Principle Of Least Action Research Articles

Lagrangian dynamics of the coupled field-medium state of light

In the recently introduced mass-polariton (MP) theory of light (Partanen et al 2017 Phys. Rev. A 95 063850), the optical force of light drives in a medium forward an atomic mass density wave. In this work, we present the Lagrangian formulation of the MP theory starting directly from the principle of least action and the well-known Lagrangian densities of the electromagnetic field and the medium within the special theory of relativity. The Lagrangian densities and the resulting Euler–Lagrange equations lead directly and without any further postulates to the unique expression of the optical Abraham force that dynamically couples the electromagnetic field and the medium in the MP theory of light. The field-medium coupling is symmetric and bi-directional and it fulfills the law of action and counteraction. The coupled dynamical equations also enable the exact description of the very small kinetic energy of the medium as a part of the total energy of the coupled state of light. Thus, the Lagrangian formulation of the present work is a complementary approach to Lorentz covariance properties of the MP theory discussed in our recent work (Partanen and Tulkki 2019 Phys. Rev. A 99 033852). We show how the coupled dynamical equations of the field and the medium can be solved analytically for a Gaussian light pulse. It is astonishing how the simple analytic results for the dynamical equations, the optical force, and the stress-energy-momentum tensor of the MP theory follow ab initio from the Lagrangian densities that have been well known for almost a century.

Dispersion of Electromagnetic, Elastic and Diffusion Waves in Crystalline Solids

The paper analyzes the dispersion characteristics of eigen oscillation frequencies of electromagnetic, elastic and diffusion waves. The analysis is based on the general invariant expression of the Lagrange function density in a solid subjected to the elastoplastic deformation with u(r,t) strain vector of its inner points, electromagnetic field potentials A(r,t) and φ(r,t ) , and concentration n(r,t) of diffusing substance with regard to a correlation between these parameters. Owing to the least-action principle, four linear, interconnected differential equations are obtained. Form their solution all the four frequency spectra ωi (k ) are derived, where i=1,2,3,4 and k is the wave vector. It is found that the obtained dispersions are the important part in the quantum case, if taking the interaction between the four components into consideration, when knowledge of the function ωi (k ) is required.

Existence of static spherically-symmetric objects in action-dependent Lagrangian theories

We study static symmetric solutions in the context of a gravitational theory based on a action-dependent Lagrangian. Such theory has been designed as a setup to implement dissipative effects into the traditional principle of least action. Dissipation appears therefore from the first principles and has a purely geometric origin. An interesting feature of this theory is the existence of a coupling four-vector $\lambda_{\mu}$, which in an expanding background is related to cosmological bulk viscosity. General Relativity is recovered with a vanishing $\lambda_{\mu}$. We analyse the existence of equilibrium solutions of static configurations aiming to describe astrophysical objects. We find out that the existence of static spherically symmetric configurations occurs only in the particular scenario with vanishing $\lambda_t$, $\lambda_r$ and $\lambda_{\phi}$ components i.e, $\lambda_{\mu}=\{0,0,\lambda_{\theta},0\}$. Thus, the component $\lambda_{\theta}$ is the unique available parameter of the theory in the astrophysical context. This result severely constrains the existence of this sort of gravitational theories. We proceed then verifying the impact of $\lambda_{\theta}$ on the stability and the mass-radius configurations for a reasonable equation of state for the cold dense matter inside compact stars. We further investigate the relativistic spherical collapse in order to track the structure of geometrical singularities appearing in the theory.

