Experience
Industry
Vortico
Co-Founder
Málaga, Spain
Jan 2022 - Present
Helping businesses enhance and expand their AI and technology capabilities.
Adevinta
Machine Learning Enabler
Berlin, Germany
Mar 2023 - Present
Machine Learning OPs: Help the company with their strategic move towards full-adoption of AI. Usage of industry standards, build template repositories, systematise ML workflows with KubeFlow, and other MLOps standards. Machine Learning Enabler: Deliver recurrent talks, and live coding sessions about ML Engineering in Action, besides designing a standard route for the productionalisation of ML projects.
Stratyfy
Machine Learning Specialist
New York, USA
Jul 2022 - Mar 2023
Machine Learning: Build and productionalise ML models as APIs for credit-card fraud detection. Data Engineering: Design and implement Data Lake of the company.
Proportunity
Senior Data Manager
London, UK
Jun 2021 - Mar 2023
Machine Learning: Productionalising ML models as production-ready and low-latency APIs. Research about house market in the UK to assess investing decisions. Data Engineering: Design and implement the Data Lake of the company, and maintain data pipelines.
Allfunds Bank
Head of Data Innovation Lab
Madrid, Spain
Mar 2020 - Jun 2021
Management: Executive board member of the monthly IT & Operational board. Lead a team of 8 engineers and data scientists. Budget management and forecasting. Machine Learning: Design-develop-release ML solutions positioning the bank amongst top FinTech leaders. Envisage, research and enable new data-driven/ML revenue streams. Digital transformation: Lead and execute the integration of new acquired fund platforms (Credit Suisse Invest Lab, with more than €350 billion AUAs).
Allfunds Bank
Lead Cloud Solutions Architect
Madrid, Spain
May 2019 - Mar 2020
Cloud Computing & Architecture: Design and implementation of rebate calculation ecosystem (+€750 billion AUAs). Design and develop cloud solutions architecture of the core banking system. Migration from legacy mainframe systems to Google Cloud. Data Analysis: Quantitative and machine-learning models for anti-money laundering detection and prevention. Daily calculation and reporting of the flows and volumes. Datalake: Implementation and maintenance of infrastructure, data acquisition pipelines and ETLs from DB2 databases to Google Cloud ecosystem.
Ebury
Senior Quantitative Analyst
London, UK
May 2018 - May 2019
Machine Learning: ML forecasting company’s liquidity risks and hedging strategies. Design and implement ML forecaster of clients’ behaviour to price financial derivatives. Quant Finance: Monte Carlo simulations for pricing financial derivatives in combination with ML forecasting clients behaviour. Develop quantitative treasury system to daily track mark-to-market of company’s portfolio for reconciliation purposes.
Academic
Lecturer in Computer Science & Machine Learning
Department of Telematics & Computer Science, Comillas Pontifical University
Madrid, Spain
Sep 2021 - Sep 2022
Lecturer of the subjects: Machine Learning for Engineers; Architecture of Network Systems: Cloud Computing & Big Data; Social Analytics.
Honorary Research Fellow
Department of Chemical Engineering, Imperial College London
London, UK
May 2018 - Present
Co-direct MSc and PhD projects on the use of ML and data-driven frameworks to efficiently simulate and accurately predict complex systems, using families of continuous deep architectures, neural ODEs and physics-informed neural networks. Research on the application of ML to complex systems, data-driven modelling, statistical physics, and financial markets.
Postdoctoral Research Associate
Department of Chemical Engineering, Imperial College London
London, UK
Oct 2014 - May 2018
Research on usage of deep learning used as closure for irreversible processes within the context of stochastic processes; Derivation of a general framework for non-classical nucleation; Molecular dynamics study of the macroscopic relations for microscopic properties at the interface between solid substrates and dense fluids; Study of instability, rupture and fluctuations in thin liquid films with stochastic partial differential equations; Unification of classical nucleation theories via unified Ito-Stratonovich stochastic equation; Derivation of a novel dynamical density functional theory for orientable colloids including inertia and hydrodynamic interactions; Derivation of a general framework for fluctuating dynamic density functional theory.
