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Showing papers by "Brown University published in 1974"


Book
01 Jan 1974
TL;DR: In this paper, the authors proposed a method to detect cracks in a crack-penetrization model, based on the Griffith criterion, which is used to detect the presence of a crack at a crack tip.
Abstract: I Principles.- 1 Summary of basic problems and concepts.- 1.1 Introduction.- 1.2 A crack in a structure.- 1.3 The stress at a crack tip.- 1.4 The Griffith criterion.- 1.5 The crack opening displacement criterion.- 1.6 Crack propagation.- 1.7 Closure.- 2 Mechanisms of fracture and crack growth.- 2.1 Introduction.- 2.2 Cleavage fracture.- 2.3 Ductile fracture.- 2.4 Fatigue cracking.- 2.5 Environment assisted cracking.- 2.6 Service failure analysis.- 3 The elastic crack-tip stress field.- 3.1 The Airy stress function.- 3.2 Complex stress functions.- 3.3 Solution to crack problems.- 3.4 The effect of finite size.- 3.5 Special cases.- 3.6 Elliptical cracks.- 3.7 Some useful expressions.- 4 The crack tip plastic zone.- 4.1 The Irwin plastic zone correction.- 4.2 The Dugdale approach.- 4.3 The shape of the plastic zone.- 4.4 Plane stress versus plane strain.- 4.5 Plastic constraint factor.- 4.6 The thickness effect.- 5 The energy principle.- 5.1 The energy release rate.- 5.2 The criterion for crack growth.- 5.3 The crack resistance (R curve).- 5.4 Compliance.- 5.5 The J integral.- 5.6 Tearing modulus.- 5.7 Stability.- 6 Dynamics and crack arrest.- 6.1 Crack speed and kinetic energy.- 6.2 The dynamic stress intensity and elastic energy release rate.- 6.3 Crack branching.- 6.4 The principles of crack arrest.- 6.5 Crack arrest in practice.- 6.6 Dynamic fracture toughness.- 7 Plane strain fracture toughness.- 7.1 The standard test.- 7.2 Size requirements.- 7.3 Non-linearity.- 7.4 Applicability.- 8 Plane stress and transitional behaviour.- 8.1 Introduction.- 8.2 An engineering concept of plane stress.- 8.3 The R curve concept.- 8.4 The thickness effect.- 8.5 Plane stress testing.- 8.6 Closure.- 9 Elastic-plastic fracture.- 9.1 Fracture beyond general yield.- 9.2 The crack tip opening displacement.- 9.3 The possible use of the CTOD criterion.- 9.4 Experimental determination of CTOd.- 9.5 Parameters affecting the critical CTOD.- 9.6 Limitations, fracture at general yield.- 9.7 Use of the J integral.- 9.8 Limitations of the J integral.- 9.9 Measurement of JIc and JR.- 9.10 Closure.- 10 Fatigue crack propagation.- 10.1 Introduction.- 10.2 Crack growth and the stress intensity factor.- 10.3 Factors affecting crack propagation.- 10.4 Variable amplitude service loading.- 10.5 Retardation models.- 10.6 Similitude.- 10.7 Small cracks.- 10.8 Closure.- 11 Fracture resistance of materials.- 11.1 Fracture criteria.- 11.2 Fatigue cracking criteria.- 11.3 The effect of alloying and second phase particles.- 11.4 Effect of processing, anisotropy.- 11.5 Effect of temperature.- 11.6 Closure.- II Applications.- 12 Fail-safety and damage tolerance.- 12.1 Introduction.- 12.2 Means to provide fail-safety.- 12.3 Required information for fracture mechanics approach.- 12.4 Closure.- 13 Determination of stress intensity factors.- 13.1 Introduction.- 13.2 Analytical and numerical methods.- 13.3 Finite element methods.- 13.4 Experimental methods.- 14 Practical problems.- 14.1 Introduction.- 14.2 Through cracks emanating from holes.- 14.3 Corner cracks at holes.- 14.4 Cracks approaching holes.- 14.5 Combined loading.- 14.6 Fatigue crack growth under mixed mode loading.- 14.7 Biaxial loading.- 14.8 Fracture toughness of weldments.- 14.9 Service failure analysis.- 15 Fracture of structures.- 15.1 Introduction.- 15.2 Pressure vessels and pipelines.- 15.3 "Leak-bcfore-break" criterion.- 15.4 Material selection.- 15.5 The use of the J integral for structural analysis.- 15.6 Collapse analysis.- 15.7 Accuracy of fracture calculations.- 16 Stiffened sheet structures.- 16.1 Introduction.- 16.2 Analysis.- 16.3 Fatigue crack propagation.- 16.4 Residual strength.- 16.5 The R curve and the residual strength of stiffened panels.- 16.6 Other analysis methods.- 16.7 Crack arrest.- 16.8 Closure.- 17 Prediction of fatigue crack growth.- 17.1 Introduction.- 17.2 The load spectrum.- 17.3 Approximation of the stress spectrum.- 17.4 Generation of a stress history.- 17.5 Crack growth integration.- 17.6 Accuracy of predictions.- 17.7 Safety factors.- Author index.

