Low Momentum Region Research Articles

Unthrottled Flows with Complex Background Waves in Curved Isolators

The unthrottled flows in curved isolators are studied experimentally and numerically. Wind-tunnel tests are conducted at a freestream Mach number of 4.92. The internal flowfield is visualized and measured. Large-scale separation bubbles in the inlet are observed, and the downstream duct curvature is found to be able to decrease the separation bubble size via lowering the local pressure downstream of the separation bubble. Complex background waves appear in these isolators, and the increase of duct curvature tends to intensify the reflected shocks. Particularly, the strength distributions along the shock direction of the background shocks behave differently under the influence of duct curvature. For the right-running shocks, the strength distribution changes from a descending trend to an ascending trend with the increase of duct curvature, whereas the strength of left-running shocks always descends with an increasing speed. The strength of background shocks is particularly related to the left-running expansion waves, which get intensified and become the dominant expansion waves in the isolators as the duct curvature increases. The schlieren images indicate a significant transverse density gradient and pressure gradient in the curved isolators. The wall pressure distributions further show that the radial pressure gradient in small curvature isolators switches between centripetal and centrifugal repeatedly; whereas it remains centripetal consistently in large curvature isolators, which is also determined by the left-running expansion waves. As a result, the secondary flow gets stronger as the duct curvature increases, resulting in a larger low-momentum flow region near the bottom wall. In general, the compression capability of the isolator gets attenuated with the increase of the duct curvature.

Up- and down-quark contributions to the nucleon electromagnetic form factors at low Q2

The spatial distribution of charge and magnetization within the nucleon (proton and neutron) is encoded in the elastic electromagnetic form factors and . These form factors have been precisely measured utilizing elastic electron scattering, and the combination of proton and neutron form factors allows for the separation of the up- and down-quark contributions to the nucleon form factors. We expand on our original analyses and extract the up- and down-quark contributions to the nucleon electromagnetic form factors from worldwide data with an emphasis on precise new data covering the low-momentum region, which is sensitive to the large-scale structure of the nucleon. From these, we construct the flavor-separated Dirac and Pauli form factors and their ratios, and compare the results to recent extractions and theoretical calculations and models.

Phenomenological extraction of two-photon exchange amplitudes from elastic electron-proton scattering cross section data

In this work, I improve on and extend to low and high $Q^2$ values the extractions of the $\varepsilon$ dependence of the real parts of the two-photon exchange (TPE) amplitudes relative to the magnetic form factor, as well as the ratio $P_l/P_l^{Born} (\varepsilon,Q^2)$ by using world data on $\sigma_R(\varepsilon,Q^2)$ with an emphasis on precise new data covering the low-momentum region which is sensitive to the large-scale structure of the nucleon. I provide simple parametrizations of the TPE amplitudes, along with an estimate of the fit uncertainties. The extracted TPE amplitudes are compared with previous phenomenological extractions and TPE calculations. The $P_l/P_l^{Born}$ ratio is extracted by using the new parametrizations of the TPE amplitudes and compared to previous extractions, TPE calculations, and direct measurements at $Q^2$ = 2.50 (GeV/c)$^2$. The extracted TPE amplitudes are on the few-percentage-points level and behave roughly linearly with increasing $Q^2$ where they become nonlinear at high $Q^2$. Contrary to $Y_M$, which is influenced mainly by elastic contributions, I find $Y_E$ to be influenced by inelastic contributions at large $Q^2$ values. While $Y_E$ and $Y_3$ differ in magnitude, they have opposite sign and tend to partially cancel each other. This suggests that the TPE correction to $\sigma_R(\varepsilon,Q^2)$ is driven mainly by $Y_M$ and to a lesser extent by $Y_3$ in agreement with previous phenomenological extractions and hadronic TPE calculations.

