Showing papers by "Brown University published in 1980"

Slightly curved or kinked cracks

Abstract: A solution is presented for the elastic stress intensity factors at the tip of a slightly curved or kinked two-dimensional crack. The solution is accurate to first order in the deviation of the crack surface from a straight line and is carried out by perturbation procedures analogous to those of Banichuk [1] and Goldstein and Salganik [2, 3]. Comparison with exact solutions for circular arc cracks and straight cracks with kinks indicates that the first order solution is numerically accurate for considerable deviations from straightness. The solution is applied to fromulate an equation for the path of crack growth, on the assumption that the path is characterized by pure Mode I conditions (i.e., K II=0) at the advancing tip. This method confirms the dependence of the stability, under Mode I loading, of a straight crack path on the sign of the non-singular stress term, representing tensile stress T acting parallel to the crack, in the Irwin-Williams expansion of the crack tip field. The straight path is shown to be stable under Mode I loading for T 0.

Void Nucleation Effects in Biaxially Stretched Sheets

Abstract: The effects of void nucleation occurring during the deformation history on forming limit curves are considered for both in-plane and punch stretching employing a constitutive model of a porous plastic solid. Both plastic strain controlled and stress controlled nucleation processes are simulated by a two parameter void nucleation criterion. For in-plane stretching, plastic strain controlled nucleation can have, in certain circumstances, a significantly destabilizing effect on the forming limit curve. However, within the framework of plane stress theory which neglects the enhance­ ment of the hydrostatic stress due to necking, a stress controlled nucleation process is not found to be significantly destabilizing. In punch stretching a ductile rupture criterion, which limits the maximum volume fraction of voids, as well as the ap­ pearance of a well defined thickness trough, is adopted as a localized necking criterion. Only plastic strain controlled void nucleation is considered here in out-ofplane stretching. The resulting forming limit curves have the same shape as those obtained previously with void nucleation neglected.

Modeling the Climatic Response to Orbital Variations

Abstract: According to the astronomical theory of climate, variations in the earth's orbit are the fundamental cause of the succession of Pleistocene ice ages. This article summarizes how the theory has evolved since the pioneer studies of James Croll and Milutin Milankovitch, reviews recent evidence that supports the theory, and argues that a major opportunity is at hand to investigate the physical mechanisms by which the climate system responds to orbital forcing. After a survey of the kinds of models that have been applied to this problem, a strategy is suggested for building simple, physically motivated models, and a time-dependent model is developed that simulates the history of planetary glaciation for the past 500,000 years. Ignoring anthropogenic and other possible sources of variation acting at frequencies higher than one cycle per 19,000 years, this model predicts that the long-term cooling trend which began some 6000 years ago will continue for the next 23,000 years.

Traffic Equilibrium and Variational Inequalities

Abstract: We consider the general traffic equilibrium network model where the travel cost on each link of the transportation network may depend on the flow on this as well as other links of the network. The model has been designed in order to handle situations where there is interaction between traffic on different links e.g., two-way streets, intersections or between different modes of transportation on the same link. For this model, we use the techniques of the theory of variational inequalities to establish existence of a traffic equilibrium pattern, to design an algorithm for the construction of this pattern and to derive estimates on the speed of convergence of the algorithm.

The McMaster Model of Family Functioning.

Abstract: The model of family functioning being presented is the product of over twenty years of research in clinical work with family units. A method of family therapy has been developed based upon this model and will be described in a future issue. The model utilizes a general systems theory approach in an attempt to describe the structure, organization, and transactional patterns of the family unit. It allows examination of families along the total spectrum ranging from healthy to severely pathological in their functioning. It is based upon a Judaeo-Christian value set, and allows attention to be paid to cultural differences and other issues of cultural relativity.

Tensile Cracks in Creeping Solids

Abstract: The aim of the paper is to answer the question: which loading parameter determines the stress and strain fields near a crack tip, and thereby the growth of the crack, under creep conditions? As candidates for relevant loading parameters, the stress intensity factor K I , the path-independent integral C*, and the net section stress σ n e t have been proposed in the literature. The answer, which is attempted in this paper, is based on the time-dependent stress analysis of a stationary crack in Mode I tension. The material behavior is modeled as elastic-nonlinear viscous, where the nonlinear term describes power law creep. At the time t = 0, load is applied to the cracked specimen, and in the first instant the stress distribution is elastic. Subsequently, creep deformation relaxes the initial stress concentration at the crack tip, and creep strains develop rapidly near the crack tip. These processes may be analytically described by self-similar solutions for short times t. An important result of the analysis is that small-scale yielding may be defined. In creep problems, this means that elastic strains dominate almost everywhere except in a small "creep zone" which grows around the crack tip. If crack growth ensues while the creep zone is still small compared with the crack length and the specimen size, the stress intensity factor governs crack growth behavior. If, however, the calculated creep zone becomes larger than the specimen size, the stresses become finally time-independent and the elastic strain rates can be neglected. In this limiting case, the stress field is the same as in the fully-plastic limit of power law hardening plasticity that has been treated in the literature. The loading parameter that determines the near tip fields uniquely is then the path-independent integral C*. It should be emphasized that K 1 and C* characterize opposite limiting cases. Which case applies in a given situation can be decided by comparing the creep zone size with the specimen size and the crack length. Criteria for small-scale yielding are worked out in several alternative forms. Besides several methods of estimating the creep zone size, a convenient expression for a characteristic time is derived also, which characterizes the transition from small-scale yielding to extensive creep of the whole specimen.

