22,132 research outputs found
Lower bounds on the blow-up rate of the axisymmetric Navier-Stokes equations II
Consider axisymmetric strong solutions of the incompressible Navier-Stokes
equations in with non-trivial swirl. Let denote the axis of symmetry
and measure the distance to the z-axis. Suppose the solution satisfies
either or, for some \e > 0, for and
allowed to be large. We prove that is regular at time zero.Comment: More explanations and a new appendi
Spontaneous Crystallization of Skyrmions and Fractional Vortices in the Fast-rotating and Rapidly-quenched Spin-1 Bose-Einstein Condensates
We investigate the spontaneous generation of crystallized topological defects
via the combining effects of fast rotation and rapid thermal quench on the
spin-1 Bose-Einstein condensates. By solving the stochastic projected
Gross-Pitaevskii equation, we show that, when the system reaches equilibrium, a
hexagonal lattice of skyrmions, and a square lattice of half-quantized vortices
can be formed in a ferromagnetic and antiferromagnetic spinor BEC, respetively,
which can be imaged by using the polarization-dependent phase-contrast method
Quantifying effective slip length over micropatterned hydrophobic surfaces
We employ micro-particle image velocimetry (-PIV) to investigate laminar
micro-flows in hydrophobic microstructured channels, in particular the slip
length. These microchannels consist of longitudinal micro-grooves, which can
trap air and prompt a shear-free boundary condition and thus slippage
enhancement. Our measurements reveal an increase of the slip length when the
width of the micro-grooves is enlarged. The result of the slip length is
smaller than the analytical prediction by Philip et al. [1] for an infinitely
large and textured channel comprised of alternating shear-free and no-slip
boundary conditions. The smaller slip length (as compared to the prediction)
can be attributed to the confinement of the microchannel and the bending of the
meniscus (liquid-gas interface). Our experimental studies suggest that the
curvature of the meniscus plays an important role in microflows over
hydrophobic micro-ridges.Comment: 8 page
On the Scale-Invariant Distribution of the Diffusion Coefficient for Classical Particles Diffusing in Disordered Media.-
The scaling form of the whole distribution P(D) of the random diffusion
coefficient D(x) in a model of classically diffusing particles is investigated.
The renormalization group approach above the lower critical dimension d=0 is
applied to the distribution P(D) using the n-replica approach. In the annealed
approximation (n=1), the inverse gaussian distribution is found to be the
stable one under rescaling. This identification is made based on symmetry
arguments and subtle relations between this model and that of fluc- tuating
interfaces studied by Wallace and Zia. The renormalization-group flow for the
ratios between consecutive cumulants shows a regime of pure diffusion for small
disorder, in which P(D) goes to delta(D-), and a regime of strong disorder
where the cumulants grow infinitely large and the diffusion process is ill
defined. The boundary between these two regimes is associated with an unstable
fixed-point and a subdiffusive behavior: =Ct**(1-d/2). For the quenched
case (n goes to 0) we find that unphysical operators are generated raisng
doubts on the renormalizability of this model. Implications to other random
systems near their lower critical dimension are discussed.Comment: 21 pages, 1 fig. (not included) Use LaTex twic
Entropy production and equilibration in Yang-Mills quantum mechanics
The Husimi distribution provides for a coarse grained representation of the
phase space distribution of a quantum system, which may be used to track the
growth of entropy of the system. We present a general and systematic method of
solving the Husimi equation of motion for an isolated quantum system, and we
construct a coarse grained Hamiltonian whose expectation value is exactly
conserved. As an application, we numerically solve the Husimi equation of
motion for two-dimensional Yang-Mills quantum mechanics (the x-y model) and
calculate the time evolution of the coarse grained entropy of a highly excited
state. We show that the coarse grained entropy saturates to a value that
coincides with the microcanonical entropy corresponding to the energy of the
system.Comment: 23 pages, 23 figure
Interstitial gas and density-segregation in vertically-vibrated granular media
We report experimental studies of the effect of interstitial gas on
mass-density-segregation in a vertically-vibrated mixture of equal-sized bronze
and glass spheres. Sufficiently strong vibration in the presence of
interstitial gas induces vertical segregation into sharply separated bronze and
glass layers. We find that the segregated steady state (i.e., bronze or glass
layer on top) is a sensitive function of gas pressure and viscosity, as well as