Multiplicity and transverse momentum evolution of charge-dependent correlations in pp, p-Pb, and Pb-Pb collisions at the LHC

We report measurements of two-particle charge-dependent correlations in pp, p-Pb, and Pb-Pb collisions at , and 2.76 TeV, respectively, as a function of pseudorapidity and azimuthal angle differences. These measurements, carried out using the balance function, probe the charge creation time and the development of collectivity in the produced systems. The balance function is studied as a function of the event multiplicity as well as the transverse momentum (pT) of charged particles detected in the range |η| < 0.8. In the low transverse momentum region, 0.2 < pT < 2.0 GeV/c, the balance function becomes narrower in both Δη and Δφ directions in all three systems for events with higher multiplicity. For higher values of transverse momenta, the balance function becomes even narrower but exhibits no significant multiplicity dependence, indicating that the observed narrowing with increasing multiplicity at low pT is a feature of bulk particle production.

ALICE measures pA collisions: Collectivity in small systems?

Proton-nucleus collisions provide a reference for heavy ion-collisions, to study the signatures deriving from the presence of a complex nuclear structure in the initial state, which confirm that the suppression of high-pThadron production observed in heavy-ion collisions is a genuine effect of the hot deconfined QGP. However, several measurements of particle production in the low and intermediate momentum region indicate the presence of coherent and collective effects, already in small systems, such as the ones produced in p-Pb collisions. Measurements from proton-lead collisions at √sNN = 5.02 TeV obtained by the ALICE experiment at the CERN LHC will be presented and compared to p-p, A-A and d-A experimental results at different collision energies and to the available theoretical model predictions.

Low-frequency dynamics in a shock-induced separated flow

The low-frequency unsteadiness in the direct numerical simulation of a Mach 2.9 shock wave/turbulent boundary layer interaction with mean flow separation is analysed using dynamic mode decomposition (DMD). The analysis is applied both to three-dimensional and spanwise-averaged snapshots of the flow. The observed low-frequency DMD modes all share a common structure, characterized by perturbations along the shock, together with streamwise-elongated regions of low and high momentum that originate at the shock foot and extend into the downstream flow. A linear superposition of these modes, with dynamics governed by their corresponding DMD eigenvalues, accurately captures the unsteadiness of the shock. In addition, DMD analysis shows that the downstream regions of low and high momentum are unsteady and that their unsteadiness is linked to the unsteadiness of the shock. The observed flow structures in the downstream flow are reminiscent of Görtler-like vortices that are present in this type of flow due to an underlying centrifugal instability, suggesting a possible physical mechanism for the low-frequency unsteadiness in shock wave/turbulent boundary layer interactions.

Shock Train/Boundary-Layer Interaction in Rectangular Isolators

Shock trains in rectangular isolators with inflow Mach number of 2.5 and ARs of 3.0 and 6.0 are investigated. Knowledge gained is used to propose a rectangular isolator modification to existing empirical shock train length relations based on circular ducts. A novel, multiplane shadowgraph concept allows simultaneous flow visualization from multiple perspectives. Boundary-layer separation in the low-momentum corner flow regions is observed to occur upstream of the center-flow field by approximately one duct height. The leading edge shock train structure is composed of a hybrid oblique–normal shock front, with oblique shocks spawning from the corner flow separation transforming into a normal shock front near the centerline. Dynamic wall pressure measurements made along the duct major axis allow for direct comparison between the outboard and centerline sensor’s ability to detect incipient unstart, with the outboard sensor detecting the separation-induced pressure rise well ahead of centerline measurements. A modified shock train length relation for rectangular isolators accounts for the effects of potential boundary-layer momentum thickness asymmetry, upstream corner flow separation length scale, and AR magnitude. Improvements in correlation strength are discussed for both ARs, with coefficient of determination and root mean square error improvements on the order of 60% observed for the highest AR tested.

