arXiv subjects

Naresh Kumar

Publications and source records attributed to Naresh Kumar.

11 recordsLinked to original sources

arXiv2026

A High-Order Conformal FEM for Multidimensional Nonlinear Collisional Breakage Equations: Analysis and Computation

Particle breakage due to collisional interactions plays a vital role in the development of several phenomena in science and engineering. The nonlinear collisional breakage equations (NCBEs) are a significant set of equations in this context. Solving the NCBE is computationally challenging due to its nonlinearity, high dimensionality, and complex kernel interactions. Solving NCBE problems is more complex in two- and three-dimensional problems. In these problems, it is more challenging to evaluate multidimensional moments and integrals, maintain solution stability, and achieve computational efficiency. Despite the importance of the NCBE in science and engineering, the development of efficient numerical methods for solving it in two- and three-dimensional problems has not been adequately explored. In this work, we have introduced a new framework for solving the NCBE across multiple dimensions using the conformal finite element method (FEM). To the best of our knowledge, this is the first work to solve the NCBE using the conformal FEM. The new framework employs high-order Lagrange elements in conjunction with the BDF2 scheme for time discretization. The present method preserves the important physical quantities such as the total count and hypervolume of the population particles. Convergence results for error estimates have also been derived for both semidiscrete and fully discrete schemes. Numerical experiments have been carried out for one-, two-, and three-dimensional problems. The numerical experiments have shown that the proposed method achieved high accuracy, optimal convergence rates, and computational efficiency.

math.NA↗

arXiv2026

Error Analysis of a Conforming FEM for Multidimensional Fragmentation Equations

In this work, we develop and analyze a higher-order finite element method for the multidimensional fragmentation equation. To the best of our knowledge, this is the first study to establish a rigorous, conforming finite element framework for high-order spatial approximation of multidimensional fragmentation models. The scheme is formulated in a variational setting, and its stability and convergence properties are derived through a detailed mathematical analysis. In particular, the $L^2$ projection operator is used to obtain optimal-order spatial error estimates under suitable regularity assumptions on the exact solution. For temporal discretization, a second-order backward differentiation formula (BDF2) is adopted, yielding a fully discrete scheme that achieves second-order convergence in time. The theoretical analysis establishes $ L^2$-optimal convergence rates of ${\cal O}(h^{r+1})$ in space, together with second-order accuracy in time. The theoretical findings are validated through a series of numerical experiments in two and three space dimensions. The computational results confirm the predicted error estimates and demonstrate the robustness of the proposed method for various choices of fragmentation kernels and selection functions.

math.NA↗

arXiv2024

Error Analysis of a Fully Discrete Scheme for The Cahn--Hilliard Cross-Diffusion Model in Lymphangiogenesis

This paper introduces a stabilized finite element scheme for the Cahn--Hilliard cross-diffusion model, which is characterized by strongly coupled mobilities, nonlinear diffusion, and complex cross-diffusion terms. These features pose significant analytical and computational challenges, particularly due to the destabilizing effects of cross-diffusion and the absence of standard structural properties. To address these issues, we establish discrete energy stability and prove the existence of a finite element solution for the proposed scheme. A key contribution of this work is the derivation of rigorous error estimates, utilizing the novel $L^{\frac{4}{3}}(0,T; L^{\frac{6}{5}}(\Omega))$ norm for the chemical potential. This enables a comprehensive convergence analysis, where we derive error estimates in the $L^{\infty}(H^1(\Omega))$ and $L^{\infty}(L^2(\Omega))$ norms, and establish convergence of the numerical solution in the $L^{\frac{4}{3}}(0,T; W^{1,\frac{6}{5}}(\Omega))$ norm. Furthermore, the convergence analysis relies on a uniform bound of the form $\sum_{k=0}^n\tau\|\nabla(\cdot)\|_{L^{\frac{6}{5}}}^{\frac{4}{3}}$ to control the chemical potentials, marking a clear departure from the classical $\sum_{k=0}^n\tau\|\nabla(\cdot)\|_{L^{2}}^{2}$ estimate commonly used in Cahn--Hilliard-type models. Our approach builds upon and extends existing frameworks, effectively addressing challenges posed by cross-diffusion effects and the lack of uniform estimates. Numerical experiments validate the theoretical results and demonstrate the scheme's ability to capture phase separation dynamics consistent with the Cahn--Hilliard equation.