Graduate Teaching Assistant
Department of Chemical Engineering, Imperial College London
London, UK
Sep 2015 - May 2016
Teaching assistant of the subject: Properties of Matter CE1-09. Nominated twice for the Student Academic Choice Award, Imperial College Union’s flagship event for empowering students to recognise, reward and celebrate excellence amongst College staff.
Education
PhD Statistical Physics
Menéndez Pelayo International University
Madrid, Spain
Mar 2015
Doctoral Programme in Science and Technology. Thesis: Non-classical Nucleation Theories (Summa Cum Laude)
MSc. International Financial Markets
Spanish National University for Distance Education (UNED)
Madrid, Spain
Jun 2018
Thesis: Big Data & VaR calculations
MSc. Crystallography and Crystallisation
Menéndez Pelayo International University
Madrid, Spain
Jul 2011
Thesis: A Brownian model for crystal nucleation
MSc. Medical Physics
University of Seville
Sevilla, Spain
Jul 2010
Thesis: Introduction to the theory of P-systems and their application to the study of stochastic processes.
BSc.+MSc. Physics
University of Seville
Sevilla, Spain
Jul 2009
Research
Projects
Machine learning for modelling of complex multiscale systems with applications to financial markets
Imperial College London, UK
Co-director - PhD Research Project
Sep 2021 - Present
SMART-water: Selecting precipitation inhibitors using machine learning for sustainable water technologies
Spanish National Research Council (CSIC), Spain
Co-director - PhD Research Project
Apr 2023 - Present
Tool for automatic extraction of data from insurance policies
Universidad Pontificia Comillas, Spain
Director - MSc Research Project
Sep 2021 - Sep 2022
Single and Multi-Phase Fluids: From Atomistic to Continuum Simulations
Imperial College London, UK
Co-director - PhD Research Project
Sep 2016 - Sep 2021
Data-driven ML modelling and prediction of complex systems
Imperial College London, UK
Co-director - MSc Research Project
Sep 2020 - Sep 2021
Numerical simulations of phase transitions and nucleation processes
Imperial College London, UK
Co-director - MSc Research Project
Sep 2017 - Sep 2018
Phase transitions and nucleation processes using density-functional theory
Imperial College London, UK
Co-director - MSc Research Project
Sep 2015 - Sep 2016
Refereed publications
Forecasting with an N-dimensional Langevin equation and a neural-ordinary differential equation
Chaos 34, 043105 (2024)
https://doi.org/10.1063/5.0189402Accurate prediction of electricity day-ahead prices is essential in competitive electricity markets. Although stationary electricity-price forecasting techniques have received considerable attention, research on non-stationary methods is comparatively scarce, despite the common prevalence of non-stationary features in electricity markets. Specifically, existing non-stationary techniques will often aim to address individual non-stationary features in isolation, leaving aside the exploration of concurrent multiple non-stationary effects. Our overarching objective here is the formulation of a framework to systematically model and forecast non-stationary electricity-price time series, encompassing the broader scope of non-stationary behavior. For this purpose, we develop a data-driven model that combines an N-dimensional Langevin equation (LE) with a neural-ordinary differential equation (NODE). The LE captures fine-grained details of the electricity-price behavior in stationary regimes but is inadequate for non-stationary conditions. To overcome this inherent limitation, we adopt a NODE approach to learn, and at the same time predict, the difference between the actual electricity-price time series and the simulated price trajectories generated by the LE. By learning this difference, the NODE reconstructs the non-stationary components of the time series that the LE is not able to capture. We exemplify the effectiveness of our framework using the Spanish electricity day-ahead market as a prototypical case study. Our findings reveal that the NODE nicely complements the LE, providing a comprehensive strategy to tackle both stationary and non-stationary electricity-price behavior. The framework's dependability and robustness is demonstrated through different non-stationary scenarios by comparing it against a range of basic naïve methods.
Physics-informed Bayesian inference of external potentials in classical density-functional theory
J. Chem. Phys 159:104109 (2023)
https://doi.org/10.1063/5.0146920The 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 capillarity, to name a few.
