arXiv subjects

Rajarshi Ray

Publications and source records attributed to Rajarshi Ray.

At least 37 records · Page 2Linked to original sources

arXiv2017

Centrality dependence of chemical freeze-out parameters from net-proton and net-charge fluctuations using hadron resonance gas model

We estimate chemical freeze-out parameters in HRG and EVHRG model by fitting the experimental information of net-proton and net-charge fluctuations measured in Au + Au collisions by the STAR collaboration at RHIC. We observe that chemical freeze-out parameters obtained from lower and higher order fluctuations are though almost same for $\sqrt{s_{NN}} > 27$ GeV, tend to deviate from each other at lower $\sqrt{s_{NN}}$. Moreover, these separations increase with decrease of $\sqrt{s_{NN}}$ and for a fixed $\sqrt{s_{NN}}$ increase towards central collisions. Furthermore, we observe an approximate scaling behaviour of $(μ_B/T)/(μ_B/T)_{central}$ with $(N_{part})/(N_{part})_{central}$ for the parameters estimated from lower order fluctuations for 11.5 GeV $\le \sqrt{s_{NN}} \le$ 200 GeV. Scaling is violated for the parameters estimated from higher order fluctuations for $\sqrt{s_{NN}}= 11.5$ and 19.6 GeV. It is observed that the chemical freeze-out parameter, which can describe $σ^2/M$ of net-proton very well in all energies and centralities, can not describe the $sσ$ equally well and vice versa.

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arXiv2017

Exact Synthesis of Reversible Logic Circuits using Model Checking

Synthesis of reversible logic circuits has gained great atten- tion during the last decade. Various synthesis techniques have been pro- posed, some generate optimal solutions (in gate count) and are termed as exact, while others are scalable in the sense that they can handle larger functions but generate sub-optimal solutions. Although scalable synthe- sis is very much essential for circuit design, exact synthesis is also of great importance as it helps in building design library for the synthesis of larger functions. In this paper, we propose an exact synthesis technique for re- versible circuits using model checking. We frame the synthesis problem as a model checking instance and propose an iterative bounded model checking calls for an optimal synthesis. Experiments on reversible logic benchmarks shows successful synthesis of optimal circuits. We also illus- trate optimal synthesis of random functions with as many as 10 variables and up to 10 gates.

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arXiv2017

Polyakov--Nambu--Jona-Lasinio model in finite volumes

We discuss the 2+1 flavor Polyakov loop enhanced Nambu--Jona-Lasinio model in a finite volume. The main objective is to check the volume scaling of thermodynamic observables for various temperatures and chemical potentials. We observe the possible violation of the scaling with system size in a considerable window along the whole transition region in the $T-μ_q$ plane.

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arXiv2016

An Efficient Algorithm for Vertex Enumeration of Two-Dimensional Projection of Polytopes

An efficient algorithm to enumerate the vertices of a two-dimensional (2D) projection of a polytope, is presented in this paper. The proposed algorithm uses the support function of the polytope to be projected and enumerated for vertices. The complexity of our algorithm is linear in the number of vertices of the projected polytope and we show empirically that the performance is significantly better in comparison to some known efficient algorithms of projection and enumeration.

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arXiv2016

Exploring effects of magnetic field on the Hadron Resonance Gas

We present a study of the effects of magnetic fields on fluctuations and correlations in hadron resonance gas model. We find significant changes in the fluctuations of net baryon number, electric charge and strangeness. This is also reflected in various fluctuation ratios along the freezeout curve.

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arXiv2016

Solving Batched Linear Programs on GPU and Multicore CPU

Linear Programs (LPs) appear in a large number of applications and offloading them to the GPU is viable to gain performance. Existing work on offloading and solving an LP on GPU suggests that performance is gained from large sized LPs (typically 500 constraints, 500 variables and above). In order to gain performance from GPU for applications involving small to medium sized LPs, we propose batched solving of a large number of LPs in parallel. In this paper, we present the design and CUDA implementation of our batched LP solver library, keeping memory coalescent access, reduced CPU-GPU memory transfer latency and load balancing as the goals. The performance of the batched LP solver is compared against sequential solving in the CPU using an open source solver GLPK (GNU Linear Programming Kit). The performance is evaluated for three types of LPs. The first type is the initial basic solution as feasible, the second type is the initial basic solution as infeasible and the third type is the feasible region as a Hyperbox. For the first type, we show a maximum speedup of $18.3\times$ when running a batch of $50k$ LPs of size $100$ ($100$ variables, $100$ constraints). For the second type, a maximum speedup of $12\times$ is obtained with a batch of $10k$ LPs of size $200$. For the third type, we show a significant speedup of $63\times$ in solving a batch of nearly $4$ million LPs of size 5 and $34\times$ in solving 6 million LPs of size $28$. In addition, we show that the open source library for solving linear programs-GLPK, can be easily extended to solve many LPs in parallel with multi-threading. The thread parallel GLPK implementation runs $9.6\times$ faster in solving a batch of $1e5$ LPs of size $100$, on a $12$-core Intel Xeon processor. We demonstrate the application of our batched LP solver in the domain of state-space exploration of mathematical models of control systems design.

