INVERSE PATCHWORK TRANSFORM

Fractals ◽  
1994 ◽  
Vol 02 (03) ◽  
pp. 429-431
Author(s):  
P. D. CHARLES ◽  
C. A. BROWN ◽  
W. A. JOHNSEN
Keyword(s):  
Surface Topography ◽  
Surface Area ◽  
Patch Size ◽  
Basis Functions ◽  
Patch Area ◽  
Mathematical Basis ◽  
Surface Design ◽  
Surface Data ◽  
Design And Manufacture

The patchwork method uses triangular patches to estimate surface area as a function of patch size. The patch area can be interpreted as a scale of observation. Using the patchwork method, one can identify crossover scales, or thresholds, which distinguish scales where a surface is best described by Euclidean or fractal geometries. An inverse patchwork transform is proposed by which a set of relative areas and crossover data can be transformed to derive topographical data. The inverse patchwork transform and patchwork method provide mathematical basis functions for conversion between two domains-scales of observation and surface topography, providing a system for synthesizing surface data with desired characteristics. This method can also serve as a tool for aiding in surface design and manufacture.

Heat/mass transport in shear flow over a heterogeneous surface with first-order surface-reactive domains

2015 ◽  
Vol 782 ◽  
pp. 260-299 ◽  
Author(s):  
Preyas N. Shah ◽  
Eric S. G. Shaqfeh
Keyword(s):  
Mass Transfer ◽  
Shear Rate ◽  
Shear Flow ◽  
Reaction Rate ◽  
Patch Size ◽  
Patch Area ◽  
First Order ◽  
Effective Boundary ◽  
Order Surface ◽  
Slip Distance

Surfaces that include heterogeneous mass transfer at the microscale are ubiquitous in nature and engineering. Many such media are modelled via an effective surface reaction rate or mass transfer coefficient employing the conventional ansatz of kinetically limited transport at the microscale. However, this assumption is not always valid, particularly when there is strong flow. We are interested in modelling reactive and/or porous surfaces that occur in systems where the effective Damköhler number at the microscale can be $O(1)$ and the local Péclet number may be large. In order to expand the range of the effective mass transfer surface coefficient, we study transport from a uniform bath of species in an unbounded shear flow over a flat surface. This surface has a heterogeneous distribution of first-order surface-reactive circular patches (or pores). To understand the physics at the length scale of the patch size, we first analyse the flux to a single reactive patch. We use both analytic and boundary element simulations for this purpose. The shear flow induces a 3-D concentration wake structure downstream of the patch. When two patches are aligned in the shear direction, the wakes interact to reduce the per patch flux compared with the single-patch case. Having determined the length scale of the interaction between two patches, we study the transport to a periodic and disordered distribution of patches again using analytic and boundary integral techniques. We obtain, up to non-dilute patch area fraction, an effective boundary condition for the transport to the patches that depends on the local mass transfer coefficient (or reaction rate) and shear rate. We demonstrate that this boundary condition replaces the details of the heterogeneous surfaces at a wall-normal effective slip distance also determined for non-dilute patch area fractions. The slip distance again depends on the shear rate, and weakly on the reaction rate, and scales with the patch size. These effective boundary conditions can be used directly in large-scale physics simulations as long as the local shear rate, reaction rate and patch area fraction are known.

Hierarchical Nano/Micro-structured Surfaces with High Surface Area/Volume Ratios

2021 ◽  
pp. 1-36
Author(s):  
Ketki Lichade ◽  
Yizhou Jiang ◽  
Yayue Pan
Keyword(s):  
Surface Structure ◽  
Surface Area ◽  
Light Trapping ◽  
High Surface ◽  
High Surface Area ◽  
Three Dimensional ◽  
Structure Design ◽  
Surface Structures ◽  
Structured Surfaces ◽  
Design And Manufacture