Thermodynamic Merger of Fluctuation Theorem and Principle of Least Action: Case of Rayleigh–Taylor Instability

Abstract Entropy fluctuations with time occur in finite-sized time-evolving dissipative systems. There is a need to comprehend the role of these fluctuations on the fluctuations-averaged entropy generation rate, over a large enough observation time interval. In this non-equilibrium thermodynamic investigation, the Fluctuation Theorem (FT) and Principle of Least Action are re-visited to articulate their implications for dissipative systems. The Principle of Maximum Entropy Production (MaxEP: the entropy generation rate of a dissipative system is maximized by paths of least action) is conceptually identified as the Principle of Least Action for dissipative systems. A Thermodynamic Fusion Theorem that merges the FT and the MaxEP is introduced for addressing the role of fluctuations in entropy production. It identifies “entropy fluctuations” as the “least-action path” for maximizing the time-averaged entropy production in a dissipative system. The validity of this introduced theorem is demonstrated for the case of entropy fluctuations in Rayleigh–Taylor flow instability.

Theoretical Stable Hydraulic Section based on the Principle of Least Action

Despite decades of effort, stable hydraulic geometry for an open channel water flow has hardly been established because of too many unknown variables for too few rational relationships. This article derives the most efficient channel cross section using calculus of variations for the given flow area at the minimum wetting perimeter length, which is equivalent to the principle of least action. Analysis indicates that water can most efficiently flow in a semi-ellipse section channel with minimum friction and erosion. Anisotropy in channel erodibility was found to be necessary in the natural stable channel characterization because gravitation force and channel bank consolidation cannot be ignored in earth surface material. This channel cross section, based on the principle of least action, may be regarded as the theoretical stable hydraulic section for erodible bed, which was comparable to the observed river cross-sections during high flow periods.

Dynamic modeling of a dielectric elastomeric spherical actuator: an energy-based approach

ABSTRACT The present work is concerned with the dynamic modeling of a dielectric elastomeric spherical actuator subjected to an inflation pressure and an electrical DC step voltage across the actuator wall. Herein, we report an alternative method to obtain the static and dynamic instability parameters based on establishing the energy balance principle at the point of maximum stretch in an oscillation cycle. Additionally, we proposed a new energy density function, which accounts the electrostriction phenomenon for a class of an incompressible isotropic dielectric elastomeric material. We first deduce an explicit analytical Lagrange equation of motion based on the Hamiltonian principle of least action for a dielectric elastomeric spherical actuator. Further, a quantitative comparison is presented between the static and dynamic instability parameters. Finally, the numerical results obtained from the developed equation of motion are discussed in line with the parallel results presented in the literature. In summary, the present study brings out the effect of an inflation pressure on the onset of dynamic response in a dielectric elastomeric spherical actuator. In addition, the proposed method is so versatile, and can also be used in other systems of interest.

The Cognitive Lens: a primer on conceptual tools for analysing information processing in developmental and regenerative morphogenesis.

Brains exhibit plasticity, multi-scale integration of information, computation and memory, having evolved by specialization of non-neural cells that already possessed many of the same molecular components and functions. The emerging field of basal cognition provides many examples of decision-making throughout a wide range of non-neural systems. How can biological information processing across scales of size and complexity be quantitatively characterized and exploited in biomedical settings? We use pattern regulation as a context in which to introduce the Cognitive Lens-a strategy using well-established concepts from cognitive and computer science to complement mechanistic investigation in biology. To facilitate the assimilation and application of these approaches across biology, we review tools from various quantitative disciplines, including dynamical systems, information theory and least-action principles. We propose that these tools can be extended beyond neural settings to predict and control systems-level outcomes, and to understand biological patterning as a form of primitive cognition. We hypothesize that a cognitive-level information-processing view of the functions of living systems can complement reductive perspectives, improving efficient top-down control of organism-level outcomes. Exploration of the deep parallels across diverse quantitative paradigms will drive integrative advances in evolutionary biology, regenerative medicine, synthetic bioengineering, cognitive neuroscience and artificial intelligence. This article is part of the theme issue 'Liquid brains, solid brains: How distributed cognitive architectures process information'.

