes at the nano- and microscales that we find hold particular promise for a new understanding of science at the nanoscale and the development of new kinds of nanotechnologies for chemical transport, chemical communication and integration with living systems.
Programming reaction-diffusion: From theory to micro- and nanofabrication
NASA Astrophysics Data System (ADS)
Campbell, Christopher James
Nature often uses reaction-diffusion(RD) as a means of making structures and materials of unique properties or morphologies on scales from macro- (e.g., stripes in zebras, tigers, and seashells, and formations in trees, agates, and rocks) to microscopic (e.g., cellular growth, chemotaxis and biological waves). However, reaction-diffusion phenomena have not yet been applied in modern materials science and micro-/nanotechnology. In this context, RD systems are particularly promising for micropatterning of surfaces. Unlike conventional micropatterning techniques that modify the properties of the substrate only at the locations to which a modifying agent - be it a chemical or radiation - is delivered, RD can, in principle, evolve chemicals delivered onto a surface into structures of characteristic dimensions significantly smaller than those of the original pattern. In this Dissertation, I describe how reaction-diffusions are programmed and executed via a new micropatterning technique called Wet Stamping to (i) transform microscopic patterns of chemicals delivered onto thin films of dry gelatin into regular arrays of lines of submicrometer thicknesses, multicolor arrays on the micrometer scale, or three-dimensional microstructured surfaces; (ii) modify the properties of a surface by precisely delivering an oxidant to change hydrophilicity or deliver silanes or thiols to build a self-assembling monolayer; or (iii) cut into a metal, glass, or crystal surface by delivery of an etchant to form binary and curvilinear three-dimensional microstructures. This technique has allowed for a fundamental understanding and control of reaction-diffusion processes down to the nanoscale. In addition, this platform has allowed for the development of a range of applications on the micro- and nanoscale, including microlenses, microfluidic devices, and templates for studying cell motility and cancer metastasis.
Reaction rates for a generalized reaction-diffusion master equation
Hellander, Stefan; Petzold, Linda
2016-01-01
It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model, and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is on the order of the reaction radius of a reacting pair of molecules. PMID:26871190
Reaction rates for a generalized reaction-diffusion master equation
NASA Astrophysics Data System (ADS)
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.
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.
Reaction-diffusion processes and metapopulation models on duplex networks
NASA Astrophysics Data System (ADS)
Xuan, Qi; Du, Fang; Yu, Li; Chen, Guanrong
2013-03-01
Reaction-diffusion processes, used to model various spatially distributed dynamics such as epidemics, have been studied mostly on regular lattices or complex networks with simplex links that are identical and invariant in transferring different kinds of particles. However, in many self-organized systems, different particles may have their own private channels to keep their purities. Such division of links often significantly influences the underlying reaction-diffusion dynamics and thus needs to be carefully investigated. This article studies a special reaction-diffusion process, named susceptible-infected-susceptible (SIS) dynamics, given by the reaction steps β→α and α+β→2β, on duplex networks where links are classified into two groups: α and β links used to transfer α and β particles, which, along with the corresponding nodes, consist of an α subnetwork and a β subnetwork, respectively. It is found that the critical point of particle density to sustain reaction activity is independent of the network topology if there is no correlation between the degree sequences of the two subnetworks, and this critical value is suppressed or extended if the two degree sequences are positively or negatively correlated, respectively. Based on the obtained results, it is predicted that epidemic spreading may be promoted on positive correlated traffic networks but may be suppressed on networks with modules composed of different types of diffusion links.
Reaction-diffusion in the NEURON simulator.
McDougal, Robert A; Hines, Michael L; Lytton, William W
2013-01-01
In order to support research on the role of cell biological principles (genomics, proteomics, signaling cascades and reaction dynamics) on the dynamics of neuronal response in health and disease, NEURON's Reaction-Diffusion (rxd) module in Python provides specification and simulation for these dynamics, coupled with the electrophysiological dynamics of the cell membrane. Arithmetic operations on species and parameters are overloaded, allowing arbitrary reaction formulas to be specified using Python syntax. These expressions are then transparently compiled into bytecode that uses NumPy for fast vectorized calculations. At each time step, rxd combines NEURON's integrators with SciPy's sparse linear algebra library. PMID:24298253
Parametric Pattern Selection in a Reaction-Diffusion Model
Stich, Michael; Ghoshal, Gourab; Pérez-Mercader, Juan
2013-01-01
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. PMID:24204813
Exact solutions for logistic reaction-diffusion equations in biology
NASA Astrophysics Data System (ADS)
Broadbridge, P.; Bradshaw-Hajek, B. H.
2016-08-01
Reaction-diffusion equations with a nonlinear source have been widely used to model various systems, with particular application to biology. Here, we provide a solution technique for these types of equations in N-dimensions. The nonclassical symmetry method leads to a single relationship between the nonlinear diffusion coefficient and the nonlinear reaction term; the subsequent solutions for the Kirchhoff variable are exponential in time (either growth or decay) and satisfy the linear Helmholtz equation in space. Example solutions are given in two dimensions for particular parameter sets for both quadratic and cubic reaction terms.
Reaction rates for mesoscopic reaction-diffusion kinetics
Hellander, Stefan; Hellander, Andreas; Petzold, Linda
2016-01-01
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. PMID:25768640
Reaction rates for mesoscopic reaction-diffusion kinetics
NASA Astrophysics Data System (ADS)
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.
The possible role of reaction-diffusion in leaf shape.
Franks, N R; Britton, N F
2000-01-01
We consider mechanisms that may determine certain simple leaf shapes. Compared with other aspects of plant morphogenesis, such as phyllotaxis or spiral leaf arrangement, rather little is known about leaf-shape-determining mechanisms. We develop mathematical models for the gross pattern of leaf shape based on reaction diffusion systems. These models are consistent with what is known about factors that might determine leaf shape. They show that diverse leaf shapes may be obtained from a single reaction diffusion system. This has implications in terms of both convergent and divergent evolution. The models make predictions that can be tested experimentally. We predict the form of pre-patterns of growth promoters in leaf primordia of different sizes when the morphogens either diffuse into the primordia or are produced locally. We also predict the effects on leaf shape of removing parts of primordia at different times. The models can also predict the effects on leaf shape of the topical application of activators and inhibitors to leaf primordia. PMID:10972123
Reaction rates for mesoscopic reaction-diffusion kinetics.
Hellander, Stefan; Hellander, Andreas; Petzold, Linda
2015-02-01
The mesoscopic reaction-diffusion master equation (RDME) is a popular modeling framework frequently applied to stochastic reaction-diffusion kinetics in systems biology. The RDME is derived from assumptions about the underlying physical properties of the system, and it may produce unphysical results for models where those assumptions fail. In that case, other more comprehensive models are better suited, such as hard-sphere Brownian dynamics (BD). Although the RDME is a model in its own right, and not inferred from any specific microscale model, it proves useful to attempt to approximate a microscale model by a specific choice of mesoscopic reaction rates. In this paper we derive mesoscopic scale-dependent reaction rates by matching certain statistics of the RDME solution to statistics of the solution of a widely used microscopic BD model: the Smoluchowski model with a Robin boundary condition at the reaction radius of two molecules. We also establish fundamental limits on the range of mesh resolutions for which this approach yields accurate results and show both theoretically and in numerical examples that as we approach the lower fundamental limit, the mesoscopic dynamics approach the microscopic dynamics. We show that for mesh sizes below the fundamental lower limit, results are less accurate. Thus, the lower limit determines the mesh size for which we obtain the most accurate results.
Reaction-diffusion controlled growth of complex structures
NASA Astrophysics Data System (ADS)
Noorduin, Willem; Mahadevan, L.; Aizenberg, Joanna
2013-03-01
Understanding how the emergence of complex forms and shapes in biominerals came about is both of fundamental and practical interest. Although biomineralization processes and organization strategies to give higher order architectures have been studied extensively, synthetic approaches to mimic these self-assembled structures are highly complex and have been difficult to emulate, let alone replicate. The emergence of solution patterns has been found in reaction-diffusion systems such as Turing patterns and the BZ reaction. Intrigued by this spontaneous formation of complexity we explored if similar processes can lead to patterns in the solid state. We here identify a reaction-diffusion system in which the shape of the solidified products is a direct readout of the environmental conditions. Based on insights in the underlying mechanism, we developed a toolbox of engineering strategies to deterministically sculpt patterns and shapes, and combine different morphologies to create a landscape of hierarchical multi scale-complex tectonic architectures with unprecedented levels of complexity. These findings may hold profound implications for understanding, mimicking and ultimately expanding upon nature's morphogenesis strategies, allowing the synthesis of advanced highly complex microscale materials and devices. WLN acknowledges the Netherlands Organization for Scientific Research for financial support
Reaction-diffusion processes and metapopulation models in heterogeneous networks
NASA Astrophysics Data System (ADS)
Colizza, Vittoria; Pastor-Satorras, Romualdo; Vespignani, Alessandro
2007-04-01
Dynamical reaction-diffusion processes and metapopulation models are standard modelling approaches for a wide array of phenomena in which local quantities-such as density, potentials and particles-diffuse and interact according to the physical laws. Here, we study the behaviour of the basic reaction-diffusion process (given by the reaction steps B-->A and B+A-->2B) defined on networks with heterogeneous topology and no limit on the nodes' occupation number. We investigate the effect of network topology on the basic properties of the system's phase diagram and find that the network heterogeneity sustains the reaction activity even in the limit of a vanishing density of particles, eventually suppressing the critical point in density-driven phase transitions, whereas phase transition and critical points independent of the particle density are not altered by topological fluctuations. This work lays out a theoretical and computational microscopic framework for the study of a wide range of realistic metapopulation and agent-based models that include the complex features of real-world networks.
Instabilities and patterns in coupled reaction-diffusion layers
NASA Astrophysics Data System (ADS)
Catllá, Anne J.; McNamara, Amelia; Topaz, Chad M.
2012-02-01
We study instabilities and pattern formation in reaction-diffusion layers that are diffusively coupled. For two-layer systems of identical two-component reactions, we analyze the stability of homogeneous steady states by exploiting the block symmetric structure of the linear problem. There are eight possible primary bifurcation scenarios, including a Turing-Turing bifurcation that involves two disparate length scales whose ratio may be tuned via the interlayer coupling. For systems of n-component layers and nonidentical layers, the linear problem's block form allows approximate decomposition into lower-dimensional linear problems if the coupling is sufficiently weak. As an example, we apply these results to a two-layer Brusselator system. The competing length scales engineered within the linear problem are readily apparent in numerical simulations of the full system. Selecting a 2:1 length-scale ratio produces an unusual steady square pattern.
Instabilities and patterns in coupled reaction-diffusion layers.
Catllá, Anne J; McNamara, Amelia; Topaz, Chad M
2012-02-01
We study instabilities and pattern formation in reaction-diffusion layers that are diffusively coupled. For two-layer systems of identical two-component reactions, we analyze the stability of homogeneous steady states by exploiting the block symmetric structure of the linear problem. There are eight possible primary bifurcation scenarios, including a Turing-Turing bifurcation that involves two disparate length scales whose ratio may be tuned via the interlayer coupling. For systems of n-component layers and nonidentical layers, the linear problem's block form allows approximate decomposition into lower-dimensional linear problems if the coupling is sufficiently weak. As an example, we apply these results to a two-layer Brusselator system. The competing length scales engineered within the linear problem are readily apparent in numerical simulations of the full system. Selecting a sqrt[2]:1 length-scale ratio produces an unusual steady square pattern. PMID:22463307
Instabilities and patterns in coupled reaction-diffusion layers.
Catllá, Anne J; McNamara, Amelia; Topaz, Chad M
2012-02-01
We study instabilities and pattern formation in reaction-diffusion layers that are diffusively coupled. For two-layer systems of identical two-component reactions, we analyze the stability of homogeneous steady states by exploiting the block symmetric structure of the linear problem. There are eight possible primary bifurcation scenarios, including a Turing-Turing bifurcation that involves two disparate length scales whose ratio may be tuned via the interlayer coupling. For systems of n-component layers and nonidentical layers, the linear problem's block form allows approximate decomposition into lower-dimensional linear problems if the coupling is sufficiently weak. As an example, we apply these results to a two-layer Brusselator system. The competing length scales engineered within the linear problem are readily apparent in numerical simulations of the full system. Selecting a sqrt[2]:1 length-scale ratio produces an unusual steady square pattern.
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.
Cox process representation and inference for stochastic reaction-diffusion processes
NASA Astrophysics Data System (ADS)
Schnoerr, David; Grima, Ramon; Sanguinetti, Guido
2016-05-01
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to the social sciences, yet they are notoriously difficult to simulate and calibrate to observational data. Here we use ideas from statistical physics and machine learning to provide a solution to the inverse problem of learning a stochastic reaction-diffusion process from data. Our solution relies on a non-trivial connection between stochastic reaction-diffusion processes and spatio-temporal Cox processes, a well-studied class of models from computational statistics. This connection leads to an efficient and flexible algorithm for parameter inference and model selection. Our approach shows excellent accuracy on numeric and real data examples from systems biology and epidemiology. Our work provides both insights into spatio-temporal stochastic systems, and a practical solution to a long-standing problem in computational modelling.
Guiding brine shrimp through mazes by solving reaction diffusion equations
NASA Astrophysics Data System (ADS)
Singal, Krishma; Fenton, Flavio
Excitable systems driven by reaction diffusion equations have been shown to not only find solutions to mazes but to also to find the shortest path between the beginning and the end of the maze. In this talk we describe how we can use the Fitzhugh-Nagumo model, a generic model for excitable media, to solve a maze by varying the basin of attraction of its two fixed points. We demonstrate how two dimensional mazes are solved numerically using a Java Applet and then accelerated to run in real time by using graphic processors (GPUs). An application of this work is shown by guiding phototactic brine shrimp through a maze solved by the algorithm. Once the path is obtained, an Arduino directs the shrimp through the maze using lights from LEDs placed at the floor of the Maze. This method running in real time could be eventually used for guiding robots and cars through traffic.
Reaction-diffusion patterns in plant tip morphogenesis: bifurcations on spherical caps.
Nagata, Wayne; Zangeneh, Hamid R Z; Holloway, David M
2013-12-01
We study a chemical reaction-diffusion model (the Brusselator) for pattern formation on developing plant tips. A family of spherical cap domains is used to represent tip flattening during development. Applied to conifer embryos, we model the chemical prepatterning underlying cotyledon ("seed leaf") formation, and demonstrate the dependence of patterns on tip flatness, radius, and precursor concentrations. Parameters for the Brusselator in spherical cap domains can be chosen to give supercritical pitchfork bifurcations of patterned solutions of the nonlinear reaction-diffusion system that correspond to the cotyledon patterns that appear on the flattening tips of conifer embryos. PMID:24072659
On the dynamics of a forced reaction-diffusion model for biological pattern formation.
Tsonis, A A; Elsner, J B; Tsonis, P A
1989-01-01
Ideas from the theory of dynamical systems are applied in biological pattern formation. By considering a simple reaction-diffusion model subjected to an external excitation, we find that the system can give rise to a great variety of periodic, quasiperiodic, and chaotic evolutions. PMID:2740333
Field theory of propagating reaction-diffusion fronts
Escudero, C.
2004-10-01
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.
Delay-induced Turing instability in reaction-diffusion equations.
Zhang, Tonghua; Zang, Hong
2014-11-01
Time delays have been commonly used in modeling biological systems and can significantly change the dynamics of these systems. Quite a few works have been focused on analyzing the effect of small delays on the pattern formation of biological systems. In this paper, we investigate the effect of any delay on the formation of Turing patterns of reaction-diffusion equations. First, for a delay system in a general form, we propose a technique calculating the critical value of the time delay, above which a Turing instability occurs. Then we apply the technique to a predator-prey model and study the pattern formation of the model due to the delay. For the model in question, we find that when the time delay is small it has a uniform steady state or irregular patterns, which are not of Turing type; however, in the presence of a large delay we find spiral patterns of Turing type. For such a model, we also find that the critical delay is a decreasing function of the ratio of carrying capacity to half saturation of the prey density. PMID:25493859
Delay-induced Turing instability in reaction-diffusion equations
NASA Astrophysics Data System (ADS)
Zhang, Tonghua; Zang, Hong
2014-11-01
Time delays have been commonly used in modeling biological systems and can significantly change the dynamics of these systems. Quite a few works have been focused on analyzing the effect of small delays on the pattern formation of biological systems. In this paper, we investigate the effect of any delay on the formation of Turing patterns of reaction-diffusion equations. First, for a delay system in a general form, we propose a technique calculating the critical value of the time delay, above which a Turing instability occurs. Then we apply the technique to a predator-prey model and study the pattern formation of the model due to the delay. For the model in question, we find that when the time delay is small it has a uniform steady state or irregular patterns, which are not of Turing type; however, in the presence of a large delay we find spiral patterns of Turing type. For such a model, we also find that the critical delay is a decreasing function of the ratio of carrying capacity to half saturation of the prey density.
Reaction diffusion Voronoi diagrams: from sensors data to computing.
Vázquez-Otero, Alejandro; Faigl, Jan; Dormido, Raquel; Duro, Natividad
2015-05-29
In this paper, a new method to solve computational problems using reaction diffusion (RD) systems is presented. The novelty relies on the use of a model configuration that tailors its spatiotemporal dynamics to develop Voronoi diagrams (VD) as a part of the system's natural evolution. The proposed framework is deployed in a solution of related robotic problems, where the generalized VD are used to identify topological places in a grid map of the environment that is created from sensor measurements. The ability of the RD-based computation to integrate external information, like a grid map representing the environment in the model computational grid, permits a direct integration of sensor data into the model dynamics. The experimental results indicate that this method exhibits significantly less sensitivity to noisy data than the standard algorithms for determining VD in a grid. In addition, previous drawbacks of the computational algorithms based on RD models, like the generation of volatile solutions by means of excitable waves, are now overcome by final stable states.
Reaction diffusion Voronoi diagrams: from sensors data to computing.
Vázquez-Otero, Alejandro; Faigl, Jan; Dormido, Raquel; Duro, Natividad
2015-01-01
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. PMID:26035349
Reaction-diffusion processes in scale-free networks
NASA Astrophysics Data System (ADS)
Gallos, Lazaros K.; Argyrakis, Panos
2003-05-01
In this work we investigate the dynamics of reaction-diffusion processes on scale-free networks. Particles of two types, A and B, are randomly distributed on such a network and diffuse using random walk models by hopping to nearest neighbor nodes only. Here we treat the case where one species is immobile and the other is mobile. The immobile species acts as a trap, i.e. when particles of the other species encounter a trap node they are immediately annihilated. We numerically compute Φ(n,c), the survival probability of mobile species at time n, as a function of the concentration of trap nodes, c. We compare our results to the mean-field result (Rosenstock approximation), and the exact result for lattices of Donsker-Varadhan. We find that for high connectivity networks and high trap concentrations the mean-field result of a simple exponential decay is also valid here. But for low connectivity networks and low c the behavior is much more complicated. We explain these trends in terms of the number of sites visited, S(n), the system size, and the concentration of traps.
Adaptive mesh refinement for stochastic reaction-diffusion processes
Bayati, Basil; Chatelain, Philippe; Koumoutsakos, Petros
2011-01-01
We present an algorithm for adaptive mesh refinement applied to mesoscopic stochastic simulations of spatially evolving reaction-diffusion processes. The transition rates for the diffusion process are derived on adaptive, locally refined structured meshes. Convergence of the diffusion process is presented and the fluctuations of the stochastic process are verified. Furthermore, a refinement criterion is proposed for the evolution of the adaptive mesh. The method is validated in simulations of reaction-diffusion processes as described by the Fisher-Kolmogorov and Gray-Scott equations.
Stable Squares and Other Oscillatory Turing Patterns in a Reaction-Diffusion Model
NASA Astrophysics Data System (ADS)
Yang, Lingfa; Zhabotinsky, Anatol M.; Epstein, Irving R.
2004-05-01
We study the Brusselator reaction-diffusion model under conditions where the Hopf mode is supercritical and the Turing band is subcritical. Oscillating Turing patterns arise in the system when bulk oscillations lose their stability to spatial perturbations. Spatially uniform external periodic forcing can generate oscillating Turing patterns when both the Turing and Hopf modes are subcritical in the autonomous system. Most of the symmetric patterns show period doubling in both space and time. Patterns observed include squares, rhombi, stripes, and hexagons.
Analysis of some identification problems for the reaction-diffusion-convection equation
NASA Astrophysics Data System (ADS)
Alekseev, G. V.; Mashkov, D. V.; Yashenko, E. N.
2016-04-01
Identification problems for a linear stationary reaction-diffusion-convection model, considered in the bounded domain under Dirichlet boundary condition, are studied. Using an optimization method these problems are reduced to respective control problems. The reaction coefficient and the volume density of substance source play the role of controls in this control problem. The solvability of the direct and control problems is proved, the optimality system, which describes the necessary optimality conditions, is derived and the numerical algorithm is developed.
Alonso, Sergio; John, Karin; Bär, Markus
2011-03-01
An effective medium theory is employed to derive a simple qualitative model of a pattern forming chemical reaction in a microemulsion. This spatially heterogeneous system is composed of water nanodroplets randomly distributed in oil. While some steps of the reaction are performed only inside the droplets, the transport through the extended medium occurs by diffusion of intermediate chemical reactants as well as by collisions of the droplets. We start to model the system with heterogeneous reaction-diffusion equations and then derive an equivalent effective spatially homogeneous reaction-diffusion model by using earlier results on homogenization in heterogeneous reaction-diffusion systems [S.Alonso, M.Bär, and R.Kapral, J. Chem. Phys. 134, 214102 (2009)]. We study the linear stability of the spatially homogeneous state in the resulting effective model and obtain a phase diagram of pattern formation, that is qualitatively similar to earlier experimental results for the Belousov-Zhabotinsky reaction in an aerosol OT (AOT)-water-in-oil microemulsion [V.K.Vanag and I.R.Epstein, Phys. Rev. Lett. 87, 228301 (2001)]. Moreover, we reproduce many patterns that have been observed in experiments with the Belousov-Zhabotinsky reaction in an AOT oil-in-water microemulsion by direct numerical simulations.
Reaction-diffusion master equation in the microscopic limit
NASA Astrophysics Data System (ADS)
Hellander, Stefan; Hellander, Andreas; Petzold, Linda
2012-04-01
Stochastic modeling of reaction-diffusion kinetics has emerged as a powerful theoretical tool in the study of biochemical reaction networks. Two frequently employed models are the particle-tracking Smoluchowski framework and the on-lattice reaction-diffusion master equation (RDME) framework. As the mesh size goes from coarse to fine, the RDME initially becomes more accurate. However, recent developments have shown that it will become increasingly inaccurate compared to the Smoluchowski model as the lattice spacing becomes very fine. Here we give a general and simple argument for why the RDME breaks down. Our analysis reveals a hard limit on the voxel size for which no local RDME can agree with the Smoluchowski model and lets us quantify this limit in two and three dimensions. In this light we review and discuss recent work in which the RDME has been modified in different ways in order to better agree with the microscale model for very small voxel sizes.
Untangling Knots Via Reaction-Diffusion Dynamics of Vortex Strings.
Maucher, Fabian; Sutcliffe, Paul
2016-04-29
We introduce and illustrate a new approach to the unknotting problem via the dynamics of vortex strings in a nonlinear partial differential equation of reaction-diffusion type. To untangle a given knot, a Biot-Savart construction is used to initialize the knot as a vortex string in the FitzHugh-Nagumo equation. Remarkably, we find that the subsequent evolution preserves the topology of the knot and can untangle an unknot into a circle. Illustrative test case examples are presented, including the untangling of a hard unknot known as the culprit. Our approach to the unknotting problem has two novel features, in that it applies field theory rather than particle mechanics and uses reaction-diffusion dynamics in place of energy minimization. PMID:27176541
Untangling Knots Via Reaction-Diffusion Dynamics of Vortex Strings.
Maucher, Fabian; Sutcliffe, Paul
2016-04-29
We introduce and illustrate a new approach to the unknotting problem via the dynamics of vortex strings in a nonlinear partial differential equation of reaction-diffusion type. To untangle a given knot, a Biot-Savart construction is used to initialize the knot as a vortex string in the FitzHugh-Nagumo equation. Remarkably, we find that the subsequent evolution preserves the topology of the knot and can untangle an unknot into a circle. Illustrative test case examples are presented, including the untangling of a hard unknot known as the culprit. Our approach to the unknotting problem has two novel features, in that it applies field theory rather than particle mechanics and uses reaction-diffusion dynamics in place of energy minimization.
Untangling Knots Via Reaction-Diffusion Dynamics of Vortex Strings
NASA Astrophysics Data System (ADS)
Maucher, Fabian; Sutcliffe, Paul
2016-04-01
We introduce and illustrate a new approach to the unknotting problem via the dynamics of vortex strings in a nonlinear partial differential equation of reaction-diffusion type. To untangle a given knot, a Biot-Savart construction is used to initialize the knot as a vortex string in the FitzHugh-Nagumo equation. Remarkably, we find that the subsequent evolution preserves the topology of the knot and can untangle an unknot into a circle. Illustrative test case examples are presented, including the untangling of a hard unknot known as the culprit. Our approach to the unknotting problem has two novel features, in that it applies field theory rather than particle mechanics and uses reaction-diffusion dynamics in place of energy minimization.
Field theory for a reaction-diffusion model of quasispecies dynamics.
Pastor-Satorras, R; Solé, R V
2001-11-01
RNA viruses are known to replicate with extremely high mutation rates. These rates are actually close to the so-called error threshold. This threshold is in fact a critical point beyond which genetic information is lost through a second-order phase transition, which has been dubbed as the "error catastrophe." Here we explore this phenomenon using a field theory approximation to the spatially extended Swetina-Schuster quasispecies model [J. Swetina and P. Schuster, Biophys. Chem. 16, 329 (1982)], a single-sharp-peak landscape. In analogy with standard absorbing-state phase transitions, we develop a reaction-diffusion model whose discrete rules mimic the Swetina-Schuster model. The field theory representation of the reaction-diffusion system is constructed. The proposed field theory belongs to the same universality class as a conserved reaction-diffusion model previously proposed [F. van Wijland et al., Physica A 251, 179 (1998)]. From the field theory, we obtain the full set of exponents that characterize the critical behavior at the error threshold. Our results present the error catastrophe from a different point of view and suggest that spatial degrees of freedom can modify several mean-field predictions previously considered, leading to the definition of characteristic exponents that could be experimentally measurable. PMID:11735970
Reaction-diffusion modelling of bacterial colony patterns
NASA Astrophysics Data System (ADS)
Mimura, Masayasu; Sakaguchi, Hideo; Matsushita, Mitsugu
2000-07-01
It is well known from experiments that bacterial species Bacillus subtilis exhibit various colony patterns. These are essentially classified into five types in the morphological diagram, depending on the substrate softness and nutrient concentration. (A) diffusion-limited aggregation-like; (B) Eden-like; (C) concentric ring-like; (D) disk-like; and (E) dense branching morphology-like. There arises the naive question of whether the diversity of colony patterns observed in experiments is caused by different effects or governed by the same underlying principles. Our research has led us to propose reaction-diffusion models to describe the morphological diversity of colony patterns except for Eden-like ones.
Explosive instabilities of reaction-diffusion equations including pinch effects
Wilhelmsson, H. Laboratoire de Physique des Milieux Ionises, Ecole Polytechnique, F-91128 Palaiseau Laboratoire de Physique Theorique et Mathematique, Universite Paris VII, Tour centrale, 3 etage, 2 place Jussieu, Paris CEDEX 05 )
1993-01-01
Particular solutions of reaction-diffusion equations for temperature are obtained for explosively unstable situations. As a result of the interplay between inertial, diffusion, pinch, and source processes, certain bell-shaped'' distributions may grow explosively in time while preserving the shape of the spatial distribution. The effect of the pinch, which requires a density inhomogeneity, is found to diminish the effect of diffusion, or inversely to support the inertial and source processes in creating the explosion. The results may be described in terms of elliptic integrals or, more simply, by means of expansions in the spatial coordinate. An application is the temperature evolution of a burning fusion plasma.
Stable squares and other oscillatory turing patterns in a reaction-diffusion model.
Yang, Lingfa; Zhabotinsky, Anatol M; Epstein, Irving R
2004-05-14
We study the Brusselator reaction-diffusion model under conditions where the Hopf mode is supercritical and the Turing band is subcritical. Oscillating Turing patterns arise in the system when bulk oscillations lose their stability to spatial perturbations. Spatially uniform external periodic forcing can generate oscillating Turing patterns when both the Turing and Hopf modes are subcritical in the autonomous system. Most of the symmetric patterns show period doubling in both space and time. Patterns observed include squares, rhombi, stripes, and hexagons. PMID:15169455
NASA Astrophysics Data System (ADS)
Dulos, E.; Hunding, A.; Boissonade, J.; de Kepper, P.
Since the seminal paper "The chemical basis of morphogenesis" by Alan Turing, the temporal and spatial self-organization phenomena produced in chemically reacting and diffusing systems are often thought as paradigms for biological development. The basic theoretical principles on which the development of stationary concentration patterns (Turing structures) rely on are briefly presented. We review different aspects of our contribution to the experimental observation of reaction-diffusion patterns in iodine-oxychlorine systems. The experimental techniques are emphasized. Phase diagrams gathering different standing and travelling patterns are presented, analyzed and modeled. A special attention is also given to some peculiar pattern growth dynamics (spot division, finger splitting).
Reaction-diffusion models of within-feather pigmentation patterning.
Prum, Richard O; Williamson, Scott
2002-04-22
Feathers are complex, branched keratin structures that exhibit a diversity of pigmentation patterns. Feather pigments are transferred into developing feather keratinocytes from pigment cells that migrate into the tubular feather germ from the dermis. Within-feather pigment patterns are determined by differential pigmentation of keratinocytes within independent barb ridges during feather development. Little is known about the molecular mechanisms that determine which keratinocytes receive pigment. We apply reaction-diffusion models to the growth of within-feather pigment patterns based on a realistic model of feather growth. These models accurately simulate the growth of a diversity of the within-feather pigmentation patterns found in real feathers, including a central patch, a 'hollow' central patch, concentric central patches, bars, chevrons, a central circular spot, rows of paired spots, and arrays of offset dots. The models can also simulate the complex transitions between distinct pigmentation patterns among feathers observed in real avian plumages, including transitions from bars to chevrons, bars to paired dots, and bars to arrays of dots. The congruence between the developmental dynamics of the simulated and observed feather patterns indicates that the reaction-diffusion models provide a realistic and accurate description of the determination of pigment pattern within avian feather follicles. The models support the hypothesis that within-feather pigmentation patterning is determined by antagonistic interactions among molecular expression gradients within the tubular follicle and feather germ.
NASA Astrophysics Data System (ADS)
Tian, Bo; Li, Wei; Gao, Yi-Tian
The direct reduction method and computerized symbolic computation are extended to the Brusselator reaction-diffusion model, which describes a biochemical system and consists of two coupled nonlinear partial differential equations. New similarity reductions are obtained, which could be of biochemical interest. The resulting nonlinear ordinary differential equation in one dynamical variable cannot be transformed into any of the six standard forms which have solutions in terms of the Painlevé transcendents. Thus, the Brusselator model is not integrable according to the Painlevé conjecture.
Reaction-diffusion models of growing plant tips: bifurcations on hemispheres.
Nagata, Wayne; Harrison, Lionel G; Wehner, Stephan
2003-07-01
We study two chemical models for pattern formation in growing plant tips. For hemisphere radius and parameter values together optimal for spherical surface harmonic patterns of index l = 3, the Brusselator model gives an 84% probability of dichotomous branching pattern and 16% of annular pattern, while the hyperchirality model gives 88% probability of dichotomous branching and 12% of annular pattern. The models are two-morphogen reaction-diffusion systems on the surface of a hemispherical shell, with Dirichlet boundary conditions. Bifurcation analysis shows that both models give possible mechanisms for dichotomous branching of the growing tips. Symmetries of the models are used in the analysis. PMID:12875335
Small-scale properties of a stochastic cubic-autocatalytic reaction-diffusion model
NASA Astrophysics Data System (ADS)
Gagnon, Jean-Sébastien; Hochberg, David; Pérez-Mercader, Juan
2015-10-01
We investigate the small-scale properties of a stochastic cubic-autocatalytic reaction-diffusion (CARD) model using renormalization techniques. We renormalize noise-induced ultraviolet divergences and obtain β functions for the decay rate and coupling at one loop. Assuming colored (power-law) noise, our results show that the behavior of both decay rate and coupling with scale depends crucially on the noise exponent. Interpreting the CARD model as a proxy for a (very simple) living system, our results suggest that power-law correlations in environmental fluctuations can both decrease or increase the growth of structures at smaller scales.
Small-scale properties of a stochastic cubic-autocatalytic reaction-diffusion model.
Gagnon, Jean-Sébastien; Hochberg, David; Pérez-Mercader, Juan
2015-10-01
We investigate the small-scale properties of a stochastic cubic-autocatalytic reaction-diffusion (CARD) model using renormalization techniques. We renormalize noise-induced ultraviolet divergences and obtain β functions for the decay rate and coupling at one loop. Assuming colored (power-law) noise, our results show that the behavior of both decay rate and coupling with scale depends crucially on the noise exponent. Interpreting the CARD model as a proxy for a (very simple) living system, our results suggest that power-law correlations in environmental fluctuations can both decrease or increase the growth of structures at smaller scales.
Turing patterns in a reaction-diffusion model with the Degn-Harrison reaction scheme
NASA Astrophysics Data System (ADS)
Li, Shanbing; Wu, Jianhua; Dong, Yaying
2015-09-01
In this paper, we consider a reaction-diffusion model with Degn-Harrison reaction scheme. Some fundamental analytic properties of nonconstant positive solutions are first investigated. We next study the stability of constant steady-state solution to both ODE and PDE models. Our result also indicates that if either the size of the reactor or the effective diffusion rate is large enough, then the system does not admit nonconstant positive solutions. Finally, we establish the global structure of steady-state bifurcations from simple eigenvalues by bifurcation theory and the local structure of the steady-state bifurcations from double eigenvalues by the techniques of space decomposition and implicit function theorem.
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 < x < L(t), where L(t) is the domain length. The present work is an extension of our previous study, and we illustrate how to solve a system of coupled 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.
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.
Breakdown of the reaction-diffusion master equation with nonelementary rates
NASA Astrophysics Data System (ADS)
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.
Studies of the accuracy of time integration methods for reaction-diffusion equations
NASA Astrophysics Data System (ADS)
Ropp, David L.; Shadid, John N.; Ober, Curtis C.
2004-03-01
In this study we present numerical experiments of time integration methods applied to systems of reaction-diffusion equations. Our main interest is in evaluating the relative accuracy and asymptotic order of accuracy of the methods on problems which exhibit an approximate balance between the competing component time scales. Nearly balanced systems can produce a significant coupling of the physical mechanisms and introduce a slow dynamical time scale of interest. These problems provide a challenging test for this evaluation and tend to reveal subtle differences between the various methods. The methods we consider include first- and second-order semi-implicit, fully implicit, and operator-splitting techniques. The test problems include a prototype propagating nonlinear reaction-diffusion wave, a non-equilibrium radiation-diffusion system, a Brusselator chemical dynamics system and a blow-up example. In this evaluation we demonstrate a "split personality" for the operator-splitting methods that we consider. While operator-splitting methods often obtain very good accuracy, they can also manifest a serious degradation in accuracy due to stability problems.
Order and localization in reaction-diffusion pattern
NASA Astrophysics Data System (ADS)
Holloway, David M.; Harrison, Lionel G.
1995-02-01
The present work is concerned with two aspects of pattern formation: pattern localization and degree of pattern order. In reaction-diffusion models, there are three major effects. These stem from the reaction terms, the diffusion terms and the presence or absence of precursor gradients. Global analysis of reaction terms at late stages of pattern formation is at present unavailable. Therefore, we study the effect of the diffusion terms and of precursor gradients with numerical solution in two models: the Brusselator and the Gierer-Meinhardt. Differences in response to changes in the diffusion terms and the precursor gradients are related to contrasts between the nonlinear kinetics of the two models. These models both have Hill coefficient 2; effects of higher cooperativities have recently been discussed by Hunding and Engelhardt [1].
