Asymptotic expansions for a remarkable class of random walks

This paper extends the research of Wiegel (J. Math. Phys. 21 (1980) 2111) on random walks which differ from free random walks through the occurrence of an extra weightfactor (−1) at every crossing of a half-line. Starting from a new closed-form expression for the weight distribution of these walks, we derive various integral representations and asymptotic expansions for the total weight of all walks

Renormalization group theory of the critical properties of the interacting bose fluid

Starting from a functional integral representation of the partition function we apply the renormalization group to the interacting Bose fluid. A closed form for the renormalization equation is derived and the critical exponents are calculated in 4-ε dimensions

Fractional exponential decay in the capture of ligands by randomly distributed traps in one dimension

In many biophysical and biochemical experiments one observes the decay of some ligand population by an appropriate system of traps. We analyse this decay for a one-dimensional system of radomly distributed traps, and show that one can distinguish three different regimes. The decay starts with a fractional exponential of the form exp[− (t/t0)1/2], which changes into a fractional exponential of the form exp[− (t/t1)1/3] for long times, which in its turn changes into a pure exponential time dependence, i.e. exp[−t/t2] for very long times. With these three regimes, we associate three time scales, related to the average trap density and the diffusion constant characterizing the motion of the ligands

Chaotic motion of a harmonically bound charged particle in a magnetic field, in the presence of a half-plane barrier

The motion in the plane of an harmonically bound charged particle interacting with a magnetic field and a half-plane barrier along the positive x-axis is studied. The magnetic field is perpendicular to the plane in which the particle moves. This motion is integrable in between collisions of the particle with the barrier. However, the overall motion of the particle is very complicated. Chaotic regions in phase space exist next to island structures associated with linearly stable periodic orbits. We study in detail periodic orbits of low period and in particular their bifurcation behavior. Independent sequences of period doubling bifurcations and resonant bifurcations are observed associated with independent fixed points in the Poincaré section. Due to the perpendicular magnetic field an orientation is induced on the plane and time-reversal symmetry is broken.\u

Crosslinking and gelation between linear polymers: DNA-antibody complexes in systemic lupus erythematosus

In the autoimmune disease systemic lupus erythematosus the DNA molecules of an individual are attacked by its own antibodies. As these antibodies are bivalent they can crosslink different DNA molecules which can lead to the formation of DNA-antibody complexes and gels. Statistical properties of these complexes are derived and evaluated analytically in the limit of very long DNA molecules, as well as the concentrations at which a gel is being formed. The authors also present various numerical results for DNA molecules of intermediate lengths. This work can also be considered as a theory of the crosslinking and gelation of linear polymer

Adoption of organic farming systems in Missouri

The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file.Title from PDF of title page (University of Missouri--Columbia, viewed January 20, 2010).Thesis advisor: Dr. Georgeanne Artz.Includes bibliographical references.M.S. University of Missouri--Columbia 2009.Dissertations, Academic -- University of Missouri--Columbia -- Agricultural economics.Organic agricultural production in Missouri has grown since the inception of national organic production and labeling standards in 2002. Underlying the growth of certified organic operations and land area in Missouri are producers' motivations and perceptions regarding organic conversion. The main objective of this research is to compare organic farmers' perceptions and motives by the type of agricultural products produced on their farms. Using a multiple case study methodology, this study compares the elements of the organic adoption decision among Missouri's organic produce, row crop, livestock, and dairy farmers. In order to make comparisons between the farmer types, the study employs the concept of adoption from diffusion of innovations theory as a framework for understanding the elements of the farmers' organic adoption decisions. Five attributes of innovations are used as a foundation for a comparative analysis of farmers' perceptions regarding organic farming - relative advantage, compatibility, complexity, trialability, and observability. Comparing interview responses from organic farmers reveals that motivational and perceptual differences exist between farming sectors. In general, farmers from the organic produce, row crop, and dairy farming categories have more positive views of the attributes of organic farming than livestock farmers do

Computing probabilities of very rare events for Langevin processes: a new method based on importance sampling

Langevin equations are used to model many processes of physical interest, including low-energy nuclear collisions. In this paper we develop a general method for computing probabilities of very rare events (e.g. small fusion cross-sections) for processes described by Langevin dynamics. As we demonstrate with numerical examples as well as an exactly solvable model, our method can converge to the desired answer at a rate which is orders of magnitude faster than that achieved with direct simulations of the process in question.Comment: 18 pages + 7 figures, to appear in Nucl.Phys.

Continuous-flow IRMS technique for determining the 17O excess of CO2 using complete oxygen isotope exchange with cerium oxide

This paper presents an analytical system for analysis of all single substituted isotopologues (¹²C¹⁶O¹⁷O, ¹²C¹⁶O¹⁸O, ¹³C¹⁶O¹⁶O) in nanomolar quantities of CO₂ extracted from stratospheric air samples. CO₂ is separated from bulk air by gas chromatography and CO₂ isotope ratio measurements (ion masses 45 / 44 and 46 / 44) are performed using isotope ratio mass spectrometry (IRMS). The ¹⁷O excess (Δ¹⁷O) is derived from isotope measurements on two different CO₂ aliquots: unmodified CO₂ and CO₂ after complete oxygen isotope exchange with cerium oxide (CeO₂) at 700 °C. Thus, a single measurement of Δ¹⁷O requires two injections of 1 mL of air with a CO₂ mole fraction of 390 μmol mol⁻¹ at 293 K and 1 bar pressure (corresponding to 16 nmol CO₂ each). The required sample size (including flushing) is 2.7 mL of air. A single analysis (one pair of injections) takes 15 minutes. The analytical system is fully automated for unattended measurements over several days. The standard deviation of the ¹⁷O excess analysis is 1.7‰. Multiple measurements on an air sample reduce the measurement uncertainty, as expected for the statistical standard error. Thus, the uncertainty for a group of 10 measurements is 0.58‰ for Δ ¹⁷O in 2.5 h of analysis. 100 repeat analyses of one air sample decrease the standard error to 0.20‰. The instrument performance was demonstrated by measuring CO₂ on stratospheric air samples obtained during the EU project RECONCILE with the high-altitude aircraft Geophysica. The precision for RECONCILE data is 0.03‰ (1σ) for δ¹³C, 0.07‰ (1σ) for δ¹⁸O and 0.55‰ (1σ) for δ¹⁷O for a sample of 10 measurements. This is sufficient to examine stratospheric enrichments, which at altitude 33 km go up to 12‰ for δ¹⁷O and up to 8‰ for δ¹⁸O with respect to tropospheric CO₂ : δ¹⁷O ~ 21‰ Vienna Standard Mean Ocean Water (VSMOW), δ¹⁸O ~ 41‰ VSMOW (Lämmerzahl et al., 2002). The samples measured with our analytical technique agree with available data for stratospheric CO₂

Thermodynamic properties of confined interacting Bose gases - a renormalization group approach

A renormalization group method is developed with which thermodynamic properties of a weakly interacting, confined Bose gas can be investigated. Thereby effects originating from a confining potential are taken into account by periodic boundary conditions and by treating the resulting discrete energy levels of the confined degrees of freedom properly. The resulting density of states modifies the flow equations of the renormalization group in momentum space. It is shown that as soon as the characteristic length of confinement becomes comparable to the thermal wave length of a weakly interacting and trapped Bose gas its thermodynamic properties are changed significantly. This is exemplified by investigating characteristic bunching properties of the interacting Bose gas which manifest themselves in the second order coherence factor