A New Empirical Relation for Free Surface Roughening

2011 ◽  
Vol 133 (1) ◽  
Author(s):  
Sergei Alexandrov ◽  
Ken-Ichi Manabe ◽  
Tsuyoshi Furushima
Keyword(s):  
Free Surface ◽  
Dimensional Space ◽  
Empirical Relation ◽  
Three Dimensional ◽  
Geometric Interpretation ◽  
Surface Roughening ◽  
Material Surface ◽  
Reasonable Assumption ◽  
Axis Of Symmetry ◽  
Geometric Surface

A new empirical relation for the conventional measures of free surface roughness is proposed. Its geometric interpretation is a surface in three-dimensional space. A set of tests feasible for practical realization is discussed. Some available experimental and numerical results are used to reveal various qualitative features of the geometric surface. In particular, a reasonable assumption is that it is a ruled surface for a class of materials. A typical cross section of the surface, which is a curve, has an axis of symmetry if the roughening rate is independent of the sense of the strain rate normal to the material surface, where the roughness parameters should be predicted. The curve has a minimum at the axis of symmetry. Finally, there are two points, where the curve has a maximum. A simple analytic expression to specify the relation proposed for a given material is provided to fit experimental data.

scholarly journals Powers of Elliptic Scator Numbers

2021 ◽  
Author(s):  
Manuel Fernandez-Guasti
Keyword(s):  
Rational Number ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Geometric Interpretation ◽  
Two Dimensional ◽  
Closed Curves ◽  
Complex Algebra ◽  
The Real ◽  
Polar Representation ◽  
Three Dimensional Space

Elliptic scator algebra is possible in 1+n dimensions, n∈N. It is isomorphic to complex algebra in 1+1 dimensions, when the real part and any one hypercomplex component are considered. It is endowed with two representations: an additive one, where the scator components are represented as a sum; and a polar representation, where the scator components are represented as products of exponentials. Within the scator framework, De Moivre’s formula is generalized to 1+n dimensions in the so called victoria equation. This novel formula is then used to obtain compact expressions for the integer powers of scator elements. A scator in S1+n can be factored into a product of n scators that are geometrically represented as its projections onto n two dimensional planes. A geometric interpretation of scator multiplication in terms of rotations with respect to the scalar axis is expounded. The powers of scators, when the ratio of their director components is a rational number, lie on closed curves. For 1+2 dimensional scators, twisted curves in a three dimensional space are obtained. Collecting previous results, it is possible to evaluate the exponential of a scator element in 1+2 dimensions.

scholarly journals Powers of Elliptic Scator Numbers

Axioms ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 250
Author(s):  
Manuel Fernandez-Guasti
Keyword(s):  
Rational Number ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Geometric Interpretation ◽  
Two Dimensional ◽  
Closed Curves ◽  
Complex Algebra ◽  
Polar Representation ◽  
De Moivre’S Formula ◽  
Three Dimensional Space

Elliptic scator algebra is possible in 1+n dimensions, n∈N. It is isomorphic to complex algebra in 1 + 1 dimensions, when the real part and any one hypercomplex component are considered. It is endowed with two representations: an additive one, where the scator components are represented as a sum; and a polar representation, where the scator components are represented as products of exponentials. Within the scator framework, De Moivre’s formula is generalized to 1+n dimensions in the so called Victoria equation. This novel formula is then used to obtain compact expressions for the integer powers of scator elements. A scator in S1+n can be factored into a product of n scators that are geometrically represented as its projections onto n two dimensional planes. A geometric interpretation of scator multiplication in terms of rotations with respect to the scalar axis is expounded. The powers of scators, when the ratio of their director components is a rational number, lie on closed curves. For 1 + 2 dimensional scators, twisted curves in a three dimensional space are obtained. Collecting previous results, it is possible to evaluate the exponential of a scator element in 1 + 2 dimensions.

Three-Dimensional Numerical Modeling of Pier Scour Under Current and Waves Using Level-Set Method

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Mohammad Saud Afzal ◽  
Hans Bihs ◽  
Arun Kamath ◽  
Øivind A. Arntsen
Keyword(s):  
Free Surface ◽  
Level Set Method ◽  
Level Set ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Reasonable Assumption ◽  
Cfd Model ◽  
Time Step ◽  
Pier Scour

A three-dimensional (3D) computational fluid dynamics (CFD) model is used to calculate the scour and the deposition pattern around a pier for two different boundary conditions: constant discharge and regular waves. The CFD model solves Reynolds-Averaged Navier–Stokes (RANS) equations in all three dimensions. The location of the free-surface is represented using the level-set method (LSM), which calculates the complex motion of the free-surface in a very realistic manner. For the implementation of waves, the CFD code is used as a numerical wave tank. For the geometric representation of the moveable sediment bed, the LSM is used. The numerical results for the local scour prediction are compared with physical experiments. The decoupling of the hydrodynamic and the morphodynamic time step is tested and found to be a reasonable assumption. For the two situations of local pier scour under current and wave conditions, the numerical model predicts the general evolution (geometry, location, and maximum scour depth) and time development of the scour hole accurately.

