Dynamic Formulation Research Articles

Extremum seeking control for the trajectory tracking of a skid steering vehicle via averaged sub-gradient integral sliding-mode theory

This study introduces the development of a novel extremum-seeking controller designed to stabilize the tracking trajectory of a fully actuated four-wheeled skid steering vehicle. The controller design employs a class of averaged sub-gradient optimization strategies for a suitable convex function that depends on the enforced tracking trajectory achieved through an integral sliding mode implementation. The application of this controller necessitates a nonlinear coordinate transformation of the skid steering vehicle dynamics, resulting in a perturbed multi-input–multi-output linear system. Using the proposed controller, a multidimensional sliding surface remains remarkably stable despite tracking errors. The surface design defines a manifold that aligns with the sub-gradient of a convex function, contingent upon the integral of the tracking error. This connection establishes a link between the extremum-seeking problem and the sliding mode control design. Employing the cascade design strategy, commonly referred to as backstepping, enables the calculation of torques for the four wheels of the mobile vehicle using a sequence of auxiliary sliding surfaces, each with its corresponding complementary function for every stage. The dynamic formulation for the wheel torques is derived from the integral sliding mode methodology. A series of numerical evaluations are conducted to assess the controller’s effectiveness in terms of functional performance. A comparison between the control action based on sliding mode and the traditional state feedback formulation validates the efficacy of the proposed design. This comparison demonstrates advancements in robustness in the face of modeling uncertainties and optimization of the performance function, which are theoretically supported by the suggested control design. Implementing the proposed controller in an experimental platform for a wheeled skid steering vehicle reaffirms the control design methodology presented in this study. This platform includes the application of an image processing algorithm to determine the non-inertial position of the autonomous vehicle using integral sliding mode control. This information completes the necessary data for implementing the on-site version of the proposed controller.

Religious beliefs and their reasons, according to Raymond Boudon

The sociologist Raymond Boudon sought to explain increasingly complex social phenomena. After studying collective actions, he focused on collective beliefs: he was first interested in positivist beliefs, such as science, and then turned to normative beliefs, such as morality or politics. At the end of his career, he increasingly homed in on religious beliefs. This article aims to bring together the elements of his final contribution. First, a modeling of each person’s reasons to believe is presented, along with a dynamic formulation of the rational evolution of religious beliefs. This then allows me to position this theory in relation to the theories it coincides with—those of classical sociologists such as Alexis de Tocqueville, Max Weber, and Émile Durkheim—and those it refutes, namely the naturalistic theories of suspicion from Jean-Jacques Rousseau, Auguste Comte, and Karl Marx to the most extreme neuroscientists. To enhance the analysis, I will contrast this theory with Peter Berger’s, who uses similar sources, and with the epistemology of religious beliefs, which criticizes the same opponents.

A port-Hamiltonian model of airplane longitudinal dynamics

This paper contributes to the application of port-Hamiltonian systems (pHs) theory in the context of fixed-wing airplanes, an area challenged by the difficulty of introducing aerodynamics in this framework. Expanding on recent initiatives that applied pHs theory to fixed-wing airplane dynamics - a move that simplified thrust and aerodynamics - our study introduces a comprehensive longitudinal dynamics formulation. This approach not only clarifies these earlier models by aligning more closely with traditional airplane dynamics equations but also integrates physical parameters from an A300 airplane model. By addressing and enhancing the thrust and aerodynamic representations, our formulation achieves a more accurate depiction of airplane dynamics. This work marks a step forward in the ongoing efforts to adapt pHs theory for aerospace engineering, laying the groundwork for more effective modeling and control strategies in this field.

