The Experts below are selected from a list of 14973 Experts worldwide ranked by ideXlab platform

R Sahoo - One of the best experts on this subject based on the ideXlab platform.

  • elliptic flow of hadrons via quark coalescence mechanism using Boltzmann Transport Equation for pb pb collision at sqrt s_ nn 2 76 tev
    Advances in High Energy Physics, 2020
    Co-Authors: Mohammed Younus, Sushanta Tripathy, Swatantra Kumar Tiwari, R Sahoo
    Abstract:

    Elliptic flow of hadrons observed at relativistic heavy ion collision experiments at relativistic heavy ion collider (RHIC) and large hadron collider (LHC) provides us an important signature of possible deconfinement transition from the hadronic phase to partonic phase. However, hadronization processes of deconfined partons back into final hadrons are found to play a vital role in the observed hadronic flow. In the present work, we use a coalescence mechanism also known as recombination (ReCo) to combine quarks into hadrons. To get there, we have used the Boltzmann Transport Equation in relaxation time approximation to Transport the quarks into equilibration and finally to freeze-out the surface, before coalescence takes place. A Boltzmann-Gibbs blast wave (BGBW) function is taken as an equilibrium function to get the final distribution and a power-like function to describe the initial distributions of partons produced in heavy ion collisions. In the present work, we try to estimate the elliptic flow of identified hadrons such as , , and , produced in Pb+Pb collisions at at the LHC for different centralities. The elliptic flow ( ) of identified hadrons seems to be described quite well in the available range. After the evolution of quarks until freeze-out time has been calculated using BTE-RTA, the approach used in this paper consists of combining two or more quarks to explain the produced hadrons at intermediate momenta regions. The formalism is found to describe the elliptic flow of hadrons produced in Pb+Pb collisions to a large extent.

  • elliptic flow in pb pb collisions at sqrt s_ rm nn 2 76 tev at the lhc using Boltzmann Transport Equation with non extensive statistics
    European Physical Journal A, 2018
    Co-Authors: Sushanta Tripathy, Swatantra Kumar Tiwari, Mohammed Younus, R Sahoo
    Abstract:

    Elliptic flow in heavy-ion collisions is an important signature of a possible de-confinement transition from hadronic phase to partonic phase. In the present work, we use non-extensive statistics, which has been used for transverse momentum ( $p_{{\rm T}}$ ) distribution in proton+proton ( $ p+p$ ) collisions, as the initial particle distribution function in Boltzmann Transport Equation (BTE). A Boltzmann-Gibbs Blast Wave (BGBW) function is taken as an equilibrium function to get the final distribution to describe the particle production in heavy-ion collisions. In this formalism, we try to estimate the elliptic flow in Pb+Pb collisions at $\sqrt{s_{{\rm NN}}} = 2.76$ TeV at the LHC for different centralities. The elliptic flow ( $ v_{2}$ ) of identified particles seems to be described quite well in the available $p_{{\rm T}}$ range. An approach which combines the non-extensive nature of particle production in $ p+p$ collisions through an evolution in kinetic theory using BTE, with BGBW as an equilibrium distribution is successful in describing the spectra and elliptic flow in heavy-ion collisions.

  • elliptic flow of hadrons via quark coalescence mechanism using Boltzmann Transport Equation for pb pb collision at sqrt s_ nn 2 76 tev
    arXiv: High Energy Physics - Phenomenology, 2018
    Co-Authors: Mohammed Younus, Sushanta Tripathy, Swatantra Kumar Tiwari, R Sahoo
    Abstract:

    Elliptic flow of hadrons observed at relativistic heavy-ion collision experiments at Relativistic Heavy-Ion Collider (RHIC) and Large Hadron Collider (LHC), provides us an important signature of possible de-confinement transition from hadronic phase to partonic phase. However, hadronization processes of de-confined partons back into final hadrons are found to play a vital role in the observed hadronic flow. In the present work, we use coalescence mechanism also known as Recombination (ReCo) to combine quarks into hadrons. To get there, we have used Boltzmann Transport Equation in relaxation time approximation to Transport the quarks into equilibration and finally to freeze-out surface, before coalescence takes place. A Boltzmann-Gibbs Blast Wave (BGBW) function is taken as an equilibrium function to get the final distribution and a power-like function to describe the initial distributions of partons produced in heavy-ion collisions. In the present work, we try to estimate the elliptic flow of identified hadrons such as $\pi$, $K$, $p$ etc., produced in Pb+Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV at the LHC for different centralities. The elliptic flow ($v_2$) of identified hadrons seems to be described quite well in the available $p_{\rm T}$ range. After the evolution of quarks until freeze-out time, has been calculated using BTE-RTA, the approach used in this paper consists of combining two or more quarks to explain the produced hadrons at intermediate momenta regions. The formalism is found to describe elliptic flow of hadrons produced in Pb+Pb collisions to a large extent.

