Cutoff Effects Research Articles

Analysis of wavy leading-edge noise reduction and source mechanism in rod-airfoil interactions

Inspired by the wings of owls and the tubercles present on humpback whales' flippers, leading-edge serrations have demonstrated the potential to mitigate airfoil–turbulence interaction noise. To deepen our understanding of the underlying mechanisms driving this noise reduction, we conducted compressible large-eddy simulations on a rod-airfoil configuration equipped with wavy leading edges (WLEs) of varying amplitudes. All tested serrations exhibited some degree of noise reduction, with the amplitude of the WLE exerting a significant influence on the overall noise reduction effect. Notably, the wavy airfoil with the largest amplitude demonstrated the most substantial noise reduction in the mid-frequency range, achieving a remarkable decrease in up to 2.2 dB in noise levels. Applying multi-process acoustic theory, we delved into sound production on surfaces and near-field structures responsible for generating noise sources. Our findings underscore a crucial mechanism contributing to noise reduction—the source cutoff effects manifested through the significant weakening of noise sources at hill regions along the serrations' surface. Stronger source cutoff effects were observed with larger WLE amplitudes. Furthermore, our study reveals that destructive relationships among sources also play a pivotal role in reducing flow noise. The reduction in mid-frequency noise results from a synergy of the source cutoff effect and destructive source relationships induced by WLEs, while the decrease in low-frequency noise primarily emanates from the source cutoff effect.

Effect of Data Reduction Techniques on Daily Moderate to Vigorous Physical Activity Collected with ActiGraph® in People with COPD.

ActiGraph® is a valid, frequently used, accelerometer to quantify moderate to vigorous physical activities (MVPA) in people with COPD. The impact of ActiGraph processing techniques on this population is unknown. This study aimed to explore the effect of data reduction techniques on MVPA in people with COPD. MVPA/day, through ActiGraph GT3X+, was estimated using: Troiano, Freedson 98 and FreedsonVM3 cutoffs, 15-s and 60-s epochs, and normal and low-frequency extension (LFE) filters. Cutoff, epoch, and filter effects were explored with Aligned Rank Transform-ANOVA. Lin's concordance correlation coefficients and Bland-Altman plots were used to evaluate agreement and bias between different techniques. The analysis included 136 people with COPD (79% male; 68 ± 8 years; FEV1 51 ± 17% predicted). MVPA/day differed according to cutoff, filter, and epoch selection (p-value < 0.001). FreedsonVM3 cutoff, 15-s epochs, and LFE yielded the highest MVPA (45 min/day, 68% of physically active participants). Troiano cutoff, 60-s epochs, and normal filter yielded the lowest MVPA (8 min/day, 20% of physically active participants). Only comparisons between Troiano and Freedson98 cutoffs presented an almost perfect agreement. ActiGraph data reduction techniques affected MVPA/day estimates and their interpretation at the individual and group level. Studies using different processing criteria should not be compared in people with COPD. Future studies with a gold standard are required to ascertain which processing technique produces the most accurate MVPA estimates in COPD. Meanwhile, future trials employing the ActiGraph GT3X+ may consider estimating MVPA based on Freedson VM3 cutofffs, 60-s epochs, and normal filter.

Holographic n-partite information in hyperscaling violating geometry

The n-partite information (nI) is formulated as a measure of multi-partite entanglement. Field theory computation revealed that the sign of nI is indefinite for n ≥ 3, while holographic studies conjectured a sign property that holographic nI is non-negative/non-positive for even/odd n, with tripartite information (TI, n = 3) proved. We investigate the aspects of nI with holographic duality in hyperscaling violating geometry. We confirm the conjectured sign property for strips of equal length with equal separation distance, and disprove this conjecture for n > 3 with general configurations. Therefore, nI in field theories and holography exhibits compatibility except for n = 3. We also discuss other properties of holographic nI with analytic computation: the monotonicity, linearity, relation to hyperscaling violating parameters, temperature and UV cutoff effects, and the physical implications. It is doubtful that nI is an effective measure of entanglement considering the indefinite sign, non-monotonicity, and quasi-linearity of its holographic dual. In this respect, we propose constraints on the multi-partite entanglement measures.

