Moment Expansion Research Articles

Moments of the Boltzmann collision operator for Coulomb interactions

Exact moments of the Boltzmann collision operator are calculated in the irreducible Hermitian moment expansion written in terms of the random-velocity variable of each species. The formulas are presented in closed, algebraic form and can be straightforwardly implemented in computer algebra systems. They are valid for two arbitrary masses, temperatures, and flow velocities, and hence include all other existing results derived for distribution functions expanded with respect to reference states of one temperature and flow velocity. In comparison, the Landau collisional moments are good approximations for large Coulomb logarithm and small relative flow velocity, but they fail to predict the correct behavior of most collisional moments for large relative flow even for weakly coupled plasmas.

Improving the accuracy and efficiency of quantum connected moments expansions * *This manuscript has been authored by UT-Battelle, LLC, under Contract No. DE-AC0500OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce

The still-maturing noisy intermediate-scale quantum technology faces strict limitations on the algorithms that can be implemented efficiently. In the realm of quantum chemistry, the variational quantum eigensolver (VQE) algorithm has become ubiquitous, with many variations. Alternatively, a promising new avenue has been unraveled by the quantum variants of techniques grounded on expansions of the moments of the Hamiltonian, notably the connected moments expansion (CMX) and the Peeters–Devreese–Soldatov (PDS) energy functional. Common to those approaches is that, upon preparing an approximate ground state used to compute the necessary moments, the accuracy of the estimated ground state energy depends on the degree of overlap between the prepared state and the true ground state. Thus, we use the ADAPT-VQE algorithm to test shallow circuit construction strategies for the purpose of increasing the overlap with the exact ground state, validated by the sizable accuracy improvement herein reported in the PDS and CMX ground state energies. We also show that we can take advantage of the fact that the terms to be measured are highly recurring in different moments, incurring a substantial reduction in the number of necessary measurements. By coupling this measurement caching with a threshold that determines whether a given term is to be measured based on its associated scalar coefficient, we observe a further reduction in the number of circuit implementations while allowing for tunable accuracy.

Is Externally Corrected Coupled Cluster Always Better Than the Underlying Truncated Configuration Interaction?

The short answer to the question in the title is "no". We identify classes of truncated configuration interaction (CI) wave functions for which the externally corrected coupled-cluster (ec-CC) approach using the three-body (T3) and four-body (T4) components of the cluster operator extracted from CI does not improve the results of the underlying CI calculations. Implications of our analysis, illustrated by numerical examples, for the ec-CC computations using truncated and selected CI methods are discussed. We also introduce a novel ec-CC approach using the T3 and T4 amplitudes obtained with the selected CI scheme abbreviated as CIPSI, correcting the resulting energies for the missing T3 correlations not captured by CIPSI with the help of moment expansions similar to those employed in the completely renormalized CC methods.

Variational quantum solver employing the PDS energy functional

Recently a new class of quantum algorithms that are based on the quantum computation of the connected moment expansion has been reported to find the ground and excited state energies. In particular, the Peeters-Devreese-Soldatov (PDS) formulation is found variational and bearing the potential for further combining with the existing variational quantum infrastructure. Here we find that the PDS formulation can be considered as a new energy functional of which the PDS energy gradient can be employed in a conventional variational quantum solver. In comparison with the usual variational quantum eigensolver (VQE) and the original static PDS approach, this new variational quantum solver offers an effective approach to navigate the dynamics to be free from getting trapped in the local minima that refer to different states, and achieve high accuracy at finding the ground state and its energy through the rotation of the trial wave function of modest quality, thus improves the accuracy and efficiency of the quantum simulation. We demonstrate the performance of the proposed variational quantum solver for toy models, H2 molecule, and strongly correlated planar H4 system in some challenging situations. In all the case studies, the proposed variational quantum approach outperforms the usual VQE and static PDS calculations even at the lowest order. We also discuss the limitations of the proposed approach and its preliminary execution for model Hamiltonian on the NISQ device.

Clinical Observation of Intraosseous Anesthesia in Percutaneous Kyphoplasty.

