scholarly journals Dynamics of wormhole formation in fractured limestones

2019 ◽  
Vol 23 (4) ◽  
pp. 1995-2014 ◽  
Author(s):  
Wolfgang Dreybrodt ◽  
Franci Gabrovšek
Keyword(s):  
Reactive Transport ◽  
Dissolution Kinetics ◽  
Critical Distance ◽  
Homogeneous Distribution ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Single Plane ◽  
One Dimensional ◽  
Aperture Width ◽  
Dissolution Front

Abstract. Reactive transport in porous or fractured media often results in an evolution of highly conductive flow channels, often referred to as “wormholes”. The most spectacular wormholes are caves in fractured limestone terrains. Here, a model of their early evolution is presented. The modeling domain is a two-dimensional square net consisting of one-dimensional fractures intersecting each other in a rectangular grid. Fractures have given width b and length l, and to each fracture a constant aperture width, a (homogeneous net), or an aperture width taken from a lognormal statistical distribution (heterogeneous net) is assigned. The boundary conditions are constant head h at the input driving the water downstream to the output at h=0. Linear dissolution kinetics, controlled by surface kinetics and diffusion, are active. First we discuss the simple case of a homogeneous net. Two steps in its evolution are observed. In the first, all fractures are widened evenly and a homogeneous even dissolution front progresses slowly into the aquifer. The second step is triggered by an instability when, due to small perturbations, some of the foremost fractures gain length compared to the neighboring ones. Then, these fractures discharge flow using the parallel resistances of the net. This way they attract more fresh aggressive water and their propagation is enhanced. Several wormholes (caves) are penetrating into the aquifer but only one reaches the output, whereas the others stop growing due to the redistribution of hydraulic heads caused by the leading wormhole. The mechanisms governing the evolution of a single wormhole are explored by increasing the aperture width of one selected input fracture by Δa≪a. In this case, only one single wormhole is created and inspection of the flow rates along it reveal the mechanism of flow enhancement in detail. If one uses a heterogeneous net, the first step of evolution is suppressed because of the large perturbations, and wormholes start to grow immediately. We have also modeled the case of several competing wormholes in a homogeneous net by inserting appropriate seeds. We find that there is a critical distance between the wormholes. Within this distance only one wormhole survives, whereas there is no interaction between them when they are separated by more than the critical distance. We also answer the following question: why do wormholes in a two-dimensional model exhibit breakthrough times at least 1 order of magnitude smaller than a one-dimensional model representing the aquifer by one single plane-parallel fracture of the same dimensions? Finally, we present several scenarios with non-homogeneous distribution of initial aperture widths. In these, a uniform dissolution front does not develop and wormholes start to grow immediately, which is more likely expected in nature.

Mine Impact Burial Prediction From One to Three Dimensions

2008 ◽  
Vol 62 (1) ◽  
Author(s):  
Peter C. Chu
Keyword(s):  
Three Dimensional ◽  
Time History ◽  
Three Dimensions ◽  
Vertical Position ◽  
Burial Depth ◽  
Prediction Errors ◽  
Two Dimensional ◽  
Dimensional Model ◽  
One Dimensional ◽  
Dimensional Models

The Navy’s mine impact burial prediction model creates a time history of a cylindrical or a noncylindrical mine as it falls through air, water, and sediment. The output of the model is the predicted mine trajectory in air and water columns, burial depth/orientation in sediment, as well as height, area, and volume protruding. Model inputs consist of parameters of environment, mine characteristics, and initial release. This paper reviews near three decades’ effort on model development from one to three dimensions: (1) one-dimensional models predict the vertical position of the mine’s center of mass (COM) with the assumption of constant falling angle, (2) two-dimensional models predict the COM position in the (x,z) plane and the rotation around the y-axis, and (3) three-dimensional models predict the COM position in the (x,y,z) space and the rotation around the x-, y-, and z-axes. These models are verified using the data collected from mine impact burial experiments. The one-dimensional model only solves one momentum equation (in the z-direction). It cannot predict the mine trajectory and burial depth well. The two-dimensional model restricts the mine motion in the (x,z) plane (which requires motionless for the environmental fluids) and uses incorrect drag coefficients and inaccurate sediment dynamics. The prediction errors are large in the mine trajectory and burial depth prediction (six to ten times larger than the observed depth in sand bottom of the Monterey Bay). The three-dimensional model predicts the trajectory and burial depth relatively well for cylindrical, near-cylindrical mines, and operational mines such as Manta and Rockan mines.

Quantum entanglement in some topological insulator models

2019 ◽  
Vol 33 (24) ◽  
pp. 1950284 ◽  
Author(s):  
L. S. Lima
Keyword(s):  
Quantum Entanglement ◽  
Topological Insulator ◽  
Topological Charge ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Model Case ◽  
Topological Transition ◽  
One Dimensional ◽  
Zhang Model ◽  
The One

Quantum entanglement is studied in the neighborhood of a topological transition in some topological insulator models such as the two-dimensional Qi–Wu–Zhang model or Chern insulator. The system describes electrons hopping in two-dimensional chains. For the one-dimensional model case, there exist staggered hopping amplitudes. Our results show a strong effect of sudden variation of the topological charge Q in the neighborhood of phase transition on quantum entanglement for all the cases analyzed.

