12,500 research outputs found
Non-Abelian Stokes Theorem for Wilson Loops Associated with General Gauge Groups
A formula constituting the non-Abelian Stokes theorem for general semi-simple
compact gauge groups is presented. The formula involves a path integral over a
group space and is applicable to Wilson loop variables irrespective of the
topology of loops. Some simple expressions analogous to the 't Hooft tensor of
a magnetic monopole are given for the 2-form of interest. A special property in
the case of the fundamental representation of the group SU(N) is pointed out.Comment: 11 pages, PTPTEX, corrected some typo
Integrable Top Equations associated with Projective Geometry over Z_2
We give a series of integrable top equations associated with the projective
geometry over Z_2 as a (2^n-1)-dimensional generalisation of the 3D Euler top
equations. The general solution of the (2^n-1)D top is shown to be given by an
integration over a Riemann surface with genus (2^{n-1}-1)^2.Comment: 8 pages, Late
Consistency Conditions of the Faddeev-Niemi-Periwal Ansatz for the SU(N) Gauge Field
The consistency condition of the Faddeev-Niemi ansatz for the gauge-fixed
massless SU(2) gauge field is discussed. The generality of the ansatz is
demonstrated by obtaining a sufficient condition for the existence of the
three-component field introduced by Faddeev and Niemi. It is also shown that
the consistency conditions determine this three-component field as a functional
of two arbitrary functions. The consistency conditions corresponding to the
Periwal ansatz for the SU(N) gauge field with N larger than 2 are also
obtained. It is shown that the gauge field obeying the Periwal ansatz must
satisfy extra (N-1)(N-2)/2 conditions.Comment: PTP Tex, 15 pages, Eq.(3.18) inserte
Non-Abelian Stokes Theorem for Loop Variables Associated with Nontrivial Loops
The non-Abelian Stokes theorem for loop variables associated with nontrivial
loops (knots and links) is derived. It is shown that a loop variable is in
general different from unity even if the field strength vanishes everywhere on
the surface surrounded by the loop.Comment: 18 pages,10 Postscript figures, PTP Tex, Journal-ref adde
Integrable Hierarchies and Contact Terms in u-plane Integrals of Topologically Twisted Supersymmetric Gauge Theories
The -plane integrals of topologically twisted supersymmetric gauge
theories generally contain contact terms of nonlocal topological observables.
This paper proposes an interpretation of these contact terms from the point of
view of integrable hierarchies and their Whitham deformations. This is inspired
by Mari\~no and Moore's remark that the blowup formula of the -plane
integral contains a piece that can be interpreted as a single-time tau function
of an integrable hierarchy. This single-time tau function can be extended to a
multi-time version without spoiling the modular invariance of the blowup
formula. The multi-time tau function is comprised of a Gaussian factor
and a theta function. The time variables play the
role of physical coupling constants of 2-observables carried by the
exceptional divisor . The coefficients of the Gaussian part are
identified to be the contact terms of these 2-observables. This identification
is further examined in the language of Whitham equations. All relevant
quantities are written in the form of derivatives of the prepotential.Comment: latex, 17 pages, no figures; final version for publicatio
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Using data from connected thermostats to track large power outages in the United States
The detection of power outages is an essential activity for electric utilities. A large, national dataset of Internet-connected thermostats was used to explore and illustrate the ability of Internet-connected devices to geospatially track outages caused by hurricanes and other major weather events. The method was applied to nine major outage events, including hurricanes and windstorms. In one event, Hurricane Irma, a network of about 1000 thermostats provided quantitatively similar results to detailed utility data with respect to the number of homes without power and identification of the most severely affected regions. The method generated regionally uniform outage data that would give emergency authorities additional visibility into the scope and magnitude of outages. The network of thermostat-sensors also made it possible to calculate a higher resolution version of outage duration (or SAIDI) at a level of customer-level visibility that was not previously available
The correspondence between Tracy-Widom (TW) and Adler-Shiota-van Moerbeke (ASvM) approaches in random matrix theory: the Gaussian case
Two approaches (TW and ASvM) to derivation of integrable differential
equations for random matrix probabilities are compared. Both methods are
rewritten in such a form that simple and explicit relations between all TW
dependent variables and -functions of ASvM are found, for the example of
finite size Gaussian matrices. Orthogonal function systems and Toda lattice are
seen as the core structure of both approaches and their relationship.Comment: 20 pages, submitted to Journal of Mathematical Physic
Renormalization-group and numerical analysis of a noisy Kuramoto-Sivashinsky equation in 1+1 dimensions
The long-wavelength properties of a noisy Kuramoto-Sivashinsky (KS) equation
in 1+1 dimensions are investigated by use of the dynamic renormalization group
(RG) and direct numerical simulations. It is shown that the noisy KS equation
is in the same universality class as the Kardar-Parisi-Zhang (KPZ) equation in
the sense that they have scale invariant solutions with the same scaling
exponents in the long-wavelength limit. The RG analysis reveals that the RG
flow for the parameters of the noisy KS equation rapidly approach the KPZ fixed
point with increasing the strength of the noise. This is supplemented by the
numerical simulations of the KS equation with a stochastic noise, in which the
scaling behavior of the KPZ equation can be easily observed even in the
moderate system size and time.Comment: 12pages, 7figure
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