Related papers: Localisation of directional scale-discretised wave…
This paper provides quantitative Central Limit Theorems for nonlinear transforms of spherical random fields, in the high frequency limit. The sequences of fields that we consider are represented as smoothed averages of spherical Gaussian…
This paper has three main contributions. The first is the construction of wavelet transforms from B-spline scaling functions defined on a grid of non-equispaced knots. The new construction extends the equispaced, biorthogonal, compactly…
The potential breakdown of the notion of a metric at high energy scales could imply the existence of a fundamental minimal length scale below which distances cannot be resolved. One approach to realizing this minimum length scale is…
In this paper, we introduce a new wavelet tool for studying the degree of non-periodicity of time series that is based on some recently defined tools, such as the \textit{windowed scalogram} and the \textit{scale index}. It is especially…
We discuss how the kernel convolution approach can be used to accurately approximate the spatial covariance model on a sphere using spherical distances between points. A detailed derivation of the required formulas is provided. The proposed…
Anisotropically wetting substrates enable useful control of droplet behavior across a range of applications. Usually, these involve chemically or physically patterning the substrate surface, or applying gradients in properties like…
Controlling the spatial distribution of liquid droplets on surfaces via surface energy patterning can be used to control material delivery to specified regions via selective liquid/solid wetting. While studies of the equilibrium shape of…
We establish spectral rigidity for spherically symmetric manifolds with boundary and interior interfaces determined by discontinuities in the metric under certain conditions. Rather than a single metric, we allow two distinct metrics in…
Symmetries are known to dictate important physical properties and can be used as a design principle in particular in wave physics, including wave structures and the resulting propagation dynamics. Local symmetries, in the sense of a…
Spiral waves are ubiquitous in two-dimensional systems of chemical or biological oscillators coupled locally by diffusion. At the center of such spirals is a phase singularity, a topological defect where the oscillator amplitude drops to…
We report on existence and properties of discrete gap solitons in zigzag arrays of alternating waveguides with positive and negative refractive indices. Zigzag quasi-one-dimensional configuration of waveguide array introduces strong…
A complete discrete set of spherical single-particle wave functions for studies of weakly-bound many-body systems is proposed. The new basis is obtained by means of a local-scale point transformation of the spherical harmonic oscillator…
Many phenomena taking place in the solar photosphere are controlled by plasma motions. Although the line-of-sight component of the velocity can be estimated using the Doppler effect, we do not have direct spectroscopic access to the…
We study synchronization phenomena in scale-free networks of asymetrically coupled dynamical systems featuring degree-degree correlation in the connection wiring. We show that when the interaction is dominant from the high-degree to the…
We strengthen a result of two of us on the existence of effective interactions for discretised continuous-spin models. We also point out that such an interaction cannot exist at very low temperatures. Moreover, we compare two ways of…
The structure of discrete resonances in water-wave turbulence is studied. It is shown that the number of exact 4-wave resonances is huge (hundreds million) even in comparatively small spectral domain when both scale and angle energy…
Nonlinear waves are a robust phenomenon observed in complex systems ranging from mechanics to ecology. Fronts are fundamental due to their robustness against perturbations and capacity to propagate one state over another. Controlling and…
Understanding the drift motion and dynamical locking of crystalline clusters on patterned substrates is important for the diffusion and manipulation of nano- and micro-scale objects on surfaces. In a previous work, we studied the…
The discrete-dipole approximation (DDA) is a powerful method for calculating absorption and scattering by targets that have sizes smaller than or comparable to the wavelength of the incident radiation. We present a new prescription -- the…
Reconstructing magnetizations from measurements of the generated magnetic potential is generally non-unique. The non-uniqueness still remains if one restricts the magnetization to those induced by an ambient magnetic dipole field (i.e., the…