One-Dimensional and Two-Dimensional Estimates of Abutment Scour Prediction Variables

1998 ◽  
Vol 1647 (1) ◽  
pp. 18-26 ◽  
Author(s):  
Terry W. Sturm ◽  
Antonis Chrisochoides
Keyword(s):  
Vertical Wall ◽  
Two Dimensional ◽  
One Dimensional ◽  
Bridge Abutment ◽  
Overbank Flow ◽  
Bridge Approach ◽  
Surface Profiles ◽  
Abutment Scour ◽  
The One ◽  
D Model

An experimental study of the estimation of hydraulic parameters needed in bridge abutment scour formulas is presented. Two different compound channel geometries are studied with rough floodplains in shallow overbank flow. Vertical-wall and spill-through abutment shapes are included in the study, with the abutment face located on the floodplain for various embankment lengths. Water surface profiles and velocity distributions are measured and compared with predictions made by the one-dimensional (1-D) model WSPRO and a two-dimensional k-ε turbulence model developed in previous research. The results show that a 1-D model can predict scour parameters reasonably well in the bridge approach section but not in the bridge contraction section.

Regions-based Two-dimensional Continua: The Euclidean Case

2018 ◽  
Author(s):  
Geoffrey Hellman ◽  
Stewart Shapiro
Keyword(s):  
Mathematical Induction ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Entire Space ◽  
Euclidean Case ◽  
Free Basis ◽  
One Dimensional ◽  
Archimedean Property ◽  
The One

This chapter develops a Euclidean, two-dimensional, regions-based theory. As with the semi-Aristotelian account in Chapter 2, the goal here is to recover the now orthodox Dedekind–Cantor continuum on a point-free basis. The chapter derives the Archimedean property for a class of readily postulated orientations of certain special regions, what are called “generalized quadrilaterals” (intended as parallelograms), by which the entire space is covered. Then the chapter generalizes this to arbitrary orientations, and then establishes an isomorphism between the space and the usual point-based one. As in the one-dimensional case, this is done on the basis of axioms which contain no explicit “extremal clause”, and we have no axiom of induction other than ordinary numerical (mathematical) induction.

scholarly journals Validation of a one-dimensional model of the systemic arterial tree

2009 ◽  
Vol 297 (1) ◽  
pp. H208-H222 ◽  
Author(s):  
Philippe Reymond ◽  
Fabrice Merenda ◽  
Fabienne Perren ◽  
Daniel Rüfenacht ◽  
Nikos Stergiopulos
Keyword(s):  
Constitutive Law ◽  
Distributed Model ◽  
Arterial Tree ◽  
One Dimensional ◽  
Continuity Equations ◽  
Nonlinear Viscoelastic ◽  
Model Predictions ◽  
The One ◽  
D Model ◽  
Systemic Arterial Tree

A distributed model of the human arterial tree including all main systemic arteries coupled to a heart model is developed. The one-dimensional (1-D) form of the momentum and continuity equations is solved numerically to obtain pressures and flows throughout the systemic arterial tree. Intimal shear is modeled using the Witzig-Womersley theory. A nonlinear viscoelastic constitutive law for the arterial wall is considered. The left ventricle is modeled using the varying elastance model. Distal vessels are terminated with three-element windkessels. Coronaries are modeled assuming a systolic flow impediment proportional to ventricular varying elastance. Arterial dimensions were taken from previous 1-D models and were extended to include a detailed description of cerebral vasculature. Elastic properties were taken from the literature. To validate model predictions, noninvasive measurements of pressure and flow were performed in young volunteers. Flow in large arteries was measured with MRI, cerebral flow with ultrasound Doppler, and pressure with tonometry. The resulting 1-D model is the most complete, because it encompasses all major segments of the arterial tree, accounts for ventricular-vascular interaction, and includes an improved description of shear stress and wall viscoelasticity. Model predictions at different arterial locations compared well with measured flow and pressure waves at the same anatomical points, reflecting the agreement in the general characteristics of the “generic 1-D model” and the “average subject” of our volunteer population. The study constitutes a first validation of the complete 1-D model using human pressure and flow data and supports the applicability of the 1-D model in the human circulation.

MUTUAL EXCLUSION ON OPTICAL BUSES

2002 ◽  
Vol 12 (03n04) ◽  
pp. 341-358
Author(s):  
KRISHNA M. KAVI ◽  
DINESH P. MEHTA
Keyword(s):  
Mutual Exclusion ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Array ◽  
Propagation Delays ◽  
Optical Buses ◽  
The One

This paper presents two algorithms for mutual exclusion on optical bus architectures including the folded one-dimensional bus, the one-dimensional array with pipelined buses (1D APPB), and the two-dimensional array with pipelined buses (2D APPB). The first algorithm guarantees mutual exclusion, while the second guarantees both mutual exclusion and fairness. Both algorithms exploit the predictability of propagation delays in optical buses.

