Related papers: Capillary-Wave Description of Rapid Directional So…

Planes and circular cylinders are models of interfaces of a fluid when the support surface is translationally invariant in a direction of the space. After a study of the eigenvalues of the Jacobi operator, it is investigated when planar…

We consider unsupervised learning methods for characterizing the disordered microscopic structure of supercooled liquids and glasses. Specifically, we perform dimensionality reduction of smooth structural descriptors that describe radial…

Understanding rapid solidification behavior at velocities relevant to additive manufacturing (AM) is critical to controlling microstructure selection. Although in-situ visualization of solidification dynamics is now possible, systematic…

The addition of small amounts of a secondary fluid to a suspension can, through the attractive capillary force, lead to particle bridging and network formation. The capillary bridging phenomenon can be used to stabilize particle suspensions…

We present a mathematical formulation of a multiscale model for solidification with convective flow in the liquid phase. The model is an extension of the dendritic needle network approach for crystal growth in a binary alloy. We propose a…

In this letter we introduce the concept of stabilized vector solitons as nonlinear waves constructed by addition of mutually incoherent Townes solitons that are stabilized under the effect of a periodic modulation of the nonlinearity. We…

This study presents a detailed investigation of the modulational stability of interfacial wave packets in a two-layer inviscid incompressible fluid with finite layer thicknesses and interfacial surface tension. The stability analysis is…

Linear stability analysis currently fails to predict turbulence transition in canonical viscous flows. We show that two alternative models of the boundary condition for incipient perturbations at solid walls produce linear instabilities…

We investigate wavelet-like localized solutions in nonlinear waveguides, enabled by complementary propagation constants embedded in domains of anomalous dispersion. They are carrier-envelope-phase stable and independent of fine details of…

We introduce a model which gives rise to self-trapping of fundamental and higher-order localized states in a one-dimensional nonlinear Schr\"odinger equation with fractional diffraction and the strength of the self-defocusing nonlinearity…

This paper is concerned with analysis of coupled fractional reaction-diffusion equations. It provides analytical comparison for the fractional and regular reaction-diffusion systems. As an example, the reaction-diffusion model with cubic…

We present an analytical stability theory for the onset of the Faraday instability, applying over a wide frequency range between shallow water gravity and deep water capillary waves. For sufficiently thin fluid layers the surface is…

In this paper we establish a rigorous spectral stability analysis for solitary waves associated to a generalized fractional Benjamin-Bona-Mahony type equation. Besides the well known smooth and positive solitary wave with large wave speed,…

Capillary imbibition underpins many processes of fundamental and applied relevance in fluid mechanics. A limitation to the flow is the coupling to the confining solid, which induces friction forces. Our work proposes a general theoretical…

Recently, the Whitham and capillary-Whitham equations were shown to accurately model the evolution of surface waves on shallow water. In order to gain a deeper understanding of these equations, we compute periodic, traveling-wave solutions…

We use a one-scale similarity analysis which gives specific relations between the velocity, amplitude and width of localized solutions of nonlinear differential equations, whose exact solutions are generally difficult to obtain. We also…

A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. They depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation in the…

We investigate how two finite-amplitude, transverse, plane body waves may be superposed to propagate in a deformed hyperelastic incompressible solid. We find that the equations of motion reduce to a well-determined system of partial…

We analyze the existence and stability of nonlinear localized waves in a periodic medium described by the Kronig-Penney model with a nonlinear defect. We demonstrate the existence of a novel type of stable nonlinear band-gap localized…

Motivated by complex multi-fluid geometries currently being explored in fibre-device manufacturing, we study capillary instabilities in concentric cylindrical flows of $N$ fluids with arbitrary viscosities, thicknesses, densities, and…