Related papers: Phase space geometry and reaction dynamics near in…
We study the effect of changes in the parameters of a two-dimensional potential energy surface on the phase space structures relevant for chemical reaction dynamics. The changes in the potential energy are representative of chemical…
We investigate whether ideas from symplectic topology, in particular Gromov's non-squeezing theorem and symplectic capacity, can provide useful geometric insight into classical reaction dynamics near an index-1 saddle. Using…
The equilibrium configuration of an engineering structure, able to withstand a certain loading condition, is usually associated with a local minimum of the underlying potential energy. However, in the nonlinear context, there may be other…
The rate of a chemical reaction can often be determined by the properties of a rank-1 saddle and the associated transition state separating reactants and products. We have found evidence that such rates can be controlled and even enhanced…
In this paper we analyze a two degree of freedom Hamiltonian system constructed from two planar Morse potentials. The resulting potential energy surface has two potential wells surrounded by an unbounded flat region containing no critical…
We develop the geometrical, analytical, and computational framework for reactive island theory for three degrees-of-freedom time-independent Hamiltonian systems. In this setting, the dynamics occurs in a 5-dimensional energy surface in…
Invariant manifolds play an important role in organizing global dynamical behaviors. For example, it is found that in multi-well conservative systems where the potential energy wells are connected by index-1 saddles, the motion between…
We apply the method of Lagrangian Descriptors (LDs) to a symmetric Caldera-type potential energy surface which has three index-1 saddles surrounding a relatively flat region that contains no minimum. Using this method we show the phase…
A computational procedure that allows the detection of a new type of high-dimensional chaotic saddle in Hamiltonian systems with three degrees of freedom is presented. The chaotic saddle is associated with a so-called normally hyperbolic…
When a real saddle equilibrium in a three-dimensional vector field undergoes a homoclinic bifurcation, the associated two-dimensional invariant manifold of the equilibrium closes on itself in an orientable or non-orientable way. We are…
We analyze the dynamics of a model of a nanobeam under compression. The model is a two mode truncation of the Euler-Bernoulli beam equation subject to compressive stress. We consider parameter regimes where the first mode is unstable and…
The framework of transition state theory (TST) provides a powerful way for analyzing the dynamics of physical and chemical reactions. While TST has already been successfully used to obtain reaction rates for systems with a single…
We used for the first time the method of periodic orbit dividing surfaces in a non-integrable Hamiltonian system with three degrees of freedom. We have studied the structure of these four dimensional objects in the five dimensional phase…
The escape mechanism of orbits in a star cluster rotating around its parent galaxy in a circular orbit is investigated. A three degrees of freedom model is used for describing the dynamical properties of the Hamiltonian system. The…
Escape from a potential well through an index-1 saddle can be widely found in some important physical systems. Knowing the criteria and phase space geometry that govern escape events plays an important role in making use of such phenomenon,…
Plenty of saddles on a multidimensional potential energy surface(PES) of two-dimensional microclusters, where atoms are interacting via Morse potential, are numerically located. The reaction paths emanating from the two types of the local…
In this study, we analyze how changes in the geometry of a potential energy surface in terms of depth and flatness can affect the reaction dynamics. We formulate depth and flatness in the context of one and two degree-of-freedom (DOF)…
We investigate the fragmentation dynamics of an atomic chain under tensile stress. We have classified the location, stability type (indices) and energy of all equilibria for the general $n$-particle chain, and have highlighted the…
We study the bifurcation scenario of a three-degree-of-freedom Hamiltonian system, a model based on the Lagrange restricted 3-body problem: a test particle moving in the gravitational field of a pair of interacting dwarf galaxies. The phase…
Chemical reactions in multidimensional driven systems are typically described by a time-dependent rank-1 saddle associated with one reaction and several orthogonal coordinates (including the solvent bath). To investigate reactions in such…