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We provide an analytical approximation to the dynamics in each of the three most important low order secondary resonances (1:1, 2:1, and 3:1) bifurcating from the synchronous primary resonance in the gravitational spin-orbit problem. To…
When using a finite difference method to solve an initial--boundary--value problem, the truncation error is often of lower order at a few grid points near boundaries than in the interior. Normal mode analysis is a powerful tool to analyze…
We study Faraday patterns in quasi-one-dimensional dipolar Bose-Einstein condensates with parametrically driven dipolar interactions. We show that in the presence of a roton minimum in the excitation spectrum, the emergent Faraday waves…
When two-dimensional pattern-forming problems are posed on a periodic domain, classical techniques (Lyapunov-Schmidt, equivariant bifurcation theory) give considerable information about what periodic patterns are formed in the transition…
The formation of patterns of peaks on the free surface of a ferrofluid subject to a magnetic field normal to the undisturbed interface is investigated theoretically. The relative stability of ridge, square, and hexagon planforms is studied…
We propose two frequency-domain filters to analyze ringdown signals of binary black hole mergers. The first rational filter is constructed based on a set of (arbitrary) quasi-normal modes (QNMs) of the remnant black holes, whereas the…
We analytically compute the long-term orbital variations of a test particle orbiting a central body acted upon by an incident monochromatic plane gravitational wave. We assume that the characteristic size of the perturbed two-body system is…
The effects of a spatially periodic forcing on an oscillating chemical reaction as described by the Lengyel-Epstein model are investigated. We find a surprising competition between two oscillating patterns, where one is harmonic and the…
We study free surface water waves in a 2-D symmetric triangular channel with sides that have a 45o slope. We develop models for small amplitude nonlinear waves, extending earlier studies that have considered the linearized problem. We see…
We analyze the propagation properties of the numerical versions of one and two-dimensional wave equations, semi-discretized in space by finite difference schemes. We focus on high-frequency solutions whose propagation can be described, both…
We consider the inverse problem for the wave equation which consists of determining an unknown space-dependent force function acting on a vibrating structure from Cauchy boundary data. Since only boundary data are used as measurements, the…
Hydrodynamic instabilities are usually investigated in confined geometries where the resulting spatiotemporal pattern is constrained by the boundary conditions. Here we study the Faraday instability in domains with flexible boundaries. This…
This second part of the study develops a geometric and asymptotic description of how surface tension governs the modulational stability of interfacial waves in a two-layer fluid. Extending the analytical framework of Part~I, surface tension…
Pattern formation in parametric surface waves is studied in the limit of weak viscous dissipation. A set of quasi-potential equations (QPEs) is introduced that admits a closed representation in terms of surface variables alone. A multiscale…
The ubiquity of parametric resonance is continually evident in the repeated experimental observations of this phenomenon in multiple physical systems. The elementary case of 2 mode parametric resonance of order 1 involves the excitation of…
Building on a previous study that analyses surface waves in magnetic slabs embedded in a non-magnetic external environment, in this study the model is generalised and external magnetic fields are added. The slab is assumed to be thin, with…
Turbine blades operating in transonic-supersonic regime develop a complex shock wave system at the trailing edge, a phenomenon that leads to unfavorable pressure perturbations downstream and can interact with other turbine stages.…
It is well known that instantons are classical topological solutions existing in the context of quantum field theories that lie behind the standard model of particles. To provide a better understanding for the dynamical nature of…
In this paper, we analyse the dynamics of a pattern-forming system close to simultaneous Turing and Turing--Hopf instabilities, which have a 1:1 spatial resonance, that is, they have the same critical wave number. For this, we consider a…
We discuss the notion of resonance, as well as the existence and uniqueness of periodic solutions for a forced simple harmonic oscillator. While this topic is elementary, and well-studied for sinusoidal forcing, this does not seem to be the…