Mathematical Physics (MP)
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Modeling anomalous heat diffusion: Comparing fractional derivative and non-linear diffusivity treatments
(International Journal of Thermal Sciences, 2018-11)In the Fourier heat conduction equation, when the flux definition is expressed as the product of a constant diffusivity and the temperature gradient, the characteristic length scale evolves as the square root of time. ... -
Isotropic Bipolaron-Fermion-Exchange Theory and Unconventional Pairing in Cuprate Superconductors
(Ann. Phys. (Berl.), 2018-12-10)The discovery of high-temperature superconductors in 1986 represented a major experimental breakthrough (Nobel Prize 1987), but their theoretical explanation is still a subject of much debate. These materials have many ... -
Accuracy of Classical Conductivity Theory at Atomic Scales for Free Fermions in Disordered Media
(J. Math. Pures Appl., 2019-01-22)The growing need for smaller electronic components has recently sparked the interest in the breakdown of the classical conductivity theory near the atomic scale, at which quantum effects should dominate. In 2012, experimental ... -
Decay of Complex-time Determinantal and Pfaffian\ Correlation Functionals in Lattices
(Commun. Math. Phys., 2018-01-24)We supplement the determinantal and Pfaffian bounds of Sims and Warzel (Commun Math Phys 347:903--931, 2016) for many-body localization of quasi-free fermions, by considering the high dimensional case and complex-time ... -
Modeling non-stationarities in high-frequency financial time series
(Physica A: Statistical Mechanics and its Applications, 2019-01)We study tick-by-tick financial returns for the FTSE MIB index of the Italian Stock Exchange (Borsa Italiana). We confirm previously detected non-stationarities. Scaling properties reported before for other high-frequency ... -
Centre-of-mass like superposition of Ornstein-Uhlenbeck processes: A pathway to non-autonomous stochastic differential equations and to fractional diffusion
(Fractional Calculus and Applied Analysis, 2018-10-25)We consider an ensemble of Ornstein–Uhlenbeck processes featuring a population of relaxation times and a population of noise amplitudes that characterize the heterogeneity of the ensemble. We show that the centre-of-mass ... -
The Discreteness-driven Relaxation of Collisionless Gravitating Systems: Entropy Evolution in External Potentials, N-dependence, and the Role of Chaos
(The Astrophysical Journal, 2019-01-10)We investigate the old problem of the fast relaxation of collisionless N-body systems that are collapsing or perturbed, emphasizing the importance of (noncollisional) discreteness effects. We integrate orbit ensembles in ... -
A jacobian module for disentanglements and applications to Mond's conjecture
(Revista Matemática Complutense, 2019)Let $f:(\mathbb C^n,S)\to (\mathbb C^{n+1},0)$ be a germ whose image is given by $g=0$. We define an $\mathcal O_{n+1}$-module $M(g)$ with the property that $\mathscr A_e$-$\operatorname{codim}(f)\le \dim_\mathbb C M(g)$, ... -
RandomFront 2.3 A physical parametrisation of fire-spotting for operational fire spread models: Implementation in WRF-Sfire and response analysis with LSFire+
(Geoscientific Model Development, 2018-12)Fire-spotting is often responsible for a dangerous flare up in the wildfire and causes secondary ignitions isolated from the primary fire zone leading to perilous situations. The main aim of the present research to provide ... -
On Zariski’s multiplicity problem at infinity
(Proceedings of the American Mathematical Society, 2018-08-14)We address a metric version of Zariski's multiplicity conjecture at infinity that says that two complex algebraic affine sets which are bi-Lipschitz homeomorphic at infinity must have the same degree. More specifically, ... -
Measure-valued weak solutions to some kinetic equations with singular kernels for quantum particles
(2018-12-19)In this thesis, we present a mathematical study of three problems arising in the kinetic theory of quantum gases. In the first part, we consider a Boltzmann equation that is used to describe the time evolution of the ... -
Singularities in Geometry and Topology
(2018-06-18)This thesis consists of two different topics that are not related. The thesis has two different and independent parts that can be read in any order. The purpose of this work is to study two topics in singularity theory: ... -
Crossover from anomalous to normal diffusion: truncated power-law noise correlations and applications to dynamics in lipid bilayers
(New Journal of Physics, 2018-10-18)The emerging diffusive dynamics in many complex systems shows a characteristic crossover behaviour from anomalous to normal diffusion which is otherwise fitted by two independent power-laws. A prominent example for a ... -
Right unimodal and bimodal singularities in positive characteristic
(International Mathematics Research Notices, 2017-08-07)The problem of classification of real and complex singularities was initiated by Arnol'd in the sixties who classified simple, unimodal and bimodal singularities w.r.t. right equivalence. The classification of simple ... -
On a Boltzmann equation for Compton scattering, from non relativistic electrons at low density.
(2018-08-15)A Boltzmann equation, used to describe the Compton scattering in the non-relativistic limit is considered. A truncation of the very singular redistribution function is introduced and justified. The existence of weak solutions ... -
On a system of equations for the normal fluid - condensate interaction in a Bose gas
(2018-03-27)The existence of global solutions for a system of differential equations is proved, and some of their properties are described. The system involves a kinetic equation for quantum particles. It is a simplified version of ... -
Multiplicity and degree as bi‐Lipschitz invariants for complex sets
(Journal of Topology, 2018-08-29)We study invariance of multiplicity of complex analytic germs and degree of complex affine sets under outer bi-Lipschitz transformations (outer bi-Lipschitz homeomorphims of germs in the first case and outer bi-Lipschitz ... -
Concurent multi-scale physical parametrization of fire-spotting: A study on the role of macro- and meso-scale characteristics of the system
(Advances in Forest Fire Research, 2018)The strong impact of wildfires in terms of lives and homes lost and of damage to ecosystems, calls for an urgent improvement in the risk management. The aim of the present research is the improvement of these software ... -
Wildfire propagation modelling
(Geophysical Research Abstracts Vol. 20, 2018)Wildfires are a concrete problem with a strong impact on human life, property and the environment, because they cause disruption and are an important source of pollutants. Climate change and ... -
Langevin equation in complex media and anomalous diffusion
(Journal of the Royal Society Interface, 2018-07-30)The problem of biological motion is a very intriguing and topical issue. Many efforts are being focused on the development of novel modelling approaches for the description of anomalous diffusion in biological systems, such ...
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