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Harish Kumar

Publications and source records attributed to Harish Kumar.

At least 37 records · Page 2Linked to original sources
arXiv2023

Entropy stable schemes for the shear shallow water model Equations

The shear shallow water model is an extension of the classical shallow water model to include the effects of vertical shear. It is a system of six non-linear hyperbolic PDE with non-conservative products. We develop a high-order entropy stable finite difference scheme for this model in one dimension and extend it to two dimensions on rectangular grids. The key idea is to rewrite the system so that non-conservative terms do not contribute to the entropy evolution. Then, we first develop an entropy conservative scheme for the conservative part, which is then extended to the complete system using the fact that the non-conservative terms do not contribute to the entropy production. The entropy dissipative scheme, which leads to an entropy inequality, is then obtained by carefully adding dissipative flux terms. The proposed schemes are then tested on several one and two-dimensional problems to demonstrate their stability and accuracy.

math.NA↗
arXiv2023

High-order finite-difference entropy stable schemes for two-fluid relativistic plasma flow equations

In this article, we propose high-order finite-difference entropy stable schemes for the two-fluid relativistic plasma flow equations. This is achieved by exploiting the structure of the equations, which consists of three independent flux components. The first two components describe the ion and electron flows, which are modeled using the relativistic hydrodynamics equation. The third component is Maxwell's equations, which are linear systems. The coupling of the ion and electron flows, and electromagnetic fields is via source terms only. Furthermore, we also show that the source terms do not affect the entropy evolution. To design semi-discrete entropy stable schemes, we extend the RHD entropy stable schemes in Bhoriya et al. to three dimensions. This is then coupled with entropy stable discretization of the Maxwell's equations. Finally, we use SSP-RK schemes to discretize in time. We also propose ARK-IMEX schemes to treat the stiff source terms; the resulting nonlinear set of algebraic equations is local (at each discretization point). These equations are solved using the Newton's Method, which results in an efficient method. The proposed schemes are then tested using various test problems to demonstrate their stability, accuracy and efficiency.

math.NA↗
arXiv2023

Techniques, Tricks and Algorithms for Efficient GPU-Based Processing of Higher Order Hyperbolic PDEs

GPU computing is expected to play an integral part in all modern Exascale supercomputers. It is also expected that higher order Godunov schemes will make up about a significant fraction of the application mix on such supercomputers. It is, therefore, very important to prepare the community of users of higher order schemes for hyperbolic PDEs for this emerging opportunity. We focus on three broad and high-impact areas where higher order Godunov schemes are used. The first area is computational fluid dynamics (CFD). The second is computational magnetohydrodynamics (MHD) which has an involution constraint that has to be mimetically preserved. The third is computational electrodynamics (CED) which has involution constraints and also extremely stiff source terms. Together, these three diverse uses of higher order Godunov methodology, cover many of the most important applications areas. In all three cases, we show that the optimal use of algorithms, techniques and tricks, along with the use of OpenACC, yields superlative speedups on GPUs! As a bonus, we find a most remarkable and desirable result: some higher order schemes, with their larger operations count per zone, show better speedup than lower order schemes on GPUs. In other words, the GPU is an optimal stratagem for overcoming the higher computational complexities of higher order schemes! Several avenues for future improvement have also been identified. A scalability study is presented for a real-world application using GPUs and comparable numbers of high-end multicore CPUs. It is found that GPUs offer a substantial performance benefit over comparable number of CPUs, especially when all the methods designed in this paper are used.

math.NA↗
arXiv2023

Efficient Finite Difference WENO Scheme for Hyperbolic Systems with Non-Conservative Products

Higher order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes have been constructed for conservation laws. For multidimensional problems, they offer high order accuracy at a fraction of the cost of a finite volume WENO or DG scheme of comparable accuracy. This makes them quite attractive for several science and engineering applications. But, to the best of our knowledge, such schemes have not been extended to non-linear hyperbolic systems with non-conservative products. In this paper, we perform such an extension which improves the domain of applicability of such schemes. The extension is carried out by writing the scheme in fluctuation form. We use the HLLI Riemann solver of Dumbser and Balsara (2016) as a building block for carrying out this extension. Because of the use of an HLL building block, the resulting scheme has a proper supersonic limit. The use of anti-diffusive fluxes ensures that stationary discontinuities can be preserved by the scheme, thus expanding its domain of applicability. Our new finite difference WENO formulation uses the same WENO reconstruction that was used in classical versions, making it very easy for users to transition over to the present formulation. For conservation laws, the new finite difference WENO is shown to perform as well as the classical version of finite difference WENO, with two major advantages:- 1) It can capture jumps in stationary linearly degenerate wave families exactly. 2) It only requires the reconstruction to be applied once. Several examples from hyperbolic PDE systems with non-conservative products are shown which indicate that the scheme works and achieves its design order of accuracy for smooth multidimensional flows. Stringent Riemann ... *Abstract truncated, see PDF*

