4,416 research outputs found
Four-manifolds of Pinched Sectional Curvature
In this paper, we study closed four-dimensional manifolds. In particular, we
show that under various new pinching curvature conditions (for example, the
sectional curvature is no more than 5/6 of the smallest Ricci eigenvalue) then
the manifold is definite. If restricting to a metric with harmonic Weyl tensor,
then it must be self-dual or anti-self-dual under the same conditions.
Similarly, if restricting to an Einstein metric, then it must be either the
complex projective space with its Fubini-Study metric, the round sphere or
their quotients. Furthermore, we also classify Einstein manifolds with positive
intersection form and an upper bound on the sectional curvature.Comment: 20 pages, add a few remarks, references, and acknowledgemen
A Simple, Approximate Method for Analysis of Kerr-Newman Black Hole Dynamics and Thermodynamics
In this work we present a simple, approximate method for analysis of the
basic dynamical and thermodynamical characteristics of Kerr-Newman black hole.
Instead of the complete dynamics of the black hole self-interaction we consider
only such stable (stationary) dynamical situations determined by condition that
black hole (outer) horizon circumference holds the integer number of the
reduced Compton wave lengths corresponding to mass spectrum of a small quantum
system (representing quant of the black hole self-interaction). Then, we show
that Kerr-Newman black hole entropy represents simply the quotient of the sum
of static part and rotation part of mass of black hole on the one hand and
ground mass of small quantum system on the other hand. Also we show that
Kerr-Newman black hole temperature represents the negative value of the
classical potential energy of gravitational interaction between a part of black
hole with reduced mass and small quantum system in the ground mass quantum
state. Finally, we suggest a bosonic great canonical distribution of the
statistical ensemble of given small quantum systems in the thermodynamical
equilibrium with (macroscopic) black hole as thermal reservoir. We suggest
that, practically, only ground mass quantum state is significantly degenerate
while all other, excited mass quantum states are non-degenerate. Kerr-Newman
black hole entropy is practically equivalent to the ground mass quantum state
degeneration. Given statistical distribution admits a rough (qualitative) but
simple modeling of Hawking radiation of the black hole too.Comment: 8 pages, no figure
A continuum-microscopic method based on IRBFs and control volume scheme for viscoelastic fluid flows
A numerical computation of continuum-microscopic model for visco-elastic flows based on the Integrated Radial Basis Function (IRBF) Control Volume and the Stochastic Simulation Techniques (SST) is reported in this paper. The macroscopic flow equations are closed by a stochastic equation for the extra stress at the microscopic level. The former are discretised by a 1D-IRBF-CV method while the latter is integrated with Euler explicit or Predictor-Corrector schemes. Modelling is very efficient as it is based on Cartesian grid, while the integrated RBF approach enhances both the stability of the procedure and the accuracy of the solution. The proposed method is demonstrated with the solution of the start-up Couette flow of the Hookean and FENE dumbbell model fluids
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