Erratum: Plasma‐Filled Waveguide with Axial Magnetization. I. Variational Determination of Normal Modes

1969 ◽  
Vol 40 (12) ◽  
pp. 4999-4999
Author(s):  
K. S. Champlin ◽  
G. H. Glover ◽  
D. E. O'Connor
Keyword(s):  
Normal Modes

Statistical determination of normal modes

1987 ◽  
Vol 64 (5) ◽  
pp. 425 ◽  
Author(s):  
John F. Geldard ◽  
Lawrence R. Pratt
Keyword(s):  
Normal Modes ◽  
Statistical Determination

scholarly journals Determination of the complex frequencies for the normal modes below 1mHz after the 2010 Maule and 2011 Tohoku earthquakes

2014 ◽  
Vol 56 (5) ◽  
Author(s):  
Hao Ding ◽  
Wen-Bin Shen
Keyword(s):  
Time Series ◽  
Normal Modes ◽  
Power Spectra ◽  
Tohoku Earthquake ◽  
Superconducting Gravimeter ◽  
Width Ratio ◽  
Maule Earthquake ◽  
Attenuation Models ◽  
First Time

<p>Based upon SG (superconducting gravimeter) records, the autoregressive method proposed by Chao and Gilbert [1980] is used to determine the frequencies of the singlets of seven spheroidal modes (<sub>0</sub>S<sub>2</sub>, <sub>2</sub>S<sub>1</sub>, <sub>0</sub>S<sub>3</sub>, <sub>0</sub>S<sub>4</sub>, <sub>1</sub>S<sub>2</sub>, <sub>0</sub>S<sub>0</sub>, and <sub>3</sub>S<sub>1</sub>) and the degenerate frequencies of three toroidal modes (<sub>0</sub>T<sub>2</sub>, <sub>0</sub>T<sub>3</sub>, and <sub>0</sub>T<sub>4</sub>) below 1 mHz after two recent huge earthquakes, the 2010 Mw8.8 Maule earthquake and the 2011 Mw9.1 Tohoku earthquake. The corresponding quality factor <em>Q</em>s are also determined for those modes, of which the <em>Q</em>s of the five singlets of <sub>1</sub>S<sub>2</sub> and the five singlets (<em>m</em>=0, <em>m</em>=±2, and <em>m</em>=±3) of <sub>0</sub>S<sub>4</sub> are estimated for the first time using the SG observations. The singlet <em>m</em>=0 of <sub>3</sub>S<sub>1</sub> is clearly observed from the power spectra of the SG time series without using other special spectral analysis methods or special time series from pole station records. In addition, the splitting width ratio <em>R</em> of <sub>3</sub>S<sub>1</sub> is 0.99, and consequently we conclude that <sub>3</sub>S<sub>1</sub> is normally split. The frequencies and <em>Q</em>s of the modes below 1mHz may contribute to refining the 3D density and attenuation models of the Earth.</p>

Applications of Infrared Methods in the Structural Examination of Synthetic Rubber

1946 ◽  
Vol 19 (4) ◽  
pp. 1113-1123 ◽  
Author(s):  
J. E. Field ◽  
D. E. Woodford ◽  
S. D. Gehman
Keyword(s):  
Absorption Spectra ◽  
Organic Molecules ◽  
Normal Modes ◽  
Structural Variations ◽  
Structural Examination ◽  
Absorption Bands ◽  
Synthetic Rubber ◽  
Modes Of Vibration ◽  
Long Chain

Abstract Infrared absorption spectra have been long recognized as a convenient means for studying the structure of organic molecules. The interpretations of the spectra are based on the energy interactions of the molecule and the radiations which arise from the vibration of the constituent atoms and molecular rotations. For simple or highly symmetrical molecules, the determination of the normal modes of vibration and the calculation of the absorbing frequencies are relatively simple and straightforward. For more complicated organic molecules, this becomes increasingly difficult because with each additional atom, the number of degrees of freedom is increased by three and the determination of the normal modes of vibration becomes practically impossible. However, interpretations can be made to a useful extent through empirical comparisons with the absorption spectra of simpler known structures. The data that have been accumulated by investigators in this field have made it possible to assign rather definite absorption frequencies to some of the chemical linkages and functional groups. These correlations which have appeared in numerous places in the literature are partially reproduced in Table I. Organic compounds generally have strong absorption bands below 1300 cm−1, to which few definite assignments can be made with certainty because the vibrations of many of the atoms of the molecule may be involved rather than a specific part of it. It is clear that such empirical relationships must be relied upon in studying the structural variations of the long chain, complex molecules which occur in butadiene and isoprene polymers and copolymers and other synthetic rubbers. This procedure has been applied to determine the effects of oxidation and of variations in monomers and polymerizing conditions on the structure of synthetic rubber. It is practically certain that physical deficiencies of synthetic rubber are due principally to the structure of the long chain molecules rather than to the chemical nature of the monomers used.