Turing instability in reaction-diffusion models on complex networks
NASA Astrophysics Data System (ADS)
Ide, Yusuke; Izuhara, Hirofumi; Machida, Takuya
2016-09-01
In this paper, the Turing instability in reaction-diffusion models defined on complex networks is studied. Here, we focus on three types of models which generate complex networks, i.e. the Erdős-Rényi, the Watts-Strogatz, and the threshold network models. From analysis of the Laplacian matrices of graphs generated by these models, we numerically reveal that stable and unstable regions of a homogeneous steady state on the parameter space of two diffusion coefficients completely differ, depending on the network architecture. In addition, we theoretically discuss the stable and unstable regions in the cases of regular enhanced ring lattices which include regular circles, and networks generated by the threshold network model when the number of vertices is large enough.
NASA Astrophysics Data System (ADS)
Ohmori, Shousuke; Yamazaki, Yoshihiro
2016-01-01
Ultradiscrete equations are derived from a set of reaction-diffusion partial differential equations, and cellular automaton rules are obtained on the basis of the ultradiscrete equations. Some rules reproduce the dynamical properties of the original reaction-diffusion equations, namely, bistability and pulse annihilation. Furthermore, other rules bring about soliton-like preservation and periodic pulse generation with a pacemaker, which are not obtained from the original reaction-diffusion equations.
A deterministic particle method for one-dimensional reaction-diffusion equations
NASA Technical Reports Server (NTRS)
Mascagni, Michael
1995-01-01
We derive a deterministic particle method for the solution of nonlinear reaction-diffusion equations in one spatial dimension. This deterministic method is an analog of a Monte Carlo method for the solution of these problems that has been previously investigated by the author. The deterministic method leads to the consideration of a system of ordinary differential equations for the positions of suitably defined particles. We then consider the time explicit and implicit methods for this system of ordinary differential equations and we study a Picard and Newton iteration for the solution of the implicit system. Next we solve numerically this system and study the discretization error both analytically and numerically. Numerical computation shows that this deterministic method is automatically adaptive to large gradients in the solution.
Reaction Diffusion Modeling of Calcium Dynamics with Realistic ER Geometry
Means, Shawn; Smith, Alexander J.; Shepherd, Jason; Shadid, John; Fowler, John; Wojcikiewicz, Richard J. H.; Mazel, Tomas; Smith, Gregory D.; Wilson, Bridget S.
2006-01-01
We describe a finite-element model of mast cell calcium dynamics that incorporates the endoplasmic reticulum's complex geometry. The model is built upon a three-dimensional reconstruction of the endoplasmic reticulum (ER) from an electron tomographic tilt series. Tetrahedral meshes provide volumetric representations of the ER lumen, ER membrane, cytoplasm, and plasma membrane. The reaction-diffusion model simultaneously tracks changes in cytoplasmic and ER intraluminal calcium concentrations and includes luminal and cytoplasmic protein buffers. Transport fluxes via PMCA, SERCA, ER leakage, and Type II IP3 receptors are also represented. Unique features of the model include stochastic behavior of IP3 receptor calcium channels and comparisons of channel open times when diffusely distributed or aggregated in clusters on the ER surface. Simulations show that IP3R channels in close proximity modulate activity of their neighbors through local Ca2+ feedback effects. Cytoplasmic calcium levels rise higher, and ER luminal calcium concentrations drop lower, after IP3-mediated release from receptors in the diffuse configuration. Simulation results also suggest that the buffering capacity of the ER, and not restricted diffusion, is the predominant factor influencing average luminal calcium concentrations. PMID:16617072
Characterization of Cocycle Attractors for Nonautonomous Reaction-Diffusion Equations
NASA Astrophysics Data System (ADS)
Cardoso, C. A.; Langa, J. A.; Obaya, R.
In this paper, we describe in detail the global and cocycle attractors related to nonautonomous scalar differential equations with diffusion. In particular, we investigate reaction-diffusion equations with almost-periodic coefficients. The associated semiflows are strongly monotone which allow us to give a full characterization of the cocycle attractor. We prove that, when the upper Lyapunov exponent associated to the linear part of the equations is positive, the flow is persistent in the positive cone, and we study the stability and the set of continuity points of the section of each minimal set in the global attractor for the skew product semiflow. We illustrate our result with some nontrivial examples showing the richness of the dynamics on this attractor, which in some situations shows internal chaotic dynamics in the Li-Yorke sense. We also include the sublinear and concave cases in order to go further in the characterization of the attractors, including, for instance, a nonautonomous version of the Chafee-Infante equation. In this last case we can show exponentially forward attraction to the cocycle (pullback) attractors in the positive cone of solutions.
A Reaction-Diffusion Model of Cholinergic Retinal Waves
Lansdell, Benjamin; Ford, Kevin; Kutz, J. Nathan
2014-01-01
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. PMID:25474327
Turing instabilities in reaction-diffusion systems with cross diffusion
NASA Astrophysics Data System (ADS)
Fanelli, Duccio; Cianci, Claudia; Di Patti, Francesca
2013-04-01
The Turing instability paradigm is revisited in the context of a multispecies diffusion scheme derived from a self-consistent microscopic formulation. The analysis is developed with reference to the case of two species. These latter share the same spatial reservoir and experience a degree of mutual interference due to the competition for the available resources. Turing instability can set in for all ratios of the main diffusivities, also when the (isolated) activator diffuses faster then the (isolated) inhibitor. This conclusion, at odd with the conventional vision, is here exemplified for the Brusselator model and ultimately stems from having assumed a generalized model of multispecies diffusion, fully anchored to first principles, which also holds under crowded conditions.
Spatiotemporal patterns in a reaction-diffusion model with the Degn-Harrison reaction scheme
NASA Astrophysics Data System (ADS)
Peng, Rui; Yi, Feng-qi; Zhao, Xiao-qiang
Spatial and temporal patterns generated in ecological and chemical systems have become a central object of research in recent decades. In this work, we are concerned with a reaction-diffusion model with the Degn-Harrison reaction scheme, which accounts for the qualitative feature of the respiratory process in a Klebsiella aerogenes bacterial culture. We study the global stability of the constant steady state, existence and nonexistence of nonconstant steady states as well as the Hopf and steady state bifurcations. In particular, our results show the existence of Turing patterns and inhomogeneous periodic oscillatory patterns while the system parameters are all spatially homogeneous. These results also exhibit the critical role of the system parameters in leading to the formation of spatiotemporal patterns.
Taylor-Couette Flow with Hourglass Geometry of Varying Lengths Simulated by Reaction-Diffusion
NASA Astrophysics Data System (ADS)
Zhao, Yunjie; Halmstad, Andrew; Olsen, Thomas; Wiener, Richard
2008-11-01
Previously, we have observed chaotic formation of Taylor-Vortex pairs in Modified Taylor- Couette Flow with Hourglass Geometry. In the experiment, the chaotic formation in a shorter system has been restricted to a narrow band about the waist of the hourglass. Such behavior has been modeled by The Reaction-Diffusion equation, which has been previously studied, by Riecke and Paap. Their calculation suggested that quadrupling length of the system would lead to spatial chaos in the vortex formation. We present a careful recreation of this result and consider an intermediate length. We demonstrate that doubling the length should be sufficient to observe spatially chaotic behavior. Richard J. Wiener et al, Phys. Rev. E 55, 5489 (1997). H. Riecke and H.-G. Paap, Europhys. Lett. 14, 1235 (1991).
A reaction-diffusion model of human brain development.
Lefèvre, Julien; Mangin, Jean-François
2010-04-01
Cortical folding exhibits both reproducibility and variability in the geometry and topology of its patterns. These two properties are obviously the result of the brain development that goes through local cellular and molecular interactions which have important consequences on the global shape of the cortex. Hypotheses to explain the convoluted aspect of the brain are still intensively debated and do not focus necessarily on the variability of folds. Here we propose a phenomenological model based on reaction-diffusion mechanisms involving Turing morphogens that are responsible for the differential growth of two types of areas, sulci (bottom of folds) and gyri (top of folds). We use a finite element approach of our model that is able to compute the evolution of morphogens on any kind of surface and to deform it through an iterative process. Our model mimics the progressive folding of the cortical surface along foetal development. Moreover it reveals patterns of reproducibility when we look at several realizations of the model from a noisy initial condition. However this reproducibility must be tempered by the fact that a same fold engendered by the model can have different topological properties, in one or several parts. These two results on the reproducibility and variability of the model echo the sulcal roots theory that postulates the existence of anatomical entities around which the folding organizes itself. These sulcal roots would correspond to initial conditions in our model. Last but not least, the parameters of our model are able to produce different kinds of patterns that can be linked to developmental pathologies such as polymicrogyria and lissencephaly. The main significance of our model is that it proposes a first approach to the issue of reproducibility and variability of the cortical folding. PMID:20421989
Hybrid approaches for multiple-species stochastic reaction-diffusion models
NASA Astrophysics Data System (ADS)
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.
An FTLE analysis for reaction-diffusion fronts in fluid flows
NASA Astrophysics Data System (ADS)
Mahoney, John; Mitchell, Kevin
2012-11-01
The theory of advective transport depends heavily on the elucidation of organizing structures within the fluid. In a time-independent or time-periodic flow, one can define invariant manifolds. In a time-aperiodic flow, one often employs the finite-time-lyapunov-exponent (FTLE) and Lagrangian coherent structures. It has been recently demonstrated that fronts, e.g. reaction-diffusion fronts, propagating in time-periodic flows can also depend on such organizing invariant manifolds. In this talk, we describe an FTLE analysis for propagating fronts in two-dimensional fluid flows. In particular, we employ a dimension reduction technique to the front system so that a two-dimensional FTLE approach is feasible. NSF PHY-0748828.
Symmetry breaking in a bulk-surface reaction-diffusion model for signalling networks
NASA Astrophysics Data System (ADS)
Rätz, Andreas; Röger, Matthias
2014-08-01
Signalling molecules play an important role for many cellular functions. We investigate here a general system of two membrane reaction-diffusion equations coupled to a diffusion equation inside the cell by a Robin-type boundary condition and a flux term in the membrane equations. A specific model of this form was recently proposed by the authors for the GTPase cycle in cells. We investigate here a putative role of diffusive instabilities in cell polarization. By a linearized stability analysis, we identify two different mechanisms. The first resembles a classical Turing instability for the membrane subsystem and requires (unrealistically) large differences in the lateral diffusion of activator and substrate. On the other hand, the second possibility is induced by the difference in cytosolic and lateral diffusion and appears much more realistic. We complement our theoretical analysis by numerical simulations that confirm the new stability mechanism and allow us to investigate the evolution beyond the regime where the linearization applies.
Liang, Xiao; Wang, Linshan; Wang, Yangfan; Wang, Ruili
2016-09-01
In this paper, we focus on the long time behavior of the mild solution to delayed reaction-diffusion Hopfield neural networks (DRDHNNs) driven by infinite dimensional Wiener processes. We analyze the existence, uniqueness, and stability of this system under the local Lipschitz function by constructing an appropriate Lyapunov-Krasovskii function and utilizing the semigroup theory. Some easy-to-test criteria affecting the well-posedness and stability of the networks, such as infinite dimensional noise and diffusion effect, are obtained. The criteria can be used as theoretic guidance to stabilize DRDHNNs in practical applications when infinite dimensional noise is taken into consideration. Meanwhile, considering the fact that the standard Brownian motion is a special case of infinite dimensional Wiener process, we undertake an analysis of the local Lipschitz condition, which has a wider range than the global Lipschitz condition. Two samples are given to examine the availability of the results in this paper. Simulations are also given using the MATLAB.
A reaction-diffusion-advection model of harmful algae growth with toxin degradation
NASA Astrophysics Data System (ADS)
Wang, Feng-Bin; Hsu, Sze-Bi; Zhao, Xiao-Qiang
2015-10-01
This paper is devoted to the study of a reaction-diffusion-advection system modeling the dynamics of a single nutrient, harmful algae and algal toxin in a flowing water habitat with a hydraulic storage zone. We introduce the basic reproduction ratio R0 for algae and show that R0 serves as a threshold value for persistence and extinction of the algae. More precisely, we prove that the washout steady state is globally attractive if R0 < 1, while there exists a positive steady state and the algae is uniformly persistent if R0 > 1. With an additional assumption, we obtain the uniqueness and global attractivity of the positive steady state in the case where R0 > 1.
Scalable implicit methods for reaction-diffusion equations in two and three space dimensions
Veronese, S.V.; Othmer, H.G.
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.
Spread of infectious diseases in a hyperbolic reaction-diffusion susceptible-infected-removed model
NASA Astrophysics Data System (ADS)
Barbera, Elvira; Consolo, Giancarlo; Valenti, Giovanna
2013-11-01
A one-dimensional hyperbolic reaction-diffusion model of epidemics is developed to describe the dynamics of diseases spread occurring in an environment where three kinds of individuals mutually interact: the susceptibles, the infectives, and the removed. It is assumed that the disease is transmitted from the infected population to the susceptible one according to a nonlinear convex incidence rate. The model, based upon the framework of extended thermodynamics, removes the unphysical feature of instantaneous diffusive effects, which is typical of parabolic models. Linear stability analyses are performed to study the nature of the equilibrium states against uniform and nonuniform perturbations. Emphasis is given to the occurrence of Hopf and Turing bifurcations, which break the temporal and the spatial symmetry of the system, respectively. The existence of traveling wave solutions connecting two steady states is also discussed. The governing equations are also integrated numerically to validate the analytical results and to characterize the spatiotemporal evolution of diseases.
Reaction-diffusion processes and epidemic metapopulation models in complex networks
NASA Astrophysics Data System (ADS)
Vespignani, A.
2008-08-01
The correct description of reaction-diffusion phenomena requires a detailed knowledge of the contact networks defining the interactions between individuals and groups of individuals. For this reason, the study of reaction-diffusion processes has been recently widened with opportune models and methods dealing with the heterogeneity and large scale fluctuations observed in many real world networks. Here we present a brief overview of some recent results on reaction-diffusion processes in complex networks which provide useful insights into the dynamic behavior of epidemic metapopulation models.
Modeling of Turing Structures in the Chlorite-Iodide-Malonic Acid-Starch Reaction System
NASA Astrophysics Data System (ADS)
Lengyel, Istivan; Epstein, Irving R.
1991-02-01
Recent experiments on the chlorite-iodide-malonic acid-starch reaction in a gel reactor give the first evidence of the existence of the symmetry breaking, reaction-diffusion structures predicted by Turing in 1952. A five-variable model that describes the temporal behavior of the system is reduced to a two-variable model, and its spatial behavior is analyzed. Structures have been found with wavelengths that are in good agreement with those observed experimentally. The gel plays a key role by binding key iodine species, thereby creating the necessary difference in the effective diffusion coefficients of the activator and inhibitor species, iodide and chlorite ions, respectively.
NASA Astrophysics Data System (ADS)
Ghosh, Atiyo; Leier, Andre; Marquez-Lago, Tatiana
2014-03-01
Spatial stochastic effects are prevalent in many biological systems spanning a variety of scales, from intracellular (e.g. gene expression) to ecological (plankton aggregation). The most common ways of simulating such systems involve drawing sample paths from either the Reaction Diffusion Master Equation (RDME) or the Smoluchowski Equation, using methods such as Gillespie's Simulation Algorithm, Green's Function Reaction Dynamics and Single Particle Tracking. The simulation times of such techniques scale with the number of simulated particles, leading to much computational expense when considering large systems. The Spatial Chemical Langevin Equation (SCLE) can be simulated with fixed time intervals, independent of the number of particles, and can thus provide significant computational savings. However, very little work has been done to investigate the behavior of the SCLE. In this talk we summarize our findings on comparing the SCLE to the well-studied RDME. We use both analytical and numerical procedures to show when one should expect the moments of the SCLE to be close to the RDME, and also when they should differ.
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.
Modeling reaction--diffusion pattern formation in the Couette flow reactor
Elezgaray, J. ); Arneodo, A. )
1991-07-01
We report on a numerical and theoretical study of spatio--temporal pattern forming phenomena in a one-dimensional reaction--diffusion system with equal diffusion coefficients. When imposing a concentration gradient through the system, this model mimics the sustained stationary and periodically oscillating front structures'' observed in a recent experiment conducted in the Couette flow reactor. Conditions are also found under which oscillations of the nontrivial spatial patterns become chaotic. Singular perturbation techniques are used to study the existence and the linear stability of single-front and multi-front patterns. A nonlinear analysis of bifurcating patterns is carried out using a center manifold/normal form approach. The theoretical predictions of the normal form calculations are found in quantitative agreement with direct simulations of the Hopf bifurcation from steady to oscillating front patterns. The remarkable feature of these sustained spatio--temporal phenomena is the fact that they organize due to the interaction of the diffusion process with a chemical reaction which itself would proceed in a stationary manner if diffusion was negligible. This study clearly demonstrates that complex spatio--temporal patterns do not necessarily result from the coupling of oscillators or nonlinear transport.
tiReaction Diffusion Voronoi Diagrams: From Sensors Data to Computing
Vázquez-Otero, Alejandro; Faigl, Jan; Dormido, Raquel; Duro, Natividad
2015-01-01
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. PMID:26035349
Local Perturbation Analysis: A Computational Tool for Biophysical Reaction-Diffusion Models
Holmes, William R.; Mata, May Anne; Edelstein-Keshet, Leah
2015-01-01
Diffusion and interaction of molecular regulators in cells is often modeled using reaction-diffusion partial differential equations. Analysis of such models and exploration of their parameter space is challenging, particularly for systems of high dimensionality. Here, we present a relatively simple and straightforward analysis, the local perturbation analysis, that reveals how parameter variations affect model behavior. This computational tool, which greatly aids exploration of the behavior of a model, exploits a structural feature common to many cellular regulatory systems: regulators are typically either bound to a membrane or freely diffusing in the interior of the cell. Using well-documented, readily available bifurcation software, the local perturbation analysis tracks the approximate early evolution of an arbitrarily large perturbation of a homogeneous steady state. In doing so, it provides a bifurcation diagram that concisely describes various regimes of the model’s behavior, reducing the need for exhaustive simulations to explore parameter space. We explain the method and provide detailed step-by-step guides to its use and application. PMID:25606671
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. PMID:26986201
NASA Astrophysics Data System (ADS)
Hellander, Andreas; Lawson, Michael J.; Drawert, Brian; Petzold, Linda
2014-06-01
The efficiency of exact simulation methods for the reaction-diffusion master equation (RDME) is severely limited by the large number of diffusion events if the mesh is fine or if diffusion constants are large. Furthermore, inherent properties of exact kinetic-Monte Carlo simulation methods limit the efficiency of parallel implementations. Several approximate and hybrid methods have appeared that enable more efficient simulation of the RDME. A common feature to most of them is that they rely on splitting the system into its reaction and diffusion parts and updating them sequentially over a discrete timestep. This use of operator splitting enables more efficient simulation but it comes at the price of a temporal discretization error that depends on the size of the timestep. So far, existing methods have not attempted to estimate or control this error in a systematic manner. This makes the solvers hard to use for practitioners since they must guess an appropriate timestep. It also makes the solvers potentially less efficient than if the timesteps were adapted to control the error. Here, we derive estimates of the local error and propose a strategy to adaptively select the timestep when the RDME is simulated via a first order operator splitting. While the strategy is general and applicable to a wide range of approximate and hybrid methods, we exemplify it here by extending a previously published approximate method, the diffusive finite-state projection (DFSP) method, to incorporate temporal adaptivity.
NASA Astrophysics Data System (ADS)
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.
Bifurcation analysis of brown tide by reaction-diffusion equation using finite element method
Kawahara, Mutsuto; Ding, Yan
1997-03-01
In this paper, we analyze the bifurcation of a biodynamics system in a two-dimensional domain by virtue of reaction-diffusion equations. The discretization method in space is the finite element method. The computational algorithm for an eigenspectrum is described in detail. On the basis of an analysis of eigenspectra according to Helmholtz`s equation, the discrete spectra in regards to the physical variables are numerically obtained in two-dimensional space. In order to investigate this mathematical model in regards to its practical use, we analyzed the stability of two cases, i.e., hydranth regeneration in the marine hydroid Tubularia and a brown tide in a harbor in Japan. By evaluating the stability according to the linearized stability definition, the critical parameters for outbreaks of brown tide can be theoretically determined. In addition, results for the linear combination of eigenspectrum coincide with the distribution of the observed brown tide. Its periodic characteristic was also verified. 10 refs., 8 figs., 5 tabs.
Reaction-diffusion waves in neuronal tissue and the window of cortical excitability
NASA Astrophysics Data System (ADS)
Dahlem, M. A.; Müller, S. C.
2004-07-01
Spreading depression (SD) is a dynamic wave phenomenon occurring in all gray matter regions of the central nervous systems (CNS). It is characterized by a sudden breakdown of neuronal activity and accompanied by a massive influx and efflux of ions across the membrane of neurons. The retina is a constituent of the CNS in which one can easily observe the dynamic behavior of the SD wave fronts, because SD changes the optical properties of the tissue. There is ample evidence that SD belongs to the self-organization processes due to the coupling of reaction with diffusion in excitable medium. It is assumed that the occurrence of SD is associated with some neurological symptoms of migraine with aura. A frequently reported aura symptom is a traveling visual blind region (scotoma) with a preceding figure of scintillating line segments. The characteristic form and development of the scotoma suggests that the underlying phenomenon is a wave propagating through the primary visual cortex, most likely the cortical spreading depression. In this article we discuss similarities between SD waves and the migraine aura on the basis of properties of reaction-diffusion waves known from other excitable media. In particular, the propagation velocities, the shape and the dynamics of the waves are compared with each other. We find that the assumption of the neuronal tissue to be in a state of only weak excitability explains some properties of the migraine aura, such as the confined appearance and its propagation with a stable velocity.
Gan, Qintao; Lv, Tianshi; Fu, Zhenhua
2016-04-01
In this paper, the synchronization problem for a class of generalized neural networks with time-varying delays and reaction-diffusion terms is investigated concerning Neumann boundary conditions in terms of p-norm. The proposed generalized neural networks model includes reaction-diffusion local field neural networks and reaction-diffusion static neural networks as its special cases. By establishing a new inequality, some simple and useful conditions are obtained analytically to guarantee the global exponential synchronization of the addressed neural networks under the periodically intermittent control. According to the theoretical results, the influences of diffusion coefficients, diffusion space, and control rate on synchronization are analyzed. Finally, the feasibility and effectiveness of the proposed methods are shown by simulation examples, and by choosing different diffusion coefficients, diffusion spaces, and control rates, different controlled synchronization states can be obtained.
Reaction-diffusion processes on interconnected scale-free networks
NASA Astrophysics Data System (ADS)
Garas, Antonios
2015-08-01
We study the two-particle annihilation reaction A +B →∅ on interconnected scale-free networks, using different interconnecting strategies. We explore how the mixing of particles and the process evolution are influenced by the number of interconnecting links, by their functional properties, and by the interconnectivity strategies in use. We show that the reaction rates on this system are faster than what was observed in other topologies, due to the better particle mixing that suppresses the segregation effect, in line with previous studies performed on single scale-free networks.
A new Sumudu transform iterative method for time-fractional Cauchy reaction-diffusion equation.
Wang, Kangle; Liu, Sanyang
2016-01-01
In this paper, a new Sumudu transform iterative method is established and successfully applied to find the approximate analytical solutions for time-fractional Cauchy reaction-diffusion equations. The approach is easy to implement and understand. The numerical results show that the proposed method is very simple and efficient. PMID:27386314
Stability and bifurcations in a nonlocal delayed reaction-diffusion population model
NASA Astrophysics Data System (ADS)
Chen, Shanshan; Yu, Jianshe
2016-01-01
A nonlocal delayed reaction-diffusion equation with Dirichlet boundary condition is considered in this paper. It is shown that a positive spatially nonhomogeneous equilibrium bifurcates from the trivial equilibrium. The stability/instability of the bifurcated positive equilibrium and associated Hopf bifurcation are investigated, providing us with a complete picture of the dynamics.
Stability and bifurcation in a reaction-diffusion model with nonlocal delay effect
NASA Astrophysics Data System (ADS)
Guo, Shangjiang
2015-08-01
In this paper, the existence, stability, and multiplicity of spatially nonhomogeneous steady-state solution and periodic solutions for a reaction-diffusion model with nonlocal delay effect and Dirichlet boundary condition are investigated by using Lyapunov-Schmidt reduction. Moreover, we illustrate our general results by applications to models with a single delay and one-dimensional spatial domain.
Pointwise nonlinear stability of nonlocalized modulated periodic reaction-diffusion waves
NASA Astrophysics Data System (ADS)
Jung, Soyeun; Zumbrun, Kevin
2016-10-01
In this paper, extending previous results of [2], we obtain pointwise nonlinear stability of periodic traveling reaction-diffusion waves, assuming spectral linearized stability, under nonlocalized perturbations. More precisely, we establish pointwise estimate of nonlocalized modulational perturbation under a small initial perturbation consisting of a nonlocalized modulation plus a localized perturbation decaying algebraically.
Reaction-diffusion constraints in living tissue: effectiveness factors in skeletal muscle design.
Dasika, S K; Kinsey, S T; Locke, B R
2011-01-01
A mathematical model was developed to analyze the effects of intracellular diffusion of O(2) and high-energy phosphate metabolites on aerobic energy metabolism in skeletal muscle. We tested the hypotheses that in a range of muscle fibers from different species (1) aerobic metabolism was not diffusion limited and (2) that fibers had a combination of rate and fiber size that placed them at the brink of substantial diffusion limitation. A simplified chemical reaction rate law for mitochondrial oxidative phosphorylation was developed utilizing a published detailed model of isolated mitochondrial function. This rate law was then used as a boundary condition in a reaction-diffusion model that was further simplified using the volume averaging method and solved to determine the rates of oxidative phosphorylation as functions of the volume fraction of mitochondria, the size of the muscle cell, and the amount of oxygen delivered by the capillaries. The effectiveness factor, which is the ratio of reaction rate in the system with finite rates of diffusion to those in the absence of any diffusion limitations, defined the regions where intracellular diffusion of metabolites and O(2) may limit aerobic metabolism in both very small, highly oxidative fibers as well as in larger fibers with lower aerobic capacity. Comparison of model analysis with experimental data revealed that none of the fibers was strongly limited by diffusion, as expected. However, while some fibers were near substantial diffusion limitation, most were well within the domain of reaction control of aerobic metabolic rate. This may constitute a safety factor in muscle that provides a level of protection from diffusion constraints under conditions such as hypoxia.
Periodic travelling waves in cyclic populations: field studies and reaction-diffusion models.
Sherratt, Jonathan A; Smith, Matthew J
2008-05-01
Periodic travelling waves have been reported in a number of recent spatio-temporal field studies of populations undergoing multi-year cycles. Mathematical modelling has a major role to play in understanding these results and informing future empirical studies. We review the relevant field data and summarize the statistical methods used to detect periodic waves. We then discuss the mathematical theory of periodic travelling waves in oscillatory reaction-diffusion equations. We describe the notion of a wave family, and various ecologically relevant scenarios in which periodic travelling waves occur. We also discuss wave stability, including recent computational developments. Although we focus on oscillatory reaction-diffusion equations, a brief discussion of other types of model in which periodic travelling waves have been demonstrated is also included. We end by proposing 10 research challenges in this area, five mathematical and five empirical.
NASA Astrophysics Data System (ADS)
Gal, Ciprian G.; Warma, Mahamadi
2016-08-01
We investigate the long term behavior in terms of finite dimensional global and exponential attractors, as time goes to infinity, of solutions to a semilinear reaction-diffusion equation on non-smooth domains subject to nonlocal Robin boundary conditions, characterized by the presence of fractional diffusion on the boundary. Our results are of general character and apply to a large class of irregular domains, including domains whose boundary is Hölder continuous and domains which have fractal-like geometry. In addition to recovering most of the existing results on existence, regularity, uniqueness, stability, attractor existence, and dimension, for the well-known reaction-diffusion equation in smooth domains, the framework we develop also makes possible a number of new results for all diffusion models in other non-smooth settings.
Effect of mixing on reaction-diffusion kinetics for protein hydrogel-based microchips.
Zubtsov, D A; Ivanov, S M; Rubina, A Yu; Dementieva, E I; Chechetkin, V R; Zasedatelev, A S
2006-03-01
Protein hydrogel-based microchips are being developed for high-throughput evaluation of the concentrations and activities of various proteins. To shorten the time of analysis, the reaction-diffusion kinetics on gel microchips should be accelerated. Here we present the results of the experimental and theoretical analysis of the reaction-diffusion kinetics enforced by mixing with peristaltic pump. The experiments were carried out on gel-based protein microchips with immobilized antibodies under the conditions utilized for on-chip immunoassay. The dependence of fluorescence signals at saturation and corresponding saturation times on the concentrations of immobilized antibodies and antigen in solution proved to be in good agreement with theoretical predictions. It is shown that the enhancement of transport with peristaltic pump results in more than five-fold acceleration of binding kinetics. Our results suggest useful criteria for the optimal conditions for assays on gel microchips to balance high sensitivity and rapid fluorescence saturation kinetics.
NASA Astrophysics Data System (ADS)
Yochelis, Arik; Bar-On, Tomer; Gov, Nir S.
2016-04-01
Unconventional myosins belong to a class of molecular motors that walk processively inside cellular protrusions towards the tips, on top of actin filament. Surprisingly, in addition, they also form retrograde moving self-organized aggregates. The qualitative properties of these aggregates are recapitulated by a mass conserving reaction-diffusion-advection model and admit two distinct families of modes: traveling waves and pulse trains. Unlike the traveling waves that are generated by a linear instability, pulses are nonlinear structures that propagate on top of linearly stable uniform backgrounds. Asymptotic analysis of isolated pulses via a simplified reaction-diffusion-advection variant on large periodic domains, allows to draw qualitative trends for pulse properties, such as the amplitude, width, and propagation speed. The results agree well with numerical integrations and are related to available empirical observations.
Fourier spectral method for higher order space fractional reaction-diffusion equations
NASA Astrophysics Data System (ADS)
Pindza, Edson; Owolabi, Kolade M.
2016-11-01
Evolution equations containing fractional derivatives can provide suitable mathematical models for describing important physical phenomena. In this paper, we propose a fast and accurate method for numerical solutions of space fractional reaction-diffusion equations. The proposed method is based on an exponential integrator scheme in time and the Fourier spectral method in space. The main advantages of this method are that it yields a fully diagonal representation of the fractional operator, with increased accuracy and efficiency, and a completely straightforward extension to high spatial dimensions. Although, in general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives, we introduce them to describe fractional hyper-diffusions in reaction diffusion. The scheme justified by a number of computational experiments, this includes two and three dimensional partial differential equations. Numerical experiments are provided to validate the effectiveness of the proposed approach.
Sato, Makoto; Yasugi, Tetsuo; Minami, Yoshiaki; Miura, Takashi; Nagayama, Masaharu
2016-08-30
Notch-mediated lateral inhibition regulates binary cell fate choice, resulting in salt and pepper patterns during various developmental processes. However, how Notch signaling behaves in combination with other signaling systems remains elusive. The wave of differentiation in the Drosophila visual center or "proneural wave" accompanies Notch activity that is propagated without the formation of a salt and pepper pattern, implying that Notch does not form a feedback loop of lateral inhibition during this process. However, mathematical modeling and genetic analysis clearly showed that Notch-mediated lateral inhibition is implemented within the proneural wave. Because partial reduction in EGF signaling causes the formation of the salt and pepper pattern, it is most likely that EGF diffusion cancels salt and pepper pattern formation in silico and in vivo. Moreover, the combination of Notch-mediated lateral inhibition and EGF-mediated reaction diffusion enables a function of Notch signaling that regulates propagation of the wave of differentiation. PMID:27535937
Sato, Makoto; Yasugi, Tetsuo; Minami, Yoshiaki; Miura, Takashi; Nagayama, Masaharu
2016-01-01
Notch-mediated lateral inhibition regulates binary cell fate choice, resulting in salt and pepper patterns during various developmental processes. However, how Notch signaling behaves in combination with other signaling systems remains elusive. The wave of differentiation in the Drosophila visual center or “proneural wave” accompanies Notch activity that is propagated without the formation of a salt and pepper pattern, implying that Notch does not form a feedback loop of lateral inhibition during this process. However, mathematical modeling and genetic analysis clearly showed that Notch-mediated lateral inhibition is implemented within the proneural wave. Because partial reduction in EGF signaling causes the formation of the salt and pepper pattern, it is most likely that EGF diffusion cancels salt and pepper pattern formation in silico and in vivo. Moreover, the combination of Notch-mediated lateral inhibition and EGF-mediated reaction diffusion enables a function of Notch signaling that regulates propagation of the wave of differentiation. PMID:27535937
Delay-induced Turing-like waves for one-species reaction-diffusion model on a network
NASA Astrophysics Data System (ADS)
Petit, Julien; Carletti, Timoteo; Asllani, Malbor; Fanelli, Duccio
2015-09-01
A one-species time-delay reaction-diffusion system defined on a complex network is studied. Traveling waves are predicted to occur following a symmetry-breaking instability of a homogeneous stationary stable solution, subject to an external nonhomogeneous perturbation. These are generalized Turing-like waves that materialize in a single-species populations dynamics model, as the unexpected byproduct of the imposed delay in the diffusion part. Sufficient conditions for the onset of the instability are mathematically provided by performing a linear stability analysis adapted to time-delayed differential equations. The method here developed exploits the properties of the Lambert W-function. The prediction of the theory are confirmed by direct numerical simulation carried out for a modified version of the classical Fisher model, defined on a Watts-Strogatz network and with the inclusion of the delay.
Wang, Jin-Liang; Wu, Huai-Ning; Huang, Tingwen; Ren, Shun-Yan
2016-04-01
Two types of coupled neural networks with reaction-diffusion terms are considered in this paper. In the first one, the nodes are coupled through their states. In the second one, the nodes are coupled through the spatial diffusion terms. For the former, utilizing Lyapunov functional method and pinning control technique, we obtain some sufficient conditions to guarantee that network can realize synchronization. In addition, considering that the theoretical coupling strength required for synchronization may be much larger than the needed value, we propose an adaptive strategy to adjust the coupling strength for achieving a suitable value. For the latter, we establish a criterion for synchronization using the designed pinning controllers. It is found that the coupled reaction-diffusion neural networks with state coupling under the given linear feedback pinning controllers can realize synchronization when the coupling strength is very large, which is contrary to the coupled reaction-diffusion neural networks with spatial diffusion coupling. Moreover, a general criterion for ensuring network synchronization is derived by pinning a small fraction of nodes with adaptive feedback controllers. Finally, two examples with numerical simulations are provided to demonstrate the effectiveness of the theoretical results.
Contribution to an effective design method for stationary reaction-diffusion patterns
NASA Astrophysics Data System (ADS)
Szalai, István; Horváth, Judit; De Kepper, Patrick
2015-06-01
The British mathematician Alan Turing predicted, in his seminal 1952 publication, that stationary reaction-diffusion patterns could spontaneously develop in reacting chemical or biochemical solutions. The first two clear experimental demonstrations of such a phenomenon were not made before the early 1990s when the design of new chemical oscillatory reactions and appropriate open spatial chemical reactors had been invented. Yet, the number of pattern producing reactions had not grown until 2009 when we developed an operational design method, which takes into account the feeding conditions and other specificities of real open spatial reactors. Since then, on the basis of this method, five additional reactions were shown to produce stationary reaction-diffusion patterns. To gain a clearer view on where our methodical approach on the patterning capacity of a reaction stands, numerical studies in conditions that mimic true open spatial reactors were made. In these numerical experiments, we explored the patterning capacity of Rabai's model for pH driven Landolt type reactions as a function of experimentally attainable parameters that control the main time and length scales. Because of the straightforward reversible binding of protons to carboxylate carrying polymer chains, this class of reaction is at the base of the chemistry leading to most of the stationary reaction-diffusion patterns presently observed. We compare our model predictions with experimental observations and comment on agreements and differences.
Contribution to an effective design method for stationary reaction-diffusion patterns.
