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.

Two-dimensional analysis of spatial pattern in vegetation for site comparison

1990 ◽  
Vol 68 (1) ◽  
pp. 149-158 ◽  
Author(s):  
M. R. T. Dale
Keyword(s):  
Spatial Pattern ◽  
Dimensional Analysis ◽  
Satellite Imagery ◽  
Two Dimensions ◽  
Vegetation Classification ◽  
New Method ◽  
Two Dimensional ◽  
Vegetation Composition ◽  
Artificial Data ◽  
Rectangular Grids

A new method for the analysis of spatial pattern in two dimensions is described. The technique uses data collected in square or rectangular grids of quadrats to examine the scale of pattern in vegetation, no matter how the grids are oriented with respect to the pattern. Its usefulness is demonstrated by application to artificial data. The method is also applied to vegetation classification data derived from LANDSAT TM satellite imagery of a valley in the Yukon, Canada, in which the effects of experimental manipulations on boreal communities are being studied. A set of 2 × 2 km squares of the valley were selected for analysis in which the vegetation composition squares varies considerably. The analysis shows that most of the squares had one and only one scale of two dimensional pattern, consistently in the range of 360–780 m.

EXPLORING INSIDE TILING RECOGNIZABLE PICTURE LANGUAGES TO FIND DETERMINISTIC SUBCLASSES

2011 ◽  
Vol 22 (07) ◽  
pp. 1519-1532
Author(s):  
DORA GIAMMARRESI
Keyword(s):  
Two Dimensions ◽  
Two Dimensional ◽  
Picture Languages

Tiling recognizable two-dimensional languages, also known as REC, generalize recognizable string languages to two dimensions and share with them several theoretical properties. Nevertheless family REC is not closed under complementation and this implies that it is intrinsically non-deterministic. We consider different notions of unambiguity and determinism and the corresponding REC subclasses: they define a hierarchy inside REC. We show that some definitions of unambiguity are equivalent to particular notions of determinism and therefore the corresponding classes have linear parsing algorithms and are closed under complementation.

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.

Response Curves for Cellular Automata in One and Two Dimensions

2010 ◽  
Vol 1 (3) ◽  
pp. 85-99 ◽  
Author(s):  
Henryk Fuks ◽  
Andrew Skelton
Keyword(s):  
Cellular Automata ◽  
Response Curve ◽  
Initial Density ◽  
Two Dimensions ◽  
Initial Configuration ◽  
Two Dimensional ◽  
Response Curves ◽  
Special Case

In this paper, the authors consider the problem of computing a response curve for binary cellular automata, that is, the curve describing the dependence of the density of ones after many iterations of the rule on the initial density of ones. The authors demonstrate how this problem could be approached using rule 130 as an example. For this rule, preimage sets of finite strings exhibit recognizable patterns; therefore, it is possible to compute both cardinalities of preimages of certain finite strings and probabilities of occurrence of these strings in a configuration obtained by iterating a random initial configuration n times. Response curves can be rigorously calculated in both one- and two-dimensional versions of CA rule 130. The authors also discuss a special case of totally disordered initial configurations, that is, random configurations where the density of ones and zeros are equal to 1/2.

Response Curves for Cellular Automata in One and Two Dimensions

2012 ◽  
pp. 291-305
Author(s):  
Henryk Fuks ◽  
Andrew Skelton
Keyword(s):  
Cellular Automata ◽  
Response Curve ◽  
Initial Density ◽  
Two Dimensions ◽  
Initial Configuration ◽  
Two Dimensional ◽  
Response Curves ◽  
Special Case

In this paper, the authors consider the problem of computing a response curve for binary cellular automata, that is, the curve describing the dependence of the density of ones after many iterations of the rule on the initial density of ones. The authors demonstrate how this problem could be approached using rule 130 as an example. For this rule, preimage sets of finite strings exhibit recognizable patterns; therefore, it is possible to compute both cardinalities of preimages of certain finite strings and probabilities of occurrence of these strings in a configuration obtained by iterating a random initial configuration n times. Response curves can be rigorously calculated in both one- and two-dimensional versions of CA rule 130. The authors also discuss a special case of totally disordered initial configurations, that is, random configurations where the density of ones and zeros are equal to 1/2.

