Cumulant Expansion Research Articles

Thermodynamic Properties and Anharmonic Effects in XAFS Based on Anharmonic Correlated Debye Model Debye–Waller Factors

Thermodynamic properties and anharmonic effects in X‐ray absorption fine structure (XAFS) have been studied based on the anharmonic correlated Debye model Debye–Waller factors presented in terms of cumulant expansion. The derived analytical expressions of three first XAFS cumulants involve more information on phonon‐phonon interactions taken from integration over the first Brillouin zone. Many‐body effects are taken into account in the present one‐dimensional model based on the first shell near neighbor contributions to the vibrations between absorber and backscatterer atoms. Morse potential is assumed to describe single‐pair atomic interaction included in the derived anharmonic interatomic effective potential. The present theory can be applied to any crystal structure including complex systems. Numerical results for Cu and Ni are found to be in good agreement with experiment and with those of the other theories.

Linear and nonlinear spectroscopy from quantum master equations.

We investigate the accuracy of the second-order time-convolutionless (TCL2) quantum master equation for the calculation of linear and nonlinear spectroscopies of multichromophore systems. We show that even for systems with non-adiabatic coupling, the TCL2 master equation predicts linear absorption spectra that are accurate over an extremely broad range of parameters and well beyond what would be expected based on the perturbative nature of the approach; non-equilibrium population dynamics calculated with TCL2 for identical parameters are significantly less accurate. For third-order (two-dimensional) spectroscopy, the importance of population dynamics and the violation of the so-called quantum regression theorem degrade the accuracy of TCL2 dynamics. To correct these failures, we combine the TCL2 approach with a classical ensemble sampling of slow microscopic bath degrees of freedom, leading to an efficient hybrid quantum-classical scheme that displays excellent accuracy over a wide range of parameters. In the spectroscopic setting, the success of such a hybrid scheme can be understood through its separate treatment of homogeneous and inhomogeneous broadening. Importantly, the presented approach has the computational scaling of TCL2, with the modest addition of an embarrassingly parallel prefactor associated with ensemble sampling. The presented approach can be understood as a generalized inhomogeneous cumulant expansion technique, capable of treating multilevel systems with non-adiabatic dynamics.

Cumulant expansion for fast estimate of non-Condon effects in vibronic transition profiles

When existing, cumulants can provide valuable information about a given distribution and can in principle be used to either fully reconstruct or approximate the parent distribution function. A previously reported cumulant expansion approach for Franck–Condon profiles [Faraday Discuss., 150, 363 (2011)] is extended to describe also the profiles of vibronic transitions that are weakly allowed or forbidden in the Franck–Condon approximation (non-Condon profiles). In the harmonic approximation the cumulants of the vibronic profile can be evaluated analytically and numerically with a coherent state-based generating function that accounts for the Duschinsky effect. As illustration, the one-photon 1 1Ag → 1 1B2u UV absorption profile of benzene in the electric dipole and (linear) Herzberg–Teller approximation is presented herein for zero Kelvin and finite temperatures.

Advances in theoretical and experimental XAFS studies of thermodynamic properties, anharmonic effects and structural determination of fcc crystals

Thermodynamic properties, anharmonic effects and structural determination of fcc crystals have been studied based on the theoretical and experimental Debye–Waller factors presented in terms of cumulant expansion up to the third order, thermal expansion coefficient, X-ray absorption fine structure (XAFS) spectra and their Fourier transform magnitudes. The advances in these studies are performed by the further development of the anharmonic correlated Einstein model primary only for approximating three first XAFS cumulants into the method using that all the considered theoretical and experimental XAFS parameters have been provided based on only the calculated and measured second cumulants. The obtained cumulants describe the anharmonic effects in XAFS contributing to the accurate structural determination. Numerical results for Cu are found to be in good agreement with the experimental values extracted by using the present advanced method and with those obtained by the other measurements.

