We present linearized stability analyses of the effect of slow anisotropic compression or expansion on the growth of perturbations at accelerated fluid interfaces in both planar and spherical geometries. The interface separates two fluids with different densities, compressibilities, and compression rates. We show that a perturbation of large mode number on a spherical interface grows at precise...

In this paper we consider the problem of determining the boundary perturbations of an object from far-field electric or acoustic measurements. Assuming that the unknown scatterer boundary is a small perturbation of a circle, we develop a linearized relation between the far-field data and the shape of the object. This relation is used to find the Fourier coefficients of the perturbation of the s...

We study the dynamics of perturbations around an inhomogeneous stationary state Vlasov-HMF (Hamiltonian Mean-Field) model, satisfying a linearized stability criterion (Penrose criterion). consider solutions equation steady state, and prove algebraic decay in time Fourier modes their density. moreover that these exhibit scattering behavior to modified implying linear damping effect with rate dam...

(6) Let G be a column Y-constant line Y-increasing matrix over E2 T and i1, i2, j1, j2 be natural numbers. Suppose 〈i1, j1〉 ∈ the indices of G and 〈i2, j2〉 ∈ the indices of G. If (G◦ (i1, j1))2 = (G◦ (i2, j2))2, then j1 = j2. (7) Let G be a line X-constant column X-increasing matrix over E2 T and i1, i2, j1, j2 be natural numbers. Suppose 〈i1, j1〉 ∈ the indices of G and 〈i2, j2〉 ∈ the indices o...

We extend the standard theory of cosmological perturbations to homogeneous but anisotropic universes. We present an exhaustive computation for the case of a Bianchi I model, with a residual isotropy between two spatial dimensions, which is undergoing complete isotropization at the onset of inflation; we also show how the computation can be further extended to more general backgrounds. In presen...

We prove the existence of quasi-periodic, small amplitude, solutions for quasi-linear and fully nonlinear forced perturbations of KdV equations. For Hamiltonian or reversible nonlinearities we also obtain the linear stability of the solutions. The proofs are based on a combination of different ideas and techniques: (i) a Nash-Moser iterative scheme in Sobolev scales. (ii) A regularization proce...

This paper presents several new open-loop guidance methods for spacecraft swarms composed of hundreds to thousands of agents with each spacecraft having modest capabilities. These methods have three main goals: preventing relative drift of the swarm, preventing collisions within the swarm, and minimizing the propellant used throughout the mission. The development of these methods progresses by ...

Fluid flows that are smooth at low speeds become unstable and then turbulent at higher speeds. This phenomenon has traditionally been investigated by linearizing the equations of flow and testing for unstable eigenvalues of the linearized problem, but the results of such investigations agree poorly in many cases with experiments. Nevertheless, linear effects play a central role in hydrodynamic ...

The articles [8], [11], [10], [5], [1], [7], [12], [4], [3], [2], [9], and [6] provide the notation and terminology for this paper. In this paper i, j, k, k1, k2, n, m, i1, i2, j1, j2 are natural numbers. Let us consider i1, i2. We say that i1 and i2 are adjacent if and only if: (Def. 1) i2 = i1 + 1 or i1 = i2 + 1. One can prove the following propositions: (1) For all i1, i2 such that i1 and i2...