arXiv subjects

Suman Pal

Publications and source records attributed to Suman Pal.

16 recordsLinked to original sources

arXiv2026

Non-Local Energy Dissipation and Topological Obstructions in the Second-Order Positive Modified Burgers' Equation

We study the higher-order flows of the modified Burgers' equation generated by its standard recursion operator. In particular, we show that the second-order positive flow takes the form of a non-local integro-differential equation. After reducing the equation to a traveling-wave form, we investigate its asymptotic energy behavior. The resulting analysis shows that the non-local energy flux prevents the formation of both topological kink and bell-shaped solitary waves. We show that the non-local dissipation permanently breaks the asymptotic equilibrium between nonlinear convection and linear dispersion, forcing an irreversible energy imbalance. Our analysis shows that the solitary waves are unstable. The non-local term causes continuous energy loss through radiation. As a result, the traveling wave cannot keep a stable and symmetric shape.

math.AP↗

arXiv2026

On the Second-Order Positive Burgers' Equation: Integrability, Lax Pair, Darboux Transformations, and Lie Symmetry Reduction

This paper derives the second-order positive Burgers' equation from the standard Burgers' hierarchy to explore its complete integrability and exact analytical solutions. We construct this higher-order nonlinear evolution equation by systematically applying the recursion operator to the classical Burgers' equation. Expanding on this structural framework, we then derive the explicit third-order equation and use Complete Bell Polynomials to generalize the $n$-th order hierarchy. Through the Cole-Hopf transformation, the second-order nonlinear equation rigorously maps to the linear third-order dispersion equation. We establish complete integrability by explicitly formulating the scalar Lax pair (zero-curvature representation), which allows us to directly derive the associated differential and algebraic Darboux transformations. To systematically classify explicit stationary, time-dependent traveling wave, and self-similar profiles, we apply several techniques to the linear domain: separation of variables, the Hirota perturbation method, traveling wave reduction via the Complete Discrimination System for Polynomial Method (CDSPM), and Lie similarity reduction. Crucially, our analysis demonstrates the exact finite truncation of the Hirota perturbation series. We conclude by outlining how this equation impacts the theoretical understanding of fluid dynamics, nonlinear transport phenomena, and higher-order wave propagation.

nlin.SI↗

arXiv2026

Can average speed of sound and thermodynamic response functions signal the exotic phases in neutron star cores?

The speed of sound in dense nuclear matter is crucial for understanding neutron star structure and constraining the EOS. We have discussed in details the decomposition of speed of sound via the average speed of sound and its logarithmic derivative and have connected it to the other two decomposition schemes via slope and curvature of the energy per particle or through the normalized trace anomaly and its derivative. These thermodynamic variables provide important diagnostic tools for the composition of the inner core of the compact stars. We discuss a new method of understanding phase transition and the microphysics of dense matter through the thermodynamic response functions like isothermal compressibility, baryon number susceptibility and bulk modulus in order to distinguish between local (sharp interface) and global charge (mixed phase) neutrality conditions, thereby revealing the signatures of the phase transition. The corresponding neutron-star mass--radius relations demonstrate that all considered equations of state satisfy current astrophysical constraints, while the most massive stable configurations contain either an extended mixed phase or a quark core depending on the phase-transition construction.

nucl-th↗

arXiv2026

Characterizing the quark-hadron mixed phase in compact star cores : sensitivity to nuclear saturation and quark-model parameters at finite-temperature

A thorough knowledge of the quark-hadron phase transition in hot and dense matter is essential for constraining the equation of state of neutron stars. In this work, we study the thermodynamics of the quark-hadron mixed phase at finite temperature using the Gibbs construction and examine its impact on hybrid star matter. We systematically explore the role of nuclear saturation properties, including the effective nucleon mass, incompressibility, symmetry energy coefficient, and its slope, together with quark matter parameters such as the bag constant and the vector coupling strength. We find that the width of the mixed phase is mainly controlled by the effective mass and symmetry energy, while the roles of incompressibility and symmetry energy slope are comparatively weak, particularly at higher temperatures. Thermal effects substantially modify the phase structure: increasing temperature reduces the mixed-phase width and softens the equation of state in the coexistence region due to Gibbs phase equilibrium constraints. These effects are reflected in the behavior of the speed of sound, the trace anomaly, and its derivative. Variations in the symmetry energy, effective mass, and quark parameters significantly affect the hadron-quark transition, stellar radii, and maximum mass, while finite temperature softens the equation of state and enhances radius jumps in the mixed phase. Strong vector repulsion is essential to reconcile massive pulsar observations with NICER constraints, whereas weaker repulsion favors more compact, low-mass configurations.

nucl-th↗

arXiv2026

Can a hybrid star with constant sound speed parametrization explain the new NICER mass-radius measurements ?

