20,105 research outputs found
New expression for the K-shell ionization
A new expression for the total K-shell ionization cross section by electron
impact based on the relativistic extension of the binary encounter Bethe (RBEB)
model, valid from ionization threshold up to relativistic energies, is
proposed. The new MRBEB expression is used to calculate the K-shell ionization
cross sections by electron impact for the selenium atom. Comparison with all,
to our knowledge, available experimental data shows good agreement
Central limit theorem for fluctuations in the high temperature region of the Sherrington-Kirkpatrick spin glass model
In a region above the Almeida-Thouless line, where we are able to control the
thermodynamic limit of the Sherrington-Kirkpatrick model and to prove replica
symmetry, we show that the fluctuations of the overlaps and of the free energy
are Gaussian, on the scale N^{-1/2}, for N large. The method we employ is based
on the idea, we recently developed, of introducing quadratic coupling between
two replicas. The proof makes use of the cavity equations and of concentration
of measure inequalities for the free energy.Comment: 18 page
The Ising-Sherrington-Kirpatrick model in a magnetic field at high temperature
We study a spin system on a large box with both Ising interaction and
Sherrington-Kirpatrick couplings, in the presence of an external field. Our
results are: (i) existence of the pressure in the limit of an infinite box.
When both Ising and Sherrington-Kirpatrick temperatures are high enough, we
prove that: (ii) the value of the pressure is given by a suitable replica
symmetric solution, and (iii) the fluctuations of the pressure are of order of
the inverse of the square of the volume with a normal distribution in the
limit. In this regime, the pressure can be expressed in terms of random field
Ising models
On the Stability Functional for Conservation Laws
This note is devoted to the explicit construction of a functional defined on
all pairs of \L1 functions with small total variation, which is equivalent to
the \L1 distance and non increasing along the trajectories of a given system
of conservation laws. Two different constructions are provided, yielding an
extension of the original stability functional by Bressan, Liu and Yang.Comment: 26 page
Photoexcitation of lasers and chemical reactions for NASA missions: A theoretical study
The possibility of obtaining CW laser oscillation by optical pumping in the infrared at an elevated gas pressure is reviewed. A specific example utilizing a mixture of CO and NO gases is included. The gas pressures considered are in excess of several atmospheres. Laser frequency tuning over a broad region becomes possible at such elevated gas pressures due to collisional broadening of the amplifying transitions. The prior-rate and surprisal analysis are applied to obtain detailed VV and VT rates for CO and NO molecules and the transfer rates in a CO-NO gas mixture. The analysis is capable of giving temperature dependence of the rate constants. Computer estimates of the rates are presented for vibrational levels up to v = 50. The results show that in the high-lying vibrational states the VV transfer rates with Delta nu = 2 become appreciable
The replica symmetric behavior of the analogical neural network
In this paper we continue our investigation of the analogical neural network,
paying interest to its replica symmetric behavior in the absence of external
fields of any type. Bridging the neural network to a bipartite spin-glass, we
introduce and apply a new interpolation scheme to its free energy that
naturally extends the interpolation via cavity fields or stochastic
perturbations to these models. As a result we obtain the free energy of the
system as a sum rule, which, at least at the replica symmetric level, can be
solved exactly. As a next step we study its related self-consistent equations
for the order parameters and their rescaled fluctuations, found to diverge on
the same critical line of the standard Amit-Gutfreund-Sompolinsky theory.Comment: 17 page
The Compressible to Incompressible Limit of 1D Euler Equations: the Non Smooth Case
We prove a rigorous convergence result for the compressible to incompressible
limit of weak entropy solutions to the isothermal 1D Euler equations.Comment: 16 page
General properties of overlap probability distributions in disordered spin systems. Toward Parisi ultrametricity
For a very general class of probability distributions in disordered Ising
spin systems, in the thermodynamical limit, we prove the following property for
overlaps among real replicas. Consider the overlaps among s replicas. Add one
replica s+1. Then, the overlap q(a,s+1) between one of the first s replicas,
let us say a, and the added s+1 is either independent of the former ones, or it
is identical to one of the overlaps q(a,b), with b running among the first s
replicas, excluding a. Each of these cases has equal probability 1/s.Comment: LaTeX2e, 11 pages. Submitted to Journal of Physics A: Mathematical
and General. Also available at
http://rerumnatura.zool.su.se/stefano/ms/ghigu.p
Spin Glass Computations and Ruelle's Probability Cascades
We study the Parisi functional, appearing in the Parisi formula for the
pressure of the SK model, as a functional on Ruelle's Probability Cascades
(RPC). Computation techniques for the RPC formulation of the functional are
developed. They are used to derive continuity and monotonicity properties of
the functional retrieving a theorem of Guerra. We also detail the connection
between the Aizenman-Sims-Starr variational principle and the Parisi formula.
As a final application of the techniques, we rederive the Almeida-Thouless line
in the spirit of Toninelli but relying on the RPC structure.Comment: 20 page
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