296 research outputs found
A Generalization of Chetaev's Principle for a Class of Higher Order Non-holonomic Constraints
The constraint distribution in non-holonomic mechanics has a double role. On
one hand, it is a kinematic constraint, that is, it is a restriction on the
motion itself. On the other hand, it is also a restriction on the allowed
variations when using D'Alembert's Principle to derive the equations of motion.
We will show that many systems of physical interest where D'Alembert's
Principle does not apply can be conveniently modeled within the general idea of
the Principle of Virtual Work by the introduction of both kinematic constraints
and variational constraints as being independent entities. This includes, for
example, elastic rolling bodies and pneumatic tires. Also, D'Alembert's
Principle and Chetaev's Principle fall into this scheme. We emphasize the
geometric point of view, avoiding the use of local coordinates, which is the
appropriate setting for dealing with questions of global nature, like
reduction.Comment: 27 pages. Journal of Mathematical Physics (to zappear
A transient network of telechelic polymers and microspheres : structure and rheology
We study the structure and dynamics of a transient network composed of
droplets of microemulsion connected by telechelic polymers. The polymer induces
a bridging attraction between droplets without changing their shape. A
viscoelastic behaviour is induced in the initially liquid solution,
characterised in the linear regime by a stretched exponential stress
relaxation. We analyse this relaxation in the light of classical theories of
transient networks. The role of the elastic reorganisations in the deformed
network is emphasized. In the non linear regime, a fast relaxation dynamics is
followed by a second one having the same rate as in the linear regime. This
behaviour, under step strain experiments, should induce a non monotonic
behaviour in the elastic component of the stress under constant shear rate.
However, we obtain in this case a singularity in the flow curve very different
from the one observed in other systems, that we interpret in terms of fracture
behaviour.Comment: 9 pages, 4 figure
Projective dynamics and classical gravitation
Given a real vector space V of finite dimension, together with a particular
homogeneous field of bivectors that we call a "field of projective forces", we
define a law of dynamics such that the position of the particle is a "ray" i.e.
a half-line drawn from the origin of V. The impulsion is a bivector whose
support is a 2-plane containing the ray. Throwing the particle with a given
initial impulsion defines a projective trajectory. It is a curve in the space
of rays S(V), together with an impulsion attached to each ray. In the simplest
example where the force is identically zero, the curve is a straight line and
the impulsion a constant bivector. A striking feature of projective dynamics
appears: the trajectories are not parameterized.
Among the projective force fields corresponding to a central force, the one
defining the Kepler problem is simpler than those corresponding to other
homogeneities. Here the thrown ray describes a quadratic cone whose section by
a hyperplane corresponds to a Keplerian conic. An original point of view on the
hidden symmetries of the Kepler problem emerges, and clarifies some remarks due
to Halphen and Appell. We also get the unexpected conclusion that there exists
a notion of divergence-free field of projective forces if and only if dim V=4.
No metric is involved in the axioms of projective dynamics.Comment: 20 pages, 4 figure
On two-dimensional Bessel functions
The general properties of two-dimensional generalized Bessel functions are
discussed. Various asymptotic approximations are derived and applied to analyze
the basic structure of the two-dimensional Bessel functions as well as their
nodal lines.Comment: 25 pages, 17 figure
Structure factor of polymers interacting via a short range repulsive potential: application to hairy wormlike micelles
We use the Random Phase Approximation (RPA) to compute the structure factor,
S(q), of a solution of chains interacting through a soft and short range
repulsive potential V. Above a threshold polymer concentration, whose magnitude
is essentially controlled by the range of the potential, S(q) exhibits a peak
whose position depends on the concentration. We take advantage of the close
analogy between polymers and wormlike micelles and apply our model, using a
Gaussian function for V, to quantitatively analyze experimental small angle
neutron scattering profiles of semi-dilute solutions of hairy wormlike
micelles. These samples, which consist in surfactant self-assembled flexible
cylinders decorated by amphiphilic copolymer, provide indeed an appropriate
experimental model system to study the structure of sterically interacting
polymer solutions
One pendulum to run them all
The analytical solution for the three-dimensional linear pendulum in a rotating frame of reference is obtained, including Coriolis and centrifugal accelerations, and expressed in terms of initial conditions. This result offers the possibility of treating Foucault and Bravais pendula as trajectories of the same system of equations, each of them with particular initial conditions. We compare them with the common two-dimensional approximations in textbooks. A previously unnoticed pattern in the three-dimensional Foucault pendulum attractor is presented
