The Mean Amplitudes of Thermal Vibrations in Polyatomic Molecules. II. An Approximate Method for Calculating Mean Square Amplitudes

1953 ◽  
Vol 21 (11) ◽  
pp. 1927-1933 ◽  
Author(s):  
Yonezo Morino ◽  
Kôzo Kuchitsu ◽  
Akira Takahashi ◽  
Keiji Maeda
Keyword(s):  
Approximate Method ◽  
Polyatomic Molecules ◽  
Mean Square ◽  
The Mean ◽  
Thermal Vibrations

scholarly journals Melting Criterion for Cubic Metals Based on a Modified Angular Force Model

1974 ◽  
Vol 27 (1) ◽  
pp. 129 ◽  
Author(s):  
Jyoti Prakash ◽  
MP Hemkar
Keyword(s):  
Melting Point ◽  
Periodic Table ◽  
Lattice Dynamics ◽  
Force Model ◽  
Mean Square ◽  
Interatomic Spacing ◽  
Cubic Metals ◽  
The Mean ◽  
Thermal Vibrations

A modified angular force model for the lattice dynamics of metals is used to test Lindemann's melting criterion by computing the ratio Ym of the mean square amplitude of thermal vibrations to the square of the interatomic spacing at the melting point for a number of cubic metals belonging to different groups in the periodic table.

The Mean Amplitudes of Thermal Vibrations in Polyatomic Molecules. I. CF2=CF2 and CH2=CF2

1952 ◽  
Vol 20 (4) ◽  
pp. 726-733 ◽  
Author(s):  
Yonezo Morino ◽  
Kôzo Kuchitsu ◽  
Takehiko Shimanouchi
Keyword(s):  
Polyatomic Molecules ◽  
The Mean ◽  
Thermal Vibrations

Krebs's model and Lindemann's melting law

1968 ◽  
Vol 46 (15) ◽  
pp. 1677-1679 ◽  
Author(s):  
A. K. Singh ◽  
P. K. Sharma
Keyword(s):  
Melting Temperature ◽  
Periodic Table ◽  
Lattice Dynamics ◽  
Mean Square Displacement ◽  
Mean Square ◽  
Interatomic Spacing ◽  
Cubic Metals ◽  
The Mean ◽  
Thermal Vibrations

Lindemann's melting criterion for cubic metals is examined using Krebs's model for the lattice dynamics of metals by computing the ratio, xm, of the mean square displacement of thermal vibrations and the square of interatomic spacing at the melting temperature for a number of cubic metals belonging to different groups of the periodic table. This ratio has nearly the same value for elements of one particular group, but exhibits wide variation from one group to another. It is concluded that Lindemann's melting law is inadequate.

Predicting some Effects of Lattice Vibrations on Proton Scattering Patterns

1970 ◽  
Vol 14 ◽  
pp. 1-10
Author(s):  
C. S. Barrett
Keyword(s):  
Temperature Factor ◽  
Lattice Vibrations ◽  
Proton Scattering ◽  
Mean Square ◽  
X Ray Diffraction ◽  
X Ray ◽  
Structure Factors ◽  
Integrated Intensity ◽  
The Mean ◽  
Thermal Vibrations

AbstractA method of predicting the approximate relative intensities of lines in proton blocking patterns recently proposed, which is based on summing the squares of structure factors for the various orders of reflection of a plane, is found to predict certain effects of lattice vibrations on the lines in some recently reported patterns. The mean square amplitude of vibration enters the calculations through a Debye-Waller temperature factor like that used in X-ray diffraction. When patterns are compared for groups of crystals that are nearly identical except for this temperature factor, the qualitative predictions by this method agree with the observations. If it is also arbitrarily assumed that the integrated intensity dip at a spot where lines intersect is approximated by summing the calculated Integrated intensity dips for all of the lines crossing at the spot, one has a simple and convenient method of predicting relative spot intensities. Such calculations have been successful in establishing the order of decreasing intensity for most of the spots along a given line, with several different kinds of crystals. This method also serves to predict qualitatively how prominent the spots appear relative to the lines, in general, in patterns of crystals that differ appreciably only in the amplitude of the thermal vibrations.

The Bordeaux Automatic Meridian Circle

1978 ◽  
Vol 48 ◽  
pp. 227-228
Author(s):  
Y. Requième
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Meridian Circle ◽  
The Mean ◽  
Full Automation

In spite of important delays in the initial planning, the full automation of the Bordeaux meridian circle is progressing well and will be ready for regular observations by the middle of the next year. It is expected that the mean square error for one observation will be about ±0.”10 in the two coordinates for declinations up to 87°.

