## Publications

211 results found

Chapman SJ, Dallaston MC, Kalliadasis S,
et al., 2023, The role of exponential asymptotics and complex singularities in self-similarity, transitions, and branch merging of nonlinear dynamics, *Physica D: Nonlinear Phenomena*, Vol: 453, Pages: 1-14, ISSN: 0167-2789

We study a prototypical example in nonlinear dynamics where transition to self-similarity in asingular limit is fundamentally changed as a parameter is varied. Here, we focus on the complicateddynamics that occur in a generalised unstable thin-film equation that yields finite-time rupture. Aparameter, n, is introduced to model more general disjoining pressures. For the standard case ofvan der Waals intermolecular forces, n = 3, it was previously established that a countably infinitenumber of self-similar solutions exist leading to rupture. Each solution can be indexed by a parameter,ϵ = ϵ1 > ϵ2 > · · · > 0, and the prediction of the discrete set of solutions requires examination ofterms beyond-all-orders in ϵ. However, recent numerical results have demonstrated the surprisingcomplexity that exists for general values of n. In particular, the bifurcation structure of self-similarsolutions now exhibits branch merging as n is varied. In this work, we shall present key ideas of howbranch merging can be interpreted via exponential asymptotics.

Malpica-Morales A, Yatsyshin P, Durán-Olivencia MA,
et al., 2023, Physics-informed Bayesian inference of external potentials in classical density-functional theory., *J Chem Phys*, Vol: 159

The swift progression and expansion of machine learning (ML) have not gone unnoticed within the realm of statistical mechanics. In particular, ML techniques have attracted attention by the classical density-functional theory (DFT) community, as they enable automatic discovery of free-energy functionals to determine the equilibrium-density profile of a many-particle system. Within classical DFT, the external potential accounts for the interaction of the many-particle system with an external field, thus, affecting the density distribution. In this context, we introduce a statistical-learning framework to infer the external potential exerted on a classical many-particle system. We combine a Bayesian inference approach with the classical DFT apparatus to reconstruct the external potential, yielding a probabilistic description of the external-potential functional form with inherent uncertainty quantification. Our framework is exemplified with a grand-canonical one-dimensional classical particle ensemble with excluded volume interactions in a confined geometry. The required training dataset is generated using a Monte Carlo (MC) simulation where the external potential is applied to the grand-canonical ensemble. The resulting particle coordinates from the MC simulation are fed into the learning framework to uncover the external potential. This eventually allows us to characterize the equilibrium density profile of the system by using the tools of DFT. Our approach benchmarks the inferred density against the exact one calculated through the DFT formulation with the true external potential. The proposed Bayesian procedure accurately infers the external potential and the density profile. We also highlight the external-potential uncertainty quantification conditioned on the amount of available simulated data. The seemingly simple case study introduced in this work might serve as a prototype for studying a wide variety of applications, including adsorption, wetting, and capillar

Russo A, Duran-Olivencia MA, Kevrekidis IG,
et al., 2022, Machine learning memory kernels as closure for non-Markovian stochastic processes, *IEEE Transactions on Neural Networks and Learning Systems*, Pages: 1-13, ISSN: 1045-9227

Finding the dynamical law of observable quantities lies at the core of physics. Within the particular field of statistical mechanics, the generalized Langevin equation (GLE) comprises a general model for the evolution of observables covering a great deal of physical systems with many degrees of freedom and an inherently stochastic nature. Although formally exact, GLE brings its own great challenges. It depends on the complete history of the observables under scrutiny, as well as the microscopic degrees of freedom, all of which are often inaccessible. We show that these drawbacks can be overcome by adopting elements of machine learning from empirical data, in particular coupling a multilayer perceptron (MLP) with the formal structure of GLE and calibrating the MLP with the data. This yields a powerful computational tool capable of describing noisy complex systems beyond the realms of statistical mechanics. It is exemplified with a number of representative examples from different fields: from a single colloidal particle and particle chains in a thermal bath to climatology and finance, showing in all cases excellent agreement with the actual observable dynamics. The new framework offers an alternative perspective for the study of nonequilibrium processes opening also a new route for stochastic modeling.

