Showing papers on "Rarefaction published in 2019"

Origami-based impact mitigation via rarefaction solitary wave creation

Abstract: The principles underlying the art of origami paper folding can be applied to design sophisticated metamaterials with unique mechanical properties. By exploiting the flat crease patterns that determine the dynamic folding and unfolding motion of origami, we are able to design an origami-based metamaterial that can form rarefaction solitary waves. Our analytical, numerical, and experimental results demonstrate that this rarefaction solitary wave overtakes initial compressive strain waves, thereby causing the latter part of the origami structure to feel tension first instead of compression under impact. This counterintuitive dynamic mechanism can be used to create a highly efficient—yet reusable—impact mitigating system without relying on material damping, plasticity, or fracture.

Mouse models of Alzheimer's disease cause rarefaction of pial collaterals and increased severity of ischemic stroke.

Abstract: Vascular dysfunction contributes to the progression and severity of Alzheimer’s disease (AD). Patients with AD also sustain larger infarctions after ischemic stroke; however, the responsible mechanisms are unknown. Pial collaterals are the primary source of protection in stroke. Unfortunately, natural aging and other vascular risk factors cause a decline in collateral number and diameter (rarefaction) and an increase in stroke severity. Herein, we tested the hypothesis that AD accelerates age-induced collateral rarefaction and examined potential underlying mechanisms. Triple and double transgenic mouse models of AD both sustained collateral rarefaction by 8 months of age, well before the onset of rarefaction caused by aging alone (16 months of age). Rarefaction, which did not progress further at 18 months of age, was accompanied by a twofold increase in infarct volume after MCA occlusion. AD did not induce rarefaction of similarly sized pial arterioles or penetrating arterioles. Rarefaction was minimal and occurred only at 18 months of age in a parenchymal vascular amyloid-beta model of AD. Rarefaction was not associated with amyloid-beta deposition on collaterals or pial arteries, nor was plaque burden or CD11b+ cell density greater in brain underlying the collateral zones versus elsewhere. However, rarefaction was accompanied by increased markers of oxidative stress, inflammation, and aging of collateral endothelial and mural cells. Moreover, rarefaction was lessened by deletion of CX3CR1 and prevented by overexpression of eNOS. These findings demonstrate that mouse models of AD promote rarefaction of pial collaterals and implicate inflammation-induced accelerated aging of collateral wall cells. Strategies that reduce vascular inflammation and/or increase nitric oxide may preserve collateral function.

Evolution of initial discontinuity for the defocusing complex modified KdV equation

Abstract: The complete classification of solutions to the defocusing complex modified Korteweg-de Vries (cmKdV) equation with the step-like initial condition is given by Whitham theory. The process of studying the solution of cmKdV equation can be reduced to explore four quasi-linear equations, which predicts the evolution of dispersive shock wave. The results obtained here are quite different from the defocusing nonlinear Schrodinger equation: the bidirectionality of defocusing nonlinear Schrodinger equation determines that there are two basic rarefaction and shock structures while in the cmKdV case three basic rarefaction structures and four basic dispersive shock structures are constructed which lead to more complicated classification of step-like initial condition, and wave patterns even consisted of six different regions while each of wave patterns is consisted of five regions in the defocusing nonlinear Schrodinger equation. Direct numerical simulations of cmKdV equation are agreed well with the solutions corresponding to Whitham theory.

Propagation of elastic solitons in chains of pre-deformed beams

Abstract: We use a combination of experiments, numerical analysis and theory to investigate the nonlinear dynamic response of a chain of precompressed elastic beams. Our results show that this simple system offers a rich platform to study the propagation of large amplitude waves. Compression waves are strongly dispersive, whereas rarefaction pulses propagate in the form of solitons. Further, we find that the model describing our structure closely resembles those introduced to characterize the dynamics of several molecular chains and macromolecular crystals, suggesting that our macroscopic system can provide insights into the effect of nonlinear vibrations on molecular mechanisms.