Objective Percutaneous kyphoplasty (PKP) is an effective minimally invasive technique in spine surgery in recent years. General anesthesia and local anesthesia are the main ways of anesthesia in PKP, and epidural anesthesia is also applied to PKP to some extent. However, all these three anesthetic methods have their respective advantages and disadvantages. It is essential to compare and evaluate the effects of different anesthesia methods on PKP for treating spinal fractures. Method A total of 45 patients (53 vertebral bodies were included) were divided into two groups. Group A included 24 patients (29 vertebral bodies) with an average of 71 years old and Group B included 21 patients (24 vertebral bodies) with an average of 74 years old. Visual analogue scale (VAS) scores were recorded preoperatively; balloon expansion and bone cement injection were conducted intraoperatively. Then, they were recorded immediately after operation, 6 h postoperatively, to assess the pain level of the patient. Moreover, hospitalization time (days), operation duration (minutes), and bone cement injection amount (mL) had also been recorded. Results There was no significant difference in preoperative general information and VAS score. However, the VAS scores were statistically significant at both the moment of balloon expansion and injection of bone cement. At the moment of immediate postoperation, the VAS scores showed no statistically significant difference, while it showed a statistically significant difference 6 h postoperatively. Conclusion The anesthesia method by injection of 1% lidocaine hydrochloride (5 ml) into vertebral body can effectively relieve patients' pain in intraoperation and postoperation.

Transmissibility Enhanced Inverse Chatter Stability Solution

Abstract The structural dynamics of a machine tool at the tool center point characterizes its vibration response and machining stability which affects productivity. The dynamics are mostly dominated by the spindle-holder-tool assembly whose main vibration mode can change during machining due to centrifugal forces, thermal expansion, and gyroscopic moments generated at high spindle speeds. This paper proposes the identification of the spindle's in-process modal parameters: natural frequency, damping ratio and modal constant, by using a limited number of vibration transmissibility and critical chatter stability measurements. The classical inverse stability solution, which tunes the modal parameters to minimize prediction errors in chatter stability limits, is augmented with vibration transmissibility under two methods: (1) transmissibility-enhanced inverse stability solution: the modal parameters are updated to minimize prediction errors in chatter stability, and vibration transmissibility; (2) artificial neural network (ANN)-integrated inverse stability solution: the ANN uses vibration transmissibility to estimate the natural frequency and damping ratio, such that the inverse stability solution only needs to identify the modal constant. While both methods are experimentally validated, it is shown that the transmissibility-enhanced inverse stability solution is a more effective approach than the time-consuming ANN alternative for the estimation of in-process spindle dynamics.

A minimal power-spectrum-based moment expansion for CMB B-mode searches

The characterization and modeling of polarized foregrounds has become a critical issue in the quest for primordial B-modes. A typical method to proceed is to factorize and parametrize the spectral properties of foregrounds and their scale dependence (i.e. assuming that foreground spectra are well described everywhere by their sky average). Since in reality foreground properties vary across the Galaxy, this assumption leads to inaccuracies in the model that manifest themselves as biases in the final cosmological parameters (in this case the tensor-to-scalar ratio r). This is particularly relevant for surveys over large fractions of the sky, such as the Simons Observatory (SO), where the spectra should be modeled over a distribution of parameter values. Here we propose a method based on the existing “moment expansion” approach to address this issue in a power-spectrum-based analysis that is directly applicable in ground-based multi-frequency data. Additionally, the method uses only a small set of parameters with simple physical interpretation, minimizing the impact of foreground uncertainties on the final B-mode constraints. We validate the method using SO-like simulated observations, recovering an unbiased estimate of the tensor-to-scalar ratio r with standard deviation σ(r) ≃ 0.003, compatible with official forecasts. When applying the method to the public BICEP2/Keck data, we find an upper bound r < 0.06 (95% C.L.), compatible with the result found by BICEP2/Keck when parametrizing spectral index variations through a scale-independent frequency decorrelation parameter. We also discuss the formal similarities between the power spectrum-based moment expansion and methods used in the analysis of CMB lensing.

Oil and Financialization: Another Relation

ABSTRACT The conception of financialization and the impacts of the oil market will be presented in this work from an alternative perspective. Financialization will not be analyzed as a dominance of finance over industry, as if these two sides of the productive process were dissociated. Financialization will be understood as a moment of expansion of a mechanism of domination, reaching not only the state-form and enterprise, but also the own constitution of the social being as an “individual capitalist,” being part of the process of constitution of form-value. Oil, from production to the market, cannot be seen only in a reduced view of its high incomes. Oil must be understood as a social relationship. Oil from the 1980s onwards became one of the central elements of support for the US dollar, therefore, of support for the international monetary system. In addition to this new social role of sustaining the international currency that oil now has, this commodity also incorporates a determined form of social relation through its imposition as an energy source. Therefore, the main purpose of this paper is to show how both financialization and recent developments in the oil market are part of the actual constellation of the forms of capitalist social relations.