Magaletti F, Gallo M, Perez SP,
et al., 2022, A positivity-preserving scheme for fluctuating hydrodynamics, *Journal of Computational Physics*, Vol: 463, Pages: 111248-1-111248-19, ISSN: 0021-9991

A finite-difference hybrid numerical method for the solution of the isothermal fluctuating hydrodynamic equations is proposed. The primary focus is to ensure the positivity-preserving property of the numerical scheme, which is critical for its functionality and reliability especially when simulating fluctuating vapour systems. Both cases of single- and two-phase flows are considered by exploiting the van der Waals' square-gradient approximation to model the fluid (often referred to as “diffuse-interface” model). The accuracy and robustness of the proposed scheme is verified against several benchmark theoretical predictions for the statistical properties of density, velocity fluctuations and liquid-vapour interface, including the static structure factor of the density field and the spectrum of the capillary waves excited by thermal fluctuations at interface. Finally, the hybrid scheme is applied to the challenging bubble nucleation process, and is shown to capture the salient features of the phenomenon, namely nucleation rate and subsequent bubble-growth dynamics.

Yatsyshin P, Kalliadasis S, Duncan AB, 2022, Physics-constrained Bayesian inference of state functions in classical density-functional theory, *Journal of Chemical Physics*, Vol: 156, Pages: 074105-1-074105-10, ISSN: 0021-9606

We develop a novel data-driven approach to the inverse problem of classical statistical mechanics: given experimental data on the collective motion of a classical many-body system, how does one characterise the free energy landscape of that system? By combining non-parametric Bayesian inference with physically-motivated constraints, we develop an efficient learning algorithm which automates the construction of approximate free energy functionals. In contrast to optimisation-based machine learning approaches, which seek to minimise a cost function, the centralidea of the proposed Bayesian inference is to propagate a set of prior assumptions through the model, derived from physical principles. The experimental data is usedto probabilistically weigh the possible model predictions. This naturally leads to humanly interpretable algorithms with full uncertainty quantification of predictions. In our case, the output of the learning algorithm is a probability distribution over a family of free energy functionals, consistent with the observed particle data. We find that surprisingly small data samples contain sufficient information for inferring highly accurate analytic expressions of the underlying free energy functionals, making our algorithm highly data efficient. We consider excluded volume particle interactions, which are ubiquitous in nature, whilst being highly challenging for modelling in terms of free energy. To validate our approach we consider the paradigmaticcase of one-dimensional fluid and develop inference algorithms for the canonical and grand-canonical statistical-mechanical ensembles. Extensions to higher dimensional systems are conceptually straightforward, whilst standard coarse-graining techniques allow one to easily incorporate attractive interactions

Duran-Olivencia M, Kalliadasis S, 2021, Understanding soaring corona virus cases and the effect of contagion policies in the UK, *Vaccines*, Vol: 9, Pages: 1-7, ISSN: 2076-393X

The number of new daily SARS-CoV-2 infections is frantically risingin almost every country of the EU. The phenomenological explanationoffered is a new mutation of the virus, first identified in the UK.We use publicly available data in combination with a controlled SIRmodel, which captures the effects of preventive measures on the activecases, to show that the current wave of infections is consistentwith a single transmission rate. This suggests that the new SARSCoV-2 variant is as transmissible as previous strains. Our findingsindicate that the relaxation of preventive measures is closely relatedwith the ongoing surge in cases. We simulate the effects of newrestrictions and vaccination campaigns in 2021, demonstrating thatlockdown policies are not fully effective to flatten the curve. For effectivemitigation, it is critical that the public keeps on high alert untilvaccination reaches a critical threshold.

Carrillo JA, Kalliadasis S, Liang F,
et al., 2021, Enhancement of damaged-image prediction through Cahn-Hilliard image inpainting., *Royal Society Open Science*, Vol: 8, Pages: 1-17, ISSN: 2054-5703

We assess the benefit of including an image inpainting filter before passing damaged images into a classification neural network. We employ an appropriately modified Cahn-Hilliard equation as an image inpainting filter which is solved numerically with a finite-volume scheme exhibiting reduced computational cost and the properties of energy stability and boundedness. The benchmark dataset employed is Modified National Institute of Standards and Technology (MNIST) dataset, which consists of binary images of handwritten digits and is a standard dataset to validate image-processing methodologies. We train a neural network based on dense layers with MNIST, and subsequently we contaminate the test set with damages of different types and intensities. We then compare the prediction accuracy of the neural network with and without applying the Cahn-Hilliard filter to the damaged images test. Our results quantify the significant improvement of damaged-image prediction by applying the Cahn-Hilliard filter, which for specific damages can increase up to 50% and is advantageous for low to moderate damage.

