Related papers: A closed-form solution of the three-dimensional co…
We present a three dimensional, time dependent model for bone regeneration in the presence of porous scaffolds to bridge critical size bone defects. Our approach uses homogenized quantities, thus drastically reducing computational cost…
The linear (Winkler) foundation is a simple model widely used for decades to account for the surface response of elastic bodies. It models the response as purely local, linear, and perpendicular to the surface. We extend this model to the…
We consider a viscoelastic body occupying a smooth bounded domain of $R^3$ under the effects of volumic traction forces. Inertial effects are considered: hence, the equation describing the evolution of displacements is of the second order…
This paper deals with a hyperbolic system of two nonlinear conservation laws, where the phase space contains two contact manifolds. The governing equations are modelling bidisperse suspensions, which consist of two types of small particles…
Multiphase field models have emerged as an important computational tool for understanding biological tissue while resolving single-cell properties. While they have successfully reproduced many experimentally observed behaviors of living…
A one-dimensional system of two trapped bosons which interact through a contact potential is studied using the optimized configuration interaction method. The rapid convergence of the method is demonstrated for trapping potentials of convex…
The modelling of heterogeneous and architected materials poses a significant challenge, demanding advanced homogenisation techniques. However, the complexity of this task can be considerably simplified through the application of micropolar…
The mechanical response of cellular materials with spinodal topologies is numerically and experimentally investigated. Spinodal microstructures are generated by the numerical solution of the Cahn-Hilliard equation. Two different topologies…
On contact manifolds we describe a notion of (contact) finite-type for linear partial differential operators satisfying a natural condition on their leading terms. A large class of linear differential operators are of finite-type in this…
Recent experimental advances in realizing degenerate quantum dipolar gases in optical lattices and the flexibility of experimental setups in attaining various geometries offer the opportunity to explore exotic quantum many-body phases…
Following the Cartans's original method of equivalence supported by methods of parabolic geometry, we provide a complete solution for the equivalence problem of quaternionic contact structures, that is, the problem of finding a complete…
We investigate the nature of the ordered phase and the orientational correlations between adjacent layers of the confined three-dimensional self-assembled rigid rod model, on the cubic lattice. We find that the ordered phase at finite…
A mechanical interaction of compressible viscoelastic fluids with viscoelastic solids in Kelvin-Voigt rheology using the concept of higher-order (so-called 2nd-grade multipolar) viscosity is investigated in a quasistatic variant. The…
Cross-sections of cell shapes in a tissue monolayer typically resemble a tiling of convex polygons. Yet, examples exist where the polygons are not convex with curved cell-cell interfaces, as seen in the adaxial epidermis. To date,…
This paper is concerned with the time-dependent acoustic-elastic interaction problem associated with a bounded elastic body immersed in a homogeneous air or fluid above an unbounded rough surface. The well-posedness and stability of the…
It is well known that for many semilinear parabolic equations there is a global attractor which has a cell complex structure with finite dimensional cells. Additionally, many semilinear parabolic equations have equilibria with finite…
In order to describe two-dimensionally packed cells in epithelial tissues both mathematically and physically, there have been developed several sorts of geometrical models, such as the vertex model, the finite element model, the…
A geometric analysis of the $sdg$ interacting boson model is performed. A coherent-state is used in terms of three types of deformation: axial quadrupole ($\beta_2$), axial hexadecapole ($\beta_4$) and triaxial ($\gamma_2$). The…
We investigate a system of two- and three-body constrained dipolar bosons in a pair of one-dimensional optical lattices coupled to each other by the non-local dipole-dipole interactions. Assuming attractive dipole-dipole interactions, we…
The three-phase contact line formed by the intersection of a liquid-vapor interface of an electrolyte solution with a charged planar substrate is studied in terms of classical density functional theory applied to a lattice model. The…