scholarly journals A geometrical argument for a theorem of G. E. Welters

1999 ◽  
Vol 232 (3) ◽  
pp. 505-509
Author(s):  
Giambattista Marini
Keyword(s):  
Geometrical Argument

scholarly journals X-ray studies of the structure of hair, wool, and related fibres - III—The configuration of the keratin molecule and its orientation in the biological cell

1935 ◽  
Vol 150 (871) ◽  
pp. 533-551 ◽  
Keyword(s):  
Average Distance ◽  
Three Dimensional ◽  
Side Chains ◽  
X Ray ◽  
Molecular Arrangement ◽  
Proposed Model ◽  
Basic Features ◽  
Geometrical Argument ◽  
Diffraction Effects ◽  
Physical And Chemical

One of the difficulties associated with the X-ray study of biological structures arises from the fact that such structures, while not in general unorganized “powders,” are nevertheless usually built up of numerous submicroscopic individuals of continuously varying orientation: in the typical biological “fibre,” for example, the imperfectly crystalline mole­cular aggregates all lie with one and the same crystallographic direction either approximately parallel to the fibre-axis or spirally inclined at some approximately constant angle to it; but subject to this limitation there may be present within the compass of the X-ray beam all orientations up to the maximum possible consistent with axial symmetry. This means that though we may not be condemned to work in the least profitable field of X-ray technique, that of the completely random “powder photograph,” yet we are debarred from the full geometrical advantages to be derived from operating with a single macroscopic crystal. Speaking briefly, the main trouble lies in the difficulty or impossibility of measuring sufficient inter-directional angles to define the molecular arrangement without ambiguity. Sometimes it is possible to draw very plausible conclusions, or even conclusions almost certainly correct; but in others the diffraction effects are so ill-defined as to preclude altogether the use of direct geometrical argument, and compel us to fall back on indirect reasoning based on evidence from various sources, including comparative photographs of related structures. The X-ray investigation of proteins in particular is a many-sided enquiry of this nature, for the diffraction effects are susceptible of interpretation only in relation to other physical and chemical data. The X-ray photographs then serve to give form, so to speak, to such data—to provide the three-dimensional framework necessary to build them into a coherent whole. Papers I and II in this series show how, working along these lines, it has been found possible to derive the basic features of the keratin molecule or complex, both in its unextended form (α) and in its extended form ((β), and to apply the proposed model to the interpretation of the long-range elasticity and other characteristic properties of mammalian hairs. The structure of β-keratin may be described most simply as that of a flat “polypeptide grid,” in which a succession of fully extended main-chains are bound side by side through linkages, both electrostatic and co-valent, between certain of their side-chains; while that of α-keratin (the normal equilibrium form) may be thought of as derived from (β-keratin by a regular folding of the main-chains in planes transverse to the side-chains. By this means the length of the molecule in the direction of the main-chains is reduced to approximately one-half (the average distance apart of the side-chains is decreased from rather less than 3·4 A to about 1·7 A), while the average separation of the main-chains in the plane of the side-chains (the plane of the “grid”) remains roughly constant (9·8 A). In the β-keratin crystallites the grids are piled one on top of another with the main-chains parallel and separated by a distance of 4·65 A.

Imaging salt with turning seismic waves

Geophysics ◽  
1992 ◽  
Vol 57 (11) ◽  
pp. 1453-1462 ◽  
Author(s):  
Dave Hale ◽  
N. Ross Hill ◽  
Joe Stefani
Keyword(s):  
Seismic Waves ◽  
Computational Cost ◽  
Salt Dome ◽  
Seismic Survey ◽  
Seismic Wave Velocity ◽  
Salt Domes ◽  
Reflection Time ◽  
Before And After ◽  
Migration Method ◽  
Geometrical Argument

Turning seismic waves, which first travel downward and then upward before (and after) reflection, have been recorded in a 3-D seismic survey conducted over an overhanging salt dome. Careful processing of these turning waves enables the imaging of the underside of the salt dome and of intrusions of salt into vertical faults radiating from the dome. When seismic wave velocity increases with depth, waves that initially travel downward are reflected and may turn so as to travel upward before reflection. A simple geometrical argument suggests that these turning waves are likely to exhibit abnormal moveout in common‐midpoint (CMP) gathers, in that reflection time decreases with increasing source‐receiver offset. This abnormal moveout and the attenuation of turning waves by most migration methods suggest that conventional seismic processing does not properly image turning waves. The most important step in imaging turning waves, assuming that they have been recorded, is the migration process. Simple and inexpensive modifications to the conventional phase‐shift migration method enable turning waves to be imaged for little additional computational cost. The examples provided in this paper suggest that these and other such modifications to conventional processing should be used routinely when imaging salt domes.

Mechanistically based, allometric models to predict tree diameter and height in even-aged monoculture of Eucalyptusregnans F. Muell.

