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We study the convergence of the empirical measure of moderately interacting particle systems subject to singular forces derived by Lennard-Jones potential. Although the classical Lennard-Jones force is widely used in molecular dynamics,…
We construct solutions to the two dimensional parabolic-elliptic Keller-Segel model for chemotaxis that blow up in finite time $T$. The solution is decomposed as the sum of a stationary state concentrated at scale $\lambda$ and of a…
We consider the Lam\'{e} system arising from high-contrast composite materials whose inclusions (fibers) are nearly touching the matrix boundary. The stress, which is the gradient of the solution, always concentrates highly in the narrow…
We develop a bonded-particle model for magneto-elastic rods that unifies large deformations, contact, and long-range magnetic interactions within a single discrete-element framework. The rod is discretized into orientable particles…
The structure, thermodynamics and slow activated dynamics of the equilibrated metastable regime of glass-forming fluids remains a poorly understood problem of high theoretical and experimental interest. We apply a highly accurate…
We investigate the dynamics of a binary mixture Lennard-Jones system of different system sizes with respect to the importance of the properties of the underlying potential energy landscape (PEL). We show that the dynamics of small systems…
Singularities arise in diverse disciplines and play a key role in both exploring fundamental laws of physics and making highly-sensitive sensors. Higher-order (>3) singularities, with further improved performance, however, usually require…
A family of explicit modified Euler methods (MEMs) is constructed for long-time approximations of super-linear SODEs driven by multiplicative noise. The proposed schemes can preserve the same Lyapunov structure as the continuous problems.…
Localization of normal modes is used in recent microelectromechanical systems (MEMS) technologies with orders of magnitude improvements in sensitivity. A pair of eigenvalues veer, or avoid crossing each other, as a single parameter of a…
Mobility edges (MEs) constitute the energies separating the localized states from the extended ones in disordered systems. Going beyond this conventional definition, recent proposal suggests for an ME which separates the localized and…
Reversible electropermeabilization, commonly referred to as electroporation, is a transient increase in cell membrane permeability induced by short, high-voltage electric pulses. We present a stochastically perturbed version of a…
This paper gives an overview of recent results concerning the long time dynamics of repeated interaction quantum systems in a deterministic and random framework. We describe the non equilibrium steady states (NESS) such systems display and…
We revisit the classical concept of near-decomposability in complex systems, introduced by Herbert Simon in his foundational article The Architecture of Complexity, by developing an explicit quantitative analysis based on singular…
So far most studies on mathematical models for microelectromechanical systems (MEMS) are focused on the so-called small aspect ratio model which is a wave or beam equation with a singular source term. It is formally derived by setting the…
Two approaches to incorporate heterogeneity in discrete models are compared. In the first, standard approach, the heterogeneity is dictated by geometrical structure of the discrete system. In the second approach, the heterogeneity is…
This is a summary of the article with the same title, accepted for publication in Advances in Chemical Engineering, 47: 193-277 (2015). Gas-solid fluidization is a typical nonlinear nonequilibrium system with multiscale structure. In…
Great progress has been made in the last several years towards understanding the properties of disordered electronic systems. In part, this is made possible by recent advances in quantum effective medium methods which enable the study of…
The fluctuations of two-dimensional extended objects membranes is a rich and exciting field with many solid results and a wide range of open issues. We review the distinct universality classes of membranes, determined by the local order,…
A collision of a rubber rod to a hard floor is regarded as a simple example of obstacle problems for elastic material. In this article we have proposed a new mathematical model for the collision phenomenon by applying beam equations with…
This paper shows finite time singularity formation for the Muskat problem in a stable regime. The framework we found is with a dry region, where the density and the viscosity are set equal to $0$ (the gradient of the pressure is equal to…