Szalai, István; Horváth, Judit; De Kepper, Patrick
2015-06-01
The British mathematician Alan Turing predicted, in his seminal 1952 publication, that stationary reaction-diffusion patterns could spontaneously develop in reacting chemical or biochemical solutions. The first two clear experimental demonstrations of such a phenomenon were not made before the early 1990s when the design of new chemical oscillatory reactions and appropriate open spatial chemical reactors had been invented. Yet, the number of pattern producing reactions had not grown until 2009 when we developed an operational design method, which takes into account the feeding conditions and other specificities of real open spatial reactors. Since then, on the basis of this method, five additional reactions were shown to produce stationary reaction-diffusion patterns. To gain a clearer view on where our methodical approach on the patterning capacity of a reaction stands, numerical studies in conditions that mimic true open spatial reactors were made. In these numerical experiments, we explored the patterning capacity of Rabai's model for pH driven Landolt type reactions as a function of experimentally attainable parameters that control the main time and length scales. Because of the straightforward reversible binding of protons to carboxylate carrying polymer chains, this class of reaction is at the base of the chemistry leading to most of the stationary reaction-diffusion patterns presently observed. We compare our model predictions with experimental observations and comment on agreements and differences.
Contribution to an effective design method for stationary reaction-diffusion patterns
Szalai, István; Horváth, Judit; De Kepper, Patrick
2015-06-15
The British mathematician Alan Turing predicted, in his seminal 1952 publication, that stationary reaction-diffusion patterns could spontaneously develop in reacting chemical or biochemical solutions. The first two clear experimental demonstrations of such a phenomenon were not made before the early 1990s when the design of new chemical oscillatory reactions and appropriate open spatial chemical reactors had been invented. Yet, the number of pattern producing reactions had not grown until 2009 when we developed an operational design method, which takes into account the feeding conditions and other specificities of real open spatial reactors. Since then, on the basis of this method, five additional reactions were shown to produce stationary reaction-diffusion patterns. To gain a clearer view on where our methodical approach on the patterning capacity of a reaction stands, numerical studies in conditions that mimic true open spatial reactors were made. In these numerical experiments, we explored the patterning capacity of Rabai's model for pH driven Landolt type reactions as a function of experimentally attainable parameters that control the main time and length scales. Because of the straightforward reversible binding of protons to carboxylate carrying polymer chains, this class of reaction is at the base of the chemistry leading to most of the stationary reaction-diffusion patterns presently observed. We compare our model predictions with experimental observations and comment on agreements and differences.
Contribution to an effective design method for stationary reaction-diffusion patterns.
Szalai, István; Horváth, Judit; De Kepper, Patrick
2015-06-01
The British mathematician Alan Turing predicted, in his seminal 1952 publication, that stationary reaction-diffusion patterns could spontaneously develop in reacting chemical or biochemical solutions. The first two clear experimental demonstrations of such a phenomenon were not made before the early 1990s when the design of new chemical oscillatory reactions and appropriate open spatial chemical reactors had been invented. Yet, the number of pattern producing reactions had not grown until 2009 when we developed an operational design method, which takes into account the feeding conditions and other specificities of real open spatial reactors. Since then, on the basis of this method, five additional reactions were shown to produce stationary reaction-diffusion patterns. To gain a clearer view on where our methodical approach on the patterning capacity of a reaction stands, numerical studies in conditions that mimic true open spatial reactors were made. In these numerical experiments, we explored the patterning capacity of Rabai's model for pH driven Landolt type reactions as a function of experimentally attainable parameters that control the main time and length scales. Because of the straightforward reversible binding of protons to carboxylate carrying polymer chains, this class of reaction is at the base of the chemistry leading to most of the stationary reaction-diffusion patterns presently observed. We compare our model predictions with experimental observations and comment on agreements and differences. PMID:26117122
NASA Astrophysics Data System (ADS)
Musho, Matthew K.; Kozak, John J.
1984-10-01
A method is presented for calculating exactly the relative width (σ2)1/2/
Threshold dynamics of a time periodic reaction-diffusion epidemic model with latent period
NASA Astrophysics Data System (ADS)
Zhang, Liang; Wang, Zhi-Cheng; Zhao, Xiao-Qiang
2015-05-01
In this paper, we first propose a time-periodic reaction-diffusion epidemic model which incorporates simple demographic structure and the latent period of infectious disease. Then we introduce the basic reproduction number R0 for this model and prove that the sign of R0 - 1 determines the local stability of the disease-free periodic solution. By using the comparison arguments and persistence theory, we further show that the disease-free periodic solution is globally attractive if R0 < 1, while there is an endemic periodic solution and the disease is uniformly persistent if R0 > 1.
Wang, Chi-Jen
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.
Reaction-Diffusion Processes on Random and Scale-Free Networks
NASA Astrophysics Data System (ADS)
Banerjee, Subhasis; Mallick, Shrestha Basu; Bose, Indrani
We study the discrete Gierer-Meinhardt model of reaction-diffusion on three different types of networks: regular, random and scale-free. The model dynamics lead to the formation of stationary Turing patterns in the steady state in certain parameter regions. Some general features of the patterns are studied through numerical simulation. The results for the random and scale-free networks show a marked difference from those in the case of the regular network. The difference may be ascribed to the small world character of the first two types of networks.
Conservation Laws of a Family of Reaction-Diffusion-Convection Equations
NASA Astrophysics Data System (ADS)
Bruzón, M. S.; Gandarias, M. L.; de la Rosa, R.
Ibragimov introduced the concept of nonlinear self-adjoint equations. This definition generalizes the concept of self-adjoint and quasi-self-adjoint equations. Gandarias defined the concept of weak self-adjoint. In this paper, we found a class of nonlinear self-adjoint nonlinear reaction-diffusion-convection equations which are neither self-adjoint nor quasi-self-adjoint nor weak self-adjoint. From a general theorem on conservation laws proved by Ibragimov we obtain conservation laws for these equations.
A reaction-diffusion SIS epidemic model in an almost periodic environment
NASA Astrophysics Data System (ADS)
Wang, Bin-Guo; Li, Wan-Tong; Wang, Zhi-Cheng
2015-12-01
A susceptible-infected-susceptible almost periodic reaction-diffusion epidemic model is studied by means of establishing the theories and properties of the basic reproduction ratio {R0}. Particularly, the asymptotic behaviors of {R0} with respect to the diffusion rate {DI} of the infected individuals are obtained. Furthermore, the uniform persistence, extinction and global attractivity are presented in terms of {R0}. Our results indicate that the interaction of spatial heterogeneity and temporal almost periodicity tends to enhance the persistence of the disease.
Self-assembly and plasticity of synaptic domains through a reaction-diffusion mechanism.
Haselwandter, Christoph A; Kardar, Mehran; Triller, Antoine; da Silveira, Rava Azeredo
2015-09-01
Signal transmission across chemical synapses relies crucially on neurotransmitter receptor molecules, concentrated in postsynaptic membrane domains along with scaffold and other postsynaptic molecules. The strength of the transmitted signal depends on the number of receptor molecules in postsynaptic domains, and activity-induced variation in the receptor number is one of the mechanisms of postsynaptic plasticity. Recent experiments have demonstrated that the reaction and diffusion properties of receptors and scaffolds at the membrane, alone, yield spontaneous formation of receptor-scaffold domains of the stable characteristic size observed in neurons. On the basis of these experiments we develop a model describing synaptic receptor domains in terms of the underlying reaction-diffusion processes. Our model predicts that the spontaneous formation of receptor-scaffold domains of the stable characteristic size observed in experiments depends on a few key reactions between receptors and scaffolds. Furthermore, our model suggests novel mechanisms for the alignment of pre- and postsynaptic domains and for short-term postsynaptic plasticity in receptor number. We predict that synaptic receptor domains localize in membrane regions with an increased receptor diffusion coefficient or a decreased scaffold diffusion coefficient. Similarly, we find that activity-dependent increases or decreases in receptor or scaffold diffusion yield a transient increase in the number of receptor molecules concentrated in postsynaptic domains. Thus, the proposed reaction-diffusion model puts forth a coherent set of biophysical mechanisms for the formation, stability, and plasticity of molecular domains on the postsynaptic membrane.
3D choroid neovascularization growth prediction based on reaction-diffusion model
NASA Astrophysics Data System (ADS)
Zhu, Shuxia; Chen, Xinjian; Shi, Fei; Xiang, Dehui; Zhu, Weifang; Chen, Haoyu
2016-03-01
Choroid neovascularization (CNV) is a kind of pathology from the choroid and CNV-related disease is one important cause of vision loss. It is desirable to predict the CNV growth rate so that appropriate treatment can be planned. In this paper, we seek to find a method to predict the growth of CNV based on 3D longitudinal Optical Coherence Tomography (OCT) images. A reaction-diffusion model is proposed for prediction. The method consists of four phases: pre-processing, meshing, CNV growth modeling and prediction. We not only apply the reaction-diffusion model to the disease region, but also take the surrounding tissues into consideration including outer retinal layer, inner retinal layer and choroid layer. The diffusion in these tissues is considered as isotropic. The finite-element-method (FEM) is used to solve the partial differential equations (PDE) in the diffusion model. The curve of CNV growth with treatment are fitted and then we can predict the CNV status in a future time point. The preliminary results demonstrated that our proposed method is accurate and the validity and feasibility of our model is obvious.
Turing-Hopf bifurcation in the reaction-diffusion equations and its applications
NASA Astrophysics Data System (ADS)
Song, Yongli; Zhang, Tonghua; Peng, Yahong
2016-04-01
In this paper, we consider the Turing-Hopf bifurcation arising from the reaction-diffusion equations. It is a degenerate case and where the characteristic equation has a pair of simple purely imaginary roots and a simple zero root. First, the normal form theory for partial differential equations (PDEs) with delays developed by Faria is adopted to this degenerate case so that it can be easily applied to Turing-Hopf bifurcation. Then, we present a rigorous procedure for calculating the normal form associated with the Turing-Hopf bifurcation of PDEs. We show that the reduced dynamics associated with Turing-Hopf bifurcation is exactly the dynamics of codimension-two ordinary differential equations (ODE), which implies the ODE techniques can be employed to classify the reduced dynamics by the unfolding parameters. Finally, we apply our theoretical results to an autocatalysis model governed by reaction-diffusion equations; for such model, the dynamics in the neighbourhood of this bifurcation point can be divided into six categories, each of which is exactly demonstrated by the numerical simulations; and then according to this dynamical classification, a stable spatially inhomogeneous periodic solution has been found.
Hallock, Michael J.; Stone, John E.; Roberts, Elijah; Fry, Corey; Luthey-Schulten, Zaida
2014-01-01
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. PMID:24882911
NASA Astrophysics Data System (ADS)
Schwarz, Karsten; Rieger, Heiko
2013-03-01
We present an efficient Monte Carlo method to simulate reaction-diffusion processes with spatially varying particle annihilation or transformation rates as it occurs for instance in the context of motor-driven intracellular transport. Like Green's function reaction dynamics and first-passage time methods, our algorithm avoids small diffusive hops by propagating sufficiently distant particles in large hops to the boundaries of protective domains. Since for spatially varying annihilation or transformation rates the single particle diffusion propagator is not known analytically, we present an algorithm that generates efficiently either particle displacements or annihilations with the correct statistics, as we prove rigorously. The numerical efficiency of the algorithm is demonstrated with an illustrative example.
NASA Astrophysics Data System (ADS)
Hepburn, I.; Chen, W.; De Schutter, E.
2016-08-01
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.
Hepburn, I; Chen, W; De Schutter, E
2016-08-01
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. PMID:27497550
NASA Astrophysics Data System (ADS)
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.
A reaction-diffusion-based coding rate control mechanism for camera sensor networks.
Yamamoto, Hiroshi; Hyodo, Katsuya; Wakamiya, Naoki; Murata, Masayuki
2010-01-01
A wireless camera sensor network is useful for surveillance and monitoring for its visibility and easy deployment. However, it suffers from the limited capacity of wireless communication and a network is easily overflown with a considerable amount of video traffic. In this paper, we propose an autonomous video coding rate control mechanism where each camera sensor node can autonomously determine its coding rate in accordance with the location and velocity of target objects. For this purpose, we adopted a biological model, i.e., reaction-diffusion model, inspired by the similarity of biological spatial patterns and the spatial distribution of video coding rate. Through simulation and practical experiments, we verify the effectiveness of our proposal. PMID:22163620
Reaction-diffusion-advection equation in binary tree networks and optimal size ratio.
Sakaguchi, Hidetsugu
2014-10-01
A simple reaction-diffusion-advection equation is proposed in a dichotomous tree network to discuss an optimal network. An optimal size ratio r is evaluated by the principle of maximization of total reaction rate. In the case of reaction-limited conditions, the optimal ratio can be larger than (1/2)(1/3) for a fixed value of branching number n, which is consistent with observations in mammalian lungs. We find furthermore that there is an optimal branching number nc when the Péclet number is large. Under the doubly optimal conditions with respect to the size ratio and branching number, the optimal value of r is close to (1/2)(1/3).
Reaction-diffusion-advection equation in binary tree networks and optimal size ratio
NASA Astrophysics Data System (ADS)
Sakaguchi, Hidetsugu
2014-10-01
A simple reaction-diffusion-advection equation is proposed in a dichotomous tree network to discuss an optimal network. An optimal size ratio r is evaluated by the principle of maximization of total reaction rate. In the case of reaction-limited conditions, the optimal ratio can be larger than (1/2)1/3 for a fixed value of branching number n, which is consistent with observations in mammalian lungs. We find furthermore that there is an optimal branching number nc when the Péclet number is large. Under the doubly optimal conditions with respect to the size ratio and branching number, the optimal value of r is close to (1/2)1/3.
Hepburn, I; Chen, W; De Schutter, E
2016-08-01
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.
Using adaptive proper orthogonal decomposition to solve the reaction-diffusion equation
Singer, M A; Green, W H
2007-12-03
We introduce an adaptive POD method to reduce the computational cost of reacting flow simulations. The scheme is coupled with an operator-splitting algorithm to solve the reaction-diffusion equation. For the reaction sub-steps, locally valid basis vectors, obtained via POD and the method of snapshots, are used to project the minor species mass fractions onto a reduced dimensional space thereby decreasing the number of equations that govern combustion chemistry. The method is applied to a one-dimensional laminar premixed CH{sub 4}-air flame using GRImech 3.0; with errors less than 0:25%, a speed-up factor of 3:5 is observed. The speed-up results from fewer source term evaluations required to compute the Jacobian matrices.
A Reaction-Diffusion-Based Coding Rate Control Mechanism for Camera Sensor Networks
Yamamoto, Hiroshi; Hyodo, Katsuya; Wakamiya, Naoki; Murata, Masayuki
2010-01-01
A wireless camera sensor network is useful for surveillance and monitoring for its visibility and easy deployment. However, it suffers from the limited capacity of wireless communication and a network is easily overflown with a considerable amount of video traffic. In this paper, we propose an autonomous video coding rate control mechanism where each camera sensor node can autonomously determine its coding rate in accordance with the location and velocity of target objects. For this purpose, we adopted a biological model, i.e., reaction-diffusion model, inspired by the similarity of biological spatial patterns and the spatial distribution of video coding rate. Through simulation and practical experiments, we verify the effectiveness of our proposal. PMID:22163620
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. PMID:27415276
Numerical methods for one-dimensional reaction-diffusion equations arising in combustion theory
NASA Technical Reports Server (NTRS)
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.
NASA Astrophysics Data System (ADS)
Olsen, Thomas; Hou, Yu; Kowalski, Adam; Wiener, Richard
2006-05-01
The Reaction-Diffusion model predicted a period doubling cascade to chaos in a situation analagous Taylor- Couette flow with hourglass geometry. This cascade to chaos was discovered in the actual fluid flow experiments. We model Taylor-Couette flow in a cylindrical geometry with multiple waists of super-critical flow connected by regions of barely super-critical flow by corresponding Reaction-Diffusion models. We compare our results to the findings of an ongoing experimental program. H. Riecke and H.-G. Paap, Europhys. Lett. 14, 1235 (1991). Richard J. Wiener et al, Phys. Rev. E 55, 5489 (1997).
Scarle, Simon
2009-08-01
In the arsenal of tools that a computational modeller can bring to bare on the study of cardiac arrhythmias, the most widely used and arguably the most successful is that of an excitable medium, a special case of a reaction-diffusion model. These are used to simulate the internal chemical reactions of a cardiac cell and the diffusion of their membrane voltages. Via a number of different methodologies it has previously been shown that reaction-diffusion systems are at multiple levels Turing complete. That is, they are capable of computation in the same manner as a universal Turing machine. However, all such computational systems are subject to a limitation known as the Halting problem. By constructing a universal logic gate using a cardiac cell model, we highlight how the Halting problem therefore could limit what it is possible to predict about cardiac tissue, arrhythmias and re-entry. All simulations for this work were carried out on the GPU of an XBox 360 development console, and we also highlight the great gains in computational power and efficiency produced by such general purpose processing on a GPU for cardiac simulations.
NASA Astrophysics Data System (ADS)
Vlad, Marcel Ovidiu; Ross, John
2002-12-01
We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are described by a set of transformation rates, which are nonlinear functions of the local concentrations of the different types of individuals. We use the time interval between two jumps (the transition time) as an additional state variable and obtain a set of evolution equations, which are local in time. In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations of the so-called generalized master equations. The method leads under different specified conditions to various types of nonlocal transport equations including a nonlinear generalization of fractional diffusion equations, hyperbolic reaction-diffusion equations, and delay-differential reaction-diffusion equations. Thus in the analysis of a given problem we can fit to the data the type of reaction-diffusion equation and the corresponding physical and kinetic parameters. The method is illustrated, as a test case, by the study of the neolithic transition. We introduce a set of assumptions which makes it possible to describe the transition from hunting and gathering to agriculture economics by a differential delay reaction-diffusion equation for the population density. We derive a delay evolution equation for the rate of advance of agriculture, which illustrates an application of our analysis.
Doi, Kentaro; Toyokita, Yukihiro; Akamatsu, Shingo; Kawano, Satoyuki
2014-01-01
Deoxyribonucleic acid (DNA) is a vital molecule for life since it contains genetic information. However, DNA has recently been reported to have unique properties that make it suitable for bionanoelectronic applications, such as the possibility of electrical conductivity and self-organisation. Self-assembled DNA network structures have been observed on several substrates, but the detailed self-assembly mechanism has yet to be determined. The present study investigates self-assembled structures of DNA both theoretically and experimentally. We developed a reaction-diffusion model and used it to investigate pattern formations observed by atomic force microscopy. The computational results qualitatively replicate the network patterns of DNA molecules based on a quantitative agreement with the surface size and timescale. The model can account for the effect of the DNA concentration on pattern formation. Furthermore, peculiar geometric patterns are simulated for mica and highly oriented pyrolytic graphite surfaces.
NASA Astrophysics Data System (ADS)
Aziz, Taha; Fatima, Aeeman; Khalique, Chaudry Masood
An analytical approach based on the compatibility concept is employed to solve a nonlinear reaction-diffusion model arising in mathematical biology. The solution process makes it extremely easy to obtain a relatively accurate closed-form solution of the model. The pencil-and-paper solution procedure can be extended to other class of nonlinear problems of similar kind.
Reaction diffusion model of the enzymatic erosion of insoluble fibrillar matrices.
Tzafriri, Abraham R; Bercovier, Michel; Parnas, Hanna
2002-01-01
Predicting the time course of in vivo biodegradation is a key issue in the design of an increasing number of biomedical applications such as sutures, tissue analogs and drug-delivery devices. The design of such biodegradable devices is hampered by the absence of quantitative models for the enzymatic erosion of solid protein matrices. In this work, we derive and simulate a reaction diffusion model for the enzymatic erosion of fibrillar gels that successfully reproduces the main qualitative features of this process. A key aspect of the proposed model is the incorporation of steric hindrance into the standard Michaelis-Menten scheme for enzyme kinetics. In the limit of instantaneous diffusion, the model equations are analogous to the standard equations for enzymatic degradation in solution. Invoking this analogy, the total quasi-steady-state approximation is used to derive approximate analytical solutions that are valid for a wide range of in vitro conditions. Using these analytical approximations, an experimental-theoretical method is derived to unambiguously estimate all the kinetic model parameters. Moreover, the analytical approximations correctly describe the characteristic hyperbolic dependence of the erosion rate on enzyme concentration and the zero-order erosion of thin fibers. For definiteness, the analysis of published experimental results of enzymatic degradation of fibrillar collagen is demonstrated, and the role of diffusion in these experiments is elucidated. PMID:12124264
Local traps as nanoscale reaction-diffusion probes: B clustering in c-Si
Pawlak, B. J.; Cowern, N. E. B.; Ahn, C.; Vandervorst, W.; Gwilliam, R.; Berkum, J. G. M. van
2014-12-01
A series of B implantation experiments into initially amorphized and not fully recrystallized Si, i.e., into an existing a/c-Si bi-layer material, have been conducted. We varied B dose, energy, and temperature during implantation process itself. Significant B migration has been observed within c-Si part near the a/c-interface and near the end-of-range region before any activation annealing. We propose a general concept of local trapping sites as experimental probes of nanoscale reaction-diffusion processes. Here, the a/c-Si interface acts as a trap, and the process itself is explored as the migration and clustering of mobile BI point defects in nearby c-Si during implantation at temperatures from 77 to 573 K. We find that at room temperature—even at B concentrations as high as 1.6 atomic %, the key B-B pairing step requires diffusion lengths of several nm owing to a small, ∼0.1 eV, pairing energy barrier. Thus, in nanostructures doped by ion implantation, the implant distribution can be strongly influenced by thermal migration to nearby impurities, defects, and interfaces.
NASA Astrophysics Data System (ADS)
Ding, Hongxia; Chen, Shangbin; Zeng, Shuai; Zeng, Shaoqun; Liu, Qian; Luo, Qingming
2008-12-01
Spreading depression (SD) shows as propagating suppression of electrical activity, which relates with migraine and focal cerebral ischaemia. The putative mechanism of SD is the reaction-diffusion hypothesis involving potassium ions. In part inspired by optical imaging of two SD waves collision, we aimed to show the merged and large wavefront but not annihilation during collision by experimental and computational study. This paper modified Reggia et al established bistable equation with recovery to compute and visualize SD. Firstly, the media tissue of SD was assumed as one-dimensional continuum. The Crank-Nicholson method was used to solve the modified equations with recovery term. Then, the computation results were extended to two-dimensional space by symmetry. One individual SD was visualized as a concentric wave initiating from the stimulation point. The mergence but not annihilation of two colliding waves of SD was demonstrated. In addition, the dynamics of SD depending on the parameters was studied and presented. The results allied SD with the emerging concepts of volume transmission. This work not only supplied a paradigm to compute and visualize SD but also became a tool to explore the mechanisms of SD.
Cubic autocatalysis in a reaction-diffusion annulus: semi-analytical solutions
NASA Astrophysics Data System (ADS)
Alharthi, M. R.; Marchant, T. R.; Nelson, M. I.
2016-06-01
Semi-analytical solutions for cubic autocatalytic reactions are considered in a circularly symmetric reaction-diffusion annulus. The Galerkin method is used to approximate the spatial structure of the reactant and autocatalyst concentrations. Ordinary differential equations are then obtained as an approximation to the governing partial differential equations and analyzed to obtain semi-analytical results for this novel geometry. Singularity theory is used to determine the regions of parameter space in which the different types of steady-state diagram occur. The region of parameter space, in which Hopf bifurcations can occur, is found using a degenerate Hopf bifurcation analysis. A novel feature of this geometry is the effect, of varying the width of the annulus, on the static and dynamic multiplicity. The results show that for a thicker annulus, Hopf bifurcations and multiple steady-state solutions occur in a larger portion of parameter space. The usefulness and accuracy of the semi-analytical results are confirmed by comparison with numerical solutions of the governing partial differential equations.
A reaction-diffusion model for migmatization in high-grade metamorphic terrains
NASA Astrophysics Data System (ADS)
Baruah, Amiya; Roy, Manas Kumar; Mandal, Nibir; Misra, Santanu
2016-04-01
Migmatitic rocks evolve through a complex interaction of metamorphism, anatectic melting and solid-state chemical mixing of two principal components: leucosome (quartzofeldspathic materials- L) and melanosome (ferromagnesian materials- M). Melt segregation and their migration are central to generate the features commonly observed in migmatitic rocks. Such L-M interaction leads to melt transport often maintaining a sharp interface between the two units. Existing theoretical and experimental models predicts melt segregation to occur under the combined effects of gravity-driven flow, local stress drop, convection, and advection. However, the efficiency of these processes in large scale transport of melts is largely uncertain. The present study theorizes the migmatization process, treating interactions of the two components (L and M) in the framework of prey-predator dynamics. We propose a reaction-diffusion (RD) model to explore the micro-scale attributes to explain various migmatitic structures observed in the Chotonagpur Granite Gneissic Complex, India. Our simulation couples the L-M phases to a pinning field, accounting linear and non-linear interactions in the diffusion process. The RD model shows that migration of the L-phase into M-phase produces a simple, planar to a complex, multi-ordered geometrical pattern at their interfaces, depending upon the contrast in diffusion coefficients (D) and the pinning factor (W). Furthermore, our models suggest that the linear and the non-linear coupling between L and M phases are critical for the formation of migmatitic structures.
A nonlocal and periodic reaction-diffusion-advection model of a single phytoplankton species.
Peng, Rui; Zhao, Xiao-Qiang
2016-02-01
In this article, we are concerned with a nonlocal reaction-diffusion-advection model which describes the evolution of a single phytoplankton species in a eutrophic vertical water column where the species relies solely on light for its metabolism. The new feature of our modeling equation lies in that the incident light intensity and the death rate are assumed to be time periodic with a common period. We first establish a threshold type result on the global dynamics of this model in terms of the basic reproduction number R0. Then we derive various characterizations of R0 with respect to the vertical turbulent diffusion rate, the sinking or buoyant rate and the water column depth, respectively, which in turn give rather precise conditions to determine whether the phytoplankton persist or become extinct. Our theoretical results not only extend the existing ones for the time-independent case, but also reveal new interesting effects of the modeling parameters and the time-periodic heterogeneous environment on persistence and extinction of the phytoplankton species, and thereby suggest important implications for phytoplankton growth control.
A reaction-diffusion model of the Darien Gap Sterile Insect Release Method
NASA Astrophysics Data System (ADS)
Alford, John G.
2015-05-01
The Sterile Insect Release Method (SIRM) is used as a biological control for invasive insect species. SIRM involves introducing large quantities of sterilized male insects into a wild population of invading insects. A fertile/sterile mating produces offspring that are not viable and the wild insect population will eventually be eradicated. A U.S. government program maintains a permanent sterile fly barrier zone in the Darien Gap between Panama and Columbia to control the screwworm fly (Cochliomyia Hominivorax), an insect that feeds off of living tissue in mammals and has devastating effects on livestock. This barrier zone is maintained by regular releases of massive quantities of sterilized male screwworm flies from aircraft. We analyze a reaction-diffusion model of the Darien Gap barrier zone. Simulations of the model equations yield two types of spatially inhomogeneous steady-state solutions representing a sterile fly barrier that does not prevent invasion and a barrier that does prevent invasion. We investigate steady-state solutions using both phase plane methods and monotone iteration methods and describe how barrier width and the sterile fly release rate affects steady-state behavior.
Competing computational approaches to reaction-diffusion equations in clusters of cells
NASA Astrophysics Data System (ADS)
Stella, Sabrina; Chignola, Roberto; Milotti, Edoardo
2014-03-01
We have developed a numerical model that simulates the growth of small avascular solid tumors. At its core lies a set of partial differential equations that describe diffusion processes as well as transport and reaction mechanisms of a selected number of nutrients. Although the model relies on a restricted subset of molecular pathways, it compares well with experiments, and its emergent properties have recently led us to uncover a metabolic scaling law that stresses the common mechanisms that drive tumor growth. Now we plan to expand the biochemical model at the basis of the simulator to extend its reach. However, the introduction of additional molecular pathways requires an extensive revision of the reaction-diffusion part of the C++ code to make it more modular and to boost performance. To this end, we developed a novel computational abstract model where the individual molecular species represent the basic computational building blocks. Using a simple two-dimensional toy model to benchmark the new code, we find that the new implementation produces a more modular code without affecting performance. Preliminary results also show that a factor 2 speedup can be achieved with OpenMP multithreading, and other very preliminary results indicate that at least an order-of-magnitude speedup can be obtained using an NVidia Fermi GPU with CUDA code.
NASA Astrophysics Data System (ADS)
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.
Bifurcation analysis of a delay reaction-diffusion malware propagation model with feedback control
NASA Astrophysics Data System (ADS)
Zhu, Linhe; Zhao, Hongyong; Wang, Xiaoming
2015-05-01
With the rapid development of network information technology, information networks security has become a very critical issue in our work and daily life. This paper attempts to develop a delay reaction-diffusion model with a state feedback controller to describe the process of malware propagation in mobile wireless sensor networks (MWSNs). By analyzing the stability and Hopf bifurcation, we show that the state feedback method can successfully be used to control unstable steady states or periodic oscillations. Moreover, formulas for determining the properties of the bifurcating periodic oscillations are derived by applying the normal form method and center manifold theorem. Finally, we conduct extensive simulations on large-scale MWSNs to evaluate the proposed model. Numerical evidences show that the linear term of the controller is enough to delay the onset of the Hopf bifurcation and the properties of the bifurcation can be regulated to achieve some desirable behaviors by choosing the appropriate higher terms of the controller. Furthermore, we obtain that the spatial-temporal dynamic characteristics of malware propagation are closely related to the rate constant for nodes leaving the infective class for recovered class and the mobile behavior of nodes.
NASA Astrophysics Data System (ADS)
Cherniha, Roman; King, John R.; Kovalenko, Sergii
2016-07-01
Complete descriptions of the Lie symmetries of a class of nonlinear reaction-diffusion equations with gradient-dependent diffusivity in one and two space dimensions are obtained. A surprisingly rich set of Lie symmetry algebras depending on the form of diffusivity and source (sink) in the equations is derived. It is established that there exists a subclass in 1-D space admitting an infinite-dimensional Lie algebra of invariance so that it is linearisable. A special power-law diffusivity with a fixed exponent, which leads to wider Lie invariance of the equations in question in 2-D space, is also derived. However, it is shown that the diffusion equation without a source term (which often arises in applications and is sometimes called the Perona-Malik equation) possesses no rich variety of Lie symmetries depending on the form of gradient-dependent diffusivity. The results of the Lie symmetry classification for the reduction to lower dimensionality, and a search for exact solutions of the nonlinear 2-D equation with power-law diffusivity, also are included.
Guterl, Jerome Smirnov, R. D.; Krasheninnikov, S. I.
2015-07-28
Desorption phase of thermal desorption spectroscopy (TDS) experiments performed on tungsten samples exposed to flux of hydrogen isotopes in fusion relevant conditions is analyzed using a reaction-diffusion model describing hydrogen retention in material bulk. Two regimes of hydrogen desorption are identified depending on whether hydrogen trapping rate is faster than hydrogen diffusion rate in material during TDS experiments. In both regimes, a majority of hydrogen released from material defects is immediately outgassed instead of diffusing deeply in material bulk when the evolution of hydrogen concentration in material is quasi-static, which is the case during TDS experiments performed with tungsten samples exposed to flux of hydrogen isotopes in fusion related conditions. In this context, analytical expressions of the hydrogen outgassing flux as a function of the material temperature are obtained with sufficient accuracy to describe main features of thermal desorption spectra (TDSP). These expressions are then used to highlight how characteristic temperatures of TDSP depend on hydrogen retention parameters, such as trap concentration or activation energy of detrapping processes. The use of Arrhenius plots to characterize retention processes is then revisited when hydrogen trapping takes place during TDS experiments. Retention processes are also characterized using the shape of desorption peaks in TDSP, and it is shown that diffusion of hydrogen in material during TDS experiment can induce long desorption tails visible aside desorption peaks at high temperature in TDSP. These desorption tails can be used to estimate activation energy of diffusion of hydrogen in material.
NASA Astrophysics Data System (ADS)
Lubuma, J. M.-S.; Mureithi, E.; Terefe, Y. A.
2011-11-01
The classical SIS epidemiological model is extended in two directions: (a) The number of adequate contacts per infective in unit time is assumed to be a function of the total population in such a way that this number grows less rapidly as the total population increases; (b) A diffusion term is added to the SIS model and this leads to a reaction diffusion equation, which governs the spatial spread of the disease. With the parameter R0 representing the basic reproduction number, it is shown that R0 = 1 is a forward bifurcation for the model (a), with the disease-free equilibrium being globally asymptotic stable when R0 is less than 1. In the case when R0 is greater than 1, traveling wave solutions are found for the model (b). Nonstandard finite difference (NSFD) schemes that replicate the dynamics of the continuous models are presented. In particular, for the model (a), a nonstandard version of the Runge-Kutta method having high order of convergence is investigated. Numerical experiments that support the theory are provided.
Nucleic acid based logical systems.
Han, Da; Kang, Huaizhi; Zhang, Tao; Wu, Cuichen; Zhou, Cuisong; You, Mingxu; Chen, Zhuo; Zhang, Xiaobing; Tan, Weihong
2014-05-12
Researchers increasingly visualize a significant role for artificial biochemical logical systems in biological engineering, much like digital logic circuits in electrical engineering. Those logical systems could be utilized as a type of servomechanism to control nanodevices in vitro, monitor chemical reactions in situ, or regulate gene expression in vivo. Nucleic acids (NA), as carriers of genetic information with well-regulated and predictable structures, are promising materials for the design and engineering of biochemical circuits. A number of logical devices based on nucleic acids (NA) have been designed to handle various processes for technological or biotechnological purposes. This article focuses on the most recent and important developments in NA-based logical devices and their evolution from in vitro, through cellular, even towards in vivo biological applications.
Boric Acid Reclamation System (BARS)
Kniazewycz, B.G.; Markind, J.
1986-03-01
KLM Technologies' personnel have identified a Boric Acid Reclamation System (BARS) utilizing reverse osmosis and ultrafiltration to produce a recyclable grade of otherwise waste boric acid at PWRs, thus reducing a major source of low-level radwaste. The design of a prototype BARS as a compact volume reduction system was the result of KLM's Phase 1 Program, and based upon a preliminary feasibility program, which assessed the applicability of membrane technology to refurbish and recycle waste boric acid from floor and equipment drain streams. The analysis of the overall program indicated a substantial savings regarding off-site disposal costs. Today's economic scenario indicates that optimization of volume reduction operation procedures could significantly reduce waste management costs, especially where burial penalties have become more severe. As a reaction to the economic burden imposed by final disposal, many nuclear plants are currently modifying their design and operating philosophies concerning liquid radwaste processing systems to meet stricter environmental regulations, and to derive potential economic benefits by reducing the ever-increasing volumes of wastes that are produced. To effect these changes, innovative practices in waste management and more efficient processing technologies are being successfully implemented.
NASA Astrophysics Data System (ADS)
Rothman, D.; Petroff, A. P.; Liang, B.; Sim, M.; Bosak, T.
2009-12-01
Laminated and lithified sedimentary structures called stromatolites are commonly thought to record the presence of microbes in sediments as old as 3.4 billion years. Conical stromatolites are considered the most robust indicators of past biological presence or activity. This inference, however, is largely drawn from the qualitative similarity in shape between modern conical stromatolites and ancient rocks. Here we relate the growth and organization of a field of conical stromatolites to competition between individual cones for a diffusing nutrient. The predictions of this reaction-diffusion model are compared with laboratory experiments and field observations of modern conical stromatolites from Yellowstone National Park. We observe that cone-forming bacteria respond to diffusion limitation by forming mm-scale clumps that can develop into cm-size cones. Competition between clumps occur over the distance nutrients diffuse while bacteria are continuously active, thus linking physical form to metabolic forcing. Furthermore, we find that the spacing between these clumps can be varied in the lab by changing the day length, suggesting the central role of photosynthesis in the growth of clumps. Although all modern microbial communities that build stromatolites are fueled by the energy of the sun, it is unclear whether there is any specific textural or chemical evidence for photosynthesis in many ancient stromatolites. However, we find that the spacing between many ancient conical stromatolites and all modern examples is consistent with diurnal forcing, thus providing quantitative morphological evidence of photosynthetic activity. This result provides a biological mechanism for the cm-scale spacing between many small conical stromatolites of all ages. The earliest manifestation of cm-spaced cones about three billion years ago may therefore record the earliest photosynthetic microbial communities.
