Analytical Description Research Articles

Two-dimensional analytical description of the plasma potential in a magnetron discharge

Simple analytical formulas are proposed to describe the plasma potential in a steady-state magnetron discharge, based on the results of various experiments and numerical simulations reported in the literature. The description is two-dimensional (2D), covering two main regions, the cathode sheath and the ionization region, both contributing to electron energization. A parabolic potential in the axial direction governs the cathode sheath. The thickness of the cathode sheath is obtained from the 1D collisionless Child–Langmuir law. A parabolic or linear potential in the axial direction characterizes the ionization region. The local ion current density to the cathode, estimated from the target erosion profile, sets the radial dependence of the potential. The proposed formulas use a set of input parameters that can be experimentally obtained. The analytical description captures all characteristics of the highly inhomogeneous plasma potential of a steady-state magnetron discharge operated in a reduced magnetic field BRT/p lower than 0.1 T/Pa, as revealed by the comparison to self-consistent 2D numerical simulations.

Modelling the loosening of rock in the experimental rock mining method

Analytical description of the process of rock discontinuity caused by the operation of an experimental cutting head, in which a combination of cutting and loosening methods was used, is presented. Loosening of the rock fragment takes place after reaching the tensile or shear strength of the rock, what is more favourable compared to the classical mining methods. An analytical model of the stress in the crack initiation plane was developed using the models of rock loosening using the disc tools and relationships formulated in fracture mechanism. The special integral of the differential equation of the loosening line was determined by geometric integration. Numerical simulations of the chip loosening were also carried out using the model of the solid rock built using the Finite Element Method. The developed models of losing the rock continuity were used in numerical simulations of loosening the rock fragment to analyze the impact of the selected parameters of the mining technology, of the rock properties and geometrical features of the experimental cutting head, on the shape of the loosening line and its extend. Using the stand test results, the qualitative compliance of the shape of the loosening line, determined using the analytical model and the numerical model, with the geometrical features of the rock chips obtained in the laboratory, was confirmed. It was found that the proper selection of the design features of the cutting head, such as: a small angle of the loosening disc and a small angle of inclination of the head axis, cause a qualitative increase in the loosening range.

Recent advances in the SISSO method and their implementation in the SISSO++ code.

Accurate and explainable artificial-intelligence (AI) models are promising tools for accelerating the discovery of new materials. Recently, symbolic regression has become an increasingly popular tool for explainable AI because it yields models that are relatively simple analytical descriptions of target properties. Due to its deterministic nature, the sure-independence screening and sparsifying operator (SISSO) method is a particularly promising approach for this application. Here, we describe the new advancements of the SISSO algorithm, as implemented into SISSO++, a C++ code with Python bindings. We introduce a new representation of the mathematical expressions found by SISSO. This is a first step toward introducing "grammar" rules into the feature creation step. Importantly, by introducing a controlled nonlinear optimization to the feature creation step, we expand the range of possible descriptors found by the methodology. Finally, we introduce refinements to the solver algorithms for both regression and classification, which drastically increase the reliability and efficiency of SISSO. For all these improvements to the basic SISSO algorithm, we not only illustrate their potential impact but also fully detail how they operate both mathematically and computationally.

Toward a Unified Analytical Description of Internal Conversion and Intersystem Crossing in the Photodissociation of Thioformaldehyde. I. Diabatic Singlet States.

The photodissociation of thioformaldehyde is an archetypal system for the study of competition between internal conversion and intersystem crossing, which involves its two singlet states (S0 and S1) and two triplet states (T1 and T2). In order to perform accurate dynamic simulations, either quantum or quasi-classical, it is essential to construct an analytical representation for all necessary electronic structure data. In this work, a diabatic potential energy matrix (DPEM), Hd, for the two singlet states (S0 and S1) is reported. The analytical form of DPEM is symmetrized and constructed to reproduce adiabatic energies, energy gradients, and derivative couplings obtained from high-level multireference configuration interaction wave functions. The Hd is fully saturated in the molecular configuration space with a trajectory-guided point sampling approach. This Hd can provide the accurate description of the photodissociation of thioformaldehyde on its singlet states and is also a necessary part for incorporating the spin-orbit couplings into a unified diabatic framework. Preliminary quasi-classical trajectory simulations show that a roaming mechanism also exists in the molecular dissociation channel of thioformaldehyde.

Heuristic construction of field line random walk diffusion coefficients

To understand the statistics of magnetic field lines in turbulence is complicated. Previous descriptions have been based on either pure numerical treatments, often called simulations, or analytical theory. In the latter case one operates with nonlinear integral or differential equations which are difficult to solve. In order to achieve a complete analytical description, one needs to employ a set of approximations which are often difficult to justify. Although, previously developed numerical and analytical treatments of field line random walk agree with each other, they do not provide simple arguments for the analytical form of field line diffusion coefficients. It is the purpose of the current article to derive field line random walk coefficients entirely based on simple heuristic arguments. Special cases such as slab, two-dimensional, three-dimensional, and two-component turbulence are considered. Heuristically constructed diffusion parameters are compared with previously obtained analytical results. It is shown that the heuristic arguments provide the same scaling behavior as the formulas derived by employing systematic analytical theories.

