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Song Zhang

Song Zhang contributes to research discovery and scholarly infrastructure.

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Published work

21 published item(s)

preprint2026arXiv

Beyond GSD-as-Token: Continuous Scale Conditioning for Remote Sensing VLMs

Remote sensing vision-language models (RS-VLMs) face a fundamental mismatch with natural-image counterparts: the same geographic object exhibits radically different visual evidence across ground sampling distances (GSDs) spanning multiple orders of magnitude. Yet existing RS-VLMs often discard GSD or inject it as a discrete text token, forcing a single static parameter set to absorb the entire scale spectrum. We introduce ScaleEarth, a parameter-efficient fine-tuning framework built on Qwen3-VL that treats GSD as a continuous conditioning variable governing the model's computation path. At its core, CS-HLoRA (Continuous Scale-Conditioned Hyper-LoRA) modulates the LoRA low-rank subspace through a GSD-driven gate, enabling the model to dynamically route computation by physical scale. To remove reliance on sensor metadata at deployment, we pair CS-HLoRA with SSE-U, a lightweight heteroscedastic sub-head that predicts GSD and its uncertainty from visual features. To provide matching supervision, we construct GeoScale-VQA, a 1.5M-sample scale-layered RS-VQA corpus whose question-answer generation is conditioned on the same physical scalar that drives CS-HLoRA, forming a closed method-data loop. Trained with QLoRA on an 8B backbone, ScaleEarth achieves state-of-the-art results on remote-sensing benchmarks covering diverse Earth-system tasks, including XLRS-Bench and OmniEarth-Bench.

preprint2024arXiv

Effects of the $α$-cluster structure and the intrinsic momentum component of nuclei on the longitudinal asymmetry in relativistic heavy-ion collisions

The longitudinal asymmetry in relativistic heavy ion collisions arises from the fluctuation in the number of nucleons involved. This asymmetry causes a rapidity shift in the center of mass of the participating zone. Both the rapidity shift and the longitudinal asymmetry have been found to be significant at the top CERN Large Hadron Collider (LHC) energy for collisions of identical nuclei, and the longitudinal asymmetry is important for reconstructing the colliding vertex and correcting the rapidity shift. However, much discussion of the longitudinal asymmetry has treated the initial condition as a nonzero momentum contributed only by the number of participants, i.e., the asymmetry depends only on the number of participating nucleons. So we naturally raise a physical problem, can other initial conditions, such as two typical initial conditions for nuclei, geometric configuration, and momentum distribution, provide effects on the longitudinal asymmetry? Therefore, in this work we consider other effects on the longitudinal asymmetry other than the fluctuation in the number of participants, e.g., the α clustering structure as well as the intrinsic momentum distribution in the target and projectile nuclei for the collisions in the framework of a multiphase transport (AMPT) model. By introducing systems with different α-clustering structure and intrinsic momentum distribution, we calculated the ratio of the rapidity distributions of different systems and extracted expansion coefficients to analyze the difference contributed by these factors. ...

preprint2023arXiv

Collective flows of protons and deuterons in Au + Au collisions at $E_{beam}$ = 1.23$A$ GeV by the IQMD model

Collective flows of protons and deuterons for Au + Au collisions at beam energy $E_{beam}$ = 1.23 $A$ GeV were simulated by an Isospin dependent Quantum Molecular Dynamics (IQMD) model. Two coalescence models, namely naive coalescence and dynamical coalescence models, for the formation of deuterons are compared. After reasonable match of rapidity spectra of protons and deuterons to the High Acceptance DiElectron Spectrometer (HADES) data is reached, we apply an event-plane method to calculate the first four-order collective flow coefficients as well as the ratios of $<v_4>/<v_2>^2$ and $<v_3>/<v_1><v_2>$, and observe the number of constituent nucleon scaling among protons and deuterons. In addition, the dependence of $ε_n$ and $v_n$ as well as the ratio $<v_n>$/$ε_n$ on the centrality is obtained. Lastly, we further investigate the Pearson coefficients $corr(v_n,v_m)$ between the first four harmonic flows for protons and deuterons as a function of rapidity and centrality.

preprint2023arXiv

Simulations of momentum correlation functions of light (anti)nuclei in relativistic heavy-ion collisions at $\sqrt{s_{NN}}$ = 39 GeV

