arXiv subjects

Sarvesh Kumar

Publications and source records attributed to Sarvesh Kumar.

14 recordsLinked to original sources

arXiv2026

A virtual element method for Kelvin--Voigt viscoelasticity

Considering the computational advantages of virtual element methods (VEM), this work employs a conforming VEM for the numerical approximation of the Kelvin--Voigt model of viscoelasticity. For clarity and simplicity, we focus on the primal formulation. The spatial discretization is carried out using the virtual element method, while the temporal discretization is handled via the {second-order Crank--Nicolson} scheme. We establish the well-posedness of both the semi-discrete and fully discrete problems and derive {\it a priori} error estimates. Several representative numerical examples are presented to validate the theoretical results and to demonstrate the effectiveness of the proposed formulation.

math.NA↗

arXiv2026

Stability estimates for systems of nonlocal balance laws with memory

In this work, we investigate entropy solutions for a class of systems of nonlocal {balance laws in which the convective flux and the source involves terms where the state variable convolved with kernels} in both spatial and temporal variables. This formulation captures the dependence of the flux on the solution within its spatial neighborhood (spatial nonlocality) as well as on its past states (temporal nonlocality), thereby incorporating memory effects. The resulting systems are coupled through these nonlocal interactions. We establish stability estimates for entropy solutions with respect to perturbations in the flux, the spatial and temporal kernels, and the initial data for the corresponding initial value problems. Finally, we present numerical experiments to illustrate the theoretical results and to highlight the influence of memory and source terms on the solution dynamics.

math.AP↗

arXiv2025

SCULPT: An Interactive Machine Learning Platform for Analyzing Multi-Particle Coincidence Data from Cold Target Recoil Ion Momentum Spectroscopy

We present SCULPT (Supervised Clustering and Uncovering Latent Patterns with Training), a comprehensive software platform for analyzing tabulated high-dimensional multi-particle coincidence data from Cold Target Recoil Ion Momentum Spectroscopy (COLTRIMS) experiments. The software addresses critical challenges in modern momentum spectroscopy by integrating advanced machine learning techniques with physics-informed analysis in an interactive web-based environment. SCULPT implements Uniform Manifold Approximation and Projection (UMAP) for non-linear dimensionality reduction to reveal correlations in highly dimensional data. We also discuss potential extensions to deep autoencoders for feature learning, and genetic programming for automated discovery of physically meaningful observables. A novel adaptive confidence scoring system provides quantitative reliability assessments by evaluating user-selected clustering quality metrics with predefined weights that reflect each metric's robustness. The platform features configurable molecular profiles for different experimental systems, interactive visualization with selection tools, and comprehensive data filtering capabilities. Utilizing a subset of SCULPT's capabilities, we analyze photo double ionization data measured using the COLTRIMS method for 3-body dissociation of the D2O molecule, revealing distinct fragmentation channels and their correlations with physics parameters. The software's modular architecture and web-based implementation make it accessible to the broader atomic and molecular physics community, significantly reducing the time required for complex multi-dimensional analyses. This opens the door to finding and isolating rare events exhibiting non-linear correlations on the fly during experimental measurements, which can help steer exploration and improve the efficiency of experiments.

physics.atm-clus↗

arXiv2025

Mixed virtual element methods for a stress-velocity-rotation formulation in viscoelasticity

In this paper we propose a new mixed virtual element formulation for the numerical approximation of viscoelasticity equations with weakly imposed stress symmetry. The governing equations use the Zener model and are expressed in terms of the principal unknowns of additively decomposed stress into elastic and internal viscoelastic contributions, while the rotation tensor and velocity act as Lagrange multipliers. The time discretisation uses Crank--Nicolson's scheme. We demonstrate the unique solvability of both semi-discrete and fully-discrete problems by leveraging the properties of suitable local projectors. Moreover, we establish optimal a priori error estimates for all variables that appear in the mixed formulation. To validate our theoretical findings, we present several representative numerical examples that also highlight the features of the proposed formulation.

