Coordinate Space Research Articles

FISHER-SHANNON ENTROPIC UNCERTAINTY RELATIONS AND THEIR POWER-PRODUCTS AS A MEASURE OF ELECTRONIC CORRELATION

In this paper, we have presented an analytical model of two electron systems consisting of a many particle correlated wave function with some variational parameters α, λ and µ and used it to quantify the electron-electron correlation described by the wave function containing explicitly r12 (inter atomic distance between two electrons) dependent term. The single particle wave functions and the charge densities have been extracted from the said correlated wave function both for the uncorrelated and correlated systems in coordinate space and its momentum analogs have been obtained by taking the Fourier transform of the coordinate analogs. We have computed and presented the results of the numerical values of the theoretic information entropies of the Shannon entropy, Fisher information entropy, Shannon power and the FisherShannon product. The numerical values are consistently found to satisfy the Beckner, Bialynicki-Birula and Mycielski (BBM ) inequality relation; Stam-Cramer-Rao inequalities or Fisher based uncertainty relation and Fisher-Shannon product relation for the uncorrelated and correlated systems in both the coordinate and momentum spaces.

Shannon Information Entropy Sum of a Free Particle in Three Dimensions Using Cubical and Spherical Symmetry

In this paper, the plane wave solutions of a free particle in three dimensions for Cubical and Spherical Symmetry have been considered. The coordinate space wave functions for the Cubical and Spherical Symmetry are obtained by solving the Schrdinger differential equation. The momentum space wave function is obtained by using the operator form of an observable in the case of Cubical Symmetry. For Spherical Symmetry, the same is obtained by taking the Fourier transform of the respective coordinate space wave function. The wave functions have been used to constitute probability densities in coordinate and momentum space for both the symmetries. Further, the Shannon information entropy has been computed both in coordinate and momentum space respectively for (L is the length of the side of the cubical box) values for Cubical Symmetry and for values in Spherical Symmetry keeping (k is the wave vector and p is the momentum of the free particle) constant. The values obtained for the Shannon information entropies are found to satisfy the Bialynicki-Birula and Myceilski (BBM) inequality at larger values () in case of Cubical Symmetry and for values of and in Spherical Symmetry.

Unification of kinetic and hydrodynamic approaches in the theory of dense gases and liquids far from equilibrium

A system of non-Markovian transport equations is obtained for the non-equilibrium one-particle distribution function of particles and the non-equilibrium average value of the density of the potential energy of the interaction of the system particles far from the equilibrium state. Expressions for entropy, the partition function of the non-equilibrium state of the system, as well as non-equilibrium thermodynamic relations were obtained. The generalized structure of transfer nuclei is revealed in detail with the selection of short-range and long-range contributions of interactions between particles. The connection of transport nuclei with generalized diffusion coefficients, friction in the space of coordinates and momentum and the potential part of the thermal conductivity coefficient is established.

Modeling Supercontinuum Lasers to Simulate Damage Thresholds on the Retina

Laser damage thresholds depend on the amount of energy absorbed, and in this specific case, energy absorbed by the retina. The goal of our research is to simulate a supercontinuum laser source and compare the resulting damage to that of the current ANSI approach. To calculate retinal damage we utilize the Arrhenius integral, which returns numerical values for laser-induced damage with values ranging from zero to one depending on the severity. Our simulations use numerical analysis to iterate through different coordinates in space and time to return data representative of the physical situation after we expose the eye to a gaussian laser beam. We have performed simulations ranging from a singular laser source up to a three-laser source and are currently working towards an automated method of generating these complex configurations in the hopes of more efficiently replicating the damage properties of a specific laser product and comparing it to the existing ANSI approach.

The diagrammatic method of Berezinskii for one-dimensional disordered wire with spin–orbit interaction

We extend Berezinskii’s diagram technique to the one-dimensional disordered wire containing Rashba and Dresselhaus spin–orbit interactions. The retarded and advanced Green’s functions are factorized in coordinates space in the presence of spin–orbit interactions. This factorization allows us to transform all coordinate dependence of the Green’s functions from lines to the impurity vertices. Our calculations show that all possible impurity vertices giving a contribution to the correlators do not differ from those given in the conventional technique, except that they are written in a 2 × 2 matrix form and the Fermi velocity vF∗ now depends on the spin–orbit coupling constants. The diagrammatic method of Berezinskii with spin–orbit interaction is used to obtain the distribution of the electron density of the localized state p∞(y).

