6,264 research outputs found
Quasi-local charges and asymptotic symmetry generators
The quasi-local formulation of conserved charges through the off-shell
approach is extended to cover the asymptotic symmetry generators. By
introducing identically conserved currents which are appropriate for asymptotic
Killing vectors, we show that the asymptotic symmetry generators can be
understood as quasi-local charges. We also show that this construction is
completely consistent with the on-shell method.Comment: 19 pages; v2 typos fixe
Thermodynamic Volume and the Extended Smarr Relation
We continue to explore the scaling transformation in the reduced action
formalism of gravity models. As an extension of our construction, we consider
the extended forms of the Smarr relation for various black holes, adopting the
cosmological constant as the bulk pressure as in some literatures on black
holes. Firstly, by using the quasi-local formalism for charges, we show that,
in a general theory of gravity, the volume in the black hole thermodynamics
could be defined as the thermodynamic conjugate variable to the bulk pressure
in such a way that the first law can be extended consistently. This, so called,
thermodynamic volume can be expressed explicitly in terms of the metric and
field variables. Then, by using the scaling transformation allowed in the
reduced action formulation, we obtain the extended Smarr relation involving the
bulk pressure and the thermodynamic volume. In our approach, we do not resort
to Euler's homogeneous scaling of charges while incorporating the would-be
hairy contribution without any difficulty.Comment: 1+21 pages, plain LaTeX; v2 typo fixed and references adde
Tau functions as Widom constants
We define a tau function for a generic Riemann-Hilbert problem posed on a
union of non-intersecting smooth closed curves with jump matrices analytic in
their neighborhood. The tau function depends on parameters of the jumps and is
expressed as the Fredholm determinant of an integral operator with block
integrable kernel constructed in terms of elementary parametrices. Its
logarithmic derivatives with respect to parameters are given by contour
integrals involving these parametrices and the solution of the Riemann-Hilbert
problem. In the case of one circle, the tau function coincides with Widom's
determinant arising in the asymptotics of block Toeplitz matrices. Our
construction gives the Jimbo-Miwa-Ueno tau function for Riemann-Hilbert
problems of isomonodromic origin (Painlev\'e VI, V, III, Garnier system, etc)
and the Sato-Segal-Wilson tau function for integrable hierarchies such as
Gelfand-Dickey and Drinfeld-Sokolov.Comment: 26 pages, 6 figure
Computer Model Development on Contact-Stabilization Wastewater Treatment Systems
Computer model is developed to relate parameters that determine the performance of a contact-stabilization system. Based on mass and substrate balance in the system, relationships between the variables are developed, then simulations using various values of the parameters can produce trend lines indicating the behavior of a system as well as the required conditions to reach an expected performance. When the operating conditions, such as recycled sludge and wasted sludge are changed, the model demonstrates alterations of the performance consistent to the developed mathematical relationships. Additionally, the computer model shows that the results could produce further explanation on phenomena of biological processes in contact-stabilization systems
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