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The exact solutions for the Navier–Stokes–Fourier equations in the case of plane shock waves for dilute monatomic gases with constant transport coefficients were found by Becker in 1922. The solutions obtained are limited for a Prandtl's number given by Pr=3/4$Pr=3/4$. Besides the solutions for the speed and temperature, profiles were given in an implicit way. In this paper, we consider Becker's model to find some exact explicit solutions for dilute polyatomic gases. [ABSTRACT FROM AUTHOR]

This paper considers the exact solutions for plane shock waves in dilute polyatomic gases. The local enthalpy in the steady state plays an important role and fixes the Prandtl's number to write the temperature profile in an exact way. The condition for the Prandtl's number is a generalisation of Becker's result and now it considers the bulk viscosity. The velocity profile can also be found in an exact implicit way when the viscosity index is an arbitrary positive number. [ABSTRACT FROM AUTHOR]

It is shown that for a binary mixture of dilute gases characterized by the Boltzmann equation the Burnett contribution for the fluxes can be evaluated without solving the integrodifferential equations for the corrections to the distribution function to third order in the Chapman–Enskog method. The conservation equations can be closed knowing only the second-order solution (in the Chapman–Enskog method) to the Boltzmann equation which is well known. By considering a trace component of light particles in a heavy gas (Lorentz approximation) all the higher-order transport coefficients for the soft-sphere model can be evaluated and from these results an estimation of the Burnett corrections to the Navier–Stokes regime is given. Other pertinent results of this calculation are also discussed. [ABSTRACT FROM AUTHOR]

In 1922 Becker found an exact solution for shock waves in gases using the Navier-Stokes-Fourier constitutive equations for a Prandtl number of value 3/4 with constant transport coefficients. His analysis has been extended to study some cases where an implicit solution can be found in an exact way. In this work we consider this problem for the so-called soft-spheres model in which the viscosity and thermal conductivity are proportional to a power of the temperature η, κ ∝ T σ. In particular, we give implicit exact solutions for the Maxwell model (σ = 1), hard spheres (σ = 1 / 2), and when σ (the viscosity index) is a natural number. [ABSTRACT FROM AUTHOR]

In this work we present a phenomenological model to look for a better understanding of the shock-wave structure in dilute monatomic gases. The model is based on the principles of linear irreversible thermodynamics, where we have been aware of the flow anisotropy caused by the shock-wave propagation. Then a new coupling appears between the stress tensor and the heat flux. The comparisons with the experimental data available for argon as well as the direct simulation Monte Carlo method calculations are done and shown to support our proposal. [ABSTRACT FROM AUTHOR]

We use the Navier-Stokes-Fourier constitutive equations to study plane shock waves in dilute gases. It is shown that the experimental information on the normalized density profiles can be fit by using the so-called soft sphere model, in which the viscosity and thermal conductivity are proportional to a power of the temperature. [ABSTRACT FROM AUTHOR]

Several continuum theories for shock waves give rise to a set of differential equations in which the analysis of the underlying vector field can be done using the tools of the theory of dynamical systems. We illustrate the importance of the divergences associated with the vector field by considering the ideas by Maxwell and Cattaneo and apply them to study shock waves in dilute gases. By comparing the predictions of the Maxwell-Cattaneo equations with shock wave experiments we are lead to the following conclusions: (a) For low compressions (low Mach numbers: M) the results from the Maxwell-Cattaneo equations provide profiles that are in fair agreement with the experiments, (b) as the Mach number is increased we find a range of Mach numbers (1.27≈M1M2) shock wave solutions can be found though they differ significantly from experiments. [ABSTRACT FROM AUTHOR]

In this work, we establish some fluctuation relations for a classical two-dimensional system of independent charged harmonic oscillators in the presence of an electromagnetic field. The main fluctuation relation quantifies irreversible behavior by comparing probabilities of observing particular trajectories during forward and backward processes and is expressed in terms of the work performed by the externally time-dependent electric field when the system is driven away from equilibrium. In the absence of a harmonic force and assuming a constant electric field, our theoretical results reduce to the fluctuation relations for a classical two-dimensional system of noninteracting electrons under the influence of externally crossed electric and magnetic fields, which were recently studied [D. Roy and N. Kumar, Phys. Rev. E 78, 052102 (2008)]. Finally, by considering the dragging of the center of the harmonic trap potential given by the presence of the arbitrary time-dependent electric field, the work-fluctuation theorem and the Jarzynski equality are verified.

