Fundamental Equations

2009 ◽  
pp. 7-13
Keyword(s):  
Fundamental Equations

On submersions of the complex indicatrix

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5081-5092
Author(s):  
Elena Popovicia
Keyword(s):  
Fixed Point ◽  
Complex Projective Space ◽  
Finsler Space ◽  
Hermitian Manifold ◽  
Almost Hermitian Manifold ◽  
Codimension One ◽  
Real Submanifold ◽  
Fundamental Equations ◽  
Complex Projective ◽  
Extrinsic Sphere

In this paper we study the complex indicatrix associated to a complex Finsler space as an embedded CR - hypersurface of the holomorphic tangent bundle, considered in a fixed point. Following the study of CR - submanifolds of a K?hler manifold, there are investigated some properties of the complex indicatrix as a real submanifold of codimension one, using the submanifold formulae and the fundamental equations. As a result, the complex indicatrix is an extrinsic sphere of the holomorphic tangent space in each fibre of a complex Finsler bundle. Also, submersions from the complex indicatrix onto an almost Hermitian manifold and some properties that can occur on them are studied. As application, an explicit submersion onto the complex projective space is provided.

Stresses in a Metal Tube Under Both High Radial Temperature Variation and Internal Pressure

1954 ◽  
Vol 21 (2) ◽  
pp. 101-108
Author(s):  
Chieh-Chien Chang ◽  
Wen-Hwa Chu
Keyword(s):  
Stress Distribution ◽  
Temperature Variation ◽  
Modulus Of Elasticity ◽  
Coefficient Of Thermal Expansion ◽  
Metal Tube ◽  
Radial Temperature ◽  
Variation Of Parameters ◽  
Effects Of Temperature ◽  
Fundamental Equations ◽  
Very High

Abstract The paper treats the stress distribution in a metal tube which is subject to a very high radial temperature variation and pressure. The radial temperature distribution across the tube wall and the variations of the modulus of elasticity and the coefficient of thermal expansion are obtained from experimental data, and all these effects of temperature are taken into account in the calculations. The fundamental equations in the case of plane strain and plane stress can be formulated as the nonhomogeneous Whittaker differential equations. The corresponding solutions are obtained by the method of variation of parameters and in terms of Kummer series. An example is shown, and the stress distribution across the wall is given. For comparison, the stress distribution of the case of constant modulus of elasticity and coefficient of expansion is included.

Local Scale Covariance and Its Radical Implications for Cosmology

Galaxies ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 76
Author(s):  
Yehonatan Knoll
Keyword(s):  
Local Scale ◽  
Covariant Theory ◽  
De Sitter ◽  
Cosmological Redshift ◽  
Physical Limit ◽  
Scale Covariance ◽  
The Status ◽  
Scale Motion ◽  
Fundamental Equations ◽  
Conceptual Foundations

Local scale covariance posits that no privileged length scales should appear in the fundamental equations of local, Minkowskian physics—why should nature have scale, but not position preferences?—yet, they clearly do. A resolution is proposed wherein scale covariance is promoted to the status of Poincaré covariance, and privileged scales emerge as a result of `scale clustering’, similarly to the way privileged positions emerge in a translation covariant theory. The implied ability of particles to `move in scale’ has recently been shown by the author to offer a possible elegant solution to the missing matter problem. For cosmology, the implications are: (a) a novel component of the cosmological redshift, due to scale-motion over cosmological times; (b) a radically different scenario for the early universe, during which the conditions for such scale clustering are absent. The former is quantitatively analyzed, resulting in a unique cosmological model, empirically coinciding with standard Einstein–de-Sitter cosmology, only in some non-physical limit. The latter implication is qualitatively discussed as part of a critique of the conceptual foundations of ΛCDM which ignores scale covariance altogether.

