arXiv subjects

Robert Evans

Publications and source records attributed to Robert Evans.

At least 19 recordsLinked to original sources

arXiv2026

Using test particle sum rules to improve approximations in classical DFT : White-Bear and White-Bear mark II versions of the Lutsko Functional

In a recent paper [M. G\"ul et al., Phys. Rev. E, 110 (6), 064115] we showed that test particle sum rules, which address the excess chemical potential and isothermal compressibility, could be used to develop new and accurate classical density functionals for hard-sphere (HS) fluids. Here we extend our approach to the construction of HS functionals building upon the state of art White-Bear (WB) and White-Bear mark II functionals. Employing the same test-particle sum rules we determine the two free parameters in the Lutsko [James F. Lutsko, Phys. Rev. E, 102, 062137] formulation of fundamental measure theory (FMT) by minimizing the relative errors between different routes to the two thermodynamic quantities. The resulting optimized Lutsko WB functionals, especially Lutsko WB mark II, are generally more accurate and consistent than those obtained in earlier treatments.

cond-mat.soft↗

arXiv2026

Binary colloidal mixtures in near-critical binary solvents

The phase behavior of a single type of colloid C suspended in near-critical solvents is known to be very rich. Motivated in part by recent experiments we consider a mixture of two colloidal types C1 and C2 in a binary solvent close to its demixing critical point. We extend a mean-field description of a lattice model, previously used to investigate systems with a single type of colloid in two dimensions, to the binary colloid case in three dimensions. The model treats the system as a full four-component mixture. For simplicity we choose C1 and C2 to be hard spheres with the same radius but with different affinities for one species, B, of the AB binary solvent. We show that intricate interplay between couplings of C1 and solvent, C2 and solvent as well as solvent-solvent interactions and hard sphere packing drive significant changes in the topology of the colloidal phase diagram when the relative volume fractions of the two different colloid types change. The behavior of the two lines of triple points is particularly interesting. Our results can provide some insight into the control of the self-assembly process for colloidal 'alloys' mediated by a near-critical solvent and therefore controlled by temperature in a reversible manner

cond-mat.soft↗

arXiv2025

Learning the bulk and interfacial physics of liquid-liquid phase separation with neural density functionals

We use simulation-based supervised machine learning and classical density functional theory to investigate bulk and interfacial phenomena associated with phase coexistence in binary mixtures. For a prototypical symmetrical Lennard-Jones mixture our trained neural density functional yields accurate liquid-liquid and liquid-vapour binodals together with predictions for the variation of the associated interfacial tensions across the entire fluid phase diagram. From the latter we determine the contact angles at fluid-fluid interfaces along the line of triple-phase coexistence and confirm there can be no wetting transition in this symmetrical mixture.

cond-mat.soft↗

arXiv2024

Metadensity functional theory for classical fluids: Extracting the pair potential

The excess free energy functional of classical density functional theory depends upon the type of fluid model, specifically on the choice of (pair) potential, is unknown in general, and is approximated reliably only in special cases. We present a machine learning scheme for training a neural network that acts as a generic metadensity functional for truncated but otherwise arbitrary pair potentials. Automatic differentiation and neural functional calculus then yield, for one-dimensional fluids, accurate predictions for inhomogeneous states and immediate access to the pair distribution function. The approach provides a means of addressing a fundamental problem in the physics of liquids, and for soft matter design: How best to invert structural data to obtain the pair potential?

cond-mat.soft↗

arXiv2024

Using test particle sum rules to construct accurate functionals in classical Density Functional Theory

Fundamental Measure Theory (FMT) is a successful and versatile approach for describing the properties of the hard-sphere fluid and hard-sphere mixtures within the framework of classical density functional theory (DFT). Lutsko [Phys. Rev. E 102, 062137 (2020)] introduced a version of FMT containing two free parameters, to be fixed by additional physical constraints. Whereas Lutsko focused on the stability of crystalline phases, we introduce and employ two statistical mechanical sum rules pertinent for the fluid phase, that are not automatically satisfied by FMT. By minimizing the relative deviation between different routes to calculate the excess chemical potential and the isothermal compressibility we determine the two free parameters of the theory. Our results indicate that requiring consistency with these sum rules can improve the quality of predictions of FMT for properties of the hard-sphere fluid phase. We suggest that employing these (test particle) sum rules, which apply for any interparticle pair-potential, might provide a means of testing the performance and accuracy of general DFT approximations.

