21,979 research outputs found
Elastic scattering and the proton form factor
We compute the differential and the total cross sections for scattering
using the QCD pomeron model proposed by Landshoff and Nachtmann. This model is
quite dependent on the experimental electromagnetic form factor, and it is not
totally clear why this form factor gives good results even at moderate
transferred momentum. We exchange the eletromagnetic form factor by the
asymptotic QCD proton form factor determined by Brodsky and Lepage (BL) plus a
prescription for its low energy behavior dictated by the existence of a
dynamically generated gluon mass. We fit the data with this QCD inspired form
factor and a value for the dynamical gluon mass consistent with the ones
determined in the literature. Our results also provide a new determination of
the proton wave function at the origin, which appears in the BL form factor.Comment: 10 pages, 2 figures. Submitted to Physics Letters B. Submitted to
Phys. Lett.
Charge reversal of colloidal particles
A theory is presented for the effective charge of colloidal particles in
suspensions containing multivalent counterions. It is shown that if colloids
are sufficiently strongly charged, the number of condensed multivalent
counterion can exceed the bare colloidal charge leading to charge reversal.
Charge renormalization in suspensions with multivalent counterions depends on a
subtle interplay between the solvation energies of the multivalent counterions
in the bulk and near the colloidal surface. We find that the effective charge
is {\it not} a monotonically decreasing function of the multivalent salt
concentration. Furthermore, contrary to the previous theories, it is found that
except at very low concentrations, monovalent salt hinders the charge reversal.
This conclusion is in agreement with the recent experiments and simulations
Metastability of Asymptotically Well-Behaved Potential Games
One of the main criticisms to game theory concerns the assumption of full
rationality. Logit dynamics is a decentralized algorithm in which a level of
irrationality (a.k.a. "noise") is introduced in players' behavior. In this
context, the solution concept of interest becomes the logit equilibrium, as
opposed to Nash equilibria. Logit equilibria are distributions over strategy
profiles that possess several nice properties, including existence and
uniqueness. However, there are games in which their computation may take time
exponential in the number of players. We therefore look at an approximate
version of logit equilibria, called metastable distributions, introduced by
Auletta et al. [SODA 2012]. These are distributions that remain stable (i.e.,
players do not go too far from it) for a super-polynomial number of steps
(rather than forever, as for logit equilibria). The hope is that these
distributions exist and can be reached quickly by logit dynamics.
We identify a class of potential games, called asymptotically well-behaved,
for which the behavior of the logit dynamics is not chaotic as the number of
players increases so to guarantee meaningful asymptotic results. We prove that
any such game admits distributions which are metastable no matter the level of
noise present in the system, and the starting profile of the dynamics. These
distributions can be quickly reached if the rationality level is not too big
when compared to the inverse of the maximum difference in potential. Our proofs
build on results which may be of independent interest, including some spectral
characterizations of the transition matrix defined by logit dynamics for
generic games and the relationship of several convergence measures for Markov
chains
Can Maxwell's equations be obtained from the continuity equation?
We formulate an existence theorem that states that given localized scalar and
vector time-dependent sources satisfying the continuity equation, there exist
two retarded fields that satisfy a set of four field equations. If the theorem
is applied to the usual electromagnetic charge and current densities, the
retarded fields are identified with the electric and magnetic fields and the
associated field equations with Maxwell's equations. This application of the
theorem suggests that charge conservation can be considered to be the
fundamental assumption underlying Maxwell's equations.Comment: 14 pages. See the comment: "O. D. Jefimenko, Causal equations for
electric and magnetic fields and Maxwell's equations: comment on a paper by
Heras [Am. J. Phys. 76, 101 (2008)].
Scale Dependence of the Retarded van der Waals Potential
We study the ground state energy for a system of two hydrogen atoms coupled
to the quantized Maxwell field in the limit together with the
relative distance between the atoms increasing as , . In particular we determine explicitly the crossover function from the
van der Waals potential to the retarded van der Waals
potential, which takes place at scale .Comment: 19 page
Using state space differential geometry for nonlinear blind source separation
Given a time series of multicomponent measurements of an evolving stimulus,
nonlinear blind source separation (BSS) seeks to find a "source" time series,
comprised of statistically independent combinations of the measured components.
In this paper, we seek a source time series with local velocity cross
correlations that vanish everywhere in stimulus state space. However, in an
earlier paper the local velocity correlation matrix was shown to constitute a
metric on state space. Therefore, nonlinear BSS maps onto a problem of
differential geometry: given the metric observed in the measurement coordinate
system, find another coordinate system in which the metric is diagonal
everywhere. We show how to determine if the observed data are separable in this
way, and, if they are, we show how to construct the required transformation to
the source coordinate system, which is essentially unique except for an unknown
rotation that can be found by applying the methods of linear BSS. Thus, the
proposed technique solves nonlinear BSS in many situations or, at least,
reduces it to linear BSS, without the use of probabilistic, parametric, or
iterative procedures. This paper also describes a generalization of this
methodology that performs nonlinear independent subspace separation. In every
case, the resulting decomposition of the observed data is an intrinsic property
of the stimulus' evolution in the sense that it does not depend on the way the
observer chooses to view it (e.g., the choice of the observing machine's
sensors). In other words, the decomposition is a property of the evolution of
the "real" stimulus that is "out there" broadcasting energy to the observer.
The technique is illustrated with analytic and numerical examples.Comment: Contains 14 pages and 3 figures. For related papers, see
http://www.geocities.com/dlevin2001/ . New version is identical to original
version except for URL in the bylin
Investing in Socially Responsible Mutual Funds
We construct optimal portfolios of mutual funds whose objectives include socially responsible investment (SRI). Comparing portfolios of these funds to those constructed from the broader fund universe reveals the cost of imposing the SRI constraint on investors seeking the highest Sharpe ratio. This SRI cost depends crucially on the investor\u27s views about asset pricing models and stock-picking skill by fund managers. To an investor who believes strongly in the CAPM and rules out managerial skill, i.e. a market-index investor, the cost of the SRI constraint is typically just a few basis points per month, measured in certainly-equivalent loss. To an investor who still disallows skill but instead believes to some degree in pricing models that associate higher returns with exposures to size, value, and momentum factors, the SRI constraint is much costlier, typically by at least 30 basis points per month. The SRI constraint imposes large costs on investors whose beliefs allow a substantial amount of fund-manager skill, i.e., investors who rely heavily on individual funds\u27 track records to predict future performance
Thermoelastic Noise and Homogeneous Thermal Noise in Finite Sized Gravitational-Wave Test Masses
An analysis is given of thermoelastic noise (thermal noise due to
thermoelastic dissipation) in finite sized test masses of laser interferometer
gravitational-wave detectors. Finite-size effects increase the thermoelastic
noise by a modest amount; for example, for the sapphire test masses tentatively
planned for LIGO-II and plausible beam-spot radii, the increase is less than or
of order 10 per cent. As a side issue, errors are pointed out in the currently
used formulas for conventional, homogeneous thermal noise (noise associated
with dissipation which is homogeneous and described by an imaginary part of the
Young's modulus) in finite sized test masses. Correction of these errors
increases the homogeneous thermal noise by less than or of order 5 per cent for
LIGO-II-type configurations.Comment: 10 pages and 3 figures; RevTeX; submitted to Physical Review
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