math.NA↗

arXiv2024

NH3 gas sensing over 2D Phosphorene sheet: A First-Principles Study

First-principles based calculations were executed to investigate the sensing properties of ammonia gas molecules on two-dimensional pristine black phosphorene towards its application as a gas sensor and related applications. We discuss in detail, the interaction of ammonia gas molecules on the phosphorene single sheet through the structural change analysis, electronic band gap, Bader charge transfer, and density-of-states calculations. Our calculations indicate that the phosphorene could be used as a detector of ammonia, where good sensitivity and very short recovery time at room temperature have confirmed the potential use of phosphorene in the detection of ammonia.

cond-mat.mtrl-sci↗

arXiv2024

Epidemic Modeling using Hybrid of Time-varying SIRD, Particle Swarm Optimization, and Deep Learning

Epidemiological models are best suitable to model an epidemic if the spread pattern is stationary. To deal with non-stationary patterns and multiple waves of an epidemic, we develop a hybrid model encompassing epidemic modeling, particle swarm optimization, and deep learning. The model mainly caters to three objectives for better prediction: 1. Periodic estimation of the model parameters. 2. Incorporating impact of all the aspects using data fitting and parameter optimization 3. Deep learning based prediction of the model parameters. In our model, we use a system of ordinary differential equations (ODEs) for Susceptible-Infected-Recovered-Dead (SIRD) epidemic modeling, Particle Swarm Optimization (PSO) for model parameter optimization, and stacked-LSTM for forecasting the model parameters. Initial or one time estimation of model parameters is not able to model multiple waves of an epidemic. So, we estimate the model parameters periodically (weekly). We use PSO to identify the optimum values of the model parameters. We next train the stacked-LSTM on the optimized parameters, and perform forecasting of the model parameters for upcoming four weeks. Further, we fed the LSTM forecasted parameters into the SIRD model to forecast the number of COVID-19 cases. We evaluate the model for highly affected three countries namely; the USA, India, and the UK. The proposed hybrid model is able to deal with multiple waves, and has outperformed existing methods on all the three datasets.

cs.LG↗

arXiv2022

Faked Speech Detection with Zero Prior Knowledge

Audio is one of the most used ways of human communication, but at the same time it can be easily misused to trick people. With the revolution of AI, the related technologies are now accessible to almost everyone, thus making it simple for the criminals to commit crimes and forgeries. In this work, we introduce a neural network method to develop a classifier that will blindly classify an input audio as real or mimicked; the word 'blindly' refers to the ability to detect mimicked audio without references or real sources. We propose a deep neural network following a sequential model that comprises three hidden layers, with alternating dense and drop out layers. The proposed model was trained on a set of 26 important features extracted from a large dataset of audios to get a classifier that was tested on the same set of features from different audios. The data was extracted from two raw datasets, especially composed for this work; an all English dataset and a mixed dataset (Arabic plus English) (The dataset can be provided, in raw form, by writing an email to the first author). For the purpose of comparison, the audios were also classified through human inspection with the subjects being the native speakers. The ensued results were interesting and exhibited formidable accuracy, as we were able to get at least 94% correct classification of the test cases, as against the 85% accuracy in the case of human observers.

cs.SD↗

arXiv2021

A Systematic Study on Weak Galerkin Finite Element Method for Second Order Parabolic Problems

A systematic numerical study on weak Galerkin (WG) finite element method for second order linear parabolic problems is presented by allowing polynomial approximations with various degrees for each local element. Convergence of both semidiscrete and fully discrete WG solutions are established in $L^{\infty}(L^2)$ and $L^{\infty}(H^1)$ norms for a general WG element $({\cal P}_{k}(K),\;{\cal P}_{j}(\partial K),\;\big[{\cal P}_{l}(K)\big]^2)$, where $k\ge 1$, $j\ge 0$ and $l\ge 0$ are arbitrary integers. The fully discrete space-time discretization is based on a first order in time Euler scheme. Our results are intended to extend the numerical analysis of WG methods for elliptic problems [J. Sci. Comput., 74 (2018), 1369-1396] to parabolic problems. Numerical experiments are reported to justify the robustness, reliability and accuracy of the WG finite element method.

