Search

This analysis uses the case of the Better Math Teaching Network (BMTN) to explore whether individuals participating in a networked improvement community (NIC) experienced common developmental trajectories on known dimensions of engagement. The analysis included quantitative data from annual network member surveys and qualitative data from annual member interviews. Evidence suggests potential developmental trajectories on three key dimensions of network participation: (1) learning how to engage in a network; (2) learning to use the tools of improvement science; and (3) learning to take up the theory of improvement. Additional findings show preliminary variations based on participant characteristics such as teaching tenure, whether they participated in the network with a colleague they knew prior to joining the network or with a school-based colleague, the context of their school, and how student centered they were at the outset of their participation.

From 2016 to 2021, the Better Math Teaching Network (BMTN) aimed to transform high school mathematics teaching in New England. Researchers and teachers worked together to make high school Algebra I classes more student centered. The BMTN was piloted with a group of nine teachers during the 2015-2016 school year and added teachers the following three years. In all, a total of 63 teachers engaged in the BMTN. Selected from a pool of volunteers that applied to join the network, participating teachers worked in urban, suburban, and rural contexts and taught at least one Algebra I course to 9th grade students. They engaged collaboratively to continuously improve their teaching, enhancing learning for thousands of high school math students throughout New England. Each year, BMTN teachers tested self-identified strategies for making their classrooms more student centered. Their testing was guided by the network's definition of Deep Engagement in Algebra (DEA): connect, justify, and solve. Using learning gleaned from the network, the BMTN hub launched a professional learning community (PLC) in another school district. Involvement in the BMTN has changed teacher practice for all 63 teachers directly involved in the network. Beyond the network participants, many of the routines, tools, and practices will be used in their local contexts in a variety of ways. The BMTN hub's formalized effort to support BMTN teachers in spreading the learning of the network into local contexts (through PLCs) yielded effects on the instructional practices of local teachers in schools, districts, and states throughout New England as well as insight into how networked improvement communities (NICs) might organize for scale.

From the fall of 2017 to the winter of 2020, the Student-Centered Assessment Network (SCAN) aimed to transform high school teaching in Rhode Island. Researchers and teachers worked together to make high school classes more student centered by increasing teachers' use of student-centered formative assessment. Network leaders (the hub) organized SCAN as an improvement network to address a shared problem of practice using improvement science. By joining the network, SCAN teachers committed to working collaboratively to make their formative assessment practice more student centered, using iterative testing cycles--Plan-Do-Study-Act (PDSA) cycles--to hone their instructional practices. SCAN was launched with a group of 23 high school teachers during the 2017-2018 school year. New teachers joined in the fall of 2018 and in the fall of 2019. The network was made up of educators from three public high schools that served a wide range of student demographics. In all, a total of 59 teachers representing seven content areas participated in SCAN. They engaged collaboratively to continuously improve their teaching, enhancing learning for thousands of Rhode Island high school students. This developmental evaluation of SCAN aims to: (1) infuse an evidence-based critical friend/thought partner perspective into the network development process; (2) track growth and the development of the Networked Improvement Community (NIC) as a learning organization; (3) produce useable knowledge for the education field and specifically for other educators, policymakers, funders, and researchers interested in the NIC model as a way to organize for improvement and address high-leverage practical problems; and (4) advance the evaluation field by testing and refining models for evaluating improvement processes and NICs in education contexts.

As the Better Math Teaching Network (BMTN) matured, different strategies for sharing network learning emerged. These strategies became more formalized and intentional as BMTN members developed tools and routines to spread the learning. Our multi-year evaluation sought to understand the affordances and constraints of each strategy. In the sections below, we present the five strategies that reflect this developmental trajectory. We begin by providing examples of each strategy. We then identify the resources necessary for implementation and reflect on the affordances and constraints of the strategy. To understand the possibilities for scaling the learning of the BMTN--and other improvement networks--we analyze each strategy using Coburn's four dimensions of scale: widespread use, depth of implementation, shift in reform ownership, and sustainability.

