104,624 research outputs found
ENO-wavelet transforms for piecewise smooth functions
We have designed an adaptive essentially nonoscillatory (ENO)-wavelet transform for approximating discontinuous functions without oscillations near the discontinuities. Our approach is to apply the main idea from ENO schemes for numerical shock capturing to standard wavelet transforms. The crucial point is that the wavelet coefficients are computed without differencing function values across jumps. However, we accomplish this in a different way than in the standard ENO schemes. Whereas in the standard ENO schemes the stencils are adaptively chosen, in the ENO-wavelet transforms we adaptively change the function and use the same uniform stencils. The ENO-wavelet transform retains the essential properties and advantages of standard wavelet transforms such as concentrating the energy to the low frequencies, obtaining maximum accuracy, maintained up to the discontinuities, and having a multiresolution framework and fast algorithms, all without any edge artifacts. We have obtained a rigorous approximation error bound which shows that the error in the ENO-wavelet approximation depends only on the size of the derivative of the function away from the discontinuities. We will show some numerical examples to illustrate this error estimate
Ultrafast and octave-spanning optical nonlinearities from strongly phase-mismatched cascaded interactions
Cascaded nonlinearities have attracted much interest, but ultrafast
applications have been seriously hampered by the simultaneous requirements of
being near phase-matching and having ultrafast femtosecond response times. Here
we show that in strongly phase-mismatched nonlinear frequency conversion
crystals the pump pulse can experience a large and extremely broadband
self-defocusing cascaded Kerr-like nonlinearity. The large cascaded
nonlinearity is ensured through interaction with the largest quadratic tensor
element in the crystal, and the strong phase-mismatch ensures an ultrafast
nonlinear response with an octave-spanning bandwidth. We verify this
experimentally by showing few-cycle soliton compression with noncritical
cascaded second-harmonic generation: Energetic 47 fs infrared pulses are
compressed in a just 1-mm long bulk lithium niobate crystal to 17 fs (under 4
optical cycles) with 80% efficiency, and upon further propagation an
octave-spanning supercontinuum is observed. Such ultrafast cascading is
expected to occur for a broad range of pump wavelengths spanning the near- and
mid-IR using standard nonlinear crystals.Comment: resubmitted, revised version, accepted for Phys. Rev. Let
SPSA-Based Tracking Method for Single-Channel-Receiver Array
A novel tracking method in the phased antenna array with a single-channel receiver for the moving signal source is presented in this paper. And the problems of the direction-of-arrival track and beamforming in the array system are converted to the power maximization of received signal in the free-interference conditions, which is different from the existing algorithms that maximize the signal to interference and noise ratio. The proposed tracking method reaches the global optimum rather than local by injecting the extra noise terms into the gradient estimation. The antenna beam can be steered to coincide with the direction of the moving source fast and accurately by perturbing the output of the phase shifters during motion, due to the high efficiency and easy implementation of the proposed beamforming algorithm based on the simultaneous perturbation stochastic approximation (SPSA). Computer simulations verify that the proposed tracking scheme is robust and effective
Instrumentation of the variable-angle magneto-optic ellipsometer and its application to M-O media and other non-magnetic films
A new and comprehensive dielectric tensor characterization instrument is presented for characterization of magneto-optical recording media and non-magnetic thin films. Random and systematic errors of the system are studied. A series of TbFe, TbFeCo, and Co/Pt samples with different composition and thicknesses are characterized for their optical and magneto-optical properties. The optical properties of several non-magnetic films are also measured
Ground-state configuration space heterogeneity of random finite-connectivity spin glasses and random constraint satisfaction problems
We demonstrate through two case studies, one on the p-spin interaction model
and the other on the random K-satisfiability problem, that a heterogeneity
transition occurs to the ground-state configuration space of a random
finite-connectivity spin glass system at certain critical value of the
constraint density. At the transition point, exponentially many configuration
communities emerge from the ground-state configuration space, making the
entropy density s(q) of configuration-pairs a non-concave function of
configuration-pair overlap q. Each configuration community is a collection of
relatively similar configurations and it forms a stable thermodynamic phase in
the presence of a suitable external field. We calculate s(q) by the
replica-symmetric and the first-step replica-symmetry-broken cavity methods,
and show by simulations that the configuration space heterogeneity leads to
dynamical heterogeneity of particle diffusion processes because of the entropic
trapping effect of configuration communities. This work clarifies the fine
structure of the ground-state configuration space of random spin glass models,
it also sheds light on the glassy behavior of hard-sphere colloidal systems at
relatively high particle volume fraction.Comment: 26 pages, 9 figures, submitted to Journal of Statistical Mechanic
Obtaining correct orbital ground states in electron systems using a nonspherical self-interaction corrected LDA+ method
The electronic structure of lanthanide and actinide compounds is often
characterized by orbital ordering of localized -electrons.
Density-functional theory (DFT) studies of such systems using the currently
available LDA+ method are plagued by significant orbital-dependent
self-interaction, leading to erroneous orbital ground states. An alternative
scheme that modifies the exchange, not Hartree, energy is proposed as a remedy.
We show that our LDA+ approach reproduces the expected degeneracy of
and states in free ions and the correct ground states in solid PrO.
We expect our method to be useful in studying compounds of - and heavy-
elements.Comment: 11 pages, 4 figure
Nuclear spin qubits in a trapped-ion quantum computer
Physical systems must fulfill a number of conditions to qualify as useful
quantum bits (qubits) for quantum information processing, including ease of
manipulation, long decoherence times, and high fidelity readout operations.
Since these conditions are hard to satisfy with a single system, it may be
necessary to combine different degrees of freedom. Here we discuss a possible
system, based on electronic and nuclear spin degrees of freedom in trapped
ions. The nuclear spin yields long decoherence times, while the electronic
spin, in a magnetic field gradient, provides efficient manipulation, and the
optical transitions of the ions assure a selective and efficient initialization
and readout.Comment: 7 page
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