The Influence of Wood Specimen Surface Coating on Moisture Movement during Drying

Holzforschung ◽  
2002 ◽  
Vol 56 (5) ◽  
pp. 541-546 ◽  
Author(s):  
R. Baronas ◽  
F. Ivanauskas
Keyword(s):  
Surface Coating ◽  
Transverse Section ◽  
Wood Specimen ◽  
Two Dimensional ◽  
Drying Process ◽  
Dimensional Model ◽  
Wood Drying ◽  
Moisture Movement ◽  
One Dimensional ◽  
The One

Summary A model of wood drying under isothermal conditions taking into consideration coating of the surface of a specimen is presented in this paper in a two-dimensional formulation. The influence of the surface coating degree as well as geometrical shape of a wood specimen on the dynamics of drying is investigated. Exponentials, describing the dependence of the halfdrying time on the degree of coating of the edges, as well as on the ratio of the width to the thickness of the transverse section of specimens from the northern red oak (Quercus rubra), are presented for drying from above the fiber saturation point. This paper describes the conditions of usage of the two-dimensional moisture transfer model in contrast to the one-dimensional model for accurate prediction of the drying process taking into consideration the coating of edges of specimens having a rectangular transverse section. A measure of reliability of the one-dimensional model to predict the wood drying process of sawn boards is introduced in this paper.

scholarly journals Detecting isolation by distance using phylogenies of genes.

Genetics ◽  
1990 ◽  
Vol 126 (1) ◽  
pp. 249-260 ◽  
Author(s):  
M Slatkin ◽  
W P Maddison
Keyword(s):  
Migration Rate ◽  
Regression Coefficient ◽  
Isolation By Distance ◽  
Alternative Methods ◽  
Simple Relationship ◽  
Two Dimensional ◽  
Dimensional Model ◽  
One Dimensional ◽  
Structured Population ◽  
Two Dimensional Model

Abstract We introduce a method for analyzing phylogenies of genes sampled from a geographically structured population. A parsimony method can be used to compute s, the minimum number of migration events between pairs of populations sampled, and the value of s can be used to estimate the effective migration rate M, the value of Nm in an island model with local populations of size N and a migration rate m that would yield the same value of s. Extensive simulations show that there is a simple relationship between M and the geographic distance between pairs of samples in one- and two-dimensional models of isolation by distance. Both stepping-stone and lattice models were simulated. If two demes k steps apart are sampled, then, s, the average value of s, is a function only of k/(Nm) in a one-dimensional model and is a function only of k/(Nm)2 in a two-dimensional model. Furthermore, log(M) is approximately a linear function of log(k). In a one-dimensional model, the regression coefficient is approximately -1 and in a two-dimensional model the regression coefficient is approximately -0.5. Using data from several locations, the regression of log(M) on log(distance) may indicate whether there is isolation by distance in a population at equilibrium and may allow an estimate of the effective migration rate between adjacent sampling locations. Alternative methods for analyzing DNA sequence data from a geographically structured population are discussed. An application of our method to the data of R. L. Cann, M. Stoneking and A. C. Wilson on human mitochondrial DNA is presented.

scholarly journals Thermal Analysis of a Double Glazed Window with a Between-Panes Pleated Blind

2021 ◽  
Author(s):  
Rasesh Dalal
Keyword(s):  
Fluid Dynamics ◽  
Thermal Analysis ◽  
Thermal Performance ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Number Range ◽  
One Dimensional ◽  
U Value ◽  
Shading Devices ◽  
The Impact

A simplified two-dimensional numerical model of a window with a between-panes pleated blind has been developed using commercial computational fluid dynamics software. Knowledge of the effect of blinds on the free convection is important for understanding and predicting the impact of shading devices on the overall thermal performance of a window. Numerical results have been obtained for three fill gases (air, argon and krypton) and several blind geometries over the Rayleigh number range 10³ [less than or equal to]Ra[less than or equal to]10[to the exponent of 5]. The results show that pleated blinds can have a strong effect on window thermal performance. In addition, it has been shown that the data from a convection-only model can be combined with a simplified one-dimensional model to estimate the overall U-value of the enclosure. Using this procedure, the convection data can be applied to a window/blind assembly with arbitrary radiation parameters.

scholarly journals Which Task Characteristics Do Students Rely on When They Evaluate Their Abilities to Solve Linear Function Tasks? – A Task-Specific Assessment of Self-Efficacy

2021 ◽  
Vol 12 ◽  
Author(s):  
Katharina Siefer ◽  
Timo Leuders ◽  
Andreas Obersteiner
Keyword(s):  
Linear Function ◽  
Self Efficacy ◽  
Real Life ◽  
Linear Functions ◽  
Task Characteristics ◽  
Two Dimensional ◽  
Dimensional Model ◽  
One Dimensional ◽  
Life Context ◽  
Specific Assessment

