scholarly journals Theory of Motion of Jupiter’s Galilean Satellites

1978 ◽  
Vol 41 ◽  
pp. 207-207
Author(s):  
J.H. Lieske
Keyword(s):  
Analytic Functions ◽  
Digital Computer ◽  
Algebraic Manipulation ◽  
Physical Parameters ◽  
Galilean Satellites ◽  
Partial Derivatives ◽  
Theory Of Motion ◽  
Analytic Expressions ◽  
Free Libration ◽  
Future Revision

AbstractThe final results for the theory enabling one to calculate the positions of the Galilean satellites and their partial derivatives are presented, following the techniques outlined in earlier papers. Extensive use of algebraic manipulation software on a digital computer is employed to generate the final expressions. The new theory is, in effect, a revitalization of Sampson’s theory in which we (a) remove algebraic and mathematical errors existing in Sampson’s work, (b) introduce some neglected effects due to solar interactions and the 3-7 commensurability, (c) allow for non-zero amplitude and phase of the free libration, (d) express the final results as analytic functions of variations in 49 arbitrary constants of integration and physical parameters, (e) construct the theory in a manner which readily allows for future revision, and (f) provide analytic expressions for the partial derivatives with respect to the 49 parameters.

Theory of motion controllability of a wheel machine-tractor aggregate

2016 ◽  
Vol 3 (2) ◽  
pp. 3-10 ◽  
Author(s):  
V. Adamchuk ◽  
V. Bulgakov ◽  
V. Nadykto ◽  
I. Golovach
Keyword(s):  
Vertical Plane ◽  
Rectilinear Motion ◽  
Transport Mode ◽  
Longitudinal Plane ◽  
Theory Of Motion ◽  
Non Linear ◽  
Analytic Expressions ◽  
Computer Calculations ◽  
External Forces

Aim. To obtain analytically new dependencies, determining the indicator of motion controllability of a wheel machine-tractor aggregate, taking into consideration external forces, constructive and kinematic parameters of the aggregate while the latter moves in the transport mode. Methods. The methods of tractor and vehicle theories, theoretical mechanics, the theory of dynamic stability, and methods of numeric computer calculations. Results. A new theory of motion controllability of a wheel machine-tractor aggregate during its non-linear mo- tion along the surface of the soil at an angle to the horizontal was elaborated. The analytic expressions for the determination of the actual indicator of aggregate controllability, including force and constructive parameters of a machine-tractor aggregate, affecting this indicator in the longitudinal-vertical plane were made. The ana- lytic expressions were obtained for the transport mode of the aggregate movement. The conditions, in which cross slips of the directive wheels of the tractor with implements in the longitudinal plane were analytically considered for the fi rst time. The analytic expressions for the determination of the required indicator of the controllability of the machine-tractor aggregate in the longitudinal plane, excluding any possibility of a cross slip of the aggregate while turning its directive wheels at a certain angle, were defi ned. Conclusions. Computer calculations demonstrated that during the non-linear movement along the surface of the soil at an angle of 12 ° to the horizontal the wheel machine-tractor aggregate will be controllable only if the wheel turning angles for the tractor with implements do not exceed 9 ° . In case of the working motion of this aggregate along the slope, its controllability is preserved on condition that the turning angle of directive wheels does not exceed 11 ° . It was established that the controllability of the wheel machine-tractor aggregate is determined by the actual λ d and required λ о indicators of controllability, which take into consideration the values of the vertical load on the directive wheels of the power source, the possibility of their turn in the longitudinal plane, and the pull during the deviation from rectilinear motion when it moves along the surface at an angle to the horizontal.

Guiding properties of multilayer dielectric planar waveguides

1988 ◽  
Vol 66 (10) ◽  
pp. 914-940 ◽  
Author(s):  
John W. Y. Lit ◽  
Yi-Fan Li ◽  
Daniel W. Hewak
Keyword(s):  
Phase Shift ◽  
Planar Waveguides ◽  
Mode Number ◽  
Physical Parameters ◽  
Field Distributions ◽  
Guided Modes ◽  
New Concepts ◽  
Analytic Expressions ◽  
Multilayer Dielectric

Eigenvalue equations for guided modes in multilayer waveguides are given, along with equations for the field distributions. Closed analytic expressions are given to calculate the mode number of the guides. Two new concepts—fictitious half-phase shift and effective guide thickness—are extremely useful in the analysis of the field and in calculating the power carried by the different layers. General formulas for the dispersions caused by changes in various physical parameters are given. The study ends with illustrations using three-layer, four-layer, W-structure, and symmetrical seven-layer waveguides, as well as symmetrical periodic multilayer waveguides.

