710 research outputs found
On the pulsating strings in AdS_4 x CP3
We study the class of pulsating strings on AdS_4 x CP3. Using a generalized
ansatz for pulsating string configurations we find new solutions of this class.
Further we quasi-classically quantize the theory and obtain the first
corrections to the energy. The latter, due to AdS/CFT correspondence, is
supposed to give the anomalous dimensions of operators of the gauge theory dual
N=6 Chern-Simons theory.Comment: references adde
Large J expansion in ABJM theory revisited
Recently there has been progress in the computation of the anomalous
dimensions of gauge theory operators at strong coupling by making use of
AdS/CFT correspondence. On string theory side they are given by dispersion
relations in the semiclassical regime. We revisit the problem of large charges
expansion of the dispersion relations for simple semiclassical strings in
background. We present the calculation of the
corresponding anomalous dimensions of the gauge theory operators to an
arbitrary order using three different methods. Although the results of the
three methods look different, power series expansions show their consistency.Comment: 24 pages, 2 figure
On the pulsating strings in Sasaki-Einstein spaces
We study the class of pulsating strings in AdS_5 x Y^{p,q} and AdS_5 x
L^{p,q,r}. Using a generalized ansatz for pulsating string configurations, we
find new solutions for this class in terms of Heun functions, and derive the
particular case of AdS_5 x T^{1,1}, which was analyzed in arXiv:1006.1539
[hep-th]. Unfortunately, Heun functions are still little studied, and we are
not able to quantize the theory quasi-classically and obtain the first
corrections to the energy. The latter, due to AdS/CFT correspondence, is
supposed to give the anomalous dimensions of operators of the gauge theory dual
N=1 superconformal field theory.Comment: 9 pages, talk given at the 2nd Int. Conference AMiTaNS, 21-26 June
2010, Sozopol, Bulgaria, organized by EAC (Euro-American Consortium) for
Promoting AMiTaNS, to appear in the Proceedings of 2nd Int. Conference
AMiTaN
Generalized pulsating strings
In this paper we consider new solutions for pulsating strings. For this
purpose we use tha idea of the generalized ansatz for folded and circular
strings in hep-th/0311004. We find the solutions to the resulting
Neumann-Rosochatius integrable system and the corrections to the energy. To do
that we use the approach developed by Minahan in hep-th/0209047 and find that
the corrections are quite different from those obtained in that paper and
hep-th/0310188. We conclude with comments on our solutions and obtained
corrections to the energy, expanded to the leading order in lambda.Comment: v.2 references added, citations corrected, 18 page
Monte Carlo Study of Particle Transport Problem in Air Pollution
2002 Mathematics Subject Classification: 65C05.The actual transport of the air pollutants is due to the wind.
This normally called “advection of the air pollutants”. Diffusion and deposition are other two major physical processes, which take place during the transport of pollutants in the atmosphere.
In this paper we study two classes of grid-free Monte Carlo (MC) algorithms for solving an elliptic boundary value problem, where the partial differential equation contains advection, diffusion and deposition parts. The grid-free MC approach to solve the above equation uses a local integral representation and leads to a stochastic process called a random “Walk on balls” (WOB).
In the first class of algorithms, the choice of a transition density function in the Markov chain depends on the radius of the maximal ball, lying inside the domain, in which the problem is defined, and on the parameters of the differential operator. While the choice of a transition density function in
the second class of algorithms does not depend on the deposition part of the problem.
The computational complexity of both classes of grid-free MC algorithms was investigated using varied numerical tests on a PowerPC (G4 w/AltiVec) 450 MHz running YDL 2.0.Supported by Center of Excellence BIS-21 grant ICA1-2000-70016 and by the NSF of Bulgaria under Grants #I 811/98 and #MM 902/9
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