Straight Cylindrical Tube Research Articles

Self-consistent nanoflare heating in model active regions: MHD avalanches in curved coronal arcades

AbstractMHD avalanches involve small, narrowly localized instabilities spreading across neighbouring areas in a magnetic field. Cumulatively, many small events release vast amounts of stored energy. Straight cylindrical flux tubes are easily modelled, between two parallel planes, and can support such an avalanche: one unstable flux tube causes instability to proliferate, via magnetic reconnection, and then an ongoing chain of like events. True coronal loops, however, are visibly curved, between footpoints on the same solar surface. With 3D MHD simulations, we verify the viability of MHD avalanches in the more physically realistic, curved geometry of a coronal arcade. MHD avalanches thus amplify instability across strong solar magnetic fields and disturb wide regions of plasma. Contrasting with the behaviour of straight cylindrical models, a modified ideal MHD kink mode occurs, more readily and preferentially upwards in the new, curved geometry. Instability spreads over a region far wider than the original flux tubes and than their footpoints. Consequently, sustained heating is produced in a series of ‘nanoflares’ collectively contributing substantially to coronal heating. Overwhelmingly, viscous heating dominates, generated in shocks and jets produced by individual small events. Reconnection is not the greatest contributor to heating, but is rather the facilitator of those processes that are. Localized and impulsive, heating shows no strong spatial preference, except a modest bias away from footpoints, towards the loop’s apex. Remarkable evidence emerges of ‘campfire’ like events, with simultaneous, reconnection-induced nanoflares at separate sites along coronal strands, akin to recent results from Solar Orbiter. Effects of physically realistic plasma parameters, and the implications for thermodynamic models, with energetic transport, are discussed.

Resonant absorption of kink MHD waves in inclined and asymmetric coronal loops

ABSTRACT This paper separately evaluates the effects of inclination and asymmetry of solar coronal loops on the resonant absorption of kink magnetohydrodynamic oscillations. We modelled a typical coronal loop by a straight and axisymmetric cylindrical magnetic flux tube filled with cold plasma. We solved the dispersion relation numerically for different values of the longitudinal mass density stratification. We show that, in inclined and asymmetric loops, the frequencies and their corresponding damping rates of the fundamental and first-overtone modes of kink oscillations are smaller in comparison with semi-circular uninclined loops with the same lengths. The results also indicate that, the period ratio P1/P2, increases with increasing the inclination of the loop, but it decreases less than $2{{\ \rm per\ cent}}$ while imposing the asymmetry to each loop side, up to $9.66{{\ \rm per\ cent}}$ of the loop length. The ratio of each mode frequency to its corresponding damping rate remain unchanged approximately while the inclination or the asymmetry imposed. Hence, we conclude that these ratios are reliable for inferring the physical parameters of coronal loops and coronal medium, regardless of the loop shape or the state of its inclination. In addition, in contrast with the effect of asymmetry, which is not significant on the period ratio P1/P2, when an observed oscillating loop has a smaller apex height, the state of its inclination is an important factor that should be considered, especially when the period ratio P1/P2, is taken into consideration for coronal seismology.

Full-wave numerical simulation of nonlinear dissipative acoustic standing waves in wind instruments

A finite volume full-wave method is used to simulate nonlinear dissipative acoustic propagation in ducts with a circular cross-section. Thermoviscous dissipative effects, due to bulk viscosity and shear viscosity in the boundary layer adjacent to the duct walls, are also considered. The propagation is assumed to be axisymmetric, and two different geometries are considered: a straight cylindrical tube, and a cylindrical tube joined smoothly to a slowly-flaring bell. Of special interest is the study of the onset of standing waves in the nonlinear regime. The full-wave numerical scheme is particularly well-adapted for this purpose, as it is not necessary to impose boundary conditions at the open end of the duct. A simplified model of excitation is adopted, where the lips are replaced by a spring–mass system which behaves like a pressure valve with a single degree of freedom. The full system behaves as expected, with a feedback cycle established between the pressure valve and the air column. The simulation is validated successfully in the linear regime using a theoretical solution. It is shown that increasing the stiffness of the lips leads to discrete jumps in playing frequency, which is behaviour typical of brass instruments. In the nonlinear regime, shock formation is observed for sufficiently high amplitudes of oscillation, and the radiation of these shock waves by the open end of the ducts can be visualised in the time-domain, along with edge-diffraction effects. The formation and evolution of standing waves in the nonlinear regime, where the effect of these shocks is very noticeable, is also examined.

