Related papers: Towards a Nano Geometry? Geometry and Dynamics on …
The biological membrane, which compartmentalizes the cell and its organelles, exhibit wide variety of macroscopic shapes of varying morphology and topology. A systematic understanding of the relation of membrane shapes to composition,…
This paper concerns a model for tumor cell migration through the surrounding extracellular matrix by considering mass balance phenomena involving the chemical interactions produced on the cell surface. The well-posedness of this model is…
While it is commonly observed that the shape dynamics of mammalian cells can undergo large random fluctuations, theoretical models aiming at capturing cell mechanics often focus on the deterministic part of the motion. In this paper, we…
This article covers thermodynamic, dynamic, and kinetic models that are suitable for the analysis of wetting, adsorption, and related interfacial phenomena in colloidal and multiphase systems. Particular emphasis is made on describing…
Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck scale, one of the many problems one has to face in this enterprise is to find the…
In cell membranes, proteins and lipids are organized into sub-micrometric nanodomains of varying size, shape and composition, performing specific functions. Despite their biological importance, the detailed morphology of these nanodomains…
Heterogeneities in the cell membrane due to coexisting lipid phases have been conjectured to play a major functional role in cell signaling and membrane trafficking. Thereby the material properties of multiphase systems, such as the line…
In the era of foundation models and Large Language Models (LLMs), Euclidean space has been the de facto geometric setting for machine learning architectures. However, recent literature has demonstrated that this choice comes with…
A molecular rotor mechanism is proposed to explain weak magnetic field effects in biology. Despite being nanoscale (1 nm), this rotor exhibits quantum superposition and interference. Analytical modeling shows its quantum dynamics are highly…
Granular and nanoscale materials containing a relatively small number of constituents have been studied to discover how their properties differ from their macroscopic counterparts. These studies are designed to test how far the known…
We analyse symmetry breaking in general gauge theories paying particular attention to the underlying geometry of the theory. In this context we find two natural metrics upon the vacuum manifold: a Euclidean metric associated with the scalar…
This work investigates the geometrical properties of self-gravitating $N$-body systems from the perspective established by Henri Poincar\'e and Albert Einstein concerning the operational nature of measured geometry. Utilizing recent…
An attempt is made to extend some of the basic paradigms of dynamics, from the viewpoint of (continuous) flows, to non-metric manifolds.
Mechanical cues from the extracellular microenvironment play a central role in regulating the structure, function and fate of living cells. Nevertheless, the precise nature of the mechanisms and processes underlying this crucial cellular…
Experience collected in mesoscopic dynamic modeling of externally driven systems indicates absence of potentials that could play role of equilibrium or nonequilibrium thermodynamic potentials yet their thermo-dynamics-like modeling is often…
We elaborate on a recently proposed geometric framework for scalar effective field theories. Starting from the action, a metric can be identified that enables the construction of geometric quantities on the associated functional manifold.…
The relationship between micro-structure and macro-structure of complex systems using information geometry has been dealt by several authors. From this perspective, we are going to apply it as a geometrical structure connecting both…
This manuscript introduces novel approaches to three phenomena. First, we extend the algebraic formulation of kinetic theory within the contact framework by making explicit the gauge freedom, thereby obtaining a formulation in which the…
Water behaves very differently at surfaces and under extreme confinement, but the boundary between these two regimes has remained unclear. Despite evidence that interfacial effects persist under sub-nanometre confinement, the…
Cell membranes separate the cell interior from the external environment. They are constituted by a variety of lipids; their composition determines the dynamics of membrane proteins and affects the ability of the cells to adapt. Even though…