Momentum correlation functions of light (anti)nuclei formed by the coalescence mechanism of (anti)nucleons are calculated for several central heavy-ion collision systems, namely $_{5}^{10}\textrm{B}+_{5}^{10}\textrm{B}$, $_{8}^{16}\textrm{O}+_{8}^{16}\textrm{O}$, $_{20}^{40}\textrm{Ca}+_{20}^{40}\textrm{Ca}$ as well as $_{79}^{197}\textrm{Au}+_{79}^{197}\textrm{Au}$ in different centralities at center of mass energy $\sqrt{s_{NN}}$ = 39 GeV within the framework of A Multi-Phase Transport (AMPT) model complemented by the Lednick$\acute{y}$ and Lyuboshitz analytical method. Momentum correlation functions for identical or nonidentical light (anti)nuclei are constructed and analyzed for the above collision systems. The Au + Au results demonstrate that emission of light (anti)nuclei occurs from a source with smaller space extent in more peripheral collisions. The effect of system-size on the momentum correlation functions of identical or nonidentical light (anti)nuclei is also explored by several collision system in central collisions. The results indicate that the emission source-size of light (anti)nuclei pairs deduced from their momentum correlation functions and system-size is self-consistent. Momentum correlation functions of nonidentical light nuclei pairs gated on velocity are applied to infer the average emission sequence of them. The results illustrate that protons are emitted in average on a similar time scale with neutrons but earlier than deuterons or tritons in the small relative momentum region. In addition, larger interval of the average emission order among them is exhibited for smaller collision systems or at more peripheral collisions.

preprint2022arXiv

A Polyphone BERT for Polyphone Disambiguation in Mandarin Chinese

Grapheme-to-phoneme (G2P) conversion is an indispensable part of the Chinese Mandarin text-to-speech (TTS) system, and the core of G2P conversion is to solve the problem of polyphone disambiguation, which is to pick up the correct pronunciation for several candidates for a Chinese polyphonic character. In this paper, we propose a Chinese polyphone BERT model to predict the pronunciations of Chinese polyphonic characters. Firstly, we create 741 new Chinese monophonic characters from 354 source Chinese polyphonic characters by pronunciation. Then we get a Chinese polyphone BERT by extending a pre-trained Chinese BERT with 741 new Chinese monophonic characters and adding a corresponding embedding layer for new tokens, which is initialized by the embeddings of source Chinese polyphonic characters. In this way, we can turn the polyphone disambiguation task into a pre-training task of the Chinese polyphone BERT. Experimental results demonstrate the effectiveness of the proposed model, and the polyphone BERT model obtain 2% (from 92.1% to 94.1%) improvement of average accuracy compared with the BERT-based classifier model, which is the prior state-of-the-art in polyphone disambiguation.

preprint2022arXiv

Azimuthal-sensitive three-dimensional HBT radius in Au-Au collisions at $E_{beam} = 1.23$$A$ GeV by the IQMD model

We used an Isospin dependent Quantum Molecular Dynamics (IQMD) model to simulate Au + Au collisions at beam energy $E_{beam}$ = 1.23$A$ GeV, which corresponds to center of mass energy $\sqrt{s_{NN}} = 2.4$ GeV. Firstly, we obtained reasonable rapidity and transverse mass spectra of $π^-$ and $π^+$ as well as &#34;apparent&#34; temperature parameters in comparison with the HADES data. Then by calculating three-dimensional Hanbury Brown and Twiss (HBT) radius of same charged pion-pairs, we obtained the square difference of outward radius and sideward radius, i.e. $R_{out}^{2}-R_{side}^{2}$, as well as the freeze-out volume ($V_{fo}$), which were basically consistent with the trend of HADES experimental results. The azimuthal dependence of the HBT radii was also calculated by a matrix method, and corrected by the rotation matrix. In addition, the eccentricities of the $xy$- and $zy$- planes of pion-pair emissions were also extracted for different pair transverse momentum and collision centrality, which show that the $xy$-eccentricity increases with pair transverse momentum as well as centrality but not for $zy$-eccentricity, indicating a more asymmetric transverse emission of particle-pairs with higher transverse momentum in off-central collisions.

preprint2022arXiv

Impact of nuclear structure on the CME background in $^{96}_{44}$Ru + $^{96}_{44}$Ru and $^{96}_{40}$Zr + $^{96}_{40}$Zr collisions at $\sqrt{s_{NN}}$ = 7.7 $\sim$ 200 GeV from a multiphase transport model