  • transverse momentum spectra and nuclear modification factor using Boltzmann Transport Equation with flow in pb pb collisions at sqrt s_ nn 2 76 tev
    European Physical Journal A, 2017
    Co-Authors: Sushanta Tripathy, Swatantra Kumar Tiwari, Arvind Khuntia, R Sahoo
    Abstract:

    In the continuation of our previous work, the transverse-momentum (\(p_{T}\)) spectra and nuclear modification factor (\(R_{AA}\)) are derived using the relaxation time approximation of Boltzmann Transport Equation (BTE). The initial \(p_{T}\)-distribution used to describe p + p collisions has been studied with the perturbative-Quantum Chromodynamics (pQCD) inspired power-law distribution, Hagedorn's empirical formula and with the Tsallis non-extensive statistical distribution. The non-extensive Tsallis distribution is observed to describe the complete range of the transverse-momentum spectra. The Boltzmann-Gibbs Blast Wave (BGBW) distribution is used as the equilibrium distribution in the present formalism, to describe the \(p_{T}\)-distribution and nuclear modification factor in nucleus-nucleus collisions. The experimental data for Pb+Pb collisions at \(\sqrt{s_{NN}} = 2.76\) TeV at the Large Hadron Collider at CERN have been analyzed for pions, kaons, protons, \(K^{\ast0}\) and \(\phi\). It is observed that the present formalism while explaining the transverse-momentum spectra up to 5 GeV/c, explains the nuclear modification factor very well up to 8 GeV/c in \(p_{T}\) for all these particles except for protons. \(R_{AA}\) is found to be independent of the degree of non-extensivity, \(q_{pp}\) after \(p_{T} \sim 8\) GeV/c.

  • transverse momentum spectra and nuclear modification factor using Boltzmann Transport Equation with flow in pb pb collisions at sqrt s_ nn 2 76 tev
    arXiv: Nuclear Theory, 2017
    Co-Authors: Sushanta Tripathy, Swatantra Kumar Tiwari, Arvind Khuntia, R Sahoo
    Abstract:

    In the continuation of our previous work, the transverse momentum ($p_T$) spectra and nuclear modification factor ($R_{AA}$) are derived using relaxation time approximation of Boltzmann Transport Equation (BTE). The initial $p_T$-distribution used to describe $p+p$ collisions has been studied with the pQCD inspired power-law distribution, the Hagedorn's empirical formula and with the Tsallis non-extensive statistical distribution. The non-extensive Tsallis distribution is observed to describe the complete range of the transverse momentum spectra. The Boltzmann-Gibbs Blast Wave (BGBW) distribution is used as the equilibrium distribution in the present formalism, to describe the $p_T$-distribution and nuclear modification factor in nucleus-nucleus collisions. The experimental data for Pb+Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV at the Large Hadron Collider at CERN have been analyzed for pions, kaons, protons, $K^{*0}$ and $\phi$. It is observed that the present formalism while explaining the transverse momentum spectra upto 5 GeV/c, explains the nuclear modification factor very well upto 8 GeV/c in $p_T$ for all these particles except for protons. $R_{AA}$ is found to be independent of the degree of non-extensivity, $q_{pp}$ after $p_T \sim$ 8 GeV/c.

Gang Chen - One of the best experts on this subject based on the ideXlab platform.

  • variational approach to solving the spectral Boltzmann Transport Equation in transient thermal grating for thin films
    Journal of Applied Physics, 2016
    Co-Authors: Vazrik Chiloyan, Lingping Zeng, Samuel Huberman, A A Maznev, Keith A Nelson, Gang Chen
    Abstract:

    The phonon Boltzmann Transport Equation (BTE) is widely utilized to study non-diffusive thermal Transport. We find a solution of the BTE in the thin film transient thermal grating (TTG) experimental geometry by using a recently developed variational approach with a trial solution supplied by the Fourier heat conduction Equation. We obtain an analytical expression for the thermal decay rate that shows excellent agreement with Monte Carlo simulations. We also obtain a closed form expression for the effective thermal conductivity that demonstrates the full material property and heat transfer geometry dependence, and recovers the limits of the one-dimensional TTG expression for very thick films and the Fuchs-Sondheimer expression for very large grating spacings. The results demonstrate the utility of the variational technique for analyzing non-diffusive phonon-mediated heat Transport for nanostructures in multi-dimensional Transport geometries, and will assist the probing of the mean free path distribution of...