From 2016 to 2021, the Better Math Teaching Network (BMTN) aimed to transform high school mathematics teaching in New England. Researchers and teachers worked together to make high school Algebra I classes more student centered. Network leaders organized the BMTN as a networked improvement community (NIC) to address a common problem of practice using improvement science. The BMTN was piloted with a group of nine teachers during the 2015-2016 school year and added teachers the following three years. In all, a total of 63 teachers engaged in the BMTN. Selected from a pool of volunteers that applied to join the network, participating teachers worked in urban, suburban, and rural contexts and taught at least one Algebra I course to 9th grade students. They engaged collaboratively to continuously improve their teaching, enhancing learning for thousands of high school math students throughout New England. This report is a developmental evaluation that studied and supported the networked improvement community's (NIC) initiation, development, outcomes, and dissemination of lessons learned. The developmental evaluation of BMTN aimed to: (1) infuse an evidence-based critical friend/thought partner perspective into the network development process; (2) track growth and the development of the NIC as a learning organization; (3) produce useable knowledge for the education field and specifically for other educators, policymakers, funders, and researchers interested in the NIC model as a way to organize for improvement and address high-leverage practical problems; and (4) advance the evaluation field by testing and refining models for evaluating improvement processes and NICs in education contexts.

The Beam Energy Scan Theory (BEST) Collaboration was formed with the goal of providing a theoretical framework for analyzing data from the Beam Energy Scan (BES) program at the relativistic heavy ion collider (RHIC) at Brookhaven National Laboratory. The physics goal of the BES program is the search for a conjectured QCD critical point as well as for manifestations of the chiral magnetic effect. We describe progress that has been made over the previous five years. This includes studies of the equation of state and equilibrium susceptibilities, the development of suitable initial state models, progress in constructing a hydrodynamic framework that includes fluctuations and anomalous transport effects, as well as the development of freezeout prescriptions and hadronic transport models. Finally, we address the challenge of integrating these components into a complete analysis framework. This document describes the collective effort of the BEST Collaboration and its collaborators around the world., Comment: 103 pages

We present a new determination of $\hat{q}$, the jet transport coefficient of the quark-gluon plasma. Using the JETSCAPE framework, we use Bayesian parameter estimation to constrain the dependence of $\hat{q}$ on the jet energy, virtuality, and medium temperature from experimental measurements of inclusive hadron suppression in Au-Au collisions at RHIC and Pb-Pb collisions at the LHC. These results are based on a multi-stage theoretical approach to in-medium jet evolution with the MATTER and LBT jet quenching models. The functional dependence of $\hat{q}$ on jet energy, virtuality, and medium temperature is based on a perturbative picture of in-medium scattering, with components reflecting the different regimes of applicability of MATTER and LBT. The correlation of experimental systematic uncertainties is accounted for in the parameter extraction. These results provide state-of-the-art constraints on $\hat{q}$ and lay the groundwork to extract additional properties of the quark-gluon plasma from jet measurements in heavy-ion collisions., Comment: contribution to the 2021 QCD session of the 55th Recontres de Moriond

We develop a far-from-equilibrium hydrodynamic model to evolve ultrarelativistic heavy-ion collisions in event-by-event simulations. Anisotropic hydrodynamics is designed to better handle the strong and highly anisotropic expansion during the early stages of the collision. The large gradients cause conventional second-order viscous hydrodynamic approaches to break down at early times. Anisotropic hydrodynamics evolves the large pressure anisotropies present in the quark-gluon plasma non-perturbatively, which prevents negative longitudinal pressures from developing even under extreme conditions. This increased stability allows us to start anisotropic hydrodynamics already at a very early longitudinal proper time to evolve the pre-hydrodynamic stage. In current pre-hydrodynamic models, the equation of state is not consistent with the QCD equation of state used in the subsequent fluid dynamic stage. Since our approach avoids this inconsistency, we are able to achieve a smooth transition to non-conformal viscous hydrodynamics as the gradients decrease over time. For our first phenomenological application, we apply our new simulation to model fluctuating Pb+Pb collisions at LHC energies ($\sqrt{s_\text{NN}} = 2.76$ TeV) and find that our preliminary calculations for the hadronic observables are in excellent agreement with the experimental data., Comment: PhD thesis, 332 pages

