Oscillations and chaos in CO+O(2) combustion

The gas-phase reaction between carbon monoxide and oxygen (in the presence of small amounts of hydrogen) shows bistability and oscillatory behavior. Typically, the oscillatory ignition has a period-1 relaxation waveform. The limit cycle is born at a saddle-node loop and terminates via a supercritical Hopf bifurcation. For a mean residence time of 8 s there is a period-doubling to a period-2 solution followed by period-halving to quasisinusoidal period-1 oscillations. At longer residence times, more period-doublings forming a full cascade to chaos with subsequent periodic windows are observed. The chaotic attractor has an underlying single-humped next maximum map.     

On a symmetry of turbulence

This paper presents results on symmetries of the spectrum of singularities for random cascades found in the statistical theory of turbulence. It is shown that empirical dimension curves possess a natural symmetry whose presence restricts the class of allowable probability distributions of the cascade generator in a simple manner. In particular, necessary and sufficient conditions on the probability distribution of the generator are obtained for symmetry of the singularity spectrum within a large class of cascade models.     

Smart Geodesic Tracing in GRworkbench

We have developed a new tool for numerical work in General Relativity: GRworkbench. We discuss how GRworkbench's implementation of a numerically-amenable analogue to Differential Geometry facilitates the development of robust and chart-independent numerical algorithms. We consider, as an example, geodesic tracing on two charts covering the exterior Schwarzschild space-time.     

MR detection of mechanical vibrations using a radiofrequency field gradient

A new method for NMR characterization of mechanical waves, based upon radiofrequency field gradient for motion encoding, is proposed. A binomial B1 gradient excitation scheme was used to visualize the mobile spins undergoing a periodic transverse mechanical excitation. A simple model was designed to simulate the NMR signal as a function of the wave frequency excitation and the periodicity of the NMR pulse sequence. The preliminary results were obtained on a gel phantom at low vibration frequencies (0-200 Hz) by using a ladder-shaped coil generating a nearly constant RF field gradient along a specific known direction. For very small displacements and/or B1 gradients, the NMR signal measured on a gel phantom was proportional to the vibration amplitude and the pulse sequence was shown to be selective with respect to the vibration frequency. A good estimation of the direction of vibrations was obtained by varying the angle between the motion direction and the B1 gradient. The method and its use in parallel to more conventional MR elastography techniques are discussed. The presented approach might be of interest for noninvasive investigation of elastic properties of soft tissues and other materials.     

MuSR study of weakly magnetic Y(Co1−x Al x )2

All previous experiments have suggested that Y(Co_1−x Al _x )₂ is a weak itinerant ferromagnet for 0.12<x<0.20. The muon transverse damping rate (λ) increases rapidly near the Curie point forx≥0.155 and for one sample withx=0.145. The value of λ increases with decreasing temperature for other samples withx<0.155 but shows no feature at the Curie point.     

Nuclear quantum effects in liquid water from path-integral simulations using an ab initio force-matching approach

We have applied path integral simulations, in combination with new ab initio based water potentials, to investigate nuclear quantum effects in liquid water. Because direct ab initio path integral simulations are computationally expensive, a flexible water model is parameterised by force-matching to density functional theory-based molecular dynamics simulations. Static and dynamic properties of liquid water at ambient conditions are presented and the role of nuclear quantum effects, exchange-correlation functionals and dispersion corrections are discussed in regards to reproducing the experimental properties of liquid water.     

Infrared Absorption Study of Some Cyclic Ureas,Cyclic Thioureas and Their N,N′-Dialkyl Derivatives

Abstract

In his communication on the detection limits for thermal emission spectroscopy of metallic species in flame media, Fassel (¹) attacks our previous statement that detection limits for Al, Be and Mo were available only for turbulent oxygen-supported hydrogen or acetylene flames. It should be borne in mind that he was referring to a preliminary communication (²) which naturally does not carry an extensive bibliography. It should also be noted that we were concerned, in context, with a comparison of the separated flame with conventional flames, not with highly unconventional flames such as those to which he refers. Whilst the point with which he takes issue was a very minor one, incorporated in our preliminary communication mainly as an “aside”, we firmly disagree with his observation. The flame he refers to (³) (⁴) is, in fact, a diluted oxy-acetylene flame which is supported by venting some air (and therefore nitrogen) to dilute the fuel-oxygen mixture. Fassel's communication (¹) erroneously refers to this as a 'premixed oxy-acetylene flame', whereas elsewhere (⁵) it is described more correctly as an oxygen-nitrogen-acetylene flame. The burner he long-pathlength carbonaceous flames (¹⁰). They also allow more sensitive molecular emission spectroscopy of sulphur in an air-hydrogen flame (¹¹), etc. We hope that this unfortunate correspondence will not distract attention from the main issue of our previous or previous preliminary communication on the separated nitrous oxide-acetylene flime.     

Implementing and using high-order finite element methods

We present theoretical analyses of and detailed timings for two programs which use high-order finite element methods to solve the Navier- Strokes equations in two and three dimensions. The analyses show that algorithms popular in low-order finite element implementations are not always appropriate for high-order methods. The timings show that with the proper algorithms high-order finite element methods are viable for solving the Navier-Stokes equations. We show that it is more efficient, both in time and storage, not to precompute element matrices as the degree of approximating functions increases. We also study the cost of assembling the stiffness matrix versus directly evaluating bilinear forms in two and three dimensions. We show that it is more efficient not to assemble the full stiffness matrix for high-order methods in some cases. We consider the computational issues with regard to both Euclidean and isoparametric elements. We show that isoparametric elements may be used with higher-order elements without increasing the order of computational complexity.