scholarly journals Hydrodynamic descriptions for surface roughness in fracture front propagation

Author(s):  
Abhik Basu ◽  
Bikas K. Chakrabarti

Fracture is ubiquitous in a crystalline material. Inspired by the observed phenomenological similarities between the spatial profile of a fractured surface and velocities in hydrodynamic turbulence, we set up a hydrodynamic description for the dynamics of fracture surface propagation mode I or opening fracture front. We consider several related continuum hydrodynamic models and use them to extract the similarities between the profile of a fractured surface and velocities in hydrodynamic turbulence. We conclude that a fractured surface should be generically self-similar with an underlying multifractal behaviour. This article is part of the theme issue ‘Statistical physics of fracture and earthquakes’.

Author(s):  
Martin Verlaan ◽  
Annette Zijderveld ◽  
Hans de Vries ◽  
Jan Kroos

The accurate forecasting of storm surges is an important issue in the Netherlands. With the emergence of the first numerical hydrodynamic models for surge forecasting at the beginning of the 1980s, new demands and possibilities were raised. This article describes the main phases of the development and the present operational set-up of the Dutch continental shelf model, which is the main hydrodynamic model for storm surges in the Netherlands. It includes a brief discussion of applied data-assimilation techniques, such as Kalman filtering, the model calibration process and some thoughts on quality assurance in an operational environment. After further describing some select recent investigations, the paper concludes with some remarks on future developments in a European context.


2015 ◽  
Author(s):  
Ali Daneshy ◽  
Chad Touchet ◽  
Fred Hoffman ◽  
Mike McKown

Abstract This paper presents the analysis results of 60 single stage fracturing treatments performed in a horizontal well using cemented casing sleeves and a coiled tubing deployed frac isolation system as the completion method. In this carefully set-up and executed treatment, separation between the toe stages was 97 feet, and near the heel it was 55 feet. Pressure data was collected above and below the retrievable plug used for stage isolation. This data was used for analysis of fracturing treatment data which included mode of propagation, completion efficiency, and a rough estimate of fracture orientation. The analysis showed that; There was no interaction between adjacent fractures during five of the sixty fracturing stages. None of these was in the well interval with shorter fracture spacingFracture shadowing occurred during six fracture stages, again none in the shorter spacing intervalMinor cement defects (micro-annuli) caused some fluid migration into the passive segment of the well. This happened in 27 stages. Of these; In eleven cases the cement defects were plugged after a while, causing the migration of fracturing fluid into the passive interval to stop.In sixteen other cases the fluid migration through cement micro-annuli continued during fracturing.During ten stages, defective zone isolation and fluid migration caused a pressure increase of several hundred psi in the passive segment of the well. But this did not result in extension of passive fractures.The volume of migrated slurry due to inadequate zone isolation was mostly a very small fraction of the injected volume.During five stages poor cement quality hampered stage isolation and caused immediate link between adjacent active and passive intervals and extension of passive fractures.The data indicate possible connection between the active and one passive fracture in four stages.Shorter spacing between stages increased the incidents of fluid migration due to poor cement qualityThe fracturing pressure variations during the treatments did not indicate presence of large stress shadowingA rough estimation of fracture orientation indicates that they were likely to be vertical and nearly perpendicular to the wellbore.The fracture growth pattern can best be described as off-balance. To our knowledge, this is the first time existence of direct communication between adjacent fractures has been observed through actual pressure interference data.


2020 ◽  
Vol 22 (3) ◽  
pp. 510-527
Author(s):  
Maarten van Ormondt ◽  
Kees Nederhoff ◽  
Ap van Dongeren

Abstract The open-source program Delft Dashboard (DDB) is a graphical user interface designed to quickly create, edit input parameters and visualize model inputs for a number of hydrodynamic models, using private or publicly available local and global datasets. It includes a number of toolboxes that facilitate the generation of spatially varying inputs. These include new model schematizations (grids, bathymetry, boundary conditions, etc.), cyclonic wind fields and initial tsunami waves. The use of DDB can have significant benefits. It can save modellers considerable time and effort. Furthermore, the automated nature of both data collection and pre-processing within the program reduces the likelihood of errors that could occur when setting up models manually. Three case studies are presented: simulation of tides in the North Sea, storm surge and wave modelling under tropical cyclone conditions and the simulation of a tsunami. The test cases show that models created with DDB can be set up efficiently while maintaining a predictive skill that is only slightly lower than that of extensively calibrated models.


