A model for the movement of large solids in small sewers

2005 ◽  
Vol 52 (5) ◽  
pp. 69-76 ◽  
Author(s):  
D. Butler ◽  
K. Littlewood ◽  
N. Orman
Keyword(s):  
Amorphous Solids ◽  
Small Time ◽  
Model Parameters ◽  
Transport Distance ◽  
Long Run ◽  
Series Of Experiments ◽  
Calibration And Verification ◽  
Solid Transport ◽  
Solid Movement ◽  
Experimental Rig

An extensive series of experiments has been carried out to investigate the movement mechanisms and behaviour of large solids in small sewers. This paper describes the development, calibration and verification of a model (SOLID) based on data obtained from the experimental rig. It is used to predict solid movement with respect to ‘limiting solid transport distance’. Key model parameters are the coefficients of static and dynamic friction, the shape factor of amorphous solids and the flow bypass coefficient. The model is shown to successfully represent the movement of a large solid down a small pipe, where the solid is moving as a sliding, leaking dam, particularly the first ‘hop’. Limitations of the model include a limited facility to well represent multiple hops and the need for closely spaced computational nodes leading to small time steps, and long run times.

Movement mechanisms of gross solids in intermittent flow

2003 ◽  
Vol 47 (4) ◽  
pp. 45-50 ◽  
Author(s):  
K. Littlewood ◽  
D. Butler
Keyword(s):  
Flow Regime ◽  
Water Conservation ◽  
Small Diameter ◽  
Intermittent Flow ◽  
Transport Distance ◽  
Photographic Evidence ◽  
Transport Behaviour ◽  
Series Of Experiments ◽  
Solid Transport ◽  
Solid Movement

Gross solids, such as used tampons, sanitary towels and faecal stools, are introduced into the sewer network via the WC. Although small diameter pipes (≤ 150mm diameter) make up a large proportion of most sewer networks, the transport behaviour of gross solids in these smaller pipes is not fully established. In particular, there are concerns about the effect of water conservation measures on the transport of gross solids in the intermittent flow regime prevalent in small pipes. This paper introduces a study carried out on the movement of solids in this flow regime. An extensive series of experiments has been carried out to investigate the movement mechanisms and behaviour in detail. It was found that there are three different mechanisms of movement, and photographic evidence is provided in the paper. The concept and implications of the “limiting solid transport distance” is also introduced. It is argued that solid movement is dependent on factors other than just WC flush volume and that increased blockage potential is not inevitable.

scholarly journals Exploitation of a Productive Asset in the Presence of Strategic Behavior and Pollution Externalities

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1682
Author(s):  
N. Baris Vardar ◽  
Georges Zaccour
Keyword(s):  
Strategic Behavior ◽  
Piecewise Linear ◽  
Growth Function ◽  
Piecewise Linear Approximation ◽  
Stable Steady State ◽  
Model Parameters ◽  
State Variables ◽  
Long Run ◽  
Productive Asset ◽  
Asset Growth

We study the strategic behavior of firms competing in the exploitation of a common-access productive asset, in the presence of pollution externalities. We consider a differential game with two state variables (asset stock and pollution stock), and by using a piecewise-linear approximation of the nonlinear asset growth function, we provide a tractable characterization of the symmetric feedback–Nash equilibrium with asymptotically stable steady state(s). The results show that the firm’s strategy takes three forms depending on the pair of state variables and that different options for the model parameters lead to contrasting outcomes in both the short- and long-run equilibria.

A Modification of the Modified Stollsteimer Location Moled

1975 ◽  
Vol 7 (1) ◽  
pp. 159-164 ◽  
Author(s):  
Stephen Fuller
Keyword(s):  
Cost Function ◽  
Optimal Solution ◽  
Computer Time ◽  
Solution Procedure ◽  
Plant Location ◽  
Model Parameters ◽  
Basic Model ◽  
Long Run ◽  
Large Numbers ◽  
Cost Parameters

The Stollsteimer plant location model is a normative tool appropriate for deterrmning least-cost number, size and location of a subindustry's marketing facilities. Several modification and extensions of the basic model have increased its value to the applied economist. Ladd and Halvorson developed a procedure to determine sensitivity of the optimal solution to variation in model parameters, i.e., the researcher may resolve how magnitude cost parameters are altered before the solution becomes non-optimal. The basic model's solution procedure prevented application where large numbers of potential plant sites were involved. A recent modification by Warrack and Fletcher effects a reduction in required computer time by approximating optimization, thus increasing size of plant location problems investigated. Polopolus extended the basic model to encompass multiple product plants and, in collaboration with Chern, modified the basic Stollsteimer model to permit substitution of a discontinuous, long-run plant cost function for the strategically assumed continuous linear form. Prior to the latter modification, the basic model accommodated only a long-run total plant cost function which was linear with a positive intercept.

