Cumulant Expansion Research Articles

Equation-of-Motion Coupled-Cluster Cumulant Green's Function for Excited States and X-Ray Spectra.

Green’s function methods provide a robust, general framework within many-body theory for treating electron correlation in both excited states and x-ray spectra. Conventional methods using the Dyson equation or the cumulant expansion are typically based on the GW self-energy approximation. In order to extend this approximation in molecular systems, a non-perturbative real-time coupled-cluster cumulant Green’s function approach has been introduced, where the cumulant is obtained as the solution to a system of coupled first order, non-linear differential equations. This approach naturally includes non-linear corrections to conventional cumulant Green’s function techniques where the cumulant is linear in the GW self-energy. The method yields the spectral function for the core Green’s function, which is directly related to the x-ray photoemission spectra (XPS) of molecular systems. The approach also yields very good results for binding energies and satellite excitations. The x-ray absorption spectrum (XAS) is then calculated using a convolution of the core spectral function and an effective, one-body XAS. Here this approach is extended to include the full coupled-cluster-singles (CCS) core Green’s function by including the complete form of the non-linear contributions to the cumulant as well as all single, double, and triple cluster excitations in the CC amplitude equations. This approach naturally builds in orthogonality and shake-up effects analogous to those in the Mahan-Noizeres-de Dominicis edge singularity corrections that enhance the XAS near the edge. The method is illustrated for the XPS and XAS of NH3.

Superradiant lasing in inhomogeneously broadened ensembles with spatially varying coupling.

Background: Theoretical studies of superradiant lasing on optical clock transitions predict a superb frequency accuracy and precision closely tied to the bare atomic linewidth. Such a superradiant laser is also robust against cavity fluctuations when the spectral width of the lasing mode is much larger than that of the atomic medium. Recent predictions suggest that this unique feature persists even for a hot and thus strongly broadened ensemble, provided the effective atom number is large enough. Methods: Here we use a second-order cumulant expansion approach to study the power, linewidth and lineshifts of such a superradiant laser as a function of the inhomogeneous width of the ensemble including variations of the spatial atom-field coupling within the resonator. Results: We present conditions on the atom numbers, the pump and coupling strengths required to reach the buildup of collective atomic coherence as well as scaling and limitations for the achievable laser linewidth. Conclusions: We show how sufficiently large numbers of atoms subject to strong optical pumping can induce synchronization of the atomic dipoles over a large bandwidth. This generates collective stimulated emission of light into the cavity mode leading to narrow-band laser emission at the average of the atomic frequency distribution. The linewidth is orders of magnitudes smaller than that of the cavity as well as the inhomogeneous gain broadening and exhibits reduced sensitivity to cavity frequency noise.

Solvent randomness and intramolecular considerations of optical responses in four-wave mixing

We determined the optical profiles of a molecular system coupled with a thermal bath in presence of intramolecular coupling. Solvent effects were explicitly considered as a random variable by modelling the non-radiative interaction with the solute. Optical susceptibilities of stochastic origin were solved through cumulant expansions in Gaussian distributions considering a white noise as a correlation function. We examined the behaviour of these properties for the solvent noise parameter and intramolecular coupling parameters. Our results show that the intensity of the nonlinear optical properties decreases with the insertion of either of the two effects considered. Finally, other considerations related to the determination of relaxation times from the symmetry properties of the optical responses in frequency space are presented.

Effect of the non-ideal axial ratio c/a on anharmonic EXAFS oscillation of h.c.p. crystals.

The temperature and wavenumber dependence of the extended X-ray absorption fine-structure (EXAFS) oscillation of hexagonal close-packed (h.c.p.) crystals have been calculated and analyzed under the effect of the non-ideal axial ratio c/a. The anharmonic EXAFS oscillation is presented in terms of the Debye-Waller factor using the cumulant expansion approach up to the fourth order. An effective calculation model is expanded and developed from the many-body perturbation approach and correlated Debye model using the anharmonic effective potential. This potential, depending on the non-ideal axial ratio c/a, is obtained from the first-shell near-neighbor contribution approach. A suitable analysis procedure is performed by evaluating the influence of EXAFS cumulants on the phase shift and amplitude reduction of the anharmonic EXAFS oscillation. The numerical results for crystalline zinc are found to be in good agreement with those obtained from experiments and other theoretical methods at various temperatures. The obtained results show that the present theoretical model is essential and effective in improving the accuracy for analyzing the experimental data of anharmonic EXAFS signals of h.c.p. crystals with a non-ideal axial ratio c/a.

