Topological ManifoldsMarzio De Corato
Topological ManifoldsComputational physics and the topology of nanostructures
02 / Computational physics and the topology of nanostructures

Computational physics and the topology of nanostructures.

Research background in physics

Graphene nanoribbons

Graphene nanoribbons

Cutting a graphene sheet leaves an atomic edge whose properties can be investigated through spectroscopy and calculations. The two views make armchair and zigzag terminations recognisable.

Formula and scientific context ↗
Deformed nanoribbon

Deformed nanoribbon

Twisting moves the hexagons out of plane and changes the orientation of ribbon regions, providing a visual introduction to the relationship between structural distortion and electronic properties.

Formula and scientific context ↗
Bilayer graphene nanoflakes

Bilayer graphene nanoflakes

Two overlapping graphene fragments reveal how a relative shift changes ring alignment, introducing the role of interlayer interactions in the study of optical properties.

Formula and scientific context ↗
P688 schwarzite

P688 schwarzite

The carbon lattice's hexagons remain visible as the framework curves around its openings. Octagons connect the saddle regions, where the bonds reveal the narrowing and subsequent widening of the structure.

Formula and scientific context ↗
Research problem

Which properties of a nanostructure depend on its geometry and bond arrangement?

Graphene nanoribbons and nanoflakes, schwarzites and other carbon structures allow the study of how bond configurations affect a system’s electronic, optical and vibrational behaviour, while topological descriptions of negatively curved networks provide tools for relating structural organisation to the physical properties under consideration.

Approach and tools

Ab initio calculations have been compared with spectroscopic results to identify Raman and vibrational signatures associated with nanoribbon edges. Other work examines how structural distortion changes the bandgap, the optical properties of coupled nanoflakes and the mathematical indices used to compare carbon networks.

Ab initio calculationsMolecular topologyVibrational propertiesCarbon nanostructures

Related activities

PhD in Physics and Nanosciences: “Vibrational and optical fingerprints in graphene-based nanostructures” (2013–2016).

Research experience at CNR–NANO, Modena, on the optical properties of carbon nanostructures (2012–2013).

Related work

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Graph theory and cyber-attacks

Unaffected nodeCompromised node

When devices, services and identities are described through their relationships, system security can be studied as a structural problem in which both a vulnerability and the paths through which it could expose other resources matter.

From connections to attack paths

A graph G = (V, E) consists of vertices V and edges E. In an asset network, vertices may represent devices or services, while edges describe connections, dependencies or trust relationships. An attack graph instead represents conditions, actions or system states, depending on the model, to examine how several steps can combine into a compromise.

G = (V, E)

The analogy with an epidemic helps illustrate how a compromise can spread between nodes, provided that the conditions for each transition are considered. Credentials, permissions, vulnerabilities and configurations determine which paths are feasible; a connection alone describes a possibility of communication.

How this supports defence

Path analysis helps identify the resources reachable from an initial position and the connections that form critical passages. Comparing the graph before and after a change shows how network segmentation, reduced privileges or a vulnerability fix can interrupt particular sequences. A node’s importance depends on its role and context, so its number of connections gives only a partial account of risk.

Reading this figure

Red nodes marked with a cross represent compromised systems in the scenario; green nodes remain unaffected, while pale pulses follow the propagation paths. The map provides a conventional geographical layout for an illustrative network whose links and timing are constructed to clarify the phenomenon. It does not show observed attacks or estimate compromise probabilities.

References

Sheyner et al. — Automated Generation and Analysis of Attack Graphs, Carnegie Mellon University

NIST IR 7788 — Security Risk Analysis of Enterprise Networks Using Probabilistic Attack Graphs

Natural Earth cartography — public-domain data

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Relations, assumptions and study references. These are not empirical results from the author’s research.

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Marzio De Corato

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