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Abstract A thermo‐time domain reflectometry (thermo‐TDR) sensor combines a heat‐pulse sensor with a TDR waveguide to simultaneously measure coupled processes of water, heat, and solute transfer. The sensor can provide repeated in situ measurements of several soil state properties (temperature, soil water content, and ice content), thermal properties (thermal diffusivity, thermal conductivity, heat capacity), and electromagnetic properties (dielectric constant and bulk electrical conductivity) with minimal soil disturbance. Combined with physical or empirical models, structural indicators, such as bulk density and air‐filled porosity, can be derived from measured soil thermal and electrical properties. Successful applications are available to determine fine‐scale heat, water, and vapor fluxes with thermo‐TDR sensors. Applications of thermo‐TDR sensors in complicated scenarios, such as heterogeneous root zones and saline environments, are also possible. Therefore, the multi‐functional uses of thermo‐TDR sensors are invaluable for in situ observations of several soil physical properties and processes in critical zone soils.
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On the heat kernel of the Rumin complex and Calderón reproducing formula
Abstract We derive several properties of the heat equation with the Hodge operator associated with the Rumin’s complex on Heisenberg groups and prove several properties of the fundamental solution. As an application, we use the heat kernel for Rumin’s differential forms to construct a Calderón reproducing formula on Rumin’s forms.
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- Award ID(s):
- 2154219
- PAR ID:
- 10513152
- Publisher / Repository:
- De Gruyter
- Date Published:
- Journal Name:
- Analysis and Geometry in Metric Spaces
- Volume:
- 12
- Issue:
- 1
- ISSN:
- 2299-3274
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1515/agms-2024-0002