Using Element Birth and Death Technique in Modeling Cumulative Molded Substrate Expansion before Singulation

Semiconductor packages are commonly assembled and molded in array format on a substrate strip before they are singulated into individual units. However, cumulative substrate expansion causes problems such as machine vacuum error or misaligned cut during singulation if the substrate expansion is not factored in. This study uses element birth and death technique in modeling the overall expansion of the molded substrate strip so that the predicted expansion could be considered in the singulation tooling design offsets. The expansion of the substrate was modeled with the different package assembly processes and thermal conditions. Modeling results showed that there is a cumulative increase in the length of the substrate as it passes through the different processes. The results are in agreement with actual substrate expansion prior to package singulation. This would not be captured when simulation is done only for the molded substrate without considering the cumulative contribution of the preceding processes. With the element birth and death technique in process-based thermomechanical modeling, substrate expansion could already be forecasted, and package assembly problems avoided.

Comparative analysis of signal models for microscopic fractional anisotropy estimation using q-space trajectory encoding

Microscopic diffusion anisotropy imaging using diffusion-weighted MRI and multidimensional diffusion encoding is a promising method for quantifying clinically and scientifically relevant microstructural properties of neural tissue. Several methods for estimating microscopic fractional anisotropy (µFA), a normalized measure of microscopic diffusion anisotropy, have been introduced but the differences between the methods have received little attention thus far. In this study, the accuracy and precision of µFA estimation using q-space trajectory encoding and different signal models were assessed using imaging experiments and simulations. Three healthy volunteers and a microfibre phantom were imaged with five non-zero b-values and gradient waveforms encoding linear and spherical b-tensors. Since the ground-truth µFA was unknown in the imaging experiments, Monte Carlo random walk simulations were performed using axon-mimicking fibres for which the ground truth was known. Furthermore, parameter bias due to time-dependent diffusion was quantified by repeating the simulations with tuned waveforms, which have similar power spectra, and with triple diffusion encoding, which, unlike q-space trajectory encoding, is not based on the assumption of time-independent diffusion. The truncated cumulant expansion of the powder-averaged signal, gamma-distributed diffusivities assumption, and q-space trajectory imaging, a generalization of the truncated cumulant expansion to individual signals, were used to estimate µFA. The gamma-distributed diffusivities assumption consistently resulted in greater µFA values than the second order cumulant expansion, 0.1 greater when averaged over the whole brain. In the simulations, the generalized cumulant expansion provided the most accurate estimates. Importantly, although time-dependent diffusion caused significant overestimation of µFA using all the studied methods, the simulations suggest that the resulting bias in µFA is less than 0.1 in human white matter.

Expansion series of the pairwise velocity generating function and its implications on redshift space distortion modeling

The pairwise velocity generating function G has a deep connection with both the pairwise velocity probability distribution function and modeling of redshift space distortion (RSD). Its implementation into RSD modeling is often faciliated by expansion into a series of pairwise velocity moments . Motivated by the logrithmic transformation of the cosmic density field, we investigate an alternative expansion into series of pairwise velocity cumulants . We numerically evaluate the convergence rate of the two expansions, with three 30723 particle simulations of the CosmicGrowth N-body simulation series. (1) We find that the cumulant expansion performs significantly better, for all the halo samples and redshifts investigated. (2) For modeling RSD at k ∥ < 0.1h Mpc−1, including only the n = 1,2 cumulants is sufficient. (3) But for modeling RSD at k ∥ = 0.2h Mpc−1, we need and only need the n = 1,2,3,4 cumulants. These results provide specific requirements on RSD modeling in terms of m-th order statistics of the large-scale structure.

