Zeroth Moments Research Articles

Charm quark mass with calibrated uncertainty

We determine the charm quark mass hat{m}_c from QCD sum rules of the moments of the vector current correlator calculated in perturbative QCD at mathcal{O} (hat{alpha }_s^3). Only experimental data for the charm resonances below the continuum threshold are needed in our approach, while the continuum contribution is determined by requiring self-consistency between various sum rules, including the one for the zeroth moment. Existing data from the continuum region can then be used to bound the theoretic uncertainty. Our result is hat{m}_c(hat{m}_c) = 1272 pm 8 MeV for hat{alpha }_s(M_Z) = 0.1182, where the central value is in very good agreement with other recent determinations based on the relativistic sum rule approach. On the other hand, there is considerably less agreement regarding the theory dominated uncertainty and we pay special attention to the question how to quantify and justify it.

Mixture of Quark and Gluon Fluids Described in Terms of Anisotropic Hydrodynamics

A system of equations of anisotropic hydrodynamics that describes mixture of quark and gluon fluids is studied. The equations are based on the zeroth, first, and second moments of the RTA kinetic equations. Tests of this formulation are performed by comparing the results of anisotropic hydorodynamics with the exact solutions of the Boltzmann equations for a mixture of fluids in the Bjorken flow limit. One finds a very good agreement between the hydrodynamic and kinetic-theory results.

Numerical solution of the population balance equation using an efficiently modified cell average technique

Abstract In order to increase the accuracy of the modified cell average technique (mCAT) alongside the zeroth and first moments and increase the speed of the technique, a new supplemental solver has been developed in the region of high amount time, a region where the ratio of the zeroth moment to the initial zeroth moment (μ0(t)/μ0(0)) is too small or too large depending on the process and the amount of error is high there. The solver is conceptually easy to understand and straightforward for programming. A number of analytically solved problems were simulated by incorporating this solver into the mCAT and the results were compared with the previous solver. Significant improvements for different phenomenon especially the aggregation related systems were observed.

Moments of fusion-barrier distributions

A study of fusion-barrier distributions through an analysis of their moments is presented. The moments can be obtained from least-squares fits of the energy-weighted fusion cross sections without the need of calculating second derivatives. The zeroth and first moments determine the fusion radius $R$ and the Coulomb barrier ${V}_{C}$. These two quantities are the same as the parameters $R$ and ${V}_{C}$ that are used in the well-known expression, $E\ensuremath{\sigma}=\ensuremath{\pi}{R}^{2}(E\ensuremath{-}{V}_{C})$, for the fusion cross section at high energies. The second and third moments, ${M}_{2}$ and ${M}_{3}$, determine the width and skewness of the barrier distribution, respectively. From these global parameters new correlations for the study of heavy-ion-induced fusion reactions can be obtained. Systems exhibiting a large coupling to transfer reactions show a small fusion radius as well as a large second moment. A negative third moment is correlated with a prolate deformation of the target nucleus.

Moment-of-fluid analytic reconstruction on 2D Cartesian grids

Moment-of-Fluid (MoF) is a piecewise linear interface reconstruction method that tracks fluid through its volume fraction and centroid, which are deduced from the zeroth and first moments. We present a method that replaces the original minimization stage by an analytic reconstruction algorithm on bi-dimensional Cartesian grids. This algorithm provides accurate results for a lower computational cost than the original minimization algorithm. When more than two fluids are involved, this algorithm can be used coupled with the minimization algorithm. Although this paper deals with Cartesian grids, everything remains valid for any meshes that are made of rectangular cells.

Anisotropic matching principle for the hydrodynamic expansion

Following the recent success of anisotropic hydrodynamics we propose a new, general prescription for the hydrodynamics expansion around an anisotropic background. The anisotropic distribution is fixing exactly the complete energy-momentum tensor, just like the effective temperature is fixing the proper energy density in the ordinary expansion around local equilibrium. This means that momen- tum anisotropies are already included at the leading order, allowing for large pressure anisotropies without the need of a next to leading order treatment. The first moment of the Boltzmann equation (local four-momentum conservation) provides the time evolution of the proper energy density and the four velocity. Differently from previous prescriptions, the dynamic equations for the pressure corrections are not derived from the zeroth or second moment of the Boltzmann equation, but they are taken directly from the exact evolution given by the Boltzmann equation. We check the effec- tiveness of this new approach by matching with the exact solution of the Boltzmann equation in the Bjorken limit with the collisional kernel treated in relaxation time approximation, finding an unprecedented agreement.

