A one-dimensional model for theoretical analysis of single molecule experiments

In this paper we compare two polymer stretching experiments. The outcome of both experiments is a force-extension relation. We use a one-dimensional model to show that in general the two quantities are not equal. In certain limits, however, both force-extension relations coincide.Comment: 11 pages, 5 figure

A two-parameter random walk with approximate exponential probability distribution

We study a non-Markovian random walk in dimension 1. It depends on two parameters eps_r and eps_l, the probabilities to go straight on when walking to the right, respectively to the left. The position x of the walk after n steps and the number of reversals of direction k are used to estimate eps_r and eps_l. We calculate the joint probability distribution p_n(x,k) in closed form and show that, approximately, it belongs to the exponential family.Comment: 12 pages, updated reference to companion paper cond-mat/060126

A generalized quantum microcanonical ensemble

We discuss a generalized quantum microcanonical ensemble. It describes isolated systems that are not necessarily in an eigenstate of the Hamilton operator. Statistical averages are obtained by a combination of a time average and a maximum entropy argument to resolve the lack of knowledge about initial conditions. As a result, statistical averages of linear observables coincide with values obtained in the canonical ensemble. Non-canonical averages can be obtained by taking into account conserved quantities which are non-linear functions of the microstate.Comment: improved version, new titl

Grand canonical ensemble in generalized thermostatistics

We study the grand-canonical ensemble with a fluctuating number of degrees of freedom in the context of generalized thermostatistics. Several choices of grand-canonical entropy functional are considered. The ideal gas is taken as an example.Comment: 14 pages, no figure

Unravelling the functions of biogenic volatiles in boreal and temperate forest ecosystems

Living trees are the main source of biogenic volatile organic compounds (BVOCs) in forest ecosystems, but substantial emissions originate from leaf and wood litter, the rhizosphere and from microorganisms. This review focuses on temperate and boreal forest ecosystems and the roles of BVOCs in ecosystem function, from the leaf to the forest canopy and from the forest soil to the atmosphere level. Moreover, emphasis is given to the question of how BVOCs will help forests adapt to environmental stress, particularly biotic stress related to climate change. Trees use their vascular system and emissions of BVOCs in internal communication, but emitted BVOCs have extended the communication to tree population and whole community levels and beyond. Future forestry practices should consider the importance of BVOCs in attraction and repulsion of attacking bark beetles, but also take an advantage of herbivore-induced BVOCs to improve the efficiency of natural enemies of herbivores. BVOCs are extensively involved in ecosystem services provided by forests including the positive effects on human health. BVOCs have a key role in ozone formation but also in ozone quenching. Oxidation products form secondary organic aerosols that disperse sunlight deeper into the forest canopy, and affect cloud formation and ultimately the climate. We also discuss the technical side of reliable BVOC sampling of forest trees for future interdisciplinary studies that should bridge the gaps between the forest sciences, health sciences, chemical ecology, conservation biology, tree physiology and atmospheric science

Generalized pricing formulas for stochastic volatility jump diffusion models applied to the exponential Vasicek model

Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a Fokker-Planck differential equation and that, consequently, neglect jumps and only describe drift and diffusion. We present a method to adapt formulas for both the path-integral propagators and the option prices themselves, so that jump processes are taken into account in conjunction with the usual drift and diffusion terms. In particular, we focus on stochastic volatility models, such as the exponential Vasicek model, and extend the pricing formulas and propagator of this model to incorporate jump diffusion with a given jump size distribution. This model is of importance to include non-Gaussian fluctuations beyond the Black-Scholes model, and moreover yields a lognormal distribution of the volatilities, in agreement with results from superstatistical analysis. The results obtained in the present formalism are checked with Monte Carlo simulations.Comment: 9 pages, 2 figures, 1 tabl

Brownian motion with dry friction: Fokker-Planck approach

We solve a Langevin equation, first studied by de Gennes, in which there is a solid-solid or dry friction force acting on a Brownian particle in addition to the viscous friction usually considered in the study of Brownian motion. We obtain both the time-dependent propagator of this equation and the velocity correlation function by solving the associated time-dependent Fokker-Planck equation. Exact results are found for the case where only dry friction acts on the particle. For the case where both dry and viscous friction forces are present, series representations of the propagator and correlation function are obtained in terms of parabolic cylinder functions. Similar series representations are also obtained for the case where an external constant force is added to the Langevin equation.Comment: 18 pages, 13 figures (in color