116 research outputs found
Condensing Momentum Modes in 2-d 0A String Theory with Flux
We use a combination of conformal perturbation theory techniques and matrix
model results to study the effects of perturbing by momentum modes two
dimensional type 0A strings with non-vanishing Ramond-Ramond (RR) flux. In the
limit of large RR flux (equivalently, mu=0) we find an explicit analytic form
of the genus zero partition function in terms of the RR flux and the
momentum modes coupling constant alpha. The analyticity of the partition
function enables us to go beyond the perturbative regime and, for alpha>> q,
obtain the partition function in a background corresponding to the momentum
modes condensation. For momenta such that 0<p<2 we find no obstruction to
condensing the momentum modes in the phase diagram of the partition function.Comment: 22 page
Ramanujan and Extensions and Contractions of Continued Fractions
If a continued fraction is known to converge
but its limit is not easy to determine, it may be easier to use an extension of
to find the limit. By an extension of
we mean a continued fraction whose odd or even part is . One can
then possibly find the limit in one of three ways:
(i) Prove the extension converges and find its limit;
(ii) Prove the extension converges and find the limit of the other
contraction (for example, the odd part, if is the
even part);
(ii) Find the limit of the other contraction and show that the odd and even
parts of the extension tend to the same limit.
We apply these ideas to derive new proofs of certain continued fraction
identities of Ramanujan and to prove a generalization of an identity involving
the Rogers-Ramanujan continued fraction, which was conjectured by Blecksmith
and Brillhart.Comment: 16 page
I.B.S. coatings on large substrates: Towards an improvement of the mechanical and optical performances
présenté par A. RemillieuxLarge mirrors (350 mm), having extremely low optical loss (absorption, scattering, wavefront) were coated for the VIRGO interferometer. The new mirror generation needs better wavefront and lower mechanical loss. The first results are discussed
Original optical metrologies of large components
présentée par A. RemillieuxThe coating deposition on large optical components (diameter 350 mm) has required the development of new metrology tools at 1064 nm. To give realistic values of the optical performances, the whole surface of the component needs to be scanned. Our scatterometer (commercial system) has been upgraded to support large and heavy samples. The other metrology tools are prototypes we have developed. We can mention the absorption (photothermal effect) and birefringence bench, a control interferometer equipped with an original stitching option, the optical profilometer (RMS roughness and small defect measurements). A detailed description of these metrology benches will be exposed. Their sensitivity, accuracy and capability to map the optical properties of substrates or mirrors will be discussed. We will describe the recent developments: the stitching option adapted to the Micromap profilometer to measure the RMS roughness on larger area (exploration of a new spatial frequency domain), the accurate bulk absorption calibration
Exact Analytic Solutions for the Rotation of an Axially Symmetric Rigid Body Subjected to a Constant Torque
New exact analytic solutions are introduced for the rotational motion of a
rigid body having two equal principal moments of inertia and subjected to an
external torque which is constant in magnitude. In particular, the solutions
are obtained for the following cases: (1) Torque parallel to the symmetry axis
and arbitrary initial angular velocity; (2) Torque perpendicular to the
symmetry axis and such that the torque is rotating at a constant rate about the
symmetry axis, and arbitrary initial angular velocity; (3) Torque and initial
angular velocity perpendicular to the symmetry axis, with the torque being
fixed with the body. In addition to the solutions for these three forced cases,
an original solution is introduced for the case of torque-free motion, which is
simpler than the classical solution as regards its derivation and uses the
rotation matrix in order to describe the body orientation. This paper builds
upon the recently discovered exact solution for the motion of a rigid body with
a spherical ellipsoid of inertia. In particular, by following Hestenes' theory,
the rotational motion of an axially symmetric rigid body is seen at any instant
in time as the combination of the motion of a "virtual" spherical body with
respect to the inertial frame and the motion of the axially symmetric body with
respect to this "virtual" body. The kinematic solutions are presented in terms
of the rotation matrix. The newly found exact analytic solutions are valid for
any motion time length and rotation amplitude. The present paper adds further
elements to the small set of special cases for which an exact solution of the
rotational motion of a rigid body exists.Comment: "Errata Corridge Postprint" version of the journal paper. The
following typos present in the Journal version are HERE corrected: 1)
Definition of \beta, before Eq. 18; 2) sign in the statement of Theorem 3; 3)
Sign in Eq. 53; 4)Item r_0 in Eq. 58; 5) Item R_{SN}(0) in Eq. 6
Euler configurations and quasi-polynomial systems
In the Newtonian 3-body problem, for any choice of the three masses, there
are exactly three Euler configurations (also known as the three Euler points).
In Helmholtz' problem of 3 point vortices in the plane, there are at most three
collinear relative equilibria. The "at most three" part is common to both
statements, but the respective arguments for it are usually so different that
one could think of a casual coincidence. By proving a statement on a
quasi-polynomial system, we show that the "at most three" holds in a general
context which includes both cases. We indicate some hard conjectures about the
configurations of relative equilibrium and suggest they could be attacked
within the quasi-polynomial framework.Comment: 21 pages, 6 figure
The Hamiltonian formulation of General Relativity: myths and reality
A conventional wisdom often perpetuated in the literature states that: (i) a
3+1 decomposition of space-time into space and time is synonymous with the
canonical treatment and this decomposition is essential for any Hamiltonian
formulation of General Relativity (GR); (ii) the canonical treatment
unavoidably breaks the symmetry between space and time in GR and the resulting
algebra of constraints is not the algebra of four-dimensional diffeomorphism;
(iii) according to some authors this algebra allows one to derive only spatial
diffeomorphism or, according to others, a specific field-dependent and
non-covariant four-dimensional diffeomorphism; (iv) the analyses of Dirac
[Proc. Roy. Soc. A 246 (1958) 333] and of ADM [Arnowitt, Deser and Misner, in
"Gravitation: An Introduction to Current Research" (1962) 227] of the canonical
structure of GR are equivalent. We provide some general reasons why these
statements should be questioned. Points (i-iii) have been shown to be incorrect
in [Kiriushcheva et al., Phys. Lett. A 372 (2008) 5101] and now we thoroughly
re-examine all steps of the Dirac Hamiltonian formulation of GR. We show that
points (i-iii) above cannot be attributed to the Dirac Hamiltonian formulation
of GR. We also demonstrate that ADM and Dirac formulations are related by a
transformation of phase-space variables from the metric to lapse
and shift functions and the three-metric , which is not canonical. This
proves that point (iv) is incorrect. Points (i-iii) are mere consequences of
using a non-canonical change of variables and are not an intrinsic property of
either the Hamilton-Dirac approach to constrained systems or Einstein's theory
itself.Comment: References are added and updated, Introduction is extended,
Subsection 3.5 is added, 83 pages; corresponds to the published versio
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