МОДЕЛЮВАННЯ ЗАДАЧ ОПТИМІЗАЦІЇ УПРАВЛІННЯ ІТ-ПРОЕКТАМИ

Abstract. The article focuses on exploring mathematical models for optimizing business processes in project management within IT companies in the context of contemporary trends and challenges. Project management involves the process of guiding and coordinating people's activities, as well as managing material and financial resources throughout the project's lifecycle. This process encompasses applying modern management methods and techniques to achieve project goals. The dynamic allocation modeling of IT projects among teams to ensure high-quality development at maximum efficiency with minimal costs is a pertinent task in IT project management. The article's objective is to select a mathematical framework for decision-making regarding the optimal IT project management program to enhance the efficiency of each IT team and the entire IT company. The research involved an analysis of scientific literature on modeling project management in IT companies. The article proposes focusing on developing dynamic multi-criteria optimization models for human resource management, emphasizing the distribution of IT projects among executing teams. The research aims to elevate the strategic and operational levels of IT personnel management to achieve optimal outcomes in information technology. The analysis concludes that despite the advantages of various mathematical modeling methods, none of them in isolation allows for constructing a sufficiently detailed mathematical model. Methods and models addressing IT enterprise modeling problems may oversimplify the issue or, conversely, overly complicate it, complicating the selection of input data. The functioning of the IT enterprise was analyzed through the lens of external and internal indicators concerning the solved task. A verbal model of IT project distribution among teams, considering the time factor, was developed. This model formulated a system of basic concepts and ideas, allowing the dynamic formulation of the problem using widely accepted linear optimization models. This will facilitate finding optimal solutions for IT project distribution tasks over a specific period. Future research should focus on selecting a solution method for the model and implementing the constructed mathematical model using appropriate tools. The research findings presented can serve as a basis for further academic exploration and practical application in the field of IT project management. Keywords: modeling, optimization, business processes, project management, labor resources, IT projects.

On the geometry and dynamical formulation of the Sinkhorn algorithm for optimal transport

On the geometry and dynamical formulation of the Sinkhorn algorithm for optimal transport

Damage quantification of a metallic beam under thermo-mechanical loads using novel empirical correlations and neural network

This research examines the interactions between fracture depth and crack location on a cantilever beam’s dynamic response under thermomechanical loads. The structure’s stiffness is significantly influenced by temperature, and changes in stiffness can alter the response’s damping, frequency, and amplitude. The basis for measuring damage to an Aluminium 2024 specimen under thermomechanical loads is provided by these variations. Cantilever beams are used in experiments that are carried out at elevated temperatures, such as 50°C, 100°C, 150°C, and 200°C, as well as at room temperature (non-heating). This analysis takes into account a cantilever beam with different initial fracture depths and positions. The outcomes of the experimental, analytical, and numerical work are found to be in good accord. This research mainly fill the gaps of recent techniques for structure health monitoring of metallic structures where the coupled loads exist. Dynamic response formulation is presented experimentally on beam for the first time under thermo-mechanical loads. The dynamic parameters vary with material stiffness, thus; this change is also investigated by introducing the temperature as a key variable using a specially designed temperature controller. A novel technique is presented for damage estimation in metallic structures using the experimental data that is currently accessible which is later compared with the neural network approach. This tool helps in finding out and quantifying damagesusing dynamic response, temperature along withfinding of subsurface cracks. The results establisha clearway of diagnosing the crack growth at any particular instant under thermo-mechanical loads within the operational condition.

STRENGTH AND DUCTILITY CHARACTERISTICS OF METAL ALLOYS AND STAINLESS STEELS CREATED BY WIRE-ARC SURFACING IN A WIDE RANGE OF STRAIN RATES

To select rational parameters of the process of hybrid additive manufacturing of structures made of structural metal alloys and stainless steels, mechanical characteristics capable of serving as indicators of material quality were determined. The most advanced technologies of additive manufacturing by wire-arc surfacing (plasma, plasma arc with a melting electrode, including cold metal transfer) with layer-by-layer forging with a pneumatic impact tool and subsequent heat treatment were used. Aluminum-magnesium alloy AlMg5, titanium alloy Ti-6Al-4V, austenitic stainless steels 12Cr18Ni10Ti (AISI 321) and AISI 308LSi have been studied. Samples were cut from the blanks created by additive manufacturing – blades for standard tests for static uniaxial tension and cylinders for high-speed compression tests by the Kolsky method on a Hopkinson split bar. According to the registered and processed stress–strain curves for all materials, standard strength and ductility characteristics and the Johnson – Cook law of deformation and speed hardening were determined. For a correct assessment of the mechanical properties of additively produced materials, these tests were also carried out for each of them in the form of annealed rolled products. It is established that to compare the efficiency of various technological parameters of additive manufacturing, it is advisable to use static tensile strength and uniform elongation to rupture, having the smallest statistical variation. It was also found acceptable to approximate the Johnson – Cook law of the deformation curves of each of the studied materials according to averaged data, including various technological modes. Certain mechanical characteristics seem to be necessary for the search for effective modes of hybrid additive manufacturing and numerical calculation of various elastic-plastic problems in a dynamic formulation for the studied materials for design and technological needs.

