Shell models in three dimensions

1995 ◽  
pp. 163-182 ◽  
Author(s):  
Przemyslaw Prusinkiewicz ◽  
Deborah R. Fowler
Keyword(s):  
Three Dimensions ◽  
Shell Models

Shell models in three dimensions

2003 ◽  
pp. 163-182
Author(s):  
Przemyslaw Prusinkiewicz ◽  
Deborah R. Fowler
Keyword(s):  
Three Dimensions ◽  
Shell Models

Automated generation of turbulence shell models by the methods of computer algebra

2021 ◽  
pp. 65-80
Author(s):  
Глеб Михайлович Водинчар ◽  
Любовь Константиновна Фещенко
Keyword(s):  
Conservation Laws ◽  
Computer Algebra ◽  
Quadratic Forms ◽  
Main Idea ◽  
Physical Space ◽  
Turbulence Models ◽  
Three Dimensions ◽  
Conserved Quantities ◽  
Automated Generation ◽  
Shell Models

Описана разработанная методика генерации уравнений каскадных моделей турбулентности с помощью систем компьютерной алгебры. Методика позволяет варьировать размер масштабной нелокальности модели, вид квадратичных законов сохранения и спектральных законов, знаменатель геометрической прогрессии масштабов. Ее использование позволяет быстро и безошибочно генерировать целые классы моделей. Может использоваться для разработки каскадных моделей гидродинамических, магнитогидродинамических и конвективных турбулентных систем. There is a great variety of shell turbulence models. Such models reproduce certain characteristics of turbulence. A model that could reproduce all turbulence regimes does not exist at the moment. Information about a particular model is contained in a set of persistent quantities, which are some quadratic forms of turbulent fields. These quadratic forms should be formal analogs of the exact conserved quantities. It is important to note that the main idea of Shell models presupposes a refusal to describe the geometric structure of movements. At the same time, it is well known that turbulent processes in spaces of two and three dimensions behave differently. Therefore, the provision of certain combinations of conserved quantities allows indirect introducing into the shell model the information about the dimension of the physical space in which the turbulent process develops. Purpose. The aim of this work was to create software tools that would quickly generate classes of models that satisfy one or another set of conservation laws. The choice of a specific model within these classes can then be specified using additional physical considerations, for example, the existence of a given probability distribution for the interaction of certain shells. Methods. The developed technique for generating equations of shell turbulence models is carried out using symbolic computation systems (computer algebra systems - CAS). Note that symbolic packages are used not for studying ready-made shell models, but for the automated generation of the equations of these models themselves. The technique allows varying the value of the scale nonlocality of the model, the form of the quadratic conservation laws and spectral laws, the denominator of the geometric progression of scales. It allows quickly and accurately generating the entire set of classes of the models. It can be used to develop shell models of hydrodynamic, magnetohydrodynamic and convective turbulent systems. Findings. It seems that the proposed technique will be useful for studying the properties of turbulence in the framework of cascade models

Shell models in three dimensions

1998 ◽  
pp. 163-182
Author(s):  
Przemyslaw Prusinkiewicz ◽  
Deborah R. Fowler
Keyword(s):  
Three Dimensions ◽  
Shell Models

High-resolution scanning electron microscopy (HRSEM) of mitochondria from various rat tissues

1988 ◽  
Vol 46 ◽  
pp. 14-15
Author(s):  
P.J. Lea ◽  
M.J. Hollenberg
Keyword(s):  
Electron Microscopy ◽  
Pigment Epithelium ◽  
Retinal Pigment ◽  
Rat Hepatocytes ◽  
Three Dimensions ◽  
Objective Lens ◽  
Rat Tissues ◽  
Thin Sections ◽  
Reconstruction Methods ◽  
Scanning Electron