math.NA↗

arXiv2025

Convergence Analysis of Virtual Element Methods for the Sobolev Equation with Convection

We explore the potential applications of virtual elements for solving the Sobolev equation with a convective term. A conforming virtual element method is employed for spatial discretization, while an implicit Euler scheme is used to approximate the time derivative. To establish the optimal rate of convergence, a novel intermediate projection operator is introduced. We discuss and analyze both the semi-discrete and fully discrete schemes, deriving optimal error estimates for both the energy norm and L2-norm. Several numerical experiments are conducted to validate the theoretical findings and assess the computational efficiency of the proposed numerical methods.

math.NA↗

arXiv2024

Convergence analysis of a nonconforming virtual element method for compressible miscible displacement problems in porous media

This article presents a priori error estimates of the miscible displacement of one compressible fluid by another in a porous medium. The study utilizes the $H(\rm div)$ conforming virtual element method (VEM) for the approximation of the velocity, while a non-conforming virtual element approach is employed for the concentration. The pressure is discretised using the standard piecewise discontinuous polynomial functions. These spatial discretization techniques are combined with a backward Euler difference scheme for time discretization. Error estimates are established for velocity, pressure and concentration. The article also includes numerical results that validate the theoretical estimates.

math.NA↗

arXiv2024

Nonconforming virtual element method for an incompressible miscible displacement problem in porous media

This article presents a priori error estimates of the miscible displacement of one incompressible fluid by another through a porous medium characterized by a coupled system of nonlinear elliptic and parabolic equations. The study utilizes the $H(\rm{div})$ conforming virtual element method (VEM) for the approximation of the velocity, while a non-conforming virtual element approach is employed for the concentration. The pressure is discretised using the standard piecewise discontinuous polynomial functions. These spatial discretization techniques are combined with a backward Euler difference scheme for time discretization. The article also includes numerical results that validate the theoretical estimates presented.

math.NA↗

arXiv2023

Morley Type Virtual Element Method for Von K\'{a}rm\'{a}n Equations

This paper analyses the nonconforming Morley type virtual element method to approximate a regular solution to the von K\'{a}rm\'{a}n equations that describes bending of very thin elastic plates. Local existence and uniqueness of a discrete solution to the non-linear problem is discussed. A priori error estimate in the energy norm is established under minimal regularity assumptions on the exact solution. Error estimates in piecewise $H^1$ and $L^2$ norm are also derived. A working procedure to find an approximation for the discrete solution using Newtons method is discussed. Numerical results that justify theoretical estimates are presented.

math.NA↗

arXiv2023

Numerical solution of the Biot/elasticity interface problem using virtual element methods

We propose, analyze and implement a virtual element discretization for an interfacial poroelasticity-elasticity consolidation problem. The formulation of the time-dependent poroelasticity equations uses displacement, fluid pressure, and total pressure, and the elasticity equations are written in the displacement-pressure formulation. The construction of the virtual element scheme does not require Lagrange multipliers to impose the transmission conditions (continuity of displacement and total traction, and no-flux for the fluid) on the interface. We show the stability and convergence of the virtual element method for different polynomial degrees, and the error bounds are robust with respect to delicate model parameters (such as Lame constants, permeability, and storativity coefficient). Finally, we provide numerical examples that illustrate the properties of the scheme.

math.NA↗

arXiv2021

Understanding the L-shell ionization mechanism through osmium atoms bombarded by 4-6 MeV/u fluorine ions

