Form Of Analytical Formulas Research Articles

Alternativni teorijski model zemljinog EM polja zasnovan na hipotezama o dve komponente polja

Introduction/purpose: The paper describes an alternative theoretical model of the Earth's EM field based on two-component field hypotheses. The paper consists of several parts, one part of which is a model showing the rotation of the magnetically conducting sphere of magnetization M in a foreign magnetic field. The last part defines theoretical models for the calculation of the components of the electromagnetic field of electrically conductive, dielectric and magnetically conductive spheres which are exposed to the influence of a foreign electromagnetic field. Methods: In the work, the responses of electrically conductive, dielectric and magnetically conductive spheres to the influence of external EM fields were investigated using the analytical method. Results: The obtained solutions in the form of analytical formulas will be applied to research the impact of the Sun's EM field on the planets and especially on the Earth. Conclusion: The resulting formulas of the electric and magnetic field strength and induction and their solutions can be applied to electrically conductive, dielectric and magnetically conductive spheres. In comparison to already known formulas, they are simple and have higher accuracy.

Cosmogenic tsunamic risk assessment: a first application to the European Atlantic coasts

We address the question of cosmogenic tsunamis, i.e., tsunamis due to the fall of an asteroid in the ocean, in particular on the Atlantic coasts of Europe. We apply Ward and Asphaug's method (Deep-Sea Res II 49:1073–1079, 2002) for assessing this probabilistic return period of tsunami waves, with simplifying assumptions allowing writing their results in the form of analytic formulae, some of them involving simple integrals to be computed by numerical quadrature. We also account for uncertainties, (still following Ward and Asphaug (Deep-Sea Res II 49:1073–1079, 2002) on a simplified line. An upper bound of continental shelf shoaling is estimated ad hoc. The influence of several parameters is also analyzed, in particular the effect of tide is briefly addressed.

Simultaneous learning of several materials properties from incomplete databases with multi-task SISSO

The identification of descriptors of materials properties and functions that capture the underlying physical mechanisms is a critical goal in data-driven materials science. Only such descriptors will enable a trustful and efficient scanning of materials spaces and possibly the discovery of new materials. Recently, the sure-independence screening and sparsifying operator (SISSO) has been introduced and was successfully applied to a number of materials-science problems. SISSO is a compressed sensing based methodology yielding predictive models that are expressed in form of analytical formulas, built from simple physical properties. These formulas are systematically selected from an immense number (billions or more) of candidates. In this work, we describe a powerful extension of the methodology to a ‘multi-task learning’ approach, which identifies a single descriptor capturing multiple target materials properties at the same time. This approach is specifically suited for a heterogeneous materials database with scarce or partial data, e.g. in which not all properties are reported for all materials in the training set. As showcase examples, we address the construction of materials properties maps for the relative stability of octet-binary compounds, considering several crystal phases simultaneously, and the metal/insulator classification of binary materials distributed over many crystal prototypes.

Development of the algorithm for aircraft control at inaccurate measurement of the state vector and variable accuracy parameter

A parametric method of the synthesis of control in the closed circuit, taking into account explicitly generalized error of the inertial module, is presented. The law of control in the form of analytical formulas is typically assigned to the control program and does not change during flight of an unmanned aerial vehicle. This decreases the capabilities of the autonomous flight control system to overcome control errors, which occur for various reasons. To verify assumptions about a possibility of improving the accuracy of an aerial vehicle control by the data of the strapdown inertial navigation system on a certain time interval of autonomous operation, the calculation experiment was conducted with the use of the developed software complex, simulating operation of the automatic flight control system. Parametrization of the law of control is considered as the main contribution (the outcome). Introduction of the parameter made it possible to decrease a negative impact of measurement errors and other disturbing factors on accuracy of reaching by the point of flight destination. Through computer modeling, it was shown that it is possible to decrease the impact of a generalized measurement error on generation of values of control functions by changing the value of the parameter. Analytical expressions for the estimation of accuracy of automatic control at the known generalized error of the inertial module and limited disturbing influences were obtained. After analyzing the influence of these factors on accuracy of the object control, a set of recommendations on selection of a variable parameter of synthesis of control depending on precision level of the sensors, used in the inertial module of measuring sensors, was generated.

