Continuum Scheme Research Articles

Self-renormalization of quasi-light-front correlators on the lattice

In applying large-momentum effective theory, renormalization of the Euclidean correlators in lattice regularization is a challenge due to linear divergences in the self-energy of Wilson lines. Based on lattice QCD matrix elements of the quasi-PDF operator at lattice spacing a=0.03fm ∼ 0.12fm with clover and overlap valence quarks on staggered and domain-wall sea, we design a strategy to disentangle the divergent renormalization factors from finite physics matrix elements, which can be matched to a continuum scheme at short distance such as dimensional regularization and minimal subtraction. Our results indicate that the renormalization factors are universal in the hadron state matrix elements. Moreover, the physical matrix elements appear independent of the valence fermion formulations. These conclusions remain valid even with HYP smearing which reduces the statistical errors albeit reducing control of the renormalization procedure. Moreover, we find a large non-perturbative effect in the popular RI/MOM and ratio renormalization scheme, suggesting favor of the hybrid renormalization procedure proposed recently.

BAL and non-BAL quasars: continuum, emission, and absorption properties establish a common parent sample

ABSTRACT Using a sample of ≃144 000 quasars from the Sloan Digital Sky Survey Data Release 14, we investigate the outflow properties, evident in both absorption and emission, of high-ionization broad absorption line (BAL) and non-BAL quasars with redshifts 1.6 ≲ $z$ ≤ 3.5 and luminosities 45.3 erg s−1 < log10(Lbol) < 48.2 erg s−1. Key to the investigation is a continuum and emission-line reconstruction scheme, based on mean-field independent component analysis, that allows the kinematic properties of the C iv λ1550 emission line to be compared directly for both non-BAL and BAL quasars. C iv emission blueshift and equivalent width (EW) measurements are thus available for both populations. Comparisons of the emission-line and BAL trough properties reveal strong systematic correlations between the emission and absorption properties. The dependence of quantitative outflow indicators on physical properties such as quasar luminosity and luminosity relative to Eddington luminosity is also shown to be essentially identical for the BAL and non-BAL populations. There is an absence of BALs in quasars with the hardest spectral energy distributions (SEDs), revealed by the presence of strong He ii λ1640 emission, large C iv λ1550 emission EW, and no measurable blueshift. In the remainder of the C iv emission blueshift versus EW space, BAL and non-BAL quasars are present at all locations; for every BAL quasar, it is possible to identify non-BAL quasars with the same emission-line outflow properties and SED hardness. The co-location of BAL and non-BAL quasars as a function of emission-line outflow and physical properties is the key result of our investigation, demonstrating that (high-ionization) BALs and non-BALs represent different views of the same underlying quasar population.

A Semianalytical Model for Simulating Fluid Flow in Naturally Fractured Reservoirs With Nonhomogeneous Vugs and Fractures

Summary Carbonate reservoirs comprise fractures, vugs, and cavities. Vugs have a large contribution to reserves of oil and gas, and the fractures provide effective paths for fluid flow in the reservoir. The triple-porosity (TP) model is an effective conceptual method for capturing rock matrix and vugs and the microfractures connecting them. However, these fractures and vugs are always nonhomogeneous. Macrofractures and vugs cannot be handled with a continuum scheme because of their low density and high conductivity. In this approach, the TP conceptual model is implemented to characterize rock matrix, microvugs, and fractures. To capture the heterogeneity of fractures and vugs, macrofractures and vugs are represented explicitly with the discontinuum model. The boundaries of macrovugs and macrofractures are discretized into several elements. The boundary-element method (BEM) is used to handle flow into macrofractures and vugs. The finite-difference method is applied to handle flow within macrofractures. The flow within macrovugs is assumed to be pseudosteady state. With a simple discretization of the boundaries of macrovugs and macrofractures, the proposed model is shown to efficiently simulate the behavior of fractured carbonate reservoirs with heterogeneity. The computational accuracy is demonstrated using an analytical model and numerical simulation. On the basis of the proposed model, the effect of the heterogeneity of macrofractures and vugs on pressure-transient behavior is analyzed. The results show that macrofractures and vugs cannot be handled with triple-continuum models analytically. There will be several “dips” on the derivative of the pressure curve if macrovugs are discretely handled. Also, discretely handling the fractures and vugs will make the calculated dimensionless pressure and the derivative pressure lower than those calculated with the triple-continuum models. After increasing the porosity of macrovugs, the pressure and the derivative will go down in the flow regimes dominated by macrovugs. The conductivity of macrofractures has a great impact on almost all the flow regimes except for boundary-dominated flow. Finally, a field case is used to show the application of the proposed semianalytical model. The novelty of the new model is its ability to model the transient behavior of carbonate reservoirs with nonhomogeneous fractures and vugs. Furthermore, it provides an efficient method for characterizing the heterogeneity of multiscaled fractures and vugs.

