Principle Of Least Action Research Articles

기적이란 무엇인가? 기적에 관한 양자역학적 해석을 통한 과학적 설명 시도

We generally define a miracle as follows: miracles are surprising events that transcend everyday empirical facts, abnormalities that cannot be properly explained by the laws of nature and the principles of science, especially as a result of supernatural and mysterious actions. However, when a miracle is defined in this way, the miraculous ‘divine actions’ should be considered completely separate from all ‘natural actions’ in our nature/universe. Since both natural order/law and miracles are given to this world by God’s common divine actions, we need a new interpretation beyond such a complete separation of the two.
 So now we may ask if we can find a single law/principle given by the same God and explain natural actions and transcendental divine actions as one comprehensive concept of ‘the divine actions’ by that law/principle. Therefore, if the natural order/law given by God the Creator in this nature/universe can be expanded to include miraculous divine actions, it will be possible to explain miracles through the ‘expanded natural order/law’.
 This article attempts to expand the ‘principle of least action’, which has been accepted as the most important principle in existing physics, to include the ‘divine action’. In particular, I would like to show that the quantum version of the ‘principle of least divine action’ is the principle that allows even supernatural miracles to be explained. This article attempts to present a modern, scientific, and original interpretation of the concept of miracles through the introduction of the new principle.

Lightlike singular hypersurfaces in quadratic gravity

Using the principle of least action, the motion equations for a singular hypersurface of arbitrary type in quadratic gravity are derived. Equations containing the “external pressure” and the “external flow” components of the surface energy–momentum tensor together with the Lichnerowicz conditions serve to find the hypersurface itself, while the remaining ones define arbitrary functions that arise due to the implicit presence of the delta function derivative. It turns out that neither double layers nor thin shells exist for the quadratic Gauss–Bonnet term. It is shown that there is no “external pressure” for null singular hypersurfaces. The Lichnerowicz conditions imply the continuity of the scalar curvature in the case of spherically symmetric null singular hypersurfaces. These hypersurfaces must be thin shells if the Lichnerowicz conditions are necessary. It is shown that for this particular case the Lichnerowicz conditions can be completely removed therefore a spherically symmetric null double layer exists. Spherically symmetric null singular hypersurfaces in conformal gravity are explored as application.

On Derivation of Equations of Electrodynamics and Gravitation from the Principle of Least Action, the Hamilton–Jacobi Method, and Cosmological Solutions

In classical texts, equations for fields are proposed without derivation of right-hand sides. Below, the right-hand sides of the Maxwell and Einstein equations are derived within the framework of the Vlasov–Maxwell–Einstein equations from a classical, but slightly more general principle of least action and Hamilton–Jacobi equations are used to obtain cosmological solutions.

Derivation of the Equations of Electrodynamics and Gravity from the Principle of Least Action

Derivation of the Equations of Electrodynamics and Gravity from the Principle of Least Action

Ergonomics for indoor air environments: Problems, reflections and investigations

<p indent="0mm">People spend over 80% of their time indoors. Indoor environmental quality has a significant impact on human health, comfort and productivity. Applying energy-efficient and low-carbon methods to create a healthy and comfortable indoor environment is strongly requested by the national strategies of “Healthy China” and “Peak Carbon Dioxide Emissions and Carbon Neutrality”. The traditional paradigm of studying indoor air environments has the following limitations: Human thermal comfort information mainly comes from questionnaire surveys; human health information is mainly based on the investigations of morbility and mortality rate; indoor air parameters that are monitored are very limited regarding their types and spatial and temporal distributions; the traditional method to optimize the heat and mass transfer processes of indoor air is based upon engineering thermodynamics and heat and mass transfer, in which the former is only applicable to the heat-work conversion processes under equilibrium states, while the latter lacks the concept of optimization and thus encounters substantial difficulties when dealing with complex non-equilibrium processes involving heat, mass, and work. Due to these intrinsic limitations, the following fundamental problems cannot be solved: The key influencing factors and mechanisms of indoor air environments on human responses have not been well identified and interpreted; and the ideal heat and mass transfer processes for a desired indoor air environment and the corresponding optimized engineering approach have not been determined. To address these problems, we put forward a framework of “Ergonomics for Indoor Air Environments”. It is based upon modern technologies (e.g., online sensing technology for indoor air parameters and human responses, and big data collecting and analyzing technologies, including machine learning). By referring to the key parameter in the building energy efficiency field, COP (coefficient of performance), we put forward two new parameters, COH (coefficient of health-benefit) and COE (coefficient of economy-benefit). The theory can identify an ideal heat and mass transfer process by using the principle of least action and taking COE as the index of “action”, where the “ideal” means that the target indoor air environment can meet all healthy and thermal comfort requirements while the economic cost is minimal. This approach is also helpful for researchers to develop Ergonomics for Indoor Air Environments.

