13,567 research outputs found
Measuring the Weibull modulus of microscope slides
The objectives are that students will understand why a three-point bending test is used for ceramic specimens, learn how Weibull statistics are used to measure the strength of brittle materials, and appreciate the amount of variation in the strength of brittle materials with low Weibull modulus. They will understand how the modulus of rupture is used to represent the strength of specimens in a three-point bend test. In addition, students will learn that a logarithmic transformation can be used to convert an exponent into the slope of a straight line. The experimental procedures are explained
A DEIM Induced CUR Factorization
We derive a CUR matrix factorization based on the Discrete Empirical
Interpolation Method (DEIM). For a given matrix , such a factorization
provides a low rank approximate decomposition of the form ,
where and are subsets of the columns and rows of , and is
constructed to make a good approximation. Given a low-rank singular value
decomposition , the DEIM procedure uses and to
select the columns and rows of that form and . Through an error
analysis applicable to a general class of CUR factorizations, we show that the
accuracy tracks the optimal approximation error within a factor that depends on
the conditioning of submatrices of and . For large-scale problems,
and can be approximated using an incremental QR algorithm that makes one
pass through . Numerical examples illustrate the favorable performance of
the DEIM-CUR method, compared to CUR approximations based on leverage scores
Photon scattering by a three-level emitter in a one-dimensional waveguide
We discuss the scattering of photons from a three-level emitter in a
one-dimensional waveguide, where the transport is governed by the interference
of spontaneously emitted and directly transmitted waves. The scattering problem
is solved in closed form for different level structures. Several possible
applications are discussed: The state of the emitter can be switched
deterministically by Raman scattering, thus enabling applications in quantum
computing such as a single photon transistor. An array of emitters gives rise
to a photonic band gap structure, which can be tuned by a classical driving
laser. A disordered array leads to Anderson localization of photons, where the
localization length can again be controlled by an external driving.Comment: 17 pages, 8 figure
Quantum emitters coupled to surface plasmons of a nano-wire: A Green function approach
We investigate a system consisting of a single, as well as two emitters
strongly coupled to surface plasmon modes of a nano-wire using a Green function
approach. Explicit expressions are derived for the spontaneous decay rate into
the plasmon modes and for the atom-plasmon coupling as well as a
plasmon-mediated atom-atom coupling. Phenomena due to the presence of losses in
the metal are discussed. In case of two atoms, we observe Dicke sub- and
superradiance resulting from their plasmon-mediated interaction. Based on this
phenomenon, we propose a scheme for a deterministic two-qubit quantum gate. We
also discuss a possible realization of interesting many-body Hamiltonians, such
as the spin-boson model, using strong emitter-plasmon coupling.Comment: 12 pages, 16 figure
Mixed mode stress intensity factors for semielliptical surface cracks
The three-dimensional equations of elasticity are solved for a flat elliptical crack which has nonuniform shear stresses applied to its surfaces. An alternating method is used to determine the mode two and mode three stress intensity factors for a semielliptical surface crack in the surface of a finite thickness solid. These stress intensity factors are presented as a function of position along the crack border for a number of crack shapes and crack depths. This same technique is followed to determine the mode one stress intensity factors for the semielliptical surface crack which has normal loading applied to its surface. Mode one stress intensity factors are presented and compared with the results obtained from previous work
Fractional quantum Hall states of atoms in optical Lattices
We describe a method to create fractional quantum Hall states of atoms
confined in optical lattices. We show that the dynamics of the atoms in the
lattice is analogous to the motion of a charged particle in a magnetic field if
an oscillating quadrupole potential is applied together with a periodic
modulation of the tunneling between lattice sites. We demonstrate that in a
suitable parameter regime the ground state in the lattice is of the fractional
quantum Hall type and we show how these states can be reached by melting a Mott
insulator state in a super lattice potential. Finally we discuss techniques to
observe these strongly correlated states.Comment: 4+epsilon pages including 3 figures. V2: Changes in the presentatio
Correlated Gaussian method for dilute bosonic systems
The weakly interacting trapped Bose gases have been customarily described
using the mean-field approximation in the form of the Gross-Pitaevskii
equation. The mean-field approximation, however, has certain limitations, in
particular it can not describe correlations between particles. We introduce
here an alternative variational approach, based on the correlated Gaussian
method, which in its simplest form is as fast and simple as the mean-field
approximation, but which allows successive improvements of the trial
wave-function by including correlations between particles.Comment: 9 pages, Workshop on Nuclei and Mesoscopic Physics, NSCL MSU, 200
Strong coupling of single emitters to surface plasmons
We propose a method that enables strong, coherent coupling between individual
optical emitters and electromagnetic excitations in conducting nano-structures.
The excitations are optical plasmons that can be localized to sub-wavelength
dimensions. Under realistic conditions, the tight confinement causes optical
emission to be almost entirely directed into the propagating plasmon modes via
a mechanism analogous to cavity quantum electrodynamics. We first illustrate
this result for the case of a nanowire, before considering the optimized
geometry of a nanotip. We describe an application of this technique involving
efficient single-photon generation on demand, in which the plasmons are
efficiently out-coupled to a dielectric waveguide. Finally we analyze the
effects of increased scattering due to surface roughness on these
nano-structures.Comment: 34 pages, 7 figure
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