vibration frequency and amplitude. In particular, we identify distinct regimes
of behavior that characterize the change from bronze-on-top to glass-on-top
steady-state.Comment: 4 pages, 5 figures, submitted to PRL; accepted in PRE as rapid
communication, with revised text and reference
Searching For Anomalous Couplings
The capability of current and future measurements at low and high energy
colliders to probe for the existence of anomalous, CP conserving,
dipole moment-type couplings is examined. At present, constraints
on the universality of the tau charged and neutral current interactions as well
as the shape of the energy spectrum provide the strongest
bounds on such anomalous couplings. The presence of these dipole moments are
shown to influence, e.g., the extraction of from
decays and can lead to apparent violations of CVC expectations.Comment: 24 pages, 9 figure
Impact of Baseline Magnetic Resonance Imaging on Neurologic, Functional, and Safety Outcomes in Patients With Acute Traumatic Spinal Cord Injury
Study Design: Systematic review. Objective: To perform a systematic review to evaluate the utility of magnetic resonance imaging (MRI) in patients with acute spinal cord injury (SCI). Methods: An electronic search of Medline, EMBASE, the Cochrane Collaboration Library, and Google Scholar was conducted for literature published through May 12, 2015, to answer key questions associated with the use of MRI in patients with acute SCI. Results: The literature search yielded 796 potentially relevant citations, 8 of which were included in this review. One study used MRI in a protocol to decide on early surgical decompression. The MRI-protocol group showed improved outcomes; however, the quality of evidence was deemed very low due to selection bias. Seven studies reported MRI predictors of neurologic or functional outcomes. There was moderate-quality evidence that longer intramedullary hemorrhage (2 studies) and low-quality evidence that smaller spinal canal diameter at the location of maximal spinal cord compression and the presence of cord swelling are associated with poor neurologic recovery. There was moderate-quality evidence that clinical outcomes are not predicted by SCI lesion length and the presence of cord edema. Conclusions: Certain MRI characteristics appear to be predictive of outcomes in acute SCI, including length of intramedullary hemorrhage (moderate-quality evidence), canal diameter at maximal spinal cord compression (low-quality evidence), and spinal cord swelling (low-quality evidence). Other imaging features were either inconsistently (presence of hemorrhage, maximal canal compromise, and edema length) or not associated with outcomes. The paucity of literature highlights the need for well-designed prospective studies. © 2017, © The Author(s) 2017
Non-Ergodic Dynamics of the 2D Random-phase Sine-Gordon Model: Applications to Vortex-Glass Arrays and Disordered-Substrate Surfaces
The dynamics of the random-phase sine-Gordon model, which describes 2D
vortex-glass arrays and crystalline surfaces on disordered substrates, is
investigated using the self-consistent Hartree approximation. The
fluctuation-dissipation theorem is violated below the critical temperature T_c
for large time t>t* where t* diverges in the thermodynamic limit. While above
T_c the averaged autocorrelation function diverges as Tln(t), for T<T_c it
approaches a finite value q* proportional to 1/(T_c-T) as q(t) = q* -
c(t/t*)^{-\nu} (for t --> t*) where \nu is a temperature-dependent exponent. On
larger time scales t > t* the dynamics becomes non-ergodic. The static
correlations behave as Tln{x} for T>T_c and for T<T_c when x < \xi* with \xi*
proportional to exp{A/(T_c-T)}. For scales x > \xi*, they behave as (T/m)ln{x}
where m is approximately T/T_c near T_c, in general agreement with the
variational replica-symmetry breaking approach and with recent simulations of
the disordered-substrate surface. For strong- coupling the transition becomes
first-order.Comment: 12 pages in LaTeX, Figures available upon request, NSF-ITP 94-10
Near-Equilibrium Dynamics of Crystalline Interfaces with Long-Range Interactions in 1+1 Dimensional Systems
The dynamics of a one-dimensional crystalline interface model with long-range
interactions is investigated. In the absence of randomness, the linear response
mobility decreases to zero when the temperature approaches the roughening
transition from above, in contrast to a finite jump at the critical point in
the Kosterlitz-Thouless (KT) transition. In the presence of substrate disorder,
there exists a phase transition into a low-temperature pinning phase with a
continuously varying dynamic exponent . The expressions for the non-linear
response mobility of a crystalline interface in both cases are also derived.Comment: 14 Pages, Revtex3.0, accepted to be published in Phys. Rev. E Rapid
Communicatio
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