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Abstract The fate of nutrients and contaminants in fluvial ecosystems is strongly affected by the mixing dynamics between surface water and groundwater within the hyporheic zone, depending on the combination of the sediment's hydraulic heterogeneity and dune morphology. This study examines the effects of hydraulic conductivity stratification on steady‐state, two‐dimensional, hyporheic flows and solute residence time distribution. First, we derive an integral transform‐based semi‐analytical solution for the flow field, capable of accounting for the effects of any functional shape of the vertically varying hydraulic conductivity. The solution considers the uneven distribution of pressure at the water‐sediment interface (i.e., the pumping process) dictated by the presence of dune morphology. We then simulate solute transport using particle tracking. Our modeling framework is validated against numerical and tracer data from flume experiments and used to explore the implication of hydraulic conductivity stratification on the statistics andpdfof the residence time. Finally, reduced‐order models are used to enlighten the dependence of key residence time statistics on the parameters characterizing the hydraulic conductivity stratification.
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On the Su–Schrieffer–Heeger model of electron transport: Low‐temperature optical conductivity by the Mellin transform
Abstract We describe the low‐temperature optical conductivity as a function of frequency for a quantum‐mechanical system of electrons that hop along a polymer chain. To this end, we invoke the Su–Schrieffer–Heegertight‐bindingHamiltonian for noninteracting spinless electrons on a one‐dimensional (1D) lattice. Our goal is to show via asymptotics how the interband conductivity of this system behaves as the smallest energy bandgap tends to close. Our analytical approach includes: (i) the Kubo‐type formulation for the optical conductivity with a nonzero damping due to microscopic collisions, (ii) reduction of this formulation to a 1D momentum integral over the Brillouin zone, and (iii) evaluation of this integral in terms of elementary functions via the three‐dimensional Mellin transform with respect to key physical parameters and subsequent inversion in a region of the respective complex space. Our approach reveals an intimate connection of the behavior of the conductivity to particular singularities of its Mellin transform. The analytical results are found in good agreement with direct numerical computations.
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- Award ID(s):
- 1922165
- PAR ID:
- 10419784
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- Studies in Applied Mathematics
- Volume:
- 151
- Issue:
- 2
- ISSN:
- 0022-2526
- Page Range / eLocation ID:
- p. 555-584
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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