XFEM formulation with sub‐interpolation, and equivalence to zero‐thickness interface elements

SummaryThis paper describes a particular formulation of the extended finite element method (XFEM) specifically conceived for application to existing discontinuities of fixed location, for instance, in geological media. The formulation is based on two nonstandard assumptions: (1) the use of sub‐interpolation functions for each subdomain and (2) the use of fictitious displacement variables on the nodes across the discontinuity (instead of the more traditional jump variables). Thanks to the first of those assumptions, the proposed XFEM formulation may be shown to be equivalent to the standard finite element method with zero‐thickness interface elements for the discontinuities (FEM+z). The said equivalence is theoretically proven for the case of quadrangular elements cut in two quadrangles by the discontinuity, and only approximate for other types of intersections of quadrangular or triangular elements, in which the XFEM formulation corresponds to a kinematically restricted version of the corresponding interface plus continuum scheme. The proposed XFEM formulation with sub‐interpolation, also helps improving spurious oscillations of the results obtained with natural interpolation functions when the discontinuity runs skew to the mesh. A possible explanation for these oscillations is provided, which also explains the improvement observed with sub‐interpolation. The paper also discusses the oscillations observed in the numerical results when some nodes are too close to the discontinuity and proposes the remedy of moving those nodes onto the discontinuity itself. All the aspects discussed are illustrated with some examples of application, the results of which are compared with closed‐form analytical solutions or to existing XFEM results from the literature.

Nano-particle drag prediction at low Reynolds number using a direct Boltzmann–BGK solution approach

This paper outlines a novel approach for solution of the Boltzmann–BGK equation describing molecular gas dynamics applied to the challenging problem of drag prediction of a 2D circular nano-particle at transitional Knudsen number (0.0214) and low Reynolds number (0.25–2.0). The numerical scheme utilises a discontinuous-Galerkin finite element discretisation for the physical space representing the problem particle geometry and a high order discretisation for molecular velocity space describing the molecular distribution function. The paper shows that this method produces drag predictions that are aligned well with the range of drag predictions for this problem generated from the alternative numerical approaches of molecular dynamics codes and a modified continuum scheme. It also demonstrates the sensitivity of flow-field solutions and therefore drag predictions to the wall absorption parameter used to construct the solid wall boundary condition used in the solver algorithm. The results from this work has applications in fields ranging from diagnostics and therapeutics in medicine to the fields of semiconductors and xerographics.

Low-order mixed finite element analysis of progressive failure in pressure-dependent materials within the framework of the Cosserat continuum

PurposeThis paper aims to develop a finite element analysis strategy, which is suitable for the analysis of progressive failure that occurs in pressure-dependent materials in practical engineering problems.Design/methodology/approachThe numerical difficulties stemming from the strain-softening behaviour of the frictional material, which is represented by a non-associated Drucker–Prager material model, is tackled using the Cosserat continuum theory, while the mixed finite element formulation based on Hu–Washizu variational principle is adopted to allow the utilization of low-order finite elements.FindingsThe effectiveness and robustness of the low-order finite element are verified, and the simulation for a real-world landslide which occurred at the upstream side of Carsington embankment in Derbyshire reconfirms the advantages of the developed elastoplastic Cosserat continuum scheme in capturing the entire progressive failure process when the strain-softening and the non-associated plastic law are involved.Originality/valueThe permit of using low-order finite elements is of great importance to enhance computational efficiency for analysing large-scale engineering problems. The case study reconfirms the advantages of the developed elastoplastic Cosserat continuum scheme in capturing the entire progressive failure process when the strain-softening and the non-associated plastic law are involved.

Hybrid business models for peace and reconciliation

Despite growing interest in business for peace, there is little insight into how the organizations involved combine societal aims with economic ones in their business models. Literature has exemplified ‘hybrid organizations’ that seek to pursue both for-profit and non-profit activities and are specifically set up with this mission, usually in stable Western countries. However, already existing, traditional organizations that aim for mixed forms of economic and social value creation have been underexposed, and that applies even more for organizational forms that address peace in difficult settings. To help fill these gaps, this article sheds light on different degrees of hybridity of a range of organizations operating in a (post-)conflict region. It shows how 53 organizations in between the non-profit/for-profit extremes pursue different combinations of social and economic goals, maintain and develop relationships with stakeholders, and interact progressively with markets and institutions. We also present a hybridization continuum and classification scheme that is applicable beyond our specific context. While different degrees of hybridity in objectives, perspectives, and relationships exist, key dimensions are frequent interactions with stakeholders, awareness of development and reconciliation issues, and personal commitment. We identify hybridity aspects relevant to management and discuss implications for business scholars and practitioners.

