Quantifying Disorder through Conditional Entropy: An Application to Fluid Mixing

Brandani, Giovanni B.; Schor, Marieke; MacPhee, Cait E.; Grubmüller, Helmut; Zachariae, Ulrich; Marenduzzo, Davide

doi:10.1371/journal.pone.0065617

Cited by 38 publications

(32 citation statements)

References 28 publications

(42 reference statements)

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“…In comparison to the one used in 37,38 , this formula is based on normalized populations x j and y j (rather than n j and m j ) and is therefore more suited to describe binary mixtures where the species feature a particle-number imbalance (moreover the contribution of each site j to the total entropy of mixing is not fixed, but it is weighted by the fractions of particles present therein). As shown in Fig.…”

Section: Resultsmentioning

confidence: 99%

The mixing-demixing phase diagram of ultracold heteronuclear mixtures in a ring trimer

Richaud

Zenesini

Penna

2019

Sci Rep

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We derive the complete mixing-demixing phase-diagram relevant to a bosonic binary mixture confined in a ring trimer and modeled within the Bose-Hubbard picture. The mixing properties of the two quantum fluids, which are shown to be strongly affected by the fragmented character of the confining potential, are evaluated by means of a specific indicator imported from Statistical Thermodynamics and are shown to depend only on two effective parameters incorporating the asymmetry between the heteronuclear species. To closely match realistic experimental conditions, our study is extended also beyond the pointlike approximation of potential wells by describing the systems in terms of two coupled Gross-Pitaevskii equations. The resulting mean-field analysis confirms the rich scenario of mixing-demixing transitions of the mixture and also constitutes an effective springboard towards a viable experimental realization. We additionally propose an experimental realization based on a realistic optical-tweezers system and on the bosonic mixture 23 Na + 39 K, thanks to the large tunability of their intra- and inter-species scattering lengths.

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Section: Resultsmentioning

confidence: 99%

The mixing-demixing phase diagram of ultracold heteronuclear mixtures in a ring trimer

Richaud

Zenesini

Penna

2019

Sci Rep

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“…as described by Brandani et al [ 38 ], where p ( x i , n b i ) is the probability to find a lipid of type x i neighboured to a lipid of type n b i , and p ( x i ∣ n b i ) indicates the conditional probability that a lipid is of type x i given that its neighbour is of type n b i . To calculate the entropy, a distance vector is established between the phosphorous atoms on each lipid in a leaflet to determine the nearest neighbouring lipid and its type.…”

Section: Methodsmentioning

confidence: 99%

Membrainy: a ‘smart’, unified membrane analysis tool

Carr

MacPhee

2015

Source Code Biol Med

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BackgroundThe study of biological membranes using Molecular Dynamics has become an increasingly popular means by which to investigate the interactions of proteins, peptides and potentials with lipid bilayers. These interactions often result in changes to the properties of the lipids which can modify the behaviour of the membrane. Membrainy is a unified membrane analysis tool that contains a broad spectrum of analytical techniques to enable: measurement of acyl chain order parameters; presentation of 2D surface and thickness maps; determination of lateral and axial headgroup orientations; measurement of bilayer and leaflet thickness; analysis of the annular shell surrounding membrane-embedded objects; quantification of gel percentage; time evolution of the transmembrane voltage; area per lipid calculations; and quantification of lipid mixing/demixing entropy.ResultsEach analytical component within Membrainy has been tested on a variety of lipid bilayer systems and was found to be either comparable to or an improvement upon existing software. For the analytical techniques that have no direct comparable software, our results were confirmed with experimental data.ConclusionsMembrainy is a user-friendly, intelligent membrane analysis tool that automatically interprets a variety of input formats and force fields, is compatible with both single and double bilayers, and capable of handling asymmetric bilayers and lipid flip-flopping. Membrainy has been designed for ease of use, requiring no installation or configuration and minimal user-input to operate.

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“…, M types of monomers can be quantified by computing the Shannon entropy (i.e. entropy of mixing) [46]…”

Section: Entropy Of Mixing Quantifies Composite Macrostructurementioning

confidence: 99%

Maximally stiffening composites require maximally coupled rather than maximally entangled polymer species

2019

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Polymer composites are ideal candidates for next generation biomimetic soft materials because of their exquisite bottom-up designability. However, the richness of behaviours comes at a price: the need for precise and extensive characterisation of material properties over a highly-dimensional parameter space, as well as a quantitative understanding of the physical principles underlying desirable features. Here we couple large-scale Molecular Dynamics simulations with optical tweezers microrheology to characterise the viscoelastic response of DNA-actin composites. We discover that the previously observed non-monotonic stress-stiffening of these composites is robust, yet tunable, in a broad range of the parameter space that spans two orders of magnitude in DNA length. Importantly, we discover that the most pronounced stiffening is achieved when the species are maximally coupled, i.e. have similar number of entanglements, and not when the number of entanglements per DNA chain is largest. We further report novel dynamical oscillations of the microstructure of the composites, alternating between mixed and bundled phases, opening the door to future investigations. The generic nature of our system renders our results applicable to the behaviour of a broad class of polymer composites. arXiv:1907.12164v1 [cond-mat.soft]

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Quantifying Disorder through Conditional Entropy: An Application to Fluid Mixing

Cited by 38 publications

References 28 publications

The mixing-demixing phase diagram of ultracold heteronuclear mixtures in a ring trimer

The mixing-demixing phase diagram of ultracold heteronuclear mixtures in a ring trimer

Membrainy: a ‘smart’, unified membrane analysis tool

Maximally stiffening composites require maximally coupled rather than maximally entangled polymer species

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