The right and role of critiquing the contemporary patchwork of protection

The right and role of critiquing the contemporary patchwork of protection

Description of Resonant Inelastic X-Ray Scattering in Correlated Metals

To fully capitalize on the potential and versatility of resonant inelastic x-ray scattering (RIXS), it is essential to develop the capability to interpret different RIXS contributions through calculations, including the dependence on momentum transfer, from first-principles for correlated materials. Toward that objective, we present new methodology for calculating the full RIXS response of a correlated metal in an unbiased fashion. Through comparison of measurements and calculations that tune the incident photon energy over a wide portion of the Fe L$_3$ absorption resonance of the example material BaFe$_2$As$_2$, we show that the RIXS response in BaFe$_2$As$_2$ is dominated by the direct channel contribution, including the Raman-like response below threshold, which we explain as a consequence of the finite core-hole lifetime broadening. Calculations are initially performed within the first-principles Bethe-Salpeter framework, which we then significantly improve by convolution with an effective spectral function for the intermediate-state excitation. We construct this spectral function, also from first-principles, by employing the cumulant expansion of the Green's function and performing a real-time time dependent density functional theory calculation of the response of the electronic system to the perturbation of the intermediate-state excitation. Importantly, this allows us to evaluate the indirect RIXS response from first-principles, accounting for the full periodicity of the crystal structure and with dependence on the momentum transfer.

Superradiant lasing in inhomogeneously broadened ensembles with spatially varying coupling

Background: Theoretical studies of superradiant lasing on optical clock transitions predict a superb frequency accuracy and precision closely tied to the bare atomic linewidth. Such a superradiant laser is also robust against cavity fluctuations when the spectral width of the lasing mode is much larger than that of the atomic medium. Recent predictions suggest that this unique feature persists even for a hot and thus strongly broadened ensemble, provided the effective atom number is large enough. Methods: Here we use a second-order cumulant expansion approach to study the power, linewidth and lineshifts of such a superradiant laser as a function of the inhomogeneous width of the ensemble including variations of the spatial atom-field coupling within the resonator. Results: We present conditions on the atom numbers, the pump and coupling strengths required to reach the buildup of collective atomic coherence as well as scaling and limitations for the achievable laser linewidth. Conclusions: We show how sufficiently large numbers of atoms subject to strong optical pumping can induce synchronization of the atomic dipoles over a large bandwidth. This generates collective stimulated emission of light into the cavity mode leading to narrow-band laser emission at the average of the atomic frequency distribution. The linewidth is orders of magnitudes smaller than that of the cavity as well as the inhomogeneous gain broadening and exhibits reduced sensitivity to cavity frequency noise.

Gaussian Local Phase Approximation in a Cylindrical Tissue Model

In NMR or MRI, the measured signal is a function of the accumulated magnetization phase inside the measurement voxel, which itself depends on microstructural tissue parameters. Usually the phase distribution is assumed to be Gaussian and higher-order moments are neglected. Under this assumption, only thex-component of the total magnetization can be described correctly, and information about the local magnetization and they-component of the total magnetization is lost. The Gaussian Local Phase (GLP) approximation overcomes these limitations by considering the distribution of the local phase in terms of a cumulant expansion. We derive the cumulants for a cylindrical muscle tissue model and show that an efficient numerical implementation of these terms is possible by writing their definitions as matrix differential equations. We demonstrate that the GLP approximation with two cumulants included has a better fit to the true magnetization than all the other options considered. It is able to capture both oscillatory and dampening behavior for different diffusion strengths. In addition, the introduced method can possibly be extended for models for which no explicit analytical solution for the magnetization behavior exists, such as spherical magnetic perturbers.

Proteinase-activated receptor-2 (PAR2) on blood pressure and electrolyte handling in the late pregnant rat.

