30.—The Chord Locus of a Certain Curve in [n]

1974 ◽  
Vol 71 (4) ◽  
pp. 337-343
Author(s):  
W. L. Edge
Keyword(s):  
Three Dimensional ◽  
Single Equation

SynopsisThe sharing of a common self-polar simplex by n−1 quadrics in [n] confers special features on their curve of intersection Γn. The three-dimensional locus Mn of chords of Γn. has certain singularities, some of which are described. In conclusion, a few comments refer to the case n = 4 when Mn is defined by a single equation.

scholarly journals LIMA (v1.0): a two-moment microphysical scheme driven by a multimodal population of cloud condensation and ice freezing nuclei

2015 ◽  
Vol 8 (9) ◽  
pp. 7767-7820 ◽  
Author(s):  
B. Vié ◽  
J.-P. Pinty ◽  
S. Berthet ◽  
M. Leriche
Keyword(s):  
Mesoscale Model ◽  
Cloud Condensation Nuclei ◽  
Three Dimensional ◽  
Single Equation ◽  
Ice Crystals ◽  
Growth Mode ◽  
Squall Line ◽  
Complex Nature ◽  
Cloud Droplets ◽  
Ice Clouds

Abstract. The paper describes the 2-moment microphysical scheme LIMA (Liquid Ice Multiple Aerosols), which relies on the prognostic evolution of a three-dimensional (3-D) aerosol population, and the careful description of the nucleating properties that enable cloud droplets and pristine ice crystals to form. LIMA uses the aerosol nucleating properties to form cloud droplets and pristine ice crystals. Several modes of Cloud Condensation Nuclei (CCN) and Ice Freezing Nuclei (IFN) are considered individually. A special class of partially soluble IFN is also introduced. These "aged" IFN act first as CCN and then as IFN by immersion nucleation at low temperatures. All the CCN modes are in competition with each other, as expressed by the single equation of maximum supersaturation. The IFN are insoluble aerosols that nucleate ice in several ways (condensation, deposition and immersion freezing) assuming the singular hypothesis. The scheme also includes the homogeneous freezing of cloud droplets, the Hallett–Mossop ice multiplication process and the freezing of haze at very low temperature. LIMA assumes that water vapour is in thermodynamic equilibrium with the population of cloud droplets (adjustment to saturation in warm clouds). In ice clouds, the prediction of the number concentration of the pristine ice crystals is used to compute explicit deposition and sublimation rates (leading to free under/supersaturation over ice). The formation of hydrometeors is standard. The autoconversion, accretion and self-collection processes shape the raindrop spectra. The initiation of the large crystals and aggregates category is the result of the depositional growth of large crystals beyond a critical size. Aggregation and riming are computed explicitly. Heavily rimed crystals (graupel) can experience a dry or wet growth mode. An advanced version of the scheme includes a separate hail category of particles forming and growing exclusively in the wet growth mode. The sedimentation of all particle types is included. The LIMA scheme is inserted in the cloud-resolving mesoscale model Meso-NH. The flexibility of LIMA is illustrated by two 2-D experiments. The first one highlights the sensitivity of orographic ice clouds to IFN types and IFN concentrations. Then a squall line case discusses the microstructure of a mixed-phase cloud and the impacts of pure CCN and IFN polluting plumes. The experiments show that LIMA captures the complex nature of aerosol-cloud interactions leading to different pathways for cloud and precipitation formation.

scholarly journals Bending and free vibrational analysis of bi-directional functionally graded beams with circular cross-section

2020 ◽  
Vol 41 (10) ◽  
pp. 1497-1516 ◽  
Author(s):  
Yong Huang
Keyword(s):  
Three Dimensional ◽  
Circular Cross Section ◽  
Vibrational Analysis ◽  
Beam Theory ◽  
Single Equation ◽  
Auxiliary Function ◽  
Functionally Graded ◽  
Beam Model ◽  
Various Boundary Conditions ◽  
Differential Motion

