A theory of the dielectric polarization of polar substances

1956 ◽  
Vol 238 (1213) ◽  
pp. 235-244 ◽  
Keyword(s):  
Dielectric Constant ◽  
Short Range ◽  
Approximate Equation ◽  
Mean Square ◽  
Dielectric Polarization ◽  
Bulk Properties ◽  
Classical Statistical Mechanics ◽  
Spherical Sample ◽  
The Mean ◽  
Onsager Equation

With the aid of classical statistical mechanics, a general expression for the static dielectric constant is derived. It is found, as in earlier work, that the dielectric constant is dependent upon the mean-square dipole moment of a macroscopic spherical sample of the substance. This mean-square moment is expanded as a series in powers of the mean molecular polarizability, and the terms proportional to the zero and first powers are evaluated in detail and in such a way that the long- and the short-range effects are separated. The former are determined with the aid of macroscopic arguments, so that a purely molecular theory remains. In the limit when short-range directional forces are zero, the formula reduces to the well-known Onsager equation. It is found that it is not in general legitimate to replace the surroundings of a macroscopic sample by a continuum having the bulk properties of the substance, and for this reason the approximate equation of Harris & Alder is found to lead to doubtful conclusions. The general equations are applied to the experimental data for water and other liquids, and the results are not unsatisfactory.

Study of collision-induced rotational perturbations in gases via the wing shape of infrared bands

1984 ◽  
Vol 62 (12) ◽  
pp. 1306-1314 ◽  
Author(s):  
M. O. Bulanin ◽  
M. V. Tonkov ◽  
N. N. Filippov
Keyword(s):  
High Frequency ◽  
Short Range ◽  
Analytical Approximation ◽  
Wing Shape ◽  
Rotational Relaxation ◽  
Mean Square ◽  
Dense Gases ◽  
Rotational Perturbation ◽  
Relaxation Parameters ◽  
The Mean

A theoretical analysis of the infrared absorption band wings is presented. The wing shape is expressed in terms of the spectral density of rotational perturbations experienced by absorbing molecules in moderately dense gases. The developed formalism is applied to the absorption in the high-frequency wing of the ν3 CO2 band. Analytical approximation of the experimental rotational perturbation densities is used to deduce the rotational relaxation parameters as well as the mean square torques, which provide information on the short-range anisotropic intermolecular interactions.

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.

scholarly journals Prediction of shallow bit position based on vibration signal monitoring of bit broken rock

2021 ◽  
Vol 17 (1) ◽  
pp. 155014772199170
Author(s):  
Jinping Yu ◽  
Deyong Zou
Keyword(s):  
Acoustic Emission ◽  
Time Domain ◽  
Vibration Signal ◽  
Rock Breaking ◽  
Drill String ◽  
Mean Square ◽  
Drilling Force ◽  
Emission Signal ◽  
Force Signal ◽  
The Mean

The speed of drilling has a great relationship with the rock breaking efficiency of the bit. Based on the above background, the purpose of this article is to predict the position of shallow bit based on the vibration signal monitoring of bit broken rock. In this article, first, the mechanical research of drill string is carried out; the basic changes of the main mechanical parameters such as the axial force, torque, and bending moment of drill string are clarified; and the dynamic equilibrium equation theory of drill string system is analyzed. According to the similarity criterion, the corresponding relationship between drilling process parameters and laboratory test conditions is determined. Then, the position monitoring test system of the vibration bit is established. The acoustic emission signal and the drilling force signal of the different positions of the bit in the process of vibration rock breaking are collected synchronously by the acoustic emission sensor and the piezoelectric force sensor. Then, the denoised acoustic emission signal and drilling force signal are analyzed and processed. The mean value, variance, and mean square value of the signal are calculated in the time domain. The power spectrum of the signal is analyzed in the frequency domain. The signal is decomposed by wavelet in the time and frequency domains, and the wavelet energy coefficients of each frequency band are extracted. Through the wavelet energy coefficient calculated by the model, combined with the mean, variance, and mean square error of time-domain signal, the position of shallow buried bit can be analyzed and predicted. Finally, by fitting the results of indoor experiment and simulation experiment, it can be seen that the stress–strain curve of rock failure is basically the same, and the error is about 3.5%, which verifies the accuracy of the model.

