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Prashant Kumar

Publications and source records attributed to Prashant Kumar.

70 records · Page 4Linked to original sources
arXiv2019

On local Fourier analysis of multigrid methods for PDEs with jumping and random coefficients

In this paper, we propose a novel non-standard Local Fourier Analysis (LFA) variant for accurately predicting the multigrid convergence of problems with random and jumping coefficients. This LFA method is based on a specific basis of the Fourier space rather than the commonly used Fourier modes. To show the utility of this analysis, we consider, as an example, a simple cell-centered multigrid method for solving a steady-state single phase flow problem in a random porous medium. We successfully demonstrate the prediction capability of the proposed LFA using a number of challenging benchmark problems. The information provided by this analysis helps us to estimate a-priori the time needed for solving certain uncertainty quantification problems by means of a multigrid multilevel Monte Carlo method.

math.NA↗
arXiv2018

Stochastic turbulence modeling in RANS simulations via Multilevel Monte Carlo

A multilevel Monte Carlo (MLMC) method for quantifying model-form uncertainties associated with the Reynolds-Averaged Navier-Stokes (RANS) simulations is presented. Two, high-dimensional, stochastic extensions of the RANS equations are considered to demonstrate the applicability of the MLMC method. The first approach is based on global perturbation of the baseline eddy viscosity field using a lognormal random field. A more general second extension is considered based on the work of [Xiao et al.(2017)], where the entire Reynolds Stress Tensor (RST) is perturbed while maintaining realizability. For two fundamental flows, we show that the MLMC method based on a hierarchy of meshes is asymptotically faster than plain Monte Carlo. Additionally, we demonstrate that for some flows an optimal multilevel estimator can be obtained for which the cost scales with the same order as a single CFD solve on the finest grid level.

physics.comp-ph↗
arXiv2018

Composite fermion Hall conductivity and the half-filled Landau level

We consider the Hall conductivity of composite fermions in the theory of Halperin, Lee, and Read (HLR). We present a fully quantum mechanical numerical calculation that shows, under suitable conditions, the HLR theory exhibits a particle-hole symmetric dc electrical Hall response in the presence of quenched disorder. Remarkably, this response of the HLR theory remains robust even when the disorder range is of the order of the Fermi wavelength. We find that deviations from particle-hole symmetric response can appear in the ac Hall conductivity at frequencies sufficiently large compared to the inverse system size. Our results agree with a recent semi-classical analysis by Wang et al., Phys. Rev. X 7, 031029 (2017) and complement the arguments based on the fully quantum-mechanical model by Kumar et al., Phys. Rev. B 98, 11505 (2018). These results provide further evidence that the HLR theory is compatible with an emergent particle-hole symmetry.

cond-mat.str-el↗
arXiv2018

Why is the HLR theory particle-hole symmetric?

Long wavelength descriptions of a half-filled lowest Landau level ($ν= 1/2$) must be consistent with the experimental observation of particle-hole (PH) symmetry. The traditional description of the $ν=1/2$ state pioneered by Halperin, Lee and Read (HLR) naively appears to break PH symmetry. However, recent studies have shown that the HLR theory with weak quenched disorder can exhibit an emergent PH symmetry. We find that such inhomogeneous configurations of the $ν=1/2$ fluid, when described by HLR mean-field theory, are tuned to a topological phase transition between an integer quantum Hall state and an insulator of composite fermions with a dc Hall conductivity $σ_{xy}^{\rm (cf)} = - {1 \over 2} {e^2 \over h}$. Our observations help explain why the HLR theory exhibits PH symmetric dc response.

cond-mat.str-el↗
arXiv2017

Transfer of temporal coherence in parametric down-conversion

We show that in parametric down-conversion the coherence properties of a temporally partially coherent pump field get entirely transferred to the down-converted entangled two-photon field. Under the assumption that the frequency-bandwidth of the down-converted signal-idler photons is much larger than that of the pump, we derive the temporal coherence functions for the down-converted field, for both infinitely-fast and time-averaged detection schemes. We show that in each scheme the coherence function factorizes into two separate coherence functions with one of them carrying the entire statistical information of the pump field. In situations in which the pump is a Gaussian Schell-model field, we derive explicit expressions for the coherence functions. Finally, we show that the concurrence of time-energy-entangled two-qubit states is bounded by the degree of temporal coherence of the pump field. This study can have important implications for understanding how correlations of the pump field manifest as two-particle entanglement as well as for harnessing energy-time entanglement for long-distance quantum communication protocols.

quant-ph↗
arXiv2014

Investigation of Kelvin-like solid foams for potential engineering applications: An attractive set of geometrical and thermo-hydraulic properties

Open cell foams have diverse industrial applications e.g. heat exchangers, structured reactors, filtration due to their unique properties such as high porosity and high specific surface area. In order to theoretically determine the geometric specific surface area and relationships between geometrical parameters of isotropic open cell foams, a generalized mathematical correlation was developed. For this purpose the tetrakaidecahedron geometry was used and different shapes of strut cross-sections of foam structures were taken explicitly into account. The derived correlation to predict geometrical properties can be easily extended to different strut shapes. 3-D numerical simulations at pore scale were performed to study the pressure drop characteristics and effective thermal conductivity. Fluid flow through open cell foam was performed in three different regimes: Darcy regime, transition regime and inertia regime. Importance of geometrical properties on fluid flow characteristics and their inclusion in the proposed correlations for predicting pressure drop is discussed. Can Ergun parameters have constant numerical values or not is also extensively discussed. Three different correlations were derived to predict the effective thermal conductivity for both, isotropic and anisotropic open cell foams. Geometrical parameters of foam matrix were introduced in the correlations to predict effective thermal conductivity.

