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A phenomenological theory is proposed to analyze the asymptotic dynamics of perturbed inviscid Kolmogorov shear flows in two dimensions. The phase diagram provided by the theory is in qualitative agreement with numerical observations, which…
We characterize equilibrium properties and relaxation dynamics of a two-dimensional lattice containing, at each site, two particles connected by a double-well potential (dumbbell). Dumbbells are oriented in the orthogonal direction with…
Motivated by a stochastic differential equation describing the dynamics of interfaces, we study the bifurcation behavior of a more general class of such equations. These equations are characterized by a 2-dimensional phase space (describing…
A Landau model is used to study the phase behavior of the surface layer for magnetic and cholesteric liquid crystal systems that are at or near a Lifshitz point marking the boundary between modulated and homogeneous bulk phases. The model…
We examine the phase space structures that govern reaction dynamics in the absence of critical points on the potential energy surface. We show that in the vicinity of hyperbolic invariant tori it is possible to define phase space dividing…
We propose a generalized dynamic phasor (DP) framework to analyze inverter-based resources (IBRs) connected to multi-machine systems under balanced and unbalanced conditions. It captures subsynchronous oscillations (SSOs) induced by…
We present a new solution of the asymmetric two-matrix model in the large $N$ limit which only involves a saddle point analysis. The model can be interpreted as Ising in the presence of a magnetic field, on random dynamical lattices with…
Abridged abstract: Inert interactions between randomly moving entities and spatial disorder play a crucial role in quantifying the diffusive properties of a system. These interactions affect only the movement of the entities, and examples…
This article investigates the properties of a few interacting particles trapped in a few wells and how these properties change under adiabatic tuning of interaction strength and inter-well tunneling. While some system properties are…
In many engineering systems operating with a working fluid, the best efficiency is reached close to a condition of flow separation, which makes its prediction very crucial in industry. Providing that wall-based quantities can be measured,…
Chemical reactions in multidimensional systems are often described by a rank-1 saddle, whose stable and unstable manifolds intersect in the normally hyperbolic invariant manifold (NHIM). Trajectories started on the NHIM in principle never…
We introduce a massively parallel replica-exchange grand-canonical sampling algorithm to simulate materials at realistic conditions, in particular surfaces and clusters in reactive atmospheres. Its purpose is to determine in an automated…
We study numerically and analytically the instabilities associated with phase separation in a solid layer on which an external material ux is imposed. The first instability is localized within a boundary layer at the exposed free surface by…
The basic formal and numerical aspects of different degree interpolated moving least-squares (IMLS) methods are studied using sixteen different combinations of coordinate system for fitting and weight functions. For the application we use…
A novel modular modeling and control framework based on Lagrangian mechanics is proposed for multibody systems, motivated by the challenges of modular control of systems with closed kinematic chains and by the need for a modeling framework…
We investigate the nonlinear evolution of cosmic morphologies of the large-scale structure by examining the Lagrangian dynamics of various tensors of a cosmic fluid element, including the velocity gradient tensor, the Hessian matrix of the…
We investigate relaxation dynamics along the entire first-order phase transition line by analyzing the time evolution of the free energy landscape in the three-dimensional kinetic Ising model. Near the critical temperature $T_{\rm c}$, the…
Research in cell biology is steadily contributing new knowledge about many different aspects of physiological processes like polymerization, both with respect to the involved molecular structures as well as their related function.…
The morphogenesis of cells and tissues involves an interplay between chemical signals and active forces on their surrounding surface layers. The complex interaction of hydrodynamics and material flows on such active surfaces leads to…
We investigate the scaling behaviour of a singular perturbation model within the geometrically linearized theory of elasticity involving data of higher lamination order. We study boundary data which are of staircase type and show rather…