We introduce a positive definite single-particle distribution that is suitable for describing the transition from a macroscopic hydrodynamic to a microscopic kinetic description during the late stages of heavy-ion collisions in the presence of moderately large viscous corrections. The modified equilibrium distribution function can be constructed with hydrodynamic input from either relativistic viscous fluid dynamics or anisotropic fluid dynamics. We test the modified equilibrium distribution's hydrodynamic output for a stationary hadron resonance gas subject to either shear stress, bulk pressure, or baryon diffusion current at a given freeze-out temperature and baryon chemical potential. While it does not reproduce all components of the net baryon current and energy-momentum tensor exactly, it significantly improves upon the customary linearized approximations for the non-equilibrium correction $\delta f_n$ which typically lead to unphysical negative distribution functions at large particle momenta. A comparison of particle spectra and $p_T$-differential elliptic flow coefficients from the Cooper-Frye formula computed with the modified equilibrium distribution and with linearized $\delta f_n$ corrections is presented, for two different (2+1)-dimensional hypersurfaces corresponding to central and non-central Pb+Pb collisions at the Large Hadron Collider (LHC)., Comment: 23 pages, 10 figures

We report a new determination of $\hat{q}$, the jet transport coefficient of the Quark-Gluon Plasma. We use the JETSCAPE framework, which incorporates a novel multi-stage theoretical approach to in-medium jet evolution and Bayesian inference for parameter extraction. The calculations, based on the MATTER and LBT jet quenching models, are compared to experimental measurements of inclusive hadron suppression in Au+Au collisions at RHIC and Pb+Pb collisions at the LHC. The correlation of experimental systematic uncertainties is accounted for in the parameter extraction. The functional dependence of $\hat{q}$ on jet energy or virtuality and medium temperature is based on a perturbative picture of in-medium scattering, with components reflecting the different regimes of applicability of MATTER and LBT. In the multi-stage approach, the switch between MATTER and LBT is governed by a virtuality scale $Q_0$. Comparison of the posterior model predictions to the RHIC and LHC hadron suppression data shows reasonable agreement, with moderate tension in limited regions of phase space. The distribution of $\hat{q}/T^3$ extracted from the posterior distributions exhibits weak dependence on jet momentum and medium temperature $T$, with 90\% Credible Region (CR) depending on the specific choice of model configuration. The choice of MATTER+LBT, with switching at virtuality $Q_0$, has 90\% CR of $2<\hat{q}/T^3<4$ for $p_\mathrm{T}^\mathrm{jet}>40$ GeV/c. The value of $Q_0$, determined here for the first time, is in the range 2.0-2.7 GeV., Comment: Published in Phys Rev C

We present VAH, a (3+1)-dimensional simulation that evolves the far-from-equilibrium quark-gluon plasma produced in ultrarelativistic heavy-ion collisions with anisotropic fluid dynamics. We solve the hydrodynamic equations on an Eulerian grid using the Kurganov-Tadmor algorithm in combination with a new adaptive Runge-Kutta method. Our numerical scheme allows us to start the simulation soon after the nuclear collision, largely avoiding the need to integrate it with a separate pre-equilibrium dynamics module. We test the code's performance by simulating on the Eulerian grid conformal and non-conformal Bjorken flow as well as conformal Gubser flow, whose (0+1)-dimensional solutions are precisely known. Finally, we compare non-conformal anisotropic hydrodynamics to second-order viscous hydrodynamics in central Pb+Pb collisions and find that the former's longitudinal flow profile responds more consistently to the fluid's gradients along the spacetime rapidity direction.

We study the properties of the strongly-coupled quark-gluon plasma with a multistage model of heavy ion collisions that combines the T$_\mathrm{R}$ENTo initial condition ansatz, free-streaming, viscous relativistic hydrodynamics, and a relativistic hadronic transport. A model-to-data comparison with Bayesian inference is performed, revisiting assumptions made in previous studies. The role of parameter priors is studied in light of their importance towards the interpretation of results. We emphasize the use of closure tests to perform extensive validation of the analysis workflow before comparison with observations. Our study combines measurements from the Large Hadron Collider and the Relativistic Heavy Ion Collider, achieving a good simultaneous description of a wide range of hadronic observables from both colliders. The selected experimental data provide reasonable constraints on the shear and the bulk viscosities of the quark-gluon plasma at $T\sim$ 150-250 MeV, but their constraining power degrades at higher temperatures $T \gtrsim 250$ MeV. Furthermore, these viscosity constraints are found to depend significantly on how viscous corrections are handled in the transition from hydrodynamics to the hadronic transport. Several other model parameters, including the free-streaming time, show similar model sensitivity while the initial condition parameters associated with the T$_\mathrm{R}$ENTo ansatz are quite robust against variations of the particlization prescription. We also report on the sensitivity of individual observables to the various model parameters. Finally, Bayesian model selection is used to quantitatively compare the agreement with measurements for different sets of model assumptions, including different particlization models and different choices for which parameters are allowed to vary between RHIC and LHC energies., Comment: 51 pages, including 35 figures and 8 appendices, long companion paper to arXiv:2010.03928. A useful visualization tool to see the effect of varying individual model parameters on physical observables can be found at jetscape.org/sims-widget. Some references and discussion added. This version submitted for publication

