A method to actively localize a small perturbation in a multiple scattering medium using a collection of remote acoustic sensors is presented. The approach requires only minimal modeling and no knowledge of the scatterer distribution and properties of the scattering medium and the perturbation. The medium is ensonified before and after a perturbation is introduced. The coherent difference betwe...

We prove two stability results for the scale invariant solutions of the nonlinear heat equation @ t u = u?juj p?1 u with 1 < p < 1+ 2 n , n being the spatial dimension. The rst result is that a small perturbation of a scale invariant solution vanishes as t ! 1. The second result is global, with a positivity condition on the initial data.

A theoretical study analyzing three-dimensional combustion acoustic instabilities in a liquid propellant rocket engine combustor has been conducted. A linear theory based on Crocco’s pressure sensitive time lag model is used. To apply this theory the combustor is divided into two main components, including the combustion chamber and the converging part of the nozzle. The assumption of concentra...

In this paper, the homotopy perturbation method (HPM) is considered for finding approximate solutions of two-dimensional viscous flow. This technique provides a sequence of functions which converges to the exact solution of the problem. The HPM does not need a small parameters in the equations, but; the perturbation method depends on small parameter assumption and the obtained results. In most ...

We consider weakly asymmetric exclusion processes whose initial density profile is a small perturbation of constant. show that in the diffusive time-scale, all dimensions, defect evolves as solution viscous Burgers equation.

We prove two stability results for the scale invariant solutions of the nonlinear heat equation ∂ t u = ∆u−|u| p−1 u with 1 < p < 1+ 2 n , n being the spatial dimension. The first result is that a small perturbation of a scale invariant solution vanishes as t → ∞. The second result is global, with a positivity condition on the initial data.

We calculate the time evolution of a far-from-equilibrium initial state of a non-relativistic ultracold Bose gas in one spatial dimension. The non-perturbative approximation scheme is based on a systematic expansion of the two-particle irreducible effective action in powers of the inverse number of field components. This yields dynamic equations which contain direct scattering, memory and off-s...

The robust control and active vibration control for free-floating space flexible manipulator with parameter uncertainties are studied. The dynamic equations of the system are developed by using the Lagrangian assumed modes methods, it is verified that the dynamic equation can be linearly dependent on a group of inertial parameters. Based on the results and under the assumption of two-time scale...

For the Broadwell model of the nonlinear Boltzmann equation, there are shock profile solutions, i.e. smooth traveling waves that connect two equilibrium states. For weak shock waves, we prove asymptotic (in time) stability with respect to small perturbations of the initial data. Following the work of Liu [7] on shock wave stability for viscous conservation laws, the method consists of analyzing...

We derive, from first principle, the Fokker-Planck equation describing the non-perturbative real-time evolution of a gauge field at high temperatures on the spatial scale (g 2 T) −1 and the time scale (g 4 T) −1 , where g is the gauge coupling and T is the temperature. The knowledge of the effective dynamics on such spatial and time scales is crucial for the understanding and quantitative calcu...