  • su c brc 02 accelerating linear Boltzmann Transport Equation by an asymptotic preserving scheme
    Medical Physics, 2016
    Co-Authors: Gang Chen, Xiang Hong, Haifeng Chen, Min Tang, Hao Gao
    Abstract:

    Purpose: Linear Boltzmann Transport Equation (LBTE) is as accurate as the Monte Carlo method for dose calculation. This work is to develop an asymptotic-preserving (AP) scheme to accelerate the LBTE, i.e., to achieve the same accuracy with significantly reduced number of spatial grids. Methods: In this proof-of-concept study, two-dimensional LBTE is solved by the discrete ordinate method. The Level-Symmetric (LQn) quadrature set is employed for angular discretization of LBTE. The Henyey-Greenstein scattering function is used for simulating the anisotropic scattering. For the AP scheme, the anisotropic scattering kernel is discretized as a scattering matrix and its difference with the analytical form is minimized with some constraints that are introduced to preserve the diffusive limit. Since LBTE is linear, the solution on each grid is approximated by linear combination of characteristic solutions and a special solution. A four-point cell-centered scheme is used to establish the linear system of the final solution with unknowns and a finite difference scheme connects the unknowns at four edge centers of the cell to solve this system. Results: First, compared with the exact analytical solution, the discrete L2 norm of the numerical error of the proposed method is less than 0.03 percents when the order of quadrature set is larger than 6 (i.e., more than 48 angles), even when the spatial grid is reduced to 8 by 8. Second, when using fewer spatial grids, the proposed method is more accurate than the conventional Source Iteration method. Conclusion: The AP scheme is developed for accelerating LBTE, and the accurate results can be achieved with significantly reduced number of spatial grids. The authors were partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000), and the Shanghai Pujiang Talent Program (#14PJ1404500).

  • tu ab brc 01 spherical harmonic based finite element method shfem a new angular discretization of linear Boltzmann Transport Equation for accurate dose calculation
    Medical Physics, 2016
    Co-Authors: Xiang Hong, Gang Chen, Hao Gao
    Abstract:

    Purpose: As a deterministic method for dose calculation, the linear Boltzmann Transport Equation (LBTE) can reach the same accuracy as the Monte Carlo method (MC). In terms of speed, LBTE can be significantly accelerated through various state-of-art numerical techniques. The angular discretization is crucial since the accuracy of LBTE highly depends on it and the computational time of LBTE is quadratic with respect to number of discretized angles. This work proposes a new angular discretization scheme that synergizes spherical harmonics method and finite element method. Methods: The LBTE is solved by the discrete ordinate method with a new quadrature scheme, i.e., Spherical Harmonics based Finite Element Method (SHFEM) for discretizing the angular variable. The proposed SHFEM is free from unphysical negative weights that often appear in a Level-Symmetric (LQn) quadrature set when the order is beyond 20. Moreover, the proposed SHFEM can accurately deal with directional sources. The spatial variables are discretized on the structured grid using the diamond-difference scheme. The Source Iteration method (SI) is utilized to solve the discretized LBTE, with the acceleration by the Diffusion Synthetic Acceleration method (DSA). Results: The SHFEM is compared with LQn and Legendre-Chebyshev (PN-TN) quadrature set respectively. With a three-dimensional (3D) MC method as the benchmark, the proposed SHFEM had the best performance, especially for the directional-source problems. Conclusion: SHFEM, a novel angular discretization method for LBTE that integrates spherical harmonics method and finite element method, is proposed for dose calculation with improved accuracy from LQn and PN-TN, particularly in the presence of directional sources. The authors were partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000), and the Shanghai Pujiang Talent Program (#14PJ1404500)

  • variational approach to solving the spectral Boltzmann Transport Equation in transient thermal grating for thin films
    arXiv: Mesoscale and Nanoscale Physics, 2016
    Co-Authors: Vazrik Chiloyan, Lingping Zeng, Samuel Huberman, A A Maznev, Keith A Nelson, Gang Chen
    Abstract:

    The phonon Boltzmann Transport Equation (BTE) is widely utilized to study non-diffusive thermal Transport. We find a solution of the BTE in the thin film transient thermal grating (TTG) experimental geometry by using a recently developed variational approach with a trial solution supplied by the Fourier heat conduction Equation. We obtain an analytical expression for the thermal decay rate that shows excellent agreement with Monte Carlo simulations. We also obtain a closed form expression for the effective thermal conductivity that demonstrates the full material property and heat transfer geometry dependence, and recovers the limits of the one-dimensional TTG expression for very thick films and the Fuchs-Sondheimer expression for very large grating spacings. The results demonstrate the utility of the variational technique for analyzing non-diffusive phonon-mediated heat Transport for nanostructures in multi-dimensional Transport geometries, and will assist the probing of the mean free path (MFP) distribution of materials via transient grating experiments.

  • variational approach to extracting the phonon mean free path distribution from the spectral Boltzmann Transport Equation
    Physical Review B, 2016
    Co-Authors: Vazrik Chiloyan, Lingping Zeng, Samuel Huberman, A A Maznev, Keith A Nelson, Gang Chen
    Abstract:

    The phonon Boltzmann Transport Equation (BTE) is a powerful tool for studying nondiffusive thermal Transport. Here, we develop a new universal variational approach to solving the BTE that enables extraction of phonon mean free path (MFP) distributions from experiments exploring nondiffusive Transport. By utilizing the known Fourier heat conduction solution as a trial function, we present a direct approach to calculating the effective thermal conductivity from the BTE. We demonstrate this technique on the transient thermal grating experiment, which is a useful tool for studying nondiffusive thermal Transport and probing the MFP distribution of materials. We obtain a closed form expression for a suppression function that is materials dependent, successfully addressing the nonuniversality of the suppression function used in the past, while providing a general approach to studying thermal properties in the nondiffusive regime.