Revealing the excellent properties of minimal surface lattice structures based on additive manufacturing through the principle of least action

Revealing the excellent properties of minimal surface lattice structures based on additive manufacturing through the principle of least action

Design and Optimization of a Decision Support System for Sports Training Based on Data Mining Technology

This paper presents an in-depth study and analysis of sports training decision support systems through data mining techniques, and designs a corresponding sports training decision support system for application in practical situations. It investigates the application of data mining techniques in solving the problem of optimal analysis of sports training indicators. The Apriori algorithm is used to find out the hidden correlations behind the data, while the correlation study applicable to college students’ physical fitness indicators is proposed and practiced, and the potential hidden relationships between the indicator data are found. The analysis results are further verified by the improved AP algorithm, FP algorithm, which provides important opinions for college physical education curriculum reform and youth physical culture development. Then, the Shi-Tomasi algorithm is used for feature point tracking and the support vector machine approach for human motion posture recognition. Considering that the collected action data contain a large amount of stationary action data, a threshold-based action segmentation algorithm is designed to extract useful action segments; after extracting the action segments, common action features are extracted from both statistical features, such as mean, variance, skewness, kurtosis, and physical features, such as acceleration and plantar pressure, to give a specific description of human daily actions. Thus, the fatigue of different postures is judged according to their number of occurrences and a preliminary assessment result is obtained. Then, the surface EMG data collected by the sensors are pre-processed to reduce noise, and the surface EMG signals are fused at the feature level based on the wavelet change algorithm, and the feature vectors are trained with BP neural networks to evaluate the fatigue of human muscle movements and obtain a preliminary evaluation result. Finally, by studying the application of information fusion technology at the decision level, the assessment results of the comprehensive human movement analysis are obtained using D-S evidence theory. In addition, a web platform is built on this basis to display and manage human exercise data and assessment results, and to facilitate the storage and query of historical exercise records.

A variational theory of lift

In this paper we revive a special, less-common, variational principle in analytical mechanics (Hertz’ principle of least curvature) to develop a novel variational analogue of Euler's equations for the dynamics of an ideal fluid. The new variational formulation is fundamentally different from those formulations based on Hamilton's principle of least action. Using this new variational formulation, we generalize the century-old problem of the flow over a two-dimensional body; we developed a variational closure condition that is, unlike the Kutta condition, derived from first principles. The developed variational principle reduces to the classical Kutta–Zhukovsky condition in the special case of a sharp-edged airfoil, which challenges the accepted wisdom about the Kutta condition being a manifestation of viscous effects. Rather, we found that it represents conservation of momentum. Moreover, the developed variational principle provides, for the first time, a theoretical model for lift over smooth shapes without sharp edges where the Kutta condition is not applicable. We discuss how this fundamental divergence from current theory can explain discrepancies in computational studies and experiments with superfluids.

