A REDUCTION OF THE BOLTZMANN-PEIERLS EQUATION

2005 ◽  
Vol 02 (02) ◽  
pp. 213-229 ◽  
Author(s):  
MATTHIAS KUNIK ◽  
SHAMSUL QAMAR ◽  
GERALD WARNECKE
Keyword(s):  
Kinetic Equation ◽  
Numerical Test ◽  
Three Dimensional ◽  
Entropy Density ◽  
Test Cases ◽  
Initial Value ◽  
Phase Density ◽  
One Dimensional ◽  
Kinetic Schemes ◽  
The One

This paper deals with the solutions of initial value problems of the Boltzmann-Peierls equation (BPE). This integro-differential equation describes the evolution of heat in crystalline solids at very low temperatures. The BPE describes the evolution of the phase density of a phonon gas. The corresponding entropy density is given by the entropy density of a Bose-gas. We derive a reduced three-dimensional kinetic equation which has a much simpler structure than the original BPE. By using special coordinates in the one-dimensional case, we can perform a further reduction of the kinetic equation. By assuming one-dimensionality on the initial phase density one can show that this property is preserved for all later times. We derive kinetic schemes for the kinetic equation as well as for the derived moment systems. Several numerical test cases are presented to validate the theory.

scholarly journals Performance Investigation of a Turbocharger Compressor

2012 ◽  
Author(s):  
A. L. de Wet ◽  
T. W. von Backström ◽  
S. J. van der Spuy
Keyword(s):  
Pressure Ratio ◽  
Three Dimensional ◽  
Rotating Stall ◽  
Test Case ◽  
Test Cases ◽  
Vaned Diffuser ◽  
One Dimensional ◽  
Verification Process ◽  
The One ◽  
Modelling Methods

The compressor section of a diesel locomotive turbocharger was re-designed to increase its maximum total-to-total pressure ratio and efficiency. Tests conducted on the prototype compressor showed possible rotating stall in the diffuser section before the designed higher pressure ratio could be achieved. It was decided to simulate the prototype compressor’s operation by using one-dimensional theory [1], followed by a three-dimensional CFD analysis of the compressor. This publication focuses on implementation of the impeller, vaneless annular passage and vaned diffuser one-dimensional theories. A verification process was followed to show the accuracy of the one- and three-dimensional modelling methods using two well-known centrifugal compressor test cases found in the literature [2–5]. Comparing the test case modelling results to available experimental results indicated sufficient accuracy to investigate the prototype compressor’s impeller and diffuser. Conclusions drawn on the prototype compressor’s performance using the one- and three-dimensional modelling methods led to a recommendation to redesign the impeller and diffuser of the prototype compressor.

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.

A TWELFTH-ORDER FOUR-STEP FORMULA FOR THE NUMERICAL INTEGRATION OF THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION

2003 ◽  
Vol 14 (08) ◽  
pp. 1087-1105 ◽  
Author(s):  
ZHONGCHENG WANG ◽  
YONGMING DAI
Keyword(s):  
Schrödinger Equation ◽  
Numerical Integration ◽  
Schrodinger Equation ◽  
Numerical Test ◽  
New Method ◽  
Step Method ◽  
One Dimensional ◽  
The Stability ◽  
The One ◽  
Order Four

A new twelfth-order four-step formula containing fourth derivatives for the numerical integration of the one-dimensional Schrödinger equation has been developed. It was found that by adding multi-derivative terms, the stability of a linear multi-step method can be improved and the interval of periodicity of this new method is larger than that of the Numerov's method. The numerical test shows that the new method is superior to the previous lower orders in both accuracy and efficiency and it is specially applied to the problem when an increasing accuracy is requested.

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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