- Dept. of Chemistry, University of Calcutta
Rajabazar Science College Campus
92, APC Road, Kolkata 700 009 - 09433477217
Kamal Bhattacharyya
University of Calcutta, DEPARTMENT OF CHEMISTRY, Faculty Member
Department of Chemistry, University of Calcutta, 92, Acharya Prafulla Chandra Road, Kolkata-700 009, India <em>E</em>-<em>mail:</em> pcsdhatt@gmail.com, pchemkb@gmail.com Department of Chemistry, AJC Bose College,... more
Department of Chemistry, University of Calcutta, 92, Acharya Prafulla Chandra Road, Kolkata-700 009, India <em>E</em>-<em>mail:</em> pcsdhatt@gmail.com, pchemkb@gmail.com Department of Chemistry, AJC Bose College, 1/1B, Acharya Jagadish Chandra Bose Road, Kolkata-700 020, India <em>E</em>-<em>mail:</em> kbpchem@gmail.com <em>Manuscript received 20 June 2018, accepted 21 June 2018</em> Different graphical plots involving the catalytic rate and the (initial) substrate concentration exist in the enzyme kinetics literature to estimate the reaction constants. But, none of these standard plots can unambiguously distinguish between the two important mechanisms of rate enhancement: positive cooperativity among the active sites of an oligomeric enzyme and auto-catalysis of the intermediate complex of an enzyme with a single active site. In the simplest situation of a direct autocatalysis, at least, we have achieved this distinctio...
Department of Chemistry, University of Calcutta, Kolkata-700 009, India E-mail : pcsdhatt@gmail.com, pchemkb@gmail.com Manuscript received 04 November 2017, accepted 17 November 2017 Reaction constants in traditional Michaelis-Menten type... more
Department of Chemistry, University of Calcutta, Kolkata-700 009, India E-mail : pcsdhatt@gmail.com, pchemkb@gmail.com Manuscript received 04 November 2017, accepted 17 November 2017 Reaction constants in traditional Michaelis-Menten type enzyme kinetics are most often determined through a few linear plots. Such graphical plots sometimes provide reasonably good data. But, for a comparative survey, visual examinations are not enough. Instead, it is always advisable to go simultaneously for a few associated numerical tests. They can assess how far the measured values of the quantities sought are reliable, furnishing along with appropriate error estimates that can be checked against the corresponding nonlinear methods. Here, we explicitly deal with a few such situations to stress the importance of these tests with specific examples. Also, we advocate a new scheme to mainly highlight how cases may appear with negative reaction constants and explore the origin of such bizarre findings. T...
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Two special situations where the standard uncertainty product inequality appears to be useless are modified. One such case is noted to also trivialize the recently-introduced alternatives [Phys. Rev. Lett. 113, 260401 (2014); Sci. Rep. 6,... more
Two special situations where the standard uncertainty product inequality appears to be useless are modified. One such case is noted to also trivialize the recently-introduced alternatives [Phys. Rev. Lett. 113, 260401 (2014); Sci. Rep. 6, 23201 (2016)] involving sums of variances. A careful discussion is presented on the experimental justifications of some of the relations [Phys. Rev. A 93, 052108 (2016)] using qutrit and qubit states. Alternative bypass routes are put forward to tackle this situation, with and without involving any auxiliary state. This latter strategy is noted to be vital in an entirely different context concerned with the quality of approximate stationary states. The other case is more frustrating, but an effective method is advanced. En route, the recent alternatives are also simplified to easily accommodate even the cases of more than two observables. In favorable circumstances, an easy option in function space is obtained by virtue of symmetry that does not in...
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Different graphical plots involving the catalytic rate with the (initial) substrate concentration exist in the enzyme kinetics literature to estimate the reaction constants. But, none of these standard plots can unambiguously distinguish... more
Different graphical plots involving the catalytic rate with the (initial) substrate concentration exist in the enzyme kinetics literature to estimate the reaction constants. But, none of these standard plots can unambiguously distinguish between the two important mechanisms of rate enhancement: positive cooperativity among the active sites of an oligomeric enzyme and auto-catalysis of the intermediate complex of an enzyme with a single active site. We achieve this distinction here by providing a nice linear plot for the latter. Importantly, to accomplish this task, no extra information other than the steady-state rate as a function of substrate concentration is required.