Abstract Recently, many studies have investigated additive manufacturing of hierarchical surfaces with high surface area/volume (SA/V) ratios, and their performance has been characterized for applications in next-generation functional devices. Despite recent advances, it remains challenging to design and manufacture high SA/V ratio structures with desired functionalities. In this study, we established the complex correlations among the SA/V ratio, surface structure geometry, functionality, and manufacturability in the Two-Photon Polymerization (TPP) process. Inspired by numerous natural structures, we proposed a 3-level hierarchical structure design along with the mathematical modeling of the SA/V ratio. Geometric and manufacturing constraints were modeled to create well-defined three-dimensional hierarchically structured surfaces with a high accuracy. A process flowchart was developed to design the proposed surface structures to achieve the target functionality, SA/V ratio, and geometric accuracy. Surfaces with varied SA/V ratios and hierarchy levels were designed and printed. The wettability and antireflection properties of the fabricated surfaces were characterized. It was observed that the wetting and antireflection properties of the 3-level design could be easily tailored by adjusting the design parameter settings and hierarchy levels. Furthermore, the proposed surface structure could change a naturally-hydrophilic surface to near-superhydrophobic. Geometrical light trapping effects were enabled and the antireflection property could be significantly enhanced (>80% less reflection) by the proposed hierarchical surface structures. Experimental results implied the great potential of the proposed surface structures for various applications such as microfluidics, optics, energy, and interfaces.

The Analysis and Design of a New Type Wedge Surfaces of Sprag Overrunning Clutch

2013 ◽  
Vol 823 ◽  
pp. 43-46 ◽  
Author(s):  
Feng Zhang ◽  
Zhi Fu Gao ◽  
Wu Hui Lu
Keyword(s):  
Carrying Capacity ◽  
High Performance ◽  
Failure Modes ◽  
Meaningful Work ◽  
Surface Design ◽  
Analysis And Design ◽  
Wedge Surface ◽  
New Type ◽  
Design And Manufacture ◽  
Working Situation

Sprag overrunning clutch is one of key components in the drive system. Its a meaningful work to design and manufacture high performance sprag clutch to meet the practical working situation. In order to design reliable and durable clutch with good dynamic characteristics, this paper put forward a new type wedge surfaces which is a combination of involute and eccentric arc. On the basis of analysis of a clutch structure, work principles and failure modes, the sprag ,key element of the clutch, was demonstrated the feasibility of involute in the use of wedge surface design by analyzing the characteristics of involute, and the main sprag parameters were designed and analysized. The design of the new wedge surface, increasing the strut angle and effective cam rise, increased carrying capacity, reducing the contact stress, and extending service life, which laid the foundation for the sprag overrunning clutch design improvements.

scholarly journals Bayesian estimation of basal conditions on Rutford Ice Stream, West Antarctica, from surface data

2011 ◽  
Vol 57 (202) ◽  
pp. 315-324 ◽  
Author(s):  
Mélanie Raymond Pralong ◽  
G. Hilmar Gudmundsson
Keyword(s):  
Steady State ◽  
Surface Topography ◽  
Surface Elevation ◽  
Surface Velocity ◽  
West Antarctica ◽  
Elevation Change ◽  
Surface Geometry ◽  
Inference Problem ◽  
Ice Stream ◽  
Surface Data

AbstractThe determination of basal properties on ice streams from surface data is formulated as a Bayesian statistical inference problem. The theory is applied to a flowline on Rutford Ice Stream, West Antarctica. Estimates of bed topography and basal slipperiness are updated using measurements of surface topography and the horizontal and vertical components of the surface velocity. The surface topography is allowed to vary within measurement errors. We calculate the transient evolution of the surface until rates of surface elevation change are within limits given by measurements. For our final estimation of basal properties, modelled rates of elevation change are in full agreement with estimates of surface elevation changes. Results are discarded from a section of the flowline where the distribution of surface residuals is not consistent with error estimates. Apart from a general increase in basal slipperiness toward the grounding line, we find no evidence for any spatial variations in basal slipperiness. In particular, we find that short-scale variability (<10 × ice thickness) in surface topography and surface velocities can be reproduced by the model by variations in basal topography only. Assuming steady-state conditions, an almost perfect agreement is found between modelled and measured surface geometry, suggesting that Rutford Ice Stream is currently close to a steady state.

The effect of patch area on birds in central Australian mulga (Acacia aneura) woodland of different times-since-fire.

