arXiv subjects

Carmela Moschella

Publications and source records attributed to Carmela Moschella.

4 recordsLinked to original sources

arXiv2026

First order non-instantaneous corrections in collisional kinetic alignment models

In this work the standard kinetic theory assumption of instantaneous collisions is lifted. As a continuation of of a previous paper by Kanzler, Schmeiser, and Tora [KRM, 2024], a model for higher order non-instantaneous alignment collisions is presented and studied in the asymptotic regime of short collision duration. A first order accurate approximative model is derived as a correction to the instantaneous limit. Rigorous results on its well-posedness and on the instantaneous limit are proven. The approximative model is a system of two equations. An equally accurate scalar approximation is suggested.

math.AP↗

arXiv2026

Steady States of Transport-Coagulation-Nucleation Models

To model the dynamics of polymers formed through nucleation, elongated by polymerisation, shortened by depolymerisation and subject to aggregation reactions, we study a nonlinear integro-differential equation. Growth and shrinkage are described by transport terms, nucleation by a positive boundary condition, and aggregation by a Smoluchowski coagulation kernel. Our main result is the existence of steady states for the multiplicative coagulation kernel despite this kernel producing gelation in finite time for the pure coagulation equation. This is made possible by a sufficiently strong decay rate for large polymers. Beyond the existence result, the qualitative properties of the steady states are illustrated through explicit examples and numerical experiments. The analytical results connect the growth behaviour of the transport velocity and of the coagulation kernel to the decay properties of steady states.

math.AP↗

arXiv2025

The Vicsek-Kuramoto model in collective dynamics: macroscopic equations and pattern formation

In this work, we investigate an individual-based model (IBM) for self-propelled agents interacting locally on a plane. Agents are characterized by their position, the angle determining their direction of motion, and their angular velocity. The dynamics combine features of the well-known Vicsek and Kuramoto models, which describe collective dynamics and synchronization, respectively. The evolution of the directions of motion follows a Vicsek model, where agents align their orientations with the mean orientation of their neighbors, subject to some noise. Similarly, the angular velocities relax towards the average angular velocity of the neighboring agents, also subject to noise. From the IBM we derive the corresponding kinetic equation in the limit of a large number of agents and formally obtain the macroscopic equations through a macroscopic (hydrodynamic) limit. Numerical simulations of the IBM reveal a variety of patterns, including rotating clusters, traveling orientation waves, and globally synchronized rotational motion. A qualitative comparison with simulations of the macroscopic system show the ability of the macroscopic model to reproduce some emergent behavior of the IBM.

math-ph↗

arXiv2025

Modeling Protein Diffusion Across ER-Nuclear Envelope Junctions Reveals Efficient Transport via Simple Diffusion

The endoplasmic reticulum (ER) is the largest continuous membrane-bound organelle in the cell and plays a central role in the synthesis and turnover of many lipids and proteins. It connects directly to the nucleus through specialized contact points known as ER-nuclear envelope (NE) junctions. In our recent study, we found that these ER-NE junctions are both narrow and infrequent, measuring less than 20 nanometers in diameter and occurring at a frequency of approximately 0.1 per square micrometer. However, it remains unclear whether such limited and narrow connections are sufficient to support efficient transport between the ER and NE. Here, we built a mathematical model of ER-to-NE protein diffusion, incorporating ultrastructural parameters, the frequency of ER-NE junctions, and the diffusion coefficient of proteins within the ER lumen. To validate the model, we experimentally quantified the transport rate of ER luminal proteins to the NE using fluorescence recovery after photobleaching (FRAP). Our model and experimental data demonstrate that simple diffusion is sufficient to account for the rapid transport of proteins from the ER to the NE, despite the limited and narrow nature of the connecting junctions. Together, these findings offer mechanistic insight into how ER-NE connectivity enables rapid protein transport and lay the groundwork for future studies on ER-nucleus communication.

math-ph↗