Sushanta Tripathy - One of the best experts on this subject based on the ideXlab platform.

  • elliptic flow of hadrons via quark coalescence mechanism using Boltzmann Transport Equation for pb pb collision at sqrt s_ nn 2 76 tev
    Advances in High Energy Physics, 2020
    Co-Authors: Mohammed Younus, Sushanta Tripathy, Swatantra Kumar Tiwari, R Sahoo
    Abstract:

    Elliptic flow of hadrons observed at relativistic heavy ion collision experiments at relativistic heavy ion collider (RHIC) and large hadron collider (LHC) provides us an important signature of possible deconfinement transition from the hadronic phase to partonic phase. However, hadronization processes of deconfined partons back into final hadrons are found to play a vital role in the observed hadronic flow. In the present work, we use a coalescence mechanism also known as recombination (ReCo) to combine quarks into hadrons. To get there, we have used the Boltzmann Transport Equation in relaxation time approximation to Transport the quarks into equilibration and finally to freeze-out the surface, before coalescence takes place. A Boltzmann-Gibbs blast wave (BGBW) function is taken as an equilibrium function to get the final distribution and a power-like function to describe the initial distributions of partons produced in heavy ion collisions. In the present work, we try to estimate the elliptic flow of identified hadrons such as , , and , produced in Pb+Pb collisions at at the LHC for different centralities. The elliptic flow ( ) of identified hadrons seems to be described quite well in the available range. After the evolution of quarks until freeze-out time has been calculated using BTE-RTA, the approach used in this paper consists of combining two or more quarks to explain the produced hadrons at intermediate momenta regions. The formalism is found to describe the elliptic flow of hadrons produced in Pb+Pb collisions to a large extent.

  • elliptic flow in pb pb collisions at sqrt s_ rm nn 2 76 tev at the lhc using Boltzmann Transport Equation with non extensive statistics
    European Physical Journal A, 2018
    Co-Authors: Sushanta Tripathy, Swatantra Kumar Tiwari, Mohammed Younus, R Sahoo
    Abstract:

    Elliptic flow in heavy-ion collisions is an important signature of a possible de-confinement transition from hadronic phase to partonic phase. In the present work, we use non-extensive statistics, which has been used for transverse momentum ( $p_{{\rm T}}$ ) distribution in proton+proton ( $ p+p$ ) collisions, as the initial particle distribution function in Boltzmann Transport Equation (BTE). A Boltzmann-Gibbs Blast Wave (BGBW) function is taken as an equilibrium function to get the final distribution to describe the particle production in heavy-ion collisions. In this formalism, we try to estimate the elliptic flow in Pb+Pb collisions at $\sqrt{s_{{\rm NN}}} = 2.76$ TeV at the LHC for different centralities. The elliptic flow ( $ v_{2}$ ) of identified particles seems to be described quite well in the available $p_{{\rm T}}$ range. An approach which combines the non-extensive nature of particle production in $ p+p$ collisions through an evolution in kinetic theory using BTE, with BGBW as an equilibrium distribution is successful in describing the spectra and elliptic flow in heavy-ion collisions.

  • elliptic flow of hadrons via quark coalescence mechanism using Boltzmann Transport Equation for pb pb collision at sqrt s_ nn 2 76 tev
    arXiv: High Energy Physics - Phenomenology, 2018
    Co-Authors: Mohammed Younus, Sushanta Tripathy, Swatantra Kumar Tiwari, R Sahoo
    Abstract:

    Elliptic flow of hadrons observed at relativistic heavy-ion collision experiments at Relativistic Heavy-Ion Collider (RHIC) and Large Hadron Collider (LHC), provides us an important signature of possible de-confinement transition from hadronic phase to partonic phase. However, hadronization processes of de-confined partons back into final hadrons are found to play a vital role in the observed hadronic flow. In the present work, we use coalescence mechanism also known as Recombination (ReCo) to combine quarks into hadrons. To get there, we have used Boltzmann Transport Equation in relaxation time approximation to Transport the quarks into equilibration and finally to freeze-out surface, before coalescence takes place. A Boltzmann-Gibbs Blast Wave (BGBW) function is taken as an equilibrium function to get the final distribution and a power-like function to describe the initial distributions of partons produced in heavy-ion collisions. In the present work, we try to estimate the elliptic flow of identified hadrons such as $\pi$, $K$, $p$ etc., produced in Pb+Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV at the LHC for different centralities. The elliptic flow ($v_2$) of identified hadrons seems to be described quite well in the available $p_{\rm T}$ range. After the evolution of quarks until freeze-out time, has been calculated using BTE-RTA, the approach used in this paper consists of combining two or more quarks to explain the produced hadrons at intermediate momenta regions. The formalism is found to describe elliptic flow of hadrons produced in Pb+Pb collisions to a large extent.

