Monte Carlo simulation of a hard-sphere gas in the planar Fourier flow with a gravity field

By means of the Direct Simulation Monte Carlo method, the Boltzmann equation is numerically solved for a gas of hard spheres enclosed between two parallel plates kept at different temperatures and subject to the action of a gravity field normal to the plates. The profiles of pressure, density, temperature and heat flux are seen to be quite sensitive to the value of the gravity acceleration $g$. If the gravity field and the heat flux are parallel ($g>0$), the magnitudes of both the temperature gradient and the heat flux are smaller than in the opposite case ($g<0$). When considering the actual heat flux relative to the value predicted by the Fourier law, it is seen that, if $g>0$, the ratio increases as the reduced local field strength increases, while the opposite happens if $g<0$. The simulation results are compared with theoretical predictions for Maxwell moleculesComment: 18 pages (LaTex), 7 figures (eps

Non-Newtonian Couette-Poiseuille flow of a dilute gas

The steady state of a dilute gas enclosed between two infinite parallel plates in relative motion and under the action of a uniform body force parallel to the plates is considered. The Bhatnagar-Gross-Krook model kinetic equation is analytically solved for this Couette-Poiseuille flow to first order in the force and for arbitrary values of the Knudsen number associated with the shear rate. This allows us to investigate the influence of the external force on the non-Newtonian properties of the Couette flow. Moreover, the Couette-Poiseuille flow is analyzed when the shear-rate Knudsen number and the scaled force are of the same order and terms up to second order are retained. In this way, the transition from the bimodal temperature profile characteristic of the pure force-driven Poiseuille flow to the parabolic profile characteristic of the pure Couette flow through several intermediate stages in the Couette-Poiseuille flow are described. A critical comparison with the Navier-Stokes solution of the problem is carried out.Comment: 24 pages, 5 figures; v2: discussion on boundary conditions added; 10 additional references. Published in a special issue of the journal "Kinetic and Related Models" dedicated to the memory of Carlo Cercignan

An exact solution of the inelastic Boltzmann equation for the Couette flow with uniform heat flux

In the steady Couette flow of a granular gas the sign of the heat flux gradient is governed by the competition between viscous heating and inelastic cooling. We show from the Boltzmann equation for inelastic Maxwell particles that a special class of states exists where the viscous heating and the inelastic cooling exactly compensate each other at every point, resulting in a uniform heat flux. In this state the (reduced) shear rate is enslaved to the coefficient of restitution $\alpha$, so that the only free parameter is the (reduced) thermal gradient $\epsilon$. It turns out that the reduced moments of order $k$ are polynomials of degree $k-2$ in $\epsilon$, with coefficients that are nonlinear functions of $\alpha$. In particular, the rheological properties ($k=2$) are independent of $\epsilon$ and coincide exactly with those of the simple shear flow. The heat flux ($k=3$) is linear in the thermal gradient (generalized Fourier's law), but with an effective thermal conductivity differing from the Navier--Stokes one. In addition, a heat flux component parallel to the flow velocity and normal to the thermal gradient exists. The theoretical predictions are validated by comparison with direct Monte Carlo simulations for the same model.Comment: 16 pages, 4 figures,1 table; v2: minor change

Kinetic Theory of a Dilute Gas System under Steady Heat Conduction

The velocity distribution function of the steady-state Boltzmann equation for hard-core molecules in the presence of a temperature gradient has been obtained explicitly to second order in density and the temperature gradient. Some thermodynamical quantities are calculated from the velocity distribution function for hard-core molecules and compared with those for Maxwell molecules and the steady-state Bhatnagar-Gross-Krook(BGK) equation. We have found qualitative differences between hard-core molecules and Maxwell molecules in the thermodynamical quantities, and also confirmed that the steady-state BGK equation belongs to the same universality class as Maxwell molecules.Comment: 36 pages, 4 figures, 5 table

