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A microscopic heterogeneous system under random influence is considered. The randomness enters the system at physical boundary of small scale obstacles as well as at the interior of the physical medium. This system is modeled by a…
This article proposes a new way to construct computationally efficient `wrappers' around fine scale, microscopic, detailed descriptions of dynamical systems, such as molecular dynamics, to make predictions at the macroscale `continuum'…
Heterogeneous multiscale methods (HMM) combine molecular accuracy of particle-based simulations with the computational efficiency of continuum descriptions to model flow in soft matter liquids. In these schemes, molecular simulations…
We investigate the automatic differentiation of hybrid models, viz. models that may contain delays, logical tests and discontinuities or loops. We consider differentiation with respect to parameters, initial conditions or the time. We…
I prove that a centre manifold approach to creating finite difference models will consistently model linear dynamics as the grid spacing becomes small. Using such tools of dynamical systems theory gives new assurances about the quality of…
Hydroclimatic processes are characterized by heterogeneous spatiotemporal correlation structures and marginal distributions that can be continuous, mixed-type, discrete or even binary. Simulating exactly such processes can greatly improve…
For economic nonlinear model predictive control and dynamic real-time optimization fast and accurate models are necessary. Consequently, the use of dynamic surrogate models to mimic complex rigorous models is increasingly coming into focus.…
In this paper, we construct and analyze a multiscale (finite element) method for parabolic problems with heterogeneous dynamic boundary conditions. As origin, we consider a reformulation of the system in order to decouple the discretization…
A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely…
We present a new theoretical and numerical assessment methodology for a one-dimensional process chain with general applicability to management problems such as the optimization of decision chains or production chains. The process is thereby…
This paper aims at an accurate and efficient computation of effective quantities, e.g., the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods…
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
We review recent developments of slow/fast stochastic differential equations, and also present a new result on Diffusion Homogenisation Theory with fractional and non-strong-mixing noise and providing new examples. The emphasise of the…
We develop an automated computational modeling framework for rapid gradient-based design of multistable soft mechanical structures composed of non-identical bistable unit cells with appropriate geometric parameterization. This framework…
This paper presents novel solutions of the data-based synchronization problem for continuous-time multiagent systems. We consider the cases of homogeneous and heterogeneous systems. First, we obtain a data-based representation of the…
Micromechanical constitutive parameters are important for many engineering materials, typically in microelectronic applications and material design. Their accurate identification poses a three-fold experimental challenge: (i) deformation of…
Standandard Hamiltonian mechanics in its homogeneous formulation is applied to the study of discontinuities representing rapid changes of Hamiltonians. Different formulations of Hamiltonian mechanics are reviewed. An original representation…
In this paper, we provide an analysis of a recently proposed multicontinuum homogenization technique. The analysis differs from those used in classical homogenization methods for several reasons. First, the cell problems in multicontinuum…
In recent years hypergraphs have emerged as a powerful tool to study systems with multi-body interactions which cannot be trivially reduced to pairs. While highly structured methods to generate synthetic data have proved fundamental for the…
Dynamical heterogeneity (DH) in non-equilibrium systems is a topic of profound interest yet an open question. In a model system of constantly driven oppositely charged binary colloidal suspension, we explore DH in a model lane-forming…