Phi meson spectral moments and QCD condensates in nuclear matter

A detailed analysis of the lowest two moments of the ϕ meson spectral function in vacuum and nuclear matter is performed. The consistency is examined between the constraints derived from finite energy QCD sum rules and the spectra computed within an improved vector dominance model, incorporating the coupling of kaonic degrees of freedom with the bare ϕ meson. In the vacuum, recent accurate measurements of the e+e−→K+K− cross section allow us to determine the spectral function with high precision. In nuclear matter, the modification of the spectral function can be described by the interactions of the kaons from ϕ→KK‾ with the surrounding nuclear medium. This leads primarily to a strong broadening and an asymmetric deformation of the ϕ meson peak structure. We confirm that, both in vacuum and nuclear matter, the zeroth and first moments of the corresponding spectral functions satisfy the requirements of the finite energy sum rules to a remarkable degree of accuracy. Limits on the strangeness sigma term of the nucleon are examined in this context. Applying our results to the second moment of the spectrum, we furthermore discuss constraints on four-quark condensates and the validity of the commonly used ground state saturation approximation.

An accurate and efficient discrete formulation of aggregation population balance equation

An efficient and accurate discretization method based on a finite volume approach is presented for solving aggregation population balance equation. The principle of the method lies in the introduction of an extra feature that is beyond the essential requirement of mass conservation. The extra feature controls more precisely the behaviour of a chosen integral property of the particle size distribution that does not remain constant like mass, but changes with time. The new method is compared to the finite volume scheme recently proposed by Forestier and Mancini (SIAM J. Sci. Comput., 34, B840 - B860). It retains all the advantages of this scheme, such as simplicity, generality to apply on uniform or nonuniform meshes and computational efficiency, and improves the prediction of the complete particle size distribution as well as of its moments. The numerical results of particle size distribution using the previous finite volume method are consistently overpredicting, which is reflected in the form of the diverging behaviour of second or higher moments for large extent of aggregation. However, the new method controls the growth of higher moments very well and predicts the zeroth moment with high accuracy. Consequently, the new method becomes a powerful tool for the computation of gelling problems. The scheme is validated and compared with the existing finite volume method against several aggregation problems for suitably selected aggregation kernels, including analytically tractable and physically relevant kernels.

Finite volume approximations of breakage population balance equation

In this work, a comparative study of two newly introduced numerical methods approximating the pure multiple breakage PBEs based on the finite volume scheme is performed. For a numerical scheme it is a very essential criterion to keep the total mass of the system constant. But approximating the pure multiple breakage PBEs by mid-point quadrature rules, it is found that the total mass does not remain constant. So, suitable adjustments are made in the discrete formulation such that the mass conservation is achieved. This idea has led to the development of a new mass conserving finite volume approximation of the pure multiple breakage PBEs. In some applications, besides conserving the total mass of the system, the estimation of the zeroth moment is of great importance. Therefore, some suitable adjustments are made in the scheme such that the zeroth moment is predicted as good as the exact result. Thus a new numerical method is obtained to approximate the pure multiple breakage PBEs. Several test problems are considered in order to assess the accuracy of the two different schemes numerically.

Modeling of dissociation and energy transfer in shock-heated nitrogen flows

This work addresses the modeling of dissociation and energy transfer processes in shock heated nitrogen flows by means of the maximum entropy linear model and a newly proposed hybrid bin vibrational collisional model. Both models aim at overcoming two of the main limitations of the state of the art non-equilibrium models: (i) the assumption of equilibrium between rotational and translational energy modes of the molecules and (ii) the reliance on the quasi-steady-state distribution for the description of the population of the internal levels. The formulation of the coarse-grained models is based on grouping the energy levels into bins, where the population is assumed to follow a Maxwell-Boltzmann distribution at its own temperature. Different grouping strategies are investigated. Following the maximum entropy principle, the governing equations are obtained by taking the zeroth and first-order moments of the rovibrational master equations. The accuracy of the proposed models is tested against the rovibrational master equation solution for both flow quantities and population distributions. Calculations performed for free-stream velocities ranging from 5 km/s to 10 km/s demonstrate that dissociation can be accurately predicted by using only 2-3 bins. It is also shown that a multi-temperature approach leads to an under-prediction of dissociation, due to the inability of the former to account for the faster excitation of high-lying vibrational states.

Anisotropic hydrodynamics for a mixture of quark and gluon fluids

A system of equations for anisotropic hydrodynamics is derived that describes a mixture of anisotropic quark and gluon fluids. The consistent treatment of the zeroth, first and second moments of the kinetic equations allows us to construct a new framework with more general forms of the anisotropic phase-space distribution functions than those used before. In this way, the main difficiencies of the previous formulations of anisotropic hydrodynamics for mixtures have been overcome and the good agreement with the exact kinetic-theory results is obtained.

