Numerical evidence of persisting surface roughness when deposition stops

Abstract Do evolving surfaces become flat or not with time evolving when material deposition stops? As one qualitative exploration of this interesting issue, modified stochastic models for persisting roughness have been proposed by Schwartz and Edwards (2004 Phys. Rev. E 70 061602). In this work, we perform numerical simulations on the modified versions of Edwards–Wilkinson (EW) and Kardar–Parisi–Zhang (KPZ) systems when the angle of repose is introduced. Our results show that the evolving surface always presents persisting roughness during the flattening process, and sand dune-like morphology could gradually appear, even when the angle of repose is very small. Nontrivial scaling properties and differences of evolving surfaces between the modified EW and KPZ systems are also discussed.

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Scaling Properties of Network Traffic

Encyclopedia of Internet Technologies and Applications ◽

10.4018/978-1-59140-993-9.ch068 ◽

2008 ◽

pp. 483-489

Author(s):

David Rincón ◽

Sebastià Sallent

Keyword(s):

Size Distribution ◽

Stochastic Models ◽

Network Traffic ◽

Arrival Rate ◽

Interarrival Time ◽

Statistical Characterization ◽

Scaling Properties ◽

Network Equipment

The availability of good stochastic models of network traffic is the key to developing protocols and services. A precise statistical characterization of packet interarrival time, size distribution, and connection arrival rate help network engineers to design network equipment and evaluate its performance.

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Technique for reflection prospecting in the Rub’ Al‐Khali

Geophysics ◽

10.1190/1.1441377 ◽

1982 ◽

Vol 47 (8) ◽

pp. 1135-1152 ◽

Cited By ~ 16

Author(s):

Don K. Robinson ◽

Moujahed I. Al‐Husseini

Keyword(s):

Average Velocity ◽

Sand Dune ◽

Sand Dunes ◽

Angle Of Repose ◽

Low Velocity ◽

High Quality ◽

Reflected Waves ◽

Common Depth Point ◽

Receiver Arrays

The Rub’ Al‐Khali desert with its extensive and massive sand dunes presents difficult technical and logistic problems for reflection prospecting. The steep angle of repose of the sand dune faces and the low velocity of the air‐filled sand cause significant delays to the reflected waves. In the dunes, in order to maintain the fidelity of both the downgoing and upcoming waves, small dynamite source and receiver arrays are each contoured to a single elevation. In the flat sabkhas, larger arrays are maintained. After application of dune statics (which are derived initially from an average velocity for the sand and then refined with residual refraction statics), the small arrays are summed so as to simulate the larger arrays used on the flat sabkhas. When the terrain is dominated by dunes, increased use of small arrays reduces the maximum spread length to the detriment of the deeper reflections. Where this occurs, a second set of dynamite patterns is fired so as to increase the effective receiver arrays from 120 to 240. In this manner the simulated spread length is maintained at a minimum of 12,000 ft. The traces resulting from the array simulation on the dunes are then gathered, along with the sabkha traces, into mixed fold common‐depth‐point (CDP) gathers and processed conventionally. This technique results in the recording of high‐quality, broadband reflection profiles with improved continuity beneath the dunes.

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High-order evolving surface finite element method for parabolic problems on evolving surfaces

IMA Journal of Numerical Analysis ◽

10.1093/imanum/drx013 ◽

2017 ◽

Vol 38 (1) ◽

pp. 430-459 ◽

Cited By ~ 6

Author(s):

Balázs Kovács

Keyword(s):

Finite Element Method ◽

Finite Element ◽

High Order ◽

Parabolic Problems ◽

Evolving Surface ◽

Evolving Surfaces ◽

Element Method

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A Stefan problem on an evolving surface

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2014.0279 ◽

2015 ◽

Vol 373 (2050) ◽

pp. 20140279 ◽

Cited By ~ 5

Author(s):

Amal Alphonse ◽

Charles M. Elliott

Keyword(s):

Fixed Point ◽

Stefan Problem ◽

Continuous Dependence ◽

Existence Of Solutions ◽

Well Posedness ◽

Duality Method ◽

Uniform Estimates ◽

Natural Treatment ◽

Evolving Surface ◽

Evolving Surfaces

We formulate a Stefan problem on an evolving hypersurface and study the well posedness of weak solutions given L 1 data. To do this, we first develop function spaces and results to handle equations on evolving surfaces in order to give a natural treatment of the problem. Then, we consider the existence of solutions for data; this is done by regularization of the nonlinearity. The regularized problem is solved by a fixed point theorem and then uniform estimates are obtained in order to pass to the limit. By using a duality method, we show continuous dependence, which allows us to extend the results to L 1 data.