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arXiv2016

Parallel Reachability Analysis for Hybrid Systems

We propose two parallel state-space exploration algorithms for hybrid systems with the goal of enhancing performance on multi-core shared memory systems. The first is an adaption of the parallel breadth first search in the SPIN model checker. We show that the adapted algorithm does not provide the desired load balancing for many hybrid systems benchmarks. The second is a task parallel algorithm based on cheaply precomputing cost of post (continuous and discrete) operations for effective load balancing. We illustrate the task parallel algorithm and the cost precomputation of post operators on a support-function-based algorithm for state-space exploration. The performance comparison of the two algorithms displays a better CPU utilization/load-balancing of the second over the first, except for certain cases. The algorithms are implemented in the model checker XSpeed and our experiments show a maximum speed-up of $900\times$ on a navigation benchmark with respect to SpaceEx LGG scenario, comparing on the basis of equal number of post operations evaluated.

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arXiv2015

Fluctuation of strongly interacting matter in Polyakov Nambu Jona-Lasinio model in finite volume

We have estimated the susceptibilities of conserved charges for 2-flavor strongly interacting matter with varying system sizes, using the Polyakov loop enhanced Nambu Jona-Lasinio model. The susceptibilities for vanishing baryon densities are found to show a scaling with the system volume in the hadronic as well as partonic phase. This scaling breaks down for a temperature range of about 30-50 MeV around the cross-over region. Simultaneous measurements of the various susceptibilities may thus indicate how close to the cross-over region the freeze-out occurs for the fireball created in heavy-ion collision experiments.

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arXiv2015

Thermodynamics and fluctuations of conserved charges in Hadron Resonance Gas model in finite volume

The thermodynamics of hot and dense matter created in heavy-ion collision experiments are usually studied as a system of infinite volume. Here we report on possible effects for considering a finite system size for such matter in the framework of the Hadron Resonance Gas model. The bulk thermodynamic variables as well as the fluctuations of conserved charges are considered. We find that the finite size effects are insignificant once the observables are scaled with the respective volumes. The only substantial effect is found in the fluctuations of electric charge which may therefore be used to extract information about the volume of fireball created in heavy-ion collision experiments.

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arXiv2014

The consequences of SU(3) colorsingletness, Polyakov Loop and Z(3) symmetry on a quark-gluon gas

Based on quantum statistical mechanics we show that the $SU(3)$ color singlet ensemble of a quark-gluon gas exhibits a $Z(3)$ symmetry through the normaized character in fundamental representation and also becomes equivalent, within a stationary point approximation, to the ensemble given by Polyakov Loop. Also Polyakov Loop gauge potential is obtained by considering spatial gluons along with the invariant Haar measure at each space point. The probability of the normalized character in $SU(3)$ vis-a-vis Polyakov Loop is found to be maximum at a particular value exhibiting a strong color correlation. This clearly indicates a transition from a color correlated to uncorrelated phase or vise-versa. When quarks are included to the gauge fields, a metastable state appears in the temperature range $145\le T({\rm{MeV}}) \le 170$ due to the explicit $Z(3)$ symmetry breaking in the quark-gluon system. Beyond $T\ge 170$ MeV the metastable state disappears and stable domains appear. At low temperature a dynamical recombination of ionized $Z(3)$ color charges to a color singlet $Z(3)$ confined phase is evident along with a confining background that originates due to circulation of two virtual spatial gluons but with conjugate $Z(3)$ phases in a closed loop. We also discuss other possible consequences of the center domains in the color deconfined phase at high temperature.

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arXiv2014

Shear Viscosity and Phase Diagram from Polyakov$-$Nambu$-$Jona-Lasinio model

We discuss a detailed study of the variation of shear viscosity, $η$, with temperature and baryon chemical potential within the framework of Polyakov$-$Nambu$-$Jona-Lasinio model. $η$ is found to depend strongly on the spectral width of the quasi-particles present in the model. The variation of $η$ across the phase diagram has distinctive features for different kinds of transitions. These variations have been used to study the possible location of the Critical End Point (CEP), and cross-checked with similar studies of variation of specific heat. Finally using a parameterization of freeze-out surface in heavy-ion collision experiments, the variation of shear viscosity to entropy ratio has also been discussed as a function of the center of mass energy of collisions.