cond-mat.soft↗

arXiv2024

Neural density functional theory of liquid-gas phase coexistence

We use supervised machine learning together with the concepts of classical density functional theory to investigate the effects of interparticle attraction on the pair structure, thermodynamics, bulk liquid-gas coexistence, and associated interfacial phenomena in many-body systems. Local learning of the one-body direct correlation functional is based on Monte Carlo simulations of inhomogeneous systems with randomized thermodynamic conditions, randomized planar shapes of the external potential, and randomized box sizes. Focusing on the prototypical Lennard-Jones system, we test predictions of the resulting neural attractive density functional across a broad spectrum of physical behavior associated with liquid-gas phase coexistence in bulk and at interfaces. We analyse the bulk radial distribution function $g(r)$ obtained from automatic differentiation and the Ornstein-Zernike route and determine i) the Fisher-Widom line, i.e. the crossover of the asymptotic (large distance) decay of $g(r)$ from monotonic to oscillatory, ii) the (Widom) line of maximal correlation length, iii) the line of maximal isothermal compressibility and iv) the spinodal by calculating the poles of the structure factor in the complex plane. The bulk binodal and the density profile of the free liquid-gas interface are obtained from density functional minimization and the corresponding surface tension from functional line integration. We also show that the neural functional describes accurately the phenomena of drying at a hard wall and of capillary evaporation for a liquid confined in a slit pore. Our neural framework yields results that improve significantly upon standard mean-field treatments of interparticle attraction. Comparison with independent simulation results demonstrates a consistent picture of phase separation even when restricting the training to supercritical states only.

cond-mat.soft↗

arXiv2024

What is the best simulation approach for measuring local density fluctuations near solvo/hydrophobes?

Measurements of local density fluctuations are crucial to characterizing the interfacial properties of equilibrium fluids. A specific case that has been well-explored involves the heightened compressibility of water near hydrophobic entities. Commonly, a spatial profile of local fluctuation strength is constructed from measurements of the mean and variance of solvent particle number fluctuations in a set of contiguous sub-volumes of the system adjacent to the solvo/hydrophobe. An alternative measure proposed by Evans and Stewart (J. Phys.: Condens. Matter 27, 194111 (2015)) defines a local compressibility profile in terms of the chemical potential derivative of the spatial number density profile. Using Grand Canonical Monte Carlo simulation, we compare and contrast the efficacy of these two approaches for a Lennard-Jones solvent at spherical and planar solvophobic interfaces, and SPC/E water at a hydrophobic spherical solute. Our principal findings are that: (i) the local compressibility profile $χ({\bf r})$ of Evans and Stewart is considerably more sensitive to variations in the strength of local density fluctuations than the spatial fluctuation profile $F({\bf r})$ and can resolve much more detailed structure; (ii) while the local compressibility profile is essentially independent of the choice of spatial discretization used to construct the profile, the spatial fluctuation profile exhibits strong systematic dependence on the size of the subvolumes on which the profile is defined. We clarify the origin and nature of this finite-size effect.

cond-mat.soft↗

arXiv2023

Numerical Evidence for a refinement of Deligne's Period Conjecture for Jacobians of Curves

Let $A/\mathbb{Q}$ be a Jacobian variety and let $F$ be a totally real, tamely ramified, abelian number field. Given a character $ψ$ of $F/\mathbb{Q}$, Deligne's Period Conjecture asserts the algebraicity of the suitably normalised value $\mathcal{L}(A,ψ,1)$ at $z=1$ of the Hasse-Weil-Artin $L$-function of the $ψ$-twist of $A$. We formulate a conjecture regarding the integrality properties of the family of normalised $L$-values $(\mathcal{L}(A,ψ,1))_ψ$, and its relation to the Tate-Shafarevich group of $A$ over $F$. We numerically investigate our conjecture through $p$-adic congruence relations between these values.