Mendes J, Russo A, Perez SP,
et al., 2021, A finite-volume scheme for gradient-flow equations with non-homogeneous diffusion, *Computers & Mathematics with Applications*, Vol: 89, Pages: 150-162, ISSN: 0898-1221

We develop a first- and second-order finite-volume scheme to solve gradient flow equations with non-homogeneous properties, obtained in the framework of dynamical-density functional theory. The scheme takes advantage of an upwind approach for the space discretization to ensure positivity of the density under a CFL condition and decay of the discrete free energy. Our computational approach is used to study several one- and two-dimensional systems, with a general free-energy functional accounting for external fields and inter-particle potentials, and placed in non-homogeneous thermal baths characterized by anisotropic, space-dependent and time-dependent properties.

Yatsyshin P, Kalliadasis S, 2021, Surface nanodrops and nanobubbles: a classical density functional theory study, *Journal of Fluid Mechanics*, Vol: 913, Pages: 1-16, ISSN: 0022-1120

We present a fully microscopic study of the interfacial thermodynamics of nanodrops and nanobubbles, adsorbed on flat substrates with first-order wetting. We show that both nanodrops and nanobubbles are thermodynamically accessible in regions, demarcated by the spinodals of planar wetting films, with nanobubbles occupying a relatively bigger portion of the phase space. While nanodrops can be described as near-spherical caps of Laplace radius, the radius of nanobubbles is very different from the Laplace value. Additionally, nanobubbles are accompanied by a thin gas film adsorbed on the substrate. By computing the interface binding potential, we relate the sphericity of nanodrops to the thin–thick liquid film coexistence (prewetting transition), whereas nanobubble shapes are determined only by the decay of the fluid–substrate forces.

Duran-Olivencia M, Kalliadasis S, 2021, More than a year after the onset of the CoVid-19 pandemic in the UK: lessons learned from a minimalistic model capturing essential features including social awareness and policy making, Publisher: MedRxiv

The number of new daily SARS-CoV-2 infections experienced an abrupt increase during the last quarter of 2020 in almost every European country. The phenomenological explanation offered was a new mutation of the virus, first identified in the UK. We use publicly available data in combination with a time-delayed controlled SIR model, which captures the effects of preventive measures and concomitant social response on the spreading of the virus. The model, which has a unique transmission rate, enables us to reproduce the waves of infection occurred in the UK. This suggests that the new SARS-CoV-2 UK variant is as transmissible as previous strains. Our findings reveal that the sudden surge in cases was in fact related to the relaxation of preventive measures and social awareness. We also simulate the combined effects of restrictions and vaccination campaigns in 2021, demonstrating that lockdown policies are not fully effective to flatten the curve; fully effective mitigation can only be achieved via a vigorous vaccination campaign. As a matter of fact, incorporating recent data about vaccine efficacy, our simulations advocate that the UK might have overcome the worse of the CoVid-19 pandemic, provided that the vaccination campaign maintains a rate of approximately 140k jabs per day.

Russo A, Perez SP, Durán-Olivencia MA,
et al., 2021, A finite-volume method for fluctuating dynamical density functional theory, *Journal of Computational Physics*, Vol: 428, ISSN: 0021-9991

We introduce a finite-volume numerical scheme for solving stochastic gradient flow equations. Such equations are of crucial importance within the framework of fluctuating hydrodynamics and dynamic density functional theory. Our proposed scheme deals with general free-energy functionals, including, for instance, external fields or interaction potentials. This allows us to simulate a range of physical phenomena where thermal fluctuations play a crucial role, such as nucleation and other energy-barrier crossing transitions. A positivity-preserving algorithm for the density is derived based on a hybrid space discretization of the deterministic and the stochastic terms and different implicit and explicit time integrators. We show through numerous applications that not only our scheme is able to accurately reproduce the statistical properties (structure factor and correlations) of physical systems, but also allows us to simulate energy barrier crossing dynamics, which cannot be captured by mean-field approaches.