We present a reanalysis of NICER observations of PSR J0740+6620 and PSR J0030+0451 to test the consistency of various nuclear equations of state (EoS) within the framework of hybrid star models. In particular, we examine how different surface temperature models for PSR J0030+0451, categorized as Scenarios A, B, and C, lead to significantly different mass-radius estimates. We perform a comprehensive study constraining the parameters of the constant speed of sound (CSS) model based on representative observational categories. Our findings indicate that for certain hadronic equations of state, including both density-independent and density-dependent cases, the results remain consistent for lower values of the energy density discontinuity, while discrepancies emerge as the discontinuity increases. Scenarios involving large jumps in energy density are generally disfavored by the requirement of supporting massive neutron stars, whereas higher values of the speed of sound in the quark matter phase tend to yield better agreement with observational trends. These results underscore the importance of phase transition characteristics in aligning hybrid star models with current astrophysical observations. We further constrain the CSS parameters using observational data from PSR J0740+6620 and PSR J0952-0607 by computing the maximum mass supported by these parameter sets.

nucl-th↗

arXiv2026

Calculation of the transport coefficients in neutron star

In this work, we have calculated the transport coefficients: shear viscosity and thermal conductivity inside the neutron star core. Our calculation is based on the relativistic kinetic theory approach using a modified BUU equation for quasi-particles whose mass and the chemical-potential and thus in turn the Fermi surface varies with the baryonic density $\rho_{B}$ and the temperature of the medium, and we have used the relaxation time approximation. For the description of the hadronic matter inside the neutron star, we consider the relativistic mean field model with three different kinds of parameterizations. We have found that the shear viscosity is predominantly influenced by neutrons, while thermal conductivity is primarily dominated by electrons.

nucl-th↗

arXiv2026

Radial Oscillations and Stability of Neutron Stars with Antikaon Condensates

Radial oscillations provide a direct probe of the stability and compressibility of neutron stars and are highly sensitive to the equation of state of dense matter. In this work, we investigate the impact of antikaon condensates on the radial oscillation properties of neutron stars. We model neutron star matter using equations of state with a wide range of stiffness. For this purpose, both non-linear and density-dependent relativistic mean-field frameworks are employed to develop equations of state that are consistent with current astrophysical constraints. We further consider the emergence of antikaon condensates ($K^-$ and $\bar{K}^0$) in the stellar core, which modifies the pressure--energy density relation of dense matter. We find that the nature of the transition from nuclear matter to the condensed phase is sensitive to the antikaon optical potential depth and underlying equation of state. We compute the fundamental and higher-order radial oscillation modes for neutron stars containing antikaon condensates over a range of antikaon optical potential depths. Our results demonstrate that the antikaon optical potential depth plays a decisive role in governing the systematic shifts observed in the radial oscillation frequencies, while also significantly reducing the stability limits and maximum masses of neutron stars. These imprints of antikaon condensation on radial oscillation spectra provide a promising avenue for future multi-messenger observations and high-frequency gravitational-wave searches to directly probe and constrain the internal composition and equation of state of neutron stars.

nucl-th↗

arXiv2025

Density dependent speed of sound and its consequences in neutron stars

We introduce a parametrized density-dependent speed of sound and construct an ensemble of equations of state for neutron stars which are found to closely resemble the realistic equations of state calculated using relativistic mean field theory. We show that each of these parameters display an unique feature relevant to the properties of the compact stars. The emergence of special points in the Mass-Radius plot is a significant outcome for neutron stars which is more commonly seen in case of hybrid stars. We have also shown that the curvature term in the speed of sound changes its sign for these hadronic equations of state without the matter reaching the conformal limit or undergoing any phase transition. It is related to the 1st derivative of the energy per nucleon reaching a maximum. We have also examined the detailed behavior of the trace anomaly and polytropic index for RMF models, as well as for a density-dependent parametrized speed of sound. Our analysis demonstrates that the sign of the trace anomaly at high densities is sensitive to the stiffness or softness of the EOS. Different observational constraints from mass-radius and tidal deformability can restrict the range of parameters in the proposed speed of sound model.

