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Knotted reaction—diffusion waves
Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2002Using an eikonal formulation the authors demonstrated the existence and stability of both rigidly rotating knotted-waveforms and stationary solutions, and showed that the full reaction-diffusion system supports knotted wave, with good quantitative agreement.
McDermott, S. +2 more
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Compartmentalized reaction-diffusion systems
Physical Review E, 2000Reaction-diffusion systems consisting of a collection of reactive domains separated by chemically inactive regions are considered. The reactive dynamics is governed by a multistep reaction mechanism and each reactive domain is specific to a particular elementary step or collection of elementary steps of the global reaction mechanism.
F, Chávez, R, Kapral
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Physica A: Statistical Mechanics and its Applications, 2000
Abstract We derive a fractional reaction–diffusion equation from a continuous-time random walk model with temporal memory and sources. The equation provides a general model for reaction–diffusion phenomena with anomalous diffusion such as occurs in spatially inhomogeneous environments. As a first investigation of this equation we consider the special
B.I Henry, S.L Wearne
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Abstract We derive a fractional reaction–diffusion equation from a continuous-time random walk model with temporal memory and sources. The equation provides a general model for reaction–diffusion phenomena with anomalous diffusion such as occurs in spatially inhomogeneous environments. As a first investigation of this equation we consider the special
B.I Henry, S.L Wearne
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Proceedings of the 18th annual conference on Computer graphics and interactive techniques, 1991
We present a method for texture synthesis based on the simulation of a process of local nonlinear interaction, called reaction-diffusion, which has been proposed as a model of biological pattern formation. We extend traditional reaction-diffusion systems by allowing anisotropic and spatially non-uniform diffusion, as well as multiple competing ...
Andrew Witkin, Michael Kass
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We present a method for texture synthesis based on the simulation of a process of local nonlinear interaction, called reaction-diffusion, which has been proposed as a model of biological pattern formation. We extend traditional reaction-diffusion systems by allowing anisotropic and spatially non-uniform diffusion, as well as multiple competing ...
Andrew Witkin, Michael Kass
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2015
This chapter discusses different aspects of the Reaction-Diffusion (RD) model used to interpret dissociation and reformation of the Si−H bonds (in other words, creation and reverse-anneal of dangling Si-bonds or interface traps) present at the silicon/oxide interfaces of a CMOS transistor.
Ahmad Ehteshamul Islam +3 more
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This chapter discusses different aspects of the Reaction-Diffusion (RD) model used to interpret dissociation and reformation of the Si−H bonds (in other words, creation and reverse-anneal of dangling Si-bonds or interface traps) present at the silicon/oxide interfaces of a CMOS transistor.
Ahmad Ehteshamul Islam +3 more
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2010
Traveling waves are typical nonequilibrium phenomena encountered in numerous instances in physics, chemistry, biology, and other areas [129, 82, 309, 310]. Reacting and diffusing systems described by the RD equation (2.3) represent a particular well-studied class of applications.
Vicenç Méndez +2 more
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Traveling waves are typical nonequilibrium phenomena encountered in numerous instances in physics, chemistry, biology, and other areas [129, 82, 309, 310]. Reacting and diffusing systems described by the RD equation (2.3) represent a particular well-studied class of applications.
Vicenç Méndez +2 more
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2020
Symmetry and non-symmetry in some overdetermined boundary value problems asymptotical behaviour of solutions of some reaction-diffusion systems nonlinear singular parabolic equations nonlinear Liouville theorem existence and regularity results for quasilinear parabolic equations elliptic systems with various growth a strong comparison principle for the
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Symmetry and non-symmetry in some overdetermined boundary value problems asymptotical behaviour of solutions of some reaction-diffusion systems nonlinear singular parabolic equations nonlinear Liouville theorem existence and regularity results for quasilinear parabolic equations elliptic systems with various growth a strong comparison principle for the
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2009
In this chapter numerical methods for singularly perturbed reaction-diffusion equations on the square are studied. Find \( u \in C^2 (\Omega ) \cup C(\bar \Omega ) \) such that $$ Lu: = - \varepsilon ^2 \Delta u + cu = f\text{ in }\Omega \text{ = (0,1)}^\text{2} ,\text{ }u|\partial \Omega = g, $$ (8.1) where the parameter satisfies \( 0 0 ...
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In this chapter numerical methods for singularly perturbed reaction-diffusion equations on the square are studied. Find \( u \in C^2 (\Omega ) \cup C(\bar \Omega ) \) such that $$ Lu: = - \varepsilon ^2 \Delta u + cu = f\text{ in }\Omega \text{ = (0,1)}^\text{2} ,\text{ }u|\partial \Omega = g, $$ (8.1) where the parameter satisfies \( 0 0 ...
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2013
In this chapter we shall focus on models in which reaction and diffusion are in competition. Of particular interest is the study of the asymptotic behavior of the solutions as time goes on and to explore the existence and the stability properties of limiting steady states.
Sandro Salsa +3 more
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In this chapter we shall focus on models in which reaction and diffusion are in competition. Of particular interest is the study of the asymptotic behavior of the solutions as time goes on and to explore the existence and the stability properties of limiting steady states.
Sandro Salsa +3 more
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International Journal of Modern Physics C, 2023
The recently introduced Theory of the Adjacent Possible (TAP) is a model of combinatorial innovation aiming to explain the “hockey-stick” upward trend of human technological evolution, where an explosion in the number of produced items with increasing complexity suddenly occurs.
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The recently introduced Theory of the Adjacent Possible (TAP) is a model of combinatorial innovation aiming to explain the “hockey-stick” upward trend of human technological evolution, where an explosion in the number of produced items with increasing complexity suddenly occurs.
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