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A New Method for Automated Measurement of Sand Dune Migration Based on Multi-Temporal LiDAR-Derived Digital Elevation Models

Remote Sensing ◽

10.3390/rs13163084 ◽

2021 ◽

Vol 13 (16) ◽

pp. 3084

Author(s):

Pinliang Dong ◽

Jisheng Xia ◽

Ruofei Zhong ◽

Zhifang Zhao ◽

Shucheng Tan

Keyword(s):

Sand Dune ◽

Digital Elevation Models ◽

Angle Of Repose ◽

Sensitivity Analyses ◽

Sampling Point ◽

Automated Measurement ◽

Dune Field ◽

Digital Elevation ◽

Multi Temporal ◽

Dune Migration

While remote sensing methods have long been used for coastal and desert sand dune studies, few methods have been developed for the automated measurement of dune migration in large dune fields. To overcome a major limitation of an existing method named “pairs of source and target points (PSTP)”, this paper proposes a toe line tracking (TLT) method for the automated measurement of dune migration rate and direction using multi-temporal digital elevation models (DEM) derived from light detection and ranging (LiDAR) data. Based on a few simple parameters, the TLT method automatically extracts the base level of a dune field and toe lines of individual dunes. The toe line polygons derived from two DEMs are processed using logical operators and other spatial analysis methods implemented in the Python programming language in a geographic information system. By generating thousands of random sampling points along source toe lines, dune migration distances and directions are calculated and saved with the sampling point feature class. The application of the TLT method was demonstrated using multi-temporal LiDAR-derived DEMs for a 9 km by 2.4 km area in the White Sands Dune Field in New Mexico (USA). Dune migration distances and directions for three periods (24 January 2009–26 September 2009, 26 September 2009–6 June 2010, and 24 January 2009–6 January 2010) were calculated. Sensitivity analyses were carried out using different window sizes and toe heights. The results suggest that both PSTP and TLT produce similar sand dune migration rates and directions, but TLT is a more generic method that works for dunes with or without slipfaces that reach the angle of repose.

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Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

Journal of Applied Probability ◽

10.1017/s0021900200003041 ◽

2007 ◽

Vol 44 (02) ◽

pp. 393-408 ◽

Cited By ~ 1

Author(s):

Allan Sly

Keyword(s):

Stochastic Process ◽

Brownian Motion ◽

White Noise ◽

Gaussian Process ◽

Discrete Data ◽

Hölder Exponent ◽

Scaling Properties ◽

Multifractional Brownian Motion ◽

Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

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Advances in Stem Instrumentation for Biology

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100180562 ◽

1990 ◽

Vol 48 (1) ◽

pp. 362-363

Author(s):

J. S. Wall

Keyword(s):

Scanning Transmission Electron Microscope ◽

Carbon Films ◽

Specimen Preparation ◽

Material Deposition ◽

Active User ◽

Percent Improvement ◽

Scanning Transmission ◽

The Moment ◽

Film Substrate ◽

High Level

The forte of the Scanning transmission Electron Microscope (STEM) is high resolution imaging with high contrast on thin specimens, as demonstrated by visualization of single heavy atoms. of equal importance for biology is the efficient utilization of all available signals, permitting low dose imaging of unstained single molecules such as DNA.Our work at Brookhaven has concentrated on: 1) design and construction of instruments optimized for a narrow range of biological applications and 2) use of such instruments in a very active user/collaborator program. Therefore our program is highly interactive with a strong emphasis on producing results which are interpretable with a high level of confidence.The major challenge we face at the moment is specimen preparation. The resolution of the STEM is better than 2.5 A, but measurements of resolution vs. dose level off at a resolution of 20 A at a dose of 10 el/A2 on a well-behaved biological specimen such as TMV (tobacco mosaic virus). To track down this problem we are examining all aspects of specimen preparation: purification of biological material, deposition on the thin film substrate, washing, fast freezing and freeze drying. As we attempt to improve our equipment/technique, we use image analysis of TMV internal controls included in all STEM samples as a monitor sensitive enough to detect even a few percent improvement. For delicate specimens, carbon films can be very harsh-leading to disruption of the sample. Therefore we are developing conducting polymer films as alternative substrates, as described elsewhere in these Proceedings. For specimen preparation studies, we have identified (from our user/collaborator program ) a variety of “canary” specimens, each uniquely sensitive to one particular aspect of sample preparation, so we can attempt to separate the variables involved.

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