Now showing items 49-68 of 126

• Kinetic energy estimates for the accuracy of the time-dependent Hartree-Fock approximation with Coulomb interaction ﻿

(Journal des Mathematiques Pures et Appliquees, 2016-01-01)
We study the time evolution of a system of $N$ spinless fermions in $\mathbb{R}^3$ which interact through a pair potential, e.g., the Coulomb potential. We compare the dynamics given by the solution to Schrödinger's equation ...
• 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 ...
• A Lê-Greuel type formula for the image Milnor number ﻿

(Hokkaido Mathematical Journal, 2019-02)
• Macroscopic conductivity of free fermions in disordered media ﻿

(Reviews in Mathematical Physics, 2014-12-31)
We conclude our analysis of the linear response of charge transport in lattice systems of free fermions subjected to a random potential by deriving general mathematical properties of its conductivity at the macroscopic ...
• 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 ...
• Microscopic conductivity of lattice fermions at equilibrium. I. Non-interacting particles ﻿

(Journal of Mathematical Physics, 2015-12-31)
We consider free lattice fermions subjected to a static bounded potential and a timeand space-dependent electric field. For any bounded convex region R âŠ‚ â„ (d (d â‰¥ 1) of space, electric fields Îµ within R drive currents. ...
• Microscopic Conductivity of Lattice Fermions at Equilibrium. Part II: Interacting Particles ﻿

(Letters in Mathematical Physics, 2016-01-01)
We apply Liebâ€“Robinson bounds for multi-commutators we recently derived (Bru and de Siqueira Pedra, Liebâ€“Robinson bounds for multi-commutators and applications to response theory, 2015) to study the (possibly non-linear) ...
• Microscopic Conductivity of Lattice Fermions at Equilibrium. Part II: Interacting Particles ﻿

(Letters in Mathematical Physics, 2015-12-31)
We apply Lieb–Robinson bounds for multi-commutators we recently derived (Bru and de Siqueira Pedra, Lieb–Robinson bounds for multi-commutators and applications to response theory, 2015) to study the (possibly non-linear) ...
• Mixed tête-à-tête twists as monodromies associated with holomorphic function germs ﻿

(2018-04-01)
Tête-à-tête graphs were introduced by N. A’Campo in 2010 with the goal of modeling the monodromy of isolated plane curves. Mixed tête-à-tête graphs provide a generalization which define mixed tête-à-tête twists, which ...
• 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. ...
• 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 ...
• Modeling of birth-death and diffusion processes in biological complex environments ﻿

(2018-04-20)
This thesis is centered on the theory of stochastic processes and their applications in biological systems characterized by a complex environment. Three case studies have been modeled by the use of the three fundamental ...
• Modelling and simulation of wildland fire in the framework of the level set method ﻿

(Ricerche di Matematica, 2016-01-01)
Among the modelling approaches that have been proposed for the simulation of wildfire propagation, two have gained considerable attention in recent years: the one based on a reaction-diffusion equation, and the one based ...
• Modelling wildland fire propagation by tracking random fronts ﻿

(Natural Hazards and Earth System Sciences, 2014-12-31)
Abstract. Wildland fire propagation is studied in the liter- ature by two alternative approaches, namely the reaction– diffusion equation and the level-set method. These two ap- proaches are considered alternatives to each ...
• Moderately Discontinuous Algebraic Topology for Metric Subanalytic Germs ﻿

(2019-10-31)
We have developed both a homology theory and a homotopy theory in the context of metric subanalytic germs (see Definition 2.1). The former is called MD homology and is covered in Chapter 2, which contains a paper that is ...
• Monodromies as tête-à-tête graphs ﻿

(2018-05-08)
• 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 ...
• Multiplicity of singularities is not a bi-Lipschitz invariant ﻿

(Mathematische Annalen, 2020-01-17)
It was conjectured that multiplicity of a singularity is bi-Lipschitz invariant. We disprove this conjecture constructing examples of bi-Lipschitz equivalent complex algebraic singularities with different values of multiplicity.