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Alberto Fraile

Publications and source records attributed to Alberto Fraile.

8 recordsLinked to original sources

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

Patterns in Growth and Distribution of Unbounded Prime Number Walks

In our previous work, we defined a prime walk (PW) on a square grid and presented several intriguing numerical results. Here, we demonstrate the main conjecture presented there, namely, that the area covered by the prime walk is unbounded. Taking this fact into account, we examine in further detail the properties of the PW and explore new questions that arise naturally in this analysis.

math.NT

Differential tissue sparing of FLASH ultra high dose rates: an {\it in-silico} study

Purpose: To propose a theory for the differential tissue sparing of FLASH ultra high dose rates (UHDR) through inter-track reaction-diffusion mechanism. Methods: We calculate the time-evolution of particle track-structures using a system of coupled reaction-diffusion equations on a random network designed for molecular transport in porous and disordered media. The network is representative of the intra- and inter-cellular diffusion channels in tissues. Spatial cellular heterogeneities over the scale of track spacing have been constructed by incorporating random fluctuations in the connectivity among network sites. Results: We demonstrate the occurrence of phase separation among the tracks as the complexity in intra- and inter-cellular structural increases. At the weak limit of disorder, such as in water and normal tissue, neighboring tracks melt into each other and form a percolated network of nonreactive species. In contrast, at the strong limit of disorder, tracks evolve individually like isolated islands with negligible inter-track overlap. Thus, the spatio-temporal correlation among the chemical domains decreases as the inter-cellular complexity of the tissue increases (e.g. from normal tissue to fractal-type malignant tissue). Conclusions: The differential sparing of FLASH UHDR in normal and tumor tissue may be explained by differences in inter- and intra-cellular structural complexities between the tissue types. The structural complexities of cancerous cells prevent clustering and chemical interaction of tracks, whereas this interaction prevails and thus leads to sparing in normal tissue.

physics.med-ph

Persistent order in Schramm-Loewner Evolution driven by the primes last digit sequence

We report on a peculiar effect regarding the use of the prime's last digit sequence which is equivalent to a quaternary symbolic sequence. This was used as a driving sequence for the recently introduced Schramm-Loewner Evolution after using two different classes of possible binary encodings. We report on a clear deviation from the standard space-filling curves normally expected from such a process. We also contrast this behavior with others produced via a symbolic dynamics applied on standard noise sources as well as deterministic sequences produced by simple automata. Our findings include the well known, Morse-Thue sequence as the simplest model exhibiting such behavior apart from some strongly biased Levy walks.

physics.gen-ph

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

Jacob's Ladder: Prime numbers in 2d

Prime numbers are one of the most intriguing figures in mathematics. Despite centuries of research, many questions remain still unsolved. In recent years, computer simulations are playing a fundamental role in the study of an immense variety of problems. In this work, we present a simple representation of prime numbers in two dimensions that allows us to formulate a number of conjectures that may lead to important avenues in the field of research on prime numbers. In particular, although the zeroes in our representation grow in a somewhat erratic, hardly predictable way, the gaps between them present a remarkable and intriguing property: a clear exponential decay in the frequency of gaps vs gap size. The smaller the gaps, the more frequently they appear. Additionally, the sequence of zeroes, despite being non-consecutive numbers, contains a number of primes approximately equal to n/log(n) , being n the number of terms in the sequence.

math.HO

Long-lived discrete breathers in free-standing graphene

Intrinsic localized modes or discrete breathers are investigated by molecular dynamics simulations in free-standing graphene. Discrete breathers are generated either through thermal quenching of the graphene lattice or by proper initialization, with frequencies and lifetimes sensitively depending on the interatomic potential describing the carbon-carbon interaction. In the most realistic scenario, for which temperature-dependent molecular dynamics simulations in three dimension using a graphene-specific interatomic potential are performed, the breather lifetimes increase to hundreds of picoseconds even at relatively high temperatures. These lifetimes are much higher than those anticipated from earlier calculations, and may enable direct breather observation in Raman spectroscopy experiments.

cond-mat.mes-hall

Interatomic potential for the compound-forming Li-Pb liquid alloy

Atomistic simulations of liquid alloys face the challenge of correctly modeling basic thermodynamic properties. In this work we present an interatomic potential for the Li-Pb system, as well as a study of physical properties of Li-Pb alloys. Despite the complexity due to Li-Pb being a compound forming system where charge transfer is expected, we show here how the empirical EAM formalism is able to satisfactorily describe several physical properties in a wide range of Li concentration. Application of our potential to Li-Pb eutectic allows us to correctly predict many physical properties observed experimentally and calculated with ab initio techniques, providing in this way a potential suitable for future studies in the context of tritium breeder blanket designs in Fusion technology.

cond-mat.mtrl-sci