On head-on collisions between two solitary waves

Abstract: We consider a head-on collision between two solitary waves on the surface of an inviscid homogeneous fluid. A perturbation method which in principle can generate an asymptotic series of all orders, is used to calculate the effects of the collision. We find that the waves emerging from (i.e. long after) the collision preserve their original identities to the third order of accuracy we have calculated. However a collision does leave imprints on the colliding waves with phase shifts and shedding of secondary waves. Each secondary wave group trails behind its primary, a solitary wave. The amplitude of the wave group diminishes in time because of dispersion. We have also calculated the maximum run-up amplitude of two colliding waves. The result checks with existing experiments.

The Raft and the Pyramid: Coherence versus Foundations in the Theory of Knowledge

Abstract: Contemporary epistemology must choose between the solid security of the ancient foundationalist pyramid and the risky adventure of the new coherentist raft. Our main objective will be to understand, as deeply as we can, the nature of the controversy and the reasons for and against each of the two options. But first of all we take note of two underlying assumptions. TWO ASSUMPTIONS (A1) Not everything believed is known, but nothing can be known without being at least believed (or accepted, presumed, taken for granted, or the like) in some broad sense. What additional requirements must a belief fill in order to be knowledge? There are surely at least the following two: (a) it must be true, and (b) it must be justified (or warranted, reasonable, correct, or the like). (A2) Let us assume, moreover, with respect to the second condition A1(b): first, that it involves a normative or evaluative property; and, second, that the relevant sort of justification is that which pertains to knowledge: epistemic (or theoretical) justification. Someone seriously ill may have two sorts of justification for believing he will recover: the practical justification that derives from the contribution such belief will make to his recovery and the theoretical justification provided by the lab results, the doctor's diagnosis and prognosis, and so on. Only the latter is relevant to the question whether he knows.

Corticopontine visual projections in macaque monkeys

Abstract: These experiments were designed to study the projections to the pons from visual and visual association cortex of monkeys by degeneration staining and horseradisch peroxidase (HRP) methods. When lesions were made in these cortical visual areas, degenerated fibers were found in the rostral dorsolateral area of the pontine nuclei. When HRP was injected among visually responsive cells in this region of the pons, layer V cortical pyramidal cells were labeled. These labeled cells were concentrated most heavily on both banks of the superior temporal and intraparietal fissures, and on the rostral bank of the parieto-occipital fissure. The efferent targets and receptive field properties of these cortical regions are consistent with their possible role in visual guidance of movement.

Eyeblinks and visual suppression

Abstract: A technique for bypassing the eyelids permits equivalent visual stimulation of the retina before, during, or after a blink. Sensitivity to these stimuli decreases during voluntary blinks. This indicates that the source of the deficit is neural rather than optical. Such a visual loss may help to explain the common experience that most blinks go unnoticed.

Tertiary δ18O record and glacio-eustatic sea-level fluctuations

Abstract: Previous interpretation of the Tertiary δ 18 O record of plaiiktic and benthic foraminifers has emphasized comparison to the modern ocean, assumed an ice-free world prior to middle Miocene time, and thereby calculated surprisingly cool temperatures for the tropical sea surface. We propose an alternative interpretation, which compares Tertiary data to average late Pleistocene, assumes constant tropical sea-surface temperature, and thereby estimates global ice volume. This approach suggests that Earth has had a significant ice budget (and therefore glacio-eustatic sea-level fluctuations) at least since Eocene and perhaps even throughout much of Cretaceous time.

Electrical wiring configurations and childhood leukemia in rhode island

Abstract: The study of the relationship between childhood leukemia and electric power line configurations in the greater Denver, Colorado, area by Wertheimer and Leeper (Am J Epidemiol 109:273-284, 1979) was repeated in Rhode Island, focusing on leukemia (age at onset, 0-20 years; year of onset, 1964-1978). The addresses of 119 leukemia patients and 240 controls were studied by mapping power lines within 50 yards (45.72 m) of each residence. The shortest distance between each power line and the point of the residence closest to it was found; the number and types of wires in each power line were noted. Exposure weights were assigned each type of wire using Wertheimer and Leeper's median field strength reading for each. Assuming that the strength of the field decreases with the square of the distance from its source, and that fields generated by different wires grouped in the same power line are simply additive, a summary value of relative exposure was calculated for each address. Quartile exposure values for controls were used to group patient exposures. Contrary to Wertheimer and Leeper's results, no relationship was found between leukemia and electric power line configurations.

Arithmetic on Elliptic Curves with Complex Multiplication

Abstract: Acknowledgements.- Notation and conventions.- The theory of complex multiplication.- A classification.- Local arithmetic.- Global arithmetic.- The Q-curve A(p).

