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Double-diffusive convection, often referred to as semi-convection in astrophysics, occurs in thermally and compositionally stratified systems which are stable according to the Ledoux-criterion but unstable according to the Schwarzchild…
Exact solutions of the linear water-wave problem describing oblique waves over a submerged horizontal cylinder of small (but otherwise fairly arbitrary) cross-section in a two-layer fluid are constructed in the form of convergent series in…
We establish connections between the problem of learning a two-layer neural network and tensor decomposition. We consider a model with feature vectors $\boldsymbol x \in \mathbb R^d$, $r$ hidden units with weights $\{\boldsymbol w_i\}_{1\le…
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 investigate dynamics of large scale and slow deformations of layered structures. Starting from the respective model equations for a non-conserved system, a conserved system and a binary fluid, we derive the interface equations which are…
A simple generalization of the Swift-Hohenberg equation is proposed as a model for the pattern-forming dynamics of a two-dimensional field with two unstable length scales. The equation is used to study the dynamics of surface waves in a…
In this paper, we study exponential random graph models subject to certain constraints. We obtain some general results about the asymptotic structure of the model. We show that there exists non-trivial regions in the phase plane where the…
This paper is devoted to the unidimensional analysis of a 2-ports silicon resonator vibrating in thickness--extensional mode. Both excitation and detection ports are capacitive transducers used to control the system of longitudinal elastic…
We describe the families of periodic orbits in the 2-dimensional 1/2 retrograde resonance at mass ratio 0.001, analyzing their stability and bifurcations into 3-dimensional periodic orbits. We explain the role played by periodic orbits in…
Presenting exact solutions for the two dimensional periodic Anderson model with finite and nonzero on-site interaction U>0, we are describing a rigorous non-Fermi liquid phase in normal phase and 2D. This new state emerges in multi-band…
Mixing layers can grow in time or space by vortex pairings that succeed each other in a nearly self-similar way. We use a point vortex model to study how confinement eventually limits this growth process, leading us to propose a wavelength…
We study a model of two layers, each consisting of a d-dimensional elastic object driven over a random substrate, and mutually interacting through a viscous coupling. For this model, the mean-field theory (i.e. a fully connected model)…
We rigorously apply the sum rules to the sum-over-states expression to calculate the fundamental limits of the dispersion of the two-photon absorption cross-section. A comparison of the theory with the data suggests that the truncated sum…
Some phase space transport properties for a conservative bouncer model are studied. The dynamics of the model is described by using a two-dimensional measure preserving mapping for the variables velocity and time. The system is…
Buoyant shear layers are encountered in many engineering and environmental applications and have been studied by researchers in the context of experiments and modeling for decades. Often, these flows have high Reynolds and Richardson…
Recently, complex horizontal patterns of umbral oscillations have been reported, but their physical nature and origin are still not fully understood. Here we show that the two-dimensional patterns of umbral oscillations of slow waves are…
Multi-photon emitters are a sought-after resource in quantum photonics. Nonlinear interactions between a multi-level atomic system and a coherent drive can lead to resonant two-photon emission, but harvesting light from this process has…
The collective excitation of the conduction electrons in subwavelength structures gives rise to the Localized Surface Plasmon(LSP). The system consisting of two such LSPs, known as the dimer system,is of fundamental interest and is being…
Layers of two-dimensional materials arranged at a twist angle with respect to each other lead to enlarged unit cells with potentially strongly altered band structures, offering a new arena for novel and engineered many-body ground states.…
The Minneart resonance is a low frequency resonance in which the wavelength is much larger than the size of the resonators. It is interesting to study the interaction between two adjacent bubbles when they are brought close together.…