Determination of hydraulic resistance of channels using spectral geometry methods

In this paper, we propose a new method for calculation of hydraulic resistance of channels with constant cross-section. The method is based on the obtained estimates for the average energy dissipation rate in a turbulent flow. The first part of the paper is devoted to theoretical justification of the method. The second part is devoted to calculation of hydraulic resistance of various channels using the abovementioned method and comparison of these values with the known results. The proposed method allows for calculation of hydraulic resistance of various channels with sufficiently high accuracy and is based only on the information about the channel geometry.

Mathematical Tools to Understand the Field Theories of the Standard Model and Beyond

Since Isaac Newton the understanding of the physical world is more and more complex. The Euclidean space of three dimensions , independent of time is replaced in Enstein’s vision by the Lorentzian space-time at first, then by four dimensions manifold to unify space and matter. String theorists add to space more dimensions to make their theory consistent. Complex topological invariants which characterize different kind of spaces are developed. Space is discretized at the quantum scale in the loop quantum gravity theory. A non-commutative and spectral geometry is defined from the theory of operator algebra by Alain Connes. In this review, our goal is to enumerate different approaches implementing algebra and topology in order to understand the standard model of particles and beyond

Spectral Geometry of Black Holes in 4D Gauged Supergravity

In this work we show that the area of the event horizon of the Chong–Cvetic–Lu–Pope black hole can be reconstructed in terms of the spectra of the Laplacian on the event horizon. This result, which extends previous works regarding the de Sitter–Kerr–Newman case, points towards a possible description of the black hole degrees of freedom in terms of the spectra of canonical operators defined on the event horizon.