Regional Deposition: Deposition Models.

Modeling particle deposition in the human lung requires information about the morphology of the lung in terms of simple geometric units, e.g., characterizing bronchial airways by straight cylindrical tubes. Five different regional deposition models are discussed in this section with respect to morphometric lung models and related mathematical modeling techniques: 1) one-dimensional cross-section or "trumpet" model, 2) deterministic symmetric generation or "single-path" model, 3) deterministic asymmetric generation or "multiple-path" model, 4) stochastic asymmetric generation or "multiple-path" model, and 5) single-path computational fluid and particle dynamics (CFPD) model. Current deposition models can predict the following regional deposition quantities relevant for the administration of medical aerosols: 1) regional bronchial and alveolar deposition, 2) generational lung deposition, 3) lobar deposition, 4) generational lobar deposition, and 5) generational surface deposition. Although deposition fractions predicted by the different models depend on the selection of a specific morphometric lung model and a specific set of analytical deposition equations, all models predict the same trends as functions of particle diameter and breathing parameters. In general, the overall agreement between the modeling predictions obtained by the various deposition models and the available experimental evidence indicates that current deposition models correctly predict regional and generational deposition.

Transport in nanotube tree

The paper proposes the nanotube tree which can efficiently transfer the liquid mass or/and the heat by the pressure driven flow. This nanotube tree is equivalent to a straight cylindrical tube with a significantly large radius when the number of the branches and the number of the branch levels of the tree are respectively sufficiently large. In the pressure driven flow, the mass flow rate through the main trunk tube of the tree can be great and this can carry a great amount of flowing media and heat. The nanotube tree can be used to very efficiently collect the flowing media and heat through extensively spreading nanotubes on its end. The working principles and design guides for this nanotube tree are presented.

On the apparent permeability of porous media in rarefied gas flows

The apparent gas permeability of a porous medium is an important parameter in the prediction of unconventional gas production, which was first investigated systematically by Klinkenberg in 1941 and found to increase with the reciprocal mean gas pressure (or equivalently, the Knudsen number). Although the underlying rarefaction effects are well known, the reason that the correction factor in Klinkenberg’s famous equation decreases when the Knudsen number increases has not been fully understood. Most of the studies idealize the porous medium as a bundle of straight cylindrical tubes; however, according to the gas kinetic theory, this only results in an increase of the correction factor with the Knudsen number, which clearly contradicts Klinkenberg’s experimental observations. Here, by solving the Bhatnagar–Gross–Krook equation in simplified (but not simple) porous media, we identify, for the first time, two key factors that can explain Klinkenberg’s experimental results: the tortuous flow path and the non-unitary tangential momentum accommodation coefficient for the gas–surface interaction. Moreover, we find that Klinkenberg’s results can only be observed when the ratio between the apparent and intrinsic permeabilities is ${\lesssim}30$; at large ratios (or Knudsen numbers) the correction factor increases with the Knudsen number. Our numerical results could also serve as benchmarking cases to assess the accuracy of macroscopic models and/or numerical schemes for the modelling/simulation of rarefied gas flows in complex geometries over a wide range of gas rarefaction. Specifically, we point out that the Navier–Stokes equations with the first-order velocity-slip boundary condition are often misused to predict the apparent gas permeability of the porous medium; that is, any nonlinear dependence of the apparent gas permeability with the Knudsen number, predicted from the Navier–Stokes equations, is not reliable. Worse still, for some types of gas–surface interactions, even the ‘filtered’ linear dependence of the apparent gas permeability with the Knudsen number is of no practical use since, compared to the numerical solution of the Bhatnagar–Gross–Krook equation, it is only accurate when the ratio between the apparent and intrinsic permeabilities is ${\lesssim}1.5$.

