12,051 research outputs found
Rotating gravity currents: small-scale and large-scale laboratory experiments and a geostrophic model
Laboratory experiments simulating gravity-driven coastal surface currents produced by estuarine fresh-water discharges into the ocean are discussed. The currents are generated inside a rotating tank filled with salt water by the continuous release of buoyant fresh water from a small source at the fluid surface. The height, the width and the length of the currents are studied as a function of the background rotation rate, the volumetric discharge rate and the density difference at the source. Two complementary experimental data sets are discussed and compared with each other. One set of experiments was carried out in a tank of diameter 1 m on a small-scale rotating turntable. The second set of experiments was conducted at the large-scale Coriolis Facility (LEGI, Grenoble) which has a tank of diameter 13 m. A simple geostrophic model predicting the current height, width and propagation velocity is developed. The experiments and the model are compared with each other in terms of a set of non-dimensional parameters identified in the theoretical analysis of the problem. These parameters enable the corresponding data of the large-scale and the small-scale experiments to be collapsed onto a single line. Good agreement between the model and the experiments is found
Deeply subrecoil two-dimensional Raman cooling
We report the implementation of a two-dimensional Raman cooling scheme using
sequential excitations along the orthogonal axes. Using square pulses, we have
cooled a cloud of ultracold Cesium atoms down to an RMS velocity spread of
0.39(5) recoil velocity, corresponding to an effective temperature of 30 nK
(0.15 T_rec). This technique can be useful to improve cold atom atomic clocks,
and is particularly relevant for clocks in microgravity.Comment: 8 pages, 6 figures, submitted to Phys. Rev.
Some Heuristic Semiclassical Derivations of the Planck Length, the Hawking Effect and the Unruh Effect
The formulae for Planck length, Hawking temperature and Unruh-Davies
temperature are derived by using only laws of classical physics together with
the Heisenberg principle. Besides, it is shown how the Hawking relation can be
deduced from the Unruh relation by means of the principle of equivalence; the
deep link between Hawking effect and Unruh effect is in this way clarified.Comment: LaTex file, 6 pages, no figure
Quantum Algorithms for Matrix Products over Semirings
In this paper we construct quantum algorithms for matrix products over
several algebraic structures called semirings, including the (max,min)-matrix
product, the distance matrix product and the Boolean matrix product. In
particular, we obtain the following results.
We construct a quantum algorithm computing the product of two n x n matrices
over the (max,min) semiring with time complexity O(n^{2.473}). In comparison,
the best known classical algorithm for the same problem, by Duan and Pettie,
has complexity O(n^{2.687}). As an application, we obtain a O(n^{2.473})-time
quantum algorithm for computing the all-pairs bottleneck paths of a graph with
n vertices, while classically the best upper bound for this task is
O(n^{2.687}), again by Duan and Pettie.
We construct a quantum algorithm computing the L most significant bits of
each entry of the distance product of two n x n matrices in time O(2^{0.64L}
n^{2.46}). In comparison, prior to the present work, the best known classical
algorithm for the same problem, by Vassilevska and Williams and Yuster, had
complexity O(2^{L}n^{2.69}). Our techniques lead to further improvements for
classical algorithms as well, reducing the classical complexity to
O(2^{0.96L}n^{2.69}), which gives a sublinear dependency on 2^L.
The above two algorithms are the first quantum algorithms that perform better
than the -time straightforward quantum algorithm based on
quantum search for matrix multiplication over these semirings. We also consider
the Boolean semiring, and construct a quantum algorithm computing the product
of two n x n Boolean matrices that outperforms the best known classical
algorithms for sparse matrices. For instance, if the input matrices have
O(n^{1.686...}) non-zero entries, then our algorithm has time complexity
O(n^{2.277}), while the best classical algorithm has complexity O(n^{2.373}).Comment: 19 page
Derivation of the Blackbody Radiation Spectrum from a Natural Maximum-Entropy Principle Involving Casimir Energies and Zero-Point Radiation
By numerical calculation, the Planck spectrum with zero-point radiation is
shown to satisfy a natural maximum-entropy principle whereas alternative
choices of spectra do not. Specifically, if we consider a set of
conducting-walled boxes, each with a partition placed at a different location
in the box, so that across the collection of boxes the partitions are uniformly
spaced across the volume, then the Planck spectrum correspond to that spectrum
of random radiation (having constant energy kT per normal mode at low
frequencies and zero-point energy (1/2)hw per normal mode at high frequencies)
which gives maximum uniformity across the collection of boxes for the radiation
energy per box. The analysis involves Casimir energies and zero-point radiation
which do not usually appear in thermodynamic analyses. For simplicity, the
analysis is presented for waves in one space dimension.Comment: 11 page
Optical properties of potential-inserted quantum wells in the near infrared and Terahertz ranges
We propose an engineering of the optical properties of GaAs/AlGaAs quantum
wells using AlAs and InAs monolayer insertions. A quantitative study of the
effects of the monolayer position and the well thickness on the interband and
intersubband transitions, based on the extended-basis sp3d5s* tight-binding
model, is presented. The effect of insertion on the interband transitions is
compared with existing experimental data. As for intersubband transitions, we
show that in a GaAs/AlGaAs quantum well including two AlAs and one InAs
insertions, a three level {e1 , e2 , e3 } system where the transition energy
e3-e2 is lower and the transition energy e2-e1 larger than the longitudinal
optical phonon energy (36 meV) can be engineered together with a e3-e2
transition energy widely tunable through the TeraHertz range
Hydrodynamic reductions of the heavenly equation
We demonstrate that Pleba\'nski's first heavenly equation decouples in
infinitely many ways into a triple of commuting (1+1)-dimensional systems of
hydrodynamic type which satisfy the Egorov property. Solving these systems by
the generalized hodograph method, one can construct exact solutions of the
heavenly equation parametrized by arbitrary functions of a single variable. We
discuss explicit examples of hydrodynamic reductions associated with the
equations of one-dimensional nonlinear elasticity, linearly degenerate systems
and the equations of associativity.Comment: 14 page
Generating anisotropic fluids from vacuum Ernst equations
Starting with any stationary axisymmetric vacuum metric, we build anisotropic
fluids. With the help of the Ernst method, the basic equations are derived
together with the expression for the energy-momentum tensor and with the
equation of state compatible with the field equations. The method is presented
by using different coordinate systems: the cylindrical coordinates
and the oblate spheroidal ones. A class of interior solutions matching with
stationary axisymmetric asymptotically flat vacuum solutions is found in oblate
spheroidal coordinates. The solutions presented satisfy the three energy
conditions.Comment: Version published on IJMPD, title changed by the revie
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