Related papers: Geometrical modeling of dendritic structures
The complex arrangements of atoms near grain boundaries are difficult to understand theoretically. We propose a phenomenological (Ginzburg-Landau-like) description of crystalline phases based on symmetries and fairly general stability…
Dissipative phenomena manifest in multiple mechanical systems. In this dissertation, different geometric frameworks for modelling non-conservative dynamics are considered. The objective is to generalize several results from conservative…
Quadratic descent of hermitian and skew hermitian forms over division algebras with involution of the first kind in arbitrary characteristic is investigated and a criterion, in terms of systems of quadratic forms, is obtained. A refined…
The structural properties of packed soft-core particles provide a platform to understand the cross-pollinated physical concepts in solid-state- and soft-matter physics. Confined on spherical surface, the traditional differential geometry…
The study of quadric surfaces of revolution is a cornerstone of classical Euclidean geometry, but its extension to the three-dimensional sphere $\mathbb{S}^3$ has not been sufficiently explored. This article addresses this important gap by…
We present a method for discovering dense packings of general convex hard particles and apply it to study the dense packing behavior of a one-parameter family of particles with tetrahedral symmetry representing a deformation of the ideal…
With tangent angle perturbation approach the axial symmetry deformation of a spherical vesicle in large under the pressure changes is studied by the elasticity theory of Helfrich spontaneous curvature model.Three main results in axial…
The conformational behavior of a coarse-grained finite polymer chain near an attractive spherical surface was investigated by means of multicanonical Monte Carlo computer simulations. In a detailed analysis of canonical equilibrium data…
We present a new method for assessing the intrinsic 3D shape of prestellar cores from molecular column densities. We have employed hydrodynamic simulations of contracting, isothermal cores considering three intrinsic geometries: spherical,…
The geometry of closed surfaces equipped with a Euclidean metric with finitely many conical points of arbitrary angle is studied. The main result is that the image of a non-closed geodesic has 0 distance from the set of conical points.…
We investigated the equilibrium properties of a one-dimensional system of classical particles which interact in pairs through a bounded repulsive potential with a Gaussian shape. Notwithstanding the absence of a proper fluid-solid phase…
The complexity of condensed matter arises from emergent behaviors that cannot be understood by analyzing individual constituents in isolation. While traditional condensed-matter approaches-developed primarily for ideal crystalline…
Understanding crystal growth over arbitrary curved surfaces with arbitrary boundaries is a formidable challenge, stemming from the complexity of formulating non-linear elasticity using geometric invariant quantities. Solutions are generally…
We study static and dynamical properties that distinguish two dimensional crystals constrained to lie on a curved substrate from their flat space counterparts. A generic mechanism of dislocation unbinding in the presence of varying Gaussian…
We study avenues to shape multistability and shape-morphing in flexible crystalline membranes of cylindrical topology, enabled by glide mobility of dislocations. Using computational modeling, we obtain states of mechanical equilibrium…
We investigate morphologies of semiflexible polymer rings, such as circular DNA, which are adsorbed onto topographically or chemically structured substrate surfaces. We classify all equilibrium morphologies for two striped surface…
One of the greatest challenges facing our society is the discovery of new innovative crystal materials with specific properties. Recently, the problem of generating crystal materials has received increasing attention, however, it remains…
We apply our deformation theory of periodic bar-and-joint frameworks to tetrahedral crystal structures. The deformation space is investigated in detail for frameworks modelled on quartz, cristobalite and tridymite.
The growth of quasicrystals, i.e., aperiodic structures with long-range order, seeded from the melt is investigated using a dynamical phase field crystal model. Depending on the thermodynamic conditions, two different growth modes are…
Interface energy and kinetic coefficient of crystal growth strongly depend on the face of the crystalline lattice. To investigate the kinetic anisotropy and velocity of different crystallographic faces we use the hyperbolic (modified) phase…