scholarly journals River landscapes and optimal channel networks

2018 ◽  
Vol 115 (26) ◽  
pp. 6548-6553 ◽  
Author(s):  
Paul Balister ◽  
József Balogh ◽  
Enrico Bertuzzo ◽  
Béla Bollobás ◽  
Guido Caldarelli ◽  
...  
Keyword(s):  
Minimum Energy ◽  
Height Function ◽  
Gravitational Energy ◽  
Constant Factor ◽  
Channel Networks ◽  
Arbitrary Graph ◽  
Tree Structures ◽  
Dimensional Lattice ◽  
Natural Forms ◽  
Flow Directions

We study tree structures termed optimal channel networks (OCNs) that minimize the total gravitational energy loss in the system, an exact property of steady-state landscape configurations that prove dynamically accessible and strikingly similar to natural forms. Here, we show that every OCN is a so-called natural river tree, in the sense that there exists a height function such that the flow directions are always directed along steepest descent. We also study the natural river trees in an arbitrary graph in terms of forbidden substructures, which we call k-path obstacles, and OCNs on a d-dimensional lattice, improving earlier results by determining the minimum energy up to a constant factor for everyd≥2. Results extend our capabilities in environmental statistical mechanics.

scholarly journals Determining flow directions in river channel networks using planform morphology and topology

2020 ◽  
Vol 8 (1) ◽  
pp. 87-102 ◽  
Author(s):  
Jon Schwenk ◽  
Anastasia Piliouras ◽  
Joel C. Rowland
Keyword(s):  
Flow Direction ◽  
Remotely Sensed ◽  
River Channel ◽  
Braided River ◽  
Channel Network ◽  
Channel Networks ◽  
Braided Rivers ◽  
Morphologic Characteristic ◽  
Network Topologies ◽  
Flow Directions

Abstract. The abundance of global, remotely sensed surface water observations has accelerated efforts toward characterizing and modeling how water moves across the Earth's surface through complex channel networks. In particular, deltas and braided river channel networks may contain thousands of links that route water, sediment, and nutrients across landscapes. In order to model flows through channel networks and characterize network structure, the direction of flow for each link within the network must be known. In this work, we propose a rapid, automatic, and objective method to identify flow directions for all links of a channel network using only remotely sensed imagery and knowledge of the network's inlet and outlet locations. We designed a suite of direction-predicting algorithms (DPAs), each of which exploits a particular morphologic characteristic of the channel network to provide a prediction of a link's flow direction. DPAs were chained together to create “recipes”, or algorithms that set all the flow directions of a channel network. Separate recipes were built for deltas and braided rivers and applied to seven delta and two braided river channel networks. Across all nine channel networks, the recipe-predicted flow directions agreed with expert judgement for 97 % of all tested links, and most disagreements were attributed to unusual channel network topologies that can easily be accounted for by pre-seeding critical links with known flow directions. Our results highlight the (non)universality of process–form relationships across deltas and braided rivers.

Atomistic characterization of three-dimensional lattice trapping barriers to brittle fracture

2006 ◽  
Vol 462 (2070) ◽  
pp. 1741-1761 ◽  
Author(s):  
Ting Zhu ◽  
Ju Li ◽  
Sidney Yip
Keyword(s):  
Brittle Fracture ◽  
Crack Front ◽  
Interatomic Potential ◽  
Reaction Pathway ◽  
Minimum Energy ◽  
Three Dimensional ◽  
Pair Formation ◽  
Cleavage Crack ◽  
Dimensional Lattice ◽  
Kink Pair

We present a detailed account of an atomistic study of three-dimensional lattice trapping barriers to brittle fracture in Si. By means of a prototypical interatomic potential model, we map out the molecular details of the evolution of atomically sharp cracks in the (111) cleavage plane with straight crack fronts along the and directions, respectively. The thermally activated processes of bond rupturing along the crack front are quantitatively characterized using a reaction pathway sampling scheme. The calculated minimum energy paths reveal a mechanism of kink-pair formation and migration in facilitating the crack front advancement. We show that the physical origin of directional anisotropy in cleavage crack propagation can be attributed to a difference in the kink-pair formation energy for different crack orientations. The effects of interatomic potentials are delineated by comparing the Stillinger–Weber model with an environment-dependent model.

scholarly journals Determining flow directions in river channel networks using planform morphology and topology

2019 ◽  
Author(s):  
Jon Schwenk ◽  
Anastasia Piliouras ◽  
Joel C. Rowland
Keyword(s):  
Flow Direction ◽  
Remotely Sensed ◽  
River Channel ◽  
Braided River ◽  
Channel Network ◽  
Channel Networks ◽  
Braided Rivers ◽  
Morphologic Characteristic ◽  
Network Topologies ◽  
Flow Directions