‘Motorways in London’ and Transport Planning

1970 ◽  
Vol 2 (2) ◽  
pp. 137-151 ◽  
Author(s):  
M. E. Beesley
Keyword(s):  
Land Use ◽  
Census Data ◽  
Transport Model ◽  
Substantial Reduction ◽  
Model Parameters ◽  
Transport Planning ◽  
Economic Implications ◽  
Long Run ◽  
Job Opportunities ◽  
Journey To Work

Motorways in London proposes a substantial reduction in the planned motorway network in London, and its redistribution away from the centre, but it is argued that the book does not justify its case by the measurements presented, and pays too little attention to amenities and compensation. The article is largely concerned with problems for transport planning arising from the book and the official transport and planning documents of 1968 and 1969. The latter's land use and transport model is criticised for its neglect of the economic implications of its ‘suppression’ of trips where networks are overloaded. The model parameters should be required to conform to observed distributions of journey lengths, especially those to work, based on workplace data and recognising the influences, inter alia, of variations in income and levels of skill. A key question in making present models better reflect the long-run interaction between transport and land use is predicting journey-to-work lengths. A model to explain their past change is proposed, based on Census data, measuring the effect of changes in job opportunities, housing demands, and population shifts.

scholarly journals Computer numerical control vertical machining centre feed drive modelling using the transmission line technique

2014 ◽  
Vol 229 (9) ◽  
pp. 1578-1599 ◽  
Author(s):  
DG Ford ◽  
VYM Castaneda ◽  
AP Longstaff ◽  
C Pislaru ◽  
A Myers
Keyword(s):  
Transmission Line ◽  
High Performance ◽  
Computing System ◽  
Computer Numerical Control ◽  
Small Time ◽  
Numerical Control ◽  
Ball Screw ◽  
Model Parameters ◽  
Signal Acquisition ◽  
Cnc Machine

This study presents a novel application of the Transmission Line Matrix Method (TLM) for the modelling of the dynamic behaviour of non-linear hybrid systems for computer numerical control (CNC) machine tool drives. The application of the TLM technique implies the dividing of the ball-screw shaft into a number of identical elements in order to achieve the synchronisation of events in the simulation, and to provide an acceptable resolution according to the maximum frequency of interest. This entails the use of a high performance computing system with due consideration to the small time steps being applied in the simulation. Generally, the analysis of torsion and axial dynamic effects on a shaft implies the development of independent simulated models. This study presents a new procedure for the modelling of a ball-screw shaft by the synchronisation of the axial and torsion dynamics into the same model. The model parameters were obtained with equipments such as laser interferometer, ball bar, electronic levels, signal acquisition systems, etc. The MTLM models for single and two-axis configurations have been simulated and matches well with the measured responses of machines. The new modelling approach designated the Modified Transmission Line Method (MTLM) extends the TLM approach retaining all its inherent qualities but gives improved convergence and processing speeds. Further work since, not the subject of this paper, have identified its potential for real-time application.

Prediction of Performance and Pollutant Emission From Bituminous and Sub-Bituminous Coals in Utility Boilers

2007 ◽  
Author(s):  
Roman Saveliev ◽  
Boris Chudnovsky ◽  
Ben-Zion Kogan ◽  
Efim Korytnyi ◽  
Miron Perelman ◽  
...  
Keyword(s):  
Kinetic Parameters ◽  
Coal Combustion ◽  
Fluid Dynamic ◽  
Test Facility ◽  
Pollutant Emission ◽  
Model Parameters ◽  
Cfd Models ◽  
Utility Boilers ◽  
Series Of Experiments ◽  
Bituminous Coals

Computational Fluid Dynamic (CFD) models give good predictions of coal combustion in utility boilers if the coal combustion kinetic parameters are known. We developed a three-step methodology to provide reliable prediction of the behavior of a coal in a utility boiler: (1) Obtaining the combustion kinetic model parameters from a series of experiments in a test facility, CFD codes and optimization algorithm. (2) Validation of the combustion kinetic parameters by comparison of different experimental data with simulation results obtained by the set of combustion kinetic parameters. (3) The extracted kinetic parameters are then used for simulations of full-scale boilers using the same CFD code. Three to four bituminous and sub-bituminous coals with known behavior in Israel Electric Corporation (IEC) 550MW opposite-wall (3 coals) and 575MW tangential-fired (4 coals) boilers were used to show the capability of the method. An unfamiliar bituminous coal was then examined prior of its firing in the utility boilers and prediction of its combustion behavior in the two boilers was carried out. This methodology was used to examine a Venezuelan coal that was found to yield high LOI.

scholarly journals Parameter Estimation for the Forest Fire Propagation Model

2020 ◽  
Vol 75 (1) ◽  
pp. 1-22
Author(s):  
Martin Ambroz ◽  
Karol Mikula ◽  
Marek Fraštia ◽  
Marián Marčiš
Keyword(s):  
Data Assimilation ◽  
Forest Fire ◽  
Hausdorff Distance ◽  
Small Time ◽  
Propagation Model ◽  
Model Parameters ◽  
Normal Velocity ◽  
Fire Propagation ◽  
Rate Of Spread ◽  
Fire Front

