Moment Correlation Function Research Articles

Field theory of enzyme-substrate systems with restricted long-range interactions.

Enzyme-substrate kinetics form the basis of many biomolecular processes. The interplay between substrate binding and substrate geometry can give rise to long-range interactions between enzyme binding events. Here we study a general model of enzyme-substrate kinetics with restricted long-range interactions described by an exponent -γ. We employ a coherent-state path integral and renormalization group approach to calculate the first moment and two-point correlation function of the enzyme-binding profile. We show that starting from an empty substrate the average occupancy follows a power law with an exponent 1/(1-γ) over time. The correlation function decays algebraically with two distinct spatial regimes characterized by exponents -γ on short distances and -(2/3)(2-γ) on long distances. The crossover between both regimes scales inversely with the average substrate occupancy. Our work allows associating experimental measurements of bound enzyme locations with their binding kinetics and the spatial conformation of the substrate.

Study of permeability and permittivity of [formula omitted]-Fe[formula omitted]O[formula omitted] using computer simulation method

This study proposes a computational method to directly obtain the frequency-dependent permeability and permittivity of materials from computer simulation data. The method combines first-principles calculations, Green’s function formalism, and magnetic moment dynamics simulations. Using α-Fe2O3 as an example, we demonstrate the validation process of the computational approach. By calculating the time correlation functions of electric and magnetic dipole moments and applying linear response theory, we successfully obtained the frequency-dependent permeability and permittivity of α-Fe2O3 at 300 K. The calculated results agree well with experimental values, proving the efficacy of the proposed computational method. This study provides a reliable computational pathway to predict electromagnetic parameters of materials using computer simulations.

Fast-forwarding quantum simulation with real-time quantum Krylov subspace algorithms

Quantum subspace diagonalization (QSD) algorithms have emerged as a competitive family of algorithms that avoid many of the optimization pitfalls associated with parameterized quantum circuit algorithms. While the vast majority of the QSD algorithms have focused on solving the eigenpair problem for ground, excited-state, and thermal observable estimation, there has been a lot less work in considering QSD algorithms for the problem of quantum dynamical simulation. In this work, we propose several quantum Krylov fast-forwarding (QKFF) algorithms capable of predicting long-time dynamics well beyond the coherence time of current quantum hardware. Our algorithms use real-time evolved Krylov basis states prepared on the quantum computer and a multi-reference subspace method to ensure convergence towards high-fidelity, long-time dynamics. In particular, we show that the proposed multi-reference methodology provides a systematic way of trading off circuit depth with classical post-processing complexity. We also demonstrate the efficacy of our approach through numerical implementations for several quantum chemistry problems including the calculation of the auto-correlation and dipole moment correlation functions

Dynamics of non-Gaussian fluctuations in model A

Motivated by the experimental search for the QCD critical point we perform simulations of a stochastic field theory with purely relaxational dynamics (model A). We verify the expected dynamic scaling of correlation functions. Using a finite size scaling analysis we obtain the dynamic critical exponent $z=2.026(56)$. We investigate time dependent correlation functions of higher moments $M^n(t)$ of the order parameter $M(t)$ for $n=1,2,3,4$. We obtain dynamic scaling with the same critical exponent $z$ for all $n$, but the relaxation constant depends on $n$. We also study the relaxation of $M^n(t)$ after a quench, where the simulation is initialized in the high temperature phase, and the dynamics is studied at the critical temperature $T_c$. We find that the evolution does not follow simple scaling with the dynamic exponent $z$, and that it involves an early time rise followed by late stage relaxation.

Computational Evidence for the Crucial Role of Dipole Cross-Correlations in Polar Glass-Forming Liquids.

