Related papers: Path collective variables without paths
If a given behavior of a multi-agent system restricts the phase variable to a invariant manifold, then we define a phase transition as change of physical characteristics such as speed, coordination, and structure. We define such a phase…
We consider noise-induced transition paths in randomly perturbed dynami- cal systems on a smooth manifold. The classical Freidlin-Wentzell large devia- tion theory in Euclidean spaces is generalized and new forms of action functionals are…
Oscillation of macroscopic variables is discovered in a metastable state in the Hamiltonian dynamical system of mean field XY model, the duration of which is divergent with the system size. This long-lasting periodic or quasiperiodic…
In contrast with classical approaches, we present the project based on considering Collective Behaviours as coherent sequences of states adopted by different single systems consisting of the same elements interacting over time in different…
The free energy landscapes of several fundamental processes are characterized by high barriers separating long-lived metastable states. In order to explore these type of landscapes enhanced sampling methods are used. While many such methods…
We study the long-time dynamics in non-Markovian single-population stochastic models, where one or more reactions are modelled as a stochastic process with a fat-tailed non-exponential distribution of waiting times, mimicking long-term…
Phase diagrams are an invaluable tool for material synthesis and provide information on the phases of the material at any given thermodynamic condition. Conventional phase diagram generation involves experimentation to provide an initial…
We present a method to sample reactive pathways via biased molecular dynamics simulations in trajectory space. We show that the use of enhanced sampling techniques enables unconstrained exploration of multiple reaction routes. Time…
The committor function is a central object of study in understanding transitions between metastable states in complex systems. However, computing the committor function for realistic systems at low temperatures is a challenging task, due to…
Transition paths are rare events occurring when a system, thanks to the effect of fluctuations, crosses successfully from one stable state to another by surmounting an energy barrier. Even though they are of great significance in many…
We study a special case of the problem of statistical learning without the i.i.d. assumption. Specifically, we suppose a learning method is presented with a sequence of data points, and required to make a prediction (e.g., a classification)…
High dimensional random dynamical systems are ubiquitous, including -- but not limited to -- cyber-physical systems, daily return on different stocks of S&P 1500 and velocity profile of interacting particle systems around McKeanVlasov…
The microscopic approach to the description of the phase behaviour and critical phenomena in binary fluid mixtures is proposed. It is based on the method of collective variables with a reference system. The physical nature of the order…
Using ensemble methods for regression has been a large success in obtaining high-accuracy prediction. Examples are Bagging, Random forest, Boosting, BART (Bayesian additive regression tree), and their variants. In this paper, we propose a…
Static and dynamic structure factors and various transport coefficients are computed for a Lennard-Jones model of a binary fluid (A,B) with a symmetrical miscibility gap, varying both temperature and relative concentration of the mixture.…
We study in detail the role of covariant Lyapunov vectors and their respective angles for detecting transitions between metastable states in dynamical systems, as recently discussed in several atmospheric science applications. The…
In this paper, we study the phase transition behavior emerging from the interactions among multiple agents in the presence of noise. We propose a simple discrete-time model in which a group of non-mobile agents form either a fixed connected…
We find analytical solutions to the Cahn-Hilliard equation for the dynamics of an interface in a system with a conserved order parameter (Model B). We show that, although steady-state solutions of Model B are unphysical in the far-field,…
In many dynamical systems there is a large separation of time scales between typical events and "rare" events which can be the cases of interest. Rare-event rates are quite difficult to compute numerically, but they are of considerable…
The viscous flow of two immiscible fluids in a porous medium on the Darcy scale is governed by a system of nonlinear parabolic equations. If infinite mobility of one phase can be assumed (e.g. in soil layers in contact with the atmosphere)…