1989 ◽  
Vol 19 (2) ◽  
pp. 270-273 ◽  
Author(s):  
P. W. West ◽  
C. L. Beadle ◽  
C. R. A. Turnbull
Keyword(s):  
Tree Height ◽  
Allometric Relationships ◽  
Allometric Models ◽  
Tree Diameter ◽  
Diameter At Breast Height ◽  
Breast Height ◽  
Vertical Stability ◽  
Structural Argument ◽  
Individual Trees ◽  
Geometrical Argument

A randomly selected sample of 22 trees was felled in a stand in a 20-year-old monoculture of Eucalyptusregnans F. Muell. in southern Tasmania. One-half of the trees were from a section of the stand that had been heavily thinned 10 years previously, and the remainder were from the unthinned section. The trees were sectioned and the fresh weights of their stems (including bark) and crowns (leaves plus branches) determined. By combining a geometrical argument about the shape of tree stems with a structural argument about their vertical stability, allometric relationships were established relating tree diameter at breast height or tree height to total aboveground weight and the ratio of crown to stem weight. These relationships were found to hold in both the thinned and unthinned sections of the experiment. When combined with a model to predict biomass of individual trees, these models can be used to predict diameter or height of individual trees in E. regnans monoculture.

Epitaxy in the Presence of Very Large Misfit: High Resolution TEM Study of Al/Si, Ag/Si, Al/CaF2/Si and Ag/CaF2/Si

1987 ◽  
Vol 94 ◽  
Author(s):  
F. K LeGoues ◽  
M. Liehr ◽  
M. Renier
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
High Resolution ◽  
Lattice Models ◽  
High Angle ◽  
Multilayered Structures ◽  
Metal Insulator ◽  
Transmission Electron ◽  
High Resolution Tem ◽  
Geometrical Argument

ABSTRACTWe summarize high resolution transmission electron microscopy studies of interfaces with 33% misfit. We explain the existence of epitaxial interfaces for this systems by a geometrical argument similar to the 0-lattice models used to study high angle grain boundaries. Differences between systems very similar in structures are explained. We use the thus found epitaxial interfaces to build multilayered structures of the type metal/insulator/semiconductor.

Geometry Dependent Resistivity in Single-walled Carbon Nanotube Films Patterned Down to Submicron Dimensions

2006 ◽  
Vol 963 ◽  
Author(s):  
Ashkan Behnam ◽  
Leila Noriega ◽  
Yongho Choi ◽  
Zhuangchun Wu ◽  
Andrew G Rinzler ◽  
...  
Keyword(s):  
Carbon Nanotube ◽  
Power Law ◽  
Vital Role ◽  
Fabrication Technology ◽  
Top Down ◽  
Single Walled Carbon Nanotube ◽  
Inverse Power Law ◽  
Device Structures ◽  
Geometrical Argument ◽  
Nanotube Films

ABSTRACTWe demonstrate patterning of SWNT films down to 200 nm lateral dimensions using e-beam lithography and reactive ion etching with good selectivity and directionality and then we fabricate standard four-point-probe structures to characterize the resistivity of these films as a function of device geometry. The resistivity is found to be independent of device length for a given width and thickness, while increasing over three orders of magnitude compared to bulk films, as the width and the thickness of the films shrink. In particular, the resistivity of SWNT films starts to increase with decreasing device width below 20 μm, exhibiting an inverse power law dependence on device width at sub-micron dimensions. We explain this behavior by a purely geometrical argument. Although the “top-down” patterning of nanotube films allows for their use in sub-micron device structures and perhaps their integration into standard silicon fabrication technology, the resistivity scaling is an important effect that needs to be taken into account when fabricating small devices in which nanotube film transport characteristics play a vital role.

Lower Bounds for the Ramsey Numbers

1970 ◽  
Vol 13 (2) ◽  
pp. 227-229 ◽  
Author(s):  
Pierre Robillard
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Ramsey Numbers ◽  
Geometrical Argument

Abstract.A lower bound for a family of Ramsey numbers is derived using a geometrical argument.

The culture of flat earth and its consequences

2020 ◽  
Vol 3 (2) ◽  
pp. 173-193 ◽  
Author(s):  
Dónal Mac Erlaine
Keyword(s):  
History Of Science ◽  
Communication Technologies ◽  
The Internet ◽  
Popular Discourse ◽  
The Earth ◽  
History Of ◽  
Ancient Times ◽  
Geometrical Argument

Tracing some elements of the history of science, such as the tradition of map-making beginning in ancient times, this article aims to link together some factors that have led to the contemporary phenomenon of flat earth belief. Springing from a political fringe culture steeped in a ‘will-to-mistrust’, flat earth belief has gained huge popularity in recent years. The total rejection of science in favour of opinion is today a feature of the discursive landscape, and nowhere it is more poignant than in flat earth belief. Furthermore, it leaks from a mistrust of science to mistrust of culture itself. Ultimately it falls to the agency of recent communication technologies, that is, the internet, where this culture is able to gain traction in popular discourse. Through a very simple geometrical argument needing no equipment, I demonstrate that the earth must be spherical (or near-so), and this ultimately points to the technocratic culture today that has paradoxically led to this unpredicted phenomenon. Moreover it is a dangerous trend, and this piece aims to highlight why this is so.

Sign in / Sign up

Export Citation Format

Share Document