Determining the operational window of green antiscalants: A case study for calcium sulfate
Desalination 544:116128 (2022)
https://doi.org/10.1016/j.desal.2022.116128The detrimental effects of inorganic scaling in industrial and domestic applications are often mitigated with scale inhibitors. Increasing environmental awareness and stringent regulations require developing more sustainable antiscalants. Testing of suitable candidates is often the rate-limiting step in development cycles, therefore we developed a high-throughput methodology to rapidly evaluate the antiscaling potential of new additives under different application conditions. Using this method we determined the performance of two potential green additives – a chelating agent and a threshold inhibitor – in delaying CaSO4 precipitation over a wide range of supersaturations, temperatures and salinities. The threshold inhibitor strongly delayed CaSO4 scaling, but its performance is highly dependent on the physicochemical conditions, with the appropriate application window comprising low salinities and mild temperatures. In contrast, the chelating agent showed a lower inhibiting capacity, but its performance remained relatively constant throughout the entire matrix of physicochemical conditions. Noteworthy, we also observed that at intermediate salinities the absolute induction time for CaSO4 precipitation is dramatically prolonged, offering a sustainable strategy to mitigate scaling. Overall, our method allows simultaneously benchmarking the scaling kinetics and testing the scale-inhibiting performance of additives, providing a direct route to a more rational design of antiscaling technologies.
Multistep nucleation compatible with a single energy barrier: catching the non-classical culprit
Faraday Discussions 235: 95-108 (2022)
https://doi.org/10.1039/D1FD00092FIn this work we link experimental results of SrSO4 precipitation with a nucleation model based on mesoscopic nucleation theory (MeNT) to stride towards a cohesive view of the nucleation process that integrates both classical and non-classical views. When SrCl2 and Na2SO4 are co-titrated at slow dosing rates, time-resolved turbidity, conductivity and ion-specific data reveal that the initial stage of the nucleation process is driven by neutral species, i.e. ion-pairs or larger, akin to the prenucleation cluster model. However, when co-titrations are conducted at higher rates, the onset of nucleation is dominated by the consumption of free ions, akin to the explanation provided by classical nucleation theory (CNT). The occurrence of both mechanisms for the same system is explained by a toy model that includes both the thermodynamics (consisting of a single energy barrier) and kinetics of cluster formation formally obtained from MeNT. This gives rise to an effective energy barrier exhibiting a local intermediate minimum, which does not originate from a minimum in the thermodynamic free energy. Rather, it is associated with an increased probability of observing a specific class (in terms of size/density) of precursor clusters due to their slower kinetics. At high supersaturations this minimum in the kinetics of cluster formation becomes less pronounced and the effective barrier is also significantly lowered. Consequently, the probability of observing an intermediate state is blurred and we recover a nucleation pathway more closely following the one envisaged by the classical model. Thus, our model is capable of capturing both single and multistep nucleation mechanisms observed experimentally considering only a single energy barrier.
Machine Learning Memory Kernels as Closure for Non-Markovian Stochastic Processes
IEEE Trans. Neural Netw. Learn. Syst. (2022)
https://doi.org/10.1109/TNNLS.2022.3210695Finding 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.
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
medRxiv (2021)
https://doi.org/10.1101/2021.04.15.21255510The 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.
Understanding soaring coronavirus cases and the effect of contagion policies in the UK
Vaccines 9(7):735 (2021)
https://doi.org/10.3390/vaccines9070735The 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 on the spreading of the virus. We are able to reproduce the waves of infection occurred in the UK with a unique transmission rate, suggesting that the new SARS-CoV-2 variant is as transmissible as previous strains. Our findings indicate 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. For effective mitigation, it is critical that the public keeps on high alert until vaccination reaches a critical threshold.
