8,793 research outputs found
Probability distribution of the maximum of a smooth temporal signal
We present an approximate calculation for the distribution of the maximum of
a smooth stationary temporal signal X(t). As an application, we compute the
persistence exponent associated to the probability that the process remains
below a non-zero level M. When X(t) is a Gaussian process, our results are
expressed explicitly in terms of the two-time correlation function,
f(t)=.Comment: Final version (1 major typo corrected; better introduction). Accepted
in Phys. Rev. Let
Kowalevski's analysis of the swinging Atwood's machine
We study the Kowalevski expansions near singularities of the swinging
Atwood's machine. We show that there is a infinite number of mass ratios
where such expansions exist with the maximal number of arbitrary constants.
These expansions are of the so--called weak Painlev\'e type. However, in view
of these expansions, it is not possible to distinguish between integrable and
non integrable cases.Comment: 30 page
Tau mesonic decays and strong anomaly of PCAC
Strong anomaly of the PCAC is found in and
in the chiral limit. It originates in WZW anomaly. Theoretical
result of agrees with data well and the
measurement of will confirm the strong anomaly
of PCAC. The strong anomaly of PCAC is studied.Comment: 27 page
A Mathematical Theory of Stochastic Microlensing II. Random Images, Shear, and the Kac-Rice Formula
Continuing our development of a mathematical theory of stochastic
microlensing, we study the random shear and expected number of random lensed
images of different types. In particular, we characterize the first three
leading terms in the asymptotic expression of the joint probability density
function (p.d.f.) of the random shear tensor at a general point in the lens
plane due to point masses in the limit of an infinite number of stars. Up to
this order, the p.d.f. depends on the magnitude of the shear tensor, the
optical depth, and the mean number of stars through a combination of radial
position and the stars' masses. As a consequence, the p.d.f.s of the shear
components are seen to converge, in the limit of an infinite number of stars,
to shifted Cauchy distributions, which shows that the shear components have
heavy tails in that limit. The asymptotic p.d.f. of the shear magnitude in the
limit of an infinite number of stars is also presented. Extending to general
random distributions of the lenses, we employ the Kac-Rice formula and Morse
theory to deduce general formulas for the expected total number of images and
the expected number of saddle images. We further generalize these results by
considering random sources defined on a countable compact covering of the light
source plane. This is done to introduce the notion of {\it global} expected
number of positive parity images due to a general lensing map. Applying the
result to microlensing, we calculate the asymptotic global expected number of
minimum images in the limit of an infinite number of stars, where the stars are
uniformly distributed. This global expectation is bounded, while the global
expected number of images and the global expected number of saddle images
diverge as the order of the number of stars.Comment: To appear in JM
Symmetries of modules of differential operators
Let be the space of tensor densities of degree (or
weight) on the circle . The space of -th order linear differential operators from
to is a natural module over
, the diffeomorphism group of . We determine the
algebra of symmetries of the modules , i.e.,
the linear maps on commuting with the
-action. We also solve the same problem in the case of
straight line (instead of ) and compare the results in the
compact and non-compact cases.Comment: 29 pages, LaTeX, 4 figure
Photon Splitting in a Very Strong Magnetic Field
Photon splitting in a very strong magnetic field is analyzed for energy
. The amplitude obtained on the base of operator-diagram technique
is used. It is shown that in a magnetic field much higher than critical one the
splitting amplitude is independent on the field. Our calculation is in a good
agreement with previous results of Adler and in a strong contradiction with
recent paper of Mentzel et al.Comment: 5 pages,Revtex , 4 figure
Generalization of Linearized Gouy-Chapman-Stern Model of Electric Double Layer for Nanostructured and Porous Electrodes: Deterministic and Stochastic Morphology
We generalize linearized Gouy-Chapman-Stern theory of electric double layer
for nanostructured and morphologically disordered electrodes. Equation for
capacitance is obtained using linear Gouy-Chapman (GC) or
Debye-ckel equation for potential near complex
electrode/electrolyte interface. The effect of surface morphology of an
electrode on electric double layer (EDL) is obtained using "multiple scattering
formalism" in surface curvature. The result for capacitance is expressed in
terms of the ratio of Gouy screening length and the local principal radii of
curvature of surface. We also include a contribution of compact layer, which is
significant in overall prediction of capacitance. Our general results are
analyzed in details for two special morphologies of electrodes, i.e.
"nanoporous membrane" and "forest of nanopillars". Variations of local shapes
and global size variations due to residual randomness in morphology are
accounted as curvature fluctuations over a reference shape element.
Particularly, the theory shows that the presence of geometrical fluctuations in
porous systems causes enhanced dependence of capacitance on mean pore sizes and
suppresses the magnitude of capacitance. Theory emphasizes a strong influence
of overall morphology and its disorder on capacitance. Finally, our predictions
are in reasonable agreement with recent experimental measurements on
supercapacitive mesoporous systems
Dynamical Reduction Models: present status and future developments
We review the major achievements of the dynamical reduction program, showing
why and how it provides a unified, consistent description of physical
phenomena, from the microscopic quantum domain to the macroscopic classical
one. We discuss the difficulties in generalizing the existing models in order
to comprise also relativistic quantum field theories. We point out possible
future lines of research, ranging from mathematical physics to phenomenology.Comment: 12 pages. Contribution to the Proceedings of the "Third International
Workshop DICE2006", Castello di Piombino (Tuscany), September 11-15, 2006.
Minor changes mad
- …