A fluctuation removal based univariate integration over prescribed nodes

This work aims at the evaluation of a univariate integral whose integrand except the weight function is assumed to be analytic inside a region containing the integration interval as an interior line in the complex plane of the independent variable. The method developed here is based on the idea of fluctuation removal which is the basic root of fluctuation free integration and Gauss quadratures. To this end, first, weight function generating subspaces are constructed. Then various possibilities to use a true weight function in the integration are discussed. All analyses here are for one node integration although higher order fluctuation removal possibilities are also restrictedly discussed. Certain illustrative applications are also distributed in side the sections to support the ideas of the work.     

No fluctuation approximation in any desired precision for univariate function matrix representations

The operator involving problems are mostly handled by using the matrix representations of the operators over a finite set of appropriately chosen basis functions in a Hilbert space as long as the related problem permits. The algebraic operator which multiplies its operand by a function is the focus of this work. We deal with the univariate case for simplicity. We show that a rapidly converging scheme can be constructed by defining an appropriate fluctuation operator which projects, in fact, to the complement of the space spanned by appropriately chosen finite number of basis functions. What we obtain here can be used in efficient numerical integration also.     

Three-dimensional-IR spectroscopy: beyond the two-point frequency fluctuation correlation function

Three-dimensional-IR spectroscopy is proposed as a new spectroscopic technique that is sensitive to three-point frequency fluctuation correlation functions. This will be important when the statistics of the underlying stochastic process is non-Gaussian, and hence when the system does not follow the linear response hypothesis. Furthermore, a very general classification of nonlinear spectroscopy in terms of higher order frequency fluctuation correlation functions is introduced, according to which certain moments of a multidimensional spectrum are related to certain frequency fluctuation correlation functions. The classification is rigorous in the so-called inhomogeneous limit, but remains valid approximately also when motional narrowing becomes important. The work also puts a recent paper [J. Bredenbeck et al., Phys. Rev. Lett. 95, 083201 (2005)] onto solid theoretical grounds, where we have shown for the first time that fifth-order spectroscopy--in this case transient two-dimensional spectroscopy--is indeed sensitive to the three-point frequency fluctuation correlation function.     

Constancy maximization based weight optimization in high dimensional model representation for multivariate functions

High Dimensional Model Representation (HDMR) method is a technique that represents a multivariate function in terms of less-variate functions. Even though the method has a finite expansion, to determine the components of this expansion is very expensive due to integration based natures of the components. Hence, the HDMR expansion is generally truncated at certain multivariance level and such approximations are produced to represent the given multivariate function approximately. The weight function selection becomes an important issue for the HDMR based applications when it is desired to give different importances to function values at different points. An appropriately chosen weight function may increase the quality of the approximation incredibly. This work aims at a multivariate weight function optimization to obtain high quality approximations through the HDMR method to represent multivariate functions. The proposed optimization considers constancy measurer maximization which produces a quadratic vector equation to be solved. Another contribution of this work is to use a recently developed method, fluctuation free integration, with HDMR, to solve this equation easily. This work is an extension of a previous work about weight optimization in HDMR for univariate functions.     

Frequency spectra of transport properties in lonic liquids: contribution of charge fluctuation modes

Abstract

The influence of charge fluctuation modes on the frequency spectra for shear viscosity, self-diffusion and thermal diffusion is discussed. Both the one-component plasma, and modifications which are anticipated in real ionic liquids to the charge fluctuation modes, are considered. The latter treatment utilizes a simple model into which is incorporated plasmon dispersion and plasmon damping, the damping being both at zero wave number k and at order k²

The main emphasis of the paper is on non-analytic behaviour with frequency, and the modifications which occur for damped charge fluctuation modes. Because of the dominant influence of mass fluctuation modes at very long time, which are not considered quantitatively here, the theory discussed should have relevance at intermediate times, such as are treated in present molecular dynamical calculations. Contact is made with such computer simulation of molten BeF₂ and a model of molten salts     

Extending the fluctuation theorem to describe reaction coordinates

The fluctuation theorem describes the distribution of work done on small systems which have been pushed out of equilibrium in response to an external field. The theorem has recently been a subject of much interest for describing single-molecule experiments and simulations. In this communication, it is shown how the fluctuation theorem can be extended to describe fluctuations not only in the work done on a system, but also in a reaction coordinate. The extension explored in this work allows for a generalized derivation of Hummer and Szabo's expression (G. Hummer and A. Szabo, Proc. Natl. Acad. Sci. 98, 3658 (2001)) for reconstructing the potential of mean force from nonequilibrium trajectories. The derivation demonstrates how implementation of this expression can be more easily facilitated. Atomistic simulations of a biomolecular system are presented which support these results.     