cond-mat.mtrl-sci↗
arXiv2014

Geometric Critical Exponents in Classical and Quantum Phase Transitions

We define geometric critical exponents for systems that undergo continuous second order classical and quantum phase transitions. These relate scalar quantities on the information theoretic parameter manifolds of such systems, near criticality. We calculate these exponents by approximating the metric and thereby solving geodesic equations analytically, near curvature singularities of two dimensional parameter manifolds. The critical exponents are seen to be the same for both classical and quantum systems that we consider, and we provide evidence about the possible universality of our results.

cond-mat.stat-mech↗
arXiv2013

List Sort: A New Approach for Sorting List to Reduce Execution Time

In this paper we are proposing a new sorting algorithm, List Sort algorithm, is based on the dynamic memory allocation. In this research study we have also shown the comparison of various efficient sorting techniques with List sort. Due the dynamic nature of the List sort, it becomes much more fast than some conventional comparison sorting techniques and comparable to Quick Sort and Merge Sort. List sort takes the advantage of the data which is already sorted either in ascending order or in descending order.

cs.DS↗
arXiv2012

Geodesics in Information Geometry : Classical and Quantum Phase Transitions

We study geodesics on the parameter manifold, for systems exhibiting second order classical and quantum phase transitions. The coupled non-linear geodesic equations are solved numerically for a variety of models which show such phase transitions, in the thermodynamic limit. It is established that both in the classical as well as in the quantum case, geodesics are confined to a single phase, and exhibit turning behavior near critical points. Our results are indicative of a geometric universality in widely different physical systems.

cond-mat.stat-mech↗
arXiv2012

Large photoresponse of Cu:TCNQ nanowire arrays formed as aligned nanobridges

We report for the first time a large photoresponse in an array of charge transfer complex Cu:TCNQ nanowires (average diameter 30 nm) fabricated as a nanobridge device. The device shows highest photoresponse for excitation with 405 nm light which matches with its absorption peak. The current gain at zero bias can reach ~104 with an illumination power density of 2x106 W/m2. The zero bias responsivity is ~0.3 mA/W which increases on applying bias reaching 1.0 A/W or more for a bias of 2.0 Volt. Dark and illuminated I-V data are analyzed by two back-to-back Schottky diodes model, which shows the predominant photocurrent in the device arising from the photoconductive response of the nanowires.

cond-mat.mtrl-sci↗
arXiv2012

Observation of a Large Photo-response in a Single Nanowire (Diameter ~30 nm) of Charge Transfer Complex Cu:TCNQ

We report for the first time large photoresponse in a single NW of the charge transfer complex Cu:TCNQ. We fabricate a metal-semiconductor-metal device with a single NW and focus ion beam deposited Pt. We observe large photocurrent even at zero bias. The spectral dependence of the photoresponse follows the main absorption at ~ 405 nm which has the primarily responsible for photogenerated carriers. We have quantitatively analyzed the bias dependent photocurrent by a model of two back to back Schottky diodes connected by a series resistance. The observation shows that the large photoresponse of the device primarily occurs due to the reduction of the barrier at the contact regions due to illumination along with the photoconductive contribution. There is also a bias driven reduction of the nanowire resistance that is a unique feature for the material.

cond-mat.mtrl-sci↗
arXiv2012

Geodesic Congruences and Their Deformations in Bertrand Space-times

We study the energy conditions and geodesic deformations in Bertrand space-times. We show that these can be thought of as interesting physical space-times in certain regions of the underlying parameter space, where the weak and strong energy conditions hold. We further compute the ESR parameters and analyze them numerically. The focusing of radial time-like and radial null geodesics is shown explicitly, which verifies the Raychaudhuri equation.

gr-qc↗
arXiv2012

Parameterized Complexity on a New Sorting Algorithm: A Study in Simulation

Sundararajan and Chakraborty (2007) introduced a new sorting algorithm by modifying the fast and popular Quick sort and removing the interchanges. In a subsequent empirical study, Sourabh, Sundararajan and Chakraborty (2007) demonstrated that this algorithm sorts inputs from certain probability distributions faster than others and the authors made a list of some standard probability distributions in decreasing order of speed, namely, Continuous uniform < Discrete uniform < Binomial < Negative Binomial < Poisson < Geometric < Exponential < Standard Normal. It is clear from this interesting second study that the algorithm is sensitive to input probability distribution. Based on these pervious findings, in the present paper we are motivated to do some further study on this sorting algorithm through simulation and determine the appropriate empirical model which explains its average sorting time with special emphasis on parameterized complexity.

stat.CO↗
arXiv2011

Possible potentials responsible for stable circular relativistic orbits

Bertrand's theorem in classical mechanics of the central force fields attracts us because of its predictive power. It categorically proves that there can only be two types of forces which can produce stable, circular orbits. In the present article an attempt has been made to generalize Bertrand's theorem to the central force problem of relativistic systems. The stability criterion for potentials which can produce stable, circular orbits in the relativistic central force problem has been deduced and a general solution of it is presented in the article. It is seen that the inverse square law passes the relativistic test but the kind of force required for simple harmonic motion does not. Special relativistic effects do not allow stable, circular orbits in presence of a force which is proportional to the negative of the displacement of the particle from the potential center.

physics.class-ph↗
arXiv2010

Graphene produced by radiation-induced reduction of graphene oxide

Effect of irradiation on graphene oxide by sunlight, UV light and KrF excimer laser has been investigated in detail. Both sunlight and ultraviolet light reduce graphene oxide well after prolonged irradiation, but laser irradiation produces graphene with negligible oxygen functionalities within a short time. Laser irradiation is also useful for one-step synthesis of metal particle decorated graphene. Laser irradiation of graphene oxide appears to be an efficient procedure for large-scale synthesis of graphene.

cond-mat.mes-hall↗