arXiv subjects

Christopher G. Jesudason

Publications and source records attributed to Christopher G. Jesudason.

11 recordsLinked to original sources

arXiv2014

Fourier Heat Conduction as a phenomenon described within the scope of the Second Law

The historical development of the Carnot cycle necessitated the construction of isothermal and adiabatic pathways within the cycle that were also mechanically "reversible" which lead eventually to the Kelvin-Clausius development of the entropy function where the heat absorption is for the diathermal (isothermal) paths of the cycle only. It is deduced from traditional arguments that Fourier heat conduction involves mechanically "reversible" heat transfer with irreversible entropy increase. Here we model heat conduction as a thermodynamically reversible but mechanically irreversible process. The MD simulations conducted shows excellent agreement with the theory. Such views and results as these, if developed to a successful conclusion could imply that the Carnot cycle be viewed as describing a local process of energy-work conversion and that irreversible local processes might be brought within the scope of this cycle, implying a unified treatment of thermodynamically (i) irreversible, (ii) reversible, (iii) isothermal and (iv) adiabatic processes.

physics.gen-ph↗

arXiv2013

Reduced variable optimization methods via implicit functional dependence with applications

Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an arbitrary number of variables for classes (i) and (ii) by the minimization of a function of a single variable. Algorithms that focus on a reduced variable set also avoid problems associated with multiple minima and maxima that arise because of the large numbers of parameters. The methods described could have applications in the physical sciences where the optimization of one physically significant variable has priority over the other variables. For (i), we develop both an approximate but computationally more tractable method and an exact method where the single controlling variable k of all the other variables (P,k) passes through the local stationary point of the least squares (LS) metric. For (ii), an exact theory is developed whereby the optimized function of an independent variation of all parameters coincides with that due to single parameter optimization. The implicit function theorem has to be further qualified to arrive at this result. The topology of the surfaces of constant value of the target or cost function are considered for all the methods. A real world application of the above implicit methodology to rate constant and final concentration parameter determination for first and second order chemical reactions from published data. This work is different from and more general than all the reduction schemes for conditional linear parameters nor is it a subset of the Adomian decomposition method (ADM) used for estimating solutions of differential equations, which still require boundary conditions that do not feature in topics (i) and (ii).

math.OC↗

arXiv2011

Discrete Charge Effects on an Infinitely Long Cylindrical Rod Model

Two methods for determining the potential (ψ) around a discretely charged rod have been devised. The methods utilize the potential around the continuously charged rod (\barψ) as the reference where \barψ isdetermined by the Poisson-Boltzmann equation. The potential data are used to determine the theoretical radial distribution function (RDF) which is compared with MD simulation data. It is shown that the magnitude of the charge and size parameters very strongly affects the shape of the RDF's and consequently the thermodynamics.

physics.comp-ph↗

arXiv2011

I. Determination of chemical reaction rate constants by numerical nonlinear analysis: differential methods

The primary emphasis of this work on kinetics is to illustrate the a posteriori approach to applications, where focus on data leads to novel outcomes, rather than the a priori tendencies of applied analysis which imposes constructs on the nature of the observable. The secondary intention is the development of appropriate methods consonant with experimental definitions. By focusing on gradients, it is possible to determine both the average and instantaneous rate constants that can monitor changes in the rate constant with concentration changes as suggested by this theory. Here, methods are developed and discussed utilizing nonlinear analysis which does not require exact knowledge of initial concentrations. These methods are compared with those derived from standard methodology. These gradient methods are shown to be consistent with the ones from standard methods and could readily serve as alternatives for studies where there are limits or unknowns in the initial conditions, such as in the burgeoning fields of astrophysics and astrochemistry, forensics, archeology and biology . All four reactions studied exhibited semi sinusoidal-like change with reactant concentration change which standard methods cannot detect, which seems to constitute the observation of a new effect that is not predicted by current formulations, where the possibility that the observations are due to artifacts from instrumental errors or the optimization method is reasoned as unlikely since the experiments were conducted by different groups at very different times with different classes of reactions.

physics.gen-ph↗

arXiv2010

Induced parameter-dependent optimization method applied to reaction rate determination

Parameter fitting of data to a proposed equation almost always consider these parameters as independent variables. Here, the method proposed optimizes an arbitrary number of variables by the minimization of a function of a single variable. Such a technique avoids problems associated with multiple minima and maxima because of the large number of parameters, and could increase the accuracy of the determination by cutting down on machine errors. An algorithm for this optimization scheme is provided and applied to the determination of the rate constant and final concentration parameters for a first order and second order chemical reaction.

physics.chem-ph↗

arXiv2009

Determination of Rate Constant of Chemical Reactions by Simple Numerical Nonlinear Analysis

For some centuries, first order chemical rate constants were determined mainly by a linear logarithmic plot of reagent concentration terms against time where the initial concentration was required, which is experimentally often a challenging task to derive accurate estimates. By definition, the rate constant was deemed to be invariant and the kinetic equations were developed with this assumption. A reason for these developments was the ease in which linear graphs could be plotted. Here, different methods are discussed that does not require exact knowledge of initial concentrations and which require elementary nonlinear analysis and the ensuing results are compared with those derived from the standard methodology from an actual chemical reaction, with its experimental determination of the initial concentration with a degree of uncertain. We verify experimentally our previous theoretical conclusion based on simulation data [ J. Math . Chem {\bf 43} (2008) 976--1023, arXiv:physics/0608073] that the so called rate constant is never constant even for elementary reactions and that all the rate laws and experimental determinations to date are actually averaged quantities over the reaction pathway. We conclude that nonlinear methods in conjunction with experiments could in the future play a crucial role in extracting information of various kinetic parameters.