Carrillo JA, Castro MJ, Kalliadasis S,
et al., 2021, High-order well-balanced finite-volume schemes for hydrodynamic equations with nonlocal free energy, *SIAM Journal on Scientific Computing*, Vol: 43, Pages: A828-A858, ISSN: 1064-8275

We propose high-order well-balanced finite-volume schemes for a broad class of hydrodynamic systems with attractive-repulsive interaction forces and linear and nonlinear damping. Our schemes are suitable for free energies containing convolutions of an interaction potential with the density, which are essential for applications such as the Keller--Segel model, more general Euler--Poisson systems, or dynamic-density functional theory. Our schemes are also equipped with a nonnegative-density reconstruction which allows for vacuum regions during the simulation. We provide several prototypical examples from relevant applications highlighting the benefit of our algorithms and also elucidate some of our analytical results.

Russo A, Duran-Olivencia MA, Yatsyshin P,
et al., 2020, Memory effects in fluctuating dynamic density-functional theory: theory and simulations, *Journal of Physics A: Mathematical and Theoretical*, Vol: 53, ISSN: 1751-8113

This work introduces a theoretical framework to describe the dynamics of reacting multi-species fluid systems in-and-out of equilibrium. Our starting point is the system of generalised Langevin equations which describes the evolution of the positions and momenta of the constituent particles. One particular difficulty that this system of generalised Langevin equations exhibits is the presence of a history-dependent (i.e. non-Markovian) term, which in turn makes the system's dynamics dependent on its own past history. With the appropriate definitions of the local number density and momentum fields, we are able to derive a non-Markovian Navier–Stokes-like system of equations constituting a generalisation of the Dean–Kawasaki model. These equations, however, still depend on the full set of particles phase-space coordinates. To remove this dependence on the microscopic level without washing out the fluctuation effects characteristic of a mesoscopic description, we need to carefully ensemble-average our generalised Dean–Kawasaki equations. The outcome of such a treatment is a set of non-Markovian fluctuating hydrodynamic equations governing the time evolution of the mesoscopic density and momentum fields. Moreover, with the introduction of an energy functional which recovers the one used in classical density-functional theory and its dynamic extension (DDFT) under the local-equilibrium approximation, we derive a novel non-Markovian fluctuating DDFT (FDDFT) for reacting multi-species fluid systems. With the aim of reducing the fluctuating dynamics to a single equation for the density field, in the spirit of classical DDFT, we make use of a deconvolution operator which makes it possible to obtain the overdamped version of the non-Markovian FDDFT. A finite-volume discretization of the derived non-Markovian FDDFT is then proposed. With this, we validate our theoretical framework in-and-out-of-equilibrium by comparing results against atomistic simulations. Fi

Ruyer-Quil C, Trevelyan P, Giorgiutti-Dauphiné F,
et al., 2020, Modelling film flows down a fibre – ERRATUM, *Journal of Fluid Mechanics*, Vol: 890, ISSN: 0022-1120

[Erratum]

Carrillo de la Plata JA, Kalliadasis S, Perez Perez S,
et al., 2020, Well-balanced finite volume schemes for hydrodynamic equations with general free energy, *SIAM: Multiscale Modeling and Simulation*, Vol: 18, Pages: 502-541, ISSN: 1540-3459

Well-balanced and free energy dissipative first- and second-order accurate finite volume schemes are proposed for a general class of hydrodynamic systems with linear and nonlinear damping. The variation of the natural Liapunov functional of the system, given by its free energy, allows, for a characterization of the stationary states by its variation. An analog property at the discrete level enables us to preserve stationary states at machine precision while keeping the dissipation of the discrete free energy. These schemes can accurately analyse the stability properties of stationary states in challenging problems such as: phase transitions in collective behavior, generalized Euler-Poisson systems in chemotaxis and astrophysics, and models in dynamic density functional theories; having done a careful validation in a battery of relevant test cases.

