1,795 research outputs found
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
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