Impacts of nuclear structure on multiplicity ($N_{ch}$) and anisotropic flows ($v_{2}$ and $v_{3}$) in the isobaric collisions of $^{96}_{44}$Ru + $^{96}_{44}$Ru and $^{96}_{40}$Zr + $^{96}_{40}$Zr at $\sqrt{s_{NN}}$ = 7.7, 27, 62.4 and 200 GeV are investigated by using the string melting version of A MultiPhase Transport (AMPT) model. In comparison with the experimental data released recently by the STAR collaboration, it is found that the impact of quadrupole deformation $β_{2}$ on the $v_{2}$ difference is mainly manifested in the most central collisions, while the octupole deformation $β_{3}$ is in the near-central collisions, and the neutron skin effect dominates in the mid-central collisions. Viewing from the energy dependence, these effects are magnified at lower energies.

preprint2022arXiv

Machine Learning for Continuous Quantum Error Correction on Superconducting Qubits

Continuous quantum error correction has been found to have certain advantages over discrete quantum error correction, such as a reduction in hardware resources and the elimination of error mechanisms introduced by having entangling gates and ancilla qubits. We propose a machine learning algorithm for continuous quantum error correction that is based on the use of a recurrent neural network to identify bit-flip errors from continuous noisy syndrome measurements. The algorithm is designed to operate on measurement signals deviating from the ideal behavior in which the mean value corresponds to a code syndrome value and the measurement has white noise. We analyze continuous measurements taken from a superconducting architecture using three transmon qubits to identify three significant practical examples of non-ideal behavior, namely auto-correlation at temporal short lags, transient syndrome dynamics after each bit-flip, and drift in the steady-state syndrome values over the course of many experiments. Based on these real-world imperfections, we generate synthetic measurement signals from which to train the recurrent neural network, and then test its proficiency when implementing active error correction, comparing this with a traditional double threshold scheme and a discrete Bayesian classifier. The results show that our machine learning protocol is able to outperform the double threshold protocol across all tests, achieving a final state fidelity comparable to the discrete Bayesian classifier.

preprint2022arXiv

NTIRE 2022 Challenge on High Dynamic Range Imaging: Methods and Results

This paper reviews the challenge on constrained high dynamic range (HDR) imaging that was part of the New Trends in Image Restoration and Enhancement (NTIRE) workshop, held in conjunction with CVPR 2022. This manuscript focuses on the competition set-up, datasets, the proposed methods and their results. The challenge aims at estimating an HDR image from multiple respective low dynamic range (LDR) observations, which might suffer from under- or over-exposed regions and different sources of noise. The challenge is composed of two tracks with an emphasis on fidelity and complexity constraints: In Track 1, participants are asked to optimize objective fidelity scores while imposing a low-complexity constraint (i.e. solutions can not exceed a given number of operations). In Track 2, participants are asked to minimize the complexity of their solutions while imposing a constraint on fidelity scores (i.e. solutions are required to obtain a higher fidelity score than the prescribed baseline). Both tracks use the same data and metrics: Fidelity is measured by means of PSNR with respect to a ground-truth HDR image (computed both directly and with a canonical tonemapping operation), while complexity metrics include the number of Multiply-Accumulate (MAC) operations and runtime (in seconds).

preprint2022arXiv

Practical Adoption of Cloud Computing in Power Systems- Drivers, Challenges, Guidance, and Real-world Use Cases

Motivated by The Federal Energy Regulatory Commission&#39;s (FERC) recent direction and ever-growing interest in cloud adoption by power utilities, a Task Force was established to assist power system practitioners with secure, reliable and cost-effective adoption of cloud technology to meet various business needs. This paper summarizes the business drivers, challenges, guidance, and best practices for cloud adoption in power systems from the Task Force&#39;s perspective, after extensive review and deliberation by its members, including grid operators, utility companies, software vendors, and cloud providers. The paper begins by enumerating various business drivers for cloud adoption in the power industry. It follows with the discussion of the challenges and risks of migrating power grid utility workloads to the cloud. Next, for each corresponding challenge or risk, the paper provides appropriate guidance. Notably, the guidance is directed toward power industry professionals who are considering cloud solutions and are yet hesitant about the practical execution. Finally, to tie all the sections together, the paper documents various real-world use cases of cloud technology in the power system domain, which both the power industry practitioners and software vendors can look toward to design and select their own future cloud solutions. We hope that the information in this paper will serve as helpful guidance for the development of NERC guidelines and standards relevant to cloud adoption in the industry.

