Extended Tomlinson Model for Rheological Response

1998 ◽  
Vol 543 ◽  
Author(s):  
V. Zaloj ◽  
M. Urbakh ◽  
J. Klafter
Keyword(s):  
Nonlinear Behavior ◽  
Normal Direction ◽  
Surface Forces Apparatus ◽  
One Dimensional ◽  
Additional Information ◽  
Frictional Properties ◽  
Tomlinson Model ◽  
Harmonic Chain ◽  
The One ◽  
Normal Coupling

AbstractWe investigate the response of a confined harmonic chain to an external harmonic driving force. A model is introduced which extends the one-dimensional Tomlinson model to include motion in the normal direction. This model with lateral-normal coupling mimics recent measurements on friction, using surface forces apparatus (SFA). The model predicts a critical driving amplitude below which the response is linear. For higher amplitudes the system exhibits a nonlinear behavior and an apparent shear thinning. We discuss the effects of shear induced dilatancy, which results from the lateral-normal coupling, on the energy dissipation, and therefore on the frictional properties. It is demonstrated that measurements of response in the normal direction provide additional information on the mechanisms of friction.

THE ESTIMATION OF MAGNETOTELLURIC IMPEDANCE TENSOR ELEMENTS FROM MEASURED DATA

Geophysics ◽  
1971 ◽  
Vol 36 (5) ◽  
pp. 938-942 ◽  
Author(s):  
W. E. Sims ◽  
F. X. Bostick ◽  
H. W. Smith
Keyword(s):  
Mean Square Error ◽  
Random Noise ◽  
Measured Data ◽  
Impedance Tensor ◽  
Mean Square ◽  
Signal To Noise ◽  
One Dimensional ◽  
Additional Information ◽  
The One ◽  
Mean Square Error Criterion

Six different estimates of the magnetotelluric impedance tensor elements may be computed from measured data by use of auto‐power and cross‐power density spectra. We show that each of the estimates satisfies a mean‐square error criterion. Two of the six estimates are relatively unstable in the one‐dimensional case when the incident fields are unpolarized. For the remaining four estimates, it is shown that two are unaffected by random noise on the H signal, but are biased upward by random noise on the E signal. The remaining two estimates are unaffected by random noise on the E signal, but are biased downward by random noise on the H signal. Computation of all of the estimates provides a measure of the total amount of noise present, as indicated by a stability coefficient for the estimates. In the absence of additional information as to the relative signal‐to‐noise ratios of the E and H signals, we suggest that a mean estimate be used. A numerical example is included.

scholarly journals COMPARATIVE ANALYSIS OF NUMERICAL METHODS OF THE SOLUTION OF A ONEDIMENSIONAL INVERSE PROBLEM OF ACOUSTICS

2020 ◽  
Vol 17 (34) ◽  
pp. 321-334
Author(s):  
Gulnur A TYULEPBERDINOVA ◽  
Zhanar O ORALBEKOVA ◽  
Gulnur G GAZIZ ◽  
Bota A MAXUTOVA ◽  
Saltanat A BAITENOVA
Keyword(s):  
Comparative Analysis ◽  
Numerical Methods ◽  
Difference Scheme ◽  
Practical Significance ◽  
Inversion Method ◽  
One Dimensional ◽  
Additional Information ◽  
The Difference ◽  
The One ◽  
The University

Nowadays, a large number of methods for solving inverse problems arising in electrodynamics and acoustics have been developed, but the development of practical systems is necessary to combine a large number of equations that contribute to the substantiation of numerical methods for solving various multidimensional problems. Therefore, the main goal of the work is a comparative analysis of statistical methods for solving the one-dimensional inverse acoustic problem, as well as in the search for acoustic resistance. To achieve this goal, the means of description and comparison, which contributed to the identification of the characteristics of acoustic impedance, were used. Also, the finite-difference solution method, the differential circuit circulation method, and the Landweber iteration method were used. It was established that the inversion method of the difference scheme is expedient to apply in the case when additional information is known accurately enough, and the reconstructed solution is quite smooth. It was determined that if one of these conditions is violated, the method of reversing the difference scheme becomes unstable. The problems of the correctness of the issues for the wave equation with complex velocity in the one-dimensional and spatial cases were investigated. Formulas for solving these problems were obtained – analogs of classical formulas. Numerical computations show the kind of results that may be expected from the method under consideration. The materials of the paper imply the practical significance for the university teachers of the information technology specializations.

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.

Adiabatic large polarons in anisotropic molecular crystals

2011 ◽  
Vol 35 (1) ◽  
pp. 15-27
Author(s):  
Zoran Ivić ◽  
Željko Pržulj
Keyword(s):  
Energy Transfer ◽  
Effective Mass ◽  
Molecular Crystals ◽  
Single Chain ◽  
Proper Understanding ◽  
One Dimensional ◽  
Interchain Coupling ◽  
Large Polaron ◽  
The One

Adiabatic large polarons in anisotropic molecular crystals We study the large polaron whose motion is confined to a single chain in a system composed of the collection of parallel molecular chains embedded in threedimensional lattice. It is found that the interchain coupling has a significant impact on the large polaron characteristics. In particular, its radius is quite larger while its effective mass is considerably lighter than that estimated within the one-dimensional models. We believe that our findings should be taken into account for the proper understanding of the possible role of large polarons in the charge and energy transfer in quasi-one-dimensional substances.

Modelling Techniques in Applied Glaciology: Numerical Modelling of Avalanches

1983 ◽  
Vol 4 ◽  
pp. 297-297
Author(s):  
G. Brugnot
Keyword(s):  
Finite Difference Method ◽  
Transverse Velocity ◽  
Longitudinal Velocity ◽  
Momentum Conservation ◽  
Dimensional Model ◽  
One Dimensional ◽  
Modelling Techniques ◽  
Reference Grid ◽  
The One ◽  
Near Future

We consider the paper by Brugnot and Pochat (1981), which describes a one-dimensional model applied to a snow avalanche. The main advance made here is the introduction of the second dimension in the runout zone. Indeed, in the channelled course, we still use the one-dimensional model, but, when the avalanche spreads before stopping, we apply a (x, y) grid on the ground and six equations have to be solved: (1) for the avalanche body, one equation for continuity and two equations for momentum conservation, and (2) at the front, one equation for continuity and two equations for momentum conservation. We suppose the front to be a mobile jump, with longitudinal velocity varying more rapidly than transverse velocity.We solve these equations by a finite difference method. This involves many topological problems, due to the actual position of the front, which is defined by its intersection with the reference grid (SI, YJ). In the near future our two directions of research will be testing the code on actual avalanches and improving it by trying to make it cheaper without impairing its accuracy.

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