Adaptive and Recursive Time Relaxed Monte Carlo methods for rarefied gas dynamics

Recently a new class of Monte Carlo methods, called Time Relaxed Monte Carlo (TRMC), designed for the simulation of the Boltzmann equation close to fluid regimes have been introduced. A generalized Wild sum expansion of the solution is at the basis of the simulation schemes. After a splitting of the equation the time discretization of the collision step is obtained from the Wild sum expansion of the solution by replacing high order terms in the expansion with the equilibrium Maxwellian distribution; in this way speed up of the methods close to fluid regimes is obtained by efficiently thermalizing particles close to the equilibrium state. In this work we present an improvement of such methods which allows to obtain an effective uniform accuracy in time without any restriction on the time step and subsequent increase of the computational cost. The main ingredient of the new algorithms is recursivity. Several techniques can be used to truncate the recursive trees generated by the schemes without deteriorating the accuracy of the numerical solution. Techniques based on adaptive strategies are presented. Numerical results emphasize the gain of efficiency of the present simulation schemes with respect to standard DSMC methods

Hybrid Entrepreneurship

In contrast to previous efforts to model the individual’s movement from wage work into entrepreneurship, we consider that individuals might transition incrementally by retaining their wage job while entering into self-employment. We show that these hybrid entrepreneurs represent a significant share of all entrepreneurial activity. Theoretical arguments are proposed to suggest why hybrid entrants are distinct from self-employment entrants, and why hybrid entry may facilitate subsequent entry into full self-employment. We demonstrate that there are significant theoretical and empirical consequences for this group and our understanding of self-employment entry and labor market dynamics. Using matched employee-employer data over eight years, we test the model on a population of Swedish wage earners in the knowledge-intensive sector.Hybrid entrepreneurship; Self-employment; Labour market dynamics; Transition determinants; Employee-employer data

The impact of anticipation in dynamical systems

Collective motion in biology is often modelled as a dynamical system, in which individuals are represented as particles whose interactions are determined by the current state of the system. Many animals, however, including humans, have predictive capabilities, and presumably base their behavioural decisions---at least partially---upon an anticipated state of their environment. We explore a minimal version of this idea in the context of particles that interact according to a pairwise potential. Anticipation enters the picture by calculating the interparticle forces from linear extrapolations of the particle positions some time $\tau$ into the future. Simulations show that for intermediate values of $\tau$, compared to a transient time scale defined by the potential and the initial conditions, the particles form rotating clusters in which the particles are arranged in a hexagonal pattern. Analysis of the system shows that anticipation induces energy dissipation and we show that the kinetic energy asymptotically decays as $1/t$. Furthermore, we show that the angular momentum is not necessarily conserved for $\tau >0$, and that asymmetries in the initial condition therefore can cause rotational movement. These results suggest that anticipation could play an important role in collective behaviour, since it induces pattern formation and stabilises the dynamics of the system.Comment: Major revision compared to previous version. All figures replaced. Only introduction and discussion remain intac

Simultaneous, in situ measurements of OH and HO_2 in the stratosphere

Stratospheric OH and HO_2 radical densities have been measured between 36 and 23 km using a balloon-borne, in situ instrument launched from Palestine, TX on August 25, 1989. OH is detected using the laser-induced fluorescence technique (LIF) employing a Cu-vapor-laser pumped dye laser coupled with an enclosed-flow detection chamber. HO_2 is detected nearly simultaneously by adding No to the sample flow to convert ambient HO_2 to OH. Observed OH and HO_2 densities ranged from 8.0 ± 2.8 × 10^6 and 1.4 ± 0.5 × 10^7 molec cm^(−3), respectively, at 36 km, to 1.4± 0.5 × 10^6 and 3.0± 1.0 × 10^6 at 23 km, where the uncertainty is ±1σ. The HO_2 density exhibits a maximum in the 34–30 km of 1.7±0.6 × 10^7. The data were obtained over a solar zenith angle variation of 51° at 36 km to 61° at 23 km. O_3 and H_2O densities also were measured simultaneously with separate instruments

Observation of isoprene hydroxynitrates in the southeastern United States and implications for the fate of NO_x

Isoprene hydroxynitrates (IN) are tracers of the photochemical oxidation of isoprene in high NO_x environments. Production and loss of IN have a significant influence on the NO_x cycle and tropospheric O_3 chemistry. To better understand IN chemistry, a series of photochemical reaction chamber experiments was conducted to determine the IN yield from isoprene photooxidation at high NO concentrations (> 100 ppt). By combining experimental data and calculated isomer distributions, a total IN yield of 9(+4/−3) % was derived. The result was applied in a zero-dimensional model to simulate production and loss of ambient IN observed in a temperate forest atmosphere, during the Southern Oxidant and Aerosol Study (SOAS) field campaign, from 27 May to 11 July 2013. The 9 % yield was consistent with the observed IN/(MVK+MACR) ratios observed during SOAS. By comparing field observations with model simulations, we identified NO as the limiting factor for ambient IN production during SOAS, but vertical mixing at dawn might also contribute (~ 27 %) to IN dynamics. A close examination of isoprene's oxidation products indicates that its oxidation transitioned from a high-NO dominant chemical regime in the morning into a low-NO dominant regime in the afternoon. A significant amount of IN produced in the morning high NO regime could be oxidized in the low NO regime, and a possible reaction scheme was proposed

On Strong Convergence to Equilibrium for the Boltzmann Equation with Soft Potentials