2,539 citations


Journal ArticleDOI
TL;DR: In this article, a necessary criterion for brittle fracture in crystals is established, in terms of the spontaneous emission of dislocations from an atomically sharp cleavage crack, and the stability of a sharp crack against emission of a blunting dislocation for a number of crystals and crystal types in two dimensions and the energy to form a stable loop of dislocation from the crack tip in three dimensions.
Abstract: A necessary criterion for brittle fracture in crystals is established, in terms of the spontaneous emission of dislocations from an atomically sharp cleavage crack. We have calculated the stability of a sharp crack against emission of a blunting dislocation for a number of crystals and crystal types in two dimensions and the energy to form a stable loop of dislocation from the crack tip in three dimensions. We find that contrary to previous expectations, an atomically sharp cleavage crack is stable in a wide range of crystal types, but that in the face centred cubic metals investigated, blunting reactions occur spontaneously. Of the body centred metals investigated, iron is an intermediate case between the brittle and ductile cases, and the ionic and covalent crystals investigated are all stable against dislocation emission. Qualitatively, we find that crystals whose dislocations have wide cores, and small values of the parameter μb/γ (μb/γ⋦7·5 to 10) are ductile while crystals with narrow cores ...

1,413 citations


Journal ArticleDOI
D. M. Parks1
TL;DR: In this article, a finite element technique for determination of elastic crack tip stress intensity factors is presented, based on the energy release rate, and the solution for only a single crack length is required, where the crack is 'advanced' by moving nodal points rather than by removing nodal tractions at the crack tip and performing a second analysis.
Abstract: A finite element technique for determination of elastic crack tip stress intensity factors is presented. The method, based on the energy release rate, requires no special crack tip elements. Further, the solution for only a single crack length is required, and the crack is 'advanced' by moving nodal points rather than by removing nodal tractions at the crack tip and performing a second analysis. The promising straightforward extension of the method to general three-dimensional crack configurations is presented and contrasted with the practical impossibility of conventional energy methods.

736 citations



Journal ArticleDOI
Alden Speare1
TL;DR: A model of residential mobility in which residential satisfaction acts as an intervening variable between individual and residence variables and mobility is developed, showing that residential satisfaction at the first interview is related to the wish to move and to mobility in the year following the interview.
Abstract: The stress-threshold model (Wolpert, 1965; Brown and Moore, 1970) assumes that people do not consider moving unless they experience residential stress. This paper develops a similar model of residential mobility in which residential satisfaction acts as an intervening variable between individual and residence variables and mobility. The model is tested with data from a panel study of Rhode Island residents. The results indicate that residential satisfaction at the first interview is related to the wish to move and to mobility in the year following the interview. Individual and residence characteristics such as age of head duration of residence, home ownership, and room crowding are shown to affect mobility through their effect on residential satisfaction.

660 citations


Journal ArticleDOI
James R. Rice1
TL;DR: In this article, the non-singular stress term for crack tip deformations and fracturing is examined and its effect on crack tip parameters, such as the opening displacement and J-integral, is less pronounced than the effect on the yield zone size.
Abstract: Recent finite-element results by S G Larsson and A J Carlsson suggest a limited range of validity to the 'small scale yielding approximation,' whereby small crack tip plastic zones are correlated in terms of the elastic stress intensity factor It is shown with the help of a model for plane strain yielding that their results may be explained by considering the non-singular stress, acting parallel to the crack at its tip, which accompanies the inverse square-root elastic singularity Further implications of the non-singular stress term for crack tip deformations and fracturing are examined It is suggested that its effect on crack tip parameters, such as the opening displacement and J-integral, is less pronounced than its effect on the yield zone size