Using combined data from the Relativistic Heavy Ion and Large Hadron Colliders, we constrain the shear and bulk viscosities of quark-gluon plasma (QGP) at temperatures of ${\sim\,}150{-}350$ MeV. We use Bayesian inference to translate experimental and theoretical uncertainties into probabilistic constraints for the viscosities. With Bayesian Model Averaging we account for the irreducible model ambiguities in the transition from a fluid description of the QGP to hadronic transport in the final evolution stage, providing the most reliable phenomenological constraints to date on the QGP viscosities., Comment: 8 pages, 3 figures

The dynamics of shower development for a jet traveling through the QGP involves a variety of scales, one of them being the heavy quark mass. Even though the mass of the heavy quarks plays a subdominant role during the high virtuality portion of the jet evolution, it does affect longitudinal drag and diffusion, stimulating additional radiation from heavy quarks. These emissions partially compensate the reduction in radiation from the dead cone effect. In the lower virtuality part of the shower, when the mass is comparable to the transverse momenta of the partons, scattering and radiation processes off heavy quarks differ from those off light quarks. All these factors result in a different nuclear modification factor for heavy versus light flavors and thus for heavy-flavor tagged jets. In this study, the heavy quark shower evolution and the fluid dynamical medium are modeled on an event by event basis using the JETSCAPE Framework. We present a multi-stage calculation that explores the differences between various heavy quark energy-loss mechanisms within a realistically expanding quark-gluon plasma (QGP). Inside the QGP, the highly virtual and energetic portion of the shower is modeled using the MATTER generator, while the LBT generator models the showers induced by energetic and close-to-on-shell heavy quarks. Energy-momentum exchange with the medium, essential for the study of jet modification, proceeds using a weak coupling recoil approach. The JETSCAPE framework allows for transitions, on the level of individual partons, from one energy-loss prescription to the other depending on the parton's energy and virtuality and the local density. This allows us to explore the effect and interplay between the different regimes of energy loss on the propagation and radiation from hard heavy quarks in a dense medium., Comment: arXiv admin note: substantial text overlap with arXiv:2002.06643

It is now well established that jet modification is a multistage effect; hence a single model alone cannot describe all facets of jet modification. The JETSCAPE framework is a multistage framework that uses several modules to simulate different stages of jet propagation through the QGP medium. These simulations require a set of parameters to ensure a smooth transition between stages. We fine tune these parameters to successfully describe a variety of observables, such as the nuclear modification factors of leading hadrons and jets, jet shape, and jet fragmentation function. Photons can be produced in the hard scattering or as radiation from quarks inside jets. In this work, we study photon-jet transverse momentum imbalance and azimuthal correlation for both $p-p$ and $Pb-Pb$ collision systems. All the photons produced in each event, including the photons from hard scattering, radiation from the parton shower, and radiation from hadronization are considered with an isolation cut to directly compare with experimental data. The simulations are conducted using the same set of tuned parameters as used for the jet analysis. No new parameters are introduced or tuned. We demonstrate a significantly improved agreement with photons from $Pb-Pb$ collisions compared to prior efforts. This work provides an independent, parameter free verification of the multistage evolution framework., Comment: 4 pages, 7 figures

"Hybrid Hadronization" is a new Monte Carlo package to hadronize systems of partons. It smoothly combines quark recombination applicable when distances between partons in phase space are small, and string fragmentation appropriate for dilute parton systems, following the picture outlined by Han et al. [PRC 93, 045207 (2016)]. Hybrid Hadronization integrates with PYTHIA 8 and can be applied to a variety of systems from $e^++e^-$ to $A+A$ collisions. It takes systems of partons and their color flow information, for example from a Monte Carlo parton shower generator, as input. In addition, if for $A+A$ collisions a thermal background medium is provided, the package allows sampling thermal partons that contribute to hadronization. Hybrid Hadronization is available for use as a standalone code and is also part of JETSCAPE since the 2.0 release. In these proceedings we review the physics concepts underlying Hybrid Hadronization and demonstrate how users can use the code with various parton shower Monte Carlos. We present calculations of hadron chemistry and fragmentation functions in small and large systems when Hybrid Hadronization is combined with parton shower Monte Carlos MATTER and LBT. In particular, we discuss observable effects of the recombination of shower partons with thermal partons., Comment: 4 pages, 3 figures, Proceedings of Hard Probes 2020, 1-6 June 2020, Austin, Texas; Updated Author list

