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Fausto Martelli

Publications and source records attributed to Fausto Martelli.

29 records · Page 2Linked to original sources
arXiv2018

Water between membranes: Structure and Dynamics

An accurate description of the structure and dynamics of interfacial water is essential for phospholipid membranes, since it determines their function and their interaction with other molecules. Here we consider water confined in stacked membranes with hydration from poor to complete, as observed in a number of biological systems. Experiments show that the dynamics of water slows down dramatically when the hydration level is reduced. All-atom molecular dynamics simulations identify three (inner, hydration and outer) regions, within a distance of approximately 1 nm from the membrane, where water molecules exhibit different degrees of slowing down in the dynamics. The slow-down is a consequence of the robustness of the hydrogen bonds between water and lipids and the long lifetime of the hydrogen bonds between water molecules near the membrane. The interaction with the interface, therefore, induces a structural change in the water that can be emphasized by calculating its intermediate range order. Surprisingly, at distances as far as ~ 2.5 nm from the interface, although the bulk-like dynamics is recovered, the intermediate range order of water is still slightly higher than that in the bulk at the same thermodynamic conditions. Therefore, the water-membrane interface has a structural effect at ambient conditions that propagates further than the often-invoked 1 nm length scale. Membrane fluctuations smear out this effect macroscopically, but an analysis performed by considering local distances and instantaneous configurations is able to reveal it, possibly contributing to our understanding of the role of water at biomembrane interfaces.

cond-mat.soft↗
arXiv2018

Root-Growth of Boron Nitride Nanotubes: Experiments and \textit{Ab Initio} Simulations

We have synthesized boron nitride nanotubes (BNNTs) in an arc in presence of boron and nitrogen species only, without transition metals. We find that BNNTs are often attached to pure boron nanoparticles, suggesting that root-growth is a likely mechanism for their formation. To gain further insight into this process we have studied key mechanisms for root growth of BNNTs on the surface of a liquid boron droplet by ab initio molecular dynamics simulations. We find that nitrogen atoms reside predominantly on the droplet surface where they organize to form boron nitride islands below 2400 K. To minimize contact with the liquid particle underneath, the islands assume non-planar configurations that are likely precursors for the thermal nucleation of cap structures. Once formed, the caps are stable and can easily incorporate nitrogen and boron atoms at their base, resulting in further growth. Our simulations support the root-growth mechanism of BNNTs and provide comprehensive evidence of the active role played by liquid boron.

physics.chem-ph↗
arXiv2018

Searching for crystal-ice domains in amorphous ices

We employ classical molecular dynamics simulations to investigate the molecular-level structure of water during the isothermal compression of hexagonal ice (I$h$) and low-density amorphous (LDA) ice at low temperatures. In both cases, the system transforms to high-density amorphous ice (HDA) via a first-order-like phase transition. We employ a sensitive local order metric (LOM) [Martelli et. al., Phys. Rev. B, 97, 064105 (2018)], that can discriminate among different crystalline and non crystalline ice structures and is based on the positions of the oxygen atoms in the first and/or second hydration shell. Our results confirm that LDA and HDA are indeed amorphous, i.e., they lack of polydispersed ice domains. Interestingly, HDA contains a small number of domains that are reminiscent of the unit cell of ice IV, although the hydrogen-bond network (HBN) of these domains differ from the HBN of ice IV. The presence of ice IV-like domains provides some support to the hypothesis that HDA could be the result of a detour on the HBN rearrangement along the I$h$-to-ice IV pressure induced transformation. Both nonequilibrium LDA-to-HDA and I$h$-to-HDA transformations are two-steps processes where a small distortion of the HBN first occurs at low pressures and then, a sudden, extensive re-arrangement of hydrogen bonds at the corresponding transformation pressure follows. Interestingly, the I$h$-to-HDA and LDA-to-HDA transformations occur when LDA and I$h$ have similar local order, as quantified by the site-averaged LOMs. Since I$h$ has a perfect tetrahedral HBN, while LDA does not, it follows that higher pressures are needed to transform I$h$ into HDA than that for the conversion of LDA to HDA. In correspondence with both first-order-like phase transitions, the samples are composed of a large HDA cluster that percolates within the I$h$/LDA samples.

physics.chem-ph↗
arXiv2018

The structure factor of primes

Although the prime numbers are deterministic, they can be viewed, by some measures, as pseudo-random numbers. In this article, we numerically study the pair statistics of the primes using statistical-mechanical methods, especially the structure factor $S(k)$ in an interval $M \leq p \leq M + L$ with $M$ large, and $L/M$ smaller than unity. We show that the structure factor of the prime-number configurations in such intervals exhibits well-defined Bragg-like peaks along with a small "diffuse" contribution. This indicates that the primes are appreciably more correlated and ordered than previously thought. Our numerical results definitively suggest an explicit formula for the locations and heights of the peaks. This formula predicts infinitely many peaks in any non-zero interval, similar to the behavior of quasicrystals. However, primes differ from quasicrystals in that the ratio between the location of any two predicted peaks is rational. We also show numerically that the diffuse part decays slowly as $M$ and $L$ increases. This suggests that the diffuse part vanishes in an appropriate infinite-system-size limit.

