Movement Scheme Research Articles

Mathematical Modeling of Forwarder Operation When Collecting Logs in the Forest Swath

Optimization of the machines allows you to increase their productivity and reduce the labor costs for performing individual elements of the technological cycle of their work in the forest. In this regard, the authors offer theoretical studies that take into account the peculiarities of the work of one of the most popular logging machines today, namely, a machine for collecting and forwarding logs (forwarder). The article discusses the technological features of the functioning of these machines, identifies ways to reduce the cost of collecting logs, justifies the rational width of apiaries, which allows collecting logs with a minimum number of movements between work positions. The main purpose of the study is to substantiate the mathematical dependence for determining the rational values of such interrelated parameters of the forwarder's operation as the distance between the working positions of collecting logs and the width of apiaries. The authors propose an analytical approach to solving the problem. On the basis of the standard technological scheme of the harvester's movement through the swath, geometric regularities of the trajectory of the manipulator movement, dimensional characteristics and location of the prepared logs are revealed. As a result of the work, mathematical dependencies are constructed that make it possible to determine the rational values of the desired parameters. The results can be used by research organizations in planning the production process of logging operations. The introduction of author's recommendations into production will contribute to improving the efficiency and operation of forestry equipment.

Perspektif Jean Piaget pada Proses Pewarisan Reog Obyog: Studi Kasus pada Masyarakat Transmigran Kota Banjarbaru Provinsi Kalimantan Selatan

This research aims to examine the process of inheritance in the Reog Obyog art in the Singo Budoyo community in Banjarbaru City, South Kalimantan. This inheritance process uses the theory put forward by Jean Piaget because it is considered appropriate to the conditions that occur in the field. This research uses a qualitative method with a case study approach. Data collection techniques use observation, interviews, and documentation. The data analysis carried out was by collecting data in the field then carrying out the coding and data reduction process and drawing conclusions. The results of the entire series of research that have been carried out have obtained answers to the research problem, namely the process of inheritance of the Reog Obyog art, there are four stages of development, namely sensorimotor, pre-personal, concrete operational, and formal operational which occur as a series of forms of cognitive development processes in children as inheritors of this art in society. transmigrants in Banjarbaru City. According to the results that have been found, this research concludes that in the dance context, children assimilate new movements by incorporating them into movement schemes that they already know. This is because the environment in which they live is not far from what they study.

Existence results for Cahn–Hilliard-type systems driven by nonlocal integrodifferential operators with singular kernels

We introduce a fractional variant of the Cahn–Hilliard equation settled in a bounded domain and with a possibly singular potential. We first focus on the case of homogeneous Dirichlet boundary conditions, and show how to prove the existence and uniqueness of a weak solution. The proof relies on the variational method known as minimizing movements scheme, which fits naturally with the gradient-flow structure of the equation. The interest of the proposed method lies in its extreme generality and flexibility. In particular, relying on the variational structure of the equation, we prove the existence of a solution for a general class of integrodifferential operators, not necessarily linear or symmetric, which include fractional versions of the q-Laplacian.In the second part of the paper, we adapt the argument in order to prove the existence of solutions in the case of regional fractional operators. As a byproduct, this yields an existence result in the interesting cases of homogeneous fractional Neumann boundary conditions or periodic boundary conditions.

Competing effects in fourth‐order aggregation–diffusion equations

AbstractWe give sharp conditions for global in time existence of gradient flow solutions to a Cahn–Hilliard‐type equation, with backwards second‐order degenerate diffusion, in any dimension and for general initial data. Our equation is the 2‐Wasserstein gradient flow of a free energy with two competing effects: the Dirichlet energy and the power‐law internal energy. Homogeneity of the functionals reveals critical regimes that we analyse. Sharp conditions for global in time solutions, constructed via the minimising movement scheme, also known as JKO scheme, are obtained. Furthermore, we study a system of two Cahn–Hilliard‐type equations exhibiting an analogous gradient flow structure.

Operating Scheme of The Combined Unit Implementing The Resource-Saving Technology of Soil Working

The article presents the results of a study of the movement scheme of a combined unit that implements resource-saving technology of soil cultivation. At the same time, the aggregate is loosened in one pass with an interval of 1800 mm between the rows, forming two fertilized rows, and four rows of rows with an interval of 90 cm are formed in the return.

