Eikonal equations and pathwise solutions to fully non-linear SPDEs

We study the existence and uniqueness of the stochastic viscosity solutions of fully nonlinear, possibly degenerate, second order stochastic pde with quadratic Hamiltonians associated to a Riemannian geometry. The results are new and extend the class of equations studied so far by the last two authors

Stochastic axial compressor variable geometry schedule optimisation

The design of axial compressors is dictated by the maximisation of flow efficiency at on design conditions whereas at part speed the requirement for operation stability prevails. Among other stability aids, compressor variable geometry is employed to rise the surge line for the provision of an adequate surge margin. The schedule of the variable vanes is in turn typically obtained from expensive and time consuming rig tests that go through a vast combination of possible settings. The present paper explores the suitability of stochastic approaches to derive the most flow efficient schedule of an axial compressor for a minimum variable user defined value of the surge margin. A genetic algorithm has been purposely developed and its satisfactory performance validated against four representative benchmark functions. The work carries on with the necessary thorough investigation of the impact of the different genetic operators employed on the ability of the algorithm to find the global extremities in an effective and efficient manner. This deems fundamental to guarantee that the algorithm is not trapped in local extremities. The algorithm is then coupled with a compressor performance prediction tool that evaluates each individual's performance through a user defined fitness function. The most flow efficient schedule that conforms to a prescribed surge margin can be obtained thereby fast and inexpensively. Results are produced for a modern eight stage high bypass ratio compressor and compared with experimental data available to the research. The study concludes with the analysis of the existent relationship between surge margin and flow efficiency for the particular compressor under scrutiny. The study concludes with the analysis of the existent relationship between surge margin and flow efficiency for the particular compressor under scrutiny

Mean-Reverting Stochastic Processes, Evaluation of Forward Prices and Interest Rates

We consider mean-reverting stochastic processes and build self-consistent models for forward price dynamics and some applications in power industries. These models are built using the ideas and equations of stochastic differential geometry in order to close the system of equations for the forward prices and their volatility. Some analytical solutions are presented in the one factor case and for specific regular forward price/interest rates volatility. Those models will also play a role of initial conditions for a stochastic process describing forward price and interest rates volatility. Subsequently, the curved manifold of the internal space i.e. a discrete version of the bond term space (the space of bond maturing) is constructed. The dynamics of the point of this internal space that correspond to a portfolio of different bonds is studied. The analysis of the discount bond forward rate dynamics, for which we employed the Stratonovich approach, permitted us to calculate analytically the regular and the stochastic volatilities. We compare our results with those known from the literature.: Stochastic Differential Geometry, Mean-Reverting Stochastic Processes and Term Structure of Specific (Some) Economic/Finance Instruments

KV. Cohomology and some applications

Two versions of the KV-cohomology are presented and some algebraic and geometrical applications are given. We will see some applications to stochastic manifold. As a consequence, we can apply these ideas in Lorentzian geometry, in particular in the theory of null hypersurfaces where it is defined a non Levi-Civitta connection as an auxiliary tool, and so, there is a stochastic structure.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech