A MODEL OF COLUMNAR JOINTING

2012 ◽  
Vol 22 (02) ◽  
pp. 1150006 ◽  
Author(s):  
MATHIAS JUNGEN
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Fracture Process ◽  
Variational Model ◽  
Minimal Energy ◽  
Rigorous Derivation ◽  
Basalt Flow ◽  
Columnar Jointing ◽  
Schwarz Symmetrization ◽  
High Degree

We propose to use nonlinear elasticity to model the propagation of cracks in cooling lava. In particular, our work aims to understand the enigmatic fracture process that leads to the formation of column joints. Column joints are plane fracture surfaces fragmenting a basalt flow into prismatic columns. These columns are characterized by their polygonal cross-section and usually exhibit a strikingly high degree of regularity. We present a variational model with the assumption that the fracture process seeks to minimize the total energy of the system. The expression for the elastic energy is simplified and the configuration of minimal energy is analytically determined by a rigorous derivation. Further, we study the behavior of the energy under Steiner and Schwarz symmetrization of the column cross-section. In particular, we prove that the minimum of the energy among all possible convex and bounded column cross-sections B ⊂ ℝ2 is attained when B is the two-disk. Our results thus give strong evidence supporting the conjecture that the minimal energy is attained for a regular hexagon when the column cross-section is further required to tile the plane.

Photoneutron Cross Sections in 14N

1972 ◽  
Vol 50 (15) ◽  
pp. 1689-1696 ◽  
Author(s):  
R. W. Gellie ◽  
K. H. Lokan ◽  
N. K. Sherman ◽  
R. G. Johnson ◽  
J. I. Lodge
Keyword(s):  
Excited States ◽  
Cross Section ◽  
Cross Sections ◽  
Neutron Emission ◽  
Giant Resonance ◽  
Sequential Decay ◽  
Dipole Resonance ◽  
Intermediate States ◽  
Integrated Cross Section ◽  
High Degree

Photoneutron distributions from 14N have been obtained by time-of-flight methods, for bremsstrahlung end-point energies increasing in 2 MeV steps from 15.5 to 29.5 MeV. A large part of the neutron yield is associated with the sequential decay of 14N to 12C, through well-defined intermediate states of 13C, at 7.55, 8.86, and 11.80 MeV, which are unstable against neutron emission. The (γ,n0) cross section for neutron emission to the ground state of 13N is found to agree very closely with the corresponding (γ,p0) cross section, implying a high degree of isospin purity for the giant dipole resonance of 14N. It is observed that the decay of the giant resonance proceeds freely through those odd-parity excited states of the A = 13 nuclei which are single hole states formed by the removal of a p-shell nucleon from the parent 14N.The integrated cross section for all neutron-producing interactions is found to be 88 ± 5 MeV mb.

scholarly journals THE DYNAMIC SWEPT PRISM

1980 ◽  
Vol 1 (17) ◽  
pp. 63
Author(s):  
David M. Chapman ◽  
A.W. Smith
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Lower Surface ◽  
Gold Coast ◽  
Nearshore Zone ◽  
Intensive Study ◽  
Maximum Probability ◽  
Time Period ◽  
Profile Line ◽  
High Degree

In the course of an intensive study of beach and inshore morphodynamics associated with a nourishment project on the Lower Gold Coast, Australia (Chapman, 1978), approximately 400 profile lines were surveyed from backshore to the point of zero change in the nearshore zone, to a high degree of accuracy (Chapman & Smith, 1977). Analysis of this data base has led, inter alia, to the development of the concept of the dynamic swept prism, since the maximum and minimum ordinates on a shore-normal profile line, over a specified time period, form the vertices of an irregular polygon which may be regarded as the cross-section of the prism of sand which is worked over by waves during that time period. Representative prism cross-sections from the Lower Gold Coast are displayed in Figure 1 . The important limits of the swept prism, viz., the landward and seaward extremities and the lower surface, are probabilistically, not deterministically defined. Prism cross sections a -:• illustrated are not isotropic with respect to the probability of disturbance by waves. Isolines of probability may be conceptually defined, with the zone of maximum probability of disturbance corresponding to that zone which is re-worked during the tidal cycle (cf. Duncan, 1964).

scholarly journals The capture of neutrons by deuterons

1948 ◽  
Vol 192 (1029) ◽  
pp. 156-166 ◽  
Keyword(s):  
Magnetic Dipole ◽  
Cross Section ◽  
Cross Sections ◽  
Group Structure ◽  
Wave Functions ◽  
Fast Neutrons ◽  
Dipole Radiation ◽  
Exchange Character ◽  
The Cross ◽  
High Degree

The cross-sections for capture of neutrons by deuterons, involving emission of both electric and magnetic dipole radiation, are calculated using the wave functions obtained by Buckingham & Massey (1941) in the course of an application of the resonating-group structure method to the elastic scattering of neutrons by deuterons. The value found for capture of neutrons with emission of magnetic dipole radiation is found to be very sensitive to the particular form taken for the various wave functions, owing to a very high degree of cancellation that occurs in the integrations. As a result it is out of the question at present to provide accurate theoretical values for this process. All that can be said is that the cross-section for capture of thermal neutrons by deuterons is likely to be abnormally small. It may well be 10 -28 cm. 2 or less. This is in general agreement with observation. For capture of fast neutrons with emission of electric dipole radiation there is much less uncertainty in the calculated values although the cross-sections are very small, of the order of a few times 10 -29 cm. 2. The actual value of the cross-section in this case depends on the assumed type of nucleonic interaction, i.e. whether it is of exchange character or not. Results are also given for the inverse process—the photodisintegration of the triton.

Longitudinally inhomogeneous deformation patterns in isotropic tubes under pure bending

2006 ◽  
Vol 462 (2067) ◽  
pp. 817-838 ◽  
Author(s):  
M. Khurram Wadee ◽  
M. Ahmer Wadee ◽  
Andrew P Bassom ◽  
Andreas A Aigner
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Small Strain ◽  
Variational Model ◽  
Pure Bending ◽  
Elastic Tubes ◽  
Physical Experiments ◽  
Gradual Process ◽  
Nonlinear Elastic ◽  
Deformation Patterns

A variational model is formulated that accounts for the localization of deformation due to buckling under pure bending of thin-walled elastic tubes with circular cross-sections. Previous studies have successfully modelled the gradual process of ovalization of the cross-section with an accompanying progressive reduction in stiffness but these theories have had insufficient freedom to incorporate any longitudinal variation in the tube. Here, energy methods and small-strain nonlinear elastic theory are used to model the combined effects of cross-section deformation and localized longitudinal buckling. Results are compared with a number of case studies, including a nanotube, and it is found that the model gives rise to behaviours that correlate well with some published physical experiments and numerical studies.

Electron Irradiation Effects in Polyoxymethylene Crystals Grown Inside Trioxane Crystals

1971 ◽  
Vol 29 ◽  
pp. 78-79
Author(s):  
J. P. Colson ◽  
D. H. Reneker
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Detailed Examination ◽  
The Other ◽  
Electron Micrograph ◽  
Irradiation Effects ◽  
Threefold Axis ◽  
Typical Sample ◽  
Polymer Crystals ◽  
Chain Axis

Polyoxymethylene (POM) crystals grow inside trioxane crystals which have been irradiated and heated to a temperature slightly below their melting point. Figure 1 shows a low magnification electron micrograph of a group of such POM crystals. Detailed examination at higher magnification showed that three distinct types of POM crystals grew in a typical sample. The three types of POM crystals were distinguished by the direction that the polymer chain axis in each crystal made with respect to the threefold axis of the trioxane crystal. These polyoxymethylene crystals were described previously.At low magnifications the three types of polymer crystals appeared as slender rods. One type had a hexagonal cross section and the other two types had rectangular cross sections, that is, they were ribbonlike.

A quantitative approach to inner shell losses

1978 ◽  
Vol 36 (1) ◽  
pp. 526-527 ◽  
Author(s):  
R.D. Leapman ◽  
P. Rez ◽  
D.F. Mayers
Keyword(s):  
Energy Transfer ◽  
Cross Section ◽  
Cross Sections ◽  
Accurate Determination ◽  
Background Intensity ◽  
Core Excitation ◽  
Quantitative Basis ◽  
Cross Section Differential ◽  
Bound Electrons

Microanalysis by EELS has been developing rapidly and though the general form of the spectrum is now understood there is a need to put the technique on a more quantitative basis (1,2). Certain aspects important for microanalysis include: (i) accurate determination of the partial cross sections, σx(α,ΔE) for core excitation when scattering lies inside collection angle a and energy range ΔE above the edge, (ii) behavior of the background intensity due to excitation of less strongly bound electrons, necessary for extrapolation beneath the signal of interest, (iii) departures from the simple hydrogenic K-edge seen in L and M losses, effecting σx and complicating microanalysis. Such problems might be approached empirically but here we describe how computation can elucidate the spectrum shape.The inelastic cross section differential with respect to energy transfer E and momentum transfer q for electrons of energy E0 and velocity v can be written as

Oxygen K near edge structures studied with multiple scattering calculations

1988 ◽  
Vol 46 ◽  
pp. 504-505
Author(s):  
Xudong Weng ◽  
Peter Rez
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Partial Cross Section ◽  
Energy Window ◽  
Edge Structure ◽  
Fine Structures ◽  
Hydrogenic Model ◽  
Electron Energy Loss ◽  
Quantitative Chemical

In electron energy loss spectroscopy, quantitative chemical microanalysis is performed by comparison of the intensity under a specific inner shell edge with the corresponding partial cross section. There are two commonly used models for calculations of atomic partial cross sections, the hydrogenic model and the Hartree-Slater model. Partial cross sections could also be measured from standards of known compositions. These partial cross sections are complicated by variations in the edge shapes, such as the near edge structure (ELNES) and extended fine structures (ELEXFS). The role of these solid state effects in the partial cross sections, and the transferability of the partial cross sections from material to material, has yet to be fully explored. In this work, we consider the oxygen K edge in several oxides as oxygen is present in many materials. Since the energy window of interest is in the range of 20-100 eV, we limit ourselves to the near edge structures.

Absolute inner-shell cross section determination for EELS analysis

1988 ◽  
Vol 46 ◽  
pp. 534-535
Author(s):  
P.A. Crozier
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Absolute Cross Section ◽  
Specimen Thickness ◽  
Mass Thickness ◽  
Scattering Cross ◽  
Before And After ◽  
Estimated Error ◽  
Scattering Cross Sections ◽  
Electron Microscopist

Absolute inelastic scattering cross sections or mean free paths are often used in EELS analysis for determining elemental concentrations and specimen thickness. In most instances, theoretical values must be used because there have been few attempts to determine experimental scattering cross sections from solids under the conditions of interest to electron microscopist. In addition to providing data for spectral quantitation, absolute cross section measurements yields useful information on many of the approximations which are frequently involved in EELS analysis procedures. In this paper, experimental cross sections are presented for some inner-shell edges of Al, Cu, Ag and Au.Uniform thin films of the previously mentioned materials were prepared by vacuum evaporation onto microscope cover slips. The cover slips were weighed before and after evaporation to determine the mass thickness of the films. The estimated error in this method of determining mass thickness was ±7 x 107g/cm2. The films were floated off in water and mounted on Cu grids.

A technique for preparing semiconductor cross sections for both TEM and SEM analysis

1989 ◽  
Vol 47 ◽  
pp. 712-713
Author(s):  
Stanley J. Klepeis ◽  
J.P. Benedict ◽  
R.M Anderson
Keyword(s):  
Sample Preparation ◽  
Cross Section ◽  
Cross Sections ◽  
Sem Analysis ◽  
Preparation Technique ◽  
Ion Milling ◽  
Tem Analysis ◽  
Polished Cross Section ◽  
Area Of Interest ◽  
Polished Side

The ability to prepare a cross-section of a specific semiconductor structure for both SEM and TEM analysis is vital in characterizing the smaller, more complex devices that are now being designed and manufactured. In the past, a unique sample was prepared for either SEM or TEM analysis of a structure. In choosing to do SEM, valuable and unique information was lost to TEM analysis. An alternative, the SEM examination of thinned TEM samples, was frequently made difficult by topographical artifacts introduced by mechanical polishing and lengthy ion-milling. Thus, the need to produce a TEM sample from a unique,cross-sectioned SEM sample has produced this sample preparation technique.The technique is divided into an SEM and a TEM sample preparation phase. The first four steps in the SEM phase: bulk reduction, cleaning, gluing and trimming produces a reinforced sample with the area of interest in the center of the sample. This sample is then mounted on a special SEM stud. The stud is inserted into an L-shaped holder and this holder is attached to the Klepeis polisher (see figs. 1 and 2). An SEM cross-section of the sample is then prepared by mechanically polishing the sample to the area of interest using the Klepeis polisher. The polished cross-section is cleaned and the SEM stud with the attached sample, is removed from the L-shaped holder. The stud is then inserted into the ion-miller and the sample is briefly milled (less than 2 minutes) on the polished side. The sample on the stud may then be carbon coated and placed in the SEM for analysis.

Experimental Studies Of Multilayer Glass Structures On Compression, Compression With Bending And Simple Bending

2019 ◽  
pp. 22-30
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Applied Load ◽  
Experimental Studies ◽  
Strength Properties ◽  
Research Topic ◽  
Normative Values ◽  
Laminated Glass ◽  
The Cross ◽  
Experimental Values

The work of multilayer glass structures for central and eccentric compression and bending are considered. The substantiation of the chosen research topic is made. The description and features of laminated glass for the structures investigated, their characteristics are presented. The analysis of the results obtained when testing for compression, compression with bending, simple bending of models of columns, beams, samples of laminated glass was made. Overview of the types and nature of destruction of the models are presented, diagrams of material operation are constructed, average values of the resistance of the cross-sections of samples are obtained, the table of destructive loads is generated. The need for development of a set of rules and guidelines for the design of glass structures, including laminated glass, for bearing elements, as well as standards for testing, rules for assessing the strength, stiffness, crack resistance and methods for determining the strength of control samples is emphasized. It is established that the strength properties of glass depend on the type of applied load and vary widely, and significantly lower than the corresponding normative values of the strength of heat-strengthened glass. The effect of the connecting polymeric material and manufacturing technology of laminated glass on the strength of the structure is also shown. The experimental values of the elastic modulus are different in different directions of the cross section and in the direction perpendicular to the glass layers are two times less than along the glass layers.

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