  • transverse momentum spectra and nuclear modification factor using Boltzmann Transport Equation with flow in pb pb collisions at sqrt s_ nn 2 76 tev
    European Physical Journal A, 2017
    Co-Authors: Sushanta Tripathy, Swatantra Kumar Tiwari, Arvind Khuntia, R Sahoo
    Abstract:

    In the continuation of our previous work, the transverse-momentum (\(p_{T}\)) spectra and nuclear modification factor (\(R_{AA}\)) are derived using the relaxation time approximation of Boltzmann Transport Equation (BTE). The initial \(p_{T}\)-distribution used to describe p + p collisions has been studied with the perturbative-Quantum Chromodynamics (pQCD) inspired power-law distribution, Hagedorn's empirical formula and with the Tsallis non-extensive statistical distribution. The non-extensive Tsallis distribution is observed to describe the complete range of the transverse-momentum spectra. The Boltzmann-Gibbs Blast Wave (BGBW) distribution is used as the equilibrium distribution in the present formalism, to describe the \(p_{T}\)-distribution and nuclear modification factor in nucleus-nucleus collisions. The experimental data for Pb+Pb collisions at \(\sqrt{s_{NN}} = 2.76\) TeV at the Large Hadron Collider at CERN have been analyzed for pions, kaons, protons, \(K^{\ast0}\) and \(\phi\). It is observed that the present formalism while explaining the transverse-momentum spectra up to 5 GeV/c, explains the nuclear modification factor very well up to 8 GeV/c in \(p_{T}\) for all these particles except for protons. \(R_{AA}\) is found to be independent of the degree of non-extensivity, \(q_{pp}\) after \(p_{T} \sim 8\) GeV/c.

  • transverse momentum spectra and nuclear modification factor using Boltzmann Transport Equation with flow in pb pb collisions at sqrt s_ nn 2 76 tev
    arXiv: Nuclear Theory, 2017
    Co-Authors: Sushanta Tripathy, Swatantra Kumar Tiwari, Arvind Khuntia, R Sahoo
    Abstract:

    In the continuation of our previous work, the transverse momentum ($p_T$) spectra and nuclear modification factor ($R_{AA}$) are derived using relaxation time approximation of Boltzmann Transport Equation (BTE). The initial $p_T$-distribution used to describe $p+p$ collisions has been studied with the pQCD inspired power-law distribution, the Hagedorn's empirical formula and with the Tsallis non-extensive statistical distribution. The non-extensive Tsallis distribution is observed to describe the complete range of the transverse momentum spectra. The Boltzmann-Gibbs Blast Wave (BGBW) distribution is used as the equilibrium distribution in the present formalism, to describe the $p_T$-distribution and nuclear modification factor in nucleus-nucleus collisions. The experimental data for Pb+Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV at the Large Hadron Collider at CERN have been analyzed for pions, kaons, protons, $K^{*0}$ and $\phi$. It is observed that the present formalism while explaining the transverse momentum spectra upto 5 GeV/c, explains the nuclear modification factor very well upto 8 GeV/c in $p_T$ for all these particles except for protons. $R_{AA}$ is found to be independent of the degree of non-extensivity, $q_{pp}$ after $p_T \sim$ 8 GeV/c.

J St. Aubin - One of the best experts on this subject based on the ideXlab platform.

  • sci thur pm colourful interactions highlights 02 a deterministic solution to the first order linear Boltzmann Transport Equation including magnetic fields
    Medical Physics, 2016
    Co-Authors: J St. Aubin, A Keyvanloo, O. Vassiliev, Gino B Fallone
    Abstract:

    Purpose: To develop a novel formalism including magnetic force in the linear Boltzmann Transport Equation (LBTE) and to solve this Equation deterministically by developing a new numerical framework. Methods: The continuity Equation in six dimensions was used to derive the magnetic force term in the LBTE. The phase space variables were discretized using the multigroup method for energy variables, the discontinuous finite element method (DFEM) for the spatial variables, and using two approaches for the angular variables: the standard discrete ordinates method (DOM), and a novel angular DFEM. The calculated dose for both techniques was compared to Monte Carlo. Results: It was found that the standard source iteration approach was unstable using the DOM with magnetic fields. The Krylov solver restarted GMRES(m) overcame the instability except for cases characterized by very low media densities and large magnetic fields where convergence stagnated using smaller restart parameters. Our novel angular DFEM framework overcame these instabilities for all cases tested. Comparison with Monte Carlo showed greater than 99% of points passing a 2%/2mm gamma criterion for the DOM, and 99% of points passing for the angular DFEM. Conclusion: A novel formalism to include magnetic force within the LBTE was derived and a new numerical framework to solve the resultant Equations was developed and tested using two different angular discretization techniques. Both techniques provided excellent accuracy, but the angular DFEM proved to be more stable. Dose calculations with this formalism were proven to be highly accurate, equivalent to advanced Monte Carlo algorithms.

