Related papers: The Relation between Approximation in Distribution…
The biomolecules in and around a living cell -- proteins, nucleic acids, lipids, carbohydrates -- continuously sample myriad conformational states that are thermally accessible at physiological temperatures. Simultaneously, a given…
Molecular search phenomena are observed in a variety of chemical and biological systems. During the search the participating particles frequently move in complex inhomogeneous environments with random transitions between different dynamic…
The powerful molecular dynamics (MD) simulation is basically based on a picture that the atoms experience classical-like trajectories under the exertion of classical force field determined by the quantum mechanically solved electronic…
An approach to find a weak form of shadowing is developed. We consider homeomorphisms of a compact metric space. It is proved that every pseudotrajectory with sufficiently small errors contains at least one subsequence that can be shadowed…
Diffusive molecular dynamics is a novel model for materials with atomistic resolution that can reach diffusive time scales. The main ideas of diffusive molecular dynamics are to first minimize an approximate variational Gaussian free energy…
Molecular dynamics (MD) has become a powerful tool for studying biophysical systems, due to increasing computational power and availability of software. Although MD has made many contributions to better understanding these complex…
The nucleation of crystals in liquids is one of nature's most ubiquitous phenomena, playing an important role in areas such as climate change and the production of drugs. As the early stages of nucleation involve exceedingly small time and…
Event-driven molecular dynamics is a valuable tool in condensed and soft matter physics when particles can be modeled as hard objects or more generally if their interaction potential can be modeled in a stepwise fashion. Hard spheres model…
Complex systems often have features that can be modeled by advanced mathematical tools [1]. Of special interests are the features of complex systems that have a network structure as such systems are important for modeling technological and…
Several physical systems in condensed matter have been modeled approximating their constituent particles as hard objects. The hard spheres model has been indeed one of the cornerstones of the computational and theoretical description in…
All-atom and coarse-grained molecular dynamics are two widely used computational tools to study the conformational states of proteins. Yet, these two simulation methods suffer from the fact that without access to supercomputing resources,…
Molecular dynamics simulation is used to investigate the crystallization of a classical two-dimensional electron system, in which electrons interact with the Coulomb repulsion. From the positional and the orientational correlation…
Due to its non-crystalline nature, the glassy state has remained one the most exciting scientific challenges. To study such materials, Molecular Dynamics (MD) simulations have been extensively used because they provide a direct view into…
We study compressible fluid flow in narrow two-dimensional channels using a novel molecular dynamics simulation method. In the simulation area, an upstream source is maintained at constant density and temperature while a downstream…
We extend the phase field crystal model to accommodate exact atomic configurations and vacancies by requiring the order parameter to be non-negative. The resulting theory dictates the number of atoms and describes the motion of each of…
Protein dynamics is a fundamental element to comprehend their biological functions. However, a theoretical picture providing microscopic-detail explanation of its relevant features is still missing. One of the outmost relevant properties…
When addressing spatial biological questions using mathematical models, symmetries within the system are often exploited to simplify the problem by reducing its physical dimension. In a reduced-dimension model molecular movement is…
Endothelial cells are responsible for the formation of the capillary blood vessel network. We describe a system of endothelial cells by means of two-dimensional molecular dynamics simulations of point-like particles. Cells' motion is…
Cancer is a complex disease that is characterized by uncontrolled growth and division of cells. It involves a complex interplay between genetic and environmental factors that lead to the initiation and progression of tumors. Recent advances…
Molecular dynamics (MD) is a widely-used tool for simulating the molecular and materials properties. It is a common wisdom that molecular dynamics simulations should obey physical laws and, hence, lots of effort is put into ensuring that…