Flat flow solution to the mean curvature flow with volume constraint

Abstract In this paper I will revisit the construction of a global weak solution to the volume preserving mean curvature flow via discrete minimizing movement scheme by Mugnai, Seis and Spadaro [L. Mugnai, C. Seis and E. Spadaro, Global solutions to the volume-preserving mean-curvature flow, Calc. Var. Partial Differential Equations 55 2016, 1, Article ID 18]. This method is based on the gradient flow approach due to Almgren, Taylor and Wang [F. Almgren, J. E. Taylor and L. Wang, Curvature-driven flows: a variational approach, SIAM J. Control Optim. 31 1993, 2, 387–438] and Luckhaus and Sturzenhecker [S. Luckhaus and T. Sturzenhecker, Implicit time discretization for the mean curvature flow equation, Calc. Var. Partial Differential Equations 3 1995, 2, 253–271] and my aim is to replace the volume penalization with the volume constraint directly in the discrete scheme, which from practical point of view is perhaps more natural. A technical novelty is the proof of the density estimate which is based on second variation argument.

Photon, A New Principle for Justification of Its Structure and Process of Motion

The work relates to the basics of quantum physics and photonics, in particular to the formation of photons in two states: as elementary particles and their electromagnetic radiation. The study of these problems is an urgent and important scientific task, which has not been fully resolved in terms of their structure and principle of action. In modern science, the photon is considered a fundamental elementary particle, which has neither its own structure nor dimensions, but only wave parameters. However, the denial of the material state of the photon contradicts the general conditions for the formation of the material world within the framework of the principles of dualism. Eliminating this shortcoming is the main goal of the work being performed. Its scientific novelty lies in the development of strict physical foundations for explaining the structure, parameters and process of photon motion. Working methods. The work was performed at the level of scientific discoveries for which reliable methods and techniques are not yet known, therefore, it used general methods and principles of scientific research, as well as the author’s method of accessing the initial level of the material world. Results of the work and their discussion. A new structure of the photon is substantiated, which includes not only its wave, but also a material particle. The substant particle of the photon is formed in the form of a regular hexagonal prism from 6 trihedral prisms, which are quarks, 3 of which are real quarks, and the empty space between them are virtual quarks. The transition of energy from real quarks to virtual ones, and then back, leads to virtual rotation of the photon, which ensures its stability, and the absence of losses in this process ensures the “eternity” of its life. A complete revolution of the quarks of the real part of the photon occurs in 6 quantum jumps, during which it moves translationally by the photon wavelength λ. When moving according to the proposed scheme, virtual sinusoids are formed, characteristic of the action of electromagnetic fields, which confirms the correctness of the proposed structure and scheme of photon movement. Conclusion The proposed structure and pattern of photon movement implements the principle of least action, which dominates in the material world. At the same time, there are no contradictions with the real laws of the material world, as well as the need for uncertain physical processes and energies for its implementation, which is the evidence base for the work.

Design and Simulation of Hydraulic Integrated Valve based on SLM Technology

Intelligent robots put forward the need for miniaturization and integration of hydraulic systems. Based on SLM technology, this paper designs a hydraulic integrated valve, integrates flow channels, adapters and other facilities on the valve body, replaces the original linear movement scheme with a rotating spool scheme, studies parameters such as runner diameter and minimum wall thickness, and simulates and analyzes the flow performance of liquid when the main control runner and a single valve work. The results show that the integrated valve has the advantages of light weight, small size and good performance.

Weak Solutions of Mullins–Sekerka Flow as a Hilbert Space Gradient Flow

We propose a novel weak solution theory for the Mullins–Sekerka equation in dimensions d=2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d=2$$\\end{document} and 3, primarily motivated from a gradient flow perspective. Previous existence results on weak solutions due to Luckhaus and Sturzenhecker (Calc. Var. PDE 3, 1995) or Röger (SIAM J. Math. Anal. 37, 2005) left open the inclusion of both a sharp energy dissipation principle and a weak formulation of the contact angle at the intersection of the interface and the domain boundary. To incorporate these, we introduce a functional framework encoding a weak solution concept for Mullins–Sekerka flow essentially relying only on (i) a single sharp energy dissipation inequality in the spirit of De Giorgi, and (ii) a weak formulation for an arbitrary fixed contact angle through a distributional representation of the first variation of the underlying capillary energy. Both ingredients are intrinsic to the interface of the evolving phase indicator and an explicit distributional PDE formulation with potentials can be derived from them. The existence of weak solutions is established via subsequential limit points of the naturally associated minimizing movements scheme. Smooth solutions are consistent with the classical Mullins–Sekerka flow, and even further, we expect our solution concept to be amenable, at least in principle, to the recently developed relative entropy approach for curvature driven interface evolution.

