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Significant progress in the development of efficient and fast algorithms for quantum chemical calculations has been made in the past two decades. The main focus has always been the desire to be able to treat ever larger molecules or…
Droplet coalescence is essential in a host of biological and industrial processes, involving complex systems as diverse as cellular aggregates, colloidal suspensions, and polymeric liquids. Classical solutions for the time evolution of…
Column chromatography is an important process in downstream biopharmaceutical manufacturing that enables high-selectivity separation of proteins through various modalities, such as affinity, ion exchange, hydrophobic interactions, or a…
We consider adaptive finite element methods for solving a multiscale system consisting of a macroscale model comprising a system of reaction-diffusion partial differential equations coupled to a microscale model comprising a system of…
This paper investigates connections between discrete and continuous approaches for decomposable submodular function minimization. We provide improved running time estimates for the state-of-the-art continuous algorithms for the problem…
A variety of problems in device and materials design require the rapid forward modeling of Maxwell's equations in complex micro-structured materials. By combining high-order accurate integral equation methods with classical multiple…
Osmosis plays a central role in the function of living and soft matter systems. While the thermodynamics of osmosis is well understood, the underlying microscopic dynamical mechanisms remain the subject of discussion. Unraveling these…
A multiscale QM/classical approach is presented, that is able to model the optical properties of complex nanostructures composed of a molecular system adsorbed on metal nanoparticles. The latter are described by a combined…
Metastable condensed matter typically fluctuates about local energy minima at the femtosecond time scale before transitioning between local minima after nanoseconds or microseconds. This vast scale separation limits the applicability of…
We describe an approach for modeling fluid concentration profiles in grid-based microfluidic chips for fluid mixing. This approach provides an algorithm that predicts fluid concentrations at the chip outlets. Our algorithm significantly…
Equilibrium sampling of biomolecules remains an unmet challenge after more than 30 years of atomistic simulation. Efforts to enhance sampling capability, which are reviewed here, range from the development of new algorithms to…
We make the case for studying the complexity of approximately simulating (sampling) quantum systems for reasons beyond that of quantum computational supremacy, such as diagnosing phase transitions. We consider the sampling complexity as a…
Multiphysics incompressible fluid dynamics simulations play a crucial role in understanding intricate behaviors of many complex engineering systems that involve interactions between solids, fluids, and various phases like liquid and gas.…
Machine learning (ML) can be used to construct surrogate models for the fast prediction of a property of interest. ML can thus be applied to chemical projects, where the usual experimentation or calculation techniques can take hours or days…
We construct importance sampling schemes for stochastic differential equations with small noise and fast oscillating coefficients. Standard Monte Carlo methods perform poorly for these problems in the small noise limit. With multiscale…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
Large-scale electrification is vital to addressing the climate crisis, but several scientific and technological challenges remain to fully electrify both the chemical industry and transportation. In both of these areas, new electrochemical…
We present a multiscale simulation of liquid water where a spatially adaptive molecular resolution procedure allows for changing on-the-fly from a coarse-grained to an all-atom representation. We show that this approach leads to the correct…
In this study, we develop computational models and methodology for accurate multi-component-flow simulation in under-resolved multi-scale porous structures. It is generally impractical to fully resolve the flow in porous structures with…
Strongly correlated quantum impurity problems appear in a wide variety of contexts ranging from nanoscience and surface physics to material science and the theory of strongly correlated lattice models, where they appear as auxiliary systems…