Smearing Width Research Articles

Evaluation of the Effects of Actuator Line Force Smearing on Wind Turbines Near-Wake Development

In the present study, the effects of the actuator line force smearing on the predicted near-wake development of a model wind turbine are evaluated. To exclude the uncertainties related to the blade loads computation, the loads of a corresponding blade-resolving simulation are imposed. Three force projection functions are applied, which all radially scale with the local chord length: an isotropic Gauss force distribution, an anisotropic Gauss distribution with distinct projection widths in the chord and thickness directions, and a Gauss-Gumbel projection function which creates an airfoil-like force distribution in the chord direction. Comparisons with corresponding blade-resolving simulations and experimental results show a good agreement of the tip vortex core size, position and circulation. Comparison of the mid-wake instantaneous streamwise velocity with blade-resolving simulations shows a thinner vortex sheet and stronger effects of the trailed vortices in the actuator line simulation. Although the bound vortex shape scales with the projection function, no significant difference was observed in the resulting tip vortices and near-wake flow field between the three projection functions used. It is attributed to the similar projection width in the tip vortex region for all cases considered. With the chosen grid refinement in the tip vortex area and a smearing width that scales with the chord length, tip vortices that compare with high-resolution experiments and high-fidelity blade-resolving simulation could be generated with the actuator line approach.

Probing granular inhomogeneity of a particle-emitting source by imaging two-pion Bose–Einstein correlations

Using the source imaging technique in two-pion interferometry, we study the image of the hydrodynamic particle-emitting source with the HIJING initial conditions for relativistic heavy-ion collisions on an event-by-event basis. It is shown that the initial-state fluctuations may give rise to bumpy structures of the medium during hydrodynamical evolution, which affects the two-pion emission space and leads to a visible two-tiered shape in the source function imaged using the two-pion Bose–Einstein correlations. This two-tiered shape can be understood within a similar but more analytic granular source model and is found to be closely related to the introduced quantity $$\xi$$ , which characterizes the granular inhomogeneity of the source. By fitting the imaged source function with a granular source parametrization, we extract the granular inhomogeneity of the hydrodynamic source, which is found to be sensitive to both the Gaussian smearing width of the HIJING initial condition and the centrality of the collisions.

Study of collective anisotropies v_2 and v_3 and their fluctuations in pA collisions at LHC within a relativistic transport approach

We have developed a relativistic transport approach at fixed eta /s(T) that incorporates initial space fluctuations generated by wounded quark model to study the hadron observables in 5.02 TeV p + Pb collisions. We find that our approach is able to correctly predict quite well several existing experimental measurements assuming a matter with eta /s=1/4pi , a result similar to previous studies within a viscous hydrodynamics approach. Besides, we further discuss the sensitivity of the results on both eta /s(T) and the smearing width. Our transport approach has the possibility to include in initial conditions the power law tail associated to minijet, and this improvement extends the agreement with the experimental data to higher p_T ranges. We also perform a comparison to Pb + Pb collisions pointing out that even if the collective flows have a similar magnitude the features of the matter created are different. By studying the correlation between collective flows and initial geometry, we find that the correlation decreases faster in small systems with the increase of n and centrality. In particular we show that the variance of sigma _{v_n}/langle v_nrangle has a quite different evolution with centrality for p + Pb, so their measurement could provide some further hint about the correctness of current modelling.

Excited-state effects in nucleon structure on the lattice using hybrid interpolators

It would be very useful to find a way of reducing excited-state effects in lattice QCD calculations of nucleon structure that has a low computational cost. We explore the use of hybrid interpolators, which contain a nontrivial gluonic excitation, in a variational basis together with the standard interpolator with tuned smearing width. Using the clover discretization of the field strength tensor, a calculation using a fixed linear combination of standard and hybrid interpolators can be done using the same number of quark propagators as a standard calculation, making this a cost-effective option. We find that such an interpolator, optimized by solving a generalized eigenvalue problem, reduces excited-state contributions in two-point correlators. However, the effect in three-point correlators, which are needed for computing nucleon matrix elements, is mixed: for some matrix elements such as the tensor charge, excited-state effects are suppressed, whereas for others such as the axial charge, they are enhanced. The results illustrate that the variational method is not guaranteed to reduce the net contribution from excited states except in its asymptotic regime, and suggest that it may be important to use a large basis of interpolators capable of isolating all of the relevant low-lying states.

