scholarly journals Polaron in Electric Field and Vibrational Spectrum of Polyacetylene

2019 ◽  
Vol 14 (1) ◽  
pp. 150-159 ◽  
Author(s):  
T.Yu. Astakhova ◽  
G.A. Vinogradov
Keyword(s):  
Electric Field ◽  
Vibrational Spectrum ◽  
Phase Velocity ◽  
Additional Condition ◽  
Fourier Spectrum ◽  
Optical Branch ◽  
System A ◽  
Second Derivatives ◽  
The Matrix ◽  
Derivatives Of

In the present paper, the evolution of a polaron in polyacetylene in electric field is studied in detail. It is shown that the dependence of the polaron velocity on the applied field is determined by the peculiarities of the vibrational spectrum of polyacetylene. The spectrum is calculated numerically using the Hessian, the matrix of the second derivatives of the potential energy of the system. A supersonic polaron moving in an electric field generates coherent vibrations of the optical branch of the spectrum of the polyacetylene. The phase velocity of these oscillations is equal to the polaron velocity. An additional condition for the excitation of a mode with a certain phase velocity is its correspondence to the Fourier spectrum of an impulse with polaron shape.

scholarly journals GOCE gradients in various reference frames and their accuracies

2003 ◽  
Vol 1 ◽  
pp. 33-38 ◽  
Author(s):  
J. Müller ◽  
M. Wermut
Keyword(s):  
Gravity Field ◽  
Ocean Circulation ◽  
Reference Frames ◽  
Terrestrial Reference Frame ◽  
Second Derivatives ◽  
Gravitational Gradients ◽  
The Matrix ◽  
Along Track ◽  
Derivatives Of

Abstract. The objective of GOCE (Gravity Field and Steady-State Ocean Circulation Explorer) is the determination of the Earth’s gravity field with high spatial resolution. The main science sensor (the gradiometer) measures differential accelerations, from which the gravitational gradients, i.e. the matrix of the second derivatives of the gravitational potential, are derived. Some of them (the diagonal components of the gravitational tensor) are observed with highest accuracy, 4 mE/√Hz in a frequency range from 5 mHz to 100 mHz, whereas the off-diagonals are obtained less accurately. The gradients will be observed in the instrument frame, which approximates the along-track oriented, local orbital frame. For the transformation of the gradients in other frames (e.g. in the strictly earth-pointing frame or a local geodetic frame), the transformation parameters (orientation angles) and all components of the gravity tensor have to be known with sufficient accuracy. We show how the elements of the gravitational tensor and their accuracies look like in the various frames as well as their spectral behaviour, if only the GOCE observations are used for the transformation. Only V'zz keeps approximately its original accuracy in all frames discussed, except in the earth-fixed frame ITRF (International Terrestrial Reference Frame). Therefore we recommend to analyse the gradients as ‘close’ as possible in the observation frame.Key words. Satellite gradiometry, GOCE mission, reference frames, transformation errors

scholarly journals Analysis of optimal controlling system using Chebyshev Wavelets

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
V. Ramalakshmi ◽  
T. Balasubramanian ◽  
B.Ramesh Kumar
Keyword(s):  
Numerical Analysis ◽  
Explicit Formula ◽  
Chebyshev Polynomial ◽  
Chebyshev Wavelets ◽  
Numerical Example ◽  
System A ◽  
Controlling System ◽  
The Matrix ◽  
Matrix Derivatives ◽  
Derivatives Of

<div><p><em>In this paper, we derive new explicit formula for the matrix derivatives of chebyshev polynomial third degree because of this kind of polynomial is an important tool for numerical analysis of optimal controlling system. A numerical example is included to demonstrate the validity and applicability of the technique.</em></p></div>

Earth's gravity field parameters determination by the space geodesy dynamical approach

2017 ◽  
Vol 919 (1) ◽  
pp. 7-12
Author(s):  
N.A Sorokin
Keyword(s):  
Coordinate System ◽  
Gravitational Potential ◽  
Coefficient Matrix ◽  
Measured Quantity ◽  
Second Derivative ◽  
Measured Variable ◽  
Second Derivatives ◽  
Rectangular Coordinates ◽  
Cartesian Coordinate ◽  
Derivatives Of

The method of the geopotential parameters determination with the use of the gradiometry data is considered. The second derivative of the gravitational potential in the correction equation on the rectangular coordinates x, y, z is used as a measured variable. For the calculated value of the measured quantity required for the formation of a free member of the correction equation, the the Cunningham polynomials were used. We give algorithms for computing the second derivatives of the Cunningham polynomials on rectangular coordinates x, y, z, which allow to calculate the second derivatives of the geopotential at the rectangular coordinates x, y, z.Then we convert derivatives obtained from the Cartesian coordinate system in the coordinate system of the gradiometer, which allow to calculate the free term of the correction equation. Afterwards the correction equation coefficients are calculated by differentiating the formula for calculating the second derivative of the gravitational potential on the rectangular coordinates x, y, z. The result is a coefficient matrix of the correction equations and corrections vector of the free members of equations for each component of the tensor of the geopotential. As the number of conditional equations is much more than the number of the specified parameters, we go to the drawing up of the system of normal equations, from which solutions we determine the required corrections to the harmonic coefficients.