Inference of the Universal Constancy of Planck Constant based on First Principles

Since its discovery by Max Planck in 1900, the Planck constant h has been demonstrated to be a universal constant for all (quasi-) stationary dynamical processes of all particles and fields, whenever an energy quantum h× frequency is exchanged or transmitted. Its numerical value has been accurately determined based on experiments. The physical origin of this fundamental constant h has however not been well understood up to the present, and its numerical value has not been ab initio predicted. This paper presents a theoretical inquiry into the first respect, a mathematical inference of the universal constancy of h based on the second law of thermodynamics and the principle of least action combined with probability theory. We consequently conclude that the universal constancy of h is the result of Maupertuis-Jacobi’s least action and entropy maximum principles governing the global system, the observable part of the cosmos at least.

Modified general relativity

In a Lorentzian spacetime there exists a smooth regular line element field $(\bm{X},-\bm{X}) $ and a unit vector $ \bm{u} $ collinear with one of the pair of vectors in the line element field. An orthogonal decomposition of symmetric tensors can be constructed in terms of the Lie derivative along $ \bm{X} $ of the metric and a product of the unit vectors; and a linear sum of divergenceless symmetric tensors. A modified Einstein equation of general relativity is then obtained by using the principle of least action, the decomposition and a fundamental postulate of general relativity. The decomposition introduces a new symmetric tensor $ \varPhi_{\alpha\beta} $ which describes the energy-momentum of the gravitational field. It completes Einstein's equation and addresses the energy localization problem. Variation of the action with respect to $ X^{\mu} $ restricts $u_{\mu}$ to a particular value, which defines the possible Lorentzian metrics. $ \Phi $, the trace of $ \varPhi_{\alpha\beta} $, describes dark energy. The cosmological constant is dynamically replaced by $ \Phi $. A cyclic universe that developed after the Big Bang is described. The dark energy density provides a natural explanation of why the vacuum energy density is so small, and why it dominates the present epoch. Assuming dark matter does not exist, a solution to the modified Einstein equation introduces two additional terms into the Newtonian radial force equation, from which the baryonic Tully-Fisher relation is obtained.

Coupling in ATP synthesis: Test of thermodynamic consistency and formulation in terms of the principle of least action

Abstract The coupled nonequilibrium processes of ATP synthesis in oxidative phosphorylation (OX PHOS) are tuned such that the system operates at optimal thermodynamic efficiency, η. This state is compatible with maximum free energy dissipation, Φ under the imposed constraints. These results are shown to be consistent with nonequilibrium thermodynamics. Analysis of experimental data on rat liver mitochondria with succinate as substrate demonstrates that the total action of the system for a selected final state is a maximum compatible with the constraints, and that the system evolves with time to a minimum average unit action of 1.4 × 10−3 J s natom O−1 mg protein−1. This value of least average unit action corresponds to the highest efficiency of the system, compatible with the constraints to which the system is subject.

How and why the present tectonic setting in the Apennine belt has developed

The building of the Apennine belt slowed down or ceased around the Early Pleistocene. Since then, the belt has undergone strong uplift and considerable distortion. This change, from belt-normal to belt-parallel shortening, has been determined by the fact that the continental Adriatic domain (Adria) was almost completely surrounded by buoyant orogenic structures. In that context, the mobility of Adria underwent a considerable reduction, whereas uplift and deformation of its southern part was strongly emphasized as an effect of the convergence of the confining plates. Around the middle Pleistocene, the deformation pattern in the peri-Adriatic zones changed again, in response to acceleration of Adria. The outer (Adriatic) sector of the Apennine belt underwent belt-parallel shortening, accommodated by uplift and outward escape of upper crustal wedges. The separation between the extruding wedges and the almost stable inner belt has generated a series of extensional or transtensional fault systems along the axial part of the Apennines, which now correspond to the main seismogenic sources. The spatio-temporal distribution of major tectonic events in the study area can plausibly be explained as an effect of the least-action principle. Thematic collection: This article is part of the ‘Apennines and Tyrrhenian system’ collection available at: https://www.lyellcollection.org/cc/the-apennines-tyrrhenian-system

Einstein-Maxwell Theory without Symmetry and Examples of Geodesics in Space with Torsion

The propagation of light and electromagnetic-gravity field in Y n space is studied. Our aims are to obtain the equations that described gravitational field in vacuum from the principle of least action in Y n space, and derive the law of motion of free point particles in Y n ; we showed that free point particles move along geodesics of space. The geodesic in Y n are depended on metric and torsion and this situation are considered in several non-trivial examples of the geodesics in the three-dimensional space without gravitational force; as result, we obtained that even in space without gravity geodesics are depending on torsion of space.