In this Letter, we analyze the dipole-dipole correlations obtained from the molecular dynamics simulations for strongly and weakly polar model liquids. As a result, we find that the cross-correlations' contribution to the system's total dipole moment correlation function, which is directly measured in the dielectric spectroscopy experiment, is negligible for weakly polar liquids. In contrast, the cross-correlations' term dominates over the self-correlations' term for the examined strongly polar liquid. Consequently, our studies strongly support the interpretation of the dielectric spectra nature of glass-forming liquids recently proposed by Pabst etal.

Spectroscopy of Vibronically Coupled and Duschinskcally Rotated Polyatomic Molecules.

Electron-vibration coupling (or vibronic coupling) of polyatomic molecules in the condensed phase has received considerable attention experimentally and theoretically using linear spectroscopy and four-wave mixing techniques in an effort to probe the structure and dynamics of the system at hand. For this reason, a detailed study of vibronic coupling in harmonic polyatomic molecules featuring a greater degree of computational efficiency is presented. A full treatment of non-Condon systems whereupon linear and nonlinear Herzberg-Teller vibronic coupling and Duschinsky mixing effects in harmonic systems taking place upon electronic excitation is provided. The utilization of an exponential function to express the nuclear dependence of the electronic transition dipole moment, thereby avoiding the finite sum and eigenstate representation that is normally used in computing a non-Condon interaction, leads to a simpler electronic transition dipole moment time correlation function with rapid convergence and better numerical stability than previously reported works. A closed-form expression is obtained for the electronic transition dipole moment time correlation function of polyatomic molecules in which linear and nonlinear Herzberg-Teller vibronic coupling and Duschinsky mixing effects are accounted for. An important numerical observation regarding dealing with branch cuts, which manifest themselves as discontinuities in the function itself or its first derivative, and are often exhibited by complex-valued correlation functions, is noted and treated using the Riemann surface approach. The resultant dipole moment correlation function is in turn employed to calculate linear absorption and hole-burning signals, accounting for the aforementioned spectroscopic effects. A link between wavelets and the electronic transition dipole moment time correlation function in multidimensional harmonic systems is made in the concluding remarks.

Theory of Spin Hall Magnetoresistance from a Microscopic Perspective.

We present a theory of the spin Hall magnetoresistance of metals in contact with magnetic insulators. We express the spin mixing conductances, which govern the phenomenology of the effect, in terms of the microscopic parameters of the interface and the spin-spin correlation functions of the local moments on the surface of the magnetic insulator. The magnetic-field and temperature dependence of the spin mixing conductances leads to a rich behavior of the resistance due to an interplay between the Hanle effect and the spin mixing at the interface. We describe an unusual negative magnetoresistance originating from a nonlocal Hanle effect. Our theory provides a useful tool for understanding the experiments on heavy metals in contact with magnetic insulators of different kinds, and it enables the spin Hall magnetoresistance effect to be used as a technique to study magnetism at interfaces.

Application of Kendall’s rank function for digital image correlation

Digital image correlation (DIC) is a widely used technique for measuring the surface deformation of solid materials and structures. A new criterion, called Kendall’s rank correlation function (KRCF), has been applied to replace the traditional Pearson’s product moment correlation function (PPMCF), which is a zero-mean normalized cross-correlation criterion in essence. By comparing the rank information of the reference and target subsets, the difference between the concordant and discordant pairs is larger and their correlation is higher. Simulations and experiments show that the performance of KRCF is better than PPMCF in an environment with: (1) salt-and-pepper noise; (2) monotone nonlinear light intensity distortion; (3) a fixed bright spot; and (4) cracks.

OSNR monitoring technique based on multi-order statistical moment method and correlation function for PM-16QAM in presence of fiber nonlinearities

Abstract We propose an improved optical signal-to-noise ratio (OSNR) monitoring technique in presence of optical fiber nonlinearity-induced distortions, in which traditional multi-order statistical moments based (MOSMB) OSNR monitoring method is corrected by a calibration factor α and correlation functions between neighboring received symbols. This OSNR monitoring technique is performed for the first time in a 224-Gb/s polarization-multiplexed quadrature amplitude modulation (PM-16QAM) system. We explore relationships between α , transmission distances and channel launch powers for further convenient usage considerations. The proposed monitoring technique shows much better performances than existing OSNR monitoring techniques in highly nonlinear systems, where OSNR estimation errors are below 1 dB with actual OSNR ranging 18–28 dB and the channel launch powers reach as highly as 4 dBm and the transmission distances are up to 2000 km. Besides, this proposed technique is applicable to different modulation formats and corresponding performances are compared.

