Related papers: Gabor frames from contact geometry in models of th…
Interface states in photonic crystals (PCs) have attracted attention for the special properties, such as high transmission efficiency in bend waveguides, and their generation related to the topological phase. Previous works on interface…
Accurately rendering the appearance of fabrics is challenging, due to their complex 3D microstructures and specialized optical properties. If we model the geometry and optics of fabrics down to the fiber level, we can achieve unprecedented…
Motivated by recent experimental work on multicomponent lipid membranes supported by colloidal scaffolds, we report an exhaustive theoretical investigation of the equilibrium configurations of binary mixtures on curved substrates. Starting…
We study quantum vortex states of strongly interacting bosons in a two-dimensional rotating optical lattice. The system is modeled by Bose-Hubbard Hamiltonian with rotation. We consider lattices of different geometries, such as square,…
A three-dimensional unilateral contact problem for articular cartilage layers attached to subchondral bones shaped as elliptic paraboloids is considered in the framework of the biphasic cartilage model. The main novelty of the study is in…
Modeling membrane interactions with arbitrarily shaped colloidal particles, such as environmental micro- and nanoplastics, at the cell scale remains particularly challenging, owing to the complexity of particle geometries and the need to…
In this paper, we study the global behaviour of contact structures on oriented manifolds V which are circle bundles over a closed orientable surface S of genus g>0. We establish in particular contact analogs of a number of classical results…
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…
The phenomenom of emerging regular spectral features from random interactions is addressed in the context of the vibron model. A mean-field analysis links different regions of the parameter space with definite geometric shapes. The results…
We obtain a sub-Riemannian version of the classical Gauss-Bonnet theorem. We consider subsurfaces of a three dimensional contact sub-Riemannian manifolds, and using a family of taming Riemannian metric, we obtain a pure sub-Riemannian…
We study a two-dimensional system of spin-polarized fermions on the kagome lattice at filling fraction f=1/3 interacting through a nearest-neighbor interaction V. Above a critical interaction strength V_c a charge-density wave with a broken…
Frames normal for linear connections in vector bundles are defined and studied. In particular, such frames exist at every fixed point and/or along injective path. Inertial frames for gauge fields are introduced and on this ground the…
Multiplicative gating is widely used in neural architectures and has recently been applied to attention layers to improve performance and training stability in large language models. Despite the success of gated attention, the mathematical…
Let $P(M,G)$ be a principal fiber bundle, let $\omega$ be a connection form on $P(M,G)$, and consider a projectable connection $\nabla^{P}$ on $P(M,G)$. The aim of this work is to determine the $\nabla^{P}$-martingales in $P(M,G)$. Our…
The reconfigurability of radio environments with programmable metasurfaces is considered a key feature of next-generation wireless networks. Identifying suitable metasurface configurations for desired wireless functionalities requires a…
Strongly interacting dipolar bosons in optical lattices exhibit diverse quantum phases that are rich in physics. As the strength of the long-range boson-boson interaction increases, the system transitions across different phases: from a…
Given a null-cobordant oriented framed link $L$ in a closed oriented $3$--manifold $M$, we determine those links in $M \setminus L$ which can be realized as the singular point set of a generic map $M \to \mathbb{R}^2$ that has $L$ as an…
We consider plumbings of symplectic disk bundles over spheres admitting concave contact boundary, with the goal of understanding the geometric properties of the boundary contact structure in terms of the data of the plumbing. We focus on…
We have observed with STM moir\'e patterns corresponding to the rotation of one graphene layer on HOPG surface. The moir\'e patterns were characterized by rotation angle and extension in the plane. Additionally, by identifying border…
Gabor functions have wide-spread applications in image processing and computer vision. In this paper, we prove that 2D Gabor functions are translation-invariant positive-definite kernels and propose a novel formulation for the problem of…