Memory effects in dynamic density functional theory with fluctuation: Theory and simulations
J. Phys. A: Math. Theor. 53:445007 (2020)
https://doi.org/10.1088/1751-8121/ab9e8dThis 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. Finally, we illustrate the influence of non-Markovian effects on the dynamics of non-linear chemically reacting fluid systems with a detailed study of memory-driven Turing patterns
Classical Density Functional Theory and Nanofluidics: Adsorption and the Interface Binding Potential
21st Century Nanoscience – A Handbook [Chapter] (2020)
https://doi.org/10.1201/9780429347313This chapter discusses the prototypical problem of droplet adsorption on a flat surface and discuss the application of classical density functional theory (DFT) to the computation of drop shapes and contact angles. It highlights a connection to the well-known Derjaguin’s disjoining pressure approach and demonstrates how DFT can be used rationally and systematically to determine an approximate interface binding potential, whose derivative gives the disjoining pressure. Interest in wetting has been rapidly growing over the past few decades across different applied and theoretical fields of study. On the applied front, it plays a crucial role in many technological processes, from the vapor-liquid-solid growth of nanowires, to labs-on-chip and to applications in superhydrophobicity and nanofluidics. The fact that intermolecular interactions at small scales are non-local, as well as the typical presence of a wide range of length scales in problems of wetting, spurs on theoreticians to develop appropriate microscopic approaches.
A finite-volume method for fluctuating dynamical density functional theory
J. Comput. Phys. 412:109796 (2020)
https://doi.org/10.1016/j.jcp.2020.109796We 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.
Macroscopic relations for microscopic properties at the interface between solid substrates and dense fluids
J. Chem. Phys. 150:214705 (2019)
https://doi.org/10.1063/1.5094911Strongly 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.
General framework for nonclassical nucleation
New J. Phys. 20:083019 (2018)
https://10.1088/1367-2630/aad170A 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.
Microscopic aspects of wetting using classical density-functional theory
J. Phys. Condens. Matter 30:274003 (2018)
https://doi.org/10.1088/1361-648X/aabf3bWetting is a rather efficient mechanism for nucleation of a phase (typically liquid) on the interface between two other phases (typically solid and gas). In many experimentally accessible cases of wetting, the interplay between the substrate structure, and the fluid–fluid and fluid–substrate intermolecular interactions brings about an entire 'zoo' of possible fluid configurations, such as liquid films with a thickness of a few nanometers, liquid nanodrops and liquid bridges. These fluid configurations are often associated with phase transitions occurring at the solid–gas interface and at lengths of just several molecular diameters away from the substrate. In this special issue article, we demonstrate how a fully microscopic classical density-functional framework can be applied to the efficient, rational and systematic exploration of the rich phase space of wetting phenomena. We consider a number of model prototype systems such as wetting on a planar wall, a chemically patterned wall and a wedge. Through density-functional computations we demonstrate that for these simply structured substrates the behaviour of the solid–gas interface is already highly complex and non-trivial.
Instability, rupture and fluctuations in thin liquid films: Theory and computations
J. Stat. Phys. 174:579–604 (2018)
https://doi.org/10.1007/s10955-018-2200-0Thin 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.
General framework for fluctuating dynamic density functional theory
New J. Phys. 19:123022 (2017)
https://doi.org/10.1088/1367-2630/aa9041We introduce a versatile bottom-up derivation of a formal theoretical framework to describe (passive) soft-matter systems out of equilibrium subject to fluctuations. We provide a unique connection between the constituent-particle dynamics of real systems and the time evolution equation of their measurable (coarse-grained) quantities, such as local density and velocity. The starting point is the full Hamiltonian description of a system of colloidal particles immersed in a fluid of identical bath particles. Then, we average out the bath via Zwanzig's projection-operator techniques and obtain the stochastic Langevin equations governing the colloidal-particle dynamics. Introducing the appropriate definition of the local number and momentum density fields yields a generalisation of the Dean–Kawasaki (DK) model, which resembles the stochastic Navier–Stokes description of a fluid. Nevertheless, the DK equation still contains all the microscopic information and, for that reason, does not represent the dynamical law of observable quantities. We address this controversial feature of the DK description by carrying out a nonequilibrium ensemble average. Adopting a natural decomposition into local-equilibrium and nonequilibrium contribution, where the former is related to a generalised version of the canonical distribution, we finally obtain the fluctuating-hydrodynamic equation governing the time-evolution of the mesoscopic density and momentum fields. Along the way, we outline the connection between the ad hoc energy functional introduced in previous DK derivations and the free-energy functional from classical density-functional theory. The resultant equation has the structure of a dynamical density-functional theory (DDFT) with an additional fluctuating force coming from the random interactions with the bath. We show that our fluctuating DDFT formalism corresponds to a particular version of the fluctuating Navier–Stokes equations, originally derived by Landau and Lifshitz. Our framework thus provides the formal apparatus for ab initio derivations of fluctuating DDFT equations capable of describing the dynamics of soft-matter systems in and out of equilibrium.