preprint2022arXiv

Production of $ΩNN$ and $ΩΩN$ in ultra-relativistic heavy ion collisions

Even though lots of $Λ$-hypernuclei have been found and measured, multi-strangeness hypernuclei consisting of $Ω$ are not yet discovered. The studies of multi-strangeness hypernuclei help us further understand the interaction between hyperons and nucleons. Recently the $ΩN$ and $ΩΩ$ interactions as well as binding energies were calculated by the HAL-QCD&#39;s lattice Quantum Chromo-Dynamics (LQCD) simulations and production rates of $Ω$-dibaryon in Au + Au collisions at RHIC and Pb + Pb collisions at LHC energies were estimated by a coalescence model. The present work discusses the production of more exotic triple-baryons including $Ω$, namely $ΩNN$ and $ΩΩN$ as well as their decay channels. A variation method is used in calculations of bound states and binding energy of $ΩNN$ and $ΩΩN$ with the potentials from the HAL-QCD&#39;s results. The productions of $ΩNN$ and $ΩΩN$ are predicted by using a blast-wave model plus coalescence model in ultra-relativistic heavy-ion collisions at $\sqrt{s_{NN}} = 200$ GeV and $2.76$ TeV. Furthermore, plots for baryon number dependent yields of different baryons ($N$ and $Ω$), their dibaryons and hypernuclei are made and the production rate of a more exotic tetra-baryon ($ΩΩNN$) is extrapolated.

preprint2022arXiv

Specific heat and its high-order moments in relativistic heavy-ion collisions from a multiphase transport model

Energy dependence of specific heat extracted from temperature fluctuation of Au + Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV to 200 GeV was investigated by using a multiphase transport (AMPT) model. The results were compared with those from other models and some differences at low $\sqrt{s_{NN}}$ were found. To explain the above differences and describe the properties of the hot dense matter at low $\sqrt{s_{NN}}$, a new quantity $C_v^{*}$ was derived for describing specific heat in heavy-ion collisions. It was found that, by using $C_v^{*}$ together with its high order moments (skewness and kurtosis), thermal properties of the hot dense matter can be described and different thermal properties with or without parton process can be clearly distinguished. The proposed observable provides a way to learn the property of QCD matter % phase transition %along with critical point in heavy-ion collisions.

preprint2022arXiv

System dependence of away-side broadening and $α$-clustering light nuclei structure effect in dihadron azimuthal correlations

A collision system scan involving $α$-clustered $^{12}$C and $^{16}$O is studied by using a multiphase transport model for central collisions at $\sqrt{s_{NN}} = 6.37$ TeV. Background subtracted away-side dihadron azimuthal correlation is performed via the zero yield at minimum (ZYAM) method from raw signals, and the quantitative parameters, such as RMS width and Kurtosis, seem nicely follow the $A^{-1/3}$ law of the system size if the nucleus has the normal Woods-Saxon nucleon distribution. However, for $α$-clustering light nuclei, specifically for $^{12}$C and $^{16}$O, the RMS width and Kurtosis of away-side azimuthal correlation are deviated from the baseline of $A^{-1/3}$ law. In addition, the momentum dependence of away-side broadening parameters is also presented. The results show that there is a distinction in away-side broadening parameters of dihadron correlation function between the Woods-Saxon distribution and the $α$-clustered structures, which sheds light on that the collision system scan for dihadron azimuthal correlation as a potential probe to distinguish $α$-clustered nuclei.

preprint2021arXiv

Collision centrality and system size dependences of light nuclei production via dynamical coalescence mechanism

