Infinite Train Research Articles

Effect of Relaxation and Retardation Time on Peristaltic Transport of the Oldroydian Viscoelastic Fluid

The influence of relaxation and retardation time on peristaltic transport of an incompressible Oldroydian viscoelastic fluid by means of an infinite train of sinusoidal waves traveling along the walls of a two-dimensional flexible channel is investigated. A perturbation solution is obtained for the case in which the amplitude ratio (wave amplitude to channel half-width) is small. The results show that the values of the mean axial velocity of an Oldroydian viscoelastic fluid is smaller than that for a Newtonian fluid. The reflux phenomena are discussed. It is found that the critical reflux pressure gradient decreases with increasing retardation time and increases with increasing relaxation time. Numerical results are reported for different values of the physical parameters of interest.

Peristaltic transport of Johnson‐Segalman fluid under effect of a magnetic field

The peristaltic transport of Johnson‐Segalman fluid by means of an infinite train of sinusoidal waves traveling along the walls of a two‐dimensional flexible channel is investigated. The fluid is electrically conducted by a transverse magnetic field. A perturbation solution is obtained for the case in which amplitude ratio is small. Numerical results are reported for various values of the physical parameters of interest.

The interaction of an infinite wheel-train with a constant spacing between the wheels moving uniformly over a rail track

A periodic model of rail track in the form of an infinite Timoshenko beam held by massive elastoviscous supports with constant spacing is considered. The sprung part of the carriage is separated from the wheel by an elastic spring, and its action on the wheel in a first approximation is therefore represented by a static load. The steady vertical vibrations of the rail under the action of an infinite train of wheels moving uniformly over the rail are investigated. The distances between the wheels are identical, and all the wheels have the same mass and carry the same load. The static stiffness of the track over a sleeper exceeds that of track in the space between sleepers. Therefore, under the action of a constant load, each wheel performs vertical parametric vibrations with the frequency of passage of the sleepers. These vibrations are an extension of parametric vibrations described using the well-known Mathieu and Hill equations.

A Numerical Investigation of Peristaltic Waves in Circular Tubes

Peristaltic pumping is a process of fluid transport arising from the progressive waves, which travel along the walls of a flexible channel. It is a primary physiological transport mechanism that is inherent in many tubular organs of the human body such as the ureter, the gastro-intestinal tract, the urethra, and so on. Many studies exist in literature with the aim of understanding the characteristics of peristaltic flow under the assumption of low Reynolds number and infinitely long wavelength in a two-dimensional channel. However, peristaltic pumping is also the mechanism used in other industrial applications such as the blood pump for which the Reynolds number has a moderately high value. As studies concerning moderate to high Reynolds number flow in the circular tube are rare in literature, in the present study, the peristaltic flow of an incompressible fluid is numerically simulated using the finite volume method for solving the incompressible Navier-Stokes equations in primitive variable formulation by means of an infinite train of sinusoidal waves traveling along the wall of an axi-symmetric tube. The computational model presented in this work covers a wider range of Reynolds number (0.01-100), wave amplitude (0-0.8), and wavelength (0.01-0.4) than the those attempted in previous studies reported in literature and some new results pertaining to the distribution of velocity, pressure, wall shear stress for different peristaltic flow conditions characterizing flow at moderately higher Reynolds number have been obtained. The effect of the wave amplitude, wavelength, and Reynolds number on the "flow trapping" mechanism induced by peristalsis has also been investigated here for higher ranges of values of the parameters characterizing peristalsis.

One-dimensional co-ordination polymers formed by crown ether metal cation bridges: synthesis and crystal structure of nickel(II) dithiolene complexes [{Na(benzo-15-crown-5)}2 Ni(i-mnt)2]n · nCH2Cl2 and [{Na(benzo-15-crown-5)}2Ni(mnt)2

Reaction of NiCl2 · 6H2O, Na2[i-mnt] and benzo-15-crown-5 in CH3OH⧹CH2Cl2 at room temperature leads to [{Na(benzo-15-crown-5)}2Ni(i-mnt)2]n · nCH2Cl2 (1). The same reaction with Na2[mnt] instead of Na2[i-mnt] affords [{Na(benzo-15-crown-5)}2Ni(mnt)2]n (2). Both complexes were isolated as crystalline products. X-ray diffraction analyses reveal that the main segments of 1 and 2 are infinite train structures, in which the building blocks Ni(i-mnt)2 or Ni(mnt)2 in end-to-end arrangements act as body frames and crown cycles standing by the body frames play the role of cartwheel. They are joined with each other through sodium ions.

