845 research outputs found
Partial Regularity of solutions to the Four-dimensional Navier-Stokes equations at the first blow-up time
The solutions of incompressible Navier-Stokes equations in four spatial
dimensions are considered. We prove that the two-dimensional Hausdorff measure
of the set of singular points at the first blow-up time is equal to zero.Comment: 19 pages, a comment regarding five or higher dimensional case is
added in Remark 1.3. accepted by Comm. Math. Phy
Marginal deformation of N=4 SYM and Penrose limits with continuum spectrum
We study the Penrose limit about a null geodesic with 3 equal angular momenta
in the recently obtained type IIB solution dual to an exactly marginal
-deformation of N=4 SYM. The resulting background has non-trivial NS
3-form flux as well as RR 5- and 3-form fluxes. We quantise the light-cone
Green-Schwarz action and show that it exhibits a continuum spectrum. We show
that this is related to the dynamics of a charged particle moving in a Landau
plane with an extra interaction induced by the deformation. We interpret the
results in the dual N=1 SCFT.Comment: 26 pages, 2 figures; v2: typos corrected, field theory interpretation
extende
Reduced contextually induced muscle thermogenesis in rats with calorie restriction and lower aerobic fitness but not monogenic obesity
We have previously identified predator odor as a potent stimulus activating thermogenesis in skeletal muscle in rats. As this may prove relevant for energy balance and weight loss, the current study investigated whether skeletal muscle thermogenesis was altered with negative energy balance, obesity propensity seen in association with low intrinsic aerobic fitness, and monogenic obesity. First, weight loss subsequent to three weeks of 50% calorie restriction suppressed the muscle thermogenic response to predator odor. Next, we compared rats bred based on artificial selection for intrinsic aerobic fitness—high- and low-capacity runners (HCR, LCR)—that display robust leanness and obesity propensity, respectively. Aerobically fit HCR showed enhanced predator odor-induced muscle thermogenesis relative to the less-fit LCR. This contrasted with the profound monogenic obesity displayed by rats homozygous for a loss of function mutation in Melanocortin 4 receptor (Mc4rK314X/K314X rats), which showed no discernable deficit in thermogenesis. Taken together, these data imply that body size or obesity per se are not associated with deficient muscle thermogenesis. Rather, the physiological phenotype associated with polygenic obesity propensity may encompass pleiotropic mechanisms in the thermogenic pathway. Adaptive thermogenesis associated with weight loss also likely alters muscle thermogenic mechanisms.</p
Surface tension of the isotropic-nematic interface
We present the first calculations of the pressure tensor profile in the
vicinity of the planar interface between isotropic liquid and nematic liquid
crystal, using Onsager's density functional theory and computer simulation.
When the liquid crystal director is aligned parallel to the interface, the
situation of lowest free energy, there is a large tension on the nematic side
of the interface and a small compressive region on the isotropic side. By
contrast, for perpendicular alignment, the tension is on the isotropic side.
There is excellent agreement between theory and simulation both in the forms of
the pressure tensor profiles, and the values of the surface tension.Comment: Minor changes; to appear in Phys. Rev.
Rotating Strings with Two Unequal Spins in Lunin-Maldacena Background
We study a string motion in the Lunin-Maldacena background, that is, the
\beta-deformed AdS_5 \times \tilde{S}^5 background dual to a \beta-deformation
of \mathcal{N} = 4 super Yang-Mills theory. For real \beta we construct a
rotating and wound string solution which has two unequal spins in \tilde{S}^5.
