scholarly journals Complex Reaction Kinetics in Chemistry: A Unified Picture Suggested by Mechanics in Physics

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Elena Agliari ◽  
Adriano Barra ◽  
Giulio Landolfi ◽  
Sara Murciano ◽  
Sarah Perrone
Keyword(s):  
Reaction Kinetics ◽  
Substrate Concentration ◽  
Classical Mechanics ◽  
Elementary Reactions ◽  
Cooperative Effects ◽  
Molecular Binding ◽  
Least Action ◽  
Consistent Picture ◽  
The Hill ◽  
Cooperative Kinetics

Complex biochemical pathways can be reduced to chains of elementary reactions, which can be described in terms of chemical kinetics. Among the elementary reactions so far extensively investigated, we recall the Michaelis-Menten and the Hill positive-cooperative kinetics, which apply to molecular binding and are characterized by the absence and the presence, respectively, of cooperative interactions between binding sites. However, there is evidence of reactions displaying a more complex pattern: these follow the positive-cooperative scenario at small substrate concentration, yet negative-cooperative effects emerge as the substrate concentration is increased. Here, we analyze the formal analogy between the mathematical backbone of (classical) reaction kinetics in Chemistry and that of (classical) mechanics in Physics. We first show that standard cooperative kinetics can be framed in terms of classical mechanics, where the emerging phenomenology can be obtained by applying the principle of least action of classical mechanics. Further, since the saturation function plays in Chemistry the same role played by velocity in Physics, we show that a relativistic scaffold naturally accounts for the kinetics of the above-mentioned complex reactions. The proposed formalism yields to a unique, consistent picture for cooperative-like reactions and to a stronger mathematical control.

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 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.

Chemical Reaction Kinetics in Solution

2004 ◽  
Author(s):  
W. Ronald Fawcett
Keyword(s):  
Reaction Kinetics ◽  
Chemical Reactions ◽  
Chemical Reaction ◽  
Physical Property ◽  
Theoretical Description ◽  
Time Range ◽  
Chemical Changes ◽  
Elementary Reactions ◽  
Chemical Reaction Kinetics ◽  
Liquid Solutions

The kinetics of chemical reactions were first studied in liquid solutions. These experiments involved mixing two liquids and following the change in the concentration of a reactant or product with time. The concentration was monitored by removing a small sample of the solution and stopping the reaction, for example, by rapidly lowering the temperature, or by following a physical property of the system in situ, for example, its color. Although the experiments were initially limited to slow reactions, they established the basic laws governing the rate at which chemical changes occur. The variables considered included the concentrations of the reactants and of the products, the temperature, and the pressure. Thus, the reacting system was examined using the variables normally considered for a system at equilibrium. Most reactions were found to be complex, that is, to be made up of several elementary steps which involved one or two reactants. As the fundamental concepts of chemical kinetics developed, there was a strong interest in studying chemical reactions in the gas phase. At low pressures the reacting molecules in a gaseous solution are far from one another, and the theoretical description of equilibrium thermodynamic properties was well developed. Thus, the kinetic theory of gases and collision processes was applied first to construct a model for chemical reaction kinetics. This was followed by transition state theory and a more detailed understanding of elementary reactions on the basis of quantum mechanics. Eventually, these concepts were applied to reactions in liquid solutions with consideration of the role of the non-reacting medium, that is, the solvent. An important turning point in reaction kinetics was the development of experimental techniques for studying fast reactions in solution. The first of these was based on flow techniques and extended the time range over which chemical changes could be observed from a few seconds down to a few milliseconds. This was followed by the development of a variety of relaxation techniques, including the temperature jump, pressure jump, and electrical field jump methods. In this way, the time for experimental observation was extended below the nanosecond range.

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.

scholarly journals The Principle of Least Action for Reversible Thermodynamic Processes and Cycles

Entropy ◽  
2018 ◽  
Vol 20 (7) ◽  
pp. 542 ◽  
Author(s):  
Tian Zhao ◽  
Yu-Chao Hua ◽  
Zeng-Yuan Guo
Keyword(s):  
Heat Release ◽  
Optimization Problems ◽  
Optimal Path ◽  
Classical Mechanics ◽  
Carnot Cycle ◽  
Heat Absorption ◽  
Least Action ◽  
Principle Of Least Action ◽  
Thermodynamic Processes ◽  
Release Processes

The principle of least action, which is usually applied to natural phenomena, can also be used in optimization problems with manual intervention. Following a brief introduction to the brachistochrone problem in classical mechanics, the principle of least action was applied to the optimization of reversible thermodynamic processes and cycles in this study. Analyses indicated that the entropy variation per unit of heat exchanged is the mode of action for reversible heat absorption or heat release processes. Minimizing this action led to the optimization of heat absorption or heat release processes, and the corresponding optimal path was the first or second half of a Carnot cycle. Finally, the action of an entire reversible thermodynamic cycle was determined as the sum of the actions of the heat absorption and release processes. Minimizing this action led to a Carnot cycle. This implies that the Carnot cycle can also be derived using the principle of least action derived from the entropy concept.

The whole of physics

2017 ◽  
Author(s):  
Jennifer Coopersmith
Keyword(s):  
Physical Chemistry ◽  
General Relativity ◽  
Electromagnetic Waves ◽  
Materials Science ◽  
Classical Mechanics ◽  
Least Action ◽  
Principle Of Least Action ◽  
Theory Of Gravitation ◽  
Mathematical Equations ◽  
Deep Significance

How the Principle of Least Action underlies all physics (all physics that can be reduced to mathematical equations) is explained at a qualitative, semi-popular level. It even applies to smartphones. The domains of classical mechanics, continuum mechanics, materials science, light and electromagnetic waves, special and general relativity (Einstein’s Theory of Gravitation), electrodynamics, quantumelectrodynamics (QED), hydrodynamics, physical chemistry, statistical mechanics, and the quantum world, are examined. It is shown that the Principles of Least Time, Least Resistance, and Maximal Ageing, and Lenz’s Law are, in fact, examples of the Principle of Least Action. It is also shown how Planck’s constant is a measure of “absolute smallness,” and its units are the units of action. Never again, post quantum mechanics, can there be any doubt about the deep significance of action in physics.

scholarly journals Co-operativity and the methods of plotting binding and steady-state kinetic data

1978 ◽  
Vol 171 (2) ◽  
pp. 501-504 ◽  
Author(s):  
E P Whitehead
Keyword(s):  
Steady State ◽  
Ligand Binding ◽  
Substrate Concentration ◽  
Kinetic Data ◽  
Free Ligand ◽  
Free Energies ◽  
Steady State Kinetic ◽  
Second Derivatives ◽  
The Hill ◽  
State Kinetic

The features that distinguish positive from negative co-operativity in double-reciprocal Eadie-Hofstee-Scatchard and Hanes plots, often incorrectly stated to be the sign of curvature or second derivatives, are explained. It is shown how to determine the ‘Hill exponent’ and interaciton free energies from curves in these plots, and in the simple plot of ligand binding or velocity against free ligand or substrate concentration. New types of plots, where the kind of co-operative behaviour is more obvious than in the traditional ones, are proposed.

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