  • su g tep1 15 toward a novel gpu accelerated deterministic solution to the linear Boltzmann Transport Equation
    Medical Physics, 2016
    Co-Authors: R Yang, J St. Aubin, B. G. Fallone
    Abstract:

    Purpose: To develop a Graphic Processor Unit (GPU) accelerated deterministic solution to the Linear Boltzmann Transport Equation (LBTE) for accurate dose calculations in radiotherapy (RT). A deterministic solution yields the potential for major speed improvements due to the sparse matrix-vector and vector-vector multiplications and would thus be of benefit to RT. Methods: In order to leverage the massively parallel architecture of GPUs, the first order LBTE was reformulated as a second order self-adjoint Equation using the Least Squares Finite Element Method (LSFEM). This produces a symmetric positive-definite matrix which is efficiently solved using a parallelized conjugate gradient (CG) solver. The LSFEM formalism is applied in space, discrete ordinates is applied in angle, and the Multigroup method is applied in energy. The final linear system of Equations produced is tightly coupled in space and angle. Our code written in CUDA-C was benchmarked on an Nvidia GeForce TITAN-X GPU against an Intel i7-6700K CPU. A spatial mesh of 30,950 tetrahedral elements was used with an S4 angular approximation. Results: To avoid repeating a full computationally intensive finite element matrix assembly at each Multigroup energy, a novel mapping algorithm was developed which minimized the operations required at each energy. Additionally, a parallelized memory mapping for the kronecker product between the sparse spatial and angular matrices, including Dirichlet boundary conditions, was created. Atomicity is preserved by graph-coloring overlapping nodes into separate kernel launches. The one-time mapping calculations for matrix assembly, kronecker product, and boundary condition application took 452±1ms on GPU. Matrix assembly for 16 energy groups took 556±3s on CPU, and 358±2ms on GPU using the mappings developed. The CG solver took 93±1s on CPU, and 468±2ms on GPU. Conclusion: Three computationally intensive subroutines in deterministically solving the LBTE have been formulated on GPU, resulting in two orders of magnitude speedup. Funding support from Natural Sciences and Engineering Research Council and Alberta Innovates Health Solutions. Dr. Fallone is a co-founder and CEO of MagnetTx Oncology Solutions (under discussions to license Alberta bi-planar linac MR for commercialization).

  • discontinuous finite element space angle treatment of the first order linear Boltzmann Transport Equation with magnetic fields application to mri guided radiotherapy
    Medical Physics, 2015
    Co-Authors: J St. Aubin, A Keyvanloo, B. G. Fallone
    Abstract:

    Purpose: The advent of magnetic resonance imaging(MRI) guided radiotherapy systems demands the incorporation of the magnetic field into dose calculation algorithms of treatment planning systems. This is due to the fact that the Lorentz force of the magnetic field perturbs the path of the relativistic electrons, hence altering the dose deposited by them. Building on the previous work, the authors have developed a discontinuous finite element space-angle treatment of the linear Boltzmann Transport Equation to accurately account for the effects of magnetic fields on radiotherapy doses. Methods: The authors present a detailed description of their new formalism and compare its accuracy to geant4Monte Carlo calculations for magnetic fields parallel and perpendicular to the radiation beam at field strengths of 0.5 and 3 T for an inhomogeneous 3D slab geometry phantom comprising water, bone, and air or lung. The accuracy of the authors’ new formalism was determined using a gamma analysis with a 2%/2 mm criterion. Results: Greater than 98.9% of all points analyzed passed the 2%/2 mm gamma criterion for the field strengths and orientations tested. The authors have benchmarked their new formalism against Monte Carlo in a challenging radiationTransport problem with a high density material (bone) directly adjacent to a very low density material (dry air at STP) where the effects of the magnetic field dominate collisions. Conclusions: A discontinuous finite element space-angle approach has been proven to be an accurate method for solving the linear Boltzmann Transport Equation with magnetic fields for cases relevant to MRI guided radiotherapy. The authors have validated the accuracy of this novel technique against geant4, even in cases of strong magnetic field strengths and low density air.