Cutoff effects in Hartree-Fock calculations at leading order of chiral effective field theory

Cutoff effects in Hartree-Fock calculations at leading order of chiral effective field theory

Extended GUP formulation and the role of momentum cut-off

We analyze the extension of the GUP theory deriving from the modified uncertainty principle in agreement with the string low energy limit, which represents one of the most general formulations satisfying the Jacobi identity, in the context of the associative algebras. After providing some physical insights on the nature of the considered approaches exploiting the cosmological arena, first, we show how a natural formulation of the theory in an infinite momentum space does not lead to the emergence of a nonzero minimal uncertainty in position, then we construct a truncated formulation of the theory in momentum space, proving that only in this case we can recover the desired feature of the presence of a nonzero minimal uncertainty in position, which – as usual in these theories – can be interpreted as a phenomenological manifestation of cut-off physics effects. Both quantization schemes are completely characterized and finally applied to study wave packets’ behavior and their evolution in time. The obtained results can shed light on which generalizations of the GUP theory are more coherent with the string low energy limit, in view of the existence of a minimum length in the form of a minimal uncertainty in position.

The charm-quark contribution to light-by-light scattering in the muon (g-2) from lattice QCD

We compute the hadronic light-by-light scattering contribution to the muon g-2 from the charm quark using lattice QCD. The calculation is performed on ensembles generated with dynamical (u, d, s) quarks at the SU(3)_mathrm{f} symmetric point with degenerate pion and kaon masses of around 415 MeV. It includes the connected charm contribution, as well as the leading disconnected Wick contraction, involving the correlation between a charm and a light-quark loop. Cutoff effects turn out to be sizeable, which leads us to use lighter-than-physical charm masses, to employ a broad range of lattice spacings reaching down to 0.039 fm and to perform a combined charm-mass and continuum extrapolation. We use the eta _c meson to define the physical charm-mass point and obtain a final value of a_mu ^mathrm{HLbL,c}= (2.8pm 0.5) times 10^{-11}, whose uncertainty is dominated by the systematics of the extrapolation. Our result is consistent with the estimate based on a simple charm-quark loop, whilst being free of any perturbative scheme dependence on the charm mass. The mixed charm–light disconnected contraction contributes a small negative amount to the final value.

Inclusive rates from smeared spectral densities in the two-dimensional O(3) non-linear σ-model

This work employs the spectral reconstruction approach of ref. [1] to determine an inclusive rate in the 1 + 1 dimensional O(3) non-linear σ-model, analogous to the QCD part of e+e− → hadrons. The Euclidean two-point correlation function of the conserved current j is computed using Monte Carlo lattice field theory simulations for a variety of spacetime volumes and lattice spacings. The spectral density of this correlator is related to the inclusive rate for j → X in which all final states produced by the external current are summed. The ill-posed inverse problem of determining the spectral density from the correlation function is made tractable through the determination of smeared spectral densities in which the desired density is convolved with a set of known smearing kernels of finite width ϵ. The smooth energy dependence of the underlying spectral density enables a controlled ϵ → 0 extrapolation in the inelastic region, yielding the real-time inclusive rate without reference to individual finite-volume energies or matrix elements. Systematic uncertainties due to cutoff effects and residual finite-volume effects are estimated and taken into account in the final error budget. After taking the continuum limit, the results are consistent with the known analytic rate to within the combined statistical and systematic errors. Above energies where 20-particle states contribute, the overall precision is sufficient to discern the four-particle contribution to the spectral density.

The asymptotic approach to the continuum of lattice QCD spectral observables

We consider spectral quantities in lattice QCD and determine the asymptotic behaviour of their discretization errors. Wilson fermion with O(a)-improvement, (Möbius) Domain wall fermion (DWF), and overlap Dirac operators are considered in combination with the commonly used gauge actions. Wilson fermions and DWF with domain wall height M5=1+O(g02) have the same, approximate, form of the asymptotic cutoff effects: Ka2[g¯2(a−1)]0.760. A domain wall height M5=1.8, as often used, introduces large mass-dependent K′(m)a2[g¯2(a−1)]0.518 effects. Massless twisted mass fermions have the same form as Wilson fermions when the Sheikholeslami-Wohlert term [1] is included. For their mass-dependent cutoff effects we have information on the exponents Γˆi of g¯2(a−1) but not for the pre-factors. For staggered fermions there is only partial information on the exponents.We propose that tree-level O(a2) improvement, which is easy to do [2], should be used in the future – both for the fermion and the gauge action. It improves the asymptotic behaviour in all cases.

