Related papers: Solutions for a free-boundary problem modeling mul…
In this manuscript, we extend the variational multiscale enrichment (VME) method to model the dynamic response of hyperelastic materials undergoing large deformations. This approach enables the simulation of wave propagation under…
The linear instability of a surfactant-laden two-layer falling film over an inclined slippery wall is analyzed under an influence of external shear which is imposed on the top surface of the flow. The free surface of the flow as well as the…
A fluid in contact with a flat structureless wall constitutes the simplest interface system, but the fluid-wall interfacial tension cannot be trivially and even unequivocally determined due to the ambiguity in identifying the precise…
A pinned or free-floating rigid plate lying on the free surface of a thin film of viscous fluid, which itself lies on top of a horizontal substrate that is moving to the right at a constant speed is considered. The focus of the present work…
The purpose of this paper is to provide analytical and numerical solutions of the formation and evolution of the localized plastic zone in a uniaxially loaded bar with variable cross-sectional area. An energy-based variational approach is…
Previous experimental and numerical studies showed that two-dimensional roughness elements can stabilize disturbances inside a hypersonic boundary layer, and eventually delay the transition onset. The objective of this paper is to evaluate…
We consider a coupled bulk-surface system of partial differential equations with nonlinear coupling modelling receptor-ligand dynamics. The model arises as a simplification of a mathematical model for the reaction between cell surface…
By introducing height dependency in the surface energy density, we propose a novel regularized variational model to simulate wetting/dewetting problems. The regularized model leads to the appearance of a precursor layer which covers the…
Turbulent boundary layers exhibit a universal structure which nevertheless is rather complex, being composed of a viscous sub-layer, a buffer zone, and a turbulent log-law region. In this letter we present a simple analytic model of…
This paper makes the first attempt to show how information exchange rules represented by a network having multiple layers (multiplex information networks) can be designed for enabling spatially evolving multiagent formations. Toward this…
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…
It is known from both experiments and molecular dynamics simulations that chemically patterning a solid surface has an effect on the flow of an adjacent liquid. This fact is in stark contrast with predictions of classical fluid mechanics…
Starting from the equations of Stokes flow and the mass conservation of particles as determined by shear-induced diffusion, we derive the coupled equations for the dynamics of particle concentration and film thickness for the free-surface…
Compressive mechanical stress exceeding a critical value leads to the formation of periodic surface buckling patterns in film-substrate systems. A comprehensive understanding of this buckling phenomenon is desired in applications where the…
We discuss instabilities of fluid films of nanoscale thickness, with a particular focus on films where the destabilising mechanism allows for linear instability, metastability, and absolute stability. Our study is motivated by nematic…
For the first time, a nonlinear interface problem on an unbounded domain with nonmonotone set-valued transmission conditions is analyzed. The investigated problem involves a nonlinear monotone partial differential equation in the interior…
Out-of-equilibrium systems, inherently complex and challenging to understand, are prevalent across various disciplines, including physics where they arise in contexts such as fluid dynamics. In particular, critical out-of-equilibrium…
Analysing the dynamics of phase-changing liquid films is essential for enhancing the performance of thermal management systems. Still, direct simulation of the full governing equations is computationally expensive. To circumvent this…
In this article, we propose a mathematical model which explains the formation of strong bonds during the relaxation process of a soft solid on a hard surface. As a result, the soft solid relaxes to a non zero residual stress level. The…
In this thesis we find an upper bound for the stretch factor of an elastic incompressible material subject to multiaxial traction, under which one can ensure that there is still no coalescence. The problem involves classical elliptic…