8,350 research outputs found
Invariant and polynomial identities for higher rank matrices
We exhibit explicit expressions, in terms of components, of discriminants,
determinants, characteristic polynomials and polynomial identities for matrices
of higher rank. We define permutation tensors and in term of them we construct
discriminants and the determinant as the discriminant of order , where
is the dimension of the matrix. The characteristic polynomials and the
Cayley--Hamilton theorem for higher rank matrices are obtained there from
A random number generator for continuous random variables
A FORTRAN 4 routine is given which may be used to generate random observations of a continuous real valued random variable. Normal distribution of F(x), X, E(akimas), and E(linear) is presented in tabular form
Mechanical Unfolding of a Simple Model Protein Goes Beyond the Reach of One-Dimensional Descriptions
We study the mechanical unfolding of a simple model protein. The Langevin
dynamics results are analyzed using Markov-model methods which allow to
describe completely the configurational space of the system. Using transition
path theory we also provide a quantitative description of the unfolding
pathways followed by the system. Our study shows a complex dynamical scenario.
In particular, we see that the usual one-dimensional picture: free-energy vs
end-to-end distance representation, gives a misleading description of the
process. Unfolding can occur following different pathways and configurations
which seem to play a central role in one-dimensional pictures are not the
intermediate states of the unfolding dynamics.Comment: 10 pages, 6 figure
Universal field equations for metric-affine theories of gravity
We show that almost all metric--affine theories of gravity yield Einstein
equations with a non--null cosmological constant . Under certain
circumstances and for any dimension, it is also possible to incorporate a Weyl
vector field and therefore the presence of an anisotropy. The viability
of these field equations is discussed in view of recent astrophysical
observations.Comment: 13 pages. This is a copy of the published paper. We are posting it
here because of the increasing interest in f(R) theories of gravit
On the geometry of four qubit invariants
The geometry of four-qubit entanglement is investigated. We replace some of
the polynomial invariants for four-qubits introduced recently by new ones of
direct geometrical meaning. It is shown that these invariants describe four
points, six lines and four planes in complex projective space . For
the generic entanglement class of stochastic local operations and classical
communication they take a very simple form related to the elementary symmetric
polynomials in four complex variables. Moreover, their magnitudes are
entanglement monotones that fit nicely into the geometric set of -qubit ones
related to Grassmannians of -planes found recently. We also show that in
terms of these invariants the hyperdeterminant of order 24 in the four-qubit
amplitudes takes a more instructive form than the previously published
expressions available in the literature. Finally in order to understand two,
three and four-qubit entanglement in geometric terms we propose a unified
setting based on furnished with a fixed quadric.Comment: 19 page
Recycling of quantum information: Multiple observations of quantum systems
Given a finite number of copies of an unknown qubit state that have already
been measured optimally, can one still extract any information about the
original unknown state? We give a positive answer to this question and quantify
the information obtainable by a given observer as a function of the number of
copies in the ensemble, and of the number of independent observers that, one
after the other, have independently measured the same ensemble of qubits before
him. The optimality of the protocol is proven and extensions to other states
and encodings are also studied. According to the general lore, the state after
a measurement has no information about the state before the measurement. Our
results manifestly show that this statement has to be taken with a grain of
salt, specially in situations where the quantum states encode confidential
information.Comment: 4 page
Canonical formulation of the embedded theory of gravity equivalent to Einstein's General Relativity
We study the approach in which independent variables describing gravity are
functions of the space-time embedding into a flat space of higher dimension. We
formulate a canonical formalism for such a theory in a form, which requires
imposing additional constraints, which are a part of Einstein's equations. As a
result, we obtain a theory with an eight-parameter gauge symmetry. This theory
becomes equivalent to Einstein's general relativity either after partial gauge
fixing or after rewriting the metric in the form that is invariant under the
additional gauge transformations. We write the action for such a theory.Comment: LaTeX, 17 page
Experimental evidence of shock mitigation in a Hertzian tapered chain
We present an experimental study of the mechanical impulse propagation
through a horizontal alignment of elastic spheres of progressively decreasing
diameter , namely a tapered chain. Experimentally, the diameters of
spheres which interact via the Hertz potential are selected to keep as close as
possible to an exponential decrease, , where the
experimental tapering factor is either ~% or ~%.
In agreement with recent numerical results, an impulse initiated in a
monodisperse chain (a chain of identical beads) propagates without shape
changes, and progressively transfer its energy and momentum to a propagating
tail when it further travels in a tapered chain. As a result, the front pulse
of this wave decreases in amplitude and accelerates. Both effects are
satisfactorily described by the hard spheres approximation, and basically, the
shock mitigation is due to partial transmissions, from one bead to the next, of
momentum and energy of the front pulse. In addition when small dissipation is
included, a better agreement with experiments is found. A close analysis of the
loading part of the experimental pulses demonstrates that the front wave adopts
itself a self similar solution as it propagates in the tapered chain. Finally,
our results corroborate the capability of these chains to thermalize
propagating impulses and thereby act as shock absorbing devices.Comment: ReVTeX, 7 pages with 6 eps, accepted for Phys. Rev. E (Related papers
on http://www.supmeca.fr/perso/jobs/
Wave localization in strongly nonlinear Hertzian chains with mass defect
We investigate the dynamical response of a mass defect in a one-dimensional
non-loaded horizontal chain of identical spheres which interact via the
nonlinear Hertz potential. Our experiments show that the interaction of a
solitary wave with a light intruder excites localized mode. In agreement with
dimensional analysis, we find that the frequency of localized oscillations
exceeds the incident wave frequency spectrum and nonlinearly depends on the
size of the intruder and on the incident wave strength. The absence of tensile
stress between grains allows some gaps to open, which in turn induce a
significant enhancement of the oscillations amplitude. We performed numerical
simulations that precisely describe our observations without any adjusting
parameters.Comment: 4 pages, 5 figures, submitted for publicatio
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