Related papers: Convergence of the Discrete Minimum Energy Path
We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy minimisation approach. More…
A modification of the nudged elastic band (NEB) method is presented that enables stable optimisations to be run using both the limited-memory quasi-Newton (L-BFGS) and slow-response quenched velocity Verlet (SQVV) minimisers. The…
Stochastic electronic structure theories, e.g., Quantum Monte Carlo methods, enable highly accurate total energy calculations which in principle can be used to construct highly accurate potential energy surfaces. However, their stochastic…
An analysis of the network defined by the potential energy minima of multi-atomic systems and their connectivity via reaction pathways that go through transition states allows to understand important characteristics like thermodynamic,…
Maximum entropy principle (MEP) offers an effective and unbiased approach to inferring unknown probability distributions when faced with incomplete information, while neural networks provide the flexibility to learn complex distributions…
The recently introduced method of excess collisions (MEC) is modified to estimate diffusion-controlled reaction times inside systems of arbitrary size. The resulting MEC-E equations contain a set of empirical parameters, which have to be…
When examining dynamics occurring at non-zero temperatures, both energy and entropy must be taken into account while describing activated barrier crossing events. Furthermore, good reaction coordinates need to be constructed to describe…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
Given a chemical reaction going from reactant (R) to the product (P) on a potential energy surface (PES) and a collective variable (CV) that discriminates between R and P, one can define a free-energy profile (FEP) as the logarithm of the…
We develop a neuroevolution-potential (NEP) framework for generating neural network based machine-learning potentials. They are trained using an evolutionary strategy for performing large-scale molecular dynamics (MD) simulations. A…
A possible mechanism for the formation of a 90{\deg} misfit dislocation at the Ge/Si(001) interface through homogeneous nucleation is identified from atomic scale calculations where a minimum energy path connecting the coherent epitaxial…
We introduce a rigorous method to microscopically compute the observables which characterize the thermodynamics and kinetics of rare macromolecular transitions for which it is possible to identify a priori a slow reaction coordinate. In…
An exact approach to compute physical properties for general multi-electronic-state (MES) systems in thermal equilibrium is presented. The approach is extended from our recent progress on path integral molecular dynamics (PIMD) [J. Chem.…
Continuous-discrete models with dynamics described by stochastic differential equations are used in a wide variety of applications. For these systems, the maximum a posteriori (MAP) state path can be defined as the curves around which lie…
A critical metric of the coverage quality in Wireless Sensor Networks (WSNs) is the Minimal Exposure Path (MEP), a path through the environment that least exposes an intruder to the sensor detecting nodes. Many approaches have been proposed…
A method for computing minimum ignition energies for gaseous fuel mixtures with detailed and reduced chemistry, by numerical integration of time-dependent conservation equations in a spherically symmetrical configuration, is presented and…
We present a numerical method for computing optimal transition pathways and transition rates in systems of stochastic differential equations (SDEs). In particular, we compute the most probable transition path of stochastic equations by…
The minimum action method (MAM) is to calculate the most probable transition path in randomly perturbed stochastic dynamics, based on the idea of action minimization in the path space. The accuracy of the numerical path between different…
The porous medium equation (PME) is a typical nonlinear degenerate parabolic equation. We have studied numerical methods for PME by an energetic variational approach in [C. Duan et al, J. Comput. Phys., 385 (2019) 13-32], where the…
The industrial drying process consumes approximately 12% of the total energy used in manufacturing, with the potential for a 40% reduction in energy usage through improved process controls and the development of new drying technologies. To…