Probabilistic evolution approach to the expectation value dynamics of quantum mechanical operators,part II: the use of mathematical fluctuation theory

The first part of these two companion papers has been devoted to the extension of Hausdorff moment problem to the sequences over integrals of Kronecker powers of an appropriate vector under a generating function in the kernel. The relations between this generating function and weight function properties have been investigated over there in a quite detailed manner. This second companion paper focuses on the utilization of the “mathematical fluctuation theory” amenities in the construction of approximations to the solutions of the expectation value dynamics of the quantum dynamical systems. The fluctuation freee approximation matching with the classical mechanical behaviour is followed by the first and then the second order fluctuation approximations. Beside the well known “Energy Conservation Law”s counterparts in these approximations of quantum expectation value dynamics are also presented.     

Dynamical fluctuation effects in glassy colloidal suspensions

Fundamental understanding of heterogeneous dynamics in concentrated glassy hard sphere fluids and colloidal suspensions, even at the single particle level, requires major theoretical advances. Recent simulations and confocal microscopy experiments suggest strong nongaussian dynamical fluctuation effects and activated transport emerge well before an apparent kinetic glass transition is reached. New theoretical approaches that can predict the observable signatures of intermittent large amplitude motions and the associated fluctuation phenomena are discussed. Comparisons are made with experiments, computer simulations, and prior theory for average dynamical properties.     

Efficiency of alchemical free energy simulations. II. Improvements for thermodynamic integration

We attempt to optimize the efficiency of thermodynamic integration, as defined by the minimal number of unphysical intermediate states required for the computation of accurate and precise free energy differences. The suitability of various numerical quadrature methods is tested. In particular, we compare the trapezoidal rule, Simpson's rule, Gauss-Legendre, Gauss-Kronrod-Patterson, and Clenshaw-Curtis integration, as well as integration based on a cubic spline approximation of the integrand. We find that Simpson's rule and spline integration are already significantly more efficient that the trapezoidal rule, i.e., correct free energy differences can be obtained using fewer λ-states. We demonstrate that Simpson's rule can be used advantageously with nonequidistant values of the abscissa, which increases the flexibility of the method. Efficiency is enhanced even further if higher order methods, such as Gauss-Legendre, Gauss-Kronrod-Patterson, or Clenshaw-Curtis integration, are used; no more than seven λ-states, which in the case of Clenshaw-Curtis integration include the physical end states, were required for accurate results in all test problems studied. Thus, the performance of thermodynamic integration can equal that of Bennett's acceptance ratio method. We also show, however, that the high efficiency found here relies on the particular functional form of the soft-core potential used; overall, thermodynamic integration is more susceptible to the details of the hybrid Hamiltonian used than Bennett's acceptance ratio method. Therefore, we recommend Bennett's acceptance ratio method as the most robust method to compute alchemical free energy differences; nevertheless, scenarios when thermodynamic integration may be preferable are discussed.     

Steepest descent reaction path integration using a first-order predictor-corrector method

The theoretical treatment of chemical reactions inevitably includes the integration of reaction pathways. After reactant, transition structure, and product stationary points on the potential energy surface are located, steepest descent reaction path following provides a means for verifying reaction mechanisms. Accurately integrated paths are also needed when evaluating reaction rates using variational transition state theory or reaction path Hamiltonian models. In this work an Euler-based predictor-corrector integrator is presented and tested using one analytic model surface and five chemical reactions. The use of Hessian updating, as a means for reducing the overall computational cost of the reaction path calculation, is also discussed.     

