Related papers: Pattern formation of a nonlocal, anisotropic inter…
Anisotropic inflation is an interesting model with an U(1) gauge field and it predicts the statistical anisotropy of the curvature perturbation characterized by a parameter $g_*$. However, we find that the background gauge field does not…
We study spatial anisotropy effects on the bulk and finite-size critical behavior of the O$(n)$ symmetric anisotropic $\phi^4$ lattice model with periodic boundary conditions in a $d$-dimensional hypercubic geometry above, at and below…
A wide variety of morphologies arise due to the tetragonal anisotropy in interfacial free energy. In this paper, we report on a family of Extended Cahn-Hilliard (ECH) models for incorporating tetragonal anisotropy in interfacial free…
A Self Consistent Field Theory description of equilibrium, but non uniform, configurations adopted by semi flexible liquid crystal molecules is presented. Two cases are considered, isotropic-nematic phase boundaries, and topological defects…
We propose a phase prediction method for the pattern formation in the uniaxial two-dimensional kinetic Ising model with the dipole-dipole interactions under the time-dependent Ginzburg-Landau dynamics. Taking the effects of the material…
We consider a modification of the Winter model describing a quantum particle in presence of a spherical barrier given by a fixed generalized point interaction. It is shown that the three classes of such interactions correspond to three…
The study of pattern emergence together with exploration of the exemplar Turing model is enjoying a renaissance both from theoretical and experimental perspective. Here, we implement a stability analysis of spatially dependent reaction…
A non-perturbative local moment approach to single-particle dynamics of the general asymmetric Anderson impurity model is developed. The approach encompasses all energy scales and interaction strengths. It captures thereby strong coupling…
Pattern formation is a visual understanding of the dynamics of complex systems. Patterns arise in many ways, such as the segmentation of animals, bacterial colonies during growth, vegetation, chemical reactions, etc. In most cases, the…
Neutrino-electron scattering is a purely leptonic fundamental interaction and therefore provides an important channel to test the Standard Model, especially at the low energy-momentum transfer regime. We derived constraints on neutrino…
The microscopic structure of several amorphous substances often reveals complex patterns such as medium- or long-range order, spatial heterogeneity, and even local polycrystallinity. To capture all these features, models usually incorporate…
Our interest lies in exploring the ability of a coupled nonlocal system of two quasilinear parabolic partial differential equations to produce phase separation patterns. The obtained patterns are referred here as morphologies. Our target…
The Johnson--Kendall--Roberts model of frictionless adhesive contact is extended to the case of a thin transversely isotropic elastic layer bonded to a rigid base. The leading-order asymptotic models are obtained for both compressible and…
The quantitative knowledge of interface anisotropy in lattice models is a major issue, both for the parametrization of continuum interface models, and for the analysis of experimental observations. In this paper, we focus on the anisotropy…
Stress-strain measurements and ultrasound propagation experiments in glass bead packs have been simultaneously conducted to characterize the stress-induced anisotropy under uniaxial loading. These measurements, realized respectively with…
The representation degeneration problem is a phenomenon that is widely observed among self-supervised learning methods based on Transformers. In NLP, it takes the form of anisotropy, a singular property of hidden representations which makes…
In this paper, we numerically study Turing patterns by the Finsler geometry (FG) modeling technique on thermally fluctuating triangular lattices, which are often used for modeling cell membranes or lipid membranes, focusing on the origin of…
We identify a mechanism for biological spatial pattern formation arising when the signals that mediate interactions between individuals in a population have pulsed character. Our general population-signal framework shows that while for a…
We present a phase-field model for simulating the solid-state dewetting of anisotropic crystalline films on non-planar substrates. This model exploits two order parameters to trace implicitly the crystal free surface and the substrate…
In this paper the thermodynamics of thin ferromagnetic films are studied in the framework of the classical Heisenberg model with uniaxial anisotropy and long--range dipole interaction. The dependence of the order of the reorientation…