Extraction of Bs→Ds(*) form factors from Nf=2 lattice QCD

We report on a two-flavor lattice QCD study of the ${B}_{s}\ensuremath{\rightarrow}{D}_{s}$ and ${B}_{s}\ensuremath{\rightarrow}{D}_{s}^{*}$ transitions parametrized, in the heavy quark limit, by the form factors $\mathcal{G}$, and ${h}_{{A}_{1}}$, ${h}_{{A}_{2}}$, and ${h}_{{A}_{3}}$, respectively. In the search for New Physics through tests of lepton flavor universality, ${B}_{s}$ decay channels are complementary to the $B$ decays widely studied at $B$ factories and LHCb, while on the theory side they can be better controlled than the ${B}_{c}$ and ${\mathrm{\ensuremath{\Lambda}}}_{b}$ decays. The purpose of this exploratory two-flavor study is, in preparation for future analyses of lattice QCD simulations with ${N}_{f}&gt;2$ and physical quark masses, to gain experience on a suitable method for a lattice extraction of form factors associated with $b\ensuremath{\rightarrow}c$ currents that may yield tighter control over systematic effects like contamination from excited states and cutoff effects. We obtain the zero-recoil values ${\mathcal{G}}^{{B}_{s}\ensuremath{\rightarrow}{D}_{s}}(1)=1.03(14)$ and ${h}^{{B}_{s}\ensuremath{\rightarrow}{D}_{s}^{*}}(1)=0.85(16)$.

Taming lattice artifacts with Pauli-Villars fields

As fermions are added to a lattice gauge theory, one is driven to stronger bare coupling in order to maintain the same renormalized coupling. Stronger bare couplings are usually associated with larger gauge fluctuations, leading to larger cutoff effects and more expensive simulations. In theories with many light fermions, sometimes the desired physical region cannot be reached before encountering a phase boundary. We show that these undesired effects can be reduced by adding Pauli--Villars fields. We reach significantly larger renormalized couplings while at the same time damping short-distance fluctuations of the gauge field. This may allow for controlled continuum extrapolations from large lattice spacings.

Bottomonium melting from screening correlators at high temperature

We study the bottomonium screening masses in a 2+1 flavor QCD medium on the lattice using the Highly Improved Staggered Quark(HISQ) discretization for the quarks. We focus on a wide temperature range in the region $350~{\rm MeV}\le T < 1000 ~{\rm MeV}$, and perform our calculations on three different lattice spacings to control the lattice cut-off effects, corresponding to temporal lattice extent of $N_\tau=8,10,12$. From a detailed study of the temperature dependence of screening masses we conclude that while the $\eta_b(1S)$ and $\Upsilon(1S)$ states melt at $T>500$ MeV, the scalar and axial-vector states $\chi_{b0}(1P)$ and $h_b(1P)$ melt already at $T>350$ MeV.

Seismic Slope Displacement of Tailings Dam: A Comparative Study between Modified Newmark and Mohr-Coulomb Models

ABSTRACT Modified Newmark method is proposed including the equivalent seismic loading and critical acceleration dependant on the dynamically exerted plastic yielding and tension cutoff effects along the base of the sliding mass. The fully nonlinear FE analysis is based on elasto-plastic Mohr-Coulomb material model. The proposed algorithm was validated in an example of 72 m high tailings dam. The Newmark permanent displacements were compared with the average plastic deformations resulting from the nonlinear Mohr-Coulomb model. The comparison shows satisfactory agreement for low to moderate nonlinear slope behavior. For deep nonlinearity, the modified Newmark method can be used as a decision-making tool only.

Regulator dependence of inhomogeneous phases in the ( 2+1 )-dimensional Gross-Neveu model

The phase diagram of the Gross-Neveu model in $2+1$ space-time dimensions at nonzero temperature and chemical potential is studied in the limit of infinitely many flavors, focusing on the possible existence of inhomogeneous phases, where the order parameter $\ensuremath{\sigma}$ is nonuniform in space. To this end, we analyze the stability of the energetically favored homogeneous configuration $\ensuremath{\sigma}(\mathbf{x})=\overline{\ensuremath{\sigma}}=\text{const}$ with respect to small inhomogeneous fluctuations, employing lattice field theory with two different lattice discretizations as well as a continuum approach with Pauli-Villars regularization. Within lattice field theory, we also perform a full minimization of the effective action, allowing for arbitrary 1-dimensional modulations of the order parameter. For all methods special attention is paid to the role of cutoff effects. For one of the two lattice discretizations, no inhomogeneous phase was found. For the other lattice discretization and within the continuum approach with a finite Pauli-Villars cutoff parameter $\mathrm{\ensuremath{\Lambda}}$, we find a region in the phase diagram where an inhomogeneous order parameter is favored. This inhomogeneous region shrinks, however, when the lattice spacing is decreased or $\mathrm{\ensuremath{\Lambda}}$ is increased, and finally disappears for all nonzero temperatures when the cutoff is removed completely. For vanishing temperature, we find hints for a degeneracy of homogeneous and inhomogeneous solutions, in agreement with earlier findings.

