169 research outputs found
Properties of equations of the continuous Toda type
We study a modified version of an equation of the continuous Toda type in 1+1
dimensions. This equation contains a friction-like term which can be switched
off by annihilating a free parameter \ep. We apply the prolongation method,
the symmetry and the approximate symmetry approach. This strategy allows us to
get insight into both the equations for \ep =0 and \ep \ne 0, whose
properties arising in the above frameworks are mutually compared. For \ep =0,
the related prolongation equations are solved by means of certain series
expansions which lead to an infinite- dimensional Lie algebra. Furthermore,
using a realization of the Lie algebra of the Euclidean group , a
connection is shown between the continuous Toda equation and a linear wave
equation which resembles a special case of a three-dimensional wave equation
that occurs in a generalized Gibbons-Hawking ansatz \cite{lebrun}. Nontrivial
solutions to the wave equation expressed in terms of Bessel functions are
determined.
For \ep\,\ne\,0, we obtain a finite-dimensional Lie algebra with four
elements. A matrix representation of this algebra yields solutions of the
modified continuous Toda equation associated with a reduced form of a
perturbative Liouville equation. This result coincides with that achieved in
the context of the approximate symmetry approach. Example of exact solutions
are also provided. In particular, the inverse of the exponential-integral
function turns out to be defined by the reduced differential equation coming
from a linear combination of the time and space translations. Finally, a Lie
algebra characterizing the approximate symmetries is discussed.Comment: LaTex file, 27 page
Calculation of gluon and four-quark condensates from the operator expansion
The magnitudes of gluon and four-quark condensates are found from the
analysis of vector mesons consisting of light quarks (the families of
and mesons) in the 3 loops approximation. The QCD model with infinite
number of vector mesons is used to describe the function . This model
describes well the experimental function . Polarization operators
calculated with this model coincide with the Wilson operator expansion at large
. The improved perturbative theory, such that the polarization operators
have correct analytical properties, is used. The result is . The electronic widths of and
are calculated.Comment: 18 pages, latex, changed content slightl
Sixth-Order Vacuum-Polarization Contribution to the Lamb Shift of the Muonic Hydrogen
The sixth-order electron-loop vacuum-polarization contribution to the
Lamb shift of the muonic hydrogen ( bound
state) has been evaluated numerically. Our result is 0.007608(1) meV. This
eliminates the largest uncertainty in the theoretical calculation. Combined
with the proposed precision measurement of the Lamb shift it will lead to a
very precise determination of the proton charge radius.Comment: 4 pages, 5 figures the totoal LS number is change
A class of nonlinear wave equations containing the continuous Toda case
We consider a nonlinear field equation which can be derived from a binomial
lattice as a continuous limit. This equation, containing a perturbative
friction-like term and a free parameter , reproduces the Toda case (in
absence of the friction-like term) and other equations of physical interest, by
choosing particular values of . We apply the symmetry and the
approximate symmetry approach, and the prolongation technique. Our main purpose
is to check the limits of validity of different analytical methods in the study
of nonlinear field equations. We show that the equation under investigation
with the friction-like term is characterized by a finite-dimensional Lie
algebra admitting a realization in terms of boson annhilation and creation
operators. In absence of the friction-like term, the equation is linearized and
connected with equations of the Bessel type. Examples of exact solutions are
displayed, and the algebraic structure of the equation is discussed.Comment: Latex file + [equations.sty], 22 p
Improving the energy efficiency of wind turbines for charging batteries
The article describes the method for determining the optimal angular velocity and the number of turns of the generator winding on permanent magnets powered by a wind turbine operating in specific operating conditions according to the wind speed regime. The optimization criterion is the maximum potential of energy that can be used to charge the battery. The permissible power of the generator and wind turbine, current and battery charging voltage are accepted as limiting factors. The restriction is provided by connecting a ballast resistor to the generator output. The power developed by the turbine is determined taking into account the wind energy utilization factor, which depends on the angular velocity of its shaft and wind speed. Two variants of power limitation are compared: by limiting the angular velocity by aerodynamic means and by stopping the wind turbine. The return of energy to charging in both cases is determined taking into account the distribution of wind speeds, obeying the Weibull probability distribution law. As an example, the calculation of the possible annual power generation for charging a battery with a capacity of 200 A∙h with a voltage of 24 volts from a synchron generator with a number of poles of 48 driven by a wind turbine with a radius of 2 meters, operating in an area with an average wind speed of 5 m/s. The calculation shows that for the parameters and operating conditions of the electrical installation used in the example, the maximum annual energy output (3.3 × 103 kWh) is observed at optimal 11 turns of the winding at each of the poles of the generator. The deviation of the number of turns from the optimal one in both directions by 2 times leads, with the same dimensions of the wind turbine, to a decrease in annual energy output by 3...5 times, which is a clear proof of the need to carry out such a calculation for each specific wind turbine