Non-equilibrium effects on flow past a circular cylinder in the slip and early transition regime

Abstract: This paper presents a comprehensive investigation into flow past a circular cylinder where compressibility and rarefaction effects play an important role. The study focuses on steady subsonic flow in the Reynolds-number range 0.1–45. Rarefaction, or non-equilibrium, effects in the slip and early transition regime are accounted for using the method of moments and results are compared to data from kinetic theory obtained from the direct simulation Monte Carlo method. Solutions obtained for incompressible continuum flow serve as a baseline to examine non-equilibrium effects on the flow features. For creeping flow, where the Reynolds number is less than unity, the drag coefficient predicted by the moment equations is in good agreement with kinetic theory for Knudsen numbers less than one. When flow separation occurs, we show that the effects of rarefaction and velocity slip delay flow separation and will reduce the size of the vortices downstream of the cylinder. When the Knudsen number is above 0.028, the vortex length shows an initial increase with the Reynolds number, as observed in the standard no-slip continuum regime. However, once the Reynolds number exceeds a critical value, the size of the downstream vortices decreases with increasing Reynolds number until they disappear. An existence criterion, which identifies the limits for the presence of the vortices, is proposed. The flow physics around the cylinder is further analysed in terms of velocity slip, pressure and skin friction coefficients, which highlights that viscous, rarefaction and compressibility effects all play a complex role. We also show that the local Knudsen number, which indicates the state of the gas around the cylinder, can differ significantly from its free-stream value and it is essential that computational studies of subsonic gas flows in the slip and early transition regime are able to account for these strong non-equilibrium effects.

Influences of relative humidity on the quality factors of MEMS cantilever resonators in gas rarefaction

Abstract: In this paper, the effect of relative humidity of moist air is discussed on the quality factor (Q factor) of micro-electro-mechanical systems (MEMS) cantilever resonators in wide range of gas rarefaction (ambient pressure and accommodation coefficients, ACs). The modified molecular gas lubrication (MMGL) equation is used to model the squeeze film damping problem of MEMS cantilever resonators. Dynamic viscosity and Poiseuille flow rate are used to modify the MMGL equation to consider the coupled effects of relative humidity and gas rarefaction. Thermoelastic damping and anchor loss, which are dominant damping mechanisms of MEMS cantilever resonators, are also included to calculate total Q factor. Thus, the influences of relative humidity are discussed on the Q factors of MEMS cantilever resonators in wide range of gas rarefaction and dimension of cantilever. The results showed that the Q factor decreases as relative humidity increases in wide range of gas rarefaction (pressure, and ACs) and dimension of cantilever (length, width, and thickness). The influences of relative humidity on the Q factor become more significantly in larger length, larger width, smaller thickness of cantilever, and higher gas rarefaction (lower pressure and ACs). Whereas, the influences of relative humidity on the Q factor reduce or are neglected in smaller length, larger thickness of cantilever and lower gas rarefaction (higher pressure and ACs).

Asymptotic stability of shock profiles and rarefaction waves under periodic perturbations for 1-d convex scalar viscous conservation laws

Abstract: This paper studies the asymptotic stability of shock profiles and rarefaction waves under space-periodic perturbations for one-dimensional convex scalar viscous conservation laws. For the shock profile, we show that the solution approaches the background shock profile with a constant shift in the $ L^\infty(\mathbb{R}) $ norm at exponential rates. The new phenomena contrasting to the case of localized perturbations is that the constant shift cannot be determined by the initial excessive mass in general, which indicates that the periodic oscillations at infinities make contributions to this shift. And the vanishing viscosity limit for the shift is also shown. The key elements of the poof consist of the construction of an ansatz which tends to two periodic solutions as $ x \rightarrow \pm\infty, $ respectively, and the anti-derivative variable argument, and an elaborate use of the maximum principle. For the rarefaction wave, we also show the stability in the $ L^\infty(\mathbb{R}) $ norm.