Finite-temperature infrared and Raman spectra of high-pressure hydrogen from first-principles molecular dynamics

Finite-temperature infrared and Raman spectra of theoretically proposed stable structures $C2/c$ and $Pc$ of high-pressure solid hydrogen are calculated from time correlation functions of dipole moments and polarizabilities extracted from first-principles molecular dynamics simulations. Calculated spectra are much improved compared with those obtained from density functional perturbation theory at zero temperature, which suggests the significance of finite-temperature effects in both spectra. The excellent agreement between the calculated spectra of the $C2/c$ structure and experimental results supports the theory that $C2/c$ is the structure of phase III. The high-frequency Raman vibron mode of the $Pc$ structure is also well reproduced compared with experimental spectra. However, the energy of the low-frequency Raman vibron mode of the $Pc$ structure is underestimated up to 16%. This suggests that the atomic structure of the strongly bonded layer in phase IV is well predicted, while the weakly bonded layer still differs from the real structure somehow. In addition, we find that diffusion in the weakly bonded layer of the $Pc$ structure is strong and the layer displays several features of a two-dimensional liquid.

Molecular dynamics simulation of collision-induced absorption spectra of neon-krypton mixture thin layer confined between graphite walls

Molecular dynamics (MD) simulations have been used to calculate interaction-induced absorption spectra of neon-krypton mixture confined between graphite plates. The continuous phenomenological model with parameters fitted to couple clusters (CC) quantum mechanical method has been applied to calculate collision-induced dipole moments. The collision-induced dipole moment correlation functions and its 2, 3, 4-body contributions of Ne-Kr binary mixture at three temperatures have been calculated and analyzed. The dynamics of neon and krypton atoms between graphite slabs have been investigated by the mean square displacement functions and z-profile functions. The phase separation between neon and krypton has been observed at T=100K in the direction perpendicular to the graphite surface. We have found that collision-induced absorption spectra reflect the mobility of noble gas atoms in binary mixture between graphite slabs.

Influence of hydrogen bonds and temperature on dielectric properties.

Dielectric properties are evaluated by means of molecular dynamics simulations on two model systems made up of dipolar molecules. One of them mimics methanol, whereas the other differs from the former only in the ability to form hydrogen bonds. Static dielectric properties such as the permittivity and the Kirkwood factor are evaluated, and results are analyzed by considering the distribution of relative orientations between molecular dipoles. Dipole moment-time correlation functions are also evaluated. The relevance of contributions associated with autocorrelations of molecular dipoles and with cross-correlations between dipoles belonging to different molecules has been investigated. For methanol, the Debye approximation for the overall dipole moment correlation function is not valid at room temperature. The model applies when hydrogen bonds are suppressed, but it fails upon cooling the nonassociated liquid. Important differences between relaxation times associated with dipole auto- versus cross-correlations as well as their relative relevance are at the root of the Debye model breakdown.

The Spatial Chemical Langevin Equation and Reaction Diffusion Master Equations: moments and qualitative solutions.