Lead(II) soaps: Crystal structures, polymorphism, solid and liquid mesophases
Phys. Chem. Chem. Phys. 19: 16907-16917 (2017)
https://doi.org/10.1039/C7CP02351KThe long-chain members of the lead(II) alkanoate series or soaps, from octanoate to octadecanoate, have been thoroughly characterized by means of XRD, PDF analysis, DSC, FTIR, ssNMR and other techniques, in all their phases and mesophases. The crystal structures at room temperature of all of the members of the series are now solved, showing the existence of two polymorphic forms in the room temperature crystal phase, different to short and long-chain members. Only nonanoate and decanoate present both forms, and this polymorphism is proven to be monotropic. At higher temperature, these compounds present a solid mesophase, defined as rotator, a liquid crystal phase and a liquid phase, all of which have a similar local arrangement. Since some lead(II) soaps appear as degradation compounds in oil paintings, the solved crystal structures of lead(II) soaps can now be used as fingerprints for their detection using X-ray diffraction. Pair distribution function analysis on these compounds is very similar in the same phases and mesophases for the different members, showing the same short range order. This observation suggests that this technique could also be used in the detection of these compounds in disordered phases or in the initial stages of formation in paintings.
Dynamical density functional theory for orientable colloids including inertia and hydrodynamic interactions
J. Stat. Phys. 164:785–809 (2016)
https://doi.org/10.1007/s10955-016-1545-5Over the last few decades, classical density-functional theory (DFT) and its dynamic extensions (DDFTs) have become powerful tools in the study of colloidal fluids. Recently, previous DDFTs for spherically-symmetric particles have been generalised to take into account both inertia and hydrodynamic interactions, two effects which strongly influence non-equilibrium properties. The present work further generalises this framework to systems of anisotropic particles. Starting from the Liouville equation and utilising Zwanzig’s projection-operator techniques, we derive the kinetic equation for the Brownian particle distribution function, and by averaging over all but one particle, a DDFT equation is obtained. Whilst this equation has some similarities with DDFTs for spherically-symmetric colloids, it involves a translational-rotational coupling which affects the diffusivity of the (asymmetric) particles. We further show that, in the overdamped (high friction) limit, the DDFT is considerably simplified and is in agreement with a previous DDFT for colloids with arbitrary-shape particles.
Step crowding effects dampen the stochasticity of crystal growth kinetics
Phys. Rev. Lett. 116–015501 (2016)
https://doi.org/10.1103/PhysRevLett.116.015501Crystals grow by laying down new layers of material which can either correspond in size to the height of one unit cell (elementary steps) or multiple unit cells (macrosteps). Surprisingly, experiments have shown that macrosteps can grow under conditions of low supersaturation and high impurity density such that elementary step growth is completely arrested. We use atomistic simulations to show that this is due to two effects: the fact that the additional layers bias fluctuations in the position of the bottom layer towards growth and by a transition, as step height increases, from a 2D to a 3D nucleation mechanism.
Unification of classical nucleation theories via a unified Ito-Stratonovich stochastic equation
Phys. Rev. E 92:032407 (2015)
https://doi.org/10.1103/PhysRevE.92.032407Classical nucleation theory (CNT) is the most widely used framework to describe the early stage of first-order phase transitions. Unfortunately, the different points of view adopted to derive it yield different kinetic equations for the probability density function, e.g., Zeldovich-Frenkel or Becker-Döring-Tunitskii equations. Starting from a phenomenological stochastic differential equation, a unified equation is obtained in this work. In other words, CNT expressions are recovered by selecting one or another stochastic calculus. Moreover, it is shown that the unified CNT thus obtained produces the same Fokker-Planck equation as that from a recent update of CNT [J.F. Lutsko and M.A. Durán-Olivencia, J. Chem. Phys. 138, 244908 (2013)] when mass transport is governed by diffusion. Finally, we derive a general induction-time expression along with specific approximations of it to be used under different scenarios, in particular, when the mass-transport mechanism is governed by direct impingement, volume diffusion, surface diffusion, or interface transfer.