AbstractThis paper first gives a brief overview of the Lagrangian forest fire propagation model [Ambroz, M.—Balažovjech, M.—Medl’a, M.—Mikula, K.: Numerical modeling of wildland surface fire propagation by evolving surface curves, Adv. Comput. Math. 45 (2019), no. 2, 1067–1103], which we apply to grass-field areas. Then, we aim to estimate the optimal model parameters. To achieve this goal, we use data assimilation of the measured data. From the data, we are able to estimate the normal velocity of the fire front (rate of spread), dominant wind direction and selected model parameters. In the data assimilation process, we use the Hausdorff distance as well as the Mean Hausdorff distance as a criterion. Moreover, we predict the fire propagation in small time intervals.

scholarly journals Modeling multi-sensory feedback control of zebrafish in a flow

2021 ◽  
Vol 17 (1) ◽  
pp. e1008644
Author(s):  
Daniel A. Burbano-L. ◽  
Maurizio Porfiri
Keyword(s):  
Critical Role ◽  
Autonomous Systems ◽  
Water Channel ◽  
Model Parameters ◽  
Complex Environments ◽  
Counter Flow ◽  
Complex Process ◽  
Series Of Experiments ◽  
Constant Distance

Understanding how animals navigate complex environments is a fundamental challenge in biology and a source of inspiration for the design of autonomous systems in engineering. Animal orientation and navigation is a complex process that integrates multiple senses, whose function and contribution are yet to be fully clarified. Here, we propose a data-driven mathematical model of adult zebrafish engaging in counter-flow swimming, an innate behavior known as rheotaxis. Zebrafish locomotion in a two-dimensional fluid flow is described within the finite-dipole model, which consists of a pair of vortices separated by a constant distance. The strength of these vortices is adjusted in real time by the fish to afford orientation and navigation control, in response to of the multi-sensory input from vision, lateral line, and touch. Model parameters for the resulting stochastic differential equations are calibrated through a series of experiments, in which zebrafish swam in a water channel under different illumination conditions. The accuracy of the model is validated through the study of a series of measures of rheotactic behavior, contrasting results of real and in-silico experiments. Our results point at a critical role of hydromechanical feedback during rheotaxis, in the form of a gradient-following strategy.

scholarly journals Response Properties of an Integrate-and-Fire Model That Receives Subthreshold Inputs

2005 ◽  
Vol 17 (12) ◽  
pp. 2571-2601 ◽  
Author(s):  
Xuedong Zhang ◽  
Laurel H. Carney
Keyword(s):  
Low Frequency ◽  
Auditory Brainstem ◽  
Small Time ◽  
Computational Technique ◽  
Model Parameters ◽  
Fire Model ◽  
Response Properties ◽  
Integrate And Fire ◽  
Output Synchronization ◽  
Model Cell

A computational technique is described for calculation of the inter-spike interval and poststimulus time histograms for the responses of an integrate-and-fire model to arbitrary inputs. The effects of the model parameters on the response statistics were studied systematically. Specifically, the probability distribution of the membrane potential was calculated as a function of time, and the mean interspike interval and PST histogram were calculated for arbitrary inputs. For stationary inputs, the regularity of the output was studied in detail for various model parameters. For nonstationary inputs, the effects of the model parameters on the output synchronization index were explored. The results show that enhanced synchronization in response to low-frequency stimuli required a large number (n > 25) of weak inputs. Irregular responses and a linear input-output rate relationship required strong (but subthreshold) inputs with a small time constant. A model cell with mixed-amplitude synaptic inputs can respond to stationary inputs irregularly and have enhanced synchronization to nonstationary inputs that are phase-locked to low-frequency inputs. Both of these response properties have been reported for some cells in the ventral cochlear nucleus in the auditory brainstem.

scholarly journals Method of Determining Trajectories in a Neighbourhood of Long-Run Equilibrium in Neoclassical Models of Exogenous Economic Growth

2019 ◽  
Vol 65 (4) ◽  
pp. 394-421
Author(s):  
Adam Krawiec ◽  
Aleksander Stachowski ◽  
Marek Szydłowski
Keyword(s):  
Economic Growth ◽  
Power Series ◽  
Growth Models ◽  
The State ◽  
Model Parameters ◽  
State Function ◽  
Initial State ◽  
Long Run ◽  
Estimation Of Model Parameters ◽  
Long Run Equilibrium

We consider economic growth models in the form of dynamical systems. We show a method of determining trajectories in a neighbourhood of a long-run equilibrium in some neoclassical models of exogenous economic growth. This method is applied primarily to these models which in general have no analytical solution. We propose the general method of finding solutions of arbitrarily dimensional dynamical system in the form of power series. We expand the state function in Taylor's series in the neighbourhood of the initial state. The coefficients of expansion represent the parameters of the variation of the state of the system and are calculated algebraically in Mathematica. We present the method of finding solutions for the Solow-Swan model and the Mankiw-Romer-Weil model. We use also the Padé aproximant method to obtain a better convergence of the power series. This method allows to obtain a solution in the form of a series for trajectories in a neighbourhood of a long-run equilibrium in two models of exogenous economic growth. We show that obtained solutions are a good approximation of time paths, along which the long-run equilibrium is reached. We show a possibility of estimation of model parameters for which solutions in the form of series are known.

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