2020 ◽  
Vol 494 (1) ◽  
pp. 1143-1164 ◽  
Author(s):  
David J Barnes ◽  
Rahul Kannan ◽  
Mark Vogelsberger ◽  
Federico Marinacci

ABSTRACT Feedback from accreting supermassive black holes (BHs), active galactic nuclei (AGNs), is now a cornerstone of galaxy formation models. In this work, we present radiation-hydrodynamic simulations of radiative AGN feedback using the novel arepo-rt code. A central BH emits radiation at a constant luminosity and drives an outflow via radiation pressure on dust grains. Utilizing an isolated Navarro–Frenk–White (NFW) halo we validate our set-up in the single- and multiscattering regimes, with the simulated shock front propagation in excellent agreement with the expected analytic result. For a spherically symmetric NFW halo, an examination of the simulated outflow properties with radiation collimation demonstrates a decreasing mass outflow rate and momentum flux, but increasing kinetic power and outflow velocity with decreasing opening angle. We then explore the impact of a central disc galaxy and the assumed dust model on the outflow properties. The contraction of the halo during the galaxy’s formation and modelling the production of dust grains result in a factor 100 increase in the halo’s optical depth. Radiation then couples momentum more efficiently to the gas, driving a stronger shock and producing a mass-loaded $\sim \!10^{3}\, \mathrm{M}_{\odot }\, \mathrm{yr}^{-1}$ outflow with a velocity of $\sim \!2000\, \mathrm{km}\, \mathrm{s}^{-1}$. However, the inclusion of dust destruction mechanisms, like thermal sputtering, leads to the rapid destruction of dust grains within the outflow, reducing its properties below the initial NFW halo. We conclude that radiative AGN feedback can drive outflows, but a thorough numerical and physical treatment is required to assess its true impact.


10.14311/1027 ◽  
2008 ◽  
Vol 48 (4) ◽  
Author(s):  
J. Sokoll ◽  
S. Fingerhuth

1202, Fibonacci set up one of the most interesting sequences in number theory. This sequence can be represented by so-called Fibonacci Numbers, and by a binary sequence of zeros and ones. If such a binary Fibonacci Sequence is played back as an audio file, a very dissonant sound results. This is caused by the “almost-periodic”, “self-similar” property of the binary sequence. The ratio of zeros and ones converges to the golden ratio, as do the primary and secondary spectral components intheir frequencies and amplitudes. These Fibonacci Sequences will be characterized using listening tests and psychoacoustic analyses. 


2011 ◽  
Vol 63 (3) ◽  
pp. 648-688 ◽  
Author(s):  
Sze-Man Ngai

AbstractWe set up a framework for computing the spectral dimension of a class of one-dimensional self-similar measures that are defined by iterated function systems with overlaps and satisfy a family of second-order self-similar identities. As applications of our result we obtain the spectral dimension of important measures such as the infinite Bernoulli convolution associated with the golden ratio and convolutions of Cantor-type measures. The main novelty of our result is that the iterated function systems we consider are not post-critically finite and do not satisfy the well-known open set condition.


1997 ◽  
Vol 11 (13) ◽  
pp. 1519-1544 ◽  
Author(s):  
Yoshiyuki Usami ◽  
Masatoshi Kitaoka

We introduce statistical physics approaches to the traveling salesman problem (TSP). TSP is a kind of combinatorial optimization problem which is known to be difficult to solve exactly for large size systems. We develop a new method for solving the TSP based on an idea of real space renormalization theory. It will be shown that the TSP has self similar characteristics, hence the renormalization frame works well for solving the problem. Statistical physics formalism is also presented on solving the TSP by simulated annealing (SA) algorithm. Analytic expression for temperature dependence of the path length is given and compared to numerical simulation. Throughout this work we will provide a new insight to this kind of optimization problem from a viewpoint of statistical physics.


1989 ◽  
Vol 41 (2) ◽  
pp. 263-280 ◽  
Author(s):  
G. J. Pert

Analytic modelling of laser-produced plasmas has generally been restricted to one-dimensional flow. Multi-dimensional hydrodynamic approximations are available, and are explored in this paper. Two configurations are examined. The explosive mode in which the entire body of material is uniformly heated is treated by the self-similar form, and the aspect ratio of the resulting expansion is determined. Ablative flows can be approximated by the hybrid model, and the self-regulating flow from a solid target can be calculated in this way.


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