A two-parameter extension of classical nucleation theory
J. Phys. Condens. Matter 27:235101 (2015)
https://doi.org/10.1088/0953-8984/27/23/235101A two-variable stochastic model for diffusion-limited nucleation is developed using a formalism derived from fluctuating hydrodynamics. The model is a direct generalization of the standard classical nucleation theory (CNT). The nucleation rate and pathway are calculated in the weak-noise approximation and are shown to be in good agreement with direct numerical simulations for the weak-solution/strong-solution transition in globular proteins. We find that CNT underestimates the time needed for the formation of a critical cluster by two orders of magnitude and that this discrepancy is due to the more complex dynamics of the two variable model and not, as often is assumed, a result of errors in the estimation of the free energy barrier.
Mesoscopic nucleation theory for confined systems: a one-parameter model
Phys. Rev. E 91:022402 (2015)
https://doi.org/10.1103/PhysRevE.91.022402Classical nucleation theory has been recently reformulated based on fluctuating hydrodynamics [J.F. Lutsko and M.A. Durán-Olivencia, Classical nucleation theory from a dynamical approach to nucleation, J. Chem. Phys. 138, 244908 (2013).]. The present work extends this effort to the case of nucleation in confined systems such as small pores and vesicles. The finite available mass imposes a maximal supercritical cluster size and prohibits nucleation altogether if the system is too small. We quantity the effect of system size on the nucleation rate. We also discuss the effect of relaxing the capillary-model assumption of zero interfacial width resulting in significant changes in the nucleation barrier and nucleation rate.
Crystal growth cessation revisited – the physical basis of step pinning
Cryst. Growth Des. 14:6129–6134 (2014)
https://doi.org/10.1021/cg501307yThe growth of crystals from solution is a fundamental process of relevance to such diverse areas as X-ray diffraction structural determination and the role of mineralization in living organisms. A key factor determining the dynamics of crystallization is the effect of impurities on step growth. For over 50 years, all discussions of impurity–step interaction have been framed in the context of the Cabrera–Vermilyea (CV) model for step blocking, which has nevertheless proven difficult to validate experimentally. Here we report on extensive computer simulations which clearly falsify the CV model, suggesting a more complex picture. While reducing to the CV result in certain limits, our approach is more widely applicable, encompassing nontrivial impurity–crystal interactions, mobile impurities, and negative growth, among others.
Observing classical nucleation theory at work by monitoring phase transitions with molecular precision
Nat. Commun. 5:5598 (2014)
https://doi.org/10.1038/ncomms6598It is widely accepted that many phase transitions do not follow nucleation pathways as envisaged by the classical nucleation theory. Many substances can traverse intermediate states before arriving at the stable phase. The apparent ubiquity of multi-step nucleation has made the inverse question relevant: does multistep nucleation always dominate single-step pathways? Here we provide an explicit example of the classical nucleation mechanism for a system known to exhibit the characteristics of multi-step nucleation. Molecular resolution atomic force microscopy imaging of the two-dimensional nucleation of the protein glucose isomerase demonstrates that the interior of subcritical clusters is in the same state as the crystalline bulk phase. Our data show that despite having all the characteristics typically associated with rich phase behaviour, glucose isomerase 2D crystals are formed classically. These observations illustrate the resurfacing importance of the classical nucleation theory by re-validating some of the key assumptions that have been recently questioned.
Classical nucleation theory from a dynamical approach to nucleation
J. Chem. Phys. 138:244908 (2013)
https://doi.org/10.1063/1.4811490It is shown that diffusion-limited classical nucleation theory (CNT) can be recovered as a simple limit of the recently proposed dynamical theory of nucleation based on fluctuating hydrodynamics. The same framework is also used to construct a more realistic theory in which clusters have finite interfacial width. When applied to the dilute solution/dense solution transition in globular proteins, it is found that the extension gives corrections to the nucleation rate even for the case of small supersaturations due to changes in the monomer distribution function and to the excess free energy. It is also found that the monomer attachment/detachment picture breaks down at high supersaturations corresponding to clusters smaller than about 100 molecules. The results also confirm the usual assumption that most important corrections to CNT can be achieved by means of improved estimates of the free energy barrier. The theory also illustrates two topics that have received considerable attention in the recent literature on nucleation: the importance sub-dominant corrections to the capillary model for the free energy and of the correct choice of the reaction coordinate.
