Topologija, geometrija in mehanika naravnih tesnih pakiranj
Oznaka in naziv projekta
J1-60013 Topologija, geometrija in mehanika naravnih tesnih pakiranj
J1-60013 Topology, geometry, and mechanics of natural space-filling packings
Logotipi ARIS in drugih sofinancerjev
Projektna skupina
Vodja projekta: dr. Matej Krajnc
Raziskovalec: dr. Tanmoy Sarkar
Raziskovalec: dr. Anton Gradisek
Sestava projektne skupine: Povezava na SICRIS
Vsebinski opis projekta
Natural space-filling packings play a fundamental role in shaping the structure and function across diverse biological and physical systems. Our proposed research will consist of two parts. In part I, we will study the honeycomb construction in bee societies. While it is widely understood that bees build regular hexagonal honeycomb due to its optimal perimeter-to-area ratio, thus minimizing the construction costs, it is not at all known how they manage to collectively build this structure to such a precision. We will employ a novel approach by presenting bees an optimization problem in form of irregular 3D-printed honeycomb templates. By observing how bees solve the optimization problem, we will learn about their construction strategies and for the first time mathematically define, through a cost function, honeycomb construction as a mathematical optimization problem. In part II, we will study the physics of tumors and tumors spheroids. In the field of tissue mechanics, most theoretical studies conducted over the past 20 years have focused on epithelia, i.e., tissues consisting of cells arranged in a surface-like manner, while tumors and tumor spheroids have remained largely unexplored. The main reason behind this stagnation lies in technical difficulties related to implementing mechanical models with a single-cell resolution (e.g., vertex model). Our recently developed computational method, Graph vertex model, overcomes these technical difficulties and in the proposed project, we will use it to address various aspects of the mechanics of tumors and tumor spheroids. The research will include exploring the solid-fluid phase diagram, the mechanical stability of tumor shapes and mechanics-driven transition to metastasis, and interaction of tumors with their surrounding media. Our results will significantly improve our understanding of the fundamental physical mechanisms underlying the topology, geometry, and mechanics of natural space-filling tilings
Osnovni podatki sofinanciranja so dostopni na spletni strani SICRIS.
Faze projekta in opis njihove realizacije
1. faza: Real-estate management in honeybee hives (2D polyonal packings)
• Task I.a: Prepare honeycomb templates (9 months + 2 months) o Deliverable D(I.a): Honeycomb templates ready.
• Task I.b: Monitor and analyze honeycomb construction (6 months + 6 months + 6 months) o Deliverable D(I.b): Digitalized images of constructed honeycombs analyzed.
• Task I.c: Model the construction-cost function (5 months + 2 months + 2 months) o Deliverable D(I.c): Cost function developed.
• Task I.d: Solve the optimization problem (5 months + 2months + 2 months) o Deliverable D(I.d): Numerical solutions of the optimization problem obtained.
• Task I.e: Explore other types of honeycomb perturbation (12 months) o Deliverable D(I.e): /
2. faza: Topology, geometry, and mechanics of tumors and tumor spheroids (3D polyhedral packings)
• Task II.a: Study active-noise-driven solid-fluid transition in 3D cell aggregates (12 months) o Deliverable D(II.a): Paper ready for submission.
• Task II.b: Develop graph-topological transformations of cell divisions (5 months) o Deliverable D(II.b): GVM with divisions developed.
• Task II.c: Characterize the shape of growing cell aggregates (9 months) o Deliverable D(II.c): Paper ready for submission.
• Task II.d: Model rheology experiments (10 months) o Deliverable D(II.d): Paper ready for submission.
• Task II.e: Develop 3D hybrid VM-FEM model (10 months) o Deliverable D(II.e): Hybrid VM-FEM model developed.
• Task II.f: Study interactions between growing aggregates and elastic substrates (10 months) o Deliverable D(II.f): Paper ready for submission.