Resonant absorption of kink magnetohydrodynamic waves by a magnetic twist in coronal loops

There is ample evidence of twisted magnetic structures in the solar corona. This motivates us to consider the magnetic twist as the cause of Alfven frequency continuum in the coronal loops, which can support the resonant absorption as a rapid damping mechanism for the observed coronal kink magnetohydrodynamic (MHD) oscillations. We model a coronal loop with a straight cylindrical magnetic flux tube which has constant but different densities in the interior and exterior regions. The magnetic field is assumed to be constant and aligned with the cylinder axis everywhere except a thin layer near the boundary of the flux tube which has an additional small magnetic field twist. Then, we investigate a number of possible instabilities that may arise in our model. In the thin tube thin boundary approximation, we derive the dispersion relation and solve it analytically to obtain the frequencies and damping rates of the fundamental (l=1) and first/second overtone (l=2,3) kink (m=1) MHD modes. We conclude that the resonant absorption by the magnetic twist can justify the rapid damping of kink MHD waves observed in coronal loops. Furthermore, the magnetic twist in the inhomogeneous layer can cause deviations from P1/P2=2 and P1/P3=3 which are comparable with the observations.

Navier–Stokes flow in converging–diverging distensible tubes

We use a method based on the lubrication approximation in conjunction with a residual-based mass-continuity iterative solution scheme to compute the flow rate and pressure field in distensible converging–diverging tubes for Navier–Stokes fluids. We employ an analytical formula derived from a one-dimensional version of the Navier–Stokes equations to describe the underlying flow model that provides the residual function. This formula correlates the flow rate to the boundary pressures in straight cylindrical elastic tubes with constant-radius. We validate our findings by the convergence toward a final solution with fine discretization as well as by comparison to the Poiseuille-type flow in its convergence toward analytic solutions found earlier in rigid converging–diverging tubes. We also tested the method on limiting special cases of cylindrical elastic tubes with constant-radius where the numerical solutions converged to the expected analytical solutions. The distensible model has also been endorsed by its convergence toward the rigid Poiseuille-type model with increasing the tube wall stiffness. Lubrication-based one-dimensional finite element method was also used for verification. In this investigation five converging–diverging geometries are used for demonstration, validation and as prototypes for modeling converging–diverging geometries in general.

A 3D kinematic study of the northern ejecta ‘jet’ of the Crab nebula

We present [O III] 4959,5007 emission line spectra (FWHM = 40 km/s) of the Crab Nebula's northern ejecta `jet'. These data, along with a recent [O III] image of the Crab, are used to build 3-dimensional models of the jet and adjacent remnant nebulosity to better understand the jet's properties and possible formation. We find that the jet's radial velocities range from -190 to +480 km/s with transverse velocities from 1600 to 2650 km/s from base to tip. The jet appears virtually hollow in [O III] emission with the exception of some material at the jet's base where the it connects with the remnant. Our 3D reconstructions indicate that the jet is elliptical in shape and slightly funnel-like rather than a straight cylindrical tube as previously thought. At the base of the jet we find evidence for a significant opening or "channel" in the Crab's main nebula shell. Our analysis of the jet's expansion properties and location supports the theory that the jet may simply represent the highest velocity component of the Crab's N-S bipolar expansion.

Vibration of a spatial elastica constrained inside a straight tube

Abstract In this paper we study the dynamic behavior of a clamped–clamped spatial elastica under edge thrust constrained inside a straight cylindrical tube. Attention is focused on the calculation of the natural frequencies and mode shapes of the planar and spatial one-point-contact deformations. The main issue in determining the natural frequencies of a constrained rod is the movement of the contact point during vibration. In order to capture the physical essence of the contact-point movement, an Eulerian description of the equations of motion based on director theory is formulated. After proper linearization of the equations of motion, boundary conditions, and contact conditions, the natural frequencies and mode shapes of the elastica can be obtained by solving a system of eighteen first-order differential equations with shooting method. It is concluded that the planar one-point-contact deformation becomes unstable and evolves to a spatial deformation at a bifurcation point in both displacement and force control procedures.