587 citations


Book ChapterDOI
J. Tauc1
01 Jan 1974
TL;DR: The sharp structure observed in the fundamental optical spectra of crystals, both vibrational and electronic, can be classified and interpreted by symmetry arguments based explicitly on the existence of long-range order as mentioned in this paper.
Abstract: The sharp structure observed in the fundamental optical spectra of crystals, both vibrational and electronic, can be classified and interpreted by symmetry arguments based explicitly on the existence of long-range order. Indeed, this is one of the few properties of crystals which cannot be accounted for on the basis of short-range order alone: If the long-range order is destroyed, the sharp structural detail, which is typical for crystals, disappears. However, the broad features of the spectra are similar if the short-range order is similar.

579 citations


Book
Philip J. Davis1
01 Jan 1974
TL;DR: The Schwarz Function of the analytic arc as mentioned in this paper is an analytic function of a complex variable that can be expressed as an antianalytic mapping of the complex conjugate of the function.
Abstract: H A Schwarz showed us how to extend the notion of reflection in straight lines and circles to reflection in an arbitrary analytic arc Notable applications were made to the symmetry principle and to problems of analytic continuation Reflection, in the hands of Schwarz, is an antianalytic mapping By taking its complex conjugate, we arrive at an analytic function that we have called here the Schwarz Function of the analytic arc This function is worthy of study in its own right and this essay presents such a study In dealing with certain familiar topics, the use of the Schwarz Function lends a point of view, a clarity and elegance, and a degree of generality which might otherwise be missing It opens up a line of inquiry which has yielded numerous interesting things in complex variables; it illuminates some functional equations and a variety of iterations which interest the numerical analyst The perceptive reader will certainly find here some old wine in relabelled bottles But one of the principles of mathematical growth is that the relabelling process often suggests a new generation of problems Means become ends; the medium rapidly becomes the message This book is not wholly self-contained Readers will find that they should be familiar with the elementary portions of linear algebra and of the theory of functions of a complex variable

384 citations


Journal ArticleDOI
TL;DR: In this paper, a finite element program suitable for solving incompressible, viscous free surface problems in steady axisymmetric or plane flows is presented. But the authors do not consider the non-Newtonian flow, non-zero Reynolds numbers, and transient flow.
Abstract: : The authors discuss the creation of a finite element program suitable for solving incompressible, viscous free surface problems in steady axisymmetric or plane flows. For convenience in extending program capability to non-Newtonian flow, non-zero Reynolds numbers, and transient flow, a Galerkin formulation of the governing equations is chosen, rather than an extremum principle. The resulting program is used to solve the Newtonian die-swell problem for creeping jets free of surface tension constraints. The authors conclude that a Newtonian jet expands about 13%, in substantial agreement with experiments made with both small finite Reynolds numbers and small ratios of surface tension to viscous forces. The solutions to the related stick-slip problem and the tube inlet problem, both of which also contain stress singularities, are also given. (Modified author abstract)

277 citations


Journal ArticleDOI
Peter D. Eimas1
TL;DR: In this paper, two and three-month-old infants were found to discriminate the acoustic cues for the phonetic feature of place of articulation in a categorical manner; that is, evidence for the discriminability of two synthetic speech patterns was present only when the stimuli signaled a change in phonetic features of place.
Abstract: Two- and 3-month-old infants were found to discriminate the acoustic cues for the phonetic feature of place of articulation in a categorical manner; that is, evidence for the discriminability of two synthetic speech patterns was present only when the stimuli signaled a change in the phonetic feature of place. No evidence of discriminability was found when two stimuli, separated by the same acoustic difference, signaled acoustic variations of the same phonetic feature. Discrimination of the same acoustic cues in a nonspeech context was found, in contrast, to be noncategorical or continuous. The results were discussed in terms of infants’ ability to process acoustic events in either an auditory or a linguistic mode.

237 citations


Journal ArticleDOI
TL;DR: Results indicate the need to reevaluate the role of perivascular spaces in net fluid exchange between brain and cerebrospinal fluid and indicate that Blue Dextran is transported away from the injection site by bulk flow of cerebral ISF, possibly along the course of cerebral blood vessels.

