Related papers: Field patterns without blow up
We address an experimental observation of pattern formation in a magnetised rf plasma. The experiments are carried out in a electrically grounded aluminium chamber which is housed inside a rotatable superconducting magnetic coil. The plasma…
A theoretical study of small thermal and electromagnetic perturbations in type-II superconductors is studied in the flux creep regime with a power-law voltage-current characteristics. The space-time evolution of temperature and electric…
Geometric singular perturbation theory provides a powerful mathematical framework for the analysis of 'stationary' multiple time-scale systems which possess a critical manifold, i.e. a smooth manifold of steady states for the limiting fast…
Recurrence plots exhibit line structures which represent typical behaviour of the investigated system. The local slope of these line structures is connected with a specific transformation of the time scales of different segments of the…
Dynamical coherent structure (pattern) formation in the Klein-Gordon lattice excited by periodic external field near the optical resonance is studied. It is shown that besides spatial patterns discovered recently (V.M.Burlakov,…
Non-reciprocal interactions between scalar fields that represent the concentrations of two active species are known to break the parity and time-reversal (PT) symmetries of the equilibrium state, as manifested in the emergence of travelling…
Temporal metamaterials are artificial materials whose electromagnetic properties change over time. In analogy with spatial media and metamaterials, where their properties change smoothly or abruptly over space, temporal metamaterials can…
We study the perturbative unitarity of noncommutative scalar field theories. Field theories with space-time noncommutativity do not have a unitary S-matrix. Field theories with only space noncommutativity are perturbatively unitary. This…
Scattering of electromagnetic fields by a defect layer embedded in a slow-light periodically layered ambient medium exhibits phenomena markedly different from typical scattering problems. In a slow-light periodic medium, constructed by…
Spontaneous symmetry breaking is a cornerstone of modern physics, defining a wealth of phenomena in condensed-matter and high-energy physics, and beyond. It requires an infinite number of degrees of freedom, and even then, for continuous…
Patterns in reaction-diffusion systems often contain two spatial scales; a long scale determined by a typical wavelength or domain size, and a short scale pertaining to front structures separating different domains. Such patterns naturally…
Nonlinear instabilities are responsible for spontaneous pattern formation in a vast number of natural and engineered systems ranging from biology to galaxies build-up. We propose a new instability mechanism leading to pattern formation in…
In this paper, we study the spatiotemporal distribution of the photon electric field produced by the scattering of a single photon narrow pulse from a system of two identical qubits coupled to continuum modes in a one-dimensional (1D) open…
Stack-theoretic blow-ups have proven to be efficient in resolving singularities over fields of characteristic zero. In this article, we move forward towards positive characteristic where new challenges arise. In particular, the dimension of…
The ordering of scalar fields after a phase transition in which a group $G$ of global symmetries is spontaneously broken to a subgroup $H$ provides a possible explanation for the origin of structure in the universe, as well as leading to…
A complex system comprises multiple interacting entities whose interdependencies form a unified whole, exhibiting emergent behaviours not present in individual components. Examples include the human brain, living cells, soft matter, Earth's…
Scattering problems with locally perturbed periodic surfaces have been studied both theoretically and numerically in recent years. In this paper, we will discuss the regularity results of the Bloch transform of the total fields. The idea is…
The spectrum of electromagnetic waves in periodic linear structures, such as periodic waveguides or chains of microelements i.e. spheres, cavities, exhibit the sequence of stop bands for propagating waves. Breaking the translational…
In this article, we study the time-reversal properties of a generic Markovian stochastic field dynamics with Gaussian noise. We introduce a convenient functional geometric formalism that allows us to straightforwardly generalize known…
The evolution of stripe patterns in type-I superconductors subject to a rotating in-plane magnetic field is investigated magneto-optically. The experimental results reveal a very rich and interesting behavior of the patterns. For small…