Clebsch representation of relativistic plasma and generalized enstrophy

The theory of relativistic plasmas is attracting interest as a model of high-energy astronomical objects. The topological constraints, built in the governing equations, play an essential role in characterizing the structures of plasmas. Among various invariants of ideal models, the circulation is one of the most fundamental quantities, being included in other invariants like the helicity. The conventional enstrophy, known to be constant in a two-dimensional flow, can be generalized, by invoking Clebsch variables, to the topological charge of a three-dimensional fluid element, which essentially measures circulations. Since the relativistic effect imparts space-time coupling into the metric, such invariants must be modified. The non-relativistic generalized enstrophy is no longer conserved in a relativistic plasma, implying that the conservation of circulation is violated. In this work, we extend the generalized enstrophy to a Lorentz covariant form. We formulate the Clebsch representation in relativity using the principle of least action and derive a relativistically modified generalized enstrophy that is conserved in the relativistic model.

An energy-based model of dielectric elastomer minimum energy structures with stiffeners: Equilibrium configuration and the electromechanical response

The Dielectric Elastomer-based Minimum Energy Structures (DEMES) pertain to an equilibrium configuration attained by the assembly of a pre-stretched electroactive polymer film and a compliant boundary frame. Because of their unique characteristics, such as fast response and a large reversible stroke; DEMES have been used widely in the development of soft robotic transducers. However, their utility is typically restricted because of the warping resulting from anticlastic curvature. The present investigation examines the effectiveness of stiffeners in controlling this warping, as well as their effect on the resulting electromechanical response when the DEMES is driven electrically. To this end, we devise an energy-based analytical model that predicts the initial equilibrium configuration of an elementary rectangular DEMES with a finite number of stiffeners adhered to the boundary frame. The proposed framework uses the neo-Hookean hyperelasticity model for the polymer film and the linear elastic constitutive model for both the frame and the stiffeners. Predictive capability of the proposed analytical model is established through comparisons with 3 D finite element simulations and experimental observations. The analytical model is then extended in the setting of the least-action principle to investigate the complex nonlinear dynamic behavior of the DEMES emanating from the interplay between material and geometric nonlinearities. The proposed dynamic model provides crucial insights into the role of varying levels of geometric and material parameters on the attainment of the initial equilibrium configuration of DEMES and its DC dynamic response when driven by a Heaviside electric load. In particular, we highlight the favorable impact of adding stiffeners in enhancing the stroke of the DEMES and an amplification in the attained equilibrium angle with an increasing spacing between the stiffeners. The analytical model and the results reported in this investigation can be of potential use in pre-designing the geometrical and material properties of DEMES for enhancing its electromechanical performance.

An Extension of the Explicit Calculation of the Principle of Least Action to a Power Series Potential

Published from 1956, the Bulgarian Journal of Physics accepts articles in the fields of: General and Mathematical Physics; Particle Physics and Field Theory; Atomic and Molecular Physics; Nuclear Physics; Fundamental Areas of Phenomenology; Theory of Relativity and Astrophysics; Condensed Matter, Statistical Physics; Cross-Disciplinary Physics; and Related Areas of Science and Technology.

Novel molecular insights into ATP synthesis in oxidative phosphorylation based on the principle of least action

In previous papers in Chemical Physics Letters, the author has analyzed the coupled nonequilibrium processes of ATP synthesis in oxidative phosphorylation (OXPHOS) with succinate as substrate. It was shown experimentally that the system evolves with time to a minimum unit action of 1.4×10-3 J s natom O–1 mg protein–1. Here the experimental value of the average unit action is suitably normalized. It is shown that the average unit action per elementary ion (proton or anion/countercation) translocation event through the FO portion of the FOF1-ATP synthase yields a value of 6.70×10-34 J s. This is equal to the value of the Planck’s constant, h to within1%. The results provide a novel molecular interpretation of energy transduction by ATP synthase in OXPHOS under optimal conditions, linking it to a fundamental physical constant.

