Optimal rotations of deformable bodies and orbits in magnetic fields

Deformations can induce rotation with zero angular momentum where dissipation is a natural "cost function." This gives rise to an optimization problem of finding the most effective rotation with zero angular momentum. For certain plastic and viscous media in two dimensions the optimal path is the orbit of a charged particle on a surface of constant negative curvature with a magnetic field whose total flux is half a quantum unit.     

Experimental study of the stochastic nature of the pulsation self-starting process in passive mode locking

We present an experimental study of the probabilistic nature of pulsation self-starting in passively mode-locked lasers. It is a Poissonian process that results from a noise-activated switching barrier. The switching rate from cw operation to pulsation when the laser pump level is turned on has an exponential dependence that is inversely proportional to the square of the laser power.     

Making an honest measurement scale out of the oxygen isotope delta-values

The differential measurement of the abundance of oxygen isotopes based on reference materials, such as VSMOW for the case of water, was used because the precision of the absolute mass-spectrometric determination of the abundance fell short of the differences to be measured. Since then these measurements have been much improved, so that a calibration scheme of the oxygen isotope abundance in water, carbonates, silica, phosphates, sulfates, nitrates and organic materials is suggested, based on an accredited primary standard of oxygen in air and using standard fluorination and O(2) to CO(2) conversion techniques.     

Chebyshev reduced basis function applied to option valuation

We present a numerical method for the frequent pricing of financial derivatives that depends on a large number of variables. The method is based on the construction of a polynomial basis to interpolate the value function of the problem by means of a hierarchical orthogonalization process that allows to reduce the number of degrees of freedom needed to have an accurate representation of the value function. In the paper we consider, as an example, a GARCH model that depends on eight parameters and show that a very large number of contracts for different maturities and asset and parameters values can be valued in a small computational time with the proposed procedure. In particular the method is applied to the problem of model calibration. The method is easily generalizable to be used with other models or problems.