Related papers: Field patterns without blow up
Type II string theory and M-theory admit flux configurations that break supersymmetry below the Kaluza-Klein scale. These backgrounds play a central role in most models of the string landscape. I argue that the behavior of such backgrounds…
The "Fluid Mechanic Sewing Machine" creates periodic patterns through the coiling nature of a viscous fluid falling onto a moving surface. At relatively moderate heights, the reported patterns are translating coiling, alternating loops, W…
We present a comprehensive and self-contained discussion of the use of the transfer matrix to study propagation in one-dimensional lossless systems, including a variety of examples, such as superlattices, photonic crystals, and optical…
Time crystals are many-body systems that spontaneously break time-translation symmetry, and thus exhibit long-range spatiotemporal order and robust periodic motion. Recent results have demonstrated how to build time-crystal phases in driven…
We consider co-rotational wave maps from the $(1+d)$-dimensional Minkowski space into the $d$-sphere for $d\geq 3$ odd. This is an energy-supercritical model which is known to exhibit finite-time blowup via self-similar solutions. Based on…
In non-commutative field theories conventional wisdom is that the unitarity is non-compatible with the perturbation analysis when time is involved in the non-commutative coordinates. However, as suggested by Bahns et.al. recently, the root…
Emergence is a concept that is easy to exhibit, but very hard to formally handle. This paper is about cubic sand grains moving around on nicely packed columns in one dimension (the physical sandpile is two dimensional, but the support of…
This paper presents a novel approach for computing substructure characteristic modes. This method leverages electromagnetic scattering matrices and spherical wave expansion to directly decompose electromagnetic fields. Unlike conventional…
A model in which pointlike defects are randomly embedded in Minkowski spacetime is considered. The distribution of spacetime defects is constructed to be Lorentz-invariant. It does not introduce a preferred reference frame, because it is…
We define a simple model of conformal field theory in random space-time environments, which we refer to as stochastic conformal field theory. This model accounts for the effects of dilute random impurities in strongly interacting critical…
The scattering formulation of characteristic mode decomposition is utilized to extend modal analysis to lossless scatterers breaking time-reversal symmetry. This enables characteristic modes analysis on devices containing gyrotropic or…
Photonic time crystals (PhTCs) are spatially uniform media whose material parameters vary periodically in time, opening momentum bandgaps within which the fields of electromagnetic modes can grow exponentially in time. To date, PhTCs have…
In the field of metamaterials, many intriguing phenomena arise from having a structure which is periodic in space. In time-dependent structures, conceptually similar properties can arise, which nevertheless have fundamentally different…
Conventional superconductors are strong diamagnets that through the Meissner effect expel magnetic fields. It would therefore be surprising if a superconducting ground state would support spontaneous magnetics fields. Such time-reversal…
Polarity fields are known to exhibit long distance patterns, in both physical and biological systems. The mechanisms behind such patterns are poorly understood. Here, we describe the dynamics of polarity fields using an original physical…
Punctured polygons are polygons with internal holes which are also polygons. The external and internal polygons are of the same type, and they are mutually as well as self-avoiding. Based on an assumption about the limiting area…
Pattern formation in biological, chemical and physical problems has received considerable attention, with much attention paid to dissipative systems. For example, the Ginzburg--Landau equation is a normal form that describes pattern…
Suspended microparticles subjected to AC electrical fields collectively organize into band patterns perpendicular to the field direction. The bands further develop into zigzag shaped patterns, in which the particles are observed to…
The Hubbard model is reformulated in terms of different ``colored'' fermion species for the electrons or holes at different lattice sites. Antiferromagnetic ordering or d-wave superconductivity can then be described in terms of…
Pattern formation from homogeneity is well-studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is nontrivial to separate observed spatial patterning due to inherent spatial heterogeneity from…