We present a multi-stage model for jet evolution through a quark-gluon plasma within the JETSCAPE framework. The multi-stage approach in JETSCAPE provides a unified description of distinct phases in jet shower contingent on the virtuality. We demonstrate a simultaneous description of leading hadron and integrated jet observables as well as jet $v_n$ using tuned parameters. Medium response to the jet quenching is implemented based on a weakly-coupled recoil prescription. We also explore the cone-size dependence of jet energy loss inside the plasma., Comment: 4 pages, 4 figures, Proceedings of Hard Probes 2020, 1-6 June 2020, Austin, Texas

We study the medium response to jet evolution in the quark-gluon plasma within the JETSCAPE framework. Recoil partons' medium response in the weakly coupled description is implemented in the multi-stage jet energy-loss model in the framework. As a further extension, the hydrodynamic description is rearranged to include in-medium jet transport based on a strong-coupling picture. To interface hydrodynamics with jet energy-loss models, the hydrodynamic source term is modeled by a causal formulation employing the relativistic diffusion equation. The jet shape and fragmentation function are studied via realistic simulations with weakly coupled recoils. We also demonstrate modifications in the medium caused by the hydrodynamic response., Comment: 4 pages, 2 figures, contribution to the Quark Matter 2019 proceedings

We present a jet quenching model within a unified multi-stage framework and demonstrate for the first time a simultaneous description of leading hadrons, inclusive jets, and elliptic flow observables which spans multiple centralities and collision energies. This highlights one of the major successes of the JETSCAPE framework in providing a tool for setting up an effective parton evolution that includes a high-virtuality radiation dominated energy loss phase (MATTER), followed by a low-virtuality scattering dominated (LBT) energy loss phase. Measurements of jet and charged-hadron $R_{AA}$ set strong constraints on the jet quenching model. Jet-medium response is also included through a weakly-coupled transport description., Comment: 4 pages, 4 figures, contribution to the Quark Matter 2019 proceedings

The interaction of heavy flavor with the quark-gluon plasma (QGP) in relativistic heavy-ion collisions is studied using JETSCAPE, a publicly available software package containing a framework for Monte Carlo event generators. Multi-stage (and multi-model) evolution of heavy quarks within JETSCAPE provides a cohesive description of heavy flavor quenching inside the QGP. As the parton shower develops, a model becomes active as soon as its kinematic region of validity is reached. Two combinations of heavy-flavor energy-loss models are explored within a realistic QGP medium, using parameters which were tuned to describe {\it light-flavor} partonic energy-loss., Comment: 4 pages, 2 figures, contribution to the Quark Matter 2019 proceedings

Multistage models based on relativistic viscous hydrodynamics have proven successful in describing hadron measurements from relativistic nuclear collisions. These measurements are sensitive to the shear and the bulk viscosities of QCD and provide a unique opportunity to constrain these transport coefficients. Bayesian analyses can be used to obtain systematic constraints on the viscosities of QCD, through methodical model-to-data comparisons. In this manuscript, we discuss recent developments in Bayesian analyses of heavy ion collision data. We highlight the essential role of closure tests in validating a Bayesian analysis before comparison with measurements. We discuss the role of the emulator that is used as proxy for the multistage theoretical model. We use an ongoing Bayesian analysis of soft hadron measurements by the JETSCAPE Collaboration as context for the discussion., Comment: 4 pages, 1 figure, contribution to the Quark Matter 2019 proceedings

We resum the non-equilibrium gradient corrections to a single-particle distribution function evolved by the Boltzmann equation in the relaxation time approximation (RTA). We first study a system undergoing Bjorken expansion and show that, for a constant relaxation time, the exact solution of the RTA Boltzmann equation at late times (i.e. after the decay of non-hydrodynamic modes) generates the Borel resummed Chapman-Enskog series. Extending this correspondence to systems without Bjorken symmetry, we construct a (3+1)-dimensional hydrodynamic generator for RTA kinetic theory, which is an integral representation of the Chapman-Enskog series in the limit of vanishing non-hydrodynamic modes. Relaxing this limit we find at earlier times a set of non-hydrodynamic modes coupled to the Chapman-Enskog expansion. Including the dynamics of these non-hydrodynamic modes is shown to control the emergence of hydrodynamics as an effective field theory description of non-equilibrium fluids, which works well even for far-off-equilibrium situations where the Knudsen number is initially large.