What is the central question of this study? Pregnancy requires marked renal sodium and potassium retention and cumulative plasma volume expansion, in the setting of reduced blood pressure. Research in male rodents has shown that activation of PAR2 can produce peripheral vasodilatation, stimulate renal sodium chloride reabsorption and inhibit renal potassium secretion. Here, we investigate PAR2 activation in virgin and normal pregnant rats. What is the main finding and its importance? PAR2 expression and sensitivity to activation are increased in pregnancy. This implicates a possible role for PAR2 in supporting the renal/vascular adaptations of pregnancy required for normal maternal plasma volume expansion. A healthy pregnancy involves renal and systemic haemodynamic adaptations, which allow renal sodium and potassium retention and cumulative plasma volume expansion, accompanied by a decline in blood pressure attributable to a reduction in the total peripheral vascular resistance. When these adaptations do not occur, pregnancy is compromised. The mechanisms permitting these opposing adaptations are largely unknown. Research in male rodents has shown that activation of PAR2 can produce peripheral vasodilatation, stimulate renal sodium chloride reabsorption and inhibit renal potassium secretion. Here, we investigate PAR2 activation in female virgin and normal late pregnant (LP) rats. We measured the mRNA expression of PAR2 in the renal cortex, outer medulla and inner medulla of virgin and LP rats using quantitative real-time PCR. We also measured in vivo blood pressure, natriuretic and kaliuretic responses to PAR2-activating peptide (SLIGRL-NH2 ) in anaesthetized virgin and LP rats. We found that PAR2 mRNA was increased in the inner medulla of LP rats. We also found that LP rats had larger decreases in blood pressure and increases in net sodium retention compared with virgin rats. These findings suggest that pregnancy enhances sensitivity to the blood pressure-lowering and sodium-retaining effects of PAR2.

The Lyα forest flux correlation function: a perturbation theory perspective

The Lyα forest provides one of the best means of mapping large-scale structure at high redshift, including our tightest constraint on the distance-redshift relation before cosmic noon. We describe how the large-scale correlations in the Lyα forest can be understood as an expansion in cumulants of the optical depth field, which itself can be related to the density field by a bias expansion. This provides a direct connection between the observable and the statistics of the matter fluctuations which can be computed in a systematic manner. We discuss the way in which complex, small-scale physics enters the predictions, the origin of the much-discussed velocity bias and the `renormalization' of the large-scale bias coefficients. Our calculations are within the context of perturbation theory, but we also make contact with earlier work using the peak-background split. Using the structure of the equations of motion we demonstrate, to all orders in perturbation theory, that the large-scale flux power spectrum becomes the linear spectrum times the square of a quadratic in the cosine of the angle to the line of sight. Unlike the case of galaxies, both the isotropic and anisotropic pieces receive contributions from small-scale physics.

Rapid microscopic fractional anisotropy imaging via an optimized linear regression formulation

Water diffusion anisotropy in the human brain is affected by disease, trauma, and development. Microscopic fractional anisotropy (μFA) is a diffusion MRI (dMRI) metric that can quantify water diffusion anisotropy independent of neuron fiber orientation dispersion. However, there are several different techniques to estimate μFA and few have demonstrated full brain imaging capabilities within clinically viable scan times and resolutions. Here, we present an optimized spherical tensor encoding (STE) technique to acquire μFA directly from the 2nd order cumulant expansion of the powder averaged dMRI signal obtained from direct linear regression (i.e. diffusion kurtosis) which requires fewer powder-averaged signals than other STE fitting techniques and can be rapidly computed. We found that the optimal dMRI parameters for white matter μFA imaging were a maximum b-value of 2000 s/mm2 and a ratio of STE to LTE tensor encoded acquisitions of 1.7 for our system specifications. We then compared two implementations of the direct regression approach to the well-established gamma model in 4 healthy volunteers on a 3 Tesla system. One implementation used mean diffusivity (D) obtained from a 2nd order fit of the cumulant expansion, while the other used a linear estimation of D from the low b-values. Both implementations of the direct regression approach showed strong linear correlations with the gamma model (ρ = 0.97 and ρ = 0.90) but mean biases of −0.11 and − 0.02 relative to the gamma model were also observed, respectively. All three μFA measurements showed good test-retest reliability (ρ ≥ 0.79 and bias = 0). To demonstrate the potential scan time advantage of the direct approach, 2 mm isotropic resolution μFA was demonstrated over a 10 cm slab using a subsampled data set with fewer powder-averaged signals that would correspond to a 3.3-min scan. Accordingly, our results introduce an optimization procedure that has enabled nearly full brain μFA in only several minutes.

