We study collisions between two strongly interacting atomic Fermi gas clouds. We observe exotic nonlinear hydrodynamic behavior, distinguished by the formation of a very sharp and stable density peak as the clouds collide and subsequent evolution into a boxlike shape. We model the nonlinear dynamics of these collisions by using quasi-1D hydrodynamic equations. Our simulations of the time-depend...

This report is a documentation of analytical techniques for characterizing the degree of nonlinearity implicit to active networks designed to achieve nominally linear performance input -tooutput performance characteristics. It addresses such metrics as total harmonic distortion, intermodulation levels, intercept points, and spurious free dynamic range. Aside from addressing the theoretic nature...

In this paper, a state observer is proposed for the reconstruction of the concentration profiles in a simulated moving bed. The approach is based on a simple Luenberger-like correction term. Validating simulations are proposed to assess the efficiency of the proposed profile reconstruction and its robustness against uncertainties on modelling parameters. Comparisons are also done with open-loop...

Plasma-wakefield excitation by positron beams is examined in a regime for which the plasma dynamics are highly nonlinear. Three dimensional particle-in-cell simulations and physical models are presented. In the nonlinear wake regime known as the blowout regime for electrons, positron wakes exhibit an analogous "suck-in" behavior. Although analogous, the two wakefield cases are quite different i...

We rigorously derive nonlinear instability of Hele-Shaw flows moving with a constant velocity in the presence of smooth viscosity profiles where the viscosity upstream is lower than the viscosity downstream. This is a single-layer problem without any material interface. The instability of the basic flow is driven by a viscosity gradient as opposed to conventional interfacial Saffman–Taylor inst...

This work establishes nonlinear orbital asymptotic stability of scalar radiative shock profiles, namely, traveling wave solutions to the simplified model system of radiating gas [8], consisting of a scalar conservation law coupled with an elliptic equation for the radiation flux. The method is based on the derivation of pointwise Green function bounds and description of the linearized solution ...

A self-regulating method for the control of spontaneous instabilities of the transversal beam profile in nonlinear optical systems is experimentally realized. The control method is the high-dimensional analogue of classical negative feedback regulators. An all-optical implementation with its capabilities of parallel processing is essential for the experimental feasibility. Unstable system-inher...

Many modern industrial processes are capable of generating rich and complex data records that do not readily permit the use of traditional statistical process control techniques. For example, a “single observation” from a process might consist of n pairs of (x, y) data that can be described as y = f(x) when the process is in-control. Such data structures or relationships between y and x have be...

In many quality control applications, use of a single (or several distinct) quality characteristic(s) is insufficient to characterize the quality of a produced item. In an increasing number of cases, a response curve (profile), is required. Such profiles can frequently be modeled using linear or nonlinear regression models. In recent research others have developed multivariate T 2 control chart...