Finger Growth and Selection in a Poisson Field

McDonald, N. Robb

doi:10.1007/s10955-019-02454-6

Cited by 3 publications

(2 citation statements)

References 15 publications

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“…As noted in Ref 44 , such an approach provides also another method of regularizing the Laplacian growth at short wavelengths, without the need of introducing the surface tension. This model has been used for the analysis of fingered growth in both the Laplacian [45][46][47][48] and Poissonian fields 49,50 .…”

Section: The Modelmentioning

confidence: 99%

Through history to growth dynamics: deciphering the evolution of spatial networks

Żukowski

Morawiecki

Seybold

et al. 2022

Sci Rep

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Many ramified, network-like patterns in nature, such as river networks or blood vessels, form as a result of unstable growth of moving boundaries in an external diffusive field. Here, we pose the inverse problem for the network growth—can the growth dynamics be inferred from the analysis of the final pattern? We show that by evolving the network backward in time one can not only reconstruct the growth rules but also get an insight into the conditions under which branch splitting occurs. Determining the growth rules from a single snapshot in time is particularly important for growth processes so slow that they cannot be directly observed, such as growth of river networks and deltas or cave passages. We apply this approach to analyze the growth of a real river network in Vermont, USA. We determine its growth rule and argue that branch splitting events are triggered by an increase in the tip growth velocity.

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Section: The Modelmentioning

confidence: 99%

Through history to growth dynamics: deciphering the evolution of spatial networks

Żukowski

Morawiecki

Seybold

et al. 2022

Sci Rep

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“…Physically, accretion results in groundwater mounds whose summits hydraulically command the regional discharge zones (the curve G in Figure 1, see e.g., [31]). Analytical and numerical solutions to these BVPs are used in groundwater hydrology, agricultural and geotechncial engineering, geomorphology, among others (see e.g., [20,[25][26][27][32][33][34][35][36][37]). If wells are pumped in D, the mound is drained causing a near-well drawdown of the water table.…”

Section: F I G U R E 1 Plan (Aerial) View Of An Unconfined Aquifermentioning

confidence: 99%

The Saint‐Venant type isoperimetric inequalities for assessing saturated water storage in lacunary shallow perched aquifers

Avkhadiev

Kacimov

2022

Z Angew Math Mech

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The Dupuit-Forchheimer (DF) approximation for unconfined groundwater flows is reduced to 2D Poisson's equation (PE), the right hand side of which involves an intensive evapotranspiration (ET) rate. A shallow water table dips inward from a constant piezometric head boundary (closed curve) such that a "dry gap," demarcated by another closed curve (unknown front), may emerge. Apriori estimates of the volume of the saturated zone and of the "dry gap" area are important for water resources management in drylands. We use the results from the theory of linear elasticity, torsion of elastic bars, for which PE is solved for the Prandtl function. Using the Poincaré metrics with the Gaussian constant curvature 𝑐 = −4, isoperimetric inequalities are obtained for steady-state DF flows. Conformal moments and confromal radii of the domains and 2-D Hardy's type inequalities in domains, modeling the Saint Venant bar torsion problem, are involved in the obtained estimates. The studied boundary value problems (BVPs) are nonlinear for ET rates depending on the depth of the water table.In the DF model, the vadose zone (VZ) is considered as a "distributed sink" (similar to a standard "distributed source," which models recharge to the water table in humid climates). The analytical VZ is collated with one obtained from a numerical solution to BVP for Richards' equation in a 3-D saturated-unsaturated flow. BVPs for Richards' equation in cylindrical domains, solved by HYDRUS software, give the pressure head, moisture content, Darcian velocity fields, and streamlines.

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On Normal and Non-Normal Wave Statistics Implied by a Canonical–Microcanonical Gibbs Ensemble of the Truncated KdV System

Sun

Moore

2022

J Stat Phys

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Finger Growth and Selection in a Poisson Field

Cited by 3 publications

References 15 publications

Through history to growth dynamics: deciphering the evolution of spatial networks

Through history to growth dynamics: deciphering the evolution of spatial networks

The Saint‐Venant type isoperimetric inequalities for assessing saturated water storage in lacunary shallow perched aquifers

On Normal and Non-Normal Wave Statistics Implied by a Canonical–Microcanonical Gibbs Ensemble of the Truncated KdV System

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