Convergence of methods for coupling of microscopic and mesoscopic reaction-diffusion simulations
Flegga, Mark B.; Hellander, Stefan; Erban, Radek
2015-01-01
In this paper, three multiscale methods for coupling of mesoscopic (compartment-based) and microscopic (molecular-based) stochastic reaction-diffusion simulations are investigated. Two of the three methods that will be discussed in detail have been previously reported in the literature; the two-regime method (TRM) and the compartment-placement method (CPM). The third method that is introduced and analysed in this paper is called the ghost cell method (GCM), since it works by constructing a “ghost cell” in which molecules can disappear and jump into the compartment-based simulation. Presented is a comparison of sources of error. The convergent properties of this error are studied as the time step Δt (for updating the molecular-based part of the model) approaches zero. It is found that the error behaviour depends on another fundamental computational parameter h, the compartment size in the mesoscopic part of the model. Two important limiting cases, which appear in applications, are considered: (i) Δt → 0 and h is fixed; (ii) Δt → 0 and h → 0 such that √Δt/h is fixed. The error for previously developed approaches (the TRM and CPM) converges to zero only in the limiting case (ii), but not in case (i). It is shown that the error of the GCM converges in the limiting case (i). Thus the GCM is superior to previous coupling techniques if the mesoscopic description is much coarser than the microscopic part of the model. PMID:26568640
NASA Astrophysics Data System (ADS)
Mena, Andres; Ferrero, Jose M.; Rodriguez Matas, Jose F.
2015-11-01
Solving the electric activity of the heart possess a big challenge, not only because of the structural complexities inherent to the heart tissue, but also because of the complex electric behaviour of the cardiac cells. The multi-scale nature of the electrophysiology problem makes difficult its numerical solution, requiring temporal and spatial resolutions of 0.1 ms and 0.2 mm respectively for accurate simulations, leading to models with millions degrees of freedom that need to be solved for thousand time steps. Solution of this problem requires the use of algorithms with higher level of parallelism in multi-core platforms. In this regard the newer programmable graphic processing units (GPU) has become a valid alternative due to their tremendous computational horsepower. This paper presents results obtained with a novel electrophysiology simulation software entirely developed in Compute Unified Device Architecture (CUDA). The software implements fully explicit and semi-implicit solvers for the monodomain model, using operator splitting. Performance is compared with classical multi-core MPI based solvers operating on dedicated high-performance computer clusters. Results obtained with the GPU based solver show enormous potential for this technology with accelerations over 50 × for three-dimensional problems.
NASA Astrophysics Data System (ADS)
Fu, Jin; Wu, Sheng; Li, Hong; Petzold, Linda R.
2014-10-01
The inhomogeneous stochastic simulation algorithm (ISSA) is a fundamental method for spatial stochastic simulation. However, when diffusion events occur more frequently than reaction events, simulating the diffusion events by ISSA is quite costly. To reduce this cost, we propose to use the time dependent propensity function in each step. In this way we can avoid simulating individual diffusion events, and use the time interval between two adjacent reaction events as the simulation stepsize. We demonstrate that the new algorithm can achieve orders of magnitude efficiency gains over widely-used exact algorithms, scales well with increasing grid resolution, and maintains a high level of accuracy.
Wu, Sheng; Li, Hong; Petzold, Linda R.
2015-01-01
The inhomogeneous stochastic simulation algorithm (ISSA) is a fundamental method for spatial stochastic simulation. However, when diffusion events occur more frequently than reaction events, simulating the diffusion events by ISSA is quite costly. To reduce this cost, we propose to use the time dependent propensity function in each step. In this way we can avoid simulating individual diffusion events, and use the time interval between two adjacent reaction events as the simulation stepsize. We demonstrate that the new algorithm can achieve orders of magnitude efficiency gains over widely-used exact algorithms, scales well with increasing grid resolution, and maintains a high level of accuracy. PMID:26609185
Experimental studies of coherent structures in an advection-reaction-diffusion system.
Gowen, Savannah; Solomon, Tom
2015-08-01
We present experimental studies of reaction front propagation in a single vortex flow with an imposed external wind. The fronts are produced by the excitable, ferroin-catalyzed Belousov-Zhabotinsky chemical reaction. The flow is generated using an electromagnetic forcing technique: an almost-radial electrical current interacts with a magnetic field from a magnet below the fluid layer to produce the vortex. The magnet is mounted on crossed translation stages allowing for movement of the vortex through the flow. Reaction fronts triggered in or in front of the moving vortex form persistent structures that are seen experimentally for time-independent (constant motion), time-periodic, and time-aperiodic flows. These results are examined with the use of burning invariant manifolds that act as one-way barriers to front motion in the flows. We also explore the usefulness of finite-time Lyapunov exponent fields as an instrument for analyzing front propagation behavior in a fluid flow. PMID:26328574
A reaction-diffusion system modeling the spread of resistance to an antimalarial drug.
Bacaer, Nicolas; Sokhna, Cheikh
2005-04-01
A mathematical model representing the difusion of resistance to an antimalarial drug is developed. Resistance can spread only when the basic reproduction number of the resistant parasites is bigger than the basic reproduction number of the sensitive parasites (which depends on the fraction of infected people treated with the antimalarial drug). Based on a linearization study and on numerical simulations, an expression for the speed at which resistance spreads is conjectured. It depends on the ratio of the two basic reproduction numbers, on a coefficient representing the difusion of mosquitoes, on the death rate of mosquitoes infected by resistant parasites, and on the recovery rate of nonimmune humans infected by resistant parasites.
Reaction diffusion in the nickel-chromium-aluminum and cobalt-chromium-aluminum systems
NASA Technical Reports Server (NTRS)
Levine, S. R.
1977-01-01
The effects of MCrAl coating-substrate interdiffusion on oxidation life and the general mutliphase, multicomponent diffusion problem were examined. Semi-infinite diffusion couples that had sources representing coatings and sinks representing gas turbine alloys were annealed at 1,000, 1,095, 1,150, or 1,205 C for as long as 500 hours. The source and sink aluminum and chromium contents and the base metal (cobalt or nickel) determined the parabolic diffusion rate constants of the couples and predicted finite coating lives. The beta source strength concept provided a method (1) for correlating beta recession rate constants with composition; (2) for determining reliable average total, diffusion, and constitutional activation energies; and (3) for calculating interdiffusion coefficients.
Reaction-diffusion systems in natural sciences and new technology transfer
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Mena, Andres; Ferrero, Jose M.; Rodriguez Matas, Jose F.
2015-11-01
Solving the electric activity of the heart possess a big challenge, not only because of the structural complexities inherent to the heart tissue, but also because of the complex electric behaviour of the cardiac cells. The multi-scale nature of the electrophysiology problem makes difficult its numerical solution, requiring temporal and spatial resolutions of 0.1 ms and 0.2 mm respectively for accurate simulations, leading to models with millions degrees of freedom that need to be solved for thousand time steps. Solution of this problem requires the use of algorithms with higher level of parallelism in multi-core platforms. In this regard the newer programmable graphic processing units (GPU) has become a valid alternative due to their tremendous computational horsepower. This paper presents results obtained with a novel electrophysiology simulation software entirely developed in Compute Unified Device Architecture (CUDA). The software implements fully explicit and semi-implicit solvers for the monodomain model, using operator splitting. Performance is compared with classical multi-core MPI based solvers operating on dedicated high-performance computer clusters. Results obtained with the GPU based solver show enormous potential for this technology with accelerations over 50 × for three-dimensional problems.
Simulating Stochastic Reaction-Diffusion Systems on and within Moving Boundaries
Ghosh, Atiyo; Marquez-Lago, Tatiana T.
2015-01-01
Chemical reactions inside cells are generally considered to happen within fixed-size compartments. However, cells and their compartments are highly dynamic. Thus, such stringent geometrical assumptions may not reflect biophysical reality, and can highly bias conclusions from simulation studies. In this work, we present an intuitive algorithm for particle-based diffusion in and on moving boundaries, for both point particles and spherical particles. We first benchmark our proposed stochastic method against solutions of partial differential equations in appropriate scenarios, and further demonstrate that moving boundaries can give rise to super-diffusive motion as well as time-inhomogeneous reaction rates. Finally, we conduct a numerical experiment representing photobleaching of diffusing fluorescent proteins in dividing Saccharomyces cerevisiae cells to demonstrate that moving boundaries might cause important effects neglected in previously published studies of cell compartmentalization. PMID:26230406
Manifolds and front propagation barriers in advection-reaction-diffusion systems
NASA Astrophysics Data System (ADS)
Solomon, Tom
2015-03-01
We present experiments on the propagation of reaction fronts in laminar, vortex-dominated flows. The fronts are produced by the excitable Belousov-Zhabotinsky chemical reaction. The flows studied are driven by magnetohydrodynamic forcing techniques and are composed of a single vortex, chains or arrays of vortices, or spatially-disordered flows. In all of these cases, one-way barriers appear that either inhibit front propagation or, in some cases, pin the reactions fronts. We analyze this behavior with a recent theory of burning invariant manifolds (BIMs) that are a generalization of the theory of invariant manifolds developed in the past to characterize chaotic mixing and transport of passive impurities. We demonstrate that the BIMs are responsible for the reaction barriers observed experimentally, and we discuss the applicability of this BIM formalism to a range of flows: time-independent, time-periodic and time-aperiodic. Supported by NSF Grants DMR-1004744, DMR-1361881 and PHY-1156964.
Hormuth, David A; Weis, Jared A; Barnes, Stephanie L; Miga, Michael I; Rericha, Erin C; Quaranta, Vito; Yankeelov, Thomas E
2015-06-04
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.
NASA Astrophysics Data System (ADS)
Hormuth, David A., II; Weis, Jared A.; Barnes, Stephanie L.; Miga, Michael I.; Rericha, Erin C.; Quaranta, Vito; Yankeelov, Thomas E.
2015-07-01
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.
NASA Astrophysics Data System (ADS)
Kengne, Emmanuel; Saydé, Michel; Ben Hamouda, Fathi; Lakhssassi, Ahmed
2013-11-01
Analytical entire traveling wave solutions to the 1+1 density-dependent nonlinear reaction-diffusion equation via the extended generalized Riccati equation mapping method are presented in this paper. This equation can be regarded as an extension case of the Fisher-Kolmogoroff equation, which is used for studying insect and animal dispersal with growth dynamics. The analytical solutions are then used to investigate the effect of equation parameters on the population distribution.
Prabhu, Vivek M.; Kang, Shuhui; Sha, Jing; Bonnesen, Peter V; Satija, Sushil K.; Wu, Wen-li; Ober, Christoper K.
2012-01-01
Lithographic feature size requirements have approached a few radius of gyration of photoresist polymers used in thin-film patterning. Furthermore, the feature dimensions are commensurate with the photoacid diffusion length that defines the underlying latent image. Smaller imaging building blocks may enable reduced feature sizes; however, resolution limits are also dependent upon the spatial extent of the photoacid-catalyzed reaction diffusion front and subsequent dissolution mechanism. The reaction-diffusion front was characterized by neutron reflectivity for ccc stereoisomer-purified, deuterium-labeled tert-butoxycarbonyloxy calix[4]resorcinarene molecular resists. The spatial extent of the reaction front exceeds the size of the molecular resist with an effective diffusion constant of (0.13 0.06) nm2/s for reaction times longer than 60 s, with the maximum at shorter times. Comparison to a mean-field reaction-diffusion model shows that a photoacid trapping process provides bounds to the spatial and extent of reaction via a reaction-limited mechanism whereas the ratio of the reaction rate to trapping rate constants recovers the effective diffusion peak. Under the ideal step-exposure conditions, surface roughness was observed after either positive- or negative-tone development. However, negative-tone development follows a surface restructuring mechanism rather than etch-like dissolution in positive-tone development.
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 0
Beaghton, Andrea; Beaghton, Pantelis John; Burt, Austin
2016-04-01
Some genes or gene complexes are transmitted from parents to offspring at a greater-than-Mendelian rate, and can spread and persist in populations even if they cause some harm to the individuals carrying them. Such genes may be useful for controlling populations or species that are harmful. Driving-Y chromosomes may be particularly potent in this regard, as they produce a male-biased sex ratio that, if sufficiently extreme, can lead to population elimination. To better understand the potential of such genes to spread over a landscape, we have developed a series of reaction-diffusion models of a driving-Y chromosome in 1-D and radially-symmetric 2-D unbounded domains. The wild-type system at carrying capacity is found to be unstable to the introduction of driving-Y males for all models investigated. Numerical solutions exhibit travelling wave pulses and fronts, and analytical and semi-analytical solutions for the asymptotic wave speed under bounded initial conditions are derived. The driving-Y male invades the wild-type equilibrium state at the front of the wave and completely replaces the wild-type males, leaving behind, at the tail of the wave, a reduced- or zero-population state of females and driving-Y males only. In our simplest model of a population with one life stage and density-dependent mortality, wave speed depends on the strength of drive and the diffusion rate of Y-drive males, and is independent of the population dynamic consequences (suppression or elimination). Incorporating an immobile juvenile stage of fixed duration into the model reduces wave speed approximately in proportion to the relative time spent as a juvenile. If females mate just once in their life, storing sperm for subsequent reproduction, then wave speed depends on the movement of mated females as well as Y-drive males, and may be faster or slower than in the multiple-mating model, depending on the relative duration of juvenile and adult life stages. Numerical solutions are shown for
Beaghton, Andrea; Beaghton, Pantelis John; Burt, Austin
2016-04-01
Some genes or gene complexes are transmitted from parents to offspring at a greater-than-Mendelian rate, and can spread and persist in populations even if they cause some harm to the individuals carrying them. Such genes may be useful for controlling populations or species that are harmful. Driving-Y chromosomes may be particularly potent in this regard, as they produce a male-biased sex ratio that, if sufficiently extreme, can lead to population elimination. To better understand the potential of such genes to spread over a landscape, we have developed a series of reaction-diffusion models of a driving-Y chromosome in 1-D and radially-symmetric 2-D unbounded domains. The wild-type system at carrying capacity is found to be unstable to the introduction of driving-Y males for all models investigated. Numerical solutions exhibit travelling wave pulses and fronts, and analytical and semi-analytical solutions for the asymptotic wave speed under bounded initial conditions are derived. The driving-Y male invades the wild-type equilibrium state at the front of the wave and completely replaces the wild-type males, leaving behind, at the tail of the wave, a reduced- or zero-population state of females and driving-Y males only. In our simplest model of a population with one life stage and density-dependent mortality, wave speed depends on the strength of drive and the diffusion rate of Y-drive males, and is independent of the population dynamic consequences (suppression or elimination). Incorporating an immobile juvenile stage of fixed duration into the model reduces wave speed approximately in proportion to the relative time spent as a juvenile. If females mate just once in their life, storing sperm for subsequent reproduction, then wave speed depends on the movement of mated females as well as Y-drive males, and may be faster or slower than in the multiple-mating model, depending on the relative duration of juvenile and adult life stages. Numerical solutions are shown for
NASA Astrophysics Data System (ADS)
Benguria, R. D.; Depassier, M. C.
2016-04-01
We study the dynamics of the equation obtained by Schryer and Walker for the motion of domain walls. The reduced equation is a reaction diffusion equation for the angle between the applied field and the magnetization vector. If the hard-axis anisotropy Kd is much larger than the easy-axis anisotropy Ku, there is a range of applied fields where the dynamics does not select the Schryer-Walker solution. We give an analytic expression for the speed of the domain wall in this regime and the conditions for its existence.
Tan, Jie; Li, Chuandong; Huang, Tingwen
2015-04-01
The global asymptotic stability of impulsive stochastic Cohen-Grossberg neural networks with mixed delays and reaction-diffusion terms is investigated. Under some suitable assumptions and using Lyapunov-Krasovskii functional method, we apply the linear matrix inequality technique to propose some new sufficient conditions for the global asymptotic stability of the addressed model in the stochastic sense. The mixed time delays comprise both the time-varying and continuously distributed delays. The effectiveness of the theoretical result is illustrated by a numerical example.
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 0
Comte, J C; Marquié, P; Remoissenet, M
1999-12-01
We introduce a nonlinear Klein-Gordon lattice model with specific double-well on-site potential, additional constant external force and dissipation terms, which admits exact discrete kink or traveling wave fronts solutions. In the non-dissipative or conservative regime, our numerical simulations show that narrow kinks can propagate freely, and reveal that static or moving discrete breathers, with a finite but long lifetime, can emerge from kink-antikink collisions. In the general dissipative regime, the lifetime of these breathers depends on the importance of the dissipative effects. In the overdamped or diffusive regime, the general equation of motion reduces to a discrete reaction diffusion equation; our simulations show that, for a given potential shape, discrete wave fronts can travel without experiencing any propagation failure but their collisions are inelastic. PMID:11970697
One-Dimensional Reaction-Diffusion Simulation of Cu Migration in Polycrystalline CdTe Solar Cells
Guo, Da; Akis, Richard; Brinkman, Daniel; Sankin, Igor; Fang, Tian; Vasileska, Dragica; Ringhofer, Christain
2014-06-13
In this work, we report on developing 1D reaction-diffusion solver to understand the kinetics of p-type doping formation in CdTe absorbers and to shine some light on underlying causes of metastabilities observed in CdTe PV devices. Evolution of intrinsic and Cu-related defects in CdTe solar cell has been studied in time-space domain self-consistently with free carrier transport and Poisson equation. Resulting device performance was simulated as a function of Cu diffusion anneal time showing pronounced effect the evolution of associated acceptor and donor states can cause on device characteristics. Although 1D simulation has intrinsic limitations when applied to poly-crystalline films, the results suggest strong potential of the approach in better understanding of the performance and metastabilities of CdTe photovoltaic device.
Comte, J C; Marquié, P; Remoissenet, M
1999-12-01
We introduce a nonlinear Klein-Gordon lattice model with specific double-well on-site potential, additional constant external force and dissipation terms, which admits exact discrete kink or traveling wave fronts solutions. In the non-dissipative or conservative regime, our numerical simulations show that narrow kinks can propagate freely, and reveal that static or moving discrete breathers, with a finite but long lifetime, can emerge from kink-antikink collisions. In the general dissipative regime, the lifetime of these breathers depends on the importance of the dissipative effects. In the overdamped or diffusive regime, the general equation of motion reduces to a discrete reaction diffusion equation; our simulations show that, for a given potential shape, discrete wave fronts can travel without experiencing any propagation failure but their collisions are inelastic.
NASA Astrophysics Data System (ADS)
Ma, Manjun; Wang, Zhi-An
2015-08-01
This paper is devoted to studying a reaction-diffusion-chemotaxis model with a volume-filling effect in a bounded domain with Neumann boundary conditions. We first establish the global existence of classical solutions bounded uniformly in time. Then applying the asymptotic analysis and bifurcation theory, we obtain both the local and global structure of steady states bifurcating from the homogeneous steady states in one dimension by treating the chemotactic coefficient as a bifurcation parameter. Moveover we find the stability criterion of the bifurcating steady states and give a sufficient condition for the stability of steady states with small amplitude. The pattern formation of the model is numerically shown and the stability criterion is verified by our numerical simulations.
NASA Astrophysics Data System (ADS)
Weis, Jared A.; Miga, Michael I.; Arlinghaus, Lori R.; Li, Xia; Bapsi Chakravarthy, A.; Abramson, Vandana; Farley, Jaime; Yankeelov, Thomas E.
2013-09-01
There is currently a paucity of reliable techniques for predicting the response of breast tumors to neoadjuvant chemotherapy. The standard approach is to monitor gross changes in tumor size as measured by physical exam and/or conventional imaging, but these methods generally do not show whether a tumor is responding until the patient has received many treatment cycles. One promising approach to address this clinical need is to integrate quantitative in vivo imaging data into biomathematical models of tumor growth in order to predict eventual response based on early measurements during therapy. In this work, we illustrate a novel biomechanical mathematical modeling approach in which contrast enhanced and diffusion weighted magnetic resonance imaging data acquired before and after the first cycle of neoadjuvant therapy are used to calibrate a patient-specific response model which subsequently is used to predict patient outcome at the conclusion of therapy. We present a modification of the reaction-diffusion tumor growth model whereby mechanical coupling to the surrounding tissue stiffness is incorporated via restricted cell diffusion. We use simulations and experimental data to illustrate how incorporating tissue mechanical properties leads to qualitatively and quantitatively different tumor growth patterns than when such properties are ignored. We apply the approach to patient data in a preliminary dataset of eight patients exhibiting a varying degree of responsiveness to neoadjuvant therapy, and we show that the mechanically coupled reaction-diffusion tumor growth model, when projected forward, more accurately predicts residual tumor burden at the conclusion of therapy than the non-mechanically coupled model. The mechanically coupled model predictions exhibit a significant correlation with data observations (PCC = 0.84, p < 0.01), and show a statistically significant >4 fold reduction in model/data error (p = 0.02) as compared to the non-mechanically coupled model.
21 CFR 862.1450 - Lactic acid test system.
Code of Federal Regulations, 2013 CFR
2013-04-01
....1450 Lactic acid test system. (a) Identification. A lactic acid test system is a device intended to measure lactic acid in whole blood and plasma. Lactic acid measurements that evaluate the acid-base status... 21 Food and Drugs 8 2013-04-01 2013-04-01 false Lactic acid test system. 862.1450 Section...
21 CFR 862.1450 - Lactic acid test system.
Code of Federal Regulations, 2011 CFR
2011-04-01
....1450 Lactic acid test system. (a) Identification. A lactic acid test system is a device intended to measure lactic acid in whole blood and plasma. Lactic acid measurements that evaluate the acid-base status... 21 Food and Drugs 8 2011-04-01 2011-04-01 false Lactic acid test system. 862.1450 Section...
21 CFR 862.1450 - Lactic acid test system.
Code of Federal Regulations, 2012 CFR
2012-04-01
....1450 Lactic acid test system. (a) Identification. A lactic acid test system is a device intended to measure lactic acid in whole blood and plasma. Lactic acid measurements that evaluate the acid-base status... 21 Food and Drugs 8 2012-04-01 2012-04-01 false Lactic acid test system. 862.1450 Section...
21 CFR 862.1450 - Lactic acid test system.
Code of Federal Regulations, 2014 CFR
2014-04-01
....1450 Lactic acid test system. (a) Identification. A lactic acid test system is a device intended to measure lactic acid in whole blood and plasma. Lactic acid measurements that evaluate the acid-base status... 21 Food and Drugs 8 2014-04-01 2014-04-01 false Lactic acid test system. 862.1450 Section...
Tomography of reaction-diffusion microemulsions reveals three-dimensional Turing patterns.
Bánsági, Tamás; Vanag, Vladimir K; Epstein, Irving R
2011-03-11
Spatially periodic, temporally stationary patterns that emerge from instability of a homogeneous steady state were proposed by Alan Turing in 1952 as a mechanism for morphogenesis in living systems and have attracted increasing attention in biology, chemistry, and physics. Patterns found to date have been confined to one or two spatial dimensions. We used tomography to study the Belousov-Zhabotinsky reaction in a microemulsion in which the polar reactants are confined to aqueous nanodroplets much smaller than the scale of the stationary patterns. We demonstrate the existence of Turing patterns that can exist only in three dimensions, including curved surfaces, hexagonally packed cylinders, spots, and labyrinthine and lamellar patterns.
Tomography of reaction-diffusion microemulsions reveals three-dimensional Turing patterns.
Bánsági, Tamás; Vanag, Vladimir K; Epstein, Irving R
2011-03-11
Spatially periodic, temporally stationary patterns that emerge from instability of a homogeneous steady state were proposed by Alan Turing in 1952 as a mechanism for morphogenesis in living systems and have attracted increasing attention in biology, chemistry, and physics. Patterns found to date have been confined to one or two spatial dimensions. We used tomography to study the Belousov-Zhabotinsky reaction in a microemulsion in which the polar reactants are confined to aqueous nanodroplets much smaller than the scale of the stationary patterns. We demonstrate the existence of Turing patterns that can exist only in three dimensions, including curved surfaces, hexagonally packed cylinders, spots, and labyrinthine and lamellar patterns. PMID:21310963
Acid sensing by the Drosophila olfactory system.
Ai, Minrong; Min, Soohong; Grosjean, Yael; Leblanc, Charlotte; Bell, Rati; Benton, Richard; Suh, Greg S B
2010-12-01
The odour of acids has a distinct quality that is perceived as sharp, pungent and often irritating. How acidity is sensed and translated into an appropriate behavioural response is poorly understood. Here we describe a functionally segregated population of olfactory sensory neurons in the fruitfly, Drosophila melanogaster, that are highly selective for acidity. These olfactory sensory neurons express IR64a, a member of the recently identified ionotropic receptor (IR) family of putative olfactory receptors. In vivo calcium imaging showed that IR64a+ neurons projecting to the DC4 glomerulus in the antennal lobe are specifically activated by acids. Flies in which the function of IR64a+ neurons or the IR64a gene is disrupted had defects in acid-evoked physiological and behavioural responses, but their responses to non-acidic odorants remained unaffected. Furthermore, artificial stimulation of IR64a+ neurons elicited avoidance responses. Taken together, these results identify cellular and molecular substrates for acid detection in the Drosophila olfactory system and support a labelled-line mode of acidity coding at the periphery. PMID:21085119
Sulfuric acid thermoelectrochemical system and method
Ludwig, Frank A.
1989-01-01
A thermoelectrochemical system in which an electrical current is generated between a cathode immersed in a concentrated sulfuric acid solution and an anode immersed in an aqueous buffer solution of sodium bisulfate and sodium sulfate. Reactants consumed at the electrodes during the electrochemical reaction are thermochemically regenerated and recycled to the electrodes to provide continuous operation of the system.
Micro-electro-mechanical systems phosphoric acid fuel cell
Sopchak, David A.; Morse, Jeffrey D.; Upadhye, Ravindra S.; Kotovsky, Jack; Graff, Robert T.
2010-08-17
A phosphoric acid fuel cell system comprising a porous electrolyte support, a phosphoric acid electrolyte in the porous electrolyte support, a cathode electrode contacting the phosphoric acid electrolyte, and an anode electrode contacting the phosphoric acid electrolyte.
Micro-electro-mechanical systems phosphoric acid fuel cell
Sopchak, David A.; Morse, Jeffrey D.; Upadhye, Ravindra S.; Kotovsky, Jack; Graff, Robert T.
2010-12-21
A phosphoric acid fuel cell system comprising a porous electrolyte support, a phosphoric acid electrolyte in the porous electrolyte support, a cathode electrode contacting the phosphoric acid electrolyte, and an anode electrode contacting the phosphoric acid electrolyte.
NASA Astrophysics Data System (ADS)
Vlad, Marcel Ovidiu; Moran, Federico; Tsuchiya, Masa; Cavalli-Sforza, L. Luca; Oefner, Peter J.; Ross, John
2002-06-01
We study a general class of nonlinear macroscopic evolution equations with ``transport'' and ``reaction'' terms which describe the dynamics of a species of moving individuals (atoms, molecules, quasiparticles, organisms, etc.). We consider that two types of individuals exist, ``not marked'' and ``marked,'' respectively. We assume that the concentrations of both types of individuals are measurable and that they obey a neutrality condition, that is, the kinetic and transport properties of the ``not marked'' and ``marked'' individuals are identical. We suggest a response experiment, which consists in varying the fraction of ``marked'' individuals with the preservation of total fluxes, and show that the response of the system can be represented by a linear superposition law even though the underlying dynamics of the system is in general highly nonlinear. The linear response law is valid even for large perturbations and is not the result of a linearization procedure but rather a necessary consequence of the neutrality condition. First, we apply the response theorem to chemical kinetics, where the ``marked species'' is a molecule labeled with a radioactive isotope and there is no kinetic isotope effect. The susceptibility function of the response law can be related to the reaction mechanism of the process. Secondly we study the geographical distribution of the nonrecurrent, nonreversible neutral mutations of the nonrecombining portion of the Y chromosome from human populations and show that the fraction of mutants at a given point in space and time obeys a linear response law of the type introduced in this paper. The theory may be used for evaluating the geographic position and the moment in time where and when a mutation originated.
A Refined Reaction-Diffusion Model of Tau-Microtubule Dynamics and Its Application in FDAP Analysis
Igaev, Maxim; Janning, Dennis; Sündermann, Frederik; Niewidok, Benedikt; Brandt, Roland; Junge, Wolfgang
2014-01-01
Fluorescence decay after photoactivation (FDAP) and fluorescence recovery after photobleaching (FRAP) are well established approaches for studying the interaction of the microtubule (MT)-associated protein tau with MTs in neuronal cells. Previous interpretations of FDAP/FRAP data have revealed dwell times of tau on MTs in the range of several seconds. However, this is difficult to reconcile with a dwell time recently measured by single-molecule analysis in neuronal processes that was shorter by two orders of magnitude. Questioning the validity of previously used phenomenological interpretations of FDAP/FRAP data, we have generalized the standard two-state reaction-diffusion equations by 1), accounting for the parallel and discrete arrangement of MTs in cell processes (i.e., homogeneous versus heterogeneous distribution of tau-binding sites); and 2), explicitly considering both active (diffusion upon MTs) and passive (piggybacking upon MTs at rates of slow axonal transport) motion of bound tau. For some idealized cases, analytical solutions were derived. By comparing them with the full numerical solution and Monte Carlo simulations, the respective validity domains were mapped. Interpretation of our FDAP data (from processes of neuronally differentiated PC12 cells) in light of the heterogeneous formalism yielded independent estimates for the association (∼2 ms) and dwell (∼100 ms) times of tau to/on a single MT rather than in an MT array. The dwell time was shorter by orders of magnitude than that in a previous report where a homogeneous topology of MTs was assumed. We found that the diffusion of bound tau was negligible in vivo, in contrast to an earlier report that tau diffuses along the MT lattice in vitro. Methodologically, our results demonstrate that the heterogeneity of binding sites cannot be ignored when dealing with reaction-diffusion of cytoskeleton-associated proteins. Physiologically, the results reveal the behavior of tau in cellular processes
Pursuit-and-Evasion Reaction-Diffusion Waves in Microreactors with Tailored Geometry.
Zambrano, A; Zadorin, A S; Rondelez, Y; Estévez-Torres, A; Galas, J-C
2015-04-30
Out-of-equilibrium chemical systems may self-organize into structures displaying spatiotemporal order, such as traveling waves and Turing patterns. Because of its predictable chemistry, DNA has recently appeared as an interesting candidate to engineer these spatiotemporal structures. However, in addition to the intrinsic chemical parameters, initial and boundary conditions have a major impact on the final structure. Here we take advantage of microfluidics to design controlled reactors and investigate pursuit-and-evasion chemical waves generated by a DNA-based reaction network with Predator-Prey dynamics. We first propose two complementary microfabrication strategies to either control the initial condition or the two-dimensional geometry of the reactor where the waves develop. We subsequently use them to investigate the effect of curvature in wave propagation. We finally show that DNA-based waves can compute the optimal path within a maze. We thus suggest that coupling configurable microfluidics to programmable DNA-based dissipative reaction networks is a powerful route to investigate spatiotemporal order formation in chemistry. PMID:25839240
Spreading of infection in a two species reaction-diffusion process in networks.
Korosoglou, Paschalis; Kittas, Aristotelis; Argyrakis, Panos
2010-12-01
We study the dynamics of the infection of a two mobile species reaction from a single infected agent in a population of healthy agents. Historically, the main focus for infection propagation has been through spreading phenomena, where a random location of the system is initially infected and then propagates by successfully infecting its neighbor sites. Here both the infected and healthy agents are mobile, performing classical random walks. This may be a more realistic picture to such epidemiological models, such as the spread of a virus in communication networks of routers, where data travel in packets, the communication time of stations in ad hoc mobile networks, information spreading (such as rumor spreading) in social networks, etc. We monitor the density of healthy particles ρ(t), which we find in all cases to be an exponential function in the long-time limit in two-dimensional and three-dimensional lattices and Erdős-Rényi (ER) and scale-free (SF) networks. We also investigate the scaling of the crossover time t(c) from short- to long-time exponential behavior, which we find to be a power law in lattices and ER networks. This crossover is shown to be absent in SF networks, where we reveal the role of the connectivity of the network in the infection process. We compare this behavior to ER networks and lattices and highlight the significance of various connectivity patterns, as well as the important differences of this process in the various underlying geometries, revealing a more complex behavior of ρ(t).
21 CFR 862.1290 - Fatty acids test system.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 21 Food and Drugs 8 2013-04-01 2013-04-01 false Fatty acids test system. 862.1290 Section 862.1290....1290 Fatty acids test system. (a) Identification. A fatty acids test system is a device intended to measure fatty acids in plasma and serum. Measurements of fatty acids are used in the diagnosis...
21 CFR 862.1295 - Folic acid test system.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 21 Food and Drugs 8 2013-04-01 2013-04-01 false Folic acid test system. 862.1295 Section 862.1295....1295 Folic acid test system. (a) Identification. A folic acid test system is a device intended to measure the vitamin folic acid in plasma and serum. Folic acid measurements are used in the diagnosis...
An exact and efficient first passage time algorithm for reaction-diffusion processes on a 2D-lattice
NASA Astrophysics Data System (ADS)
Bezzola, Andri; Bales, Benjamin B.; Alkire, Richard C.; Petzold, Linda R.
2014-01-01
We present an exact and efficient algorithm for reaction-diffusion-nucleation processes on a 2D-lattice. The algorithm makes use of first passage time (FPT) to replace the computationally intensive simulation of diffusion hops in KMC by larger jumps when particles are far away from step-edges or other particles. Our approach computes exact probability distributions of jump times and target locations in a closed-form formula, based on the eigenvectors and eigenvalues of the corresponding 1D transition matrix, maintaining atomic-scale resolution of resulting shapes of deposit islands. We have applied our method to three different test cases of electrodeposition: pure diffusional aggregation for large ranges of diffusivity rates and for simulation domain sizes of up to 4096×4096 sites, the effect of diffusivity on island shapes and sizes in combination with a KMC edge diffusion, and the calculation of an exclusion zone in front of a step-edge, confirming statistical equivalence to standard KMC simulations. The algorithm achieves significant speedup compared to standard KMC for cases where particles diffuse over long distances before nucleating with other particles or being captured by larger islands.
Holloway, D. M.
1999-01-01
Semi-cell morphogenesis in unicellular desmid algae of the genus Micrasterias generates a stellar shape by repeated dichotomous branching of growing tips of the cell surface. The numerous species of the genus display variations of the branching pattern that differ markedly in number of branchings, lobe width and lobe length. We have modelled this morphogenesis, following previous work by D. M. Harrison and M. Kolar (1988), on the assumptions that patterning occurs by chemical reaction-diffusion activity within the plasma membrane, leading to morphological expression by patterned catalysis of the extension of the cell surface. The latter has been simulated in simplified form by two-dimensional computations. Our results indicate that for generation of repeated branchings and for the control of diverse species-specific shapes, the loss of patterning activity and of rapid growth in regions separating the active growing tips is an essential feature. We believe this conclusion to be much more general than the specific details of our model. We discuss the limitations of the model especially in terms of what extra features might be addressed in three-dimensional computation.
NASA Astrophysics Data System (ADS)
Simmons, Alex; Yang, Qianqian; Moroney, Timothy
2015-04-01
The numerical solution of fractional partial differential equations poses significant computational challenges in regard to efficiency as a result of the spatial nonlocality of the fractional differential operators. The dense coefficient matrices that arise from spatial discretisation of these operators mean that even one-dimensional problems can be difficult to solve using standard methods on grids comprising thousands of nodes or more. In this work we address this issue of efficiency for one-dimensional, nonlinear space-fractional reaction-diffusion equations with fractional Laplacian operators. We apply variable-order, variable-stepsize backward differentiation formulas in a Jacobian-free Newton-Krylov framework to advance the solution in time. A key advantage of this approach is the elimination of any requirement to form the dense matrix representation of the fractional Laplacian operator. We show how a banded approximation to this matrix, which can be formed and factorised efficiently, can be used as part of an effective preconditioner that accelerates convergence of the Krylov subspace iterative solver. Our approach also captures the full contribution from the nonlinear reaction term in the preconditioner, which is crucial for problems that exhibit stiff reactions. Numerical examples are presented to illustrate the overall effectiveness of the solver.
