288 research outputs found
Compressible potential flows around round bodies: Janzen-Rayleigh expansion inferences
The subsonic, compressible, potential flow around a hypersphere can be
derived using the Janzen-Rayleigh expansion (JRE) of the flow potential in even
powers of the incident Mach number . JREs were carried out
with terms polynomial in the inverse radius to high orders in two
dimensions (2D), but were limited to order in three
dimensions (3D). We derive general JRE formulae to arbitrary order, adiabatic
index, and dimension. We find that powers of can creep into the
expansion, and are essential in 3D beyond order . Such
terms are apparently absent in the 2D disk, as we confirm up to order
, although they do show in other dimensions (e.g. at
order in 4D) and in non-circular 2D bodies. This
suggests that the disk, which was extensively used to study basic flow
properties, has additional symmetry. Our results are used to improve the
hodograph-based approximation for the flow in front of a sphere. The
symmetry-axis velocity profiles of axisymmetric flows around different prolate
spheroids are approximately related to each other by a simple, Mach-independent
scaling.Comment: 24 pages, 6 figures, 5 tables, comments welcom
Gravitational Trapping Near Domain Walls and Stable Solitons
In this work, the behavior of test particles near a domain wall of a stable
false vacuum bubble is studied. It is shown that matter is naturally trapped in
the vicinity of a static domain wall, and also, that there is a discontinuity
in the test particle's velocity when crossing the domain wall. The latter is
unexpected as it stands in contrast to Newtonian theory, where infinite forces
are not allowed. The weak field limit is defined in order to show that there is
no conflict with the non-relativistic behavior of gravitational fields and
particle motions under these conditions.Comment: 8 pages, 1 figure, problem is reanalyzed using a continuous
coordinate syste
Stabilization of Neutral Thin Shells By Gravitational Effects From Electric Fields
We study the properties of a system consisting of an uncharged spherically
symmetric two dimensional extended object which encloses a stationary point
charge placed in the shell's center. We show that there can be a static and
stable configuration for the neutral shell, using only the gravitational field
of the charged source as a stabilizing mechanism. In particular, two types of
shells are studied: a dust shell and a string gas shell. The dynamical
possibilities are also analyzed, including the possibility of child universe
creation.Comment: 5 pages, 1 figur
Direct measurement of the flow field around swimming microorganisms
Swimming microorganisms create flows that influence their mutual interactions
and modify the rheology of their suspensions. While extensively studied
theoretically, these flows have not been measured in detail around any
freely-swimming microorganism. We report such measurements for the microphytes
Volvox carteri and Chlamydomonas reinhardtii. The minute ~0.3% density excess
of V. carteri over water leads to a strongly dominant Stokeslet contribution,
with the widely-assumed stresslet flow only a correction to the subleading
source dipole term. This implies that suspensions of V. carteri have features
similar to suspensions of sedimenting particles. The flow in the region around
C. reinhardtii where significant hydrodynamic interaction is likely to occur
differs qualitatively from a "puller" stresslet, and can be described by a
simple three-Stokeslet model.Comment: 4 pages, 4 figures, accepted for publication in PR
Descemet's membrane detachment management following trabeculectomy
Purpose: To present a case of total Descemet's membrane detachment (DMD) after trabeculectomy and its surgical management. Case Report: A 68-year-old woman presented with large DMD and corneal edema one day after trabeculectomy. Intracameral air injection on day 3 was not effective. Choroidal effusion complicated the clinical picture with Descemet's membrane (DM) touching the lens. Choroidal tap with air injection on day 6 resulted in DM attachment and totally clear cornea on the next day. However, on day 12 the same scenario was repeated with choroidal effusion, shallow anterior chamber (AC), and DM touching the lens. The third surgery included transconjunctival closure of the scleral flap with 10/0 nylon sutures, choroidal tap, and intracameral injection of 20 sulfur hexafluoride. After the third surgery, DM remained attached with clear cornea. Suture removal and needling bleb revision preserved bleb function. Lens opacity progressed, and the patient underwent uneventful cataract surgery 4 months later. Conclusion: Scleral flap closure using transconjunctival sutures can be used for DMD after trabeculectomy to make the eye a closed system. Surgical drainage of choroidal effusions should be considered to increase the AC depth. © 2016 Journal of Ophthalmic and Vision Research
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Trace Formulae and Spectral Statistics for Discrete Laplacians on Regular Graphs (I)
Trace formulae for d-regular graphs are derived and used to express the
spectral density in terms of the periodic walks on the graphs under
consideration. The trace formulae depend on a parameter w which can be tuned
continuously to assign different weights to different periodic orbit
contributions. At the special value w=1, the only periodic orbits which
contribute are the non back- scattering orbits, and the smooth part in the
trace formula coincides with the Kesten-McKay expression. As w deviates from
unity, non vanishing weights are assigned to the periodic walks with
back-scatter, and the smooth part is modified in a consistent way. The trace
formulae presented here are the tools to be used in the second paper in this
sequence, for showing the connection between the spectral properties of
d-regular graphs and the theory of random matrices.Comment: 22 pages, 3 figure
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Functional Network Dynamics of the Language System
During linguistic processing, a set of brain regions on the lateral surfaces of the left frontal, temporal, and parietal cortices exhibit robust responses. These areas display highly correlated activity while a subject rests or performs a naturalistic language comprehension task, suggesting that they form an integrated functional system. Evidence suggests that this system is spatially and functionally distinct from other systems that support high-level cognition in humans. Yet, how different regions within this system might be recruited dynamically during task performance is not well understood. Here we use network methods, applied to fMRI data collected from 22 human subjects performing a language comprehension task, to reveal the dynamic nature of the language system. We observe the presence of a stable core of brain regions, predominantly located in the left hemisphere, that consistently coactivate with one another. We also observe the presence of a more flexible periphery of brain regions, predominantly located in the right hemisphere, that coactivate with different regions at different times. However, the language functional ROIs in the angular gyrus and the anterior temporal lobe were notable exceptions to this trend. By highlighting the temporal dimension of language processing, these results suggest a trade-off between a region's specialization and its capacity for flexible network reconfiguration
Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach
Mixing fluid in a container at low Reynolds number - in an inertialess
environment - is not a trivial task. Reciprocating motions merely lead to
cycles of mixing and unmixing, so continuous rotation, as used in many
technological applications, would appear to be necessary. However, there is
another solution: movement of the walls in a cyclical fashion to introduce a
geometric phase. We show using journal-bearing flow as a model that such
geometric mixing is a general tool for using deformable boundaries that return
to the same position to mix fluid at low Reynolds number. We then simulate a
biological example: we show that mixing in the stomach functions because of the
"belly phase": peristaltic movement of the walls in a cyclical fashion
introduces a geometric phase that avoids unmixing.Comment: Revised, published versio
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