Application of a strip-yield model to predict crack growth under variable-amplitude and spectrum loading – Part 1: Compact specimens

Fatigue-crack-growth tests were conducted on compact, C(T), specimens made of D16Cz (clad) aluminum alloy under constant-amplitude loading, a single spike overload, and simulated aircraft spectrum loading. Constant-amplitude tests were conducted to generate crack-growth-rate data from threshold to near fracture over a wide range of stress ratios (R = Pmin/Pmax = 0.1–0.75) using the new compression pre-cracking test methods. Comparisons were made between test data generated on the C(T) specimens with test data from the literature on middle-crack-tension, M(T), specimens machined from the same sheet. A crack-closure analysis was used to collapse the rate data from both specimen types into a narrow band over many orders of magnitude in rates using proper constraint factors. The constraint factors were established from constant-amplitude (CA) and single-spike overload tests. The life-prediction code, FASTRAN, which is based on the strip-yield model concept, was used to calculate crack-length-against-cycles under CA loading and a single-spike overload (OL) test, and to predict crack growth under simulated aircraft spectrum loading tests on C(T)specimens. The calculated crack-growth lives under CA loading were generally within about ±25% of the test results, but slower crack growth under the double-shear fatigue mode, unlike the single-shear mode (45° slant crack growth), may be the reason for some of the larger differences. The predicted results under the single-spike overload and the Mini-Falstaff+ spectrum were within 10% of the test data

Application of a strip-yield model to predict crack growth under variable-amplitude and spectrum loading – Part 1: Compact specimens

Fatigue-crack-growth tests were conducted on compact, C(T), specimens made of D16Cz (clad) aluminum alloy under constant-amplitude loading, a single spike overload, and simulated aircraft spectrum loading. Constant-amplitude tests were conducted to generate crack-growth-rate data from threshold to near fracture over a wide range of stress ratios (R = Pmin/Pmax = 0.1–0.75) using the new compression pre-cracking test methods. Comparisons were made between test data generated on the C(T) specimens with test data from the literature on middle-crack-tension, M(T), specimens machined from the same sheet. A crack-closure analysis was used to collapse the rate data from both specimen types into a narrow band over many orders of magnitude in rates using proper constraint factors. The constraint factors were established from constant-amplitude (CA) and single-spike overload tests. The life-prediction code, FASTRAN, which is based on the strip-yield model concept, was used to calculate crack-length-against-cycles under CA loading and a single-spike overload (OL) test, and to predict crack growth under simulated aircraft spectrum loading tests on C(T)specimens. The calculated crack-growth lives under CA loading were generally within about ±25% of the test results, but slower crack growth under the double-shear fatigue mode, unlike the single-shear mode (45° slant crack growth), may be the reason for some of the larger differences. The predicted results under the single-spike overload and the Mini-Falstaff+ spectrum were within 10% of the test data

The three-dimensional random field Ising magnet: interfaces, scaling, and the nature of states

The nature of the zero temperature ordering transition in the 3D Gaussian random field Ising magnet is studied numerically, aided by scaling analyses. In the ferromagnetic phase the scaling of the roughness of the domain walls, $w\sim L^\zeta$, is consistent with the theoretical prediction $\zeta = 2/3$. As the randomness is increased through the transition, the probability distribution of the interfacial tension of domain walls scales as for a single second order transition. At the critical point, the fractal dimensions of domain walls and the fractal dimension of the outer surface of spin clusters are investigated: there are at least two distinct physically important fractal dimensions. These dimensions are argued to be related to combinations of the energy scaling exponent, $\theta$, which determines the violation of hyperscaling, the correlation length exponent $\nu$, and the magnetization exponent $\beta$. The value $\beta = 0.017\pm 0.005$ is derived from the magnetization: this estimate is supported by the study of the spin cluster size distribution at criticality. The variation of configurations in the interior of a sample with boundary conditions is consistent with the hypothesis that there is a single transition separating the disordered phase with one ground state from the ordered phase with two ground states. The array of results are shown to be consistent with a scaling picture and a geometric description of the influence of boundary conditions on the spins. The details of the algorithm used and its implementation are also described.Comment: 32 pp., 2 columns, 32 figure

Line Graphs of Weighted Networks for Overlapping Communities

In this paper, we develop the idea to partition the edges of a weighted graph in order to uncover overlapping communities of its nodes. Our approach is based on the construction of different types of weighted line graphs, i.e. graphs whose nodes are the links of the original graph, that encapsulate differently the relations between the edges. Weighted line graphs are argued to provide an alternative, valuable representation of the system's topology, and are shown to have important applications in community detection, as the usual node partition of a line graph naturally leads to an edge partition of the original graph. This identification allows us to use traditional partitioning methods in order to address the long-standing problem of the detection of overlapping communities. We apply it to the analysis of different social and geographical networks.Comment: 8 Pages. New title and text revisions to emphasise differences from earlier paper

