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Jan Lange

Publications and source records attributed to Jan Lange.

5 recordsLinked to original sources

Cascading Failures and Critical Infrastructures in Future Renewable European Power Systems

The world's power systems are undergoing a rapid transformation, shifting away from carbon-intensive power generation to renewable sources. As a result, electricity is being transported over ever longer distances, while the intrinsic system inertia provided by thermal power plants decreases. Together, these developments raise the probability of cascading line failures and reduce the stability of the system after a system split. In this article, we assess the risk of cascading failures and system splits in the European power grid for different carbon reduction scenarios. We analyze the most likely and most dangerous splits, and identify critical transmission infrastructures and we discuss potential countermeasures that can address the problem of cascades. Our results show that while the risks of splits causing power failures rises with decarbonization, it can be mitigated cost efficiently.

physics.soc-ph

Torsion order and irrationality of complete intersections

We provide new logarithmic lower bounds for the torsion order of a very general complete intersection in projective space as well as a very general hypersurface in products of projective spaces and Grassmannians, in particular we prove their retract irrationality.

math.AG

On the rationality problem for low degree hypersurfaces

We show that a very general hypersurface of degree d at least 4 and dimension at most $(d+1)2^{d-4}$ over a field of characteristic different from 2 does not admit a decomposition of the diagonal; hence, it is neither stably nor retract rational, nor $\mathbb{A}^1$-connected. Similar results hold in characteristic 2 under a slightly weaker degree bound. This improves earlier results by the second named author and Moe.

math.AG

On zero-cycles of varieties over Laurent fields

We generalize a recent result of Pavic--Schreieder regarding the surjectivity of the obstruction morphism defined in [PS23]. As a consequence of this result, we show that geometrically (retract) rational varieties over a Laurent field of characteristic 0, which admit a strictly semi-stable model, have trivial Chow group of zero-cycles. Our key new ingredient comes from toric geometry.

math.AG

The diagonal of (3,3) fivefolds

We show that a very general (3,3) complete intersection in $\mathbb{P}^7$ over an algebraically closed uncountable field of characteristic different from 2 admits no decomposition of the diagonal, in particular it is not retract rational. This strengthens Nicaise--Ottem's result, where stable irrationality in characteristic 0 was shown. The main tool is a Chow-theoretic obstruction which was found by Pavic--Schreieder, where quartic fivefolds are studied.

math.AG