scholarly journals Computer-assisted Existence Proofs for One-dimensional Schrödinger-Poisson Systems

2020 ◽  
Vol 24 (3) ◽  
pp. 373-391
Author(s):  
Jonathan Wunderlich ◽  
Michael Plum
Keyword(s):  
Approximate Solution ◽  
Ritz Method ◽  
Three Dimensional ◽  
Computer Assisted ◽  
Poisson System ◽  
Eigenvalue Bounds ◽  
One Dimensional ◽  
Existence Proofs ◽  
Norm Bound ◽  
The One

Motivated by the three-dimensional time-dependent Schrödinger-Poisson system we prove the existence of non-trivial solutions of the one-dimensional stationary Schrödinger-Poisson system using computer-assisted methods. Starting from a numerical approximate solution, we compute a bound for its defect, and a norm bound for the inverse of the linearization at the approximate solution. For the latter, eigenvalue bounds play a crucial role, especially for the eigenvalues "close to" zero. Therefor, we use the Rayleigh-Ritz method and a corollary of the Temple-Lehmann Theorem to get enclosures of the crucial eigenvalues of the linearization below the essential spectrum. With these data in hand, we can use a fixed-point argument to obtain the desired existence of a non-trivial solution "nearby" the approximate one. In addition to the pure existence result, the used methods also provide an enclosure of the exact solution.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

Lower Bounds to the Eigenvalues in One-Dimensional Problems by a Shift in the Weight Function

1970 ◽  
Vol 37 (2) ◽  
pp. 267-270 ◽  
Author(s):  
D. Pnueli
Keyword(s):  
Lower Bound ◽  
Weight Function ◽  
Lower Bounds ◽  
Variational Formulation ◽  
Ritz Method ◽  
The Other ◽  
One Dimensional ◽  
Systematic Shift ◽  
The One ◽  
Detailed Computation

A method is presented to obtain both upper and lower bound to eigenvalues when a variational formulation of the problem exists. The method consists of a systematic shift in the weight function. A detailed procedure is offered for one-dimensional problems, which makes improvement of the bounds possible, and which involves the same order of detailed computation as the Rayleigh-Ritz method. The main contribution of this method is that it yields the “other bound;” i.e., the one which cannot be obtained by the Rayleigh-Ritz method.

On the numerical study of thermohydrodynamics and biochemistry of inland water bodies

2021 ◽  
Author(s):  
Daria Gladskikh ◽  
Evgeny Mortikov ◽  
Victor Stepanenko
Keyword(s):  
Mixed Layer ◽  
Numerical Study ◽  
Three Dimensional ◽  
Water Bodies ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
One Dimensional ◽  
Lake Model ◽  
Upper Mixed Layer ◽  
The One

<p>The study of thermodynamic and biochemical processes of inland water objects using one- and three-dimensional RANS numerical models was carried out both for idealized water bodies and using measurements data. The need to take into account seiche oscillations to correctly reproduce the deepening of the upper mixed layer in one-dimensional (vertical) models is demonstrated. We considered the one-dimensional LAKE model [1] and the three-dimensional model [2, 3, 4] developed at the Research Computing Center of Moscow State University on the basis of a hydrodynamic code combining DNS/LES/RANS approaches for calculating geophysical turbulent flows. The three-dimensional model was supplemented by the equations for calculating biochemical substances by analogy with the one-dimensional biochemistry equations used in the LAKE model. The effect of mixing processes on the distribution of concentration of greenhouse gases, in particular, methane and oxygen, was studied.</p><p>The work was supported by grants of the RF President’s Grant for Young Scientists (MK-1867.2020.5, MD-1850.2020.5) and by the RFBR (19-05-00249, 20-05-00776). </p><p>1. Stepanenko V., Mammarella I., Ojala A., Miettinen H., Lykosov V., Timo V. LAKE 2.0: a model for temperature, methane, carbon dioxide and oxygen dynamics in lakes // Geoscientific Model Development. 2016. V. 9(5). P. 1977–2006.<br>2. Mortikov E.V., Glazunov A.V., Lykosov V.N. Numerical study of plane Couette flow: turbulence statistics and the structure of pressure-strain correlations // Russian Journal of Numerical Analysis and Mathematical Modelling. 2019. 34(2). P. 119-132.<br>3. Mortikov, E.V. Numerical simulation of the motion of an ice keel in stratified flow // Izv. Atmos. Ocean. Phys. 2016. V. 52. P. 108-115.<br>4. Gladskikh D.S., Stepanenko V.M., Mortikov E.V. On the influence of the horizontal dimensions of inland waters on the thickness of the upper mixed layer // Water Resourses. 2021.V. 45, 9 pages. (in press) </p>

scholarly journals The three dimensional stabilization of superconductivity at 12 K in the one dimensional organic superconductor (TMTSF)2PF6 under 11 kbar

1981 ◽  
Vol 42 (19) ◽  
pp. 445-449 ◽  
Author(s):  
A. Fournel ◽  
C. More ◽  
G. Roger ◽  
J.P. Sorbier ◽  
J.M. Delrieu ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Organic Superconductor ◽  
One Dimensional ◽  
The One

scholarly journals Hydraulic modeling of combined sewers overflow integrating the results of the SWMM and CFX models.