Deconfinement critical point of lattice QCD with Nf=2 Wilson fermions

The ${\rm SU}(3)$ pure gauge theory exhibits a first-order thermal deconfinement transition due to spontaneous breaking of its global $Z_3$ center symmetry. When heavy dynamical quarks are added, this symmetry is broken explicitly and the transition weakens with decreasing quark mass until it disappears at a critical point. We compute the critical hopping parameter and the associated pion mass for lattice QCD with $N_f=2$ degenerate standard Wilson fermions on $N_\tau\in\{6,8,10\}$ lattices, corresponding to lattice spacings $a=0.12\, {\rm fm}$, $a=0.09\, {\rm fm}$, $a=0.07\, {\rm fm}$, respectively. Significant cut-off effects are observed, with the first-order region growing as the lattice gets finer. While current lattices are still too coarse for a continuum extrapolation, we estimate $m_\pi^c\approx 4 {\rm GeV}$ with a remaining systematic error of $\sim 20\%$. Our results allow to assess the accuracy of the LO and NLO hopping expanded fermion determinant used in the literature for various purposes. We also provide a detailed investigation of the statistics required for this type of calculation, which is useful for similar investigations of the chiral transition.

Chiral phase structure of three flavor QCD in a background magnetic field

We investigate the chiral phase structure of three flavor QCD in a background $U(1)$ magnetic field using the standard staggered action and the Wilson plaquette gauge action. We perform simulations on lattices with a temporal extent of $N_\tau=4$ and four spatial extents of $N_\sigma = 8,16, 20$ and 24. We choose a smaller-than-physical quark mass in lattice spacing as $am = 0.030$ such that there exists a crossover transition at vanishing magnetic fields, and adopt two values of magnetic field strength in lattice spacing $a \sqrt{ e{B}}\simeq 1.5$ and 2. We find that the transition becomes stronger in the presence of a background magnetic field, and turns into a first order as seen from the volume scaling of the order parameter susceptibility as well as the metastable states in the time history of the chiral condensate. On the other hand, the chiral condensate and transition temperature always increase with $B$ even within the regime of a first order phase transition. This suggests that the discrepancy in the behavior of chiral condensates and transition temperature as a function of $B$ between earlier lattice studies using larger-than-physical pion masses with standard staggered fermions and those using physical pions with improved staggered fermions is mainly due to lattice cutoff effects.

Asymptotic behavior of cutoff effects in Yang\u2013Mills theory and in Wilson\u2019s lattice QCD

Discretization effects of lattice QCD are described by Symanzik’s effective theory when the lattice spacing, a, is small. Asymptotic freedom predicts that the leading asymptotic behavior is sim a^{n_{mathrm{min}}}[{bar{g}}^2(a^{-1})]^{hat{gamma }_1} sim a^{n_{mathrm{min}}}left[ frac{1}{-log (aLambda )}right] ^{hat{gamma }_1}. For spectral quantities, {n_{mathrm{min}}}=d is given in terms of the (lowest) canonical dimension, d+4, of the operators in the local effective Lagrangian and hat{gamma }_1 is proportional to the leading eigenvalue of their one-loop anomalous dimension matrix gamma ^{(0)}. We determine gamma ^{(0)} for Yang–Mills theory ({n_{mathrm{min}}}=2) and discuss consequences in general and for perturbatively improved short distance observables. With the help of results from the literature, we also discuss the {n_{mathrm{min}}}=1 case of Wilson fermions with perturbative mathrm{O}(a) improvement and the discretization effects specific to the flavor currents. In all cases known so far, the discretization effects are found to vanish faster than the naive sim a^{n_{mathrm{min}}} behavior with rather small logarithmic corrections – in contrast to the two-dimensional O(3) sigma model.

Finite size and cut-off effects on the Roberge-Weiss transition in Nf=2 QCD with staggered fermions

In the absence of a genuine solution to the sign problem, lattice studies at imaginary quark chemical potential are an important tool to constrain the QCD phase diagram. We calculate the values of the tricritical quark masses in the Roberge-Weiss plane, $\mu=\imath\pi T/3$, which separate mass regions with chiral and deconfinement phase transitions from the intermediate region, for QCD with $N_\text{f}=2$ unimproved staggered quarks on $N_\tau=6$ lattices. A quantitative measure for the quality of finite size scaling plots is developed, which significantly reduces the subjective judgement required for fitting. We observe that larger aspect ratios are necessary to unambiguously determine the order of the transition than at $\mu=0$. Comparing with previous results from $N_\tau=4$ we find a $\sim50$% reduction in the light tricritical pion mass. The heavy tricritical pion mass stays roughly the same, but is too heavy to be resolved on $N_\tau=6$ lattices and thus equally afflicted with cut-off effects. Further comparison with other discretizations suggests that current cut-off effects on the light critical masses are likely to be larger than $\sim100$%, implying a drastic shrinking of the chiral first-order region to possibly zero.