LES of Turbulent Separated Flow and Heat Transfer in a Symmetric Expansion Plane Channel

2005 ◽  
Vol 127 (5) ◽  
pp. 865-871 ◽  
Author(s):  
Kazuaki Sugawara ◽  
Hiroyuki Yoshikawa ◽  
Terukazu Ota
Keyword(s):  
Heat Transfer ◽  
Finite Difference ◽  
Plane Channel ◽  
Separated Flow ◽  
Expansion Ratio ◽  
Vortical Flow ◽  
Flow And Heat Transfer ◽  
Finite Difference Equations ◽  
Separated And Reattached Flow ◽  
Fundamental Equations

The LES method was applied to analyze numerically an unsteady turbulent separated and reattached flow and heat transfer in a symmetric expansion plane channel of expansion ratio 2.0. The Smagorinsky model was used in the analysis and fundamental equations were discretized by means of the finite difference method, and their resulting finite difference equations were solved using the SMAC method. The calculations were conducted for Re=15,000. It is found that the present numerical results, in general, agree well with the previous experimental ones. The complicated vortical flow structures in the channel and their correlations with heat transfer characteristics are visualized through various fields of flow quantities.

scholarly journals Model experiments on large tabular iceberg evolution: ablation and strain thinning

2005 ◽  
Vol 51 (174) ◽  
pp. 363-372 ◽  
Author(s):  
Daniela Jansen ◽  
Henner Sandhäger ◽  
Wolfgang Rack
Keyword(s):  
Environmental Parameters ◽  
Constant Density ◽  
Active Components ◽  
Ice Shelf ◽  
Ice Dynamics ◽  
Model Experiments ◽  
Flow And Heat Transfer ◽  
Sensitivity Studies ◽  
Basal Melting ◽  
Fundamental Equations

AbstractAntarctic tabular icebergs are important active components of the ice–ocean system. To investigate the relevance of inherent ice dynamics to iceberg evolution, we developed a numerical model based on the fundamental equations of ice-shelf flow and heat transfer, forced by environmental parameters of the ice–ocean–atmosphere system. Model experiments with idealized icebergs of constant density show that the strain thinning rate for a typical iceberg with a thickness of 250 m and a temperature of −15°C is about 1 m a−1. Sensitivity studies for different scenarios of environmental conditions confirmed the reliability of our model. A 5 year simulation of the evolution of iceberg A-38B yielded a mean decrease in thickness from 220 m to 106.3 m, 95% of which was caused by basal melting, 1% by surface melting and 4% by strain thinning. We found iceberg spreading decelerating by about 75%, and ice temperatures being strongly affected by progressive erosion of the relatively warm basal layers and warming in the uppermost part. According to the model results, basal melting is the primary cause of change of iceberg geometry during drift, whereas strain thinning is only relevant in cold areas where basal melting is low.

Calculation of whole blood CO2 content

1988 ◽  
Vol 65 (1) ◽  
pp. 473-477 ◽  
Author(s):  
A. R. Douglas ◽  
N. L. Jones ◽  
J. W. Reed
Keyword(s):  
Whole Blood ◽  
Hemoglobin Concentration ◽  
Healthy Male ◽  
Co2 Solubility ◽  
Computer Technique ◽  
Solubility Coefficient ◽  
Blood Ph ◽  
Fundamental Equations ◽  
Male Subjects

Currently used methods for calculating whole blood CO2 content from calculated plasma content, measured blood pH, hemoglobin concentration ([Hb]), and O2 saturation yield materially different results. In this study the constants of the fundamental equations relating blood CO2 content to plasma content have been reevaluated. An iterative computer technique was used to empirically derive appropriate constants from data obtained from nine healthy male subjects at rest and at several exercise work loads. A calculation was derived that fitted the data well [difference 0.02 +/- 1.19 ml/100 (SD) ml, r = 0.98] blood CCO2 = plasma CCO2 (Formula: see text) where plasma CCO2 = 2.226.s.plasma PCO2.(1 + 10pH-pK'), CCO2 is CO2 content, SO2 is O2 saturation, s is the plasma CO2 solubility coefficient, and pK' is the apparent pK [s and pK' are from the equations of Kelman (Respir. Physiol. 3: 111-115, 1967)].

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