Karakasidis T, Kalliadasis S, Koumoutsakos P,
et al., 2019, Preface, *Computational Materials Science*, Vol: 169, Pages: 109096-109096, ISSN: 0927-0256

Thompson AB, Gomes SN, Denner F,
et al., 2019, Robust low-dimensional modelling of falling liquid films subject to variable wall heating, *Journal of Fluid Mechanics*, Vol: 877, Pages: 844-881, ISSN: 0022-1120

Accurate low-dimensional models for the dynamics of falling liquid films subject to localized or time-varying heating are essential for applications that involve patterning or control. However, existing modelling methodologies either fail to respect fundamental thermodynamic properties or else do not accurately capture the effects of advection and diffusion on the temperature profile. We argue that the best-performing long-wave models are those that give the surface temperature implicitly as the solution of an evolution equation in which the wall temperature alone (and none of its derivatives) appears as a source term. We show that, for both flat and non-uniform films, such a model can be rationally derived by expanding the temperature field about its free-surface values. We test this model in linear and nonlinear regimes, and show that its predictions are in remarkable quantitative agreement with full Navier–Stokes calculations regarding the surface temperature, the internal temperature field and the surface displacement that would result from temperature-induced Marangoni stresses.

Radhakrishnan ANP, Pradas M, Sorensen E,
et al., 2019, Hydrodynamic characterization of phase separation in devices with microfabricated capillaries, *Langmuir*, Vol: 35, Pages: 8199-8209, ISSN: 0743-7463

Capillary microseparators have been gaining interest in downstream unit operations, especially for pharmaceutical, space, and nuclear applications, offering efficient separation of two-phase flows. In this work, a detailed analysis of the dynamics of gas-liquid separation at the single meniscus level helped to formulate a model to map the operability region of microseparation devices. A water-nitrogen segmented flow was separated in a microfabricated silicon-glass device, with a main channel (width, W = 600 μm; height, H = 120 μm) leading into an array of 276 capillaries (100 μm long; width = 5 μm facing the main channel and 25 μm facing the liquid outlet), on both sides of the channel. At optimal pressure differences, the wetting phase (water) flowed through the capillaries into the liquid outlet, whereas the nonwetting phase (nitrogen) flowed past the capillaries into the gas outlet. A high-speed imaging methodology aided by computational analysis was used to quantify the length of the liquid slugs and their positions in the separation zone. It was observed that during stable separation, the position of the leading edge of the liquid slugs (advancing meniscus), which became stationary in the separation zone, was dependent only on the outlet pressure difference. The trailing edge of the liquid slugs (receding meniscus) approached the advancing meniscus at a constant speed, thus leading to a linear decrease of the liquid slug length. Close to the liquid-to-gas breakthrough point, that is, when water exited through the gas outlet, the advancing meniscus was no longer stationary, and the slug lengths decreased exponentially. The rates of decrease of the liquid slug length during separation were accurately estimated by the model, and the calculated liquid-to-gas breakthrough pressures agreed with experimental measurements.

Russo A, Durán-Olivencia MA, Kalliadasis S,
et al., 2019, Macroscopic relations for microscopic properties at the interface between solid substrates and dense fluids, *Journal of Chemical Physics*, Vol: 150, ISSN: 0021-9606

Strongly confined fluids exhibit inhomogeneous properties due to atomistic structuring in close proximity to a solid surface. State variables and transport coefficients at a solid-fluid interface vary locally and become dependent on the properties of the confining walls. However, the precise mechanisms for these effects are not known as of yet. Here, we make use of nonequilibrium molecular dynamics simulations to scrutinize the local fluid properties at the solid-fluid interface for a range of surface conditions and temperatures. We also derive microscopic relations connecting fluid viscosity and density profiles for dense fluids. Moreover, we propose empirical ready-to-use relations to express the average density and viscosity in the channel as a function of temperature, wall interaction strength, and bulk density or viscosity. Such relations are key to technological applications such as micro-/nanofluidics and tribology but also natural phenomena.

Hatipogullari M, Wylock C, Pradas M,
et al., 2019, Contact angle hysteresis in a microchannel: Statics, *Physical Review Fluids*, Vol: 4, ISSN: 2469-990X

We study contact angle hysteresis in a chemically heterogeneous microchannel by tracking static meniscus configurations in the microchannel upon varying the volume of liquid. We first construct a graphical force balance similar to a previous approach by Joanny and de Gennes for this system, though here with a straight contact line. It is shown that hysteresis is induced by wettability gradients above a finite threshold value. This is also visualized in a phase-plane plot enabling to easily predict stick-slip events of the contact line and the occurrence of hysteresis. Above the threshold and for nonoverlapping Gaussian defects, we find good agreement with the expressions by Joanny and de Gennes for the hysteresis amplitude induced by a dilute system of defects. In particular, the hysteresis amplitude is found to be proportional to the square of the defect force and to the defect concentration. For a model sinusoidal heterogeneity, decreasing the ratio between the heterogeneity wavelength and the microchannel gap size brings the system from a subthreshold regime, to a stick-slip dominated regime, and finally to a regime with a quasiconstant advancing and receding angle. In the latter case, the hysteresis amplitude is found to be proportional to the defect force. We also consider an unusual heterogeneity for which the gradients of increasing and decreasing wettability are different. In such a situation breaking the left/right symmetry, whether or not hysteresis is observed will depend on the side the liquid enters the microchannel.