Retraction: Einstein–Maxwell theory without symmetry and examples of geodesics in space with torsion

The propagation of light and electromagnetic-gravity field in Y n space is studied. Our aims are to obtain the equations that described gravitational field in vacuum from the principle of least action in Y n space, and derive the law of motion of free point particles in Y n ; we showed that free point particles move along geodesics of space. The geodesic in Y n are depended on metric and torsion and this situation are considered in several non-trivial examples of the geodesics in the three-dimensional space without gravitational force; as result, we obtained that even in space without gravity geodesics are depending on torsion of space.

Numerical complete solution for random genetic drift by energetic variational approach

In this paper, we focus on numerical solutions for random genetic drift problem, which is governed by a degenerated convection-dominated parabolic equation. Due to the fixation phenomenon of genes, Dirac delta singularities will develop at boundary points as time evolves. Based on an energetic variational approach (EnVarA), a balance between the maximal dissipation principle (MDP) and least action principle (LAP), we obtain the trajectory equation. In turn, a numerical scheme is proposed using a convex splitting technique, with the unique solvability (on a convex set) and the energy decay property (in time) justified at a theoretical level. Numerical examples are presented for cases of pure drift and drift with semi-selection. The remarkable advantage of this method is its ability to catch the Dirac delta singularity close to machine precision over any equidistant grid.

Maupertuis’s Principle of Least Action: Epistemology and Metaphysics

The paper deals with Pierre-Louis Moreau de Maupertuis’s (1698-1759) writings on the principle of least action (PLA). I discuss Maupertuis’s philosophical interpretation of the PLA by analysing three of his papers (1740, 1744, 1746), in order to assess the overall consistency of his argument. As I shall argue, Maupertuis presents the PLA as a universal principle of nature, this being at odds with the empiricist inspiration of his epistemology. Maupertuis’s attempt to introduce conceptual elements borrowed from the Leibnizian tradition into a Newtonian-inspired framework creates in fact a tension that is difficult to overcome.

BAO reconstruction: a swift numerical action method for massive spectroscopic surveys

A new fully non-linear reconstruction algorithm for the accurate recovery of the Baryonic Acoustic Oscillations (BAO) scale in two-point correlation functions is proposed, based on the least-action principle and extending the Fast Action Minimisation method by Nusser & Branchini (2000). Especially designed for massive spectroscopic surveys, it is tested on dark-matter halo catalogues extracted from the DEUS-FUR $\Lambda$CDM simulation to trace the trajectories of up to $\sim207,000$ haloes backward-in-time, well beyond the first-order Lagrangian approximation. The new algorithm successfully recovers the BAO feature in real and redshift-space in both the monopole and the anisotropic two-point correlation function, also for anomalous samples showing misplaced or absent signature of BAO. In redshift-space the non-linear displacement parameter $\Sigma_\mathrm{NL}$ is reduced from $11.8\pm0.3h^{-1}$Mpc at redshift $z=0$ (pre-reconstruction) to $4.0\pm0.5h^{-1}$Mpc at $z\simeq37$ after reconstruction. A comparison with the first-order Lagrangian reconstruction is presented, showing that this techniques outperforms the linear approximation in recovering an unbiased measurement of the acoustic scale.

