| 1. |
- Breznau, Nate, et al.
(författare)
-
Observing many researchers using the same data and hypothesis reveals a hidden universe of uncertainty
- 2022
-
Ingår i: Proceedings of the National Academy of Sciences of the United States of America. - : National Academy of Sciences. - 0027-8424 .- 1091-6490. ; 119:44
-
Tidskriftsartikel (refereegranskat)abstract
- This study explores how researchers analytical choices affect the reliability of scientific findings. Most discussions of reliability problems in science focus on systematic biases. We broaden the lens to emphasize the idiosyncrasy of conscious and unconscious decisions that researchers make during data analysis. We coordinated 161 researchers in 73 research teams and observed their research decisions as they used the same data to independently test the same prominent social science hypothesis: that greater immigration reduces support for social policies among the public. In this typical case of social science research, research teams reported both widely diverging numerical findings and substantive conclusions despite identical start conditions. Researchers expertise, prior beliefs, and expectations barely predict the wide variation in research outcomes. More than 95% of the total variance in numerical results remains unexplained even after qualitative coding of all identifiable decisions in each teams workflow. This reveals a universe of uncertainty that remains hidden when considering a single study in isolation. The idiosyncratic nature of how researchers results and conclusions varied is a previously underappreciated explanation for why many scientific hypotheses remain contested. These results call for greater epistemic humility and clarity in reporting scientific findings.
|
|
| 2. |
- Betancourt, Fernando, et al.
(författare)
-
A Model of Froth Flotation with Drainage : Simulations and Comparison with Experiments
- 2023
-
Ingår i: Minerals. - : MDPI AG. - 2075-163X. ; 13:3
-
Tidskriftsartikel (refereegranskat)abstract
- The operation of a froth flotation column can be described by a nonlinear convection–diffusion partial differential equation that incorporates the solids–flux and drift–flux theories as well as a model of foam drainage. The resulting model predicts the bubble and (gangue) particle volume fractions as functions of height and time. The steady-state (time-independent) version of the model defines so-called operating charts that map conditions on the gas and pulp feed rates that allow for operation with a stationary froth layer. Operating charts for a suitably adapted version of the model are compared with experimental results obtained with a laboratory flotation column. Experiments were conducted with a two-phase liquid–bubble flow. The results indicate good agreement between the predicted and measured conditions for steady states. Numerical simulations for transient operation, in part for the addition of solid particles, are presented.
|
|
| 3. |
- Betancourt, Fernando, et al.
(författare)
-
A random sampling method for a family of Temple-class systems of conservation laws
- 2018
-
Ingår i: Numerische Mathematik. - : Springer Science and Business Media LLC. - 0029-599X .- 0945-3245. ; 138:1, s. 37-73
-
Tidskriftsartikel (refereegranskat)abstract
- The Aw–Rascle–Zhang traffic model, a model of sedimentation, and other applications lead to nonlinear (Formula presented.) systems of conservation laws that are governed by a single scalar system velocity. Such systems are of the Temple class since rarefaction wave curves and Hugoniot curves coincide. Moreover, one characteristic field is genuinely nonlinear almost everywhere, and the other is linearly degenerate. Two well-known problems associated with these systems are handled via a random sampling approach. Firstly, Godunov’s and related methods produce spurious oscillations near contact discontinuities since the numerical solution invariably leaves the invariant region of the exact solution. It is shown that alternating between averaging (Av) and remap steps similar to the approach by Chalons and Goatin (Commun Math Sci 5:533–551, 2007) generates numerical solutions that do satisfy an invariant region property. If the remap step is made by random sampling (RS), then combined techniques due to Glimm (Commun Pure Appl Math 18:697–715, 1965), LeVeque and Temple (Trans Am Math Soc 288:115–123, 1985) prove that the resulting Av–RS scheme converges to a weak solution. Numerical examples illustrate that the new scheme is superior to Godunov’s method in accuracy and resolution. Secondly, the vacuum state, which may form even from positive initial data, causes potential problems of non-uniqueness and instability. This is resolved by introducing an alternative Riemann solution concept.
|
|
| 4. |
- Betancourt, Fernando, et al.
(författare)
-
Advanced methods of flux identification for clarifier–thickener simulation models
- 2014
-
Ingår i: Minerals Engineering. - : Elsevier BV. - 0892-6875. ; 63:August 2014, s. 2-15
-
Tidskriftsartikel (refereegranskat)abstract
- Mathematical models for the simulation of batch settling and continuous clarifier-thickeners can usually be expressed as a convection-diffusion partial differential equation (PDE). Reliable numerical methods require that the nonlinear flux function of this PDE has been identified for a given material. This contribution summarizes, and applies to experimental data, a recent approach [Bürger, R., Diehl, S., 2013. Inverse Problems 29, 045008] for the flux identification in the case of a suspension that shows no compressive behavior. The experimental Kynch test and the Diehl test, which are based on an initially homogenous suspension either filling the whole settling column or being initially located above clear liquid, respectively, provide data points that represent a convex and concave, respectively, suspension-supernate interface. A provably convex (concave) smooth approximation of this interface is obtained by solving a constrained least-squares minimization problem. The interface-approximating function can be converted uniquely into an explicit formula for a convex (concave) part of the flux function.
|
|
| 5. |
- Betancourt, Fernando, et al.
