arXiv subjects

Patrick E. Müller

Publications and source records attributed to Patrick E. Müller.

3 recordsLinked to original sources

arXiv2016

Path large deviations for interacting diffusions with local mean-field interactions in random environment

We consider a system of $N^{d}$ spins in random environment with a random local mean field type interaction. Each spin has a fixed spatial position on the torus $\mathbb{T}^{d}$, an attached random environment and a spin value in $\mathbb{R}$ that evolves according to a space and environment dependent Langevin dynamic. The interaction between two spins depends on the spin values, on the spatial distance and the random environment of both spins. We prove the path large deviation principle from the hydrodynamic (or local mean field McKean-Vlasov) limit and derive different expressions of the rate function for the empirical process and for the empirical measure of the paths. To this end, we generalize an approach of Dawson and Gärtner. By the space and random environment dependency, this requires new ingredients compared to mean field type interactions. Moreover, we prove the large deviation principle by using a second approach. This requires a generalisation of Varadhan's lemma to nowhere continuous functions.

math.PR↗

arXiv2014

Rotating massive O stars with non-spherical 2D winds

We present solutions for the velocity field and mass-loss rates for 2D axisymmetric outflows, as well as for the case of mass accretion through the use of the Lambert W-function. For the case of a rotating radiation-driven wind the velocity field is obtained analytically using a parameterised description of the line acceleration that only depends on radius r at any given latitude $θ$. The line acceleration g(r) is obtained from Monte-Carlo multi-line radiative transfer calculations. The critical/sonic point of our equation of motion varies with latitude $θ$. Furthermore, an approximate analytical solution for the supersonic flow of a rotating wind is derived, which is found to closely resemble the exact solution. For the simultaneous solution of the mass-loss rate and velocity field, we use the iterative method of our 1D method extended to the non-spherical 2D case. We apply the new theoretical expressions with our iterative method to the stellar wind from a differentially rotating 40 $M_{sun}$ O5-V main sequence star as well as to a 60 $M_{sun}$ O-giant star, and we compare our results to previous studies that are extensions of the Castor et al. (1975, ApJ, 195, 157) CAK formalism. Next, we account for the effects of oblateness and gravity darkening. Our numerical results predict an equatorial decrease of the mass-loss rate, which would imply that (surface-averaged) total mass-loss rates are lower than for the spherical 1D case, in contradiction to the Maeder & Meynet (2000, A&A, 361, 159) formalism that is oftentimes employed in stellar evolution calculations for rotating massive stars. To clarify the situation in nature we discuss observational tests to constrain the shapes of large-scale 2D stellar winds.

astro-ph.SR↗

arXiv2008

A consistent solution for the velocity field and mass-loss rate of massive stars

Stellar winds are an important aspect of our understanding of the evolution of massive stars and their input into the interstellar medium. Here we present solutions for the velocity field and mass-loss rates for stellar outflows as well as for the case of mass accretion through the use of the so-called Lambert W-function. For the case of a radiation-driven wind, the velocity field is obtained analytically using a parameterised description for the line acceleration that only depends on radius, which we obtain from Monte-Carlo multi-line radiative transfer calculations. In our form of the equation of motion the critical point is the sonic point. We also derive an approximate analytical solution for the supersonic flow which closely resembles our exact solution. For the simultaneous solution of the mass-loss rate and velocity field, we describe a new iterative method. We apply our theoretical expressions and our iterative method to the stellar wind from a typical O5-V main sequence star, and find good agreement with empirical values. Our computations represent a self-consistent mass-loss calculation including the effect of multi-line scattering for an O-type star, opening up the possibility of applying Monte Carlo mass-loss calculations in regions of the Universe for which empirical constraints cannot be readily obtained.

astro-ph↗