Structure and Instability of the Ekman Spiral in the Presence of Surface Gravity Waves

Abstract The physical processes responsible for maintaining the mixed layer am examined by considering the velocity structure. The low-frequency Ekman response in the interior of unstratified mixed layers is much less sheared than is predicted using eddy viscosity models that reproduce the temperature structure. However, the response is more sheared than predicted by models that parameterize the mixed layer as a slab. An explanation is sought by considering the effect of an infinite train of surface gravity waves on the mean Ekman spiral. For some realistic conditions, the Ekman spiral predicted by assuming small-scale diffusion alone is strongly unstable to Langmuir cells driven by wave-current interaction. In the Northern Hemisphere, these cells are oriented to the right of the wind, the result of a balance between maximizing the wave-current forcing, maximizing the efficiency of this forcing in producing cells, and minimizing the crosscell shear. The cells are capable of replacing small-scale turbulent...

Repetitive activity of a branched Hodgkin-Huxley axon with multiple encoding sites.

Afferent activity in a receptor afferent fiber with several encoding sites is generally believed to represent the activity of the fastest pacemaker that resets all more slowly encoding sites. Alternatively, some impulse mixing as well as some nonlinear summation of receptor current to a single encoder have been considered. In this article the repetitive firing activity of a Hodgkin-Huxley axon consisting of two branches that join into a single stem axon was investigated. The model axon was stimulated by constant-current injection into either the right or the left or both branches. It was found that the model axon generated an (infinite) train of action potentials if the input current was large enough. The discharge frequency found was constant, and on combined stimulation of both branches with different current, the site of impulse initiation was always in the branch receiving the higher input current, excluding a simple impulse mixing. On the other hand, the combined stimulation of both branches evoked repetitive firing with a higher frequency than expected by the pacemaker-resetting hypothesis. Moreover, a stimulus that is subthreshold for repetitive firing if injected into one branch yields repetitive firing when it is injected into both branches, a behavior inconsistent with impulse mixing and pacemaker resetting. On the other hand, current injection into one branch allowed repetitive activity only within a rather limited range of firing frequencies. Using distributed current injection into both branches, however, allowed many more different firing frequencies. Such behavior is inconsistent with both pacemaker resetting and (nonlinear) input current summation. Consequently, the repetitive firing behavior of a branched Hodgkin-Huxley axon with multiple encoding sites appears to be more complex than postulated in the simple hypotheses.

Influence of ion pairs on the dynamical behaviour of Er3+-doped fibre lasers

We demonstrate experimentally the influence of ion-pair concentration on the dynamical behaviour of erbium-doped fibre lasers. At low pair densities, the laser has a CW output, while at higher densities it exhibits a self-pulsing behaviour. For intermediate pair concentrations, the output intensity evolves continuously from an infinite train of pulses to a CW steady state as the pumping ratio is increased.

Self-pulsing in Er3+-doped fibre laser

The output intensity of an erbium-doped fibre laser was studied. Experiments were performed with three pumping wavelengths: 514.5 nm, 810 nm and 980 nm. The laser output intensity exhibits three different dynamical behaviours: steady-state, sinusoidal variation or self-pulsing. In particular, in a bad (high-loss) cavity configuration, when the pumping ratio is increased above the lasing threshold the output intensity changes continuously from a steady-state to an infinite train of pulses. We also show that, depending on the cavity configuration, the transient oscillations display different forms.

Dynamical Behaviour of the Bonhoeffer-van der Pol Model11The project supported by Sino-British Friendship Scholarship Foundation and National Natural Science Foundation of China.