The string energy is expressed in terms of the spins, the winding numbers and
the deformation parameter. In the expansion of \lambda/J^2 with the total spin
J and the string tension \sqrt{\lambda} we present ``one-loop" and ``two-loop"
energy corrections. The ``one-loop" one agrees with the one-loop anomalous
dimension of the corresponding gauge-theory scalar operators obtained in
hep-th/0503192 from the \beta-deformed Bethe equation as well as the
anisotropic Landau-Lifshitz equation.Comment: 13 pages, LaTeX, no figure
Gravity duals for the Coulomb branch of marginally deformed N=4 Yang-Mills
Supergravity backgrounds dual to a class of exactly marginal deformations of
N supersymmetric Yang-Mills can be constructed through an SL(2,R) sequence of
T-dualities and coordinate shifts. We apply this transformation to multicenter
solutions and derive supergravity backgrounds describing the Coulomb branch of
N=1 theories at strong 't Hooft coupling as marginal deformations of N=4
Yang-Mills. For concreteness we concentrate to cases with an SO(4)xSO(2)
symmetry preserved by continuous distributions of D3-branes on a disc and on a
three-dimensional spherical shell. We compute the expectation value of the
Wilson loop operator and confirm the Coulombic behaviour of the heavy
quark-antiquark potential in the conformal case. When the vev is turned on we
find situations where a complete screening of the potential arises, as well as
a confining regime where a linear or a logarithmic potential prevails depending
on the ratio of the quark-antiquark separation to the typical vev scale. The
spectra of massless excitations on these backgrounds are analyzed by turning
the associated differential equations into Schrodinger problems. We find
explicit solutions taking into account the entire tower of states related to
the reduction of type-IIB supergravity to five dimensions, and hence we go
beyond the s-wave approximation that has been considered before for the
undeformed case. Arbitrary values of the deformation parameter give rise to the
Heun differential equation and the related Inozemtsev integrable system, via a
non-standard trigonometric limit as we explicitly demonstrate.Comment: 43 pages, Latex, 2 figures. v2: References added. v3: small typos
corrected, published versio
Persistent precordial "hyperacute" T-waves signify proximal left anterior descending artery occlusion
gamma_i Deformed Lax Pair for Rotating Strings in the Fast Motion Limit
A 3-parameter generalization of the Lunin-Maldacena background has recently
been constructed by Frolov. This gamma_i-deformed background is
non-supersymmetric. We consider strings in this gamma_i-deformed R \times S^5
background rotating in three orthogonal planes (the 3-spin sector) in a fast
motion limit, in which the total angular momentum J is assumed to be large. We
show that there exists a consistent transformation which takes the undeformed
equations of motion into the gamma_i-deformed equations of motion. This
transformation is used to construct a Lax pair for the bosonic part of the
gamma_i-deformed theory in the fast motion limit. This implies the
integrability of the bosonic part of the gamma_i-deformed string sigma model in
the fast motion limit.Comment: 21 page
Semiclassical Strings, Dipole Deformations of N=1 SYM and Decoupling of KK Modes
In this paper we investigate the recently found -deformed
Maldacena-Nunez background by studying the behavior of different semiclassical
string configurations. This background is conjectured to be dual to dipole
deformations of SYM. We compare our results to those in the pure
Maldacena-Nunez background and show that the energies of our string
configurations are higher than in the undeformed background. Thinking in the
lines of (hep-th/0505100) we argue that this is an evidence for better
decoupling of the Kaluza-Klein modes from the pure SYM theory excitations.
Moreover we are able to find a limit of the background in which the string
energy is independent of , these strings are interpreted as
corresponding to pure gauge theory effects.Comment: 31 pages, references added, new solutions in Section 7 presented, an
appendix added, to appear in JHE
Deformed PP-waves from the Lunin-Maldacena Background
In this article we study a pp-wave limit of the Lunin-Maldacena background.
We show that the relevant string theory background is a homogeneous pp-wave. We
obtain the string spectrum. The dual field theory is a deformation of N=4 super
Yang-Mills theory. We have shown that, for a class of operators, at O(g_{YM}^2)
and at leading order in N, all contributions to the anomalous dimension come
from F-terms. We are able to identify the operator in the deformed super
Yang-Mills which is dual to the lowest string mode. By studying the undeformed
theory we are able to provide some evidence, directly in the field theory, that
a small set of nearly protected operators decouple. We make some comments on
operators in the Yang-Mills theory that are dual to excited string modes.Comment: 22 pages, 1 figure; Final version to appear in JHE
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