Computer-aided simulation of the influence of collective effects on polymer-melt dynamics in a straight cylindrical tube: Observation of the onset stage of the corset effect

The results of the computer-aided simulation of the dynamics of a polymer melt consisting of Fraenkel chains in straight cylindrical tubes and in bulk are discussed. Two different models are studied. In the first model, the dynamics of the polymer melt is simulated via the molecular dynamics simulation. The interaction of unbound polymer segments is described by the Lennard-Jones potential, which excludes any chain crossing of macromolecules and generates collective acoustic waves. In the second model, which serves as a reference, the system is studied via the Brownian dynamics method, in which intermolecular interactions are allowed for phenomenologically via friction and stochastic Langevin forces. In this case, cooperative effects are absent and the effect of spatial confinements makes itself evident only in a narrow near-wall layer. For the two models under consideration, there is a significant difference in the decay of dynamic correlation functions C αβ(t) = 〈b α(t)b β(t)b α(0)b β(0)〉〈b α 2 b β 2 〉−1, where averaging is performed over all macromolecular segments and b α (t) is the component of the end-to-end-segment vector (α ≠ β = x,y, and the cylindrical axis of the tube is directed along the z axis). For the first model allowing for collective effects, the dynamics of decay of C αβ (t)functions is much slower than that for the melt in bulk, and for the second model, in which the presence of the tube leads only to spatial confinements for the polymer segments in the direct vicinity of walls. This difference indicates the fundamental significance of the collective effects in the dynamics of polymer melts confined in porous media. This phenomenon is the first computer-simulated evidence of the onset stage of the so-called corset effect, which was first observed experimentally with the use of NMR relaxometry.

Knudsen Diffusion Through Cylindrical Tubes of Varying Radii: Theory and Monte Carlo Simulations

In this study, Knudsen diffusion of low-pressure gases of infinite mean free path through various tubes is studied using the integral equation theory (IET), standard diffusion theory, and Monte Carlo (MC) simulations. We investigated the transmission probabilities (TPs) of linearly diverging–converging, sinusoidally bulging, and periodic tubes as compared with TPs of conventional straight cylinders. An exact analytic solution for the TP through the straight cylindrical tube was developed using the standard diffusion theory with a linear concentration approximation. IET for the TPs through the diverging–converging and bulging tubes were developed. MC simulation techniques were applied to calculate TPs through all the tube types azimuthal symmetry of which was held with tube radius changing only along the axial coordinate (z). The linearly diverging–converging and sinusoidally bulging tubes provide noticeably higher TPs than those of the equivalent straight tubes. Periodic tubes show that if the tube length scaled by the equivalent diameter is of an order of or greater than the periodicity coefficient (equal to the number of peaks on the tube wall), then the TP of the periodic tube is larger than that of the equivalent straight tube.

인간 이도의 소리응답특성과 음향공간의 재현

The human ear canal amplifies the sound pressure level at specific frequency bands. The characteristics of the ear canal are very similar to those of curved cylindrical tube. In this study, the characteristics of sound transfer in human ear canal were measured and the acoustical space of ear canal was reproduced from the canal cavity geometry. For the measurement of sound transfer function in ear canal, a probe microphone and a reference microphone were used. The sound transfer functions were measured for 5 human subjects. To reproduce the acoustical space of the ear canal, two kinds of ear simulator were designed. The first one is a straight cylindrical tube type and the other is a real-shape ear of which geometry was taken from a micro-CT scanning of a human ear. The characteristics of the reproduced apparatus were compared with those of the human and a commercial ear simulator, RA0045 of G.R.A.S. Inc. The comparison results show that the developed apparatus well represent the ear canal characteristics in the low frequency, but have limited coincidence in level over high frequency range.

