Diffusion, Fragmentation and Coagulation Processes: Analytical and Numerical Results

We formulate dynamical rate equations for physical processes driven by a combination of diffusive growth, size fragmentation and fragment coagulation. Initially, we consider processes where coagulation is absent. In this case we solve the rate equation exactly leading to size distributions of Bessel type which fall off as $\exp(-x^{3/2})$ for large $x$-values. Moreover, we provide explicit formulas for the expansion coefficients in terms of Airy functions. Introducing the coagulation term, the full non-linear model is mapped exactly onto a Riccati equation that enables us to derive various asymptotic solutions for the distribution function. In particular, we find a standard exponential decay, $\exp(-x)$, for large $x$, and observe a crossover from the Bessel function for intermediate values of $x$. These findings are checked by numerical simulations and we find perfect agreement between the theoretical predictions and numerical results.Comment: (28 pages, 6 figures, v2+v3 minor corrections

Pitch Dynamics of Unmanned Aerial Vehicles

Dynamic stability requirements for manned aircraft have been in place for many years. However, we cannot expect stability constraints for UAVs to match those for manned aircraft; and dynamic stability requirements specific to UAVs have not been developed. The boundaries of controllability for both remotely-piloted and auto-piloted aircraft must be established before UAV technology can reach its full potential. The development of dynamic stability requirements specific to UAVs could improve flying qualities and facilitate more efficient UAV designs to meet specific mission requirements. As a first step to developing UAV stability requirements in general, test techniques must be established that will allow the stability characteristics of current UAVs to be quantified. This paper consolidates analytical details associated with procedures that could be used to experimentally determine the pitch stability boundaries for good UAV flying qualities. The procedures require determining only the maneuver margin and pitch radius of gyration and are simple enough to be used in an educational setting where resources are limited. The premise is that these procedures could be applied to UAVs now in use, in order to characterize the longitudinal flying qualities of current aircraft. This is but a stepping stone to the evaluation of candidate metrics for establishing flying-quality constraints for unmanned aircraft

Fossil shark teeth from upland Fleurieu Peninsula, South Australia: evidence for previously unknown Tertiary marine sediments

Neville S Pledge, Anthony R Milnes, Robert P Bourman, and Neville F Alle

Short-wavelength collective modes in a binary hard-sphere mixture

We use hard-sphere generalized hydrodynamic equations to discuss the extended hydrodynamic modes of a binary mixture. The theory presented here is analytic and it provides us with a simple description of the collective excitations of a dense binary mixture at molecular length scales. The behavior we predict is in qualitative agreement with molecular-dynamics results for soft-sphere mixtures. This study provides some insight into the role of compositional disorder in forming glassy configurations.Comment: Published; withdrawn since already published. Ordering in the archive gives misleading impression of new publicatio

Hydrodynamic fluctuations in the Kolmogorov flow: Linear regime

The Landau-Lifshitz fluctuating hydrodynamics is used to study the statistical properties of the linearized Kolmogorov flow. The relative simplicity of this flow allows a detailed analysis of the fluctuation spectrum from near equilibrium regime up to the vicinity of the first convective instability threshold. It is shown that in the long time limit the flow behaves as an incompressible fluid, regardless of the value of the Reynolds number. This is not the case for the short time behavior where the incompressibility assumption leads in general to a wrong form of the static correlation functions, except near the instability threshold. The theoretical predictions are confirmed by numerical simulations of the full nonlinear fluctuating hydrodynamic equations.Comment: 20 pages, 4 figure

A Delayed Choice Quantum Eraser

This paper reports a "delayed choice quantum eraser" experiment proposed by Scully and Dr\"{u}hl in 1982. The experimental results demonstrated the possibility of simultaneously observing both particle-like and wave-like behavior of a quantum via quantum entanglement. The which-path or both-path information of a quantum can be erased or marked by its entangled twin even after the registration of the quantum.Comment: twocolumn, 4pages, submitted to PR

