Weak discontinuities in one-dimensional compressible nonideal gas dynamics

This article concerns the study of various parameter effects on the propagation of weak discontinuities by using the method of characteristics. Analytical solutions of the quasi-linear system of hyperbolic partial differential equations (PDEs) are obtained and examined the evolutionary behavior of shock in the characteristic plane. The general behavior of solutions to the Bernoulli equation, which determines the evolution of weak discontinuity in a nonlinear system, is studied in detail. Also, we discuss the formation and distortion of compressive and expansive discontinuities under the van der Waals parameter effect and small particles for planar and cylindrical symmetric flow. The comparison between planar flow and cylindrical symmetric flow is studied under the influence of nonidealness and mass fraction of dust particles. It is found that the compressive waves become shock after a certain lapse of time. The medium considered here is the mixture of van der Waals gas with small dust particles.

Study of shocks in a nonideal dusty gas using Maslov, Guderley, and CCW methods for shock exponents

In this work, we consider the system of partial differential equations describing one-dimensional (1D) radially symmetric (i.e., cylindrical or spherical) flow of a nonideal gas with small solid dust particles. We analyze the implosion of cylindrical and spherical symmetric strong shock waves in a mixture of a nonideal gas with small solid dust particles. An evolution equation for the strong cylindrical and spherical shock waves is derived by using the Maslov technique based on the kinematics of 1D motion. The approximate value of the similarity exponent describing the behavior of strong shocks is calculated by applying a first-order truncation approximation. The obtained approximate values of similarity exponent are compared with the values of the similarity exponent obtained from Whitham’s rule and Guderley’s method. All the above computations are performed for the different values of mass fraction of dust particles, relative specific heat, and the ratio of the density of dust particle to the density of the mixture and van der Waals excluded volume.

An Approach of Statistical Corrections to Interactions in Hadron Resonance Gas

We propose a new model for hadrons with quantum mechanical attractive and repulsive interactions sensitive to some spatial correlation length parameter inspired by the Beth-Uhlenbeck quantum mechanical nonideal gas model (Uhlenbeck and Beth, 1937). We confront the thermodynamics calculated using our model with a corresponding recent lattice data at four different values of the baryon chemical potential, μ b = 0 , 170 , 340 , 425 MeV over temperatures ranging from 130 MeV to 200 MeV and for five values for the correlation length ranging from 0 to 0.2 fm. For equilibrium temperatures up to the vicinity of the chiral phase transition temperature ≃160 MeV, a decent fitting between the model and the lattice data is observed for different values of r , especially at μ b , r = 170 , 0.05 , 340 , 0.1 , and 340 , 0.15 , where μ b is in MeV and r is in fm. For the vanishing chemical potential, the uncorrelated model r = 0 , which corresponds to the ideal hadron resonance gas model, seems to offer the best fit. The quantum hadron correlations seem to be more probable at nonvanishing chemical potentials, especially within the range μ b ∈ 170 , 340 MeV .

Systems of Interacting Particles

This chapter presents two examples of the application of Boltzmann statistics to systems with nontrivial interactions between particles. The first example is a nonideal gas, treated approximately using a series expansion that we can visualize in terms of simple diagrams. The second example is a model of a ferromagnet as a collection of two-state particles interacting with their nearest neighbors. It is easy to solve this model exactly in one dimension, and to gain a semi-quantitative understanding of why the system magnetizes below a critical temperature in two or three dimensions. The most powerful tool for studying this model, however, is numerical simulation on a computer using a random-sampling algorithm based on the Boltzmann distribution.

Amplification of Operational Uncertainty Induced by Nonideal Flows in Supersonic Turbine Cascades

In high-temperature transcritical organic Rankine cycles (ORCs), the expansion process may take place in the neighborhood of the thermodynamic critical point. In this region, many organic fluids feature a value of the fundamental derivative of gas dynamics Γ that is less than unity. As a consequence, severe nonideal gas-dynamic effects can be possibly observed. Examples of these nonideal effects are the nonmonotonic variation of the Mach number along an isentropic expansion, oblique shocks featuring an increase of the Mach number, and a significant dependence of the flow field on the upstream total state. To tackle this latter nonideal effect, an uncertainty-quantification strategy combined with Reynolds-averaged flow simulations is devised to evaluate the turbine performance in presence of operational uncertainty. The results clearly indicate that a highly nonideal expansion process leads to an amplification of the operational uncertainty. Specifically, given an uncertainty in the order of 1% in cycle nominal conditions, the mass flow rate and cascade losses vary ±4% and ±0.75 percentage points, respectively. These variations are four and six times larger than those prompted by an ideal-like expansion process. The flow delivered to the first rotating cascade is severely altered as well, leading to local variations in the rotor incidence angle up to 10 deg. A decomposition of variance contributions reveals that the uncertainty in the upstream total temperature is mainly responsible for these variations. Finally, the understanding of the physical mechanism behind these changes allows us to generalize the present findings to other organic-fluid flows.

Olfactory Detection Thresholds for Primary Aliphatic Alcohols in Mice

Probing the neural mechanisms that underlie each sensory system requires the presentation of perceptually appropriate stimulus concentrations. This is particularly relevant in the olfactory system as additional odorant receptors typically respond with increasing stimulus concentrations. Thus, perceptual measures of olfactory sensitivity provide an important guide for functional experiments. This study focuses on aliphatic alcohols because they are commonly used to survey neural activity in a variety of olfactory regions, probe the behavioral limits of odor discrimination, and assess odor-structure activity relationships in mice. However, despite their frequent use, a systematic study of the relative sensitivity of these odorants in mice is not available. Thus, we assayed the ability of C57BL/6J mice to detect a homologous series of primary aliphatic alcohols (1-propanol to 1-heptanol) using a head-fixed Go/No-Go operant conditioning assay combined with highly reproducible stimulus delivery. To aid in the accessibility of our data, we report the animal’s threshold to each odorant according to the 1) ideal gas condition, 2) nonideal gas condition (factoring in the activity of the odorant in the solvent), and 3) the liquid dilution of the odorant in the olfactometer. Of the odorants tested, mice were most sensitive to 1-hexanol and least sensitive to 1-butanol. These updated measures of murine sensitivity will hopefully guide experimenters in choosing appropriate stimulus concentrations for experiments using these odorants.