Conditionally Averaged Large-Scale Motions in the Neutral Atmospheric Boundary Layer: Insights for Aeolian Processes

Aeolian erosion of flat, arid landscapes is induced (and sustained) by the aerodynamic surface stress imposed by flow in the atmospheric surface layer. Conceptual models typically indicate that sediment mass flux, Q (via saltation or drift), scales with imposed aerodynamic stress raised to some exponent, n, where $$n > 1$$ . This scaling demonstrates the importance of turbulent fluctuations in driving aeolian processes. In order to illustrate the importance of surface-stress intermittency in aeolian processes, and to elucidate the role of turbulence, conditional averaging predicated on aerodynamic surface stress has been used within large-eddy simulation of atmospheric boundary-layer flow over an arid, flat landscape. The conditional-sampling thresholds are defined based on probability distribution functions of surface stress. The simulations have been performed for a computational domain with $$\approx 25 H$$ streamwise extent, where H is the prescribed depth of the neutrally-stratified boundary layer. Thus, the full hierarchy of spatial scales are captured, from surface-layer turbulence to large- and very-large-scale outer-layer coherent motions. Spectrograms are used to support this argument, and also to illustrate how turbulent energy is distributed across wavelengths with elevation. Conditional averaging provides an ensemble-mean visualization of flow structures responsible for erosion ‘events’. Results indicate that surface-stress peaks are associated with the passage of inclined, high-momentum regions flanked by adjacent low-momentum regions. Fluid in the interfacial shear layers between these adjacent quasi-uniform momentum regions exhibits high streamwise and vertical vorticity.

Appearance of novel modes ofD¯mesons with negative velocity in the dual chiral density wave

We calculate dispersion relations for $\bar{D}(0^-)$, $\bar{D}^*(1^-)$, $\bar{D}_0^*(0^+)$ and $\bar{D}_1(1^+)$ mesons in the Dual Chiral Density Wave (DCDW) where the chiral symmetry is spontaneously broken by inhomogeneous chiral condensate. Employing the Bloch's theorem, we show that all the modes have opposite group velocity to the momentum in the low-momentum region and the energy is minimized at non-zero momentum. Furthermore, the magnitude of momentum which realizes the minimum energy is equal to the wave number of the density wave.

Electron momentum spectroscopy of aniline taking account of nuclear dynamics in the initial electronic ground state

The electronic structure, electron binding energy spectrum and (e, 2e) momentum distributions of aniline have been theoretically predicted at an electron impact energy of 1.500 keV on the basis of Born–Oppenheimer molecular dynamical simulations, in order to account for thermally induced nuclear motions in the initial electronic ground state. Most computed momentum profiles are rather insensitive to thermally induced alterations of the molecular structure, with the exception of the profiles corresponding to two ionization bands at electron binding energies comprised between ∼10.0 and ∼12.0 eV (band C) and between ∼16.5 and ∼20.0 eV (band G). These profiles are found to be strongly influenced by nuclear dynamics in the electronic ground state, especially in the low momentum region. The obtained results show that thermal averaging smears out most generally the spectral fingerprints that are induced by nitrogen inversion.

Numerical Investigation of Kelvin–Helmholtz Instability in a Centrifugal Compressor Operating Near Stall

The present work details the occurrence of the Kelvin–Helmholtz instability in a centrifugal compressor operating near stall. The analysis is based on unsteady three-dimensional simulations performed on a calculation domain covering the full annulus for the impeller and the vaned diffuser. A detailed investigation of the flow structure is presented, together with its evolution consequent to the mass flow reduction. It is demonstrated that this reduction leads to an enlargement of the low-momentum flow region initially induced by the combination of the secondary and leakage flows. When the compressor operates near stall, the shear layer at the interface between the main flow and this low-momentum flow becomes unstable and induces a periodic vortex shedding. The frequency of such an unsteady phenomenon is not correlated with the blade-passing frequency. Its signature is thus easily isolated from the deterministic rotor/stator interaction. Its detection requires full-annulus simulations with an accurate resolution in time and space, which explains why it has never been previously observed in centrifugal compressors.