The iS3D particlization module simulates the emission of hadrons from heavy-ion collisions via Monte-Carlo sampling of the Cooper-Frye formula which converts fluid dynamical information into local phase-space distributions for hadrons. The code package includes multiple choices for the non-equilibrium correction to these distribution functions: the 14-moment approximation, first-order Chapman-Enskog expansion, and two types of modified equilibrium distributions. This makes it possible to explore to what extent heavy-ion experimental data are sensitive to different choices for $\delta f_n$, presently the main source of theoretical uncertainty in the particlization stage. We validate our particle sampler with a high degree of precision by generating several million hadron emission events from a longitudinally boost-invariant hypersurface and comparing the event-averaged particle spectra and space-time distributions to the Cooper-Frye formula.

The JETSCAPE framework is a modular and versatile Monte Carlo software package for the simulation of high energy nuclear collisions. In this work we present a new tune of JETSCAPE, called PP19, and validate it by comparison to jet-based measurements in $p+p$ collisions, including inclusive single jet cross sections, jet shape observables, fragmentation functions, charged hadron cross sections, and dijet mass cross sections. These observables in $p+p$ collisions provide the baseline for their counterparts in nuclear collisions. Quantifying the level of agreement of JETSCAPE results with $p+p$ data is thus necessary for meaningful applications of JETSCAPE to A+A collisions. The calculations use the JETSCAPE PP19 tune, defined in this paper, based on version 1.0 of the JETSCAPE framework. For the observables discussed in this work calculations using JETSCAPE PP19 agree with data over a wide range of collision energies at a level comparable to standard Monte Carlo codes. These results demonstrate the physics capabilities of the JETSCAPE framework and provide benchmarks for JETSCAPE users., Comment: 23 pages, 23 figures; v1.1: minor bug fixes in author information

The JETSCAPE simulation framework is an overarching computational envelope for developing complete event generators for heavy-ion collisions. It allows for modular incorporation of a wide variety of existing and future software that simulates different aspects of a heavy-ion collision. The default JETSCAPE package contains both the framework, and an entire set of indigenous and third party routines that can be used to directly compare with experimental data. In this article, we outline the algorithmic design of the JETSCAPE framework, define the interfaces and describe the default modules required to carry out full simulations of heavy-ion collisions within this package. We begin with a description of the various physics elements required to simulate an entire event in a heavy-ion collision, and distribute these within a flowchart representing the event generator and statistical routines for comparison with data. This is followed by a description of the abstract class structure, with associated members and functions required for this flowchart to work. We then define the interface that will be required for external users of JETSCAPE to incorporate their code within this framework and to modify existing elements within the default distribution. We conclude with a discussion of some of the physics output for both $p$-$p$ and $A$-$A$ collisions from the default distribution, and an outlook towards future releases. In the appendix, we discuss various architectures on which this code can be run and outline our benchmarks on similar hardware., Comment: 93 pages, 13 figures

The JETSCAPE Collaboration has recently announced the first release of the JETSCAPE package that provides a modular, flexible, and extensible Monte Carlo event generator. This innovative framework makes it possible to perform a comprehensive study of multi-stage high-energy jet evolution in the Quark-Gluon Plasma. In this work, we illustrate the performance of the event generator for different algorithmic approaches to jet energy loss, and reproduce the measurements of several jet and hadron observables as well as correlations between the hard and soft sector. We also carry out direct comparisons between different approaches to energy loss to study their sensitivity to those observables.

The modification of jet substructure in relativistic heavy-ion collisions is studied using JETSCAPE, a publicly available software package containing a framework for Monte Carlo event generators. Multi-stage jet evolution in JETSCAPE provides an integrated description of jet quenching by combining multiple models, with each becoming active at a different stage of the parton shower evolution. Jet substructure modification due to different aspects of jet quenching is studied using jet shape and jet fragmentation observables. Various combinations of jet energy loss models are exploed, with medium background provided by (2 + 1)-D VISHNU with TRENTo+freestreaming initial conditions. Results reported here are from simulations performed within JETSCAPE framework., Comment: 4 pages, 3 figures, Proceedings of Hard Probes 2018, 30 September-5 October, Aix-Les-Bains, France

