Universal Function Research Articles

Trajectory Re-Planning and Tracking Control for a Tractor–Trailer Mobile Robot Subject to Multiple Constraints

Autonomous tractor–trailer robots possess a broad spectrum of applications but pose significant challenges in control due to their nonlinear and underactuated dynamics. Unlike the tractor, the motion of the trailer cannot be directly actuated, which often results in a deviation from the intended path. In this study, we introduce a novel method for generating and following trajectories that circumvent obstacles, tailored for a tractor–trailer robotic system constrained by multiple factors. Firstly, leveraging the state information of both the obstacles and the desired trajectory, we formulate an improved trajectory for obstacle avoidance using the nonlinear least squares method. Subsequently, we propose an innovative tracking controller that integrates a universal barrier function with a state transformation strategy. This amalgamation facilitates the accurate tracking of the prescribed trajectory. Our theoretical analysis substantiates that the proposed control methodology ensures exponential convergence of the line-of-sight (LOS) distance and angle tracking errors, while enhancing the transient performance. To validate the efficacy of our approach, we present a series of simulation results, which demonstrate the applicability of the developed control strategy in managing the complex dynamics of tractor–trailer robots.

Research on optimization method of evaporation duct prediction model based on particle swarm algorithm

The sea surface roughness parameterization and universal stability functions, as key components of the evaporation duct prediction models rooted in the Monin-Obukhov similarity theory, dictate the model performance which further impacts the efficiency and accuracy of offshore electromagnetic applications. In this paper, layered meteorological and hydrological observations are collected during two cruises and processed to obtain the reference modified refractivity profiles close to the sea surface, and then particle swarm algorithm is utilized to optimize the parameters of the sea surface roughness parameterization and universal stability functions. The results show that compared with the pre-optimization model, the prediction accuracy of the optimized model is improved by 5.09% and 8.12% under stable conditions, and by 9.97% and 31.51% under unstable conditions for observation dataset from each cruise, which proves the feasibility of the proposed method for evaporation duct prediction model optimization.

Cooperative Control for Stochastic Multiagent Systems With Deferred Dynamic Constraints via a Novel Universal Barrier Function Approach.

This article investigates the cooperative control problem for stochastic multiagent systems (MASs) with dynamic constraints. A new universal barrier function is proposed, which is applicable to many systems with different types of constraint functions, even unconstrained systems. Several mapping functions are constructed to constrain the state variables directly without feasibility conditions, and the tracking control is achieved for stochastic MASs with deferred full-state constraints under the backstepping framework. In order to regulate the tracking error more precisely, the funnel error transformation is improved and the deferred funnel controller is developed by introducing a preassigned finite-time function. Based on the deferred funnel controller, the tracking error can be maintained within the predetermined funnel in the preassigned time. The convergence time can be defined according to the actual requirements, and it is independent of the design controller parameters and initial conditions. Finally, some simulation results are given to demonstrate the effectiveness of the proposed control algorithm.

Composite adaptive fuzzy bipartite consensus of fractional-order multiagent systems with a switched event-triggered mechanism

This paper focuses on online recorded-data-based composite adaptive fuzzy bipartite consensus control for uncertain fractional-order multiagent systems with interconnected terms and external disturbances by employing a switched-threshold-based event-triggered mechanism (ETM) under the backstepping structure. Fuzzy logic system is used as a universal function approximation to deal with function uncertainties that are not prone to model in the system. A new composite learning adaptive parameter design scheme that synthesizes both prediction error and tracking error is developed to enhance the tracking performance, where the prediction error is raised from the utilization of online recorded data and instantaneous data. A unique switched-threshold-based ETM is introduced, in which the information transmission between the sensor and the controller is imposed on one of the individuals. One merit of this work consists in that it can automatically and rapidly switch and adjust between the fixed threshold and relative threshold ETM according to the amplitude of input signals to balance the network resources and impede the occurrence of pulse phenomenon. In addition, it is theoretically proven that the proposed scheme can ensure that all internal signals of the closed-loop system are bounded and achieve local bipartite consistent errors through the fractional Lyapunov stability criterion. Finally, a numerical example is provided to confirm the feasibility of the proposed approach.