physics.chem-ph↗

arXiv2006

The form of the rate constant for elementary reactions at equilibrium from MD: framework and proposals for thermokinetics

The rates or formation and concentration distributions of a dimer reaction showing hysteresis behavior are examined in an ab initio chemical reaction designed as elementary and where the hysteresis structure precludes the formation of transition states (TS) with pre-equilibrium and internal sub-reactions. It was discovered that the the reactivity coefficients, defined as a measure of departure from the zero density rate constant for the forward and backward steps had a ratio that was equal to the activity coefficient ratio for the product and reactant species. From the above observations, a theory is developed with the aid of some proven elementary theorems in thermodynamics, and expressions are derived whereby a feasible experimental and computational method for determining the activity coefficients from the rate constants may be obtained The theory developed is applied to ionic reactions where the standard Bronsted-Bjerrum rate equation and exceptions to this are rationalized, and by viewing ion association as a n-meric process, ion activity coefficients may in principle be determined under varying applicable assumptions.

physics.chem-ph↗

arXiv2005

Equilibrium properties of a hysteresis dimer molecule from MD simulations using two-body potentials

Recent experiments indicate that electromagnetic hysteresis behavior can be exhibited at the molecular level.A MD simulation using 2-body potentials and switches to form and break bonds is implemented to determine whether chemical reaction pathways might also exhibit analogous behavior whilst preserving conventional thermodynamical outcomes. The results of various common thermodynamical and kinetic properties are presented, where no unusual thermodynamics is observed. A potential switching technique circumvents the problem of computer intensive three-body calculations which makes this model particularly suitable for numerical investigations in both equilibrium and nonequilibrium states . A new algorithm for the conservation of energy and momentum is incorporated. The thermodynamical parameters determined include the standard free energy, enthalpy and entropy, the activity coefficient ratios, the equilibrium constant and the many energy distribution functions of the molecule, all of which are compared to the Maxwell distribution function. The results do not support recent MNET theories nor the principle of local equilibrium as fundamental principles. A non-cosine dependent rotational variable is suggested for first order relaxation processes. A revision of time reversibility concepts is suggested.

physics.comp-ph↗

arXiv2005

An energy interconversion principle applied in reaction dynamics for the determination of equilibrium standard states

Chemical theories involving thermodynamical equilibrium states invariably utilize statistical mechanical equilibrium density distributions. Here, a definition of heat-work transformation termed thermo mechanical coherence is first made, and it is conjectured that most molecular bonds have the above heat-work transformation property, which models a chemical bond as a "`centrifugal heat engine"' . Expressions are derived for the standard Gibbs free energy, enthalpy, and entropy where the bond coordinates need not conform to a non degenerate Boltzmann state, since bond breakdown and formation are processes that have direction, whereas equilibrium distributions are derived when the Hamiltonian is of fixed form, which is not the case for chemical reactions using localized Hamiltonians. The empirically determined Gibbs free energy from a known molecular dynamics simulation of a dimer reaction 2A--> A_2, accords rather well with the theoretical estimate. A relation connecting the rate of reaction with the equilibrium constant and other kinetic parameters is derived and could place the commonly observed linear relationship between the logarithms of the rate constant and equilibrium constant on a firmer theoretical footing. These relationships could include analogues of the Hammett correlations used extensively in physical organic chemistry, as well as others which are temperature dependent.

physics.chem-ph↗

arXiv2003

New Entropy and other state functions from analysis of open system Carnot cycle

A first principles analysis of an open system thermodynamical Carnot cycle is provided, and the results are compared to those proposed by Gibbs for open systems. The Kelvin-Clausius statement concerning heat transfer for reversible cycles is taken as an axiom, from which several rigorous theorems are proven.An equation is derived that resembles a Gibbs-Duhem relation relating convected entropies, from which two distinguishable forms of entropy are proven to exist for such systems, which questions prevailing developments which presume a singular or characteristic entropic form which couple all work and heat flows, such as in Onsager first order thermodynamics. In particular, a closed path undergone by the system does not return to the environment to the initial state for one of these entropic forms. The Biot assertion that the entropy contribution due to diathermal heat transfer does not form a state function is therefore contradicted and a local entropy is shown to exist. Several other new composite state functions for work and heat flow are shown to exist for open systems. From Gibbs' results, it is suggested that the ensuing chemical potentials used routinely may possibly ignore heat effects. The functions developed here are suitable for application since the functions are proven to exist, rather than presumed to exist.

math.GM↗

arXiv2000

General Non-Applicability of the Liouville Equation in Statistical Mechanics and a New μ-space Stochastic Equation for Dynamical Systems

By examining both the divergence of the velocity vector in orthogonal Cartesian coordinate space $\mathbfΓ $ of dimension $\R^{\textrm {2fN}}$ and the structure of the Hamiltonian determining a system trajectory, it is shown that the standard Liouville equation cannot describe anything more than linear motion for typical Hamiltonians with separated momentum and space variables and some significant consequences such as the Poincare recurrence theorem do not obtain for such Hamiltonians. A new stochastic equation which is everywhere in principle discontinuous is developed for dynamical systems described by a general Hamiltonian which is a functional of the space and momentum variables, and where the average trajectory of a system point is proven to be orthogonal to any constant energy surface consonant with the system energy at equilibrium. This equation does not assume the presence of binary collision only, as required in the standard first-order Boltzmann equation, and is therefore suitable to describe dense systems as well, and may be viewed as an alternative to the latter. Some new macroscopic variational principles for non-equilibrium thermodynamical systems are proposed, where one object for future work would be to relate the microscopic description given here with the macroscopic principles.

nlin.CD↗