Insight into the electron–positron correlations in metals through the looking glass

A semi-empirical analysis of the positron annihilation experimental spectra indicates for a strong sensitivity of the two-particle electron–positron (e–p) enhancement factor to the l=s, p, d, f character of the initial electronic state [1,2]. The essential discrepancy between the models consists in the dependence of the relevant correlation functions on the energy of the annihilating electron. The present contribution contains a theoretical study of the e–p enhancement factors for s, p, d and f states as a function of the electron energy. The slope of the resulting characteristics is directly related to the degree of localisation of the s, p, d and f electrons in the electron density of states. This effect occurs especially for d electrons in transition metals, in favour to the approach of Ref. [1].The energy dependence of the two-particle correlation functions is also a source of controversy between various theoretical approaches. The energy dependent enhancement factors describe properly the positron interaction with delocalised s and p electrons, but this approach overestimates the high momentum components of the e–p momentum densities, dominated by the localised d and f states. On the contrary, the calculations that employ the energy averaged enhancement factors match better with experiment for localised d and f electrons, but they hardly reproduce experimental spectra for nearly-free electron populations. An attempt to visit two sides of the looking glass is made in the theory of the present work. The model combines the properties of both approaches. The resulting e–p momentum densities and enhancement factors are in good agreement with the experimental data for simple, noble and transition metals, both in the low and high momentum region.

Multiplicity and transverse momentum evolution of charge-dependent correlations in pp, p-Pb, and Pb-Pb collisions at the LHC.

We report on two-particle charge-dependent correlations in pp, p–Pb, and Pb–Pb collisions as a function of the pseudorapidity and azimuthal angle difference, Delta eta and Delta varphi respectively. These correlations are studied using the balance function that probes the charge creation time and the development of collectivity in the produced system. The dependence of the balance function on the event multiplicity as well as on the trigger and associated particle transverse momentum (p_{{mathrm {T}}}) in pp, p–Pb, and Pb–Pb collisions at sqrt{s_{mathrm {NN}}}= 7, 5.02, and 2.76 TeV, respectively, are presented. In the low transverse momentum region, for 0.2 < p_{{mathrm {T}}} < 2.0 GeV/c, the balance function becomes narrower in both Delta eta and Delta varphi directions in all three systems for events with higher multiplicity. The experimental findings favor models that either incorporate some collective behavior (e.g. AMPT) or different mechanisms that lead to effects that resemble collective behavior (e.g. PYTHIA8 with color reconnection). For higher values of transverse momenta the balance function becomes even narrower but exhibits no multiplicity dependence, indicating that the observed narrowing with increasing multiplicity at low p_{{mathrm {T}}} is a feature of bulk particle production.

Forward heavy quarkonium productions at the LHC

We investigate the low transverse momentum heavy quarkonium ($J/\psi$, $\Upsilon$) productions in the forward rapidity region of $pp$ and $pA$ collisions at the LHC as an important probe to the transverse momentum tomography of the gluons in hadrons in the Color Glass Condensate (CGC) framework. By implementing the Sudakov resummation consistently in the CGC formalism, we achieve an excellent agreement between the improved CGC calculations and the LHC data. We show that both the small-$x$ and the Sudakov effects are essential for a complete description of heavy quarkonium productions in the low transverse momentum region. This provides a solid foundation to study the small-$x$ gluon saturation in a big nucleus with the future $pA$ programs at the LHC.