Random Matrix Statistics in Propagating Correlation Fronts of Fermions.

We theoretically study propagating correlation fronts in noninteracting fermions on a one-dimensional lattice starting from an alternating state, where the fermions occupy every other site. We find that, in the long-time asymptotic regime, all the moments of dynamical fluctuations around the correlation fronts are described by the universal correlation functions of Gaussian orthogonal and symplectic random matrices at the soft edge. Our finding here sheds light on a hitherto unknown connection between random matrix theory and correlation propagation in quantum dynamics.

Nonlinear response in diffusive systems

Nonintegrable systems thermalize, leading to the emergence of fluctuating hydrodynamics. Typically, this hydrodynamics is diffusive. We use the effective field theory (EFT) of diffusion to compute higher-point functions of conserved densities. We uncover a simple scaling behavior of correlators at late times, and, focusing on three and four-point functions, derive the asymptotically exact universal scaling functions that characterize nonlinear response in diffusive systems. This allows for precision tests of thermalization beyond linear response in quantum and classical many-body systems. We confirm our predictions in a classical lattice gas.

Variation-Difference Method of Calculation of Layered Rubber-Metal Vibration Isolators Used for Protection of Reinforced Concrete Buildings from Anthropogenic Vibration

In the modern construction complex of the city of Moscow for the protection of buildings and structures from man-made vibration arising from the movement of trains of rail transportation (subway trains, railroad lines and trams). To protect buildings and structures from anthropogenic vibration arising from the movement of rail transport trains (subway trains, railroad lines and streetcars), Moscow uses layered rubber-metal vibration isolators [1]. Most often, to determine their static and dynamic characteristics, the finite element method (FEM) is used, which makes it possible to determine all components of the stress-strain state and frequencies of free oscillations in the loaded state practically for any structural forms of isolators. However, for the most popular software packages that implement FEM, the problem of optimizing the structural shape of the vibration isolator still requires significant time expenditures for multiple changes of the finite element mesh, repeated setting of boundary conditions and implementation of a series of calculations. Only some of the software packages implementing the FEM solve optimization problems of the shape of the product being calculated, most often it is related to foreign software products with universal functionality. Variation-difference method (VDM) is the closest to the finite element method (FEM) in terms of its computational capabilities. It is possible to create program modules that repeatedly and automatically solve three-dimensional problems of elasticity theory taking into account the changed geometry of the vibration isolator: the dimensions of the product, the location of perforations within the rubber layers, as well as the thickness of the rubber layer and other parameters important for obtaining an effective technical solution for vibration isolation of buildings. Further, the article describes the method of implementation of the variational-difference method (VDM) as applied to the solution of the problem of determining the components of the stress-strain state inside a three-dimensional layered vibration isolator with perforations of different sizes having different locations relative to the contour of the vibration isolator, i.e., the solution of the problem of optimizing the three-dimensional shape of the vibration isolator is given.

A novel fault location method for the active distribution network based on dynamic quantum genetic algorithm

The fault location of an active distribution network is a vital analysis to prevent major outages in the power system. Considering the influence of renewable distributed generations on fault characteristics, this paper proposes a novel location method based on a dynamic quantum genetic algorithm to solve for fault locations in active distribution networks. In the method, the fault current code is measured based on feeder terminal units. A universal switching function is presented to convert the feeder switch status into an uploaded fault current code. The fault location model is defined as an optimization problem that presents the evaluation objective function with an anti-false-positive factor. The dynamic quantum genetic algorithm is developed to locate the fault feeder according to the uploaded fault current code of the feeder terminal unit. The algorithm adopts dynamic rotating gate strategy and adaptive quantum crossover strategy to satisfy the requirements of quickness and accuracy for fault location. Moreover, the method avoids easily falling into a local optimum by integrating the discrete quantum mutation. The proposed fault location technique is tested and compared to other existing techniques on a 33-bus active distribution network. The simulation results show that the proposed fault location method can locate fault feeders accurately with fast computational times under conditions of single or multiple faults and with an information distortion of the feeder terminal unit.

