Prateek Gupta

Last Name

Gupta

First Name

Prateek

ORCID

0000-0003-3666-0257

Show all metadata

Search Results

Publications 1 - 6 of 6

High‐resolution numerical simulations of electrophoresis using the Fourier pseudo‐spectral method
Gupta, Prateek; Bahga, Supreet S. (2021)
Electrophoresis
We present the formulation, implementation, and performance evaluation of the Fourier pseudo‐spectral method for performing fast and accurate simulations of electrophoresis. We demonstrate the applicability of this method for simulating a wide variety of electrophoretic processes such as capillary zone electrophoresis, transient‐isotachophoresis, field amplified sample stacking, and oscillating electrolytes. Through these simulations, we show that the Fourier pseudo‐spectral method yields accurate and stable solutions on coarser computational grids compared with other nondissipative spatial discretization schemes. Moreover, due to the use of coarser grids, the Fourier pseudo‐spectral method requires lower computational time to achieve the same degree of accuracy. We have demonstrated the application of the Fourier pseudo‐spectral method for simulating realistic electrophoresis problems with current densities as high as 5000 A/m2 with over tenfold speed‐up compared to the commonly used second‐order central difference scheme, to achieve a given degree of accuracy. The Fourier pseudo‐spectral method is also suitable for simulating electrophoretic processes involving a large number of concentration gradients, which render the adaptive grid‐refinement techniques ineffective. We have integrated the numerical scheme in a new electrophoresis simulator named SPYCE, which we offer to the community as open‐source code.
Finite-temperature grain boundary properties from quasistatic atomistics
Spinola, Miguel; Saxena, Shashank; Gupta, Prateek; et al. (2024)
Computational Materials Science
Grain boundary (GB) properties greatly influence the mechanical, electrical, and thermal response of polycrystalline materials. Most computational studies of GB properties at finite temperatures use molecular dynamics (MD), which is computationally expensive, limited in the range of accessible timescales, and requires cumbersome techniques like thermodynamic integration to estimate free energies. This restricts the reasonable computation (without incurring excessive computational expense) of GB properties to regimes that are often unrealistic, such as zero temperature or extremely high strain rates. Consequently, there is a need for simulation methodology that avoids the timescale limitations of MD, while providing reliable estimates of GB properties. The Gaussian Phase-Packet (GPP) method is a temporal coarse-graining technique that can predict relaxed atomic structures at finite temperature in the quasistatic limit. This work applies GPP, combined with the quasiharmonic approximation for computing the free energy, to the problem of determining the free energy and shear coupling factor of grain boundaries in metals over a range of realistic temperatures. Validation is achieved by comparison to thermodynamic integration and quasiharmonic approximation (QHA), which confirms that the presented approach captures relaxed-energy GB structures and shear coupling factors at finite temperature with a high degree of accuracy, and it performs significantly better than QHA on hydrostatically expanded 0 K structures.
GNN-assisted phase space integration with application to atomistics
Saxena, Shashank; Bastek, Jan-Hendrik; Spinola, Miguel; et al. (2023)
Mechanics of Materials
Overcoming the time scale limitations of atomistics can be achieved by switching from the state-space representation of Molecular Dynamics (MD) to a statistical-mechanics-based representation in phase space, where approximations such as maximum-entropy or Gaussian phase packets (GPP) evolve the atomistic ensemble in a time-coarsened fashion. In practice, this requires the computation of expensive high-dimensional integrals over all of phase space of an atomistic ensemble. This, in turn, is commonly accomplished efficiently by low-order numerical quadrature. We show that numerical quadrature in this context, unfortunately, comes with a set of inherent problems, which corrupt the accuracy of simulations---especially when dealing with crystal lattices with imperfections. As a remedy, we demonstrate that Graph Neural Networks, trained on Monte-Carlo data, can serve as a replacement for commonly used numerical quadrature rules, overcoming their deficiencies and significantly improving the accuracy. This is showcased by three benchmarks: the thermal expansion of copper, the martensitic phase transition of iron, and the energy of grain boundaries. We illustrate the benefits of the proposed technique over classically used third- and fifth-order Gaussian quadrature, we highlight the impact on time-coarsened atomistic predictions, and we discuss the computational efficiency. The latter is of general importance when performing frequent evaluation of phase space or other high-dimensional integrals, which is why the proposed framework promises applications beyond the scope of atomistics.
Nonequilibrium thermomechanics of Gaussian phase packet crystals: Application to the quasistatic quasicontinuum method
Gupta, Prateek; Ortiz, Michael; Kochmann, Dennis M. (2021)
Journal of the Mechanics and Physics of Solids