Effect of temperature fluctuation on hydrate-based CO_2 separation from fuel gas

A new method of temperature fluctuation is proposed to promote the process of hydrate-based CO2 separation from fuel gas in this work according to the dual nature of CO2 solubility in hydrate forming and non-hydrate forming regions [1].The temperature fluctuation operated in the process of hydrate formation improves the formation of gas hydrate observably.The amount of the gas consumed with temperature fluctuation is approximately 35% more than that without temperature fluctuation.It is found that only the temperature fluctuation operated in the period of forming hydrate leads to a good effect on CO2 separation.Meanwhile,with the proceeding of hydrate formation,the effect of temperature fluctuation on the gas hydrate gradually reduces,and little effect is left in the completion term.The CO2 separation efficiencies in the separation processes with the effective temperature fluctuations are improved remarkably.     

Electron pairing and chemical bonds: Chemical bonds from the condition of minimum fluctuation of electron pair

The role of electron pairing in chemical bonding stressed by the Lewis electron-pair model of the chemical bond is analyzed and discussed from the point of view of the proposal that chemical bonds are the regions of space populated roughly by two electrons and which at the same time exhibit low fluctuation of an electron pair. Based on this assumption, we have been able to introduce a new localization procedure, the output of which are just the orbitals (chemical bonds) satisfying the criterion of minimum pair fluctuation. It has been shown that these orbitals remarkably well display the most important attributes of chemical bonds, namely, the localization in the regions where classical bonds are expected and there is very high transferability from one molecule to another. The applicability of this procedure as a new means of the analysis and the visualization of the molecular structure is also discussed. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 193–200, 1998     

Gliadin effect on fluctuation properties of phospholipid giant vesicles

Gliadin is a fraction of wheat gluten, a protein supramolecular complex known for its remarkable and biotechnologically relevant viscoelastic properties. Very high molecular mass characterise these systems, thus hindering high-resolution structural investigations. It is known, however, that these proteins comprise rather extended, extensively interassociated structures, which respond for their peculiar mechanical behaviour. Besides these properties, some of gluten's fractions, such as gliadin, are also known to be involved in a nutritionally relevant pathology of auto-immune character, the celiac disease, supposedly related to some unusual structural features of the protein. Despite its medical relevance, however, the role played by gliadin in the etiology of the celiac disease is not sufficiently understood to date. In this work, we investigated the role of gliadin on mechanical properties of a membrane model of dioleoylphosphatidylcholine (DOPC) giant unilamellar vesicles. The technique of micropipette aspiration, coupled to videomicroscopy, was applied. The microvesicles, produced by electric field pulsing over metal-covered plates, were suctioned into the micropipettes under varying applied pressures. A significant increase in the values of the bilayer curvature constant, k(c), was observed, with a saturation effect being verified at around 0.02-0.03 gliadin/DOPC mass ratio, indicating that the membrane becomes less elastic in the presence of the protein. Possible correlations between the observed membrane fluctuation properties and the celiac disease etiology are suggested and discussed.     

On the integration of jet ejectors into hybrid dehydration processes

Hybrid processes of distillation and membrane separation are considered as promising alternatives to azeotropic and extractive distillation. However, the membrane process, which is basically pervaporation or vapor permeation, is still a niche operation with a limited number of applications. The relatively high cost of the membrane units, and the lack of long time industrial experience are the main obstacles. Great efforts are being undertaken to improve the membrane properties and to optimize the membrane process. Additional savings in the effective cost of the membrane unit could be achieved by its proper integration into the overall process. In this work, the use of steam jet ejectors as a process integration alternative for hybrid dehydration processes is investigated. Favorable implementation regions are defined. Advantages and limitations of this modification are discussed.     

A differential fluctuation theorem

We derive a nonequilibrium thermodynamics identity (the "differential fluctuation theorem") that connects forward and reverse joint probabilities of nonequilibrium work and of arbitrary generalized coordinates corresponding to states of interest. This identity allows us to estimate the free energy difference between domains of these states. Our results follow from a general symmetry relation between averages over nonequilibrium forward and backward path functions derived by Crooks [Crooks, G. E. Phys. Rev. E 2000, 61, 2361-2366]. We show how several existing nonequilibrium thermodynamic identities can be obtained directly from the differential fluctuation theorem. We devise an approach for measuring conformational free energy differences, and we demonstrate its applicability to the analysis of molecular dynamics simulations by estimating the free energy difference between two conformers of the alanine dipeptide model system. We anticipate that these developments can be applied to the analysis of laboratory experiments.     