Erratum to “Competitive Two-Agent Scheduling and Its Applications”

Erratum to “Competitive Two-Agent Scheduling and Its Applications” The paper “Competitive Two-Agent Scheduling and Its Applications” by Leung, Pinedo, and Wan appeared in Operations Research in 2010. Because competitive agent scheduling has become an active area of research, the paper has garnered its share of citations over the years. This particular direction of scheduling research has become so popular that the book Multiagent Scheduling: Models and Algorithms by Agnetis, Billaut, Gawiejnowicz, Pacciarelli, and Soukhal appeared in 2014. However, one of the results in the Leung et al. paper had a minor error in it. The paper considers a two-agent scheduling problem with a single machine, with each one of the two agents having their own set of jobs. The first agent has as the objective the minimization of the total tardiness of her set of jobs, and the second agent has to ensure that the total completion time of her set of jobs is less than or equal to Q. Leung et al. showed, through a dynamic programming formulation, that this problem can be solved in pseudopolynomial time and determined the time complexity of their algorithm. Their proof contains a minor error. The proper algorithm is still pseudopolynomial but of a slightly higher time complexity.

Thermal pair production from photon-photon collision: Breit–Wheeler process at finite temperature

In this paper we examine the pair production through the Breit–Wheeler process γγ→e+e-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma ~\\gamma \\rightarrow e^+ e^-$$\\end{document} in a thermal background. We compute the thermal contribution to the Breit–Wheeler differential cross section within the thermofield dynamics formalism. We evaluate in details the cross section for this process, which possess a surprisingly simple expression valid for any temperature β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}, from which we discuss some physically relevant aspects. We also consider the high temperature regime of the cross section in order to have a better understanding about its thermal behavior.

Description of intruder levels in the 162,164,166Dy nuclei by two different algebraic approaches

In this paper, we tried to describe both normal and intruder levels of the ground and first excited beta and gamma rotational bands of 162,164,166Dy deformed nuclei in the framework of the interacting boson model. A normal Hamiltonian of SU(3) dynamical symmetry limit is extended by adding a 2p-2 h excitation term. Also, the results are compared with the predictions of the partial dynamical symmetry for these levels of considered nuclei. The results show that, this extension removes the degeneracy suggested by the pure SU(3) symmetry and makes satisfactory agreement with the experimental counterparts for the energy levels, too. Also, a comparison between the results of this extended formalism and partial dynamical symmetry shows the advantages of the first one in the description of intruder levels, whereas the latter, makes exact results for the normal energy levels of beta and gamma energy bands. The predictions of pure SU(3), partial dynamical symmetry SU(3) and mixed formalism for different quadrupole transition rates between normal and intruder levels of this nucleus are compared with the predictions of pseudo-SU(3) model and the advantages of each model have explained in detail.

Improved lattice Boltzmann model for moving contact-line with soluble surfactant

Modeling moving contact-line with surfactant has become a widely sought methodology due to its scientific relevance and extensive applications. Within the phase field framework, we present an improved lattice Boltzmann (LB) model for simulating moving contact-line dynamics with soluble surfactant. In this model, a LB equation is used to solve the Navier–Stokes equations, and another two LB equations are utilized to solve the two Cahn–Hilliard-like equations. The modified chemical potentials are incorporated in the LB model by using an equivalent variant of the free energy functional and the corresponding equilibrium distribution functions are also amended. These modifications could circumvent the degraded accuracy of previous LB models in capturing the interfacial behavior and surfactant distribution, and also improve the well-posedness of the LB model. In addition, a dynamic contact angle formulation is introduced to account for the surfactant effect on surface wettability and the resulting contact angle is further implemented in the LB model via a popular geometrical wetting approach. We comprehensively evaluate the numerical performance of the LB model by simulating some benchmark problems. It is found that the LB model achieves a higher accuracy than previous LB models in solving the phase field and surfactant profiles, and also numerical prediction of moving contact-line dynamics with surfactant shows good agreement with the analytical solution. Finally, the LB model is applied to investigate droplet shearing dynamics on solid substrate. The influences of capillary number and solid wetting property on droplet deformation and breakup are analyzed in detail.

Minimal Peptoid Dynamics Inform Self-Assembly Propensity.