nucl-th↗

arXiv2025

Is the central compact object in HESS J1731-347 a hybrid star with a quark core? An analysis with the constant speed of sound parametrization

In this work, we investigate the possibility of the compact object in HESS J1731-347 with $M=0.77_{-0.17}^{+0.20}M_{\odot}$ and $R=10.4_{-0.78}^{+0.86} km$ to be a hybrid star with quark matter in the inner core. The observation of this low mass compact star dictates the use of softer equation of state which on the contrary cannot explain the massive compact stars. This poses a new challenge for the astrophysicists in their search for the equation of state of compact objects. The hybrid equations of state are constructed using the IUFSU parametrization based on the relativistic mean field (RMF) theory for the hadronic part and the generic constant speed of sound parametrization (CSS) for the phase transition to quark matter.The CSS framework is characterized by three key parameters, namely the transition density $(\rho_{tr})$, the energy jumps $(\Delta\varepsilon)$ and the speed of sound $(C_s)$. Here, our primary aim is to investigate the influence of individual CSS parameters on the formation of a object of small mass and radius compatible with HESS J1731-347 parameters. We have also examined the effect of hadronic parameters such as effective mass, symmetry energy, and the slope of the symmetry energy at saturation densities on the formation of this compact object.Finally our analysis suggests that, within a 1$\sigma$ credible level, HESS J1731-347 aligns with the scenario of a stable hybrid star with early deconfinement and higher energy gap

nucl-th↗

arXiv2024

Self-consistent thermodynamical treatment for quark matter in quasi-particle model at finite temperature

In this work, we have studied the medium effects in strange quark matter in the framework of a grand-canonical ensemble using the phenomenological quasi-particle model. This model is studied with proper self-consistent thermodynamical treatment by incorporating chemical potential-dependent quark mass. We have also included the vector interaction in a self-consistent way. The main aim of this work is to explore the proper thermodynamic treatment in addressing the medium effects at both zero and finite temperatures. In the case of the finite temperature, we explore the study of self-consistent thermodynamics in the isothermal as well as the isentropic processes. The effect of finite temperature and lepton fraction have been studied on the equation of state, speed of sound, and particle fraction. The $M-R$ and $M-\Lambda$ diagrams are found to be consistent with the observational constraints.

hep-ph↗

arXiv2024

Effect of $f(R,T)$ theory of gravity on the properties of strange quark stars

In this study, we investigate strange quark stars within the framework of modified $f(R,T)$ gravity, where $R$ represents the Ricci scalar and $T$ denotes the trace of the energy-momentum tensor, specifically defined as $ f(R,T) = R + 2\chi T $. The equation of state is obtained with the different forms of the MIT bag model and quark mass model with medium effects and self-consistent thermodynamical treatment. We find that negative values of $\chi$ significantly increase both the mass and radius of the quark star. The inclusion of $\chi$ helps to satisfy recent the astrophysical constraints on the mass-radius relationship. We have also constrained the values of $\chi$ for each EoS, based on the observed maximum mass and corresponding radius, demonstrating that the inclusion of this parameter helps to address the challenges posed by both the GW190814 event and NICER observations of PSR J0030+0451. We also observe that the inclusion of $f(R,T)$ gravity leads to an increase in both the maximum mass, by about $ (0.23- 0.27)~M_{\odot}$, and the corresponding radius, by approximately (1.5-2.0)~\text{km}, depending on the chosen equation of state.

gr-qc↗

arXiv2024

Medium Effects in MIT Bag Model for quark matter: Self consistent thermodynamical treatment

The study of strange quark matter within the framework of the density-dependent MIT Bag model using the Grand Canonical ensemble is thermodynamically inconsistent. In this work, it is shown that if the medium effects are incorporated through a density-dependent Bag pressure in the Grand Canonical ensemble, then the Euler relation is violated. If Euler relation is used then the minimum of energy per baryon does not occur at zero pressure. In order to overcome this inconsistency, we propose the medium effect of the strange quark matter in the form of chemical potential dependent Bag pressure in the grand Canonical ensemble. The density dependent Bag pressure which has been used in Grand Canonical ensemble so far can however be used in Canonical ensemble without violating the laws of thermodynamics. These prescriptions will obey the Euler relation as well as the minimum energy per baryon will coincide with the zero of pressure and hence can be considered to be self consistent. These equations of state in the Grand Canonical ensemble can be further used to construct the Mass-Radius and other structural properties of the strange quark stars as well as hybrid stars. In our present work we have calculated the mass radius diagram of strange stars only using this formalism.

