Related papers: Existence of Phi-Relationship Within Regular Hexag…
In the study of pattern formation in symmetric physical systems a 3-dimensional structure in thin domains is often modelled as 2-dimensional one. We are concerned with functions in $R^3$ that are invariant under the action of a…
Since the seminal work by Nagel and Weiss, the iteration stable (STIT) tessellations have attracted considerable interest in stochastic geometry as a natural and flexible, yet analytically tractable model for hierarchical spatial…
It is shown that every scalar linear quadrilateral lattice equation lies within a family of similar equations, members of which are compatible between one another on a higher dimensional lattice. There turn out to be two such families, a…
Polymers are among the most important materials in the modern society being found almost in every activity of our daily life. Understanding their chemical and physical properties lead to improvements of their usage. The correlation…
A universal relation connecting Fermi surface (FS) to the symmetry of the gap function in BCS-like superconductors is derived. It is found that the shape of the FS can be deduced directly from the symmetry of the superconducting gap…
Triangular lattice models for pattern formation by hard-core soft-shell particles at interfaces are introduced and studied in order to determine the effect of the shell thickness and structure. In model I, we consider particles with…
We study the proximity effect between conventional superconductor and magnetic normal metal with a spin-orbit interaction of the Rashba type. Using the phenomenological Ginzburg-Landau theory and the quasiclassical Eilenberger approach it…
The results obtained from molecular dynamics simulations of the friction at an interface between polymer melts and weakly attractive crystalline surfaces are reported. We consider a coarse-grained bead-spring model of linear chains with…
By regular tessellation, we mean any hyperbolic 3-manifold tessellated by ideal Platonic solids such that the symmetry group acts transitively on oriented flags. A regular tessellation has an invariant we call the cusp modulus. For small…
In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…
Contrary to canonical expectations we show that lattice translational symmetry breaking often accompanies uniformly ordered flux phases. We demonstrate this phenomena by studying a spinless-fermion model on a square latttice with…
The signature topological feature of Maxwell lattices is their polarization, which manifests as an unbalance in stiffness between opposite edges of a finite domain. The manifestation of this asymmetry is especially dramatic in the case of…
We study a variety of Hofstadter ladders in order to probe the interplay between interactions, an applied magnetic field and crystalline or quasiperiodic geometries. Rotational motion will be induced on charged particles when a magnetic…
In many mathematical models for pattern formation, a regular hexagonal pattern is stable in an infinite region. However, laboratory and numerical experiments are carried out in finite domains, and this imposes certain constraints on the…
Simulations are used to find the zero temperature jamming threshold, $\phi_j$, for soft, bidisperse disks in the presence of small fixed particles, or "pins", arranged in a lattice. The presence of pins leads, as one expects, to a decrease…
The kinetic features of secondary magnetic reconnection in a single flux rope undergoing internal kink instability are studied by means of three-dimensional Particle-in-Cell simulations. Several signatures of secondary magnetic reconnection…
We study the intimate relationship between the Penrose and the Taylor-Socolar tilings, within both the context of double hexagon tiles and the algebraic context of hierarchical inverse sequences of triangular lattices. This unified approach…
The impact of projective lattice symmetry on electronic band structures has attracted significant attention in recent years, particularly in light of growing experimental studies of two-dimensional hexagonal materials in magnetic fields.…
In this chapter, we analyze the steady-state microscale fluid--structure interaction (FSI) between a generalized Newtonian fluid and a hyperelastic tube. Physiological flows, especially in hemodynamics, serve as primary examples of such FSI…
We analyze the geometrical background under which many Lie groups relevant to particle physics are endowed with a (possibly multiple) hexagonal structure. There are several groups appearing, either as special holonomy groups on the…