math.NA↗

arXiv2020

COVID-19 Pandemic Prediction using Time Series Forecasting Models

Millions of people have been infected and lakhs of people have lost their lives due to the worldwide ongoing novel Coronavirus (COVID-19) pandemic. It is of utmost importance to identify the future infected cases and the virus spread rate for advance preparation in the healthcare services to avoid deaths. Accurately forecasting the spread of COVID-19 is an analytical and challenging real-world problem to the research community. Therefore, we use day level information of COVID-19 spread for cumulative cases from whole world and 10 mostly affected countries; US, Spain, Italy, France, Germany, Russia, Iran, United Kingdom, Turkey, and India. We utilize the temporal data of coronavirus spread from January 22, 2020 to May 20, 2020. We model the evolution of the COVID-19 outbreak, and perform prediction using ARIMA and Prophet time series forecasting models. Effectiveness of the models are evaluated based on the mean absolute error, root mean square error, root relative squared error, and mean absolute percentage error. Our analysis can help in understanding the trends of the disease outbreak, and provide epidemiological stage information of adopted countries. Our investigations show that ARIMA model is more effective for forecasting COVID-19 prevalence. The forecasting results have potential to assist governments to plan policies to contain the spread of the virus.

physics.soc-ph↗

arXiv2012

Luminosity distance in Swiss cheese cosmology with randomized voids and galaxy halos

We study the fluctuations in luminosity distance due to gravitational lensing produced both by galaxy halos and large scale voids. Voids are represented via a "Swiss cheese" model consisting of a \LambdaCDM Friedman-Robertson-Walker background in which a number of randomly distributed, spherical regions of comoving radius 35 Mpc are removed. A fraction of the removed mass is then placed on the shells of the spheres, in the form of randomly located halos, modeled with Navarro-Frenk-White profiles. The remaining mass is placed in the interior of the spheres, either smoothly distributed, or as randomly located halos. We compute the distribution of magnitude shifts using a variant of the method of Holz & Wald (1998), which includes the effect of lensing shear. In the two models we consider, the standard deviation of this distribution is 0.065 and 0.072 magnitudes and the mean is -0.0010 and -0.0013 magnitudes, for voids of radius 35 Mpc, sources at redshift 1.5, with the voids chosen so that 90% of the mass is on the shell today. The standard deviation due to voids and halos is a factor ~ 3 larger than that due to 35 Mpc voids alone with a 1 Mpc shell thickness which we studied in our previous work. To a good approximation, the variance of the distribution depends only on the mean column depth and concentration of halos and on the fraction of the mass density that is in the form of halos (as opposed to smoothly distributed): it is independent of how the halos are distributed in space. We derive an approximate analytic formula for the variance that agrees with our numerical results to \lesssim 20% out to z\simeq 1.5.

astro-ph.CO↗

arXiv2011

Luminosity distance in Swiss cheese cosmology with randomized voids. II. Magnification probability distributions

We study the fluctuations in luminosity distances due to gravitational lensing by large scale (> 35 Mpc) structures, specifically voids and sheets. We use a simplified "Swiss cheese" model consisting of a \Lambda -CDM Friedman-Robertson-Walker background in which a number of randomly distributed non-overlapping spherical regions are replaced by mass compensating comoving voids, each with a uniform density interior and a thin shell of matter on the surface. We compute the distribution of magnitude shifts using a variant of the method of Holz & Wald (1998), which includes the effect of lensing shear. The standard deviation of this distribution is ~ 0.027 magnitudes and the mean is ~ 0.003 magnitudes for voids of radius 35 Mpc, sources at redshift z_s=1.0, with the voids chosen so that 90% of the mass is on the shell today. The standard deviation varies from 0.005 to 0.06 magnitudes as we vary the void size, source redshift, and fraction of mass on the shells today. If the shell walls are given a finite thickness of ~ 1 Mpc, the standard deviation is reduced to ~ 0.013 magnitudes. This standard deviation due to voids is a factor ~ 3 smaller than that due to galaxy scale structures. We summarize our results in terms of a fitting formula that is accurate to ~ 20%, and also build a simplified analytic model that reproduces our results to within ~ 30%. Our model also allows us to explore the domain of validity of weak lensing theory for voids. We find that for 35 Mpc voids, corrections to the dispersion due to lens-lens coupling are of order ~ 4%, and corrections to due shear are ~ 3%. Finally, we estimate the bias due to source-lens clustering in our model to be negligible.

gr-qc↗

arXiv2008

Backreaction of superhorizon perturbations in scalar field cosmologies

It has been suggested that the acceleration of the Universe may be due to the backreaction of perturbations to the Friedmann-Robertson-Walker background. For a Universe dominated by cold dark matter, it is known that the backreaction of superhorizon perturbations can not drive acceleration. We extend this result to models with cold dark matter together with a scalar field. We show that the scalar field can drive acceleration only via the standard mechanism of a constant or nearly constant piece of its potential (i.e., a cosmological constant); there is no separate mechanism involving superhorizon backreaction. This rules out some models which have been proposed in the literature.

astro-ph↗