  • A deterministic solution of the first order linear Boltzmann Transport Equation in the presence of external magnetic fields
    Medical physics, 2015
    Co-Authors: J St. Aubin, A Keyvanloo, O. Vassiliev, B. G. Fallone
    Abstract:

    Purpose: Accurate radiotherapy dose calculation algorithms are essential to any successful radiotherapy program, considering the high level of dose conformity and modulation in many of today’s treatment plans. As technology continues to progress, such as is the case with novel MRI-guided radiotherapy systems, the necessity for dose calculation algorithms to accurately predict delivered dose in increasingly challenging scenarios is vital. To this end, a novel deterministic solution has been developed to the first order linear Boltzmann Transport Equation which accurately calculates x-ray based radiotherapy doses in the presence of magnetic fields. Methods: The deterministic formalism discussed here with the inclusion of magnetic fields is outlined mathematically using a discrete ordinates angular discretization in an attempt to leverage existing deterministic codes. It is compared against the EGSnrc Monte Carlo code, utilizing the emf_macros addition which calculates the effects of electromagnetic fields. This comparison is performed in an inhomogeneous phantom that was designed to present a challenging calculation for deterministic calculations in 0, 0.6, and 3 T magnetic fields oriented parallel and perpendicular to the radiation beam. The accuracy of the formalism discussed here against Monte Carlo was evaluated with a gamma comparison using a standard 2%/2 mm and a more stringent 1%/1 mm criterion for a standard reference 10 × 10 cm2 field as well as a smaller 2 × 2 cm2 field. Results: Greater than 99.8% (94.8%) of all points analyzed passed a 2%/2 mm (1%/1 mm) gamma criterion for all magnetic field strengths and orientations investigated. All dosimetric changes resulting from the inclusion of magnetic fields were accurately calculated using the deterministic formalism. However, despite the algorithm’s high degree of accuracy, it is noticed that this formalism was not unconditionally stable using a discrete ordinate angular discretization. Conclusions: The feasibility of including magnetic field effects in a deterministic solution to the first order linear Boltzmann Transport Equation is shown. The results show a high degree of accuracy when compared against Monte Carlo calculations in all magnetic field strengths and orientations tested.

Swatantra Kumar Tiwari - One of the best experts on this subject based on the ideXlab platform.

  • elliptic flow of hadrons via quark coalescence mechanism using Boltzmann Transport Equation for pb pb collision at sqrt s_ nn 2 76 tev
    Advances in High Energy Physics, 2020
    Co-Authors: Mohammed Younus, Sushanta Tripathy, Swatantra Kumar Tiwari, R Sahoo
    Abstract:

    Elliptic flow of hadrons observed at relativistic heavy ion collision experiments at relativistic heavy ion collider (RHIC) and large hadron collider (LHC) provides us an important signature of possible deconfinement transition from the hadronic phase to partonic phase. However, hadronization processes of deconfined partons back into final hadrons are found to play a vital role in the observed hadronic flow. In the present work, we use a coalescence mechanism also known as recombination (ReCo) to combine quarks into hadrons. To get there, we have used the Boltzmann Transport Equation in relaxation time approximation to Transport the quarks into equilibration and finally to freeze-out the surface, before coalescence takes place. A Boltzmann-Gibbs blast wave (BGBW) function is taken as an equilibrium function to get the final distribution and a power-like function to describe the initial distributions of partons produced in heavy ion collisions. In the present work, we try to estimate the elliptic flow of identified hadrons such as , , and , produced in Pb+Pb collisions at at the LHC for different centralities. The elliptic flow ( ) of identified hadrons seems to be described quite well in the available range. After the evolution of quarks until freeze-out time has been calculated using BTE-RTA, the approach used in this paper consists of combining two or more quarks to explain the produced hadrons at intermediate momenta regions. The formalism is found to describe the elliptic flow of hadrons produced in Pb+Pb collisions to a large extent.

  • elliptic flow in pb pb collisions at sqrt s_ rm nn 2 76 tev at the lhc using Boltzmann Transport Equation with non extensive statistics
    European Physical Journal A, 2018
    Co-Authors: Sushanta Tripathy, Swatantra Kumar Tiwari, Mohammed Younus, R Sahoo
    Abstract:

    Elliptic flow in heavy-ion collisions is an important signature of a possible de-confinement transition from hadronic phase to partonic phase. In the present work, we use non-extensive statistics, which has been used for transverse momentum ( $p_{{\rm T}}$ ) distribution in proton+proton ( $ p+p$ ) collisions, as the initial particle distribution function in Boltzmann Transport Equation (BTE). A Boltzmann-Gibbs Blast Wave (BGBW) function is taken as an equilibrium function to get the final distribution to describe the particle production in heavy-ion collisions. In this formalism, we try to estimate the elliptic flow in Pb+Pb collisions at $\sqrt{s_{{\rm NN}}} = 2.76$ TeV at the LHC for different centralities. The elliptic flow ( $ v_{2}$ ) of identified particles seems to be described quite well in the available $p_{{\rm T}}$ range. An approach which combines the non-extensive nature of particle production in $ p+p$ collisions through an evolution in kinetic theory using BTE, with BGBW as an equilibrium distribution is successful in describing the spectra and elliptic flow in heavy-ion collisions.

