575 research outputs found
Morphometric approach to many-body correlations in hard spheres
We model the thermodynamics of local structures within the hard sphere liquid
at arbitrary volume fractions through the \textit{morphometric} calculation of
-body correlations. We calculate absolute free energies of local geometric
motifs in excellent quantitative agreement with molecular dynamics simulations
across the liquid and supercooled liquid regimes. We find a bimodality in the
density library of states where five-fold symmetric structures appear lower in
free energy than four-fold symmetric structures, and from a single reaction
path predict a relaxation barrier which scales linearly in the compressibility
factor. The method provides a new route to assess changes in the free energy
landscape at volume fractions dynamically inaccessible to conventional
techniques.Comment: 6+17 pages, 3 figure
Long-Lived Non-Equilibrium Interstitial-Solid-Solutions in Binary Mixtures
We perform particle resolved experimental studies on the heterogeneous
crystallisation process of two compo- nent mixtures of hard spheres. The
components have a size ratio of 0.39. We compared these with molecular dynamics
simulations of homogenous nucleation. We find for both experiments and
simulations that the final assemblies are interstitial solid solutions, where
the large particles form crystalline close-packed lattices, whereas the small
particles occupy random interstitial sites. This interstitial solution
resembles that found at equilibrium when the size ratios are 0.3 [Filion et
al., Phys. Rev. Lett. 107, 168302 (2011)] and 0.4 [Filion, PhD Thesis, Utrecht
University (2011)]. However, unlike these previous studies, for our system sim-
ulations showed that the small particles are trapped in the octahedral holes of
the ordered structure formed by the large particles, leading to long-lived
non-equilibrium structures in the time scales studied and not the equilibrium
interstitial solutions found earlier. Interestingly, the percentage of small
particles in the crystal formed by the large ones rapidly reaches a maximum of
around 14% for most of the packing fractions tested, unlike previous
predictions where the occupancy of the interstitial sites increases with the
system concentration. Finally, no further hopping of the small particles was
observed
Morphological thermodynamics for hard bodies from a controlled expansion
The morphometric approach is a powerful ansatz for decomposing the chemical
potential for a complex solute into purely geometrical terms. This method has
proven accuracy in hard spheres, presenting an alternative to comparatively
expensive (classical) density functional theory approaches. Despite this,
fundamental questions remain over why it is accurate and how one might include
higher-order terms to improve accuracy. We derive the morphometric approach as
the exact resummation of terms in the virial series, providing further
justification of the approach. The resulting theory is less accurate than
previous morphometric theories, but provides fundamental insights into the
inclusion of higher-order terms and to extensions to mixtures of convex bodies
of arbitrary shape.Comment: 10 pages, 2 figure
Many-body correlations from integral geometry
In a recent letter we presented a framework for predicting the concentrations
of many-particle local structures inside the bulk liquid as a route to
assessing changes in the liquid approaching dynamical arrest. Central to this
framework was the morphometric approach, a synthesis of integral geometry and
liquid state theory, which has traditionally been derived from fundamental
measure theory. We present the morphometric approach in a new context as a
generalisation of scaled particle theory, and derive several morphometric
theories for hard spheres of fundamental and practical interest. Our central
result is a new theory which is particularly suited to the treatment of
many-body correlation functions in the hard sphere liquid, which we demonstrate
by numerical tests against simulation.Comment: 12 pages, 6 figure
Resting vs. active: a meta-analysis of the intra- and inter-specific associations between minimum, sustained, and maximum metabolic rates in vertebrates
Variation in aerobic capacity has far reaching consequences for the physiology, ecology, and evolution of vertebrates. Whether at rest or active, animals are constrained to operate within the energetic bounds determined by their minimum (minMR) and sustained or maximum metabolic rates (upperMR). MinMR and upperMR can differ considerably among individuals and species but are often presumed to be mechanistically linked to one another. Specifically, minMR is thought to reflect the idling cost of the machinery needed to support upperMR. However, previous analyses based on limited datasets have come to conflicting conclusions regarding the generality and strength of their association.
Here we conduct the first comprehensive assessment of their relationship, based on a large number of published estimates of both the intra-specific (n = 176) and inter-specific (n = 41) phenotypic correlations between minMR and upperMR, estimated as either exercise-induced maximum metabolic rate (VO2max), cold-induced summit metabolic rate (Msum), or daily energy expenditure (DEE).
Our meta-analysis shows that there is a general positive association between minMR and upperMR that is shared among vertebrate taxonomic classes. However, there was stronger evidence for intra-specific correlations between minMR and Msum and between minMR and DEE than there was for a correlation between minMR and VO2max across different taxa. As expected, inter-specific correlation estimates were consistently higher than intra-specific estimates across all traits and vertebrate classes.
An interesting exception to this general trend was observed in mammals, which contrast with birds and exhibit no correlation between minMR and Msum. We speculate that this is due to the evolution and recruitment of brown fat as a thermogenic tissue, which illustrates how some species and lineages might circumvent this seemingly general association.
We conclude that, in spite of some variability across taxa and traits, the contention that minMR and upperMR are positively correlated generally holds true both within and across vertebrate species. Ecological and comparative studies should therefore take into consideration the possibility that variation in any one of these traits might partly reflect correlated responses to selection on other metabolic parameters
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