Stokes-Darcy System, Small-Darcy-Number Behaviour and Related Interfacial Conditions

We show that the Stokes-Darcy system, which governs flows through adjacent porous and pure-fluid domains in the two-domain approach without forced filtration, can be recovered from the Helmholtz minimal dissipation principle. While the continuity of normal velocity across the interface is imposed explicitly for mass conservation, only the Beavers-Joseph-Saffman-Jones (BJSJ) interface boundary condition is imposed implicitly, and the balance of the normal-force interface boundary condition appears naturally in the variational process. This set of interface boundary conditions is well-accepted in the mathematics community. We show that these interfacial boundary conditions, at the physically important small-Darcy-number regime, are consistent with continuity of pressure across the interface condition. the tangential velocity and pressure are discontinuous in general but the discontinuity is of the order of the square root of the Darcy number. Hence these interfacial conditions are all approximately consistent in the physically important small-Darcy-number regime. the leading order dynamics in the pure fluid zone is governed by the Stokes system with the no-slip no-penetration boundary condition on the interface between the free zone and porous media at a small Darcy number. the leading order non-trivial dynamics in porous media is governed by the Darcy equation with the pressure on the interface prescribed by the pressure of the leading order Stokes flow in the pure fluid zone. Such a semi-decoupled approach has long been used by the groundwater community. Our result is the first rigorous work quantifying the error of this intuitive approach and relating different interfacial conditions

Single-port laparoscopic sacrospinous ligament suspension via the natural vaginal cavity (SvNOTES) for pelvic prolapse: The first feasibility study

ObjectiveThis study aims to investigate the feasibility and short-term efficacy of single-port laparoscopic-assisted transvaginal natural cavity endoscopic sacrospinous ligament suspensions (SvNOTES).MethodsA total of 30 patients diagnosed with anterior or/and middle pelvic organ prolapse Stages III and IV underwent natural vaginal cavity (SvNOTES), and 30 patients who underwent conventional sacrospinous ligament (SSLF) were used as a control group. The operation time, blood loss, postoperative POP-Q score, length of hospital stay, and complications were compared between the two groups.ResultsThe operation time for SvNOTE was (60 ± 13) min, which was longer than (30 ± 15) min for SSLF (P = 0.04). However, the bleeding amount in SvNOTE was 29.44 ± 2.56, significantly lower than that in the SSLF group (80 ± 10; P = 0.02), and the postoperative hospital stay in the SvNOTE group was (4 ± 2) days, longer than (3 ± 1) days in SSLF (P = 0.02). However, there were no intraoperative complications in the SvNOTE group, whereas one ureteral injury occurred in the SSLF group; in addition, the postoperative POP-Q score was significantly better in the SvNOTE group than that in the SSLF group with increasing time (P < 0.001).ConclusionCompared with SSLF, single-port laparoscopic sacrospinous ligament suspension via the natural vaginal cavity is visualized, greatly improving the success rate of sacrospinous ligament fixation, with less blood loss and fewer complications, arguably a safer and minimally invasive surgical approach

Regularity of the Stokes-Darcy System

We present a proof of the elliptic regularity property for the steady state Stokes-Darcy equation in a two-dimensional domain equipped with the Beavers-Joseph-Saffman-Jones (BJSJ) interface condition. Such regularity results are fundamental to the numerical analysis of various numerical methods for the Stokes-Darcy system

A hypothetical urban layout generation model for exploring land use impacts on travel behavior

In urban planning, land-use policies are commonly applied to reduce automobile travel and encourage active transport because land use is believed to affect travel behavior. However, a debate about such effects continues in literature. Empirical studies differing in context, methodology, and geographic scale come to different results. Although questioned because of self-selection, the accumulated empirical evidence provides a solid foundation for conducting simulation research that helps systematically examine the effects of land use attributes on travel behavior. This paper introduces an urban layout generation (ULG) model specially developed for simulations. The ULG model is not a land use and transport interaction model. It generates hypothetical urban layouts corresponding directly to D-variables, a set of land use measurements widely used in empirical studies. The D-variables are controlled on multiple spatial scales in the ULG model. Besides the spatial aspects of the road network and land use commonly included in virtual city models, the ULG model also simulates the population density. Performance tests showed the ability of the ULG model to generate hypothetical though reasonable urban layouts which meet the requirements of simulation research of land use and travel behavior. Finally, several examples combing the ULG model and a travel behavior simulation model show potential applications of the ULG model

Algebraic proof of recursive relation for Boros-Moll polynomial sequence

In order to expand the basic theory of the recurrence relationship of Boros-Moll polynomial sequence, a new proof method for the recurrence relationship of Boros-Moll polynomial sequence was studied. Firstly, the recurrence relationship satisfied by the Boros-Moll polynomial sequence was appropriately deformed and partitioned. Secondly, the recursive relationship that satisfies as the difference of the sum of three parts was constructed. Finally, mathematical methods such as algebraic method and structured approach were used to find that the sum of the three parts is all zero. Furthermore, a new proof method for the recurrence relationship of Boros-Moll polynomial sequence was obtained. The results indicate that in the Boros-Moll polynomial sequence recurrence relationship, the recurrence relationship is cleverly deformed and partitioned, and the corresponding lemma is proved to be corrected, thus obtaining a new proof method. The research results enrich the relevant theory of recurrence relationship of the Boros-Moll polynomial sequence, and provide a certain theoretical reference value for the application of the Boros-Moll polynomial sequence in combinatorics, social science, information theory and other fields

Mir-5100 Mediates Proliferation, Migration and Invasion of Oral Squamous Cell Carcinoma Cells Via Targeting SCAI

Purpose We aimed to investigate the role of microRNA-5100 (miRNA-5100) in oral squamous cell carcinoma (OSCC) and its underlying mechanisms. Material/Methods: The expression of miR-5100 and suppressor of cancer cell invasion (SCAI) in OSCC cell lines were examined. A luciferase reporter assay was applied to confirm the combination between miR-5100 and SCAI. Then, miR-5100 inhibitor or small hairpin RNA (shRNA)-SCAI were transfected into cells. Cell Counting Kit-8 assay was executed for testing cell proliferation ability. Flow cytometry assay was exploited for measuring cell cycle. Invasion and migration of OSCC cells were assessed using Transwell assay and wound healing assay. The expression of proteins were detected using western blotting. Results The results demonstrated that the level of miR-5100 was upregulated while SCAI was downregulated in OSCC cells. SCAI was verified as a direct target of miR-5100. MiR-5100 silencing suppressed proliferation of OSCC cells, increased cells in the G1 and G2 phases, and reduced those in the S phase, which was reversed after transfection with shRNA-SCAI. Moreover, miR-5100 inhibitor downregulated the expression of cyclin-dependent kinase-2 (CDK-2) and cyclinD1, accompanied by upregulation in p27 expression, whereas SCAI silencing had the opposite results. The invasion and migration abilities of OSCC cells were reduced after treatment with miR-5100 inhibitor, whereas SCAI silencing suppressed the effects of miR-5100 inhibitor on OSCC cell behaviors. Conclusion These findings suggested that miR-5100 silencing inhibit proliferation, invasion and migration of OSCC cells via upregulating the expression of SCAI, which provides theoretical basis and treatment strategies for the treatment of OSCC

Procedural modeling of urban layout: population, land use, and road network

This paper introduces an urban simulation system generating urban layouts with population, road network and land use layers. The desired urban spatial structure is obtained by generating a population map based on population density models. The road network is generated at two spatial levels corresponding to the road hierarchy. The land use allocation is based on the What If? allocation model. The expected results are urban layouts suitable for academic scenario analysis