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The quasi-static problem describes a nonlinear porous body with a non-penetrating Barenblatt’s crack driven by the fracturing fluid, and its propagation is under investigation. By this, a bulk modulus of the porous body depends linearly on the density, the fracture faces allow contact with cohesion, and leak-off of the fluid into reservoir is accounted by the model. The mathematical problem consists in finding time-continuous functions of a displacement and a mean fluid pressure in the fracture, which satisfy the coupled system of the variational inequality and the fluid mass balance, which is controlled by the volume of fracking fluid pumped into the fracture. Well-posedness of the governing relations is proved rigorously by applying the method of Lagrange multipliers and using optimality conditions for the constrained minimization problem. As anillustrative example, a numerical benchmark problem of the fluid-driven fracture is presented in one dimension and computed by a Newton-type algorithm.
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Total Syntheses of Scabrolide A and Yonarolide
The concise total syntheses of oxidized norcembranoid terpenoids (−)-scabrolide A and (−)-yonarolide have been accomplished in 10 and 11 steps, respectively. The carbocyclic skeleton was efficiently constructed from two chiral-pool-derived fragments, including a [5,5]-bicyclic lactone accessed through a powerful Ni-catalyzed pentannulation of functionalized cyclopentenone with methylenecyclopropane and subsequent fragmentation. Additional features included a Liebeskind–Srogl coupling, induction of a cyclization/elimination cascade by a zinc-amido base, and installation of a sensitive enedione motif by late-stage γ-oxidation.
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- Award ID(s):
- 2154393
- PAR ID:
- 10493172
- Publisher / Repository:
- American Chemical Society
- Date Published:
- Journal Name:
- Journal of the American Chemical Society
- Volume:
- 145
- Issue:
- 16
- ISSN:
- 0002-7863
- Page Range / eLocation ID:
- 8805 to 8809
- Subject(s) / Keyword(s):
- Annulations Enones Hydrocarbons Lactones Molecular structure
- 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/10.1021/jacs.3c02317
