Related papers: Hamiltonian pitchfork bifurcation in transition ac…
In this article, we review the analytical and numerical approaches for computing the phase space structures in two degrees-of-freedom Hamiltonian systems that arise in chemical reactions. In particular, these phase space structures are the…
In this work we analyze the bifurcation of dividing surfaces that occurs as a result of a pitchfork bifurcation of periodic orbits in a two degrees of freedom Hamiltonian System. The potential energy surface of the system that we consider…
In this article we present the influence of a Hamiltonian saddle-node bifurcation on the high-dimensional phase space structures that mediate reaction dynamics. To achieve this goal, we identify the phase space invariant manifolds using…
We present a quantitative semiclassical treatment of the effects of bifurcations on the spectral rigidity and the spectral form factor of a Hamiltonian quantum system defined by two coupled quartic oscillators, which on the classical level…
In this paper, we study the quantum dynamics of a one degree-of-freedom (DOF) Hamiltonian that is a normal form for a saddle node bifurcation of equilibrium points in phase space. The Hamiltonian has the form of the sum of kinetic energy…
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)…
A transition state for a Hamiltonian system is a closed, invariant, oriented, codimension-2 submanifold of an energy-level that can be spanned by two compact codimension-1 surfaces of unidirectional flux whose union, called a dividing…
The classical pitchfork of singularity theory is a twice-degenerate bifurcation that typically occurs in dynamical system models exhibiting Z_2 symmetry. Non-classical pitchfork singularities also occur in many non-symmetric systems, where…
Many organic chemical reactions are governed by potential energy surfaces that have a region with the topographical features of a caldera. If the caldera has a symmetry then trajectories transiting the caldera region are observed to exhibit…
A study is reported of the quantum scattering resonances of dissociating molecules using a semiclassical approach based on periodic-orbit theory. The dynamics takes place on a potential energy surface with an energy barrier separating two…
General features of the $\alpha-\beta$ transition of quartz are investigated. Molecular dynamics methods are mainly used, an analytic treatment being deferred to a work in preparation. A basic preliminary observation is that the transition…
Spatial diffusion of particles in periodic potential models has provided a good framework for studying the role of chaos in global properties of classical systems. Here a bidimensional "soft" billiard, classically modeled from an optical…
We investigate the evaporation of a two-dimensional droplet on a solid surface. The solid is flat but with smooth chemical variations that lead to a space-dependent local contact angle. We perform a detailed bifurcation analysis of the…
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…
In this paper, we explore the dynamics of a Hamiltonian system after a double van der Waals potential energy surface degenerates into a single well. The energy of the system is increased from the bottom of the potential well up to the…
Asymptotic state of an open quantum system can undergo qualitative changes upon small variation of system parameters. We demonstrate it that such 'quantum bifurcations' can be appropriately defined and made visible as changes in the…
In this work we analyze the bifurcation of dividing surfaces that occurs as a result of two period-doubling bifurcations in a 2D caldera-type potential. We study the structure, the range, the minimum and maximum extents of the periodic…
The emergence of periodic oscillations is observed in various complex systems in nature and engineering. Thermoacoustic oscillations in systems comprising turbulent reactive flow exemplify such complexity in the engineering context, where…
We consider the existence of invariant manifolds in phase space governing reaction dynamics in situations where there are no saddle points on the potential energy surface in the relevant regions of configuration space. We point out that…
On a two-dimensional circular domain, we analyze the formation of spatio-temporal patterns for a class of coupled bulk-surface reaction-diffusion models for which a passive diffusion process occurring in the interior bulk domain is linearly…