Showing papers on "Rarefaction published in 2017"

An extended macro traffic flow model accounting for the driver’s bounded rationality and numerical tests

Abstract: In this paper, we propose a macro traffic flow model to explore the effects of the driver’s bounded rationality on the evolutions of traffic waves (which include shock and rarefaction waves) and small perturbation, and on the fuel consumption and emissions (that include CO, HC and NO X ) during the evolution process. The numerical results illustrate that considering the driver’s bounded rationality can prominently smooth the wavefront of the traffic waves and improve the stability of traffic flow, which shows that the driver’s bounded rationality has positive impacts on traffic flow; but considering the driver’s bounded rationality reduces the fuel consumption and emissions only at the upstream of the rarefaction wave while enhances the fuel consumption and emissions under other situations, which shows that the driver’s bounded rationality has positive impacts on the fuel consumption and emissions only at the upstream of the rarefaction wave, while negative effects on the fuel consumption and emissions under other situations. In addition, the numerical results show that the driver’s bounded rationality has little prominent impact on the total fuel consumption, and emissions during the whole evolution of small perturbation.

RTK: efficient rarefaction analysis of large datasets

Abstract: Motivation The rapidly expanding microbiomics field is generating increasingly larger datasets, characterizing the microbiota in diverse environments. Although classical numerical ecology methods provide a robust statistical framework for their analysis, software currently available is inadequate for large datasets and some computationally intensive tasks, like rarefaction and associated analysis. Results Here we present a software package for rarefaction analysis of large count matrices, as well as estimation and visualization of diversity, richness and evenness. Our software is designed for ease of use, operating at least 7x faster than existing solutions, despite requiring 10x less memory. Availability and implementation C ++ and R source code (GPL v.2) as well as binaries are available from https://github.com/hildebra/Rarefaction and from CRAN (https://cran.r-project.org/). Contact bork@embl.de or falk.hildebrand@embl.de. Supplementary information Supplementary data are available at Bioinformatics online.

Dispersive Dam-Break Flow of a Photon Fluid

Abstract: We investigate the temporal photonic analogue of the dam-break phenomenon for shallow water by exploiting a fiber optics setup. We clearly observe the decay of the steplike input (photonic dam) into a pair of oppositely propagating rarefaction wave and dispersive shock wave. Our results show evidence for a critical transition of the dispersive shock into a self-cavitating state. The detailed observation of the cavitating state dynamics allows for a fully quantitative test of the Whitham modulation theory applied to the universal defocusing nonlinear Schrodinger equation.

Hall effects on MHD natural convection flow in a vertical microchannel

Abstract: In this work, the steady fully developed magnetohydrodynamic natural convection flow in a vertical microchannel formed by two infinite vertical parallel plates due to asymmetric heating of parallel plates in the presence of Hall current is studied. Effects of velocity slip and temperature jump have been considered on the microchannel surfaces and exact solutions have been obtained for momentum and energy equations under relevant boundary conditions. The influence of each governing parameter such as Hall current parameter, Hartmann number, rarefaction parameter, fluid wall interaction parameter and wall-ambient temperature ratio on flow formation is discussed with the aid of graphs. The significant result from the study is that, increase in the value of rarefaction parameter leads to enhancement in volume flow rate. Furthermore, it is evident that volume flow rate is found to be increasing function of Hall current parameter.

Numerical simulation of unsteady cavitation in liquid hydrogen flows

Abstract: An unsteady cavitation model in liquid hydrogen flow is studied in the context of compressible, two-phase, one-fluid inviscid solver. This is accomplished by applying three conservation laws for mixture mass, mixture momentum and total energy along with gas volume fraction transport equation, with thermodynamic effects. Various mass transfers between phases are utilised to study the process under consideration. A numerical procedure is presented for the simulation of cavitation due to rarefaction and shock waves. Attention is focused on cavitation in which the simulated fluid is liquid hydrogen in cryogenic conditions. Numerical results are in close agreement with theoretical solutions for several test cases. The current numerical results show that liquid hydrogen flow can be accurately modelled using an accurate inviscid approach to describe the features of thermodynamic effects on cavitation.

