Results 191 to 200 of about 2,033 (212)
Quantifying the Uncertainty of Molecular Dynamics Simulations: Good–Turing Statistics Revisited
Journal of Computational Chemistry, Volume 47, Issue 14, 30 May 2026.A method and associated computer program are described that allow the estimation of the remaining structural uncertainty of a molecular dynamics trajectory. ABSTRACT We have previously shown that Good–Turing statistics can be applied to molecular dynamics trajectories to estimate the probability of observing completely new (thus‐far unobserved ...
Vasiliki Tsampazi, Nicholas M. Glykos
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Complex Systems, 2023
The first pattern formation model was proposed by the mathematician Alan M. Turing. This model consists of a system of reaction-diffusion equations that produces stationary patterns by means of the so-called “Turing instability.” In this paper, we found the conditions that the network and the parameters need to fulfill in order to achieve the Turing ...
Elizabeth Alejandra Ortiz Durán +1 more
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The first pattern formation model was proposed by the mathematician Alan M. Turing. This model consists of a system of reaction-diffusion equations that produces stationary patterns by means of the so-called “Turing instability.” In this paper, we found the conditions that the network and the parameters need to fulfill in order to achieve the Turing ...
Elizabeth Alejandra Ortiz Durán +1 more
openaire +1 more source
Physical Review E, 1999
We address the problem of pattern formation on the surface of a sphere using Turing equations. By considering a generic reaction-diffusion model, we numerically investigate the patterns formed under different conditions on the parameter values. Our results show that a closed surface with curvature, as a sphere, imposes geometrical restrictions on the ...
C, Varea, J L, Aragón, R A, Barrio
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We address the problem of pattern formation on the surface of a sphere using Turing equations. By considering a generic reaction-diffusion model, we numerically investigate the patterns formed under different conditions on the parameter values. Our results show that a closed surface with curvature, as a sphere, imposes geometrical restrictions on the ...
C, Varea, J L, Aragón, R A, Barrio
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Effect of obstructions on growing Turing patterns
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2022We study how Turing pattern formation on a growing domain is affected by discrete domain discontinuities. We use the Lengyel–Epstein reaction–diffusion model to numerically simulate Turing pattern formation on radially expanding circular domains containing a variety of obstruction geometries, including obstructions spanning the length of the domain ...
Milos Dolnik +3 more
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Membrane-bound Turing patterns
Physical Review E, 2005Motivated by recent observations in biological cells, we study Turing patterns in bounded regions where the nonlinear chemical reactions occur on the boundary and where reagent transport occurs in the bulk. Within a generic model, we formulate the stability problem and discuss the conditions for the occurrence of a Turing instability. By choosing other
Herbert, Levine, Wouter-Jan, Rappel
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Widening the criteria for emergence of Turing patterns
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2020The classical concept for emergence of Turing patterns in reaction–diffusion systems requires that a system should be composed of complementary subsystems, one of which is unstable and diffuses sufficiently slowly while the other one is stable and diffuses sufficiently rapidly. In this work, the phenomena of emergence of Turing patterns are studied and
Maxim Kuznetsov, Andrey Polezhaev
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1998
In the first chapter of this book, we noted the “dark age” of nearly forty years separating the work of Bray and Lotka in the early 1920s and the discovery of the BZ reaction in the late 1950s. Remarkably, the history of nonlinear chemical dynamics contains another gap of almost the same length.
Irving R. Epstein, John A. Pojman
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In the first chapter of this book, we noted the “dark age” of nearly forty years separating the work of Bray and Lotka in the early 1920s and the discovery of the BZ reaction in the late 1950s. Remarkably, the history of nonlinear chemical dynamics contains another gap of almost the same length.
Irving R. Epstein, John A. Pojman
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Turing Bifurcations and Pattern Selection
1995Pattern forming instabilities in spatially extended dissipative systems driven away from equilibrium have been the focus of a large activity for many years. The goal of this chapter is to present some theoretical concepts that have been developed to understand and describe these dissipative structures [1] from a macroscopic point of view.
Borckmans, Pierre +3 more
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Turing pattern formation in heterogenous media
Physica D: Nonlinear Phenomena, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Voroney, J.-P. +2 more
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Science, 2011
Turing patterns—self-organized structures created by systems that undergo reaction and diffusion—are a possible mechanism underlying pattern formation in living organisms. Although there are many experimental studies of two-dimensional (2D) pattern formation—three-dimensional (3D) structures, the most relevant to biology, have been difficult to observe
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Turing patterns—self-organized structures created by systems that undergo reaction and diffusion—are a possible mechanism underlying pattern formation in living organisms. Although there are many experimental studies of two-dimensional (2D) pattern formation—three-dimensional (3D) structures, the most relevant to biology, have been difficult to observe
openaire +1 more source