The Experts below are selected from a list of 155994 Experts worldwide ranked by ideXlab platform
Ulrike Feudel - One of the best experts on this subject based on the ideXlab platform.
-
multistability noise and attractor hopping the crucial role of chaotic Saddles
arXiv: Chaotic Dynamics, 2003Co-Authors: Suso Kraut, Ulrike FeudelAbstract:We investigate the hopping dynamics between different attractors in a multistable system under the influence of noise. Using symbolic dynamics we find a sudden increase of dynamical entropies, when a system parameter is varied. This effect is explained by a novel bifurcation involving two chaotic Saddles. We also demonstrate that the transient lifetimes on the saddle obey a scaling law in analogy to crisis.
-
multistability noise and attractor hopping the crucial role of chaotic Saddles
Physical Review E, 2002Co-Authors: Suso Kraut, Ulrike FeudelAbstract:We investigate the hopping dynamics between different attractors in a multistable system under the influence of noise. Using symbolic dynamics we find a sudden increase of dynamical entropies, when a system parameter is varied. This effect is explained by a bifurcation involving two chaotic Saddles. We also demonstrate that the transient lifetimes on the saddle obey a scaling law in analogy to crisis.
Stephen Wiggins - One of the best experts on this subject based on the ideXlab platform.
-
index k Saddles and dividing surfaces in phase space with applications to isomerization dynamics
Journal of Chemical Physics, 2011Co-Authors: Peter Collins, Gregory S Ezra, Stephen WigginsAbstract:In this paper, we continue our studies of the phase space geometry and dynamics associated with index k Saddles (k > 1) of the potential energy surface. Using Poincare-Birkhoff normal form (NF) theory, we give an explicit formula for a "dividing surface" in phase space, i.e., a codimension one surface (within the energy shell) through which all trajectories that "cross" the region of the index k saddle must pass. With a generic non-resonance assumption, the normal form provides k (approximate) integrals that describe the saddle dynamics in a neighborhood of the index k saddle. These integrals provide a symbolic description of all trajectories that pass through a neighborhood of the saddle. We give a parametrization of the dividing surface which is used as the basis for a numerical method to sample the dividing surface. Our techniques are applied to isomerization dynamics on a potential energy surface having four minima; two symmetry related pairs of minima are connected by low energy index 1 Saddles, with the pairs themselves connected via higher energy index 1 Saddles and an index 2 saddle at the origin. We compute and sample the dividing surface and show that our approach enables us to distinguish between concerted crossing ("hilltop crossing") isomerizing trajectories and those trajectories that are not concerted crossing (potentially sequentially isomerizing trajectories). We then consider the effect of additional "bath modes" on the dynamics, by a study of a four degree-of-freedom system. For this system we show that the normal form and dividing surface can be realized and sampled and that, using the approximate integrals of motion and our symbolic description of trajectories, we are able to choose initial conditions corresponding to concerted crossing isomerizing trajectories and (potentially) sequentially isomerizing trajectories.
-
index k Saddles and dividing surfaces in phase space with applications to isomerization dynamics
arXiv: Statistical Mechanics, 2011Co-Authors: Peter Collins, Gregory S Ezra, Stephen WigginsAbstract:In this paper we continue our studies of the phase space geometry and dynamics associated with index k Saddles (k > 1) of the potential energy surface. Using normal form theory, we give an explicit formula for a "dividing surface" in phase space, i.e. a co-dimension one surface (within the energy shell) through which all trajectories that "cross" the region of the index k saddle must pass. With a generic non-resonance assumption, the normal form provides k (approximate) integrals that describe the saddle dynamics in a neighborhood of the index k saddle. These integrals provide a symbolic description of all trajectories that pass through a neighborhood of the saddle. We give a parametrization of the dividing surface which is used as the basis for a numerical method to sample the dividing surface. Our techniques are applied to isomerization dynamics on a potential energy surface having 4 minima; two symmetry related pairs of minima are connected by low energy index one Saddles, with the pairs themselves connected via higher energy index one Saddles and an index two saddle at the origin. We compute and sample the dividing surface and show that our approach enables us to distinguish between concerted crossing ("hilltop crossing") isomerizing trajectories and those trajectories that are not concerted crossing (potentially sequentially isomerizing trajectories). We then consider the effect of additional "bath modes" on the dynamics, which is a four degree-of-freedom system. For this system we show that the normal form and dividing surface can be realized and sampled and that, using the approximate integrals of motion and our symbolic description of trajectories, we are able to choose initial conditions corresponding to concerted crossing isomerizing trajectories and (potentially) sequentially isomerizing trajectories.