Time-dependent methodology for non-stationary mass flow rate measurements in a long micro-tube: experimental and numerical analysis at arbitrary rarefaction conditions

Abstract: This paper reports the experimental and numerical analysis of time-dependent rarefied gas flows through a long metallic micro-tube. The experimental methodology was conceived on the basis of the constant volume technique and adapted to measure the evolution with time of a transient mass flow rate through a micro-tube. Furthermore, the characteristic time of each experiment, extracted from the pressure measurements in each reservoir, offered a clear indication on the dynamics of the transient flow as a function of the gas molecular mass and its rarefaction level. The measured pressure evolution with time at the inlet and outlet of the micro-tube was compared to numerical results obtained with the BGK linearized kinetic equation model. Finally, we present an original methodology to extract stationary mass flow rates by using the tube conductance, which can be associated with the characteristic time of the experiment, measured for different mean pressures between two tanks. The results were obtained in a wide range of rarefaction conditions for nitrogen ( $$N_2$$ ). A brief comparison is offered with respect to R134a (CH2FCF3), too, a heavy polyatomic gas which is typically used in the refrigeration industry.

Stability of nonlinear wave patterns to the bipolar Vlasov-Poisson-Boltzmann system

Abstract: The main purpose of the present paper is to investigate the nonlinear stability of viscous shock waves and rarefaction wave for bipolar Vlasov-Poisson-Boltzmann (VPB) system. To this end, motivated by the micro-macro decomposition to the Boltzmann equation in [21, 23], we first set up a new micro-macro decomposition around the local Maxwellian related to the bipolar VPB system and give a unified framework to study the nonlinear stability of the basic wave patterns to the system. Then, as the applications of this new decomposition, the time-asymptotic stability of the two typical nonlinear wave patterns, viscous shock waves and rarefaction wave, are proved for the 1D bipolar Vlasov-Poisson-Boltzmann system. More precisely, it is first proved that the linear superposition of two Boltzmann shock profiles in the first and third characteristic fields is nonlinearly stable to the 1D bipolar VPB system up to some suitable shifts without the zero macroscopic mass conditions on the initial perturbations. Then the time-asymptotic stability of rarefaction wave fan to compressible Euler equations is proved to 1D bipolar VPB system. These two results are concerned with the nonlinear stability of wave patterns for Boltzmann equation coupled with additional (electric) forces, which together with spectral analysis made in [18] sheds light on understanding the complicated dynamic behaviors around the wave patterns in the transportation of charged particles under the binary collisions, mutual interactions, and the effect of the electrostatic potential forces.

Analytical scalings of the linear Richtmyer-Meshkov instability when a rarefaction is reflected.

Abstract: The Richtmyer-Meshkov instability for the case of a reflected rarefaction is studied in detail following the growth of the contact surface in the linear regime and providing explicit analytical expressions for the asymptotic velocities in different physical limits. This work is a continuation of the similar problem when a shock is reflected [Phys. Rev. E 93, 053111 (2016)1539-375510.1103/PhysRevE.93.053111]. Explicit analytical expressions for the asymptotic normal velocity of the rippled surface (δv_{i}^{∞}) are shown. The known analytical solution of the perturbations growing inside the rarefaction fan is coupled to the pressure perturbations between the transmitted shock front and the rarefaction trailing edge. The surface ripple growth (ψ_{i}) is followed from t=0+ up to the asymptotic stage inside the linear regime. As in the shock reflected case, an asymptotic behavior of the form ψ_{i}(t)≅ψ_{∞}+δv_{i}^{∞}t is observed, where ψ_{∞} is an asymptotic ordinate to the origin. Approximate expressions for the asymptotic velocities are given for arbitrary values of the shock Mach number. The asymptotic velocity field is calculated at both sides of the contact surface. The kinetic energy content of the velocity field is explicitly calculated. It is seen that a significant part of the motion occurs inside a fluid layer very near the material surface in good qualitative agreement with recent simulations. The important physical limits of weak and strong shocks and high and low preshock density ratio are also discussed and exact Taylor expansions are given. The results of the linear theory are compared to simulations and experimental work [R. L. Holmes et al., J. Fluid Mech. 389, 55 (1999)JFLSA70022-112010.1017/S0022112099004838; C. Mariani et al., Phys. Rev. Lett. 100, 254503 (2008)PRLTAO0031-900710.1103/PhysRevLett.100.254503]. The theoretical predictions of δv_{i}^{∞} and ψ_{∞} show good agreement with the experimental and numerical reported values.