Nonlinear Pressure Wave Analysis by Concentrated Mass Model

A pressure wave propagating in a tube often changes to a shock wave because of the nonlinear effects in the propagation medium. The purpose of this study is to establish a practical analytical model to analyze this phenomenon. In previous reports, a concentrated mass model was proposed to analyze nonlinear pressure wave phenomena in a straight cylindrical tube. In the present paper, models of enlargement and contraction are proposed. The models of the enlargement and contraction elements consist of masses, nonlinear springs, base support dampers, and nonlinear dampers. The nonlinear damper is derived from the pressure loss at the enlargement and contraction. To confirm the validity of the proposed model, an experiment on a sound tube with an expansion-chamber muffler is performed and the experimental results are compared with the numerical results obtained by the concentrated mass model. The numerical computational results agree well with the experimental result. Therefore, it is concluded that the proposed enlargement and contraction models are valid for the numerical analysis of nonlinear pressure wave problem in a tube with an expansion-chamber muffler.

Nonlinear Pressure Wave Analysis by Concentrated Mass Model (4th Report, Modeling of Elastic Pipe Element)

A pressure wave propagating in a tube often changes to a shock wave because of the nonlinear effect of the fluid it is traveling through. The purpose of this study is to establish a practical analytical model to analyze this phenomenon. In previous reports, a concentrated mass model was proposed to analyze nonlinear pressure wave phenomena in a straight cylindrical tube. In this paper, the modeling of a branched junction is proposed. The model of the branched junction consists of masses, nonlinear pressure elements, base support dampers, and nonlinear dampers. The nonlinear damper is derived from the pressure loss at the branched junction. To confirm the validity of the proposed branch model, the numerical results obtained from the concentrated mass model are compared with the theoretical value of the transmission loss of a branch pipe. Additionally, an experiment on a sound tube with a branch pipe is performed and the experimental results are compared with the numerical result. All computational results agree very well with the theoretical value and the experimental results. Therefore, it is concluded that the proposed branch model is valid for the numerical analysis of nonlinear pressure wave problem in a tube with a branch pipe.

Nonlinear Pressure Wave Analysis by Concentrated Mass Model (4th Report, Modeling of Elastic Pipe Element)

A pressure wave propagating in a tube often changes to a shock wave because of the nonlinear effects in the propagation medium. The purpose of this study is to establish a practical analytical model to analyze this phenomenon. In the first report, a concentrated mass model was proposed to analyze a nonlinear pressure wave phenomenon in a rigid straight cylindrical tube. In this paper, we apply the model to an elastic pipe. The model in the elastic pipe consists of masses, nonlinear connecting springs, base support dampers, base support springs, and connecting dampers. The effect that the cross-sectional area of the elastic pipe changes is considered by the nonlinear connecting spring. To confirm the validity of the proposed elastic pipe model, we perform experiments on a silicone tube, and the experimental results are compared with the numerical results obtained by the concentrated mass model. The numerical computational results agree well with the experimental results. Therefore, it is concluded that the proposed elastic pipe model is valid for the numerical analysis of nonlinear pressure wave problem in an elastic pipe.

