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Break of radial symmetry for interaction energy minimizers is a phenomenon where a radial interaction potential whose associated energy minimizers are never radially symmetric. Numerically, it has been frequently observed for various types…
For a relativistic particle moving in the presence of mean scalar and vector fields, the energy at second order in the scalar field is shown to contain two contributions in general. One is a momentum-dependent repulsive interaction…
We consider a class of single-director Cosserat shell models accounting for both curvature and finite mid-plane strains. We assume a polyconvexity condition for the stored-energy function that reduces to a physically correct membrane model…
We consider a discrete-continuum model of a biomembrane with embedded particles. While the membrane is represented by a continuous surface, embedded particles are described by rigid discrete objects which are free to move and rotate in…
We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…
Dynamics near the grazing manifold and basins of attraction for a motion of a material point in a gravitational field, colliding with a moving motion-limiting stop, are investigated. The Poincare map, describing evolution from an impact to…
Given a graph $G$, we associate a path matrix $P$ whose $(i, j)$ entry represents the maximum number of vertex disjoint paths between the vertices $i$ and $j$, with zeros on the main diagonal. In this note, we resolve four conjectures from…
The energy budget and dissipation mechanisms during droplet impact on solid surfaces are studied numerically and theoretically. We find that for high impact velocities and negligible surface friction at the solid surface (i.e. free-slip),…
We consider a one-dimensional classical many-body system with interaction potential of Lennard-Jones type in the thermodynamic limit at low temperature $1/\beta\in(0,\infty)$. The ground state is a periodic lattice. We show that when the…
How local cracks can contribute to the global cracks landscape is a goal of several scientific topics, for example, how bottlenecks can impact the robustness of traffic into a city? In one direction, cracks from cascading failures into…
The motion of a forced vibro-impacting inclined energy harvester is investigated in parameter regimes with asymmetry in the number of impacts on the bottom and top of the device. This motion occurs beyond a grazing bifurcation, at which…
We discuss the properties of the distributions of energies of minima obtained by gradient descent in complex energy landscapes. We find strikingly similar phenomenology across several prototypical models. We particularly focus on the…
We study self-contact phenomena in elastic rods that are constrained to lie on a cylinder. By choosing a particular set of variables to describe the rod centerline the variational setting is made particularly simple: the strain energy is a…
The difficulty in exploring potential energy surfaces, which are nonconvex, stems from the presence of many local minima, typically separated by high barriers and often disconnected in configurational space. We obtain the global minimum on…
We consider the minimisation of power-law repulsive-attractive interaction energies which occur in many biological and physical situations. We show existence of global minimizers in the discrete setting and get bounds for their supports…
Shortest paths play an important role in mathematical modeling and image processing. Usually, shortest path problems are formulated on planar graphs that consist of vertices and weighted arcs. In this context, one is interested in finding a…
Cracks in beams and shallow arches are modeled by massless rotational springs. First, we introduce a specially designed linear operator that "absorbs" the boundary conditions at the cracks. Then the equations of motion are derived from the…
We present a variational reduced-order model for three-dimensional coplanar propagation of sharp cracks in heterogeneous perfectly brittle solids under mixed-mode I+II+III loading. The approach connects the variational fracture formulation…
The interaction of crack fronts with asperities is central to the criteria of fracture in heterogeneous materials and for predicting fracture surface formation. It is known how dynamic crack fronts respond to small, 1st-order,…
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…