Theoretical study of the defect evolution for molecular crystal under shock loading

Abstract: We simulate the shock loading process of β-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine by molecular dynamics and calculate the isoentropic curve, Hugoniot curve, temperature field, velocity field, stress field, and density field. Based on the simulation results, we develop a physical model to describe the pore collapse, crack expansion, and hot spot formation mechanisms and calculate a set of key parameters, such as pore collapsing speed, rarefaction wave speed, and crack expansion speed. A microscopic physical picture for defect evolution at the early time of shock loading is obtained.

Vanishing viscosity limit to the planar rarefaction wave for the two-dimensional compressible Navier-Stokes equations

Abstract: The vanishing viscosity limit of the two-dimensional (2D) compressible isentropic Navier-Stokes equations is studied in the case that the corresponding 2D inviscid Euler equations admit a planar rarefaction wave solution. It is proved that there exists a family of smooth solutions for the 2D compressible Navier-Stokes equations converging to the planar rarefaction wave solution with arbitrary strength for the 2D Euler equations. A uniform convergence rate is obtained in terms of the viscosity coefficients away from the initial time. In the proof, the hyperbolic wave is crucially introduced to recover the physical viscosities of the inviscid rarefaction wave profile, in order to rigorously justify the vanishing viscosity limit.

Nonlinear stability of planar rarefaction wave to the three-dimensional Boltzmann equation

Abstract: We investigate the time-asymptotic stability of planar rarefaction wave for the three-dimensional Boltzmann equation, based on the micro-macro decomposition introduced in [ 24 , 22 ] and our new observations on the underlying wave structures of the equation to overcome the difficulties due to the wave propagation along the transverse directions and its interactions with the planar rarefaction wave. Note that this is the first stability result of planar rarefaction wave for 3D Boltzmann equation, while the corresponding results for the shock and contact discontinuities are still completely open.

Dynamical structure of the pulsating atmosphere of RR Lyrae - I. A typical pulsation cycle

Abstract: Context. RRab stars are large amplitude pulsating stars in which the pulsation wave is a progressive wave. Consequently, strong shocks, stratification effects, and phase lag may exist between the variations associated with line profiles formed in different parts of the atmosphere, including the shock wake. The pulsation is associated with a large extension of the expanding atmosphere, and strong infalling motions are expected.Aims. The objective of this study is to provide a general overview of the dynamical structure of the atmosphere occurring over a typical pulsation cycle.Methods. We report new high-resolution observations with high time resolution of Hα and sodium lines in the brightest RR Lyrae star of the sky: RR Lyr (HD 182989). A detailed analysis of line profile variations over the whole pulsation cycle is performed to understand the dynamical structure of the atmosphere.Results. The main shock wave appears when it exits from the photosphere at φ ≃ 0.89, i.e., when the main Hα emission is observed. Whereas the acceleration phase of the shock is not observed, a significant deceleration of the shock front velocity is clearly present. The radiative stage of the shock wave is short: 4% of the pulsation period (0.892 > 10 is required to get such a radiative shock. The sodium layer reaches its maximum expansion well before that of Hα (Δφ = 0.135). Thus, a rarefaction wave is induced between the Hα and sodium layers. A strong atmospheric compression occurring around φ = 0.36, which produces the third Hα emission, takes place in the highest part of the atmosphere. The region located lower in the atmosphere where the sodium line is formed is not involved. The amplification of gas turbulence seems mainly due to strong shock waves propagating in the atmosphere rather than to the global compression of the atmosphere caused by the pulsation. It has not yet been clearly established whether the microturbulence velocity increases or decreases with height in the atmosphere. Furthermore, it seems very probable that an interstellar component is visible within the sodium profile.