Abstract. The abundance of global, remotely-sensed surface water observations has paved the way toward characterizing and modeling how water moves across the Earth's surface through complex channel networks. In particular, deltas and braided river channel networks may contain thousands of links that route water, sediment, and nutrients across landscapes. In order to model flows through channel networks and characterize network structure, the direction of flow for each link within the network must be known. In this work, we propose a rapid, automatic, and objective method to identify flow directions for all links of a channel network using only remotely-sensed imagery and knowledge of the network's inlet and outlet locations. We designed a suite of direction-predicting algorithms (DPAs), each of which exploits a particular morphologic characteristic of the channel network to provide a prediction of a link's flow direction. DPAs were chained together to create “recipes”, or algorithms that set all the flow directions of a channel network. Separate recipes were built for deltas and braided rivers and applied to seven delta and two braided river channel networks. Across all nine channel networks, the recipes' predicted flow directions agreed with expert judgement for 97 % of all tested links, and most disagreements were attributed to unusual channel network topologies that can easily be accounted for by pre-seeding critical links with known flow directions.

scholarly journals On the Gravitational Energy of the Hawking Wormhole

2003 ◽  
Vol 18 (23) ◽  
pp. 4251-4256 ◽  
Author(s):  
H. Culetu
Keyword(s):  
Flat Space ◽  
Gravitational Energy ◽  
Constant Factor ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Conformally Flat ◽  
Order Unity ◽  
Rindler Coordinates ◽  
System Of Particles ◽  
Rindler Acceleration

The surface energy for a conformally flat space–time which represents the Hawking wormhole in spherical (static) Rindler coordinates is computed using the Hawking–Hunter formalism for nonasymptotically flat space–times. The physical gravitational Hamiltonian is proportional to the Rindler acceleration g of the hyperbolic observer and is finite on the event horizon ξ=b (b — the Planck length, ξ — the Minkowski interval). The corresponding temperature of the system of particles associated to the massless scalar field Ψ=1-b2/ξ2, coupled conformally to Einstein's equations, is given by the Davies–Unruh temperature up to a constant factor of order unity.

scholarly journals Average Degree Conditions Forcing a Minor

10.37236/5321 ◽  
2016 ◽  
Vol 23 (1) ◽  
Author(s):  
Daniel J. Harvey ◽  
David R. Wood
Keyword(s):  
Recent Result ◽  
Complete Graph ◽  
Open Problem ◽  
Complete Bipartite Graph ◽  
Constant Factor ◽  
Average Degree ◽  
Sparse Graph ◽  
Arbitrary Graph ◽  
A Minor ◽  
High Degree

Mader first proved that high average degree forces a given graph as a minor. Often motivated by Hadwiger's Conjecture, much research has focused on the average degree required to force a complete graph as a minor. Subsequently, various authors have considered the average degree required to force an arbitrary graph $H$ as a minor. Here, we strengthen (under certain conditions) a recent result by Reed and Wood, giving better bounds on the average degree required to force an $H$-minor when $H$ is a sparse graph with many high degree vertices. This solves an open problem of Reed and Wood, and also generalises (to within a constant factor) known results when $H$ is an unbalanced complete bipartite graph.

A MINIMUM ENERGY DISSIPATION MODEL FOR RIVER NETWORKS AND THEIR ASSOCIATED TOPOGRAPHIES

Fractals ◽  
1993 ◽  
Vol 01 (03) ◽  
pp. 576-584
Author(s):  
T. SUN ◽  
P. MEAKIN ◽  
T. JØSSANG
Keyword(s):  
Energy Dissipation ◽  
Empirical Relationship ◽  
Minimum Energy ◽  
River Networks ◽  
Drainage Basins ◽  
Channel Networks ◽  
Area Distribution ◽  
Universal Power Law ◽  
Dissipation Model ◽  
Minimum Energy Dissipation

The model for the river networks presented here is based on minimum energy dissipation principles. The foundation for this model is the empirical relationship s~Qα between the link slope s in channel networks and the mean annual discharge Q in that link. The associated landscapes were constructed using a range of values for the exponent α. The surfaces appear to be more complex than simple self-affine fractals. The boundaries of drainage basins covering the entire drainage area were found to have an effective fractal dimension about 1.10 for all values of α in the range −1<α<0. A universal power-law size (area) distribution is also found for the drainage basins obtained from this minimum energy dissipation model.

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