Reemission spectra and inelastic processes at interaction of attosecond and shorter duration electromagnetic pulses with atoms

Inelastic processes and the reemission of attosecond and shorter electromagnetic pulses by atoms have been considered within the analytical solution of the Schrodinger equation in the sudden perturbation approximation. A method of calculations with the exact inclusion of spatial inhomogeneity of the field of an ultrashort pulse and the momenta of photons in the reemission processes has been developed. The probabilities of inelastic processes and spectra of reemission of ultrashort electromagnetic pulses by one- and many-electron atoms have been calculated. The results have been presented in the form of analytical formulas.

MATHEMATICAL DESCRIPTION OF RESISTANCE OF BRICK PIER WITH MORTAR FRAME TO REFERENCE FIRE EXPOSURE

The results of mathematical description of resistance of brick pier with mortar frame to reference fire exposure are viewed. New functional relations are presented in the form of analytic formulas which determine fire resistance duration of reinforced mortar frame and brick pier core. The package of measures of non-destructive testing of brick pier with mortar frame keeps down costs of fire experiment, improves testing accuracy and reduces testing time.

Inelastic processes and the reemission of attosecond and shorter electromagnetic pulses at the interaction with atoms

Inelastic processes and the reemission of attosecond and shorter electromagnetic pulses by atoms have been considered within the analytical solution of the Schrodinger equation in the sudden perturbation approximation. A method of calculations with the exact inclusion of spatial inhomogeneity of the field of an ultrashort pulse and the momenta of photons in the reemission processes has been developed. The results have been presented in the form of analytical formulas. The probabilities of inelastic processes and spectra of reemission of ultrashort electromagnetic pulses by single-electron atoms have been calculated.

Average elastic and strength characteristics of a honeycomb core and a theoretical-experimental method of their determination

To determine the average elastic and strength characteristics of a honeycomb core of hexahedral structure made of a “NOMEX” polymeric paper, tests of special specimens in compression and shear in two mutually perpendicular planes were conducted. Proceeding from the experimental and computational-experimental data found, the dimensionless correcting parameters entering into solutions derived previously in the form of analytical formulas and meant to determine the honeycomb core characteristics mentioned are identified. It is established that, in compression, the average elastic and strength characteristics of the filler considered are practically formed only at the expense of two walls glued together, but in shear in the plane of the walls — at the expense of all four walls of the cell of periodicity.

The Second Born Corrections to the Electrical and Thermal Conductivities of Dense Matter in the Liquid Metal Phase

The second Born corrections to the electrical and thermal conductivities are calculated for the dense matter in the liquid metal phase for various elemental compositions of astrophysical importance. Inclusion up to the second Born corrections is sufficiently accurate for the Coulomb scattering of the electrons by the atomic nuclei with Z < 26. Our approach is semi-analytical, and is in contrast to that of the previous authors who have used fully numerical values of the cross section for the Coulomb scattering of the electron by the atomic nucleus. The merit of the present semi-analytical approach is that this approach affords us to obtain the results with reliable Z-dependence and \rho-dependence. The previous fully numerical approach has made use of the numerical values of the cross section for the scattering of the electron off the atomic nucleus for a limited number of Z-values, Z=6, 13, 29, 50, 82, and 92, and for a limited number of electron energies, 0.05MeV, 0.1MeV, 0.2MeV, 0.4MeV, 0.7MeV, 1MeV, 2MeV, 4MeV, and 10MeV. Our study, however, has confirmed that the previous results are sufficiently accurate. They are recovered, if the terms higher than the second Born terms are taken into account. We make a detailed comparison of the present results with those of the previous authors. The numerical results are parameterized in a form of analytic formulae that would facilitate practical uses of the results. We also extend our calculations to the case of mixtures of nuclear species. The corresponding subroutine can be retrieved from http://www.ph.sophia.ac.jp/~itoh-ken/subroutine/subroutine.htm