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Received 30 September 1986 The performance of the least-squares method is compared with that of the usual (Rayleigh-Ritz) variation method (UVM) in a specific bound-state calculation. Their relative merits and demerits are carefully... more
Received 30 September 1986 The performance of the least-squares method is compared with that of the usual (Rayleigh-Ritz) variation method (UVM) in a specific bound-state calculation. Their relative merits and demerits are carefully analysed with respect to the approximate calculation of expectation vafues of particular types of observables.
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The rate of a reaction may not always show a monotonic dependence on some specific rate constant. In the context of stochastic single-substrate enzyme kinetics, such a behavior has recently [PNAS 111 (2014) 4391] been demonstrated;... more
The rate of a reaction may not always show a monotonic dependence on some specific rate constant. In the context of stochastic single-substrate enzyme kinetics, such a behavior has recently [PNAS 111 (2014) 4391] been demonstrated; specifically, rate is noted to increase with increasing dissociation rate constant of the enzyme-substrate complex, contrary to standard expectation. In this work, we identify this counter-intuitive trait in several solvable and deterministic situations too. However, these anomalies are also analytically shown to disappear after a time-averaging. Numerical results of the deterministic enzyme kinetics scheme reveal similar features. The age-old intuitive chemistry thus retains its significance as an average.
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The Carnot engine sets an upper limit to the efficiency of a practical heat engine. An arbitrary irreversible engine is sometimes believed to behave closely as the Curzon-Ahlborn engine. Efficiency of the latter is obtained commonly by... more
The Carnot engine sets an upper limit to the efficiency of a practical heat engine. An arbitrary irreversible engine is sometimes believed to behave closely as the Curzon-Ahlborn engine. Efficiency of the latter is obtained commonly by invoking the maximum power principle in a non-equilibrium framework. We outline here two plausible routes within the domain of classical thermodynamics to arrive at the same expression. Further studies on the performances of available practical engines reveal that a simpler approximate formula works much better in respect of bounds to the efficiency. Putting an intermediate-temperature reservoir between the actual source and the sink leads to a few interesting extra observations.
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ABSTRACT The kinship of a simple variational scheme involving the uncertainty product with a prevalent semiclassical nonlinear differential equation approach for finding energies of stationary states is established. This leads to a... more
ABSTRACT The kinship of a simple variational scheme involving the uncertainty product with a prevalent semiclassical nonlinear differential equation approach for finding energies of stationary states is established. This leads to a transparent physical interpretation of the embedded parameters in the latter approach, providing additionally a lower bound to the integration constant. The domain of applicability of this strategy is also extended to encompass neighbouring states. Other advantages of the simpler alternative route are stressed. Pilot calculations demonstrate nicely the efficacy of the endeavour.
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ABSTRACT The problem of slow convergence in sequential estimates of covalent lattice constants is overcome by employing a new linear convergence accelerator. Chebyshev polynomials have been exploited to generate this transformation. It is... more
ABSTRACT The problem of slow convergence in sequential estimates of covalent lattice constants is overcome by employing a new linear convergence accelerator. Chebyshev polynomials have been exploited to generate this transformation. It is simple, sufficiently accelerative and expressible in a closed form, thus providing enough computational convenience. Performance of the scheme with relation to a few others is tested. Demonstrative calculations highlighting its worth and efficiency involve the rapid and accurate evaluation of a few cubic lattice constants.
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Variational studies employing the basis functions of the quantal particle-in-a-box model are shown to lead to accurate estimates of eigenvalues, various expectation values and eigenfunctions of the stationary anharmonic oscillator... more
Variational studies employing the basis functions of the quantal particle-in-a-box model are shown to lead to accurate estimates of eigenvalues, various expectation values and eigenfunctions of the stationary anharmonic oscillator problem. Calculations involve bothzx 2α and (x 2+ zx 2α)-type oscillators, withα=2, 3 and 4, both in weak and strong coupling regime. Apart from its recommendable computational simplicity, convergence of
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A route to evaluate exact sums represented by Dirichlet eta and beta functions, both of which are alternating and divergent at negative integer arguments, is advocated. It rests on precise polynomial extrapolations and stands as a... more
A route to evaluate exact sums represented by Dirichlet eta and beta functions, both of which are alternating and divergent at negative integer arguments, is advocated. It rests on precise polynomial extrapolations and stands as a generalization of an early endeavor on lattice sums. Apart from conferring a physical meaning to anti-limits, the scheme advanced here is direct, independent and computationally appealing. A new interpretation of summability is also gained.