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
New perturbation theory representation of the conformal symmetry breaking effects in gauge quantum field theory models
We propose a hypothesis on the detailed structure for the representation of
the conformal symmetry breaking term in the basic Crewther relation generalized
in the perturbation theory framework in QCD renormalized in the scheme. We establish the validity of this representation in the
approximation. Using the variant of the generalized Crewther
relation formulated here allows finding relations between specific
contributions to the QCD perturbation series coefficients for the flavor
nonsinglet part of the Adler function for the electron-positron
annihilation in hadrons and to the perturbation series coefficients for the
Bjorken sum rule for the polarized deep-inelastic lepton-nucleon
scattering. We find new relations between the coefficients of
and . Satisfaction of one of them serves as an
additional theoretical verification of the recent computer analytic
calculations of the terms of order in the expressions for these
two quantities.Comment: 12 pages, Title modified, abstract modified, improved and extended
variant of the talks, presented at Int. Seminar "Quarks-2010" (6-12 June,
2010, Kolomna) and Int. Workshop Hadron Structure and QCD: From Low to High
Energies (5-9 July 2010, Gatchina
Lie group analysis for multi-scale plasma dynamics
An application of approximate transformation groups to study dynamics of a
system with distinct time scales is discussed. The utilization of the
Krylov-Bogoliubov-Mitropolsky method of averaging to find solutions of the Lie
equations is considered. Physical illustrations from the plasma kinetic theory
demonstrate the potentialities of the suggested approach. Several examples of
invariant solutions for the system of the Vlasov-Maxwell equations for the
two-component (electron-ion) plasma are presented.Comment: Latex, 15 pages, 7 figure. This is an enlarged contribution to
Journal of Nonlinear Mathematical Physics v.18, Suppl. 1 (2011) p.163-175
with modest stylistic corrections introduced mainly in the third Sectio
Looking through the QCD conformal window with perturbation theory
We study the conformal window of QCD using perturbation theory, starting from the perturbative upper edge and going down as much as we can towards the strongly coupled regime. We do so by exploiting the available five-loop
computation of the -function and employing Borel resummation techniques both for the ordinary perturbative series and for the Banks-Zaks conformal expansion. Large- results are also used. We argue that the perturbative series for the -function is most likely asymptotic and non-Borel resummable, yet Borel resummation techniques allow to improve on ordinary perturbation theory. We find
substantial evidence that QCD with flavours flows in the IR to a conformal field theory. Though the evidence is weaker, we find indications that also might sit within the conformal window. We also compute the value
of the mass anomalous dimension at the fixed point and compare it with the available lattice results. The conformal window might extend for lower values of , but our methods break down for n_f<11, where we expect that non-perturbative effects become important. A similar analysis is performed in the Veneziano limit
What two models may teach us about duality violations in QCD
Though the operator product expansion is applicable in the calculation of
current correlation functions in the Euclidean region, when approaching the
Minkowskian domain, violations of quark-hadron duality are expected to occur,
due to the presence of bound-state or resonance poles. In QCD finite-energy sum
rules, contour integrals in the complex energy plane down to the Minkowskian
axis have to be performed, and thus the question arises what the impact of
duality violations may be. The structure and possible relevance of duality
violations is investigated on the basis of two models: the Coulomb system and a
model for light-quark correlators which has already been studied previously. As
might yet be naively expected, duality violations are in some sense "maximal"
for zero-width bound states and they become weaker for broader resonances whose
poles lie further away from the physical axis. Furthermore, to a certain
extent, they can be suppressed by choosing appropriate weight functions in the
finite-energy sum rules. A simplified Ansatz for including effects of duality
violations in phenomenological QCD sum rule analyses is discussed as well.Comment: 17 pages, 6 figures; version to appear in JHE
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