math.NT↗

arXiv2022

Understanding the physics of hydrophobic solvation

Simulations of water near extended hydrophobic spherical solutes have revealed the presence of a region of depleted density and accompanying enhanced density fluctuations.The physical origin of both phenomena has remained somewhat obscure. We investigate these effects employing a mesoscopic binding potential analysis, classical density functional theory (DFT) calculations for a simple Lennard-Jones (LJ) solvent and Grand Canonical Monte Carlo (GCMC) simulations of a monatomic water (mw) model. We argue that the density depletion and enhanced fluctuations are near-critical phenomena. Specifically, we show that they can be viewed as remnants of the critical drying surface phase transition that occurs at bulk liquid-vapor coexistence in the macroscopic planar limit, i.e.~as the solute radius $R_s\to\infty$. Focusing on the radial density profile $ρ(r)$ and a sensitive spatial measure of fluctuations, the local compressibility profile $χ(r)$, our binding potential analysis provides explicit predictions for the manner in which the key features of $ρ(r)$ and $χ(r)$ scale with $R_s$, the strength of solute-water attraction $\varepsilon_{sf}$, and the deviation from liquid-vapor coexistence of the chemical potential, $δμ$. These scaling predictions are confirmed by our DFT calculations and GCMC simulations. As such our theory provides a firm basis for understanding the physics of hydrophobic solvation.

cond-mat.soft↗

arXiv2022

Measures of Fluctuations for a Liquid Near Critical Drying

We investigate density fluctuations in a liquid close to a solvophobic substrate at which a surface critical drying transition occurs. Using classical density functional theory, we determine three measures of the spatial extent and strength of the fluctuations, i.e., the local compressibility $χ_μ(z)$, the local thermal susceptibility $χ_T(z)$ and the reduced density $χ_*(z)$; $z$ is the distance from the substrate. Whilst the first measure is frequently used, the second and third were introduced very recently by Eckert et.al., Phys. Rev. Lett. 125, 268004 (2020). For state points in the critical drying regime, all three measures, each scaled by its bulk value, exhibit very similar forms and the ratio of $χ_T(z)$ to $χ_μ(z)$, for fixed $z$ in the vapour-liquid transition region, is constant. Using a scaling treatment of surface thermodynamics we show that such behaviour is to be expected on general grounds.

cond-mat.stat-mech↗

arXiv2022

Density depletion and enhanced fluctuations in water near hydrophobic solutes: identifying the underlying physics

We investigate the origin of the density depletion and enhanced density fluctuations that occur in water in the vicinity of an extended hydrophobic solute. We argue that both phenomena are remnants of the critical drying surface phase transition that occurs at liquid-vapor coexistence in the macroscopic planar limit, ie. as the solute radius $R_s\to\infty$. Focusing on the density profile $ρ(r)$ and a sensitive spatial measure of fluctuations, the local compressibility profile $χ(r)$, we develop a scaling theory which expresses the extent of the density depletion and enhancement in compressibility in terms of $R_s$, the strength of solute-water attraction $\varepsilon_s$, and the deviation from liquid-vapor coexistence $δμ$. Testing the predictions against results of classical density functional theory for a simple solvent and Grand Canonical Monte Carlo simulations of a popular water model, we find that the theory provides a firm physical basis for understanding how water behaves at a hydrophobe.

cond-mat.soft↗

arXiv2020

Bypassing the energy functional in density functional theory: Direct calculation of electronic energies from conditional probability densities

Density functional calculations can fail for want of an accurate exchange-correlation approximation. The energy can instead be extracted from a sequence of density functional calculations of conditional probabilities (CP-DFT). Simple CP approximations yield usefully accurate results for two-electron ions, the hydrogen dimer, and the uniform gas at all temperatures. CP-DFT has no self-interaction error for one electron, and correctly dissociates H2, both major challenges. For warm dense matter, classical CP-DFT calculations can overcome the convergence problems of Kohn-Sham DFT.

physics.chem-ph↗

arXiv2020

On a BSD-type formula for L-values of Artin twists of elliptic curves

This is an investigation into the possible existence and consequences of a Birch-Swinnerton-Dyer-type formula for L-functions of elliptic curves twisted by Artin representations. We translate expected properties of L-functions into purely arithmetic predictions for elliptic curves, and show that these force some peculiar properties of the Tate-Shafarevich group, which do not appear to be tractable by traditional Selmer group techniques. In particular we exhibit settings where the different p-primary components of the Tate-Shafarevich group do not behave independently of one another. We also give examples of "arithmetically identical" settings for elliptic curves twisted by Artin representations, where the associated L-values can nonetheless differ, in contrast to the classical Birch-Swinnerton-Dyer conjecture.