Redshift space power spectrum beyond Einstein-de Sitter kernels

We develop a framework to compute the redshift space power spectrum (PS), with kernels beyond Einstein-de Sitter (EdS), that can be applied to a wide variety of generalized cosmologies. We build upon a formalism that was recently employed for standard cosmology in Chen, Vlah & White (2020), and utilize an expansion of the density-weighted velocity moment generating function that explicitly separates the magnitude of the k-modes and their angle to the line-of-sight direction dependencies. We compute the PS for matter and biased tracers to 1-loop Perturbation Theory (PT) and show that the expansion has a correct infrared and ultraviolet behavior, free of unwanted divergences. We also add Effective Field Theory (EFT) counterterms, necessary to account for small-scale contributions to PT, and employ an IR-resummation prescription to properly model the smearing of the BAO due to large scale bulk flows within Standard-PT. To demonstrate the applicability of our formalism, we apply it on the ΛCDM and the Hu-Sawicki f(R) models, and compare our numerical results against the elephant suite of N-body simulations, finding very good agreement up to k = 0.27 Mpc-1 h at z = 0.5 for the first three non-vanishing Legendre multipoles of the PS. To our knowledge, the model presented in this work is the most accurate theoretical EFT-PT for modified gravity to date, being the only one that accounts for beyond linear local biasing in redshift-space. Hence, we argue our RSD modeling is a promising tool to construct theoretical templates in order to test deviations from ΛCDM using real data obtained from the next stage of cosmological surveys such as DESI and LSST.

Non-equilibrium properties of an active nanoparticle in a harmonic potential

Active particles break out of thermodynamic equilibrium thanks to their directed motion, which leads to complex and interesting behaviors in the presence of confining potentials. When dealing with active nanoparticles, however, the overwhelming presence of rotational diffusion hinders directed motion, leading to an increase of their effective temperature, but otherwise masking the effects of self-propulsion. Here, we demonstrate an experimental system where an active nanoparticle immersed in a critical solution and held in an optical harmonic potential features far-from-equilibrium behavior beyond an increase of its effective temperature. When increasing the laser power, we observe a cross-over from a Boltzmann distribution to a non-equilibrium state, where the particle performs fast orbital rotations about the beam axis. These findings are rationalized by solving the Fokker-Planck equation for the particle’s position and orientation in terms of a moment expansion. The proposed self-propulsion mechanism results from the particle’s non-sphericity and the lower critical point of the solution.

High-level coupled-cluster energetics by Monte Carlo sampling and moment expansions: Further details and comparisons.

We recently proposed a novel approach to converging electronic energies equivalent to high-level coupled-cluster (CC) computations by combining the deterministic CC(P;Q) formalism with the stochastic configuration interaction (CI) and CC Quantum Monte Carlo (QMC) propagations. This article extends our initial study [J. E. Deustua, J. Shen, and P. Piecuch, Phys. Rev. Lett. 119, 223003 (2017)], which focused on recovering the energies obtained with the CC method with singles, doubles, and triples (CCSDT) using the information extracted from full CI QMC and CCSDT-MC, to the CIQMC approaches truncated at triples and quadruples. It also reports our first semi-stochastic CC(P;Q) calculations aimed at converging the energies that correspond to the CC method with singles, doubles, triples, and quadruples (CCSDTQ). The ability of the semi-stochastic CC(P;Q) formalism to recover the CCSDT and CCSDTQ energies, even when electronic quasi-degeneracies and triply and quadruply excited clusters become substantial, is illustrated by a few numerical examples, including the F-F bond breaking in F2, the automerization of cyclobutadiene, and the double dissociation of the water molecule.