Peptoids are structural isomers of natural peptides, with side chain attachment at the amide nitrogen, conferring this class of compounds with the ability to access both cis and trans ω torsions as well as an increased diversity of ψ/φ states with respect to peptides. Sampling within these dimensions is controlled through side chain selection, and an expansive set of viable peptoid residues exists. It has been shown recently that "minimal" di- and tripeptoids with aromatic side chains can self-assemble into highly ordered structures, with size and morphological definition varying as a function of sequence pattern (e.g., XFF and FXF, where X = a nonaromatic peptoid monomer). Aromatic groups, such as phenylalanine, are regularly used in the design of minimal peptide assemblers. In recognition of this, and to draw parallels between these compounds classes, we have developed a series of descriptors for intramolecular dynamics of aromatic side chains to discern whether these dynamics, in a preassembly condition, can be related to experimentally observed nanoscale assemblies. To do this, we have built on the atomistic peptoid force field reported by Weiser and Santiso (CGenFF-WS) through the rigorous fitting of partial charges and the collation of Charmm General Force Field (CGenFF) parameters relevant to these systems. Our study finds that the intramolecular dynamics of side chains, for a given sequence, is dependent on the specific combination of backbone ω torsions and that homogeneity of sampling across these states correlates well with the experimentally observed ability to assemble into nanomorphologies with long-range order. Sequence patterning is also shown to affect sampling, in a manner consistent for both tripeptoids and tripeptides. Additionally, sampling similarities between the nanofiber forming tripeptoid, Nf-Nke-Nf in the cc state, and the nanotube forming dipeptide FF, highlight a structural motif which may be relevant to the emergence of extended linear assemblies. To assess these properties, a variety of computational approaches have been employed.

Stefan–Boltzmann law and Casimir effect for dark photons

In this paper, the existence of a massive dark photon, associated with a new gauge group is considered. The dark photon can be kinetically mixed with the photon. To study some applications, the thermo field dynamics formalism is used. Exploring the topological structure of this approach, the influence of dark photons on the Stefan–Boltzmann law and the Casimir effect at zero and finite temperature is calculated.

Fine Properties of Geodesics and Geodesic λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda $$\\end{document}-Convexity for the Hellinger–Kantorovich Distance

We study the fine regularity properties of optimal potentials for the dual formulation of the Hellinger–Kantorovich problem (HK\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{H}\\!\\!\ extsf{K}$$\\end{document}), providing sufficient conditions for the solvability of the primal Monge formulation. We also establish new regularity properties for the solution of the Hamilton–Jacobi equation arising in the dual dynamic formulation of HK\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{H}\\!\\!\ extsf{K}$$\\end{document}, which are sufficiently strong to construct a characteristic transport-growth flow driving the geodesic interpolation between two arbitrary positive measures. These results are applied to study relevant geometric properties of HK\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{H}\\!\\!\ extsf{K}$$\\end{document} geodesics and to derive the convex behaviour of their Lebesgue density along the transport flow. Finally, exact conditions for functionals defined on the space of measures are derived that guarantee the geodesic λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda $$\\end{document}-convexity with respect to the Hellinger–Kantorovich distance. Examples of geodesically convex functionals are provided.

Global existence and decay of small solutions for quasi-linear second-order uniformly dissipative hyperbolic-hyperbolic systems

This paper is concerned with quasilinear systems of partial differential equations consisting of two hyperbolic operators interacting dissipatively. Its main theorem establishes global-in-time existence and asymptotic stability of strong solutions to the Cauchy problem close to homogeneous reference states in d≥3 space dimensions. Notably, the operators are not required to be symmetric hyperbolic, instead merely the existence of symbolic symmetrizers is assumed. The dissipation is characterized by algebraic conditions implying the uniform decay of all Fourier modes at the reference state. On a technical level, the theory developed herein uses para-differential operators as its main tool. Apparently being the first to apply such operators in the context of global-in-time existence of small solutions for quasi-linear hyperbolic systems, the present work contains a new version of the strong Gårding inequality. In the context of theoretical physics, the theorem applies to recent formulations for the relativistic dynamics of viscous, heat-conductive fluids such as notably that of Bemfica, Disconzi and Noronha (2018) [2].

Optimized Self-Similar Borel Summation

The method of Fractional Borel Summation is suggested in conjunction with self-similar factor approximants. The method used for extrapolating asymptotic expansions at small variables to large variables, including the variables tending to infinity, is described. The method is based on the combination of optimized perturbation theory, self-similar approximation theory, and Borel-type transformations. General Borel Fractional transformation of the original series is employed. The transformed series is resummed in order to adhere to the asymptotic power laws. The starting point is the formulation of dynamics in the approximations space by employing the notion of self-similarity. The flow in the approximation space is controlled, and “deep” control is incorporated into the definitions of the self-similar approximants. The class of self-similar approximations, satisfying, by design, the power law behavior, such as the use of self-similar factor approximants, is chosen for the reasons of transparency, explicitness, and convenience. A detailed comparison of different methods is performed on a rather large set of examples, employing self-similar factor approximants, self-similar iterated root approximants, as well as the approximation technique of self-similarly modified Padé–Borel approximations.