The Ball-on-Three-Balls strength test: Effective volumes and surfaces for Weibull strength scaling

In order to compare the strength results of brittle materials from various testing methods or use the data for design purposes, it is essential to know the effective volume (Veff) or surface (Seff) for every loading scenario. For the Ball-on-Three-Balls-test (B3B), Veff and Seff have to be determined and investigated through Finite-Element-Analysis due to the lack of an accurate analytical description of the stress field. Through this work, the effective volume and surface of the B3B-test are made available as tabulated data for a wide range of specimen geometries and materials, along with the tools to utilize the data. A fitting model for the dependency of Veff and Seff on the Weibull-modulus for any given specimen geometry is provided. The influence of load-dependent non-linear effects on Veff and Seff is discussed. Finally, the necessity of Veff and Seff for statistical strength analysis is demonstrated through a practical example.

On the renormalization group fixed point of the two-dimensional Ising model at criticality

We analyze the renormalization group fixed point of the two-dimensional Ising model at criticality. In contrast with expectations from tensor network renormalization (TNR), we show that a simple, explicit analytic description of this fixed point using operator-algebraic renormalization (OAR) is possible. Specifically, the fixed point is characterized in terms of spin-spin correlation functions. Explicit error bounds for the approximation of continuum correlation functions are given.

Undulating Propulsion Underwater Robot Control Method Based on ADRC and Fuzzy Logic

The article is devoted to the development a closed-loop depth and course control algorithms for underwater robot with pair undulating fin. The controller was proposed based on the Active Disturbance Rejection Control (ADRC) technique and fuzzy logic. A brief review of the underwater robot with pair undulating fin (AUV) is carried out. The dynamic and kinematic robot model is given, and the robot model with the environment is presented in the Simscape-MATLAB library. To solve the problem of controlling course and depth of the robot, a method of Active Disturbance Rejection Control (ADRC) is proposed. This robust control method based on extension of the system model with an additional and fictitious state variable, representing everything that is not included in the mathematical description of the plant. This method allows to treat the considered system with a simpler model, since the negative effects of modeling uncertainty are compensated in real time. The advantage of the proposed method is that an exact analytical description of the system is not required, since it can be assumed that the unknown parts of the dynamics are internal noise in the installation. The fuzzy control method is used to build a non-linear relationship between controller outputs and fin parameters that determine the generated fin forces. The results of modeling of the problem of heading and depth control using a complete nonlinear dynamic model with six degrees of freedom are presented. The conducted studies confirm the operability, adequacy, and anti-disturbance ability of the ADRC controller. 

Closed-Form Analysis of the α-Beaulieu-Xie Shadowed Fading Channel

The presented research proposes the α-modification of the Beaulieu-Xie shadowed fading channel for wireless communications. For the assumed model the closed-form analytical description of the basic statistical characteristics is carried out (i.e., probability density function, cumulative distribution function, and their asymptotics). The derived statistical description is exemplified on the problems of the average bit error rate and ergodic capacity calculation, for which the exact analytic and high signal-to-noise ratio asymptotic expressions are derived. The performed extensive numerical analysis demonstrates high correspondence with the analytical work and helps to study the dependence of the channel nonlinearity effects on the bit error probability.

Description of Residual Stress Distribution in the Surface Layer After Heat Treatment and Shot Peening

Abstract The stress distribution function in the surface layer is created as a result of using stress measurements on the surfaces of C45 steel samples after shot peening. Stresses were measured by X-ray diffraction with the use of the PSF-3M device from the Rigaku Company. For measuring residual stresses, subsequent layers of the top surface of the material were used as a basis, and these were obtained through electrochemical etching. The test results i.e. distance into the material, sample hardness, shot type, stress) were entered into the stepwise multiple regression program. A record of residual stresses was obtained in the form of the second-degree regression function of three independent variables with interactions. The obtained analytical form of the residual stress function was used in the FUNVAL3.EXE program to calculate the tabular values of stresses permeating into the material. For the analytical description of the stress distribution, the REGPOLY.EXE regression program was used, which creates a polynomial functional form of the residual stress distribution. The plot form of the residual stress distribution was obtained using the EXCEL Microsoft Office 2000 program.

