120 research outputs found
Discrete Lagrangian systems on the Virasoro group and Camassa-Holm family
We show that the continuous limit of a wide natural class of the
right-invariant discrete Lagrangian systems on the Virasoro group gives the
family of integrable PDE's containing Camassa-Holm, Hunter-Saxton and
Korteweg-de Vries equations. This family has been recently derived by Khesin
and Misiolek as Euler equations on the Virasoro algebra for
-metrics. Our result demonstrates a universal nature of
these equations.Comment: 6 pages, no figures, AMS-LaTeX. Version 2: minor changes. Version 3:
minor change
Yang-Baxter maps and multi-field integrable lattice equations
A variety of Yang-Baxter maps are obtained from integrable multi-field
equations on quad-graphs. A systematic framework for investigating this
connection relies on the symmetry groups of the equations. The method is
applied to lattice equations introduced by Adler and Yamilov and which are
related to the nonlinear superposition formulae for the B\"acklund
transformations of the nonlinear Schr\"odinger system and specific
ferromagnetic models.Comment: 16 pages, 4 figures, corrected versio
Spectroscopy of Baryons Containing Two Heavy Quarks in Nonperturbative Quark Dynamics
We have studied the three quark systems in an Effective Hamiltonian approach
in QCD. With only two parameters: the string tension sigma and the strong
coupling constant alpha_s we obtain a good description of the ground state
light and heavy baryons. The prediction of masses of the doubly heavy baryons
not discovered yet are also given. In particular, a mass of 3620 MeV for the
lightest (ccu) baryon is found by employing the hyperspherical formalism to the
three quark confining potential with the string junction.Comment: 8 pages, LaTe
LR and L+R Systems
We consider coupled nonholonomic LR systems on the product of Lie groups. As
examples, we study -dimensional variants of the spherical support system and
the rubber Chaplygin sphere. For a special choice of the inertia operator, it
is proved that the rubber Chaplygin sphere, after reduction and a time
reparametrization becomes an integrable Hamiltonian system on the
--dimensional sphere. Also, we showed that an arbitrary L+R system
introduced by Fedorov can be seen as a reduced system of an appropriate coupled
LR system.Comment: 18 pages, 1 figur
Diquark and triquark correlations in the deconfined phase of QCD
We use the non-perturbative Q\bar Q potential at finite temperatures derived
in the Field Correlator Method to obtain binding energies for the lowest
eigenstates in the Q\bar Q and QQQ systems (Q=c,b). The three--quark problem is
solved by the hyperspherical method. The solution provides an estimate of the
melting temperature and the radii for the different diquark and triquark bound
states. In particular we find that J/\psi and ground states survive up to
T \sim 1.3 T_c, where T_c is the critical temperature, while the corresponding
bottomonium states survive even up to higher temperature, T \sim 2.2 T_c.Comment: 11 pages, 1 figure; published versio
Rapid changes in root HvPIP2; 2 aquaporins abundance and ABA concentration are required to enhance root hydraulic conductivity and maintain leaf water potential in response to increased evaporative demand
To address the involvement of abscisic acid (ABA) in regulating transpiration and root hydraulic conductivity (Lp(Root)) and their relative importance for maintaining leaf hydration, the ABA-deficient barley mutant Az34 and its parental wild-type (WT) genotype (cv. Steptoe) were grown in hydroponics and exposed to changes in atmospheric vapour pressure deficit (VPD) imposed by air warming. WTplants were capable of maintaining leaf water potential (psi(L)) that was likely due to increased Lp(Root) enabling higher water flow from the roots, which increased in response to air warming. The increased Lp(Root) and immunostaining for HvPIP2; 2 aquaporins (AQPs) correlated with increased root ABA content of WT plants when exposed to increased air temperature. The failure of Az34 to maintain psi(L) during air warming may be due to lower Lp(Root) than WT plants, and an inability to respond to changes in air temperature. The correlation between root ABA content and Lp(Root) was further supported by increased root hydraulic conductivity in both genotypes when treated with exogenous ABA (10(-5) M). Thus the ability of the root system to rapidly regulate ABA levels (and thence aquaporin abundance and hydraulic conductivity) seems important to maintain leaf hydration
A discrete time relativistic Toda lattice
Four integrable symplectic maps approximating two Hamiltonian flows from the
relativistic Toda hierarchy are introduced. They are demostrated to belong to
the same hierarchy and to examplify the general scheme for symplectic maps on
groups equiped with quadratic Poisson brackets. The initial value problem for
the difference equations is solved in terms of a factorization problem in a
group. Interpolating Hamiltonian flows are found for all the maps.Comment: 32 pages, LaTe
Leptonic widths of high excitations in heavy quarkonia
Agreement with the measured electronic widths of the ,
, and resonances is shown to be reached if two
effects are taken into account: a flattening of the confining potential at
large distances and a total screening of the gluon-exchange interaction at
r\ga 1.2 fm. The leptonic widths of the unobserved and
resonances: keV and
keV are predicted.Comment: 11 pages revtex
Commutator identities on associative algebras and integrability of nonlinear pde's
It is shown that commutator identities on associative algebras generate
solutions of linearized integrable equations. Next, a special kind of the
dressing procedure is suggested that in a special class of integral operators
enables to associate to such commutator identity both nonlinear equation and
its Lax pair. Thus problem of construction of new integrable pde's reduces to
construction of commutator identities on associative algebras.Comment: 12 page
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