39 research outputs found
A Laplace variational iteration strategy for the solution of differential equations
AbstractThe aim of this article is to introduce a novel Laplace variational numerical scheme, based on the variational iteration method (VIM) and Laplace transform, for the solution of certain classes of linear and nonlinear differential equations. The strategy is outlined and then illustrated through a number of test examples. The results assert that this alternative approach yields accurate results, converges rapidly and handles impulse functions and the ones with discontinuities
The shrinking instability of toroidal liquid droplets in the Stokes flow regime
We analyze the stability and dynamics of toroidal liquid droplets. In
addition to the Rayleigh instabilities akin to those of a cylindrical droplet
there is a shrinking instability that is unique to the topology of the torus
and dominates in the limit that the aspect ratio is near one (fat tori). We
first find an analytic expression for the pressure distribution inside the
droplet. We then determine the velocity field in the bulk fluid, in the Stokes
flow regime, by solving the biharmonic equation for the stream function. The
flow pattern in the external fluid is analyzed qualitatively by exploiting
symmetries. This elucidates the detailed nature of the shrinking mode and the
swelling of the cross-section following from incompressibility. Finally the
shrinking rate of fat toroidal droplets is derived by energy conservation.Comment: 6 pages, 7 figure
On an asymptotic estimate of the -loop correction in perturbative QCD
A recently proposed method of estimating the asymptotic behaviour of QCD
perturbation theory coefficients is critically reviewed and shown to contain
numerous invalid mathematical operations and unsubstantiated assumptions. We
discuss in detail why this procedure, based solely on renormalization group
(RG) considerations and analyticity constraints, cannot lead to such estimates.
We stress the importance of correct renormalization scheme (RS) dependence of
any meaningful asymptotic estimate and argue that the unambiguous summation of
QCD perturbation expansions for physical quantities requires information from
outside of perturbation theory itself.Comment: PRA-HEP-92/17, Latex, 20 pages of text plus 5 figures contained in 5
separate PS files. Four of them (corresponding to Figs.1,2,3,5) are appended
at the end of this file, the (somewhat larger one) corresponding to Fig.4 can
be obtained from any of the mentioned E-mail addresses upon request. E-mail
connections: J. Chyla - [email protected]) or h1kchy@dhhdesy3 P. Kolar -
[email protected]
Wrapped branes with fluxes in 8d gauged supergravity
We study the gravity dual of several wrapped D-brane configurations in
presence of 4-form RR fluxes partially piercing the unwrapped directions. We
present a systematic approach to obtain these solutions from those without
fluxes. We use D=8 gauged supergravity as a starting point to build up these
solutions. The configurations include (smeared) M2-branes at the tip of a G_2
cone on S^3 x S^3, D2-D6 branes with the latter wrapping a special Lagrangian
3-cycle of the complex deformed conifold and an holomorphic sphere in its
cotangent bundle T^*S^2, D3-branes at the tip of the generalized resolved
conifold, and others obtained by means of T duality and KK reduction. We
elaborate on the corresponding N=1 and N=2 field theories in 2+1 dimensions.Comment: 32 pages, LateX, v2: minor changes, reference added, v3: section
3.5.2 improve
Solitary and periodic solutions of the generalized Kuramoto-Sivashinsky equation
The generalized Kuramoto-Sivashinsky equation in the case of the power
nonlinearity with arbitrary degree is considered. New exact solutions of this
equation are presented
Calculations of binding energies and masses of heavy quarkonia using renormalon cancellation
We use various methods of Borel integration to calculate the binding ground
energies and masses of b-bbar and t-tbar quarkonia. The methods take into
account the leading infrared renormalon structure of the hard+soft part of the
binding energies E(s), and of the corresponding quark pole masses m_q, where
the contributions of these singularities in M(s) = 2 m_q + E(s) cancel.
Beforehand, we carry out the separation of the binding energy into its
hard+soft and ultrasoft parts. The resummation formalisms are applied to
expansions of m_q and E(s) in terms of quantities which do not involve
renormalon ambiguity, such as MSbar quark mass, and alpha_s. The
renormalization scales are different in calculations of m_q, E(s) and E(us).
The MSbar mass of b quark is extracted, and the binding energies of t-tbar and
the peak (resonance) energies for (t+tbar) production are obtained.Comment: 23 pages, 8 double figures, revtex4; the version to appear in
Phys.Rev.D; extended discussion between Eqs.(25) and (26); the paragraph
between Eqs.(32) and (33) is new and explains the numerical dependence of the
residue parameter on the factorization scale; several new references were
added; acknowledgments were modified; the numerical results are unchange