Flavor decomposition of the nucleon electromagnetic form factors at lowQ2

Background: The spatial distribution of charge and magnetization within the proton is encoded in the elastic form factors. These have been precisely measured in elastic electron scattering, and the combination of proton and neutron form factors allows for the separation of the up- and down-quark contributions.Purpose: In this work, we extract the proton and neutron form factors from worldwide data with an emphasis on precise new data covering the low-momentum region, which is sensitive to the large-scale structure of the nucleon. From these, we separate the up- and down-quark contributions to the proton form factors.Method: We combine cross section and polarization measurements of elastic electron-proton scattering to separate the proton form factors and two-photon exchange (TPE) contributions. We combine the proton form factors with parametrization of the neutron form factor data and uncertainties to separate the up- and down-quark contributions to the proton's charge and magnetic form factors.Results: The extracted TPE corrections are compared to previous phenomenological extractions, TPE calculations, and direct measurements from the comparison of electron and positron scattering. The flavor-separated form factors are extracted and compared to models of the nucleon structure.Conclusions: With the inclusion of the precise new data, the extracted TPE contributions show a clear change of sign at low ${Q}^{2}$, which is necessary to explain the high-${Q}^{2}$ form factor discrepancy while being consistent with the known ${Q}^{2}\ensuremath{\rightarrow}0$ limit. We find that the new Mainz data yield a significantly different result for the proton magnetic form factor and its flavor-separated contributions. We also observe that the rms radius of both the up- and down-quark distributions are smaller than the rms charge radius of the proton.

Elliptic flow of identified hadrons in Pb-Pb collisions at s N N = 2.76 $$ \sqrt{s_{\mathrm{NN}}}=2.76 $$ TeV

The elliptic flow coefficient ($v_{2}$) of identified particles in Pb-Pb collisions at $\sqrt{s_\mathrm{{NN}}} = 2.76$ TeV was measured with the ALICE detector at the LHC. The results were obtained with the Scalar Product method, a two-particle correlation technique, using a pseudo-rapidity gap of $|\Delta\eta| > 0.9$ between the identified hadron under study and the reference particles. The $v_2$ is reported for $\pi^{\pm}$, $\mathrm{K}^{\pm}$, $\mathrm{K}^0_\mathrm{S}$, p+$\overline{\mathrm{p}}$, $\mathrm{\phi}$, $\Lambda$+$\overline{\mathrm{\Lambda}}$, $\Xi^-$+$\overline{\Xi}^+$ and $\Omega^-$+$\overline{\Omega}^+$ in several collision centralities. In the low transverse momentum ($p_{\mathrm{T}}$) region, $p_{\mathrm{T}} < 2 $GeV/$c$, $v_2(p_\mathrm{T})$ exhibits a particle mass dependence consistent with elliptic flow accompanied by the transverse radial expansion of the system with a common velocity field. The experimental data for $\pi^{\pm}$ and $\mathrm{K}$ are described fairly well by hydrodynamical calculations coupled to a hadronic cascade model (VISHNU) for central collisions. However, the same calculations fail to reproduce the $v_2(p_\mathrm{T})$ for p+$\overline{\mathrm{p}}$, $\mathrm{\phi}$, $\Lambda$+$\overline{\mathrm{\Lambda}}$ and $\Xi^-$+$\overline{\Xi}^+$. For transverse momentum values larger than about 3 GeV/$c$, particles tend to group according to their type, i.e. mesons and baryons. However, the experimental data at the LHC exhibit deviations from the number of constituent quark (NCQ) scaling at the level of $\pm$20$\%$ for $p_{\mathrm{T}} > 3 $GeV/$c$.

Numerical simulation of flow over urban-like topographies and evaluation of turbulence temporal attributes

We have used large-eddy simulation with an immersed boundary method to study turbulent flows over distributions of uniform height, staggered cubes. The computational domains were designed such that both the roughness sublayer and a region of the inertial layer are resolved. With this, we record vertical profiles of time series of fluctuating streamwise and vertical velocity at different locations throughout the domain. Contour images of these fluctuating quantities shown relative to elevation and time are studied; contour images of Reynolds shear stresses owing to ‘sweeps’ and ‘ejections’ are also studied. These images show that periods of momentum excess (deficit) in the inertial-layer precede excitation (subdual) of cube-scale coherent vortices in the roughness sublayer. We compute this time lag (termed advective lag) and demonstrate that it scales linearly with wall-normal elevation. The advective lag is attributed to coherent, low- and high-momentum regions in the aloft inertial layer. Vortex identification is used to illustrate the presence of hairpin packets encapsulating low-momentum regions. Based on this, the reported inclination angle associated with hairpin packets is used to guide the development of a model for prediction of advective lag with height. The model captures the advective lag profiles reasonably well. In the interest of generality, additional cases of flow over homogeneous roughness (aerodynamic drag imposed with the equilibrium logarithmic law) are considered. We again observe that advective lag scales linearly with wall-normal elevation. Advective lag predictions from the aforementioned model agree well with results for these cases.