nucl-th↗

arXiv2024

Effect of dark matter interaction on hybrid star in the light of the recent astrophysical observations

We have explored the effect of dark matter interaction on hybrid star (HS) in the light of recent astrophysical observational constraints. The presence of dark matter is assumed to be there in both the hadron as well as the quark sector. The dark matter particle interacts with both hadron and quark matter through the exchange of a scalar as well as a vector meson. The equation of state (EOS) of the hadron part is computed using the NL3 version of the relativistic mean field(RMF) model, whereas the quark part is taken care of using the well-known MIT Bag model with the vector interaction. We investigate the effect of the dark matter density and the mass of the dark matter particle on various observables like mass, radius, tidal deformability of the dark matter admixed hybrid star(DMAHS). In this study, we have noted an intriguing aspect that is the speed of sound in the DMAHS is insensitive to both the mass as well as the density of dark matter. We also observe a striking similarity in the variation of transition mass and its corresponding radius, as well as the maximum mass of neutron stars, with dark matter density and mass. We employ observational constraints from neutron stars to narrow down the allowed range of the parameters of dark matter.

nucl-th↗

arXiv2023

Constraints on Density Dependent MIT Bag Model Parameters for Quark and Hybrid Stars

We compute the equation of state (EoS) of strange quark stars (SQSs) with the MIT Bag model using density dependent bag pressure, characterized by a Gaussian distribution function. The bag pressure's density dependence is controlled by three key parameters namely the asymptotic value ($B_{as}$), $ΔB(=B_0 - B_{as})$, and $β$. We explore various parameter combinations ($B_{as}$, $ΔB$, $β$) that adhere to the Bodmer-Witten conjecture, a criterion for the stability of SQSs. Our primary aim is to analyze the effects of these parameter variations on the structural properties of SQSs. However we find that none of the combinations can satisfy the NICER data for PSR J0030+0451 and the constraint on tidal deformability from GW170817. So it can be emphasized that this model cannot describe reasonable SQS configurations. We also extend our work to calculate structural properties of hybrid stars (HSs). With the density dependent bag model (DDBM), these astrophysical constraints are fulfilled by the HSs configurations within a very restricted range of the three parameters. The present work is the first to constrain the parameters of DDBM for both SQS and HSs using the recent astrophysical constraints on tidal deformabiity from GW170817 and that on mass-radius relationship from NICER data.

nucl-th↗

arXiv2023

Minigrid & Miniworld: Modular & Customizable Reinforcement Learning Environments for Goal-Oriented Tasks

We present the Minigrid and Miniworld libraries which provide a suite of goal-oriented 2D and 3D environments. The libraries were explicitly created with a minimalistic design paradigm to allow users to rapidly develop new environments for a wide range of research-specific needs. As a result, both have received widescale adoption by the RL community, facilitating research in a wide range of areas. In this paper, we outline the design philosophy, environment details, and their world generation API. We also showcase the additional capabilities brought by the unified API between Minigrid and Miniworld through case studies on transfer learning (for both RL agents and humans) between the different observation spaces. The source code of Minigrid and Miniworld can be found at https://github.com/Farama-Foundation/{Minigrid, Miniworld} along with their documentation at https://{minigrid, miniworld}.farama.org/.

cs.LG↗

arXiv2023

Speed of Sound in Hybrid Stars and the Role of Bag Pressure in the Emergence of Special Points on M-R Variation of Hybrid Stars

We compute the hybrid star (HS) properties with the help of Maxwell construction. For the purpose we choose a fixed hadronic model and four different forms of MIT bag model for the quark phase. We investigate thoroughly the effects of the different parameters of the bag model on the speed of sound in HS matter and the structural properties of HSs in the light of the various recent constraints on them from astrophysical observations. We also examine the importance of each parameter involved in these four forms of bag model in the context appearance of special points (SPs) in the mass-radius (M-R) variation of HSs. We find that among all these parameters the bag pressure play the most significant role in the emergence of the SPs in the M-R dependence of HSs.

nucl-th↗