Nonlinear analysis of forced vibration of nonlocal third-order shear deformable beam model of magneto–electro–thermo elastic nanobeams

This paper deals with the forced vibration behavior of nonlocal third-order shear deformable beam model of magneto–electro–thermo elastic (METE) nanobeams based on the nonlocal elasticity theory in conjunction with the von Kármán geometric nonlinearity. The METE nanobeam is assumed to be subjected to the external electric potential, magnetic potential and constant temperature rise. Based on the Hamilton principle, the nonlinear governing equations and corresponding boundary conditions are established and discretized using the generalized differential quadrature (GDQ) method. Thereafter, using a Galerkin-based numerical technique, the set of nonlinear governing equations is reduced into a time-varying set of ordinary differential equations of Duffing type. The pseudo-arc length continuum scheme is then adopted to solve the vectorized form of nonlinear parameterized equations. Finally, a comprehensive study is conducted to get an insight into the effects of different parameters such as nonlocal parameter, slenderness ratio, initial electric potential, initial external magnetic potential, temperature rise and type of boundary conditions on the natural frequency and forced vibration characteristics of METE nanobeams.

Three-phonon scattering processes and thermal conductivity in IV-chalocogenides

We present a systematic study of allowed three-phonon scattering processes, involving acoustic and optical branches, and their relative roles in explaining the low thermal conductivity of IV-chalcogenide thermoelectric materials PbTe, PbSe, PbS, and SnTe. Using numerical results for , computed by employing the isotropic continuum scheme, we have examined the extent of the additional contribution the Callaway theory and the Allen theory provide over the single-mode relaxation time theory. Within the Callaway theory, for all these materials the acoustic (, ) and transverse optical () phonons contribute between 10–25% towards at and above room temperature, with . The longitudinal optical () phonons contribute negligibly (<5%) in Pb-chalogenides, but their contribution is larger (22%) than that of phonons (18%) in SnTe. Due to the presence of high defect concentration in these materials, the high temperature conductivity varies less strongly than T−1. In confirmation with experimental measurements, our study finds that below the Debye temperature the resistivity of SnTe varies as the square-root of the point defect concentration.

Dynamic behaviors of long and curved microtubules based on an atomistic-continuum model

This paper analyses dynamic response and vibration characteristics of long microtubules. Mechanical aspects of material properties are described based on an atomistic-continuum model and the use of a higher-order Cauchy–Born rule that bridges the scale between microstructures and continuum description. Long microtubules are simulated with one-dimensional strips, which include microscale interaction among protein molecules and can be dealt with using continuum mechanical approaches under higher-order gradient continuum scheme. Based on Hamilton’s principle, the differential equation of motion is established and is incorporated in the higher-order gradient continuum mesh-free framework. The performances of structures of microtubules are determined by direct numerical integration in time domain and applying the Fourier transform technique in frequency domain. Time-histories and frequency spectrums are obtained to determine vibration characteristics. Curved shapes of microtubules are involved in the study. Different cases are considered and compared, and the results are presented and discussed.

Bottom-Up Approach to Innovative Memory Devices: I. Intrinsic and Environmental Effects on the Molecular Component

The 50 nm-thick polystyrene (PS) film, involved in some innovative memory devices, contains 8-hydroxyquinoline (8HQ) molecules and gold nanoparticles. A model where molecular localized properties directly reflect on macroscopic behavior of a complex system has been tested in the present work, which is focused on the structural and electronic properties of the 8HQ-PS mixture modeled in a continuum scheme: one 8HQ molecule with a polarizable continuum model (PCM) whose reliability has been checked by comparison with periodic DFT calculations of 8HQ-PS crystalline structures. A comprehensive study of the keto−enolic tautomerization of 8HQ has been performed, at the DFT level using B3LYP, LC-PBE, and M052X functionals and a polarized double-ζ basis set. The energetics of the obtained structures (minima and transition states) have been refined by single point calculations at the CCSD(T) level with the aug-cc-pVDZ basis set. Our calculations predict the enolic tautomer to be the most stable for the isolated and PS-solvated 8HQ in its neutral form, with a tautomerization barrier much larger than the thermal energy at the working conditions. The opposite trend has been found for the charged (both positive and negative) 8HQ, with ketonic tautomers being the most stable. In a first approximation of weak interaction with the aluminum electrodes, the electric-field effects have also been taken into account for the calculations of electron affinities and ionization potentials of 8HQ molecules. The electron and hole injection barriers issuing from these results are in good agreement with the experimental observations.