Angiotoxicity of oxygenated sterols and possible precursors

Abstract: Cell death, inflammation, and repair in rabbits' aortas and pulmonary arteries were observed at 3-, 7-, and 10-day periods after the intravenous injection of oxygenated sterols. Thus, oxygenated sterols, not cholesterol, may play the primary role in arterial wall injury and lesion development.

Elastic plastic analysis of growing cracks

Abstract: The elastic--plastic stress and deformation fields at the tip of a crack which grows in an ideally plastic solid under plane strain, shows small scale yielding conditions. Results of an asymptotic analysis suggests the existence of a crack tip stress state similar to that of the classical Prandtl field, but containing a zone of elastic unloading between the centered fan region and the trailing constant stress plastic region. The near tip expression for the rate of opening displacement delta at distance r from the growing tip is found to have the form delta-. = ..cap alpha.. J-./sigma/sub o/ + ..beta..(sigma/sub o//E) a-. ln(R/r) but the presence of the elastic wedge causes ..beta.. to have the revised value of 5.08 (for Poisson ratio ..nu.. = 0.3); also, (a = crack length, sigma/sub o/ = yield strength, E = elastic modulus, and J denotes the far-field value), and (1-..nu../sup 2/)K/sup 2//E for the small scale yielding conditions considered. The parameters ..cap alpha.. and R cannot be determined from the asymptotic analysis, but comparisons with finite element solutions suggest that, for small amounts of growth, ..cap alpha.. is approximately the same for stationary and growing cracks, and R scales approximately with the sizemore » of the plastic zone, being about 15% to 30% larger. For large scale yielding, a similar form applies with possible variations in ..cap alpha.. and ..beta.., in cases which maintain triaxial constraint at the crack tip. In the fully yielded case R is expected to be proportional to the dimension of the uncracked ligament. Model crack growth criterion requiring a critical delta at some fixed r from the tip, is re-examined in light of the more accurate solution. Results suggest that the J versus ..delta..a relation describing growth is dependent on the extent of yielding. It is suggested that this dependency might be small for highly ductile materials, provided that a similar triaxial constraint is maintained in all cases.« less

On the thermodynamics of adsorption at interfaces as it influences decohesion

Abstract: Earlier computations on the work of separation of boundaries with adsorbed solute atmospheres are reconsidered in terms of reversible work cycles. Special attention is given to two limiting cases. These are the separation of a material interface under fully equilibrated conditions, for which the chemical potential of the adsorbed solute remains constant, and separation under constrained conditions for which the surface excess solute concentration remains constant (i.e., the same on the two newly created free surfaces as present initially on the unstressed interface). The results are consistent with the limiting cases treated before and include the extension to more general cases of solute interactions, including multi-component systems. The work terms are conveniently represented on diagrams of chemical potentialvs surface excess solute concentration. A general separation process is then represented as a path in this diagram which begins on the adsorption isotherm for the unstressed interface and ends on the adsorption isotherm for the pair of newly created surfaces.

The oblique effect of stimulus identification considered with respect to two classes of oblique effects.

Abstract: Two classes of oblique effects are proposed. Oblique effects demonstrated in paradigms reflecting the basic functioning of the visual system are termed class 1, and those obtained in paradigms reflecting stimulus encoding and memory are termed class 2. The present experiments examine the class 2 oblique effect that has been obtained on reaction time (RT) tasks. Three RT tasks with different response requirements (identification, detection, and classification) were conducted to determine the basic conditions necessary for the production of the class 2 RT oblique effect. The results indicate that the source of the class 2 oblique effect obtained in RT paradigms is a greater confusability between the 45 degrees oblique lines than between the horizontal and vertical lines when identification of orientation is required.

Receptor clustering on a cell surface. I. theory of receptor cross-linking by ligands bearing two chemically identical functional groups

Abstract: We present a general mathematical analysis of the problem of bivalent ligands, containing two identical reactive groups, interacting with cell surface receptors. The initial binding of such ligands to a cell is followed by further reactions on the surface, leading to the formation of ligand-receptor clusters. If the receptors are monovalent, at most two receptors can be cross-linked by ligand. However, if the receptors are bivalent (or multivalent), large cell surface aggregates can form, the clusters being distributed in size. Our mathematical analysis of ligand binding and receptor cross-linking is based upon the equivalent-site hypothesis and encompasses both equilibrium and kinetic aspects of the problem. In principle, the mathematical description of cluster formation kinetics requires the solution of an infinite system of coupled nonlinear differential equations. We show that in the absence of ligand-receptor rings, the problem of obtaining the entire aggregate size distribution as a function of time can be reduced to the solution of two nonlinear differential equations. Approximate solutions to these equations are developed via singular perturbation methods. When ring formation is included in the model, additional equations need to be solved. We show that when the rate constant for ring closure varies inversely with chain size, the infinite system of differential equations needed to describe the growth of linear aggregates can be reduced to a system of three integral and integrodifferential equations. To determine the concentration of rings, an additional equation must be solved for each ring size of interest. The mathematical development is general and may be applicable to the analysis of a number of biological problems, including histamine release from basophils and mast cells, B-cell triggering, and the action of hormones, such as insulin and epidermal growth factor.