Acoustic field of a pulsating cylinder in a rarefied gas: Thermoviscous and curvature effects

Abstract: The impact of gas rarefaction on the acoustic field of a pulsating cylinder is studied for all Knudsen numbers The continuum-limit far field exhibits thermoviscous exponential decay Stronger attenuation occurs in the ballistic limit because of curvature-related geometric reduction of the affected layer

The piston problem in hyperelasticity with the stored energy in separable form

Abstract: The piston problem for a hyperelastic hyperbolic conservative model where the stored energy is given in separable form is studied. The eigenfields corresponding to the hyperbolic system are of three types: linearly degenerate fields (corresponding to the contact characteristics), the fields which are genuinely nonlinear in the sense of Lax (corresponding to longitudinal waves), and, finally, nonlinear fields which are not genuinely nonlinear (corresponding to transverse waves). Taking the initial state free of stresses, we presented possible auto-similar solutions to the piston problem. In particular, we have shown that the equations admit transverse shock waves having a remarkable property: the solid density is decreasing through such a shock, it is thus a ‘rarefaction’ shock.

Stability of the superposition of rarefaction wave and contact discontinuity for the non-isentropic Navier-Stokes-Poisson system

Abstract: This paper is devoted to the study of the nonlinear stability of the composite wave consisting of a rarefaction wave and a viscous contact discontinuity wave of the non-isentropic Navier–Stokes–Poisson system with free boundary. We first construct the composite wave through the quasineutral Euler equations and then prove that the composite wave is time asymptotically stable under small perturbations for the corresponding initial-boundary value problem of the non-isentropic Navier–Stokes–Poisson system. Only the strength of the viscous contact wave is required to be small. However, the strength of the rarefaction wave can be arbitrarily large. In our analysis, the domain decomposition plays an important role in obtaining the zero-order energy estimates. By introducing this technique, we successfully overcome the difficulty caused by the critical terms involved with the linear term, which does not satisfy the quasineural assumption for the composite wave. Copyright © 2016 John Wiley & Sons, Ltd.

Solution of Riemann problem for ideal polytropic dusty gas

Abstract: The Riemann problem for a quasilinear hyperbolic system of equations governing the one dimensional unsteady flow of an ideal polytropic gas with dust particles is solved analytically without any restriction on magnitude of the initial states. The elementary wave solutions of the Riemann problem, that is shock waves, rarefaction waves and contact discontinuities are derived explicitly and their properties are discussed, for a dusty gas. The existence and uniqueness of the solution for Riemann problem in dusty gas is discussed. Also the conditions leading to the existence of shock waves or simple waves for a 1-family and 3-family curves in the solution of the Riemann problem are discussed. It is observed that the presence of dust particles in an ideal polytropic gas leads to more complex expression as compared to the corresponding ideal case; however all the parallel results remain same. Also, the effect of variation of mass fraction of dust particles with fixed volume fraction (Z) and the ratio of specific heat of the solid particles and the specific heat of the gas at constant pressure on the variation of velocity and density across the shock wave, rarefaction wave and contact discontinuities are discussed.

Simulation of Underwater Explosions Initiated by High-Pressure Gas Bubbles of Various Initial Shapes

Abstract: UNDerwater EXplosions (UNDEXs) are widely used in many areas of applied engineering including oil production and warship protection. However, the three-dimensional computations of UNDEXs, especially for explosives with complex initial shapes are still lacking, which is mainly due to the difficulty in capturing the multi-medium interface with high pressure ratio. In this study, we conducted a series of three-dimensional numerical simulations of UNDEXs with different initial shapes of a high-pressure gas bubble surrounded with water, to investigate the dynamics of the explosion caused by the shape change of the gas bubble. The movement of the interface was traced with the level-set method, and the conditions at the gas–water interface were treated using the Real Ghost Fluid Method (RGFM). As a result, the temporal evolution of the pressure field during the explosion and the pressure exerted at the boundaries of the computational domain in each simulation scenario were obtained. It was found that an initial shock wave is generated by the explosion and transmitted in the water, leading to an increase of the pressure and density. Meanwhile, inside the gas bubble, a rarefaction wave is formed, causing a pressure drop of the explosive gas. The results also show that if the initial shape of the bubble filled with the explosive gas is simple (e.g., spherical, cylindrical, cuboidal), the peak pressure of the shock wave is dominated by the cross-sectional area of the initial bubble along each direction. In addition, the duration of the high pressure phase of the shock wave is dictated by the thickness of the bubble. Moreover, the simulation of a bubble with an initially bullet-like shape revealed that this specific shape enables a concentration of the energy in a well-defined direction. The peak of the pressure generated by the gas bubble of this more complex shape is approximately twice than that of the other scenarios. However, the high pressure was found to drop more rapidly than that of the other cases, which might be attributed to the comparably small thickness of the initial bubble.