  • elliptic flow of hadrons via quark coalescence mechanism using Boltzmann Transport Equation for pb pb collision at sqrt s_ nn 2 76 tev
    arXiv: High Energy Physics - Phenomenology, 2018
    Co-Authors: Mohammed Younus, Sushanta Tripathy, Swatantra Kumar Tiwari, R Sahoo
    Abstract:

    Elliptic flow of hadrons observed at relativistic heavy-ion collision experiments at Relativistic Heavy-Ion Collider (RHIC) and Large Hadron Collider (LHC), provides us an important signature of possible de-confinement transition from hadronic phase to partonic phase. However, hadronization processes of de-confined partons back into final hadrons are found to play a vital role in the observed hadronic flow. In the present work, we use coalescence mechanism also known as Recombination (ReCo) to combine quarks into hadrons. To get there, we have used Boltzmann Transport Equation in relaxation time approximation to Transport the quarks into equilibration and finally to freeze-out surface, before coalescence takes place. A Boltzmann-Gibbs Blast Wave (BGBW) function is taken as an equilibrium function to get the final distribution and a power-like function to describe the initial distributions of partons produced in heavy-ion collisions. In the present work, we try to estimate the elliptic flow of identified hadrons such as $\pi$, $K$, $p$ etc., produced in Pb+Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV at the LHC for different centralities. The elliptic flow ($v_2$) of identified hadrons seems to be described quite well in the available $p_{\rm T}$ range. After the evolution of quarks until freeze-out time, has been calculated using BTE-RTA, the approach used in this paper consists of combining two or more quarks to explain the produced hadrons at intermediate momenta regions. The formalism is found to describe elliptic flow of hadrons produced in Pb+Pb collisions to a large extent.

  • transverse momentum spectra and nuclear modification factor using Boltzmann Transport Equation with flow in pb pb collisions at sqrt s_ nn 2 76 tev
    European Physical Journal A, 2017
    Co-Authors: Sushanta Tripathy, Swatantra Kumar Tiwari, Arvind Khuntia, R Sahoo
    Abstract:

    In the continuation of our previous work, the transverse-momentum (\(p_{T}\)) spectra and nuclear modification factor (\(R_{AA}\)) are derived using the relaxation time approximation of Boltzmann Transport Equation (BTE). The initial \(p_{T}\)-distribution used to describe p + p collisions has been studied with the perturbative-Quantum Chromodynamics (pQCD) inspired power-law distribution, Hagedorn's empirical formula and with the Tsallis non-extensive statistical distribution. The non-extensive Tsallis distribution is observed to describe the complete range of the transverse-momentum spectra. The Boltzmann-Gibbs Blast Wave (BGBW) distribution is used as the equilibrium distribution in the present formalism, to describe the \(p_{T}\)-distribution and nuclear modification factor in nucleus-nucleus collisions. The experimental data for Pb+Pb collisions at \(\sqrt{s_{NN}} = 2.76\) TeV at the Large Hadron Collider at CERN have been analyzed for pions, kaons, protons, \(K^{\ast0}\) and \(\phi\). It is observed that the present formalism while explaining the transverse-momentum spectra up to 5 GeV/c, explains the nuclear modification factor very well up to 8 GeV/c in \(p_{T}\) for all these particles except for protons. \(R_{AA}\) is found to be independent of the degree of non-extensivity, \(q_{pp}\) after \(p_{T} \sim 8\) GeV/c.

  • transverse momentum spectra and nuclear modification factor using Boltzmann Transport Equation with flow in pb pb collisions at sqrt s_ nn 2 76 tev
    arXiv: Nuclear Theory, 2017
    Co-Authors: Sushanta Tripathy, Swatantra Kumar Tiwari, Arvind Khuntia, R Sahoo
    Abstract:

    In the continuation of our previous work, the transverse momentum ($p_T$) spectra and nuclear modification factor ($R_{AA}$) are derived using relaxation time approximation of Boltzmann Transport Equation (BTE). The initial $p_T$-distribution used to describe $p+p$ collisions has been studied with the pQCD inspired power-law distribution, the Hagedorn's empirical formula and with the Tsallis non-extensive statistical distribution. The non-extensive Tsallis distribution is observed to describe the complete range of the transverse momentum spectra. The Boltzmann-Gibbs Blast Wave (BGBW) distribution is used as the equilibrium distribution in the present formalism, to describe the $p_T$-distribution and nuclear modification factor in nucleus-nucleus collisions. The experimental data for Pb+Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV at the Large Hadron Collider at CERN have been analyzed for pions, kaons, protons, $K^{*0}$ and $\phi$. It is observed that the present formalism while explaining the transverse momentum spectra upto 5 GeV/c, explains the nuclear modification factor very well upto 8 GeV/c in $p_T$ for all these particles except for protons. $R_{AA}$ is found to be independent of the degree of non-extensivity, $q_{pp}$ after $p_T \sim$ 8 GeV/c.