Breakdown of self-similarity at the crests of large amplitude standing water waves

We study the limiting behavior of large-amplitude standing waves on deep water using high-resolution numerical simulations in double and quadruple precision. While periodic traveling waves approach Stokes's sharply crested extreme wave in an asymptotically self-similar manner, we find that standing waves behave differently. Instead of sharpening to a corner or cusp as previously conjectured, the crest tip develops a variety of oscillatory structures. This causes the bifurcation curve that parametrizes these waves to fragment into disjoint branches corresponding to the different oscillation patterns that occur. In many cases, a vertical jet of fluid pushes these structures upward, leading to wave profiles commonly seen in wave tank experiments. Thus, we observe a rich array of dynamic behavior at small length scales in a regime previously thought to be self-similar.Comment: 4 pages, 5 figures. Final version accepted for publicatio

Absolute Dynamical Limit to Cooling Weakly-Coupled Quantum Systems

Cooling of a quantum system is limited by the size of the control forces that are available (the "speed" of control). We consider the most general cooling process, albeit restricted to the regime in which the thermodynamics of the system is preserved (weak coupling). Within this regime, we further focus on the most useful control regime, in which a large cooling factor, and good ground-state cooling can be achieved. We present a control protocol for cooling, and give clear structural arguments, as well as strong numerical evidence, that this protocol is globally optimal. From this we obtain simple expressions for the limit to cooling that is imposed by the speed of control.Comment: 4 pages, Revetex4-1, 2 png figure

Ultra-Efficient Cooling of Resonators: Beating Sideband Cooling with Quantum Control

The present state-of-the-art in cooling mechanical resonators is a version of "sideband" cooling. Here we present a method that uses the same configuration as sideband cooling --- coupling the resonator to be cooled to a second microwave (or optical) auxiliary resonator --- but will cool significantly colder. This is achieved by varying the strength of the coupling between the two resonators over a time on the order of the period of the mechanical resonator. As part of our analysis, we also obtain a method for fast, high-fidelity quantum information-transfer between resonators.Comment: 4 pages, revtex4-1, 2 png figure

An Energy Based Discontinuous Galerkin Method for Coupled Elasto-Acoustic Wave Equations in Second Order Form

We consider wave propagation in a coupled fluid-solid region, separated by a static but possibly curved interface. The wave propagation is modeled by the acoustic wave equation in terms of a velocity potential in the fluid, and the elastic wave equation for the displacement in the solid. At the fluid solid interface, we impose suitable interface conditions to couple the two equations. We use a recently developed, energy based discontinuous Galerkin method to discretize the governing equations in space. Both energy conserving and upwind numerical fluxes are derived to impose the interface conditions. The highlights of the developed scheme include provable energy stability and high order accuracy. We present numerical experiments to illustrate the accuracy property and robustness of the developed scheme

Probing magnetic fields with multi-frequency polarized synchrotron emission

We investigate the problem of probing the local spatial structure of the magnetic field of the interstellar medium using multi-frequency polarized maps of the synchrotron emission at radio wavelengths. We focus in this paper on the three-dimensional reconstruction of the largest scales of the magnetic field, relying on the internal depolarization (due to differential Faraday rotation) of the emitting medium as a function of electromagnetic frequency. We argue that multi-band spectroscopy in the radio wavelengths, developed in the context of high-redshift extragalactic HI lines, can be a very useful probe of the 3D magnetic field structure of our Galaxy when combined with a Maximum A Posteriori reconstruction technique. When starting from a fair approximation of the magnetic field, we are able to recover the true one by using a linearized version of the corresponding inverse problem. The spectral analysis of this problem allows us to specify the best sampling strategy in electromagnetic frequency and predicts a spatially anisotropic distribution of posterior errors. The reconstruction method is illustrated for reference fields extracted from realistic magneto-hydrodynamical simulations

Optimal Filling of Shapes

We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In n-dimensional space, if the objects are polydisperse n-balls, we show that solutions correspond to sets of maximal n-balls. For polygons, we provide a heuristic for finding solutions of maximal discs. We consider the properties of ideal distributions of N discs as N approaches infinity. We note an analogy with energy landscapes.Comment: 5 page

B-spline neural networks based PID controller for Hammerstein systems

A new PID tuning and controller approach is introduced for Hammerstein systems based on input/output data. A B-spline neural network is used to model the nonlinear static function in the Hammerstein system. The control signal is composed of a PID controller together with a correction term. In order to update the control signal, the multi-step ahead predictions of the Hammerstein system based on the B-spline neural networks and the associated Jacobians matrix are calculated using the De Boor algorithms including both the functional and derivative recursions. A numerical example is utilized to demonstrate the efficacy of the proposed approaches

Minimax optimization of entanglement witness operator for the quantification of three-qubit mixed-state entanglement

We develop a numerical approach for quantifying entanglement in mixed quantum states by convex-roof entanglement measures, based on the optimal entanglement witness operator and the minimax optimization method. Our approach is applicable to general entanglement measures and states and is an efficient alternative to the conventional approach based on the optimal pure-state decomposition. Compared with the conventional one, it has two important merits: (i) that the global optimality of the solution is quantitatively verifiable, and (ii) that the optimization is considerably simplified by exploiting the common symmetry of the target state and measure. To demonstrate the merits, we quantify Greenberger-Horne-Zeilinger (GHZ) entanglement in a class of three-qubit full-rank mixed states composed of the GHZ state, the W state, and the white noise, the simplest mixtures of states with different genuine multipartite entanglement, which have not been quantified before this work. We discuss some general properties of the form of the optimal witness operator and of the convex structure of mixed states, which are related to the symmetry and the rank of states

Optimal control of circuit quantum electrodynamics in one and two dimensions

Optimal control can be used to significantly improve multi-qubit gates in quantum information processing hardware architectures based on superconducting circuit quantum electrodynamics. We apply this approach not only to dispersive gates of two qubits inside a cavity, but, more generally, to architectures based on two-dimensional arrays of cavities and qubits. For high-fidelity gate operations, simultaneous evolutions of controls and couplings in the two coupling dimensions of cavity grids are shown to be significantly faster than conventional sequential implementations. Even under experimentally realistic conditions speedups by a factor of three can be gained. The methods immediately scale to large grids and indirect gates between arbitrary pairs of qubits on the grid. They are anticipated to be paradigmatic for 2D arrays and lattices of controllable qubits.Comment: Published version