Analysis of the Statistical Moments of the Scintillation Light Distribution With dSiPMs

In $\gamma $ -ray detectors, monolithic scintillation crystals offer the possibility of preserving the scintillation light distribution especially when painted black. The statistical moments of this distribution provide accurate information on the three photon impact coordinates, including their depth of interaction (DOI). Digital SiPMs (dSiPMs) return digital information based on pixels about the collected light distribution, since the signal is a digital sum of the trigger bins. In this work we present, for the first time, an accurate analysis of the statistical moments of the light distribution using monolithic painted black crystals and state-of-the-art dSiPMs. Two $32.6 \times 32.6 ~\hbox{mm}^2$ monolithic LYSO crystals covering the entire photodetectors area have been used in coincidence with 10 mm in thickness. The photosensor tiles were kept at a stable temperature of ${\rm T} = 20\,^\circ{\hbox {C}}$ . Energy resolution of about 18% was reached in relation to the zeroth moment. The first moment, related to the impact position, determined a spatial resolution of about 3 mm near the crystal center, but quadratically degrading towards the crystal borders. The DOI resolution, measured by means of the second moment, was found to be nearing 4 mm in the crystal center region. The third order moment, the so-called skewness, is related to the degree of truncation and once calibrated minimizes the compression effects. A corrected spatial resolution of about 3 mm was then measured for the entire crystal surface. DOI resolution improved at the crystal’s center, reaching 3.5 mm, but a degradation towards the borders remained due to truncation of the scintillation light distribution.

Moments of a length function on the boundary of a hyperbolic manifold

In this paper we will study the statistics of the unit geodesic flow normal to the boundary of a hyperbolic manifold with non-empty totally geodesic boundary. Viewing the time it takes this flow to hit the boundary as a random variable, we derive a formula for its moments in terms of the orthospectrum. The first moment gives the average time for the normal flow acting on the boundary to again reach the boundary, which we connect to Bridgeman's identity (in the surface case), and the zeroth moment recovers Basmajian's identity. Furthermore, we are able to give explicit formulae for the first moment in the surface case as well as for manifolds of odd dimension. In dimension two, the summation terms are dilogarithms. In dimension three, we are able to find the moment generating function for this length function.

Ultrafast Electron and Hole Relaxation Pathways in Few-Layer MoS2

Femtosecond optical pump–probe spectroscopy is employed to elucidate the band-selective ultrafast carrier dynamics of few-layer MoS2. Following narrowband resonant photoexcitation of the exciton A transition, the subpicosecond to picosecond relaxation dynamics of the electron and the hole at the K valley are separately interrogated by a broadband probe pulse. The temporal evolution of the spectral first moment reveals nonexponential intravalley relaxation dynamics in the conduction band. Fluence dependence measurements suggest that this relaxation process is predominantly mediated by acoustic phonon emission. Intervalley scattering of carriers from the K valley to the extrema of the conduction and valence bands is also observed via the decay of the spectral zeroth moment. In addition, second-order Raman scattering leads to the emergence of sidebands in the normalized differential transmission spectra. The observed two-phonon energies and the fluence-dependent time constants suggest that the E1g longitudinal optical (LO) phonon and the LA phonon participate in intervalley scattering in the conduction and valence bands, respectively. Ab initio nonadiabatic molecular dynamics simulations yield time constants of 0.80 and 0.72 ps for intra- and intervalley electronic relaxation, respectively; the latter agrees well with experiment. Finally, the normalized differential transmission spectra reveal a two-electron shake-up satellite that originates from band-edge radiative recombination and the simultaneous excitation of a hole from Kv1 to Kv2. From its spectral position, a Kv1–Kv2 spin–orbit splitting of 1166 ± 1 cm–1 is deduced. The observation of the two-electron transition points to the existence of strong electron correlation in photoexcited few-layer MoS2.

(3 + 1)-dimensional framework for leading-order nonconformal anisotropic hydrodynamics

In this work I develop a new framework for anisotropic hydrodynamics that generalizes the leading order of the hydrodynamic expansion to the full (3+1)-dimensional anisotropic massive case. Following previous works, my considerations are based on the Boltzmann kinetic equation with the collisional term treated in the relaxation time approximation. The momentum anisotropy is included explicitly in the leading term, allowing for a large difference between the longitudinal and transverse pressures as well as for non trivial transverse dynamics. Energy and momentum conservation is expressed by the first moment of the Boltzmann equation. The system of equations is closed by using the zeroth and second moments of the Boltzmann equation. The close-to-equilibrium matching with second-order viscous hydrodynamics is demonstrated. In particular, I show that the coupling between shear and bulk pressure corrections, recently proved to be important for an accurate description of momentum anisotropy and bulk viscous dynamics, does not vanish in the close-to-equilibrium limit.

