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

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

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

Balloon borne in-situ detection of OH in the stratosphere from 37 to 23 km

The OH number density in the stratosphere has been measured over the altitude interval of 37 to 23 km at midday via a balloon-borne gondola launched from Palestine, Texas on July 6, 1988. OH radicals are detected with a laser induced fluorescence instrument employing a 17 kHz repetition rate copper vapor laser pumped dye laser optically coupled to an enclosed flow, in-situ sampling chamber. OH abundances ranged from 88±31 pptv (1.1 ± 0.4 × 10^7 molec cm^(−3)) in the 36 to 35 km interval to 0.9 ± 0.8 pptv (8.7 ± 7.7 × 10^5 molec cm^(−3)) in the 24 to 23 km interval. The stated uncertainty (±1σ) includes that from both measurement precision and accuracy. Simultaneous detection of ozone and water vapor densities was carried out with separate on-board instruments

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

Formation and Propagation of Discontinuity for Boltzmann Equation in Non-Convex Domains

The formation and propagation of singularities for Boltzmann equation in bounded domains has been an important question in numerical studies as well as in theoretical studies. Consider the nonlinear Boltzmann solution near Maxwellians under in-flow, diffuse, or bounce-back boundary conditions. We demonstrate that discontinuity is created at the non-convex part of the grazing boundary, then propagates only along the forward characteristics inside the domain before it hits on the boundary again.Comment: 39 pages, 5 Figure

Measurement of atmospheric nitrous acid at Blodgett Forest during BEARPEX2007

Nitrous acid (HONO) is an important precursor of the hydroxyl radical (OH) in the lower troposphere. Understanding HONO chemistry, particularly its sources and contribution to HO_x (=OH+HO_2) production, is very important for understanding atmospheric oxidation processes. A highly sensitive instrument for detecting atmospheric HONO based on wet chemistry followed by liquid waveguide long path absorption photometry was deployed in the Biosphere Effects on Aerosols and Photochemistry Experiment (BEARPEX) at Blodgett Forest, California in late summer 2007. The median diurnal variation shows minimum HONO levels of about 20–30 pptv during the day and maximum levels of about 60–70 pptv at night, a diurnal pattern quite different from the results at various other forested sites. Measured HONO/NO_2 ratios for a 24-h period ranged from 0.05 to 0.13 with a mean ratio of 0.07. Speciation of reactive nitrogen compounds (NO_y) indicates that HONO accounted for only ~3% of total NO_y. However, due to the fast HONO loss through photolysis, a strong HONO source (1.59 ppbv day^(−1)) existed in this environment in order to sustain the observed HONO levels, indicating the significant role of HONO in NO_y cycling. The wet chemistry HONO measurements were compared to the HONO measurements made with a Chemical Ionization Mass Spectrometer (CIMS) over a three-day period. Good agreement was obtained between the measurements from the two different techniques. Using the expansive suite of photochemical and meteorological measurements, the contribution of HONO photolysis to HO_x budget was calculated to be relatively small (6%) compared to results from other forested sites. The lower HONO mixing ratio and thus its smaller contribution to HO_x production are attributed to the unique meteorological conditions and low acid precipitation at Blodgett Forest. Further studies of HONO in this kind of environment are needed to test this hypothesis and to improve our understanding of atmospheric oxidation and nitrogen budget

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

Supplier-induced demand for psychiatric admissions in Northern New England

The development of hospital service areas (HSAs) using small area analysis has been useful in examining variation in medical and surgical care; however, the techniques of small area analysis are underdeveloped in understanding psychiatric admission rates. We sought to develop these techniques in order to understand the relationship between psychiatric bed supply and admission rates in Northern New England. Our primary hypotheses were that there would be substantial variation in psychiatric admission across geographic settings and that bed availability would be positively correlated with admission rates, reflecting a supplier-induced demand phenomenon. Our secondary hypothesis was that the construction of psychiatric HSAs (PHSAs) would yield more meaningful results than the use of existing general medical hospital service areas