SQM2.20: Semiempirical quantum-mechanical scoring function yields DFT-quality protein–ligand binding affinity predictions in minutes

Accurate estimation of protein–ligand binding affinity is the cornerstone of computer-aided drug design. We present a universal physics-based scoring function, named SQM2.20, addressing key terms of binding free energy using semiempirical quantum-mechanical computational methods. SQM2.20 incorporates the latest methodological advances while remaining computationally efficient even for systems with thousands of atoms. To validate it rigorously, we have compiled and made available the PL-REX benchmark dataset consisting of high-resolution crystal structures and reliable experimental affinities for ten diverse protein targets. Comparative assessments demonstrate that SQM2.20 outperforms other scoring methods and reaches a level of accuracy similar to much more expensive DFT calculations. In the PL-REX dataset, it achieves excellent correlation with experimental data (average R2 = 0.69) and exhibits consistent performance across all targets. In contrast to DFT, SQM2.20 provides affinity predictions in minutes, making it suitable for practical applications in hit identification or lead optimization.

An Interesting Correlation Between the Peak Slope and Peak Value of a Sunspot Cycle

The maximum slope of the sunspot number during the rising phase of a sunspot cycle has an excellent correlation with the maximum value of the sunspot number during that cycle. This is demonstrated using a Savitzky–Golay filter to both smooth and calculate the derivative of the sunspot-number data. Version 2 of the International Sunspot Number (S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$S$\\end{document}) is used to represent solar activity. The maximum of the slope during the rising phase of each cycle was correlated against the peaks of solar activity. Using three different correlation fits, the average predicted amplitude for Solar Cycle 25 is 130.7 ± 0.5, among the best correlations in solar predictions. A possible explanation for this correlation is given by the similar behavior of a shape function representing the time variation of the sunspot number. This universal function also provides the timing of the solar maximum by the time from the slope maximum to the peak in the function as late 2023 or early 2024. A Hilbert transform gives similar results, which are caused by the dominance of the 11-yr sunspot-cycle period in a Fourier fit of the sunspot number.

A formalism for extracting track functions from jet measurements

The continued success of the jet substructure program will require widespread use of tracking information to enable increasingly precise measurements of a broader class of observables. The recent reformulation of jet substructure in terms of energy correlators has simplified the incorporation of universal non-perturbative matrix elements, so called “track functions”, in jet substructure calculations. These advances make it timely to understand how these universal non-perturbative functions can be extracted from hadron collider data, which is complicated by the use jet algorithms. In this paper we introduce a new class of jet functions, which we call (semi-inclusive) track jet functions, which describe measurements of the track energy fraction in identified jets. These track jet functions can be matched onto the universal track functions, with perturbatively calculable matching coefficients that incorporate the jet algorithm dependence. We perform this matching, and present phenomenological results for the charged energy fraction in jets at the LHC and EIC/HERA at collinear next-to-leading logarithmic accuracy. We show that higher moments of the charged energy fraction directly exhibit non-linear Lorentzian renormalization group flows, allowing the study of these flows with collider data. Our factorization theorem enables the extraction of universal track functions from jet measurements, opening the door to their use for a precision jet substructure program.

Diffusion Monte Carlo calculations of the polarizability of a confined hydrogen atom: benchmarking and application to high symmetry wells

We present a non-perturbative direct method to calculate the polarizability of a hydrogen atom confined in a three-dimensional potential well of any geometry. The calculation is based on the diffusion Monte Carlo method. The advantage of the method is simplicity of implementation and immediate adaptability to any well shape. The method is validated for the well-studied spherically confined hydrogen atom, and demonstrated in the case of two other geometries (cube and octahedron), for which this paper provides the first set of results. Although demonstrated here for the confined hydrogen atom, the method can be immediately applied to any single-electron system placed in a three-dimensional potential well of any type and geometry. Results for a hydrogen atom confined in potential wells of cubic or spherical symmetry suggests that the polarizability in these cases is a universal function of the volume of the well. This result can simplify calculations for real situations such as in quantum dots.

