scholarly journals Peristatic solutions for finite one- and two-dimensional systems

2016 ◽  
Vol 22 (8) ◽  
pp. 1639-1653 ◽  
Author(s):  
Vinesh V Nishawala ◽  
Martin Ostoja-Starzewski
Keyword(s):  
Numerical Method ◽  
Continuum Mechanics ◽  
Analytical Solutions ◽  
Differential Form ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Nonlocal Continuum ◽  
One Dimensional ◽  
Static Version ◽  
Special Case

Peridynamics is a nonlocal continuum mechanics theory where its governing equation has an integro-differential form. This paper specifically uses bond-based peridynamics. Typically, peridynamic problems are solved via numerical means, and analytical solutions are not as common. This paper analytically evaluates peristatics, the static version of peridynamics, for a finite one-dimensional rod as well as a special case for two dimensions. A numerical method is also implemented to confirm the analytical results.

scholarly journals THE EFFECT OF THE THIRD DIMENSION ON ROUGH SURFACES FORMED BY SEDIMENTING PARTICLES IN QUASI-TWO-DIMENSIONS

2002 ◽  
Vol 16 (08) ◽  
pp. 1217-1223 ◽  
Author(s):  
K. V. MCCLOUD ◽  
M. L. KURNAZ
Keyword(s):  
Two Dimensions ◽  
Scaling Analysis ◽  
Silica Spheres ◽  
Two Dimensional ◽  
One Dimensional ◽  
The Third ◽  
Roughness Exponent ◽  
Third Dimension ◽  
Dimensional Cell ◽  
Roughness Exponents

The roughness exponent of surfaces obtained by dispersing silica spheres into a quasi-two-dimensional cell is examined. The cell consists of two glass plates separated by a gap, which is comparable in size to the diameter of the beads. Previous work has shown that the quasi-one-dimensional surfaces formed have two roughness exponents in two length scales, which have a crossover length about 1 cm. We have studied the effect of changing the gap between the plates to a limit of about twice the diameter of the beads. If the conventional scaling analysis is performed, the roughness exponent is found to be robust against changes in the gap between the plates; however, the possibility that scaling does not hold should be taken seriously.

DIAGRAMS FOR MAGNETOTELLURIC DATA

Geophysics ◽  
1976 ◽  
Vol 41 (4) ◽  
pp. 766-770 ◽  
Author(s):  
F. E. M. Lilley
Keyword(s):  
Impedance Tensor ◽  
Two Dimensional ◽  
Magnetotelluric Data ◽  
One Dimensional ◽  
Magnetic Components ◽  
Strike Direction ◽  
Electric And Magnetic Fields ◽  
The Relationship ◽  
Special Case ◽  
Phase Differences

Observed magnetotelluric data are often transformed to the frequency domain and expressed as the relationship [Formula: see text]where [Formula: see text] [Formula: see text] and [Formula: see text] [Formula: see text] represent electric and magnetic components measured along two orthogonal axes (in this paper, for simplicity, to be north and east, respectively). The elements [Formula: see text] comprise the magnetotelluric impedance tensor, and they are generally complex due to phase differences between the electric and magnetic fields. All quantities in equation (1) are frequency dependent. For the special case of “two‐dimensional” geology (where structure can be described as having a certain strike direction along which it does not vary), [Formula: see text] with [Formula: see text]. For the special case of “one‐dimensional” geology (where structure varies with depth only, as if horizontally layered), [Formula: see text] and [Formula: see text].

An Instrument for One- or Two-Dimensional Tracking

1965 ◽  
Vol 21 (1) ◽  
pp. 307-312
Author(s):  
William C. Roehrig
Keyword(s):  
Low Cost ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Error Signal ◽  
One Dimensional ◽  
Constant Torque ◽  
Sinusoidal Motion ◽  
The Cross ◽  
Target Path

A rugged electro-mechanical tracking apparatus of simple, low-cost construction is described. The apparatus can be used for one-dimensional tracking by connecting only the longitudinal motor, thus forcing the target to move back and forth in either simple sinusoidal motion or according to the sum of two or three sinusoids. The relative phases of the three sinusoids can be rapidly altered, as can the amplitudes (within limits) of each of the sinusoids. The frequency of the sinusoids can be changed either independently or conjointly. By also connecting the cross-feed motor, an essentially unpredictable target path in two dimensions is obtained, and this path can be rapidly altered by changing cams, and/or frequency, amplitude, and phase of the sinusoids. Movement of the cursor is by low, constant torque lathe-type controls. The distance the cursor moves per each rotation of the controls, can be altered for either or both of the controls. A continuous error signal is generated which is directly proportional to the distance the cursor is off target in any direction.