Time-dependent transient response of piles partially embedded in layered viscoelastic saturated cross-anisotropic soils using a fractional-order Merchant model

A 3D analytical method is proposed for the lateral time-dependent response of monopiles partially embedded in stratified saturated viscoelastic cross-anisotropic soils under horizontal transient loads. Nevertheless, previous studies on ocean engineering have rarely considered the rheological properties of seabed materials. In this study, depending upon Biot's dynamical formulation, the linear elastic solution of the layered cross-anisotropic saturated soils due to lateral transient and vertical loads is solved using the analytical layer-element method (ALEM). The fractional-order Merchant model is adopted to describe the rheological deformation of the seabed, and the viscoelastic solution of the laminar cross-anisotropic saturated soils is derived by combining the elastic-viscoelastic transformation theory. Using the consolidation solution of the seabed as the kernel function, the pile-soil boundary problem is analyzed by the boundary element method (BEM) to obtain the BE equation of the viscoelastic saturated soils. The Timoshenko beam is employed to simulate the monopile, and based on the finite element method (FEM), the monopile is discretized into pile units to derive the FE matrix equation. Finally, the dynamic response formulation of the partially embedded offshore monopile is obtained by coupling the BE and FE equations through the coordination conditions of close contact between the Timoshenko beam and the seabed. The accuracy of the methodology is verified by comparing with the existing solutions and the numerical results from ABAQUS. And the effects of the transient load type, seabed viscosity, and pile properties on the horizontal response of partially embedded monopiles are explored.

Unravelling the importance of cold-adapted bacterial formulations in microbial community dynamics during in situ lemongrass residue valorization under cold conditions

Unravelling the importance of cold-adapted bacterial formulations in microbial community dynamics during in situ lemongrass residue valorization under cold conditions

Closed-Form Dynamic Modeling and Performance Evaluation of a 4-Degrees-of-Freedom Parallel Driving Mechanism

Abstract Kinematic estimations and dynamic performance assessments are fundamental theoretical issues to realize the mechanism from conceptual design to engineering application. In this article, the closed-form dynamic formulations of a 4-degrees-of-freedom (DoFs) parallel driving mechanism are derived by combining the Lagrange method and the virtual work principle. The selection principle of generalized coordinates and the steps for inverse dynamics modeling of the manipulator are proposed. Simulation results verify the correctness of the dynamic model, and a physical prototype has been built. Based on the dynamic modeling, the concise algebraic expression of the operational space inertia matrix of the parallel driving mechanism is deduced. Because the translation and rotation degrees-of-freedom are inconsistent in the operational space, the Jacobian matrix is adopted to map the inertia matrix from the operational space to the joint space. Based on the inertia matrix in joint space, the average energy transfer efficiency (AETE) index is proposed. Finally, two control techniques for the manipulator implementable in joint space are compared. The AETE index and dynamic modeling method suggested in this article can be further used in other manipulators for dynamic analysis and motion system design.

Robust control of gust-induced vibration of highly flexible aircraft

This paper mainly addresses the gust suppression and alleviation of highly flexible aircraft using the model predictive controller (MPC) based on linear parameter-varying (LPV) models. The dynamic behavior of highly flexible aircraft is modeled by a coupled nonlinear aeroelastic and flight dynamic formulation. Conventional trailing-edge flaps along the main wings and tails are deployed to provide the required loads for the wing vibration control and/or longitudinal flight attitude control of the slender vehicle. The coupled dynamic equations are performed with linearization and model reduction about a series of nonlinear equilibria to derive reduced-order LPV models. This work considers two quantities as the scheduling parameters in building the LPV models: the gust-induced angle of attack and the modal magnitude of wing deformation. With the reduced-order LPV model, MPC is designed to minimize the wing vibration and rigid-body motions excited by the time-domain Dryden gust perturbation. The proposed LPV modeling is capable of describing large wing deformations, and the LPV-MPC innovatively previews the scheduling parameter and gust disturbance in the prediction horizon. The closed-loop flight responses of a highly flexible aircraft with gust disturbance are presented in the numerical studies, which demonstrate the effectiveness of controlling coupled vibrations and rigid-body dynamics of such slender vehicles.