III. The influence of stress and strain on the physical properties of matter. Part I. Elasticity (
            continued
            ). The effect of change of temperature on the internal friction and torsional elasticity of metals

The author has recently had the honour of presenting to the Society a memoir relating to the internal friction of metals when vibrating torsionally at temperatures ranging from 0° C. to 25° C. He now brings forward results which have been obtained in experiments on the effect of change of temperature on the torsional elasticity and internal friction of metals. The apparatus used and the mode of experimenting are fully described in the paper, so that it will be sufficient, perhaps, to state here that the vibration-period and the logarithmic decrement were very carefully determined at four different temperatures between 0° C. and 100° C., and that the formulæ given below were worked out by the method of least squares; these formulæ are to be found in Tables I and II.

Download Full-text

Deprotonation energetics of some nucleosides in water from EMF measurements

Canadian Journal of Chemistry ◽

10.1139/v95-010 ◽

1995 ◽

Vol 73 (1) ◽

pp. 70-78 ◽

Cited By ~ 2

Author(s):

Sonali Ganguly ◽

Kiron K. Kundu

Keyword(s):

Least Squares ◽

Thermodynamic Quantities ◽

Method Of Least Squares ◽

Emf Measurements ◽

Different Temperatures ◽

Temperature Equation

The deprotonation constants of uridine (K1 and K2), thymidine (K1 and K2), cytidine (K1 and K2), guanosine (K1, K2, and K3), and xanthosine (K1, K2, and K3) have been obtained in water from EMF measurements of Harned-Ehler type cells comprising H2 and Ag-AgI electrodes at different temperatures. The pK values were substituted in the temperature equation: pK = AT−1 + B + CT and A, B, and C were obtained by the method of least squares. Related thermodynamic quantities viz. ΔG0, TΔS0, and ΔH0 were obtained from coefficients A, B, and C of the respective nucleosides. Keywords: deprotonation energetics, uridine, thymidine, cytidine, guanosine, xanthosine.

Download Full-text

VI. The influence of stress and strain on the physical properties of matter. Part I. Elasticity— continued . The effect of magnetisation on the elasticity and the internal friction of metals

Proceedings of the Royal Society of London ◽

10.1098/rspl.1886.0063 ◽

1886 ◽

Vol 40 (242-245) ◽

pp. 447-449 ◽

Cited By ~ 1

Keyword(s):

Internal Friction ◽

Physical Properties ◽

Electric Current ◽

Stress And Strain ◽

The Wire ◽

Permanent Rotation ◽

A Current

The principal object of this investigation was to test the soundness of the view advanced by Professor G. Wiedemann respecting the cause of the internal friction of a torsionally oscillating wire. According to this view the internal friction is mainly due to permanent rotation to-and-fro of the molecules about their axes; it seemed probable, therefore, that experiments on the effects of magnetising a wire either longitudinally with a helix or circularly by passing a current through it would aid in elucidating the matter. In the experiments on the effects of longitudinal magnetisation arrangements were made so that the heat generated in the magnetising helix should not reach the wire, whilst the effect of the heat generated in the wire when an electric current was passed through it was eliminated in a manner which is fully described in the paper.

Download Full-text

I. The influence of stress and strain on the physical properties of matter. Part I. Elasticity— continued . The internal friction of metals

Proceedings of the Royal Society of London ◽

10.1098/rspl.1886.0028 ◽

1886 ◽

Vol 40 (242-245) ◽

pp. 240-242

Keyword(s):

Internal Friction ◽

Physical Properties ◽

Stress And Strain ◽

Vibrating Wire ◽

Coefficient Of Viscosity ◽

Molecular Friction

An abstract of a paper on this subject has been already published, but the paper itself was withdrawn for the purpose of revision. The fresh experiments which have been for this purpose instituted during the last year were made with improved apparatus, and the coefficient of viscosity of air redetermined, with a view of enabling the author to make more accurate correction for the effect of the resistance of the air. These more recent experiments on the loss of energy of a torsionally vibrating wire, besides confirming the results of the older ones, as far as the latter have been published, have furnished, more or less in addition, the following facts relating to the internal molecular friction of metals.

Download Full-text

I. The influence of stress and strain on the physical properties of matter.—Part I. Elasticity (continued).—The effect of magnetisation on the elasticity and the internal friction of metals

Philosophical Transactions of the Royal Society of London. (A.) ◽

10.1098/rsta.1888.0001 ◽

1888 ◽

Vol 179 ◽

pp. 1-26 ◽

Cited By ~ 9

Keyword(s):

Internal Friction ◽

Physical Properties ◽

Main Part ◽

Stress And Strain ◽

Heating Effect ◽

Vibrating Wire ◽

The Wire

According to Professor G. Wiedemann, the main part of the internal friction which occurs in a torsionally vibrating wire is due to the rotation of the molecules about their axes, first to this side and then to that, as the wire vibrates to and fro. With this view the author’s own experiments on the internal friction of metals had been so far in accordance that he wished still further to test the matter by investigating the effect of magnetisation on the internal friction. The author has already made some experiments on the effect of magnetisation on the torsional elasticity of metals, but the results of these experiments did not entirely satisfy him, inasmuch as the means of eliminating the heating effect of the magnetising solenoid were imperfect. It is true that the observed changes of temperature wrought by the solenoid were comparatively small, but so also was the apparent alteration of torsional elasticity due to magnetisation; and it seemed, therefore, advisable to reopen the inquiry, and to devise more perfect apparatus, whereby the heating effect above mentioned might be entirely done away with.

