Symmetrical Triangle Research Articles

Effect of nitrogen on high temperature low cycle fatigue behaviors in type 316L stainless steel

Strain-controlled low cycle fatigue (LCF) tests were conducted in the temperature range of RT–600°C and air atmosphere to investigate the nitrogen effect on LCF behavior of type 316L stainless steels with different nitrogen contents (0.04–0.15%). The waveform of LCF was a symmetrical triangle with a strain amplitude of ±0.5% and a constant strain rate of 2×10 −3/s was employed for most tests. Cyclic stress response of the alloys exhibited a gradual cyclic softening at RT, but a cyclic hardening at an early stage of fatigue life at 300–600°C. The hardening at high temperature was attributed to dynamic strain aging (DSA). Nitrogen addition decreased hardening magnitude (maximum cyclic stress — first cyclic stress) because nitrogen retarded DSA for these conditions. The dislocation structures were changed from cell to planar structure with increasing temperature and nitrogen addition by DSA and short range order (SRO). Fatigue life was a maximum at 0.1% nitrogen content, which was attributed to the balance between DSA and SRO.

Simulation of pseudostationary radical polymerization, 1. Chain‐length distributions for arbitrary initiation profiles

A procedure is developed which allows to treat arbitrary periodic initiation profiles (asymmetric and symmetric triangle profiles, sinusoidal profiles, Gaussian profiles etc.) in pseudostationary radical polymerization. Using an iterative method these profiles are transformed into the (likewise periodic) radical profiles and into the chain-length distributions of the resulting polymer in case of termination by disproportionation. These distributions are analysed for the position of their inflection points which may be used for experimental determination of the elementary rate constant of chain propagation kp. It turned out that for all profiles that have at least one discontinuity (e.g. asymmetric triangle profiles) the position of the point of inflection is a correct measure of kp for a conveniently wide range of experimental parameters. In case of profiles without discontinuity (symmetric triangle profiles, sinusoidal and Gaussian profiles) the position of the inflection point is shifted to lower values which means that the kp values determined on this basis will be a little too small. In most cases, however, the error introduced by this fact will not exceed the overall error of the experiment so that in practice the method of determining kp in pseudostationary polymerization is not restricted to those profiles which exhibit discontinuities.

Simulation of pseudostationary radical polymerization, 1. Chain‐length distributions for arbitrary initiation profiles

AbstractA procedure is developed which allows to treat arbitrary periodic initiation profiles (asymmetric and symmetric triangle profiles, sinusoidal profiles, Gaussian profiles etc.) in pseudostationary radical polymerization. Using an iterative method these profiles are transformed into the (likewise periodic) radical profiles and into the chain‐length distributions of the resulting polymer in case of termination by disproportionation. These distributions are analysed for the position of their inflection points which may be used for experimental determination of the elementary rate constant of chain propagation kp. It turned out that for all profiles that have at least one discontinuity (e.g. asymmetric triangle profiles) the position of the point of inflection is a correct measure of kp for a conveniently wide range of experimental parameters. In case of profiles without discontinuity (symmetric triangle profiles, sinusoidal and Gaussian profiles) the position of the inflection point is shifted to lower values which means that the kp values determined on this basis will be a little too small. In most cases, however, the error introduced by this fact will not exceed the overall error of the experiment so that in practice the method of determining kp in pseudostationary polymerization is not restricted to those profiles which exhibit discontinuities.

On the algorithms for parameter estimation in one-dimensional densities and distributions in a general purpose statistical package

The substantial details of a complex of programs for estimating in respect to maximum likelihood or x2 method the parameters in densities or distributions given in arbitrary parametric form through an iteration process of MARQUARDT type are given. As an example, the results of estimating 5 parameters in a mixture of two symmetrical triangle densities are described. The complex of programs is a component of the general purpose statistical package STATES of the Tallinn Institute of cybernetics

Space filling with identical symmetrical solids

In one dimension, a set of rods of equal length may be used to cover the line. In two dimensions, an area may be covered by joining up sets of identical symmetrical squares, equilateral triangles or regular hexagons. In three dimensions, there are at least four different symmetrical solids which can be packed together to fill space. Of these, the cube is most obvious, two others are moderately well known (see [1] for example), while I have been unable to find any record of the fourth solid.