Density Functional Theory Study of Structural and Electronic Properties of γ'-Ni3Al and γ"-Ni3Nb

In the present paper, the structural and electronic properties of ordered face-centered cubic (L12) γ'-Ni3Al and body-centered tetragonal (D022) γ"-Ni3Nb are investigated by density functional theory calculation within projector augmented wave (PAW) potentials. The structures are optimized for both the phases and the results are found in good agreement with the experimental and theoretical data. In the geometrical optimization, all the forces on each atom are converged to less than 103 eV/Å, and the total energy less than 10-6 eV/atom. The Methfessel–Paxton smearing width of 0.2 eV is used here. The formation energy of γ'-Ni3Al and γ"-Ni3Nb phases are calculated and the values are found to be -40.67 kJ/mol and -27.55 kJ/mol respectively. The bonding character is analyzed based on the density of states (DOS).

Two-scale modeling of fracturing solids using a smeared macro-to-micro discontinuity transition

We consider multiscale modeling of fracturing solids undergoing strain localization, whereby Statistical Volume Elements (SVEs) are used to compute the homogenized macroscopic stresses and the eXtended Finite Element Method (XFEM) is used to represent macroscale displacement discontinuities. These discontinuities are imposed on the localized SVEs in a smeared sense, whereby the smearing width is related to the SVE size and the orientation of the macroscopic discontinuity. This smearing width relation, which is derived within the setting of Variationally Consistent Homogenization (VCH), prevents pathological dependence of the solution on the SVE size. The SVE size insensitivity is further improved by adopting the recently proposed localization aligned weakly periodic boundary conditions. Advantages of the proposed method are that it allows multiscale modeling of localized fracture without restrictive assumptions on the SVE size and without the need to explicitly track a localized region in the SVE.

Tuned and Balanced Redistributed Charge Scheme for Combined Quantum Mechanical and Molecular Mechanical (QM/MM) Methods and Fragment Methods: Tuning Based on the CM5 Charge Model.

Tuned and balanced redistributed charge schemes have been developed for modeling the electrostatic fields of bonds that are cut by a quantum mechanical-molecular mechanical boundary in combined quantum mechanical and molecular mechanical (QM/MM) methods. First, the charge is balanced by adjusting the charge on the MM boundary atom to conserve the total charge of the entire QM/MM system. In the balanced smeared redistributed charge (BSRC) scheme, the adjusted MM boundary charge is smeared with a smearing width of 1.0 Å and is distributed in equal portions to the midpoints of the bonds between the MM boundary atom and the MM atoms bonded to it; in the balanced redistributed charge-2 (BRC2) scheme, the adjusted MM boundary charge is distributed as point charges in equal portions to the MM atoms that are bonded to the MM boundary atom. The QM subsystem is capped by a fluorine atom that is tuned to reproduce the sum of partial atomic charges of the uncapped portion of the QM subsystem. The new aspect of the present study is a new way to carry out the tuning process; in particular, the CM5 charge model, rather than the Mulliken population analysis applied in previous studies, is used for tuning the capping atom that terminates the dangling bond of the QM region. The mean unsigned error (MUE) of the QM/MM deprotonation energy for a 15-system test suite of deprotonation reactions is 2.3 kcal/mol for the tuned BSRC scheme (TBSRC) and 2.4 kcal/mol for the tuned BRC2 scheme (TBRC2). As was the case for the original tuning method based on Mulliken charges, the new tuning method performs much better than using conventional hydrogen link atoms, which have an MUE on this test set of about 7 kcal/mol. However, the new scheme eliminates the need to use small basis sets, which can be problematic, and it allows one to be more consistent by tuning the parameters with whatever basis set is appropriate for applications. (Alternatively, since the tuning parameters and partial charges obtained by the new method do not depend strongly on basis set, one can continue to use available CM5-tuned parameters even when one changes the basis set.) Furthermore, we found that, as compared to Mulliken charges, the CM5 charges describe the charge distributions in test molecules better, and they reproduce the dipole moments of full quantum mechanical calculations better; therefore the new tuning procedure is more physical and should be more reliable and robust.