In Situ Measurement of 2-D Crystal Size Distribution During Cooling Crystallization Process via a Binocular Telecentric Imaging System

In this paper, a novel in-situ measurement method with stereoscopic image analysis is proposed for monitoring crystal length and width distributions during a cooling crystallization process, based on a binocular telecentric imaging system. Firstly, a stereoscopic imaging calibration model is established for using binocular telecentric cameras to conduct in-situ measurement during a cooling crystallization process. Secondly, an enhanced algorithm is presented to improve matching crystal images from binocular image pairs, based on in-situ image preprocessing and segmentation. Thirdly, four key corners related to crystal length and width are determined by using the boundary features of matched crystal image projections. Finally, the length and width of each crystal are computed based on the reconstructed key corners in three-dimensional (3D) coordinate space, by using the established stereoscopic calibration model. Experimental validation on the proposed stereoscopic imaging calibration model and 3D reconstruction of key corners is carried out via in-situ measurement of a microscale checkerboard plate inserted into a cooling crystallizer. In-situ measurements of crystal length and width distributions during the cooling crystallization process of β-form L-glutamic acid are conducted to verify the effectiveness and advantage of the proposed measurement method.

Dynamic correction in manipulator control systems based on intelligent linear motion mechatronic module

Robotic complexes and robotic manipulators are widely used in the management of various objects and processes of control systems; their performance is directly related to the execution element. Electromagnetic actuators of multi-function control systems are structurally created separately for each adjustment body and lead to system complexity. To solve these problems, improve the executive system's weight-gauge indicators, and simplify the structural schemes, implementing intelligent mechatronic modules that perform linear and rotational movements in space coordinates is one of the urgent tasks. In this article, dynamic correction in manipulator control systems built based on an intelligent linear motion mechatronic module is considered. In manipulator control systems, the use of intelligent mechatronic modules in dynamic correction for manual and semi-automatic control manipulation systems that do not have a feedback channel for forces and moments and the relevance of the handle movement and manipulation objects with such a selection of the forces and moments vector m developed by them was seen. The article presents mathematical models for calculating vector components based on the current values of the generalized coordinates of the manipulator, their speed and acceleration, and the selection of the vector of forces and moments m developed by the intelligent mechatronic modules of the manipulator.

Schemes in thinking and the Creative Process

The article considers the role of schemes (especially visual – visual) in thinking and its research: illustration of situations, problems, correlation of concepts; use of non-standard tasks in the process of creative solution; research of certain types of schemes themselves as manifestations of some features of creative thinking. The understanding of schematism of productive creative thinking, started by I. Kant, was realized in the beginning of the XX century in a number of philosophical-theoretical and pedagogical approaches that address either their heuristic or didactic – constructive role. Special attention is paid to V. E. Steinberg's multidimensional didactic technology a number of initial aspects that were developed with the active participation of the author of the article. The method of constructing a scheme of coordinates of existence and action that not only gives a picture of the existence of a certain "subject" of consideration or field of activity, a certain social subject in a certain direction; but also revealing in their very structure the deep structures of creative thinking, hidden in the unconscious layers of the creative act: superconsciousness (as part of the frame), integral (realized in the space of many coordinates – "dimensions") thinking, dialectical synthesis of heterogeneous (incompatible, opposite).

Ultracool dwarfs in Gaia DR3

Context. Previous Gaia data releases offered the opportunity to uncover ultracool dwarfs (UCDs) through astrometric, rather than purely photometric, selection. The most recent, the third data release (DR3), offers in addition the opportunity to use low-resolution spectra to refine and widen the selection. Aims. In this work we use the Gaia DR3 set of UCD candidates and complement the Gaia spectrophotometry with additional photometry in order to characterise the global properties of the set. This includes the inference of the distances, their locus in the Gaia colour-absolute magnitude diagram, and the (biased through selection) luminosity function at the faint end of the main sequence. We study the overall changes in the Gaia RP spectra as a function of spectral type. We study the UCDs in binary systems, we attempt to identify low-mass members of nearby young associations, star-forming regions, and clusters, and we analyse their variability properties. Methods. We used a forward model and the Bayesian inference framework to produce posterior probabilities for the distribution parameters and a calibration of the colour index as a function of the absolute magnitude in the form of a Gaussian process. Additionally, we applied the hierarchical mode association clustering (HMAC) unsupervised classification algorithm for the detection and characterisation of overdensities in the space of celestial coordinates, projected velocities, and parallaxes. Results. We detect 57 young, kinematically homogeneous groups, some of which are identified as well-known star-forming regions, associations, and clusters of different ages. We find that the primary members of the 880 binary systems with a UCD belong to the thin and thick disc components of the Milky Way. We identify 1109 variable UCDs using the variability tables in the Gaia archive, 728 of which belong to the star-forming regions defined by HMAC. We define two groups of variable UCDs with extreme bright or faint outliers. Conclusions. The set of sources identified as UCDs in the Gaia archive contains a wealth of information that will require focused follow-up studies and observations. It will help advance our understanding of the nature of the faint end of the main sequence and the stellar-substellar transition.

