Structure And Dynamics Of Modulated Traveling Waves In Cellular Flames

We describe spatial and temporal patterns in cylindrical premixed flames in the cellular regime, $Le < 1$, where the Lewis number $Le$ is the ratio of thermal to mass diffusivity of a deficient component of the combustible mixture. A transition from stationary, axisymmetric flames to stationary cellular flames is predicted analytically if $Le$ is decreased below a critical value. We present the results of numerical computations to show that as $Le$ is further decreased traveling waves (TWs) along the flame front arise via an infinite-period bifurcation which breaks the reflection symmetry of the cellular array. Upon further decreasing $Le$ different kinds of periodically modulated traveling waves (MTWs) as well as a branch of quasiperiodically modulated traveling waves (QPMTWs) arise. These transitions are accompanied by the development of different spatial and temporal symmetries including period doublings and period halvings. We also observe the apparently chaotic temporal behavior of a disordered cellular pattern involving creation and annihilation of cells. We analytically describe the stability of the TW solution near its onset+ using suitable phase-amplitude equations. Within this framework one of the MTW's can be identified as a localized wave traveling through an underlying stationary, spatially periodic structure. We study the Eckhaus instability of the TW and find that in general they are unstable at onset in infinite systems. They can, however, become stable for larger amplitudes.Comment: to appear in Physica D 28 pages (LaTeX), 11 figures (2MB postscript file

Computation of acoustic waves in a jet

A numerical treatment of acoustic waves in a jet is described. The full time dependent Euler equations are used in both linear and nonlinear formulations. The computational region of integration is artificially bounded and boundary conditions are developed to simulate outgoing waves and to enable the computational domain to be substantially restricted. Higher order methods and coordinate transformations are introduced to further reduce the number of grid points as well as to increase the efficiency of the program. Numerical results are presented for time harmonic sources as well as for sources with more complicated time dependence

Once in a lifetime: the date of the Wayland's Smithy long barrow

Twenty-three radiocarbon results are now available from the Wayland’s Smithy long barrow, and are presented within an interpretive Bayesian statistical framework. Four alternative archaeological interpretations of the sequence are considered, each with a separate Bayesian model, though only two are presented in detail. The differences are based on different readings of the sequence of Wayland’s Smithy II. In our preferred interpretation of the sequence, the primary mortuary structure was some kind of lidded wooden box, accessible for deposition over a period of time, and then closed by the mound of Wayland’s Smithy I; Wayland’s Smithy II was a unitary construction, with transepted chambers, secondary kerb and secondary ditches all constructed together. In the Bayesian model for this interpretation, deposition began in the earlier 36th century cal BC, and probably lasted for a generation. A gap of probably 40–100 years ensued, before the first small mound was constructed in 3520–3470 cal BC. After another gap, probably of only 1–35 years, the second phase of the monument was probably constructed in the middle to later part of the 35th century cal BC (3460–3400 cal BC), and its use probably extended to the middle decades of the 34th century cal BC. Results are discussed in relation to the local setting, the nature of mortuary rites and the creation of tradition

Talking About My Generation: the Date of the West Kennet Long Barrow

Thirty-one radiocarbon results are now available from the West Kennet long barrow, and are presented within an interpretive Bayesian statistical framework. Two alternative archaeological interpretations of the sequence are given, each with a separate Bayesian model. In our preferred interpretation, the barrow is seen as a unitary construction (given the lack of dating samples from the old ground surface, ditches or constructional features themselves), with a series of deposits of human remains made in the chambers following construction. Primary deposition in the chambers is followed by further secondary deposition of some human remains, including children, and layers of earth and chalk, the latest identifiable finds in which are Beaker sherds. In the Bayesian model for this sequence, the construction of the monument at West Kennet, as dated from the primary mortuary deposits, occurred in 3670–3635 cal. BC, probably in the middle decades of the thirty-seventh century cal. BC. The last interments of this initial use of the chambers probably occurred in 3640–3610 cal. BC. The difference between these two distributions suggests that this primary mortuary activity probably continued for only 10–30 years. After a hiatus probably lasting for rather more than a century, the infilling of the chambers began in 3620–3240 cal. BC and continued into the second half of the third millennium cal. BC. In an alternative interpretation, we do not assume that all the people dated from the primary mortuary deposits were placed in the monument in a fleshed or partially articulated condition; they could therefore have died before the monument was built, although they must have died before the end of the formation of the mortuary deposit. In the Bayesian model for this interpretation, the monument appears to belong either to the thirty-seventh century cal. BC or the mid-thirty-sixth century cal. BC, and deposition again appears short-lived, but the model is unstable. Results are discussed in relation to the setting and sequence of the local region