pH-Responsive Delivery of Doxorubicin from Citrate-Apatite Nanocrystals with Tailored Carbonate Content
Langmuir 29:8213–8221 (2013)
https://doi.org/10.1021/la4008334In this work, the efficiency of bioinspired citrate-functionalized nanocrystalline apatites as nanocarriers for delivery of doxorubicin (DOXO) has been assessed. The nanoparticles were synthesized by thermal decomplexing of metastable calcium/citrate/phosphate solutions both in the absence (Ap) and in the presence (cAp) of carbonate ions. The presence of citrate and carbonate ions in the solution allowed us to tailor the size, shape, carbonate content, and surface chemistry of the nanoparticles. The drug-loading efficiency of the two types of apatite was evaluated by means of the adsorption isotherms, which were found to fit a Langmuir–Freundlich behavior. A model describing the interaction between apatite surface and DOXO is proposed from adsorption isotherms and ζ-potential measurements. DOXO is adsorbed as a dimer by means of a positively charged amino group that electrostatically interacts with negatively charged surface groups of nanoparticles. The drug-release profiles were explored at pHs 7.4 and 5.0, mimicking the physiological pH in the blood circulation and the more acidic pH in the endosome-lysosome intracellular compartment, respectively. After 7 days at pH 7.4, cAp-DOXO released around 42% less drug than Ap-DOXO. However, at acidic pH, both nanoassemblies released similar amounts of DOXO. In vitro assays analyzed by confocal microscopy showed that both drug-loaded apatites were internalized within GTL-16 human carcinoma cells and could release DOXO, which accumulated in the nucleus in short times and exerted cytotoxic activity with the same efficiency. cAp are thus expected to be a more promising nanocarrier for experiments in vivo, in situations where intravenous injection of nanoparticles are required to reach the targeted tumor, after circulating in the bloodstream.
Influence of Charged Polypeptides on Nucleation and Growth of CaCO3 Evaluated by Counterdiffusion Experiments
Cryst. Growth Des. 13: 4426–4433 (2013)
https://doi.org/10.1021/cg400523wMany mineralization processes occur in convection-free conditions. Understanding these processes requires knowledge of crystal nucleation and growth processes in gels or high viscous sol systems. In this work, the crystallization parameters of calcium carbonate in an agarose viscous sol using counterdiffusion crystallization were monitored as a function of time. Additionally, by comparing the precipitation parameters in the high viscous sol entrapping charged polypeptides, namely, poly-l-lysine (pLys), poly-l-aspartate (pAsp), and poly-l-glutamate (pGlu), it was possible to establish the polypeptide capability to inhibit, or eventually promote, the calcium carbonate nucleation and/or crystal growth processes. The polymorphism and morphology of the precipitates indicate that pLys only influences the growth mechanism of calcium carbonate without affecting the nucleation process. On the contrary, pAsp and, to a minor extent, pGlu affect both nucleation and growth. The application of this analysis can be extended to other additives and macromolecules able to affect crystallization processes.
A Brownian model for crystal nucleation
J. Cryst. Growth 380:247–255 (2013)
https://doi.org/10.1016/j.jcrysgro.2013.06.035In this work a phenomenological stochastic differential equation is proposed for modelling the time evolution of the radius of a pre-critical molecular cluster during nucleation (the classical order parameter). Such a stochastic differential equation constitutes the basis for the calculation of the (nucleation) induction time under Kramers' theory of thermally activated escape processes. Considering the nucleation stage as a Poisson rare-event, analytical expressions for the induction time statistics are deduced for both steady and unsteady conditions, the latter assuming the semiadiabatic limit. These expressions can be used to identify the underlying mechanism of molecular cluster formation (distinguishing between homogeneous and heterogeneous nucleation from the nucleation statistics is possible) as well as to predict induction times and induction time distributions. The predictions of this model are in good agreement with experimentally measured induction times at constant temperature, unlike the values obtained from the classical equation, but agreement is not so good for induction time statistics. Stochastic simulations truncated to the maximum waiting time of the experiments confirm that this fact is due to the time constraints imposed by experiments. Correcting for this effect, the experimental and predicted curves fit remarkably well. Thus, the proposed model seems to be a versatile tool to predict cluster size distributions, nucleation rates, (nucleation) induction time and induction time statistics for a wide range of conditions (e.g. time-dependent temperature, supersaturation, pH, etc.) where classical nucleation theory is of limited applicability.