Mori, Yoichiro; Jilkine, Alexandra; Edelstein-Keshet, Leah
2011-01-01
We describe and analyze a bistable reaction-diffusion (RD) model for two interconverting chemical species that exhibits a phenomenon of wave-pinning: a wave of activation of one of the species is initiated at one end of the domain, moves into the domain, decelerates, and eventually stops inside the domain, forming a stationary front. The second (“inactive”) species is depleted in this process. This behavior arises in a model for chemical polarization of a cell by Rho GTPases in response to stimulation. The initially spatially homogeneous concentration profile (representative of a resting cell) develops into an asymmetric stationary front profile (typical of a polarized cell). Wave-pinning here is based on three properties: (1) mass conservation in a finite domain, (2) nonlinear reaction kinetics allowing for multiple stable steady states, and (3) a sufficiently large difference in diffusion of the two species. Using matched asymptotic analysis, we explain the mathematical basis of wave-pinning, and predict the speed and pinned position of the wave. An analysis of the bifurcation of the pinned front solution reveals how the wave-pinning regime depends on parameters such as rates of diffusion and total mass of the species. We describe two ways in which the pinned solution can be lost depending on the details of the reaction kinetics: a saddle-node or a pitchfork bifurcation. PMID:22171122
NASA Astrophysics Data System (ADS)
Xie, Yongqin; Zhu, Kaixuan; Sun, Chunyou
2012-08-01
In this paper, we introduce a new class of functions satisfying spacial absolutely continuous (see Definition 3.1), denoted by L2_{sac}({R};{R}n), which are translation bounded but not normal (see [S. S. Lu, H. Q. Wu, and C. K. Zhong, "Attractors for non-autonomous 2D Navier-Stokes equations with normal external forces," Discrete Contin. Dyn. Syst. A 13(3), 701-719 (2005)], 10.3934/dcds.2005.13.701 and Definition 3.1) in L2_{loc}({R};{R}n). Then the asymptotic a priori estimate is applied to some nonlinear reaction-diffusion equations with external forces g(x,s)in L2_{sac}({R};{R}n). We obtain the existence of uniform attractor together with its structure in the bi-spaces (L2({R}n), L2({R}n)) and (L2({R}n), Lp({R}n))(p>2) without any restriction on the growing order of the nonlinear term.
21 CFR 862.1795 - Vanilmandelic acid test system.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 21 Food and Drugs 8 2013-04-01 2013-04-01 false Vanilmandelic acid test system. 862.1795 Section... Systems § 862.1795 Vanilmandelic acid test system. (a) Identification. A vanilmandelic acid test system is a device intended to measure vanilmandelic acid in urine. Measurements of vanilmandelic...
Acid mine water aeration and treatment system
Ackman, Terry E.; Place, John M.
1987-01-01
An in-line system is provided for treating acid mine drainage which basically comprises the combination of a jet pump (or pumps) and a static mixer. The jet pump entrains air into the acid waste water using a Venturi effect so as to provide aeration of the waste water while further aeration is provided by the helical vanes of the static mixer. A neutralizing agent is injected into the suction chamber of the jet pump and the static mixer is formed by plural sections offset by 90 degrees.
Docosahexaenoic acid in neural signaling systems.
Crawford, Michael A
2006-01-01
Docosahexaenoic acid has been conserved in neural signalling systems in the cephalopods, fish, amphibian, reptiles, birds, mammals, primates and humans. This extreme conservation, despite wide genomic changes over 500 million years, testifies to a uniqueness of this molecule in the brain. The brain selectively incorporates docosahexaenoic acid and its rate of incorporation into the developing brain has been shown to be greater than ten times more efficient than its synthesis from the omega 3 fatty acids of land plant origin. Data has now been published demonstrating a significant influence of dietary omega 3 fatty acids on neural gene expression. As docosahexaenoic acid is the only omega 3 fatty acid in the brain, it is likely that it is the ligand involved. The selective uptake, requirement for function and stimulation of gene expression would have conferred an advantage to a primate which separated from the chimpanzees in the forests and woodlands and sought a different ecological niche. In view of the paucity of docosahexaenoic acid in the land food chain it is likely that the advantage would have been gained from a lacustrine or marine coastal habitat with access to food rich in docosahexaenoic acid and the accessory micronutrients, such as iodine, zinc, copper, manganese and selenium, of importance in brain development and protection against peroxidation. Land agricultural development has, in recent time, come to dominate the human food chain. The decline in use and availability of aquatic resources is not considered important by Langdon (2006) as he considers the resource was not needed for human evolution and can be replaced from the terrestrial food chain. This notion is not supported by the biochemistry nor the molecular biology. He misses the point that the shoreline hypothesis is not just dependent on docosahexaenoic acid but also on the other accessory nutrients specifically required by the brain. Moreover he neglects the basic principle of Darwinian
21 CFR 862.1509 - Methylmalonic acid (nonquantitative) test system.
Code of Federal Regulations, 2012 CFR
2012-04-01
... Test Systems § 862.1509 Methylmalonic acid (nonquantitative) test system. (a) Identification. A methylmalonic acid (nonquantitative) test system is a device intended to identify methylmalonic acid in urine... 21 Food and Drugs 8 2012-04-01 2012-04-01 false Methylmalonic acid (nonquantitative) test...
21 CFR 862.1509 - Methylmalonic acid (nonquantitative) test system.
Code of Federal Regulations, 2013 CFR
2013-04-01
... Test Systems § 862.1509 Methylmalonic acid (nonquantitative) test system. (a) Identification. A methylmalonic acid (nonquantitative) test system is a device intended to identify methylmalonic acid in urine... 21 Food and Drugs 8 2013-04-01 2013-04-01 false Methylmalonic acid (nonquantitative) test...
21 CFR 862.1509 - Methylmalonic acid (nonquantitative) test system.
Code of Federal Regulations, 2014 CFR
2014-04-01
... Test Systems § 862.1509 Methylmalonic acid (nonquantitative) test system. (a) Identification. A methylmalonic acid (nonquantitative) test system is a device intended to identify methylmalonic acid in urine... 21 Food and Drugs 8 2014-04-01 2014-04-01 false Methylmalonic acid (nonquantitative) test...
21 CFR 862.1775 - Uric acid test system.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 21 Food and Drugs 8 2010-04-01 2010-04-01 false Uric acid test system. 862.1775 Section 862.1775....1775 Uric acid test system. (a) Identification. A uric acid test system is a device intended to measure uric acid in serum, plasma, and urine. Measurements obtained by this device are used in the...
21 CFR 862.1775 - Uric acid test system.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 21 Food and Drugs 8 2013-04-01 2013-04-01 false Uric acid test system. 862.1775 Section 862.1775....1775 Uric acid test system. (a) Identification. A uric acid test system is a device intended to measure uric acid in serum, plasma, and urine. Measurements obtained by this device are used in the...
21 CFR 862.1775 - Uric acid test system.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 21 Food and Drugs 8 2014-04-01 2014-04-01 false Uric acid test system. 862.1775 Section 862.1775...) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Chemistry Test Systems § 862.1775 Uric acid test system. (a) Identification. A uric acid test system is a device intended to...
21 CFR 862.1775 - Uric acid test system.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 21 Food and Drugs 8 2012-04-01 2012-04-01 false Uric acid test system. 862.1775 Section 862.1775...) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Chemistry Test Systems § 862.1775 Uric acid test system. (a) Identification. A uric acid test system is a device intended to...
Nucleic acid detection systems for enteroviruses.
Rotbart, H A
1991-01-01
The enteroviruses comprise nearly 70 human pathogens responsible for a wide array of diseases including poliomyelitis, meningitis, myocarditis, and neonatal sepsis. Current diagnostic tests for the enteroviruses are limited in their use by the slow growth, or failure to grow, of certain serotypes in culture, the antigenic diversity among the serotypes, and the low titer of virus in certain clinical specimens. Within the past 6 years, applications of molecular cloning techniques, in vitro transcription vectors, automated nucleic acid synthesis, and the polymerase chain reaction have resulted in significant progress toward nucleic acid-based detection systems for the enteroviruses that take advantage of conserved genomic sequences across many, if not all, serotypes. Similar approaches to the study of enteroviral pathogenesis have already produced dramatic advances in our understanding of how these important viruses cause their diverse clinical spectra. PMID:1649002
Jiménez, Zulma A; Steinbock, Oliver
2012-08-31
Scroll rings are three-dimensional excitation waves rotating around one-dimensional filament loops. In experiments with the Belousov-Zhabotinsky reaction we show that the collapse of these loops can be stopped by local pinning to only two unexcitable heterogeneities. The resulting vortices rotate around stationary but curved filaments. The absence of filament motion can be explained by repulsive interaction that counteracts the expected curvature-induced motion. The shape and key dependencies of the stationary filaments are well described by a curvature-flow model with additive interaction velocities that rapidly decrease with filament distance.
Phytic acid interactions in food systems.
Cheryan, M
1980-01-01
Phytic acid is present in many plant systems, constituting about 1 to 5% by weight of many cereals and legumes. Concern about its presence in food arises from evidence that it decreases the bioavailability of many essential minerals by interacting with multivalent cations and/or proteins to form complexes that may be insoluble or otherwise unavailable under physiologic conditions. The precise structure of phytic acid and its salts is still a matter of controversy and lack of a good method of analysis is also a problem. It forms fairly stable chelates with almost all multivalent cations which are insoluble about pH 6 to 7, although pH, type, and concentration of cation have a tremendous influence on their solubility characteristics. In addition, at low pH and low cation concentration, phytate-protein complexes are formed due to direct electrostatic interaction, while at pH > 6 to 7, a ternary phytic acid-mineral-protein complex is formed which dissociates at high Na+ concentrations. These complexes appear to be responsible for the decreased bioavailability of the complexed minerals and are also more resistant to proteolytic digestion at low pH. Development of methods for producing low-phytate food products must take into account the nature and extent of the interactions between phytic acid and other food components. Simple mechanical treatment, such as milling, is useful for those seeds in which phytic acid tends to be localized in specific regions. Enzyme treatment, either directly with phytase or indirectly through the action of microorganisms, such as yeast during breadmaking, is quite effective, provided pH and other environmental conditions are favorable. It is also possible to produce low-phytate products by taking advantage of some specific interactions. For example, adjustment of pH and/or ionic strength so as to dissociate phytate-protein complexes and then using centrifugation or ultrafiltration (UF) has been shown to be useful. Phytic acid can also
Acid preservation systems for food products
Tiberio, J. E.; Cirigiano, M. C.
1984-10-16
Fumaric acid is used in combination with critical amounts of acetic acid to preserve acid containing food products from microbiological spoilage in the absence of or at reduced levels of chemical preservative.
Lysophosphatidic Acid signaling in the nervous system.
Yung, Yun C; Stoddard, Nicole C; Mirendil, Hope; Chun, Jerold
2015-02-18
The brain is composed of many lipids with varied forms that serve not only as structural components but also as essential signaling molecules. Lysophosphatidic acid (LPA) is an important bioactive lipid species that is part of the lysophospholipid (LP) family. LPA is primarily derived from membrane phospholipids and signals through six cognate G protein-coupled receptors (GPCRs), LPA1-6. These receptors are expressed on most cell types within central and peripheral nervous tissues and have been functionally linked to many neural processes and pathways. This Review covers a current understanding of LPA signaling in the nervous system, with particular focus on the relevance of LPA to both physiological and diseased states. PMID:25695267
Hydroxybenzoic acid isomers and the cardiovascular system
2014-01-01
Today we are beginning to understand how phytochemicals can influence metabolism, cellular signaling and gene expression. The hydroxybenzoic acids are related to salicylic acid and salicin, the first compounds isolated that have a pharmacological activity. In this review we examine how a number of hydroxyphenolics have the potential to ameliorate cardiovascular problems related to aging such as hypertension, atherosclerosis and dyslipidemia. The compounds focused upon include 2,3-dihydroxybenzoic acid (Pyrocatechuic acid), 2,5-dihydroxybenzoic acid (Gentisic acid), 3,4-dihydroxybenzoic acid (Protocatechuic acid), 3,5-dihydroxybenzoic acid (α-Resorcylic acid) and 3-monohydroxybenzoic acid. The latter two compounds activate the hydroxycarboxylic acid receptors with a consequence there is a reduction in adipocyte lipolysis with potential improvements of blood lipid profiles. Several of the other compounds can activate the Nrf2 signaling pathway that increases the expression of antioxidant enzymes, thereby decreasing oxidative stress and associated problems such as endothelial dysfunction that leads to hypertension as well as decreasing generalized inflammation that can lead to problems such as atherosclerosis. It has been known for many years that increased consumption of fruits and vegetables promotes health. We are beginning to understand how specific phytochemicals are responsible for such therapeutic effects. Hippocrates’ dictum of ‘Let food be your medicine and medicine your food’ can now be experimentally tested and the results of such experiments will enhance the ability of nutritionists to devise specific health-promoting diets. PMID:24943896
Hydroxybenzoic acid isomers and the cardiovascular system.
Juurlink, Bernhard H J; Azouz, Haya J; Aldalati, Alaa M Z; AlTinawi, Basmah M H; Ganguly, Paul
2014-01-01
Today we are beginning to understand how phytochemicals can influence metabolism, cellular signaling and gene expression. The hydroxybenzoic acids are related to salicylic acid and salicin, the first compounds isolated that have a pharmacological activity. In this review we examine how a number of hydroxyphenolics have the potential to ameliorate cardiovascular problems related to aging such as hypertension, atherosclerosis and dyslipidemia. The compounds focused upon include 2,3-dihydroxybenzoic acid (Pyrocatechuic acid), 2,5-dihydroxybenzoic acid (Gentisic acid), 3,4-dihydroxybenzoic acid (Protocatechuic acid), 3,5-dihydroxybenzoic acid (α-Resorcylic acid) and 3-monohydroxybenzoic acid. The latter two compounds activate the hydroxycarboxylic acid receptors with a consequence there is a reduction in adipocyte lipolysis with potential improvements of blood lipid profiles. Several of the other compounds can activate the Nrf2 signaling pathway that increases the expression of antioxidant enzymes, thereby decreasing oxidative stress and associated problems such as endothelial dysfunction that leads to hypertension as well as decreasing generalized inflammation that can lead to problems such as atherosclerosis. It has been known for many years that increased consumption of fruits and vegetables promotes health. We are beginning to understand how specific phytochemicals are responsible for such therapeutic effects. Hippocrates' dictum of 'Let food be your medicine and medicine your food' can now be experimentally tested and the results of such experiments will enhance the ability of nutritionists to devise specific health-promoting diets. PMID:24943896
NASA Astrophysics Data System (ADS)
Jahani, Fereidoun
In the model for microbially induced crown corrosion, the diffusion of sulfide inside the concrete pores, its biological conversion to sulfuric acid, and the corrosion of calcium carbonate aggregates are represented. The corrosion front is modeled as a moving boundary. The location of the interface between the corrosion layer and the concrete is determined as part of the solution to the model equations. This model consisted of a system of one dimensional reaction-diffusion equations coupled to an equation describing the movement of the corrosion front. The equations were solved numerically using finite element Galerkin approximation. The concentration profiles of sulfide in the air and the liquid phases, the pH as a function of concrete depth, and the position of the corrosion front. A new equation for the corrosion rate was also derived. A more specific model for the degradation of a concrete specimen exposed to a sulfuric acid solution was also studied. In this model, diffusion of hydrogen ions and their reaction with alkaline components of concrete were expressed using Fick's Law of diffusion. The model equations described the moving boundary, the dissolution rate of alkaline components in the concrete, volume increase of sulfuric acid solution over the concrete specimen, and the boundary conditions on the surface of the concrete. An apparatus was designed and experiments were performed to measure pH changes on the surface of concrete. The data were used to calculate the dissolution rate of the concrete and, with the model, to determine the diffusion rate of sulfuric acid in the corrosion layer and corrosion layer thickness. Electrochemical Impedance Spectroscopy (EIS) was used to study the corrosion rate of iron pins embedded in the concrete sample. The open circuit potential (OCP) determined the onset of corrosion on the surface of the pins. Visual observation of the corrosion layer thickness was in good agreement with the simulation results.
Amino acid isotopic analysis in agricultural systems
Technology Transfer Automated Retrieval System (TEKTRAN)
A relatively new approach to stable isotopic analysis—referred to as compound-specific isotopic analysis (CSIA)—has emerged, centering on the measurement of 15N:14N ratios in amino acids (glutamic acid and phenylalanine). CSIA has recently been used to generate trophic position estimates among anima...
Thoron-tartaric acid systems for spectrophotometric determination of thorium
Grimaldi, F.S.; Fletcher, M.H.
1956-01-01
Thoron is commonly used for the spectrophotometric determination of thorium. An undesirable feature of its use is its high sensitivity to zirconium. This study describes the use of tartaric acid as a masking reagent for zirconium. Three tartaric acid-thoron systems, developed for the determination of thorium, differ with respect to the concentrations of thoron and tartaric acid. Mesotartaric acid, used in one of the systems, is most effective in masking zirconium. The behavior of rarer elements, usually associated with thorium ores, is determined in two systems, and a dilution method is described for the direct determination of thorium in monazite concentrates.
Tested Demonstrations: Color Oscillations in the Formic Acid-Nitric Acid-Sulfuric Acid System.
ERIC Educational Resources Information Center
Raw, C. J. G.; And Others
1983-01-01
Presented are procedures for demonstrating the production of color oscillations when nitric acid is added to a formic acid/concentrated sulfuric acid mixture. Because of safety considerations, "Super-8" home movie of the color changes was found to be satisfactory for demonstration purposes. (JN)
NASA Astrophysics Data System (ADS)
MacDonald, G.; Mackenzie, J. A.; Nolan, M.; Insall, R. H.
2016-03-01
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.
Continuous-flow free acid monitoring method and system
Strain, J.E.; Ross, H.H.
1980-01-11
A free acid monitoring method and apparatus is provided for continuously measuring the excess acid present in a process stream. The disclosed monitoring system and method is based on the relationship of the partial pressure ratio of water and acid in equilibrium with an acid solution at constant temperature. A portion of the process stream is pumped into and flows through the monitor under the influence of gravity and back to the process stream. A continuous flowing sample is vaporized at a constant temperature and the vapor is subsequently condensed. Conductivity measurements of the condensate produces a nonlinear response function from which the free acid molarity of the sample process stream is determined.
Continuous-flow free acid monitoring method and system
Strain, James E.; Ross, Harley H.
1981-01-01
A free acid monitoring method and apparatus is provided for continuously measuring the excess acid present in a process stream. The disclosed monitoring system and method is based on the relationship of the partial pressure ratio of water and acid in equilibrium with an acid solution at constant temperature. A portion of the process stream is pumped into and flows through the monitor under the influence of gravity and back to the process stream. A continuous flowing sample is vaporized at a constant temperature and the vapor is subsequently condensed. Conductivity measurements of the condensate produces a nonlinear response function from which the free acid molarity of the sample process stream is determined.
Nucleic acid detection system and method for detecting influenza
Cai, Hong; Song, Jian
2015-03-17
The invention provides a rapid, sensitive and specific nucleic acid detection system which utilizes isothermal nucleic acid amplification in combination with a lateral flow chromatographic device, or DNA dipstick, for DNA-hybridization detection. The system of the invention requires no complex instrumentation or electronic hardware, and provides a low cost nucleic acid detection system suitable for highly sensitive pathogen detection. Hybridization to single-stranded DNA amplification products using the system of the invention provides a sensitive and specific means by which assays can be multiplexed for the detection of multiple target sequences.
Amino acid auxotrophy as a system of immunological control nodes.
Murray, Peter J
2016-02-01
Cells of the immune system are auxotrophs for most amino acids, including several nonessential ones. Arginine and tryptophan are used within the regulatory immune networks to control proliferation and function through pathways that actively deplete the amino acid from the microenvironment or that create regulatory molecules such as nitric oxide or kynurenines. How immune cells integrate information about essential amino acid supplies and then transfer these signals to growth and activation pathways remains unclear but has potential for pathway discovery about amino sensing. In applied research, strategies to harness amino acid auxotrophy so as to block cancerous lymphocyte growth have been attempted for decades with limited success. Emerging insights about amino acid metabolism may lead to new strategies in clinical medicine whereby both amino acid auxotrophy and the immunoregulatory pathways controlled by amino acids can be manipulated.
System for agitating the acid in a lead-acid battery
Weintraub, Alvin; MacCormack, Robert S.
1987-01-01
A system and method for agitating the acid in a large lead-sulfuric acid storage battery of the calcium type. An air-lift is utilized to provide the agitation. The air fed to the air-lift is humidified prior to being delivered to the air-lift.
Klika, Václav; Baker, Ruth E; Headon, Denis; Gaffney, Eamonn A
2012-04-01
Understanding the mechanisms governing and regulating self-organisation in the developing embryo is a key challenge that has puzzled and fascinated scientists for decades. Since its conception in 1952 the Turing model has been a paradigm for pattern formation, motivating numerous theoretical and experimental studies, though its verification at the molecular level in biological systems has remained elusive. In this work, we consider the influence of receptor-mediated dynamics within the framework of Turing models, showing how non-diffusing species impact the conditions for the emergence of self-organisation. We illustrate our results within the framework of hair follicle pre-patterning, showing how receptor interaction structures can be constrained by the requirement for patterning, without the need for detailed knowledge of the network dynamics. Finally, in the light of our results, we discuss the ability of such systems to pattern outside the classical limits of the Turing model, and the inherent dangers involved in model reduction. PMID:22072186
Recognition of Endogenous Nucleic Acids by the Innate Immune System.
Roers, Axel; Hiller, Björn; Hornung, Veit
2016-04-19
Recognition of DNA and RNA by endosomal and cytosolic sensors constitutes a central element in the detection of microbial invaders by the innate immune system. However, the capacity of these sensors to discriminate between microbial and endogenous nucleic acids is limited. Over the past few years, evidence has accumulated to suggest that endogenous DNA or RNA species can engage nucleic-acid-sensing pattern-recognition receptors that can trigger or sustain detrimental pathology. Here, we review principles of how the activation of innate sensors by host nucleic acids is prevented in the steady state and discuss four important determinants of whether a nucleic-acid-driven innate response is mounted. These include structural features of the ligand being sensed, the subcellular location and quantity of pathogen-derived or endogenous nucleic acids, and the regulation of sensor-activation thresholds. Furthermore, we emphasize disease mechanisms initiated by failure to discriminate self from non-self in nucleic acid detection.
Amino Acid Synthesis in a Supercritical Carbon Dioxide - Water System
Fujioka, Kouki; Futamura, Yasuhiro; Shiohara, Tomoo; Hoshino, Akiyoshi; Kanaya, Fumihide; Manome, Yoshinobu; Yamamoto, Kenji
2009-01-01
Mars is a CO2-abundant planet, whereas early Earth is thought to be also CO2-abundant. In addition, water was also discovered on Mars in 2008. From the facts and theory, we assumed that soda fountains were present on both planets, and this affected amino acid synthesis. Here, using a supercritical CO2/liquid H2O (10:1) system which mimicked crust soda fountains, we demonstrate production of amino acids from hydroxylamine (nitrogen source) and keto acids (oxylic acid sources). In this research, several amino acids were detected with an amino acid analyzer. Moreover, alanine polymers were detected with LC-MS. Our research lights up a new pathway in the study of life’s origin. PMID:19582225
300 Area waste acid treatment system closure plan. Revision 1
1996-03-01
This section provides a description of the Hanford Site, identifies the proposed method of 300 Area Waste Acid Treatment System (WATS) closure, and briefly summarizes the contents of each chapter of this plan.
Acid-base homeostasis in the human system
NASA Technical Reports Server (NTRS)
White, R. J.
1974-01-01
Acid-base regulation is a cooperative phenomena in vivo with body fluids, extracellular and intracellular buffers, lungs, and kidneys all playing important roles. The present account is much too brief to be considered a review of present knowledge of these regulatory systems, and should be viewed, instead, as a guide to the elements necessary to construct a simple model of the mutual interactions of the acid-base regulatory systems of the body.
NASA Astrophysics Data System (ADS)
Zolotareva, N. D.; Nikolaev, E. S.
2016-05-01
An iterative process implementing an adaptive hp-version of the finite element method (FEM) previously proposed by the authors for the approximate solution of boundary value problems for the stationary reaction-diffusion equation is described. The method relies on piecewise polynomial basis functions and makes use of an adaptive strategy for constructing a sequence of finite-dimensional subspaces based on the computation of correction indicators. Singularly perturbed boundary value test problems with smooth and not very smooth solutions are used to analyze the efficiency of the method in the situation when an approximate solution has to be found with high accuracy. The convergence of the approximate solution to the exact one is investigated depending on the value of the small parameter multiplying the highest derivative, on the family of basis functions and the quadrature formulas used, and on the internal parameters of the method. The method is compared with an adaptive h-version of FEM that also relies on correction indicators and with its nonadaptive variant based on the bisection of grid intervals.
Denaro, Giovanni; Valenti, Davide; Spagnolo, Bernardo; Basilone, Gualtiero; Mazzola, Salvatore; Zgozi, Salem W.; Aronica, Salvatore; Bonanno, Angelo
2013-01-01
A stochastic advection-reaction-diffusion model with terms of multiplicative white Gaussian noise, valid for weakly mixed waters, is studied to obtain the vertical stationary spatial distributions of two groups of picophytoplankton, i.e., picoeukaryotes and Prochlorococcus, which account about for 60% of total chlorophyll on average in Mediterranean Sea. By numerically solving the equations of the model, we analyze the one-dimensional spatio-temporal dynamics of the total picophytoplankton biomass and nutrient concentration along the water column at different depths. In particular, we integrate the equations over a time interval long enough, obtaining the steady spatial distributions for the cell concentrations of the two picophytoplankton groups. The results are converted into chlorophyll a and divinil chlorophyll a concentrations and compared with experimental data collected in two different sites of the Sicily Channel (southern Mediterranean Sea). The comparison shows that real distributions are well reproduced by theoretical profiles. Specifically, position, shape and magnitude of the theoretical deep chlorophyll maximum exhibit a good agreement with the experimental values. PMID:23826130
Babu, Ellappan; Kanai, Yoshikatsu; Chairoungdua, Arthit; Kim, Do Kyung; Iribe, Yuji; Tangtrongsup, Sahatchai; Jutabha, Promsuk; Li, Yuewei; Ahmed, Nesar; Sakamoto, Shinichi; Anzai, Naohiko; Nagamori, Seishi; Endou, Hitoshi
2003-10-31
A cDNA that encodes a novel Na+-independent neutral amino acid transporter was isolated from FLC4 human hepatocarcinoma cells by expression cloning. When expressed in Xenopus oocytes, the encoded protein designated LAT3 (L-type amino acid transporter 3) transported neutral amino acids such as l-leucine, l-isoleucine, l-valine, and l-phenylalanine. The LAT3-mediated transport was Na+-independent and inhibited by 2-aminobicyclo[2.2.1]heptane-2-carboxylic acid, consistent with the properties of system L. Distinct from already known system L transporters LAT1 and LAT2, which form heterodimeric complex with 4F2 heavy chain, LAT3 was functional by itself in Xenopus oocytes. The deduced amino acid sequence of LAT3 was identical to the gene product of POV1 reported as a prostate cancer-up-regulated gene whose function was not determined, whereas it did not exhibit significant similarity to already identified transporters. The Eadie-Hofstee plots of LAT3-mediated transport were curvilinear, whereas the low affinity component is predominant at physiological plasma amino acid concentration. In addition to amino acid substrates, LAT3 recognized amino acid alcohols. The transport of l-leucine was electroneutral and mediated by a facilitated diffusion. In contrast, l-leucinol, l-valinol, and l-phenylalaninol, which have a net positive charge induced inward currents under voltage clamp, suggesting these compounds are transported by LAT3. LAT3-mediated transport was inhibited by the pretreatment with N-ethylmaleimide, consistent with the property of system L2 originally characterized in hepatocyte primary culture. Based on the substrate selectivity, affinity, and N-ethylmaleimide sensitivity, LAT3 is proposed to be a transporter subserving system L2. LAT3 should denote a new family of organic solute transporters. PMID:12930836
Gabboun, N H; Najib, N M; Ibrahim, H G; Assaf, S
2001-01-01
Release of salicylic acid, diclofenac acid, diclofenac diethylamine and diclofenac sodium, from lyotropic structured systems, namely; neat and middle liquid crystalline phases, across mid-dorsal hairless rat skin into aqueous buffer were studied. Release results were compared with those from the isotropic systems. The donor systems composed of the surfactant polyoxyethylene (20) isohexadecyl ether, HCl buffer of pH 1 or distilled water and the specific drug. High performance liquid chromatography (HPLC) methods were used to monitor the transfer of the drugs across the skin barrier. Results indicated that the rate-determining step in the transport process was the release of the drug from the specified donor system. Further, apparent zero order release was demonstrated with all systems. Except for diclofenac sodium, drug fluxes decreased as the donor medium changed from isotropic to anisotropic. The decrease in fluxes was probably due to the added constrains on the movement of drug molecules. By changing the anisotropic donor medium from neat to middle phase, drug flux decreased in case of salicylic acid and diclofenac sodium. In the mean time, flux increased in case of the diethylamine salt and appeared nearly similar in case of diclofenac acid. Rates of drug transfer across the skin from the anisotropic donors seemed to be largely controlled by the entropy contribution to the transport process. The type and extent of drug-liquid crystal interactions probably influenced the latter.
Microbial Nucleic Acid Sensing in Oral and Systemic Diseases.
Crump, K E; Sahingur, S E
2016-01-01
One challenge in studying chronic infectious and inflammatory disorders is understanding how host pattern recognition receptors (PRRs), specifically toll-like receptors (TLRs), sense and respond to pathogen- or damage-associated molecular patterns, their communication with each other and different components of the immune system, and their role in propagating inflammatory stages of disease. The discovery of innate immune activation through nucleic acid recognition by intracellular PRRs such as endosomal TLRs (TLR3, TLR7, TLR8, and TLR9) and cytoplasmic proteins (absent in melanoma 2 and DNA-dependent activator of interferon regulatory factor) opened a new paradigm: Nucleic acid sensing is now implicated in multiple immune and inflammatory conditions (e.g., atherosclerosis, cancer), viral (e.g., human papillomavirus, herpes virus) and bacterial (e.g., Helicobacter pylori, pneumonia) diseases, and autoimmune disorders (e.g., systemic lupus erythematosus, rheumatoid arthritis). Clinical investigations reveal the overexpression of specific nucleic acid sensors in diseased tissues. In vivo animal models show enhanced disease progression associated with receptor activation. The involvement of nucleic acid sensors in various systemic conditions is further supported by studies reporting receptor knockout mice being either protected from or prone to disease. TLR9-mediated inflammation is also implicated in periodontal diseases. Considering that persistent inflammation in the oral cavity is associated with systemic diseases and that oral microbial DNA is isolated at distal sites, nucleic acid sensing may potentially be a link between oral and systemic diseases. In this review, we discuss recent advances in how intracellular PRRs respond to microbial nucleic acids and emerging views on the role of nucleic acid sensors in various systemic diseases. We also highlight new information on the role of intracellular PRRs in the pathogenesis of oral diseases including periodontitis
21 CFR 862.1095 - Ascorbic acid test system.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 21 Food and Drugs 8 2012-04-01 2012-04-01 false Ascorbic acid test system. 862.1095 Section 862.1095 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Chemistry Test Systems §...
21 CFR 862.1095 - Ascorbic acid test system.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 21 Food and Drugs 8 2011-04-01 2011-04-01 false Ascorbic acid test system. 862.1095 Section 862.1095 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Chemistry Test Systems §...
21 CFR 862.1290 - Fatty acids test system.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 21 Food and Drugs 8 2014-04-01 2014-04-01 false Fatty acids test system. 862.1290 Section 862.1290 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Chemistry Test Systems §...
21 CFR 862.1295 - Folic acid test system.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 21 Food and Drugs 8 2012-04-01 2012-04-01 false Folic acid test system. 862.1295 Section 862.1295 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Chemistry Test Systems §...
21 CFR 862.1095 - Ascorbic acid test system.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 21 Food and Drugs 8 2014-04-01 2014-04-01 false Ascorbic acid test system. 862.1095 Section 862.1095 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Chemistry Test Systems §...
21 CFR 862.1295 - Folic acid test system.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 21 Food and Drugs 8 2011-04-01 2011-04-01 false Folic acid test system. 862.1295 Section 862.1295 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Chemistry Test Systems §...
21 CFR 862.1295 - Folic acid test system.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 21 Food and Drugs 8 2014-04-01 2014-04-01 false Folic acid test system. 862.1295 Section 862.1295 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Chemistry Test Systems §...
21 CFR 862.1290 - Fatty acids test system.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 21 Food and Drugs 8 2012-04-01 2012-04-01 false Fatty acids test system. 862.1290 Section 862.1290 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Chemistry Test Systems §...
21 CFR 862.1320 - Gastric acidity test system.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 21 Food and Drugs 8 2012-04-01 2012-04-01 false Gastric acidity test system. 862.1320 Section 862.1320 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Chemistry Test Systems §...
21 CFR 862.1290 - Fatty acids test system.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 21 Food and Drugs 8 2010-04-01 2010-04-01 false Fatty acids test system. 862.1290 Section 862.1290 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Chemistry Test Systems §...
21 CFR 862.1095 - Ascorbic acid test system.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 21 Food and Drugs 8 2013-04-01 2013-04-01 false Ascorbic acid test system. 862.1095 Section 862.1095 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Chemistry Test Systems §...
21 CFR 862.1095 - Ascorbic acid test system.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 21 Food and Drugs 8 2010-04-01 2010-04-01 false Ascorbic acid test system. 862.1095 Section 862.1095 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Chemistry Test Systems §...
21 CFR 862.1290 - Fatty acids test system.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 21 Food and Drugs 8 2011-04-01 2011-04-01 false Fatty acids test system. 862.1290 Section 862.1290 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Chemistry Test Systems §...
21 CFR 862.1295 - Folic acid test system.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 21 Food and Drugs 8 2010-04-01 2010-04-01 false Folic acid test system. 862.1295 Section 862.1295 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Chemistry Test Systems §...
21 CFR 862.1320 - Gastric acidity test system.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 21 Food and Drugs 8 2014-04-01 2014-04-01 false Gastric acidity test system. 862.1320 Section 862.1320 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Chemistry Test Systems §...
21 CFR 862.1655 - Pyruvic acid test system.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 21 Food and Drugs 8 2014-04-01 2014-04-01 false Pyruvic acid test system. 862.1655 Section 862.1655 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Chemistry Test Systems §...
21 CFR 862.1655 - Pyruvic acid test system.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 21 Food and Drugs 8 2011-04-01 2011-04-01 false Pyruvic acid test system. 862.1655 Section 862.1655 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Chemistry Test Systems §...
Dissolution state of cellulose in aqueous systems. 2. Acidic solvents.
Alves, Luis; Medronho, Bruno; Antunes, Filipe E; Topgaard, Daniel; Lindman, Björn
2016-10-20
Cellulose is insoluble in water but can be dissolved in strong acidic or alkaline conditions. How well dissolved cellulose is in solution and how it organizes are key questions often neglected in literature. The typical low pH required for dissolving cellulose in acidic solvents limits the use of typical characterization techniques. In this respect, Polarization Transfer Solid State NMR (PT ssNMR) emerges as a reliable alternative. In this work, combining PT ssNMR, microscopic techniques and X-ray diffraction, a set of different acidic systems (phosphoric acid/water, sulfuric acid/glycerol and zinc chloride/water) is investigated. The studied solvent systems are capable to efficiently dissolve cellulose, although degradation occurs to some extent. PT ssNMR is capable to identify the liquid and solid fractions of cellulose, the degradation products and it is also sensitive to gelation. The materials regenerated from the acidic dopes were found to be highly sensitive to the solvent system and to the presence of amphiphilic additives in solution. PMID:27474617
Jasmonic acid and salicylic acid activate a common defense system in rice
Tamaoki, Daisuke; Seo, Shigemi; Yamada, Shoko; Kano, Akihito; Miyamoto, Ayumi; Shishido, Hodaka; Miyoshi, Seika; Taniguchi, Shiduku; Akimitsu, Kazuya; Gomi, Kenji
2013-01-01
Jasmonic acid (JA) and salicylic acid (SA) play important roles in plant defense systems. JA and SA signaling pathways interact antagonistically in dicotyledonous plants, but, the status of crosstalk between JA and SA signaling is unknown in monocots. Our rice microarray analysis showed that more than half of the genes upregulated by the SA analog BTH are also upregulated by JA, suggesting that a major portion of the SA-upregulated genes are regulated by JA-dependent signaling in rice. A common defense system that is activated by both JA and SA is thus proposed which plays an important role in pathogen defense responses in rice. PMID:23518581
Phase diagram of a system of adipic, glutaric, and sebacic acids
NASA Astrophysics Data System (ADS)
Kolyado, A. V.; Alenova, S. M.; Garkushin, I. K.
