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We investigate the conformal and superconformal properties of a non-relativistic spinning particle propagating in a curved background coupled to a magnetic field and with a scalar potential. We derive the conditions on the couplings for a…
We use a Convolutional Recurrent Neural Network approach to learn morphological evolution driven by surface diffusion. To this aim we first produce a training set using phase field simulations. Intentionally, we insert in such a set only…
Diffusion models are powerful tools for sampling from high-dimensional distributions by progressively transforming pure noise into structured data through a denoising process. When equipped with a guidance mechanism, these models can also…
Defects are a ubiquitous feature of ordered media. They have certain universal features, independent of the underlying physical system, reflecting their topological origins. While the topological properties of defects are robust, they…
An intermittent nonlinear map generating subdiffusion is investigated. Computer simulations show that the generalized diffusion coefficient of this map has a fractal, discontinuous dependence on control parameters. An amended continuous…
Driven surface diffusion occurs, for example, in molecular beam epitaxy when particles are deposited under an oblique angle. Elastic phase transitions happen when normal modes in crystals become soft due to the vanishing of certain elastic…
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…
We used nonequilibrium molecular dynamics simulations to study the shear deformation of metallic composites composed of alternating layers of Cu and Au. Our simulations reveal the formation of "vortices" or "swirls" if the bimaterial…
Diffusion models exhibit excellent sample quality, but existing guidance methods often require additional model training or are limited to specific tasks. We revisit guidance in diffusion models from the perspective of variational inference…
Inverse design problems are common in engineering and materials science. The forward direction, i.e., computing output quantities from design parameters, typically requires running a numerical simulation, such as a FEM, as an intermediate…
We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…
Programmable structures are systems whose undeformed geometries and material property distributions are deliberately designed to achieve prescribed deformed configurations under specific loading conditions. Inflatable structures are a…
Light injected into a spherical dielectric body may be confined very efficiently via the mechanism of total internal reflection. The frequencies that are most confined are called resonances. If the shape of the body deviates from the…
From a simple model for the driven motion of a planar interface under the influence of a diffusion field we derive a damped nonlinear oscillator equation for the interface position. Inside an unstable regime, where the damping term is…
This paper deals with the formulation and numerical implementation of a fully coupled continuum model for deformation-diffusion in linearized elastic solids. The mathematical model takes into account the effect of the deformation on the…
Diffusion models provide a principled framework for generative modeling via stochastic differential equations and time-reversed dynamics. Extending spectral diffusion approaches to spherical data, however, raises nontrivial geometric and…
There are many situations when modelling environmental phenomena for which it is not appropriate to assume a stationary dependence structure. \cite{sampson1992} proposed an approach to allowing nonstationarity in dependence based on a…
We investigate spin-wave propagation in magnetic insulators in the presence of lattice dislocations. Within a continuum magnetoelastic framework, we show that the strain fields generated by dislocations induce equilibrium magnetic textures.…
By an idealized quantum mechanical model, we formally describe the dispersion of nonretarded electromagnetic waves that express charge density oscillations near a fixed plane in three spatial dimensions (3D) at zero temperature. Our goal is…
Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data,…