Weak Shock Propagation with Accretion. II. Stability of Self-similar Solutions to Radial Perturbations

Abstract: Coughlin et al. (2018) (Paper I) derived and analyzed a new regime of self-similarity that describes weak shocks (Mach number of order unity) in the gravitational field of a point mass. These solutions are relevant to low energy explosions, including failed supernovae. In this paper, we develop a formalism for analyzing the stability of shocks to radial perturbations, and we demonstrate that the self-similar solutions of Paper I are extremely weakly unstable to such radial perturbations. Specifically, we show that perturbations to the shock velocity and post-shock fluid quantities (the velocity, density, and pressure) grow with time as $t^{\alpha}$, where $\alpha \le 0.12$, implying that the ten-folding timescale of such perturbations is roughly ten orders of magnitude in time. We confirm these predictions by performing high-resolution, time-dependent numerical simulations. Using the same formalism, we also show that the Sedov-Taylor blastwave is trivially stable to radial perturbations provided that the self-similar, Sedov-Taylor solutions extend to the origin, and we derive simple expressions for the perturbations to the post-shock velocity, density, and pressure. Finally, we show that there is a third, self-similar solution (in addition to the the solutions in Paper I and the Sedov-Taylor solution) to the fluid equations that describes a rarefaction wave, i.e., an outward-propagating sound wave of infinitesimal amplitude. We interpret the stability of shock propagation in light of these three distinct self-similar solutions.

Numerical modelling of shock-bubble interactions using a pressure-based algorithm without Riemann solvers

Abstract: The interaction of a shock wave with a bubble features in many engineering and emerging technological applications, and has been used widely to test new numerical methods for compressible interfacial flows. Recently, density-based algorithms with pressure-correction methods as well as fully-coupled pressure-based algorithms have been established as promising alternatives to classical density-based algorithms based on Riemann solvers. The current paper investigates the predictive accuracy of fully-coupled pressure-based algorithms without Riemann solvers in modelling the interaction of shock waves with one-dimensional and two-dimensional bubbles in gas-gas and liquid-gas flows. For a gas bubble suspended in another gas, the mesh resolution and the applied advection schemes are found to only have a minor influence on the bubble shape and position, as well as the behaviour of the dominant shock waves and rarefaction fans. For a gas bubble suspended in a liquid, however, the mesh resolution has a critical influence on the shape, the position and the post-shock evolution of the bubble, as well as the pressure and temperature distribution.

Long-time evolution of pulses in the Korteweg-de Vries equation in the absence of solitons reexamined: Whitham method.

Abstract: We consider the long-time evolution of pulses in the Korteweg-de Vries equation theory for initial distributions which produce no soliton but instead lead to the formation of a dispersive shock wave and of a rarefaction wave. An approach based on Whitham modulation theory makes it possible to obtain an analytic description of the structure and to describe its self-similar behavior near the soliton edge of the shock. The results are compared with numerical simulations.

Rarefaction Flows and Mitigation of Imprint in Direct-Drive Implosions.

Abstract: Using highly resolved 3D radiation-hydrodynamic simulations, we identify a novel mechanism by which the deleterious impact of laser imprinting is mitigated in direct-drive inertial confinement fusion. Unsupported shocks and associated rarefaction flows, commonly produced with short laser bursts, are found to reduce imprint modulations prior to target acceleration. Optimization through the choice of laser pulse with picket(s) and target dimensions may improve the stability of lower-adiabat designs, thus providing the necessary margin for ignition-relevant implosions.

Asymptotic Stability of Rarefaction Wave for the Inflow Problem Governed by the One-Dimensional Radiative Euler Equations

Abstract: This paper is devoted to the study of the initial-boundary value problem on the half line for a one-dimensional radiative Euler equations, which is a system coupled by the classic compressible noni...