We provide here a thermodynamic analog of the Braess road-network paradox with irreversible engines working between reservoirs that are placed at vertices of the network. Paradoxes of different kinds reappear, emphasizing the specialty of... more
We provide here a thermodynamic analog of the Braess road-network paradox with irreversible engines working between reservoirs that are placed at vertices of the network. Paradoxes of different kinds reappear, emphasizing the specialty of the network.
The entropy production rate is a key quantity in irreversible thermodynamics. In this work, we concentrate on the realization of entropy production rate in chemical reaction systems in terms of the experimentally measurable reaction rate.... more
The entropy production rate is a key quantity in irreversible thermodynamics. In this work, we concentrate on the realization of entropy production rate in chemical reaction systems in terms of the experimentally measurable reaction rate. Both triangular and linear networks have been studied. They attain either thermodynamic equilibrium or a non-equilibrium steady state, under suitable external constraints. We have shown that the entropy production rate is proportional to the square of the reaction velocity only around equilibrium and not any arbitrary non-equilibrium steady state. This feature can act as a guide in revealing the nature of a steady state, very much like the minimum entropy production principle. A discussion on this point has also been presented.
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The impossibility of attaining equilibrium for cyclic chemical reaction networks with irreversible steps is apparently due to a divergent entropy production rate. A deeper reason seems to be the violation of the detailed balance... more
The impossibility of attaining equilibrium for cyclic chemical reaction networks with irreversible steps is apparently due to a divergent entropy production rate. A deeper reason seems to be the violation of the detailed balance condition. In this work, we discuss how the standard theoretical framework can be adapted to include irreversible cycles, avoiding the divergence. With properly redefined force terms, such systems are also seen to reach and sustain equilibria that are characterized by the vanishing of the entropy production rate, though detailed balance is not maintained. Equivalence of the present formulation with Onsager's original prescription is established for both reversible and irreversible cycles, with a few adjustments in the latter case. Further justification of the attainment of true equilibrium is provided with the help of the minimum entropy production principle. All the results are generalized for an irreversible cycle comprising of N number of species.
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A route to evaluate exact sums represented by Dirichlet eta and beta functions, both of which are alternating and divergent at negative integer arguments, is advocated. It rests on precise extrapolations and confers a physical meaning to... more
A route to evaluate exact sums represented by Dirichlet eta and beta functions, both of which are alternating and divergent at negative integer arguments, is advocated. It rests on precise extrapolations and confers a physical meaning to anti-limits. The scheme put forward here is direct, independent and conceptually appealing. A new interpretation of summability is also gained.
We provide here a thermodynamic analog of the Braess road-network paradox with irreversible engines working between reservoirs that are placed at vertices of the network. Paradoxes of different kinds reappear, emphasizing the specialty of... more
We provide here a thermodynamic analog of the Braess road-network paradox with irreversible engines working between reservoirs that are placed at vertices of the network. Paradoxes of different kinds reappear, emphasizing the specialty of the network.
Based on explorations in estimating certain Madelung constants, we put forward here two separate strategies to understand the meaning of two distinct classes of divergent non-power-series expansions. One class refers to alternating series... more
Based on explorations in estimating certain Madelung constants, we put forward here two separate strategies to understand the meaning of two distinct classes of divergent non-power-series expansions. One class refers to alternating series representations, the other to monotonic ones. They chiefly rest on precise and approximate polynomial extrapolations, depending on situations. In case of sawtooth sequences, e.g., the partial-sums obtainable from Dirichlet eta or beta function at negative integer arguments, exact sequence-generating polynomials are found. Extrapolations yield a graphical meaning to anti-limit here, along with the exact answer. For staircase sequences, like the ones obtained from partial-sums of series representations for lambda and zeta functions, again at negative integer arguments, anti-limits do not exist. But, correct sequence-generating polynomials are obtained. There, our recipe relies on estimation of specific, finite areas embedded by such polynomials. The ...
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Reaction constants in traditional Michaelis-Menten type enzyme kinetics are most often determined through a linear Lineweaver-Burk plot. While such a graphical plot is sometimes good to achieve the end, it is always better to go for a few... more
Reaction constants in traditional Michaelis-Menten type enzyme kinetics are most often determined through a linear Lineweaver-Burk plot. While such a graphical plot is sometimes good to achieve the end, it is always better to go for a few numerical tests that can assess the quality of the data set being used and hence offer more reliable measures of the quantities sought, furnishing along with appropriate error estimates. In this context, we specifically highlight how cases may appear with negative reaction constants and explore the origin of such bizarre findings.