Perturbations of Noise: The origins of Isothermal Flows

We make a detailed analysis of both phenomenological and analytic background for the "Brownian recoil principle" hypothesis (Phys. Rev. A 46, (1992), 4634). A corresponding theory of the isothermal Brownian motion of particle ensembles (Smoluchowski diffusion process approximation), gives account of the environmental recoil effects due to locally induced tiny heat flows. By means of local expectation values we elevate the individually negligible phenomena to a non-negligible (accumulated) recoil effect on the ensemble average. The main technical input is a consequent exploitation of the Hamilton-Jacobi equation as a natural substitute for the local momentum conservation law. Together with the continuity equation (alternatively, Fokker-Planck), it forms a closed system of partial differential equations which uniquely determines an associated Markovian diffusion process. The third Newton law in the mean is utilised to generate diffusion-type processes which are either anomalous (enhanced), or generically non-dispersive.Comment: Latex fil

Normal solutions of the Boltzmann equation for highly nonequilibrium Fourier flow and Couette flow

The state of a single-species monatomic gas from near-equilibrium to highly nonequilibrium conditions is investigated using analytical and numerical methods. Normal solutions of the Boltzmann equation for Fourier flow (uniform heat flux) and Couette flow (uniform shear stress) are found in terms of the heat-flux and shear-stress Knudsen numbers. Analytical solutions are found for inverse-power-law molecules from hard-sphere through Maxwell at small Knudsen numbers using Chapman-Enskog (CE) theory and for Maxwell molecules at finite Knudsen numbers using a moment-hierarchy (MH) method. Corresponding numerical solutions are obtained using the Direct Simulation Monte Carlo (DSMC) method of Bird. The thermal conductivity, the viscosity, and the Sonine-polynomial coefficients of the velocity distribution function from DSMC agree with CE results at small Knudsen numbers and with MH results at finite Knudsen numbers. Subtle differences between inverse-power-law, variable-soft-sphere, and variable-hard-sphere representations of Maxwell molecules are observed. The MH and DSMC results both indicate that the effective thermal conductivity and the effective viscosity for Maxwell molecules are independent of the heat-flux Knudsen number, and additional DSMC simulations indicate that these transport properties for hard-sphere molecules decrease slightly as the heat-flux Knudsen number is increased. Similarly, the MH and DSMC results indicate that the effective thermal conductivity and the effective viscosity for Maxwell molecules decrease as the shear-stress Knudsen number is increased, and additional DSMC simulations indicate the same behavior for hard-sphere molecules. These results provide strong evidence that the DSMC method can be used to determine the state of a gas under highly nonequilibrium conditionsComment: 33 pages (preprint format) + 15 figures + 3 tables; to be published in Physics of Fluids; v2: Abstract in the abstract web page has been corrected, but otherwise the paper remains the same as in v

Pathways through which health influences early retirement: a qualitative study

Background: Due to the aeging of the population, there is a societal need for workers to prolong their working lives. In the Netherlands, many employees still leave the workforce before the official retirement age of 65. Previous quantitative research showed that poor self-perceived health is a risk factor of (non-disability) early retirement. However, little is known on how poor health may lead to early retirement, and why poor health leads to early retirement in some employees, but not in others. Therefore, the present qualitative study aims to identify in which ways health influences early retirement. Methods. Face-to-face semi-structured interviews were conducted with 30 employees (60-64 years) who retired before the official retirement age of 65. Participants were selected from the Study on Transitions in Employment, Ability and Motivation. The interviews were transcribed verbatim, a summary was made including a timeline, and the interviews were open coded. Results: In 15 of the 30 persons, health played a role in early retirement. Both poor and good health influenced early retirement. For poor health, four pathways were identified. First, employees felt unable to work at all due to health problems. Second, health problems resulted in a self-perceived (future) decline in the ability to work, and employees chose to retire early. Third, employees with health problems were afraid of a further decline in health, and chose to retire early. Fourth, employees with poor health retired early because they felt pushed out by their employer, although they themselves did not experience a reduced work ability. A good health influenced early retirement, since persons wanted to enjoy life while their health still allowed to do so. The financial opportunity to retire sometimes triggered the influence of poor health on early retirement, and often triggered the influence of good health. Employees and employers barely discussed opportunities to prolong working life. Conclusions: Poor and good health influence early retirement via several different pathways. To prolong working life, a dialogue between employers and employees and tailored work-related interventions may be helpful