Urbanicity, City Delegations, and Two-Dimensional Liberalism

2018 ◽  
Author(s):  
Thomas K. Ogorzalek
Keyword(s):  
National Level ◽  
Two Dimensions ◽  
Political Order ◽  
Two Dimensional ◽  
Local Institutions ◽  
Horizontal Integration ◽  
National Politics ◽  
United Front ◽  
Strategies For Success

This theoretical chapter develops the argument that the conditions of cities—large, densely populated, heterogeneous communities—generate distinctive governance demands supporting (1) market interventions and (2) group pluralism. Together, these positions constitute the two dimensions of progressive liberalism. Because of the nature of federalism, such policies are often best pursued at higher levels of government, which means that cities must present a united front in support of city-friendly politics. Such unity is far from assured on the national level, however, because of deep divisions between and within cities that undermine cohesive representation. Strategies for success are enhanced by local institutions of horizontal integration developed to address the governance demands of urbanicity, the effects of which are felt both locally and nationally in the development of cohesive city delegations and a unified urban political order capable of contending with other interests and geographical constituencies in national politics.

scholarly journals Onset of Convection in Two-Dimensional Porous Cavities with Open and Conducting Boundaries

2021 ◽  
Vol 136 (3) ◽  
pp. 791-812
Author(s):  
Peder A. Tyvand ◽  
Jonas Kristiansen Nøland
Keyword(s):  
Critical Rayleigh Number ◽  
Numerical Results ◽  
Temperature Perturbation ◽  
Two Dimensional ◽  
Onset Of Convection ◽  
Order Problem ◽  
Fourth Order Problem ◽  
Thermally Conducting ◽  
Perturbation Pressure ◽  
Special Case

AbstractThe onset of thermal convection in two-dimensional porous cavities heated from below is studied theoretically. An open (constant-pressure) boundary is assumed, with zero perturbation temperature (thermally conducting). The resulting eigenvalue problem is a full fourth-order problem without degeneracies. Numerical results are presented for rectangular and elliptical cavities, with the circle as a special case. The analytical solution for an upright rectangle confirms the numerical results. Streamlines penetrating the open cavities are plotted, together with the isotherms for the associated closed thermal cells. Isobars forming pressure cells are depicted for the perturbation pressure. The critical Rayleigh number is calculated as a function of geometric parameters, including the tilt angle of the rectangle and ellipse. An improved physical scaling of the Darcy–Bénard problem is suggested. Its significance is indicated by the ratio of maximal vertical velocity to maximal temperature perturbation.

scholarly journals Interface Roughening in Two Dimensions

2021 ◽  
Vol 182 (3) ◽  
Author(s):  
Gernot Münster ◽  
Manuel Cañizares Guerrero
Keyword(s):  
Field Theory ◽  
Monte Carlo ◽  
Capillary Wave ◽  
System Size ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Wave Approximation ◽  
Statistical Field ◽  
Statistical Field Theory ◽  
Interface Roughening

AbstractRoughening of interfaces implies the divergence of the interface width w with the system size L. For two-dimensional systems the divergence of $$w^2$$ w 2 is linear in L. In the framework of a detailed capillary wave approximation and of statistical field theory we derive an expression for the asymptotic behaviour of $$w^2$$ w 2 , which differs from results in the literature. It is confirmed by Monte Carlo simulations.

scholarly journals Is contact angle a cause or an effect? – A cautionary tale

2020 ◽  
Vol 146 ◽  
pp. 03004
Author(s):  
Douglas Ruth
Keyword(s):  
Contact Angle ◽  
Solid Surface ◽  
Contact Angles ◽  
Two Dimensions ◽  
Experimental Results ◽  
Flow In Porous Media ◽  
Two Dimensional ◽  
Wide Range ◽  
Fluid Drop ◽  
Surrounding Fluid

The most influential parameter on the behavior of two-component flow in porous media is “wettability”. When wettability is being characterized, the most frequently used parameter is the “contact angle”. When a fluid-drop is placed on a solid surface, in the presence of a second, surrounding fluid, the fluid-fluid surface contacts the solid-surface at an angle that is typically measured through the fluid-drop. If this angle is less than 90°, the fluid in the drop is said to “wet” the surface. If this angle is greater than 90°, the surrounding fluid is said to “wet” the surface. This definition is universally accepted and appears to be scientifically justifiable, at least for a static situation where the solid surface is horizontal. Recently, this concept has been extended to characterize wettability in non-static situations using high-resolution, two-dimensional digital images of multi-component systems. Using simple thought experiments and published experimental results, many of them decades old, it will be demonstrated that contact angles are not primary parameters – their values depend on many other parameters. Using these arguments, it will be demonstrated that contact angles are not the cause of wettability behavior but the effect of wettability behavior and other parameters. The result of this is that the contact angle cannot be used as a primary indicator of wettability except in very restricted situations. Furthermore, it will be demonstrated that even for the simple case of a capillary interface in a vertical tube, attempting to use simply a two-dimensional image to determine the contact angle can result in a wide range of measured values. This observation is consistent with some published experimental results. It follows that contact angles measured in two-dimensions cannot be trusted to provide accurate values and these values should not be used to characterize the wettability of the system.

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