scholarly journals Effect of Terminal Groups on Thermomechanical and Dielectric Properties of Silica–Epoxy Composite Modified by Hyperbranched Polyester

Polymers ◽  
2021 ◽  
Vol 13 (15) ◽  
pp. 2451
Author(s):  
Jianwen Zhang ◽  
Dongwei Wang ◽  
Lujia Wang ◽  
Wanwan Zuo ◽  
Lijun Zhou ◽  
...  
Keyword(s):  
Dielectric Constant ◽  
Dielectric Properties ◽  
Binding Energy ◽  
Epoxy Resin ◽  
Volume Fraction ◽  
Epoxy Composite ◽  
Mean Square Displacement ◽  
Mean Square ◽  
Hyperbranched Polyester ◽  
Free Volume Fraction

To study the effect of hyperbranched polyester with different kinds of terminal groups on the thermomechanical and dielectric properties of silica–epoxy resin composite, a molecular dynamics simulation method was utilized. Pure epoxy resin and four groups of silica–epoxy resin composites were established, where the silica surface was hydrogenated, grafted with silane coupling agents, and grafted with hyperbranched polyester with terminal carboxyl and terminal hydroxyl, respectively. Then the thermal conductivity, glass transition temperature, elastic modulus, dielectric constant, free volume fraction, mean square displacement, hydrogen bonds, and binding energy of the five models were calculated. The results showed that the hyperbranched polyester significantly improved the thermomechanical and dielectric properties of the silica–epoxy composites compared with other surface treatments, and the terminal groups had an obvious effect on the enhancement effect. Among them, epoxy composite modified by the hyperbranched polyester with terminal carboxy exhibited the best thermomechanical properties and lowest dielectric constant. Our analysis of the microstructure found that the two systems grafted with hyperbranched polyester had a smaller free volume fraction (FFV) and mean square displacement (MSD), and the larger number of hydrogen bonds and greater binding energy, indicating that weaker strength of molecular segments motion and stronger interfacial bonding between silica and epoxy resin matrix were the reasons for the enhancement of the thermomechanical and dielectric properties.

scholarly journals Reconstruction of Diffusion Coefficients and Power Exponents from Single Lagrangian Trajectories

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 111
Author(s):  
Leonid M. Ivanov ◽  
Collins A. Collins ◽  
Tetyana Margolina
Keyword(s):  
Black Sea ◽  
Diffusion Coefficients ◽  
Current System ◽  
Mean Square Displacement ◽  
California Current ◽  
The Black Sea ◽  
Mean Square ◽  
California Current System ◽  
The Mean ◽  
Non Gaussian

Using discrete wavelets, a novel technique is developed to estimate turbulent diffusion coefficients and power exponents from single Lagrangian particle trajectories. The technique differs from the classical approach (Davis (1991)’s technique) because averaging over a statistical ensemble of the mean square displacement (<X2>) is replaced by averaging along a single Lagrangian trajectory X(t) = {X(t), Y(t)}. Metzler et al. (2014) have demonstrated that for an ergodic (for example, normal diffusion) flow, the mean square displacement is <X2> = limT→∞τX2(T,s), where τX2 (T, s) = 1/(T − s) ∫0T−s(X(t+Δt) − X(t))2 dt, T and s are observational and lag times but for weak non-ergodic (such as super-diffusion and sub-diffusion) flows <X2> = limT→∞≪τX2(T,s)≫, where ≪…≫ is some additional averaging. Numerical calculations for surface drifters in the Black Sea and isobaric RAFOS floats deployed at mid depths in the California Current system demonstrated that the reconstructed diffusion coefficients were smaller than those calculated by Davis (1991)’s technique. This difference is caused by the choice of the Lagrangian mean. The technique proposed here is applied to the analysis of Lagrangian motions in the Black Sea (horizontal diffusion coefficients varied from 105 to 106 cm2/s) and for the sub-diffusion of two RAFOS floats in the California Current system where power exponents varied from 0.65 to 0.72. RAFOS float motions were found to be strongly non-ergodic and non-Gaussian.

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