The helium atom in a strong magnetic field
We investigate the electronic structure of the helium atom in a magnetic
field b etween B=0 and B=100a.u. The atom is treated as a nonrelativistic
system with two interactin g electrons and a fixed nucleus. Scaling laws are
provided connecting the fixed-nucleus Hamiltonia n to the one for the case of
finite nuclear mass. Respecting the symmetries of the electronic Ham iltonian
in the presence of a magnetic field, we represent this Hamiltonian as a matrix
with res pect to a two-particle basis composed of one-particle states of a
Gaussian basis set. The corresponding generalized eigenvalue problem is solved
numerically, providing in the present paper results for vanish ing magnetic
quantum number M=0 and even or odd z-parity, each for both singlet and triplet
spin symmetry. Total electronic energies of the ground state and the first few
excitations in each su bspace as well as their one-electron ionization energies
are presented as a function of the magnetic fie ld, and their behaviour is
discussed. Energy values for electromagnetic transitions within the M=0 sub
space are shown, and a complete table of wavelengths at all the detected
stationary points with respect to their field dependence is given, thereby
providing a basis for a comparison with observed ab sorption spectra of
magnetic white dwarfs.Comment: 21 pages, 4 Figures, acc.f.publ.in J.Phys.
Nonparametric Information Geometry
The differential-geometric structure of the set of positive densities on a
given measure space has raised the interest of many mathematicians after the
discovery by C.R. Rao of the geometric meaning of the Fisher information. Most
of the research is focused on parametric statistical models. In series of
papers by author and coworkers a particular version of the nonparametric case
has been discussed. It consists of a minimalistic structure modeled according
the theory of exponential families: given a reference density other densities
are represented by the centered log likelihood which is an element of an Orlicz
space. This mappings give a system of charts of a Banach manifold. It has been
observed that, while the construction is natural, the practical applicability
is limited by the technical difficulty to deal with such a class of Banach
spaces. It has been suggested recently to replace the exponential function with
other functions with similar behavior but polynomial growth at infinity in
order to obtain more tractable Banach spaces, e.g. Hilbert spaces. We give
first a review of our theory with special emphasis on the specific issues of
the infinite dimensional setting. In a second part we discuss two specific
topics, differential equations and the metric connection. The position of this
line of research with respect to other approaches is briefly discussed.Comment: Submitted for publication in the Proceedings od GSI2013 Aug 28-30
2013 Pari
Unification, KK-thresholds and the top Yukawa coupling in F-theory GUTs
In a class of F-theory SU(5) GUTs the low energy chiral mass spectrum is
obtained from rank one fermion mass textures with a hierarchical structure
organised by U(1) symmetries embedded in the exceptional E_8 group. In these
theories chiral fields reside on matter `curves' and the tree level masses are
computed from integrals of overlapping wavefuctions of the particles at the
triple intersection points. This calculation requires knowledge of the exact
form of the wavefuctions. In this work we propose a way to obtain a reliable
estimate of the various quantities which determine the strength of the Yukawa
couplings. We use previous analysis of KK threshold effects to determine the
(ratios of) heavy mass scales of the theory which are involved in the
normalization of the wave functions. We consider similar effects from the
chiral spectrum of these models and discuss possible constraints on the
emerging matter content. In this approach, we find that the Yukawa couplings
can be determined solely from the U(1) charges of the states in the
`intersection' and the torsion which is a topological invariant quantity. We
apply the results to a viable SU(5) model with minimal spectrum which satisfies
all the constraints imposed by our analysis. We use renormalization group
analysis to estimate the top and bottom masses and find that they are in
agreement with the experimental values.Comment: 28 pages, 2 figure
Soft and virtual corrections to pp -> H + X at NNLO
The contributions of virtual corrections and soft gluon emission to the
inclusive Higgs production cross section pp -> H + X are computed at
next-to-next-to-leading order in the heavy top quark limit. We show that this
part of the total cross section is well behaved in the sense of perturbative
convergence, with the NNLO corrections amounting to an enhancement of the NLO
cross section by \sim 5% for LHC and 10-20% for the Tevatron. We compare our
results with an existing estimate of the full NNLO effects and argue that an
analytic evaluation of the hard scattering contributions is needed.Comment: 16 pages, 7 figures, 16 ps files embedded with epsf. Minor
modifications: references and note added, results unchange
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