A modified cell average technique for the solution of population balance equation

A new generalized discretization technique, based on the cell average technique (CAT), for solving the population balance equation and predicting the zeroth and first moments has been developed. The proposed algorithm can be easily cast into computer programs, is conceptually straightforward and demonstrated to be computationally economic. Additionally, a new type of mesh, for breakage, aggregation and combined processes is introduced. A new solver, compatible with aforementioned processes, for improving the accuracy of technique has been also proposed. A number of solvable processes were simulated by this technique and compared with the analytical solution and the CAT method. The results were very close to the analytical solution and much more accurate than CAT results.

Asymptotic, multigroup flux reconstruction and consistent discontinuity factors

Recent theoretical work has led to an asymptotically derived expression for reconstructing the neutron flux from lattice functions and multigroup diffusion solutions. The leading-order asymptotic term is the standard expression for flux reconstruction, i.e., it is the product of a shape function, obtained through a lattice calculation, and the multigroup diffusion solution. The first-order asymptotic correction term is significant only where the gradient of the diffusion solution is not small. Inclusion of this first-order correction term can significantly improve the accuracy of the reconstructed flux. One may define discontinuity factors (DFs) to make certain angular moments of the reconstructed flux continuous across interfaces between assemblies in 1-D. Indeed, the standard assembly discontinuity factors make the zeroth moment (scalar flux) of the reconstructed flux continuous. The inclusion of the correction term in the flux reconstruction provides an additional degree of freedom that can be used to make two angular moments of the reconstructed flux continuous across interfaces by using current DFs in addition to flux DFs. Numerical results demonstrate that using flux and current DFs together can be more accurate than using only flux DFs, and that making the second angular moment continuous can be more accurate than making the zeroth moment continuous.

Statistical thermodynamic properties of a new self-condensing vinyl polymerization system

A new self-condensing vinyl polymerization system consisting of AB f *-type inimers is studied by the principle of statistical mechanics. To obtain the relevant average properties of the system, a differential equation satisfied by the polymeric moment of interest is given, and as a result the zeroth, first, second, and third polymeric moments together with the size distribution function of hyperbranched polymers (HBPs) are explicitly presented. As an application of the method of statistical mechanics, several thermodynamic quantities such as the equilibrium free energy, law of mass action, isothermal compressibility, internal energy, and the specific heat associated with the polymerization are all derived. Furthermore, the scaling behavior of asymptotic size distribution function is discussed, by which a reasonable interpretation of the polydispersity index near the end of polymerization can be made. Also, the expressions of some structural parameters such as the numbers of inimers, terminal units, chain units, branched units, and the degree of branching (DB) are calculated. It is found that a high functionality is helpful to improve the DB of the resultant HBPs. These results show that the functionality f has a significant effect on the thermodynamic quantities and structural properties of HBPs.

Smoke Characterization and Feasibility of the Moment Method for Spacecraft Fire Detection

The Smoke Aerosol Measurement Experiment (SAME) has been conducted twice by the National Aeronautics and Space Administration and provided real-time aerosol data in a spacecraft micro-gravity environment. Flight experiment results have been recently analyzed with respect to comparable ground-based experiments. The ground tests included an electrical mobility analyzer as a reference instrument for measuring particle size distributions of the smoke produced from overheating five common spacecraft materials. Repeatable sample surface temperatures were obtained with the SAME ground-based hardware, and measurements were taken with the aerosol instruments returned from the International Space Station comprising two commercial smoke detectors, three aerosol instruments, which measure moments of the particle size distribution, and a thermal precipitator for collecting smoke particles for transmission electron microscopy (TEM). Moment averages from the particle number concentration (zeroth moment), the diameter co...

Different approximate models of the sectional method for nanoparticle Brownian coagulation

Purpose– The original v2-based sectional method assumes that the selected property quantity of particles is uniformly distributed in each section, which makes particle size distribution (PSD) fluctuate dramatically in the entire size range. The number concentration in each section as well as the zeroth moment of PSD also cannot be correctly predicted in case there are not enough sections used in calculation. In order to provide a more appropriate representation of PSD, different approximate models are used to close the conservation equations. The paper aims to discuss these issues.Design/methodology/approach– The uniform distribution of the selected property quantity of particles in each section is not necessarily satisfied. Instead, the distribution is approximated using an expression with an approximation factor. Different models are investigated on recovering the initial size distribution and predicting the time evolution of size distribution as well as the first three moments so that the advantages and disadvantages of each model can be compared.Findings– The approximate model with an approximation factor of 0.8 is capable of predicting the time evolution of the zeroth moment accurately no matter how many sections are used in simulations. The original v2-based model is recommended to calculate the first and second moments as long as the section number is larger than 50, otherwise, the model with an approximation factor of 0.15 would be a preferred choice.Originality/value– Different approximate models can be used to improve the accuracy of the results supposing we know which moment is of great importance in calculation.