arXiv subjects

Manas V. Upadhyay

Publications and source records attributed to Manas V. Upadhyay.

3 recordsLinked to original sources

arXiv2026

Efficient spectral Galerkin framework for nonlinear transient heat transfer in finite domains

Accurately modelling the temporal evolution of heterogeneous temperature fields requires resolving strong nonlinearities in the heat equation arising from temperature-dependent thermophysical properties, latent heats of transformation and any local heat sources/sinks. In this work, we present a spectral Galerkin (SG) framework to solve the fully nonlinear transient heat equation in finite domains to attain the accuracy of high-fidelity finite element (FE) simulations at considerably lower computational cost. The heat equation is reformulated into a linear reference problem with constant thermophysical properties and residual forcing terms. Solving the reference problem provides a complete three-dimensional orthonormal trigonometric basis, whose Galerkin projection reduces the heat equation to a set of modal ordinary differential equations (ODEs) in time; the reference operator is diagonal in the modal basis, and results in independent modal updates for a fixed nonlinear forcing. These ODEs can be integrated using exponential time differencing and iteratively corrected for nonlinearities. The SG method eliminates the global solve required by FE methods, and its use of structured grids allows efficient GPU parallelization. Applied to rapid laser-metal interactions, the SG solver reproduces high-fidelity FE temperature fields with less than 1% relative error while achieving 227-fold faster GPU runtimes. Applied to a part-scale laser scanning study [Ramani et al., Additive Manufacturing 52 (2022) 102643], the method shows that accounting for evaporation and latent heat more than halves their proposed processing metric. The source code of the SG heat solver and some worked examples are available at https://github.com/manasvupadhyay/spectral_galerkin_heat under the Apache 2.0 license.

cond-mat.mtrl-sci↗

arXiv2026

A probabilistic framework for irreversible kinetics

A probabilistic framework for irreversible kinetics is proposed in which a constrained path functional $\mathcal J$ encodes constitutive physics and observations on the admissible history space $\mathcal H_{\rm ad}$, while a discrete Gibbs-type measure proportional to $\exp(-\mathcal J/Θ)$ assigns probabilities to a candidate set $\mathcal H\subseteq\mathcal H_{\rm ad}$. The framework unifies forward-in-time evolution and inverse inference, which differ only through observations and how they constrain admissible histories. The parameter $Θ$ controls epistemic uncertainty, and the measure is interpreted as a Bayesian posterior over histories. Maximizing this posterior is equivalent to simultaneous minimization of $\mathcal J$ over $\mathcal H$, distinguishing the continuous minimizer $h_{\rm cont}$ over $\mathcal H_{\rm ad}$ from the discrete maximum a posteriori (MAP) history $h_{\rm MAP}$ over $\mathcal H$. As $Θ\to0$, the posterior concentrates on the discrete MAP set. For generalized standard material(GSM)-type incremental energy--dissipation functionals, seven forward-in-time examples show that, despite using the same incremental functionals, causal GSM evolution is generally only incrementally optimal. When minimizers are unique, observations are absent, and $h_{\rm cont}\in\mathcal H$, the strict ordering $\mathcal J(h_{\rm cont})=\mathcal J(h_{\rm MAP})<\mathcal J(h_{\rm GSM})$ holds, showing that the GSM history does not minimize the cost of the entire history. Finally, an endpoint-conditioned inverse problem with nonconvex energy demonstrates the finite-$Θ$ capability of the framework to infer unobserved states and quantify uncertainty over admissible histories.

cond-mat.stat-mech↗

arXiv2026

On the limits of the energetic coupling between field dislocation mechanics and phase field crystal

This paper investigates the energetic coupling between Field Dislocation Mechanics (FDM) and the Phase Field Crystal (PFC) model proposed in Phys. Rev. B 102, 064109, 2020. While FDM correctly solves the initial boundary value problem of a continuum body with dislocation fields, PFC captures the underlying crystallographic structure. The coupling, which penalizes the $L^2$ distance between elastic distortion from FDM and configurational distortion from PFC in the $L^2$ sense, had been proposed to reconcile dislocation mechanics with crystallography in a single continuum framework. Variational analysis reveals that the coupling term acts as a divergence-driven forcing in the phase-field evolution that matches only the compatible (curl-free) parts of the distortion fields. Consequently, its contributions are insensitive to the incompatible (divergence-free) elastic distortion carrying all the information on dislocation topology. Furthermore, the nature of the configurational distortion causes mechanical boundary conditions to be transmitted diffusively from FDM to PFC rather than elastically. Numerical simulations demonstrate that this coupling cannot prevent the unnatural core spreading in FDM. Finally, it is shown that even in the most general case, an energetic coupling suffers from the same drawbacks, which limits its ability to integrate dislocation mechanics with crystallography.

cond-mat.mtrl-sci↗