math.NA↗
arXiv2022

Investigating the Hubble Tension: Effect of Cepheid Calibration

Recent observations of Type Ia supernovae (SNe) by SH0ES collaboration (R11 and R16) diverge from the value reported by recent CMBR observations utilising the Planck satellite and application of the $ΛCDM$ cosmological model by at least $3 σ$. It is among the most challenging problems in contemporary cosmology and is known as the Hubble tension. The SNe Ia in R11 and R16 were calibrated through cepheid variables in three distinct galaxies: Milky Way, LMC, and NGC4258. Carnegie Hubble Program (CHP) observations of type Ia SNe calibrated using the tip of the red giant approach yielded a somewhat different estimate for the Hubble constant. This decreased the Hubble tension from over 3$σ$ to below 2$σ$. It is a legitimate question to answer whether there are any issues with SNe Ia calibration and to investigate whether the Hubble tension is real or not. We use statistical techniques namely, ANOVA, K-S test, and t-test to examine whether the cepheid calibration is host-dependent. Our analysis shows that (i) both R11 and R16 data suffer from non-Gaussian systematic effects, (ii) $H_0$ values in the sub-samples (different anchor-based) in both R11 and R16 groups are significantly different at a 99\% confidence level, and (iii) neglecting the metal-rich MW sample does not reduce the $H_0$ value significantly, and thus Hubble tension persists. A small reduction in the Hubble constant could be linked to the differences in the host environment. Hence instead of using a single universal relation environment based slope and zero point should be preferred.

astro-ph.CO↗
arXiv2022

Fluorite-related iridate Pr$_3$IrO$_7$: Crystal growth, structure, magnetism, thermodynamic, and optical properties

Spin-orbit coupling in heavy 5$d$ metal oxides, in particular, iridates have received tremendous interest in recent years due to the realization of exotic electronic and magnetic phases. Here, we report the synthesis, structural, magnetic, thermodynamic, and optical properties of the ternary iridate Pr$_3$IrO$_7$. Single crystals of Pr$_3$IrO$_7$ have been grown by the KF flux method. Structural analysis shows that Pr$_3$IrO$_7$ crystallizes in an orthorhombic phase with $Cmcm$ symmetry. The electron energy loss spectroscopy study indicates that Pr is in a 3+ valence state, which implies a 5+ oxidation state of Ir. Magnetization data measured at high and low magnetic fields do not exhibit any bifurcation between $M_{ZFC}$ and $M_{FC}$, however, a weak hump in $M(T)$ is observed at $T^*$$\sim$10.4~K. The specific heat data reveal two maxima at $\sim$253 K and $\sim$4.8 K. The optical conductivity $σ_1(ω)$ spectrum shows 24 infrared-active phonon modes and reveals an insulating behavior with an optical gap $Δ_{OP}$ of size $\sim$500~meV. During cooling down, the temperature-dependent reflectivity spectrum reveals eight extra phonon modes below the structural phase transition ($\sim$ 253 K). An anomaly is observed at around $T^*$ in the temperature evolution of infrared-active mode frequencies suggesting the presence of significant spin-phonon coupling in the system.

cond-mat.str-el↗
arXiv2022

Accreting White Dwarfs: Effect of WD Composition on Helium Ignition During Slow Accretion

Understanding the explosion mechanism of type Ia supernova is among the most challenging issues in astrophysics. Accretion of matter on a carbon-oxygen white dwarf from a companion star is one of the most important keys in this regard. Our aim is to study the effects of WD composition on various parameters during the accretion of helium rich matter at a slow rate. We have used the computer simulation code Modules for Experiments in Stellar Astrophysics (MESA) to understand the variations in the properties such as specific heat (\textit{$C_P$}) and degeneracy parameter (\textit{$η$}). The profile of specific heat shows a discontinuity and that of the degeneracy parameter shows a dip near the ignition region. As expected, the size of WD decreases and \textit{g} increases during the accretion. However, a red-giant-like expansion is observed after the rapid ignition towards the end. Our study explains the reason behind the delay in onset of helium ignition due to the difference in carbon abundance in a CO-WD. We find that white dwarfs of the lower abundance of carbon accrete slightly longer before the onset of helium ignition.

astro-ph.SR↗
arXiv2021

Slow Accretion of Helium Rich Matter onto C-O White Dwarf: Does Composition of WD Matter?

