4,082 research outputs found
Parameterization invariance and shape equations of elastic axisymmetric vesicles
The issue of different parameterizations of the axisymmetric vesicle shape
addressed by Hu Jian-Guo and Ou-Yang Zhong-Can [ Phys.Rev. E {\bf 47} (1993)
461 ] is reassesed, especially as it transpires through the corresponding Euler
- Lagrange equations of the associated elastic energy functional. It is argued
that for regular, smooth contours of vesicles with spherical topology,
different parameterizations of the surface are equivalent and that the
corresponding Euler - Lagrange equations are in essence the same. If, however,
one allows for discontinuous (higher) derivatives of the contour line at the
pole, the differently parameterized Euler - Lagrange equations cease to be
equivalent and describe different physical problems. It nevertheless appears to
be true that the elastic energy corresponding to smooth contours remains a
global minimum.Comment: 10 pages, latex, one figure include
Mass and pressure constraints on galaxy clusters from interferometric SZ observations
Following on our previous study of an analytic parametric model to describe
the baryonic and dark matter distributions in clusters of galaxies with
spherical symmetry, we perform an SZ analysis of a set of simulated clusters
and present their mass and pressure profiles. The simulated clusters span a
wide range in mass, 2.0 x 10^14 Msun < M200 < 1.0 x 10^15Msun, and observations
with the Arcminute Microkelvin Imager (AMI) are simulated through their
Sunyaev- Zel'dovich (SZ) effect. We assume that the dark matter density follows
a Navarro, Frenk and White (NFW) profile and that the gas pressure is described
by a generalised NFW (GNFW) profile. By numerically exploring the probability
distributions of the cluster parameters given simulated interferometric SZ data
in the context of Bayesian methods, we investigate the capability of this model
and analysis technique to return the simulated clusters input quantities. We
show that considering the mass and redshift dependency of the cluster halo
concentration parameter is crucial in obtaining an unbiased cluster mass
estimate and hence deriving the radial profiles of the enclosed total mass and
the gas pressure out to r200.Comment: 5 pages, 2 tables, 3 figure
Slow dynamics in critical ferromagnetic vector models relaxing from a magnetized initial state
Within the universality class of ferromagnetic vector models with O(n)
symmetry and purely dissipative dynamics, we study the non-equilibrium critical
relaxation from a magnetized initial state. Transverse correlation and response
functions are exactly computed for Gaussian fluctuations and in the limit of
infinite number n of components of the order parameter. We find that the
fluctuation-dissipation ratios (FDRs) for longitudinal and transverse modes
differ already at the Gaussian level. In these two exactly solvable cases we
completely describe the crossover from the short-time to the long-time
behavior, corresponding to a disordered and a magnetized initial condition,
respectively. The effects of non-Gaussian fluctuations on longitudinal and
transverse quantities are calculated in the first order in the
epsilon-expansion and reliable three-dimensional estimates of the two FDRs are
obtained.Comment: 41 pages, 9 figure
Optimal Strokes for Driftless Swimmers: A General Geometric Approach
Swimming consists by definition in propelling through a fluid by means of
bodily movements. Thus, from a mathematical point of view, swimming turns into
a control problem for which the controls are the deformations of the swimmer.
The aim of this paper is to present a unified geometric approach for the
optimization of the body deformations of so-called driftless swimmers. The
class of driftless swimmers includes, among other, swimmers in a 3D Stokes flow
(case of micro-swimmers in viscous fluids) or swimmers in a 2D or 3D potential
flow. A general framework is introduced, allowing the complete analysis of five
usual nonlinear optimization problems to be carried out. The results are
illustrated with examples coming from the literature and with an in-depth study
of a swimmer in a 2D potential flow. Numerical tests are also provided
Nuclear physics for geo-neutrino studies
Geo-neutrino studies are based on theoretical estimates of geo-neutrino
spectra. We propose a method for a direct measurement of the energy
distribution of antineutrinos from decays of long-lived radioactive isotopes.
We present preliminary results for the geo-neutrinos from Bi-214 decay, a
process which accounts for about one half of the total geo-neutrino signal. The
feeding probability of the lowest state of Bi-214 - the most important for
geo-neutrino signal - is found to be p_0 = 0.177 \pm 0.004 (stat)
^{+0.003}_{-0.001} (sys), under the hypothesis of Universal Neutrino Spectrum
Shape (UNSS). This value is consistent with the (indirect) estimate of the
Table of Isotopes (ToI). We show that achievable larger statistics and
reduction of systematics should allow to test possible distortions of the
neutrino spectrum from that predicted using the UNSS hypothesis. Implications
on the geo-neutrino signal are discussed.Comment: 8 pages RevTex format, 8 figures and 2 tables. Submitted to PR
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