The L-subshell ionization mechanism is studied in an ultra-thin osmium target bombarded by 4-6 MeV/u fluorine ions. Multiple ionization effects in the collisions are considered through the change of fluorescence and Coster-Kronig yields while determining L-subshell ionization cross sections from L-line x-ray production cross sections. The L-subshell ionization, as well as L-shell x-ray production cross sections so obtained, are compared with various theoretical approximations. The Coulomb direct ionization contributions is studied by (i) the relativistic semi-classical approximations (RSCA), (ii) the shellwise local plasma approximation (SLPA), and (iii) the ECUSAR theory, along with the inclusion of the vacancy sharing among the subshells by the coupled-states model (CSM) and the electron capture (EC) by a standard formalism. We find that the ECUSAR-CSM-EC describes the measured excitation function curves the best. However, the theoretical calculations are still about a factor of two smaller than the measured values. Such differences are resolved by re-evaluating the fluorescence and the Coster-Kronig yields. This work demonstrates that, in the present energy range, the heavy-ion induced inner-shell ionization of heavy atoms can be understood by combining the basic mechanisms of the direct Coulomb ionization, the electron capture, the multiple ionization, and the vacancy sharing among subshells, together with optimized atomic parameters.

physics.atom-ph↗

arXiv2020

Stability analysis for a new model of multispecies convection-diffusion-reaction in poroelastic tissue

We perform the linear stability analysis for a new model for poromechanical processes with inertia (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes convected in the medium. We find parameter regions that lead to spatio-temporal instabilities of the coupled system. The mutual dependences between deformation and diffusive patterns are of substantial relevance in the study of morphoelastic changes in biomaterials. We provide a set of computational examples in 2D and 3D (related to brain mechanobiology) that can be used to form a better understanding on how, and up to which extent, the deformations of the porous structure dictate the generation and suppression of spatial patterning dynamics, also related to the onset of mechano-chemical waves.

math.NA↗

arXiv2019

Virtual element methods for the three-field formulation of time-dependent linear poroelasticity

A virtual element discretisation for the numerical approximation of the three-field formulation of linear poroelasticity introduced in [R. Oyarzúa and R. Ruiz-Baier, Locking-free finite element methods for poroelasticity, SIAM J. Numer. Anal. 54 (2016) 2951--2973] is proposed. The treatment is extended to include also the transient case. Appropriate poroelasticity projector operators are introduced and they assist in deriving energy bounds for the time-dependent discrete problem. Under standard assumptions on the computational domain, optimal a priori error estimates are established. Furthermore, the accuracy of the method is verified numerically through a set of computational tests.

math.NA↗

arXiv2019

Well-posedness and discrete analysis for advection-diffusion-reaction in poroelastic media

We analyse a PDE system modelling poromechanical processes (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes in the medium. We investigate the well-posedness of the nonlinear set of equations using fixed-point theory, Fredholm's alternative, a priori estimates, and compactness arguments. We also propose a mixed finite element method and rigorously demonstrate the stability of the scheme. Error estimates are derived in suitable norms, and numerical experiments are conducted to illustrate the mechano-chemical coupling and to verify the theoretical rates of convergence.

math.NA↗

arXiv2018

Intrinsic permanent magnetic characteristics beyond Ce2Co17 with Ce/Co substitutions

By understanding the small easy axis magnetocrystalline anisotropy energy (MAE) of hexagonal Ce2Co17, an attempt has been made to improve anisotropy and consequently to obtain better characteristics for a high energy permanent magnet via site selective substitutional doping of Ce/Co with suitable elements. The present calculations of the electronic and magnetic properties of Ce2Co17 and related substituted compounds have been performed using the full potential linear augmented plane wave (FPLAPW) method within the generalized gradient approximation (GGA). Sm-substituted compounds were simulated using Coulomb corrected GGA (GGA+U) to provide a better representation of energy bands due to the strongly correlated Sm-f electrons. The formation energies for all substituted compounds are found to be negative which indicate their structural stability. Of the substitutions, Zr substitution at the Co-dumbbell site enhances uniaxial anisotropy of Ce2Co17. Furthermore, Sm-substitution at Ce-2c sites favors incremental MAE whereas a La-substitution at both 2b- and 2c-sites depletes the tiny MAE in Ce2Co17. These observed trends in the MAE have been examined in terms of contributions from various electronic states. Finally, Ce2Zr2Co15 and SmCeCo17 are foreseen as suitable materials for designing permanent magnets derived from the crystal lattice structure of hexagonal Ce2Co17.

cond-mat.mtrl-sci↗