BackgroundIt has been established that stochastic effects play an important role in spatio-temporal biochemical networks. A popular method of representing such stochastic systems is the Reaction Diffusion Master Equation (RDME). However, simulating sample paths from the RDME can be computationally expensive, particularly at large populations. Here we investigate an uncommon, but much faster alternative: the Spatial Chemical Langevin Equation (SCLE).MethodsWe investigate moment equations and correlation functions analytically, then we compare sample paths and moments of the SCLE to the RDME and associated deterministic solutions. Sample paths are generated computationally by the Next Subvolume method (RDME) and the Euler-Maruyama method (SCLE), while a deterministic solution is obtained with an Euler method. We consider the Gray-Scott model, a well-known pattern generating system, and a predator–prey system with spatially inhomogeneous parameters as sample applications.ResultsFor linear reaction networks, it is well known that the first order moments of all three approaches match, that the RDME and SCLE match to the second moment, and that all approaches diverge at third order moments. For non-linear reaction networks, differential equations governing moments do not form a closed system, but a general moment equation can be compared term wise. All approaches match at the leading order, and the RDME and SCLE match at the second leading order. As expected, the SCLE captures many dynamics of the RDME where deterministic methods fail to represent them. However, areas of the parameter space in the Gray-Scott model exist where either the SCLE and RDME give qualitatively different predictions, or the RDME predicts patterns, while the SCLE does not.ConclusionsThe SCLE provides a fast alternative to existing methods for simulation of spatial stochastic biochemical networks, capturing many aspects of dynamics represented by the RDME. This becomes very useful in search of quantitative parameters yielding desired qualitative solutions. However, there exist parameter sets where both the qualitative and quantitative behaviour of the SCLE can differ when compared to the RDME, so care should be taken in its use for applications demanding greater accuracy.Electronic supplementary materialThe online version of this article (doi:10.1186/s12976-015-0001-6) contains supplementary material, which is available to authorized users.

Long range correlation inequalities for massless Euclidean fields

In this paper, new correlation inequalities are obtained for massless Euclidean fields on the $d$ dimensional integer lattice. Some of the inequalities have been obtained previously, in the case where the Lagrangian is a very small perturbation of a quadratic, using the renormalization group method. The results of the present paper apply provided the Lagrangian is uniformly convex. They therefore hold for the Coulomb dipole gas in which particle density can be of order $1$. The approach of the present paper is based on the methodology of Naddaf–Spencer, which relates second moment correlation functions for the Euclidean field to expectations of Green’s functions for parabolic PDE with random coefficients.

Influence of magnetic fluctuations in the magnetocaloric effect on rare-earth intermetallic compounds

A theoretical model including both crystal-field and exchange interactions that considers the effect of magnetic fluctuations is developed to evaluate the temperature dependence of the isothermal magnetic entropy changes in ferromagnetic rare-earth-based intermetallic compounds. The Green's functions are derived from their equation of motion. The magnetic moment correlation functions are determined beyond the random phase approximation by incorporating a measure of magnetic spontaneous fluctuations in a way that ensures self-consistency with regard to the fluctuation-dissipation theorem. In particular, the exact magnitude of the entropy change without magnetic moment fluctuations depends on the ratio of both the crystal-field first- and the crystal-field third-order magnetic susceptibilities at the Curie temperature, ${T}_{C}$. These theoretical predictions are compared with experimental data on cubic RM${}_{2}$ ($\mathrm{R}=\mathrm{rare}\mathrm{ }\mathrm{earth}$ and $\mathrm{M}=\mathrm{Al}$ and Ni) compounds, where the principal crystal-field and exchange parameters are well known.

Effects of concentration on structure, dielectric, and dynamic properties of aqueous NaCl solutions using a polarizable model

The study of NaCl solutions in water at finite concentration, explicitly including polarization in water molecules and ions, has been carried out by molecular dynamics simulations. A comparison of the RPOL polarizable model with the rigid SPC/E potential for water has been included. Structure obtained with the two models does not show significant differences, although some deviations in the NaNa radial distribution functions at all concentrations are observed. Dielectric properties such as total and molecular dipole moment correlation functions revealed decay times of the order of 10 ps, roughly independent of concentration. The analysis of electric conductivity by means of current-current correlation functions also included the calculation of cross terms corresponding to dipole moment-current correlations, which proved to be non-neglectable at short times and especially relevant at high concentrations (m=4 mol kg(-1)). Frequency dependent dielectric constants and conductivities have been computed and the role of cross correlations has been analyzed. In all cases both concentration and cross correlations have significant influence in the results.