In binary systems, the helium accretion onto carbon-oxygen (CO) white dwarfs (WDs) plays a vital role in many astrophysical scenarios, especially in supernovae type Ia. Moreover, ignition density for accretion rate $\dot{M} \lesssim 10^{-9} M_{\odot}$ $yr^{-1}$ in helium accreting CO white dwarfs decides the triggering mechanism of a supernova explosion which could be either off-centre helium flash or central carbon flash. We aim to study the accretion of helium with a slow accretion rate $5 \times 10^{-10} M_{\odot}$ $yr^{-1}$ onto relatively cool and hot white dwarfs of different abundances of carbon and oxygen. The simulation code Modules for Experiments in Stellar Astrophysics (MESA) has been used for our study. We analyze the variation in several properties like surface gravity (g), helium luminosity ($L_{He}$), and effective temperature ($T_{eff}$) during the accretion phase of the white dwarfs. We also calculate the ignition density ($ρ_{He}$) and ignition temperature ($T_{He}$) of helium burning. As expected, the size of WD decreases and g increases during the accretion. However, a red-giant-like expansion is observed after the rapid ignition towards the end. The dependence of helium accreting WD evolution on its composition has also been explored in this study. We find that white dwarfs of the lower abundance of carbon accrete slightly longer before the onset of helium ignition.

astro-ph.SR↗
arXiv2020

Structure, magnetism and electronic properties in 3$d$-5$d$ based double perovskite (Sr$_{1-x}$Ca$_x$)$_2$FeIrO$_6$ (0 $\leq$ $x$ $\leq$ 1): A combined experimental and theoretical investigation

The 3$d$-5$d$ based double perovskites offer an ideal playground to study the interplay between electron correlation ($U$) and spin-orbit coupling (SOC) effect, showing exotic physics. The Sr$_2$FeIrO$_6$ is an interesting member in this family with ionic distribution of Fe$^{3+}$ (3$d^5$) and Ir$^{5+}$ (5$d^4$) where the later is believed to be nonmagnetic under the picture of strong SOC. Here, we report detailed investigation of structural, magnetic and electronic transport properties along with electronic structure calculations in (Sr$_{1-x}$Ca$_x$)$_2$FeIrO$_6$ series with $x$ from 0 to 1. While the basic interactions such as, $U$ and SOC are unlikely to be modified but a structural modification is expected due to ionic size difference between Sr$^{2+}$ and Ca$^{2+}$ which would influence other properties such as crystal field effect and band widths. While a nonmonotonic changes in lattice parameters are observed across the series, the spectroscopic investigations reveal that 3+/5+ charge state of Fe/Ir continue till end of the series. An analysis of magnetic data suggests similar nonmonotonic evolution of magnetic parameters with doping. Temperature dependent crystal structure as well as low temperature (5 K) magnetic structure have been determined from neutron powder diffraction measurements. The whole series shows insulating behavior. The electronic structure calculations show, SOC enhanced, a noncollinear antiferromagnetic and Mott-type insulating state is the stable ground state for present series with a substantial amount of orbital moment, but less than the spin magnetic moment, at the Ir site and the magnetocrystalline anisotropy. The obtained results imply that the Ca$^{2+}$ has large influence on the magnetic and transport properties, further showing a large agreement between experimental results as well as theoretical calculations.

cond-mat.str-el↗
arXiv2020

Entropy stable discontinuous Galerkin schemes for the Relativistic Hydrodynamic Equations

In this article, we present entropy stable discontinuous Galerkin numerical schemes for equations of special relativistic hydrodynamics with the ideal equation of state. The numerical schemes use the summation by parts (SBP) property of Gauss-Lobatto quadrature rules. To achieve entropy stability for the scheme, we use two-point entropy conservative numerical flux inside the cells and a suitable entropy stable numerical flux at the cell interfaces. The resulting semi-discrete scheme is then shown to entropy stable. Time discretization is performed using SSP Runge-Kutta methods. Several numerical test cases are presented to validate the accuracy and stability of the proposed schemes.

math.NA↗
arXiv2020

Entropy stable discontinuous Galerkin methods for ten-moment Gaussian closure equations

In this article, we propose high order discontinuous Galerkin entropy stable schemes for ten-moment Gaussian closure equations, which is based on the suitable quadrature rules (see [8]). The key components of the proposed method are the use of an entropy conservative numerical flux [31] in each cell and a suitable entropy stable numerical flux at the cell edges. This is then used in the entropy stable DG framework of [8] to obtain entropy stability of the semi-discrete scheme. We also extend these schemes to a source term that models plasma laser interaction. For the time discretization, we use strong stability preserving schemes. The proposed schemes are then tested on several test cases to demonstrate stability, accuracy, and robustness.

