arXiv subjects

Kieran Cavanagh

Publications and source records attributed to Kieran Cavanagh.

4 recordsLinked to original sources

arXiv2026

Modified scattering for semiclassical Bose-Fermi mixtures

The Vlasov-Hartree system models a mixture of bosons and fermions interacting via Coulomb forces in which the bosons are described quantum-mechanically, while the fermions are described classically. For small initial data, we prove that the system exhibits modified scattering, i.e. the bosonic and fermionic subsystems each converge to solutions of the free Schr\"odinger and Vlasov equations respectively, but with coupled logarithmic corrections owing to the long-range nature of Coulomb interactions. We use a mixed Lagrangian and Fourier-based approach to derive explicit descriptions of the asymptotic dynamics of the solution and associated fields and Lagrangian trajectories. Notably, due to our purely Lagrangian analysis on the Vlasov side, we require no derivatives on the initial fermion density, the asymptotic fermionic profile is as regular as the initial data, and convergence occurs in almost the same space as the initial data.

math.AP↗

arXiv2026

Global Existence and Time Decay for the Vlasov-Hartree System

The Vlasov-Hartree system is a mean-field model for a mixture of infinitely many interacting bosons and fermions where the bosons are described quantum mechanically and the fermions are described classically. This paper studies the well-posedness and dispersive properties of the Vlasov-Hartree system with initial data of arbitrary size. We prove that the Vlasov-Hartree system is globally well-posed in a low-regularity functional framework where the particle trajectories are meaningfully defined, but which includes discontinuous fermion densities. Moreover, when the interaction between the bosons and fermions is repulsive, we prove that the system exhibits dispersion in the form of time decay estimates for the particle densities and fields. When the interaction is attractive, we show that, at worst, the fields exhibit very mild growth in time.

math.AP↗

arXiv2022

Mandelbrot sets for fixed template iterations

We study the dynamics of template iterations, consisting of arbitrary compositions of functions chosen from a finite set of polynomials. In particular, we focus on templates using complex unicritical maps in the family $\{ z^d + c, c \in \mathbb{C}, d \ge 2 \}$. We examine the dependence on parameters of the connectedness locus for a fixed template and show that, for most templates, the connectedness locus moves upper semicontiuously. On the other hand, one does not in general have lower semicontinuous dependence, and we show this by means of a counterexample.

math.DS↗

arXiv2020

Management strategies in a SEIR model of COVID 19 community spread

The 2019 Novel Corona virus infection (COVID 19) is an ongoing public health emergency of international focus. Significant gaps persist in our knowledge of COVID 19 epidemiology, transmission dynamics, investigation tools and management, despite (or possibly because of) the fact that the outbreak is an unprecedented global threat. On the positive side, enough is currently known about the epidemic process to permit the construction of mathematical predictive models. In our work, we adapt a traditional SEIR epidemic model to the specific dynamic compartments and epidemic parameters of COVID 19, as it spreads in an age-heterogeneous community. We analyze management strategies of the epidemic course (as they were implemented through lockdown and reopening procedures in many of the US states and countries worldwide); however, to more clearly illustrate ideas, we focus on the example of a small scale college town community, with the timeline of control measures introduced in the state of New York. We generate predictions, and assess the efficiency of these control measures (closures, mobility restrictions, social distancing), in a sustainability context.

physics.soc-ph↗