SOLVING THE TWO-DIMENSIONAL INVERSE FRACTAL PROBLEM WITH THE WAVELET TRANSFORM

Fractals ◽  
1996 ◽  
Vol 04 (04) ◽  
pp. 469-475 ◽  
Author(s):  
ZBIGNIEW R. STRUZIK
Keyword(s):  
Wavelet Transform ◽  
Scale Invariance ◽  
Wavelet Decomposition ◽  
Two Dimensions ◽  
The Self ◽  
Continuous Wavelet ◽  
Two Dimensional ◽  
One Dimensional ◽  
Affine Functions ◽  
The One

The methodology of the solution to the inverse fractal problem with the wavelet transform1,2 is extended to two-dimensional self-affine functions. Similar to the one-dimensional case, the two-dimensional wavelet maxima bifurcation representation used is derived from the continuous wavelet decomposition. It possesses translational and scale invariance necessary to reveal the invariance of the self-affine fractal. As many fractals are naturally defined on two-dimensions, this extension constitutes an important step towards solving the related inverse fractal problem for a variety of fractal types.

Two Dimensional Ultrasonic Beam Distortion in the Breast: In Vivo Measurements and Effects

1992 ◽  
Vol 14 (4) ◽  
pp. 398-414 ◽  
Author(s):  
P. D. Freiburger ◽  
D. C. Sullivan ◽  
B. H. LeBlanc ◽  
S. W. Smith ◽  
G. E. Trahey
Keyword(s):  
Two Dimensions ◽  
System Response ◽  
Two Dimensional ◽  
Time Data ◽  
Phase Aberration ◽  
One Dimensional ◽  
Function Generation ◽  
Spread Function ◽  
Generation Computer

Two dimensional arrival time data was obtained for the propagation of ultrasound across the breasts of 7 female volunteers. These profiles were extracted through the use of cross-correlation measurements and a simulated annealing process that maintained phase closure while aligning the data. The phase aberration measured in two dimensions had a larger magnitude than previously reported phase aberration measured in one dimension in the breast A point spread function generation computer program was used to demonstrate the system response degrading effects of the measured phase aberration and the usefulness of current one dimensional phase aberration correction techniques. The results indicate that two dimensional correction algorithms are necessary to restore the system performance losses due to phase aberration.

Unified geometric and analytical treatment of magneto– gasdynamic shocks. Part 2. The shock polars

1973 ◽  
Vol 10 (3) ◽  
pp. 397-423 ◽  
Author(s):  
Lee A. Bertram
Keyword(s):  
Particle Velocity ◽  
Two Dimensional ◽  
Perfect Gas ◽  
Analytical Treatment ◽  
Classification Schemes ◽  
One Dimensional ◽  
The One ◽  
Shock Solution ◽  
Special Case ◽  
Alfven Velocity

Previously derived shock solutions for a perfectly conducting perfect gas are used to compute shock polars for the one-dimensional unsteady and two- dimensional non-aligned shock representations. A new special-case shock solution, having a downstream particle velocity relative to the shock equal to upstream Alfvén velocity, is obtained, in addition to exhaustive analytical classification schemes for the shock polars. Eight classes of one-dimensional polars and twelve classes of two-dimensional polars are identified.

scholarly journals Generative Aspects of Oxide Pictures by Oxide Tile Rewriting Grammar

2019 ◽  
Vol 8 (3) ◽  
pp. 1537-1543
Keyword(s):  
Two Dimensions ◽  
Two Dimensional ◽  
Silicate Network ◽  
Oxygen Ions ◽  
Tiling System ◽  
Higher Dimensional ◽  
Picture Languages ◽  
Rectangular Grids ◽  
Rewriting Rules ◽  
Special Case

In formal languages, picture language is generalization of string language theory to two dimensions. Pictures which may be regarded as two-dimensional objects occur in studies concerning recognition of patterns, images and various computational fields. Several studies have been done for generating and/or recognizing higher dimensional objects using formal models. Tile rewriting grammar (TRG) is yet another model introduced for generating picture languages. TRG combines isometric rewriting rules with the Giammaresi and Restivo’s Tiling system. This rewriting grammar generates spirals, square and rectangular grids. The power of generating pictures by tile rewriting grammar is more than REC .Sweety et al have generated hexagonal pictures, introducing hexagonal Tile Rewriting Grammar. Kuberalet al have introduced Triangular Tile Rewriting Grammar to generate Triangular Pictures. A special class of objects namely Oxide pictures have been of interest recently. Oxide network is a special case of Silicate network. The silicates are a complicated class of minerals made up of tetrahedral silicates. A basic silicate tetrahedron unit SiO4 is formed with Oxygen ions in the corners and a Silicate ion in the center. In a two dimensional plane a ring of tetrahedrons that are shared by Oxygen nodes forms a silicate sheet.In this paper, Oxide Tile Rewriting Grammar (OXTRG) is proposed for generating Oxide pictures. The motivation for the study is derived from the Oxide network which is obtained by deleting all the silicon nodes of a silicate network. Closure properties of OXTRG are discussed. When compared with schemes such as Oxide Tiling System and Oxide Sgraffito Automaton, OXTRG is found to be more powerful.