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

Substrate induced freezing, melting and depinning transitions in two-dimensional liquid crystalline systems

2022 ◽  
Author(s):  
Bharti bharti ◽  
Debabrata Deb
Keyword(s):  
Molecular Dynamics ◽  
Liquid Crystals ◽  
Molecular Dynamics Simulations ◽  
Liquid Crystalline ◽  
Two Dimensional ◽  
One Dimensional ◽  
The One ◽  
Dynamics Simulations

We use molecular dynamics simulations to investigate the ordering phenomena in two-dimensional (2D) liquid crystals over the one-dimensional periodic substrate (1DPS). We have used Gay-Berne (GB) potential to model the...

scholarly journals Water storage in wetted strips under irrigated coffee trees with different criteria of irrigation management

2013 ◽  
Vol 33 (2) ◽  
pp. 249-257 ◽  
Author(s):  
Alberto Colombo ◽  
Lívia A. Alvarenga ◽  
Myriane S. Scalco ◽  
Randal C. Ribeiro ◽  
Giselle F. Abreu
Keyword(s):  
Dimensional Analysis ◽  
Drip Irrigation ◽  
Irrigation Management ◽  
Water Storage ◽  
Moisture Distribution ◽  
Water Volume ◽  
Two Dimensional ◽  
One Dimensional ◽  
Irrigation Interval ◽  
The One

The increasing demand for water resources accentuates the need to reduce water waste through a more appropriate irrigation management. In the particular case of irrigated coffee planting, which in recent years presented growth with the predominance of drip irrigation, the improvement of drip irrigation management techniques is a necessity. The proper management of drip irrigation depends on the knowledge of the spatial pattern of soil moisture distribution inside the wetted strip formed under the irrigation lines. In this study, grids of 24 tensiometers were used to determine the water storage within the wetted strip formed under drippers, with a 3.78 L h-1 discharge, evenly spaced by 0.4 m, subjected to two different management criteria (fixed irrigation interval and 60 kPa tension). Estimates of storage based on a one-dimensional analysis, that only considers depth variations, were compared with two-dimensional estimates. The results indicate that for high-frequency irrigation the one-dimensional analysis is not appropriate. However, under less frequent irrigation, the two-dimensional analysis is dispensable, being the one-dimensional sufficient for calculating the water volume stored in the wetted strip.

Computationally Efficient Model for 2D Ion Implantation Simulation

1997 ◽  
Vol 490 ◽  
Author(s):  
Misha Temkin ◽  
Ivan Chakarov
Keyword(s):  
Ion Implantation ◽  
Efficient Method ◽  
Two Dimensional ◽  
Computationally Efficient ◽  
Crystalline Materials ◽  
One Dimensional ◽  
The One

ABSTRACTA computationally efficient method for ion implantation simulation is presented. The method allows two-dimensional ion implantation profiles in arbitrary shaped structures to be calculated and is valid for both amorphous and crystalline materials. It uses an extension of the one-dimensional dual Pearson approximation into the second dimension.

A Graphical Exposition of the Ising Problem

1971 ◽  
Vol 12 (3) ◽  
pp. 365-377 ◽  
Author(s):  
Frank Harary
Keyword(s):  
Dimensional Case ◽  
Two Dimensional ◽  
One Dimensional ◽  
Higher Dimensional ◽  
The One

Ising [1] proposed the problem which now bears his name and solved it for the one-dimensional case only, leaving the higher dimensional cases as unsolved problems. The first solution to the two dimensional Ising problem was obtained by Onsager [6]. Onsager's method was subsequently explained more clearly by Kaufman [3]. More recently, Kac and Ward [2] discovered a simpler procedure involving determinants which is not logically complete.

scholarly journals Comparison of West Balkan adult trout habitat predictions using a Pseudo-2D and a 2D hydrodynamic model

2016 ◽  
Vol 48 (6) ◽  
pp. 1697-1709 ◽  
Author(s):  
Christina Papadaki ◽  
Vasilis Bellos ◽  
Lazaros Ntoanidis ◽  
Elias Dimitriou
Keyword(s):  
Hydrodynamic Model ◽  
River Discharge ◽  
Environmental Flow ◽  
Two Dimensional ◽  
Habitat Models ◽  
One Dimensional ◽  
2D Flow ◽  
A Cell ◽  
The One ◽  
Water Depths

Abstract Hydraulic-habitat models combine the dynamic behavior of river discharge with geomorphological and ecological responses. In this study, they are used for estimating environmental flow requirements. We applied a Pseudo-two-dimensional (2D) model based on the one-dimensional (1D) HEC-RAS model and an in-house 2D (FLOW-R2D) hydrodynamic model to a section of river for several flows in respect of summer conditions of the study reach, and compared the results derived from the models in terms of water depths and velocities as well as habitat predictions in terms of weighted usable area (WUA). In general, 2D models are more promising in habitat studies since they quantify spatial variations and combinations of flow patterns important to stream flora and fauna in a higher detail than the 1D models. Relationships between WUA and discharge for the two models were examined, to compare the similarity as well as the magnitude of predictions over the modelled discharge range. The models predicted differences in the location of maxima and changes in variation of velocity and water depth. Finally, differences in spatial distribution (in terms of suitability indices and WUA) between the Pseudo-2D and the fully 2D modelling results can be considerable on a cell-by-cell basis.

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