Spin-Dependent Macroscopic Forces from New Particle Exchange

Long-range forces between macroscopic objects are mediated by light particles that interact with the electrons or nucleons, and include spin-dependent static components as well as spin- and velocity-dependent components. We parametrize the long-range potential between two fermions assuming rotational invariance, and find 16 different components. Applying this result to electrically neutral objects, we show that the macroscopic potential depends on 72 measurable parameters. We then derive the potential induced by the exchange of a new gauge boson or spinless particle, and compare the limits set by measurements of macroscopic forces to the astrophysical limits on the couplings of these particles.Comment: 37 page

Continuum theory of vacancy-mediated diffusion

We present and solve a continuum theory of vacancy-mediated diffusion (as evidenced, for example, in the vacancy driven motion of tracers in crystals). Results are obtained for all spatial dimensions, and reveal the strongly non-gaussian nature of the tracer fluctuations. In integer dimensions, our results are in complete agreement with those from previous exact lattice calculations. We also extend our model to describe the vacancy-driven fluctuations of a slaved flux line.Comment: 25 Latex pages, subm. to Physical Review

Equilibrium crystal shapes in the Potts model

The three-dimensional $q$-state Potts model, forced into coexistence by fixing the density of one state, is studied for $q=2$, 3, 4, and 6. As a function of temperature and number of states, we studied the resulting equilibrium droplet shapes. A theoretical discussion is given of the interface properties at large values of $q$. We found a roughening transition for each of the numbers of states we studied, at temperatures that decrease with increasing $q$, but increase when measured as a fraction of the melting temperature. We also found equilibrium shapes closely approaching a sphere near the melting point, even though the three-dimensional Potts model with three or more states does not have a phase transition with a diverging length scale at the melting point.Comment: 6 pages, 3 figures, submitted to PR

Nonlinear wave transmission and pressure on the fixed truncated breakwater using NURBS numerical wave tank

Fully nonlinear wave interaction with a fixed breakwater is investigated in a numerical wave tank (NWT). The potential theory and high-order boundary element method are used to solve the boundary value problem. Time domain simulation by a mixed Eulerian-Lagrangian (MEL) formulation and high-order boundary integral method based on non uniform rational B-spline (NURBS) formulation is employed to solve the equations. At each time step, Laplace equation is solved in Eulerian frame and fully non-linear free-surface conditions are updated in Lagrangian manner through material node approach and fourth order Runge-Kutta time integration scheme. Incident wave is fed by specifying the normal flux of appropriate wave potential on the fixed inflow boundary. To ensure the open water condition and to reduce the reflected wave energy into the computational domain, two damping zones are provided on both ends of the numerical wave tank. The convergence and stability of the presented numerical procedure are examined and compared with the analytical solutions. Wave reflection and transmission of nonlinear waves with different steepness are investigated. Also, the calculation of wave load on the breakwater is evaluated by first and second order time derivatives of the potential

Kernel Spectral Clustering and applications

In this chapter we review the main literature related to kernel spectral clustering (KSC), an approach to clustering cast within a kernel-based optimization setting. KSC represents a least-squares support vector machine based formulation of spectral clustering described by a weighted kernel PCA objective. Just as in the classifier case, the binary clustering model is expressed by a hyperplane in a high dimensional space induced by a kernel. In addition, the multi-way clustering can be obtained by combining a set of binary decision functions via an Error Correcting Output Codes (ECOC) encoding scheme. Because of its model-based nature, the KSC method encompasses three main steps: training, validation, testing. In the validation stage model selection is performed to obtain tuning parameters, like the number of clusters present in the data. This is a major advantage compared to classical spectral clustering where the determination of the clustering parameters is unclear and relies on heuristics. Once a KSC model is trained on a small subset of the entire data, it is able to generalize well to unseen test points. Beyond the basic formulation, sparse KSC algorithms based on the Incomplete Cholesky Decomposition (ICD) and $L_0$, $L_1, L_0 + L_1$, Group Lasso regularization are reviewed. In that respect, we show how it is possible to handle large scale data. Also, two possible ways to perform hierarchical clustering and a soft clustering method are presented. Finally, real-world applications such as image segmentation, power load time-series clustering, document clustering and big data learning are considered.Comment: chapter contribution to the book "Unsupervised Learning Algorithms