Travelling waves in a mixture of gases with bimolecular reversible reactions

Starting from the kinetic approach for a mixture of reacting gases whose particles interact through elastic scattering and a bimolecular reversible chemical reaction, the equations that govern the dynamics of the system are obtained by means of the relevant Boltzmann-like equation. Conservation laws are considered. Fluid dynamic approximations are used at the Euler level to obtain a close set of PDEs for six unknown macroscopic fields. The dispersion relation of the mixture of reacting gases is explicitly derived in the homogeneous equilibrium state. A set of ODE that governs the propagation of a plane travelling wave is obtained using the Galilei invariance. After numerical integration some solutions, including the well-known Maxwellian and the hard spheres cases, are found for various meaningful interaction laws. The main macroscopic observables for the gas mixture such as the drift velocity, temperature, total density, pressure and its chemical composition are shown.Comment: 13 pages, 2 figures, accepted on Physica

Twist operator correlation functions in O(n) loop models

Using conformal field theoretic methods we calculate correlation functions of geometric observables in the loop representation of the O(n) model at the critical point. We focus on correlation functions containing twist operators, combining these with anchored loops, boundaries with SLE processes and with double SLE processes. We focus further upon n=0, representing self-avoiding loops, which corresponds to a logarithmic conformal field theory (LCFT) with c=0. In this limit the twist operator plays the role of a zero weight indicator operator, which we verify by comparison with known examples. Using the additional conditions imposed by the twist operator null-states, we derive a new explicit result for the probabilities that an SLE_{8/3} wind in various ways about two points in the upper half plane, e.g. that the SLE passes to the left of both points. The collection of c=0 logarithmic CFT operators that we use deriving the winding probabilities is novel, highlighting a potential incompatibility caused by the presence of two distinct logarithmic partners to the stress tensor within the theory. We provide evidence that both partners do appear in the theory, one in the bulk and one on the boundary and that the incompatibility is resolved by restrictive bulk-boundary fusion rules.Comment: 18 pages, 8 figure

Effects of Turbulence, Eccentricity Damping, and Migration Rate on the Capture of Planets into Mean Motion Resonance

Pairs of migrating extrasolar planets often lock into mean motion resonance as they drift inward. This paper studies the convergent migration of giant planets (driven by a circumstellar disk) and determines the probability that they are captured into mean motion resonance. The probability that such planets enter resonance depends on the type of resonance, the migration rate, the eccentricity damping rate, and the amplitude of the turbulent fluctuations. This problem is studied both through direct integrations of the full 3-body problem, and via semi-analytic model equations. In general, the probability of resonance decreases with increasing migration rate, and with increasing levels of turbulence, but increases with eccentricity damping. Previous work has shown that the distributions of orbital elements (eccentricity and semimajor axis) for observed extrasolar planets can be reproduced by migration models with multiple planets. However, these results depend on resonance locking, and this study shows that entry into -- and maintenance of -- mean motion resonance depends sensitively on migration rate, eccentricity damping, and turbulence.Comment: 43 pages including 14 figures; accepted for publication in The Astrophysical Journa

Drones and Butterflies : A Low-Cost UAV System for Rapid Detection and Identification of Unconventional Minefields

Aerially-deployed plastic landmines in post-conflict nations present unique detection and disposal challenges. Their small size, randomized distribution during deployment, and low-metal content make these mines more difficult to identify using traditional methods of electromagnetic mine detection. Perhaps the most notorious of these mines is the Sovietera PFM-1 “butterfly mine,” widely used during the decade-long Soviet-Afghan conflict between 1979 and 1989. Predominantly used by the Soviet forces to block otherwise inaccessible mountain passages, many PFM-1 minefields remain in place due to the high associated costs of access and demining. While the total number of deployed PFM-1 mines in Afghanistan is poorly documented, PFM-1 landmines make up a considerable percentage of the estimated 10 million landmines remaining in place across Afghanistan. Their detection and disposal presents a unique logistical challenge for largely the same reasons that their deployment was rationalized in inaccessible and sparsely populated areas of the country

Percolation Crossing Formulas and Conformal Field Theory

Using conformal field theory, we derive several new crossing formulas at the two-dimensional percolation point. High-precision simulation confirms these results. Integrating them gives a unified derivation of Cardy's formula for the horizontal crossing probability $\Pi_h(r)$, Watts' formula for the horizontal-vertical crossing probability $\Pi_{hv}(r)$, and Cardy's formula for the expected number of clusters crossing horizontally $\mathcal{N}_h(r)$. The main step in our approach implies the identification of the derivative of one primary operator with another. We present operator identities that support this idea and suggest the presence of additional symmetry in $c=0$ conformal field theories.Comment: 12 pages, 5 figures. Numerics improved; minor correction

