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A conservation-consistent boundary condition is proposed for nonlinear models of soluble-surfactant-laden falling films, ensuring exact conservation of total surfactant mass. The formulation resolves an inconsistency in widely used reduced…
We developed a conformal map technique to analyze the attenuation of edge modes propagating along imperfect boundaries. In systems where the potential energy exhibits conformal invariance, the conformal transformation can straighten the…
The folded node is a singularity associated with loss of normal hyperbolicity in systems where mixtures of slow and fast timescales arise due to singular perturbations. Canards are special solutions that reveal a counteractive feature of…
A sound synthesis model for woodwind instruments is developed using modal decomposition of the input impedance, accounting for viscothermal losses as well as localized nonlinear losses at the end of the resonator. To extend the definition…
We report a critical narrowing of resonances of a driven potential well, when their eigenfrequencies approach the edge of the continuum. The resonances also obtain unusual sharp-peak shapes at the continuum boundary. The situation can be…
Gauge symmetry breaking by boundary conditions on a manifold is known to be equivalent to Wilson-line breaking through a background gauge field, and is therefore spontaneous. These equivalent pictures are related by a non-periodic gauge…
Consider the self-map F of the space of real-valued test functions on the line which takes a test function f to the test function sending a real number x to f(f(x))-f(0). We show that F is discontinuous, although its restriction to the…
This work considers the transition to unsteadiness in the wake of 2D slender bodies, and questions the relevance of the generally accepted scenario involving a region of absolute instability within the near wake. The case of a thin plate at…
We present experimental evidence that the superstructures in turbulent boundary layers comprise of smaller, geometrically self-similar coherent motions. The evidence comes from identifying and analyzing instantaneous superstructures from…
We generalise a formula of Shou-Wu Zhang, which describes local arithmetic intersection numbers of three Cartier divisors with support in the special fibre on a a self-product of a semi-stable arithmetic surface using elementary analysis.…
In this paper we study the local behavior of solutions to some free boundary problems. We relate the theory of quasi-conformal maps to the regularity of the solutions to nonlinear thin-obstacle problems; we prove that the contact set is…
Off-road semantic segmentation suffers from thick, inconsistent boundaries, sparse supervision for rare classes, and pervasive label noise. Designs that fuse only at low resolution blur edges and propagate local errors, whereas maintaining…
Localized planar patterns in spatially extended bistable systems are known to exist along intricate bifurcation diagrams, which are commonly referred to as snaking curves. Their analysis is challenging as techniques such as spatial dynamics…
Intriguing issues in one-dimensional non-reciprocal topological systems include the breakdown of usual bulk-edge correspondence and the occurrence of half-integer topological invariants. In order to understand these unusual topological…
At a border-collision bifurcation a fixed point of a piecewise-smooth map intersects a surface where the functional form of the map changes. Near a generic border-collision bifurcation there are two fixed points, each of which exists on one…
The compression of soft elastic matter and biological tissue can lead to creasing, an instability where a surface folds sharply into periodic self-contacts. Intriguingly, the unfolding of the surface upon releasing the strain is usually not…
Chemical, physical and ecological systems passing through a saddle-node bifurcation will, momentarily, find themselves balanced at a semi-stable steady state. If perturbed by noise, such systems will escape from the zero-steady state, with…
The roughness properties of two-dimensional fracture surfaces as created by the slow failure of random fuse networks are considered and compared to yield surfaces of perfect plasticity with similar disorder. By studying systems up to a…
We study nonlinear modes in subwavelength slot waveguides created by a nonlinear dielectric slab sandwiched between two metals. We present the dispersion diagrams of the families of nonlinear plasmonic modes and reveal that the symmetric…
It is known that Kolmogorov-Arnold-Moser boundaries appear in sufficiently smooth 2-dimensional area-preserving maps. When such boundaries are destroyed, they become pseudo-boundaries. We show that pseudo-boundaries can also be found in…