Our current understanding of mitochondrial ultrastructure has been derived primarily from thin sections using transmission electron microscopy (TEM). This information has been extrapolated into three dimensions by artist's impressions (1) or serial sectioning techniques in combination with computer processing (2). The resolution of serial reconstruction methods is limited by section thickness whereas artist's impressions have obvious disadvantages.In contrast, the new techniques of HRSEM used in this study (3) offer the opportunity to view simultaneously both the internal and external structure of mitochondria directly in three dimensions and in detail.The tridimensional ultrastructure of mitochondria from rat hepatocytes, retinal (retinal pigment epithelium), renal (proximal convoluted tubule) and adrenal cortex cells were studied by HRSEM. The specimens were prepared by aldehyde-osmium fixation in combination with freeze cleavage followed by partial extraction of cytosol with a weak solution of osmium tetroxide (4). The specimens were examined with a Hitachi S-570 scanning electron microscope, resolution better than 30 nm, where the secondary electron detector is located in the column directly above the specimen inserted within the objective lens.

Inelastic Electron Scattering from Valence Electrons in Aluminum

1976 ◽  
Vol 34 ◽  
pp. 462-463
Author(s):  
P. E. Batson ◽  
C. H. Chen ◽  
J. Silcox
Keyword(s):  
Electron Scattering ◽  
Single Scattering ◽  
Three Dimensions ◽  
Inelastic Electron ◽  
Weak Beam ◽  
Scattering Spectrum ◽  
Valence Electrons ◽  
Diffraction Patterns ◽  
Electronic Scattering

We wish to report in this paper measurements of the inelastic scattering component due to the collective excitations (plasmons) and single particlehole excitations of the valence electrons in Al. Such scattering contributes to the diffuse electronic scattering seen in electron diffraction patterns and has recently been considered of significance in weak-beam images (see Gai and Howie) . A major problem in the determination of such scattering is the proper correction for multiple scattering. We outline here a procedure which we believe suitably deals with such problems and report the observed single scattering spectrum.In principle, one can use the procedure of Misell and Jones—suitably generalized to three dimensions (qx, qy and #x2206;E)--to derive single scattering profiles. However, such a computation becomes prohibitively large if applied in a brute force fashion since the quasi-elastic scattering (and associated multiple electronic scattering) extends to much larger angles than the multiple electronic scattering on its own.

Advantages of Complementary Stereo Images as Viewed with the Low-Temperature Field-Emission SEM

1992 ◽  
Vol 50 (2) ◽  
pp. 1314-1315
Author(s):  
William P. Wergin ◽  
Eric F. Erbe
Keyword(s):  
Fold Increase ◽  
Horizontal Displacement ◽  
Three Dimensions ◽  
Stereo Image ◽  
Stereo Pair ◽  
Sem Micrograph ◽  
Left And Right ◽  
The Common ◽  
The Brain ◽  
Pair Analysis

The eye-brain complex allows those of us with normal vision to perceive and evaluate our surroundings in three-dimensions (3-D). The principle factor that makes this possible is parallax - the horizontal displacement of objects that results from the independent views that the left and right eyes detect and simultaneously transmit to the brain for superimposition. The common SEM micrograph is a 2-D representation of a 3-D specimen. Depriving the brain of the 3-D view can lead to erroneous conclusions about the relative sizes, positions and convergence of structures within a specimen. In addition, Walter has suggested that the stereo image contains information equivalent to a two-fold increase in magnification over that found in a 2-D image. Because of these factors, stereo pair analysis should be routinely employed when studying specimens.Imaging complementary faces of a fractured specimen is a second method by which the topography of a specimen can be more accurately evaluated.

convergent-beam diffraction from surfaces

1987 ◽  
Vol 45 ◽  
pp. 30-33
Author(s):  
J. A. Eades ◽  
A. E. Smith ◽  
D. F. Lynch
Keyword(s):  
Reciprocal Lattice ◽  
Three Dimensional ◽  
Grazing Incidence ◽  
Three Dimensions ◽  
Plane Figure ◽  
Transmission Electron ◽  
Convergent Beam ◽  
Beam Patterns ◽  
Beam Diffraction

It is quite simple (in the transmission electron microscope) to obtain convergent-beam patterns from the surface of a bulk crystal. The beam is focussed onto the surface at near grazing incidence (figure 1) and if the surface is flat the appropriate pattern is obtained in the diffraction plane (figure 2). Such patterns are potentially valuable for the characterization of surfaces just as normal convergent-beam patterns are valuable for the characterization of crystals.There are, however, several important ways in which reflection diffraction from surfaces differs from the more familiar electron diffraction in transmission.GeometryIn reflection diffraction, because of the surface, it is not possible to describe the specimen as periodic in three dimensions, nor is it possible to associate diffraction with a conventional three-dimensional reciprocal lattice.