The mean-square generalized delayed decision feedback sequence detector

2003 ◽  
Vol 14 (3) ◽  
pp. 265-268 ◽  
Author(s):  
Maurizio Magarini ◽  
Arnaldo Spalvieri ◽  
Guido Tartara
Keyword(s):  
Decision Feedback ◽  
Mean Square ◽  
The Mean

Limit tolerances for sums of measurement errors

2018 ◽  
Vol 934 (4) ◽  
pp. 59-62
Author(s):  
V.I. Salnikov
Keyword(s):  
Normal Distribution ◽  
Mean Square Error ◽  
Gaussian Distribution ◽  
Measurement Errors ◽  
Theory And Practice ◽  
Mean Square ◽  
The Mean ◽  
Limiting Values ◽  
Limiting Value

The question of calculating the limiting values of residuals in geodesic constructions is considered in the case when the limiting value for measurement errors is assumed equal to 3m, ie ∆рred = 3m, where m is the mean square error of the measurement. Larger errors are rejected. At present, the limiting value for the residual is calculated by the formula 3m√n, where n is the number of measurements. The article draws attention to two contradictions between theory and practice arising from the use of this formula. First, the formula is derived from the classical law of the normal Gaussian distribution, and it is applied to the truncated law of the normal distribution. And, secondly, as shown in [1], when ∆рred = 2m, the sums of errors naturally take the value equal to ?pred, after which the number of errors in the sum starts anew. This article establishes its validity for ∆рred = 3m. A table of comparative values of the tolerances valid and recommended for more stringent ones is given. The article gives a graph of applied and recommended tolerances for ∆рred = 3m.

scholarly journals Electrical stimulator with mechanomyography-based real-time monitoring, muscle fatigue detection, and safety shut-off: a pilot study

2020 ◽  
Vol 65 (4) ◽  
pp. 461-468
Author(s):  
Jannatul Naeem ◽  
Nur Azah Hamzaid ◽  
Amelia Wong Azman ◽  
Manfred Bijak
Keyword(s):  
Muscle Fatigue ◽  
Real Time ◽  
Isometric Force ◽  
Mean Square ◽  
Clear Indication ◽  
Initial Value ◽  
Cord Injury ◽  
The Mean ◽  
Electrical Stimulator ◽  
Fatigue Detection

AbstractFunctional electrical stimulation (FES) has been used to produce force-related activities on the paralyzed muscle among spinal cord injury (SCI) individuals. Early muscle fatigue is an issue in all FES applications. If not properly monitored, overstimulation can occur, which can lead to muscle damage. A real-time mechanomyography (MMG)-based FES system was implemented on the quadriceps muscles of three individuals with SCI to generate an isometric force on both legs. Three threshold drop levels of MMG-root mean square (MMG-RMS) feature (thr50, thr60, and thr70; representing 50%, 60%, and 70% drop from initial MMG-RMS values, respectively) were used to terminate the stimulation session. The mean stimulation time increased when the MMG-RMS drop threshold increased (thr50: 22.7 s, thr60: 25.7 s, and thr70: 27.3 s), indicating longer sessions when lower performance drop was allowed. Moreover, at thr70, the torque dropped below 50% from the initial value in 14 trials, more than at thr50 and thr60. This is a clear indication of muscle fatigue detection using the MMG-RMS value. The stimulation time at thr70 was significantly longer (p = 0.013) than that at thr50. The results demonstrated that a real-time MMG-based FES monitoring system has the potential to prevent the onset of critical muscle fatigue in individuals with SCI in prolonged FES sessions.

Die Molekülstruktur des N-Chlorsdiwefeloxiddifluoridimids ClNSOF2 / The Molecular Structure of ClNSOF2

1974 ◽  
Vol 29 (6) ◽  
pp. 901-904 ◽  
Author(s):  
O. Oberhammer ◽  
O. Glemser ◽  
H. Klüver
Keyword(s):  
Molecular Structure ◽  
Electron Diffraction ◽  
Geometric Parameters ◽  
Mean Square ◽  
The Mean

The molecular structure of ClNSOF2 was determined by electron diffraction of gases. The following geometric parameters were obtained:Cl-N=1.715(5), S=N=1.484(7), S=O=1.394(3), S-F=1.548(3) Å, ∢ ClNS=114.7 (8), ∢ FSF=92.6(.8), ∢ NSF=111.8(.9) ∢ NSO=117.4 (3.1) and ∢ OSF=108.6 (.8)°. The results for the mean square amplitudes of vibration are given in the paper and an attempt is made to explain differences in corresponding parameters of some related molecules.

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