Journal ArticleDOI
TL;DR: In this paper, a hot-wire-based line source was used to measure the thermal conductivity of gases up to 800°C and 400 atm in an absolute way.

Journal ArticleDOI
TL;DR: In this paper, the quantum-mechanical response of a two-dimensional electron gas in the presence of a strong dc magnetic field is calculated in the random-phase approximation.
Abstract: The quantum-mechanical response of a two-dimensional electron gas in the presence of a strong dc magnetic field is calculated in the random-phase approximation. The results are used to discuss the magnetoplasma oscillations of a two-dimensional electron gas. The general dispersion relation is derived, and numerical results are presented for both long and short wavelengths.

Journal ArticleDOI
K.A. Foland1
TL;DR: In this paper, a natural, nonperthitic orthoclase has been studied isothermal heating experiments between 500° and 800°C under both vacuum and hydrothermal (2 kbar) conditions.

Book ChapterDOI
01 Jan 1974
TL;DR: In this article, a one-parameter group of operators on a linear space X is considered and the behavior of U(t) f as t → ± ∞ and in the relationship between the behavior at +∞ and at −∞.
Abstract: Scattering theory compares the behavior in the distant future and past of a system evolving in time. It is called nonlinear if the system evolves in a nonlinear fashion. Consider a one-parameter group of operators on some linear space X: $$ U(t)U(s) = U(t + s);U(o) = I $$ -∞

Journal ArticleDOI
James W. Head1
01 Dec 1974
TL;DR: In this article, the authors studied the formation of the Mare Orientale basin and found that the structures and facies are related in time and mode of origin to the formation a major impact crater approximately 620 km in diam.
Abstract: The lunar Orientale basin is a 900 km diam circular topographic depression covering an area of over 700,000 sq km on the western limb of the moon. Three major rings surround the central Mare Orientale. Orientale basin structures are considered along with Orientale basin deposits and the sequence of formation of structures and deposits. It is found that the structures and facies are related in time and mode of origin to the formation of a major impact crater approximately 620 km in diam. The study suggests that the Orientale basin configuration is very nearly the same as its geometry at its time of formation. The formation of multiringed basins such as Orientale provides a mechanism for an instantaneous production of tremendous volumes of melted lunar crystal material.


Journal ArticleDOI
TL;DR: In this article, it was shown that the near tip stress field for running cracks has universal spatial dependence in a coordinate system local to the crack tip, and the rate at which energy is absorbed by the running crack can then be calculated in terms of the crack motion and the scalar stress intensity factors.
Abstract: Modifications of the linear elastodynamic uniqueness theorem are presented which extend its range of applicability so as to include running crack solutions. First, it is shown that the near tip stress field for running cracks has universal spatial dependence in a coordinate system local to the crack tip. The rate at which energy is absorbed by the running crack can then be calculated in terms of the crack motion and the scalar stress intensity factors. The fact that this rate of energy absorption is positive for any running crack plays a central role in the subsequent proof of the uniqueness theorem. The results apply for arbitrary motion of a curved crack, provided that the crack tip speed is less than the Rayleigh wave speed of the material.

Journal ArticleDOI
TL;DR: It appears that at least two possible pathogenic mechanisms may be present in aspirin intolerance, one producing bronchospasm and the other resulting in angioedema/urticaria.
Abstract: In a prospective study 1,372 patients with asthma and rhinitis and 808 normal individuals were directly questioned about symptoms of intolerance to aspirin. The frequency of aspirin intolerance in our asthmatic group was significantly greater (3.8 per cent) than the frequency in the rhinitis alone group (1.4 per cent) or in our normal group (0.9 per cent). There was no statistical difference of aspirin intolerance between rhinitis alone and our normal individuals. The predominant symptom of aspirin intolerance in our asthmatic group was bronchospasm, while the predominant symptom in our rhinitis alone group was urticaria. In our normal individuals, manifestations of aspirin intolerance were about equally divided between bronchospasm and urticaria. It appears that at least two possible pathogenic mechanisms may be present in aspirin intolerance, one producing bronchospasm and the other resulting in angioedema/urticaria.

Journal ArticleDOI
TL;DR: The nature of the platelet response to osmotic shock and its relationship to platelet viability were studied and light absorbancy changes were measured.


