Related papers: Topological methods for searching barriers and rea…
In this letter we propose the use of physics techniques for entropy determination on constrained parameter optimization problems. The main feature of such techniques, the construction of an unbiased walk on energy space, suggests their use…
We show that transport in the presence of entropic barriers exhibits peculiar characteristics which makes it distinctly different from that occurring through energy barriers. The constrained dynamics yields a scaling regime for the particle…
A massively parallel method to build large transition rate matrices from temperature accelerated molecular dynamics trajectories is presented. Bayesian Markov model analysis is used to estimate the expected residence time in the known state…
Topology is a powerful tool for categorizing magnetization textures by defining a topological index in both two-dimensional (2D) systems, such as thin films or curved surfaces, and in 3D bulk systems. In the emerging field of 3D…
Time series are ubiquitous in our data rich world. In what follows I will describe how ideas from dynamical systems and topological data analysis can be combined to gain insights from time-varying data. We will see several applications to…
In this paper, a topological classification of molecules and their chemical reactions is proposed on a single particle level . We consider zero-dimensional electronic Hamiltonians in a real-space tight-binding basis with spinless…
The analysis of global dynamics, particularly the identification and characterization of attractors and their regions of attraction, is essential for complex nonlinear and hybrid systems. Combinatorial methods based on Conley's index theory…
We give a geometrically exact treatment of percolation through voids around assemblies of randomly placed impermeable barrier particles, introducing a computationally inexpensive approach to finding critical barrier density thresholds…
Dynamics of reaction coordinates during barrier-crossing are key to understand activated processes in complex systems such as proteins. The default assumption from Kramers physical intuition is that of a diffusion process. However, the…
Starting from an algebraic approach of quantum physics it has been shown via the Tomita-Takesaki theorem and the KMS condition that the canonical density matrix contains the dynamics of the system provided we use a rescaling of time. In…
The parameter space of dynamical systems arising in applications is often found to be high-dimensional and difficult to explore. We construct a fast algorithm to numerically analyze "quantitative features" of dynamical systems depending on…
Phase separation of binary fluids quenched by contact with cold external walls is considered. Navier-Stokes, convection-diffusion, and energy equations are solved by lattice Boltzmann method coupled with finite-difference schemes. At high…
Molecular transitions -- such as protein folding, allostery, and membrane transport -- are central to biology yet remain notoriously difficult to simulate. Their intrinsic rarity pushes them beyond reach of standard molecular dynamics,…
In this extended abstract, we report on ongoing work towards an approximate multimodal optimization algorithm with asymptotic guarantees. Multimodal optimization is the problem of finding all local optimal solutions (modes) to a path…
The accuracy of rate constants calculated using transition state theory depends crucially on the correct identification of a recrossing--free dividing surface. We show here that it is possible to define such optimal dividing surface in…
The computational efficiency of stochastic simulation algorithms is notoriously limited by the kinetic trapping of the simulated trajectories within low energy basins. Here we present a new method that overcomes kinetic trapping while still…
Thermodynamics constrains the flow of matter in a reaction network to occur through routes along which the Gibbs energy decreases, implying that viable steady-state flux patterns should be void of closed reaction cycles. Identifying and…
Disentangling the mechanistic details of a chemical reaction pathway is a hard problem that often requires a considerable amount of chemical intuition and a component of luck. Experiments struggle in observing short-life metastable…
The level crossing problem and associated geometric terms are neatly formulated by using the second quantization technique both in the operator and path integral formulations. The analysis of geometric phases is then reduced to the familiar…
Topological phase transitions, which do not adhere to Landau's phenomenological model (i.e. a spontaneous symmetry breaking process and vanishing local order parameters) have been actively researched in condensed matter physics. Machine…