2016-06-01
Adipic acid-glutaric acid, glutaric acid-sebacic acid, and adipic acid-sebacic acid binary systems are studied, along with an adipic acid-glutaric acid-sebacic acid ternary system. It is shown all of these systems are eutectic. Phase equilibria for the diagram elements of the binary systems and the ternary system are described. It is concluded that the above low-melting compounds can be recommended for use as working bodies in heat accumulators, and for preparing electrolytes used in the thin-layer anodic oxidation of aluminum alloys.
Gas dilution system results and application to acid rain utilities
Jolley-Souders, K.; Geib, R.; Dunn, C.
1997-12-31
In 1997, the United States EPA will remove restrictions preventing acid rain utilities from using gas dilution systems for calibration or linearity studies for continuous emissions monitoring, Test Method 205 in 40CFR51 requires that a gas dilution system must produce calibration gases whose measured values are within {+-}2% of predicted values. This paper presents the evaluation of the Environics/CalMat 2020 Dilution System for use in calibration studies. Internal studies show that concentrations generated by this unit are within {+-}0.5% of predicted values. Studies are being conducted by several acid rain utilities to evaluate the Environics/CalMat system using single minor component calibration standards. In addition, an internally generated study is being performed to demonstrate the system`s accuracy using a multi-component gas mixture. Data from these tests will be presented in the final version of the paper.
300 Area waste acid treatment system closure plan
LUKE, S.N.
1999-05-17
The Hanford Facility Dangerous Waste Permit Application is considered to be a single application organized into a General Information Portion (document number DOERL-91-28) and a Unit-Specific Portion. The scope of the Unit-Specific Portion includes closure plan documentation submitted for individual, treatment, storage, and/or disposal units undergoing closure, such as the 300 Area Waste Acid Treatment System. Documentation contained in the General Information Portion is broader in nature and could be used by multiple treatment, storage, and/or disposal units (e.g., the glossary provided in the General Information Portion). Whenever appropriate, 300 Area Waste Acid Treatment System documentation makes cross-reference to the General Information Portion, rather than duplicating text. This 300 Area Waste Acid Treatment System Closure Plan (Revision 2) includes a Hanford Facility Dangerous Waste Permit Application, Part A, Form 3. Information provided in this closure plan is current as of April 1999.
Bile acid nuclear receptor FXR and digestive system diseases
Ding, Lili; Yang, Li; Wang, Zhengtao; Huang, Wendong
2015-01-01
Bile acids (BAs) are not only digestive surfactants but also important cell signaling molecules, which stimulate several signaling pathways to regulate some important biological processes. The bile-acid-activated nuclear receptor, farnesoid X receptor (FXR), plays a pivotal role in regulating bile acid, lipid and glucose homeostasis as well as in regulating the inflammatory responses, barrier function and prevention of bacterial translocation in the intestinal tract. As expected, FXR is involved in the pathophysiology of a wide range of diseases of gastrointestinal tract, including inflammatory bowel disease, colorectal cancer and type 2 diabetes. In this review, we discuss current knowledge of the roles of FXR in physiology of the digestive system and the related diseases. Better understanding of the roles of FXR in digestive system will accelerate the development of FXR ligands/modulators for the treatment of digestive system diseases. PMID:26579439
Bile acid nuclear receptor FXR and digestive system diseases.
Ding, Lili; Yang, Li; Wang, Zhengtao; Huang, Wendong
2015-03-01
Bile acids (BAs) are not only digestive surfactants but also important cell signaling molecules, which stimulate several signaling pathways to regulate some important biological processes. The bile-acid-activated nuclear receptor, farnesoid X receptor (FXR), plays a pivotal role in regulating bile acid, lipid and glucose homeostasis as well as in regulating the inflammatory responses, barrier function and prevention of bacterial translocation in the intestinal tract. As expected, FXR is involved in the pathophysiology of a wide range of diseases of gastrointestinal tract, including inflammatory bowel disease, colorectal cancer and type 2 diabetes. In this review, we discuss current knowledge of the roles of FXR in physiology of the digestive system and the related diseases. Better understanding of the roles of FXR in digestive system will accelerate the development of FXR ligands/modulators for the treatment of digestive system diseases. PMID:26579439
NASA Astrophysics Data System (ADS)
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
Status of commercial phosphoric acid fuel cell system development
NASA Technical Reports Server (NTRS)
Warshay, M.; Prokopius, P. R.; Simons, S. N.; King, R. B.
1981-01-01
A review of the current commercial phosphoric acid fuel cell system development efforts is presented. In both the electric utility and on-site integrated energy system applications, reducing cost and increasing reliability are important. The barrier to the attainment of these goals has been materials. The differences in approach among the three major participants are their technological features, including electrodes, matrices, intercell cooling, bipolar/separator plates, electrolyte management, fuel selection and system design philosophy.
NASA Astrophysics Data System (ADS)
Zhao, Qi; Yi, Ming; Liu, Yan
2011-10-01
The mitogen-activated protein kinase (MAPK) cascade plays a critical role in the control of cell growth. Deregulation of this pathway contributes to the development of many cancers. To better understand its signal transduction, we constructed a reaction-diffusion model for the MAPK pathway. We modeled the three layers of phosphorylation-dephosphorylation reactions and diffusion processes from the cell membrane to the nucleus. Based on different types of feedback in the MAPK cascade, four operation modes are introduced. For each of the four modes, spatial distributions and dose-response curves of active kinases (i.e. ppMAPK) are explored by numerical simulation. The effects of propagation length, diffusion coefficient and feedback strength on the pathway dynamics are investigated. We found that intrinsic bistability in the MAPK cascade can generate a traveling wave of ppMAPK with constant amplitude when the propagation length is short. ppMAPK in this mode of intrinsic bistability decays more slowly than it does in all other modes as the propagation length increases. Moreover, we examined the global and local responses to Ras-GTP of these four modes, and demonstrated how the shapes of these dose-response curves change as the propagation length increases. Also, we found that larger diffusion constant gives a higher response level on the zero-order regime and makes the ppMAPK profiles flatter under strong Ras-GTP stimulus. Furthermore, we observed that spatial responses of ppMAPK are more sensitive to negative feedback than to positive feedback in the broader signal range. Finally, we showed how oscillatory signals pass through the kinase cascade, and found that high frequency signals are damped faster than low frequency ones.
Action of chlorogenic acid on the complement system.
Ejzemberg, R; Da Silva, M H; Pinto, L; Mors, W B
1999-01-01
Previous research on plants used in folk medicine as antidotes against snake-bite revealed some constituents responsible for such protection. Chlorogenic acid (3-0-caffeoyl quinic acid) was one of these substances, studied with more attention. It has been shown that this substance binds to proteins through hydrophobic interactions and hydrogen bonds. This paper shows the preliminary results about the anti-complementary action of chlorogenic acid. Human and guinea pig sera, treated with chlorogenic acid, were added to the hemolytic system (sheep erythrocyte sensitized with hemolysin) to study its effect on the activation of the classical complement pathway. The action on the alternative pathway was studied with human serum treated with chlorogenic acid and zymosan. Our results show that chlorogenic acid presents anti-complementary action at the classical pathway, since the sera are not able to lysis the indicator system. The presence of C3b fragments on the surface of the yeast cells demonstrates that the alternative pathway was not affected. PMID:10412494
Phorbic Acid Biosynthesis in the Latex Vessel System of Euphorbia
Nordal, Arnold; Benson, A. A.
1969-01-01
Evidence is presented that phorbic acid is formed in the latex producing cell system, rather than in photosynthetic or chlorophyll-free tissues of Euphorbia resinifera Berg. When a branch of the plant was kept first in a 14CO2 atmosphere with 12 hr light-dark periods for 2 days and then left under natural conditions in the air outside for at least 2 to 3 days, radioactive phorbic acid was found in the latex. Phorbic acid synthesis appeared to be independent of the photosynthetic and respiratory activities of the plant. Besides phorbic acid 2 other major radioactive compounds were recognized in the latex, a glycoside or oligosaccharide, and a lipid belonging to the group of triterpenoid compounds characteristic of the latex in several species of Euphorbia. Images PMID:16657036
Difference between Chitosan Hydrogels via Alkaline and Acidic Solvent Systems
Nie, Jingyi; Wang, Zhengke; Hu, Qiaoling
2016-01-01
Chitosan (CS) has generated considerable interest for its desirable properties and wide applications. Hydrogel has been proven to be a major and vital form in the applications of CS materials. Among various types of CS hydrogels, physical cross-linked CS hydrogels are popular, because they avoided the potential toxicity and sacrifice of intrinsic properties caused by cross-linking or reinforcements. Alkaline solvent system and acidic solvent system are two important solvent systems for the preparation of physical cross-linked CS hydrogels, and also lay the foundations of CS hydrogel-based materials in many aspects. As members of physical cross-linked CS hydrogels, gel material via alkaline solvent system showed significant differences from that via acidic solvent system, but the reasons behind are still unexplored. In the present work, we studied the difference between CS hydrogel via alkaline system and acidic system, in terms of gelation process, hydrogel structure and mechanical property. In-situ/pseudo in-situ studies were carried out, including fluorescent imaging of gelation process, which provided dynamic visualization. Finally, the reasons behind the differences were explained, accompanied by the discussion about design strategy based on gelation behavior of the two systems. PMID:27786262
High Level Waste System Impacts from Acid Dissolution of Sludge
KETUSKY, EDWARD
2006-04-20
This research evaluates the ability of OLI{copyright} equilibrium based software to forecast Savannah River Site High Level Waste system impacts from oxalic acid dissolution of Tank 1-15 sludge heels. Without further laboratory and field testing, only the use of oxalic acid can be considered plausible to support sludge heel dissolution on multiple tanks. Using OLI{copyright} and available test results, a dissolution model is constructed and validated. Material and energy balances, coupled with the model, identify potential safety concerns. Overpressurization and overheating are shown to be unlikely. Corrosion induced hydrogen could, however, overwhelm the tank ventilation. While pH adjustment can restore the minimal hydrogen generation, resultant precipitates will notably increase the sludge volume. OLI{copyright} is used to develop a flowsheet such that additional sludge vitrification canisters and other negative system impacts are minimized. Sensitivity analyses are used to assess the processability impacts from variations in the sludge/quantities of acids.
21 CFR 862.3580 - Lysergic acid diethylamide (LSD) test system.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 21 Food and Drugs 8 2011-04-01 2011-04-01 false Lysergic acid diethylamide (LSD) test system. 862... Test Systems § 862.3580 Lysergic acid diethylamide (LSD) test system. (a) Identification. A lysergic acid diethylamide (LSD) test system is a device intended to measure lysergic acid diethylamide,...
21 CFR 862.3580 - Lysergic acid diethylamide (LSD) test system.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 21 Food and Drugs 8 2010-04-01 2010-04-01 false Lysergic acid diethylamide (LSD) test system. 862... Test Systems § 862.3580 Lysergic acid diethylamide (LSD) test system. (a) Identification. A lysergic acid diethylamide (LSD) test system is a device intended to measure lysergic acid diethylamide,...
Quasi-steady state reduction for compartmental systems
NASA Astrophysics Data System (ADS)
Goeke, Alexandra; Lax, Christian
2016-07-01
We present a method to determine an asymptotic reduction (in the sense of Tikhonov and Fenichel) for singularly perturbed compartmental systems in the presence of slow transport. It turns out that the reduction can be derived from the individual interaction terms alone. We apply the result to spatially discretized reaction-diffusion systems and obtain (based on the reduced discretized systems) a heuristic to reduce reaction-diffusion systems in presence of slow diffusion.
Fumaric acid esters: an alternative systemic treatment for psoriasis.
Ameen, M; Russell-Jones, R
1999-09-01
We report the successful clearance of severe chronic plaque psoriasis following treatment with fumaric acid esters (FAE) in two patients who had failed previous systemic therapy. FAE is gaining increasing acceptance for the treatment of psoriasis in countries such as Germany and the Netherlands, but at present remains unlicensed in Britain.
21 CFR 862.1509 - Methylmalonic acid (nonquantitative) test system.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 21 Food and Drugs 8 2010-04-01 2010-04-01 false Methylmalonic acid (nonquantitative) test system. 862.1509 Section 862.1509 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN... methylmalonic aciduria, a heritable metabolic disorder which, if untreated, may cause mental retardation....
21 CFR 862.1305 - Formiminoglutamic acid (FIGLU) test system.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 21 Food and Drugs 8 2012-04-01 2012-04-01 false Formiminoglutamic acid (FIGLU) test system. 862.1305 Section 862.1305 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical...
21 CFR 862.1305 - Formiminoglutamic acid (FIGLU) test system.
Code of Federal Regulations, 2014 CFR
2014-04-01
... 21 Food and Drugs 8 2014-04-01 2014-04-01 false Formiminoglutamic acid (FIGLU) test system. 862.1305 Section 862.1305 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical...
21 CFR 862.1305 - Formiminoglutamic acid (FIGLU) test system.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 21 Food and Drugs 8 2010-04-01 2010-04-01 false Formiminoglutamic acid (FIGLU) test system. 862.1305 Section 862.1305 Food and Drugs FOOD AND DRUG ADMINISTRATION, DEPARTMENT OF HEALTH AND HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical...
Skin delivery of ferulic acid from different vesicular systems.
Chen, Ming; Liu, Xiangli; Fahr, Alfred
2010-10-01
The aim of the present research is to evaluate the skin delivery capabilities of different vesicular systems, including conventional liposomes (CL), Tween 80-based deformable liposomes (DL), invasomes (INS) and ethosomes bearing ferulic acid (FA) being an antioxidant exhibiting a wide range of therapeutic effects against various diseases. All of the test formulations were characterized for particle size distribution, zeta-potential, vesicular shape and surface morphology, in vitro human skin permeation and skin deposition. Dynamic Light Scattering (DLS) and Transmission Electron Microscopy (TEM) defined that all of liposomal vesicles were almost spherical, displaying unilamellar structures with low polydispersity (PDI < 0.2) and nanometric size range (z-average no more than 150 nm). In addition, all the vesicular systems except conventional liposomes were negatively charged to a certain extent. In vitro skin permeation and skin deposition experiments demonstrated that the permeation profile of ferulic acid through human stratum corneum epidermis membrane (SCE) and the drug deposition in skin were both improved significantly using these vesicular liposomal systems. Permeation and skin deposition enhancing effect was highlighted by the ethosomal system containing 18.0 mg/ml of ferulic acid with an significantly (P < 0.01) enhanced skin flux (267.8 +/- 16.77 microg/cm2/h) and skin drug deposition (51.67 +/- 1.94 microg/cm2), which was 75 times and 7.3 times higher than those of ferulic acid from saturated PBS (pH 7.4) solution, respectively. This study demonstrated that ethosomes are promising vesicular carriers for delivering ferulic acid into or across the skin. PMID:21329050
Advancing polymeric delivery systems amidst a nucleic acid therapy renaissance
Burke, Paul A.; Pun, Suzie H.; Reineke, Theresa M.
2013-01-01
Nucleic acid therapeutics are attracting renewed interest due to recent clinical advances and product approvals. Most leading programs use chemical conjugates, or viral vectors in the case of gene therapy, while several use no delivery system at all. Polymer systems, which have been at the periphery of this renaissance, often involve greater molecular complexity than competing approaches, which must be justified by their advantages. Advanced analytical methods, along with biological tools for characterizing biotransformation and intracellular trafficking, are increasingly being applied to nucleic acid delivery systems including those based on polymers. These frontiers of investigation create the opportunity for an era where highly defined polymer compositions are optimized based on mechanistic insights in a way that has not been previously possible, offering the prospect of greater differentiation from alternatives. This will require integrated collaboration between polymer scientists and those from other disciplines. PMID:24683504
Advancing polymeric delivery systems amidst a nucleic acid therapy renaissance.
Burke, Paul A; Pun, Suzie H; Reineke, Theresa M
2013-10-15
Nucleic acid therapeutics are attracting renewed interest due to recent clinical advances and product approvals. Most leading programs use chemical conjugates, or viral vectors in the case of gene therapy, while several use no delivery system at all. Polymer systems, which have been at the periphery of this renaissance, often involve greater molecular complexity than competing approaches, which must be justified by their advantages. Advanced analytical methods, along with biological tools for characterizing biotransformation and intracellular trafficking, are increasingly being applied to nucleic acid delivery systems including those based on polymers. These frontiers of investigation create the opportunity for an era where highly defined polymer compositions are optimized based on mechanistic insights in a way that has not been previously possible, offering the prospect of greater differentiation from alternatives. This will require integrated collaboration between polymer scientists and those from other disciplines.
Advancing polymeric delivery systems amidst a nucleic acid therapy renaissance.
Burke, Paul A; Pun, Suzie H; Reineke, Theresa M
2013-10-15
Nucleic acid therapeutics are attracting renewed interest due to recent clinical advances and product approvals. Most leading programs use chemical conjugates, or viral vectors in the case of gene therapy, while several use no delivery system at all. Polymer systems, which have been at the periphery of this renaissance, often involve greater molecular complexity than competing approaches, which must be justified by their advantages. Advanced analytical methods, along with biological tools for characterizing biotransformation and intracellular trafficking, are increasingly being applied to nucleic acid delivery systems including those based on polymers. These frontiers of investigation create the opportunity for an era where highly defined polymer compositions are optimized based on mechanistic insights in a way that has not been previously possible, offering the prospect of greater differentiation from alternatives. This will require integrated collaboration between polymer scientists and those from other disciplines. PMID:24683504
Commercial phosphoric acid fuel cell system technology development
NASA Technical Reports Server (NTRS)
Prokopius, P. R.; Warshay, M.; Simons, S. N.; King, R. B.
1979-01-01
A review of the current commercial phosphoric acid fuel cell system technology development efforts is presented. In both the electric utility and on-site integrated energy system applications, reducing cost and increasing reliability are the technology drivers at this time. The longstanding barrier to the attainment of these goals, which manifests itself in a number of ways, has been materials. The differences in approach among the three major participants (United Technologies Corporation (UTC), Westinghouse Electric Corporation/Energy Research Corporation (ERC), and Engelhard Industries) and their unique technological features, including electrodes, matrices, intercell cooling, bipolar/separator plates, electrolyte management, fuel selection and system design philosophy are discussed.
A fully automatic system for acid-base coulometric titrations.
Cladera, A; Caro, A; Estela, J M; Cerdà, V
1990-01-01
An automatic system for acid-base titrations by electrogeneration of H(+) and OH(-) ions, with potentiometric end-point detection, was developed. The system includes a PC-compatible computer for instrumental control, data acquisition and processing, which allows up to 13 samples to be analysed sequentially with no human intervention.The system performance was tested on the titration of standard solutions, which it carried out with low errors and RSD. It was subsequently applied to the analysis of various samples of environmental and nutritional interest, specifically waters, soft drinks and wines.
Systems solutions by lactic acid bacteria: from paradigms to practice.
de Vos, Willem M
2011-08-30
Lactic acid bacteria are among the powerhouses of the food industry, colonize the surfaces of plants and animals, and contribute to our health and well-being. The genomic characterization of LAB has rocketed and presently over 100 complete or nearly complete genomes are available, many of which serve as scientific paradigms. Moreover, functional and comparative metagenomic studies are taking off and provide a wealth of insight in the activity of lactic acid bacteria used in a variety of applications, ranging from starters in complex fermentations to their marketing as probiotics. In this new era of high throughput analysis, biology has become big science. Hence, there is a need to systematically store the generated information, apply this in an intelligent way, and provide modalities for constructing self-learning systems that can be used for future improvements. This review addresses these systems solutions with a state of the art overview of the present paradigms that relate to the use of lactic acid bacteria in industrial applications. Moreover, an outlook is presented of the future developments that include the transition into practice as well as the use of lactic acid bacteria in synthetic biology and other next generation applications. PMID:21995776
Systems solutions by lactic acid bacteria: from paradigms to practice
2011-01-01
Lactic acid bacteria are among the powerhouses of the food industry, colonize the surfaces of plants and animals, and contribute to our health and well-being. The genomic characterization of LAB has rocketed and presently over 100 complete or nearly complete genomes are available, many of which serve as scientific paradigms. Moreover, functional and comparative metagenomic studies are taking off and provide a wealth of insight in the activity of lactic acid bacteria used in a variety of applications, ranging from starters in complex fermentations to their marketing as probiotics. In this new era of high throughput analysis, biology has become big science. Hence, there is a need to systematically store the generated information, apply this in an intelligent way, and provide modalities for constructing self-learning systems that can be used for future improvements. This review addresses these systems solutions with a state of the art overview of the present paradigms that relate to the use of lactic acid bacteria in industrial applications. Moreover, an outlook is presented of the future developments that include the transition into practice as well as the use of lactic acid bacteria in synthetic biology and other next generation applications. PMID:21995776
Systems solutions by lactic acid bacteria: from paradigms to practice.
de Vos, Willem M
2011-08-30
Lactic acid bacteria are among the powerhouses of the food industry, colonize the surfaces of plants and animals, and contribute to our health and well-being. The genomic characterization of LAB has rocketed and presently over 100 complete or nearly complete genomes are available, many of which serve as scientific paradigms. Moreover, functional and comparative metagenomic studies are taking off and provide a wealth of insight in the activity of lactic acid bacteria used in a variety of applications, ranging from starters in complex fermentations to their marketing as probiotics. In this new era of high throughput analysis, biology has become big science. Hence, there is a need to systematically store the generated information, apply this in an intelligent way, and provide modalities for constructing self-learning systems that can be used for future improvements. This review addresses these systems solutions with a state of the art overview of the present paradigms that relate to the use of lactic acid bacteria in industrial applications. Moreover, an outlook is presented of the future developments that include the transition into practice as well as the use of lactic acid bacteria in synthetic biology and other next generation applications.
IR-UV photochemistry of protein-nucleic acid systems
Kozub, J.; Edwards, G.
1995-12-31
UV light has often been used to induce the formation of covalent bonds between DNA (or RNA) and tightly-bound protein molecules. However, the internal photoreactions of nucleic acids and proteins limit the yield and complicate the analysis of intermolecular crosslinks. In an ongoing search for improved reaction specificity or new photoreactions in these systems, we have employed UV photons from a Nd:YAG-pumped dye laser and mid-IR photons from the Vanderbilt FEL. Having crosslinked several protein-nucleic acid systems with nanosecond UV laser pulses, we are currently studying the effect of various IR wavelengths on a model system (gene 32 protein and poly[dT]). We have found that irradiation with sufficiently intense FEL macropulses creates an altered form of gene 32 protein which was not observed with UV-only irradiation. The electrophoretic nobility of the product is consistent with the formation of a specific protein-protein crosslink. No evidence of the non-specific protein damage typically induced by UV light is found. The yield of the new photoproduct is apparently enhanced by exposure to FEL macropulses which are synchronized with UV laser pulses. With ideal exposure parameters, the two-color reaction effectively competes with UV-only reactions. Experiments designed to determine the reaction mechanism and to demonstrate FEL-induced reactions in other protein-nucleic acid systems are currently underway.
Development of an expert system for amino acid sequence identification.
Hu, L; Saulinskas, E F; Johnson, P; Harrington, P B
1996-08-01
An expert system for amino acid sequence identification has been developed. The algorithm uses heuristic rules developed by human experts in protein sequencing. The system is applied to the chromatographic data of phenylthiohydantoin-amino acids acquired from an automated sequencer. The peak intensities in the current cycle are compared with those in the previous cycle, while the calibration and succeeding cycles are used as ancillary identification criteria when necessary. The retention time for each chromatographic peak in each cycle is corrected by the corresponding peak in the calibration cycle at the same run. The main improvement of our system compared with the onboard software used by the Applied Biosystems 477A Protein/Peptide Sequencer is that each peak in each cycle is assigned an identification name according to the corrected retention time to be used for the comparison with different cycles. The system was developed from analyses of ribonuclease A and evaluated by runs of four other protein samples that were not used in rule development. This paper demonstrates that rules developed by human experts can be automatically applied to sequence assignment. The expert system performed more accurately than the onboard software of the protein sequencer, in that the misidentification rates for the expert system were around 7%, whereas those for the onboard software were between 13 and 21%.
Superabsorbent biphasic system based on poly(lactic acid) and poly(acrylic acid)
NASA Astrophysics Data System (ADS)
Sartore, Luciana; Pandini, Stefano; Baldi, Francesco; Bignotti, Fabio
2016-05-01
In this research work, biocomposites based on crosslinked particles of poly(acrylic acid), commonly used as superabsorbent polymer (SAP), and poly-L-lactic acid (PLLA) were developed to elucidate the role of the filler (i.e., polymeric crosslinked particles) on the overall physico-mechanical behavior and to obtain superabsorbent thermoplastic products. Samples prepared by melt-blending of components in different ratios showed a biphasic system with a regular distribution of particles, with diameter ranging from 5 to 10 μm, within the PLLA polymeric matrix. The polymeric biphasic system, coded PLASA i.e. superabsorbent poly(lactic acid), showed excellent swelling properties, demonstrating that cross-linked particles retain their superabsorbent ability, as in their free counterparts, even if distributed in a thermoplastic polymeric matrix. The thermal characteristics of the biocomposites evidence enhanced thermal stability in comparison with neat PLLA and also mechanical properties are markedly modified by addition of crosslinked particles which induce regular stiffening effect. Furthermore, in aqueous environments the particles swell and are leached from PLLA matrix generating very high porosity. These new open-pore PLLA foams, produced in absence of organic solvents and chemical foaming agents, with good physico-mechanical properties appear very promising for several applications, for instance in tissue engineering for scaffold production.
NASA Astrophysics Data System (ADS)
Yun, Hyejeong; Lim, Sangyong; Jo, Cheorun; Chung, Jinwoo; Kim, Soohyun; Kwon, Joong-Ho; Kim, Dongho
2008-06-01
The effects of organic acids, amino acids, and ethanol on the radio-degradation of patulin by gamma irradiation in an aqueous model system were investigated. The patulin, dissolved in distilled water at a concentration of 50 ppm, was practically degraded by the gamma irradiation at the dose of 1.0 kGy, while 33% of the patulin remained in apple juice. In the aqueous model system, the radio-degradation of patulin was partially inhibited by the addition of organic acids, amino acids, and ethanol. The proportions of remaining patulin after irradiation with the dose of 1.0 kGy in the 1% solution of malic acid, citric acid, lactic acid, acetic acid, ascorbic acid, and ethanol were 31.4%, 2.3%, 31.2%, 6.1%, 50.8%, and 12.5%, respectively. During 30 days of storage, the remaining patulin was reduced gradually in the solution of ascorbic acid and malic acid compared to being stable in other samples. The amino acids, serine, threonine, and histidine, inhibited the radio-degradation of patulin. In conclusion, it was suggested that 1 kGy of gamma irradiation (recommended radiation doses for radicidation and/or quarantine in fruits) is effective for the reduction of patulin, but the nutritional elements should be considered because the radio-degradation effects are environment dependent.
System for portable nucleic acid testing in low resource settings
NASA Astrophysics Data System (ADS)
Lu, Hsiang-Wei; Roskos, Kristina; Hickerson, Anna I.; Carey, Thomas; Niemz, Angelika
2013-03-01
Our overall goal is to enable timely diagnosis of infectious diseases through nucleic acid testing at the point-of-care and in low resource settings, via a compact system that integrates nucleic acid sample preparation, isothermal DNA amplification, and nucleic acid lateral flow (NALF) detection. We herein present an interim milestone, the design of the amplification and detection subsystem, and the characterization of thermal and fluidic control and assay execution within this system. Using an earlier prototype of the amplification and detection unit, comprised of a disposable cartridge containing flexible pouches, passive valves, and electrolysis-driven pumps, in conjunction with a small heater, we have demonstrated successful execution of an established and clinically validated isothermal loop-mediated amplification (LAMP) reaction targeting Mycobacterium tuberculosis (M.tb) DNA, coupled to NALF detection. The refined design presented herein incorporates miniaturized and integrated electrolytic pumps, novel passive valves, overall design changes to facilitate integration with an upstream sample preparation unit, and a refined instrument design that automates pumping, heating, and timing. Nucleic acid amplification occurs in a two-layer pouch that facilitates fluid handling and appropriate thermal control. The disposable cartridge is manufactured using low-cost and scalable techniques and forms a closed system to prevent workplace contamination by amplicons. In a parallel effort, we are developing a sample preparation unit based on similar design principles, which performs mechanical lysis of mycobacteria and DNA extraction from liquefied and disinfected sputum. Our next step is to combine sample preparation, amplification, and detection in a final integrated cartridge and device, to enable fully automated sample-in to answer-out diagnosis of active tuberculosis in primary care facilities of low-resource and high-burden countries.
Woo, Ji-Min; Kim, Ji-Won; Song, Ji-Won; Blank, Lars M.; Park, Jin-Byung
2016-01-01
The biosynthesis of carboxylic acids including fatty acids from biomass is central in envisaged biorefinery concepts. The productivities are often, however, low due to product toxicity that hamper whole-cell biocatalyst performance. Here, we have investigated factors that influence the tolerance of Escherichia coli to medium chain carboxylic acid (i.e., n-heptanoic acid)-induced stress. The metabolic and genomic responses of E. coli BL21(DE3) and MG1655 grown in the presence of n-heptanoic acid indicated that the GadA/B-based glutamic acid-dependent acid resistance (GDAR) system might be critical for cellular tolerance. The GDAR system, which is responsible for scavenging intracellular protons by catalyzing decarboxylation of glutamic acid, was inactive in E. coli BL21(DE3). Activation of the GDAR system in this strain by overexpressing the rcsB and dsrA genes, of which the gene products are involved in the activation of GadE and RpoS, respectively, resulted in acid tolerance not only to HCl but also to n-heptanoic acid. Furthermore, activation of the GDAR system allowed the recombinant E. coli BL21(DE3) expressing the alcohol dehydrogenase of Micrococcus luteus and the Baeyer-Villiger monooxygenase of Pseudomonas putida to reach 60% greater product concentration in the biotransformation of ricinoleic acid (i.e., 12-hydroxyoctadec-9-enoic acid (1)) into n-heptanoic acid (5) and 11-hydroxyundec-9-enoic acid (4). This study may contribute to engineering E. coli-based biocatalysts for the production of carboxylic acids from renewable biomass. PMID:27681369
21 CFR 862.1390 - 5-Hydroxyindole acetic acid/serotonin test system.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 21 Food and Drugs 8 2010-04-01 2010-04-01 false 5-Hydroxyindole acetic acid/serotonin test system... Test Systems § 862.1390 5-Hydroxyindole acetic acid/serotonin test system. (a) Identification. A 5-hydroxyindole acetic acid/serotonin test system is a device intended to measure 5-hydroxyindole acetic...
21 CFR 862.1390 - 5-Hydroxyindole acetic acid/serotonin test system.
Code of Federal Regulations, 2013 CFR
2013-04-01
... 21 Food and Drugs 8 2013-04-01 2013-04-01 false 5-Hydroxyindole acetic acid/serotonin test system... Test Systems § 862.1390 5-Hydroxyindole acetic acid/serotonin test system. (a) Identification. A 5-hydroxyindole acetic acid/serotonin test system is a device intended to measure 5-hydroxyindole acetic...
21 CFR 862.1390 - 5-Hydroxyindole acetic acid/serotonin test system.
Code of Federal Regulations, 2012 CFR
2012-04-01
... 21 Food and Drugs 8 2012-04-01 2012-04-01 false 5-Hydroxyindole acetic acid/serotonin test system... Test Systems § 862.1390 5-Hydroxyindole acetic acid/serotonin test system. (a) Identification. A 5-hydroxyindole acetic acid/serotonin test system is a device intended to measure 5-hydroxyindole acetic...
21 CFR 862.1390 - 5-Hydroxyindole acetic acid/serotonin test system.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 21 Food and Drugs 8 2011-04-01 2011-04-01 false 5-Hydroxyindole acetic acid/serotonin test system... Test Systems § 862.1390 5-Hydroxyindole acetic acid/serotonin test system. (a) Identification. A 5-hydroxyindole acetic acid/serotonin test system is a device intended to measure 5-hydroxyindole acetic...
KLM's Boric Acid Reclamation System (BARS): An update
Schuelke, D.; Kniazewycz, B.G.; Markind, J.; Brossart, M.A.; Choi, R.C.
1987-02-01
KLM Technologies has implemented its Department of Energy Phase II Small Business Innovative Research (SBIR) demonstration program for a radioactive waste Boric Acid Reclamation System (BARS). Preliminary performance indicates enhanced treatment by the BARS technique over state of the art process methods for selective removal of silica and other impurities from borated water matrices. At optimal system recovery of 96 to 97%, BARS removes nominal levels of boric acid while achieving significant rejection for soluble silica and selective radioisotopes. This is indicative of superior performance compared to existing data governing standard boric acid process treatment in the presence of silica and other contaminants. Conventional technologies have also proven to be relatively expensive, utilizing costly chemically treated disposable resins for primary waste removal. The overall BARS program indicates substantial savings regarding off-site disposal costs based on reduced waste generation. Optimization of the BARS technology could have potential impact on conventional process technologies that are essentially non-selective in removal capacities. 2 figs.
Bioluminescence regenerative cycle (BRC) system for nucleic acid quantification assays
NASA Astrophysics Data System (ADS)
Hassibi, Arjang; Lee, Thomas H.; Davis, Ronald W.; Pourmand, Nader
2003-07-01
A new label-free methodology for nucleic acid quantification has been developed where the number of pyrophosphate molecules (PPi) released during polymerization of the target nucleic acid is counted and correlated to DNA copy number. The technique uses the enzymatic complex of ATP-sulfurylase and firefly luciferase to generate photons from PPi. An enzymatic unity gain positive feedback is also implemented to regenerate the photon generation process and compensate any decay in light intensity by self regulation. Due to this positive feedback, the total number of photons generated by the bioluminescence regenerative cycle (BRC) can potentially be orders of magnitude higher than typical chemiluminescent processes. A system level kinetic model that incorporates the effects of contaminations and detector noise was used to show that the photon generation process is in fact steady and also proportional to the nucleic acid quantity. Here we show that BRC is capable of detecting quantities of DNA as low as 1 amol (10-18 mole) in 40μlit aqueous solutions, and this enzymatic assay has a controllable dynamic range of 5 orders of magnitude. The sensitivity of this technology, due to the excess number of photons generated by the regenerative cycle, is not constrained by detector performance, but rather by possible PPi or ATP (adenosine triphosphate) contamination, or background bioluminescence of the enzymatic complex.
Results of electric-vehicle propulsion system performance on three lead-acid battery systems
NASA Technical Reports Server (NTRS)
Ewashinka, J. G.
1984-01-01
Three types of state of the art 6 V lead acid batteries were tested. The cycle life of lead acid batteries as a function of the electric vehicle propulsion system design was determined. Cycle life, degradation rate and failure modes with different battery types (baseline versus state of the art tubular and thin plate batteries were compared. The effects of testing strings of three versus six series connected batteries on overall performance were investigated. All three types do not seem to have an economically feasible battery system for the propulsion systems. The tubular plate batteries on the load leveled profile attained 235 cycles with no signs of degradation and minimal capacity loss.
Results of electric-vehicle propulsion system performance on three lead-acid battery systems
NASA Technical Reports Server (NTRS)
Ewashinka, J. G.
1984-01-01
Three types of state of the art 6 V lead acid batteries were tested. The cycle life of lead acid batteries as a function of the electric vehicle propulsion system design was determined. Cycle life, degradation rate and failure modes with different battery types (baseline versus state of the art tubular and thin plate batteries) were compared. The effects of testing strings of three versus six series connected batteries on overall performance were investigated. All three types do not seem to have an economically feasible battery system for the propulsion systems. The tubular plate batteries on the load leveled profile attained 235 cycles with no signs of degradation and minimal capacity loss.