Light (anti-)nuclei in relativistic heavy-ion collisions are considered to be formed by the coalescence mechanism of (anti-)nucleons in the present work. Using a dynamical phase-space coalescence model coupled with a multi-phase transport (AMPT) model, we explore the formation of light clusters such as deuteron, triton and their anti-particles in different centralities for $^{197}$Au + $^{197}$Au collisions at $\sqrt{s_{NN}} = 39$ GeV. The calculated transverse momentum spectra of protons, deuterons, and tritons are comparable to those of experimental data from the RHIC-STAR collaboration. Both coalescence parameters $B_{2}$ for (anti-)deuteron and $B_{3}$ for triton increase with the transverse momentum as well as the collision centrality, and they are comparable with the measured values in experiments. The effect of system size on the production of light nuclei is also investigated by $^{10}$B + $^{10}$B, $^{16}$O + $^{16}$O, $^{40}$Ca + $^{40}$Ca, and $^{197}$Au + $^{197}$Au systems in central collisions. The results show that yields of light nuclei increase with system size, while the values of coalescence parameters present an opposite trend. It is interesting to see that the system size, as well as the centrality dependence of $B_A$ ($A$ = 2, 3), falls into the same group, which further demonstrates production probability of light nuclei is proportional to the size of the fireball. Furthermore, we compare our coalescence results with other models, such as the thermal model and analytic coalescence model, it seems that the description of light nuclei production is consistent with each other.

preprint2020arXiv

Clustering structure effect on Hanbury-Brown-Twiss correlation in $^{12}$C + $^{197}$Au collisions at 200 GeV}

Through $^{12}$C + $^{197}$Au collisions at $\sqrt{s_{NN}} =$ 200 GeV using a multiphase transport (AMPT) model, the azimuthal angle dependences of the Hanbury Brown-Twiss (HBT) radii relative to the second- and third-order participant plane from $π$-$π$ correlations are discussed. Three initial geometric configurations of $^{12}$C, namely three-$α$-cluster triangle, three-$α$-cluster chain and Woods-Saxon distribution of nucleons, are taken into account, and their effects on the correlations are investigated. The ratio of the third- to the second-order HBT radii $R_{o(s),3}^2/R_{o(s),2}^2$ is shown to be a clear probe for three configurations. In addition, this work presents the hadronic rescattering time evolution of the azimuthally dependent HBT radii. From the present study, one can learn that the HBT correlation from identical particles at freeze-out is able to provide the information of different initial configurations as collective flow proposed before.

preprint2020arXiv

Deep learning for smart fish farming: applications, opportunities and challenges

With the rapid emergence of deep learning (DL) technology, it has been successfully used in various fields including aquaculture. This change can create new opportunities and a series of challenges for information and data processing in smart fish farming. This paper focuses on the applications of DL in aquaculture, including live fish identification, species classification, behavioral analysis, feeding decision-making, size or biomass estimation, water quality prediction. In addition, the technical details of DL methods applied to smart fish farming are also analyzed, including data, algorithms, computing power, and performance. The results of this review show that the most significant contribution of DL is the ability to automatically extract features. However, challenges still exist; DL is still in an era of weak artificial intelligence. A large number of labeled data are needed for training, which has become a bottleneck restricting further DL applications in aquaculture. Nevertheless, DL still offers breakthroughs in the handling of complex data in aquaculture. In brief, our purpose is to provide researchers and practitioners with a better understanding of the current state of the art of DL in aquaculture, which can provide strong support for the implementation of smart fish farming.

preprint2020arXiv

Generative Feature Replay with Orthogonal Weight Modification for Continual Learning

The ability of intelligent agents to learn and remember multiple tasks sequentially is crucial to achieving artificial general intelligence. Many continual learning (CL) methods have been proposed to overcome catastrophic forgetting which results from non i.i.d data in the sequential learning of neural networks. In this paper we focus on class incremental learning, a challenging CL scenario. For this scenario, generative replay is a promising strategy which generates and replays pseudo data for previous tasks to alleviate catastrophic forgetting. However, it is hard to train a generative model continually for relatively complex data. Based on recently proposed orthogonal weight modification (OWM) algorithm which can approximately keep previously learned feature invariant when learning new tasks, we propose to 1) replay penultimate layer feature with a generative model; 2) leverage a self-supervised auxiliary task to further enhance the stability of feature. Empirical results on several datasets show our method always achieves substantial improvement over powerful OWM while conventional generative replay always results in a negative effect. Meanwhile our method beats several strong baselines including one based on real data storage. In addition, we conduct experiments to study why our method is effective.

preprint2020arXiv

Hybrid calibration procedure for fringe projection profilometry based on stereo-vision and polynomial fitting