Between Old and New Teleology. Kant on Maupertuis’ Principle of Least Action

Abstract In the Appendix to the Transcendental Dialectic, Kant formulates teleological principles, or rather ideas, and explicates them referring to concrete examples of natural science such as chemistry, astronomy, biology, empirical psychology, and physical geography. Despite the increasing interest in the systematic relevance of the Appendix to the Transcendental Dialectic and its importance for Kant’s conception of natural science, the numerous historical sources for the regulative use of reason have not yet been investigated. One that is very central is Maupertuis’ principle of least action. In 1781, Kant transformed teleology into heuristics and methodology, but in doing so, he partially develops a teleology which was disqualified by Maupertuis because its starting point lies in the construction of animals or plants, the structure of the earth, and the immensity of the celestial bodies. Based on Maupertuis’ principle of action, it can be shown that the Appendix forms a systematic interface between Universal Natural History and Theory of the Heavens and Critique of Judgement which allows the reconstruction of Kant’s regulative use of reason and its specific status in the context of natural science and his critical appraisal of Maupertuis.

Lagrangian descriptors and the action integral of classical mechanics

In this paper we bring together the method of Lagrangian descriptors and the principle of least action, or more precisely, of stationary action, in both deterministic and stochastic settings. In particular, we show how the action can be used as a Lagrangian descriptor. This provides a direct connection between Lagrangian descriptors and Hamiltonian mechanics, and we illustrate this connection with benchmark examples.

Approximate analytical solutions for one-dimensional soil water movement equation with arbitrary initial conditions

Simple analytical solutions of one-dimensional horizontal and vertical soil water movement are of great importance for the soil hydraulic parameters estimation and precision irrigation. We present the approximate analytical solutions for the problem of horizontal absorption and vertical infiltration in soil under arbitrary initial conditions and constant boundary conditions based on the principle of least action and the variational principle. The algebraic functions of soil water content (SWC) profile, cumulative infiltration, infiltration rate and infiltration time about the wetting front distance/depth (WFD) and the parameters of Brooks-Corey model are obtained. Compared with the numerical results simulated by HYDRUS-1D, the algebraic results calculated by approximate analytical solutions have high precision to predict the horizontal and vertical soil water infiltration based on the known WFD. Contrary to the linear relationship in horizontal absorption with uniform initial conditions, the relationships between cumulative infiltration and WFD, infiltration rate and reciprocal of WFD, square of WFD and infiltration time are nonlinear for the arbitrary heterogeneous initial conditions. However, the initial conditions have little effect on the relationship between infiltration rate and WFD when the initial SWCs are lower than 0.6 θs. Based on the nonlinear relationships of infiltration rate and WFD in vertical infiltration, the WFD and time of the stable infiltration are obtained.

ПРИНЦИП НАИМЕНЬШЕГО ДЕЙСТВИЯ В РАСЧЕТЕ ГЛУБИНЫ ВЫХОДНОГО СЕЧЕНИЯ ВОДОСЛИВА С ШИРОКИМ ПОРОГОМ

Purpose: development and experimental verification of a method for determining the flow depth in the outlet section of a broad-crested weir, based on the use of the variational principle of least action. Materials and methods. To develop a calculation method, the previously obtained dependences to determine the flow depth in the outlet section of a horizontal canal with a flow moving in a subcritical mode, and a method for determining the flow depth at the crest of a broad-crested weir were used. The theory was tested using a laboratory experiment and computer simulation in the ANSYS 17.0 software package. Results. The comparison of the results of experiments and computer simulation showed the conformance of the calculation results by the method based on the least action principle. The verification was carried out using the Fisher criterion, the criterion value according to the experimental data is 14.35, the criterion tabular value is 19.45, which indicates the adequacy of the proposed method to the experimental data. Conclusions. Based on the direct variational principle of least action, taking into account the influence of centrifugal forces in the flow, a calculation method that makes it possible to determine the outlet section depth of the broad-crested weir has been obtained. The resulting depth also corresponds to the transitional regime, in which the flooded regime changes to the non-flooded one, and in which the type of pool junction changes from surface to bottom one. The comparison showed a discrepancy of 0.4 % with data from outside authors. Experiments with the formation of a stuck jet in the outlet section of the weir showed that the depth in this case does not correspond to the proposed calculation method, this principle is also not implemented when the weir is flooded.

