Related papers: Learning complexity to guide light-induced self-or…
How can one design complex systems capable of learning for a given functionality? In the context of ultrafast laser-surface interaction, we unravel the nature of learning schemes tied to the emergence of complexity in dissipative…
We study pattern formation in a complex Swift Hohenberg equation with phase-sensitive (parametric) gain. Such an equation serves as a universal order parameter equation describing the onset of spontaneous oscillations in extended systems…
When ultrathin metal films are subjected to multiple cycles of rapid melting and resolidification by a ns pulsed laser, spatially correlated interfacial nanostructures can result from a competition among several possible thin film…
Spatio-temporal pattern formation in complex systems presents rich nonlinear dynamics which leads to the emergence of periodic nonequilibrium structures. One of the most prominent equations for the theoretical and numerical study of the…
Controlling laser-induced pattern formation remains a long-standing challenge. A key advance was recognising the pivotal role of intrinsic feedback mechanisms in self-organisation, which enabled self-similar patterns with long-range order…
Theories of localised pattern formation are important to understand a broad range of natural patterns, but are less well-understood than more established mechanisms of domain-filling pattern formation. Here, we extend recent work on pattern…
We study point-like polarizable particles confined in a 1D very elongated trap within the evanescent field of an optical nano-fiber or nano-structure. When illuminated transversely by coherent light, collective light scattering into…
We study the Swift-Hohenberg equation - a paradigm model for pattern formation - with "large" spatially periodic coefficients and find a Turing bifurcation that generates patterns whose leading order form is a Bloch wave modulated by…
Self-organizations of ordered patterns in far-from-equilibrium many-body systems host fundamental importance in many disciplines. Meanwhile, complex systems often feature hierarchical structures with distinct scales for different layers,…
Although coherent light is usually required for the self-organization of regular spatial patterns from optical beams, we show that peculiar light matter interaction can break this evidence. In the traditional method to record laser-induced…
Molecular building blocks interacting at the nanoscale organize spontaneously into stable mono- layers that display intriguing long-range ordering motifs on the surface of atomic substrates. The patterning process, if appropriately…
We use a combination of unsupervised clustering and sparsity-promoting inference algorithms to learn locally dominant force balances that explain macroscopic pattern formation in self-organized active particle systems. The self-organized…
We rigorously prove the bifurcation of slow-moving pattern interfaces with general direction in a two-dimensional Swift-Hohenberg-type model close to a Turing instability for a large class of nonlinearities. These interfaces describe the…
Self-organization and pattern formation in network-organized systems emerges from the collective activation and interaction of many interconnected units. A striking feature of these non-equilibrium structures is that they are often…
The capabilities of image probe experiments are rapidly expanding, providing new information about quantum materials on unprecedented length and time scales. Many such materials feature inhomogeneous electronic properties with intricate…
The formation of self-organized patterns and localized states are ubiquitous in Nature. Localized states containing trivial symmetries such as stripes, hexagons, or squares have been profusely studied. Disordered patterns with non-trivial…
Many learning problems involve symmetries, and while invariance can be built into neural architectures, it can also emerge implicitly when training on group-structured data. We study this phenomenon in classical Hopfield networks and show…
This paper investigates a Cahn-Hilliard-Swift-Hohenberg system, focusing on a three-species chemical mixture subject to physical constraints on volume fractions. The resulting system leads to complex patterns involving a separation into…
We discuss mechanisms of self-organization processes in two-level solid-state class-B laser system. The model is considered under assumptions of influence of nonlinear absorber and external force, separately. It was found that…
In some pattern-forming systems, for some parameter values, patterns form with two wavelengths, while for other parameter values, there is only one wavelength. The transition between these can be organised by a codimension-three point at…