Carlos Monago
ES

Research

My research is concerned with how microscopic molecular dynamics gives rise to effective mesoscopic stochastic dynamics. When a system is coarse-grained, many microscopic degrees of freedom are eliminated. Their influence does not disappear; it reappears as effective noise, friction, mobility, memory, and dissipation. Understanding and estimating these terms is essential for building coarse-grained models that reproduce not only equilibrium structure, but also the correct dynamics.

Dynamic coarse-graining

My work lies at the intersection of nonequilibrium statistical mechanics, stochastic dynamics, coarse-grained molecular simulation, and multiscale modeling. The central problem is to construct reduced stochastic descriptions that are not merely fitted at equilibrium, but are dynamically consistent with microscopic trajectories.

Traditional coarse-graining often emphasizes equilibrium structure: matching radial distribution functions, free energies, or average forces. My work extends this perspective by treating dynamical quantities as first-class targets. Time-correlation functions, velocity autocorrelations, displacement correlations, and distance-resolved pair observables become the windows through which the irreversible structure of the coarse-grained dynamics — friction, mobility tensors, internal dissipation, hydrodynamic interactions — is identified and estimated.

Theory

Coarse-graining and Mori–Zwanzig ideas, stochastic dynamics, and the fluctuation–dissipation structure that links eliminated microscopic variables to effective noise and dissipation.

Methodology

Self-averaging parameter estimation: inferring both reversible and irreversible parameters from microscopic averages and time-correlation functions within a single dynamical procedure.

Applications

Protein internal friction, Brownian dynamics, colloidal hydrodynamics, Lennard-Jones mixtures, and dynamically coarse-grained fluids.

Guiding questions

PhD thesis

My PhD is concerned with dynamic coarse-graining in molecular systems. The thesis focuses on stochastic coarse-grained models whose parameters are inferred from microscopic simulations by matching selected averages and time-correlation functions. The main methodological contribution is a self-averaging parameter-estimation framework that couples the coarse-grained stochastic dynamics to slow evolution equations for the model parameters. This allows both reversible parameters, such as potentials of mean force, and irreversible parameters, such as friction coefficients or configuration-dependent mobility tensors, to be estimated within a unified dynamical procedure.

Applications include analytically controlled Langevin systems, Brownian particles with hydrodynamic interactions, Lennard-Jones binary mixtures, coarse-grained protein models, interacting colloids, and dynamically defined fluid particles. Across these systems, the common goal is to identify the effective forces and transport mechanisms that emerge when microscopic degrees of freedom are eliminated.

The FPI research contract supporting this work concluded in August 2026. The thesis is now in its writing phase, alongside the completion of the colloidal-hydrodynamics and fluid-particle studies. The expected defence is in 2027.

Published · 2026

Self-averaging parameter estimation for coarse-grained stochastic models

This project develops a self-averaging framework for estimating the parameters of coarse-grained stochastic differential equations from microscopic trajectory data. Rather than fitting parameters through a separate external optimization loop, the method treats inference as a dynamical process: the coarse-grained system evolves according to a stochastic model with unknown parameters, while the parameters themselves evolve slowly under feedback equations.

These feedback equations enforce agreement between microscopic and mesoscopic averages or time-correlation functions. The combined system self-averages over time and converges toward parameter values for which the selected microscopic and mesoscopic observables coincide. It can estimate both static parameters, such as potentials of mean force, and dynamic parameters, such as friction coefficients or configuration-dependent mobility tensors — the latter being especially valuable when transport coefficients are state-dependent and difficult to compute directly from conditional averages.

The approach is validated on controlled systems — analytically tractable Langevin models and Brownian particles with hydrodynamic interactions — and then applied to molecular coarse-graining problems, including Lennard-Jones binary mixtures where the effective potential and configuration-dependent mobility of heavy tracer particles are inferred from molecular dynamics.

  • self-averaging
  • parameter inference
  • observable matching
  • coarse-grained SDEs
  • hydrodynamic mobility

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Published · 2025

Internal friction in a coarse-grained protein model

This project studies the role of internal friction in a coarse-grained model of a globular protein in water. The protein is represented by a bead model whose reversible interactions include elastic and electrostatic contributions, while its irreversible dynamics include both solvent friction and internal bead–bead friction.

The key result is that solvent friction alone is not enough to reproduce the microscopic velocity correlations of the protein beads. Internal friction, arising from the eliminated atomic degrees of freedom inside the protein, is necessary to capture the correct vibrational relaxation.

This shows that coarse-grained biomolecular models must include not only accurate equilibrium structure, but also physically meaningful dissipative mechanisms. The result is relevant for interpreting protein dynamics, viscoelastic response, and the connection between microscopic molecular motion and mesoscopic stochastic descriptions.

  • protein dynamics
  • internal friction
  • coarse-graining
  • all-atom MD
  • Mori–Zwanzig

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Manuscript in preparation

Hydrodynamic couplings between sphere-like colloids

This work develops and calibrates a model of two approximately spherical colloids in a simple fluid. It characterises single-particle diffusion and hydrodynamic radius before examining how the interaction changes when the particles approach one another.

The current analysis focuses on distance-dependent dynamic parameters, including pair friction and translational–rotational couplings. These effects are needed for a mesoscopic description that retains the hydrodynamic structure measured in the microscopic simulations.

The model and preliminary analysis are complete; validation of the dynamic parameters and revision of the manuscript are in progress.

  • colloids
  • hydrodynamic interactions
  • pair friction
  • translation–rotation coupling
  • molecular dynamics

Manuscript in preparation

Material retention in dynamically coarse-grained fluid particles

This project examines dynamically defined coarse-grained particles in a fluid and asks how much of their original microscopic material remains associated with them as they move. The question probes what information is actually preserved by a time-dependent coarse-graining map.

The equilibrium analysis is developed, and the current work extends it to the response under transverse flow. The results expose limits of simple barycentric advection and help clarify how coarse-grained fluid variables should be interpreted dynamically.

  • dynamic coarse-graining
  • fluid particles
  • material retention
  • barycentric advection
  • nonequilibrium flow

Research areas