Self-similar dynamics of two-phase flows injected into a confined porous layer

Abstract: We study the dynamics of two-phase flows injected into a confined porous layer. A model is derived to describe the evolution of the fluid–fluid interface, where the effective saturation of the injected fluid is zero. The flow is driven by pressure gradients due to injection, the buoyancy due to density contrasts and the interfacial tension between the injected and ambient fluids. The saturation field is then computed after the interface evolution is obtained. The results demonstrate that the flow behaviour evolves from early-time unconfined to late-time confined behaviours. In particular, at early times, the influence of capillary forces drives fluid flow and produces a new self-similar spreading behaviour in the unconfined limit that is distinct from the gravity current solution. At late times, we obtain two new similarity solutions, a modified shock solution and a compound wave solution, in addition to the rarefaction and shock solutions in the sharp-interface limit. A schematic regime diagram is also provided, which summarises all possible similarity solutions and the time transitions between them for the partially saturating flows resulting from fluid injection into a confined porous layer. Three dimensionless control parameters are identified and their influence on the fluid flow is also discussed, including the viscosity ratio, the pore-size distribution and the relative contributions of capillary and buoyancy forces. To underline the relevance of our results, we also briefly describe the implications of the two-phase flow model to the geological storage of , using representative geological parameters from the Sleipner and In Salah sites.

Asymptotic behavior of solutions toward the rarefaction waves to the Cauchy problem for the scalar diffusive dispersive conservation laws

Abstract: In this paper, we investigate the asymptotic behavior of solutions to the Cauchy problem for the scalar diffusive dispersive conservation laws where the far field states are prescribed. Especially, we deal with the generalized models for Korteweg–de Vries–Burgers–Kuramoto equation. When the corresponding Riemann problem for the hyperbolic part admits a Riemann solution which consists of single rarefaction wave, it is proved that the solution of the Cauchy problem tends toward the rarefaction wave as time goes to infinity.

Patterns of plasma jet arrays in the gas flow field of non-thermal atmospheric pressure plasma jets

Abstract: Schlieren photography, the state-of-art to visualize the invisible flows, has appealed gigantic attention of various researchers in the plasma community. Here, this technique is utilized to address the behavior of the plasma jet arrays in the gas flow field. The goal of this study is to probe the signatures of different parameters and their response in the gas flow field. It is concluded that every parameter exhibits its sensitivity to the plasma in the gas flow field. However, frequency has a significant impact on the reduction of the laminar flow. Furthermore, it is suggested that the flow of the higher momentum region to the lower region is the cause in establishing the instabilities. The compression and rarefaction at the rising and falling edges of the discharge pulses play the dominant role. Plasma jet arrays can be a handy tool for industrial applications unless proper parameters are selected.

Size effect on compressible flow and heat transfer in microtube with rarefaction and viscous dissipation

Abstract: In a microtube, the flow and thermal fields have very different features to the conventional tube flows. Fluid properties such as compressibility, viscous dissipation, and rarefaction are important...

Effect of heat-flux boundary conditions on the Rayleigh-Bénard instability in a rarefied gas

Abstract: The effect of heat-flux conditions on the Rayleigh-B\'enard convection in a rarefied gas is investigated, extending instability to higher rarefaction rates compared with the isothermal walls case. The deviation from the Boussinesq limit with increasing compressibility is analyzed.

Combined Effect of Rarefaction and Effective Viscosity on Micro-Elasto-Aerodynamic Lubrication Performance of Gas Microbearings.

Abstract: Elastic deformation and gaseous rarefaction effects are of great importance to the static and dynamic characteristics of gas microbearings. Based on the effective viscosity model of Veijola, the governing equations can be solved by the partial derivative method, finite element procedure, and relaxed iterative algorithm. The numerical results showed that the maximum gas pressure is relatively lower compared to a microbearing with a rigid liner at a local pressure peak region, owing to the film thickness of two converging-diverging profiles and the existence of bimodal pressure inside the elastic microbearing liner. However, the effect of bearing flexibility provides a marginal increase in the load capacity on account of the integral area of pressure distribution is larger than the rigid bearing liner. The friction coefficient and direct stiffness coefficients increase as the elastic modulus decreases while the direct damping coefficients become smaller at high eccentricity ratios and bearing numbers. Since the Poiseuille flow rate increases in connection with an increasing Knudsen number, the effective viscosity of the lubricant leads to a decreased load carrying capacity, friction coefficient, and direct stiffness coefficient, which produces an increase in the direct damping coefficients.