Analysis on the Coupling Coordination of Land Space in the Northern Metropolitan Area of Leshan City

Analysis on the Coupling Coordination of Land Space in the Northern Metropolitan Area of Leshan City

Vibration Detection for Mobile Phone Based on Digital Image Correlation Method

To solve the problem of vibration test of mobile phone, a non-contact testing method is proposed based on binocular stereo vision. The method determines the internal parameters of the lens and the external parameters of two industrial cameras by camera calibration. After obtaining the corresponding region between the two cameras by digital image correlation matching, the point coordinates of three-dimensional space are reconstructed based on laser triangulation method, and the vibration of a point with the same name is calculated by tracking its three-dimensional position in adjacent frames. The method has the advantages of non-contact and full-field measurement. The experimental results show that the proposed method has high accuracy. Compared with the measurement results of the vibrometer, the maximum deviation of the proposed method is 0.04 mm and the average deviation is 0.021mm. The proposed method can measure the vibration direction and amplitude of the designated area on the mobile phone, which provides a test method for the verification and optimization of mobile phone vibration technology.

КОЭВОЛЮЦИЯ ИННОВАЦИИ И ОБРАЗОВАТЕЛЬНОГО ПРОСТРАНСТВА

The educational space as a set of educational systems develops both as a result of selforganization and under the influence of external management factors. The phenomena of the educational system, educational space and their development have been sufficiently studied in science. The driving force behind the development of educational systems is educational innovations. System-synergetic relationships between innovation systems and the conditions of the educational space suggest that their development occurs in concert. In pedagogy, the issues of links between the development of innovations and the educational spaces in which they occur have not been sufficiently studied. Most scholars study specific innovations in specific educational spaces. The coordinated development of innovations and educational space is not enough studied. The purpose of the article is to study the general issues of the co-evolution of innovation and educational space. The methodological foundations of the study include: dialectical universal laws of development, the concretization of which makes it possible to reveal the procedural development of innovation and educational space; stages of systems development adapted to the stages of innovation; the phenomena of bifurcation, self-organization, anthroposynergism, explaining the patterns of development; concepts of sustainable development in education. The author establishes a correspondence between the stages of innovation (creation, development, testing, implementation) and the states of the educational space (actualized, transitional, established); the procedural realizations of co-evolution at each stage are characterized; the mutual adaptation of the innovation system and the coordinates of the educational space (normative-regulatory, perspective-oriented, activity-stimulating, communicative-informational) is characterized.

Charge polarization calculated with a microscopic model for the fission fragments of U-236

We investigated theoretical methods to estimate the charge polarization of the fission fragments. The method is based on the microscopic mean-field model with the nucleon degree of freedom, and is represented in the three-dimensional coordinate space for dealing with any nuclear deformation. We employed the Skyrme effective interaction for the calculations and uranium-236 as a target nucleus. We reported static and dynamic methods in which the potential energy surface of the fissioning nucleus concerning the quadrupole and octupole deformations are used. Although the static method deduced the charge polarization which indicates the nuclei with the magic number and the octupole deformation, the quantities are not consistent with the existing data library (Wahl’s systematics). The dynamic method with the iso-energy initial condition on the potential energy surface showed the finite charge polarization of light and heavy fission fragments which is consistent with the data library. Furthermore, it indicates that the charge polarization has energy dependence of the initial states of the dynamic method.

Features of accumulation of chemical elements in the volume of the lens in senile cataract

This study provides a detailed analysis of the bioinorganic chemical composition of lens substance in patients with senile cataract using classical and spatial statistics methods. The study included 30 isolated human lenses. The light scattering ability (LSA) of the lens substance was evaluated using an original method. Additionally, distribution of chemical elements in the lens substance was analyzed using a scanning electron microscope with energy dispersive spectrometer (SEM/EDS). Measurements by all methods were carried out in a single coordinate space, which made it possible to compare the spatial correlation of different parameters. Small-angle light scattering of the lens substance has been quantitatively characterized for the first time. In contrast to the conventional norm, in senile cataract the accumulation fields of the majority of ion-forming elements (including Na, P, K, Cl) are distributed along the lines repeating the geometry of the lens capsule. At the same time, the light scattering ability of certain areas of the lens is significantly correlated with changes in the concentrations of Na, P, K, Ca in these areas. In particular, one ion-forming element can be distinguished - Na: spatial change of its concentration in senile cataract is strongly associated with a local change in LSA of the lens with opacities clustering of any degree. Thus, a change in the nature of the Na accumulation in the lens volume can be considered the main marker of senile cataract formation. The distribution pattern of ion-forming elements indicates that the loss of barrier properties in the capsule plays a significant role in the development of senile cataract.