Journal ArticleDOI
TL;DR: The frequency of intolerance to aspirin in a total population of asthma and/or rhinitis was 89 out of 3,781 or 2.4 per cent; those asthmatics with negative allergy skin tests had significantly more aspirin intolerance than did those with positive skin tests.
Abstract: The frequency of intolerance to aspirin in a total population of asthma and/or rhinitis was 89 out of 3,781 or 2.4 per cent. In the asthmatic group, the frequency was 4.3 per cent. Those asthmatics with negative allergy skin tests had significantly more aspirin intolerance (6.8 per cent) than did those with positive skin tests (3.5 per cent) (p

Journal ArticleDOI
L.B. Freund1
TL;DR: In this article, the authors considered the plane strain problem of a half-plane crack in an unbounded elastic solid, and the faces of the crack were subjected to suddenly applied, equal but opposite concentrated normal forces which tend to separate the crack faces.

Journal ArticleDOI
TL;DR: In this article, the authors study the development of large-scale wavelike eddies, or instability waves, in a turbulent free shear flow, based on splitting the flow into three components: the mean flow, the instability wave and the fine-scale turbulence.
Abstract: In this paper we study the development of large-scale wavelike eddies, or instability waves, in a turbulent free shear flow. The model is based on splitting the flow into three components: the mean flow, the instability wave and the fine-scale turbulence. The wave is considered to be sufficiently weak so that it is developing in a pre-existing, known turbulent mean shear flow. The basis for the wave development is its time-averaged kinetic energy flux equation in integral form and the wave description is obtained through a shape assumption: the amplitude is determined by the energy equation; the shape function and local characteristics are determined by the local linear stability theory. The wave energy changes as it is convected into a different streamwise position where its instability properties change. The energy balancing mechanisms are production, work done by the wave pressure gradients and the energy transfer between the wave and the fine-scale turbulence via the wave-induced Reynolds stresses. The latter is taken to be dissipative via an eddy-viscosity model, inertia—elastic effects not being considered. According to forceful evidence from observations in turbulent free shear flows, the wave development is taken as being upstream controlled and begins from a distinct origin rather than being the result of local forcing by variations of the fine-scale turbulent Reynolds stresses. The wave energy flux initially grows via energy supplied by the inflexional mean flow when the shear layer is relatively thin but eventually decays through action of the finescale turbulence, directly via the dissipative energy transfer and indirectly via the turbulence-diffused, rapidly thickened mean shear flow, which renders the production mechanism less available. Numerical calculations are carried out for a turbulent mean shear flow, with speed Tie on one side and zero in the ambient region, its distribution being approximated by a sine profile in the Howarth-Dorodnitsyn co-ordinate. The flow develops from an initial boundary layer of finite thickness δ0 to a similar free-mixing layer far downstream. The wave is characterized by a dimensionless frequency parameter β0 formed from the wave frequency β*, ue, and δ0. Convection speeds, in general, increase in the downstream direction. They are subsonic initially for Mach numbers Me 2 peaking in the local intensity levels occurs when convection speeds are supersonic and this may explain the observed supersonic far-field radiation a t the higher jet speeds. Induced wave patterns in the ambient region are determined by the complex instability-wave speed rather than the real convection speed alone, consequently ambient wave patterns exist even a t subsonic convection speeds, but are more heavily damped near the origin and fan out laterally downstream for a given β0. According to the present model, if the waves are given an upstream excitation level about 10−3–10−2 times that of Ue, resembling, for instance, the levels of the upstream wall turbulent boundary-layer fluctuations over a wide, low-frequency, spectrum or other possible disturbances a t the nozzle exit, the development of the calculated near noise field as a function of downstream distance bears striking resemblances to the observed near jet noise field and is thus fully sufficient to explain such observations. This comparison leads to the suggestion that the essential energetics of the large-scale wavelike eddies are that they are formed at the origin, amplified and subsequently decay in a developing mean turbulent free shear flow. Therefore this leads also to a most important indication of shear-layer instabilities and noise control. If their historical evolution can be controlled so can the noise from the damaging wavelike eddies. Methods of control on the basis of this model are discussed.

