Related papers: Topological methods for searching barriers and rea…
The elsewhere surmised topological origin of phase transitions is given here new important evidence through the analytic study of an exactly solvable model for which both topology and thermodynamics are worked out. The model is a mean-field…
The kinetics of collective rearrangements in solution, such as protein folding and nanocrystal phase transitions, often involve free energy barriers that are both long and rough. Applying methods of transition path sampling to harvest…
Molecular dynamics is a powerful tool for studying the thermodynamics and kinetics of complex molecular events. However, these simulations can rarely sample the required time scales in practice. Transition path sampling overcomes this…
Simulations with an adaptive time-dependent bias, such as metadynamics, enable an efficient exploration of the conformational space of a system. However, the dynamic information of the system is altered by the bias. With infrequent…
Self-organization creates new order and shifts sub-boundaries while reorganizing energy and entropy within a control volume. This article examines pathway selection and tests whether maximizing the entropy generation rate can forecast…
The simulated self-assembly of molecular building blocks into functional complexes is a key area of study in computational biology and materials science. Self-assembly simulations of proteins using physically-motivated potentials for…
A local criterion of topological phase transitions is established based on the Morse theory: a topological phase transition occurs when the count of Morse critical points of the order function changes. The locations in space where this…
Hamilton's equations with noise and friction possess a hidden supersymmetry, valid for time-independent as well as periodically time-dependent systems. It is used to derive topological properties of critical points and periodic trajectories…
A version of the time-parallel algorithm parareal is analyzed and applied to stochastic models in chemical kinetics. A fast predictor at the macroscopic scale (evaluated in serial) is available in the form of the usual reaction rate…
In this work, we solve the problem of finding non-intersecting paths between points on a plane with a new approach by borrowing ideas from geometric topology, in particular, from the study of polygonal schema in mathematics. We use a…
A method evaluating the sensitivity of a given parameter to topological changes is proposed within the method of moments paradigm. The basis functions are used as degrees of freedom which, when compared to the classical pixeling technique,…
We argue that the phase transition in the mean-field XY model is related to a particular change in the topology of its configuration space. The nature of this topological transition can be discussed on the basis of elementary Morse theory…
Comparing mathematical models offers a means to evaluate competing scientific theories. However, exact methods of model calibration are not applicable to many probabilistic models which simulate high-dimensional spatio-temporal data.…
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
A new upscaling procedure that provides 1D representations of 2D mixing-limited reactive transport systems is developed and applied. A key complication with upscaled models in this setting is that the procedure must differentiate between…
The transition interface sampling (TIS) technique allows to overcome large free energy barriers within reasonable simulation time, which is impossible for straightforward molecular dynamics. Still, the method does not impose an artificial…
In addition to the Riemannian metricization of the thermodynamic state space, local relaxation times offer a natural time scale, too. Generalizing existing proposals, we relate {\it thermodynamic} time scale to the standard kinetic…
Many chemical reactions can be formulated in terms of particle diffusion in a complex energy landscape. Transition path theory (TPT) is a theoretical framework for describing the direct (reaction) pathways from reactant to product states…
Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated…
We propose a technique to detect and generate patterns in a network of locally interacting dynamical systems. Central to our approach is a novel spatial superposition logic, whose semantics is defined over the quad-tree of a partitioned…