Related papers: Formation of Liesegang Patterns
Self-organization is an ubiquitous phenomenon in nature which can be observed in a variety of different contexts and scales, with examples ranging from fish schools, swarms of birds or locusts, to flocks of bacteria. The observation of such…
We integrate numerically the nonlinear equation of motion for a collapsing spherical wavepacket in the context of theories that are expected to display behavior characteristic of classicalization. The classicalization radius sets the scale…
Spontaneous pattern formation is a phenomenon ubiquitous in nature, examples ranging from Rayleigh-Benard convection to the emergence of complex organisms from a single cell. In physical systems, pattern formation is generally associated…
The emergence of localised radial patterns from a Turing instability has been well studied in two and three dimensional settings and predicted for higher spatial dimensions. We prove the existence of localised $(n+1)$-dimensional radial…
This study proposes a coherent scenario of the formation of permanent shear bands in the flow of yield stress materials. It is a well accepted point of view that flow in disordered media is occurring via local plastic events, corresponding…
It is argued that the electron stripes as found in correlated oxides have to do with an unrecognized form of order. The manifestation of this order is the robust property that the charge stripes are at the same time anti-phase boundaries in…
The law of track formation in cloud chambers is derived from the Liouville equation with a simple Lindblad's type generator that describes coupling between a quantum particle and a classical, continuous, medium of two--state detectors.…
The equations of motion for the position and gauge invariant crystal momentum are considered for multiband wave packets of Bloch electrons. For a localized packet in a subset of bands well-separated from the rest of the band structure of…
In this work we investigate the process of pattern formation in a two dimensional domain for a reaction-diffusion system with nonlinear diffusion terms and the competitive Lotka-Volterra kinetics. The linear stability analysis shows that…
Patterns forming spontaneously in extended, three-dimensional, dissipative systems are likely to excite several homogeneous soft modes ($\approx$ hydrodynamic modes) of the underlying physical system, much more than quasi one- and…
A new class of pattern forming systems is identified and investigated: anisotropic systems that are spatially inhomogeneous along the direction perpendicular to the preferred one. By studying the generic amplitude equation of this new class…
The Talbot effect describes the emergence of periodic patterns in perturbed propagating wave fields. The effect is well studied for perturbations from structurally coherent optics such as diffraction gratings. The emergence of freeform and…
We experimentally study the occurrence of pattern formation during the slot-die coating of low-viscosity nearly Newtonian liquids onto Polyethylenterephthalat (PET)-substrates. In particular, it is demonstrated that with increase of the…
A basic understanding of the relevant features of hadron properties from first principles QCD has remained elusive, and should be understood as emergent phenomena which depend critically on the number of dimensions of physical spacetime.…
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…
A two-dimensional electron gas in a static external magnetic field exhibits two distinct collective excitation modes. The lower frequency mode propagates along the periphery of the domain almost freely with an extended lifetime, which is…
This study concerns the two-body scattering of particles in a one-dimensional periodic potential. A convenient ansatz allows for the separation of center-of-mass and relative motion, leading to a discrete Schr\"odinger equation in the…
This paper focuses on size effects in periodic mechanical metamaterials driven by reversible pattern transformations due to local elastic buckling instabilities in their microstructure. Two distinct loading cases are studied: compression…
We formulate a new information-theoretic principle--the shifted composition rule--which bounds the divergence (e.g., Kullback-Leibler or R\'enyi) between the laws of two stochastic processes via the introduction of auxiliary shifts. In this…
In this article, the possibility of generating non-classical light due to Planck-scale effects is considered. For this purpose, a widely studied model of deformation of the Heisenberg uncertainty relation is applied to single-mode and…