Roughening of a propagating planar crack front

A numerical model of the front of a planar crack propagating between two connected elastic plates is investigated. The plates are modeled as square lattices of elastic beams. The plates are connected by similar but breakable beams with a randomly varying stiffness. The crack is driven by pulling both plates at one end in Mode I at a constant rate. We find ζ=1/3, z=4/3, and β=1/4 for the roughness, dynamical, and growth exponents, respectively, that describe the front behavior. This is similar to continuum limit analyses based on a perturbative stress-intensity treatment of the front [H. Gao and J. R. Rice, J. Appl. Mech. 56, 828 (1989)]. We discuss the differences to recent experiments.Peer reviewe

Generalised epipolar constraints

The frontier of a curved surface is the envelope of contour generators showing the boundary, at least locally, of the visible region swept out under viewer motion. In general, the outlines of curved surfaces (apparent contours) from different viewpoints are generated by different contour generators on the surface and hence do not provide a constraint on viewer motion. Frontier points, however, have projections which correspond to a real point on the surface and can be used to constrain viewer motion by the epipolar constraint. We show how to recover viewer motion from frontier points and generalise the ordinary epipolar constraint to deal with points, curves and apparent contours of surfaces. This is done for both continuous and discrete motion, known or unknown orientation, calibrated and uncalibrated, perspective, weak perspective and orthographic cameras. Results of an iterative scheme to recover the epipolar line structure from real image sequences using only the outlines of curved surfaces, is presented. A statistical evaluation is performed to estimate the stability of the solution. It is also shown how the full motion of the camera from a sequence of images can be obtained from the relative motion between image pairs

Kramers-Kronig, Bode, and the meaning of zero

The implications of causality, as captured by the Kramers-Kronig relations between the real and imaginary parts of a linear response function, are familiar parts of the physics curriculum. In 1937, Bode derived a similar relation between the magnitude (response gain) and phase. Although the Kramers-Kronig relations are an equality, Bode's relation is effectively an inequality. This perhaps-surprising difference is explained using elementary examples and ultimately traces back to delays in the flow of information within the system formed by the physical object and measurement apparatus.Comment: 8 pages; American Journal of Physics, to appea

Crack dynamics and crack surfaces in elastic beam lattices

The dynamics of propagating cracks is analyzed in elastic two-dimensional lattices of beams. At early times, inertia effects and static stress enhancement combine so that the crack-tip velocity is found to behave as t1/7. At late times a minimal crack-tip model reproduces the numerical simulation results. With no disorder and for fast loading, a “mirror-mist-mirror” crack-surface pattern emerges. Introduction of disorder leads, however, to the formation of the “mirror-mist-hackle”–type interface typical in many experimental situations.Peer reviewe

Elasticity of Poissonian fiber networks

An effective-medium model is introduced for the elasticity of two-dimensional random fiber networks. These networks are commonly used as basic models of heterogeneous fibrous structures such as paper. Using the exact Poissonian statistics to describe the microscopic geometry of the network, the tensile modulus can be expressed by a single-parameter function. This parameter depends on the network density and fiber dimensions, which relate the macroscopic modulus to the relative importance of axial and bending deformations of the fibers. The model agrees well with simulation results and experimental findings. We also discuss the possible generalizations of the model.Peer reviewe

Retinoic acid induces expression of PA-FABP (psoriasis-associated fatty acid-binding protein) gene in human skin in vivo but not in cultured skin cells

: PA-FABP (psoriasis-associated fatty acid binding protein) is a new member of a group of low-molecular-weight proteins that are highly up regulated in psoriatic skin and that share similarity to fatty acid-binding proteins. In this study we demonstrate that PA-FABP transcripts are expressed in human skin in vivo and that topical application of 0.05% retinoic acid (RA) cream results in a rapid induction of PA-FABP transcripts following treatment for 16 hours and persists at increasing levels after 48 and 96 h of RA treatment. The PA-FABP mRNA response to RA was reduced by approximately 50% when patients concurrently were treated with RA and 0.025% clobelasol propionate (CLO) for 48 and 96 h, whereas treatment with CLO alone resulted in PA-FABP transcript levels not significantly different from vehicle-treated skin. When comparing the effects of a well-known irritant, sodium lauryl sulfate (SLS), to those of RA and its vehicle, 0.05% RA cream but not 2% SLS in RA vehicle caused PA-FABP mRNA induction after 16 h. SLS treatment of human skin for 96 h caused a slight increase in PA-FABP transcripts, but markedly less than that observed in response to RA treatment. Incubation of cultured human keratinocytes or skin fibroblasts with RA for up to 48 h did not significantly induce PA-FABP transcripts. Expression of PA-FABP message in keratinocytes was observed to be induced by calcium and fetal calf serum (FCS), while tetra-decanoyl phorbol acetate (TPA) caused little or no induction. Taken together, the marked inducibility of the PA-FABP gene is compatible with the possibility that this gene might be important in RA-mediated regulation of human skin growth and differentiation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72938/1/j.1600-0625.1994.tb00279.x.pd

Propagation and kinetic roughening of wave fronts in disordered lattices

The dynamics of a wave front propagating in diluted square lattices of elastic beams is analyzed. We concentrate on the propagation of the first maximum of a semi-infinite wave train. Two different limits are found for the velocity depending on the bending stiffness of the beams. If it vanishes, a one-dimensional chain model is derived for the velocity and the amplitude is found to decrease exponentially. The first maximum is localized and the average width of the wave front is always finite. For very stiff beams an effective-medium model gives the correct velocity and the amplitude of the first maximum decays according to a power law. No localization of the first maximum is observed in the simulations. In this limit scaling arguments based on Huygen’s principle suggest a growth exponent of 1/2, and a roughness exponent of 2/3. The growth exponent fits the simulation data well, but a considerably lower roughness exponent (0.5) is obtained. There is a crossover region for the bending stiffness, wherein the wave-front behavior cannot be explained by these limiting cases.Peer reviewe

Expert Control

There has been substantial progress in the theory and practice of automatic control through application of mathematical analysis and numerics. Symbolic data processing has, however, so far only had marginal influence on control systems despite the fact that the actual engineering of control systems contains a substantial amount of heuristic logic. This paper shows how the logic may be replaced by an expert system. This leads to simplification of conventional systems and makes it possible to obtain control systems with new capabilities

Steady-State Cracks in Viscoelastic Lattice Models II

We present the analytic solution of the Mode III steady-state crack in a square lattice with piecewise linear springs and Kelvin viscosity. We show how the results simplify in the limit of large width. We relate our results to a model where the continuum limit is taken only along the crack direction. We present results for small velocity, and for large viscosity, and discuss the structure of the critical bifurcation for small velocity. We compute the size of the process zone wherein standard continuum elasticity theory breaks down.Comment: 17 pages, 3 figure