Sensitivity of horizontal flows to forcing geometry

2001 ◽  
Vol 432 ◽  
pp. 419-441
Author(s):  
ISAO KANDA ◽  
P. F. LINDEN
Keyword(s):  
Reynolds Number ◽  
Analytical Solutions ◽  
Stokes Flow ◽  
Large Reynolds Number ◽  
Two Dimensional ◽  
Vortex Pattern ◽  
Inverse Energy Cascade ◽  
Horizontal Flows ◽  
Source Sink ◽  
Special Case

We investigate the horizontal flow produced by source–sink forcing in a stably stratified fluid. The forcing jets are kept laminar and are placed along the boundary of a square domain. We find that the resultant flow patterns are extremely sensitive to the forcing geometry. The single dominant vortex pattern, interpreted as the result of inverse energy cascade of two-dimensional turbulence in our previous work (Boubnov, Dalziel & Linden 1994), turns out to be a special case. We show that some of the steady patterns resemble the eigenmodes of the Helmholtz equation as the inviscid vorticity equation. Although there are significant discrepancies in the streamfunction vs. vorticity relations between the observed flows and the analytical solutions, we identify the differences as a result of viscous diffusion of vorticity from the source flows. We also study the transition from forced to decaying flow. The flow assumes the properties of Stokes flow at quite large Reynolds number, indicating transformation into patterns with small advective acceleration.

Two-Dimensional Thin-Layer Chromatography on Two-Layer Plates of Amino Acids

1970 ◽  
Vol 16 (8) ◽  
pp. 662-666 ◽  
Author(s):  
F Kraffczyk ◽  
R Helger ◽  
H Lang
Keyword(s):  
Amino Acids ◽  
Thin Layer ◽  
Thin Layer Chromatography ◽  
Two Dimensions ◽  
Two Dimensional ◽  
One Dimensional ◽  
Acid Cation ◽  
Solvent Systems ◽  
Strong Acids ◽  
Layer Chromatography

Abstract Separation of the amino acids in urine by use of thin-layer chromatography (TLC) has hitherto required that the specimen be first desalted and then chromatographed in two dimensions with at least two pairs of developing solvent systems. We wished to simplify both steps. The customary method of desalting on a column is replaced by desalting on a plate that supports a strongly acid cation-exchanger and a cellulose layer. This method, originally developed for one-dimensional TLC, is used here for two-dimensional TLC. Urine is applied to the ion-exchange layer and strong acids and neutral substances are removed with water. The amino acids are then chromatographed into the cellulose layer, and are separated there two dimensionally with a newly devised pair of developing solutions. This pair of solvents separates nearly all of the amino acids in urine.

A Comparison of Diffusion Flame Stability in One and Two Spatial Dimensions Near Cold, Inert Surfaces

2001 ◽  
Author(s):  
Robert Vance ◽  
Indrek S. Wichman
Keyword(s):  
Two Dimensions ◽  
Low Flow ◽  
Dimensional System ◽  
Flame Stability ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
One Dimensional ◽  
Cellular Flames ◽  
The One ◽  
Inert Surfaces

Abstract A linear stability analysis is performed on two simplified models representing a one-dimensional flame between oxidizer and fuel reservoirs and a two-dimensional “edge-flame” between the same reservoirs but above a cold, inert wall. Comparison of the eigenvalue spectra for both models is performed to discern the validity of extending the results from the one-dimensional problem to the two-dimensional problem. Of primary interest is the influence on flame stability of thermal-diffusive imbalances, i.e. non-unity Lewis numbers. Flame oscillations are observed when Le > 1, and cellular flames are witnessed when Le < 1. It is found that when Le > 1 the characteristics of flame behavior are consistent between the two models. Furthermore, when Le < 1, the models are found to be in good agreement with respect to the magnitude of the critical wave numbers. Results from the coarse mesh analysis of the two-dimensional system are presented and compared to the one-dimensional eigenvalue spectra. Additionally, an examination of low reactant convection is undertaken. It is concluded that for low flow rates the behavior in one and two dimensions are similar qualitatively and quantitatively.

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