A continuum–atomistic simulation of heat transfer in micro- and nano-flows

We develop a hybrid atomistic–continuum scheme for simulating micro- and nano-flows with heat transfer. The approach is based on spatial “domain decomposition” in which molecular dynamics (MD) is used in regions where atomistic details are important, while classical continuum fluid dynamics is used in the remaining regions. The two descriptions are matched in a coupling region where we ensure continuity of mass, momentum, energy and their fluxes. The scheme for including the energy equation is implemented in 1-D and 2-D, and used to study steady and unsteady heat transfer in channel flows with and without nano roughness. Good agreement between hybrid results and analytical or pure MD results is found, demonstrating the accuracy of this multiscale method and its potential applications in thermal engineering.

Long-wavelength nonequilibrium optical phonon dynamics in cubic and hexagonal semiconductors

We have investigated the relaxation of zone-center nonequilibrium optical phonons in bulk cubic and hexagonal semiconductors. Our theory is based on the application of Fermi's golden rule formula involving anharmonic interaction between phonons. Calculations of the lifetimes of the zone-center longitudinal optical (LO) and transverse optical (TO) phonons in cubic materials have been performed by modeling acoustic phonon modes within Debye's isotropic continuum scheme. Lifetimes of ${A}_{1}(\mathrm{LO})$, ${E}_{1}(\mathrm{TO})$, ${A}_{1}(\mathrm{TO})$, ${E}_{2}^{2}$ and ${E}_{2}^{1}$ modes in wurtzite semiconductors have also been calculated by employing Debye's scheme within a semi-isotropic continuum model for acoustic modes. We have obtained a few trends in the lifetime results within a crystal phase (cubic or hexagonal), and between the two crystal phases. Our results support and explain available experimental data over a large temperature range, and make some predictions.

Asymptotic waves for fast granular flows

In [1], a mathematical description of fast flows of granular materials was developed within a continuum scheme, arriving at the system of evolution equations proposed in [2] using Grad's method of moments for determining the form of balance laws including collisional transfers and productions due to inelastic effects. Here, by using the constitutive relations proposed in [3], in the one-dimensional case, we investigate the propagation of asymptotic waves either in a constant state or in a nonconstant state of the associated hyperbolic system.

Matrix elements of four-fermion operators with quenched Wilson fermions

We present results for the matrix elements of a variety of four-fermion operators calculated using quenched Wilson fermions. Our simulations are done on 170 lattices of size ${32}^{3}\ifmmode\times\else\texttimes\fi{}64$ at $\ensuremath{\beta}=6.0$. We find ${B}_{K}=0.74\ifmmode\pm\else\textpm\fi{}0.04\ifmmode\pm\else\textpm\fi{}0.05$, ${B}_{D}=0.78\ifmmode\pm\else\textpm\fi{}0.01$, ${B}_{7}^{3/2}=0.58\ifmmode\pm\else\textpm\fi{}{0.02}_{\ensuremath{-}0.03}^{+0.07}$, ${B}_{8}^{3/2}=0.81\ifmmode\pm\else\textpm\fi{}{0.03}_{\ensuremath{-}0.02}^{+0.03}$, with all results being in the NDR scheme at $\ensuremath{\mu}=2$ GeV. We also calculate the $B$ parameter for the operator ${\mathcal{Q}}_{s},$ which is needed in the study of the difference of $B$-meson lifetimes. Our best estimate is ${B}_{S}(\mathrm{NDR},\ensuremath{\mu}=1/a=2.33 \mathrm{GeV})$ $=0.80\ifmmode\pm\else\textpm\fi{}0.01$. This is given at the lattice scale since the required two-loop anomalous dimension matrix is not known. In all these estimates, the first error is statistical, while the second is due to the use of truncated perturbation theory to match continuum and lattice operators. Errors due to quenching and lattice discretization are not included. We also present new results for the perturbative matching coefficients, extending the calculation to all Lorentz scalar four-fermion operators, and using NDR as the continuum scheme.

Phonons in thin GaAs quantum wires.

Phonon frequencies and potentials for an array of thin rectangular GaAs wires embedded in AlAs are calculated within a microscopic scheme. The confined and interface character of optical modes are clearly evident from their dispersion and from the spatial profiles. Our results allow us to conclude that macroscopic models based on the dielectric continuum scheme are adequate to describe confined phonon profiles at wave vectors relevant to el-ph scattering, in contrast with approaches based on mechanical boundary conditions, which yield modes with the wrong symmetry sequence. The implications for electron-phonon scattering rates are discussed.