2021 ◽  
Vol 37 (1) ◽  
Author(s):  
D. Pulgarín ◽  
J. Plaza ◽  
J. Ruge ◽  
J. Rojas
Keyword(s):  
Three Dimensional ◽  
Hydraulic Modeling ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
One Dimensional ◽  
Ansys Cfx ◽  
Combined Sewer ◽  
The One ◽  
Swmm Model

This study proposes a methodology for the calibration of combined sewer overflow (CSO), incorporating the results of the three-dimensional ANSYS CFX model in the SWMM one-dimensional model. The procedure consists of constructing calibration curves in ANSYS CFX that relate the input flow to the CSO with the overflow, to then incorporate them into the SWMM model. The results obtained show that the behavior of the flow over the crest of the overflow weir varies in space and time. Therefore, the flow of entry to the CSO and the flow of excesses maintain a non-linear relationship, contrary to the results obtained in the one-dimensional model. However, the uncertainty associated with the idealization of flow methodologies in one dimension is reduced under the SWMM model with kinematic wave conditions and simulating CSO from curves obtained in ANSYS CFX. The result obtained facilitates the calibration of combined sewer networks for permanent or non-permanent flow conditions, by means of the construction of curves in a three-dimensional model, especially when the information collected in situ is limited.

Contractile Filament Stress in the Left Ventricle and its Relationship to Wall Stress

1979 ◽  
Vol 101 (4) ◽  
pp. 225-231 ◽  
Author(s):  
E. S. Grood ◽  
C. A. Phillips ◽  
R. E. Mates
Keyword(s):  
Three Dimensional ◽  
Wall Stress ◽  
One Dimensional ◽  
Muscle Work ◽  
Lumped Parameter ◽  
Pressure Development ◽  
The One ◽  
Active Force Generation ◽  
Muscle Models ◽  
Significant Underestimation

A three-dimensional composite model of heart muscle is proposed, consisting of one-dimensional (uniaxial) active contractile filaments embedded in a passive elastic binder. Equations are developed which relate the force developed by the filaments to the local tissue stress. An approximate analysis is employed to determine the time variation of the contractile filament stress throughout the cardiac cycle from catheterization data. Results from 15 patients with normal left ventricles demonstrate that the stress developed by the contractile filaments is up to 25 percent more tensile than the wall stress, and that the binder stress is compressive during most of systole. In contrast, the one-dimensional lumped parameter muscle models previously employed predict active (CE) stresses less tensile than the wall stress and binder (PE) stresses that are tensile. We conclude that the use of a one-dimensional muscle model results in a significant underestimation of the active force generation required for pressure development and the power requirements for ejection. Prior studies relating muscle work and power to ventricular oxygen consumption should be re-examined in this light.

Analysis of the Exit Flow Angle and Characteristics of Flow in Axial Turbine Cascades

2020 ◽  
Author(s):  
Narmin B. Hushmandi ◽  
Per Askebjer ◽  
Magnus Genrup
Keyword(s):  
Dimensional Analysis ◽  
Three Dimensional ◽  
Flow Coefficient ◽  
Reference Plane ◽  
Exit Angle ◽  
Design Work ◽  
Flow Angle ◽  
Axial Turbine ◽  
One Dimensional ◽  
The One

Abstract Despite a wealth of sophisticated CFD-methods, most designs are still based on one-dimensional and two-dimensional inviscid analytical tools. In such methods, realistic loss and angle assessment are indeed critical in order to arrive at correct loading, flow coefficient and reaction. The selected values are normally retained through the detailed design sequence for each iteration. This means that the throat sizing and hence the gauge angle is largely based on the early design work within the through-flow environment. Even one-degree error in angle estimation will turn into a rather large capacity error. For most designs, the exchange rate between capacity and gauge angle is on the order of 3–5 percent, per degree exit angle. In a previous publication, a methodology and equations were presented to assess the exit flow in an axial turbine blade row by Mamaev in Russian nomenclature and the tangential coordinate system. The approach, provided a unified and flow-physics based method for assessing exit angles from the geometry features like gauge angle, uncovered turning and flow features like Laval number, etc. Analysis of those formulas showed good agreement with physical flow pattern in real cascades for sub and transonic blade cascades. In this work, the same basic principal procedure is followed by employing the more international agreed nomenclature of blades such as an axial reference plane and Mach number. In the current work, the one-dimensional analysis results were compared with the three dimensional numerical modelling of a full annulus two-stage turbine. Analysis of the results showed the inherent unsteadiness specially outside the rotor blade cascades, however, comparison of the mass averaged exit angle with the one dimensional analysis showed satisfactory agreement.

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