We study the statistical properties of the total work associated with the Langevin equation for an electrically charged Brownian particle in a two-dimensional harmonic trap and in the presence of a uniform magnetic field. The calculations are performed under the overdamped approximation. The center of the harmonic trap is dragged in an arbitrary time-dependent way. As a result we have found the relation of the averaged work and the variance in the work distribution in the presence of the magnetic field. In addition, the Jarzynski equality (JE) is considered when the potential associated with the working force contains a time-dependent term, giving a way to calculate the change in the free energy. The particular cases in Jayannavar and Sahoo's work [Phys. Rev. E 75, 032102 (2007)] and their use of the JE are also discussed.

In this paper, the stochastic diffusion process of a charged classical harmonic oscillator in a constant magnetic field is exactly described through the analytical solution of the associated Langevin equation. Due to the presence of the magnetic field, stochastic diffusion takes place across and along the magnetic field. Along the magnetic field, the Brownian motion is exactly the same as that of the ordinary one-dimensional classical harmonic oscillator, which was very well described in Chandrasekhar's celebrated paper [Rev. Mod. Phys. 15, 1 (1943)]. Across the magnetic field, the stochastic process takes place on a plane, perpendicular to the magnetic field. For internally Gaussian white noise, this planar-diffusion process is exactly described through the first two moments of the positions and velocities and their corresponding cross correlations. In the absence of the magnetic field, our analytical results are the same as those calculated by Chandrasekhar for the ordinary harmonic oscillator. The stochastic planar diffusion is also well characterized in the overdamped approximation, through the solutions of the Langevin equation.

In this work we show that moment methods devised to solve the Boltzmann kinetic equation for a simple gas exhibit some inconsistencies. This puzzle, which also appears for the Chapman-Enskog method, is solved resorting to a perturbative expansion in the Knudsen number, thus allowing for a clear way to arrive at a closure condition.

We show that while Eu's claim is true that we made a mistake regarding the asymptotic behavior of his theory is true, the correct asymptotic behavior cannot have a physical meaning. We analyze in more detail his theory for a dilute gas of rigid spheres, and show that in some cases it predicts a negative value of the xx component of the pressure tensor.

Two recent works have shown that at small Knudsen number (K) the pressure and temperature profiles in plane Poiseuille flow exhibit a different qualitative behavior from the profiles obtained by the Navier-Stokes equations. Tij and Santos [J. Stat. Phys. 76, 1399 (1994)] used the Bhatnagar-Gross-Kook model to show that the temperature profile is bimodal and the pressure profile is nonconstant. Malek-Mansour, Baras, and Garcia [Physica A 240, 255 (1997)] qualitatively confirmed these predictions in computer experiments using the direct simulation Monte Carlo method (DSMC). In this paper we compare the DSMC measurements of hydrodynamic variables and non-equilibrium fluxes with numerical solutions of the Burnett equations. Given that they are in better agreement with molecular-dynamics simulations [E. Salomons and M. Mareschal, Phys. Rev. Lett. 69, 269 (1992)] of strong shock waves than Navier-Stokes [F. J. Uribe, R. M. Velasco, and L. S. García-Colín, Phys. Rev. Lett. 81, 2044 (1998)], and that they are second order in Knudsen number suggests that the Burnett equations may provide a better description for large K. We find that for plane Poiseuille flow the Burnett equations do not predict the bimodal temperature profile but do recover many of the other anomalous features (e.g., nonconstant pressure and nonzero parallel heat flux).

The Grad ten-moment approximation (no heat flux) is analyzed for cylindrical symmetry in a stationary situation in which the gradients of the fluxes are assumed to be small. We show that if the collision term in the transport equation, resulting from the ten-moment approximation, is linearized in the fluxes, we can obtain a viscosity (etal) that depends on the gradient of the velocity with the correct limiting behavior for small gradients. The nonlinear contribution of the fluxes to the collision term are then taken into account to derive an expression for the viscosity (eta(nl)) as a function of the gradient of the velocity. A comparison between etal and eta(nl) is performed finding that the maximum percentage deviation between them is 0.52% when the gradient of the hydrodynamic velocity is positive, but when the gradient is negative the situation changes dramatically.

A 4.5-mm filarial worm was removed from the anterior chamber of the left eye of a 56-year-old man who had lost the sight in the right eye due to trauma some years earlier. The worm was removed intact through an upper scleral incision with a corneal based flap. Within 2 months vision was normal. The worm was identified as a sexually mature male of an undescribed species of Loaina Eberhard and Orihel 1984, a genus related to Loa and Dirofilaria.