Magnetic moment of a single vacancy in graphene and semiconducting nanoribbons

Calculations of single-vacancy-induced magnetism in graphene have found different values within a large range, which restricts the understanding of magnetism in defected graphene. Here we report first-principles simulations to examine the accuracy of magnetic moment calculations of a single vacancy with respect to the smearing width and $k$-points sampling in calculations of total density of states, based on which the magnetic moment is calculated. We show that the magnetic moment of a single vacancy arises from the asymmetry between spin-up and spin-down electrons in a small energy window of 1 eV that contains a sharp resonance close to the Fermi level. A small smearing width is important to accurately describe the sharp resonance. However, we find that even with a very large number of $k$ points (thousands per unit cell), the magnetic moment value is still sensitive to the smearing width, and that the total density of states still shows spikes, which leads to unreliable evaluation of the magnetic moment. Calculations of a single vacancy in semiconducting graphene nanoribbons further illustrate the balance between smearing width and $k$-points sampling, and indicate a 2 ${\ensuremath{\mu}}_{B}$ ground state as in semiconducting graphene nanoflakes.

The thermal flux–flux correlation function and classical-quantum correspondence

Exact quantum thermal flux–flux correlations are obtained for the inverted parabolic barrier and free particle by smearing and scaling corresponding two-surface classical correlations. The smearing width is identified as a dynamical uncertainty in x associated with imaginary time evolution by −iħβ/2. The scaling is just the ratio of the high temperature asymptotic form of this dynamical uncertainty to the dynamical uncertainty itself. It represents a sort of quantum amplification. This quantum adaptation of classical flux–flux correlation is generalized to generic one-dimensional barrier systems, and applied to the symmetric and asymmetric Eckart barriers. Good agreement between model and converged numerical results is obtained down to temperatures where tunnelling begins to predominate above-barrier transmission. The model does, however, fail further into the tunnelling regime.

E1strength inPb208within the shell model

The dipole response of the doubly magic nuclide $^{208}\mathrm{Pb}$ was studied in photon-scattering experiments at the electron linear accelerator ELBE with bremsstrahlung produced at kinetic electron energies of 9.0 and 15.0 MeV. The present $(\ensuremath{\gamma},{\ensuremath{\gamma}}^{\ensuremath{'}})$ data combined with $(\ensuremath{\gamma},n)$ data from the literature are compared with results of shell-model calculations and calculations using a quasiparticle random-phase approximation. The shell-model calculations including (2p-2h) excitations describe the experimental $E1$ strength well and reproduce the spreading of the giant dipole resonance by applying a small smearing width only.

Phonon dispersion relations and soft modes of 4 A carbon nanotubes

The phonon dispersion relations of three kinds of 4 Å carbon nanotubes are calculated by using the density functional perturbation theory. It is found that the frequencies of some phonon modes are very sensitive to the smearing width used in the calculations, and eventually become negative at low electronic temperature. Moreover, two kinds of soft modes are identified for the (5,0) tube which are quite different from those reported previously. Our results suggest that the (5,0) tube remains metallic at very low temperature, instead of the metallic-semiconducting transition claimed before.