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A coupled linear-nonlinear variational strategy is adopted to study resonances in the quartic anharmonic oscillator system via the stabilisation method. Quite a few hitherto unexplored features show up in this case. The observed... more
A coupled linear-nonlinear variational strategy is adopted to study resonances in the quartic anharmonic oscillator system via the stabilisation method. Quite a few hitherto unexplored features show up in this case. The observed dependence of the energy of such quasi-bound states on the coupling parameter is employed to explain the unsuitability of a perturbative approach. Localised quasi-bound states are found even when there are no classical turning points. The origin of this peculiar quantum effect is traced. Finally, level-crossing problems and the associated quasi-degenerate situation are also noted and analysed.
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ABSTRACT The problem of representing an observable F(z) in the Padé scheme from its formal perturbative (Taylor) expansion in z is considered. It is demonstrated how the representation could be improved by incorporating in a simple... more
ABSTRACT The problem of representing an observable F(z) in the Padé scheme from its formal perturbative (Taylor) expansion in z is considered. It is demonstrated how the representation could be improved by incorporating in a simple manner, in the course of constructing such approximants, the knowledge of asymptotic (z → ∞) power-law behavior of F(z). Comparison with the usual approximants is made with a thorough numerical survey on error estimates and variations of error with z, input information, and quantum number. Spectacular performance of the new strategy is exemplified. Test calculations chiefly involve various properties of the first five eigenenergy states of the quartic anharmonic oscillator system. A few consistency requirements, including the virial theorem, are also studied. © 1993 John Wiley &amp; Sons, Inc.
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A non-equilibrium steady state is characterized by a non-zero steady dissipation rate. Chemical reaction systems under suitable conditions may generate such states. We propose here a method that is able to distinguish states with... more
A non-equilibrium steady state is characterized by a non-zero steady dissipation rate. Chemical reaction systems under suitable conditions may generate such states. We propose here a method that is able to distinguish states with identical values of the steady dissipation rate. This necessitates a study of the variation of the entropy production rate with the experimentally observable reaction rate in regions close to the steady states. As an exactly-solvable test case, we choose the problem of enzyme catalysis. Link of the total entropy production with the enzyme efficiency is also established, offering a desirable connection with the inherent irreversibility of the process. The chief outcomes are finally noted in a more general reaction network with numerical demonstrations.
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ABSTRACT The Carnot engine sets an upper limit to the efficiency of a practical heat engine. An arbitrary variety of the latter, however, is believed to behave closely as the Curzon-Ahlborn engine. Efficiency of this engine is obtained... more
ABSTRACT The Carnot engine sets an upper limit to the efficiency of a practical heat engine. An arbitrary variety of the latter, however, is believed to behave closely as the Curzon-Ahlborn engine. Efficiency of this engine is obtained commonly by invoking the maximum power principle in a non-equilibrium framework. We outline here some plausible routes within the domain of classical thermodynamics to arrive at the same expression for efficiency. Further, studies on the performances of quite a few practical engines lead us to a simpler approximate formula with better bounds, on the basis of just the second law.
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We distinguish two extreme classes of perturbation problems depending on the signs of second-order energy corrections and argue why it is generally much more probable to obtain a negative value of the same for any state in the standard... more
We distinguish two extreme classes of perturbation problems depending on the signs of second-order energy corrections and argue why it is generally much more probable to obtain a negative value of the same for any state in the standard Rayleigh-Schrödinger perturbation theory. The classes are seen to differ in reproducing results of finite-dimensional matrix perturbations. A few related issues are also discussed, some of which are based on available analytical results.
Within the framework of the method of variation of constants, time-dependent perturbation theory is presented in a form that naturally eliminates the undesirable ‘secular ’ terms for a time-independent perturbation, permits an... more
Within the framework of the method of variation of constants, time-dependent perturbation theory is presented in a form that naturally eliminates the undesirable ‘secular ’ terms for a time-independent perturbation, permits an order-by-order calculation of the exact wavefunction for a ‘resonant’ harmonic perturbation and offers a simple route to establish the adiabatic hypothesis in quantum mechanics. The formulation rests on the introduction of a flexibility in the choice of the phase factors associated with the varying amplitudes, together with development of a perturbation procedure that closely resembles the Brillouin-Wigner formalism in the static case, and which exploits the flexibility of the phase factors at each order of the theory.
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ABSTRACT Variational studies on spiked oscillators with the potential form x2 + lambda/xbeta in [0, ∞) reveal certain limitations of the conventional choices for wave functions in the beta &gt;= 2 regime. A careful analysis shows the... more
ABSTRACT Variational studies on spiked oscillators with the potential form x2 + lambda/xbeta in [0, ∞) reveal certain limitations of the conventional choices for wave functions in the beta &gt;= 2 regime. A careful analysis shows the necessity of properly incorporating the Dirichlet boundary condition at x = 0. Subsequent pilot calculations on this notion perform nicely, justifying the worth of the endeavor.
