1,791 research outputs found
Solitons and kinks in a general car-following model
We study a car-following model of traffic flow which assumes only that a
car's acceleration depends on its own speed, the headway ahead of it, and the
rate of change of headway, with only minimal assumptions about the functional
form of that dependence. The velocity of uniform steady flow is found
implicitly from the acceleration function, and its linear stability criterion
can be expressed simply in terms of it. Crucially, unlike in previously
analyzed car-following models, the threshold of absolute stability does not
generally coincide with an inflection point in the steady velocity function.
The Burgers and KdV equations can be derived under the usual assumptions, but
the mKdV equation arises only when absolute stability does coincide with an
inflection point. Otherwise, the KdV equation applies near absolute stability,
while near the inflection point one obtains the mKdV equation plus an extra,
quadratic term. Corrections to the KdV equation "select" a single member of the
one-parameter set of soliton solutions. In previous models this has always
marked the threshold of a finite- amplitude instability of steady flow, but
here it can alternatively be a stable, small-amplitude jam. That is, there can
be a forward bifurcation from steady flow. The new, augmented mKdV equation
which holds near an inflection point admits a continuous family of kink
solutions, like the mKdV equation, and we derive the selection criterion
arising from the corrections to this equation.Comment: 25 page
The Goldberger -- Treiman Relation, and at
The Goldberger-Treiman relation is shown to persist in the chiral limit at
finite temperatures to order . The dependence of turns out to
be the same as for , , while is temperature independent to this order. The baryon octet and
couplings also behave as if only pions are massless in the
pseudoscalar meson octet.Comment: 7p, NSF-ITP-93-145, BUTP-93/27, PUTP-1433, November 199
Can one see the number of colors in eta, eta-prime --> pi^+ pi^- gamma?
We investigate the decays eta, eta-prime --> pi^+ pi^- gamma up to
next-to-leading order in the framework of the combined 1/N_c and chiral
expansions. Counter terms of unnatural parity at next-to-leading order with
unknown couplings are important to acommodate the results both to the
experimental decay width and the photon spectrum. The presence of these
coefficients does not allow for a determination of the number of colors from
these decays.Comment: 8 pages, 2 figure
Sigma-term physics in the perturbative chiral quark model
We apply the perturbative chiral quark model (PCQM) at one loop to analyse
meson-baryon sigma-terms. Analytic expressions for these quantities are
obtained in terms of fundamental parameters of low-energy pion-nucleon physics
(weak pion decay constant, axial nucleon coupling, strong pion-nucleon form
factor) and of only one model parameter (radius of the nucleonic three-quark
core). Our result for the piN sigma term of about 45 MeV is in good agreement
with the value deduced by Gasser, Leutwyler and Sainio using
dispersion-relation techniques and exploiting the chiral symmetry constraints.Comment: 19 pages, LaTeX-file, 2 Figure
Critical Analysis of Baryon Masses and Sigma-Terms in Heavy Baryon Chiral Perturbation Theory
We present an analysis of the octet baryon masses and the and
--terms in the framework of heavy baryon chiral perturbation theory. At
next-to-leading order, , knowledge of the baryon masses and
allows to determine the three corresponding finite
low--energy constants and to predict the the two --terms
. We also include the spin-3/2 decuplet in the
effective theory. The presence of the non--vanishing energy scale due to the
octet--decuplet splitting shifts the average octet baryon mass by an infinite
amount and leads to infinite renormalizations of the low--energy constants. The
first observable effect of the decuplet intermediate states to the baryon
masses starts out at order . We argue that it is not sufficient to retain
only these but no other higher order terms to achieve a consistent description
of the three--flavor scalar sector of baryon CHPT. In addition, we critically
discuss an SU(2) result which allows to explain the large shift of via intermediate states.Comment: 18 pp, TeX, BUTP-93/05 and CRN-93-0
Parity-Violating Electron Scattering and Neucleon Structure
The measurement of parity violation in the helicity dependence of
electron-nucleon scattering provides unique information about the basic quark
structure of the nucleons. In this review, the general formalism of
parity-violating electron scattering is presented, with emphasis on elastic
electron-nucleon scattering. The physics issues addressed by such experiments
is discussed, and the major goals of the presently envisioned experimental
program are identified. %General aspects of the experimental technique are
reviewed and A summary of results from a recent series of experiments is
presented and the future prospects of this program are also discussed.Comment: 45 pages, 9 figure
Pion Mass Effects in the Large Limit of \chiPT
We compute the large effective action of the non-linear
sigma model including the effect of the pion mass to order
. This action is more complex than the one corresponding
to the chiral limit not only because of the pion propagators but also because
chiral symmetry produce new interactions proportional to .
We renormalize the action by including the appropriate counter terms and find
the renormalization group equations for the corresponding couplings. Then we
estudy the unitarity propierties of the scattering amplitudes. Finally our
results are applied to the particular case of the linear sigma model and also
are used to fit the pion scattering phase shifts.Comment: FT/UCM/18/9
Stringent constraints on the scalar K pi form factor from analyticity, unitarity and low-energy theorems
We investigate the scalar K pi form factor at low energies by the method of
unitarity bounds adapted so as to include information on the phase and modulus
along the elastic region of the unitarity cut. Using at input the values of the
form factor at t=0 and the Callan-Treiman point, we obtain stringent
constraints on the slope and curvature parameters of the Taylor expansion at
the origin. Also, we predict a quite narrow range for the higher order ChPT
corrections at the second Callan-Treiman point.Comment: 5 pages latex, uses EPJ style files, 3 figures, replaced with version
accepted by EPJ
Two loops calculation in chiral perturbation theory and the unitarization program of current algebra
In this paper we compare two loop Chiral Perturbation Theory (ChPT)
calculation of pion-pion scattering with the unitarity second order correction
to the current algebra soft-pion theorem. It is shown that both methods lead to
the same analytic structure for the scattering amplitude.Comment: 13 pages, Revtex 3.0, no figures, submitted to Phys. Lett.
Contributions of order to form factors and unitarity of the CKM matrix
The form factors for the semileptonic decay are computed to
order in generalized chiral perturbation theory. The main difference
with the standard expressions consists in contributions quadratic in
quark masses, which are described by a single divergence-free low-energy
constant, . A new simultaneous analysis is presented for the CKM matrix
element , the ratio , decay rates and the
scalar form factor slope . This framework easily accommodates the
precise value for deduced from superallowed nuclear -decays
- …