Visualization during Crystallization in Minkowski Spacetime

2017 ◽  
Vol 269 ◽  
pp. 7-13
Author(s):  
Vitaliy S. Borovik ◽  
Vitaliy V. Borovik ◽  
Dmitry A. Skorobogatchenko
Keyword(s):  
Crystallization Process ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Minkowski Spacetime ◽  
Model Space ◽  
Geometric Interpretation ◽  
Software Systems ◽  
Multidimensional Space ◽  
Factors Affecting ◽  
Minkowski Space Time

It was achieved a visual representation of information about the crystallization process in the multidimensional space, which creates prerequisites for the development of software systems to solve a wide class of problems. With the geometric interpretation Minkowski space-time, quasi-Lorentz and Einstein's concept concerning the concept of giving time physical sense, simulated the process of formation of crystals in the four-dimensional space. The 4D model space combines the physical three-dimensional space of the factors affecting the formation of crystals, and time. Visualization of the crystallization process in spacetime plays an important role, as having great cognitive and probative value, and contributes to a better understanding of crystallization processes, creates conditions to control the properties of materials in the process of crystallization.

scholarly journals Granular flow in equilibrium with the bottom: experimental analysis and theoretical prediction

2002 ◽  
Vol 9 (3/4) ◽  
pp. 207-220 ◽  
Author(s):  
B. Zanuttigh ◽  
A. Lamberti
Keyword(s):  
Free Surface ◽  
Granular Flow ◽  
Empirical Relation ◽  
Three Dimensional ◽  
Velocity Profiles ◽  
Surface Velocity ◽  
Wave Effects ◽  
Wave Development ◽  
Semi Empirical ◽  
Supercritical Flows

Abstract. The paper presents measurements performed on the granular flow that develops in a drum partially filled with sand grains and rotating at various speeds. The aims of the paper are: to provide experimental evidence and measurements on grain flow in a drum; to compare theoretical and experimental velocity profiles; to point out discrepancies among theory and experiments. Velocity and "temperature" profiles were obtained with a Laser Doppler Anemometer (LDA) in the mid-section of the stream, where the flow is usually uniform; image analysis and visual observations of the flow were also carried out to evaluate the local slope, the depths of the characteristic flow regions and the concentration of the granular material. A semi-empirical relation that fits the experimental velocity profiles is presented and compared with Takahashi's velocity distributions for rigid and erodible bed. As proven by the distributions of free surface elevation, velocity, volumetric concentration and grain size across the drum, the three-dimensional nature of the flow field is not negligible. By increasing the drum rotation speed, in correspondence with critical and supercritical flows, changes in the flow regime are observed with formation of quasi-stationary surface waves. Wave development is described by analysing the extension and form of the experimental and theoretical velocity profiles. Wave effects on measurements are quantified and checked comparing the free-surface velocity-discharge relation obtained from experiments and from Takahashi's model for erodible bed.

scholarly journals MESOSCALE DEFORMATION-INDUCED SURFACE PHENOMENA IN LOADED POLYCRYSTALS

2021 ◽  
Vol 19 (2) ◽  
pp. 187
Author(s):  
Varvara Romanova ◽  
Ruslan Balokhonov ◽  
Olga Zinovieva
Keyword(s):  
Free Surface ◽  
Plastic Strain ◽  
Grain Boundaries ◽  
Uniaxial Tension ◽  
Three Dimensional ◽  
Grain Structure ◽  
Surface Roughening ◽  
Surface Phenomena ◽  
Stress Concentrations

The paper reviews the results of numerical analyses for the micro-and mesoscale deformation-induced surface phenomena in three-dimensional polycrystals with the explicit account for the grain structure. The role of the free surface and grain boundaries in the appearance of the grain-scale stress concentrations and plastic strain nucleation is illustrated on the examples of aluminum polycrystals. Special attention is paid to the discussion of mesoscale deformation-induced surface roughening under uniaxial tension.