math.NA↗
arXiv2020

Magnetic and transport properties in pyrochlore iridates (Y$_{1-x}$Pr$_x$)$_2$Ir$_2$O$_7$: The role of $f$-$d$ exchange interaction and $d$-$p$ orbital hybridization

The $f$-$d$ magnetic exchange interaction is considered to be a key ingredient for many exotic topological phases in pyrochlore iridates. Here, we have investigated the evolution of structural, magnetic and electronic properties in doped pyrochlore iridate, (Y$_{1-x}$Pr$_x$)$_2$Ir$_2$O$_7$. Apart from geometrical frustration, pyrochlore iridates are well known for its active spin-orbit coupling effect. The substitution of Pr$^{3+}$ (4$f^2$) for the nonmagnetic Y$^{3+}$ (4$d^0$) acts as a magnetic doping, which provides an ideal platform to study $f$-$d$ exchange interaction without altering the Ir-sublattice. With Pr substitution, system retains its original cubic structural symmetry but the local structural parameters show an evolution with the doping concentration $x$. The robust magnetic-insulating state in Y$_2$Ir$_2$O$_7$ is drastically weakened, while Pr$_2$Ir$_2$O$_7$ ($x$ = 1.0) shows a paramagnetic-metallic behavior. A metal-insulator transition is observed for $x$ = 0.8 sample. This evolution of magnetic and electronic properties are believed to be induced by an exchange interaction between localized Pr-4$f$ and itinerant Ir-5$d$ electrons as well as by an increased hybridization between Ir-$t_{2g}$ and (basal) O-$p$ orbitals as observed in XAS study. The resistivity in insulating materials follows a power-law behavior with a decreasing exponent with $x$. A negative magnetoresistance is observed for present series of samples at low temperature and where the magnetoresistance shows a quadratic field dependence at higher fields.

cond-mat.str-el↗
arXiv2019

Manufacturing cosmic rays in the evolving dynamical states of galaxy clusters

Galaxy clusters are known to be reservoirs of Cosmic Rays (CRs), as inferred from theoretical calculations or detection of CR-derived observables. CR acceleration in clusters is mostly attributed to the dynamical activity that produces shocks. Shocks in clusters emerge out of merger or accretion, but which one is more effective in producing CRs? at which dynamical phase? and why? To this aim, we study the production or injection of CRs through shocks and its evolution in the galaxy clusters using cosmological simulations with the {\sc enzo} code. Particle acceleration model considered here is primarily the Diffusive Shock Acceleration (DSA) of thermal particles, but we also report a tentative study with pre-existing CRs. Defining appropriate dynamical states using the concept of virialization, we studied a sample of merging and non-merging clusters. We report that the merger shocks (with Mach number $\mathcal{M}\sim2-5$) are the most effective CR producers, while high-Mach peripheral shocks (i.e. $\mathcal{M}>5$) are mainly responsible for the brightest phase of CR injection in clusters. Clusters once merged, permanently deviate from CR and X-ray mass scaling of non-merging systems, enabling us to use it as a tool to determine the state of merger. Through a temporal and spatial evolution study, we found a strong correlation between cluster merger dynamics and CR injection. We observed that the brightest phase of X-ray and CR injection from clusters occur respectively at about 1.0 and 1.5 Gyr after every mergers, and CR injection peaks near to the cluster virial radius (i.e $r_{200}$). Delayed CR injection peaks found in this study deserve further investigation for possible impact on the evolution of CR-derived observables from galaxy clusters.

astro-ph.CO↗
arXiv2019

Nonmagnetic substitution in pyrochlore iridate Y$_2$(Ir$_{1-x}$Ti$_{x}$)$_2$O$_7$: Structure, magnetism and electronic properties