Lager, Susanne; Gaccioli, Francesca; Ramirez, Vanessa I; Jones, Helen N; Jansson, Thomas; Powell, Theresa L
2013-03-01
Obese women have an increased risk to deliver large babies. However, the mechanisms underlying fetal overgrowth in these pregnancies are not well understood. Obese pregnant women typically have elevated circulating lipid levels. We tested the hypothesis that fatty acids stimulate placental amino acid transport, mediated via toll-like receptor 4 (TLR4) and mammalian target of rapamycin (mTOR) signaling pathways. Circulating NEFA levels and placental TLR4 expression were assessed in women with varying prepregnancy body mass index (BMI). The effects of oleic acid on system A and system L amino acid transport, and on the activation of the mTOR (4EBP1, S6K1, rpS6), TLR4 (IĸB, JNK, p38 MAPK), and STAT3 signaling pathways were determined in cultured primary human trophoblast cells. Maternal circulating NEFAs (n = 33), but not placental TLR4 mRNA expression (n = 16), correlated positively with BMI (P < 0.05). Oleic acid increased trophoblast JNK and STAT3 phosphorylation (P < 0.05), whereas mTOR activity was unaffected. Furthermore, oleic acid doubled trophoblast system A activity (P < 0.05), without affecting system L activity. siRNA-mediated silencing of TLR4 expression prevented the stimulatory effect of oleic acid on system A activity. Our data suggest that maternal fatty acids can increase placental nutrient transport via TLR4, thereby potentially affecting fetal growth.
21 CFR 862.1187 - Conjugated sulfolithocholic acid (SLCG) test system.
Code of Federal Regulations, 2012 CFR
2012-04-01
... HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Chemistry Test Systems § 862.1187 Conjugated sulfolithocholic acid (SLCG) test system. (a) Identification....
21 CFR 862.1187 - Conjugated sulfolithocholic acid (SLCG) test system.
Code of Federal Regulations, 2013 CFR
2013-04-01
... HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Chemistry Test Systems § 862.1187 Conjugated sulfolithocholic acid (SLCG) test system. (a) Identification....
21 CFR 862.1187 - Conjugated sulfolithocholic acid (SLCG) test system.
Code of Federal Regulations, 2010 CFR
2010-04-01
... HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Chemistry Test Systems § 862.1187 Conjugated sulfolithocholic acid (SLCG) test system. (a) Identification....
21 CFR 862.1187 - Conjugated sulfolithocholic acid (SLCG) test system.
Code of Federal Regulations, 2011 CFR
2011-04-01
... HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Chemistry Test Systems § 862.1187 Conjugated sulfolithocholic acid (SLCG) test system. (a) Identification....
21 CFR 862.1187 - Conjugated sulfolithocholic acid (SLCG) test system.
Code of Federal Regulations, 2014 CFR
2014-04-01
... HUMAN SERVICES (CONTINUED) MEDICAL DEVICES CLINICAL CHEMISTRY AND CLINICAL TOXICOLOGY DEVICES Clinical Chemistry Test Systems § 862.1187 Conjugated sulfolithocholic acid (SLCG) test system. (a) Identification....
Preparation and evaluation of microemulsion systems containing salicylic acid.
Badawi, Alia A; Nour, Samia A; Sakran, Wedad S; El-Mancy, Shereen Mohamed Sameh
2009-01-01
Microemulsions (MEs) are clear, thermodynamically stable systems. They were used to solubilize drugs and to improve topical drug availability. Salicylic acid (SA) is a keratolytic agent used in topical products with antimicrobial actions. The objective of this work was to prepare and evaluate SA ME systems. Different concentrations of SA were incorporated in an ME base composed of isopropyl myristate, water, and Tween 80: propylene glycol in the ratio of 15:1. Three ME systems were prepared: S2%, S5%, and S10% which contain 2%, 5%, and 10% of SA, respectively. Evaluation by examination under cross-polarizing microscope, measuring of percent transmittance, pH measurement, determination of the specific gravity, assessment of rheological properties, and accelerated stability study were carried out. The data showed that the addition of SA markedly affected the physical properties of the base. All systems were not affected by accelerated stability tests. Stability study for 6 months under ambient conditions was carried out for S10%. No remarkable changes were recorded except a decrease in the viscosity value after 1 month. The results suggested that ME could be a suitable vehicle for topical application of different concentrations of SA. PMID:19757081
Preparation and evaluation of microemulsion systems containing salicylic acid.
Badawi, Alia A; Nour, Samia A; Sakran, Wedad S; El-Mancy, Shereen Mohamed Sameh
2009-01-01
Microemulsions (MEs) are clear, thermodynamically stable systems. They were used to solubilize drugs and to improve topical drug availability. Salicylic acid (SA) is a keratolytic agent used in topical products with antimicrobial actions. The objective of this work was to prepare and evaluate SA ME systems. Different concentrations of SA were incorporated in an ME base composed of isopropyl myristate, water, and Tween 80: propylene glycol in the ratio of 15:1. Three ME systems were prepared: S2%, S5%, and S10% which contain 2%, 5%, and 10% of SA, respectively. Evaluation by examination under cross-polarizing microscope, measuring of percent transmittance, pH measurement, determination of the specific gravity, assessment of rheological properties, and accelerated stability study were carried out. The data showed that the addition of SA markedly affected the physical properties of the base. All systems were not affected by accelerated stability tests. Stability study for 6 months under ambient conditions was carried out for S10%. No remarkable changes were recorded except a decrease in the viscosity value after 1 month. The results suggested that ME could be a suitable vehicle for topical application of different concentrations of SA.
Contributions of Cell Metabolism and H+ Diffusion to the Acidic pH of Tumors1
Schornack, Paul A; Gillies, Robert J
2003-01-01
Abstract The tumor microenvironment is hypoxic and acidic. These conditions have a significant impact on tumor progression and response to therapies. There is strong evidence that tumor hypoxia results from inefficient perfusion due to a chaotic vasculature. Consequently, some tumor regions are well oxygenated and others are hypoxic. It is commonly believed that hypoxic regions are acidic due to a stimulation of glycolysis through hypoxia, yet this is not yet demonstrated. The current study investigates the causes of tumor acidity by determining acid production rates and the mechanism of diffusion for H+ equivalents through model systems. Two breast cancer cell lines were investigated with divergent metabolic profiles: nonmetastatic MCF-7/s and highly metastatic MDA-mb-435 cells. Glycolysis and acid production are inhibited by oxygen in MCF-7/s cells, but not in MDA-mb-435 cells. Tumors of MDAmb-435 cells are significantly more acidic than are tumors of MCF-7/s cells, suggesting that tumor acidity is primarily caused by endogenous metabolism, and not the lack of oxygen. Metabolically produced protons are shown to diffuse in association with mobile buffers, in concordance with previous studies. The metabolic and diffusion data were analyzed using a reaction-diffusion model to demonstrate that the consequent pH profiles conform well to measured pH values for tumors of these two cell lines. PMID:12659686
Development of PNA-Surfactant Systems for Nucleic Acid Separations
NASA Astrophysics Data System (ADS)
Vernille, James; Armitage, Bruce; Schneider, James
2002-03-01
We have been exploring the use of novel peptide nucleic acid (PNA) surfactants for use in sequence specific, scalable DNA separations. While the synthetic and physical characteristics of PNA make it a useful molecule for bioseparations, PNA shows limited water solubility. Here we describe a molecular design strategy to improve water solubility while maintaining sequence specificity. A candidate molecule has been identified which contains lysine residues and a short alkane tail. Melting temperature data show that lipid tail interactions with the DNA nucleobases have a small but significant effect on stability while the added lysines stabilize the complex in an ionic strength dependent way. We also discuss the incorporation of these surfactants into micellar systems for novel separations.
Amine-based systems for carboxylic acid recovery
King, C.J.
1992-05-01
Several carboxylic acids are prominent commercial products, and their number and importance will probably grow. Getting these acids out of aqueous solution is necessary in petrochemical manufacture, fermentation, and the environmentally and economically important recovery from waste streams. In this paper, the authors discuss the methods possible to extract acids such as citric, lactic, and succinic from complex mixtures. Carboxylic acids are also readily made by fermentation and are among the most attractive substances that could be manufactured from biomass. Branches of this cycle lead to acetic, lactic, propionic, and formic acids, among others. Carboxylic acids are promising intermediates in a bioprocessing complex, because the oxygen of the biomass is placed in a form that is useful for further reaction with many other products. Citric acid is manufactured on a large scale by fermentation, and lactic and fumaric acids, among others, were manufactured that way in the past.
21 CFR 862.1320 - Gastric acidity test system.
Code of Federal Regulations, 2011 CFR
2011-04-01
... intended to measure the acidity of gastric fluid. Measurements of gastric acidity are used in the diagnosis...-secreting tumor of the pancreas), and related gastric disorders. (b) Classification. Class I...
Genotype, production system and sex effects on fatty acid composition of meat from goat kids.
Özcan, Mustafa; Demirel, Gulcan; Yakan, Akın; Ekiz, Bülent; Tölü, Cemil; Savaş, Türker
2015-02-01
Two trials were performed to assess the meat fatty acid profile of goat kids from different genotypes, production systems and sex. In the first trial, genotype effect was determined in 24 suckling male kids from Turkish Saanen, Maltese and Gokceada breeds. In the second trial, male and female Gokceada Goat kids were used to compare the effect of extensive and semi-intensive production systems on fatty acid composition of meat. Significant genotype effect was observed in the percentages of myristic acid (C14:0), palmitic acid (C16:0), oleic acid (C18:1 n-9), linolenic acid (C18:3 n-3), arachidonic acid (C20:4 n-6) and docosahexaenoic acid (C22:6 n-3), despite no differences on the ratios of polyunsaturated fatty acids to saturated fatty acids (PUFA/SFA) and n-6/n-3 (P > 0.05). The effect of production system had also significant effects on fatty acids, but sex only influenced significantly stearic acid (C18:0), C18:1 n-9 and C18:3 n-3 fatty acids and total PUFA level and PUFA/SFA ratio. This study confirms that dairy breeds are prone to produce higher levels of unsaturated fatty acids in their muscle. Meanwhile, meat from Gokceada goat kids, which is one of the indigenous breeds in Turkey, had similar PUFA/SFA and n-6/n-3 ratios to Turkish Saanen and Maltase.
Lactic acid bacteria as oral delivery systems for biomolecules.
Berlec, A; Ravnikar, M; Strukelj, B
2012-11-01
Lactic acid bacteria (LAB) have become increasingly studied over the last two decades as potential delivery systems for various biological molecules to the gastrointestinal tract. This article presents an overview of characteristics of LAB as delivery systems and of the applications which have already been developed. The majority of LAB strains are able to survive the intestinal passage and some are also able to persist and colonize the intestine. Several strains were in fact described as members of the human commensal flora. They can interact with their host and are able to deliver large molecular weight biomolecules across the epithelium via M-cells or dendritic cells. The most widely applied LAB species has been Lactococcus lactis; however species from genus Lactobacillus are gaining popularity and the first examples from genus Bifidobacterium are starting to emerge. Bacteria are mostly applied live and enable continuous delivery of the biomolecules. However, killed bacteria (e.g. gram-positive enhancer matrix), with bound biomolecules or as adjuvants, are also being developed. The techniques for genetic modification of LAB are well known. This review focuses on the delivery of recombinant proteins and DNA, which can cause either local or systemic effects. We divide recombinant proteins into antigens and therapeutic proteins. Delivery of antigens for the purpose of vaccination represents the most abundant application with numerous successful demonstrations of the efficacy on the animal model. Therapeutic proteins have mostly been developed for the treatment of the inflammatory bowel disease, by the delivery of anti-inflammatory cytokines, or downregulation of proinflammatory cytokines. Delivery of allergens for the modulation of allergic disorders represents the second most popular application of therapeutic proteins. The delivery of DNA by LAB was demonstrated and offers exciting opportunities, especially as a vaccine. New discoveries may eventually lead to the
Combined cycle phosphoric acid fuel cell electric power system
Mollot, D.J.; Micheli, P.L.
1995-12-31
By arranging two or more electric power generation cycles in series, combined cycle systems are able to produce electric power more efficiently than conventional single cycle plants. The high fuel to electricity conversion efficiency results in lower plant operating costs, better environmental performance, and in some cases even lower capital costs. Despite these advantages, combined cycle systems for the 1 - 10 megawatt (MW) industrial market are rare. This paper presents a low noise, low (oxides of nitrogen) NOx, combined cycle alternative for the small industrial user. By combining a commercially available phosphoric acid fuel cell (PAFC) with a low-temperature Rankine cycle (similar to those used in geothermal applications), electric conversion efficiencies between 45 and 47 percent are predicted. While the simple cycle PAFC is competitive on a cost of energy basis with gas turbines and diesel generators in the 1 to 2 MW market, the combined cycle PAFC is competitive, on a cost of energy basis, with simple cycle diesel generators in the 4 to 25 MW market. In addition, the efficiency and low-temperature operation of the combined cycle PAFC results in a significant reduction in carbon dioxide emissions with NO{sub x} concentration on the order of 1 parts per million (per weight) (ppmw).
An Efficient Biodelivery System for Antisense Polyamide Nucleic Acid (PNA)
Mehiri, Mohamed; Upert, Gregory; Tripathi, Snehlata; Di Giorgio, Audrey; Condom, Roger
2008-01-01
With the aim of developing a general and straightforward procedure for the intracellular delivery of naked peptide nucleic acids (PNAs), we designed an intracellularly biodegradable triphenylphosphonium (TPP) cation based transporter system. In this system, TPP is linked, via a biolabile disulfide bridge, to an activated mercaptoethoxycarbonyl moiety, allowing its direct coupling to the N-terminal extremity of a free PNA through a carbamate bond. We found that such TPP-PNA-carbamate conjugates were highly stable in a cell culture medium containing fetal calf serum. In a glutathione-containing medium mimicking the cytosol, the conjugates were rapidly degraded into an unstable intermediate, which spontaneously decomposed, releasing the free PNA. Using a fluorescence-labeled PNA–TPP conjugate, we demonstrated that conjugates were taken up by cells. Efficient cellular uptake and release of the PNA into the cytosol was further confirmed by the anti-HIV activity measured for the TPP-conjugate of a 16-mer PNA targeting the TAR region of the HIV-1 genome. This conjugate exhibited an IC50 value of 1 μM, while the free 16-mer PNA did not inhibit replication of HIV in the same cellular test. PMID:18707540
NASA Astrophysics Data System (ADS)
Degtev, M. I.; Popova, O. N.; Yuminova, A. A.
2014-08-01
The ability of antipyrine and its derivatives (diantipyryl alkanes) to form separating systems in the presence of salicylic (sulfosalicylic) acid and hydrochloric acid and water is studied. The optimum volume of the organic phase, the composition of complexes, and the mechanism for the distribution of metal ions are determined, depending on the concentrations of the main components and the salting-out agent. The complex distribution and extraction constants are calculated.
Self-powered switch-controlled nucleic acid extraction system.
Han, Kyungsup; Yoon, Yong-Jin; Shin, Yong; Park, Mi Kyoung
2016-01-01
Over the past few decades, lab-on-a-chip (LOC) technologies have played a great role in revolutionizing the way in vitro medical diagnostics are conducted and transforming bulky and expensive laboratory instruments and labour-intensive tests into easy to use, cost-effective miniaturized systems with faster analysis time, which can be used for near-patient or point-of-care (POC) tests. Fluidic pumps and valves are among the key components for LOC systems; however, they often require on-line electrical power or batteries and make the whole system bulky and complex, therefore limiting its application to POC testing especially in low-resource setting. This is particularly problematic for molecular diagnostics where multi-step sample processing (e.g. lysing, washing, elution) is necessary. In this work, we have developed a self-powered switch-controlled nucleic acid extraction system (SSNES). The main components of SSNES are a powerless vacuum actuator using two disposable syringes and a switchgear made of PMMA blocks and an O-ring. In the vacuum actuator, an opened syringe and a blocked syringe are bound together and act as a working syringe and an actuating syringe, respectively. The negative pressure in the opened syringe is generated by a restoring force of the compressed air inside the blocked syringe and utilized as the vacuum source. The Venus symbol shape of the switchgear provides multiple functions including being a reagent reservoir, a push-button for the vacuum actuator, and an on-off valve. The SSNES consists of three sets of vacuum actuators, switchgears and microfluidic components. The entire system can be easily fabricated and is fully disposable. We have successfully demonstrated DNA extraction from a urine sample using a dimethyl adipimidate (DMA)-based extraction method and the performance of the DNA extraction has been confirmed by genetic (HRAS) analysis of DNA biomarkers from the extracted DNAs using the SSNES. Therefore, the SSNES can be widely
[Study of antioxidant and membrane activity of rosmarinic acid using different model systems].
Popov, A M; Osipov, A N; Korepanova, E A; Krivoshapko, O N; Artiukov, A A
2013-01-01
Rosmarinic acid is found in many species of different families of higher plants and its chemical structure is phenol propanoid with various biological activity. In this paper, we conducted a comparative study of antioxidant (radical-scavenging) properties of rosmarinic acid in systems of 2,2'-azo-bis(2-methylpropionamidin)dihydrochloride-luminol and hemoglobin-hydrogen peroxide-lu- minol, determined its protective potential in preventing peroxidation of linoleic acid, and evaluated the effect on the permeability of planar bilayer lipid membranes. Linoleic acid peroxidation was assessed by iron-thiocyanate method. In these studies, trolox was used as a reference antioxidant, and ascorbic acid, and dihydroquercetin were taken as standards. Rosmarinic acid is significantly superior to trolox, ascorbic acid and dihydroquercetin in the tests for antioxidant activity in the systems studied, as well as in inhibition of linoleic acid peroxidation. According to their activity the investigated substances can be arranged in the following order: rosmarinic acid > dihydroquercetin trolox > ascorbic acid. Rosmarinic acid does not cause significant changes in the permeability of planar bilayer membranes in a dose range of 0.5 to 10 mkg/mL. Antioxidant activity of rosmarinic acid is due to the neutralization of reactive oxygen species and/or luminol radicals generated in model systems. The observed features of the antioxidant and membrane activity of rosmarinic acid, which may underlie the previously mentioned pharmacological effects are discussed. PMID:25481945
Impact of acid rain and deposition on aquatic biological systems
Not Available
1984-01-01
This book presents the papers given at a conference which examined the biological effects of acid rain on aquatic ecosystems. Topics considered at the conference included acidic lakes, the effects of acidification on biomass, hydrology, the sensitivity of stream invertebrates to pH depression, automated biomonitoring, remote computer platforms with satellite data retrieval in acidified streams, toxicity test, and a simple method of measuring pH accurately in acid rain.
Federal Register 2010, 2011, 2012, 2013, 2014
2013-06-19
... Nucleic Acid-Based Systems for Mycobacterium tuberculosis Complex in Respiratory Specimens AGENCY: Food...) is proposing to reclassify nucleic acid-based in vitro diagnostic devices for the detection of... Controls Guideline: Nucleic Acid-Based In Vitro Diagnostic Devices for the Detection of...
Gerardy-Schahn, Rita; Hildebrandt, Herbert
2014-01-01
Every cell in nature carries a rich surface coat of glycans, its glycocalyx, which constitutes the cell's interface with its environment. In eukaryotes, the glycocalyx is composed of glycolipids, glycoproteins, and proteoglycans, the compositions of which vary among different tissues and cell types. Many of the linear and branched glycans on cell surface glycoproteins and glycolipids of vertebrates are terminated with sialic acids, nine-carbon sugars with a carboxylic acid, a glycerol side-chain, and an N-acyl group that, along with their display at the outmost end of cell surface glycans, provide for varied molecular interactions. Among their functions, sialic acids regulate cell-cell interactions, modulate the activities of their glycoprotein and glycolipid scaffolds as well as other cell surface molecules, and are receptors for pathogens and toxins. In the brain, two families of sialoglycans are of particular interest: gangliosides and polysialic acid. Gangliosides, sialylated glycosphingolipids, are the most abundant sialoglycans of nerve cells. Mouse genetic studies and human disorders of ganglioside metabolism implicate gangliosides in axon-myelin interactions, axon stability, axon regeneration, and the modulation of nerve cell excitability. Polysialic acid is a unique homopolymer that reaches >90 sialic acid residues attached to select glycoproteins, especially the neural cell adhesion molecule in the brain. Molecular, cellular, and genetic studies implicate polysialic acid in the control of cell-cell and cell-matrix interactions, intermolecular interactions at cell surfaces, and interactions with other molecules in the cellular environment. Polysialic acid is essential for appropriate brain development, and polymorphisms in the human genes responsible for polysialic acid biosynthesis are associated with psychiatric disorders including schizophrenia, autism, and bipolar disorder. Polysialic acid also appears to play a role in adult brain plasticity
Characterization of a broad-scope amino acid transport system in sand dollars
Davis, J.P.; Bellis, S.; Stephens, G.C. )
1988-03-01
Both echinoderm embryos and adults take up {sup 14}C-labelled-{alpha}-amino acids by an apparent broad-scope transport system. This transporter can be characterized as follows: alanine transport is not blocked by {alpha}-(methylamino)isobutyric acid. Leucine and other lipophilic neutral amino acids are preferentially transported. Transport is sodium dependent and blocked by 2-aminobicyclo-(2,2,1)heptane-2-carboxyclic acid. Lysine and aspartate transport is inhibited by lipophilic neutral amino acids. Taurine, a {beta}-neutral amino acid is translocated via a second and independent carrier.
Abscisic Acid: Hidden Architect of Root System Structure
Harris, Jeanne M.
2015-01-01
Plants modulate root growth in response to changes in the local environment, guided by intrinsic developmental genetic programs. The hormone Abscisic Acid (ABA) mediates responses to different environmental factors, such as the presence of nitrate in the soil, water stress and salt, shaping the structure of the root system by regulating the production of lateral roots as well as controlling root elongation by modulating cell division and elongation. Curiously, ABA controls different aspects of root architecture in different plant species, perhaps providing some insight into the great diversity of root architecture in different plants, both from different taxa and from different environments. ABA is an ancient signaling pathway, acquired well before the diversification of land plants. Nonetheless, how this ancient signaling module is implemented or interacts within a larger signaling network appears to vary in different species. This review will examine the role of ABA in the control of root architecture, focusing on the regulation of lateral root formation in three plant species, Arabidopsis thaliana, Medicago truncatula and Oryza sativa. We will consider how the implementation of the ABA signaling module might be a target of natural selection, to help contribute to the diversity of root architecture in nature. PMID:27135341
Effect of fatty acids on self-assembly of soybean lecithin systems.
Godoy, C A; Valiente, M; Pons, R; Montalvo, G
2015-07-01
With the increasing interest in natural formulations for drug administration and functional foods, it is desirable a good knowledge of the phase behavior of lecithin/fatty acid formulations. Phase structure and properties of ternary lecithin/fatty acids/water systems are studied at 37°C, making emphasis in regions with relatively low water and fatty acid content. The effect of fatty acid saturation degree on the phase microstructure is studied by comparing a fully saturated (palmitic acid, C16:0), monounsaturated (oleic acid, C18:1), and diunsaturated (linoleic acid, C18:2) fatty acids. Phase determinations are based on a combination of polarized light microscopy and small-angle X-ray scattering measurements. Interestingly, unsaturated (oleic acid and linoleic acid) fatty acid destabilizes the lamellar bilayer. Slight differences are observed between the phase diagrams produced by the unsaturated ones: small lamellar, medium cubic and large hexagonal regions. A narrow isotropic fluid region also appears on the lecithin-fatty acid axis, up to 8wt% water. In contrast, a marked difference in phase microsctructure was observed between unsaturated and saturated systems in which the cubic and isotropic fluid phases are not formed. These differences are, probably, a consequence of the high Krafft point of the C16 saturated chains that imply rather rigid chains. However, unsaturated fatty acids result in more flexible tails. The frequent presence of, at least, one unsaturated chain in phospholipids makes it very likely a better mixing situation than in the case of more rigid chains. This swelling potential favors the formation of reverse hexagonal, cubic, and micellar phases. Both unsaturated fatty acid systems evolve by aging, with a reduction of the extension of reverse hexagonal phase and migration of the cubic phase to lower fatty acid and water contents. The kinetic stability of the systems seems to be controlled by the unsaturation of fatty acids.
NASA Astrophysics Data System (ADS)
Wang, Feng; Huang, Wei; Wang, Yanwei; Tang, Bo
2010-04-01
In this paper, nucleic acid can greatly enhance the fluorescence of Ellagic acid (EA) in the presence of cetylpyridine bromide (CPB). Experiments indicate that under the optimum conditions, the enhanced intensity of fluorescence is proportional to the concentration of nucleic acid in the range of 5.0 × 10 -9-3.5 × 10 -5 g mL -1 for hsDNA, 5.0 × 10 -9-3.5 × 10 -5 g mL -1 for ctDNA and 5.0 × 10 -9-3.5 × 10 -5 g mL -1 for yRNA. Their detection limits (S/N = 3) are 7.6 × 10 -9 g mL -1, 8.6 × 10 -9 g mL -1 and 6.1 × 10 -9 g mL -1, respectively. The method has been satisfactorily used for the determination of nucleic acid in actual samples. Resonance Light Scattering, Ultraviolet and other means are used to discuss its mechanism. It is considered that the charge-transfer complex EA-CPB aggregate in the extended nucleic acids by hydrogen bond and electric attraction. The hydrophobic microenvironment of nucleic acid makes the fluorescence intensity of EA-CPB-nucleic acid system much stronger.
Berenstein, Igal; Bullara, Domenico; De Decker, Yannick
2014-09-01
This paper studies the spatiotemporal dynamics of a reaction-diffusion-advection system corresponding to an extension of the Oregonator model, which includes two inhibitors instead of one. We show that when the reaction-diffusion, two-dimensional problem displays stationary patterns the addition of a plug flow can induce the emergence of new types of stationary structures. These patterns take the form of spots or arcs, the size and the spacing of which can be controlled by the flow.
Akbaridoust, Ghazal; Plozza, Tim; Trenerry, V Craige; Wales, William J; Auldist, Martin J; Ajlouni, Said
2015-08-01
The influence of different pasture-based feeding systems on fatty acids, organic acids and volatile organic flavour compounds in yoghurt was studied. Pasture is the main source of nutrients for dairy cows in many parts of the world, including southeast Australia. Milk and milk products produced in these systems are known to contain a number of compounds with positive effects on human health. In the current study, 260 cows were fed supplementary grain and forage according to one of 3 different systems; Control (a traditional pasture based diet offered to the cows during milking and in paddock), PMR1 (a partial mixed ration which contained the same supplement as Control but was offered to the cows as a partial mixed ration on a feedpad), PMR 2 (a differently formulated partial mixed ration compared to Control and PMR1 which was offered to the cows on a feedpad). Most of the yoghurt fatty acids were influenced by feeding systems; however, those effects were minor on organic acids. The differences in feeding systems did not lead to the formation of different volatile organic flavour compounds in yoghurt. Yet, it did influence the relative abundance of these components. PMID:26143651
Akbaridoust, Ghazal; Plozza, Tim; Trenerry, V Craige; Wales, William J; Auldist, Martin J; Ajlouni, Said
2015-08-01
The influence of different pasture-based feeding systems on fatty acids, organic acids and volatile organic flavour compounds in yoghurt was studied. Pasture is the main source of nutrients for dairy cows in many parts of the world, including southeast Australia. Milk and milk products produced in these systems are known to contain a number of compounds with positive effects on human health. In the current study, 260 cows were fed supplementary grain and forage according to one of 3 different systems; Control (a traditional pasture based diet offered to the cows during milking and in paddock), PMR1 (a partial mixed ration which contained the same supplement as Control but was offered to the cows as a partial mixed ration on a feedpad), PMR 2 (a differently formulated partial mixed ration compared to Control and PMR1 which was offered to the cows on a feedpad). Most of the yoghurt fatty acids were influenced by feeding systems; however, those effects were minor on organic acids. The differences in feeding systems did not lead to the formation of different volatile organic flavour compounds in yoghurt. Yet, it did influence the relative abundance of these components.
Viscosity and surface tension of dilute salicylic acid-cetrimide systems.
Wan, L S
1977-12-01
The viscosity and surface tension of systems containing small amounts of salicylic acid in aqueous solutions of cetrimide were determined. An abrupt increase in viscosity was observed, and the molar ratio of salicylic acid to certrimide at which this viscosity increase occurred was 1:2. The surface tension of these systems also increased sharply after an initial lowering. The salicylic acid concentration at which this behavior was demonstrated was almost the same as that at maximum solubility in the surfactant solution.
DimaSense™: A Novel Nucleic Acid Detection System
Stadler, A.
2011-05-18
sensors. These sensors operate with very low concentrations of target, can utilize standard instrumentation, produce detection results rapidly, and are robust enough to function in the presence of many competing genetic targets. Many current genetic target detection products/approaches/technologies rely upon methods (such as qPCR) which are more complicated, cumbersome, and costly to perform, and are not well suited to point-of-care diagnostic applications. Several clinical diagnostic applications, particularly point-of-care (POC) diagnostics for infectious diseases, are possible and appear to be a good fit for the technology. In addition, the advent of personalized medicine will create opportunities for molecular diagnostic companies with the capabilities of rapidly and quantitatively detecting nucleic acid sequences. The global POC market was {approx}$7.7B in 2010, with a recent annual growth rate of {approx}7%. A specific disease or disease-class diagnostic would need to be identified before a more meaningful sub-market value could be stated. Additional validation of the technology to show that it displays appropriate performance parameters for a commercial application on 'real world' samples is required for true commercial readiness. In addition, optimization of sensor design parameters, to effect a 10-fold increase in sensitivity, may be required to produce a commercially ready sensor system. These validation and sensor design optimization are estimated to require 3-4 months and {approx}$75k. For an unregulated product to give this sensor system a distinct competitive advantage, 2-3 years of product development and $1.5-3M are likely required. For regulated markets, time to market (through clinic) and cost would depend upon the product.
Systemic distribution and speciation of diphenylarsinic acid fed to rats
Naranmandura, Hua Suzuki, Noriyuki; Takano, Juniti; McKnight-Whitford, Tony; Ogra, Yasumitsu; Suzuki, Kazuo T.; Le, X. Chris
2009-06-01
Diphenylarsinic acid (DPAA) is an environmental degradation product of diphenylarsine chloride or diphenylarsine cyanide, which were chemical warfare agents produced by Japan during the World War II. DPAA is now considered a dangerous environmental pollutant in Kamisu, Japan, where it is suspected of inducing health effects that include articulation disorders (cerebellar ataxia of the extremities and trunk), involuntary movements (myoclonus and tremor), and sleep disorders. In order to elucidate the toxic mechanism of DPAA, we focused on the distribution and metabolism of DPAA in rats. Systemic distribution of DPAA was determined by administering DPAA orally to rats at a single dose of 5.0 mg As/kg body weight, followed by speciation analysis of selected organs and body fluids. Most of the total arsenic burden was recovered in the urine (23% of the dose) and feces (27%), with the distribution in most other organs/tissues being less than 1%. However, compared with the typical distribution of inorganic dietary arsenic, DPAA administration resulted in elevated levels in the brain, testes and pancreas. In contrast to urine, in which DPAA was found mostly in its unmodified form, the tissues and organs contained arsenic that was mostly bound to non-soluble and soluble high molecular weight proteins. These bound arsenic species could be converted back to DPAA after oxidation with H{sub 2}O{sub 2}, suggesting that the DPAA bound to proteins had been reduced within the body and was in a trivalent oxidation state. Furthermore, we also detected two unknown arsenic metabolites in rat urine, which were assumed to be hydroxylated arsenic metabolites.
Abscisic acid ameliorates the systemic sclerosis fibroblast phenotype in vitro
Bruzzone, Santina; Battaglia, Florinda; Mannino, Elena; Parodi, Alessia; Fruscione, Floriana; Basile, Giovanna; Salis, Annalisa; Sturla, Laura; Negrini, Simone; Kalli, Francesca; Stringara, Silvia; Filaci, Gilberto; and others
2012-05-25
Highlights: Black-Right-Pointing-Pointer ABA is an endogenous hormone in humans, regulating different cell responses. Black-Right-Pointing-Pointer ABA reverts some of the functions altered in SSc fibroblasts to a normal phenotype. Black-Right-Pointing-Pointer UV-B irradiation increases ABA content in SSc cultures. Black-Right-Pointing-Pointer SSc fibroblasts could benefit from exposure to ABA and/or to UV-B. -- Abstract: The phytohormone abscisic acid (ABA) has been recently identified as an endogenous hormone in humans, regulating different cell functions, including inflammatory processes, insulin release and glucose uptake. Systemic sclerosis (SSc) is a chronic inflammatory disease resulting in fibrosis of skin and internal organs. In this study, we investigated the effect of exogenous ABA on fibroblasts obtained from healthy subjects and from SSc patients. Migration of control fibroblasts induced by ABA was comparable to that induced by transforming growth factor-{beta} (TGF-{beta}). Conversely, migration toward ABA, but not toward TGF-{beta}, was impaired in SSc fibroblasts. In addition, ABA increased cell proliferation in fibroblasts from SSc patients, but not from healthy subjects. Most importantly, presence of ABA significantly decreased collagen deposition by SSc fibroblasts, at the same time increasing matrix metalloproteinase-1 activity and decreasing the expression level of tissue inhibitor of metalloproteinase (TIMP-1). Thus, exogenously added ABA appeared to revert some of the functions altered in SSc fibroblasts to a normal phenotype. Interestingly, ABA levels in plasma from SSc patients were found to be significantly lower than in healthy subjects. UV-B irradiation induced an almost 3-fold increase in ABA content in SSc cultures. Altogether, these results suggest that the fibrotic skin lesions in SSc patients could benefit from exposure to high(er) ABA levels.
21 CFR 862.1655 - Pyruvic acid test system.
Code of Federal Regulations, 2010 CFR
2010-04-01
... measure pyruvic acid (an intermediate compound in the metabolism of carbohydrate) in plasma. Measurements obtained by this device are used in the evaluation of electrolyte metabolism and in the diagnosis...
21 CFR 862.1655 - Pyruvic acid test system.
Code of Federal Regulations, 2012 CFR
2012-04-01
... measure pyruvic acid (an intermediate compound in the metabolism of carbohydrate) in plasma. Measurements obtained by this device are used in the evaluation of electrolyte metabolism and in the diagnosis...
21 CFR 862.1655 - Pyruvic acid test system.
Code of Federal Regulations, 2013 CFR
2013-04-01
... measure pyruvic acid (an intermediate compound in the metabolism of carbohydrate) in plasma. Measurements obtained by this device are used in the evaluation of electrolyte metabolism and in the diagnosis...
Nasarabadi, Shanavaz
2011-01-11
A polymerase chain reaction system for analyzing a sample containing nucleic acid includes providing magnetic beads; providing a flow channel having a polymerase chain reaction chamber, a pre polymerase chain reaction magnet position adjacent the polymerase chain reaction chamber, and a post pre polymerase magnet position adjacent the polymerase chain reaction chamber. The nucleic acid is bound to the magnetic beads. The magnetic beads with the nucleic acid flow to the pre polymerase chain reaction magnet position in the flow channel. The magnetic beads and the nucleic acid are washed with ethanol. The nucleic acid in the polymerase chain reaction chamber is amplified. The magnetic beads and the nucleic acid are separated into a waste stream containing the magnetic beads and a post polymerase chain reaction mix containing the nucleic acid. The reaction mix containing the nucleic acid flows to an analysis unit in the channel for analysis.
Omega-3 fatty acids differentially modulate enzymatic anti-oxidant systems in skeletal muscle cells.
da Silva, E P; Nachbar, R T; Levada-Pires, A C; Hirabara, S M; Lambertucci, R H
2016-01-01
During physical activity, increased reactive oxygen species production occurs, which can lead to cell damage and in a decline of individual's performance and health. The use of omega-3 polyunsaturated fatty acids as a supplement to protect the immune system has been increasing; however, their possible benefit to the anti-oxidant system is not well described. Thus, the aim of this study was to evaluate whether the omega-3 fatty acids (docosahexaenoic acid and eicosapentaenoic acid) can be beneficial to the anti-oxidant system in cultured skeletal muscle cells. C2C12 myocytes were differentiated and treated with either eicosapentaenoic acid or docosahexaenoic acid for 24 h. Superoxide content was quantified using the dihydroethidine oxidation method and superoxide dismutase, catalase, and glutathione peroxidase activity, and expression was quantified. We observed that the docosahexaenoic fatty acids caused an increase in superoxide production. Eicosapentaenoic acid induced catalase activity, while docosahexaenoic acid suppressed superoxide dismutase activity. In addition, we found an increased protein expression of the total manganese superoxide dismutase and catalase enzymes when cells were treated with eicosapentaenoic acid. Taken together, these data indicate that the use of eicosapentaenoic acid may present both acute and chronic benefits; however, the treatment with DHA may not be beneficial to muscle cells.