Serious mortality: the date of the Fussell's Lodge long barrow

Twenty-seven radiocarbon results are now available from the Fussell’s Lodge long barrow, and are presented within an interpretive Bayesian statistical framework. Three alternative archaeological interpretations of the sequence are given, each with a separate Bayesian model. It is hard to decide between these, though we prefer the third. In the first (following the excavator), the construction is a unitary one, and the human remains included are by definition already old. In the second, the primary mortuary structure is seen as having two phases, and is set within a timber enclosure; these are later closed by the construction of a long barrow. In that model of the sequence, deposition began in the 38th century cal BC and the mortuary structure was extended probably in the 3660s–3650s cal BC; the long barrow was probably built in the 3630s–3620s cal BC; ancestral remains are not in question; and the use of the primary structure may have lasted for a century or so. In the third, preferred model, a variant of the second, we envisage the inclusion of some ancestral remains in the primary mortuary structure alongside fresh remains. This provides different estimates of the date of initial construction (probably in the last quarter of the 38th century cal BC or the first half of the 37th century cal BC) and the duration of primary use, but agrees in setting the date of the long barrow probably in the 3630s–3620s cal BC. These results are discussed in relation to the development and meanings of long barrows at both national and local scales

Effective Improvement of Symptoms in Patients with Acute Migraine by GR43175 Administered in Dispersible Tablets

GR43175, a selective 5-HT1-like agonist, was administered as oral dispersible tablets in an open, uncontrolled dose-ranging study to assess its efficacy as an agent for acute migraine. Nine patients, all with well established attacks, were assessed for changes in severity of headache and associated symptoms over 2 h. Drug absorption was compared during and between attacks in five patients. Doses of 140 mg and 280 mg resulted in complete relief of all symptoms within 2 h. Treatment was well tolerated in all patients

Radiation of sound from unflanged cylindrical ducts

Calculations of sound radiated from unflanged cylindrical ducts are presented. The numerical simulation models the problem of an aero-engine inlet. The time dependent linearized Euler equations are solved from a state of rest until a harmonic solution is attained. A fourth order accurate finite difference scheme is used and solutions are obtained from a fully vectorized Cyber-203 computer program. Cases of both plane waves and spin modes are treated. Spin modes model the sound generated by a turbofan engine. Boundary conditions for both plane waves and spin modes are treated. Solutions obtained are compared with experiments conducted at NASA Langley Research Center

Simulation of the fluctuating field of a forced jet

The fluctuating field of a jet excited by transient mass injection is simulated numerically. The model is developed by expanding the state vector as a mean state plus a fluctuating state. Nonlinear terms are not neglected and the effect of nonlinearity is studied. The results show a significant spectral broadening in the flow field due to the nonlinearity. In addition, large scale structures are broken down into smaller scales

Boundary conditions for the numerical solution of elliptic equations in exterior regions

Elliptic equations in exterior regions frequently require a boundary condition at infinity to ensure the well-posedness of the problem. Examples of practical applications include the Helmholtz equation and Laplace's equation. Computational procedures based on a direct discretization of the elliptic problem require the replacement of the condition on a finite artificial surface. Direct imposition of the condition at infinity along the finite boundary results in large errors. A sequence of boundary conditions is developed which provides increasingly accurate approximations to the problem in the infinite domain. Estimates of the error due to the finite boundary are obtained for several cases. Computations are presented which demonstrate the increased accuracy that can be obtained by the use of the higher order boundary conditions. The examples are based on a finite element formulation but finite difference methods can also be used

Numerical Study of Three-dimensional Spatial Instability of a Supersonic Flat Plate Boundary Layer

The behavior of spatially growing three-dimensional waves in a supersonic boundary layer was studied numerically by solving the complete Navier-Stokes equations. Satisfactory comparison with linear parallel and non-parallel stability theories, and experiment are obtained when a small amplitude inflow disturbance is used. The three-dimensional unsteady Navier-Stokes equations are solved by a finite difference method which is fourth-order and second-order accurate in the convection and viscous terms respectively, and second-order accurate in time. Spanwise periodicity is assumed. The inflow disturbance is composed of eigenfunctions from linear stability theory. By increasing the amplitude of the inflow disturbance, nonlinear effects in the form of a relaxation type oscillation of the time signal of rho(u) are observed