Technological solution of a modular family farm

The technological solution of a modular family farm for producing high-quality and environmentally friendly beef is presented. The development aims to make beef using bulls-producers of meat and graded dairy cows. The family farm project was developed considering the generalisation of the best practices of organising peasant farms and scientific research of SIBNIPTIZH. It assumes a comprehensive solution for a family farm, including, in addition to industrial housing facilities with outbuildings and a personal plot, the introduction of the most acceptable methods for keeping animals, type of feeding, design parameters of industrial buildings and elements of technology equipment, small-sized machinery, as well as the organisation of labour and production. The technological solution is to grow and fatten young animals using the low-cost technology of beef cattle breeding "cow-calf" from culled dairy cows suitable for reproduction. The optimal scheme of placement and movement of technological groups of cows and repair young animals has been determined. Variants of space-planning solutions for building a modular family farm for 26 cows have been developed. Cows, repair heifers and calves are kept in a lightweight cowshed. Cows are kept on a leash. Calves are kept loose. Young animals, after weaning from cows, are transferred to another room. From the age of 6 months, heifers and bulls are kept separately. Young animals in winter are in a lightweight room with a deep litter. Bulls older than 12 months are not grazed. They are intensively reared and fattened up to 17 months when they reach a live weight of 439 kg.

Minimizing movement scheme for intrinsic aggregation on compact Riemannian manifolds

Minimizing movement scheme for intrinsic aggregation on compact Riemannian manifolds

Effective organization of acceleration of local train movement at railway transport departments

In the mentioned article, an analysis was conducted on the delay in providing services to local wagons due to the distance of up to 200 km between the sections located in the “UTY” joint-stock company. In this regard, works to improve the schedule of local trains have been carried out by extending the distance between two technical stations to 600-800 km. As a result of analyzing the options for transporting local wagons to technical stations in this article, movement schemes for local trains have been developed. The proposed schemes specify the movement of local trains from the initial station to the final station within the sections, as well as determining the movement from the initial station to halfway through the section. Through these schemes, operations carried out at intermediate and freight stations between two section stations in a mathematical manner have been investigated. These operations include operations such as coupling, uncoupling, and providing technical and cargo services to the wagons within the movement composition. In providing services to local trains on the section, two options were analyzed to obtain results: with the help of the second scheme we developed, during the movement of each train within the section, a possibility of saving 16 minutes of time was created.

З історії участі волинських студентів у масових гімнастичних виступах

Topicality. Mass gymnastics performances are a powerful spectacle that can significantly influence a person, his or her spiritual world, in particular, the world of emotions, aesthetic tastes, ethical and worldview ideas. Students have always been participants in these mass sporting events held in Volyn, and studying the experience of the past will help to find new opportunities and forms of gymnastic performances of our time. The Purpose of the Work is to highlight information about the organization and content of students` mass gymnastic performances of Lesya Ukrainka Lutsk State Pedagogical Institute (LULSPI) in the 80s of the XXth century. Research Methods: analysis and generalization of scientific, methodical and special literature; analysis of materials from the State Archive of Volyn Region; interviews and conversations with teachers (former students of LULSPI) who were involved in the organization of mass gymnastic performances at that time; analysis of individual mass gymnastic performances` scenarios preserved on paper media. Results of the Reserch. Organizing and conducting various mass gymnastic performances and sports festivals is just one of the ways to increase the physical activity of citizens. The article collects and analyzes information about the experience of holding mass gymnastic performances at parades and sports festivals, in which students of all existing faculties, as well as boys and girls of the Faculty of Physical Education of LULSPI took part. Particular attention is paid to the organization of preparation and conducting of performances, their chronology is highlighted, scenarios of mass sports performances are presented (description of the performance, musical accompaniment, performance time, schemes of movement and rearrangements, thematic inscriptions) of 1980, 1982, 1983. Conclusions. Since 1970, Lutsk has established a tradition of holding artistic and sports festivals, which included mass gymnastic performances. These events were mainly dedicated to Victory Day. LULSPI students were their constant participants. They demonstrated the scenario of mass gymnastic performances developed by the teachers not only for the audience, but also acquired the appropriate motor and creative skills.

Consistency of the Flat Flow Solution to the Volume Preserving Mean Curvature Flow

We consider the flat flow solution, obtained via a discrete minimizing movement scheme, to the volume preserving mean curvature flow starting from C1,1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^{1,1}$$\\end{document}-regular set. We prove the consistency principle, which states that (any) flat flow solution agrees with the classical solution as long as the latter exists. In particular the flat flow solution is unique and smooth up to the first singular time. We obtain the result by proving the full regularity for the discrete time approximation of the flat flow such that the regularity estimates are stable with respect to the time discretization. Our method can also be applied in the case of the mean curvature flow and thus it provides an alternative proof, not relying on comparison principle, for the consistency between the flat flow solution and the classical solution for C1,1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^{1,1}$$\\end{document}-regular initial sets.