KELVIN–HELMHOLTZ INSTABILITY IN CORONAL MAGNETIC FLUX TUBES DUE TO AZIMUTHAL SHEAR FLOWS

Transverse oscillations of coronal loops are often observed and have been theoretically interpreted as kink magnetohydrodynamic (MHD) modes. Numerical simulations by Terradas et al. (2008, ApJ 687, L115) suggest that shear flows generated at the loop boundary during kink oscillations could give rise to a Kelvin-Helmholtz instability (KHI). Here, we investigate the linear stage of the KHI in a cylindrical magnetic flux tube in the presence of azimuthal shear motions. We consider the basic, linearized MHD equations in the beta = 0 approximation, and apply them to a straight and homogeneous cylindrical flux tube model embedded in a coronal environment. Azimuthal shear flows with a sharp jump of the velocity at the cylinder boundary are included in the model. We obtain an analytical expression for the dispersion relation of the unstable MHD modes supported by the configuration, and compute analytical approximations of the critical velocity shear and the KHI growth rate in the thin tube limit. A parametric study of the KHI growth rates is performed by numerically solving the full dispersion relation. We find that fluting-like modes can develop a KHI in time-scales comparable to the period of kink oscillations of the flux tube. The KHI growth rates increase with the value of the azimuthal wavenumber and decrease with the longitudinal wavenumber. However, the presence of a small azimuthal component of the magnetic field can suppress the KHI. Azimuthal motions related to kink oscillations of untwisted coronal loops may trigger a KHI, but this phenomenon has not been observed to date. We propose that the azimuthal component of the magnetic field is responsible for suppressing the KHI in a stable coronal loop. The required twist is small enough to prevent the development of the pinch instability.

The emergence of toroidal flux tubes from beneath the solar photosphere

Context. Models of flux emergence frequently use a twisted cylindrical loop as the initial starting configuration and ignore the coupling between the radiation field and plasma. In these models, the axis of the original tube never emerges through the photosphere. Without the axis emerging, it is very difficult to form a realistic sunspot. Aims. The aim is to use a toroidal flux loop, placed beneath the solar photosphere and study whether the axis of the system emerges fully into the atmosphere. The toroidal curvature means that the plasma can drain more effectively than in a straight cylindrical tube. Methods. Three-dimensional magnetohydrodynamic numerical simulations of an emerging magnetic flux tube are presented for an initial toroidal loop model. The simulations use a Lagrangian-Remap code that is particularly suited to dealing with shocks and strong current sheets. Results. The evolution of the toroidal loop is followed and the characteristics of the emergence process are compared with the traditional cylindrical loops. The flux sources seen at the photosphere are more circular, and there are less shearing motions in the upper photosphere. When the initial magnetic field strength is relatively weak the evolution of the system is similar to the cylindrical loop case, with the formation of a new flux rope above the photosphere. A striking result is that for large values of field strength the axial field of the toroidal loop emerges fully into the corona. This is reported for the first time in experiments of flux emergence in a highly stratified atmosphere that do not solve self-consistently the radiation transfer problem. In addition, the new flux rope forms below the original axis of the toroidal tube when the field strength is sufficiently strong.

Optimized molecule supply from nozzle-based gas injection systems for focused electron- and ion-beam induced deposition and etching: simulation and experiment

We simulated and measured near-field distributions of molecules impinging on a flat substrate from tube-based nozzles with varying exit aperture geometries (straight, bevelled and doubly perforated). Simulations were performed with the test-particle Monte Carlo approach taking into account the Knudsen number (molecular/transient flow) at the nozzle exit. Distributions were measured via thermal decomposition of Co2(CO)8 molecules on a homogeneously heated substrate. For all geometries and Knudsen numbers a good match between the simulation and experiment was found. For the first time the maximum accessible molecule flux with respect to the total flux exiting the nozzle could be quantified: it is around 7% for a straight cylindrical tube, around 27% for a bevelled tube and around 32% for a doubly perforated tube, all nozzles being 300 µm distant from the substrate and having a 400 µm aperture. Optimum substrate–nozzle angles were determined and shadow effects quantified.

Axisymmetric deformations of straight cylindrical tubes under shock wave loading

The tube strains caused by shock waves passing through the tube are investigated. The tubes are straight and cylindrical and the deformations axisymmetric. Two models are developed that allow the computation of the strains for differently fixed tubes. The models are simple and lead to equation of motions that can easily be solved. The characteristics of the tube deformations caused by shock waves can be studied and described by these models. It is shown that the chosen approach to compute the tube strains is suited to reproduce experimental results. The comparison between computation and experiment also indicates that the structural damping activated by these high speed waves may be small.