scholarly journals BOHMIAN TRAJECTORIES AND THE PATH INTEGRAL PARADIGM: COMPLEXIFIED LAGRANGIAN MECHANICS

2009 ◽  
Vol 19 (07) ◽  
pp. 2335-2346 ◽  
Author(s):  
VALERIY I. SBITNEV
Keyword(s):  
Probability Density ◽  
Path Integral ◽  
Balance Equation ◽  
Classical Mechanics ◽  
Nonlinear Function ◽  
Quantum Potential ◽  
Energy Term ◽  
Entropy Balance ◽  
Least Action ◽  
The Difference

David Bohm had shown that the Schrödinger equation, that is a "visiting card" of quantum mechanics, can be decomposed onto two equations for real functions — action and probability density. The first equation is the Hamilton–Jacobi (HJ) equation, a "visiting card" of classical mechanics, is modified by the Bohmian quantum potential. This potential is a nonlinear function of the probability density. And the second is the continuity equation. The latter can be transformed to the entropy balance equation. The Bohmian quantum potential is transformed into two Bohmian quantum correctors. The first corrector modifies the kinetic energy term of the HJ equation, and the second one modifies the potential energy term. The unification of the quantum HJ equation and the entropy balance equation gives a complexified HJ equation containing complex kinetic and potential terms. The imaginary parts of these terms have an order of smallness about the Planck constant. The Bohmian quantum corrector is an indispensable term modifying the Feynman's path integral by expanding coordinates and momenta to an imaginary sector. The difference between the Bohmian and Feynman's trajectories is that the former satisfies the principle of least action and they bifurcate on interfaces. The latter covers all possible paths from a source to a detector. They can split and annihilate.

Study of pumping effect in flow-through electrolysers

1983 ◽  
Vol 48 (8) ◽  
pp. 2232-2248 ◽  
Author(s):  
Ivo Roušar ◽  
Michal Provazník ◽  
Pavel Stuhl
Keyword(s):  
Natural Convection ◽  
Balance Equation ◽  
Volume Fraction ◽  
Industrial Applications ◽  
Pumping Effect ◽  
Flow Through ◽  
The Mean ◽  
The Difference

In electrolysers with recirculation, where a gas is evolved, the pumping of electrolyte from a lower to a higher level can be effected by natural convection due to the difference between the densities of the inlet electrolyte and the gaseous emulsion at the outlet. An accurate balance equation for calculation of the rate of flow of the pumped liquid is derived. An equation for the calculation of the mean volume fraction of bubbles in the space between the electrodes is proposed and verified experimentally on a pilot electrolyser. Two examples of industrial applications are presented.

scholarly journals A least action principle for interceptive walking

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Soon Ho Kim ◽  
Jong Won Kim ◽  
Hyun Chae Chung ◽  
MooYoung Choi
Keyword(s):  
Social Systems ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Action Principle ◽  
Lagrange Equations ◽  
Least Action Principle ◽  
Least Action ◽  
The Least Action Principle ◽  
Principle Of Least Action ◽  
Human Participants

AbstractThe principle of least effort has been widely used to explain phenomena related to human behavior ranging from topics in language to those in social systems. It has precedence in the principle of least action from the Lagrangian formulation of classical mechanics. In this study, we present a model for interceptive human walking based on the least action principle. Taking inspiration from Lagrangian mechanics, a Lagrangian is defined as effort minus security, with two different specific mathematical forms. The resulting Euler–Lagrange equations are then solved to obtain the equations of motion. The model is validated using experimental data from a virtual reality crossing simulation with human participants. We thus conclude that the least action principle provides a useful tool in the study of interceptive walking.

scholarly journals Thermodynamic Analysis of Relaxation Model for Non-Equilibrium Phase Behavior of Hydrocarbon Mixtures

2021 ◽  
Vol 2090 (1) ◽  
pp. 012138
Author(s):  
I M Indrupskiy ◽  
P A Chageeva
Keyword(s):  
Relaxation Time ◽  
Phase Behavior ◽  
Relaxation Process ◽  
Thermodynamic Analysis ◽  
Balance Equation ◽  
Equilibrium Phase ◽  
Characteristic Relaxation Time ◽  
Relaxation Model ◽  
Entropy Balance ◽  
Non Equilibrium