(författare)
-
Modeling and controlling clarifier–thickeners fed by suspensions with time-dependent properties
- 2014
-
Ingår i: Minerals Engineering. - : Elsevier BV. - 0892-6875. ; 62, s. 91-101
-
Tidskriftsartikel (refereegranskat)abstract
- A one-dimensional model of the process of continuous sedimentation in a clarifier–thickener unit is presented. The governing model is expressed as a system of two nonlinear partial differential equations for the solids volume fraction and the varying settling velocity of the solids as functions of depth and time. This model extends the well-known model for the dynamics of a flocculated suspension in a clarifier–thickener advanced by Bürger et al. (2005). Operating charts are calculated to be used for the control of steady states, in particular, to keep the sediment level and the underflow volume fraction at desired values. A numerical scheme and a simple regulator are proposed and numerical simulations are performed.
|
|
| 6. |
- Burger, Friedrich Anton, et al.
(författare)
-
Comparison of Theory and Experiments on van der Waals Forces in Media-A Survey
- 2020
-
Ingår i: The Journal of Physical Chemistry C. - : American Chemical Society (ACS). - 1932-7447 .- 1932-7455. ; 124:44, s. 24179-24186
-
Tidskriftsartikel (refereegranskat)abstract
- We present a critical overview comparing theoretical predictions and measurements of van der Waals dispersion forces in media on the basis of the respective Hamaker constants. To quantify the agreement, we complement the reported experimental errors with those for the theoretical predictions, which are because of the uncertainties in the underlying spectroscopic data. Our main finding is that the theoretical errors are often larger than their experimental counterparts. Within these uncertainties, the comparison confirms the standard Lifshitz theory based on the Abraham electromagnetic stress tensor against the recently suggested alternative account on the basis of the Maxwell stress tensor.
|
|
| 7. |
|
|
| 8. |
- Bürger, Raimund, et al.
(författare)
-
A consistent modelling methodology for secondary settling tanks: A reliable numerical method.
- 2013
-
Ingår i: Water Science and Technology. - : IWA Publishing. - 0273-1223 .- 1996-9732. ; 68:1, s. 192-208
-
Tidskriftsartikel (refereegranskat)abstract
- The consistent modelling methodology for secondary settling tanks (SSTs) leads to a partial differential equation (PDE) of nonlinear convection–diffusion type as a one-dimensional model for the solids concentration as a function of depth and time. This PDE includes a flux that depends discontinuously on spatial position modelling hindered settling and bulk flows, a singular source term describing the feed mechanism, a degenerating term accounting for sediment compressibility, and a dispersion term for turbulence. In addition, the solution itself is discontinuous. A consistent, reliable and robust numerical method that properly handles these difficulties is presented. Many constitutive relations for hindered settling, compression and dispersion can be used within the model, allowing the user to switch on and off effects of interest depending on the modelling goal as well as investigate the suitability of certain constitutive expressions. Simulations show the effect of the dispersion term on effluent suspended solids and total sludge mass in the SST. The focus is on correct implementation whereas calibration and validation are not pursued.
|
|
| 9. |
- Bürger, Raimund, et al.
(författare)
-
A consistent modelling methodology for secondary settling tanks in wastewater treatment
- 2011
-
Ingår i: Water Research. - : Elsevier BV. - 1879-2448 .- 0043-1354. ; 45:6, s. 2247-2260
-
Tidskriftsartikel (refereegranskat)abstract
- The aim of this contribution is partly to build consensus on a consistent modelling methodology (CMM) of complex real processes in wastewater treatment by combining classical concepts with results from applied mathematics, and partly to apply it to the clarification-thickening process in the secondary settling tank. In the CMM, the real process should be approximated by a mathematical model (process model; ordinary or partial differential equation (ODE or PDE)), which in turn is approximated by a simulation model (numerical method) implemented on a computer. These steps have often not been carried out in a correct way. The secondary settling tank was chosen as a case since this is one of the most complex processes in a wastewater treatment plant and simulation models developed decades ago have no guarantee of satisfying fundamental mathematical and physical properties. Nevertheless, such methods are still used in commercial tools to date. This particularly becomes of interest as the state-of-the-art practice is moving towards plant-wide modelling. Then all submodels interact and errors propagate through the model and severely hamper any calibration effort and, hence, the predictive purpose of the model. The CMM is described by applying it first to a simple conversion process in the biological reactor yielding an ODE solver, and then to the solideliquid separation in the secondary settling tank, yielding a PDE solver. Time has come to incorporate established mathematical techniques into environmental engineering, and wastewater treatment modelling in particular, and to use proven reliable and consistent simulation models.
|
|
| 10. |
- Bürger, Raimund, et al.
(författare)
-
A difference scheme for a degenerating convection-diffusion-reaction system modelling continuous sedimentation
- 2018
-
Ingår i: ESAIM: Mathematical Modelling and Numerical Analysis. - : EDP Sciences. - 0764-583X .- 1290-3841. ; 52:2, s. 365-392
-
Tidskriftsartikel (refereegranskat)abstract
- Continuously operated settling tanks are used for the gravity separation of solid-liquid suspensions in several industries. Mathematical models of these units form a topic for well-posedness and numerical analysis even in one space dimension due to the spatially discontinuous coefficients of the underlying strongly degenerate parabolic, nonlinear model partial differential equation (PDE). Such a model is extended to describe the sedimentation of multi-component particles that react with several soluble components of the liquid phase. The fundamental balance equations contain the mass percentages of the components of the solid and liquid phases. The equations are reformulated as a system of nonlinear PDEs that can be solved consecutively in each time step by an explicit numerical scheme. This scheme combines a difference scheme for conservation laws with discontinuous ux with an approach of numerical percentage propagation for multi-component ows. The main result is an invariant-region property, which implies that physically relevant numerical solutions are produced. Simulations of denitrification in secondary settling tanks in wastewater treatment illustrate the model and its discretization.
|
|