2013 ◽  
Vol 19 (1) ◽  
pp. 28 ◽  
Author(s):  
Adam J Leavesley ◽  
Geofferey J Cary
Keyword(s):  
National Park ◽  
Patch Size ◽  
Species Turnover ◽  
Bird Communities ◽  
Positive Density ◽  
Patch Area ◽  
Bird Density ◽  
Key Species ◽  
Fixed Area ◽  
Acacia Aneura

It is often assumed that a fine-scaled mosaic of different times-since-fire supports greater biodiversity than a coarsescaled mosaic — the fire mosaic hypothesis. A potential mechanism of the fire mosaic hypothesis is the effect of area on species diversity. We investigated the effect of patch area on bird communities in mulga (Acacia aneura) woodland in central Australia. The study was conducted at Uluru Kata-Tjuta National Park using 55 fixed-area sites classified to the time since last fire: burnt 2002; burnt 1976 and long unburnt. Birds were surveyed in the winter and spring of 2005 and 2006. Of 20 key species, two showed a positive density-area effect (i.e. higher density in larger patches). Patch area did not affect total bird density or species richness. However, species turnover (ß-diversity) was greater in large patches in the burnt 2002 treatment than it was in small patches. There was no effect of patch area on the composition of the bird communities in any of the time-since-fire classes. We concluded that patch area did affect the distribution of some birds in mulga woodland. However, patch area was not a mechanism of the fire mosaic hypothesis because the effects of patch size tended to increase avian diversity in larger patches rather than small.

scholarly journals Multiscale Model Reduction of the Unsaturated Flow Problem in Heterogeneous Porous Media with Rough Surface Topography

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 904
Author(s):  
Denis Spiridonov ◽  
Maria Vasilyeva ◽  
Eric T. Chung ◽  
Yalchin Efendiev ◽  
Raghavendra Jana
Keyword(s):  
Porous Media ◽  
Boundary Conditions ◽  
Surface Topography ◽  
Rough Surface ◽  
Heterogeneous Porous Media ◽  
Coarse Grid ◽  
Basis Functions ◽  
Richards Equation ◽  
Small Scale ◽  
Fine Grid

In this paper, we consider unsaturated filtration in heterogeneous porous media with rough surface topography. The surface topography plays an important role in determining the flow process and includes multiscale features. The mathematical model is based on the Richards’ equation with three different types of boundary conditions on the surface: Dirichlet, Neumann, and Robin boundary conditions. For coarse-grid discretization, the Generalized Multiscale Finite Element Method (GMsFEM) is used. Multiscale basis functions that incorporate small scale heterogeneities into the basis functions are constructed. To treat rough boundaries, we construct additional basis functions to take into account the influence of boundary conditions on rough surfaces. We present numerical results for two-dimensional and three-dimensional model problems. To verify the obtained results, we calculate relative errors between the multiscale and reference (fine-grid) solutions for different numbers of multiscale basis functions. We obtain a good agreement between fine-grid and coarse-grid solutions.

scholarly journals Discerning the painter’s hand: machine learning on surface topography

2021 ◽  
Author(s):  
Fang Ji ◽  
Michael McMaster ◽  
Samuel Schwab ◽  
Gundeep Singh ◽  
Lauryn Nicole Smith ◽  
...  
Keyword(s):  
Machine Learning ◽  
Surface Topography ◽  
Art History ◽  
Controlled Study ◽  
Art Students ◽  
Surface Data ◽  
Workshop Practice ◽  
Optical Profilometer ◽  
Different Color ◽  
Learning Analysis

Abstract Attribution of paintings is a critical problem in art history. This study extends machine learning analysis to surface topography of painted works. A controlled study of positive attribution was designed with paintings produced by a class of art students. The paintings were scanned using a confocal optical profilometer to produce surface data. The surface data were divided into virtual patches and used to train an ensemble of convolutional neural networks (CNNs) for attribution. Over a range of patch sizes from 0.5 to 60 mm, the resulting attribution was found to be 60 to 96% accurate, and, when comparing regions of different color, was nearly twice as accurate as CNNs using color images of the paintings. Remarkably, short length scales, as small as twice a bristle diameter, were the key to reliably distinguishing among artists. These results show promise for real-world attribution, particularly in the case of workshop practice.

scholarly journals A comparison between solar plage and network properties

2019 ◽  
Vol 630 ◽  
pp. A86 ◽  
Author(s):  
D. Buehler ◽  
A. Lagg ◽  
M. van Noort ◽  
S. K. Solanki
Keyword(s):  
Magnetic Field ◽  
Patch Size ◽  
Line Pair ◽  
Size Distributions ◽  
Patch Area ◽  
Magnetic Structures ◽  
Disc Centre ◽  
Network Properties ◽  
The Mean ◽  
The Continuum

