DSpace Collection:https://dspace.lboro.ac.uk/2134/902017-08-17T05:50:40Z2017-08-17T05:50:40ZThe van Hove distribution function for Brownian hard spheres: Dynamical test particle theory and computer simulations for bulk dynamics.Hopkins, PaulFortini, AndreaArcher, Andrew J.Schmidt, Matthiashttps://dspace.lboro.ac.uk/2134/260492017-08-14T13:59:12Z2010-01-01T00:00:00ZTitle: The van Hove distribution function for Brownian hard spheres: Dynamical test particle theory and computer simulations for bulk dynamics.
Authors: Hopkins, Paul; Fortini, Andrea; Archer, Andrew J.; Schmidt, Matthias
Abstract: We describe a test particle approach based on dynamical density functional theory (DDFT) for studying the correlated time evolution of the particles that constitute a fluid. Our theory provides a means of calculating the van Hove distribution function by treating its self and distinct parts as the two components of a binary fluid mixture, with the “self ” component having only one particle, the “distinct”
component consisting of all the other particles, and using DDFT to calculate the time evolution of the density profiles for the two components.We apply this approach to a bulk fluid of Brownian hard spheres and compare to results for the van Hove function and the intermediate scattering function from Brownian dynamics computer simulations. We find good agreement at low and intermediate densities using the very simple Ramakrishnan–Yussouff [Phys. Rev. B 19, 2775 (1979)] approximation
for the excess free energy functional. Since the DDFT is based on the equilibrium Helmholtz
free energy functional, we can probe a free energy landscape that underlies the dynamics. Within the mean-field approximation we find that as the particle density increases, this landscape develops a minimum, while an exact treatment of a model confined situation shows that for an ergodic fluid this landscape should be monotonic. We discuss possible implications for slow, glassy, and arrested dynamics at high densities.
Description: This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in HOPKINS, P. ...et al., 2010. The van Hove distribution function for Brownian hard spheres: Dynamical test particle theory and computer simulations for bulk dynamics. Journal of Chemical Physics , 133: 224505. and may be found at http://dx.doi.org/10.1063/1.35117192010-01-01T00:00:00ZCommunity-level regulation of temporal trends in biodiversityGotelli, Nicholas J.Shimadzu, HideyasuDornelas, MariaMcGill, BrianMoyes, FayeMagurran, Anne E.https://dspace.lboro.ac.uk/2134/260232017-08-11T09:49:09Z2017-01-01T00:00:00ZTitle: Community-level regulation of temporal trends in biodiversity
Authors: Gotelli, Nicholas J.; Shimadzu, Hideyasu; Dornelas, Maria; McGill, Brian; Moyes, Faye; Magurran, Anne E.
Abstract: Many theoretical models of community dynamics predict that species richness (S) and total abundance (N) are regulated in their temporal fluctuations. We present novel evidence for widespread regulation of biodiversity. For 59 plant and animal assemblages from around the globe monitored annually for a decade or more, the
majority exhibited regulated fluctuations compared to the null hypothesis of an unconstrained random walk. However, there was little evidence for statistical artifacts, regulation driven by correlations with average annual temperature, or local-scale compensatory fluctuations in S or N. In the absence of major environmental perturbations, such as urbanization or cropland transformation, species richness and abundance may be buffered and exhibit some resilience in their temporal trajectories. These results suggest that regulatory processes are
occurring despite unprecedented environmental change, highlighting the need for community-level assessment of biodiversity trends, as well as extensions of existing theory to address open source pools and shifting environmental conditions.
Description: This paper was accepted for publication in the journal Science Advances and is also available at http://dx.doi.org/10.1126/sciadv.1700315.2017-01-01T00:00:00ZQuasilinear systems with linearizable characteristic websAgafonov, S.I.Ferapontov, E.V.Novikov, V.S.https://dspace.lboro.ac.uk/2134/259922017-08-09T10:33:48Z2017-01-01T00:00:00ZTitle: Quasilinear systems with linearizable characteristic webs
Authors: Agafonov, S.I.; Ferapontov, E.V.; Novikov, V.S.
Abstract: We classify quasilinear systems in Riemann invariants whose characteristic webs are
linearizable on every solution. Although the linearizability of an individual web is a rather nontrivial differential constraint, the requirement of linearizability of characteristic
webs on all solutions imposes simple second-order constraints for the
characteristic speeds of the system. It is demonstrated that every such system with
n > 3 components can be transformed by a reciprocal transformation to n uncoupled
Hopf equations. All our considerations are local.
Description: This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in AGAFONOV, S.I., FERAPONTOV, E.V. and NOVIKOV, V.S., 2017. Quasilinear systems with linearizable characteristic webs. Journal of Mathematical Physics, 58 (7), 071506 and may be found at http://dx.doi.org/10.1063/1.4994198.2017-01-01T00:00:00ZThe standard mean-field treatment of inter-particle attraction in classical DFT is better than one might expectArcher, Andrew J.Chacko, BlessonEvans, Roberthttps://dspace.lboro.ac.uk/2134/258572017-08-10T14:02:43Z2017-01-01T00:00:00ZTitle: The standard mean-field treatment of inter-particle attraction in classical DFT is better than one might expect
Authors: Archer, Andrew J.; Chacko, Blesson; Evans, Robert
Abstract: In classical density functional theory (DFT) the part of the Helmholtz free energy functional arising from attractive inter-particle interactions is often treated in a mean-field or van der Waals approximation. On the face of it, this is a somewhat crude treatment as the resulting functional generates the simple random phase approximation (RPA) for the bulk fluid pair direct correlation function. We explain why using standard mean-field DFT to describe inhomogeneous fluid structure and thermodynamics is more accurate than one might expect based on this observation. By considering the pair correlation function $g(x)$ and structure factor $S(k)$ of a one-dimensional model fluid, for which exact results are available, we show that the mean-field DFT, employed within the test-particle procedure, yields results much superior to those from the RPA closure of the bulk Ornstein-Zernike equation. We argue that one should not judge the quality of a DFT based solely on the approximation it generates for the bulk pair direct correlation function.
Description: This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in ARCHER, A.J., CHACK, B. and EVANS, R., 2017. The standard mean-field treatment of inter-particle attraction in classical DFT is better than one might expect. Journal of Chemical Physics, 147 (3), 034501 and may be found at http://dx.doi.org/10.1063/1.4993175.2017-01-01T00:00:00Z