23,427 research outputs found
Orientation of particle attachment and local isotropy in diffusion limited aggregation (DLA)
We simulate 50 off-lattice DLA clusters, one million particles each. The
probability distribution of the angle of attachment of arriving particles with
respect to the local radial direction is obtained numerically. For increasing
cluster size, , the distribution crosses over extremely accurately to a
cosine, whose amplitude decreases towards zero as a power-law in . From this
viewpoint, asymptotically large DLA clusters are locally . This
contradicts previous conclusions drawn from density-density correlation
measurements [P. Meakin, and T. Viscek, Phys. Rev. A {\bf 32}, 685 (1985)]. We
present an intuitive phenomenological model random process for our numerical
findings.Comment: 10 pages, RevTex 3.0, 11-9
Recovery of continuous wave squeezing at low frequencies
We propose and demonstrate a system that produces squeezed vacuum using a
pair of optical parametric amplifiers. This scheme allows the production of
phase sidebands on the squeezed vacuum which facilitate phase locking in
downstream applications. We observe strong, stably locked, continuous wave
vacuum squeezing at frequencies as low as 220 kHz. We propose an alternative
resonator configuration to overcome low frequency squeezing degradation caused
by the optical parametric amplifiers.Comment: 9 pages, 4 figure
The diffuse Nitsche method: Dirichlet constraints on phase-field boundaries
We explore diffuse formulations of Nitsche's method for consistently imposing Dirichlet boundary conditions on phase-field approximations of sharp domains. Leveraging the properties of the phase-field gradient, we derive the variational formulation of the diffuse Nitsche method by transferring all integrals associated with the Dirichlet boundary from a geometrically sharp surface format in the standard Nitsche method to a geometrically diffuse volumetric format. We also derive conditions for the stability of the discrete system and formulate a diffuse local eigenvalue problem, from which the stabilization parameter can be estimated automatically in each element. We advertise metastable phase-field solutions of the Allen-Cahn problem for transferring complex imaging data into diffuse geometric models. In particular, we discuss the use of mixed meshes, that is, an adaptively refined mesh for the phase-field in the diffuse boundary region and a uniform mesh for the representation of the physics-based solution fields. We illustrate accuracy and convergence properties of the diffuse Nitsche method and demonstrate its advantages over diffuse penalty-type methods. In the context of imaging based analysis, we show that the diffuse Nitsche method achieves the same accuracy as the standard Nitsche method with sharp surfaces, if the inherent length scales, i.e., the interface width of the phase-field, the voxel spacing and the mesh size, are properly related. We demonstrate the flexibility of the new method by analyzing stresses in a human vertebral body
Surgical treatment of a paraspinal abscess with osteomyelitis and spinal cord compression in a rabbit
Schubert Polynomials for the affine Grassmannian of the symplectic group
We study the Schubert calculus of the affine Grassmannian Gr of the
symplectic group. The integral homology and cohomology rings of Gr are
identified with dual Hopf algebras of symmetric functions, defined in terms of
Schur's P and Q-functions. An explicit combinatorial description is obtained
for the Schubert basis of the cohomology of Gr, and this is extended to a
definition of the affine type C Stanley symmetric functions. A homology Pieri
rule is also given for the product of a special Schubert class with an
arbitrary one.Comment: 45 page
Poles of regular quaternionic functions
This paper studies the singularities of Cullen-regular functions of one
quaternionic variable. The quaternionic Laurent series prove to be
Cullen-regular. The singularities of Cullen-regular functions are thus
classified as removable, essential or poles. The quaternionic analogues of
meromorphic complex functions, called semiregular functions, turn out to be
quotients of Cullen-regular functions with respect to an appropriate division
operation. This allows a detailed study of the poles and their distribution.Comment: 14 page
Magneto-Seebeck effect in spin-valve with in-plane thermal gradient
We present measurements of magneto-Seebeck effect on a spin valve with
in-plane thermal gradient. We measured open circuit voltage and short circuit
current by applying a temperature gradient across a spin valve stack, where one
of the ferromagnetic layers is pinned. We found a clear hysteresis in these two
quantities as a function of magnetic field. From these measurements, the
magneto-Seebeck effect was found to be 0.82%.Comment: 10 Pages, 7 figure
Microlensing of gamma ray bursts by stars and MACHOs
The microlensing interpretation of the optical afterglow of GRB 000301C seems
naively surprising, since a simple estimate of the stellar microlensing rate
gives less than one in four hundred for a flat Omega_Lambda=0.7 cosmology,
whereas one event was seen in about thirty afterglows. Considering baryonic
MACHOs making up half of the baryons in the universe, the microlensing
probability per burst can be roughly 5% for a GRB at redshift z=2. We explore
two effects that may enhance the probability of observing microlensed gamma-ray
burst afterglows: binary lenses and double magnification bias. We find that the
consideration of binary lenses can increase the rate only at the ~15% level. On
the other hand, because gamma-ray bursts for which afterglow observations exist
are typically selected based on fluxes at widely separated wavebands which are
not necessarily well correlated (e.g. localization in X-ray, afterglow in
optical/infrared), magnification bias can operate at an enhanced level compared
to the usual single-bias case. We find that existing estimates of the slope of
the luminosity function of gamma-ray bursts, while as yet quite uncertain,
point to enhancement factors of more than three above the simple estimates of
the microlensing rate. We find that the probability to observe at least one
microlensing event in the sample of 27 measured afterglows can be 3-4% for
stellar lenses, or as much as 25 Omega_lens for baryonic MACHOs. We note that
the probability to observe at least one event over the available sample of
afterglows is significant only if a large fraction of the baryons in the
universe are condensed in stellar-mass objects. (ABRIDGED)Comment: 22 pages, 4 figures, 2 table
Squeezed light at sideband frequencies below 100 kHz from a single OPA
Quantum noise of the electromagnetic field is one of the limiting noise
sources in interferometric gravitational wave detectors. Shifting the spectrum
of squeezed vacuum states downwards into the acoustic band of gravitational
wave detectors is therefore of challenging demand to quantum optics
experiments. We demonstrate a system that produces nonclassical continuous
variable states of light that are squeezed at sideband frequencies below 100
kHz. A single optical parametric amplifier (OPA) is used in an optical noise
cancellation scheme providing squeezed vacuum states with coherent bright phase
modulation sidebands at higher frequencies. The system has been stably locked
for half an hour limited by thermal stability of our laboratory.Comment: 3 pages, 3 figure
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