Coalescence Parameters Research Articles

Understanding the energy dependence of B_2 in heavy ion collisions: interplay of volume and space-momentum correlations

The deuteron coalescence parameter B_2 in proton+proton and nucleus+nucleus collisions in the energy range of sqrt{s_{NN}}= 900–7000 GeV for proton + proton and sqrt{s_{NN}}= 2–2760 GeV for nucleus + nucleus collisions is analyzed with the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) transport model, supplemented by an event-by-event phase space coalescence model for deuteron and anti-deuteron production. The results are compared to data by the E866, E877, PHENIX, STAR and ALICE experiments. The B_2 values are calculated from the final spectra of protons and deuterons. At lower energies, sqrt{s_{NN}}le 20 GeV, B_2 drops drastically with increasing energy. The calculations confirm that this is due to the increasing freeze-out volume reflected in B_2sim 1/V. At higher energies, sqrt{s_{NN}}ge 20 GeV, B_2 saturates at a constant level. This qualitative change and the vanishing of the volume suppression is shown to be due to the development of strong radial flow with increasing energy. The flow leads to strong space-momentum correlations which counteract the volume effect.

Predictions for production of HΛ3 and H¯Λ¯3 in isobaric Ru4496+Ru4496 and Zr4096+Zr4096 collisions at sNN=200 GeV

The production of $\rm{^3_\Lambda H}$ and $\rm{{^3_{\overline \Lambda}\overline H}}$, as well as $\rm{^3H}$, $\rm{{^3\overline H}}$, $\rm{^3He}$, and $\rm{{^3\overline {He}}}$ are studied in central collisions of isobars $^{96}_{44}$Ru+$^{96}_{44}$Ru and $^{96}_{40}$Zr+$^{96}_{40}$Zr at $\sqrt{s_{\rm{NN}}}=200$ GeV, using the dynamically constrained phase-space coalescence model and the {\footnotesize PACIAE} model with chiral magnetic effect. The yield, yield ratio, coalescence parameters, and strangeness population factor of (anti-)hypertriton and (anti-)nuclei produced in isobaric $^{96}_{44}$Ru+$^{96}_{44}$Ru and $^{96}_{40}$Zr+$^{96}_{40}$Zr collisions are predicted. The (anti-)hypertriton and (anti-)nuclei production is found to be insensitive to the chiral magnetic effects. Experimental data of Cu+Cu, Au+Au and Pb+Pb collisions from RHIC, LHC, and the results of {\footnotesize PACIAE+DCPC} model are presented in the results for comparison.

Frozen Mode in Three-Way Periodic Microstrip Coupled Waveguide

We demonstrate theoretically and experimentally that a simple periodic fully planar three-way microstrip coupled waveguide exhibits a stationary inflection point (SIP). The SIP is a third-order exceptional point of degeneracy where three eigenmodes of the guiding system coalesce to form a stationary frozen mode with zero group velocity. Here, the frozen mode is shown in a reciprocal three-way waveguide supporting three modes in each direction. We illustrate the occurrence of the frozen mode regime by observing the dispersion diagram and by the coalescence parameter that is a measure of the separation of the three coalescing eigenvectors. Results based on full-wave simulations and measurements demonstrate the coalescence of three modes and how this coalescence is not perfect due to the presence of losses in the microstrip structure at 2 GHz. The coalescence parameter is used to determine how close the three-way system is to the ideal frozen mode condition.

Light Nuclei (d, t) Production in Au + Au Collisions at [formula omitted

In high-energy nuclear collisions, light nuclei can be regarded as a cluster of baryons and their yields are sensitive to the baryon density fluctuations. Thus, the production of light nuclei can be used to study the QCD phase transition, at which the baryon density fluctuation will be enhanced. A yield ratio of light nuclei, defined as N(t)×N(p)/N2(d), is predicted to be a sensitive observable to search for the 1st-order phase transition and/or QCD critical point in heavy-ion collisions. In this paper, we present the energy and centrality dependence of (anti)deuteron and triton production in Au+Au collisions at sNN=7.7,11.5,14.5,19.6,27,39,54.4,62.4,and200GeV measured by the STAR experiment at RHIC. We show beam-energy dependence for the coalescence parameter, B2(d) and B3(t), particle ratios, d/p, t/p, and t/d, and the yield ratio of N(t)×N(p)/N2(d). More importantly, non-monotonic energy dependence is observed for the yield ratio, N(t)×N(p)/N2(d), in 0-10% central Au+Au collisions with a peak around 20-30 GeV. Their physics implications on QCD critical point search and change of the equation of state will be discussed.