Stability of the composite wave for the inflow problem on the micropolar fluid model

Abstract: In this paper, we study the asymptotic behavior of solutions to the initial boundary value problem for the micropolar fluid model in half line $\mathbb{R}_{+}:=(0, \infty).$ Inspired by the relationship between the micropolar fluid model and Navier-Stokes system, we can prove that the composite wave consisting of the subsonic BL-solution, the contact wave, and the rarefaction wave for the inflow problem on micropolar fluid model is time-asymptotically stable. Meanwhile, we obtain the global existence of solutions based on the basic energy method.

Chiral Shock Waves

Abstract: We study the shock waves in relativistic chiral matter. We argue that the conventional Rankine-Hugoinot relations are modified due to the presence of chiral transport phenomena. We show that the entropy discontinuity in a weak shock wave is quadratic in the pressure discontinuity when the effect of chiral transport becomes sufficiently large. We also show that rarefaction shock waves, which do not exist in usual nonchiral fluids, can appear in chiral matter. The direction of shock wave propagation is found to be completely determined by the direction of the vorticity and the chirality of fermions. These features are exemplified by shock propagation in dense neutrino matter in the hydrodynamic regime.

Supersonic Indicial Response with Nonlinear Corrections by Shock and Rarefaction Waves

Abstract: In this paper, supersonic indicial pressure loads on a finite length planar surface (like those of an airfoil) subject to a strong crossflow, as caused by a gust or a sudden change of angle of attack, are studied. The unsteady pressure and force are obtained by an extension of linear theory, accounting for the nonlinear effects of shock waves on a windward surface and rarefaction waves on a leeward surface. Notably, the pressure in the nonuniform region (secondary wave) caused by interaction of the front and rear parts of the shock or rarefaction wave is assumed to be geometrically similar to that given by linear theory. The indicial force is expressed as an algebraic function of the edges of the secondary wave and pressure coefficients of uniform regions. The flow around a flat plate with a sudden change of angle of attack is used as a test case. By using a numerical simulation for comparison, it is shown that the modified theory increases the accuracy significantly at a large angle of attack, whereas th...

Effect of gas rarefaction on the quality factors of micro-beam resonators

Abstract: The external squeeze film damping (SFD) of microelectromechanical systems (MEMS) resonators is a dominant factor to lower the quality factor (Q-factor) due to their large surface area to volume ratio and small spacing. To improve the Q-factor of MEMS resonators, the effect of gas rarefaction (low gas ambient pressure in thin gas film thickness) or operating in higher mode should be considered in SFD analysis. The modified molecular gas lubrication (MMGL) equation is applied for modeling the SFD with gas rarefaction effects taken into consideration. The effects of inverse Knudsen number, surface accommodation coefficients (ACs) and operating frequency on SFD are discussed. The combined effects of SFD, thermoelastic damping (TED) and anchor loss on the total Q-factors of MEMS resonators are considered. The contribution of SFD on the total Q-factor (weighting of SFD) is also discussed. The results show that weighting of SFD could be decrease at low inverse Knudsen number or low ACs or operating at high resonant frequencies.

On Exact Solutions of Rarefaction-Rarefaction Interactions in Compressible Isentropic Flow

Abstract: Consider the interaction of two centered rarefaction waves in one-dimensional, compressible gas flow with pressure function \(p(\rho )=a^2\rho ^\gamma \) with \(\gamma >1\). The classic hodograph approach of Riemann provides linear 2nd order equations for the time and space variables t, x as functions of the Riemann invariants r, s within the interaction region. It is well known that t(r, s) can be given explicitly in terms of the hypergeometric function. We present a direct calculation (based on works by Darboux and Martin) of this formula, and show how the same approach provides an explicit formula for x(r, s) in terms of Appell functions (two-variable hypergeometric functions). Motivated by the issue of vacuum and total variation estimates for 1-d Euler flows, we then use the explicit t-solution to monitor the density field and its spatial variation in interactions of two centered rarefaction waves. It is found that the variation is always non-monotone, and that there is an overall increase in density variation if and only if \(\gamma >3\). We show that infinite duration of the interaction is characterized by approach toward vacuum in the interaction region, and that this occurs if and only if the Riemann problem defined by the extreme initial states generates a vacuum. Finally, it is verified that the minimal density in such interactions decays at rate O(1)/t.