Connecting the Failure of K Theory inside and above Vegetation Canopies and Ejection–Sweep Cycles by a Large-Eddy Simulation

AbstractParameterizations of biosphere–atmosphere interaction processes in climate models and other hydrological applications require characterization of turbulent transport of momentum and scalars between vegetation canopies and the atmosphere, which is often modeled using a turbulent analogy to molecular diffusion processes. Simple flux–gradient approaches (K theory) fail for canopy turbulence, however. One cause is turbulent transport by large coherent eddies at the canopy scale, which can be linked to sweep–ejection events and bear signatures of nonlocal organized eddy motions. The K theory, which parameterizes the turbulent flux or stress proportional to the local concentration or velocity gradient, fails to account for these nonlocal organized motions. The connection to sweep–ejection cycles and the local turbulent flux can be traced back to the turbulence triple moment . In this work, large-eddy simulation is used to investigate the diagnostic connection between the failure of K theory and sweep–ejection motions. Analyzed schemes are quadrant analysis and complete and incomplete cumulant expansion methods. The latter approaches introduce a turbulence time scale in the modeling. Furthermore, it is found that the momentum flux and sensible heat flux need different formulations for the turbulence time scale. Accounting for buoyancy in stratified conditions is also deemed important in addition to accounting for nonlocal events to predict the correct momentum or scalar fluxes.

Cumulant expansion in gluon saturation and five- and six-gluon azimuthal correlations

Correlations between the momenta of the final state hadrons measured in proton or nucleus collisions contain information that sheds light on the initial conditions and evolutionary dynamics of the collision system. These correlation measurements have revealed the long-range rapidity correlations in p-p and p-Pb systems, and they have also made it possible to extract the elliptic flow coefficient from hadron correlation measurements. In this work, we calculate five- and six-gluon correlation functions in the framework of saturation physics by using superdiagrams. We also derive the cumulant expansion of the gluon correlators that is valid in the gluon saturation limit. We show that the cumulant expansion of the gluon correlators that is used for counting the number of diagrams to be calculated does not follow the standard cumulant expansion. We also explain how these findings can be used in obtaining experimentally relevant observables such as flow coefficients calculated from correlations as well as ratios of the correlation functions of different orders.

Anharmonic correlated Debye model Debye-Waller factors of metallic Copper compared to experiment and to other theories

Debye-Waller factors (DWFs) of metallic Cu (fcc crystal) in X-ray absorption fine structure (XAFS) presented in terms of cumulant expansion have been studied using the anharmonic correlated Debye model (ACDM). This ACDM is derived using the many-body perturbation approach and the anharmonic effective potential that includes the first shell near neighbor contributions to the vibration between absorber and backscatterer atoms. Analytical expressions of three first XAFS cumulants of Cu have been derived involving more information of phonon-phonon interactions taken from integration over the first Brillouin zone. Morse potential is assumed to describe the single-pair atomic interaction. Numerical results for Cu using the present ACDM show their good agreement with experiment and with those of other theories, as well as their advantage compared to those calculated using the single-pair potential.

Precision and accuracy of diffusion kurtosis estimation and the influence of b-value selection.

Diffusion kurtosis imaging (DKI) is an extension of diffusion tensor imaging that accounts for leading non-Gaussian diffusion effects. In DKI studies, a wide range of different gradient strengths (b-values) is used, which is known to affect the estimated diffusivity and kurtosis parameters. Hence there is a need to assess the accuracy and precision of the estimated parameters as a function of b-value. This work examines the error in the estimation of mean of the kurtosis tensor (MKT) with respect to the ground truth, using simulations based on a biophysical model for both gray (GM) and white (WM) matter. Model parameters are derived from densely sampled experimental data acquired in ex vivo rat brain and in vivo human brain. Additionally, the variability of MKT is studied using the experimental data. Prevalent fitting protocols are implemented and investigated. The results show strong dependence on the maximum b-value of both net relative error and standard deviation of error for all of the employed fitting protocols. The choice of b-values with minimum MKT estimation error and standard deviation of error was found to depend on the protocol type and the tissue. Protocols that utilize two terms of the cumulant expansion (DKI) were found to achieve minimum error in GM at b-values less than 1ms/μm2 , whereas maximal b-values of about 2.5ms/μm2 were found to be optimal in WM. Protocols including additional higher order terms of the cumulant expansion were found to provide higher accuracy for the more commonly used b-value regime in GM, but were associated with higher error in WM. Averaged over multiple voxels, a net average error of around 15% for both WM and GM was observed for the optimal b-value choice. These results suggest caution when using DKI generated metrics for microstructural modeling and when comparing results obtained using different fitting techniques and b-values.