The dynamical behaviour and the threshold phenomenon for the Bonhoeffer-van der Pol model of a nerve membrane stimulated by a constant and a periodic currents are investigated. For the constant current , there are two Hopf bifurcations at and , respectively. At an infinite long train of nerve impulses (threshold phenomenon) is found. For the periodic current, there are an ordinary period-doubling to chaotic state, and a mode-locking state, as well as a reversed period-doubling from chaotic state to period-1 state. A phase diagram for the threshold phenomenon in the parameter space ( and , amplitude and frequency) is obtained. In our discussion we conclude that the period- oscillations correspond to the -shaped impulse trains, and the chaotic oscillation corresponds to the infinite-shaped impulse trains. All of these impulses of the BVP model system code the information process of the nerve fibre in neural tissue.

Cyclostrophic balance in surface gravity waves

The cyclostrophic balance (pressure forcevs. force centrifugal force) is shown to be satisfied for all fluid particles in surface gravity waves with sinusoidal form and circular particle orbits. Consequences of the cyclostrophic balance are 1) that the normal dispersion relation for deep water hold and 2) that the orbital radius decrease with increasing depth at the usual exponential rate, from which it follows that the wave pressure and particle speed also decrease with depth exponentially. In addition, the cyclostrophic and hydrostatic balances together predict wave breaking at the crests for amplitudes exceeding one divided by the wave number. In contrast to the traditional perturbation method, based on irrotational flow, the cyclostrophic method does not demand that the amplitude be much less than a wave length and does not require an infinite wave train.

Testing convergence schemes on the solution of two-dimensional boundary value problems in elasticity

This paper is the first of a three-part series in which solutions are given to two-dimensional and three-dimensional boundary value problems in elasticity. Using a new convergence technique developed here, the stress in the near zone for the case of a two-dimensional semi-infinite slab subject to static loading will be evaluated. In the next article this same technique will be applied in two ways to evaluate the dynamic response of a three-dimensional solid cylinder subject to time-dependent end loading. In addition, the third article will discuss a resonance phenomenon associated with the reflection of an infinite wave train off the free end of a semi-infinite cylindrical bar.

The singularly perturbed Hodgkin-Huxley equations as a tool for the analysis of repetitive nerve activity

A qualitative analysis of the Hodgkin-Huxley model (Hodgkin and Huxley 1952), which closely mimics the ionic processes at a real nerve membrane, is performed by means of a singular perturbation theory. This was achieved by introducing a perturbation parameter that, if decreased, "speeds up" the fast variables of the Hodgkin-Huxley equations (membrane potential and sodium activation), whereas it does not affect the slow variables (sodium inactivation and potassium activation). In the most extreme case, if the perturbation parameter is set to zero, the original four-dimensional system "degenerates" to a system with only two differential equations. This degenerate system is easier to analyze and much more intuitive than the original Hodgkin-Huxley equations. It shows, like the original model, an infinite train of action potentials if stimulated by an input current in a suitable range. Additionally, explanations for the increased sensitivity to depolarizing current steps that precedes an action potential can be found by analysis of the degenerate system. Using the theory of Mishchenko and Rozov (1980) it is shown that the degenerate system does not only represent a simplification of the original Hodgkin-Huxley equations but also gives a valid approximation of the original model at least for stimulating currents that are constant within a suitable range.

Magnetic fields in the vicinity of pulsed electron beams in space

The electric component of the fields generated by a pulsed electron beam in a magnetized plasma was derived by Harker and Banks (1987, Planet. Space Sci. 35, 11). The beam was modeled as an infinite train of square-wave pulses and the radiation was obtained by adding coherently the radiation from each individual electron in the idealized helical trajectory assumed by the beam. Here we complete the analysis by presenting the magnetic components.