Three Dimensional structure and organization of diploid chromosomes by optical section microscopy

1987 ◽  
Vol 45 ◽  
pp. 633-635
Author(s):  
David A. Agard ◽  
Yasushi Hiraoka ◽  
John W. Sedat
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Developmental State ◽  
Mitotic Cell ◽  
Biological Properties ◽  
Dimensional Structure ◽  
Specific Gene ◽  
Three Dimensional Structure ◽  
Complementary Techniques ◽  
Dynamic Structures

In an effort to understand the complex relationship between structure and biological function within the nucleus, we have embarked on a program to examine the three-dimensional structure and organization of Drosophila melanogaster embryonic chromosomes. Our overall goal is to determine how DNA and proteins are organized into complex and highly dynamic structures (chromosomes) and how these chromosomes are arranged in three dimensional space within the cell nucleus. Futher, we hope to be able to correlate structual data with such fundamental biological properties as stage in the mitotic cell cycle, developmental state and transcription at specific gene loci.Towards this end, we have been developing methodologies for the three-dimensional analysis of non-crystalline biological specimens using optical and electron microscopy. We feel that the combination of these two complementary techniques allows an unprecedented look at the structural organization of cellular components ranging in size from 100A to 100 microns.

Diffraction contrast of dislocations in icosahedral quasicrystals

1990 ◽  
Vol 48 (4) ◽  
pp. 454-455
Author(s):  
K. Urban ◽  
Z. Zhang ◽  
M. Wollgarten ◽  
D. Gratias
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Complete Characterization ◽  
Extinction Condition ◽  
Burgers Vector ◽  
Diffraction Contrast ◽  
Lattice Geometry ◽  
Reference Space ◽  
Icosahedral Quasicrystals ◽  
The One

Recently dislocations have been observed by electron microscopy in the icosahedral quasicrystalline (IQ) phase of Al65Cu20Fe15. These dislocations exhibit diffraction contrast similar to that known for dislocations in conventional crystals. The contrast becomes extinct for certain diffraction vectors g. In the following the basis of electron diffraction contrast of dislocations in the IQ phase is described. Taking account of the six-dimensional nature of the Burgers vector a “strong” and a “weak” extinction condition are found.Dislocations in quasicrystals canot be described on the basis of simple shear or insertion of a lattice plane only. In order to achieve a complete characterization of these dislocations it is advantageous to make use of the one to one correspondence of the lattice geometry in our three-dimensional space (R3) and that in the six-dimensional reference space (R6) where full periodicity is recovered . Therefore the contrast extinction condition has to be written as gpbp + gobo = 0 (1). The diffraction vector g and the Burgers vector b decompose into two vectors gp, bp and go, bo in, respectively, the physical and the orthogonal three-dimensional sub-spaces of R6.

Flavin radicals, conformational sampling and robust design principles in interprotein electron transfer: the trimethylamine dehydrogenase-electron-transferring flavoprotein complex

2004 ◽  
Vol 71 ◽  
pp. 1-14
Author(s):  
David Leys ◽  
Jaswir Basran ◽  
François Talfournier ◽  
Kamaldeep K. Chohan ◽  
Andrew W. Munro ◽  
...  
Keyword(s):  
Electron Transfer ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Kinetic Studies ◽  
Molecular Assembly ◽  
Conformational Sampling ◽  
Trimethylamine Dehydrogenase ◽  
Key Residues ◽  
Electron Transferring Flavoprotein ◽  
Electron Transfer Complex

TMADH (trimethylamine dehydrogenase) is a complex iron-sulphur flavoprotein that forms a soluble electron-transfer complex with ETF (electron-transferring flavoprotein). The mechanism of electron transfer between TMADH and ETF has been studied using stopped-flow kinetic and mutagenesis methods, and more recently by X-ray crystallography. Potentiometric methods have also been used to identify key residues involved in the stabilization of the flavin radical semiquinone species in ETF. These studies have demonstrated a key role for 'conformational sampling' in the electron-transfer complex, facilitated by two-site contact of ETF with TMADH. Exploration of three-dimensional space in the complex allows the FAD of ETF to find conformations compatible with enhanced electronic coupling with the 4Fe-4S centre of TMADH. This mechanism of electron transfer provides for a more robust and accessible design principle for interprotein electron transfer compared with simpler models that invoke the collision of redox partners followed by electron transfer. The structure of the TMADH-ETF complex confirms the role of key residues in electron transfer and molecular assembly, originally suggested from detailed kinetic studies in wild-type and mutant complexes, and from molecular modelling.

Sign in / Sign up

Export Citation Format

Share Document