Analysis of EXAFS oscillation of FCC crystals using classical anharmonic correlated Einstein model

In this work, we analyze the extended X-ray absorption fine structure (EXAFS) oscillation of face-centered cubic crystals based on the classical anharmonic correlated Einstein (CACE) model and suitable analysis procedure. The calculation of EXAFS cumulants is performed by the CACE model, where thermodynamic parameters are derived from the anharmonic effective potential that depends on the crystal structure type and obtained using the first shell near-neighbor contribution approach. Temperature and wavenumber dependence of the anharmonic EXAFS oscillation is analyzed via evaluating the contributions of the cumulants to the phase shift and amplitude reduction, in which the anharmonic EXAFS oscillation is presented in terms of the Debye-Waller factor up to the fourth-order using the cumulant expansion approach. The numerical results for crystalline nickel are found to be in good agreement with those obtained from the experiments and other theoretical methods at various temperatures. This model is very effective for analyzing experimental EXAFS data of the anharmonic EXAFS signals above the correlated Einstein temperature.

Intramolecular O-H⋯S hydrogen bonding in threefold symmetry: Line broadening dynamics from ultrafast 2DIR-spectroscopy and ab initio calculations.

The dynamics of intramolecular hydrogen-bonding involving sulfur atoms as acceptors is studied using two-dimensional infrared (2DIR) spectroscopy. The molecular system is a tertiary alcohol whose donating hydroxy group is embedded in a hydrogen-bond potential with torsional C3-symmetry about the carbon-oxygen bond. The linear and 2DIR-spectra recorded in the OH-stretching region of the alcohol can be simulated very well using Kubo's line shape theory based on the cumulant expansion for evaluating the linear and nonlinear optical response functions. The correlation function for OH-stretching frequency fluctuations reveals an ultrafast component decaying with a time constant of 700 fs, which is in line with the apparent decay of the center line slopes averaged over absorption and bleach/emission signals. In addition, a quasi-static inhomogeneity is detected, which prevents the 2DIR line shape to fully homogenize within the observation window of 4 ps. The experimental data were then analyzed in more detail using a full ab initio approach that merges time-dependent structural information from classical molecular dynamics (MD) simulations with an OH-stretching frequency map derived from density functional theory (DFT). The latter method was also used to obtain a complementary transition dipole map to account for non-Condon effects. The 2DIR-spectra obtained from the MD/DFT method are in good agreement with the experimental data at early waiting delays, thereby corroborating an assignment of the fast decay of the correlation function to the dynamics of hydrogen-bond breakage and formation.

Platelet Count Recovery after Endovascular Aneurysm Repair for Abdominal Aortic Aneurysm.

Objective: To find a new predictor of endoleak (EL) and aneurysm sac expansion after endovascular aneurysm repair (EVAR), we evaluated the platelet count recovery (PCR) process after EVAR.Materials and Methods: Two hundred five patients treated with elective EVAR from 2007 to 2015 were retrospectively analyzed. We compared the platelet count ratio until postoperative day (POD) 7 to the presurgical baseline between patients with and without persistent EL (≥ 6 months). Subsequently, we calculated the optimal platelet count ratio for distinguishing persistent EL using receiver-operating characteristics analysis. A platelet count ratio on POD7 ≥118% was defined as the PCR. We evaluated the PCR’s influence on the cumulative aneurysm sac expansion rate.Results: The average platelet count ratio on POD7 rose above baseline (112%), and the ratio was attenuated by persistent EL (103%). Of 205 patients, 126 (61%) were assigned to the disturbed PCR group (PCR(−) group). Cumulative aneurysm sac expansion rate was higher in the PCR(−) group than the PCR(+) group (34.4% vs. 12.8% in 5 years, p=0.01).Conclusion: Disturbed PCR after EVAR may be associated with ELs and eventual aneurysm sac expansion.