Comments on “Computer modelling of the growth kinetics of ledged interface boundaries I — Single step and infinite train of steps”

Comments on “Computer modelling of the growth kinetics of ledged interface boundaries I — Single step and infinite train of steps”

Computer modeling of the growth kinetics of ledged interphase boundaries—I. Single step and infinite train of steps

A computer model of the DuFort-Frankel finite difference method was developed to simulate the motion of a single step and of an infinite train of steps. Volume diffusion of solute in the matrix to the riser of the step was assumed to control the growth rate. The results for a single step are fully consistent with the Atkinson analysis, based upon the steady state diffusion field equation, and in a limited range of supersaturation also with the Jones-Trivedi results reported earlier. At long reaction times the growth rate of an infinite train of equally spaced steps became nearly proportional to t −1 2 , the time dependence of the growth kinetics of a planar disordered boundary. The thickening by the former mechanism can be faster than that by the latter when the interledge spacings are smaller than about four times the step height. Scatter in the interledge spacing among precipitate plates formed in the same specimen can account fairly well for the variations in observed thickening rates. However, simulation of thickening by an infinite train of steps proves to be not always appropriate for analyzing the actual kinetics over long reaction times.

Near fields in the vicinity of pulsed electron beams in space

Most measurements of the radio frequency emissions from artificial electron beams in space have been made in close proximity to the beam. This paper presents theory and results for the near-field radiation associated with the operation of a pulsed electron beam, taking into account the effects of the ionospheric plasma. The beam is modeled as an infinite train of square-wave pulses and the radiation is obtained by adding coherently the radiation from each individual electron in the idealized helical trajectory assumed by the beam as it traverses the magnetized plasma. The mathematical solution is obtained by taking the Fourier transform in space and time of Maxwell's equations and the driving modulated beam current, and then taking the inverse transform of the resulting electric field.Typical electric field strengths are presented for a range of modulation frequencies extending from below the ion cyclotron to the electron cyclotron frequency.

Existence of Traveling Wave Trains in Nerve Axon Equations

We establish the existence of two discrete classes of traveling wave solutions to nerve axon equations under conditions on the linearization of the system about the rest state. Each solution in one class consists of a finite train of pulses, while each solution in the other class consists of an infinite train that arises from the rest state in the leading direction. The solutions are distinguished by the spacing of the pulses in the train, and indexed by n-tuples and sequences of integers respectively in the two classes. This result is obtained from study of the resulting parametrized dynamical system, which has a a single homoclinic orbit for one parameter value. These assumptions were previously used to show the existence of the double pulse solutions and are known to hold in for some nerve models.

Radiation from long pulse train electron beams in space plasmas

A previous study of electromagnetic radiation from a finite train of electron pulses is extended to an infinite train of such pulses. The electrons are assumed to follow an idealized helical path through a space plasma in such a manner as to retain their respective position within the beam. This leads to radiation by coherent spontaneous emission. The waves of interest in this region are the whistler slow (compressional) and fast (torsional) Alfvén waves. Although a general theory is developed, analysis is then restricted to two approximations, the short and long electron beam. Formulas for the radiation per unit solid angle from the short beam are presented as a function of both propagation and ray angles, electron beam pulse width and separation and beam current, voltage, and pitch angle. Similar formulas for the total power radiated from the long beam are derived as a function of frequency, propagation angle, and ray angle. Predictions of the power radiated are presented for representative examples as determined by the long beam theory.

'Modelling and Properties of Modulated RF Signals Perturbed by Oscillator Phase Instabilities and Resulting Spectral Dispersion'

Abstract : This dissertation considers the problem of characterization and stochastic properties of oscillator phase instabilities. Spectral dispersion caused by such instabilities is also determined. The instabilities are modeled using white phase, random walk phase, random walk frequency random processes as well as drift phase and frequency terms. Auto-correlation functions and power spectral densities are derived for the oscillator rf output signal containing such instabilities. Furthermore, a procedure is proposed which involves the covariance matrix of the phase random process in conjunction with the characteristic function for determining the higher order moments of the rf signal. Stationarity and ergodicity properties of the rf signals containing phase instabilities are discussed. In each case, conditions for ergodicity are established for the mean, auto-correlation function, and the power spectral density. The spectral dispersion generated by oscillator phase instabilities imposes limits on dynamic range and Doppler resolution in radar signal processing. This spectral dispersion is determined for the phase instability models considered in this dissertation. Modulating waveforms considered as examples include the cw, the infinite pulse train and the finite pulse train.