Melting of Branched RNA Molecules

Stability of the branching structure of an RNA molecule is an important condition for its function. In this letter we show that the melting thermodynamics of RNA molecules is very sensitive to their branching geometry for the case of a molecule whose groundstate has the branching geometry of a Cayley Tree and whose pairing interactions are described by the Go model. Whereas RNA molecules with a linear geometry melt via a conventional continuous phase transition with classical exponents, molecules with a Cayley Tree geometry are found to have a free energy that seems smooth, at least within our precision. Yet, we show analytically that this free energy in fact has a mathematical singularity at the stability limit of the ordered structure. The correlation length appears to diverge on the high-temperature side of this singularity.Comment: 4 pages, 3 figure

Equilibrium and non-equilibrium dynamics of the sub-ohmic spin-boson model

Employing the non-perturbative numerical renormalization group method, we study the dynamics of the spin-boson model, which describes a two-level system coupled to a bosonic bath with spectral density J(omega) propto omega^s. We show that, in contrast to the case of ohmic damping, the delocalized phase of the sub-ohmic model cannot be characterized by a single energy scale only, due to the presence of a non-trivial quantum phase transition. In the strongly sub-ohmic regime, s<<1, weakly damped coherent oscillations on short time scales are possible even in the localized phase - this is of crucial relevance, e.g., for qubits subject to electromagnetic noise.Comment: 4 pages, 6 figures; final version, as publishe

Spectral properties of fractional Fokker-Plank operator for the L\'evy flight in a harmonic potential

We present a detailed analysis of the eigenfunctions of the Fokker-Planck operator for the L\'evy-Ornstein-Uhlenbeck process, their asymptotic behavior and recurrence relations, explicit expressions in coordinate space for the special cases of the Ornstein-Uhlenbeck process with Gaussian and with Cauchy white noise and for the transformation kernel, which maps the fractional Fokker-Planck operator of the Cauchy-Ornstein-Uhlenbeck process to the non-fractional Fokker-Planck operator of the usual Gaussian Ornstein-Uhlenbeck process. We also describe how non-spectral relaxation can be observed in bounded random variables of the L\'evy-Ornstein-Uhlenbeck process and their correlation functions.Comment: 10 pages, 5 figures, submitted to Euro. Phys. J.

Modelling Dust Evolution in Galaxies with a Multiphase, Inhomogeneous ISM

We develop a model of dust evolution in a multiphase, inhomogeneous ISM including dust growth and destruction processes. The physical conditions for grain evolution are taken from hydrodynamical simulations of giant molecular clouds in a Milky Way-like spiral galaxy. We improve the treatment of dust growth by accretion in the ISM to investigate the role of the temperature-dependent sticking coefficient and ion-grain interactions. From detailed observational data on the gas-phase Si abundances [Si/H]_{gas} measured in the local Galaxy, we derive a relation between the average [Si/H]_{gas} and the local gas density n(H) which we use as a critical constraint for the models. This relation requires a sticking coefficient that decreases with the gas temperature. The synthetic relation constructed from the spatial dust distribution reproduces the slope of -0.5 of the observed relation in cold clouds. This slope is steeper than that for the warm medium and is explained by the dust growth. We find that it occurs for all adopted values of the minimum grain size a_{min} from 1 to 5nm. For the classical cut-off of a_{min}=5 nm, the ion-grain interactions result in longer growth timescales and higher [Si/H]_{gas} than the observed values. For a_{min} below 3 nm, the ion-grain interactions enhance the growth rates, steepen the slope of [Si/H]_{gas}-n(H) relation and provide a better match to observations. The rates of dust re-formation in the ISM by far exceed the rates of dust production by stellar sources as expected from simple evolution models. After the cycle of matter in and out of dust reaches a steady state, the dust growth balances the destruction operating on similar timescales of 350 Myr.Comment: 17 pages, 11 figures, accepted to Ap

Evaluation of different sources of uncertainty in climate change impact research using a hydro-climatic model ensemble

The international research project QBic3 (Quebec-Bavarian Collaboration on Climate Change) aims at investigating the potential impacts of climate change on the hydrology of regional scale catchments in Southern Quebec (Canada) and Bavaria (Germany). Yet, the actual change in river runoff characteristics during the next 70 years is highly uncertain due to a multitude of uncertainty sources. The so-called hydro-climatic ensemble that is constructed to describe the uncertainties of this complex model chain consists of four different global climate models, downscaled by three different regional climate models, an exchangeable bias correction algorithm, a separate method to scale RCM outputs to the hydrological model scale and several hydrological models of differing complexity to assess the impact of different hydro model concepts. This choice of models and scenarios allows for the inter-comparison of the uncertainty ranges of climate and hydrological models, of the natural variability of the climate system as well as of the impact of scaling and correction of climate data on mean, high and low flow conditions. A methodology to display the relative importance of each source of uncertainty is proposed and results for past runoff and potential future changes are presented

Coupled dynamics of RNA folding and nanopore translocation

The translocation of structured RNA or DNA molecules through narrow pores necessitates the opening of all base pairs. Here, we study the interplay between the dynamics of translocation and base-pairing theoretically, using kinetic Monte Carlo simulations and analytical methods. We find that the transient formation of basepairs that do not occur in the ground state can significantly speed up translocation.Comment: 4 pages, 3 figures, to appear in Physical Review Letter

DNA nano-mechanics: how proteins deform the double helix

It is a standard exercise in mechanical engineering to infer the external forces and torques on a body from its static shape and known elastic properties. Here we apply this kind of analysis to distorted double-helical DNA in complexes with proteins. We extract the local mean forces and torques acting on each base-pair of bound DNA from high-resolution complex structures. Our method relies on known elastic potentials and a careful choice of coordinates of the well-established rigid base-pair model of DNA. The results are robust with respect to parameter and conformation uncertainty. They reveal the complex nano-mechanical patterns of interaction between proteins and DNA. Being non-trivially and non-locally related to observed DNA conformations, base-pair forces and torques provide a new view on DNA-protein binding that complements structural analysis.Comment: accepted for publication in JCP; some minor changes in response to review 18 pages, 5 figure + supplement: 4 pages, 3 figure