Aymard B, Vaes U, Pradas M,
et al., 2019, A linear, second-order, energy stable, fully adaptive finite element method for phase-field modelling of wetting phenomena, *Journal of Computational Physics: X*, Vol: 2, ISSN: 2590-0552

We propose a new numerical method to solve the Cahn-Hilliard equation coupled with non-linear wetting boundary conditions. We show that the method is mass-conservative and that the discrete solution satisfies a discrete energy law similar to the one satisfied by the exact solution. We perform several tests inspired by realistic situations to verify the accuracy and performance of the method: wetting of a chemically heterogeneous substrate in three dimensions, wetting-driven nucleation in a complex two-dimensional domain and three-dimensional diffusion through a porous medium.

Gomes SN, Kalliadasis S, Pavliotis GA,
et al., 2019, Dynamics of the Desai-Zwanzig model in multiwell and random energy landscapes, *Physical Review E*, Vol: 99, ISSN: 2470-0045

We analyze a variant of the Desai-Zwanzig model [J. Stat. Phys. 19, 1 (1978)]. In particular, we study stationary states of the mean field limit for a system of weakly interacting diffusions moving in a multiwell potential energy landscape, coupled via a Curie-Weiss type (quadratic) interaction potential. The location and depth of the local minima of the potential are either deterministic or random. We characterize the structure and nature of bifurcations and phase transitions for this system, by means of extensive numerical simulations and of analytical calculations for an explicitly solvable model. Our numerical experiments are based on Monte Carlo simulations, the numerical solution of the time-dependent nonlinear Fokker-Planck (McKean-Vlasov) equation, the minimization of the free-energy functional, and a continuation algorithm for the stationary solutions.

Durán-Olivencia MA, Gvalani RS, Kalliadasis S,
et al., 2019, Instability, rupture and fluctuations in thin liquid films: Theory and computations, *Journal of Statistical Physics*, Vol: 174, Pages: 579-604, ISSN: 0022-4715

Thin liquid films are ubiquitous in natural phenomena and technological applications. They have been extensively studied via deterministic hydrodynamic equations, but thermal fluctuations often play a crucial role that needs to be understood. An example of this is dewetting, which involves the rupture of a thin liquid film and the formation of droplets. Such a process is thermally activated and requires fluctuations to be taken into account self-consistently. In this work we present an analytical and numerical study of a stochastic thin-film equation derived from first principles. Following a brief review of the derivation, we scrutinise the behaviour of the equation in the limit of perfectly correlated noise along the wall-normal direction, as opposed to the perfectly uncorrelated limit studied by Grün et al. (J Stat Phys 122(6):1261–1291, 2006). We also present a numerical scheme based on a spectral collocation method, which is then utilised to simulate the stochastic thin-film equation. This scheme seems to be very convenient for numerical studies of the stochastic thin-film equation, since it makes it easier to select the frequency modes of the noise (following the spirit of the long-wave approximation). With our numerical scheme we explore the fluctuating dynamics of the thin film and the behaviour of its free energy in the vicinity of rupture. Finally, we study the effect of the noise intensity on the rupture time, using a large number of sample paths as compared to previous studies.

Savva N, Groves D, Kalliadasis S, 2019, Droplet dynamics on chemically heterogeneous substrates, *Journal of Fluid Mechanics*, Vol: 859, Pages: 321-361, ISSN: 0022-1120

Slow droplet motion on chemically heterogeneous substrates is considered analytically and numerically. We adopt the long-wave approximation which yields a single partial differential equation for the droplet height in time and space. A matched asymptotic analysis in the limit of nearly circular contact lines and vanishingly small slip lengths yields a reduced model consisting of a set of ordinary differential equations for the evolution of the Fourier harmonics of the contact line. The analytical predictions are found, within the domain of their validity, to be in good agreement with the solutions to the governing partial differential equation. The limitations of the reduced model when the contact line undergoes stronger deformations are partially lifted by proposing a hybrid scheme which couples the results of the asymptotic analysis with the boundary integral method. This approach improves the agreement with the governing partial differential equation, but at a computational cost which is significantly lower compared to that required for the full problem.

