2025/2026 Seminar Series

Thursday, 18th June 2026 

12:00 am, Seminari MA, Dept IMAE

Cristian Moreno-Pulido (Universitat de Girona): 

First part: "Summary of research topics on vacuum energy and cosmology" 

Abstract: In this first part, I will briefly talk about my research's initial trajectory. In particular, I will summarize the research in [1] with special emphasis on asymptotic series in the context of the vacuum energy. 

Second part: "Approximate solutions to the shrinking core model and their interpretation" 

Abstract: The shrinking core model (SCM) describes the reaction of a solid particle with a surrounding fluid. It has interesting applications in many fields [2] In this talk, we revisit the SCM by deriving it directly from the underlying physical processes and carrying out a careful non-dimensionalisation. This analysis reveals limitations of the widely used pseudo-steady-state approximation, particularly for liquid–solid systems where fluid and solid densities are comparable.

To address these limitations, we derive approximate analytical solutions using a perturbation method that improves upon the pseudo-steady-state model, and we also obtain a small-time solution that captures the early transient behaviour. A semi-implicit finite-difference scheme is implemented to solve the full model numerically and to benchmark the analytical approximations.

We show that the perturbation solution provides significantly improved accuracy over the pseudo-steady-state model, especially in diffusion-limited regimes. Finally, we present a simple fitting procedure that combines the perturbation and early-time solutions to estimate physical parameters from experimental data with minimal computational cost.

Third part: "Pore size effects in Contaminant Adsorption"

Abstract: Sorption processes, including adsorption and desorption, play a central role in many areas of interest: from the removal of contaminants from fluids to hydrogen storage technologies based on porous materials. The efficiency of these processes depends on the microstructure of the adsorbent, particularly on the distribution of pore sizes. However, most mathematical models rely on homogenized descriptions of porous media and do not account for the internal pore-size distribution. The aim of our work is to develop mathematical models that explicitly incorporate pore-size distributions to capture the impact of porous microstructure on adsorption dynamics and improve predictions of adsorption kinetics and equilibrium in nanoporous adsorbents. In particular, our approach relates it to the adsorption rates of contaminants within a probabilistic description of pore accessibility.

The modeling framework combines multiscale and size-structured approaches to link  pore characteristics with macroscopic concentration. We focus on the evolution of contaminant concentration in a batch system containing nanoporous adsorbent particles, where experimental conditions allow for simplified governing equations. Information on pore-size distributions comes from BET characterization of activated carbons in the micro/mesoporous diameter range of 0.6–24 nm, with most of the volume being contained in pores below 2 nm. Internal surfaces can reach 1500–2800 m²/g. The evolution of contaminant concentration in the batch system is tracked until equilibrium is reached. We repeat the process for several combinations of contaminant size, carbon type, and initial concentration. The resulting concentration curves and isotherms allow model parameter calibration. Preliminary results show that variations in pore-size distributions can lead to different adsorption dynamics, even under identical experimental conditions.

References:

[1] Renormalizing the vacuum energy in cosmological spacetime: implications for the cosmological constant problem   https://arxiv.org/abs/2201.05827

[2] Modelling hydrogen storage in metal hydrides https://arxiv.org/abs/2507.22083

[3] Approximate solutions to the shrinking core model and their interpretation https://arxiv.org/abs/2507.21042

Thursday, 12th March 2026 

12:00 am, Seminari MA, Dept IMAE

German Miranda (Universitat de Lund, Suècia): "Teoria espectral del Laplacià magnètic i operadors de Schrödinger"

Abstract: En aquest seminari presentarem una introducció a alguns resultats relatius als valors propis d’operadors diferencials i al seu paper en l’estudi qualitatiu de les solucions d’equacions en derivades parcials rellevants en física. En particular, ens centrarem en l'anàlisi espectral d’operadors de Schrödinger i el Laplacià magnètic. Com a cas paradigmàtic, considerem l'operador Laplacià, operador fonamental present en la modelització de multitud de fenòmens com ara la propagació del so o de la calor. Posteriorment, discutirem com la introducció d’un camp magnètic modifica aquest marc a través del Laplacià magnètic, i com l’estudi dels seus valors propis resulta rellevant en la descripció de materials superconductors.

Thursday, 16th April 2026 

15:30 am, Seminari MA, Dept IMAE

Berenguer Sabadell (Universitat de Girona): "Variacions sobre un problema clàssic" 

Abstract: L'any 1735 Leonhard Euler es feia conèixer al món matemàtic a partir de la resolució del conegut com a Problema de Basilea, és a dir, donar el valor exacte de la suma dels inversos dels nombres quadrats. La resposta a aquesta qüestió, plantejada per Jakob Bernoulli al seu Tractatus de seriebus infinitis (1689), és un d'aquells resultats matemàtics sorprenents tant per valor de la resposta, π^2/6, com pel raonament emprat pel mateix Euler per arribar a la solució. Avui sabem que Euler es va avançar gairebé 150 anys a la formalització correcta i rigorosa d'aquest càlcul.

El Problema de Basilea és un cas concret de sèrie racional, suma infinita de fraccions on tant el numerador com el denominador són polinomis amb coeficients complexos.  En aquesta xerrada intentarem donar resposta a aquest problema més general, que parteix del Problema de Basilea, i ens centrarem en el valor de les sèries racionals quan tant numerador com denominador són polinomis a coeficients enters.