Related papers: Origin of anisotropic diffusion in Turing Patterns
We present a theoretical study aimed to elucidate the origin of the inverse symmetry breaking transition observed in ultrathin magnetic films with perpendicular anisotropy. We study the behavior of the dipolar frustrated Ising model in a…
The nonlinear theory of anomalous diffusion is based on particle interactions giving an explicit microscopic description of diffusive processes leading to sub-, normal, or super-diffusion as a result competitive effects between attractive…
The different thermo-elastic properties of glass fibers and polymer matrices can generate residual thermal stresses in injection-molded fiber-reinforced plastic (FRP) objects. During cooling from mold to room temperature, these stresses can…
When smooth granular material is fluidized by vertically shaking a container, we find that the temperature in the direction of energy input always exceeds the temperature in the other directions. An analytical model is presented which shows…
We investigate properties of turbulence and turbulent transport of non-inertial particles described in terms of turbulent thermal diffusion in strongly inhomogeneous and anisotropic convection forced by two similar turbulence generators…
Classifier-free guidance (CFG) has emerged as a pivotal advancement in text-to-image latent diffusion models, establishing itself as a cornerstone technique for achieving high-quality image synthesis. However, under high guidance weights,…
Inspired by recent experiments of cells accumulating on anisotropic substrates, we study a two-dimensional, compressible, isotropic, active fluid in the presence of anisotropic friction. We find that regions of anisotropic friction that are…
When magnetohydrodynamic turbulence evolves in the presence of a large-scale mean magnetic field, an anisotropy develops relative to that preferred direction. The well-known tendency is to develop stronger gradients perpendicular to the…
The Turing instability is a paradigmatic route to patterns formation in reaction-diffusion systems. Following a diffusion-driven instability, homogeneous fixed points can become unstable when subject to external perturbation. As a…
Fully localised patterns involving cellular hexagons or squares have been found experimentally and numerically in various continuum models. However, there is currently no mathematical theory for the emergence of these localised cellular…
Thermal fluctuations of microtubules (MTs) and other cytoskeletal filaments govern to a great extent the complex rheological properties of the cytoskeleton in eukaryotic cells. In recent years, much effort has been put into capturing the…
The study is focused on the dispersion properties of a wire medium formed by a rectangular lattice of parallel wires at the frequencies close to its plasma frequency. While the effective medium theory predicts isotropic behaviour of…
This paper presents a new type of surface models constructed on the basis of Finsler geometry. A Finsler metric is defined on the surface by using an underlying vector field, which is an in-plane tilt order. According to the orientation of…
We propose a mathematical model to describe the athermal fluctuations of thin sheets driven by the type of random driving that might be experienced prior to weak crumpling. The model is obtained by merging the F\"oppl-von K\'arm\'an…
The diffusion model presents a powerful ability to capture the entire (conditional) data distribution. However, due to the lack of sufficient training and data to learn to cover low-probability areas, the model will be penalized for failing…
This essay fuses concepts and approaches used to describe fluctuating phenomena in climate systems and statistical mechanics, and explores new ideas essential for understanding such phenomena. Its starting points are the Langevin equation…
Due to the advent of antiferromagnetic (AF) spintronics there is a burgeoning interest in AF materials for a wide range of potential and actual applications. Generally, AFs are characterized via the ordering at the Neel temperature (TN)…
A key prediction of turbulence theories is frame-invariance, and in magnetohydrodynamic (MHD) turbulence, axisymmetry of fluctuations with respect to the background magnetic field. Paradoxically the power in fluctuations in the turbulent…
In this work we study the effect of density dependent nonlinear diffusion on pattern formation in the Lengyel--Epstein system. Via the linear stability analysis we determine both the Turing and the Hopf instability boundaries and we show…
Transformation media provide a fundamental paradigm for field regulation, but their tricky anisotropy challenges fabrication. Though optical conformal mapping has been utilized to eliminate anisotropy, two key factors still hinder its…