Dislocation drag from phonon wind in an isotropic crystal at large velocities

ABSTRACTThe anharmonic interaction and scattering of phonons by a moving dislocation, the photon wind, imparts a drag force on the dislocation. In early studies, the drag coefficient B was computed and experimentally determined only for dislocation velocities v much less than transverse sound speed, . In this paper, we derive analytic expressions for the velocity dependence of B up to in terms of the third-order continuum elastic constants of an isotropic crystal, in the continuum Debye approximation. In so doing we point out that the most general form of the third order elastic potential for such a crystal and the dislocation-phonon interaction requires two additional elastic constants involving asymmetric local rotational strains, which have been neglected previously. We compute the velocity dependence of the transverse phonon wind contribution to B in the range 1–90% for Al, Cu, Fe, and Nb in the isotropic Debye approximation. The drag coefficient for transverse phonons scattering from screw dislocations is finite as , whereas B is divergent for transverse phonons scattering from edge dislocations in the same limit. This divergence indicates the breakdown of the Debye approximation and sensitivity of the drag coefficient at very high velocities to the microscopic crystalline lattice cutoff. We compare our results to experimental results wherever possible and identify ways to validate and further improve the theory of dislocation drag at high velocities with realistic phonon dispersion relations, inclusion of lattice cutoff effects, MD simulation data, and more accurate experimental measurements.

Polymer representation of the Bianchi IX cosmology in the Misner variables

We analyze the Bianchi IX Universe in the Polymer Quantum Mechanics framework by facing both semiclassical and purely quantum effects near the cosmological singularity. We adopt Misner variables to describe the model dynamics, applying the polymer paradigm simultaneously to the isotropic one (linked to the Universe volume) and to the two anisotropy ones (characterizing the physical gravitational degrees of freedom). Setting two different cut-off scales for the two different variable sets, i.e. the geometrical volume and the gravity tensor modes, we demonstrate how the semiclassical properties of the Bianchi IX dynamics are sensitive to the ratio of the cut-off parameters. In particular, the semiclassical evolution turns out to be chaotic only if the parameter associated to the volume discretization is greater or equal to that one of the anisotropies. Concerning the chaotic case we perform a purely quantum polymer analysis, demonstrating that the original Misner result about the existence of quasi-classical states near the singularity (in the sense of high occupation numbers) is still valid in the revised approach and able to account for cut-off physics effects. The possibility for a comparison with the original study by Misner is possible because the singularity is still present in the semiclassical evolution of the cosmological model for all the parameter space. We interpret this surprising feature as the consequence of a geometrical volume discretization which does not prevent the volume from vanishing, i.e. restoring in the Minisuperspace analysis its zero value.

Effects of low-pass filter combinations on lower extremity joint moments in distance running

Inverse dynamics is a standard tool in biomechanics, which requires low-pass filtering of external force and kinematic signals. Unmatched filtering procedures are reported to affect joint moment amplitudes in high impact movements, like landing or cutting, but are also common in the analysis of distance running. We analyzed the effects of cut-off frequencies in 94 rearfoot runners at a speed of 3.5 m/s. Additionally, we investigated whether the evaluation of footwear interventions is affected by the choice of cut-off frequencies. We performed 3D inverse dynamics for the hip, knee and ankle joints using different low-pass filter cut-off frequency combinations for a recursive fourth-order Butterworth filter. We observed fluctuations of joint moment curves in the first half of stance, which were most pronounced for the most unmatched cut-off frequency combination (kinematics: 10 Hz; ground reaction forces (GRFs): 100 Hz) and for more proximal joints. Peak sagittal plane hip joint moments were altered by 94% on average. We observed a change in the ranking of subjects based on joint moment amplitude. We found significant (p < 0.001) footwear by cut-off frequency combination interaction effects for most peak joint moments. These findings highlight the importance of cut-off frequency choice in the analysis of joint moments and the assessment of footwear interventions in distance running. Based on our results, we propose to use matched cut-off frequencies around 20 Hz in order to avoid large artificial fluctuations in joint moment curves while at the same time avoiding a severe removal of physiological high-frequency signal content from the GRF signals.