Higher-Order Optomechanical Nonlinearity Based on the Mechanical Effect of Light

Nonlinear cavity optomechanics based on the mechanical effect of light has recently received considerable attention due to its potential applications in high-precision metrology. In this work, we theoretically studied the third-order optomechanical nonlinearity by using a perturbative approach, and an analytical solution is given, which can be extended to cases of higher-order optomechanical nonlinearity. Furthermore, the generation of a third-order sideband is analyzed in detail, and the results show that the amplitude of the third-order sideband shows a high dependence on the control field detuning, suggesting that the high-order nonlinear intensity can be enhanced by properly adjusting the detuning of the laser field rather than by a strong laser drive. In addition to providing insight into optomechanical nonlinearity, the analytical description of third-order optomechanical nonlinearity based on the mechanical effects of light may find applications in ultra-high precision measurement under low power conditions.

Disorder and Photogeneration Efficiency in Organic Semiconductors.

An analytical description of the separation probability of a geminate pair in organic semiconductors is given. The initial diffusion of "hot" twins is anomalously strong due to energy disorder. This circumstance significantly increases the photogeneration quantum yield at low temperatures and weakens its temperature dependence relative to predictions of the Onsager model, in agreement with Monte Carlo and experimental results.

Transition between metastable equilibria: Applications to binary-choice games.

Transitions between metastable equilibria in the low-temperature phase of dynamical Ising game with activity spillover are studied in the infinite time limit. It is shown that exponential enhancement due to activity spillover, which takes place in finite-time transitions, is absent in the infinite time limit. In order to demonstrate that, the analytical description for infinite time trajectory is developed. An analytical approach to estimate the probability of transition between metastable equilibria in the infinite time limit is introduced and its results are compared with those of kinetic Monte Carlo simulation. Our study sheds light on the dynamics of the Ising game and has implications for the understanding of transitions between metastable states in complex systems.

Keterkaitan Masyarakat dan Kebudayaan Sekolah Pentingnya Inklusivitas dan Adaptasi di Era Globalisasi

 The importance of the relationship between society and school culture is to create a healthy balance between these two entities. A school culture that is positive and relevant to the surrounding community can help students develop themselves and contribute positively to society. Conversely, positive influences from the community can also shape an inclusive and adaptive school culture. The method used in this paper is a qualitative approach with the type of writing analytic descriptions. The author will explain and analyze the problems encountered in the topic raised. Society can influence school culture in various ways such as providing support for school programs, providing input on school policies, and influencing student behavior outside of school. Society and school culture are two things that are interrelated and influence one another. These changes were mainly due to the implementation of the 2013 Curriculum which emphasized more active and creative learning.
 Keywords: Society, Change, Culture, School.

Performance of the cross-polarization experiment in conditions of radiofrequency field inhomogeneity and slow to ultrafast magic angle spinning (MAS).

In this paper, we provide an analytical description of the performance of the cross-polarization (CP) experiment, including linear ramps and adiabatic tangential sweeps, using effective Hamiltonians and simple rotations in 3Dspace. It is shown that radiofrequency field inhomogeneity induces a reduction in the transfer efficiency at increasing magic angle spinning (MAS)frequencies for both the ramp and the adiabatic CPexperiments. The effect depends on the ratio of the dipolar coupling constant and the sample rotation frequency. In particular, our simulations show that for small dipolar couplings (1 ) and ultrafast MAS (above 100 ) the transfer efficiency is below 40 % when extended contact times up to 20  are used and relaxation losses are ignored. New recoupling and magnetization transfer techniques that are designed explicitly to account for inhomogeneous radiofrequencyfields are needed.

AUTOMATION OF CALCULATING THE POSITION OF THE BOUNDARY COLUMN BETWEEN ADJACENT TRACKS OF DIFFERENT DESIGNS

The purpose of the study is to develop appropriate algorithms and procedures used in simulating the movement of a model car along adjacent tracks. These algorithms will automate the process of calculating the position of the boundary column between adjacent tracks of different designs with a given accuracy and compliance with traffic safety requirements. Scientific methods. In the course of the study, simulation methods were used to model the movement of the design car along the adjacent tracks. Analytical geometry methods were used to determine the main geometric characteristics of the car in terms of its relative position relative to the track axis. Results. The following conclusions were obtained as a result of the research. The multivariability of the design of adjacent tracks in the plan does not make it possible to create a universal analytical expression for determining the position of the boundary column. Existing methods for calculating the position of the boundary post provide for the maximum spread of the dimension in curved sections, which results in an excessive distance between the boundary post and the switch and inefficient use of the useful track length. The developed algorithms and procedures for determining the position of the boundary column are universal and allow automating the process of calculating the position of the boundary column between adjacent tracks of different designs in the plan, even when technical standards or parameters of the design cars change. In this case, only the initial data for the calculation need to be changed. Scientific novelty. The scientific novelty lies in the development of algorithms and procedures for formalizing the design of adjacent tracks and simulating the movement of design rolling stock on them. Practical significance. The developed algorithms and procedures can be implemented in the form of a software package for automated calculation of the position of the boundary column with high accuracy. Also, the obtained results of calculations can be used in the analysis and creation of an analytical description of the position of the boundary column for complex structures of adjacent tracks.