Asymptotic Freedom at the Berezinskii-Kosterlitz-Thouless Transition without Fine-Tuning Using a Qubit Regularization

We propose a two-dimensional hard-core loop-gas model as a way to regularize the asymptotically free massive continuum quantum field theory that emerges at the Berezinskii-Kosterlitz-Thouless transition. Without fine-tuning, our model can reproduce the universal step-scaling function of the classical lattice XY model in the massive phase as we approach the phase transition. This is achieved by lowering the fugacity of Fock-vacuum sites in the loop-gas configuration space to zero in the thermodynamic limit. Some of the universal quantities at the Berezinskii-Kosterlitz-Thouless transition show smaller finite size effects in our model as compared to the traditional XY model. Our model is a prime example of qubit regularization of an asymptotically free massive quantum field theory in Euclidean space-time and helps understand how asymptotic freedom can arise as a relevant perturbation at a decoupled fixed point without fine-tuning. Published by the American Physical Society 2024

Viscosity Anomalies of Magnetic Fluid Stabilized by a Double Layer of Surfactant in Water

Purpose to study the temperature dependence of the viscosity of a water-based magnetic fluid.Method. Consists of measuring the dynamic viscosity of a magnetic fluid based on cobalt ferrite particles stabilized in water by a double layer of surfactant. Lauric acid (first layer) and a mixture of lauric acid and sodium dodecyl sulfate (second layer) were used as a stabilizer. Measurements were performed using a Brookfield DV-II+Pro rotational viscometer equipped with a coaxial cylinder system. The measuring system of the viscometer was thermostated using a KRIO-VT-12-1 thermostat.Results. The temperature dependences of dynamic viscosity were measured for three samples of magnetic fluid based on cobalt ferrite particles of various concentrations in the temperature range 0–90C°. The obtained temperature dependences of viscosity are radically different from the temperature dependences both predicted by known theories and experimentally observed for kerosene-based magnetic fluids. According to well-known theoretical models, the ratio of the viscosity of the magnetic fluid to the viscosity of the base medium is a certain universal function of particle concentration. Different models offer different types of this feature. But it clearly follows from them that the viscosity ratio should not depend on temperature. For magnetic fluids based on kerosene, it has been experimentally established that its relative viscosity decreases with increasing temperature. However, according to the results obtained, the relative viscosity of a water-based magnetic fluid does not decrease with increasing temperature, but increases significantly. That is, the viscosity of a water-based magnetic fluid decreases more slowly with increasing temperature than the viscosity of water.Conclusion. The observed dependencies completely contradict the known patterns, both theoretical and experimentally established for kerosene-based magnetic fluids. The results obtained may be useful for the further development of the theory of aqueous colloidal solutions with particle stabilization by a double layer of surfactants.

Evidence of second-order transition and critical scaling for the dynamical ordering transition in current-driven vortices

Dynamical ordering from a disordered plastic flow to an anisotropically ordered smectic flow induced by a dc force has been studied in various many-particle systems, including vortices in type-II superconductors. However, it remains unclear whether the dynamical ordering is a true phase transition because of lack of suitable experimental methods. Here, we study the response of vortex flow to the transverse force using a cross-shaped amorphous Mox\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_{x}$$\\end{document}Ge1-x\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_{1-x}$$\\end{document} film. From transverse current-voltage (force-velocity) characteristics under various longitudinal currents, we find a change of the transverse response in low voltage (velocity) regions from a nonlinear to linear behavior at a well-defined longitudinal current that marks the dynamical ordering transition. We also find the scaling collapse of the transverse current-voltage curves to a universal scaling function, providing evidence of the second-order transition for the dynamical ordering transition.