The quasicontinuum (QC) method was originally introduced to bridge across length scales by coarse-graining an atomistic ensemble to significantly larger continuum scales at zero temperature, thus overcoming the crucial length-scale limitation of classical atomic-scale simulation techniques while solely relying on atomic-scale input (in the form of interatomic potentials). An associated challenge lies in bridging across time scales to overcome the time-scale limitations of atomistics at finite temperature. To address the biggest challenge, bridging across both length and time scales, only a few techniques exist, and most of those are limited to conditions of constant temperature. Here, we present a new general strategy for the space–time coarsening of an atomistic ensemble, which introduces thermomechanical coupling. Specifically, we evolve the statistics of an atomistic ensemble in phase space over time by applying the Liouville equation to an approximation of the ensemble’s probability distribution (which further admits a variational formulation). To this end, we approximate a crystalline solid as a lattice of lumped correlated Gaussian phase packets occupying atomic lattice sites, and we investigate the resulting quasistatics and dynamics of the system. By definition, phase packets account for the dynamics of crystalline lattices at finite temperature through the statistical variances of atomic momenta and positions. We show that momentum-space correlation allows for an exchange between potential and kinetic contributions to the crystal’s Hamiltonian. Consequently, local adiabatic heating due to atomic site motion is captured. Moreover, in the quasistatic limit, the governing equations reduce to the minimization of thermodynamic potentials (similar to maximum-entropy formulation previously introduced for finite-temperature QC), and they yield the local equation of state, which we derive for isothermal, isobaric, and isentropic conditions. Since our formulation without interatomic correlations precludes irreversible heat transport, we demonstrate its combination with thermal transport models to describe realistic atomic-level processes, and we discuss opportunities for capturing atomic-level thermal transport by including interatomic correlations in the Gaussian phase packet formulation. Overall, our Gaussian phase packet approach offers a promising avenue for finite-temperature non-equilibrium quasicontinuum techniques, which may be combined with thermal transport models and extended to other approximations of the probability distribution as well as to exploit the variational structure.
AQCNES: A Quasi-Continuum Non-Equilibrium Solver
Bräunlich, Gerhard; Saxena, Shashank; Weberndorfer, Manuel; et al. (2024)
Journal of Open Source Software
The behavior of macroscopic structures is determined by fast atomic interactions at the nanoscales. Current atomic simulation techniques, such as molecular dynamics (MD), are limited to a millions of atoms and hence a few micrometers of domain length. Moreover, finite temperature vibrational frequencies of around tens of terahertz restrict the time step of MD to femtoseconds, precluding the simulation of problems of engineering interest. Consequently, there has been a significant focus in recent decades on developing multiscale modeling techniques to extend atomistic accuracy to larger length scales and longer time frames. Existing techniques, such as the quasicontinuum (QC) method, are restricted to spatial upscaling at zero temperature, while temporal upscaling methods like the maximum entropy (max-ent) approach are constrained to fully resolved atomistic simulations at finite temperature.
A fast atomistic approach to finite-temperature surface elasticity of crystalline solids
Saxena, Shashank; Spinola, Miguel; Gupta, Prateek; et al. (2022)
Computational Materials Science
Surface energies and surface elasticity largely affect the mechanical response of nanostructures as well as the physical phenomena associated with surfaces such as evaporation and adsorption. Studying surface energies at finite temperatures is therefore of immense interest for nanoscale applications. However, calculating surface energies and derived quantities from atomistic ensembles is usually limited to zero temperature or involves cumbersome thermodynamic integration techniques at finite temperature. Here, we illustrate a computational technique to identify the energy and elastic properties of surfaces of solids at non-zero temperature based on a Gaussian phase packets (GPP) approach (which in the isothermal limit coincides with a maximum-entropy formulation). Using this technique, we investigate the effect of temperature on the surface properties of different crystal faces for six pure metals – copper, nickel, aluminium, iron, tungsten and vanadium – thus covering both FCC and BCC lattice structures. While the obtained surface energies and stresses usually show a decreasing trend with increasing temperature, the elastic constants do not show such a consistent trend across the different materials and are quite sensitive to temperature changes. Validation is performed by comparing the obtained surface energy densities of selected BCC and FCC materials to those calculated via molecular dynamics.

Publications 1 - 6 of 6

Prateek Gupta

Last Name

First Name

ORCID

Organisational unit

Filters

Search Results