scholarly journals Improving the parameterisation of horizontal density gradient in one-dimensional water column models for estuarine circulation

Ocean Science ◽  
2008 ◽  
Vol 4 (4) ◽  
pp. 239-246 ◽  
Author(s):  
S. Blaise ◽  
E. Deleersnijder
Keyword(s):  
Finite Difference ◽  
Water Column ◽  
Density Gradient ◽  
Lower Bounds ◽  
A Priori ◽  
Upwind Scheme ◽  
Upper And Lower Bounds ◽  
One Dimensional ◽  
First Order ◽  
Horizontal Density Gradient

Abstract. A new parameterisation of horizontal density gradient for a one-dimensional water column estuarine model, inspired by the first-order finite-difference upwind scheme, is presented. This parameterisation prevents stratification from growing indefinitely, a deficiency usually referred to as "runaway stratification". It is seen that, using this upwind-like parameterisation, the salinity must remain comprised between upper and lower bounds set a priori and that any initial over- or under-shooting is progressively eliminated. Simulations of idealised and realistic estuarine regimes indicate that the new parameterisation lead to results that are devoid of the runaway stratification phenomenon, as opposed to previously used models.

scholarly journals A new parameterisation of salinity advection to prevent stratification from running away in a simple estuarine model

2008 ◽  
Vol 5 (2) ◽  
pp. 187-211
Author(s):  
S. Blaise ◽  
E. Deleersnijder
Keyword(s):  
Finite Difference ◽  
Water Column ◽  
Lower Bounds ◽  
A Priori ◽  
Upwind Scheme ◽  
Upper And Lower Bounds ◽  
One Dimensional ◽  
First Order ◽  
Running Away

Abstract. A new parameterisation of horizontal salinity advection for a one-dimensional water-column estuarine model, inspired by the first-order finite-difference upwind scheme, is presented. This parameterisation prevents stratification from growing indefinitely, a numerical artefact usually referred to as "runaway stratification". It is seen that, using this upwind-like parameterisation, the salinity must remain comprised between upper and lower bounds set a priori and that any initial over- or under-shooting is progressively eliminated. Simulations of idealised and realistic estuarine regimes indicate that the new parameterisation lead to results that are devoid of the runaway stratification artefact, as opposed to previously used models.

Equivalent Composite Laminated Beams With Various Elastic Constitutive Models

1999 ◽  
Author(s):  
Izhak Sheinman ◽  
Yeoshua Frostig
Keyword(s):  
Lower Bounds ◽  
Plane Stress ◽  
Constitutive Models ◽  
Upper And Lower Bounds ◽  
Two Dimensional ◽  
Laminated Beams ◽  
Cylindrical Bending ◽  
One Dimensional ◽  
First Order ◽  
Shear Deformable

Abstract Equivalent one-dimensional constitutive models of composite laminated beams with shear deformation are derived from the classical laminate two-dimensional using first-order shear deformable theory. The present cylindrical bending constitutive models can be used — with much greater accuracy than their well known plane-strain and plane-stress counterparts — as upper and lower bounds, to one of which the behavior tends depending on the width-to-length ratio; this aspect was investigated and results are presented.

TWO PROCESSES FOR TWO PRICES

2014 ◽  
Vol 17 (01) ◽  
pp. 1450005 ◽  
Author(s):  
DILIP B. MADAN ◽  
WIM SCHOUTENS
Keyword(s):  
Lower Bounds ◽  
Markov Processes ◽  
Stochastic Dominance ◽  
Upper And Lower Bounds ◽  
One Dimensional ◽  
First Order ◽  
Order Stochastic Dominance ◽  
Bid Price ◽  
Increasing Process ◽  
Exchange Traded Fund

Postulating additivity of bid and ask prices for claims comonotone with a long or short stock position, two pricing processes are identified from data on bid and ask prices for options. It is observed that there are two separate put call parity relations in place, with the ask price for call less bid prices for put delivering an ask price for the forward-stock. Likewise the ask for puts less the bid for calls identifies the bid for the forward-stock. Two processes are introduced to determine bid and ask prices for claims comonotone with a long or short position in the stock. For a claim comonotone with a long position one uses the so-called increasing process for the ask price and the so-called decreasing process for the bid price and vice versa for a claim comonotone with a short position. As candidates for the two processes one may employ any of the traditional one-dimensional Markov processes. We illustrate the theory by using a Sato process, a model known to produce a smile conforming fit over strike and maturity. The two processes are observed to have marginals related by first order stochastic dominance. The increasing process dominates the decreasing process in this sense. These two processes are also used to construct upper and lower bounds for bid and ask prices for claims not comonotone with a long or short stock position. The two processes and their properties are illustrated with data on bid and ask prices for options on the exchange traded fund, SPY, that is the Standard and Poors' Depository Receipt tracking the S&P 500 index.

scholarly journals An exact expression of positive periodic solution for a first-order singular equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yun Xin ◽  
Xiaoxiao Cui ◽  
Jie Liu
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Lower Bounds ◽  
Topological Degree ◽  
Order Differential Equation ◽  
Positive Periodic Solution ◽  
Exact Expression ◽  
Upper And Lower Bounds ◽  
Singular Equation ◽  
First Order

