89 research outputs found
Solution of a hydrodynamic lubrication problem with Maple
A set of partial differential equations, arising in a calculation of hydrodynamic lubricationeffects, was solved using a perturbation technique. All of the algebraic manipulations required to find the solution were performed using Maple. The main challenge was the efficient handling and simplification of very long expression, which was met by the power of Maple's built-in procedures and by algebraic transformations suggested by the solution to the lowest-order approximation. As a result, the solution was obtained to a higher order, with greater reliability, than would otherwise have been possible
Matching WMAP 3-yrs results with the Cosmological Slingshot Primordial Spectrum
We consider a recently proposed scenario for the generation of primordial
cosmological perturbations, the so called Cosmological Slingshot scenario. We
firstly obtain a general expression for the Slingshot primordial power spectrum
which extends previous results by including a blue pre-bounce residual
contribution at large scales. Starting from this expression we numerically
compute the CMB temperature and polarization power spectra arising from the
Slingshot scenario and show that they excellently match the standard WMAP
3-years best-fit results. In particular, if the residual blue spectrum is far
above the largest WMAP observed scale, the Slingshot primordial spectrum fits
the data well by only fixing its amplitude and spectral index at the pivot
scale k_p=10^{-3}h x Mpc^{-1}. We finally show that all possible distinctive
Slingshot signatures in the CMB power spectra are confined to very low
multipoles and thus very hard to detect due to large cosmic variance dominated
error bars at these scales.Comment: 9 pages, 4 figures; v3 clarifications added, version accepted for
publication in Gen. Rel. Grav. 200
Resultant-based methods for plane curves intersection problems
http://www.springeronline.com/3-540-28966-6We present an algorithm for solving polynomial equations, which uses generalized eigenvalues and eigenvectors of resultant matrices. We give special attention to the case of two bivariate polynomials and the Sylvester or Bezout resultant constructions. We propose a new method to treat multiple roots, detail its numerical aspects and describe experiments on tangential problems, which show the efficiency of the approach. An industrial application of the method is presented at the end of the paper. It consists in recovering cylinders from a large cloud of points and requires intensive resolution of polynomial equations
The Effect of Negative-Energy Shells on the Schwarzschild Black Hole
We construct Penrose diagrams for Schwarzschild spacetimes joined by massless
shells of matter, in the process correcting minor flaws in the similar diagrams
drawn by Dray and 't Hooft, and confirming their result that such shells
generate a horizon shift. We then consider shells with negative energy density,
showing that the horizon shift in this case allows for travel between the
heretofore causally separated exterior regions of the Schwarzschild geometry.
These drawing techniques are then used to investigate the properties of
successive shells, joining multiple Schwarzschild regions. Again, the presence
of negative-energy shells leads to a causal connection between the exterior
regions, even in (some) cases with two successive shells of equal but opposite
total energy.Comment: 12 pages, 10 figure
Elastic deformation of a fluid membrane upon colloid binding
When a colloidal particle adheres to a fluid membrane, it induces elastic
deformations in the membrane which oppose its own binding. The structural and
energetic aspects of this balance are theoretically studied within the
framework of a Helfrich Hamiltonian. Based on the full nonlinear shape
equations for the membrane profile, a line of continuous binding transitions
and a second line of discontinuous envelopment transitions are found, which
meet at an unusual triple point. The regime of low tension is studied
analytically using a small gradient expansion, while in the limit of large
tension scaling arguments are derived which quantify the asymptotic behavior of
phase boundary, degree of wrapping, and energy barrier. The maturation of
animal viruses by budding is discussed as a biological example of such
colloid-membrane interaction events.Comment: 14 pages, 9 figures, REVTeX style, follow-up on cond-mat/021242
Renormalization Group Summation and the Free Energy of Hot QCD
Using an approach developed in the context of zero-temperature QCD to
systematically sum higher order effects whose form is fixed by the
renormalization group equation, we sum to all orders the leading log (LL) and
next-to-leading log (NLL) contributions to the thermodynamic free energy in hot
QCD. While the result varies considerably less with changes in the
renormalization scale than does the purely perturbative result, a novel
ambiguity arises which reflects the strong scheme dependence of thermal
perturbation theory.Comment: 7 pages REVTEX4, 2 figures; v2: typos correcte
Recursive Polynomial Remainder Sequence and the Nested Subresultants
We give two new expressions of subresultants, nested subresultant and reduced
nested subresultant, for the recursive polynomial remainder sequence (PRS)
which has been introduced by the author. The reduced nested subresultant
reduces the size of the subresultant matrix drastically compared with the
recursive subresultant proposed by the authors before, hence it is much more
useful for investigation of the recursive PRS. Finally, we discuss usage of the
reduced nested subresultant in approximate algebraic computation, which
motivates the present work.Comment: 12 pages. Presented at CASC 2005 (Kalamata, Greece, Septermber 12-16,
2005
Extremal limit of the regular charged black holes in nonlinear electrodynamics
The near horizon limit of the extreme nonlinear black hole is investigated.
It is shown that resulting geometry belongs to the AdS2xS2 class with different
modules of curvatures of subspaces and could be described in terms of the
Lambert functions. It is demonstrated that the considered class of Lagrangians
does not admit solutions of the Bertotti-Robinson type
Vacuum polarization in the spacetime of charged nonlinear black hole
Building on general formulas obtained from the approximate renormalized
effective action, the approximate stress-energy tensor of the quantized massive
scalar field with arbitrary curvature coupling in the spacetime of charged
black hole being a solution of coupled equations of nonlinear electrodynamics
and general relativity is constructed and analysed. It is shown that in a few
limiting cases, the analytical expressions relating obtained tensor to the
general renormalized stress-energy tensor evaluated in the geometry of the
Reissner-Nordstr\"{o}m black hole could be derived. A detailed numerical
analysis with special emphasis put on the minimal coupling is presented and the
results are compared with those obtained earlier for the conformally coupled
field. Some novel features of the renormalized stress-energy tensor are
discussed
Anomalous scaling and Lee-Yang zeroes in Self-Organized Criticality
We show that the generating functions of avalanche observables in SOC models
exhibits a Lee-Yang phenomenon. This establishes a new link between the
classical theory of critical phenomena and SOC. A scaling theory of the
Lee-Yang zeroes is proposed including finite sampling effects.Comment: 33 pages, 19 figures, submitte
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