Rarefaction Effects for Transonic Airfoil Flows at Low Reynolds Numbers

Abstract: The quantification of rarefaction effects for low-Reynolds-number (Re∞<10,000) transonic (M∞∼0.8) flows is essential for the aerodynamic design of vehicles moving in vacuum environments approaching...

Asymptotic behavior toward the combination of contact discontinuity with rarefaction waves for 1-D compressible viscous gas with radiation

Abstract: This paper is concerned with the large-time behavior toward the combination of two rarefaction waves and viscous contact wave for the Cauchy problem to a one-dimensional Navier–Stokes–Poisson coupled system, modeling the dynamics of a viscous gas in the presence of radiation. We show that the composite wave with small strength is asymptotically stable under partially large initial perturbations. The proofs are based on the more refined energy estimates to control the possible growth of the perturbations induced by two different waves and large data.

Rarefaction Waves for the Toda Equation via Nonlinear Steepest Descent

Abstract: We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Toda lattice with steplike initial data corresponding to a rarefaction wave.

Influences of temperature on the quality factors of micro-beam resonators in gas rarefaction

Abstract: In this study, the effect of temperature on the quality factor (Q-factor) of a micro-beam resonator is analyzed in a wide range of gas rarefaction conditions (ambient pressure and accommodation coefficients (ACs)). Squeeze film damping (SFD), thermoelastic damping (TED), and anchor loss, which are dominant damping mechanisms of micro-beam resonators, are included in the total Q-factor. The increase in the mean free path of gas with temperature is more significant than that of the gas viscosity in high gas rarefaction. Thus, the effect of temperature in gas rarefaction is discussed to improve the Q-factors of the resonators. The modified molecular gas lubrication (MMGL) equation is utilized to model SFD. Dynamic viscosity and Poiseuille flow rate are used to modify the MMGL equation considering the coupled effects of temperature and gas rarefaction. Finally, the effect of temperature on the Q-factors is discussed under various gas rarefaction conditions (pressure and ACs), types of gases and resonator modes. The results show that the Q-factor increases with temperature in higher gas rarefaction (lower pressure and ACs), whereas the Q-factor decreases as temperature increases in lower gas rarefaction (higher pressure and ACs). The decrease in the Q-factor with temperature is improved by the gas rarefaction effect. Furthermore, the Q-factor of a micro-beam resonator increases considerably with temperature by using hydrogen in higher gas rarefaction and the 1st mode of the resonator.

Linear theory of Richtmyer-Meshkov like flows

Abstract: The hydrodynamic flow generated by rippled shocks and rarefactions (Richtmyer–Meshkov like flows) is presented. When a corrugated shock travels inside an homogeneous fluid, it leaves pressure, density and velocity perturbations in the compressed fluid. The velocity perturbations generated in the composed fluid are inherently rotational. Vorticity is an important quantity in order to determine the asymptotic rate of growth in the linear stage. The size of the strongest vortices generated by the rippled shocks is analyzed as a function of the shock Mach number for different boundary conditions downstream. Comparison to experiments and simulations is provided for the RMI in the shock and rarefaction reflected cases and the validity of the growth law is emphasized.

Effects of surface roughness and gas rarefaction on the quality factor of micro-beam resonators

Abstract: In this paper, the average modified molecular gas lubrication (MMGL) equation is utilized to analyze the squeeze film damping (SFD) of micro-beam resonators. Under thin gas film spacing and low ambient pressure conditions, the effects of surface roughness and gas rarefaction become important due to their larger surface area to volume ratio. The external SFD and the combined structural damping [thermoelastic damping (TED) and anchor loss] are studied on the quality factor (Q-factor) of micro-beam resonators. The coupling effects of surface roughness and gas rarefaction on SFD are discussed. The results show that the effects of surface roughness are diluted by the gas rarefaction. The Q-factor of micro-beam resonators depends significantly on surface roughness (film thickness ratio, Peklenik number) in higher gas rarefaction (low ambient pressure, low accommodation coefficients) and/or higher modes of the resonators.

On doubly stochastic rarefaction of renewal processes

Abstract: In the paper, the concepts of π-mixed geometric and π-mixed binomial distributions are introduced within the setting of Bernoulli trials with a random probability of success. A generalization of the Renyi theorem concerning the asymptotic behavior of rarefied renewal processes is proved for doubly stochastic rarefaction resulting in that the limit process is mixed Poisson.