Related papers: Towards a Nano Geometry? Geometry and Dynamics on …

All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at…

A biophysical issue how the nuclear size dynamically scales with the cellular size remains mysterious. We develop a theoretical framework in which the interactions between polydisperse biomolecules and the mechanical elasticity of the cell…

The internal dynamics of strongly interacting systems and that of biomolecules such as proteins display several important analogies, despite the huge difference in their characteristic energy and length scales. For example, in all such…

In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form…

We map molecular dynamics simulations of fluid-fluid interfaces onto mesoscale continuum theories for partially miscible fluids. Unlike most previous work, we examine not only the interface order parameter and density profiles, but also the…

The migratory dynamics of cells can be influenced by the complex micro-environment through which they move. It remains unclear how the motility machinery of confined cells responds and adapts to their micro-environment. Here, we propose a…

Many intracellular processes continue to oscillate during the cell cycle. Although it is not well-understood how they are affected by discontinuities in the cellular environment, the general assumption is that oscillations remain robust…

Cell plasma membranes display a dramatically rich structural complexity characterized by functional sub-wavelength domains with specific lipid and protein composition. Under favorable experimental conditions, patterned morphologies can also…

A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell.…

Modeling membrane interactions with arbitrarily shaped colloidal particles, such as environmental micro- and nanoplastics, at the cell scale remains particularly challenging, owing to the complexity of particle geometries and the need to…

As an effective method to deliver external materials into biological cells, microinjection has been widely applied in the biomedical field. However, the cognition of cell mechanical property is still inadequate, which greatly limits the…

Geometrical aspects of quantum computing are reviewed elementarily for non-experts and/or graduate students who are interested in both Geometry and Quantum Computation. In the first half we show how to treat Grassmann manifolds which are…

We present the fundamentals of geometrothermodynamics, an approach to study the properties of thermodynamic systems in terms of differential geometric concepts. It is based, on the one hand, upon the well-known contact structure of the…

Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…

We introduce a formalism for the geometry of eukaryotic cells and organisms.Cells are taken to be star-convex with good biological reason. This allows for a convenient description of their extent in space as well as all manner of cell…

The unique plasma-specific features and physical phenomena in the organization of nanoscale solid-state systems in a broad range of elemental composition, structure, and dimensionality are critically reviewed. These effects lead to the…

The positioning of new cellular walls during cell division plays a key role in shaping plant tissue organization. The influence of cell geometry on the positioning of division planes has been previously captured into various geometrical…

The fundamental role of on-shell diagrams in quantum field theory has been recently recognized. On-shell diagrams, or equivalently bipartite graphs, provide a natural bridge connecting gauge theory to powerful mathematical structures such…

Throughout the evolution of biological species on Earth, cells and organs have developed many complex structures and processes to ensure their interactions with individual chemical molecules (small and macromolecular) and nanoscale objects…

We develop the geometric description of submanifolds in Newton--Cartan spacetime. This provides the necessary starting point for a covariant spacetime formulation of Galilean-invariant hydrodynamics on curved surfaces. We argue that this is…