The problem of compensation of infinite-dimensional actuator or sensor dynamics of more complex type than pure delay was solved recently using the backstepping method for PDEs. In this paper we construct an explicit feedback law for a multi-input LTI system which compensates the wave PDE dynamics in its input and stabilizes the overall system. Our design is based on a novel infinite-dimensional...

The coherent interaction with ultrashort light pulses is a powerful strategy for monitoring and controlling the dynamics of wave packets in all states of matter. As light presents an oscillation period of a few femtoseconds (T=2.6 fs in the near infrared spectral range), an external optical field can induce changes in a medium on the sub-cycle timescale, i.e. in a few hundred attoseconds. In ...

We survey some recent results related to three long wave asymptotic regimes for the Nonlinear-Schrödinger Equation: the Euler regime corresponding to the WKB method, the linear wave regime and finally the KdV/KP-I asymptotic dynamics.

Wave formation and propagation due to submarine landslides are complex phenomena that may be divided into four parts: Landslide dynamics, energy transfer from landslide motion to water motion, wave propagation in open water, and wave run-up along the shores. This paper focuses on the energy transfer from landslide motion to water motion, i.e. the generation of tsunamis by submarine landslides.

We are investigating possible functional roles for spiral wave activity in visual cortex. Our initial findings suggest that spiral wave formation could contribute to visual salience analysis, in particular for mediating attention to human body features. Exploiting travelling wave dynamics for visual processing offers many advantages, including template-free sensitivity to spatial patterns, robu...

The nonlinear Schrödinger (NLS) equation describing the propagation of weakly rotational wave packets in an infinitely deep fluid in Lagrangian coordinates has been derived. The vorticity is assumed to be an arbitrary function of Lagrangian coordinates and quadratic in the small parameter proportional to the wave steepness. The vorticity effects manifest themselves in a shift of the wave number...

Asymmetric intracellular signals enable cells to migrate in response to external cues. The multiprotein WAVE (also known as SCAR or WASF) complex activates the actin-nucleating Arp2/3 complex [1-4] and localizes to propagating "waves," which direct actin assembly during neutrophil migration [5, 6]. Here, we observe similar WAVE complex dynamics in other mammalian cells and analyze WAVE complex ...

We investigate the dynamics of weakly-modulated nonlinear wave trains. For reaction-diffusion systems and for the complex Ginzburg–Landau equation, we establish rigorously that slowly varying modulations of wave trains are well approximated by solutions to the Burgers equation over the natural time scale. In addition to the validity of the Burgers equation, we show that the viscous shock profil...

An approach to the quantum-classical mechanics of phase space dependent operators, which has been proposed recently, is remodeled as a formalism for wave fields. Such wave fields obey a system of coupled nonlinear equations that can be written by means of a suitable non-Hamiltonian bracket. As an example, the theory is applied to the relaxation dynamics of the spin-boson model. In the adiabatic...

An optimized and numerically stable method, based on the formalism of orthogonal polynomials, is proposed to solve the time-dependent Schrödinger equation and to construct energy-filtered wave-packets. It is compared to other methods (Runge-Kutta, Second-Order Differencing scheme). A method is also devised to study quantum diffusion in finite systems with periodic boundary conditions, which all...