Mixtures in non stable Levy processes

We analyze the Levy processes produced by means of two interconnected classes of non stable, infinitely divisible distribution: the Variance Gamma and the Student laws. While the Variance Gamma family is closed under convolution, the Student one is not: this makes its time evolution more complicated. We prove that -- at least for one particular type of Student processes suggested by recent empirical results, and for integral times -- the distribution of the process is a mixture of other types of Student distributions, randomized by means of a new probability distribution. The mixture is such that along the time the asymptotic behavior of the probability density functions always coincide with that of the generating Student law. We put forward the conjecture that this can be a general feature of the Student processes. We finally analyze the Ornstein--Uhlenbeck process driven by our Levy noises and show a few simulation of it.Comment: 28 pages, 3 figures, to be published in J. Phys. A: Math. Ge

Solutions of the Maxwell equations and photon wave functions

Properties of six-component electromagnetic field solutions of a matrix form of the Maxwell equations, analogous to the four-component solutions of the Dirac equation, are described. It is shown that the six-component equation, including sources, is invariant under Lorentz transformations. Complete sets of eigenfunctions of the Hamiltonian for the electromagnetic fields, which may be interpreted as photon wave functions, are given both for plane waves and for angular-momentum eigenstates. Rotationally invariant projection operators are used to identify transverse or longitudinal electric and magnetic fields. For plane waves, the velocity transformed transverse wave functions are also transverse, and the velocity transformed longitudinal wave functions include both longitudinal and transverse components. A suitable sum over these eigenfunctions provides a Green function for the matrix Maxwell equation, which can be expressed in the same covariant form as the Green function for the Dirac equation. Radiation from a dipole source and from a Dirac atomic transition current are calculated to illustrate applications of the Maxwell Green function.Comment: 75 pages; typo corrected, slight text chang

Propagation and Structure of Planar Streamer Fronts

Streamers often constitute the first stage of dielectric breakdown in strong electric fields: a nonlinear ionization wave transforms a non-ionized medium into a weakly ionized nonequilibrium plasma. New understanding of this old phenomenon can be gained through modern concepts of (interfacial) pattern formation. As a first step towards an effective interface description, we determine the front width, solve the selection problem for planar fronts and calculate their properties. Our results are in good agreement with many features of recent three-dimensional numerical simulations. In the present long paper, you find the physics of the model and the interfacial approach further explained. As a first ingredient of this approach, we here analyze planar fronts, their profile and velocity. We encounter a selection problem, recall some knowledge about such problems and apply it to planar streamer fronts. We make analytical predictions on the selected front profile and velocity and confirm them numerically. (abbreviated abstract)Comment: 23 pages, revtex, 14 ps file

The high-precision, charge-dependent Bonn nucleon-nucleon potential (CD-Bonn)

We present a charge-dependent nucleon-nucleon (NN) potential that fits the world proton-proton data below 350 MeV available in the year of 2000 with a chi^2 per datum of 1.01 for 2932 data and the corresponding neutron-proton data with chi^2/datum = 1.02 for 3058 data. This reproduction of the NN data is more accurate than by any phase-shift analysis and any other NN potential. The charge-dependence of the present potential (that has been dubbed `CD-Bonn') is based upon the predictions by the Bonn Full Model for charge-symmetry and charge-independence breaking in all partial waves with J <= 4. The potential is represented in terms of the covariant Feynman amplitudes for one-boson exchange which are nonlocal. Therefore, the off-shell behavior of the CD-Bonn potential differs in a characteristic and well-founded way from commonly used local potentials and leads to larger binding energies in nuclear few- and many-body systems, where underbinding is a persistent problem.Comment: 69 pages (RevTex) including 20 tables and 9 figures (ps files

Comparing Methods to Constrain Future European Climate Projections Using a Consistent Framework

Political decisions, adaptation planning, and impact assessments need reliable estimates of future climate change and related uncertainties. To provide these estimates, different approaches to constrain, filter, or weight climate model projections into probabilistic distributions have been proposed. However, an assessment of multiple such methods to, for example, expose cases of agreement or disagreement, is often hindered by a lack of coordination, with methods focusing on a variety of variables, time periods, regions, or model pools. Here, a consistent framework is developed to allow a quantitative comparison of eight different methods; focus is given to summer temperature and precipitation change in three spatial regimes in Europe in 2041–60 relative to 1995–2014. The analysis draws on projections from several large ensembles, the CMIP5 multimodel ensemble, and perturbed physics ensembles, all using the high-emission scenario RCP8.5. The methods’ key features are summarized, assumptions are discussed, and resulting constrained distributions are presented. Method agreement is found to be dependent on the investigated region but is generally higher for median changes than for the uncertainty ranges. This study, therefore, highlights the importance of providing clear context about how different methods affect the assessed uncertainty—in particular, the upper and lower percentiles that are of interest to risk-averse stakeholders. The comparison also exposes cases in which diverse lines of evidence lead to diverging constraints; additional work is needed to understand how the underlying differences between methods lead to such disagreements and to provide clear guidance to users.ISSN:0894-8755ISSN:1520-044