Constraining the production mechanism of light (anti-)nuclei in small systems with ALICE at the LHC: Parallel Session - Small systems III

The large samples of high-quality data collected at the LHC by the ALICE Collaboration allow for a systematic study of light (anti-)nuclei production in pp collisions at s=5,7and13TeV and in p–Pb collisions at sNN=5.02TeV. The excellent performance of the Inner Tracking System, Time-Projection Chamber and Time-Of-Flight detectors provide a clear identification and separation of primary produced light (anti-)nuclei from secondaries. The results on deuteron and 3He production as a function of multiplicity in pp and p–Pb collisions are shown. The goal is to study whether the production of (anti-)nuclei in small systems is better described by the coalescence model or by the statistical hadronisation model. The main observables for testing the production mechanisms are the coalescence parameter BA and the ratio between the transverse-momentum integrated yields of nuclei and protons, d/p, 3He/p and 3H/p. These observables are studied as a function of the event multiplicity and compared with the predictions of theoretical models.

Beam-energy dependence of the production of light nuclei in Au + Au collisions

We study the collision energy dependence of (anti-)deuteron and (anti-)triton production in the most central Au+Au collisions at $\sqrt{s_\mathrm{NN}}=$ 7.7, 11.5, 19.6, 27, 39, 62.4 and 200 GeV, using the nucleon coalescence model. The needed phase-space distribution of nucleons at the kinetic freeze-out is generated from a new 3D hybrid dynamical model (\texttt{iEBE-MUSIC}) by using a smooth crossover equation of state (EoS) without a QCD critical point. Our model calculations predict that the coalescence parameters of (anti-)deuteron ($B_2(d)$ and $B_2(\bar{d})$) decrease monotonically as the collision energy increases, and the light nuclei yield ratio $N_t N_p/N_d^2$ remains approximately a constant with respect to the collision energy. These calculated observables fail to reproduce the non-monotonic behavior of the corresponding data from the STAR Collaboration. Without including any effects of the critical point in our model, our results serve as the baseline predictions for the yields of light nuclei in the search for the possible QCD critical points from the experimental beam energy scan of heavy ion collisions.

Deuteron and antideuteron coalescence in heavy-ion collisions: energy dependence of the formation geometry

We investigate the collision energy dependence of deuteron and antideuteron emission in the RHIC-BES low- to mid-energy range $\sqrt{s_{NN}} = 4.6-200$ GeV where the formation rate of antinuclei compared to nuclei is strongly suppressed. In the coalescence picture, this can be understood as bulk emission for nuclei in contrast to surface emission for antinuclei. By comparison with experimental data on the coalescence parameter $B_2$, we are able to extract the respective source geometries. This interpretation is further supported by results from the UrQMD transport model, and establishes the following picture: At low energies, nucleons freeze out over the total fireball volume, while antinucleons are annihilated inside the nucleon-rich fireball and can only freeze out on its surface. Towards higher energies, this annihilation effect becomes irrelevant (due to the decreasing baryochemical potential) and the system's freeze-out is driven by the mesons. Thus, the nucleon and antinucleon freeze-out distributions become similar with increasing energy.

Large-scale simulations of antihelium production in cosmic-ray interactions

The possibility of antihelium production in interaction of cosmic rays with the interstellar gas is studied using large-scale Monte Carlo simulations. For this purpose, an energy-dependent coalescence mechanism developed previously is extended to estimate the production of light antinuclei (${}^3\overline{\text{He}}$ and ${}^4\overline{\text{He}}$). The uncertainty in the coalescence parameter and its effect on the expected antiparticle flux is also investigated. The simulated background antihelium fluxes are found to be lower than the fluxes predicted by simplified models using numerical scaling techniques.

