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Thin fluid or elastic films and membranes are found in nature and technology, for instance, as confinements of living cells or in loudspeakers. When applying a net force, resulting flows in an unbounded two-dimensional incompressible…
The control of biofilm formation is a challenging goal that has not been reached yet in many aspects. One is the role of van der Waals forces and another the importance of mutual interactions between the adsorbing and the adsorbed…
In topology optimization of compliant mechanisms, the specific placement of boundary conditions strongly affects the resulting material distribution and performance of the design. At the same time, the most effective locations of the loads…
Many problems in physics, material sciences, chemistry and biology can be abstractly formulated as a system that navigates over a complex energy landscape of high or infinite dimensions. Well-known examples include phase transitions of…
Periodically forced turbulence is used as a test case to evaluate the predictions of two-equation and multiple-scale turbulence models in unsteady flows. The limitations of the two-equation model are shown to originate in the basic…
While there have been many developments in computational probes of both strongly-correlated molecular systems and machine-learning accelerated molecular dynamics, there remains a significant gap in capabilities in simulating accurate…
We map molecular dynamics simulations of fluid-fluid interfaces onto mesoscale continuum theories for partially miscible fluids. Unlike most previous work, we examine not only the interface order parameter and density profiles, but also the…
The starting point of our analysis is a class of one-dimensional interacting particle systems with two species. The particles are confined to an interval and exert a nonlocal, repelling force on each other, resulting in a nontrivial…
Many practical approximations in physics and engineering invoke a relatively long physical domain with a relatively thin cross-section. In this scenario we typically expect the system to have structures that vary slowly in the long…
The standard Maxwell formulation of the problem of polarized dielectrics suffers from a number of difficulties, both conceptual and practical. These difficulties are particularly significant in the case of liquid interfaces, where the…
Due to the processes that occur during the functioning of modern electromechanical systems, these systems can be considered complex nonlinear dynamic systems from the point of view of the theory of dynamic systems. The movement of such…
The fluid-mechanics community is currently divided in assessing the boundaries of applicability of the macroscopic approach to fluid mechanical problems. Can the dynamics of nano-droplets be described by the same macroscopic equations as…
Simulating transition dynamics between metastable states is a fundamental challenge in dynamical systems and stochastic processes with wide real-world applications in understanding protein folding, chemical reactions and neural activities.…
This article reviews the mechanical bidomain model, a mathematical description how the extracellular matrix and intracellular cytoskeleton are coupled by integrin proteins. The fundamental hypothesis is that differences between…
Electrostatic interactions in solvents play a major role in biophysical systems. There is a consensus in the literature that the dielectric response of aqueous solutions is nonlocal: polarization depends on the electric field not only at a…
In this thesis we study the lateral electrostatic interaction between a pair of non-identical, moderately charged colloidal particles trapped at an electrolyte interface in the limit of short inter-particle separations. Using a simplified…
By means of topological methods, we provide new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of perturbed Hammerstein integral equations. In order to illustrate our theoretical…
Models of grain boundary energy are essential for predicting the behavior of polycrystalline materials. Typical models represent the minimum boundary energy as a function of macroscopic boundary parameters. An energy model may allow for…
The article proposes an algorithm to model the collision between arbitrary ellipsoids in viscous fluid. It is composed of several steps, each improving upon the standard procedure employed in the current literature. First, an efficient…
We develop a multi-scale approach to simulate hydrated nanobio systems under realistic condi- tions (e.g., nanoparticles and protein solutions at physiological conditions over time-scales up to hours). We combine atomistic simulations of…