scholarly journals Self-thermophoresis of laser-heated spherical Janus particles

2021 ◽  
Vol 44 (11) ◽  
Author(s):  
E. J. Avital ◽  
T. Miloh
Keyword(s):  
Temperature Field ◽  
Continuous Light ◽  
The Self ◽  
Soret Coefficient ◽  
Physical Parameters ◽  
Two Phase ◽  
Rayleigh Approximation ◽  
Analytic Expressions ◽  
Induced Velocity ◽  
Laser Heated

Abstract An analytic framework is presented for calculating the self-induced thermophoretic velocity of a laser-heated Janus metamaterial micro-particle, consisting of two conducting hemispheres of different thermal and electric conductivities. The spherical Janus is embedded in a quiescent fluid of infinite expanse and is exposed to a continuous light irradiation by a defocused laser beam. The analysis is carried under the electrostatic (Rayleigh) approximation (radius small compared to wavelength). The linear scheme for evaluating the temperature field in the three phases is based on employing a Fourier–Legendre approach, which renders rather simple semi-analytic expressions in terms of the relevant physical parameters of the titled symmetry-breaking problem. In addition to an explicit solution for the self-thermophoretic mobility of the heated Janus, we also provide analytic expressions for the slip-induced Joule heating streamlines and vorticity field in the surrounding fluid, for a non-uniform (surface dependent) Soret coefficient. For a ‘symmetric’ (homogeneous) spherical particle, the surface temperature gradient vanishes and thus there is no self-induced thermophoretic velocity field. The ‘inner’ temperature field in this case reduces to the well-known solution for a laser-heated spherical conducting colloid. In the case of a constant Soret phoretic mobility, the analysis is compared against numerical simulations, based on a tailored collocation method for some selected values of the physical parameters. Also presented are some typical temperature field contours and heat flux vectors prevailing in the two-phase Janus as well as light-induced velocity and vorticity fields in the ambient solute and a new practical estimate for the self-propelling velocity. Graphic abstract

scholarly journals Contributions to Born’s new theory of the electromagnetic field

1935 ◽  
Vol 150 (870) ◽  
pp. 465-477 ◽  
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Field ◽  
Field Strength ◽  
Lagrange Function ◽  
Variation Principle ◽  
Partial Derivatives ◽  
Independent Variables ◽  
Analytic Expressions ◽  
Magnetic Vectors ◽  
Derivatives Of

Born’s theory starts from describing the field by two vectors (or a “six-vector”), B, E, the magnetic induction and electric field-strength respectively. A second pair of vectors (or a second six-vector) H, D, is introduced, merely an abbreviation, if you please, for the partial derivatives of the Lagrange function with respect to the components of B and E respectively (though with the negative sign for E). H is called magnetic field and D dielectric displacement. It was pointed out by Born that it is possible to choose the independent vectors in different ways. Four different and, to a certain extent, equivalent and symmetrical representations of the theory can be given by combining each of the two “magnetic” vectors with each of the two “electric” vectors to form the set of six independent variables. Every one of these four representations can be derived from a variation principle, using, of course, entirely different Lagrange functions—physically different, that is, though their analytic expressions by the respective variables are either identical or very similar to each other. In studying Born’s theory I came across a further representation, which is so entirely different from all the aforementioned, and presents such curious analytical aspects, that I desired to have it communicated. The idea is to use two complex combinations of B, E, H, D as independent variables, but in such a way that their “conjugates,” i. e. , the partial derivatives of L , equal their complex conjugates.

scholarly journals Atmospheric tides and their consequences on the rotational dynamics of terrestrial planets

2019 ◽  
Vol 82 ◽  
pp. 81-90
Author(s):  
P. Auclair-Desrotour ◽  
J. Laskar ◽  
S. Mathis
Keyword(s):  
The Body ◽  
Rotational Dynamics ◽  
Atmospheric Tides ◽  
Terrestrial Planets ◽  
Physical Parameters ◽  
Strong Impact ◽  
Tidal Torque ◽  
Analytic Expressions ◽  
Dynamical Coupling ◽  
Neutral Stratification