Abstract The main purpose of this paper is to obtain an exact expression of the positive periodic solution for a first-order differential equation with attractive and repulsive singularities. Moreover, we prove the existence of at least one positive periodic solution for this equation with an indefinite singularity by applications of topological degree theorem, and give the upper and lower bounds of the positive periodic solution.

scholarly journals Upper and lower bounds on the speed of a one-dimensional excited random walk

2019 ◽  
Vol 12 (1) ◽  
pp. 97-115
Author(s):  
Erin Madden ◽  
Brian Kidd ◽  
Owen Levin ◽  
Jonathon Peterson ◽  
Jacob Smith ◽  
...  
Keyword(s):  
Random Walk ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
One Dimensional ◽  
Excited Random Walk

Upper and Lower Bounds for the Parameters of One-Dimensional Theories for Sandwich Fracture Specimens

2020 ◽  
Vol 88 (3) ◽  
Author(s):  
Roberta Massabò
Keyword(s):  
Crack Length ◽  
Lower Bounds ◽  
Beam Theory ◽  
Approximate Solutions ◽  
Upper And Lower Bounds ◽  
Model Parameters ◽  
One Dimensional ◽  
Limit Value ◽  
Elastic Mismatch ◽  
Fracture Specimens

Abstract Upper and lower bounds for the parameters of one-dimensional theories used in the analysis of sandwich fracture specimens are derived by matching the energy release rate with two-dimensional elasticity solutions. The theory of a beam on an elastic foundation and modified beam theory are considered. Bounds are derived analytically for foundation modulus and crack length correction in single cantilever beam (SCB) sandwich specimens and verified using accurate finite element results and experimental data from the literature. Foundation modulus and crack length correction depend on the elastic mismatch between face sheets and core and are independent of the core thickness if this is above a limit value, which also depends on the elastic mismatch. The results in this paper clarify conflicting results in the literature, explain the approximate solutions, and highlight their limitations. The bounds of the model parameters can be applied directly to specimens satisfying specific geometrical/material ratios, which are given in the paper, or used to support and validate numerical calculations and define asymptotic limits.

scholarly journals Analysis of one-dimensional models for exchange flows under strong stratification

2019 ◽  
Vol 70 (1) ◽  
pp. 41-56
Author(s):  
Steven J. Kaptein ◽  
Koen J. van de Wal ◽  
Leon P. J. Kamp ◽  
Vincenzo Armenio ◽  
Herman J. H. Clercx ◽  
...  
Keyword(s):  
Density Gradient ◽  
Turbulent Mixing ◽  
Schmidt Number ◽  
Density Gradients ◽  
One Dimensional ◽  
Exchange Flows ◽  
Dimensional Models ◽  
The One ◽  
Horizontal Density Gradient ◽  
Classical Constant

AbstractOne-dimensional models of exchange flows driven by horizontal density gradients are well known for performing poorly in situations with weak turbulent mixing. The main issue with these models is that the horizontal density gradient is usually imposed as a constant, leading to non-physically high stratification known as runaway stratification. Here, we propose two new parametrizations of the horizontal density gradient leading to one-dimensional models able to tackle strongly stratified exchange flows at high and low Schmidt number values. The models are extensively tested against results from laminar two-dimensional simulations and are shown to outperform the models using the classical constant parametrization for the horizontal density gradients. Four different flow regimes are found by exploring the parameter space defined by the gravitational Reynolds number Reg, the Schmidt number Sc, and the aspect ratio of the channel Γ. For small values of RegΓ, when diffusion dominates, all models perform well. However, as RegΓ increases, two clearly distinct regimes emerge depending on the Sc value, with an equally clear distinction of the performance of the one-dimensional models.

NOTES ON THE DISTRIBUTION OF PHASE SHIFTS

2008 ◽  
Vol 22 (23) ◽  
pp. 2163-2175 ◽  
Author(s):  
MIKLÓS HORVÁTH
Keyword(s):  
Inverse Scattering ◽  
Lower Bounds ◽  
Three Dimensional ◽  
Variational Formula ◽  
Phase Shifts ◽  
Upper And Lower Bounds ◽  
One Dimensional ◽  
Fixed Energy ◽  
Symmetrical Potential ◽  
The One

We consider three-dimensional inverse scattering with fixed energy for which the spherically symmetrical potential is nonvanishing only in a ball. We give exact upper and lower bounds for the phase shifts. We provide a variational formula for the Weyl–Titchmarsh m-function of the one-dimensional Schrödinger operator defined on the half-line.

scholarly journals A New Method to Study the Periodic Solutions of the Ordinary Differential Equations Using Functional Analysis

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 677 ◽  
Author(s):  
Kadry ◽  
Alferov ◽  
Ivanov ◽  
Korolev ◽  
Selitskaya
Keyword(s):  
Functional Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Lower Bounds ◽  
New Method ◽  
Upper And Lower Bounds ◽  
First Order ◽  
Periodic Problems ◽  
Existence And Stability

In this paper, a new theorems of the derived numbers method to estimate the number of periodic solutions of first-order ordinary differential equations are formulated and proved. Approaches to estimate the number of periodic solutions of ordinary differential equations are considered. Conditions that allow us to determine both upper and lower bounds for these solutions are found. The existence and stability of periodic problems are considered.

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