Some new generalizations for GA-convex functions

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 1009-1016 ◽  
Author(s):  
Ahmet Akdemir ◽  
Özdemir Emin ◽  
Ardıç Avcı ◽  
Abdullatif Yalçın
Keyword(s):  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
General Integral ◽  
Second Derivatives ◽  
Derivatives Of

In this paper, firstly we prove an integral identity that one can derive several new equalities for special selections of n from this identity: Secondly, we established more general integral inequalities for functions whose second derivatives of absolute values are GA-convex functions based on this equality.

System of thermodynamic quantities in the McMillan-Mayer solution theory

1985 ◽  
Vol 50 (4) ◽  
pp. 791-798 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Generating Function ◽  
Simple Form ◽  
Unit Volume ◽  
Thermodynamic Quantities ◽  
Solution Theory ◽  
Pure Solvent ◽  
Second Derivatives ◽  
Definition Of ◽  
Derivatives Of

The McMillan-Mayer (MM) free energy per unit volume of solution AMM, is employed as a generating function of the MM system of thermodynamic quantities for solutions in the state of osmotic equilibrium with pure solvent. This system can be defined by replacing the quantities G, T, P, and m in the definition of the Lewis-Randall (LR) system by AMM, T, P0, and c (P0 being the pure solvent pressure). Following this way the LR to MM conversion relations for the first derivatives of the free energy are obtained in a simple form. New relations are derived for its second derivatives.

scholarly journals The Meaning of the Matrix: Towards a Cybernetic Critical Theory of Capitalism

2018 ◽  
Vol 6 (1) ◽  
pp. 1
Author(s):  
Shay Hershkovitz
Keyword(s):  
Social Systems ◽  
Theoretical Concept ◽  
Social Actors ◽  
System A ◽  
The Social ◽  
Social Entity ◽  
Key Concepts ◽  
The Matrix ◽  
Critical Approaches ◽  
Operational Logic

Marxist criticism is most discernible; despite the oft-repeated claim that it is now irrelevant, belonging to an age now past. This essay assumes that criticism originating in the Marxist school of thought continue to be relevant also in this present time; though it may need to be further developed and improved by integrating newer critical approaches into the classic Marxist discourse. This essay therefore integrates basic Marxist ideas with key concepts from ‘social systems theory’; especially the theory of the German sociologist Niklas Luhmann's. In this light, capitalism is conceptualized here as a ‘super (social) system’: a meaning-creating social entity, in which social actors, behaviors and structures are realized. This theoretical concept and terminology emphasizes the social construction of control and stability, when discussing the operational logic of capitalism.

A State-Space Approach to the Synthesis of Random Vertical and Crosslevel Rail Irregularities

1990 ◽  
Vol 112 (1) ◽  
pp. 83-87 ◽  
Author(s):  
R. H. Fries ◽  
B. M. Coffey
Keyword(s):  
Numerical Simulation ◽  
White Noise ◽  
State Space ◽  
Spectral Characteristics ◽  
The State ◽  
Second Derivatives ◽  
Time Histories ◽  
Sample Interval ◽  
Rail Irregularities ◽  
Derivatives Of

Solution of rail vehicle dynamics models by means of numerical simulation has become more prevalent and more sophisticated in recent years. At the same time, analysts and designers are increasingly interested in the response of vehicles to random rail irregularities. The work described in this paper provides a convenient method to generate random vertical and crosslevel irregularities when their time histories are required as inputs to a numerical simulation. The solution begins with mathematical models of vertical and crosslevel power spectral densities (PSDs) representing PSDs of track classes 4, 5, and 6. The method implements state-space models of shape filters whose frequency response magnitude squared matches the desired PSDs. The shape filters give time histories possessing the proper spectral content when driven by white noise inputs. The state equations are solved directly under the assumption that the white noise inputs are constant between time steps. Thus, the state transition matrix and the forcing matrix are obtained in closed form. Some simulations require not only vertical and crosslevel alignments, but also the first and occasionally the second derivatives of these signals. To accommodate these requirements, the first and second derivatives of the signals are also generated. The responses of the random vertical and crosslevel generators depend upon vehicle speed, sample interval, and track class. They possess the desired PSDs over wide ranges of speed and sample interval. The paper includes a comparison between synthetic and measured spectral characteristics of class 4 track. The agreement is very good.

Investigation of a Technique for the Differentiation of Empirical Data

1983 ◽  
Vol 105 (3) ◽  
pp. 200-202 ◽  
Author(s):  
D. M. Trujillo ◽  
H. R. Busby
Keyword(s):  
Dynamic Programming ◽  
Differentiable Function ◽  
Empirical Data ◽  
Numerical Experiments ◽  
Random Noise ◽  
Second Derivatives ◽  
Derivatives Of

A dynamic programming filter is derived to estimate the first and second derivatives of empirical data. A series of numerical experiments are conducted using a known differentiable function with various amounts of added random noise.

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