1,244 research outputs found
A semi-relativistic approach to the circular restricted three body problem and a numerical experiment around the 3:2 resonance
A Hamiltonian that approaches the study of the three-body problem in general
relativity is obtained. We use it to study the relativistic version of the
circular restricted three-body problem in which the first body is the heaviest
and the third body is a test-particle. We focus on the orbits around the 3:2
resonance. We show that, in spite of the notable difference between the
relativistic and Newtonian orbits, most of the resonant region is preserved.
Nevertheless, differently from the Newtonian case, the frequencies between the
second and the third body are no longer commensurable.Comment: 6 eps figures, accepted to Class. Quant. Gra
Non-perturbative \lambda\Phi^4 in D=1+1: an example of the constructive quantum field theory approach in a schematic way
During the '70, several relativistic quantum field theory models in
and also in have been constructed in a non-perturbative way. That was
done in the so-called {\it constructive quantum field theory} approach, whose
main results have been obtained by a clever use of Euclidean functional
methods. Although in the construction of a single model there are several
technical steps, some of them involving long proofs, the constructive quantum
field theory approach contains conceptual insights about relativistic quantum
field theory that deserved to be known and which are accessible without
entering in technical details. The purpose of this note is to illustrate such
insights by providing an oversimplified schematic exposition of the simple case
of (with ) in . Because of the absence of
ultraviolet divergences in its perturbative version, this simple example
-although does not capture all the difficulties in the constructive quantum
field theory approach- allows to stress those difficulties inherent to the
non-perturbative definition. We have made an effort in order to avoid several
of the long technical intermediate steps without missing the main ideas and
making contact with the usual language of the perturbative approach.Comment: 63 pages. Typos correcte
The relativistic glider
We present a purely relativistic effect according to which asymmetric
oscillations of a quasi-rigid body slow down or accelerate its fall in a
gravitational background.Comment: 3 pages, 2 figures. To appear in Phys Rev
Modelling mucociliary clearance
Mathematical modelling of the fluid mechanics of mucociliary clearance (MCC) is reviewed and future challenges for researchers are discussed. The morphology of the bronchial and tracheal airway surface liquid (ASL) and ciliated epithelium are briefly introduced. The cilia beat cycle, beat frequency and metachronal coordination are described, along with the rheology of the mucous layer. Theoretical modelling of MCC from the late 1960s onwards is reviewed, and distinctions between ‘phenomenological’, ‘slender body theory’ and recent ‘fluid–structure interaction’ models are explained.\ud
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The ASL consists of two layers, an overlying mucous layer and underlying watery periciliary layer (PCL) which bathes the cilia. Previous models have predicted very little transport of fluid in the PCL compared with the mucous layer. Fluorescent tracer transport experiments on human airway cultures conducted by Matsui et al. [Matsui, H., Randell, S.H., Peretti, S.W., Davis, C.W., Boucher, R.C., 1998. Coordinated clearance of periciliary liquid and mucus from airway surfaces. J. Clin. Invest. 102 (6), 1125–1131] apparently showed equal transport in both the PCL and mucous layer. Recent attempts to resolve this discrepancy by the present authors are reviewed, along with associated modelling findings. These findings have suggested new insights into the interaction of cilia with mucus due to pressure gradients associated with the flat PCL/mucus interface. This phenomenon complements previously known mechanisms for ciliary propulsion. Modelling results are related to clinical findings, in particular the increased MCC observed in patients with pseudohypoaldosteronism. Recent important advances by several groups in modelling the fluid–structure interaction by which the cilia movement and fluid transport emerge from specification of internal mechanics, viscous and elastic forces are reviewed. Finally, we discuss the limitations of existing work, and the challenges for the next generation of models, which may provide further insight into this complex and vital system
Power-law versus exponential distributions of animal group sizes
There has been some confusion concerning the animal group-size: an
exponential distribution was deduced by maximizing the entropy; lognormal
distributions were practically used; a power-law decay with exponent {3/2} was
proposed in physical analogy to aerosol condensation. Here I show that the
animal group-size distribution follows a power-law decay with exponent 1, and
is truncated at a cut-off size which is the expected size of the groups an
arbitrary individual engages in. An elementary model of animal aggregation
based on binary splitting and coalescing on contingent encounter is presented.
The model predicted size distribution holds for various data from pelagic
fishes and mammalian herbivores in the wild.Comment: 19 pages,9 figures, to appear in J. Theor. Bio
Application of Benford-Newcomb Law with Base Change to Electoral Fraud Detection
The invariance of Benford-Newcomb law under base changing is employed to test
whether or not some data follow such distribution. Taking into account the
Brazilian senate election in 1994, changes in the numerical base were able to
evidence probable fraud.Comment: 12 pages, 4 figure
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