Schmuck M, Pavliotis GA, Kalliadasis S, 2019, Recent advances in the evolution of interfaces: Thermodynamics, upscaling, and universality, *Computational Materials Science*, Vol: 156, Pages: 441-451, ISSN: 0927-0256

We consider the evolution of interfaces in binary mixtures permeating strongly heterogeneous systems such as porous media. To this end, we first review available thermodynamic formulations for binary mixtures based on general reversible-irreversible couplings and the associated mathematical attempts to formulate a non-equilibrium variational principle in which these non-equilibrium couplings can be identified as minimizers. Based on this, we investigate two microscopic binary mixture formulations fully resolving heterogeneous/perforated domains: (a) a flux-driven immiscible fluid formulation without fluid flow; (b) a momentum-driven formulation for quasi-static and incompressible velocity fields. In both cases we state two novel, reliably upscaled equations for binary mixtures/multiphase fluids in strongly heterogeneous systems by systematically taking thermodynamic features such as free energies into account as well as the system's heterogeneity defined on the microscale such as geometry and materials (e.g. wetting properties). In the context of (a), we unravel a universality with respect to the coarsening rate due to its independence of the system's heterogeneity, i.e. the well-known O(t1/3)-behaviour for homogeneous systems holds also for perforated domains. Finally, the versatility of phase field equations and their thermodynamic foundation relying on free energies, make the collected recent developments here highly promising for scientific, engineering and industrial applications for which we provide an example for lithium batteries.

Lin T-S, Tseluiko D, Blyth MG,
et al., 2018, Continuation methods for time-periodic travelling-wave solutions to evolution equations, *Applied Mathematics Letters*, Vol: 86, Pages: 291-297, ISSN: 0893-9659

A numerical continuation method is developed to follow time-periodic travelling-wave solutions of both local and non-local evolution partial differential equations (PDEs). It is found that the equation for the speed of the moving coordinate can be derived naturally from the governing equations together with a condition that breaks the translational symmetry. The derived system of equations allows one to follow the branch of travelling-wave solutions as well as solutions that are time-periodic in a frame of reference travelling at a constant speed. Finally, we show as an example the bifurcation and stability analysis of single and double-pulse waves in long-wave models of electrified falling films.

Blyth MG, Tseluiko D, Lin T-S,
et al., 2018, Two-dimensional pulse dynamics and the formation of bound states on electrified falling films, *Journal of Fluid Mechanics*, Vol: 855, Pages: 210-235, ISSN: 0022-1120

The flow of an electrified liquid film down an inclined plane wall is investigated with the focus on coherent structures in the form of travelling waves on the film surface, in particular, single-hump solitary pulses and their interactions. The flow structures are analysed first using a long-wave model, which is valid in the presence of weak inertia, and second using the Stokes equations. For obtuse angles, gravity is destabilising and solitary pulses exist even in the absence of an electric field. For acute angles, spatially non-uniform solutions exist only beyond a critical value of the electric field strength; moreover, solitary-pulse solutions are present only at sufficiently high supercritical electric-field strengths. The electric field increases the amplitude of the pulses, can generate recirculation zones in the humps and alters the far-field decay of the pulse tails from exponential to algebraic with a significant impact on pulse interactions. A weak-interaction theory predicts an infinite sequence of bound-state solutions for non-electrified flow, and a finite set for electrified flow. The existence of single-hump pulse solutions and two-pulse bound states is confirmed for the Stokes equations via boundary-element computations. In addition, the electric field is shown to trigger a switch from absolute to convective instability, thereby regularising the dynamics, and this is confirmed by time-dependent simulations of the long-wave model.