The paper concerns $L^1$- convergence to equilibrium for weak solutions of the spatially homogeneous Boltzmann Equation for soft potentials (-4\le \gm<0), with and without angular cutoff. We prove the time-averaged $L^1$-convergence to equilibrium for all weak solutions whose initial data have finite entropy and finite moments up to order greater than 2+|\gm|. For the usual $L^1$-convergence we prove that the convergence rate can be controlled from below by the initial energy tails, and hence, for initial data with long energy tails, the convergence can be arbitrarily slow. We also show that under the integrable angular cutoff on the collision kernel with -1\le \gm<0, there are algebraic upper and lower bounds on the rate of $L^1$-convergence to equilibrium. Our methods of proof are based on entropy inequalities and moment estimates.Comment: This version contains a strengthened theorem 3, on rate of convergence, considerably relaxing the hypotheses on the initial data, and introducing a new method for avoiding use of poitwise lower bounds in applications of entropy production to convergence problem

Derivation of tropospheric methane from TCCON CH₄ and HF total column observations

The Total Carbon Column Observing Network (TCCON) is a global ground-based network of Fourier transform spectrometers that produce precise measurements of column-averaged dry-air mole fractions of atmospheric methane (CH₄). Temporal variability in the total column of CH₄ due to stratospheric dynamics obscures fluctuations and trends driven by tropospheric transport and local surface fluxes that are critical for understanding CH₄ sources and sinks. We reduce the contribution of stratospheric variability from the total column average by subtracting an estimate of the stratospheric CH₄ derived from simultaneous measurements of hydrogen fluoride (HF). HF provides a proxy for stratospheric CH₄ because it is strongly correlated to CH₄ in the stratosphere, has an accurately known tropospheric abundance (of zero), and is measured at most TCCON stations. The stratospheric partial column of CH₄ is calculated as a function of the zonal and annual trends in the relationship between CH₄ and HF in the stratosphere, which we determine from ACE-FTS satellite data. We also explicitly take into account the CH₄ column averaging kernel to estimate the contribution of stratospheric CH₄ to the total column. The resulting tropospheric CH₄ columns are consistent with in situ aircraft measurements and augment existing observations in the troposphere

In situ measurements of tropospheric volcanic plumes in Ecuador and Colombia during TC^4

A NASA DC-8 research aircraft penetrated tropospheric gas and aerosol plumes sourced from active volcanoes in Ecuador and Colombia during the Tropical Composition, Cloud and Climate Coupling (TC^4) mission in July–August 2007. The likely source volcanoes were Tungurahua (Ecuador) and Nevado del Huila (Colombia). The TC^4 data provide rare insight into the chemistry of volcanic plumes in the tropical troposphere and permit a comparison of SO_2 column amounts measured by the Ozone Monitoring Instrument (OMI) on the Aura satellite with in situ SO_2 measurements. Elevated concentrations of SO_2, sulfate aerosol, and particles were measured by DC-8 instrumentation in volcanic outflow at altitudes of 3–6 km. Estimated plume ages range from ~2 h at Huila to ~22–48 h downwind of Ecuador. The plumes contained sulfate-rich accumulation mode particles that were variably neutralized and often highly acidic. A significant fraction of supermicron volcanic ash was evident in one plume. In-plume O_3 concentrations were ~70%–80% of ambient levels downwind of Ecuador, but data are insufficient to ascribe this to O_3 depletion via reactive halogen chemistry. The TC^4 data record rapid cloud processing of the Huila volcanic plume involving aqueous-phase oxidation of SO_2 by H_2O_2, but overall the data suggest average in-plume SO_2 to sulfate conversion rates of ~1%–2% h^(−1). SO_2 column amounts measured in the Tungurahua plume (~0.1–0.2 Dobson units) are commensurate with average SO_2 columns retrieved from OMI measurements in the volcanic outflow region in July 2007. The TC^4 data set provides further evidence of the impact of volcanic emissions on tropospheric acidity and oxidizing capacity

In situ measurements of tropospheric volcanic plumes in Ecuador and Colombia during TC

A NASA DC‐8 research aircraft penetrated tropospheric gas and aerosol plumes sourced from active volcanoes in Ecuador and Colombia during the Tropical Composition, Cloud and Climate Coupling (TC4 ) mission in July–August 2007. The likely source volcanoes were Tungurahua (Ecuador) and Nevado del Huila (Colombia). The TC4 data provide rare insight into the chemistry of volcanic plumes in the tropical troposphere and permit a comparison of SO2 column amounts measured by the Ozone Monitoring Instrument (OMI) on the Aura satellite with in situ SO2 measurements. Elevated concentrations of SO2, sulfate aerosol, and particles were measured by DC‐8 instrumentation in volcanic outflow at altitudes of 3–6 km. Estimated plume ages range from ∼2 h at Huila to ∼22–48 h downwind of Ecuador. The plumes contained sulfate‐rich accumulation mode particles that were variably neutralized and often highly acidic. A significant fraction of supermicron volcanic ash was evident in one plume. In‐plume O3 concentrations were ∼70%–80% of ambient levels downwind of Ecuador, but data are insufficient to ascribe this to O3 depletion via reactive halogen chemistry. The TC4 data record rapid cloud processing of the Huila volcanic plume involving aqueous‐phase oxidation of SO2 by H2O2, but overall the data suggest average in‐plume SO2 to sulfate conversion rates of ∼1%–2% h−1 . SO2 column amounts measured in the Tungurahua plume (∼0.1–0.2 Dobson units) are commensurate with average SO2 columns retrieved from OMI measurements in the volcanic outflow region in July 2007. The TC4 data set provides further evidence of the impact of volcanic emissions on tropospheric acidity and oxidizing capacit