A new formulation of (3+1)-dimensional anisotropic hydrodynamics is presented that accounts nonperturbatively for the large longitudinal-transverse pressure anisotropy and bulk viscous pressure in heavy-ion collisions. The initialization of the anisotropic hydrodynamic stage is discussed, and a comparison to standard viscous hydrodynamics for (0+1)- dimensional Bjorken expansion is presented., Comment: 4 pages, 3 figures, Quark Matter 2018

Anisotropic hydrodynamics improves upon standard dissipative fluid dynamics by treating certain large dissipative corrections non-perturbatively. Relativistic heavy-ion collisions feature two such large dissipative effects: (i) Strongly anisotropic expansion generates a large shear stress component which manifests itself in very different longitudinal and transverse pressures, especially at early times. (ii) Critical fluctuations near the quark-hadron phase transition lead to a large bulk viscous pressure on the conversion surface between hydrodynamics and a microscopic hadronic cascade description of the final collision stage. We present a new dissipative hydrodynamic formulation for non-conformal fluids where both of these effects are treated nonperturbatively. The evolution equations are derived from the Boltzmann equation in the 14-moment approximation, using an expansion around an anisotropic leading-order distribution function with two momentum-space deformation parameters, accounting for the longitudinal and transverse pressures. To obtain their evolution we impose generalized Landau matching conditions for the longitudinal and transverse pressures. We describe an approximate anisotropic equation of state that relates the anisotropy parameters with the macroscopic pressures. Residual shear stresses are smaller and are treated perturbatively, as in standard second-order dissipative fluid dynamics. The resulting optimized viscous anisotropic hydrodynamic evolution equations are derived in 3+1 dimensions and tested in a (0+1)-dimensional Bjorken expansion, using a state-of-the-art lattice equation of state. Comparisons with other viscous hydrodynamical frameworks are presented., Comment: 27 pages, 7 figures

In this work we describe the dynamics of a highly anisotropic system undergoing boost-invariant longitudinal and azimuthally symmetric radial expansion (Gubser flow) for arbitrary shear viscosity to entropy density ratio. We derive the equations of motion of dissipative anisotropic hydrodynamics by applying to this situation the moments method recently derived by Moln\'ar et al. (MNR) [1,2], based on an expansion around an arbitrary anisotropic one-particle distribution function. One requires an additional evolution equation in order to close the conservation laws. This is achieved by selecting the relaxation equation for the longitudinal pressure with a suitable Landau matching condition. As a result one obtains two coupled differential equations for the energy density and the longitudinal pressure which respect the $SO(3)_q\otimes SO(1,1)\otimes Z_2$ symmetry of the Gubser flow in the deSitter space. These equations are solved numerically and compared with the predictions of the recently found exact solution of the relaxation-time-approximation Boltzmann equation subject to the same flow. We also compare our numerical results with other fluid dynamical models. We observe that the MNR description of anisotropic fluid dynamics reproduces the space-time evolution of the system than all other currently known hydrodynamical approaches., Comment: 4 pages, 1 Figure. Proceedings of the XXVIth International Conference on Ultrarelativistic Nucleus-Nucleus Collisions (Quark Matter 2017) Chicago, February 6-11, 2017

Exploring a variety of closing schemes to the infinite hierarchy of momentum moments of the exactly solvable Boltzmann equation for systems undergoing Gubser flow, we study the precision with which the resulting hydrodynamic equations reproduce the exact evolution of hydrodynamic moments of the distribution function. We find that anisotropic hydrodynamics, obtained by ex- panding the distribution function around a dynamically evolving locally anisotropic background whose evolution is matched to exactly reproduce the macroscopic pressure anisotropy caused by the different longitudinal and transverse expansion rates in Gubser flow, provides the most accurate macroscopic description of the microscopic kinetic evolution. This confirms a similar earlier finding for Bjorken flow [Moln\'ar, Niemi and Rischke, Phys. Rev. D 94, 125003 (2016)]. We explain the physics behind this optimal matching procedure and show that one can efficiently correct for a non- optimized matching choice by adding a residual shear stress to the energy-momentum tensor whose evolution is again determined by the Boltzmann equation. Additional insights to guide the optimal choice of a macroscopic anisotropic hydrodynamic framework for strongly-coupled systems that do not admit a microscopic kinetic description are reported., Comment: 17 pages; 4 figures