Dynamic crack propagation with cohesive elements: a methodology to address mesh dependency

In this paper, two brittle fracture problems are numerically simulated: the failure of a ceramic ring under centrifugal loading and crack branching in a PMMA strip. A three‐dimensional finite element package in which cohesive elements are dynamically inserted has been developed. The cohesive elements' strength is chosen to follow a modified weakest link Weibull distribution. The probability of introducing a weak cohesive element is set to increase with the cohesive element size. This reflects the physically based effect according to which larger elements are more likely to contain defects. The calculations illustrate how the area dependence of the Weibull model can be used to effectively address mesh dependency. On the other hand, regular Weibull distributions have failed to reduce mesh dependency for the examples shown in this paper. The ceramic ring calculations revealed that two distinct phenomena appear depending on the magnitude of the Weibull modulus. For low Weibull modulus, the fragmentation of the ring is dominated by heterogeneities. Whereas many cracks were generated, few of them could propagate to the outer surface. Monte Carlo simulations revealed that for highly heterogeneous rings, the number of small fragments was large and that few large fragments were generated. For high Weibull modulus, signifying that the ring is close to being homogeneous, the fragmentation process was very different. Monte Carlo simulations highlighted that a larger number of large fragments are generated due to crack branching. Copyright © 2003 John Wiley & Sons, Ltd.     

Hydrothermal Reaction Mechanism and Pathway for the Formation of K2Ti6O13 Nanowires

Calculations and detailed first principle and thermodynamic analyses have been performed to understand the formation mechanism of K₂Ti₆O₁₃ nanowires (NWs) by a hydrothermal reaction between bulk Na₂Ti₃O₇ crystals and a KOH solution. It is found that direct ion exchange between K⁺ and Na⁺ plus H⁺ interactions with [TiO₆] octahedra in Na₂Ti₃O₇ promote the formation of an intermediate H₂K₂Ti₆O₁₄ phase. The large lattice mismatch between this intermediate phase and the bulk Na₂Ti₃O₇ structure, and the large energy reduction associated with the formation of this intermediate phase, drive the splitting of the bulk crystal into H₂K₂Ti₆O₁₄ NWs. However, these NWs are not stable because of large [TiO₆] octahedra distortion and are subject to a dehydration process, which results in uniform K₂Ti₆O₁₃ NWs with narrowly distributed diameters of around 10 nm.     

Analysis of S-SEED''s characteristics in optical switch

This article introduces the basic structure of a symmetric self-electrooptic effect device （S-SEED）, and applies the Kirchoff＇ s current law and a purely equivalent capacitive model, to analyze S-SEED＇s switch characteristics. Linear approximation and N-segment approximation are utilized to obtain S-SEED＇s voltage-time （V-T） and characteristics. Theoretical analysis is verified by simulations, and the results demonstrate that the precision of S-SEED＇s switch time can satisfy the requirement in applications with linear approximation. Moreover, the simulations compare S-SEED＇s switch characteristics with different input powers and input contrast ratios, which reveal that increasing input contrast ratio is an effective way to improve S-SEED＇s switch characteristics.     

Self-Irradiation Cascade Simulations in Plutonium Metal: Model Behavior at High Energy

The Modified Embedded Atom Method model for Pu metal is revised so that it more accurately captures the behavior of the Ziegler-Biersack-Littmark model of ion-ion interactions. Two revision are tested with somewhat different stiffnesses in the 2-1000 eV range. The revised models show higher damage levels at 20 KeV than an earlier model, suggesting that the behavior of the models above 100 eV is dominating damage production, at least in the earlier stages of the cascade. Work was performed at Los Alamos National Laboratory under the auspices of the US Department of Energy, under contract DE-AC52-06NA25396.     

HYDRODYNAMIC FORCE ON SMOOTH HORIZONTAL CYLINDER IN UNIFORM OSCILLATORY FLOW

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Computer simulation of the effective double layer occurring on a catalyst surface under electro-chemical promotion conditions

In this work, the structural and energetic properties of two typical catalytic surfaces, Na/Pt(111) and O/Pt(111), are studied by means of quantum mechanical calculations and Monte Carlo Grand Canonical simulations. The simulations were performed with electrostatic potentials at different truncation schemes. In order to elucidate the modification of catalyst surfaces produced by the backspillover of ionic species onto Pt(111), the electrostatic field at the interface due to the electric double layer was also analyzed.     

Surface adsorption of comb polymers by Monte Carlo simulations

This paper reports off-lattice Monte Carlo simulations of highly-branched comb homopolymers weakly adsorbed on a flat, featureless surface showing only covolume and dispersion interactions with the adsorbate. A minimal coarse-grained model, described by hard spheres connected by harmonic springs, was employed. The interaction energy of the adsorbed combs and linear chains is first discussed as a function of the molecular mass and of the number of beads in contact with the surface. The molecular size is then investigated as a function of backbone length and branching density at a fixed arm size. The apparent swelling exponents of the adsorbed combs are larger than those of the corresponding linear chains, and much larger than that of the free molecules. This result indicates a surface-induced stiffening of the comb backbone, further studied through the persistence length l_pers. It is found that l_pers increases upon adsorption over the free-molecule value, more so the larger is the branching density. Finally, the thickness of the adsorbed layer, the surface-induced molecular anisotropy and the molecular aspect ratio are investigated as a function of branching density and molecular mass.     

Locality-preserving hash functions for general purpose parallel computation

Consider the problem of efficiently simulating the shared-memory parallel random access machine (PRAM) model on massively parallel architectures with physically distributed memory. To prevent network congestion and memory bank contention, it may be advantageous to hash the shared memory address space. The decision on whether or not to use hashing depends on (1) the communication latency in the network and (2) the locality of memory accesses in the algorithm.We relate this decision directly to algorithmic issues by studying the complexity of hashing in the Block PRAM model of Aggarwal, Chandra, and Snir, a shared-memory model of parallel computation which accounts for communication locality. For this model, we exhibit a universal family of hash functions having optimal locality. The complexity of applying these hash functions to the shared address space of the Block PRAM (i.e., by permuting data elements) is asymptotically equivalent to the complexity of performing a square matrix transpose, and this result is best possible for all pairwise independent universal hash families. These complexity bounds provide theoretical evidence that hashing and randomized routing need not destroy communication locality, addressing an open question of Valiant.This work was started when the author was a student at Oxford University, supported by a National Science Foundation Graduate Fellowship and a Rhodes Scholarship. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the author and do not necessarily reflect the views of the National Science Foundation or the Rhodes Trust.     

Application of an improved control-variate scheme to local neoclassical transport simulations

A new radially local neoclassical transport code is developed based on the radially global two-weight δf$\delta f$ Monte Carlo code, FORTEC-3D (Satake et al., 2008). In the collisional two-weight δf$\delta f$ method, the variance of weight increases in time due to the so-called weight spreading, which leads to an increasing numerical noise in long time simulations. A new improved control-variate scheme was proposed by Kleiber et al. (2011) to reduce the variance. We investigate the effectiveness and validity of the new control-variate scheme for a practical collisional transport problem in a plasma described by the drift kinetic equation. It is demonstrated that the new scheme reduces the variance of weight by approximately 75% in an axisymmetric magnetic field configuration. The burst-like behavior of a transport observable caused by a large numerical noise can be avoided. As a result, the time evolution of a transport observable can be successfully smoothed.