Peeling off foregrounds with the constrained moment ILC method to unveil primordial CMB B modes

ABSTRACT Galactic foregrounds are the main obstacle to observations of the cosmic microwave background (CMB) B-mode polarization. In addition to obscuring the inflationary B-mode signal by several orders of magnitude, Galactic foregrounds have non-trivial spectral signatures that are partially unknown and distorted by averaging effects along the line of sight, within the pixel/beam window, and by various analysis choices (e.g. spherical harmonic transforms and filters). Statistical moment expansion methods provide a powerful tool for modelling the effective Galactic foreground emission resulting from these averaging effects in CMB observations, while blind component separation treatments can handle unknown foregrounds. In this work, we combine these two approaches to develop a new semiblind component separation method at the intersection of parametric and blind methods, called constrained moment ILC (cMILC). This method adds several constraints to the standard ILC method to deproject the main statistical moments of the Galactic foreground emission. Applications to maps are performed in needlet space and when compared to the NILC method, this helps in significantly reducing residual foreground contamination (bias, variance, and skewness) in the reconstructed CMB B-mode map, power spectrum, and tensor-to-scalar ratio. We consider sky simulations for experimental settings similar to those of LiteBIRD and PICO, illustrating which trade-offs between residual foreground biases and degradation of the constraint on r can be expected within the new cMILC framework. We also outline several directions that require more work in preparation for the coming analysis challenges.

Comparison of explicit and mean-field models of cytoskeletal filaments with crosslinking motors.

In cells, cytoskeletal filament networks are responsible for cell movement, growth, and division. Filaments in the cytoskeleton are driven and organized by crosslinking molecular motors. In reconstituted cytoskeletal systems, motor activity is responsible for far-from-equilibrium phenomena such as active stress, self-organized flow, and spontaneous nematic defect generation. How microscopic interactions between motors and filaments lead to larger-scale dynamics remains incompletely understood. To build from motor-filament interactions to predict bulk behavior of cytoskeletal systems, more computationally efficient techniques for modeling motor-filament interactions are needed. Here, we derive a coarse-graining hierarchy of explicit and continuum models for crosslinking motors that bind to and walk on filament pairs. We compare the steady-state motor distribution and motor-induced filament motion for the different models and analyze their computational cost. All three models agree well in the limit of fast motor binding kinetics. Evolving a truncated moment expansion of motor density speeds the computation by [Formula: see text]-[Formula: see text] compared to the explicit or continuous-density simulations, suggesting an approach for more efficient simulation of large networks. These tools facilitate further study of motor-filament networks on micrometer to millimeter length scales.

Redshift-space distortions in Lagrangian perturbation theory

We present the one-loop 2-point function of biased tracers in redshift space computed with Lagrangian perturbation theory, including a full resummation of both long-wavelength (infrared) displacements and associated velocities. The resulting model accurately predicts the power spectrum and correlation function of halos and mock galaxies from two different sets of N-body simulations at the percent level for quasi-linear scales, including the damping of the baryon acoustic oscillation signal due to the bulk motions of galaxies. We compare this full resummation with other, approximate, techniques including the moment expansion and Gaussian streaming model. We discuss infrared resummation in detail and compare our Lagrangian formulation with the Eulerian theory augmented by an infrared resummation based on splitting the input power spectrum into “wiggle” and “no-wiggle” components. We show that our model is able to recover unbiased cosmological parameters in mock data encompassing a volume much larger than what will be available to future galaxy surveys. We demonstrate how to efficiently compute the resulting expressions numerically, making available a fast Python code capable of rapidly computing these statistics in both configuration and Fourier space.

A New Resonance Calculation Method Using Energy Expansion Based on a Reduced Order Model

A Resonance calculation using energy Spectrum Expansion (RSE) method is newly proposed in this paper. In this method, ultra-fine-group (UFG) spectra appearing in a resonance calculation are expanded by orthogonal bases on energy, which are extracted from the UFG spectra obtained in homogeneous geometry with various background cross sections using singular value decomposition and low-rank approximation. Namely, this method is based on the concept of a reduced order model. A neutron transport equation for flux moments (expansion coefficients) similar to the conventional one is derived and is numerically solved. This method applies to two benchmark problems in which a resonance interference effect and spatial self-shielding effect can appear. The results indicate that this method accurately predicts the reference effective cross sections and reaction rates obtained from direct UFG calculation in heterogeneous geometry.