ПРИНЦИП НАИМЕНЬШЕГО ДЕЙСТВИЯ В РАСЧЕТЕ ВОДОСЛИВА С ШИРОКИМ ПОРОГОМ

Purpose: to apply the variation principle of least action to create a theory for calculating the broad-crested weir, to compare the results obtained with the data of various domestic and foreign researchers and to draw conclusions about the accuracy of the solution obtained. Materials and methods. The minimum flow depth on a broad-crested weir was determined by minimizing the Lagrangian liquid flow. This equation is used to close the equation of specific total flow energy. The verification of the obtained method in determining the minimum depth at the weir crest was carried out by a laboratory experiment and computer simulation of the flow movement through the weir, carried out in the ANSYS 17.0 software package. The results of determining weir capacity were compared with the experimental and theoretical data of domestic and foreign authors. Results. The comparison of the results of calculations of the broad-crested weir capacity with a wide threshold with the proposed method showed good agreement with the data of various authors, the difference did not exceed 3 %. The comparison of the results of depth calculations at the weir crest showed their agreement with the data of various authors, our own laboratory experiments and computer simulation. The adequacy of the obtained dependence was confirmed on the basis of determination coefficient and the Fisher variance ratio. Conclusions. A new theoretical method for hydraulic calculation of a broad-crested weir has been obtained, which made it possible to determine the liquid flow depth at the weir crest and its capacity. An analysis of the applicability of the method showed that the depth by the principle of least action is realized only in cases where the flow has no obstacles for free discharge. The limitation of the proposed method is the mandatory presence of a section with a relatively streamline flow and hydrostatic pressure distribution on the weir crest, as well as the absence of flooding of the structure.

Can One Transmit Energy Faster Than Light

Considerations on the mechanism of why EM fields in the near-field of an antenna, and particles tunnelling through a potential barrier are both superluminal, that if this could be understood, then there may be the possibility of sending energy faster than light. Possible explanations of this mechanism are considered, the nature of tunnelling and EM fields in general and considered explaining such behaviour through Emmy Noether’s theorem (1918) and the principle of least action, and applying this to the principle of work and energy, with considerations of Wheeler – Feynman Absorber theory of advanced waves echoing back to the source, as an explanation of the principle of least action, then speculating that this can be applied to superluminal effects in tunnelling and EM fields in the near-field. That the solutions of Maxwell’s equations for advanced and retarded potentials shows a symmetry to time, reflecting the fact that there must be two-time flows, one into the past and the other, into the future. From this it is considered that the reducing of the refractive index of the vacuum, ZPF field is what causes light to be faster than light, giving an explanation of the mechanism of tunnelling and EM fields in the near-field being superluminal, and considering the engineering of the vacuum, to send energy faster than light.

Energy-based Modeling and Simulation of Shallow Water Waves in a Tube with Moving Boundary

Modeling and simulation of shallow water waves in a tube with moving boundary and arbitrary cross-section are considered. Based on the a variational formulation of the well known one dimensional Saint-Venant equations in material fixed coordinates, energy-conserving finite-dimensional approximations are directly derived by the principle of least action. A particular discretization scheme is investigated, namely, a piecewise constant approximation of the distributed variables. The approach is validated in simulation and compared with alternative discretization-schemes.

The principle of least action in the space of Kähler potentials

Given a compact Kahler manifold, the space $\mathcal H$ of its (relative) Kahler potentials is an infinite dimensional Frechet manifold, on which Mabuchi and Semmes have introduced a natural connection $\nabla$. We study certain Lagrangians on $T\mathcal H$, in particular Finsler metrics, that are parallel with respect to the connection. We show that geodesics of $\nabla$ are paths of least action, and prove a certain convexity property of the least action. This generalizes earlier results of Calabi, Chen, and Darvas.