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A novel variant of the \emph{residual-free bubble} method (RFB) for advection dominated problems is presented. Since the usual RFB still suffers from oscillations and strong under/overshoots, the bubble space is enriched by \emph{patch…
It is known that in an unbounded fluid, the inline configuration of a freely rising bubble pair is often unstable with respect to lateral disturbances. This work numerically examines the stability of this configuration in the presence of a…
In this paper we introduce a method for solving linear and nonlinear scattering problems for wave equations using a new hybrid approach. This new approach consists of a reformulation of the governing equations into a form that can be solved…
We develop a formally exact technique for obtaining steady-state distributions of non-interacting active Brownian particles in a variety of systems. Our technique draws on results from the theory of two-way diffusion equations to solve the…
A number of important results of studying large deformations of hyper-elastic shells are obtained using discrete methods of mathematical physics. In the present paper, using the variational method for solving nonlinear boundary problems of…
The galactic supershells are cavities in the interstellar medium. These shells can be explained by introducing the concept of superbubbles, the theoretical result of multiple supernova. The superbubbles can be analytically described if the…
The air entrainment due to the turbulence in a free surface boundary layer shear flow created by a horizontally moving vertical surface-piercing wall is studied through experiments and direct numerical simulations. In the experiments, a…
We study the stability and shapes of domains with spontaneous curvature in fluid films and membranes, embedded in a surrounding membrane with zero spontaneous curvature. These domains can result from the inclusion of an impurity in a fluid…
We argue that there exists a new class of completely smooth 1/8-BPS, three-charge bound state configurations that depend upon arbitrary functions of two variables. These configurations are locally 1/2-BPS objects in that if they form an…
This paper concerns the dynamic stability of the steady 3-D wave structure of a planar normal shock front intersecting perpendicularly to a planar solid wall for unsteady potential flows. The stability problem can be formulated as a free…
We report the computational discovery of complex, topologically charged, and spectrally stable states in three-dimensional multi-component nonlinear wave systems of nonlinear Schr{\"o}dinger type. While our computations relate to…
In the last two centuries and more particularly in the last decades, the geometry of foams has become an important research domain, in mathematics, physics, material sciences and biology. Most of the simplest geometrical observations of…
This paper studies the polynomial stabilization of an elastic plate with dynamical boundary conditions on a non-smooth domain. To deal with the possible loss of solution regularity induced by boundary singularities, we formulate the problem…
Most problems in electrodynamics do not have an analytical solution so much effort has been put in the development of numerical schemes, such as the finite-difference method, volume element methods, boundary element methods, and related…
The nucleation of bubbles during a first-order phase transition has recently been explored using holographic duality, which can provide an important complement to standard perturbative methods. These computations typically require finding…
We study standing-wave solutions of Born-Infeld electrodynamics, with nonzero electromagnetic field in a region between two parallel conducting plates. We consider the simplest case which occurs when the vector potential describing the…
In this article, we study the free vibration and the mechanical buckling of plates using a three dimensional consistent approach based on the scaled boundary finite element method. The in-plane dimensions of the plate are modeled by…
We question physical existence of shape invariant solitons in three dimensional nematic liquid crystals. Using modified Petviashvili's method for finding eigenvalues and eigenfunctions, we determine shape invariant solitons in a realistic…
Spiral waves are a ubiquitous feature of the nonequilibrium dynamics of a great variety of excitable systems. In the limit of a large separation in timescale between fast excitation and slow recovery, one can reduce the spiral problem to…
This paper aims to use the unified bubble dynamics equation to investigate bubble behavior in complex scenarios involving hybrid free surface/wall boundaries and interactions between multiple bubbles. The effect of singularity movement on…