Abstract Mathematical models of phase behavior are widely used to describe multiphase oil and gas-condensate systems during hydrocarbon recovery from natural petroleum reservoirs. Previously a non-equilibrium phase behavior model was proposed as an extension over generally adopted equilibrium models. It is based on relaxation of component chemical potentials difference between phases and provides accurate calculations in some typical situations when non-instantaneous changing of phase fractions and compositions in response to variations of pressure or total composition is to be considered. In this paper we present a thermodynamic analysis of the relaxation model. General equations of non-equilibrium thermodynamics for multiphase flows in porous media are considered, and reduced entropy balance equation for the relaxation process is obtained. Isotropic relaxation process is simulated for a real multicomponent hydrocarbon system with different values of characteristic relaxation time using the non-equilibrium model implemented in the PVT Designer module of the RFD tNavigator simulation software. The results are processed with a special algorithm implemented in Matlab to calculate graphs of the total entropy time derivative and its constituents in the entropy balance equation. It is shown that the constituents have different signs, and the greatest influence on the entropy is associated with the interphase flow of the major component of the mixture and the change of the total system volume in the isotropic process. The characteristic relaxation time affects the rate at which the entropy is approaching its maximum value.

scholarly journals Action in Economics: Mathematical Derivation of Laws of Economics from the Principle of Least Action in Physics

2021 ◽  
Author(s):  
Sayan Kombarov
Keyword(s):  
Mathematical Formulation ◽  
Classical Mechanics ◽  
Human Action ◽  
Fundamental Principle ◽  
Austrian School ◽  
Rate Theory ◽  
Main Stream ◽  
Marginal Value ◽  
Least Action ◽  
Principle Of Least Action

The thesis of this paper is mathematical formulation of the laws of Economics with application of the principle of Least Action of classical mechanics. This paper is proposed as the rigorous mathematical approach to Economics provided by the fundamental principle of the physical science – the Principle of Least Action. This approach introduces the principle of Action into main-stream economics and allows reconcile main principles Austrian School of Economics and the laws of market, such Say’s law and marginal value and interest rate theory, with the modern results of mathematical economics, such as Capital Asset Pricing Model (CAPM), game theory and behavioral economics. This principle is well known in classical mechanics as the law of conservation of action that governs any system as a whole and all its components. It led to the revolution in physics, as it allows to derive the laws of Newtonian and quantum mechanics and probability. Ludwig von Mises defined Economics is the science of Human Action. Action is introduced into Economics by the founder of Austrian School of Economic, Carl Menger. Production or acquisition of any goods, services and assets are results of purposeful acts in the form of expenditure of work and energy in the form of flow of money and material resources. Humans take them to achieve certain desired goals with given resources and time. Any economic good and service, financial, productive, or real estate asset is the result of such action.

Understanding single-slit experiments on the basis of Galton board experiments

2021 ◽  
Vol 34 (3) ◽  
pp. 265-267
Author(s):  
Chong Wang
Keyword(s):  
Normal Distribution ◽  
Probability Density ◽  
Least Action ◽  
Neighboring Particle ◽  
Large Particles ◽  
Pass Through ◽  
Particle Group ◽  
Slit Experiment

In a single-slit experiment conducted for microparticles, the well-aligned rough structure of the slit wall can be viewed as a Galton board. Thus, when microparticles pass through the single slit, both the particle probability density (PPD) and particle direction of motion have a normal distribution. Therefore, when the distance between the slit and the receiving film becomes large, particles with different directions of motion will separate into different particle groups. By the nature of a normal distribution, the PPD for any particle group should also be normal-distributed. Obviously, between any two neighboring particle groups, there should be a valley in the PPD and thus the particle groups are observed as discrete fringes. All phenomena observed in the single-slit experiment can be explained reasonably well from the above viewpoint. In particular, analysis shows that the PPD can be described by the square of the modulus of the average least action of particles at a given location.