An exhaustive investigation into power performance of an unmanned robotized vehicle for industrial transportations

Investigation of power performance of an unmanned robotized vehicle for industrial transportations of payloads leads to appearance of an applied research in this study. This novel aim has been chosen based on operational requirement of the vehicle. Hence, it can be highlighted that this paper is the first exhaustive investigation for power efficiencies (tractive, slip, and motion power efficiencies) of the vehicle. To this aim, various payloads mounted on a trailer (1–5 kN) were towed by the vehicle through diverse tire air pressures (20.68–55.16 kPa) and drive speeds (0.17–0.5 m/s). Results illuminate that tire air pressure and payload weight had consequential contribution to motion and slip power efficiencies. While, tractive power efficiency mainly depended on payload weight. Linear regression approximations demonstrate that dual cumulative contributory effect of payload weight and tire air pressure on the motion power efficiency (87.28–99.84 %) and slip power efficiency (66.48–98.82 %) was synergetic. Meanwhile, tractive power efficiency (66.31–94.27 %) nonlinearly dropped with augmentation of payload weight. Resultant slip and motion power inefficiency were associate with vehicle motion power loss in amplitude of 0.28–123.52 and 0.21–10.33 W, respectively. Consequently, tractive power inefficiency was associate with vehicle motion power loss in amplitude of 1.30–124.46 W. This amplitude spotlights that 5.78–33.78 % of vehicle motion power inevitably wasted inside wheel-surface interface in towing tasks. Overall, numerical and analytical descriptions of the results as well as practical suggestions provide appropriate guidelines for vehicle supervisor in order to optimize power performance.

Family Support in Online Learning for the Student's Semester Achievement Index During the Covid-19 Pandemic

The background of the research is the unfinished Covid-19 pandemic in Indonesia, and it makes public adapt to all situations and conditions that are lived, including the learning process in the study place. The government issued a regulation to reduce the Covid-19 incidence rate by applying online learning or distance learning. This condition is certainly not an easy thing for families, students, and the education management to achieve the learning purpose. This study aims to know the relationship of family support in the implementation of online learning with Student Semester Achievement Index during the Covid-19 pandemic in 2021. The research method used an analytic description, using a cross-sectional approach. The research was conducted in November 2021 in Faculty of Nursing, Cendekia Abditama University. The instrument used a questionnare, with 144 respondents of research samples. The results showed significant relationship between family support in the implementation online learning with Student Semester Achievement Index with p-value = 0.00. Studies indicate that family is a main support in the educational process.
 Keywords: Covid-19, family support, grade point average

Exact solution of the quantum integrable model associated with the Motzkin spin chain

The Motzkin spin chain is a spin-1 frustration-free model introduced by Shor & Movassagh. The ground state is constructed by mapping random walks on the upper half of the square lattice to spin configurations. It has unusually large entanglement entropy [quantum fluctuations]. The ground state of the Motzkin chain can be analytically described by the Motzkin paths. There is no analytical description of the excited states. The model is not solvable. We simplify the model by removing one of the local equivalence moves of the Motzkin paths. The system becomes integrable [similar to the XXX spin chain]. We call it free Motzkin chain. From the point of view of quantum integrability, the model is special since its R-matrix does not have crossing unitarity. We solve the periodic free Motzkin chain by generalizing the functional Bethe Ansatz method. We construct a T − Q relation with an additional parameter to formulate the energy spectrum. This new parameter is related to the roots of unity and can be described by the Möbius function in number theory. We observe further patterns of number theory.

Self-consistent dynamical models with a finite extent – III. Truncated power-law spheres

Abstract Fully analytical dynamical models usually have an infinite extent, while real star clusters, galaxies, and dark matter haloes have a finite extent. The standard method for generating dynamical models with a finite extent consists of taking a model with an infinite extent and applying a truncation in binding energy. This method, however, cannot be used to generate models with a pre-set analytical mass density profile. We investigate the self-consistency and dynamical properties of a family of power-law spheres with a general tangential Cuddeford (TC) orbital structure. By varying the density power-law slope γ and the central anisotropy β0, these models cover a wide parameter space in density and anisotropy profiles. We explicitly calculate the phase-space distribution function for various parameter combinations, and interpret our results in terms of the energy distribution of bound orbits. We find that truncated power-law spheres can be supported by a TC orbital structure if and only if γ ≥ 2β0, which means that the central density slope–anisotropy inequality is both a sufficient and a necessary condition for this family. We provide closed expressions for structural and dynamical properties such as the radial and tangential velocity dispersion profiles, which can be compared against more complex numerical modelling results. This work significantly adds to the available suite of self-consistent dynamical models with a finite extent and an analytical description.