Spectral line shapes in linear absorption and two-dimensional spectroscopy with skewed frequency distributions.

The effect of Gaussian dynamics on the line shapes in linear absorption and two-dimensional correlation spectroscopy is well understood as the second-order cumulant expansion provides exact spectra. Gaussian solvent dynamics can be well analyzed using slope line analysis of two-dimensional correlation spectra as a function of the waiting time between pump and probe fields. Non-Gaussian effects are not as well understood, even though these effects are common in nature. The interpretation of the spectra, thus far, relies on complex case to case analysis. We investigate spectra resulting from two physical mechanisms for non-Gaussian dynamics, one relying on the anharmonicity of the bath and the other on non-linear couplings between bath coordinates. These results are compared with outcomes from a simpler log-normal dynamics model. We find that the skewed spectral line shapes in all cases can be analyzed in terms of the log-normal model, with a minimal number of free parameters. The effect of log-normal dynamics on the spectral line shapes is analyzed in terms of frequency correlation functions, maxline slope analysis, and anti-diagonal linewidths. A triangular line shape is a telltale signature of the skewness induced by log-normal dynamics. We find that maxline slope analysis, as for Gaussian dynamics, is a good measure of the solvent dynamics for log-normal dynamics.

Temperature dependence of theoretical and experimental Debye-Waller factors, thermal expansion and XAFS of metallic Zinc

Debye-Waller factors presented in terms of cumulant expansion up to the third order, thermal expansion coefficient, X-ray absorption fine structure (XAFS) spectra and their Fourier transform magnitudes of Zn (hcp crystal) have been calculated and measured. The results have been obtained based on the quantum statistically derived method using that the calculations and measurements are necessary only for the second cumulants from which all other XAFS parameters have been provided. The many-body effects included in the present one-dimensional model are taken into account based on the first shell near neighbor contributions to the vibration between absorber and backscaterer atoms. Morse potential is assumed to describe the single-pair atomic interaction included in the anharmonic interatomic effective potential. Numerical results for Zn are found to be in good agreement with the obtained experimental data which show evident temperature dependence of the thermodynamic properties, anharmonic effects and structural parameters of the material.

Zonostrophic instability driven by discrete particle noise

The consequences of discrete particle noise for a system possessing a possibly unstable collective mode are discussed. It is argued that a zonostrophic instability (of homogeneous turbulence to the formation of zonal flows) occurs just below the threshold for linear instability. The scenario provides a new interpretation of the random forcing that is ubiquitously invoked in stochastic models such as the second-order cumulant expansion or stochastic structural instability theory; neither intrinsic turbulence nor coupling to extrinsic turbulence is required. A representative calculation of the zonostrophic neutral curve is made for a simple two-field model of toroidal ion-temperature-gradient-driven modes. To the extent that the damping of zonal flows is controlled by the ion–ion collision rate, the point of zonostrophic instability is independent of that rate.

Suppressing and Restoring the Dicke Superradiance Transition by Dephasing and Decay.

We show that dephasing of individual atoms destroys the superradiance transition of the Dicke model, but that adding individual decay toward the spin down state can restore this transition. To demonstrate this, we present a method to give an exact solution for the N atom problem with individual dephasing which scales polynomially with N. By comparing finite size scaling of our exact solution to a cumulant expansion, we confirm the destruction and restoration of the superradiance transition hold in the thermodynamic limit.

In situ study on liquid structure of Sn during Sn/Cu liquid–solid interfacial reaction by fluorescence XAFS

Fluorescence X-ray Absorption Fine Structure (XAFS) was used to in situ study the local structure around Cu atoms in liquid Sn solder during Sn/Cu liquid–solid interfacial reaction. The extended edge data were analyzed by cumulant expansion method. The results showed that both the atomic distance and the coordination number in the first shell decreased with the increase of temperature. It is an intrinsic trend that high-coordinated polyhedrons could transform into low-coordinated ones with relatively high stability in the liquid Sn solder with increasing temperature, and the high-coordinated polyhedrons always had larger atomic distance. The atomic distance in the first shell decreased with decreasing coordination number. Based on the fitting results, the proportion of Cu–Sn atomic coordination increased with rising soldering temperature from 250 to 310 °C. That is, Cu atoms preferred to form Cu–Sn interaction with Sn atoms, which promoted the nucleation and growth of Cu6Sn5 intermetallic compound at the Sn/Cu interface during soldering process.

