New studies of nonuniform flows: Finite length and averaged hydraulic gradient of rapid flows in prismatic channels

1998 ◽  
Vol 32 (7) ◽  
pp. 391-411 ◽  
Author(s):  
O. M. Aivazian
Keyword(s):  
Finite Length ◽  
Hydraulic Gradient ◽  
Nonuniform Flows

MGP NAPL management using hydraulic gradient modification

2006 ◽  
Vol 14 (2) ◽  
pp. 639-644
Author(s):  
G.M. Thomas ◽  
J.F. Morgan ◽  
M.J. Gefell ◽  
J. Shi
Keyword(s):  
Hydraulic Gradient

On mappings with finite length distortion on Riemann surfaces

2019 ◽  
Vol 33 ◽  
Author(s):  
Serhii Volkov ◽  
Vladimir Ryazanov
Keyword(s):  
Finite Length ◽  
Riemann Surfaces ◽  
Boundary Behavior ◽  
Main Tool ◽  
Natural Generalization ◽  
Finite Distortion ◽  
Lipschitz Mappings ◽  
Geometric Function ◽  
Mappings With Finite Distortion ◽  
Length Distortion

The present paper is a natural continuation of our previous paper (2017) on the boundary behavior of mappings in the Sobolev classes on Riemann surfaces, where the reader will be able to find the corresponding historic comments and a discussion of many definitions and relevant results. The given paper was devoted to the theory of the boundary behavior of mappings with finite distortion by Iwaniec on Riemannian surfaces first introduced for the plane in the paper of Iwaniec T. and Sverak V. (1993) On mappings with integrable dilatation and then extended to the spatial case in the monograph of Iwaniec T. and Martin G. (2001) devoted to Geometric function theory and non-linear analysis. At the present paper, it is developed the theory of the boundary behavior of the so--called mappings with finite length distortion first introduced in the paper of Martio O., Ryazanov V., Srebro U. and Yakubov~E. (2004) in the spatial case, see also Chapter 8 in their monograph (2009) on Moduli in modern mapping theory. As it was shown in the paper of Kovtonyuk D., Petkov I. and Ryazanov V. (2017) On the boundary behavior of mappings with finite distortion in the plane, such mappings, generally speaking, are not mappings with finite distortion by Iwaniec because their first partial derivatives can be not locally integrable. At the same time, this class is a generalization of the known class of mappings with bounded distortion by Martio--Vaisala from their paper (1988). Moreover, this class contains as a subclass the so-called finitely bi-Lipschitz mappings introduced for the spatial case in the paper of Kovtonyuk D. and Ryazanov V. (2011) On the boundary behavior of generalized quasi-isometries, that in turn are a natural generalization of the well-known classes of bi-Lipschitz mappings as well as isometries and quasi-isometries. In the research of the local and boundary behavior of mappings with finite length distortion in the spatial case, the key fact was that they satisfy some modulus inequalities which was a motivation for the consideration more wide classes of mappings, in particular, the Q-homeomorphisms (2005) and the mappings with finite area distortion (2008). Hence it is natural that under the research of mappings with finite length distortion on Riemann surfaces we start from establishing the corresponding modulus inequalities that are the main tool for us. On this basis, we prove here a series of criteria in terms of dilatations for the continuous and homeomorphic extension to the boundary of the mappings with finite length distortion between domains on arbitrary Riemann surfaces.

Influence of Pumps on Salinity of a Coastal Aquifer with Legal Protection (A Zone in the North of Isla Cristina, Huelva, Spain)

1991 ◽  
Vol 24 (11) ◽  
pp. 251-260 ◽  
Author(s):  
A. González ◽  
E. Romero
Keyword(s):  
Coastal Aquifer ◽  
Salt Water ◽  
Legal Protection ◽  
Hydraulic Gradient ◽  
Water Mixture ◽  
Residual Flow ◽  
Legal Requirements ◽  
The North ◽  
North Side ◽  
Rational Distribution

In this article we show that the legal measures for protection of aquifers are not enough to lessen the pumping if the users are not associated and determined to have a rational distribution of water. The expansive agriculture on the North side of Isla Cristina (Huelva, Spain), based on citrus and strawberry growing, uses high volumes of groundwater that comes from a tertiary age detritic coastal aquifer with a significant lack of resources. This causes a decrease of the residual flow to the sea, deep pumpcones, and an inversion of the hydraulic gradient, which initiates the progressive salinization of the aquifer northwards, in the sense that the fresh-salt water mixture zone is moving. The problem is worsening because the number of uncontrolled pump-works in the areais increasing. This problem could be alleviated if a Users Community for the whole aquifer were created, itself to watch over the fulfilment of the legal requirements and to regulate the water extractions.

scholarly journals Aerodynamics of a Circular Cylinder of Finite Length

1988 ◽  
Vol 1988 (36) ◽  
pp. 27-43
Author(s):  
Yasushi UEMATSU ◽  
Motohiko YAMADA ◽  
Kaoru ISHII
Keyword(s):  
Circular Cylinder ◽  
Finite Length
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