To the Solution of a Spherically Symmetric Problem of General Relativity

The paper is devoted to the spherically symmetric problem of General Relativity. Existing solutions obtained by K. Schwarzschild and V. Fock are presented and discussed. A special geometry of the Riemannian space induced by gravitation is proposed. According to this geometry the four-dimensional Riemannian space is assumed to be Euclidean with respect to the space coordinates and Riemannian with respect to the time coordinate. The solution of the Einstein equations for the empty space with this geometry coincides with the solution in Gullstand-Painlever coordinates. In application to the found solution, the problem of the light trajectory deviation in the vicinity of Sun and the problem of escape velocity are discussed.

Spherically Symmetric Problem of General Relativity for an Elastic Solid Sphere

The paper is devoted to a spherically symmetric problem of General Relativity (GR) for an elastic solid sphere. Originally developed to describe gravitation in continuum (vacuum, gas, fluid and solid) GR does not provide the complete set of equations for solids and, in contrast to the Newton gravitation theory, does not allow us to study the stresses induced by gravitation in solids, because the compatibility equations which are attracted in the Euclidean space for this purpose do not exist in the Riemannian space. To solve the problem within the framework of GR, a special geometry of the Riemannian space induced by gravitation is proposed. According to this geometry, the four-dimensional Riemannian space is assumed to be Euclidean with respect to the space coordinates and Riemannian with respect to the time coordinate. Such interpretation of the Riemannian space in GR allows us to supplement the conservation equations for the energy-momentum tensor with compatibility equations of the theory of elasticity and to arrive to the complete set of equations for stresses. The analytical solution of the Einstein equations for the empty space surrounding the sphere and the numerical solution for the internal space inside the sphere with the proposed geometry are presented and discussed.

Reconstruction of transverse phase space from transverse feedback data for real time extraction of vital LHC machine parameters

The LHC transverse feedback system (ADT) provides bunch by bunch, turn by turn, normalized and digitized beam position signals from four pick-ups per plane and for each beam. Together with already existing powerful computer-based observation systems, this data can be used to reconstruct in real-time the transverse phase space coordinates of the centre-of-charges, for each individual bunch. Such information is extremely valuable for machine operation, or transverse instability diagnostics.This paper aims on discussing and evaluating methods of combining four position signals for such analysis in the presence of noise and with active transverse feedback. Comparisons are made based on the extraction of vital parameters like the fractional tune or transverse activity. Analytical and numerical results are further benchmarked against real beam data.

Model-free cable robot control

This paper proposes a technique to control a cable robot in the total absence of a model and its parameters. The cable robot is actuated by three motors whose data, including exact positions, pulley diameters, and nominal cable length, are unknown. We just assume to have a very rough knowledge of lower and upper bounds for the partial derivatives of the relation between the cable lengths and the end-effector space coordinates. A structured-light sensor measures the end-effector position, and the goal is to drive it to a designated point. An algorithm is proposed with guaranteed convergence based on the so-called model-free plant tuning approach. No learning stage is required. Experimental results are reported.

Applications of randomly selected sets of exact Voight's solutions for vibration of thin plates

The principally new method of selected exact solutions, SES, for plate vibration based on fundamental solutions of Voigt is suggested. In contrast to similar known methods, it employs the frequency dependent functions for both space coordinates. The sets of exact solutions which depends on some arbitrary chosen parameters are constructed. This allows to choose any number of exact solutions, while the required number of them depends on the boundary conditions which should satisfy in considered collocation points. 
 The efficiency of method is demonstrated for the most unfavorable case of all sides clamped rectangular plate. Nevertheless, the accuracy is quite satisfactory for first six natural frequencies even for relatively small number of collocation boundary points, and testify about big prospects as to application for complex structures, different geometries, various boundary conditions. 
 Additionally two variants of the Galerkin method are realized and compared. First one, employs the exponential functions, while the second one –the very popular beam functions. The calculation results show the superiority of first variant as in technical realization as in accuracy, and in further applications in structural mechanics.

On the relationship between the strength of bonding between topological atoms and the exchange‐correlation energy

AbstractThe titled relationship is considered in this paper in terms of the (de)localization phenomenon and its emanation in the positional coordinate space. The similarity between the strength of bonding of a topological atom (in the sense of the population of the corresponding atomic surface) and the delocalization index is discussed. Based on the hypervirial theorem, a scalar one‐particle field is suggested to visualize the consequences of (de)localization for the formation of bonding.