Plastic instability and fracture of ultra-thin stainless-steel sheet

A new approach was used to characterise the hardening, instability and fracture behaviour of ultra-thin (0.1 mm) stainless steel sheets under stress triaxiality ranging from 0.37 to 0.66. The Swift and the linear hardening laws were used to capture the stress–strain relationship for the complete level of plastic deformation that exceeds that achievable by a uniaxial tensile test. For this, the Virtual Field Method (VFM) was applied, which uses the strain field measured on the surface of the notched samples, to output the material hardening parameters. To determine one set of hardening parameters that fits all conditions of stress triaxiality, an upper bound of major strain was selected for the VFM fitting that optimises a single set of hardening parameters across all of the stress triaxiality conditions. The void coalescence parameter in a Gurson-Tvergaard-Needleman (GTN) fracture model was calibrated and the model results for fracture initiation were validated experimentally with a quasi-biaxial stretching test.

Recent results on light (anti-)nuclei production with ALICE at the LHC

The high-statistics and high-quality data samples in pp, p–Pb and Pb–Pb collisions at various collision energies collected by the ALICE Collaboration, and the excellent tracking and particle identification capabilities of the Inner Tracking System, the Time-Projection Chamber and the Time-of-Flight detector allow for the detection of rarely produced light (anti-)(hyper-)nuclei. The first (anti-)triton p T spectra in Pb–Pb at the LHC as well as the first (anti-)4He p T spectra are presented. Moreover, the p T-integrated production yield ratios of deuteron over proton as well as 3He and triton over proton as a function of charged-particle multiplicity are shown. In addition coalescence parameters B 2 and B 3 as a function of p T/A and charge particle multiplicity for several collision systems and energies are discussed. Furthermore, light-nuclei radial and elliptic flow are presented and compared to the flow of lighter particles. These various results are compared with statistical hadronization and coalescence model predictions to provide insight in the production mechanism of light (anti-)nuclei in heavy-ion collisions.

Production of (anti-)He3 and (anti-)H3 in p-Pb collisions at sNN=5.02 TeV

The transverse momentum ($p_{\rm{T}}$) differential yields of (anti-)$^3$He and (anti-)$^3$H measured in p-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 5.02 TeV with ALICE at the Large Hadron Collider (LHC) are presented. The ratios of the $p_{\rm{T}}$-integrated yields of (anti-)$^3$He and (anti-)$^3$H to the proton yields are reported, as well as the $p_{\rm{T}}$ dependence of the coalescence parameters $B_3$ for (anti-)$^3$He and (anti-)$^3$H. For (anti-)$^3$He, the results obtained in four classes of the mean charged-particle multiplicity density are also discussed. These results are compared to predictions from a canonical statistical hadronization model and coalescence approaches. An upper limit on the total yield of $^4\bar{\mathrm{He}}$ is determined.

Investigations on multi-sheets single point incremental forming of commercial pure titanium alloys

ABSTRACT The rate of production in single point incremental forming (SPIF) approach for the sheet metals is comparatively low when comparing to multiple sheet incremental forming process (MSSPIF). This increase in production rate comes with a trade-off of reduced formability in MSSPIF. The aspiration of the current paper is to analyze the formability, the strain distribution, and the void coalescence variables as per the strain triaxiality during the MSSPIF process of the available commercially pure (CP) titanium sheets. The forming limit diagrams (FLDs) and the strain distribution analysis have been carried out for multiple sheets of two, three, and four sheets bunch while they were formed together. The outcomes proved that the uppermost sheets achieved the higher limiting principal true strain and the limiting values of the principal true strain of bottom sheets decreased in accordance with the position of the sheet and the same was reported in FLDs. The void coalescence in the fractured specimen exhibited an enhanced fracture resistance for CP sheets of titanium. The size of void (µm), thickness of ligament (LT), void (L/W) ratio, d-factor, strain triaxiality, and other void coalescence parameters also have been compared when two, three, and four sheets were formed together during MSSPIF process.

