Main Research Lines
Virus Physics: Elastic Frustration and Capsid Assembly
This research line explores the physical principles governing viral capsid assembly and structural organization, with particular emphasis on the roles of geometry, elasticity, and mechanical frustration. Using tools from statistical physics, continuum elasticity, and computational modeling, the work aims to identify generic mechanisms that control shape selection and stability in virus-like assemblies.
A central contribution of this line is the development of elastic models that describe how viral capsids emerge as a result of competing geometric and mechanical constraints. Rather than relying solely on biochemical specificity, these models show that capsid morphology can be understood as an outcome of elastic energy minimization under curvature frustration, leading to preferred shapes and characteristic defect structures.
In this framework, mis-assembly and shape selection arise naturally when local elastic preferences cannot be simultaneously satisfied on a closed shell. The resulting frustration generates an energy landscape that favors certain capsid geometries while suppressing others, providing predictive insight into the stability of viral morphologies and the role of defects during assembly.
More recently, this work has been extended to the self-assembly of tubular structures, a key process in the formation of tubular viruses. Using Classical Nucleation Theory combined with an elastic description in the stretching-dominated regime, the study identifies the conditions under which tubules emerge from free subunits and clarifies the physical mechanisms governing their assembly.
A central result is the identification of a single dimensionless parameter that controls tubule formation and polymorphism by quantifying the competition between bending elasticity and line tension. The model shows that tubule growth can proceed through distinct fluctuation mechanisms depending on which contribution dominates, and that kinetic effects may lead to final tubule radii that deviate from thermodynamic equilibrium.
Colloidal Self-Assembly: Competing Interactions and Structural Organization
This research line focuses on the physical principles governing colloidal self-assembly, with emphasis on how competing interactions, particle architecture, and external constraints lead to the spontaneous formation of ordered structures. Through theoretical modeling and numerical simulations, these studies aim to identify generic mechanisms responsible for pattern formation and structural selection in colloidal matter.
Early contributions demonstrated that relatively simple colloidal systems can self-organize into complex morphologies such as square lattices, stripe phases, and confined clusters. These structures arise from the competition between attractive and repulsive interactions acting at different length scales, showing that long-range order can emerge without requiring highly specific particle designs.
Subsequent work extended this framework to anisotropic and soft colloidal particles, revealing how particle shape, internal structure, and non-additive mixtures give rise to different assembly pathways. In two-dimensional systems, these effects give rise to a rich variety of phases, illustrating the interplay between entropy, geometry, and interaction energetics in determining collective behavior.
More recent studies have explored the role of confinement and topology in colloidal self-assembly. By examining particles confined to finite domains or curved surfaces, this work shows how boundary conditions and global geometric constraints can stabilize novel structures and defect patterns not accessible in bulk systems. Overall, this research line highlights how complex self-assembled architectures can emerge from simple physical ingredients, with relevance to soft matter physics, materials science, and the design of functional colloidal materials.
Viscosity Models for Colloidal Suspensions
This research line focuses on the development of analytical and semi-empirical models to describe the effective viscosity of colloidal suspensions over a wide range of particle concentrations. The central objective is to understand how microscopic particle properties and collective interactions translate into macroscopic flow behavior, from dilute regimes to highly concentrated systems.
The work begins with the formulation of a general viscosity model for hard-sphere suspensions, valid at arbitrary volume fractions. This model provides a continuous description of the viscosity increase as particle concentration grows, naturally bridging the dilute Einstein limit and the strongly concentrated regime approaching maximum packing. Due to its simplicity and physical transparency, this framework serves as a reference model for more complex suspensions.
Subsequent developments extend this approach to systems involving soft particles, porous or core–shell structures, emulsions, and nanoparticle dispersions. A key unifying concept introduced in these studies is the effective volume fraction, which accounts for hydrodynamic interactions, particle deformability, and microstructural constraints, allowing diverse colloidal systems to be described within a common theoretical structure.
The line culminates in a semi-empirical viscosity model applicable to multicomponent and interacting suspensions, combining physical constraints with minimal fitting parameters. Together, these models provide a scalable and predictive framework linking particle-level properties with the rheology of complex fluids, with relevance to soft matter physics, materials science, and chemical engineering.
This research line is developed in collaboration with Prof. Iván Santamaría-Holek of UNAM, and the main results are documented in Refs. [35,37,38,41,43,49].
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Epidemic Dynamics: Inhomogeneous Transmission and Asynchronic Mixing
This research line develops extended epidemic models that incorporate population heterogeneity and temporal dispersion to better describe real epidemic dynamics beyond traditional well-mixed assumptions. The focus is on understanding how differences in onset times and transmission rates across subpopulations affect the spread of infectious diseases, using COVID-19 as a prototypical case.
The work begins with the recognition that standard compartmental models (such as SIR) assume homogeneous mixing, which leads to early exponential growth of infections that often does not match empirical observations. In contrast, many real outbreaks — including COVID-19 — exhibit subexponential growth even in the absence of interventions. To explain this, the model introduces inhomogeneous transmission by treating the total population as a collection of interacting subpopulations with differing local outbreak onset times and transmission parameters.
By reformulating the SIR framework with a time-dependent transmission rate, the model captures how the effective reproduction number naturally decreases over time due to structural heterogeneity rather than solely through depletion of susceptibles or intervention measures. This approach accounts for early algebraic growth in cumulative cases and aligns closely with observed epidemic curves from multiple countries, including Mexico, without requiring externally imposed behavioral changes.
The model’s success across diverse datasets suggests that population structure and asynchronous outbreak dynamics play key roles in shaping epidemic progression. It also provides a quantitative basis for distinguishing between effects due to containment policies and those emerging from inherent heterogeneities in transmission. Beyond improving prediction accuracy, these insights may help inform public health strategies that exploit heterogeneity — such as targeted mobility restrictions — to mitigate disease spread more effectively.