3-D reconstruction and analysis of mammalian mitotic spindle structure

1992 ◽  
Vol 50 (1) ◽  
pp. 578-579
Author(s):  
Kent McDonald ◽  
David Mastronarde ◽  
Rubai Ding ◽  
Eileen O'Toole ◽  
J. Richard McIntosh
Keyword(s):  
Cross Sections ◽  
Mitotic Spindle ◽  
Experimental Studies ◽  
Video Camera ◽  
Three Dimensions ◽  
Mitotic Spindles ◽  
Black And White ◽  
Reconstruction Methods ◽  
Spindle Structure ◽  
Tissue Culture Line

Mammalian spindles are generally large and may contain over a thousand microtubules (MTs). For this reason they are difficult to reconstruct in three dimensions and many researchers have chosen to study the smaller and simpler spindles of lower eukaryotes. Nevertheless, the mammalian spindle is used for many experimental studies and it would be useful to know its detailed structure.We have been using serial cross sections and computer reconstruction methods to analyze MT distributions in mitotic spindles of PtK cells, a mammalian tissue culture line. Images from EM negatives are digtized on a light box by a Dage MTI video camera containing a black and white Saticon tube. The signal is digitized by a Parallax 1280 graphics device in a MicroVax III computer. Microtubules are digitized at a magnification such that each is 10-12 pixels in diameter.

Five-Dimensional Microscopy using Widefield-Deconvolution: Practical Considerations and Biological Applications

1996 ◽  
Vol 54 ◽  
pp. 268-269
Author(s):  
W.F. Marshall ◽  
K. Oegema ◽  
J. Nunnari ◽  
A.F. Straight ◽  
D.A. Agard ◽  
...  
Keyword(s):  
Confocal Microscopy ◽  
High Speed ◽  
Laser Scanning ◽  
Ccd Camera ◽  
Image Plane ◽  
Time Lapse ◽  
Laser Scanning Confocal Microscopy ◽  
Three Dimensions ◽  
Excitation Light ◽  
Cooled Ccd

The ability to image cells in three dimensions has brought about a revolution in biological microscopy, enabling many questions to be asked which would be inaccessible without this capability. There are currently two major methods of three dimensional microscopy: laser-scanning confocal microscopy and widefield-deconvolution microscopy. The method of widefield-deconvolution uses a cooled CCD to acquire images from a standard widefield microscope, and then computationally removes out of focus blur. Using such a scheme, it is easy to acquire time-lapse 3D images of living cells without killing them, and to do so for multiple wavelengths (using computer-controlled filter wheels). Thus, it is now not only feasible, but routine, to perform five dimensional microscopy (three spatial dimensions, plus time, plus wavelength).Widefield-deconvolution has several advantages over confocal microscopy. The two main advantages are high speed of acquisition (because there is no scanning, a single optical section is acquired at a time by using a cooled CCD camera) and the use of low excitation light levels Excitation intensity can be much lower than in a confocal microscope for three reasons: 1) longer exposures can be taken since the entire 512x512 image plane is acquired in parallel, so that dwell time is not an issue, 2) the higher quantum efficiently of a CCD detect over those typically used in confocal microscopy (although this is expected to change due to advances in confocal detector technology), and 3) because no pinhole is used to reject light, a much larger fraction of the emitted light is collected. Thus we can typically acquire images with thousands of photons per pixel using a mercury lamp, instead of a laser, for illumination. The use of low excitation light is critical for living samples, and also reduces bleaching. The high speed of widefield microscopy is also essential for time-lapse 3D microscopy, since one must acquire images quickly enough to resolve interesting events.

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