Contributions to Developments of Photoelectron Spectroscopy and X-ray Absorption Fine Structure Applied to Materials Studies

This work reviews the contributions of author to the developments and applications of Photoelectron Spectroscopy (PES) and X-ray Absorption Fine Structure (XAFS) to materials studies. Focusing on Angle resolved PES (ARPES) the energy distribution is discussed for angle-resolved photoemission from valence bands of single crystals. The important influence of the spectrometer angle of acceptance on the results of X-ray PES (XPS) is investigated in detail. The Plane Density of States (PDOS) is introduced as a new property of the electronic structure. Most meaningful contributions to XAFS consist of the developments of multiple-scattering and anharmonic XAFS theory. Anharmonic correlated Einstein model (ACEM) and anharmonic correlated Debye model (ACDM) have been derived to obtain Debye-Waller factors (DWF) presented in terms of cumulant expansion which describe the thermodynamic properties and anharmonic effects in XAFS of substances contributing to their accurate structural determination. The anharmonic effective potential (AEP) procedure and first shell near neighbor contributions approach have developed to include many-body effects in the one-dimensional model by a simple measure. Based on DWFs a thermodynamic lattice theory has been derived for studying melting curve and eutectic points of binary alloys. Several applications of the derived methods are performed and the good agreement of the calculated results with experiment illustrate the advantages and efficiencies of the achieved developments.

Gaussian accelerated molecular dynamics (GaMD): principles and applications.

Gaussian accelerated molecular dynamics (GaMD) is a robust computational method for simultaneous unconstrained enhanced sampling and free energy calculations of biomolecules. It works by adding a harmonic boost potential to smooth biomolecular potential energy surface and reduce energy barriers. GaMD greatly accelerates biomolecular simulations by orders of magnitude. Without the need to set predefined reaction coordinates or collective variables, GaMD provides unconstrained enhanced sampling and is advantageous for simulating complex biological processes. The GaMD boost potential exhibits a Gaussian distribution, thereby allowing for energetic reweighting via cumulant expansion to the second order (i.e., "Gaussian approximation"). This leads to accurate reconstruction of free energy landscapes of biomolecules. Hybrid schemes with other enhanced sampling methods, such as the replica exchange GaMD (rex-GaMD) and replica exchange umbrella sampling GaMD (GaREUS), have also been introduced, further improving sampling and free energy calculations. Recently, new "selective GaMD" algorithms including the ligand GaMD (LiGaMD) and peptide GaMD (Pep-GaMD) enabled microsecond simulations to capture repetitive dissociation and binding of small-molecule ligands and highly flexible peptides. The simulations then allowed highly efficient quantitative characterization of the ligand/peptide binding thermodynamics and kinetics. Taken together, GaMD and its innovative variants are applicable to simulate a wide variety of biomolecular dynamics, including protein folding, conformational changes and allostery, ligand binding, peptide binding, protein-protein/nucleic acid/carbohydrate interactions, and carbohydrate/nucleic acid interactions. In this review, we present principles of the GaMD algorithms and recent applications in biomolecular simulations and drug design.

Waiting Cost Based Long-Run Network Investment Decision-Making Under Uncertainty

Traditional system investment decision is costly and hard to reverse. This is aggravated by uncertainties from flexible load and renewables (FLR), which impact the accuracy of network investment decisions and could trigger a high asset risk. Thus, system operators have the incentive to postpone network reinforcement, and `wait and see' whether the request of investment can be reduced or delayed with new information. This paper proposes a novel method to evaluate network investment horizon deferral based on the trade-off between waiting profit and waiting cost under FLR uncertainties. Although deferring investment leads to waiting cost, it is worthy to wait if the cost is smaller than the waiting profits. To capture the impact of FLR uncertainties on system investment, nodal uncertainties are converted into branch flow uncertainties based on a combined cumulant and Gram-Charlier expansion method. The waiting cost is quantified by the options' cost based on real options method and waiting profit is from asset present value reduction due to the deferral. Thus, by paying waiting cost, current investment cost can be reserved until uncertainties are reduced to an acceptable level. The waiting time is evaluated by Sharp ratio and expected return, determined by the waiting cost and uncertainty level. The results show that paying waiting cost is an economical way to reduce the impact of uncertainty and avoid hastily investment.