Journal ArticleDOI
TL;DR: Suppressed deflation as mentioned in this paper describes a situation in which, at existing wages and prices, the aggregate demands for current output and labour services exceed the corresponding aggregate supplies, and therefore, sales are rationed.
Abstract: Suppressed inflation describes a situation in which, at existing wages and prices, the aggregate demands for current output and labour services exceed the corresponding aggregate supplies. Suppressed inflation is the opposite of suppressed deflation, in which aggregate supplies of output and labour exceed aggregate demands. Both suppressed inflation and suppressed deflation involve non-wage and non-price rationing. In suppressed inflation, purchases of goods and labour services are rationed. In suppressed deflation, sales are rationed. Suppressed inflation and suppressed deflation both result from the inability of wages and prices to adjust instantaneously, in response to shifts in aggregate demand or supply, to satisfy the conditions for general market clearing. This inability can result either from effective legal constraints-that is, the imposition of price and wage ceilings or floorsor from natural frictions in the workings of the market mechanism.3 However, whatever the cause of wage and price stickiness, the resulting failure of markets to clear has profound consequences for the determination of output and employment. In the case of suppressed deflation, standard macro-economic analysis has long recognized these consequences. In contrast, suppressed inflation, although empirically not a rare phenomenon, has been the subject of little systematic theoretical analysis. In addition, the standard macro-economic paradigm fails even to recognize the analogybetween suppressed inflation and suppressed deflation. A central aspect of the received theory of suppressed deflation is the demand multiplier. This theoretical construct was first discovered by Kahn [7] and expanded by Keynes [8] and quickly became part of conventional wisdom. Assume, starting from a position of general market clearing and full employment, an autonomous reduction in aggregate demand for current output.4 Maintaining full employment would require a fall in the price level and nominal wage rate, but prices and wages are sticky. The initial effect of the reduced demand will be the emergence of excess supply in the output market. This excess supply induces the representative firm to reduce output to what it can sell, which is less than what it desires to sell at current wages and prices, and to reduce its effective

Journal ArticleDOI
TL;DR: In this paper, the existence of periodic solutions for some nonautonomous neutral functional differential equations is examined, and the results are nontrivial extensions to the neutral case of existence theorems for periodic solutions.

Journal ArticleDOI
TL;DR: The results indicate that the stimulation of gluconeogenesis by glucagon or epinephrine is not restricted to substrates which enter the pathways of glucose formation prior to phosphoenolpyruvate, and support the hypothesis thatEpinephrine mediated gluc oneogenesis occurs by a cyclic adenosine 3' : 5'-monophosphate-independent mode of action distinct from that for glucagon.

Journal ArticleDOI
TL;DR: Ubersicht uber Aquotisierung, Solvolyse, Isomerisierings, Anionenaustausch, ihren experimentellen Methoden und Einflus vom Oxidationszustand und Grose des Metalls as discussed by the authors.


Journal ArticleDOI
TL;DR: In this article, a theoretical model of the folding of a free, anisotropic, linearly viscous layer of appropriate wave length/thickness ratio is analyzed, and the model of inherited asymmetry is both appropriate for the Greenport Center syncline and treatable within the present theoretical framework.
Abstract: The Greenport Center syncline is an asymmetric fold with a half wave length of about 40 m developed in the Devonian Becraft and Alsen Limestones on Becraft Mountain, New York. Twinning strains have been measured in 19 samples distributed so as to sample all of the structurally significant regions of the fold. The orientation and relative magnitudes of the observed strains are consistent with those expected from the buckling of a thick isotropic layer, but the observed magnitudes are too small by a factor of more than four. Local and nonsystematic variations in strain are much larger than those expected in the buckling of a continuous layer, and the Greenport Center syncline also contains abundant geologic evidence that slip between beds was important. A theoretical model of the folding of a free, anisotropic, linearly viscous layer of appropriate wave length/thickness ratio is analyzed. Although the smoothly distributed bedding-parallel shear of the model does not adequately represent the process of bedding slip in the real fold, it does permit the estimate of the degree of anisotropy necessary to produce observed limb dips with observed bending strains. If the viscosity coefficient for shear parallel to bedding is 0.03 times that for bending, the bending strains are reduced to the observed value; the required bedding slip could be produced by slip surfaces spaced about 30 cm apart if the average displacement on a slip surface were about 23 cm. The model of inherited asymmetry is both appropriate for the Greenport Center syncline and treatable within the present theoretical framework. Inherited asymmetry is shown to be possible for an anisotropic layer though not for an isotropic one.