Casimir-Polder effect for a plane with Chern-Simons interaction

A novel formalism for the evaluation of the Casimir-Polder potential in an arbitrary gauge of vector potentials is introduced. The ground state energy of a neutral atom in the presence of an infinite two-dimensional plane with Chern-Simons interaction is derived at zero temperature. The essential feature of the result is its dependence on the antisymmetric part of a dipole moment correlation function.

Structure and Mobility of Poly(ethylene terephthalate): A Molecular Dynamics Simulation Study

An accurate force-field has been parametrized for PET and is employed to simulate a long chain, consisting of 120 repeat units, over a wide temperature and pressure range, for long time scales. The force field has been validated against the experimental results for the pressure−volume−temperature properties, the characteristic ratio, the dipolar ratio, and the population of ethylene glycol bond conformer. In all cases the agreement with experiment is quite good. The glass transition temperature is calculated very accurately as a function of pressure. The local dynamics of the chain has been investigated by calculating phenylene reorientation, collective dipole moment, and individual dipole moment correlation functions. The calculated relaxation times for collective dipole moment and phenylene reorientation correlation functions show activation energies close to the corresponding experimental β-relaxation value. Local translational mobilities of phenylene groups in the backbone and end phenylene groups have also been investigated. It is concluded that the end groups have much higher mobility than the polymer backbone, and increasing the distance from the chain ends decreases the mobility dramatically. The long-time asymptotic slope of chain displacement at temperatures higher than the glass transition temperature is around 0.65 in close agreement with Rouse model. On the other hand at the glassy state, the polymer segments perform very restricted movements in the cages formed by their surrounding segments.

Empirical relaxation function and spectral density for underdamped vibrations at low temperatures

A new relaxation function which accounts for electronic dephasing (electronic phase loss and excited state lifetime) is presented, whose applicability for underdamped motion at low temperatures is examined in detail. This new empirical relaxation function phi(t) yields linear and nonlinear spectral/temporal profiles that render accurate dephasing time in the underdamped regime. The relaxation function phi(t) is normally expressed in terms of the coupling functions M(j) (') and M(j) (") on which the time evolution of the vibrational modes in question depends. The corresponding spectral density, which is a central quantity in probing dynamics, is derived and compared to that of the multimode Brownian oscillator model. Derivation and discussion of the new position and momentum autocorrelation functions in terms of our new spectral density are presented. While the position autocorrelation function plays a key role in representing solvation structure in polar or nonpolar medium, the momentum correlation function projects out the molecular vibrational motion. The Liouville space generating function (LGF) for harmonic and anharmonic systems is expressed in terms of our new empirical phi(t) and spectral density, leading to more physical observation. Several statistical quantities are derived from the position and momentum correlation function, which in turn contribute to LGF. Model calculations reflecting the infinite population decay in the low temperature limit in linear and nonlinear spectroscopic signals are presented. The herein quantum dipole moment correlation function is compared to that derived in [M. Toutounji, J. Chem. Phys. 118, 5319 (2003)] using mixed quantum-classical dynamics framework, yielding reasonable results, in fact identical at higher temperatures. The results herein are found to be informative, useful, and consistent with experiments.

The Kondo Lattice Model in Infinite Dimensions: I. Formalism

A Green-function formalism for the Kondo lattice model is presented, which is designed to be combined with the dynamical mean-field theory. With use of Wick's theorem only for conduction electrons, dynamical quantities are represented in terms of the t-matrix and its two-particle generalizations. By taking the high-frequency limit of the t-matrix with respect to a part of the fermion frequencies, one obtains dynamical correlation functions of localized moments. Explicit examples of calculational steps are provided with use of the continuous-time quantum Monte Carlo method.