Media architecture: Fellini’s Rimini, a town of the imagination

With this article, I would like to reflect on the role Fellini played in transforming the urban imagery of his hometown, Rimini, into something new. The idea that Fellini represents an ideal, the incarnation of a national character capable of representing twentieth-century Italy is already well known, even if not sufficiently studied. He is a director who becomes an icon of a way of being, of seeing, of imagining, which are internationally associated with a presumed national identity. The geocultural poles of this identity are Rimini, Rome and Cinecittà, and they express some antinomies rich with personal choices, of multiple belonging and full of psychological implications. The artist expresses a titanic mediation between the persistence of an ancient country and metropolitan evasions, in a negotiating process of anthropological and aesthetic tensions. In this article, I intend to analyse different moments of media expansion directly created by Fellini or born around Fellini. I will therefore try to redefine the reputation and the new public image of the native ‘borgo’ of the Italian Maestro.

Impactos da política nacional de atenção básica nas taxas de mortalidade infantil sob a ótica da estratégia de saúde da família

Este estudo buscou analisar os impactos da Política Nacional de Atenção Básica (PNAB) nas taxas de mortalidade infantil no âmbito da Estratégia de Saúde da Família (ESF). Para isso foi realizado uma revisão integrativa na Biblioteca Virtual em Saúde por meio do acesso simultâneo às bases de dados BDENF, CVSP e LILACS, utilizando os seguintes descritores: “Estratégia Saúde da Família” e “Mortalidade Infantil”. 49 publicações foram encontradas inicialmente, porém apenas oito artigos foram incluídos na análise final. Verificou-se uma redução drástica da taxa de mortalidade infantil a partir do momento de expansão da ESF pelas regiões mais carentes do Brasil, favorecendo uma queda deste indicador com consequente melhoria na qualidade da assistência à saúde e na qualidade de vida, pondo o Brasil com uma das nações de maior evolução neste âmbito, proporcionada principalmente pelas ações que a PNAB desenvolveu ao longo dos anos. Desta forma, as publicações analisadas por esta revisão demonstraram que a PNAB contribui para que as taxas de mortalidade infantil alcancem valores ainda menores, principalmente pelas ações desempenhadas pelas equipes de saúde em especial os enfermeiros.

Taylor Moment Expansion for Continuous-Discrete Gaussian Filtering

This article is concerned with Gaussian filtering in nonlinear continuous-discrete state-space models. We propose a novel Taylor moment expansion (TME) Gaussian filter, which approximates the moments of the stochastic differential equation with a temporal Taylor expansion. Differently from classical linearization or Itô-Taylor approaches, the Taylor expansion is formed for the moment functions directly and in time variable, not by using a Taylor expansion on the nonlinear functions in the model. We analyze the theoretical properties, including the positive definiteness of the covariance estimate and stability of the TME filter. By numerical experiments, we demonstrate that the proposed TME Gaussian filter significantly outperforms the state-of-the-art methods in terms of estimation accuracy and numerical stability.

Efficient analytical approach for high-pressure melting properties of iron

Abstract Iron represents the principal constituent of the Earth's core, but its high-pressure melting diagram remains ambiguous. Here we present a simple analytical approach to predict the melting properties of iron under deep-Earth conditions. In our model, anharmonic free energies of the solid phase are directly determined by the moment expansion technique in quantum statistical mechanics. This basis associated with the Lindemann criterion for a vibrational instability can deduce the melting temperature. Moreover, we correlate the thermal expansion process with the shear response to explain a discontinuity of atomic volume, enthalpy, and entropy upon melting. Our numerical calculations are quantitatively consistent with recent experiments and simulations. The obtained results would improve understanding of the Earth's structure, dynamics, and evolution.

Moment approach of the multi-species non-linear Coulomb collision operator adapted to particle-in-cell codes

In this article an approximated version of the multi-species, non-linear Coulomb collision operator is derived via the use of a truncated moment expansion of the distribution function to compute the Rosenbluth potentials. The evolution of the distribution function due to the collision operator takes the form of a Fokker–Planck equation that can be efficiently solved by a Langevin approach in the particle-in-cell (PIC) framework. This kinetic collision operator is then implemented in the global gyrokinetic PIC code ORB5 while neglecting finite Larmor effects. This collision operator ensures exact conservation of density, total momentum and energy as expected. The neoclassical physics is also successfully retrieved by the code. Numerical aspects such as the noise control and the parallelisation of the code are presented in detail.