Design Philosophy for High-Resolution Rate and Throughput Spectroscopy Systems

The paper describes the philosophy behind the design of a pulse processing system used in a semiconductor detector x-ray spectrometer to be used for plasma diagnostics at the Princeton TFTR facility. This application presents the unusual problems of very high counting rates and a high-energy neutron background while still requiring excellent resolution. To meet these requirements three specific new advances are included in the design: (i) A symmetrical triangular pulse shape is employed in the main pulse-processing channel. A new simple method of generating a close approximation to the symmetrical triangle has been developed. (ii) To cope with the very wide dynamic range of signals while maintaining a constant fast resolving time, approximately symmetrical triangular pulse shaping is also used in the fast pulse pile-up inspection channel. (iii) The demand for high throughput has resulted in a re-examination of the operation of pile-up rejectors and pulse stretchers. As a result a technique has been developed that, for a given total pulse shaping time, permits approximately a 40% increase in throughput in the system. Performance results obtained using the new techniques are presented.

A Versatile and Easy-To-Build Digital Function. Generator for Voltammetry

ABSTRACT A versatile and easy-to-build digital function generator for electrochemical applications is described. The instrument combines a 16 bit digital to analog converter (DAC) with digital control of the switching. Possible waveforms are ramp and asymmetrical or symmetrical triangle in single cycle or continuous mode. In the latter modes a timed delay at steady potential can be incorporated at the point of slope reversal. This is interesting for use in cyclic voltammetry to measure the reverse peak current when several electroactive species are present in solution.

Bootstrap theory of quarks

Combinatorial topology reveals particle quark structure to be a consequence of S-matrix causality and unitarity. The two “basic quarks” correspond to symmetrical and unsymmetrical triangles; out of these, particle faces are built belonging both to hadrons and to weakly interacting particles. Hadron quarks must themselves be built from at least three basic quarks and carry topological quantum numbers that include baryon number, four primary flavours with exact up-down symmetry and three colours. There is an infinite number of secondary flavours with successively higher thresholds, a guess for the multiplicity of the next flavour group being 32.

A novel symmetrical triangle waveform generator

The interconnection of a long tailed pair switch and a monolithic diode-transistor coupled structure facilitates the generation of a symmetrical triangle voltage waveform having a 150-V//spl mu/s edge-speed capability and a typical 5-V amplitude. Deviations from sweep linearity, as given by sweep speed error is typically <0.3 percent for the positive-going edge of the waveform; for the negative-going edge it is <3 percent, but this figure can be reduced by using a suggested modification. The circuit essentially employs a current rerouting technique but differs from existing fast types in that the waveform stays automatically symmetrical as the magnitude of the timing capacitor charging current is varied.

Method of Diatomics in Molecules. V. Theoretical Prediction of Stable Li2H+ and Almost Stable LiH2+

Diatomics-in-molecules theory is applied to the molecule—ions LiH2+ and Li2H+ using as a basis three canonical valence-bond wavefunctions in each case. The input for this theory consists of the valence-bond wavefunctions and potential-energy curves for the ground electronic states of H2, Li2, and LiH and for the ground and first excited states of H2+, Li2+, and LiH+. Experimental diatomic potential-energy curves are used if available; otherwise, best possible theoretical or semiempirical curves are used. Diatomics-in-molecules theory in this approximation leads to predictions that ground-state LiH2+ may be stable by about 2.5 kcal with respect to Li++H2 and that ground-state Li2H+ should be stable by about 10 kcal with respect to Li++LiH. The equilibrium shape for LiH2+ turns out to be a symmetrical isosceles triangle with RLiH=5.0 bohrs and RHH=1.4 bohrs; Li2H+ is symmetrical and linear with RLiH=3.4 bohrs. A stable linear excited state (1Σu+) is predicted at about 35 kcal above the ground state (1Σg+) of Li2H+.

ASYMMETRY O HE NARES: A POSITIVE DIAGNOSTIC SIGN OR ENTITY ESTABLISHING ANATOMIC DISPLACEMENT OF LOWER END OF CARTILAGINOUS NASAL SEPTUM

DEMONSTRATION O GEOMETIC PROPOSITION When a perpendicular is dropped from the apex of an isosceles triangle (a triangle having two equal sides) to its base the original triangle is divided into two similar or two symmetrical triangles. If the base of this perpendicular is moved to either side, then these two similar triangles become dissimilar or asymmetrical. The converse of this geometric proposition is equally true. The base of the nose as viewed from below is an isosceles (the two sides are equal) triangle. From the apex of this isosceles triangle the lower end of the cartilaginous septum, together with the columnar cartilages, forms a perpendicular to the base line and divides the triangular base of the nose into two symmetrical or two similar nares. If the perpendicular or lower end of the cartilaginous septum is shifted or sprung to either side from out of its septal groove