Abstract The bending and free vibrational behaviors of functionally graded (FG) cylindrical beams with radially and axially varying material inhomogeneities are investigated. Based on a high-order cylindrical beam model, where the shear deformation and rotary inertia are both considered, the two coupled governing differential motion equations for the deflection and rotation are established. The analytical bending solutions for various boundary conditions are derived. In the vibrational analysis of FG cylindrical beams, the two governing equations are firstly changed to a single equation by means of an auxiliary function, and then the vibration mode is expanded into shifted Chebyshev polynomials. Numerical examples are given to investigate the effects of the material gradient indices on the deflections, the stress distributions, and the eigenfrequencies of the cylindrical beams, respectively. By comparing the obtained numerical results with those obtained by the three-dimensional (3D) elasticity theory and the Timoshenko beam theory, the effectiveness of the present approach is verified.

Comparison of different fidelity mass analyses

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Jacek Mieloszyk ◽  
Andrzej Tarnowski ◽  
Tomasz Goetzendorf-Grabowski ◽  
Mariusz Kowalski ◽  
Bartłomiej Goliszek
Keyword(s):  
Composite Structure ◽  
Computer Aided Design ◽  
Human Factor ◽  
Three Dimensional ◽  
Single Equation ◽  
Estimation Methods ◽  
Content Type ◽  
Mass Estimation ◽  
Key Factor ◽  
Real Mass

Purpose Aircraft structure mass estimation is a very important issue in aerospace. Multiple methods of different fidelity are available, which give results with varying accuracy. Sometimes these methods are giving a high discrepancy of estimated mass compared to the real mass of the structure. The discrepancy is especially noticeable in the case of small aircraft with a composite structure. Their mass properties highly depend not only on the material but also on technology and the human factor. Moreover, methods of mass estimation for unmanned aerial vehicle (UAV) platforms are even less established and examined. The purpose of this paper is to present and discuss various methods of mass estimation. Design/methodology/approach The paper presents different procedures of mass estimation for small UAVs with a composite structure. Beginning from the simplest one, where mass is estimated basing on a single equation and finishing with a mass estimation based on finite element method model and three-dimensional computer-aided design model. The results from all methods are compared with the airworthy aircraft and conclusions are discussed. Findings Mass of flying aircraft was estimated with different methods and compared. It revealed levels of accuracy of the investigated methods. Moreover, the influence on structure mass of human factor, glueing and painting is underlined. Practical implications Mass of the structure is a key factor in aerospace, which influences the performance of the aircraft. Thorough knowledge about the accuracy of the mass estimation methods and possible sources of discrepancies in mass analyses provides an essential tool for designers, which can be used with confidence and allows for the development of new cutting-edge constructions. Originality/value There are very few comparisons of mass estimation methods with an actual mass of manufactured and functional airframes. Additionally, mass estimation inaccuracies based on technological issues are presented, which is seldom done.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

Conformation of Ribosomes from Escherichia Coli

1974 ◽  
Vol 32 ◽  
pp. 210-211
Author(s):  
M. Boublik ◽  
W. Hellmann ◽  
F. Jenkins
Keyword(s):  
Binding Sites ◽  
Ribosomal Proteins ◽  
Fluorescent Dyes ◽  
Protein Biosynthesis ◽  
Three Dimensional ◽  
Spatial Arrangement ◽  
Dimensional Structure ◽  
Complete Understanding ◽  
And Function

The present knowledge of the three-dimensional structure of ribosomes is far too limited to enable a complete understanding of the various roles which ribosomes play in protein biosynthesis. The spatial arrangement of proteins and ribonuclec acids in ribosomes can be analysed in many ways. Determination of binding sites for individual proteins on ribonuclec acid and locations of the mutual positions of proteins on the ribosome using labeling with fluorescent dyes, cross-linking reagents, neutron-diffraction or antibodies against ribosomal proteins seem to be most successful approaches. Structure and function of ribosomes can be correlated be depleting the complete ribosomes of some proteins to the functionally inactive core and by subsequent partial reconstitution in order to regain active ribosomal particles.