Tuning of spin-orbit coupling and electron correlation effects in pyrochlore iridates is considered for many interesting phenomena. We have investigated the temperature evolution of structural, magnetic and electronic properties in doped Y$_2$(Ir$_{1-x}$Ti$_{x}$)$_2$O$_7$ ($x$ = 0.0, 0.02, 0.05, 0.10 and 0.15) where the substitution of nonmagnetic Ti$^{4+}$ (3$d^0$) for Ir$^{4+}$ (5$d^5$) amounts to dilution of magnetic network and tuning of these parameters in opposite way. The system retains its original structural symmetry but local structural parameters show an evolution with Ti content. While the magnetic transition temperature is not largely influenced, both magnetic moment and magnetic frustration decreases with Ti doping. Magnetic relaxation measurement shows the parent compound Y$_2$Ir$_2$O$_7$ as well as its Ti doped analogues are in nonequilibrium magnetic state where the magnetic relaxation rate increases with Ti. Temperature dependent Raman measurements indicate no changes in structural symmetry, however, across the magnetic transition temperature an anomaly in A$_{1g}$ Raman mode is observed. Temperature dependent x-ray diffraction data also support the Raman spectroscopy data, however, an evolution of lattice parameters with temperature is observed. The electrical resistivity data of Y$_2$(Ir$_{1-x}$Ti$_{x}$)$_2$O$_7$ series exhibits insulating behavior throughout the temperature range, however, the resistivity decreases with Ti doping. The nature of charge conduction is found to follow power-law behavior in whole series but the validity of this model varies with temperature. A negative magnetoresistance has been observed at low temperature in present series which is explained with weak localized mechanism. Similar to other Ir based oxides, a crossover from negative to positive MR has been observed in present system.

cond-mat.str-el↗
arXiv2019

Polyphonic Music Composition with LSTM Neural Networks and Reinforcement Learning

In the domain of algorithmic music composition, machine learning-driven systems eliminate the need for carefully hand-crafting rules for composition. In particular, the capability of recurrent neural networks to learn complex temporal patterns lends itself well to the musical domain. Promising results have been observed across a number of recent attempts at music composition using deep RNNs. These approaches generally aim at first training neural networks to reproduce subsequences drawn from existing songs. Subsequently, they are used to compose music either at the audio sample-level or at the note-level. We designed a representation that divides polyphonic music into a small number of monophonic streams. This representation greatly reduces the complexity of the problem and eliminates an exponential number of probably poor compositions. On top of our LSTM neural network that learnt musical sequences in this representation, we built an RL agent that learnt to find combinations of songs whose joint dominance produced pleasant compositions. We present Amadeus, an algorithmic music composition system that composes music that consists of intricate melodies, basic chords, and even occasional contrapuntal sequences.

cs.SD↗
arXiv2019

Spin-phonon coupling in hole-doped pyrochlore iridates Y$_2$(Ir$_{1-x}$Ru$_x$)$_2$O$_7$: A Raman scattering study

Temperature dependent Raman scattering measurements have been performed to explore unusual coupling between magnetism and crystal structure in doped pyrochlore iridate Y$_2$(Ir$_{1-x}$Ru$_x$)$_2$O$_7$ with $x$ = 0.0, 0.05 and 0.2. The parent Y$_2$Ir$_2$O$_7$ shows an onset of magnetic ordering around $\sim$ 160 K ($T_{N}$) which monotonically decreases with Ru doping. Further, magnetic moment also decreases with progressive substitution of Ru. Substitution of Ru$^{4+}$ (4$d^4$) for Ir$^{4+}$ (5$d^5$) does not introduce significant modification in structural parameters, however, the magnetic transition temperature decreases systematically with doping. Raman scattering data show an anomalous change in $A_{1g}$ and $P_3$ Raman mode frequency and line-width across $T_{N}$ of individual samples. We further show that the shifting of Raman mode frequency with temperature exhibits a strong deviation from anharmonic decay around and below the $T_{N}$ of respective samples which underlines a spin-phonon coupling in these materials.

cond-mat.str-el↗
arXiv2017

Evolution of structure, magnetism and electronic transport in doped pyrochlore iridate Y$_2$Ir$_{2-x}$Ru$_{x}$O$_7$

The interplay between spin-orbit coupling (SOC) and electron correlation ($U$) is considered for many exotic phenomena in iridium oxides. We have investigated the evolution of structural, magnetic and electronic properties in pyrochlore iridate Y$_2$Ir$_{2-x}$Ru$_{x}$O$_7$ where the substitution of Ru has been aimed to tune this interplay. The Ru substitution does not introduce any structural phase transition, however, we do observe an evolution of lattice parameters with the doping level $x$. X-ray photoemission spectroscopy (XPS) study indicates Ru adopts charge state of Ru$^{4+}$ and replaces the Ir$^{4+}$ accordingly. Magnetization data reveal both the onset of magnetic irreversibility and the magnetic moment decreases with progressive substitution of Ru. These materials show non-equilibrium low temperature magnetic state as revealed by magnetic relaxation data. Interestingly, we find magnetic relaxation rate increases with substitution of Ru. The electrical resistivity shows an insulating behavior in whole temperature range, however, resistivity decreases with substitution of Ru. Nature of electronic conduction has been found to follow power-law behavior for all the materials.

cond-mat.str-el↗