Self-efficacy is an important predictor of learning and achievement. By definition, self-efficacy requires a task-specific assessment, in which students are asked to evaluate whether they can solve concrete tasks. An underlying assumption in previous research into such assessments was that self-efficacy is a one-dimensional construct. However, empirical evidence for this assumption is lacking, and research on students’ performance suggests that it depends on various task characteristics (e.g., the representational format). The present study explores the potential multi-dimensionality of self-efficacy in the topic of linear functions. More specifically, we investigate how three task characteristics – (1) the representational format, (2) embedding in a real-life context, or (3) the required operation – are related to students’ self-efficacy. We asked 8th and 9th graders (N = 376) to evaluate their self-efficacy on specific linear function tasks which systematically varied along the three dimensions of task characteristics. Using confirmatory factor analysis, we found that a two-dimensional model which includes the task characteristic of real-life context (i.e., with vs. without a real-life context) fitted the data better than other two-dimensional models or a one-dimensional model. These results suggest that self-efficacy with linear functions is empirically separable with respect to tasks with vs. without a real-life context. This means that in their self-evaluation of linear function tasks students particularly rely on whether or not the linear function task is embedded in a real-life context. This study highlights the fact that even within a specific content domain students’ self-efficacy can be considered a multi-dimensional construct.

Study on the Estimation Error Caused by Using One-Dimensional Model for the Evaluation of Dipole Tracer Test

2010 ◽  
Author(s):  
Yuji Ijiri ◽  
Yumi Naemura ◽  
Kenji Amano ◽  
Keisuke Maekawa ◽  
Atsushi Sawada ◽  
...  
Keyword(s):  
Estimation Error ◽  
Tracer Tests ◽  
Fracture Plane ◽  
Nuclear Waste Repository ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Transport Parameters ◽  
Experimental Conditions ◽  
One Dimensional ◽  
Longitudinal Dispersivity

In-situ tracer tests are a valuable approach to obtain parameters for a performance assessment of nuclear waste repository. A one-dimensional model is simple and is commonly used to identify radionuclide transport parameters by fitting breakthrough curves simulated using the model to those obtained from tracer tests. However, this method can increase uncertainty and introduce errors in the estimated parameters. In particular, such uncertainties and errors will be significant when evaluating parameters for tests conducted in a dipole (two-dimensional) flow field between injection and withdrawal wells. This paper describes a numerical analysis investigation into the effects of various experimental conditions on parameters estimated using a one-dimensional model for cases involving tracer tests in a two-dimensional fracture plane. Results show that longitudinal dispersivity tends to be overestimated by the one-dimensional model analysis. This overestimation is the result of several factors: smaller pumping rate, larger dipole ratio, stronger heterogeneity of the fracture hydraulic conductivity, and greater orthogonally-oriented background groundwater flow. Such information will help us to better plan and design tracer tests at underground research laboratories located in both Mizunami in central Japan and Horonobe in northern Japan. Understanding appropriate experimental conditions will help decrease the uncertainty in the results of tracer tests.

A Two-Dimensional Model of the Fluid Dynamics of an Air Reverser

1998 ◽  
Vol 65 (1) ◽  
pp. 171-177 ◽  
Author(s):  
S. Mu¨ftu¨ ◽  
T. S. Lewis ◽  
K. A. Cole ◽  
R. C. Benson
Keyword(s):  
Design Guidelines ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Web Handling ◽  
One Dimensional ◽  
Air Supply ◽  
Two Dimensional Model ◽  
The One ◽  
The Web

A theoretical analysis of the fluid mechanics of the air cushion of the air reversers used in web-handling systems is presented. A two-dimensional model of the air flow is derived by averaging the equations of conservation of mass and momentum over the clearance between the web and the reverser. The resulting equations are Euler’s equations with nonlinear source terms representing the air supply holes in the surface of the reverser. The equations are solved analytically for the one-dimensional case and numerically for the two-dimensional case. Results are compared with an empirical formula and the one-dimensional airjet theory developed for hovercraft. Conditions that maximize the air pressure supporting the web are analyzed and design guidelines are deduced.

Numerical and Analytical Solutions for Two-Dimensional Gas Distribution in Gas-Loaded Heat Pipes

1989 ◽  
Vol 111 (3) ◽  
pp. 598-604 ◽  
Author(s):  
P. F. Peterson ◽  
C. L. Tien
Keyword(s):  
Heat Pipes ◽  
Computational Effort ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Gas Distribution ◽  
Dimensional Solution ◽  
Integral Analysis ◽  
One Dimensional ◽  
Wide Range ◽  
Design Calculations

This work presents a two-dimensional axisymmetric diffusion model for the non-condensable gas distribution in gas-loaded heat pipes and thermosyphons. The new model, based on an integral analysis, has major advantages over existing, computationally time consuming, two-dimensional models. It has equal accuracy while using only the computational effort required for the cruder one-dimensional model, and also includes the effects of wall conduction and spatial variation of the condenser heat transfer coefficient. To simplify design calculations further an analytic two-dimensional solution is established, which gives excellent results over a wide range of parameters.

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