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Prashant Dwivedi

Publications and source records attributed to Prashant Dwivedi.

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Crystal forming ability of amorphous refractory metals under nanoindentation: a molecular dynamics study

Amorphous refractory metal coatings combine high hardness with chemical inertness, yet their metastability makes them prone to mechanically induced crystallisation (devitrification) under contact loading, and how readily such a glass re-orders to its parent body centred cubic (bcc) crystal is unknown across the refractory series. We prepared amorphous V, Nb, Mo, Ta and W by melt quenching to 300 K, validated each interatomic potential against ab initio liquid radial distribution functions, and probed them by large scale molecular dynamics nanoindentation. Indentation drives a localised amorphous to bcc transformation by bulk nucleation, growth and coalescence. A crystal forming ability (CFA), the maximum slope of the sigmoidal bcc fraction versus depth curve, spans about a factor of four and decreases as V > Mo > Nb > Ta > W; it falls with indenter velocity as CFA $\propto v^{-m}$ with a mean exponent of 1.08, so CFA$\cdot v$ is nearly constant and the transformation rate is almost velocity independent. Transforming atoms carry excess non affine displacement and local shear strain, not hydrostatic pressure, marking a shear associated displacive pathway; the bulk driving force is largest for the most resistant element, W, so resistance tracks cohesive bond strength rather than the thermodynamic driving force. Early bcc like order sets the sharpness and depth of the transition, whereas the mechanical work to half transformation sets the persistent nucleus density. A grain population balance links nucleation, growth and coalescence to a terminal microstructure whose completeness does not follow the CFA order.

cond-mat.mtrl-sci

Prime numbers and random walks in a square grid

In recent years, computer simulations are playing a fundamental role in unveiling some of the most intriguing features of prime numbers. In this work, we define an algorithm for a deterministic walk through a two-dimensional grid that we refer to as Prime Walk. The walk is constructed from a sequence of steps dictated by and dependent on the sequence of last digits of the primes. Despite the apparent randomness of this generating sequence, the resulting structure -- both in 2d and 3d -- created by the algorithm presents remarkable properties and regularities in its pattern that we proceed to analyze in detail.

math.NT