Atmospheric tides can have a strong impact on the rotational dynamics of planets. They are of most importance for terrestrial planets located in the habitable zone of their host star, where their competition with solid tides is likely to drive the body towards non-synchronized rotation states of equilibrium, as observed in the case of Venus. Contrary to other planetary layers, the atmosphere is sensitive to both gravitational and thermal forcings, through a complex dynamical coupling involving the effects of Coriolis acceleration and characteristics of the atmospheric structure. These key physics are usually not taken into account in modelings used to compute the evolution of planetary systems, where tides are described with parametrised prescriptions. In this work, we present a new ab initio modeling of atmospheric tides adapting the theory of the Earth’s atmospheric tides (Chapman & Lindzen 1970) to other terrestrial planets. We derive analytic expressions of the tidal torque, as a function of the tidal frequency and parameters characterizing the internal structure (e.g. the Brunt-Väisälä frequency, the radiative frequency, the pressure heigh scale). We show that stratification plays a key role, the tidal torque being strong in the case of convective atmospheres (i.e. with a neutral stratification) and weak in case of atmosphere convectively stable. In a second step, the model is used to determine the non-synchronized rotation states of equilibrium of Venus-like planets as functions of the physical parameters of the system. These results are detailed in Auclair-Desrotour et al. (2016a) and Auclair-Desrotour et al. (2016b).

Approximate Analytic Expressions of the Thermodynamic Functions of Dissociating Steam

1967 ◽  
Vol 9 (3) ◽  
pp. 226-233
Author(s):  
V. Kmoníček ◽  
V. Hoffer
Keyword(s):  
Thermodynamic Functions ◽  
Digital Computer ◽  
Compressibility Factor ◽  
Computation Time ◽  
Specific Enthalpy ◽  
Specific Entropy ◽  
Computer Storage ◽  
Analytic Expressions ◽  
Complete Calculation ◽  
Approximate Expressions

The paper presents relatively simple approximate analytic expressions showing the dependence of the compressibility factor, specific enthalpy and specific entropy of dissociating steam on pressure and temperature. The range covered by these expressions extends from 1000 to 5000°K, and from 0·01 to 100 bar. The deviations of the approximate analytic expressions deduced in the paper, from data obtained through complete thermodynamic calculations, are of the order of 1·5 per cent, i.e. practically the same as the errors of the complete calculation. The advantages offered by the use of the approximate expressions are a computation time of about 50 per cent and a digital computer storage occupation of about 60 per cent of the values corresponding to the complete calculation, while the fact that the approximate expressions are not generally thermodynamically consistent within the whole range constitutes a certain shortcoming.

The Critical and Two-Phase Flow of Steam

1961 ◽  
Vol 83 (2) ◽  
pp. 145-154 ◽  
Author(s):  
William G. Steltz
Keyword(s):  
Digital Computer ◽  
Critical Pressure ◽  
Single Phase ◽  
Unit Area ◽  
Pressure Ratio ◽  
Phase Region ◽  
Critical Flow ◽  
Two Phase ◽  
Analytic Expressions ◽  
Inlet Conditions

The results of a digital computer and analytic study of the critical flow of a compressible fluid are presented in this paper. The expanding flow of a fluid in a single-phase region as well as the expansion of a fluid to a two-phase region is considered and described by analytic expressions relating choking velocity, critical pressure ratio, and flow per unit area characteristics. A comparison is made of the analytic results which assume a constant value of the isentropic expansion exponent, with the digital computer results using the actual properties of steam. All analyses assume the fluid to be in thermodynamic equilibrium. A skeleton Mollier diagram is presented for steam showing the exponent in the wet and superheated regions. The choking velocity is presented in plot form as a function of the inlet conditions as well as state point conditions; critical pressure ratio is presented as a function of inlet conditions. The critical flow per unit area is presented in the form of a factor K plotted versus inlet conditions; this factor K when multiplied by inlet pressure produces the desired value of critical flow.

Dynamical Hysteresis and Stochastic Resonance in Driven Dissipative Quantum Two-State System

1997 ◽  
Vol 11 (20) ◽  
pp. 861-866 ◽  
Author(s):  
T. P. Pareek ◽  
Mangal C. Mahato ◽  
A. M. Jayannavar
Keyword(s):  
Stochastic Resonance ◽  
Thermal Environment ◽  
Resonance Condition ◽  
Temperature Limit ◽  
State System ◽  
Physical Parameters ◽  
High Temperature Limit ◽  
Periodically Driven ◽  
Loop Area ◽  
Analytic Expressions

We study the dynamics of a periodically driven two-state system coupled to thermal environment. In the high temperature limit we have obtained analytic expressions for the average position of the particle and hysteresis loop area. Both these quantities exhibit stochastic resonance behavior as a function of various parameters of the problem. These two resonances, however, occur at different values of the parameters. The resonance condition obtained from the study of phase delay exhibits resonance at a fixed frequency independent of other physical parameters.

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