Reduction of multiple scattering of positively charged ultra relativistic particles channeling in planar fields of single crystals

Based on the theory of multiple scattering of positively charged particles channeled in the planes of a single crystal of silicon, calculations of the rms angle of scattering have been made for particles in the range of momenta 100–7000 GeV/c. As a result of the analysis, we find that the rms angle of multiple particle scattering can be represented by in the form of (Cl)1/w/ph, where p is the particle momentum, l is the crystal thickness and C,w,h are the constant coefficients. We show that these calculation results can be represented in a unified way using the found universal function. This function is shown to be in a good agreement with the experimental data. Furthermore, our analysis is consistent with the effect (predicted by Luboshits and Podgoretsky) of reducing multiple scattering of above-barrier particles moving at small angles to the planes of the crystal. In general, the obtained results give a simple and clear description of the scattering process under consideration.

Editing function of type II thioesterases in the biosynthesis of fungal polyketides

Polyketide synthases (PKSs) are megasynthases with multiple autonomously folding domains, which operate cooperatively in the PKS assemblies to synthesize specific polyketide scaffolds. Any nonreactive intermediates tethered to acyl carrier protein (ACP) domain in the PKS will block the elongation process of polyketide chains. In this study, we systematically elucidate the editing function of fungal type II thioesterases (TEIIs) to hydrolyze ACP domain-bounded nonreactive acyl groups, which are uploaded by substrate promiscuous fungal phosphopantetheinyl transferase. Thereof, the TEIIs encoded in gene clusters of nonreducing PKS with reductase domain exhibit universal editing function. Besides, editing function was also found for TEIIs encoded in gene clusters of highly-reducing PKS with condensation domain. Hence, the editing TEIIs with function of recovery PKS are applied to improve the yield of the fungal polyketides in vivo. Our study provides valuable insights into the editing process of fungal PKSs, highlights the crucial role of TEIIs in enhancing polyketide production and introduces a novel metabolic engineering strategy for fungal polyketide biosynthesis by leveraging the editing function of TEIIs.

Research on Optimization Method of Evaporation Duct Prediction Model

The sea surface roughness parameterization and the universal stability function are key components of the evaporation duct prediction model based on the Monin–Obukhov similarity theory. They determine the model’s performance, which in turn affects the efficiency and accuracy of electromagnetic applications at sea. In this study, we collected layered meteorological and hydrological observation data and preprocessed them to obtain near-surface reference modified refractivity profiles. We then optimized the sea surface roughness parameterization and the universal stability function using particle swarm optimization and simulated annealing algorithms. The results show that the particle swarm optimization algorithm outperforms the simulated annealing algorithm. Compared to the original model, the particle swarm optimization algorithm improved the prediction accuracy of the model by 5.09% under stable conditions and by 9.97% under unstable conditions, demonstrating the feasibility of the proposed method for optimizing the evaporation duct prediction model. Subsequently, we compared the electromagnetic wave propagation path losses under two different evaporation duct heights and modified refractivity profile states, confirming that the modified refractivity profile is more suitable as the accuracy criterion for the evaporation duct prediction model.

Application of a universal reaction function to the description of heavy-ion reaction cross sections

Application of a universal reaction function to the description of heavy-ion reaction cross sections

СИСТЕМА РАННЬОГО РЕАГУВАННЯ ТА ПОПЕРЕДЖЕННЯ БАНКРУТСТВА

In the introduction, the relevance of the research topic is defined, and foreign and domestic economists who have examined the issues of the early warning and bankruptcy prevention system are cited. The main part of the article summarizes and defines the economic essence of corporate bankruptcy: the concept of "bankruptcy" is defined. The early warning and prevention system is examined: its essence is defined, and the systems (focused on internal parameters of the enterprise and the external environment) and approaches to detecting the possibility of bankruptcy (technical and fundamental) are characterized. The main models for determining the probability of bankruptcy occurrence in a company are presented (Altman's five-factor model, Springate's five-factor model, universal discriminant function) and possible ways to overcome bankruptcy (prevention, avoidance, and overcoming) are defined. In the conclusion, which summarizes the research, the main provisions of the article are specified.