Alternative coalescence model for deuteron, tritium, helium-3 and their antinuclei

Antideuteron and antihelium nuclei have been proposed as a detection channel for dark matter annihilations and decays in the Milky Way, due to the low astrophysical background expected. To estimate both the signal for various dark matter models and the astrophysical background, one employs usually the coalescence model in a Monte Carlo framework. This allows one to treat the production of antinuclei on an event-by-event basis, taking thereby into account momentum correlations between the antinucleons involved in the process. This approach lacks however an underlying microscopic picture, and the numerical value of the coalescence parameter obtained from fits to different reactions varies considerably. Here we propose instead to combine event-by-event Monte Carlo simulations with a microscopic coalescence picture based on the Wigner function representations of the produced antinuclei states. This approach allows us to include in a semi-classical picture both the size of the formation region, which is process dependent, and momentum correlations. The model contains a single, universal parameter which is fixed by fitting the production spectra of antideuterons in proton-proton interactions, measured at the Large Hadron Collider. Using this value, the model describes well the production of various antinuclei both in electron-positron annihilation and in proton-proton collisions.

Numerical investigation and modelling of the venous injection of sclerosant foam

Sclerosant foam, a mixture of a surfactant liquid and air, is injected directly into varicose veins as a treatment that causes the vein to collapse. This investigation develops a model that will allow the medical specialist to visualise how the sclerosant foam will interact with the blood and behave within the vein. The process is simulated using a multiphase computational fluid dynamics model with the sclerosant foam considered as a two-phase non-Newtonian power law viscosity liquid. The governing multiphase equations are solved using an Eulerian⁠–⁠Eulerian approach coupled with a population balance model to predict the bubble size distribution within the flow field. The computational results demonstrate similar flow characteristics and flow features to an available set of experimental results. The model predicts the mixing layers between the sclerosant foam and the ambient fluid, and the sclerosant liquid and the ambient fluid, as well as the sclerosant liquid coverage on the vein wall and the bubble size distribution within the vein. These quantities are of interest to medical specialists allowing them to assess the treatment feasibility and safety before treating the patients. 
 
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A Comparison of Fracture Limit Analysis on Titanium Grade 2 and Titanium Grade 4 Sheets During Single Point Incremental Forming

The influence of tensile properties, void coalescence parameters, strain triaxiality $$\left( {\frac{{\varepsilon_{\text{m}} }}{{\varepsilon_{\text{eff}} }}} \right)$$ and its fracture limits for various spindle rotational speeds in single point incremental forming were compared for titanium grade 2 and grade 4 sheets. The microstructure reveals the presence of α and β phase particles, as was confirmed using x-ray diffraction analysis. Forming limit diagrams and fracture limit curves were plotted for the sheets and the results were compared for both titanium grade sheets. The void coalescence in fractured samples showed an improved fracture resistance for the titanium grade 2 sheets compared with the titanium grade 4 sheets. The void size, ligament thickness, void (L/W) ratio, d-factor, strain triaxiality and further void coalescence parameters were also compared. In all cases, because of their better ductility, the titanium grade 2 sheets exhibited better forming and fracture limits (void coalescence) than that of grade 4 sheets.

Light (anti)nuclei production in Cu+Cu collisions at $\sqrt{s_{NN}} = 200$ GeV

The production of light (anti)nuclei have been investigated using the dynamically constrained phase-space coalescence model based on the final-state hadrons generated by the PACIAE model in Cu+Cu collisions at $\sqrt{s_{\rm{NN}}}=200$GeV with $|\eta|<0.5$ and $0<p_T<8$GeV/c. The results show that there is a strong centrality dependence of yields of $\rm d$, $\rm\overline d$, $\rm ^3He$, $\rm^3\overline {He}$, $\rm ^4He$, and $\rm^4\overline {He}$, i.e., their yields decrease rapidly with the increase of centrality, and the greater the mass is, the greater the dependence shows; whereas their ratio of antinucleus to nucleus and coalescence parameter $B_A$ remain constant as the centrality increases. In addition, the yields of (anti)nuclei are strongly dependent on the mass of the (anti)nuclei, indicating that the (anti)nuclei produced have mass scaling properties in high-energy heavy-ion collisions. Our results are consistent with the STAR experimental data.