Charogiannis A, Denner F, Van Wachem B,
et al., 2018, Experimental investigations of liquid falling films flowing under an inclined planar substrate, *Physical Review Fluids*, Vol: 3, ISSN: 2469-990X

We report on detailed and systematic experiments of thin liquid films flowing as a result of the action of gravity under an inverted planar substrate. A measurement technique based on planar laser-induced fluorescence (PLIF) was developed and applied to a range of such flows in order to provide detailed space- and time-resolved film-height information. Specifically, the experimental campaign spanned three inclination angles (β=−15∘, −30∘, and −45∘, in all cases negative with respect to the vertical), two water-glycerol solutions (with Kapitza numbers of Ka=13.1 and 330), and flow Reynolds numbers covering the range Re=0.6–193. The collection optics were arranged so as to interrogate a spanwise section of the flow extending about 40mm symmetrically on either side the centerline of the film span (80mm in total), at a distance 330 mm downstream of the flow inlet. A range of flow regimes, typically characterized by strong three dimensionality and pronounced rivulet formation, were observed depending on the imposed inlet flow conditions. In the lower liquid Kapitza number Ka(=13.1) flows and depending on the flow Re, the free surface of the film was populated by smooth rivulets or regular sequences of solitary pulses that traveled over the rivulets. In the higher liquid Ka(=330) flows, rivulets were observed typically above Re≈30, depending also on the inclination angle, and grew in amplitude until quasi-two-dimensional fronts developed intermittently that were associated with distinct thin-film regions of varying length and frequency. These regions are of particular interest as they are expected to affect strongly the heat and mass transfer capabilities of these flows. The occurrence of the fronts was more pronounced, with higher wave frequencies, in film flows at smaller negative inclinations for the same flow Re. The rivulet amplitude was found to increase at larger inclinations for the same Re and showed a nonmonotonic trend with in

Duran-Olivencia M, Yatsyshin P, Kalliadasis S,
et al., 2018, General framework for nonclassical nucleation, *New Journal of Physics*, Vol: 20, ISSN: 1367-2630

A great deal of experimental evidence suggests that a wide spectrum of phase transitions occur in a multistage manner via the appearance and subsequent transformation of intermediate metastable states. Such multistage mechanisms cannot be explained within the realm of the classical nucleation framework. Hence, there is a strong need to develop new theoretical tools to explain the occurrence and nature of these ubiquitous intermediate phases. Here we outline a unified and self-consistent theoretical framework to describe both classical and nonclassical nucleation. Our framework provides a detailed explanation of the whole multistage nucleation pathway showing in particular that the pathway involves a single energy barrier and it passes through a dense phase, starting from a low-density initial phase, before reaching the final stable state. Moreover, we demonstrate that the kinetics of matter inside subcritical clusters favors the formation of nucleation clusters with an intermediate density, i.e. nucleation precursors. Remarkably, these nucleation precursors are not associated with a local minimum of the thermodynamic potential, as commonly assumed in previous phenomenological approaches. On the contrary, we find that they emerge due to the competition between thermodynamics and kinetics of cluster formation. Thus, the mechanism uncovered for the formation of intermediate phases can be used to explain recently reported experimental findings in crystallization: up to now such phases were assumed a consequence of some complex energy landscape with multiple energy minima. Using fundamental concepts from kinetics and thermodynamics, we provide a satisfactory explanation for the so-called nonclassical nucleation pathways observed in experiments.

Braga C, Smith E, Nold A,
et al., 2018, The pressure tensor across a liquid-vapour interface, *Journal of Chemical Physics*, Vol: 149, ISSN: 0021-9606

Inhomogeneous fluids exhibit physical properties that are neither uniform nor isotropic. The pressure tensor is a case in point, key to the mechanical description of the interfacial region. Kirkwood and Buff and, later, Irving and Kirkwood, obtained a formal treatment based on the analysis of the pressure across a planar surface [J. G. Kirkwood and F. P. Buff, J. Chem. Phys. 17(3), 338 (1949); J. H. Irving and J. G. Kirkwood, J. Chem. Phys. 18, 817 (1950)]. We propose a generalisation of Irving and Kirkwood’s argument to fluctuating, non-planar surfaces and obtain an expression for the pressure tensor that is not smeared by thermal fluctuations at the molecular scale and corresponding capillary waves [F. P. Buff et al., Phys. Rev. Lett. 15, 621–623 (1965)]. We observe the emergence of surface tension, defined as an excess tangential stress, acting exactly across the dividing surface at the sharpest molecular resolution. The new statistical mechanical expressions extend current treatments to fluctuating inhomogeneous systems far from equilibrium.

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