Fundamental length in quantum theories withPT-symmetric Hamiltonians

One-dimensional motion of a quantum point particle is usually described by its wave function $\ensuremath{\psi}(x)$, where the argument $x\ensuremath{\in}\mathbb{R}$ represents a (measurable) coordinate and where the integrated probability density is normalized to one, $\ensuremath{\int}{\ensuremath{\psi}}^{*}(x)\ensuremath{\psi}(x)=1$. The direct observability of $x$ may be lost in $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics where a ``smeared'' metric kernel ${\ensuremath{\Theta}}_{(x,{x}^{\ensuremath{'}})}\ensuremath{\ne}\ensuremath{\delta}(x\ensuremath{-}{x}^{\ensuremath{'}})$ may enter the double-integral normalization $∬{\ensuremath{\psi}}^{*}(x){\ensuremath{\Theta}}_{(x,{x}^{\ensuremath{'}})}\ensuremath{\psi}({x}^{\ensuremath{'}})=1$. We argue that such a formalism proves particularly suitable for the introduction of a nonvanishing fundamental length $\ensuremath{\theta}g0$, which would characterize the ``smearing width'' of the kernel ${\ensuremath{\Theta}}_{(x,{x}^{\ensuremath{'}})}$. The technical feasibility of such a project is illustrated via a toy family of Hamiltonians ${H}^{(N)}(\ensuremath{\lambda})$ taken from Ref. [11]. For each element of this family the complete set of all the eligible metric kernels ${\ensuremath{\Theta}}_{(x,{x}^{\ensuremath{'}})}^{(N)}(\ensuremath{\lambda})$ is constructed in closed form. We show that at any preselected non-negative fundamental length these metrics can be made to vanish unless $|x\ensuremath{-}{x}^{\ensuremath{'}}|\ensuremath{\le}\ensuremath{\theta}$. The strictly local inner product of Ref. [11] recurs at $\ensuremath{\theta}=0$, while the popular $\mathcal{C}\mathcal{P}\mathcal{T}$-symmetric option requires $\ensuremath{\theta}=\ensuremath{\infty}$ in this language.

Self-consistent Hartree-Fock based random phase approximation and the spurious state mixing

We use a fully self-consistent Hartree$-$Fock (HF) based continuum random phase approximation (CRPA) to calculate strength functions $S(E)$ and transition densities $\rho_t(r)$ for isoscalar giant resonances with multipolarities $L = 0$, 1 and 2 in $^{80}Zr$ nucleus. In particular, we consider the effects of spurious state mixing (SSM) in the isoscalar giant dipole resonance (ISGDR) and extend the projection method to determine the mixing amplitude of spurious state so that properly normalized $S(E)$ and $\rho_t(r)$ having no contribution due to SSM can be obtained. For the calculation to be highly accurate we use a very fine radial mesh (0.04 fm) and zero smearing width in HF$-$CRPA calculations. We first use our most accurate results as a basis to establish the credibility of the projection method, employed to eliminate the SSM, and then to investigate the consequences of the common violation of self-consistency, in actual implementation of HF based CRPA and discretized RPA (DRPA), as often encountered in the published literature. The HF$-$DRPA calculations are carried out using a typical box size of 12 fm and a very large box of 72 fm, for different values of particle-hole energy cutoff ranging from 50 to 600 MeV.

Helm model interpretation of 16O form factors: application to pion photoproduction and muon capture

The available experimental data for the form factors of the T = 1 levels in 16O, obtained from electron scattering at low (Darmstadt), medium (Tohoku), and high momentum transfer (Stanford), are interpreted by the generalized Helm model. This phenomenological model reduces the form factor description of each level to the listing of a few physical parameters, i.e., the radius and smearing width of the transition densities of charge (current) and magnetization, and their corresponding strength constants. Its parameters having been determined by the form factor fits, the model may then be used to predict the results of other medium energy processes; this is done here for the photoproduction of charged pions and for muon capture in16O.