-
phase space geometry and reaction dynamics near index 2 Saddles
Journal of Physics A, 2009Co-Authors: Gregory S Ezra, Stephen WigginsAbstract:We study the phase-space geometry associated with index 2 Saddles of a potential energy surface and its influence on reaction dynamics for n degree-of-freedom (DoF) Hamiltonian systems. In recent years, similar studies have been carried out for index 1 Saddles of potential energy surfaces, and the phase-space geometry associated with classical transition state theory has been elucidated. In this case, the existence of a normally hyperbolic invariant manifold (NHIM) of saddle stability type has been shown, where the NHIM serves as the 'anchor' for the construction of dividing surfaces having the no-recrossing property and minimal flux. For the index 1 saddle case, the stable and unstable manifolds of the NHIM are co-dimension 1 in the energy surface and have the structure of spherical cylinders, and thus act as the conduits for reacting trajectories in phase space. The situation for index 2 Saddles is quite different, and their relevance for reaction dynamics has not previously been fully recognized. We show that NHIMs with their stable and unstable manifolds still exist, but that these manifolds by themselves lack sufficient dimension to act as barriers in the energy surface in order to constrain reactions. Rather, in the index 2 case there are different types of invariant manifolds, containing the NHIM and its stable and unstable manifolds, that act as co-dimension 1 barriers in the energy surface. These barriers divide the energy surface in the vicinity of the index 2 saddle into regions of qualitatively different trajectories exhibiting a wider variety of dynamical behavior than for the case of index 1 Saddles. In particular, we can identify a class of trajectories, which we refer to as 'roaming trajectories', which are not associated with reaction along the classical minimum energy path (MEP). We illustrate the significance of our analysis of the index 2 saddle for reaction dynamics with two examples. The first involves isomerization on a potential energy surface with multiple (four) symmetry equivalent minima; the dynamics in the vicinity of the saddle enables a rigorous distinction to be made between stepwise (sequential) and concerted (hilltop crossing) isomerization pathways. The second example involves two potential minima connected by two distinct transition states associated with conventional index 1 Saddles, and an index 2 saddle that sits between the two index 1 Saddles. For the case of non-equivalent index 1 Saddles, our analysis suggests a rigorous dynamical definition of 'non-MEP' or 'roaming' reactive events.
-
phase space geometry and reaction dynamics near index two Saddles
arXiv: Chaotic Dynamics, 2009Co-Authors: Gregory S Ezra, Stephen WigginsAbstract:We study the phase space geometry associated with index 2 Saddles of a potential energy surface and its influence on reaction dynamics for $n$ degree-of-freedom (DoF) Hamiltonian systems. For index 1 Saddles of potential energy surfaces (the case of classical transition state theory), the existence of a normally hyperbolic invariant manifold (NHIM) of saddle stability type has been shown, where the NHIM serves as the "anchor" for the construction of dividing surfaces having the no-recrossing property and minimal flux. For the index 1 saddle case the stable and unstable manifolds of the NHIM are co-dimension one in the energy surface, and act as conduits for reacting trajectories in phase space. The situation for index 2 Saddles is quite different. We show that NHIMs with their stable and unstable manifolds still exist, but that these manifolds by themselves lack sufficient dimension to act as barriers in the energy surface. Rather, there are different types of invariant manifolds, containing the NHIM and its stable and unstable manifolds, that act as co-dimension one barriers in the energy surface. These barriers divide the energy surface in the vicinity of the index 2 saddle into regions of qualitatively different trajectories exhibiting a wider variety of dynamical behavior than for the case of index 1 Saddles. In particular, we can identify a class of trajectories, which we refer to as "roaming trajectories", which are not associated with reaction along the classical minimum energy path (MEP). We illustrate the significance of our analysis of the index 2 saddle for reaction dynamics with two examples.