Free Vibration of Continuous Skin-Stringer Panels

1960 ◽  
Vol 27 (4) ◽  
pp. 669-676 ◽  
Author(s):  
Y. K. Lin
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Normal Modes ◽  
Time Dependent ◽  
Experimental Measurements ◽  
Structural Configuration ◽  
Modes Of Vibration ◽  
Fuselage Skin

The determination of the natural frequencies and normal modes of vibration for continuous panels, representing more or less typical fuselage skin-panel construction for modern airplanes, is discussed in this paper. The time-dependent boundary conditions at the supporting stringers are considered. A numerical example is presented, and analytical results for a particular structural configuration agree favorably with available experimental measurements.

scholarly journals A linear response theory based method for prediction of large scale protein conformational changes upon ligand binding

2021 ◽  
Author(s):  
Rajat Punia ◽  
Gaurav Goel
Keyword(s):  
Ligand Binding ◽  
Conformational Change ◽  
Linear Response ◽  
Large Scale ◽  
Normal Modes ◽  
Linear Response Theory ◽  
Conformational Space ◽  
Small Scale ◽  
Excitation Temperature

ABSTRACTPrediction of ligand-induced protein conformational transitions is a challenging task due to a large and rugged conformational space, and limited knowledge of probable direction(s) of structure change. These transitions can involve a large scale, global (at the level of entire protein molecule) structural change and occur on a timescale of milliseconds to seconds, rendering application of conventional molecular dynamics simulations prohibitive even for small proteins. We have developed a computational protocol to efficiently and accurately predict these ligand-induced structure transitions solely from the knowledge of protein apo structure and ligand binding site. Our method involves a series of small scale conformational change steps, where at each step linear response theory is used to predict the direction of small scale global response to ligand binding in the protein conformational space (dLRT) followed by construction of a linear combination of slow (low frequency) normal modes (calculated for the structure from the previous step) that best overlaps with dLRT. Protein structure is evolved along this direction using molecular dynamics with excited normal modes (MDeNM) wherein excitation energy along each normal mode is determined by excitation temperature, mode frequency, and its overlap with dLRT. We show that excitation temperature (ΔT) is a very important parameter that allows limiting the extent of structural change in any one step and develop a protocol for automated determination of its optimal value at each step. We have tested our protocol for three protein–ligand systems, namely, adenylate Kinase – di(adenosine-5’)pentaphosphate, ribose binding protein – β-D-ribopyranose, and DNA β-glucosyltransferase – uridine-5’-diphosphate, that incorporate important differences in type and range of structural changes upon ligand binding. We obtain very accurate prediction for not only the structure of final protein–ligand complex (holo-structure) having a large scale conformational change, but also for biologically relevant intermediates between the apo and the holo structures. Moreover, most relevant set of normal modes for conformational change at each step are an output from our method, which can be used as collective variables for determination of free energy barriers and transition timescales along the identified pathway.

A Mechanical Analyzer for Computing Transient Stresses in Airplane Structures

1950 ◽  
Vol 17 (3) ◽  
pp. 310-314
Author(s):  
R. L. Bisplinghoff ◽  
T. H. H. Pian ◽  
L. I. Levy
Keyword(s):  
Normal Modes ◽  
Phase Relations ◽  
Elastic Structure ◽  
Mechanical Analogy ◽  
Proper Design ◽  
Torsional Pendulum ◽  
And Function

Abstract A mechanical-analogy-type analyzer is described which is used for computing the transient stresses in an undamped elastic structure. The two main functions of the analyzer are (a) to evaluate the stresses due to the deformations of an elastic structure in its various normal modes, and (b) to superpose the effects of the modes with proper regard taken of their phase relations. Function (a) is accomplished by the use of torsional-pendulum simulators, and function (b) by the proper design of the electronic pickup and recording circuit. The analyzer is particularly useful in the determination of dynamic landing stresses in airplane structures.

scholarly journals The normal vibrations of carbonate and nitrate ions

1931 ◽  
Vol 134 (823) ◽  
pp. 265-277 ◽  
Keyword(s):  
Raman Spectrum ◽  
Raman Spectra ◽  
Raman Effect ◽  
Normal Modes ◽  
Potassium Nitrate ◽  
Nitrate Ions ◽  
Carbonate Ion ◽  
Infra Red ◽  
Modes Of Vibration

When the Raman effect was first discovered, it was believed that every line in the Raman spectrum referred to some characteristic vibration of the scatter­ing molecule. Later the tendency was to regard the lines as due to transitions between states of vibration of the molecule, so that the energies corresponded not to energies of vibration directly, but to differences in the energy of vibra­tion of two different modes. It is now realised that the infra-red spectrum of a substance and the Raman spectrum which it scatters give complementary information. Certain modes of vibration are represented solely in the infra­red spectrum, others are found only in the Raman spectrum, while others may appear in both spectra. Quite early a rough criterion on the basis of symmetry was put forward by Schaefer, for the determination of whether or not a particular vibration was to be expected in the Raman effect. Recently a selection rule has been formulated by Placzek; no vibration will appear as a fundamental in the Raman effect if it is such that any symmetrical operation upon it can change the signs of the displacements of the normal co-ordinates, without altering the energy. It is clear that a knowledge of the normal modes of vibration of the molecule under discussion must precede the application of any such rule, and it is the purpose of the present communication to discuss the normal modes of vibration of the carbonate and nitrate ions. In 1929 the writer showed that it was possible to obtain Raman spectra from powdered crystals, and the discovery was made when using powdered crystals of potassium nitrate. The method was applied first to carbonates and nitrates, so it became of interest to attempt to fix the structure of the anions of these salts by means of the Raman spectra combined with the infra-red data. In what follows the carbonate ion will first be dealt with in some detail, and then the nitrate ion can be treated summarily owing to the similarity of structure of the two ions.

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