Related papers: On resolving singularities of piecewise-smooth dis…
Recently, we introduced an ekpyrotic model based on a single, canonical scalar field that generates nearly scale invariant curvature fluctuations through a purely "adiabatic mechanism" in which the background evolution is a dynamical…
Onset of small-amplitude oscillatory and both small- and finite-amplitude steady double-component convection arising due to component different boundary conditions in an infinite slot is studied for various slot orientations to the gravity.…
A detailed study of complex-space singularities of the two-dimensional incompressible Euler equation is performed in the short-time asymptotic r\'egime when such singularities are very far from the real domain; this allows an exact…
The paper is concerned with the stability of the set of trajectories of a vector field, in the presence of impulsive perturbations. Patchy vector fields are discontinuous, piecewise smooth vector fields that were introduced in AB to study…
We describe all possible topological structures of codimension one gradient vector fields on the shpere with at most ten singular points. To describe structures, we use a graph whose edges are one-dimensional stable manifolds. The…
In this paper we study the evolution of cosmological perturbations through a nonsingular bouncing universe using covariant perturbation theory and examine the validity of linear perturbation theory. The bounce is modeled by a two component…
In this paper we prove the breakdown of the two-dimensional stable and unstable manifolds associated to two saddle-focus points which appear in the unfoldings of the Hopf-zero singulariry. The method consists in obtaining an asymptotic…
Previous experimental and numerical studies showed that two-dimensional roughness elements can stabilize disturbances inside a hypersonic boundary layer, and eventually delay the transition onset. The objective of this paper is to evaluate…
In perturbation theory, the spectral densities of two-point functions develop non-integrable threshold singularities at higher orders. In QCD, such singularities emerge when calculating the diagrams in terms of the pole quark mass, and they…
In this paper, we establish the existence of Stokes waves with piecewise smooth vorticity in a two-dimensional, infinitely deep fluid domain. These waves represent traveling water waves propagating over sheared currents in a semi-infinite…
This work investigates efficient routes to turbulence in quasi-two-dimensional shear flows. Two-dimensional disturbances require high Reynolds numbers to incite transition from a steady base flow, as transient growth is modest. With the…
We analyze the convergence of a perturbed circular interface for the two-phase Mullins-Sekerka evolution in flat two-dimensional space. Our method is based on the gradient flow structure of the evolution and captures two distinct regimes of…
Variable-exponent fractional models attract increasing attentions in various applications, while the rigorous analysis is far from well developed. This work provides general tools to address these models. Specifically, we first develop a…
We present a numerical investigation of two-dimensional decaying turbulence in the Lagrangian framework. Focusing on single particle statistics, we investigate Lagrangian trajectories in a freely evolving turbulent velocity field. The…
Spinor-vector dualities have been established in various exact string realisations like orbifold and free fermionic constructions. This paper aims to investigate possibility of having spinor-vector dualities on smooth geometries in the…
The phenomenological theory revealing the generic effects of the problem symmetry, its violation, and energy conservation law on the singularities of the Poynting vector field is presented. The bifurcation scenario of their formation…
The limiting slow dynamics of slow-fast, piecewise-linear, continuous systems of ODEs occurs on critical manifolds that are piecewise-linear. At points of non-differentiability, such manifolds are not normally hyperbolic and so the…
A general, two-way coupled, point-particle formulation that accounts for the disturbance created by the dispersed particles in obtaining the undisturbed fluid flow field needed for accurate computation of the force closure models is…
We consider the motion of the interface separating two domains of the same fluid that moves with different velocity along the tangential direction of the interface. We assume that the fluids occupying the two domains are of constant…
We investigate second order conformal perturbation theory for $\mathbb{Z}_2$ orbifolds of conformal field theories in two dimensions. To evaluate the necessary twisted sector correlation functions and their integrals, we map them from the…