45,236 research outputs found
Refinements of Some Reverses of Schwarz's Inequality in 2-Inner Product Spaces and Applications for Integrals
Refinements of some recent reverse inequalities for the celebrated
Cauchy-Bunyakovsky-Schwarz inequality in 2-inner product spaces are given.
Using this framework, applications for determinantal integral inequalities are
also provided
Warped brane-world compactification with Gauss-Bonnet term
In the Randall-Sundrum (RS) brane-world model a singular delta-function
source is matched by the second derivative of the warp factor. So one should
take possible curvature corrections in the effective action of the RS models in
a Gauss-Bonnet (GB) form. We present a linearized treatment of gravity in the
RS brane-world with the Gauss-Bonnet modification to Einstein gravity. We give
explicit expressions for the Neumann propagator in arbitrary D dimensions and
show that a bulk GB term gives, along with a tower of Kaluza-Klein modes in the
bulk, a massless graviton on the brane, as in the standard RS model. Moreover,
a non-trivial GB coupling can allow a new branch of solutions with finite
Planck scale and no naked bulk singularity, which might be useful to avoid some
of the previously known ``no--go theorems'' for RS brane-world
compactifications.Comment: 23 pages, typos in Secs. 5 & 6 corrected, expanded/published version
(IJMPA
Norm Estimates for the Difference Between Bochner's Integral and the Convex Combination of Function's Values
Norm estimates are developed between the Bochner integral of a vector-valued
function in Banach spaces having the Radon-Nikodym property and the convex
combination of function values taken on a division of the interval [a,b]
Classical Strongly Coupled QGP: VII. Shear Viscosity and Self Diffusion
We construct the Liouville operator for the SU(2) classical colored Coulomb
plasma (cQGP) for arbitrary values of the Coulomb coupling , the
ratio of the mean Coulomb to kinetic energy. We show that its resolvent in the
classical colored phase space obeys a hierarchy of equations. We use a free
streaming approximation to close the hierarchy and derive an integral equation
for the time-dependent structure factor. Its reduction by projection yields
hydrodynamical equations in the long-wavelength limit. We discuss the character
of the hydrodynamical modes at strong coupling. The shear viscosity is shown to
exhibit a minimum at near the liquid point. This minimum
follows from the cross-over between the single particle collisional regime
which drops as and the hydrodynamical collisional regime which
rises as . The self-diffusion constant drops as
irrespective of the regime. We compare our results to molecular dynamics
simulations of the SU(2) colored Coulomb plasma. We also discuss the relevance
of our results for the quantum and strongly coupled quark gluon plasma (sQGP)Comment: 36 pages, 14 figure
Spectral dimension of a quantum universe
In this paper, we calculate in a transparent way the spectral dimension of a
quantum spacetime, considering a diffusion process propagating on a fluctuating
manifold. To describe the erratic path of the diffusion, we implement a minimal
length by averaging the graininess of the quantum manifold in the flat space
case. As a result we obtain that, for large diffusion times, the quantum
spacetime behaves like a smooth differential manifold of discrete dimension. On
the other hand, for smaller diffusion times, the spacetime looks like a fractal
surface with a reduced effective dimension. For the specific case in which the
diffusion time has the size of the minimal length, the spacetime turns out to
have a spectral dimension equal to 2, suggesting a possible renormalizable
character of gravity in this regime. For smaller diffusion times, the spectral
dimension approaches zero, making any physical interpretation less reliable in
this extreme regime. We extend our result to the presence of a background field
and curvature. We show that in this case the spectral dimension has a more
complicated relation with the diffusion time, and conclusions about the
renormalizable character of gravity become less straightforward with respect to
what we found with the flat space analysis.Comment: 5 pages, 1 figure, references added, typos corrected, title changed,
final version published in Physical Review
Monopoles and Knots in Skyrme Theory
We show that the Skyrme theory actually is a theory of monopoles which allows
a new type of solitons, the topological knots made of monopole-anti-monopole
pair,which is different from the well-known skyrmions. Furthermore, we derive a
generalized Skyrme action from the Yang-Mills action of QCD, which we propose
to be an effective action of QCD in the infra-red limit. We discuss the
physical implications of our results.Comment: 4 pages. Phys. Rev. Lett. in pres
Scattering phase shifts in quasi-one-dimension
Scattering of an electron in quasi-one dimensional quantum wires have many
unusual features, not found in one, two or three dimensions. In this work we
analyze the scattering phase shifts due to an impurity in a multi-channel
quantum wire with special emphasis on negative slopes in the scattering phase
shift versus incident energy curves and the Wigner delay time. Although at
first sight, the large number of scattering matrix elements show phase shifts
of different character and nature, it is possible to see some pattern and
understand these features. The behavior of scattering phase shifts in
one-dimension can be seen as a special case of these features observed in
quasi-one-dimensions. The negative slopes can occur at any arbitrary energy and
Friedel sum rule is completely violated in quasi-one-dimension at any arbitrary
energy and any arbitrary regime. This is in contrast to one, two or three
dimensions where such negative slopes and violation of Friedel sum rule happen
only at low energy where the incident electron feels the potential very
strongly (i.e., there is a very well defined regime, the WKB regime, where FSR
works very well). There are some novel behavior of scattering phase shifts at
the critical energies where -matrix changes dimension.Comment: Minor corrections mad
Percolation Transitions in Scale-Free Networks under Achlioptas Process
It has been recently shown that the percolation transition is discontinuous
in Erd\H{o}s-R\'enyi networks and square lattices in two dimensions under the
Achlioptas Process (AP). Here, we show that when the structure is highly
heterogeneous as in scale-free networks, a discontinuous transition does not
always occur: a continuous transition is also possible depending on the degree
distribution of the scale-free network. This originates from the competition
between the AP that discourages the formation of a giant component and the
existence of hubs that encourages it. We also estimate the value of the
characteristic degree exponent that separates the two transition types.Comment: 4 pages, 6 figure
Fundamental study of flow field generated by rotorcraft blades using wide-field shadowgraph
The vortex trajectory and vortex wake generated by helicopter rotors are visualized using a wide-field shadowgraph technique. Use of a retro-reflective Scotchlite screen makes it possible to investigate the flow field generated by full-scale rotors. Tip vortex trajectories are visible in shadowgraphs for a range of tip Mach number of 0.38 to 0.60. The effect of the angle of attack is substantial. At an angle of attack greater than 8 degrees, the visibility of the vortex core is significant even at relatively low tip Mach numbers. The theoretical analysis of the sensitivity is carried out for a rotating blade. This analysis demonstrates that the sensitivity decreases with increasing dimensionless core radius and increases with increasing tip Mach number. The threshold value of the sensitivity is found to be 0.0015, below which the vortex core is not visible and above which it is visible. The effect of the optical path length is also discussed. Based on this investigation, it is concluded that the application of this wide-field shadowgraph technique to a large wind tunnel test should be feasible. In addition, two simultaneous shadowgraph views would allow three-dimensional reconstruction of vortex trajectories
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