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arXiv2014

Quark Number Susceptibility : Revisited with Fluctuation-Dissipation Theorem in mean field theories

Fluctuations of conserved quantum numbers are associated with the corresponding susceptibilities because of the symmetry of the system. The underlying fact is that these fluctuations as defined through the static correlators become identical to the direct calculation of these susceptibilities defined through the thermodynamic derivatives, due to the fluctuation-dissipation theorem. Through a rigorous exercise we explicitly show that a diagrammatic calculation of the static correlators associated with the conserved quark number fluctuations and the corresponding susceptibilities are possible in case of mean field theories, if the implicit dependence of the mean fields on the quark chemical potential are taken into account appropriately. As an aside we also give an analytical prescription for obtaining the implicit dependence of the mean fields on the quark chemical potential.

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arXiv2014

Fluctuations and correlations of conserved charges in an excluded volume hadron resonance gas model

We present temperature ($T$) and baryonic chemical potential ($μ_B$) dependence of higher order fluctuations and correlation between conserved charges in Excluded Volume Hadron Resonance Gas (EVHRG) model. Products of moments, such as ratio of variance to mean ($σ^2/M)$, product of skewness and standard deviation ($Sσ$), product of kurtosis and variance ($κσ^2$), for net-proton, net-kaon and net-charge have been evaluated on the phenomenologically determined freeze-out curve. Further, products of moments for net-proton and net-charge have been compared with the experimental data measured by STAR experiment. The dependence of the model result on the hadronic radius parameter has also been discussed.

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arXiv2014

Isospin symmetry breaking and baryon-isospin correlations from Polyakov$-$Nambu$-$Jona-Lasinio model

We present a study of the 1+1 flavor system of strongly interacting matter in terms of the Polyakov$-$Nambu$-$Jona-Lasinio model. We find that though the small isospin symmetry breaking brought in through unequal light quark masses is too small to affect the thermodynamics of the system in general, it may have significant effect in baryon-isospin correlations and have a measurable impact in heavy-ion collision experiments.

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arXiv2013

Shear viscosity due to the Landau damping from quark-pion interaction

We have calculated the shear viscosity coefficient $η$ of the strongly interacting matter in the relaxation time approximation, where a quasi particle description of quarks with its dynamical mass is considered from NJL model. Due to the thermodynamic scattering of quarks with pseudo scalar type condensate (i.e. pion), a non zero Landau damping will be acquired by the propagating quarks. This Landau damping may be obtained from the Landau cut contribution of the in-medium self-energy of quark-pion loop, which is evaluated in the framework of real-time thermal field theory.

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arXiv2013

Entropy scaling from chaotically produced particles in p-p collisions at LHC energies

Scaling of information entropy obtained from chaotically produced particles in p-p collisions, has been shown to be valid up to the highest available collision energy at LHC. Results from Monte Carlo simulation model PYTHIA 6.135 have also been compared. Based on the two com- ponent model and collision energy dependence of the chaoticity, charged particle multiplicities at proposed higher collision energies have been predicted.

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arXiv2013

Thermodynamic Properties of Strongly Interacting Matter in a Finite Volume using the Polyakov-Nambu-Jona-Lasinio model

We present the thermodynamic properties of strongly interacting matter in finite volume in the framework of Polyakov loop enhanced Nambu$-$Jona-lasinio model within mean field approximation. We considered both the 2 flavor and 2+1 flavor matter. Our primary observation was a qualitative change in the phase transition properties that resulted in the lowering of the temperature corresponding to the critical end point. This would make it favorable for detection in heavy-ion experiments that intend to create high density matter with considerably small temperatures. We further demonstrate the possibility of obtaining chiral symmetry restoration even within the confined phase in finite volumes.

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arXiv2012

Net Charge Fluctuations as a signal of QGP from Polyakov-Nambu-Jona-Lasinio model

We report the first model study of the net charge fluctuations in terms of D-measure within the framework of the Polyakov-Nambu-Jona-Lasinio model. Net charge fluctuation is estimated from the charge susceptibility evaluated using PNJL model. A parameterization of the freeze-out curve has been used to obtain D as a function of sqrt(s). We have discussed our results vis-a-vis recent experimental findings from ALICE collaboration.

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