A Bayesian Approach to Comparing Cosmic Ray Energy Spectra

A common problem in ultra-high energy cosmic ray physics is the comparison of energy spectra. The question is whether the spectra from two experiments or two regions of the sky agree within their statistical and systematic uncertainties. We develop a method to directly compare energy spectra for ultra-high energy cosmic rays from two different regions of the sky in the same experiment without reliance on agreement with a theoretical model of the energy spectra. The consistency between the two spectra is expressed in terms of a Bayes factor, defined here as the ratio of the likelihood of the two-parent source hypothesis to the likelihood of the one-parent source hypothesis. Unlike other methods, for example chi^2 tests, the Bayes factor allows for the calculation of the posterior odds ratio and correctly accounts for non-Gaussian uncertainties. The latter is particularly important at the highest energies, where the number of events is very small.Comment: 22 pages, 10 figures, accepted for publication in Ap

Production delays, supply distortions and endogenous price dynamics

It takes time to produce commodities, and different production technologies may take different lengths of time. Suppose that firms may switch between different production technologies that take different lengths of time. A natural implication of such a scenario is that not all firms would then offer their commodities in every period, i.e. firms’ total supply schedule would become a time-varying quantity. Based on a behavioral cobweb framework, we analytically demonstrate that commodity markets become unstable when firms switch too rapidly between production technologies that take different lengths of time. In particular, we observe that supply distortions lead to endogenous commodity price dynamics due to a mismatch between supply and demand

Unifying thermodynamic and kinetic descriptions of single-molecule processes: RNA unfolding under tension

We use mesoscopic non-equilibrium thermodynamics theory to describe RNA unfolding under tension. The theory introduces reaction coordinates, characterizing a continuum of states for each bond in the molecule. The unfolding considered is so slow that one can assume local equilibrium in the space of the reaction coordinates. In the quasi-stationary limit of high sequential barriers, our theory yields the master equation of a recently proposed sequential-step model. Non-linear switching kinetics is found between open and closed states. Our theory unifies the thermodynamic and kinetic descriptions and offers a systematic procedure to characterize the dynamics of the unfolding processComment: 13 pages, 3 figure

Generalized Smoluchowski equation with correlation between clusters

In this paper we compute new reaction rates of the Smoluchowski equation which takes into account correlations. The new rate K = KMF + KC is the sum of two terms. The first term is the known Smoluchowski rate with the mean-field approximation. The second takes into account a correlation between clusters. For this purpose we introduce the average path of a cluster. We relate the length of this path to the reaction rate of the Smoluchowski equation. We solve the implicit dependence between the average path and the density of clusters. We show that this correlation length is the same for all clusters. Our result depends strongly on the spatial dimension d. The mean-field term KMFi,j = (Di + Dj)(rj + ri)d-2, which vanishes for d = 1 and is valid up to logarithmic correction for d = 2, is the usual rate found with the Smoluchowski model without correlation (where ri is the radius and Di is the diffusion constant of the cluster). We compute a new rate: the correlation rate K_{i,j}^{C} (D_i+D_j)(r_j+r_i)^{d-1}M{\big(\frac{d-1}{d_f}}\big) is valid for d \leq 1(where M(\alpha) = \sum+\infty i=1i\alphaNi is the moment of the density of clusters and df is the fractal dimension of the cluster). The result is valid for a large class of diffusion processes and mass radius relations. This approach confirms some analytical solutions in d 1 found with other methods. We also show Monte Carlo simulations which illustrate some exact new solvable models