Aims. We compare the properties of kG magnetic structures in the solar network and in active region plage at high spatial resolution. Methods. Our analysis used six SP scans of the solar disc centre aboard Hinode SOT and inverted the obtained spectra of the photospheric 6302 Å line pair using the 2D SPINOR code. Results. Photospheric magnetic field concentrations in network and plage areas are on average 1.5 kG strong with inclinations of 10° −20°, and have < 400 m s−1 internal and 2−3 km s−1 external downflows. At the disc centre, the continuum intensity of magnetic field concentrations in the network are on average 10% brighter than the mean quiet Sun, whilst their plage counterparts are 3% darker. A more detailed analysis revealed that all sizes of individual kG patches in the network have 150 G higher field strengths on average, 5% higher continuum contrasts, and 800 m s−1 faster surrounding downflows than similarly sized patches in the plage. The speed of the surrounding downflows also correlates with the patch area, and patches containing pores can produce supersonic flows exceeding 11 km s−1 in individual pixels. Furthermore, the magnetic canopies of kG patches are on average 9° more horizontal in the plage compared to the network. Conclusions. Most of the differences between the network and plage are due to their different patch size distributions, but the intrinsic differences between similarly sized patches likely results from the modification of the convection photospheric convection with increasing amounts of magnetic flux.

Optimisation of the geometry of axisymmetric point-absorber wave energy converters

2021 ◽  
Vol 933 ◽  
Author(s):  
Emma C. Edwards ◽  
Dick K.-P. Yue
Keyword(s):  
Surface Area ◽  
Wave Energy ◽  
Basis Functions ◽  
Motion Constraints ◽  
Point Absorber ◽  
Wave Energy Converters ◽  
Rigorous Framework ◽  
Point Absorbers ◽  
Well Posed ◽  
Energy Converters

We propose a scientifically rigorous framework to find realistic optimal geometries of wave energy converters (WECs). For specificity, we assume WECs to be axisymmetric point absorbers in a monochromatic unidirectional incident wave, all within the context of linearised potential theory. We consider separately the problem of a WEC moving and extracting wave energy in heave only and then the more general case of motion and extraction in combined heave, surge and pitch. We describe the axisymmetric geometries using polynomial basis functions, allowing for discontinuities in slope. Our framework involves ensuring maximum power, specifying practical motion constraints and then minimising surface area (as a proxy for cost). The framework is robust and well-posed, and the optimisation produces feasible WEC geometries. Using the proposed framework, we develop a systematic computational and theoretical approach, and we obtain results and insights for the optimal WEC geometries. The optimisation process is sped up significantly by a new theoretical result to obtain roots of the heave resonance equation. For both the heave-only, and the heave-surge-pitch combined problems, we find that geometries which protrude outward below the waterline are generally optimal. These optimal geometries have up to 73 % less surface area and 90 % less volume than the optimal cylinders which extract the same power.

Cubic Uniform B-Spline Curve and Surface with Multiple Shape Parameters

2014 ◽  
Vol 543-547 ◽  
pp. 1860-1863
Author(s):  
Xi Wang ◽  
Cui Cui Gao ◽  
Chen Jiang
Keyword(s):  
Shape Control ◽  
Basis Functions ◽  
Control Parameters ◽  
Shape Parameters ◽  
Surface Design ◽  
Local Shape ◽  
B Spline ◽  
Spline Curves ◽  
Curve Fit ◽  
Polynomial Curve

In order to construct B-spline curves with local shape control parameters, a class of polynomial basis functions with two local shape parameters is presented. Properties of the proposed basis functions are analyzed and the corresponding piecewise polynomial curve is constructed with two local shape control parameters accordingly. In particular, the G1 continuous and the shapes of other segments of the curve can remain unchangeably during the manipulation on the shape of each segment on the curve. Numerical examples illustrate that the constructed curve fit to the control polygon very well. Furthermore, its applications in curve design is discussed and an extend application on surface design is also presented. Modeling examples show that the new curve is very valuable for the design of curves and surfaces.

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