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ABSTRACT We show that logarithmic perturbation theory nicely yields the wavefunction correction terms in closed forms for the spiked perturbation λ/x2 on the first excited state of the harmonic oscillator, where the conventional... more
ABSTRACT We show that logarithmic perturbation theory nicely yields the wavefunction correction terms in closed forms for the spiked perturbation λ/x2 on the first excited state of the harmonic oscillator, where the conventional Rayleigh-Schrödinger scheme is known to encounter serious problems. The study also provides a direct route to obtain several sum rules, some of which appear to be new. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005
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We highlight overlap as one of the simplest inequalities in linear space that yields a number of useful results. One obtains the Cauchy–Schwarz inequality as a special case. More importantly, a variant of it is seen to work desirably in... more
We highlight overlap as one of the simplest inequalities in linear space that yields a number of useful results. One obtains the Cauchy–Schwarz inequality as a special case. More importantly, a variant of it is seen to work desirably in certain singular situations where the celebrated inequality appears to be useless. The basic tenet generates a few other interesting relations, including the improvements over certain common uncertainty bounds. Role of projection operators in modifying the Cauchy–Schwarz relation is noted. Selected applications reveal the efficacy.Quanta 2019; 8: 36-43.
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The Carnot engine sets an upper limit to the efficiency of a practical heat engine. An arbitrary variety of the latter, however, is believed to behave closely as the Curzon-Ahlborn engine. Efficiency of this engine is obtained commonly by... more
The Carnot engine sets an upper limit to the efficiency of a practical heat engine. An arbitrary variety of the latter, however, is believed to behave closely as the Curzon-Ahlborn engine. Efficiency of this engine is obtained commonly by invoking the maximum power principle in a non-equilibrium framework. We outline here some plausible routes within the domain of classical thermodynamics to arrive at the same expression for efficiency. Further, studies on the performances of quite a few practical engines lead us to a simpler approximate formula with better bounds, on the basis of just the second law.
An iterative variant of Padé approximants (PA) is presented and employed to accelerate convergence of sequences. Pilot calculations on partial lattice sums for NaCl and CsCl crystals have been explicitly shown to offer accurate estimates... more
An iterative variant of Padé approximants (PA) is presented and employed to accelerate convergence of sequences. Pilot calculations on partial lattice sums for NaCl and CsCl crystals have been explicitly shown to offer accurate estimates of their Madelung constants.
We explore a few advantages of studying the change in information entropy of a bound quantum state with energy. It is known that the property generally increases with the quantum number for stationary states, in spite of the concomitant... more
We explore a few advantages of studying the change in information entropy of a bound quantum state with energy. It is known that the property generally increases with the quantum number for stationary states, in spite of the concomitant gradual increase in the number of constraints for higher levels. A simple semiclassical proof of this observation is presented via the Wilson-Sommerfeld quantization scheme. In the small quantum number regime, we numerically demonstrate how far the semiclassical predictions are valid for a few systems, some of which are exactly solvable and some not so. Our findings appear to be significant in a number of ways. We observe that, for most problems, information entropy tends to a maximum as the quantum number tends to infinity. This sheds some light on the Bohr limit as a classical limit. Noting that the dependence of energy on the quantum number governs the rate of increase of information entropy with the degree of excitation, we extend our analysis to include the role of the kinetic energy. The endeavor yields a relation that possesses a universal character for any one-dimensional problem. Relevance of information entropy in studying the goodness of approximate stationary states obtained from finite-basis linear variational calculations is also delineated. Finally, we expound how this property behaves in situations where shape resonances show up. A typical variation is indeed observed in such cases when we proceed to detect Siegert states via the stabilization method.
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The efficacy of a Padé-(MC)SCF strategy both in accelerating slowly convergent iterative sequences and forcing convergence in pathologically divergent problems is explored. Comparison is made with the traditional level- (root-)shifted... more
The efficacy of a Padé-(MC)SCF strategy both in accelerating slowly convergent iterative sequences and forcing convergence in pathologically divergent problems is explored. Comparison is made with the traditional level- (root-)shifted (MC)SCF approach. Finally, the performance of a coupled Padé-level-shifted (MC)SCF scheme in cases of intrinsic divergence is presented.