Omega-3 fatty acids differentially modulate enzymatic anti-oxidant systems in skeletal muscle cells.
da Silva, E P; Nachbar, R T; Levada-Pires, A C; Hirabara, S M; Lambertucci, R H
2016-01-01
During physical activity, increased reactive oxygen species production occurs, which can lead to cell damage and in a decline of individual's performance and health. The use of omega-3 polyunsaturated fatty acids as a supplement to protect the immune system has been increasing; however, their possible benefit to the anti-oxidant system is not well described. Thus, the aim of this study was to evaluate whether the omega-3 fatty acids (docosahexaenoic acid and eicosapentaenoic acid) can be beneficial to the anti-oxidant system in cultured skeletal muscle cells. C2C12 myocytes were differentiated and treated with either eicosapentaenoic acid or docosahexaenoic acid for 24 h. Superoxide content was quantified using the dihydroethidine oxidation method and superoxide dismutase, catalase, and glutathione peroxidase activity, and expression was quantified. We observed that the docosahexaenoic fatty acids caused an increase in superoxide production. Eicosapentaenoic acid induced catalase activity, while docosahexaenoic acid suppressed superoxide dismutase activity. In addition, we found an increased protein expression of the total manganese superoxide dismutase and catalase enzymes when cells were treated with eicosapentaenoic acid. Taken together, these data indicate that the use of eicosapentaenoic acid may present both acute and chronic benefits; however, the treatment with DHA may not be beneficial to muscle cells. PMID:26386577
Materials characterization of phosphoric acid fuel cell system
NASA Technical Reports Server (NTRS)
Venkatesh, Srinivasan
1986-01-01
The component materials used in the fabrication of phosphoric acid fuel cells (PAFC) must have mechanical, chemical, and electrochemical stability to withstand the moderately high temperature (200 C) and pressure (500 kPa) and highly oxidizing nature of phosphoric acid. This study discusses the chemical and structural stability, performance and corrosion data on certain catalysts, catalyst supports, and electrode support materials used in PAFC applications.
Using Acid Number as a Leading Indicator of Refrigeration and Air Conditioning System Performance
Dennis Cartlidge; Hans Schellhase
2003-07-31
This report summarizes a literature review to assess the acidity characteristics of the older mineral oil and newer polyolester (POE) refrigeration systems as well as to evaluate acid measuring techniques used in other non-aqueous systems which may be applicable for refrigeration systems. Failure in the older chlorofluorocarbon/hydrochlorofluorocarbon (CFC/HCFC) / mineral oil systems was primarily due to thermal degradation of the refrigerant which resulted in the formation of hydrochloric and hydrofluoric acids. These are strong mineral acids, which can, over time, severely corrode the system metals and lead to the formation of copper plating on iron surfaces. The oil lubricants used in the older systems were relatively stable and were not prone to hydrolytic degradation due to the low solubility of water in oil. The refrigerants in the newer hydrofluorocarbon (HFC)/POE systems are much more thermally stable than the older CFC/HCFC refrigerants and mineral acid formation is negligible. However, acidity is produced in the new systems by hydrolytic decomposition of the POE lubricants with water to produce the parent organic acids and alcohols used to prepare the POE. The individual acids can therefore vary but they are generally C5 to C9 carboxylic acids. Organic acids are much weaker and far less corrosive to metals than the mineral acids from the older systems but they can, over long time periods, react with metals to form carboxylic metal salts. The salts tend to accumulate in narrow areas such as capillary tubes, particularly if residual hydrocarbon processing chemicals are present in the system, which can lead to plugging. The rate of acid production from POEs varies on a number of factors including chemical structure, moisture levels, temperature, acid concentration and metals. The hydrolysis rate of reaction can be reduced by using driers to reduce the free water concentration and by using scavenging chemicals which react with the system acids. Total acid
Analysis of Natural Buffer Systems and the Impact of Acid Rain
ERIC Educational Resources Information Center
Powers, David C.; Yoder, Claude H.; Higgs, Andrew T.; Obley, Matt L.; Hess, Kenneth R.; Leber, Phyllis A.
2005-01-01
The environmental significance of acid rain on water systems of different buffer capacities is discussed. The most prevalent natural buffer system is created by the equilibrium between carbonate ions and carbon dioxide.
Denisenko, Y K; Novgorodtseva, T P; Zhukova, N V; Antonuk, M V; Lobanova, E G; Kalinina, E P
2016-03-01
We examined composition of plasma non-esterified fatty acids (NFAs), erythrocyte fatty acids, levels of eicosanoids in patients with asthma and chronic obstructive pulmonary disease (COPD) with different type of the inflammatory response. The results of our study show that asthma and COPD in remission are associated with changes in the composition NFAs of plasma, FA of erythrocytes, level eicosanoid despite the difference in the regulation of immunological mechanisms of systemic inflammation. These changes are characterized by excessive production of arachidonic acid (20:4n-6) and cyclooxygenase and lipoxygenase metabolites (thromboxane B2, leukotriene B4) and deficiency of their functional antagonist, eicosapentaenoic acid (20:5n-3). The recognized association between altered fatty acid composition and disorders of the immune mechanisms of regulation of systemic inflammation in COPD and asthma demonstrated the important role of fatty acids and their metabolites in persistence of inflammatory processes in diseases of the respiratory system in the condition of remission. PMID:27420629
Rudin, J. Wasan, D.T. . Dept. of Chemical Engineering)
1992-08-01
This paper reports that experimental studies are conducted in order to determine the physicochemical mechanism responsible for lowering of interfacial tension in alkali, surfactant, and surfactant-enhanced alkali/acidic oil systems. A well-defined model oil is chosen to examine the influence of various surfactants and surfactant mixtures, such as oleic acid and its ionic counterpart, sodium dodecyl sulfate, petroleum sulfonate, and isobutanol, on equilibrium interfacial tension. With added surfactant alone, the interfacial tension goes through an ultralow minimum with increasing acid concentration. This proves for the first time that the un-ionized acid species plays a major role in affecting interfacial tension, and the ionized acid species.
Hydrodynamic Instabilities of Acid-Base Reaction Fronts: Active Role of a Color Indicator
NASA Astrophysics Data System (ADS)
Riolfo, L. A.; Almarcha, C.; Trevelyan, P. M. J.; El Hasi, C.; Zalts, A.; D'Onofrio, A.; de Wit, A.
2010-11-01
Chemical reactions are able to trigger hydrodynamic flows by, for example changing the density of the solutions across the reactive interfaces. In this work we present an experimental and theoretical study of the buoyancy-driven hydrodynamic instabilities that can occur when two miscible reactive solutions of an acid-base system are put in contact in the gravity field. We compare situations where a hydrochloric acid aqueous solution is put on top of a sodium hydroxide aqueous solution with or without a color indicator (Bromocresol Green). We also analyze the situation where a hydrochloric acid is put on top of an aqueous solution of a color indicator without any base. We show that the patterns observed and the instabilities taking place strongly depend on the presence of a color indicator. Using a reaction-diffusion model for the concentrations of all species (including the color indicator) we analyze the different possible sources of destabilization of the acid-base front and explain the various instabilities observed in each experimental system.
The acid-base resistant zone in three dentin bonding systems.
Inoue, Go; Nikaido, Toru; Foxton, Richard M; Tagami, Junji
2009-11-01
An acid-base resistant zone has been found to exist after acid-base challenge adjacent to the hybrid layer using SEM. The aim of this study was to examine the acid-base resistant zone using three different bonding systems. Dentin disks were applied with three different bonding systems, and then a resin composite was light-cured to make dentin disk sandwiches. After acid-base challenge, the polished surfaces were observed using SEM. For both one- and two-step self-etching primer systems, an acid-base resistant zone was clearly observed adjacent to the hybrid layer - but with differing appearances. For the wet bonding system, the presence of an acid-base resistant zone was unclear. This was because the self-etching primer systems etched the dentin surface mildly, such that the remaining mineral phase of dentin and the bonding agent yielded clear acid-base resistant zones. In conclusion, the acid-base resistant zone was clearly observed when self-etching primer systems were used, but not so for the wet bonding system.
Singh-Blom, Amrita; Hughes, Randall A; Ellington, Andrew D
2014-05-20
Residue-specific incorporation of non-canonical amino acids into proteins is usually performed in vivo using amino acid auxotrophic strains and replacing the natural amino acid with an unnatural amino acid analog. Herein, we present an efficient amino acid depleted cell-free protein synthesis system that can be used to study residue-specific replacement of a natural amino acid by an unnatural amino acid analog. This system combines a simple methodology and high protein expression titers with a high-efficiency analog substitution into a target protein. To demonstrate the productivity and efficacy of a cell-free synthesis system for residue-specific incorporation of unnatural amino acids in vitro, we use this system to show that 5-fluorotryptophan and 6-fluorotryptophan substituted streptavidin retain the ability to bind biotin despite protein-wide replacement of a natural amino acid for the amino acid analog. We envisage this amino acid depleted cell-free synthesis system being an economical and convenient format for the high-throughput screening of a myriad of amino acid analogs with a variety of protein targets for the study and functional characterization of proteins substituted with unnatural amino acids when compared to the currently employed in vivo methodologies.
A novel enzyme-based acidizing system: Matrix acidizing and drilling fluid damage removal
Harris, R.E.; McKay, D.M.; Moses, V.
1995-12-31
A novel acidizing process is used to increase the permeability of carbonate rock cores in the laboratory and to remove drilling fluid damage from cores and wafers. Field results show the benefits of the technology as applied both to injector and producer wells.
The solubilization of fatty acids in systems based on block copolymers and nonionic surfactants
NASA Astrophysics Data System (ADS)
Mirgorodskaya, A. B.; Yatskevich, E. I.; Zakharova, L. Ya.
2010-12-01
The solubilizing action of micellar, microemulsion, and polymer-colloid systems formed on the basis of biologically compatible amphiphilic polymers and nonionic surfactants on capric, lauric, palmitic, and stearic acids was characterized quantitatively. Systems based on micelle forming oxyethyl compounds increased the solubility of fatty acids by more than an order of magnitude. Acid molecules incorporated into micelles increased their size and caused structural changes. Solubilization was accompanied by complete or partial destruction of intrinsic acid associates and an increase in their p K a by 1.5-2 units compared with water.
Control of acid mist emissions from FGD systems
Dahlin, R S; Brown, T D
1991-01-01
Improved control of acid mist emissions can be achieved by replacing or augmenting the conventional mist eliminators with a wet electrostatic precipitator (WESP). This paper describes a two-phased study performed to determine the degree of control that can be achieved with this approach. Phase I was a study of the electrical operation of a lab-scale WESP collecting an acid mist from a coal combustion pilot plant equipped with a spray chamber. The results of this study were used to develop and validate a computer model of the WESP. In Phase II, measurements were made at two utility scrubber installations to determine the loadings of acid mist, fly ash, and scrubber carryover. These measurements were used as input to the model to project the performance of a retrofitted WESP.
Wittek, Finni; Hoffmann, Thomas; Kanawati, Basem; Bichlmeier, Marlies; Knappe, Claudia; Wenig, Marion; Schmitt-Kopplin, Philippe; Parker, Jane E; Schwab, Wilfried; Vlot, A Corina
2014-11-01
Systemic acquired resistance (SAR) is a form of inducible disease resistance that depends on salicylic acid and its upstream regulator ENHANCED DISEASE SUSCEPTIBILITY1 (EDS1). Although local Arabidopsis thaliana defence responses activated by the Pseudomonas syringae effector protein AvrRpm1 are intact in eds1 mutant plants, SAR signal generation is abolished. Here, the SAR-specific phenotype of the eds1 mutant is utilized to identify metabolites that contribute to SAR. To this end, SAR bioassay-assisted fractionation of extracts from the wild type compared with eds1 mutant plants that conditionally express AvrRpm1 was performed. Using high-performance liquid chromatography followed by mass spectrometry, systemic immunity was associated with the accumulation of 60 metabolites, including the putative SAR signal azelaic acid (AzA) and its precursors 9-hydroperoxy octadecadienoic acid (9-HPOD) and 9-oxo nonanoic acid (ONA). Exogenous ONA induced SAR in systemic untreated leaves when applied at a 4-fold lower concentration than AzA. The data suggest that in planta oxidation of ONA to AzA might be partially responsible for this response and provide further evidence that AzA mobilizes Arabidopsis immunity in a concentration-dependent manner. The AzA fragmentation product pimelic acid did not induce SAR. The results link the C9 lipid peroxidation products ONA and AzA with systemic rather than local resistance and suggest that EDS1 directly or indirectly promotes the accumulation of ONA, AzA, or one or more of their common precursors possibly by activating one or more pathways that either result in the release of these compounds from galactolipids or promote lipid peroxidation.
NASA Astrophysics Data System (ADS)
Kumar, Rohitash; Kumar, Ravindra; Dixit, Ambesh
2016-05-01
Thermal properties of Acetamide (AM) - Benzoic acid (BA) and Benzoic acid (BA) - Phthalimide (PM) binary eutectic systems are theoretically calculated using thermodynamic principles. We found that the binary systems of AM-BA at 67.6 : 32.4 molar ratio, BA-PM at 89.7 : 10.3 molar ratio form eutectic mixtures with melting temperatures ~ 54.5 °C and 114.3 °C respectively. Calculated latent heat of fusion for these eutectic mixtures are 191 kJ/kg and 146.5 kJ/kg respectively. These melting temperatures and heat of fusions of these eutectic mixtures make them suitable for thermal energy storage applications in solar water heating and solar cooking systems.
NASA Astrophysics Data System (ADS)
Goto, Rensuke; Fukuda, Hiroshi; Königsberger, Erich; Königsberger, Lan-Chi
2011-03-01
The solubility data for well-defined binary, ternary, and multicomponent systems of solid-liquid type are reviewed. One component, which is 2-, 3-, and 4-hydroxybenzoic acids, 4-hydroxybenzoate alkyl esters (parabens), or hydroxybenzoic acid salts, is in the solid state at room temperature and another component is liquid water, meaning that all of the systems are aqueous solutions. The ternary or multicomponent systems include organic substances of various classes (hydrocarbons of several structural types, halogenated hydrocarbons, alcohols, acids, ethers, esters, amides, and surfactants) or inorganic substances. Systems reported in the primary literature from 1898 through 2000 are compiled. For seven systems, sufficient binary data for hydroxybenzoic acids or parabens in water are available to allow critical evaluation. Almost all data are expressed as mass and mole fractions as well as the originally reported units, while some data are expressed as molar concentration.
Co-oxidation of the sulfur-containing amino acids in an autoxidizing lipid system
Wedemeyer, G.A.; Dollar, A.M.
1963-01-01
Oxidation of the sulfur amino acids by autoxidizing lipids was studied in a model system consisting of an amino acid dispersed in cold-pressed, molecularly distilled menhaden oil (20–80% w/w). Under all conditions investigated, cysteine was oxidized completely to cystine. Preliminary results suggest that at 110°C the oxidation follows first-order kinetics for at least the first 8 hr. A specific reaction rate constant of 0.25 per hour was calculated. When fatty acids were added to the system, cystine was oxidized to its thiosulfinate ester. When the fatty acid-cystine ratio was 1:2, oxidation of cystine was a maximum. No oxidation of cystine occurred unless either a fatty acid, volatile organic acid, or ethanol was added. Under the conditions investigated, methionine was not oxidized to either its sulfoxide or its sulfone.
Impact of acid rain and deposition on aquatic biological systems
Isom, B.; Dennis, S.; Bates, J.
1986-01-01
Since little information on acid rain effects on fish and other aquatic life exists, and what is available is often inconclusive, STP 928 presents quantitative and practical information. This volume is a collection of nine diverse, peer-reviewed papers. This book discusses lake/stream acidification processes and aquatic biological effects, such as stream and lake productivity, diversity, and measurement techniques.
Thymine, adenine and lipoamino acid based gene delivery systems.
Skwarczynski, Mariusz; Ziora, Zyta M; Coles, Daniel J; Lin, I-Chun; Toth, Istvan
2010-05-14
A novel class of thymine, adenine and lipoamino acid based non-viral carriers for gene delivery has been developed. Their ability to bind to DNA by hydrogen bonding was confirmed by NMR diffusion, isothermal titration calorimetry and transmission electron microscopy experiments.
Disinfection of water in recirculating aquaculture systems with peracetic acid
Technology Transfer Automated Retrieval System (TEKTRAN)
Peracetic acid (PAA) has become a favoured alternative to chlorination in the disinfection of municipal waste water in recent years. It is also commonly used in the food industry as a disinfectant. Based on PAA concentration, the disulfide linkage in enzymes and proteins of microorganisms can be bro...
DEVELOPMENT OF SRB TREATMENT SYSTEMS FOR ACID MINE DRAINAGE
Over the past decade, significant advances have been made in the development of sulfate- reducing bacteria (SRB) technology to treat acid mine drainage (AMD), Bench-scale testing, field demonstrations, and engineered applications of SRBs for the treatment of AMD will be presented...
System for NO reduction using sublimation of cyanuric acid
Perry, R.A.
1989-01-24
An arrangement for reducing the NO content of a gas stream comprises contacting the gas stream with HNCO at a temperature effective for heat induced decomposition of HNCO and for resultant lowering of the NO content of the gas stream. Preferably, the HNCO is generated by sublimation of cyanuric acid. 1 fig.
System for NO reduction using sublimation of cyanuric acid
Perry, Robert A.
1989-01-01
An arrangement for reducing the NO content of a gas stream comprises contacting the gas stream with HNCO at a temperature effective for heat induced decomposition of HNCO and for resultant lowering of the NO content of the gas stream. Preferably, the HNCO is generated by sublimation of cyanuric acid.
Weinberger, A.J.; Marley, J.L.; Costanzo, D.A.
1980-05-01
A solvent extraction study to determine equilibrium conditions of thorium nitrate-nitric acid with 30% tributyl phosphate in normal dodecane has been completed. Experimental conditions studied were 30 to 60{sup 0}C, 0.05 to 1.5 M Th(NO{sub 3}){sub 4}, and 0.0 to 3.0 M HNO{sub 3}. The extractant concentration was constant at 30% tributyl phosphate. The equilibrium experiments have produced data which demonstrate that thorium nitrate concentration, free acid, and density are related in equilibrium behavior between the aqueous and organic phases from 30 to 60{sup 0}C in the 30% tributyl phosphate-dodecane solvent extraction system. The concentration interactions apply to both the two- and three-phase regions. A linear correlation was observed for the density (D) of the aqueous or organic phase and the concentration of thorium and free acid. The general form of the equation is D = a(C/sub Th/ + bC/sub H/) + c, where a is the slope, b is the constant, c is the intercept, and C/sub Th/ and C/sub H/ are the molar concentrations of thorium and free acid respectively. The relationship of temperature, thorium nitrate, and free acid makes possible the definitions of the boundaries between the two- and three-phase regions. This dependence, in turn, permits operational control or simulation studies of the system within the two-phase region. The data demonstrate the interactions of the components of the Thorex system and can be used to improve the mathematical description of equilibrium in the SEPHIS-Thorex computer program.
Development of anti-scale poly(aspartic acid-citric acid) dual polymer systems for water treatment.
Nayunigari, Mithil Kumar; Gupta, Sanjay Kumar; Kokkarachedu, Varaprasad; Kanny, K; Bux, F
2014-01-01
The formation of calcium sulphate and calcium carbonate scale poses major problems in heat exchangers and water cooling systems, thereby affecting the performance of these types of equipment. In order to inhibit these scale formations, new types of biodegradable water soluble single polymer and dual poly(aspartic acid-citric acid) polymers were developed and tested. The effectiveness of single polymer and four different compositions of poly aspartic acid and citric acid dual polymer systems as scale inhibitors were evaluated. Details of the synthesis, thermal stability, scale inhibition and the morphological characterization of single and dual polymers are presented in this scientific paper. It was found that the calcium sulphate scale inhibition rate was in the range 76.06-91.45%, while the calcium carbonate scale inhibition rate observed was in the range 23.37-30.0% at 65-70 °C. The finding suggests that the water soluble dual polymers are very effective in sulphate scale inhibition in comparison of calcium carbonate scale inhibition.
Development of anti-scale poly(aspartic acid-citric acid) dual polymer systems for water treatment.
Nayunigari, Mithil Kumar; Gupta, Sanjay Kumar; Kokkarachedu, Varaprasad; Kanny, K; Bux, F
2014-01-01
The formation of calcium sulphate and calcium carbonate scale poses major problems in heat exchangers and water cooling systems, thereby affecting the performance of these types of equipment. In order to inhibit these scale formations, new types of biodegradable water soluble single polymer and dual poly(aspartic acid-citric acid) polymers were developed and tested. The effectiveness of single polymer and four different compositions of poly aspartic acid and citric acid dual polymer systems as scale inhibitors were evaluated. Details of the synthesis, thermal stability, scale inhibition and the morphological characterization of single and dual polymers are presented in this scientific paper. It was found that the calcium sulphate scale inhibition rate was in the range 76.06-91.45%, while the calcium carbonate scale inhibition rate observed was in the range 23.37-30.0% at 65-70 °C. The finding suggests that the water soluble dual polymers are very effective in sulphate scale inhibition in comparison of calcium carbonate scale inhibition. PMID:25189837
Gibberellic acid production by free and immobilized cells in different culture systems.
Durán-Páramo, Enrique; Molina-Jiménez, Héctor; Brito-Arias, Marco A; Robles-Martínez, Fabián
2004-01-01
Gibberellic acid production was studied in different fermentation systems. Free and immobilized cells of Gibberella fujikuroi cultures in shake-flask, stirred and fixed-bed reactors were evaluated for the production of gibberellic acid (GA3). Gibberellic acid production with free cells cultured in a stirred reactor reached 0.206 g/L and a yield of 0.078 g of GA3/g biomass.
Transient changes in the limbic histaminergic system after systemic kainic acid-induced seizures.
Lintunen, Minnamaija; Sallmen, Tina; Karlstedt, Kaj; Panula, Pertti
2005-10-01
Increased brain histamine is reported to protect against convulsions. We used systemic kainic acid (KA) administration to study possible changes of the histaminergic system in rat brain in status epilepticus (SE). Robust increases in brain histamine concentrations and numbers of histamine-immunoreactive nerve fibers were detected in the piriform cortex (Pir) and amygdala after KA injection, suggesting a reactive increase, which is opposite to other published aminergic transmitter responses. These changes, lasting several weeks, might be coupled to a mechanism unrelated to the anticonvulsive function of histamine. Transient increases in mRNA expression of H(3) receptor isoforms with a full-length third intracellular loop, coupled to mitogen-activated protein kinase pathway, were detected first in the hippocampal CA3c area, followed by the Pir and amygdala and then the hippocampal CA1 area. These results suggest that histamine and H3 receptors, which also control the release of GABA and glutamate, might be involved in convulsive SE.
Acid and alkali doped PBI electrolyte in electrochemical system
NASA Astrophysics Data System (ADS)
Xing, Baozhong
In this work the conductivity of blank PBI membrane, acid doped PBI and alkaline doped PBI was systematically studied. A new methodology for sorption kinetics study in electrolyte solution has been established by monitoring the conductivity change during the sorption process. The model of the doping process and mechanism of conductivity are proposed. The performance of PBI (doped under optimum conditions) in fuel cell as PEM was evaluated. The experimental results show that the blank PBI in acid solution is an ionic insulator. It clarified the long time confusion in this area. The acid doped PBI membrane is an ionic conductor. The conductivity increases with the concentration of the acid solution. In high concentration acid solution, the conductivity increases with the type of acid in the order: H2SO 4 > H3PO4 > HClO4 > HNO3 > HCl. The kinetics of the doping process was studied, by a continuous method. The ionic conductivity mechanism was established. The PBI membranes doped with H2SO4 and H3PO4 exhibit better performance than NafionRTM. The doped FBI has more resistance to CO poison. 3% CO in H2 has little effect on the H3PO 4 doped PBI membrane at 185°C. The conductivity of the alkali doped PBI membrane changes with the concentration of the alkaline solution and the type of the alkalis. The conductivity has a maximum in KOH and NaOH solution. The maximum conductivity in KOH is higher than in NaOH and LiOH. It is about 5 times of that of NafionRTM in alkaline solution. The two-step sorption process in alkaline solution was observed. The first step is the permeation process of the alkalis in the PBI membrane. The permeation is the results of diffusion and interaction. It is concluded that the permeation process is controlled by the rate of interaction between the alkali and PBI molecule. The second step is the relaxation process in the membrane. This step contributes more to the conductivity for the membrane than the first step. The ionic conductivity mechanism
Reprocessing system with nuclide separation based on chromatography in hydrochloric acid solution
Suzuki, Tatsuya; Tachibana, Yu; Koyama, Shi-ichi
2013-07-01
We have proposed the reprocessing system with nuclide separation processes based on the chromatographic technique in the hydrochloric acid solution system. Our proposed system consists of the dissolution process, the reprocessing process, the minor actinide separation process, and nuclide separation processes. In the reprocessing and separation processes, the pyridine resin is used as a main separation media. It was confirmed that the dissolution in the hydrochloric acid solution is easily achieved by the plasma voloxidation and by the addition of oxygen peroxide into the hydrochloric acid solution.
Grant-Preece, Paris; Fang, Hongjuan; Schmidtke, Leigh M; Clark, Andrew C
2013-11-01
The efficiency of different white wine antioxidant systems in preventing aldehyde production from amino acids by oxidative processes is not well understood. The aim of this study was to assess the efficiency of sulphur dioxide alone and in combination with either glutathione, ascorbic acid or its stereoisomer erythorbic acid, in preventing formation of the sensorially important compounds methional and phenylacetaldehyde from methionine and phenylalanine in model white wine. UHPLC, GC-MS/MS, LC-MS/MS, flow injection analysis and luminescence sensors determined both compositional changes during storage, and sulphur dioxide-aldehyde apparent equilibrium constants. Depending on temperature (25 or 45°C) or extent of oxygen supply, sulphur dioxide was equally or more efficient in impeding the production of methional compared to the other antioxidant systems. For phenylacetaldehyde, erythorbic acid or glutathione with sulphur dioxide provided improved inhibition compared to sulphur dioxide alone, in conditions of limited oxygen consumption. The results also demonstrate the extent to which sulphur dioxide addition can lower the free aldehyde concentrations to below their aroma thresholds.
Evaluation of optimal reuse system for hydrofluoric acid wastewater.
Won, Chan-Hee; Choi, Jeongyun; Chung, Jinwook
2012-11-15
The treatment of hydrofluoric acid (HF) wastewater has been an important environmental issue in recent years due to the extensive use of hydrofluoric acid in the chemical and electronics industries, such as semiconductor manufacturers. Coagulation/precipitation and ion exchange technologies have been used to treat HF wastewater, but these conventional methods are ineffective in removing organics, salts, and fluorides, limiting its reuse for water quality and economic feasibility. One promising alternative is reverse osmosis (RO) after lime treatment. Based on pilot-scale experiment using real HF wastewater discharged from semiconductor facility, the spiral wound module equipped with polyamide membranes has shown excellent flux and chemical cleaning cycles. Our results suggest that coagulation/precipitation and spiral wound RO constitute the optimal combination to reuse HF wastewater.
The role of epoxyeicosatrienoic acids in the cardiovascular system
Yang, L; Mäki-Petäjä, K; Cheriyan, J; McEniery, C; Wilkinson, I B
2015-01-01
There is increasing evidence suggesting that epoxyeicosatrienoic acids (EETs) play an important role in cardioprotective mechanisms. These include regulating vascular tone, modulating inflammatory responses, improving cardiomyocyte function and reducing ischaemic damage, resulting in attenuation of animal models of cardiovascular risk factors. This review discusses the current knowledge on the role of EETs in endothelium-dependent control of vascular tone in the healthy and in subjects with cardiovascular risk factors, and considers the pharmacological potential of targeting this pathway. PMID:25655310
The role of epoxyeicosatrienoic acids in the cardiovascular system.
Yang, L; Mäki-Petäjä, K; Cheriyan, J; McEniery, C; Wilkinson, I B
2015-07-01
There is increasing evidence suggesting that epoxyeicosatrienoic acids (EETs) play an important role in cardioprotective mechanisms. These include regulating vascular tone, modulating inflammatory responses, improving cardiomyocyte function and reducing ischaemic damage, resulting in attenuation of animal models of cardiovascular risk factors. This review discusses the current knowledge on the role of EETs in endothelium-dependent control of vascular tone in the healthy and in subjects with cardiovascular risk factors, and considers the pharmacological potential of targeting this pathway.
Thoron-meso-tartaric acid system for determination of thorium
Fletcher, M.H.; Grimaldi, F.S.; Jenkins, L.B.
1957-01-01
In the spectrophotometric determination of thorium with thoron, mesotartaric acid is used as a masking reagent for zirconium. The effects of different experimental variables such as the concentrations of the reagents, time, and temperature, and the behavior of 35 ions which might be present in thorium ores are discussed. A dilution procedure is given for the direct determination of thorium in zircon (ZrSiO4) that is also generally applicable to other materials.
Systems metabolic engineering design: Fatty acid production as an emerging case study
Tee, Ting Wei; Chowdhury, Anupam; Maranas, Costas D; Shanks, Jacqueline V
2014-01-01
Increasing demand for petroleum has stimulated industry to develop sustainable production of chemicals and biofuels using microbial cell factories. Fatty acids of chain lengths from C6 to C16 are propitious intermediates for the catalytic synthesis of industrial chemicals and diesel-like biofuels. The abundance of genetic information available for Escherichia coli and specifically, fatty acid metabolism in E. coli, supports this bacterium as a promising host for engineering a biocatalyst for the microbial production of fatty acids. Recent successes rooted in different features of systems metabolic engineering in the strain design of high-yielding medium chain fatty acid producing E. coli strains provide an emerging case study of design methods for effective strain design. Classical metabolic engineering and synthetic biology approaches enabled different and distinct design paths towards a high-yielding strain. Here we highlight a rational strain design process in systems biology, an integrated computational and experimental approach for carboxylic acid production, as an alternative method. Additional challenges inherent in achieving an optimal strain for commercialization of medium chain-length fatty acids will likely require a collection of strategies from systems metabolic engineering. Not only will the continued advancement in systems metabolic engineering result in these highly productive strains more quickly, this knowledge will extend more rapidly the carboxylic acid platform to the microbial production of carboxylic acids with alternate chain-lengths and functionalities. PMID:24481660
Utilization of a bipolar lead acid battery for the advanced launch system
NASA Technical Reports Server (NTRS)
Gentry, William O.; Vidas, Robin; Miles, Ronald; Eckles, Steven
1991-01-01
The development of a battery comprised of bipolar lead acid modules is discussed. The battery is designed to satisfy the requirements of the Advanced Launch System (ALS). The battery will have the following design features: (1) conventional lead acid chemistry; (2) thin electrode/active materials; (3) a thin separator; (4) sealed construction (gas recombinant); and (5) welded plastic frames for the external seal.
STATE ACID RAIN RESEARCH AND SCREENING SYSTEM - VERSION 1.0 USER'S MANUAL
The report is a user's manual that describes Version 1.0 of EPA's STate Acid Rain Research and Screening System (STARRSS), developed to assist utility regulatory commissions in reviewing utility acid rain compliance plans. It is a screening tool that is based on scenario analysis...
Reaction-Diffusion Patterns in Structured Media
NASA Astrophysics Data System (ADS)
Epstein, Irving
I will look at pattern formation in the Belousov-Zhabotinsky (BZ) oscillating chemical reaction in media that are structured at length scales ranging from ten nanometers to a few centimeters. A reverse microemulsion consisting of nanometer diameter droplets of water containing the reactants dispersed in oil allows the physical structure (size, spacing) of the droplets and their chemical composition to be controlled independently, enabling one to generate a remarkable variety of stationary and moving patterns, including Turing structures, ordinary and antispirals, packet waves and spatiotemporal chaos. One- and two-dimensional arrays of aqueous droplets in oil generated by microfluidic techniques have diameters of the order of 100 micrometers and produce a different array of patterns that can be precisely controlled with light. In particular, circular arrays of droplets provide a testing ground for some of Turing's ideas about morphogenesis. By attaching the BZ catalyst to a polymer that shrinks and swells in response to changes in the redox state of the catalyst, one can construct gel materials that transduce chemical changes to mechanical motion, a phenomenon modeled with considerable success by the Balazs group. If time permits, I will also discuss the BZ reaction in coupled macroscopic flow reactors that mimic small neural networks.
Seol, Yongkoo; Javandel, Iraj
2008-03-15
Fenton's reagent, a solution of hydrogen peroxide and ferrous iron catalyst, is used for an in-situ chemical oxidation of organic contaminants. Sulfuric acid is commonly used to create an acidic condition needed for catalytic oxidation. Fenton's reaction often involves pressure buildup and precipitation of reaction products, which can cause safety hazards and diminish efficiency. We selected citric acid, a food-grade substance, as an acidifying agent to evaluate its efficiencies for organic contaminant removal in Fenton's reaction, and examined the impacts of using citric acid on the unwanted reaction products. A series of batch and column experiments were performed with varying H{sub 2}O{sub 2} concentrations to decompose selected chlorinated ethylenes. Either dissolved iron from soil or iron sulfate salt was added to provide the iron catalyst in the batch tests. Batch experiments revealed that both citric and sulfuric acid systems achieved over 90% contaminant removal rates, and the presence of iron catalyst was essential for effective decontamination. Batch tests with citric acid showed no signs of pressure accumulation and solid precipitations, however the results suggested that an excessive usage of H{sub 2}O{sub 2} relative to iron catalysts (Fe{sup 2+}/H{sub 2}O{sub 2} < 1/330) would result in lowering the efficiency of contaminant removal by iron chelations in the citric acid system. Column tests confirmed that citric acid could provide suitable acidic conditions to achieve higher than 55% contaminant removal rates.
Dietary omega-3 fatty acids modulate large-scale systems organization in the rhesus macaque brain.
Grayson, David S; Kroenke, Christopher D; Neuringer, Martha; Fair, Damien A
2014-02-01
Omega-3 fatty acids are essential for healthy brain and retinal development and have been implicated in a variety of neurodevelopmental disorders. This study used resting-state functional connectivity MRI to define the large-scale organization of the rhesus macaque brain and changes associated with differences in lifetime ω-3 fatty acid intake. Monkeys fed docosahexaenoic acid, the long-chain ω-3 fatty acid abundant in neural membranes, had cortical modular organization resembling the healthy human brain. In contrast, those with low levels of dietary ω-3 fatty acids had decreased functional connectivity within the early visual pathway and throughout higher-order associational cortex and showed impairment of distributed cortical networks. Our findings illustrate the similarity in modular cortical organization between the healthy human and macaque brain and support the notion that ω-3 fatty acids play a crucial role in developing and/or maintaining distributed, large-scale brain systems, including those essential for normal cognitive function.
Drosophila melanogaster as a model system to study long-chain fatty acid amide metabolism
Jeffries, Kristen A.; Dempsey, Daniel R.; Behari, Anita L.; Anderson, Ryan L.; Merkler, David J.
2014-01-01
Long-chain fatty acid amides are cell-signaling lipids identified in mammals and, recently, in invertebrates, as well. Many details regarding fatty acid amide metabolism remain unclear. Herein, we demonstrate that Drosophila melanogaster is an excellent model system for the study long-chain fatty acid amide metabolism as we have quantified the endogenous levels of N-acylglycines, N-acyldopamines, N-acylethanolamines, and primary fatty acid amides by LC/QTOF-MS. Growth of Drosophila melanogaster on media supplemented with [1-13C]-palmitate lead to a family of 13C-palmitate-labeled fatty acid amides in the fly heads. The [1-13C]-palmitate feeding studies provide insight into the biosynthesis of the fatty acid amides. PMID:24650760