Physical tests for Random Numbers in Simulations

We propose three physical tests to measure correlations in random numbers used in Monte Carlo simulations. The first test uses autocorrelation times of certain physical quantities when the Ising model is simulated with the Wolff algorithm. The second test is based on random walks, and the third on blocks of n successive numbers. We apply the tests to show that recent errors in high precision simulations using generalized feedback shift register algorithms are due to short range correlations in random number sequences. We also determine the length of these correlations.Comment: 16 pages, Post Script file, HU-TFT-94-

Dynamics of fluctuations in a fluid below the onset of Rayleigh-B\'enard convection

We present experimental data and their theoretical interpretation for the decay rates of temperature fluctuations in a thin layer of a fluid heated from below and confined between parallel horizontal plates. The measurements were made with the mean temperature of the layer corresponding to the critical isochore of sulfur hexafluoride above but near the critical point where fluctuations are exceptionally strong. They cover a wide range of temperature gradients below the onset of Rayleigh-B\'enard convection, and span wave numbers on both sides of the critical value for this onset. The decay rates were determined from experimental shadowgraph images of the fluctuations at several camera exposure times. We present a theoretical expression for an exposure-time-dependent structure factor which is needed for the data analysis. As the onset of convection is approached, the data reveal the critical slowing-down associated with the bifurcation. Theoretical predictions for the decay rates as a function of the wave number and temperature gradient are presented and compared with the experimental data. Quantitative agreement is obtained if allowance is made for some uncertainty in the small spacing between the plates, and when an empirical estimate is employed for the influence of symmetric deviations from the Oberbeck-Boussinesq approximation which are to be expected in a fluid with its density at the mean temperature located on the critical isochore.Comment: 13 pages, 10 figures, 52 reference

Investigation of Scaling Effects in Elastic-Plastic Ductile Fracture Using the Local Approach

This paper investigates the ability of a simple ductile local fracture model to predict the fracture initiation conditions for geometrically similar specimens of different sizes containing either sharp cracks or blunt notches. The material considered is the high strength, low hardening HY 130 steel. We simulated fracture tests on fatigue-precracked compact tension specimens and three-point bend bars containing blunt notches, using the local fracture model to control crack initiation in the finite element analyses. We compared the results of the simulations with experimental results. The comparison indicates that the model qualitatively predicts the right scaling effects for cracked specimens when a characteristic material length is adequately introduced. However, the model failed to predict the fracture initiation conditions and the scaling behavior of notched specimens. The discrepancy arises because the actual micromechanism leading to fracture initiation at the notch (void growth in a band of localized shear) is different from the mechanism underlying the model (quasi-isotropic void growth). Therefore, new or improved models capable of handling ductile failure by void growth under predominantly shear deformation must be developed to predict ductile fracture initiation conditions and scaling laws for generalized loading and geometric configurations

Stability and Nusselt number scaling for inclined differentially heated cavity flow

The flow within inclined differentially side heated square cavities is investigated with two-dimensional numerical simulations. The cavity is inclined such that the heated wall is below the cooled wall. The angle of inclination is varied from theta=0°, which produces the standard differentially heated cavity flow, up to 90° where Rayleigh Bernard flow exists. The variation in flow structure, flow stability and heat transfer is presented with angle of inclination and the Rayleigh number. Results have been obtained over Ra=10⁴ – 10⁸ with Pr=7. It is shown that when the cavity is inclined the flow structure is changed with attached jet/plumes forming adjacent to the adiabatic walls, rather than diffuse intrusions as for the non-inclined side heated cavity. At a specific angle of inclination, the flow undergoes a bifurcation so that the fully developed flow is unsteady and single mode, with a further increase in inclination leading to multimodal flow. The critical transition angle is shown to vary inversely with the Rayleigh number. A scaling relationship for the Nusselt number is proposed which approximates the effect of cavity inclination on total heat transfer

Nusselt number scaling in an inclined differentially heated square cavity

The flow structure and heat transfer in inclined two-dimensional differentially heated square cavities is investigated via numerical simulation. It is shown that the basic flow structure is changed when the cavity is inclined such that the heated wall is below the cooled wall, with attached jet/plumes forming adjacent to the adiabatic walls, rather than diffuse intrusions as for the non-inclined cavity. At a specific angle of inclination, the flow undergoes a bifurcation so that the fully developed flow is unsteady and single mode, with a further increase in inclination leading to multi-modal and then broad banded chaotic flow. The Nusselt number is obtained and plotted against the inclination angle to determine the effect of inclination on the total cavity heat transfer

DYNAMIC FRACTURE OF WELDED JOINTS

Cette communication présente une étude expérimentale et analytique de la rupture dynamique de soudures en "T" sur un acier à haute résistance. Un dispositif expérimental permettant d'atteindre des vitesses de déformation de plusieurs milliers de s-l est conçu. Les conditions expérimentales sont déterminées par ajustement de l'épaisseur de la plaque d'explosif et par la densité ou l'épaisseur du matériau écran. La vitesse initiale mesurée de la plaque d'acier constitue une donnée d'entrée dans un code aux éléments finis pour calculer les contraintes, les déformations et l'endommagement en fonction du temps dans la zone de rupture. Deux échantillons de tailles différentes ont été expérimentés pour évaluer les effets d'échelle sur les soudures. Pour les deux tailles d'échantillon, les conditions de rupture varient géométriquement. Les résultats expérimentaux sont en accord avec l'analyse basée sur un modèle de rupture ductile statistique, indépendant de la vitesse de déformation. Cet accord suggère que l'endommagement dans les soudures de cet acier est peu sensible à la vitesse de déformation.This paper presents an experimental and analytical investigation of dynamic fracture of T-shaped welded joints (stiffener on a plate) in a high strength steel. A fracture test was designed in which strain rates of several thousand per second can be reached in the weldment region by loading the specimen with tamped explosive. Test conditions can be reliably controlled by adjusting the thickness of the explosive and the density and thickness of the tamping material. The measured initial specimen plate velocity is used as input for finite element simulations of the experiments to calculate the stress and strain and fracture damage histories in the fracture region. Experiments on two specimen sizes were performed to evaluate the effect of geometric scaling of the size on fracture of the weldments. For the two sizes investigated, fracture conditions scaled geometrically. The experimental results were in good agreement with the results of an analysis that used a rate independent, statically calibrated local fracture model to describe fracture by ductile void growth. This agreement suggests that fracture damage in weldments of this particular steel is not very rate sensitive

Bifurcation of natural convection flow in an inclined differentially heated closed square cavity

The natural convection flow in an inclined differentially heated cavity is investigated numerically with two-dimensional simulations at Rayleigh number Ra = 1 x 10(7) and Ra = 1 x 10(8) for Prandtl number Pr = 7.0. At theta = 0, the problem is the standard canonical differentially heated cavity flow with isothermal "hot" and "cold" vertical walls and with adiabatic horizontal walls. As the angle of inclination is increased, with the hot wall situated below the cold wall, the flow approaches an unstable Rayleigh-Bernard type flow. Below a critical angle the fully developed flow is steady and exhibits the same basic structure of the standard cavity flow. As the angle of inclination is increased, the flow undergoes a bifurcation so that the fully developed flow is unsteady and single mode. The bifurcation takes the form of traveling waves continually circulating the periphery of the cavity. These waves are supported by convectively unstable natural convection boundary layers on the heated/cooled walls and by attached plumes on the adiabatic walls. It is the establishment of these plumes coupling the opposing boundary layers which provides the mechanism for absolutely unstable flow