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ABSTRACT
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The standard two-step model of homogeneous-catalyzed reactions had been theoretically analyzed at various levels of approximations from time to time. The primary aim was to check the validity of the quasi-steady-state approximation, and... more
The standard two-step model of homogeneous-catalyzed reactions had been theoretically analyzed at various levels of approximations from time to time. The primary aim was to check the validity of the quasi-steady-state approximation, and hence emergence of the Michaelis-Menten kinetics, with various substrate-enzyme ratios. But, conclusions vary. We solve here the desired set of coupled nonlinear differential equations by invoking a new set of dimensionless variables. Approximate solutions are obtained via the power-series method aided by Pade approximants. The scheme works very successfully in furnishing the initial dynamics at least up to the region where existence of any steady state can be checked. A few conditions for its validity are put forward and tested against the findings. Temporal profiles of the substrate and the product are analyzed in addition to that of the complex to gain further insights into legitimacy of the above approximation. Some recent observations like the reactant stationary approximation and the notions of different timescales are revisited. Signatures of the quasi-steady-state approximation are also nicely detected by following the various reduced concentration profiles in triangular plots. Conditions for the emergence of Michaelis-Menten kinetics are scrutinized and it is stressed how one can get the reaction constants even in the absence of any steady state.
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A systematic approximation scheme for studying the partition function at intermediate temperature range has been presented, referring especially to molecular free internal rotation as a test case, and compared thoroughly with quite a few... more
A systematic approximation scheme for studying the partition function at intermediate temperature range has been presented, referring especially to molecular free internal rotation as a test case, and compared thoroughly with quite a few other approximants in vogue. The relative merits of the strategies are also analysed.
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The equations governing adiabatic and isothermal quantum processes involved in an ideal two-state quantum heat engine are modified when the ideality restriction is removed. We seek and study a few situations to determine the nature and... more
The equations governing adiabatic and isothermal quantum processes involved in an ideal two-state quantum heat engine are modified when the ideality restriction is removed. We seek and study a few situations to determine the nature and magnitude of the modifications. If one confines such systems well within the classical turning point, we show how one can profitably employ the Wilson-Sommerfeld quantization rule to estimate the leading correction terms due to non-ideality. The endeavour is likely to be important in studies on practical quantum engines.
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ABSTRACT
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Efficiencies of certain methods for the determination of critical indices from power-series expansions are shown to be considerably improved by a suitable implementation of fractional differentiation. In the context of the ratio method... more
Efficiencies of certain methods for the determination of critical indices from power-series expansions are shown to be considerably improved by a suitable implementation of fractional differentiation. In the context of the ratio method (RM), kinship of the modified strategy with the ad hoc `shifted' RM is established and the advantages are demonstrated. Further, in the course of the estimation of critical points, significant betterment of convergence properties of diagonal Padé approximants is observed on several occasions by invoking this concept. Test calculations are performed on (i) various Ising spin-1/2 lattice models for susceptibility series attended with a ferromagnetic phase transition, (ii) complex model situations involving confluent and antiferromagnetic singularities and (iii) the chain-generating functions for self-avoiding walks on triangular, square and simple cubic lattices.
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We observe that ground-state energies of systems in potentials | vary with α in a peculiar manner in regions α<2. This variation is most possibly due to a quantum effect. A class of still weaker confining potentials with logarithmic rise... more
We observe that ground-state energies of systems in potentials | vary with α in a peculiar manner in regions α<2. This variation is most possibly due to a quantum effect. A class of still weaker confining potentials with logarithmic rise leads to considerably lower zero-point energies. Certain implications of the findings are indicated.
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The impossibility of attaining equilibrium for cyclic chemical reaction networks with irreversible steps is apparently due to a divergent entropy production rate. A deeper reason seems to be the violation of the detailed balance... more
The impossibility of attaining equilibrium for cyclic chemical reaction networks with irreversible steps is apparently due to a divergent entropy production rate. A deeper reason seems to be the violation of the detailed balance condition. In this work, we discuss how the standard theoretical framework can be adapted to include irreversible cycles, avoiding the divergence. With properly redefined force terms, such systems are also seen to reach and sustain equilibria that are characterized by the vanishing of the entropy production rate, though detailed balance is not maintained. Equivalence of the present formulation with Onsager's original prescription is established for both reversible and irreversible cycles, with a few adjustments in the latter case. Further justification of the attainment of true equilibrium is provided with the help of the minimum entropy production principle. All the results are generalized for an irreversible cycle comprising of N number of species.