Ultrastructural Investigations of the Contractile Filaments of Amoebae

1974 ◽  
Vol 32 ◽  
pp. 188-189
Author(s):  
P.L. Moore
Keyword(s):  
Cytoplasmic Streaming ◽  
Three Dimensional ◽  
Freeze Fracture ◽  
Amoeboid Movement ◽  
Different Types ◽  
Chemical Conditions ◽  
Complete Interpretation

Previous freeze fracture results on the intact giant, amoeba Chaos carolinensis indicated the presence of a fibrillar arrangement of filaments within the cytoplasm. A complete interpretation of the three dimensional ultrastructure of these structures, and their possible role in amoeboid movement was not possible, since comparable results could not be obtained with conventional fixation of intact amoebae. Progress in interpreting the freeze fracture images of amoebae required a more thorough understanding of the different types of filaments present in amoebae, and of the ways in which they could be organized while remaining functional.The recent development of a calcium sensitive, demembranated, amoeboid model of Chaos carolinensis has made it possible to achieve a better understanding of such functional arrangements of amoeboid filaments. In these models the motility of demembranated cytoplasm can be controlled in vitro, and the chemical conditions necessary for contractility, and cytoplasmic streaming can be investigated. It is clear from these studies that “fibrils” exist in amoeboid models, and that they are capable of contracting along their length under conditions similar to those which cause contraction in vertebrate muscles.

Structural organization of escherichia coli ribosomes as determined by immuno electron microscopy

1978 ◽  
Vol 36 (2) ◽  
pp. 166-167 ◽  
Author(s):  
G. Stöffler ◽  
R.W. Bald ◽  
J. Dieckhoff ◽  
H. Eckhard ◽  
R. Lührmann ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Escherichia Coli ◽  
Ribosomal Proteins ◽  
Structural Organization ◽  
Three Dimensional ◽  
Ribosomal Subunit ◽  
Spatial Arrangement ◽  
Small Subunit ◽  
Antibody Binding ◽  
Immuno Electron Microscopy

A central step towards an understanding of the structure and function of the Escherichia coli ribosome, a large multicomponent assembly, is the elucidation of the spatial arrangement of its 54 proteins and its three rRNA molecules. The structural organization of ribosomal components has been investigated by a number of experimental approaches. Specific antibodies directed against each of the 54 ribosomal proteins of Escherichia coli have been performed to examine antibody-subunit complexes by electron microscopy. The position of the bound antibody, specific for a particular protein, can be determined; it indicates the location of the corresponding protein on the ribosomal surface.The three-dimensional distribution of each of the 21 small subunit proteins on the ribosomal surface has been determined by immuno electron microscopy: the 21 proteins have been found exposed with altogether 43 antibody binding sites. Each one of 12 proteins showed antibody binding at remote positions on the subunit surface, indicating highly extended conformations of the proteins concerned within the 30S ribosomal subunit; the remaining proteins are, however, not necessarily globular in shape (Fig. 1).

Ribosome Structural Organization

1974 ◽  
Vol 32 ◽  
pp. 332-333
Author(s):  
James A. Lake
Keyword(s):  
Ribosomal Proteins ◽  
Structural Organization ◽  
Three Dimensional ◽  
Small Subunit ◽  
Structural Studies ◽  
X Ray Diffraction ◽  
Specific Antibodies ◽  
X Ray ◽  
E Coli ◽  
Complete Sequences

The understanding of ribosome structure has advanced considerably in the last several years. Biochemists have characterized the constituent proteins and rRNA's of ribosomes. Complete sequences have been determined for some ribosomal proteins and specific antibodies have been prepared against all E. coli small subunit proteins. In addition, a number of naturally occuring systems of three dimensional ribosome crystals which are suitable for structural studies have been observed in eukaryotes. Although the crystals are, in general, too small for X-ray diffraction, their size is ideal for electron microscopy.

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