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A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies…
We discuss the problem how to determine the quality of a nonlinear system with respect to a measurement task. Due to amplification, filtering, quantization and internal noise sources physical measurement equipment in general exhibits a…
Active matter is rapidly becoming a key paradigm of out-of-equilibrium soft matter exhibiting complex collective phenomena, yet the thermodynamics of such systems remain poorly understood. In this letter we study the nonequilbrium…
We consider a nonlinear 4th-order degenerate parabolic partial differential equation that arises in modelling the dynamics of an incompressible thin liquid film on the outer surface of a rotating horizontal cylinder in the presence of…
We develop a general criterion about coarsening for a class of nonlinear evolution equations describing one dimensional pattern-forming systems. This criterion allows one to discriminate between the situation where a coarsening process…
Emergent phenomena are ubiquitous in nature and refer to spatial, temporal, or spatiotemporal pattern formation in complex nonlinear systems driven out of equilibrium that is not contained in the microscopic descriptions at the…
We investigate a specific finite element model to study the thermoelastic behavior of an elastic body within the context of nonlinear strain-limiting constitutive relation. As a special subclass of implicit relations, the thermoelastic…
We generalize the spherical collapse model for the formation of bound objects to apply in a Universe with arbitrary positive cosmological constant. We calculate the critical condition for collapse of an overdense region and give exact…
The nonlinear dynamics associated with sliding friction forms a broad interdisciplinary research field that involves complex dynamical processes and patterns covering a broad range of time and length scales. Progress in experimental…
The properties of nonlinear PDEs that generate filtered solutions are explored with particular attention given to the constraints on the residual term. The analysis is carried out for nonlinear PDEs with an emphasis on evolution problems…
We present a general and systematic theory of non-equilibrium dynamics of multi-component fluid membranes, in general, and membranes containing transmembrane proteins, in particular. Developed based on a minimal number of principles of…
In this paper we consider a system of two coupled nonlinear diffusion--reaction partial differential equations (PDEs) which model the growth of biofilm and consumption of the nutrient. At the scale of interest the biofilm density is subject…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
We develop new dynamically orthogonal tensor methods to approximate multivariate functions and the solution of high-dimensional time-dependent nonlinear partial differential equations (PDEs). The key idea relies on a hierarchical…
We present the results of large scale simulations of 4th order nonlinear partial differential equations of dif- fusion type that are typically encountered when modeling dynamics of thin fluid films on substrates. The simulations are based…
We study the steady states and dynamics of a thin film-type equation with non-conserved mass in one dimension. The evolution equation is a nonlinear fourth-order degenerate parabolic PDE motivated by a model of volatile viscous fluid films…
Nonlinear contraction theory is a comparatively recent dynamic control system design tool based on an exact differential analysis of convergence, in essence converting a nonlinear stability problem into a linear time-varying stability…
An analysis of discrete systems is important for understanding of various physical processes, such as excitations in crystal lattices and molecular chains, the light propagation in waveguide arrays, and the dynamics of Bose-condensate…
A central challenge in neuroscience is understanding how neural system implements computation through its dynamics. We propose a nonlinear time series model aimed at characterizing interpretable dynamics from neural trajectories. Our model…
Pattern formation is a widely observed phenomenon in diverse fields including materials physics, developmental biology and ecology, among many others. The physics underlying the patterns is specific to the mechanisms, and is encoded by…