Stochastic formalism for nucleation under unsteady conditions
Acta Cryst. A67, C539 (2011)
https://doi.org/10.1063/1.4768257A Langevin-type stochastic differential equation (LT-SDE) is proposed to model the fluctuating behaviour of the cluster radius in the spherical shape approximation. Indeed, an analytical solution for the probability density function of induction time is obtained not only for steady but also unsteady work of cluster formation. The latter conditions allow for the study of time-dependent (supersaturation, pressure, temperature, etc.) nucleation processes from a stochastic point of view.
Talks and seminars
A data-driven framework for non-stationary complex systems: Blending generalized Langevin and neural ordinary-differential equations
APS March Meeting 2024
Minneapolis, USA
Mar 2024
Memory effects in fluctuating dynamic density-functional theory: theory and simulations
APS Division of Fluid Dynamics Meeting 2021
Arizona, USA
Nov 2021
Myths, facts and limitations of (non-)classical nucleation theory
Seminar at Université Grenoble Alpes - ISTerre
Grenoble, France
May 2020
Reinventing legacy systems in Google Cloud
Google Cloud Financial Services Day
Madrid, Spain
Feb 2020
A finite volume scheme for stochastic PDEs in the context of fluctuating hydrodynamics
APS Division of Fluid Dynamics Meeting 2019
Washington, USA
Nov 2019
Fluctuations in density-functional theory for fluids: Theory and computations
APS March Meeting 2018
California, USA
Mar 2018
Understanding interfacial wetting transitions with classical density functional theory
APS March Meeting 2018
California, USA
Mar 2018
Phase transitions in colloidal fluids: Kinetically or thermodynamically controlled?
APS Division of Fluid Dynamics Meeting 2017
Colorado, USA
Nov 2017
Instability, rupture and fluctuations in thin liquid films: Theory and computations
APS Division of Fluid Dynamics Meeting 2017
Colorado, USA
Nov 2017
Wetting of heterogeneous substrates. A classical density-functional-theory approach
APS Division of Fluid Dynamics Meeting 2017
Colorado, USA
Nov 2017
Non-classical nucleation theory in colloidal fluids: Kinetically persistent precursors
APS March Meeting 2017
Colorado, USA
Mar 2017
Wetting in flatland: Complex interfacial transitions at inhomogeneous solid-gas interfaces
APS March Meeting 2017
Colorado, USA
Mar 2017
Dynamic density functional theory for nucleation: Non-classical predictions of mesoscopic nucleation theory
APS Division of Fluid Dynamics Meeting 2016
Oregon, USA
Nov 2016
Dynamics of two-phase interfaces and surface tensions: A density-functional theory perspective
APS Division of Fluid Dynamics Meeting 2016
Oregon, USA
Nov 2016
Mesoscopic nucleation theory: describing multistep nucleation using fluctuating hydrodynamics
ICL Summer School: Interscale Interactions in Fluid Mechanics and beyond
Imperial College London, UK
Aug 2016
A density functional approach for systems of orientable particles
ICL Summer School: Interscale Interactions in Fluid Mechanics and beyond
Imperial College London, UK
Aug 2016
Dynamical density functional theory for systems of orientational colloids including inertia and hydrodynamic interactions
Challenges in Statistical Mechanics: from Mathematics to Molecular Dynamics to Technological Applications
Imperial College London, UK
Dec 2015
Dynamical density functional theory for arbitrary-shape colloidal fluids including inertia and hydrodynamic interactions
APS Division of Fluid Dynamics Meeting 2015
Massachusetts, USA
Nov 2015
Numerical simulations of the moving contact line problem using a diffuse-interface model
APS Division of Fluid Dynamics Meeting 2015
Massachusetts, USA
Nov 2015