math.NT↗

arXiv2019

A unified description of hydrophilic and superhydrophobic surfaces in terms of the wetting and drying transitions of liquids

Clarifying the factors that control the contact angle of a liquid on a solid substrate is a long-standing scientific problem pertinent across physics, chemistry and materials science. Progress has been hampered by the lack of a comprehensive and unified understanding of the physics of wetting and drying phase transitions. Using various theoretical and simulational techniques applied to realistic fluid models, we elucidate how the character of these transitions depends sensitively on both the range of fluid-fluid and substrate-fluid interactions and the temperature. Our calculations uncover previously unrecognised classes of surface phase diagram which differ from that established for simple lattice models and often assumed to be universal. The differences relate both to the topology of the phase diagram and to the nature of the transitions, with a remarkable feature being a difference between drying and wetting transitions which persists even in the approach to the bulk critical point. Most experimental and simulational studies of liquids at a substrate belong to one of these previously unrecognised classes. We predict that while there appears to be nothing particularly special about water with regard to its wetting and drying behavior, superhydrophobic behavior should be more readily observable in experiments conducted at high temperatures than at room temperature.

cond-mat.stat-mech↗

arXiv2019

On the decay of the pair correlation function and the line of vanishing excess isothermal compressibility in simple fluids

We re-visit the competition between attractive and repulsive interparticle forces in simple fluids and how this governs and connects the macroscopic phase behavior and structural properties as manifest in pair correlation functions. We focus on the asymptotic decay of the total correlation function $h(r)$ which is, in turn, controlled by the form of the pair direct correlation function $c(r)$. The decay of $r h(r)$ to zero can be either exponential (monotonic) if attraction dominates repulsion and exponentially damped oscillatory otherwise. The Fisher-Widom (FW) line separates the phase diagram into two regions characterized by the two different types of asymptotic decay. We show that there is a new and physically intuitive thermodynamic criterion which approximates well the actual FW line. This new criterion defines a line where the isothermal compressibility takes its ideal gas value $χ_T=χ_T^\text{id}$. We test our hypothesis by considering four commonly used models for simple fluids. In all cases the new criterion yields a line in the phase diagram that is close to the actual FW line for the thermodynamic state points that are most relevant. We also investigate (Widom) lines of maximal correlation length, emphasizing the importance of distinguishing between the true and Ornstein-Zernike correlation lengths

cond-mat.soft↗

arXiv2018

Composition inversion in mixtures of binary colloids and polymer

Understanding the phase behaviour of mixtures continues to pose challenges, even for systems that might be considered "simple". Here we consider a very simple mixture of two colloidal and one non-adsorbing polymer species which can be simplified even further to a size-asymmetrical binary mixture, in which the effective colloid-colloid interactions depend on the polymer concentration. We show that this basic system exhibits surprisingly rich phase behaviour. In particular, we enquire whether such a system features only a liquid-vapor phase separation (as in one-component colloid-polymer mixtures) or whether, additionally, liquid-liquid demixing of two colloidal phases can occur. Particle-resolved experiments show demixing-like behaviour, but when combined with bespoke Monte Carlo simulations, this proves illusory, and we reveal that only a single liquid-vapor transition occurs. Progressive migration of the small particles to the liquid phase as the polymer concentration increases gives rise to composition inversion - a maximum in the large particle concentration in the liquid phase. Near criticality the density fluctuations are found to be dominated by the larger colloids.

cond-mat.soft↗

arXiv2017

Trading Zones Revisited

We describe and then elaborate the model of trading zones first presented in Collins et al 2007, Trading Zones and Interactional Expertise. We believe this expanded version of the model includes some very important but previously overlooked ways for separate language communities to communicate. We illustrate the argument with examples.

physics.hist-ph↗

arXiv2017

The standard mean-field treatment of inter-particle attraction in classical DFT is better than one might expect

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.

cond-mat.soft↗