School of Mathematical Scienceshttps://qmro.qmul.ac.uk/xmlui/handle/123456789/34782020-06-03T22:51:52Z2020-06-03T22:51:52ZReal-Time Dynamics of Plasma Balls from HolographyBantilan, HFigueras, PMateos, Dhttps://qmro.qmul.ac.uk/xmlui/handle/123456789/646172020-06-03T10:48:35Z2020-01-01T00:00:00ZReal-Time Dynamics of Plasma Balls from Holography
Bantilan, H; Figueras, P; Mateos, D
Plasma balls are droplets of deconfined plasma surrounded by a confining vacuum. We present the first holographic simulation of their real-time evolution via the dynamics of localized, finite-energy black holes in the five-dimensional anti–de Sitter (AdS) soliton background. The dual gauge theory is four-dimensional
N
=
4
super Yang-Mills theory compactified on a circle with supersymmetry-breaking boundary conditions. We consider horizonless initial data sourced by a massless scalar field. Prompt scalar field collapse produces an excited black hole at the bottom of the geometry together with gravitational and scalar radiation. The radiation disperses to infinity in the noncompact directions and corresponds to particle production in the dual gauge theory. The black hole evolves toward the dual of an equilibrium plasma ball on a time scale longer than naively expected. This feature is a direct consequence of confinement and is caused by long-lived, periodic disturbances bouncing between the bottom of the AdS soliton and the AdS boundary.
2020-01-01T00:00:00ZLarge Fluctuations in Locational Marginal PricesNesti, TMoriarty, JZocca, AZwart, Bhttps://qmro.qmul.ac.uk/xmlui/handle/123456789/645712020-06-03T01:24:12Z2020-01-01T00:00:00ZLarge Fluctuations in Locational Marginal Prices
Nesti, T; Moriarty, J; Zocca, A; Zwart, B
This paper investigates large fluctuations of Locational Marginal Prices (LMPs) in wholesale energy markets caused by volatile renewable generation profiles. Specifically, we study events of the form ℙ(LMP∉∏ni=1[α−i,α+i]), where LMP is the vector of LMPs at the n power grid nodes, and α−,α+∈ℝn are vectors of price thresholds specifying undesirable price occurrences. By exploiting the structure of the supply-demand matching mechanism in power grids, we look at LMPs as deterministic piecewise affine, possibly discontinuous functions of the stochastic input process, modeling uncontrollable renewable generation. We utilize techniques from large deviations theory to identify the most likely ways for extreme price spikes to happen, and to rank the nodes of the power grid in terms of their likelihood of experiencing a price spike. Our results are derived in the case of Gaussian fluctuations and are validated numerically on the IEEE 14-bus test case.
2020-01-01T00:00:00ZThe higher-order spectrum of simplicial complexes: a renormalization group approachReitz, MBianconi, Ghttps://qmro.qmul.ac.uk/xmlui/handle/123456789/645602020-06-03T01:24:14Z2020-01-01T00:00:00ZThe higher-order spectrum of simplicial complexes: a renormalization group approach
Reitz, M; Bianconi, G
Network topology is a flourishing interdisciplinary subject that is relevant for different disciplines including quantum gravity and brain research. The discrete topological objects that are investigated in network topology are simplicial complexes. Simplicial complexes generalize networks by not only taking pairwise interactions into account, but also taking into account many-body interactions between more than two nodes. Higher-order Laplacians are topological operators that describe higher-order diffusion on simplicial complexes and constitute the natural mathematical objects that capture the interplay between network topology and dynamics. Higher-order up and down Laplacians can have a finite spectral dimension, characterizing the long time behaviour of the diffusion process on simplicial complexes. Here we provide a renormalization group theory for the calculation of the higher-order spectral dimension of two deterministic models of simplicial complexes: the Apollonian and the pseudo-fractal simplicial complexes. We show that the RG flow is affected by the fixed point at zero mass, which determines the higher-order spectral dimension $d_S$ of the up-Laplacians of order $m$ with $m\geq 0$. Finally we discuss how the spectral properties of the higher-order up-Laplacian can change if one considers the simplicial complexes generated by the model "Network Geometry with Flavor". These simplicial complexes are random and display a structural topological phase transition as a function of the parameter $\beta$, which is also reflected in the spectrum of higher-order Laplacians.
2020-01-01T00:00:00Z2-chains: an interesting family of posetsFayers, Mhttps://qmro.qmul.ac.uk/xmlui/handle/123456789/644682020-05-30T01:24:17Z2020-05-23T00:00:00Z2-chains: an interesting family of posets
Fayers, M
We introduce a new family of finite posets which we call 2-chains. These first arose in the study of 0-Hecke algebras, but they admit a variety of different characterisations. We give these characterisations, prove that they are equivalent and derive some numerical results concerning 2-chains.
2020-05-23T00:00:00Z