Controlled crack growth specimen for brittle systems

A pure Mode 1 fracture specimen and test procedure has been developed which provides extended, stable, through-thickness crack growth in ceramics and other brittle, nonmetallic materials. Fixed displacement loading, applied at the crack mouth, promotes stable crack extension by reducing the stored elastic strain energy. Extremely fine control of applied displacements is achieved by utilizing the Poisson's expansion of a compressively loaded cylindrical pin. Stable cracks were successfully grown in soda-lime glass and monolithic Al2O3 for lengths in excess of 20 mm without uncontrollable catastrophic failure

Integrable structure of W_3 Conformal Field Theory, Quantum Boussinesq Theory and Boundary Affine Toda Theory

In this paper we study the Yang-Baxter integrable structure of Conformal Field Theories with extended conformal symmetry generated by the W_3 algebra. We explicitly construct various T- and Q-operators which act in the irreducible highest weight modules of the W_3 algebra. These operators can be viewed as continuous field theory analogues of the commuting transfer matrices and Q-matrices of the integrable lattice systems associated with the quantum algebra U_q(\hat{sl}(3)). We formulate several conjectures detailing certain analytic characteristics of the Q-operators and propose exact asymptotic expansions of the T- and Q-operators at large values of the spectral parameter. We show, in particular, that the asymptotic expansion of the T-operators generates an infinite set of local integrals of motion of the W_3 CFT which in the classical limit reproduces an infinite set of conserved Hamiltonians associated with the classical Boussinesq equation. We further study the vacuum eigenvalues of the Q-operators (corresponding to the highest weight vector of the W_3 module) and show that they are simply related to the expectation values of the boundary exponential fields in the non-equilibrium boundary affine Toda field theory with zero bulk mass.Comment: LaTeX, 87 pages, 1 figure. Misprints correcte

Discrete Hamilton-Jacobi Theory

We develop a discrete analogue of Hamilton-Jacobi theory in the framework of discrete Hamiltonian mechanics. The resulting discrete Hamilton-Jacobi equation is discrete only in time. We describe a discrete analogue of Jacobi's solution and also prove a discrete version of the geometric Hamilton-Jacobi theorem. The theory applied to discrete linear Hamiltonian systems yields the discrete Riccati equation as a special case of the discrete Hamilton-Jacobi equation. We also apply the theory to discrete optimal control problems, and recover some well-known results, such as the Bellman equation (discrete-time HJB equation) of dynamic programming and its relation to the costate variable in the Pontryagin maximum principle. This relationship between the discrete Hamilton-Jacobi equation and Bellman equation is exploited to derive a generalized form of the Bellman equation that has controls at internal stages.Comment: 26 pages, 2 figure

Numerical calibration of the stable poisson loaded specimen

An analytical calibration of the Stable Poisson Loaded (SPL) specimen is presented. The specimen configuration is similar to the ASTM E-561 compact-tension specimen with displacement controlled wedge loading used for R-Curve determination. The crack mouth opening displacements (CMOD's) are produced by the diametral expansion of an axially compressed cylindrical pin located in the wake of a machined notch. Due to the unusual loading configuration, a three-dimensional finite element analysis was performed with gap elements simulating the contact between the pin and specimen. In this report, stress intensity factors, CMOD's, and crack displacement profiles are reported for different crack lengths and different contacting conditions. It was concluded that the computed stress intensity factor decreases sharply with increasing crack length, thus making the SPL specimen configuration attractive for fracture testing of brittle, high modulus materials