The key to accurate 3D shape measurement in Fringe Projection Profilometry (FPP) is the proper calibration of the measurement system. Current calibration techniques rely on phase-coordinate mapping (PCM) or back-projection stereo-vision (SV) methods. PCM methods are cumbersome to implement as they require precise positioning of the calibration target relative to the FPP system but produce highly accurate measurements within the calibration volume. SV methods generally do not achieve the same accuracy level. However, the calibration is more flexible in that the calibration target can be arbitrarily positioned. In this work, we propose a hybrid calibration method that leverages the SV calibration approach using a PCM method to achieve higher accuracy. The method has the flexibility of SV methods, is robust to lens distortions, and has a simple relation between the recovered phase and the metric coordinates. Experimental results show that the proposed Hybrid method outperforms the SV method in terms of accuracy and reconstruction time due to its low computational complexity.

preprint2020arXiv

Nuclear system size scan for freeze-out properties in relativistic heavy-ion collisions by using a multiphase transport model

A system size scan program was recently proposed for the STAR experiments at the Relativistic Heavy Ion Collider(RHIC). In this study, we employ a multiphase transport (AMPT) model for considering the bulk properties at the freeze-out stage for $\mathrm{^{10}B+^{10}B}$, $\mathrm{^{12}C+^{12}C}$, $\mathrm{^{16}O+^{16}O}$, $\mathrm{^{20}Ne+^{20}Ne}$, $\mathrm{^{40}Ca+^{40}Ca}$, $\mathrm{^{96}Zr+^{96}Zr}$, and $\mathrm{^{197}Au+^{197}Au}$ collisions at RHIC energies $\sqrt{s_{NN}}$ of 200, 20, and 7.7 GeV. The results for $\mathrm{^{197}Au+^{197}Au}$ collisions are comparable with those of previous experimental STAR data. The transverse momentum $p_{T}$ spectra of charged particles ($π^{\pm}$, $K^{\pm}$, $p$, and $\bar{p}$) at the kinetic freeze-out stage, based on a blast-wave model, are also discussed. In addition, we use a statistical thermal model to extract the parameters at the chemical freeze-out stage, which agree with those from other thermal model calculations. It was found that there is a competitive relationship between the kinetic freeze-out parameter $T_{kin}$ and the radial expansion velocity $β_{T}$, which also agrees with the STAR or ALICE results. We found that the chemical freeze-out strangeness potential $μ_{s}$ remains constant in all collision systems and that the fireball radius $R$ is dominated by $\left\langle \mathrm{N_{Part}}\right\rangle$, which can be well fitted by a function of $a \left\langle \mathrm{N_{Part}}\right\rangle^{b}$ with $b \approx 1/3$. In addition, we calculated the nuclear modification factors for different collision systems with respect to the $ \mathrm{{}^{10}B} + \mathrm{{}^{10}B}$ system, and found that they present a gradual suppression within a higher $p_{T}$ range from small to large systems.

preprint2020arXiv

Sample Size Calculation for Cluster Randomized Trials with Zero-inflated Count Outcomes

Cluster randomized trails (CRT) have been widely employed in medical and public health research. Many clinical count outcomes, such as the number of falls in nursing homes, exhibit excessive zero values. In the presence of zero inflation, traditional power analysis methods for count data based on Poisson or negative binomial distribution may be inadequate. In this study, we present a sample size method for CRTs with zero-inflated count outcomes. It is developed based on GEE regression directly modeling the marginal mean of a ZIP outcome, which avoids the challenge of testing two intervention effects under traditional modeling approaches. A closed-form sample size formula is derived which properly accounts for zero inflation, ICCs due to clustering, unbalanced randomization, and variability in cluster size. Robust approaches, including t-distribution-based approximation and Jackknife re-sampling variance estimator, are employed to enhance trial properties under small sample sizes. Extensive simulations are conducted to evaluate the performance of the proposed method. An application example is presented in a real clinical trial setting.

preprint2020arXiv

Vorticity in low-energy heavy-ion collisions

We study the kinematic and thermal vorticities in low-energy heavy-ion collisions by using the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model. We explore their time evolution and spatial distribution. We find that the initial vorticities have a non-monotonic dependence on the collision energy $\sqrt{s_{\rm NN}}$: as $\sqrt{s_{\rm NN}}$ grows the vorticities first increase steeply and then decrease with the turning point around $\sqrt{s_{\rm NN}}\sim 3-5$ GeV depending on the centrality.