From Hard Sphere Dynamics to the Stokes–Fourier Equations: An Analysis of the Boltzmann–Grad Limit

We derive the linear acoustic and Stokes-Fourier equations as the limiting dynamics of a system of $N$ hard spheres of diameter $\varepsilon$ in two space dimensions, when~$N\to \infty$, $\varepsilon \to 0$, $N\varepsilon =\alpha \to \infty$, using the linearized Boltzmann equation as an intermediate step. Our proof is based on Lanford's strategy \cite{lanford}, and on the pruning procedure developed in \cite{BGSR1} to improve the convergence time. The main novelty here is that uniform $L^2$ a priori estimates combined with a subtle symmetry argument provide a useful cumulant expansion describing the asymptotic decorrelation between the particles. A refined geometric analysis of recollisions is also required in order to discard the possibility of multiple recollisions.

Effect of in-vivo hepatitis B viral load suppression after interferon exposure on natural killer and T-cell responsiveness

BackgroundThere is a pressing need for new treatment strategies in chronic hepatitis B. Natural killer (NK) cells are important antiviral effectors, and are potently expanded with peginterferon alfa in chronic hepatitis B. Robust antiviral T-cell responses are crucial for resolution of this disease and can be expanded with nucleos(t)ide analogues (NAs). We assessed whether changes in the NK and T-cell pool would be altered when patients are primed with peginterferon alfa and whether these changes are modulated upon switching to sequential NAs. MethodsPeripheral blood mononuclear cells from 52 patients were analysed. 33 underwent a course of peginterferon alfa and were sampled longitudinally; 24 of them progressed to sequential NAs. 19 patients receiving de-novo NA therapy were analysed for comparison. NK cell subsets and global T cells were analysed by multicolour flow cytometry, and hepatitis B virus (HBV)-specific T cells were analysed by enzyme-linked immunospot assay and correlated with treatment outcomes. FindingsThere was cumulative expansion of CD56bright NK cells driven by peginterferon alfa, which was maintained at higher than baseline concentrations throughout subsequent sequential NAs (p=0·0039). The expansion in proliferating, functional NK cells was more pronounced after sequential NAs compared with de-novo NAs. Patients treated with peginterferon alfa progressing to sequential NAs expressed higher levels of CD69, CD62L, and CXCR3 (implicated in antifibrogenesis) than did patients on de-novo therapy. Reduction in circulating HBsAg concentrations was only achieved in patients with enhancement of NK cell interferon γ and cytotoxicity. Partial recovery of HBV-specific T cells was seen during sequential NAs after peginterferon alfa cessation. Interestingly, no difference in the magnitude of HBV-specific T-cell responses was seen in patients on sequential NAs compared with de novo NAs. InterpretationPeginterferon alfa priming expands a population of functional NK cells, with altered responsiveness to subsequent viral suppression by NAs. We have previously reported that NK cells can delete HBV-specific T cells, but our findings here suggest that the peginterferon alfa expanded NK cell pool does not exhibit this negative effect. We are investigating whether peginterferon alfa is able to protect T cells from NK cell attack, as demonstrated in a mouse model by other investigators. FundingWellcome Trust, Barts and The London Charity, National Medical Research Council Singapore.

Wave turbulence theory of elastic plates

This article presents the complete study of the long-time evolution of random waves of a vibrating thin elastic plate in the limit of small plate deformation so that modes of oscillations interact weakly. According to the wave turbulence theory a nonlinear wave system evolves in longtime creating a slow redistribution of the spectral energy from one mode to another. We derive step by step, following the method of cumulants expansion and multiscale asymptotic perturbations, the kinetic equation for the second order cumulants as well as the second and fourth order renormalization of the dispersion relation of the waves. We characterize the non-equilibrium evolution to an equilibrium wave spectrum, which happens to be the well known Rayleigh–Jeans distribution. Moreover we show the existence of an energy cascade, often called the Kolmogorov–Zakharov spectrum, which happens to be not simply a power law, but a logarithmic correction to the Rayleigh–Jeans distribution. We perform numerical simulations confirming these scenarii, namely the equilibrium relaxation for closed systems and the existence of an energy cascade wave spectrum. Both show a good agreement between theoretical predictions and numerics. We show also some other relevant features of vibrating elastic plates, such as the existence of a self-similar wave action inverse cascade which happens to blow-up in finite time. We discuss the mechanism of the wave breakdown phenomena in elastic plates as well as the limit of strong turbulence which arises as the thickness of the plate vanishes. Finally, we discuss the role of dissipation and the connection with experiments, and the generalization of the wave turbulence theory to elastic shells.