Performance Map for the Design of Liquid‐Liquid Extraction Columns

AbstractFor the fast approximation of liquid‐liquid extraction column designs via HETS (height equivalent of a theoretical stage) values and flooding points, a population balance model was developed. The model requires only one pilot‐scale column experiment to fit a coalescence parameter. The comparison of experimental data with simulations shows good agreement for a stirred extraction column. With the model, the operation domain of the column is simulated and visualized in a performance map, showing the holdup, the distance to the flooding point and HETS values.

Beam energy dependence of (anti-)deuteron production in Au + Au collisions at the BNL Relativistic Heavy Ion Collider

We report the energy dependence of mid-rapidity (anti-)deuteron production in Au+Au collisions at $\sqrt{s_\text{NN}} =\ $7.7, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200 GeV, measured by the STAR experiment at RHIC. The yield of deuterons is found to be well described by the thermal model. The collision energy, centrality, and transverse momentum dependence of the coalescence parameter $B_2$ are discussed. We find that the values of $B_2$ for anti-deuterons are systematically lower than those for deuterons, indicating that the correlation volume of anti-baryons is larger than that of baryons at $\sqrt{s_\text{NN}}$ from 19.6 to 39 GeV. In addition, values of $B_2$ are found to vary with collision energy and show a broad minimum around $\sqrt{s_\text{NN}}=\ $20 to 40 GeV, which might imply a change of the equation of state of the medium in these collisions.

CFD Analysis for Two Phase Performance in 5×5 Rod Bundle with 7 Spacer Girds

A 5×5 rod bundles with 7 spacer girds which structure mixing gird (MG) and mid span mixing gird (MSMG) are arranged alternant are studied by two phase computational fluid mechanic(CFD), and bubbles coalescence and breakup, and heat transfer are considered in the calculation, but not the interface mass change. In order to choose the reasonable two phase model parameters, 5×5 rod bundles with 2 spacer girds (MG and MSMG) based on AFA3G fuel assembly isstudied by two phase CFD, and the sensitivity and uncertainty analysis is conducted on max bubble size, bubbles coalescence and breakup model parameters, non-drag force model, drag force model parameters, inlet bubble diameter and inlet void fraction distribution. Use this model setting, the study of the two phase performance is conducted on AFA3G fuel assembly with 7 spacer grids. The calculation shows that the bubble through the spacer grid is without periodicity, but the void fraction fields of every MSMG upstream are similar and the MG upstream shows the same situation. This research is useful to choose the model setting and geometry size for the rod bundle with spacer girds in the two phase calculation, for geometry size it is possible to analyze the two phase performance on rod bundle with 2 or 3 spacer grids. Finally, the void fraction distribution of AFA3G fuel assembly and advanced fuel assembly are compared, and evaluated in terms of the improvement of the CHF. It agrees well with the experiment, which verifies the evaluation method, the research is the base for the establishment of the evaluation guideline for the thermal hydraulic performance of the fuel assembly by two phase CFD calculation.

Multiplicity dependence of (anti-)deuteron production in pp collisions at [formula omitted

In this letter, the production of deuterons and anti-deuterons in pp collisions at s=7 TeV is studied as a function of the charged-particle multiplicity density at mid-rapidity with the ALICE detector at the LHC. Production yields are measured at mid-rapidity in five multiplicity classes and as a function of the deuteron transverse momentum (pT). The measurements are discussed in the context of hadron–coalescence models. The coalescence parameter B2, extracted from the measured spectra of (anti-)deuterons and primary (anti-)protons, exhibits no significant pT-dependence for pT<3GeV/c, in agreement with the expectations of a simple coalescence picture. At fixed transverse momentum per nucleon, the B2 parameter is found to decrease smoothly from low multiplicity pp to Pb–Pb collisions, in qualitative agreement with more elaborate coalescence models. The measured mean transverse momentum of (anti-)deuterons in pp is not reproduced by the Blast-Wave model calculations that simultaneously describe pion, kaon and proton spectra, in contrast to central Pb–Pb collisions. The ratio between the pT-integrated yield of deuterons to protons, d/p, is found to increase with the charged-particle multiplicity, as observed in inelastic pp collisions at different centre-of-mass energies. The d/p ratios are reported in a wide range, from the lowest to the highest multiplicity values measured in pp collisions at the LHC.