Download Full-text

III. The influence of stress and strain on the physical properties of matter. Part III. Magnetic induction ( continued ). The internal friction of iron, nickel, and cobalt, studied by means of magnetic cycles of very minute range

Proceedings of the Royal Society of London ◽

10.1098/rspl.1889.0060 ◽

1890 ◽

Vol 47 (286-291) ◽

pp. 13-14

Keyword(s):

Internal Friction ◽

Physical Properties ◽

Magnetic Induction ◽

Stress And Strain ◽

Torsional Oscillations ◽

Dissipation Of Energy ◽

Ballistic Method ◽

Iron Nickel ◽

Magnetic Cycles ◽

Molecular Friction

The author has already studied the internal friction of metals by the method of torsional oscillations, and deduced certain simple laws relating thereto. One of the principal objects of the present enquiry was to ascertain how far the dissipation of energy resulting from statical molecular friction which occurs in magnetic cycles of very minute range would be amenable to the laws of dissipation of energy occurring in torsional cycles. The “ballistic” method of observation has been employed, the arrangements being exceedingly sensitive so as to admit of the use of very feeble magnetising forces.

Download Full-text

The limit state of concrete and reinforced concrete rods at complex and longitudinal-transverse bending

PNRPU Mechanics Bulletin ◽

10.15593/perm.mech/2020.1.05 ◽

2020 ◽

pp. 60-73

Author(s):

Yu V Nemirovskii ◽

S V Tikhonov

Keyword(s):

General Solution ◽

Least Squares ◽

Nonlinear Differential Equations ◽

Limit State ◽

Algebraic Equations ◽

Method Of Least Squares ◽

Elasticity Limit ◽

Limit Values ◽

Symbolic Calculations ◽

Deformation Diagrams

The work considers rods with a constant cross-section. The deformation law of each layer of the rod is adopted as an approximation by a polynomial of the second order. The method of determining the coefficients of the indicated polynomial and the limit deformations under compression and tension of the material of each layer is described with the presence of three traditional characteristics: modulus of elasticity, limit stresses at compression and tension. On the basis of deformation diagrams of the concrete grades B10, B30, B50 under tension and compression, these coefficients are determined by the method of least squares. The deformation diagrams of these concrete grades are compared on the basis of the approximations obtained by the limit values and the method of least squares, and it is found that these diagrams approximate quite well the real deformation diagrams at deformations close to the limit. The main problem in this work is to determine if the rod is able withstand the applied loads, before intensive cracking processes in concrete. So as a criterion of the conditional limit state this work adopts the maximum permissible deformation value under tension or compression corresponding to the points of transition to a falling branch on the deformation diagram level in one or more layers of the rod. The Kirchhoff-Lyav classical kinematic hypotheses are assumed to be valid for the rod deformation. The cases of statically determinable and statically indeterminable problems of bend of the rod are considered. It is shown that in the case of statically determinable loadings, the general solution of the problem comes to solving a system of three nonlinear algebraic equations which roots can be obtained with the necessary accuracy using the well-developed methods of computational mathematics. The general solution of the problem for statically indeterminable problems is reduced to obtaining a solution to a system of three nonlinear differential equations for three functions - deformation and curvatures. The Bubnov-Galerkin method is used to approximate the solution of this equation on the segment along the length of the rod, and specific examples of its application to the Maple system of symbolic calculations are considered.

Download Full-text

Functional ratings in sports

Journal of Quantitative Analysis in Sports ◽

10.1515/jqas-2020-0001 ◽

2020 ◽

Vol 16 (3) ◽

pp. 183-191

Author(s):

Brad Lowery ◽

Abigail Slater ◽

Kaison Thies

Keyword(s):

Least Squares ◽

Method Of Least Squares ◽

Sports Teams ◽

New Model ◽

College Basketball ◽

Division 1

AbstractIn this paper, we present a new model for ranking sports teams. Our model uses all scoring data from all games to produce a functional rating by the method of least squares. The functional rating can be interpreted as a team average point differential adjusted for strength of schedule. Using two team’s functional ratings we can predict the expected point differential at any time in the game. We looked at three variations of our model accounting for home-court advantage in different ways. We use the 2018–2019 NCAA Division 1 men’s college basketball season to test the models and determined that home-court advantage is statistically important but does not differ between teams.

Download Full-text