Rescattering effects in laser-assisted electron-atom bremsstrahlung

Rescattering effects in nonresonant spontaneous laser-assisted electron-atom bremsstrahlung (LABrS) are analyzed within the framework of time-dependent effective-range (TDER) theory. It is shown that high energy LABrS spectra exhibit rescattering plateau structures that are similar to those that are well-known in strong field laser-induced processes as well as those that have been predicted theoretically in laser-assisted collision processes. In the limit of a low-frequency laser field, an analytic description of LABrS is obtained from a rigorous quantum analysis of the exact TDER results for the LABrS amplitude. This amplitude is represented as a sum of factorized terms involving three factors, each having a clear physical meaning. The first two factors are the exact field-free amplitudes for electron-atom bremsstrahlung and for electron-atom scattering, and the third factor describes free electron motion in the laser field along a closed trajectory between the first (scattering) and second (rescattering) collision events. Finally, a generalization of these TDER results to the case of LABrS in a Coulomb field is discussed

Particle-gas dynamics in the protoplanetary nebula

In the past year we made significant progress in improving our fundamental understanding of the physics of particle-gas dynamics in the protoplanetary nebula. Having brought our code to a state of fairly robust functionality, we devoted significant effort to optimizing it for running long cases. We optimized the code for vectorization to the extent that it now runs eight times faster than before. The following subject areas are covered: physical improvements to the model; numerical results; Reynolds averaging of fluid equations; and modeling of turbulence and viscosity

Thioxoethenylidene (CCS) as a bridging ligand

The reaction of [Mo(≡CBr)(CO)2(Tp*)] (Tp* = hydrotris(3,5-dimethylpyrazol-1-yl)borate) with [Fe2(μ-SLi)2(CO)6] affords, inter alia, the unsymmetrical binuclear thioxoethenylidene complex [Mo2(μ,σ(C):η2(C′S)-CCS)(CO)4(Tp*)2], which may be more directly obtained from [Mo(≡CBr)(CO)2(Tp*)] and Li2S. The reaction presumably proceeds via the intermediacy of the bis(alkylidynyl)thioether complex S{C≡Mo(CO)2(Tp*)}2, which was, however, not directly observed but explored computationally and found to lie 78.6 kJ mol–1 higher in energy than the final thioxoethenylidene product. Computational interrogation of the molecules [M2(μ-C2S)(CO)2(Tp*)2] (M = Mo, W, Re, Os) reveals three plausible coordination modes for a thioxoethenylidene bridge which involve a progressive strengthening of the C–C bond and weakening of the M–C and M–S bonds, as might be expected from simple effective atomic number considerations.This work was supported by the Australian Research Council (DP130102598 and DP110101611)

Mechanical Characterization of Torsional Micropaddles Using Atomic Force Microscopy

The reference cantilever method is shown to act as a direct and simple method for determination of torsional spring constant. It has been applied to the characterization of micropaddle structures similar to those proposed for resonant functionalized chemical sensors and resonant thermal detectors. It is shown that this method can be used as an effective procedure to characterize a key parameter of these devices and would be applicable to characterization of other similar MEMS/NEMS devices such as micromirrors. In this study, two sets of micropaddles are manufactured (beams at centre and offset by 2.5 μm) by using LPCVD silicon nitride as a substrate. The patterning is made by direct milling using focused ion beam. The torsional spring constant is achieved through micromechanical analysis via atomic force microscopy. To obtain the gradient of force curve, the area of the micropaddle is scanned and the behaviour of each pixel is investigated through an automated developed code. The experimental results are in a good agreement with theoretical results

Scalable iterative methods for sampling from massive Gaussian random vectors

Sampling from Gaussian Markov random fields (GMRFs), that is multivariate Gaussian ran- dom vectors that are parameterised by the inverse of their covariance matrix, is a fundamental problem in computational statistics. In this paper, we show how we can exploit arbitrarily accu- rate approximations to a GMRF to speed up Krylov subspace sampling methods. We also show that these methods can be used when computing the normalising constant of a large multivariate Gaussian distribution, which is needed for both any likelihood-based inference method. The method we derive is also applicable to other structured Gaussian random vectors and, in particu- lar, we show that when the precision matrix is a perturbation of a (block) circulant matrix, it is still possible to derive O(n log n) sampling schemes.Comment: 17 Pages, 4 Figure