Related papers: Learning complexity to guide light-induced self-or…
We have observed nanopattern formation with robust and controllable spatial ordering by laser-induced dewetting in nanoscopic metal films. Pattern evolution in Co film of thickness 1\leq h\leq8 nm on SiO_{2} was achieved under multiple…
Laser-induced modification of transparent solids by intense femtosecond laser pulses allows fast integration of nanophotonic and nanofluidic devices with controlled optical properties. So far, the local and dynamic nature of the…
Arrays of nanoparticles exploited in light scattering applications commonly only feature either a periodic or a rather random arrangement of its constituents. For the periodic case, light scattering is mostly governed by the strong spatial…
We consider a paradigmatic nonvariational scalar Swift-Hohenberg equation that describes short wavenumber or large wavelength pattern forming systems. This work unveils evidence of the transition from stable stationary to moving localized…
We have studied the ordering kinetics of a two-dimensional anisotropic Swift-Hohenberg (SH) model numerically. The defect structure for this model is simpler than for the isotropic SH model. One finds only dislocations in the aligned…
We present a general approach to prove the existence, both locally and globally in amplitude, of fully localised multi-dimensional patterns in partial differential equations containing a compact spatial heterogeneity. While one-dimensional…
Self-organizing systems demonstrate how simple local rules can generate complex stochastic patterns. Many natural systems rely on such dynamics, making self-organization central to understanding natural complexity. A fundamental challenge…
We apply a recently developed unsupervised machine learning scheme for local atomic environments to characterize large-scale, disordered aggregates formed by sequence-defined macromolecules. This method provides new insight into the…
A simple generalization of the Swift-Hohenberg equation is proposed as a model for the pattern-forming dynamics of a two-dimensional field with two unstable length scales. The equation is used to study the dynamics of surface waves in a…
The Swift-Hohenberg equation describes an instability which forms finite-wavenumber patterns near onset. We study this equation posed with a spatial inhomogeneity; a jump-type parameter that renders the zero solution stable for $x<0$ and…
We analyze a 1-d ring structure composed of many two-level systems, in the limit where only one excitation is present. The two-level systems are coupled to a common environment, where the excitation can be lost, which induces super and…
Unsupervised learning enables modeling complex images without the need for annotations. The representation learned by such models can facilitate any subsequent analysis of large image datasets. However, some generative factors that cause…
The bulk of computational approaches for modeling physical systems in materials science derive from either analytical (i.e. physics based) or data-driven (i.e. machine-learning based) origins. In order to combine the strengths of these two…
We study the existence of patterns (nontrivial, stationary solutions) for one-dimensional Swift-Hohenberg Equation in a directional quenching scenario, that is, on $x\leq 0$ the energy potential associated to the equation is bistable,…
The effect of external fluctuations on the formation of spatial patterns is analysed by means of a stochastic Swift-Hohenberg model with multiplicative space-correlated noise. Numerical simulations in two dimensions show a shift of the…
We study domain coarsening of two dimensional stripe patterns by numerically solving the Swift-Hohenberg model of Rayleigh-Benard convection. Near the bifurcation threshold, the evolution of disordered configurations is dominated by grain…
We introduce a deep learning framework designed to train smoothed elastoplasticity models with interpretable components, such as a smoothed stored elastic energy function, a yield surface, and a plastic flow that are evolved based on a set…
Self-organization is ubiquitous in nature and mind. However, machine learning and theories of cognition still barely touch the subject. The hurdle is that general patterns are difficult to define in terms of dynamical equations and…
The process of pattern formation in the two dimensional Swift-Hohenberg equation is examined through numerical and analytic methods. Dynamic scaling relationships are developed for the collective ordering of convective rolls in the limit of…
When atoms scatter photons from a transverse laser into a high-finesse optical cavity, they form crystalline structures which maximize the intracavity light field and trap the atoms in the ordered array. Stable organization occurs when the…