Reflection coefficient of low energy light ions based on the theory of ion ranges

Multiple collision theory of light ion ranges in an infinite medium has been used to calculate reflection coefficient from penetration profile in the energy region where the electronic stopping is dominating and proportional to the ion velocity. Ion-target atom collisions are determined by the inverse square scattering potential. The Gaussian approximation of a penetration profile as well as reflection coefficient are found in the form of analytic formulas. Corrections for multiple crossings of the surface have been applied. The results are compared with those from our previous calculations on the basis of DP0 solution of the transport equation and with the computer simulation data.

Tuning of Digital PID Controllers Based on Ziegler - Nichols Method

A unified algorithm for auto-tuning of digital РID controllers for n-order process model have been derived in this paper. Tuning procerdure uses the identification of ARX process model parameters using recursive least squares method (RLSM) with adaptive directional forgetting. The parameter estimates serve for computing of the ultimate (critical) proportional gain and period of oscillations on the basis of modified Ziegler-Nichols method for digital control loops. The relations for setting procedures in case of the 2nd and the 3rd order model are derived in the form of analytical formulas. In case of the higher order ARX models the MATLAB Symbolic Math Toolbox was used. These algorithms are suitable for automatic tuning of digital PID controllers or of the adaptive control of technological processes. The digital PID controller with weghting factor and noise filtering constant in the derivative component has been applied for temperature control of a laboratory fermentor. There has been developed the MATLABToolbox ATC PID for designing, testing, simulating and real time of auto-tuning digital PID controllers.

Pracfical Tuning of Industrial PID Controllers

Abstract The paper deals with algorithms for auto-tuning of digital PID controllers. Tuning is based on the identification of process model parameters using recursive least squares method (RLSM) with directional forgetting. The parameters of the PID controllers are designed on the basis of modified Ziegler-Nichols method for digital control loops. The ultimate (critical) gain and period of oscillations are calculated from parameter estimates of the regression model. The relations for setting procedures in case of the 2nd and 3rd order model are relatively simple and are given in the form of analytical formulas or flow diagrams. In case of the higher order regression models the MATLAB Symbolic Math Toolbox was used. These algorithms are suitable for automatic tuning of digital PID controllers or of the adaptive control of technological processes. There has been developed the MATLAB-Toolbox ATC PID for designing, testing and simulating of auto-tuning digital PID controllers.

Parametric Optimization Problem for Control Systems with Time-Delay

The paper deals with the problem of calculation of the integral from the square of the dynamic error for systems with time-delay. The solution of this problem has been obtained in the form of analytic formulae. This enables us to obtain a relationship between the optimal values of the parameters of the controller for example PID and the parameters of the object from the requirements that the above integral attains its minimal value. The presented results and method are valid for the object described by n-th differential equation with one retarded argument. The controller may also be described in general by a differential equation of any order. It is also possible to take into account the explicity known initial function.

Neutrino-pair bremsstrahlung in dense stars. III - Low-temperature quantum corrections in the liquid metal phase

Low-temperature quantum corrections to the neutrino-pair bremsstrahlung rate are calculated for dense stellar matter in the liquid metal phase. The corrections arise from the quantum nature of semiclassical ions. The numerical results are parameterized in the form of analytic formulae in order of facilitate applications. The typical corrections are on the order of 5% or less in the density-temperature region where the present method is valid.

Averaged ionization cross sections and rate coefficients in a partially ionized gas for small and high electron energy

Averaged (with Maxwell's and Druyvesteyn's electron velocity distribution functions) electron collisional ionization cross sections and rate coefficients are given for the atoms in the ground state in the form of analytical formulas. These formulas work well either for small or for high values of mean electron energy in the partially ionized gas.