Probabilistic solution of steady-state soil water storage and plant water stress equation using cumulant expansion theory

Probabilistic solution of steady-state soil water storage and plant water stress equation using cumulant expansion theory

Gaussian Accelerated Molecular Dynamics: Theory, Implementation, and Applications.

A novel Gaussian Accelerated Molecular Dynamics (GaMD) method has been developed for simultaneous unconstrained enhanced sampling and free energy calculation of biomolecules. Without the need to set predefined reaction coordinates, GaMD enables unconstrained enhanced sampling of the biomolecules. Furthermore, by constructing a boost potential that follows a Gaussian distribution, accurate reweighting of GaMD simulations is achieved via cumulant expansion to the second order. The free energy profiles obtained from GaMD simulations allow us to identify distinct low energy states of the biomolecules and characterize biomolecular structural dynamics quantitatively. In this chapter, we present the theory of GaMD, its implementation in the widely used molecular dynamics software packages (AMBER and NAMD), and applications to the alanine dipeptide biomolecular model system, protein folding, biomolecular large-scale conformational transitions and biomolecular recognition.

Gaussian Accelerated Molecular Dynamics in NAMD.

Gaussian accelerated molecular dynamics (GaMD) is a recently developed enhanced sampling technique that provides efficient free energy calculations of biomolecules. Like the previous accelerated molecular dynamics (aMD), GaMD allows for “unconstrained” enhanced sampling without the need to set predefined collective variables and so is useful for studying complex biomolecular conformational changes such as protein folding and ligand binding. Furthermore, because the boost potential is constructed using a harmonic function that follows Gaussian distribution in GaMD, cumulant expansion to the second order can be applied to recover the original free energy profiles of proteins and other large biomolecules, which solves a long-standing energetic reweighting problem of the previous aMD method. Taken together, GaMD offers major advantages for both unconstrained enhanced sampling and free energy calculations of large biomolecules. Here, we have implemented GaMD in the NAMD package on top of the existing aMD feature and validated it on three model systems: alanine dipeptide, the chignolin fast-folding protein, and the M3 muscarinic G protein-coupled receptor (GPCR). For alanine dipeptide, while conventional molecular dynamics (cMD) simulations performed for 30 ns are poorly converged, GaMD simulations of the same length yield free energy profiles that agree quantitatively with those of 1000 ns cMD simulation. Further GaMD simulations have captured folding of the chignolin and binding of the acetylcholine (ACh) endogenous agonist to the M3 muscarinic receptor. The reweighted free energy profiles are used to characterize the protein folding and ligand binding pathways quantitatively. GaMD implemented in the scalable NAMD is widely applicable to enhanced sampling and free energy calculations of large biomolecules.

The Gaussian streaming model and convolution Lagrangian effective field theory

We update the ingredients of the Gaussian streaming model (GSM) for the redshift-space clustering of biased tracers using the techniques of Lagrangian perturbation theory, effective field theory (EFT) and a generalized Lagrangian bias expansion. After relating the GSM to the cumulant expansion, we present new results for the real-space correlation function, mean pairwise velocity and pairwise velocity dispersion including counter terms from EFT and bias terms through third order in the linear density, its leading derivatives and its shear up to second order. We discuss the connection to the Gaussian peaks formalism. We compare the ingredients of the GSM to a suite of large N-body simulations, and show the performance of the theory on the low order multipoles of the redshift-space correlation function and power spectrum. We highlight the importance of a general biasing scheme, which we find to be as important as higher-order corrections due to non-linear evolution for the halos we consider on the scales of interest to us.