Realistic Calculation of the hep Astrophysical Factor

The astrophysical factor for the proton weak capture on 3He is calculated with correlated-hyperspherical-harmonics bound and continuum wave functions corresponding to a realistic Hamiltonian consisting of the Argonne v18 two-nucleon and Urbana-IX three-nucleon interactions. The nuclear weak charge and current operators have vector and axial-vector components, that include one- and many-body terms. All possible multipole transitions connecting any of the p-3He S- and P-wave channels to the 4He bound state are considered. The S-factor at a p-3He center-of-mass energy of 10 keV, close to the Gamow-peak energy, is predicted to be 10.1 10^{-20} keV b, a factor of five larger than the standard-solar-model value. The P-wave transitions are found to be important, contributing about 40 % of the calculated S-factor.Comment: 8 pages RevTex file, submitted to Phys. Rev. Let

Is subarctic forest advance able to keep pace with climate change?

Recent climate warming and scenarios for further warming have led to expectations of rapid movement of ecological boundaries. Here we focus on the circumarctic forest-tundra ecotone (FTE), which represents an important bioclimatic zone with feedbacks from forest advance and corresponding tundra disappearance (up to 50% loss predicted this century) driving widespread ecological and climatic changes. We address FTE advance and climate history relations over the 20th century, using FTE response data from 151 sites across the circumarctic area and site-specific climate data. Specifically, we investigate spatial uniformity of FTE advance, statistical associations with 20th century climate trends, and whether advance rates match climate change velocities (CCVs). Study sites diverged into four regions (Eastern Canada; Central and Western Canada and Alaska; Siberia; and Western Eurasia) based on their climate history, although all were characterized by similar qualitative patterns of behaviour (with about half of the sites showing advancing behaviour). The main associations between climate trend variables and behaviour indicate the importance of precipitation rather than temperature for both qualitative and quantitative behaviours, and the importance of non-growing season as well as growing season months. Poleward latitudinal advance rates differed significantly among regions, being smallest in Eastern Canada (~10 m/year) and largest in Western Eurasia (~100 m/year). These rates were 1-2 orders of magnitude smaller than expected if vegetation distribution remained in equilibrium with climate. The many biotic and abiotic factors influencing FTE behaviour make poleward advance rates matching predicted 21st century CCVs (~103 -104  m/year) unlikely. The lack of empirical evidence for swift forest relocation and the discrepancy between CCV and FTE response contradict equilibrium model-based assumptions and warrant caution when assessing global-change-related biotic and abiotic implications, including land-atmosphere feedbacks and carbon sequestration.Funding was provided by the Norwegian Research Council (grants 176065/S30, 185023/S50, 160022/F40 and 244557/RI), the Government of Canada Program for International Polar Year, the US National Science Foundation, and the University of Cambridge

A mathematical framework for critical transitions: normal forms, variance and applications

Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to classify critical transitions by using bifurcation theory and normal forms in the singular limit. Based on this elementary classification, we analyze stochastic fluctuations and calculate scaling laws of the variance of stochastic sample paths near critical transitions for fast subsystem bifurcations up to codimension two. The theory is applied to several models: the Stommel-Cessi box model for the thermohaline circulation from geoscience, an epidemic-spreading model on an adaptive network, an activator-inhibitor switch from systems biology, a predator-prey system from ecology and to the Euler buckling problem from classical mechanics. For the Stommel-Cessi model we compare different detrending techniques to calculate early-warning signs. In the epidemics model we show that link densities could be better variables for prediction than population densities. The activator-inhibitor switch demonstrates effects in three time-scale systems and points out that excitable cells and molecular units have information for subthreshold prediction. In the predator-prey model explosive population growth near a codimension two bifurcation is investigated and we show that early-warnings from normal forms can be misleading in this context. In the biomechanical model we demonstrate that early-warning signs for buckling depend crucially on the control strategy near the instability which illustrates the effect of multiplicative noise.Comment: minor corrections to previous versio