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Describing the complex landscape of infinite-dimensional free energy is generally a challenging problem. This difficulty arises from the existence of numerous minimizers and, consequently, a vast number of saddle points. These factors make…
This work presents a numerical analysis of computing transition states of semilinear elliptic partial differential equations (PDEs) via the index-1 saddle dynamics, or equivalently, the gentlest ascent dynamics. To establish clear…
A general theoretical framework for investigating nonlinear dynamics of phase space zonal structures is presented in this work. It is then, more specifically, applied to the limit where the nonlinear evolution time scale is smaller or…
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…
Semi-classical analysis is used to investigate synchronous quantum tunneling in a multidimensional potential energy surface (PES) characterized by four degenerate minima, serving as a foundational model for coupled vibrational modes. The…
The formulation of a model for the evolution of the flow of a solid-liquid mixture (coal-water) in a horizontal pipeline with partial phase separation is the aim of this work. Problems of instabilities due to complex eigenvalues, observed…
In a previous paper (Voglis et al. 2006a, paper I) we demonstrated that, in a rotating galaxy with a strong bar, the unstable asymptotic manifolds of the short period family of unstable periodic orbits around the Lagrangian points L$_1$ or…
Electron plasmas confined by an external magnetic field exhibit variations in a two-dimensional plane orthogonal to the confining magnetic field. A nonlinear fluid simulation code to investigate the properties of 2-D electron plasma wave…
Chemical selectivity, as quantified by a branching ratio, is a phenomenon relevant for many organic chemical reactions. It may be exhibited on a potential energy surface that features a valley-ridge inflection point in the region between…
The majority of dynamical studies in power systems focus on the high voltage transmission grids where models consider large generators interacting with crude aggregations of individual small loads. However, new phenomena have been observed…
Flatback airfoils, characterized by a blunt trailing edge, are used at the root of large wind turbine blades. A low-drag pocket has recently been identified in the flow past these airfoils at high angles of attack, potentially offering…
We study 3D chaotic dynamics through an analysis of transport in a granular flow in a half-full spherical tumbler rotated sequentially about two orthogonal axes (a bi-axial "blinking" tumbler). The flow is essentially quasi-2D in any…
We report the structure of transient fluctuations in the liquid phase of a two-dimensional system that exhibits several ordered phases with different symmetries. The density-temperature phase diagram of the system studied, composed of…
Liquid-liquid phase separation has emerged as a fundamental mechanism underlying intracellular organization, with evidence for it being reported in numerous different systems. However, there is a growing concern regarding the lack of…
In this paper, we analyse the phase space structure of the roaming dynamics in a two degree of freedom potential energy surface consisting of two identical planar Morse potentials separated by a distance. This potential energy surface was…
The topological theory of phase transitions was proposed on the basis of different arguments, the most important of which are: a direct evidence of the relation between topology and phase transitions for some exactly solvable models; an…
Symmetry-protected topological (SPT) phases exhibit nontrivial order if symmetry is respected but are adiabatically connected to the trivial product phase if symmetry is not respected. However, unlike the symmetry-breaking phase, there is…
A three-dimensional round liquid jet within a low-speed coaxial gas flow is numerically simulated and explained via vortex dynamics ($\lambda_2$ method). The instabilities on the liquid-gas interface reflect well the vortex interactions…
Predictions and discoveries of new phases of superfluid $^3$He in confined geometries, as well as novel topological excitations confined to surfaces and edges of near a bounding surface of $^3$He, are driving the fields of superfluid $^3$He…
The chaotic diffusion for particles moving in a time dependent potential well is described by using two different procedures: (i) via direct evolution of the mapping describing the dynamics and ; (ii) by the solution of the diffusion…