Categorification of the Müller-Wichards System Performance Estimation Model: Model Symmetries, Invariants, and Closed Forms

The Müller-Wichards model (MW) is an algebraic method that quantitatively estimates the performance of sequential and/or parallel computer applications. Because of category theory’s expressive power and mathematical precision, a category theoretic reformulation of MW, i.e., CMW, is presented in this paper. The CMW is effectively numerically equivalent to MW and can be used to estimate the performance of any system that can be represented as numerical sequences of arithmetic, data movement, and delay processes. The CMW fundamental symmetry group is introduced and CMW’s category theoretic formalism is used to facilitate the identification of associated model invariants. The formalism also yields a natural approach to dividing systems into subsystems in a manner that preserves performance. Closed form models are developed and studied statistically, and special case closed form models are used to abstractly quantify the effect of parallelization upon processing time vs. loading, as well as to establish a system performance stationary action principle.

Принцип наименьшего действия в логистике

The article deals with the application of the Principle of least action in logistics, as well as some issues of building a rational logistics based on this principle; logistics is the management of the movement of material and related information and financial flows on the way from the primary source of resources to the final consumer of finished products with minimal costs; logistics is a key link between the supplier and the buyer, capable of competently constructed work to increase the utility of products and profits of the enterprise; one of the tasks of logistics is to reduce the specific energy costs of workers involved in ensuring the movement of material flows; according to the principle of least action, logistics activities should be organized so that the total cost of resources is minimal.

Composite Indicators based on the Principle of Least Action and Data Envelopment Analysis. An application to Corporate Social Responsibility Data

This paper introduces a model to construct composite indicators that is based upon the determination of the least distance from each assessed unit to a frontier estimated by Data Envelopment Analysis (DEA). The model also allows accounting for the existence of slacks in all the considered dimensions (sub-indicators), playing with the notion of Pareto-efficiency. All previous approaches based on DEA for building composite indicators maximize in some sense the sum of these slacks, determining the furthest and less credible targets and peers for the set of evaluated units. In contrast, the new model applies the Principle of Least Action (PLA), which ultimately determines the closest targets on the efficient frontier. Additionally, in order to assure the satisfaction of a set of important properties (units invariance, translation invariance, Pareto-efficiency, strong monotonicity), the model implements a new version of the Russell output measure of technical efficiency working with full dimensional efficient facets (FDEFs). This also guarantees that the weights used for the aggregation of the sub-indicators are always strictly positive. Finally, the new approach is illustrated by an application to the sphere of Corporate Social Responsibility (CSR).

Space-Time Universe versus Energy Driven Time Arrow Universe: Time-Neutrality Confronted with Fundamental Irreversibility

A dynamic interpretation of quantum phenomena based on an energy driven time arrow requires a combined description of matter and information on matter. This information around matter turned out to be gravitation and the fact that a photon is continuously recycled via this information generates an always constant light velocity. These two phenomena, simple consequences of fundamental irreversibility, have mathematically been imposed on empty space for time-neutral spacetime in General Relativity theory. In an irreversible universe such a four-dimensional spacetime would not anymore be required. Another striking difference is the role of time. Clock-time, used in Relativity Theory and found to be relative, is not associated with a generation of changes, being only a scale for measuring changes, based on selected periodic phenomena. The real time in an irreversible world, action time, is the flow of action, as generated by the principle of least action, or, alternatively, the loss of information on the past. In contrast to clock-time, action time is invariant with respect to relativistic transformation and also facilitates self-organization of matter and information. Gravitation as information on matter with the aim of imposing the principle of least action also provides the link between quantum world and cosmology, which Relativity Theory cannot provide. Relevant aspects of both theoretical approaches, with special emphasis on already experimentally verified spacetime phenomena, are critically analysed. While Relativity Theory, which is relying on time-neutral laws, is applied to support a chaotically exploding Big Bang scenario, the fundamentally irreversible universe subject to an energy driven time arrow is characterized by self-organization of energy, matter and information yielding an intelligent and creative “Self-Image” universe, which is able to periodically regenerate itself. Arguments for a fundamentally irreversible energy driven nature include, apart from explaining experimental support for Relativity Theory differently, the simple, straightforward derivation from a dynamically interpreted principle of least action, the elimination of quantum and cosmological paradoxes and the more sensitive and flexible information-technology based (digital) nature of gravitation as compared with the analogue “bent space” gravitation.