Influence of movable inner tube on the charging performance for a horizontal latent thermal energy storage exchanger

The charging performance of horizontal shell-and-tube latent thermal storage exchangers is significantly influenced by the position of the inner tube. However, the underlying mechanisms of the effect of inner tube movement on the charging performance remain unclear. Based on this, this paper proposed a horizontal shell-and-tube latent thermal energy storage exchanger whose inner tube is movable or Heat Exchanger with Movable Tube (MTHX), the two-dimensional simulation model of the MTHX was established, and the influence of the inner tube movement direction, speed, and range on the charging performance was studied, and finally this study obtained an optimized inner tube movement scheme for the charging process. The results indicate that the exchanger exhibits improved charging performance when the inner tube lies in the lower hemisphere region and moves up and down along the radius direction. Furthermore, increasing the velocity of inner tube movement enhances the charging rate. Additionally, the impact of the inner tube movement range on the charging performance depends on the direction of the movement. Moreover, compared to traditional horizontal shell-and-tube latent thermal storage exchangers, the implementation of the optimized inner tube movement scheme results in a 78.88 % reduction in charging time and a remarkable 348.71 % increase in average charging rate. This research presents novel directions for optimizing the charging performance of horizontal shell-and-tube latent thermal storage exchangers, thereby laying the foundation for the engineering application. The findings hold significant theoretical implications and engineering value.

On a minimizing movement scheme for mean curvature flow with prescribed contact angle in a curved domain and its computation

We introduce a capillary Chambolle-type scheme for mean curvature flow with prescribed contact angle. Our scheme includes a capillary functional instead of just the total variation. We show that the scheme is well-defined and has consistency with the energy minimizing scheme of Almgren–Taylor–Wang type. Moreover, for a planar motion in a strip, we give several examples of numerical computation of this scheme based on the split Bregman method instead of a duality method.

Minimizing movements for anisotropic and inhomogeneous mean curvature flows

AbstractIn this paper we address anisotropic and inhomogeneous mean curvature flows with forcing and mobility, and show that the minimizing movements scheme converges to level set/viscosity solutions and to distributional solutions à la Luckhaus–Sturzenhecker to such flows, the latter result holding in low dimension and conditionally to the convergence of the energies. By doing so we generalize recent works concerning the evolution by mean curvature by removing the hypothesis of translation invariance, which in the classical theory allows one to simplify many arguments.

The deep minimizing movement scheme

Solutions of certain partial differential equations (PDEs) are often represented by the steepest descent curves of corresponding functionals. Minimizing movement scheme was developed in order to study such curves in metric spaces. Especially, Jordan-Kinderlehrer-Otto studied the Fokker-Planck equation in this way with respect to the Wasserstein metric space. In this paper, we propose a deep learning-based minimizing movement scheme for approximating the solutions of PDEs. The proposed method is highly scalable for high-dimensional problems as it is free of mesh generation. We demonstrate through various kinds of numerical examples that the proposed method accurately approximates the solutions of PDEs by finding the steepest descent direction of a functional even in high dimensions.

Phase-Field DeepONet: Physics-informed deep operator neural network for fast simulations of pattern formation governed by gradient flows of free-energy functionals

Recent advances in scientific machine learning have shed light on the modeling of pattern-forming systems. However, simulations of real patterns still incur significant computational costs, which could be alleviated by leveraging large image datasets. Physics-informed machine learning and operator learning are two new emerging and promising concepts for this application. Here, we propose “Phase-Field DeepONet”, a physics-informed operator neural network framework that predicts the dynamic responses of systems governed by gradient flows of free-energy functionals. Examples used to validate the feasibility and accuracy of the method include the Allen–Cahn and Cahn–Hilliard equations, as special cases of reactive phase-field models for nonequilibrium thermodynamics of chemical mixtures. This is achieved by incorporating the minimizing movement scheme into the framework, which optimizes and controls how the total free energy of a system evolves, instead of solving the governing equations directly. The trained operator neural networks can work as explicit time-steppers that take the current state as the input and output the next state. This could potentially facilitate fast real-time predictions of pattern-forming dynamical systems, such as phase-separating Li-ion batteries, emulsions, colloidal displays, or biological patterns.

Energetic evolutions for linearly elastic plates with cohesive slip

A quasistatic model for a horizontally loaded thin elastic composite at small strains is studied. The composite consists of two adjacent plates whose interface behaves in a cohesive fashion with respect to the slip of the two layers. We allow for different loading–unloading regimes, distinguished by the presence of an irreversible variable describing the maximal slip reached during the evolution. Existence of energetic solutions, characterized by equilibrium conditions together with energy balance, is proved by means of a suitable version of the Minimizing Movements scheme. A crucial tool to achieve compactness of the irreversible variable are uniform estimates in Hölder spaces, obtained through the regularity theory for elliptic systems. The case in which the two plates may undergo a damage process is also considered.