Abstract 566: Experimental Investigation of Blood Flow in the Femoral Bifurcated Artery

Stent implantation is one of the most widely used interventional treatments for arterial stenosis which occurs predominantly due to atherosclerosis. Although stent placement can ensure very good patency of the lumen, stent-induced hemodynamic disturbance, which can lead to further stenosis, still remains a common clinical complication. This study investigates the degree of hemodynamic disturbance induced by stenting an idealized bifurcated popliteal artery, which branches into the anterior and posterior tibial arteries, and is known as a site prone to atherosclerosis. Both stent-free and stented bifurcated arteries were examined, and the local flow patterns analysed for the comparative disturbance through the use of Micro Particle Image Velocity (micro-PIV) system. A life-size model of the artery was reconstructed using dimensions obtained from a patient specific MRI scan. The experiments were conducted under steady flow conditions, and the flow rates across the bifurcation were visualized and measured using the micro-PIV system. It was shown that hemodynamic disturbances induced by the blood flow over the stent can further disrupt the arterial wall downstream of the stent causing further downstream vascular damage in addition to the in-stent restenosis. This downstream vascular disruption may require additional treatment depending on the type and severity of the damage. The results also support the hypothesis that links certain flow dynamic behaviour with the development of early intimal thickening, as the near wall low fluid momentum regions are found at locations where thickening was localized in bifurcated arteries in clinical studies.

Anisotropic flow of identified particles in Pb–Pb collisions at √sNN= 2.76 TeV measured with ALICE at the LHC

The anisotropic flow (υn) of identified particles is an important observable to probe the freeze-out properties, the parton energy loss and the transport coefficients of the system created in heavy-ion collisions. We report on the anisotropic flow measurements for a number of identified particles such as charged pions, kaons and (anti-)protons, as well as K0s, Λ(Λ̄), ϕ, Ξ−(Ξ̅+), and Ω−(Ω̅+). The measurements are performed in the rapidity range |y| < 0.5, over a wide range of transverse momenta, 0.2 < pT < 6 GeV/c, for Pb–Pb collisions at √sNN = 2.76 TeV recorded by ALICE at the LHC. We will present the mass ordering as a function of transverse momentum for several collision centralities compared with results allower energies. While in the low pT region hydrodynamical computations describe the experimental data points fairly well, at intermediate momenta the quark number (nq) scaling indicates that it holds at an approximate level of 20–30%. Finally, focusing on the low momentum region ALICE has recently observed a similar mass ordering behaviour of υ2 in p–Pb systems. We will present this intriguing result which may be connected to a collective effect similar to that observed in Pb–Pb collisions.

Lamb shift of energy levels in quantum rings

We study the vacuum radiative corrections to energy levels of a confined electron in quantum rings. The calculations are provided for the Lamb shift of energy levels in a low-momentum region of virtual photons and for both one-dimensional and two-dimensional quantum rings. We show that contrary to the well known case of a hydrogen atom the value of the Lamb shift increases with the magnetic momentum quantum number m. We also investigate the dependence of the Lamb shift on magnetic flux piercing the ring and demonstrate a presence of magnetic-flux-dependent oscillations. For a one-dimensional ring the value of the shift strongly depends on the radius of the ring. It is small for semiconductor rings but can attain measurable quantities in natural organic ring-shape molecules, such as benzene, cycloalcanes and porphyrins.