Suso Kraut - One of the best experts on this subject based on the ideXlab platform.
-
multistability noise and attractor hopping the crucial role of chaotic Saddles
arXiv: Chaotic Dynamics, 2003Co-Authors: Suso Kraut, Ulrike FeudelAbstract:We investigate the hopping dynamics between different attractors in a multistable system under the influence of noise. Using symbolic dynamics we find a sudden increase of dynamical entropies, when a system parameter is varied. This effect is explained by a novel bifurcation involving two chaotic Saddles. We also demonstrate that the transient lifetimes on the saddle obey a scaling law in analogy to crisis.
-
multistability noise and attractor hopping the crucial role of chaotic Saddles
Physical Review E, 2002Co-Authors: Suso Kraut, Ulrike FeudelAbstract:We investigate the hopping dynamics between different attractors in a multistable system under the influence of noise. Using symbolic dynamics we find a sudden increase of dynamical entropies, when a system parameter is varied. This effect is explained by a bifurcation involving two chaotic Saddles. We also demonstrate that the transient lifetimes on the saddle obey a scaling law in analogy to crisis.
Giorgio Parisi - One of the best experts on this subject based on the ideXlab platform.
-
on the origin of the boson peak
Journal of Physics: Condensed Matter, 2003Co-Authors: Giorgio ParisiAbstract:We show that the phonon–saddle transition in the ensemble of generalized inherent structures (minima and Saddles) happens at the same point as the dynamical phase transition in glasses, that has been studied in the framework of the mode coupling approximation. The boson peak observed in glasses at low temperature is a remnant of this transition.
-
On the origine of the Boson peak
Journal of Physics: Condensed Matter, 2003Co-Authors: Giorgio ParisiAbstract:We show that the phonon-saddle transition in the ensemble of generalized inherent structures (minima and Saddles) happens at the same point as the dynamical phase transition in glasses, that has been studied in the framework of the mode coupling approximation. The Boson peak observed in glasses at low temperature is a remanent of this transition.
Francesco Sciortino - One of the best experts on this subject based on the ideXlab platform.
-
Saddles and softness in simple model liquids
arXiv: Disordered Systems and Neural Networks, 2004Co-Authors: Luca Angelani, G Ruocco, C De Michele, Francesco SciortinoAbstract:We report a numerical study of Saddles properties of the potential energy landscape for soft spheres with different softness, i.e. different power n of the interparticle repulsive potential. We find that saddle-based quantities rescale into master curves once energies and temperatures are scaled by mode-coupling temperature T_MCT, confirming and generalizing previous findings obtained for Lennard-Jones like models.
-
A stroll in the energy landscape
Philosophical Magazine B, 2002Co-Authors: Antonio Scala, Luca Angelani, Roberto Di Leonardo, Giancarlo Ruocco, Francesco SciortinoAbstract:We review recent results on the potential energy landscape (PES) of model liquids. The role of saddle-points in the PES in connecting dynamics to statics is investigated, confirming that a change between minima-dominated and saddle-dominated regions of the PES explored in equilibrium happens around the Mode Coupling Temperature. The structure of the low-energy Saddles in the basins is found to be simple and hierarchically organized; the presence of Saddles nearby in energy to the local minima indicates that, at non-cryogenic temperatures, entropic bottlenecks limit the dynamics.
-
Saddles in the energy landscape probed by supercooled liquids
Physical Review Letters, 2000Co-Authors: Luca Angelani, Antonio Scala, R Di Leonardo, G Ruocco, Francesco SciortinoAbstract:We numerically investigate the supercooled dynamics of two simple model liquids exploiting the partition of the multidimensional configuration space in basins of attraction of the stationary points (inherent Saddles) of the potential energy surface. We find that the inherent saddle order and potential energy are well-defined functions of the temperature T. Moreover, by decreasing T, the saddle order vanishes at the same temperature (T(MCT)) where the inverse diffusivity appears to diverge as a power law. This allows a topological interpretation of T(MCT): it marks the transition from a dynamics between basins of Saddles (T > T(MCT)) to a dynamics between basins of minima (T < T(MCT)).