Time evolution of density fluctuation in supercritical region. I. Non-hydrogen-bonded fluids studied by dynamic light scattering

The time evolution of the density fluctuation of molecules inhomogeneously dispersing in a mesoscopic volume is investigated by dynamic light scattering in several fluids in supercritical states. This study is the first time-domain investigation to compare the dynamics of density fluctuation among several fluids. The samples used are non-hydrogen-bonded fluids in the supercritical states: CHF(3), C(2)H(4), CO(2), and xenon. These four molecules have different properties but are of similar size. Under these conditions, the relationship between dynamic and static density inhomogeneities is studied by measuring the time correlation function of the density fluctuation. In all cases, this function is characterized by a single exponential function, decaying within a few microseconds. While the correlation times in the four fluids show noncoincidence, those values agree well with each other when scaled to a dimensionless parameter. From the results of this scaling based on the Kawasaki theory and Landau-Placzek theory, the relation between dynamics and static structures is analyzed, and the following four insights are obtained: (i) viscosity is the main contributor to the time evolution of density fluctuation; (ii) the principle of corresponding state is observed by the use of time-domain data; (iii) the Kawasaki theory and the Landau-Placzek theory are confirmed to be applicable to polar, nonpolar, and nondipolar fluids that have no hydrogen bonding, at temperatures relatively far from critical temperature; and (iv) the density fluctuation correlation length and the value of density fluctuation are estimated from the time-domain data and agree with the values from other experiments and calculations.     

A numerical integration scheme for the evaluation of correlation energy functionals

A numerical integration scheme is presented for three-dimensional integrals occurring in electronic structure calculations, concentrating attention on the evaluation of the correlation energy through a density-functional expression. The scheme is based on the choice of density-based weight functions that naturally partition the space into “atomic” volumes (in which the integration is performed in terms of spherical coordinates) and “diatomic” volumes (in which the integration is performed in terms of confocal elliptical coordinates). Such a choice is justified on the basis of the analytical behavior of the integrand. The attainable accuracy and the required computational effort within the proposed scheme are discussed in detail in a test application on the C₆₀ molecule in the symmetrical configuration. Finally, a comparison with previously proposed schemes is presented. © 1993 John Wiley & Sons, Inc.     

A combined explicit-implicit method for high accuracy reaction path integration

We present the use of an optimal combined explicit-implicit method for following the reaction path to high accuracy. This is in contrast to most purely implicit reaction path integration algorithms, which are only efficient on stiff ordinary differential equations. The defining equation for the reaction path is considered to be stiff, however, we show here that the reaction path is not uniformly stiff and instead is only stiff near stationary points. The optimal algorithm developed in this work is a combination of explicit and implicit methods with a simple criterion to switch between the two. Using three different chemical reactions, we combine and compare three different integration methods: the implicit trapezoidal method, an explicit stabilized third order algorithm implemented in the code DUMKA3 and the traditional explicit fourth order Runge-Kutta method written in the code RKSUITE. The results for high accuracy show that when the implicit trapezoidal method is combined with either explicit method the number of energy and gradient calculations can potentially be reduced by almost a half compared with integrating either method alone. Finally, to explain the improvements of the combined method we expand on the concepts of stability and stiffness and relate them to the efficiency of integration methods.     

Molecular dynamics integration meets standard theory of molecular vibrations

An iterative SISM (split integration symplectic method) for molecular dynamics (MD) integration is described. This work explores an alternative for the internal coordinate system prediction in the SISM introduced by JaneZic et al. (J. Chem. Phys. 2005, 122, 174101). The SISM, which employs a standard theory of molecular vibrations, analytically resolves the internal high-frequency molecular vibrations. This is accomplished by introducing a translating and rotating internal coordinate system of a molecule and calculating normal modes of an isolated molecule only. The Eckart frame, which is usually used in the standard theory of molecular vibrations as an internal coordinate system of a molecule, is adopted to be used within the framework of the second order generalized leapfrog scheme. In the presented MD integrator the internal coordinate frame at the end of the integration step is predicted halfway through the integration step using a predictor-corrector type iterative approach thus ensuring the method's time reversibility. The iterative SISM, which is applicable to any system of molecules with one equilibrium configuration, was applied here to perform all-atom MD simulations of liquid CO2 and SO2. The simulation results indicate that for the same level of accuracy, this algorithm allows significantly longer integration time steps than the standard second-order leapfrog Verlet (LFV) method.