Thermodynamic Properties of Simple Systems

1993 ◽  
Author(s):  
Greg M. Anderson ◽  
David A. Crerar
Keyword(s):  
Thermodynamic Properties ◽  
Pure Substance ◽  
Energy Term ◽  
Stable States ◽  
Energy Transfers ◽  
Absolute Energy ◽  
The Absolute ◽  
The Difference ◽  
Simple Systems ◽  
Constituent Elements

We have now introduced several thermodynamic parameters that are useful in dealing with energy transfers (U, H, G, etc.). We wish now to see how these quantities are measured and where to find values for them. In later chapters we will see how they are used in detail. However, we have an immediate problem in that we cannot measure the energy parameters U, H, G and A, as discussed in Chapter 4. Because we do not know the absolute values of either the total or molar version of these variables, we are forced to deal only with their changes in processes or reactions of interest to us. But we obviously cannot tabulate these changes for every reaction of potential interest; there are too many. We must tabulate some sort of energy term for each pure substance so that the changes in any reaction between them can be calculated. In the example in §5.7 of water at — 2°C changing to ice at — 2°C, we said that AG was negative. How can we know this without carrying out a research program on the thermodynamic properties of ice and supercooled water? We begin by explaining how this is done. The problem created by not having absolute energy values is handled very conveniently by determining and tabulating, for every pure compound, the difference between the (absolute) G or H of the compound itself and the sum of the (absolute) G or H values of its constituent elements. In other words, AG or AH is determined for the reaction in which the compound is formed from its elements (in their stable states). These differences can be determined experimentally in spite of not knowing the absolute values involved.

An Observation on Least Action Principle in Classical Mechanics Oriented on the Evaluation of Relativistic Error Concerning the Measurements of Light Propagating in a Liquid

2011 ◽  
Vol 1 (3) ◽  
pp. 14-24 ◽  
Author(s):  
Alessandro Massaro ◽  
Piero Adriano Massaro
Keyword(s):  
Euler Equations ◽  
Classical Mechanics ◽  
First Integrals ◽  
Action Principle ◽  
Classical Approach ◽  
Limit Case ◽  
Least Action Principle ◽  
Calculus Of Variation ◽  
Least Action ◽  
Approximate First Integrals

The authors prove that the standard least action principle implies a more general form of the same principle by which they can state generalized motion equation including the classical Euler equation as a particular case. This form is based on an observation regarding the last action principle about the limit case in the classical approach using symmetry violations. Furthermore the well known first integrals of the classical Euler equations become only approximate first integrals. The authors also prove a generalization of the fundamental lemma of the calculus of variation and we consider the application in electromagnetism.

scholarly journals Extended harmonic mapping connects the equations in classical, statistical, fluid, quantum physics and general relativity

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Xiaobo Zhai ◽  
Changyu Huang ◽  
Gang Ren
Keyword(s):  
General Relativity ◽  
Quantum Physics ◽  
Harmonic Maps ◽  
Classical Mechanics ◽  
Harmonic Mapping ◽  
Geodesic Equation ◽  
Lagrange Equations ◽  
Least Action ◽  
Principle Of Least Action ◽  
Fundamental Equations

Abstract One potential pathway to find an ultimate rule governing our universe is to hunt for a connection among the fundamental equations in physics. Recently, Ren et al. reported that the harmonic maps with potential introduced by Duan, named extended harmonic mapping (EHM), connect the equations of general relativity, chaos and quantum mechanics via a universal geodesic equation. The equation, expressed as Euler–Lagrange equations on the Riemannian manifold, was obtained from the principle of least action. Here, we further demonstrate that more than ten fundamental equations, including that  of classical mechanics, fluid physics, statistical physics, astrophysics, quantum physics and general relativity, can be connected by the same universal geodesic equation. The connection sketches a family tree of the physics equations, and their intrinsic connections reflect an alternative ultimate rule of our universe, i.e., the principle of least action on a Finsler manifold.

SPURIONS IN FUNCTIONAL AND OPERATOR QUANTIZATION OF STRING THEORY AND HARMONIC GAUGE

1991 ◽  
Vol 06 (12) ◽  
pp. 1061-1068
Author(s):  
A.P. DEMICHEV ◽  
M.Z. IOFA
Keyword(s):  
String Theory ◽  
Path Integral ◽  
Riemann Surfaces ◽  
Ward Identity ◽  
Brst Quantization ◽  
Higher Genus ◽  
The Difference ◽  
Lagrange Approach

We discuss the difference between the Lagrange and the operator BRST quantization in string theory on Riemann surfaces of higher genus. An example of the harmonic gauge yielding the non-anomalous BRST Ward identity in the path integral Lagrange approach is studied in detail.

Sign in / Sign up

Export Citation Format

Share Document