cond-mat.stat-mech↗
arXiv2017

Large-scale structure and hyperuniformity of amorphous ices

We investigate the large-scale structure of amorphous ices and transitions between their different forms by quantifying their large-scale density fluctuations. Specifically, we simulate the isothermal compression of low-density amorphous ice (LDA) and hexagonal ice (Ih) to produce high-density amorphous ice (HDA). Remarkably, both HDA and LDA are nearly hyperuniform, meaning that they are characterized by an anomalous suppression of large-scale density fluctuations. By contrast, in correspondence with both non-equilibrium phase transitions to HDA, the presence of structural heterogeneities strongly suppresses the hyperuniformity and, remarkably, the system becomes hyposurficial (devoid of "surface-area" fluctuations). Our investigation challenges the largely accepted "frozen-liquid" picture, which views glasses as structurally arrested liquids. Beyond implications for water, our findings enrich our understanding of the structural transformations that occur in glasses with varying pressures.

cond-mat.stat-mech↗
arXiv2017

Structural properties of water confined by phospholipid membranes

Biological membranes are essential for the cell life and hydration water provides the driving force for their assembly and stability. Here we study the structural properties of water in a phospholipid membrane. We characterize local structures inspecting the intermediate range order (IRO) adopting a sensitive local order metric, recently proposed by Martelli et al., which measures and grades the degree of overlap of local environments with structures of perfect ice. Close to the membrane, water acquires high IRO and changes its dynamical properties, e.g., slowing down its translational and rotational degrees of freedom in a region that extends over $\simeq 1$ nm from the membrane interface. Surprisingly, we show that at a distance as far as $\simeq 2.5$ nm from the interface, although the bulk-like dynamics is recovered, water's IRO is still slightly higher than in bulk at the same thermodynamic conditions. Therefore, the water-membrane interface has a structural effect at ambient conditions that propagates further than the often-invoked $1$ nm-length scale, a results that should be taken carefully into account when analyzing experimental data of water confined by membranes and could help us understanding the role of water in biological systems.

cond-mat.soft↗
arXiv2016

A local order metric for condensed phase environments

We introduce a local order metric (LOM) that measures the degree of order in the neighborhood of an atomic or molecular site in a condensed medium. The LOM maximizes the overlap between the spatial distribution of sites belonging to that neighborhood and the corresponding distribution in a suitable reference system. The LOM takes a value tending to zero for completely disordered environments and tending to one for environments that match perfectly the reference. The site averaged LOM and its standard deviation define two scalar order parameters, $S$ and $δS$, that characterize with excellent resolution crystals, liquids, and amorphous materials. We show with molecular dynamics simulations that $S$, $δS$ and the LOM provide very insightful information in the study of structural transformations, such as those occurring when ice spontaneously nucleates from supercooled water or when a supercooled water sample becomes amorphous upon progressive cooling.

physics.comp-ph↗
arXiv2016

Density and bond-orientational relaxations in supercooled water

Recent computational studies have reported evidence of a metastable liquid-liquid phase transition (LLPT) in molecular models of water under deeply supercooled conditions. A competing hypothesis suggests, however, that non-equilibrium artifacts associated with coarsening of the stable crystal phase have been mistaken for an LLPT in these models. Such artifacts are posited to arise due to a separation of time scales in which density fluctuations in the supercooled liquid relax orders of magnitude faster than those associated with bond-orientational order. Here, we use molecular simulation to investigate the relaxation of density and bond-orientational fluctuations in three molecular models of water (ST2, TIP5P and TIP4P/2005) in the vicinity of their reported LLPT. For each model, we find that density is the slowly relaxing variable under such conditions. We also observe similar behavior in the coarse-grained mW model of water. Our findings therefore challenge the key physical assumption underlying the competing hypothesis.e find that density relaxes significantly faster than bond-orientational order, as incorrectly predicted by this competing hypothesis.

cond-mat.stat-mech↗
arXiv2015

Local Structure Analysis in $Ab$ $Initio$ Liquid Water

Within the framework of density functional theory, the inclusion of exact exchange and non-local van der Waals/dispersion (vdW) interactions is crucial for predicting a microscopic structure of ambient liquid water that quantitatively agrees with experiment. In this work, we have used the local structure index (LSI) order parameter to analyze the local structure in such highly accurate $ab$ $initio$ liquid water. At ambient conditions, the LSI probability distribution, P($I$), was unimodal with most water molecules characterized by more disordered high-density-like local environments. With thermal excitations removed, the resultant bimodal P($I$) in the inherent potential energy surface (IPES) exhibited a 3:1 ratio between high- and low-density-like molecules, with the latter forming small connected clusters amid the predominant population. By considering the spatial correlations and hydrogen bond network topologies $among$ water molecules with the same LSI identities, we demonstrate that the signatures of the experimentally observed low- (LDA) and high-density (HDA) amorphous phases of ice are present in the IPES of ambient liquid water. Analysis of the LSI autocorrelation function uncovered a persistence time of $\sim$ 4 ps---a finding consistent with the fact that natural thermal fluctuations are responsible for transitions between these distinct yet transient local aqueous environments in ambient liquid water.

cond-mat.soft↗
arXiv2013

Dealing with prime numbers I.: On the Goldbach conjecture

In this paper we present some observations about the well-known Goldbach conjecture. In particular we list and interpret some numerical results which allow us to formulate a relation between prime numbers and even integers. We can also determine very thin and low diverging ranges in which the probability of finding a prime is one.

math.NT↗