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Francesco Maddalena

Publications and source records attributed to Francesco Maddalena.

At least 19 recordsLinked to original sources

Scaling Up Purcell-Enhanced Self-Assembled Nanoplasmonic Perovskite Scintillators into the Bulk Regime

Scintillators convert high-energy radiation into detectable photons and play a crucial role in medical imaging and security applications. The enhancement of scintillator performance through nanophotonics and nanoplasmonics, specifically using the Purcell effect, has shown promise but has so far been limited to ultrathin scintillator films because of the localized nature of this effect. This study introduces a method to expand the application of nanoplasmonic scintillators to the bulk regime. By integrating 100-nm-sized plasmonic spheroid and cuboid nanoparticles with perovskite scintillator nanocrystals, we enable nanoplasmonic scintillators to function effectively within bulk-scale devices. We experimentally demonstrate power and decay rate enhancements of up to (3.20 $\pm$ 0.20) and (4.20 $\pm$ 0.31) folds for plasmonic spheroid and cuboid nanoparticles, respectively, in a 5-mm thick CsPbBr$_{3}$ nanocrystal-polymer scintillator at RT. Theoretical modeling also predicts similar enhancements of up to (2.26 $\pm$ 0.31) and (3.02 $\pm$ 0.69) folds for the same nanoparticle shapes and dimensions. Moreover, we demonstrate a (2.07 $\pm$ 0.39) fold increase in light yield under $^{241}$Am $γ$-excitation. These findings provide a viable pathway for utilizing nanoplasmonics to enhance bulk scintillator devices, advancing radiation detection technology.

physics.optics

Frequency-dependent damping in the linear wave equation

We propose a model for frequency-dependent damping in the linear wave equation. After proving well-posedness of the problem, we study qualitative properties of the energy. In the one-dimensional case, we provide an explicit analysis for special choices of the damping operator. Finally, we show, in special cases, that solutions split into a dissipative and a conservative part.

math.AP

Comparison between solutions to the linear peridynamics model and solutions to the classical wave equation

In this paper, we consider an equation inspired by linear peridynamics and we establish its connection with the classical wave equation. In particular, given a horizon $δ>0$ accounting for the region of influence around a material point, we prove existence and uniqueness of a solution $u_δ$ and demonstrate the convergence of $u_δ$ to solutions to the classical wave equation as $δ\to 0$. Moreover, we prove that the solutions to the peridynamics model with small frequency initial data are close to solutions to the classical wave equation.

math.AP

Exponential convergence to steady-states for trajectories of a damped dynamical system modelling adhesive strings

We study the global well-posedness and asymptotic behavior for a semilinear damped wave equation with Neumann boundary conditions, modelling a one-dimensional linearly elastic body interacting with a rigid substrate through an adhesive material. The key feature of of the problem is that the interplay between the nonlinear force and the boundary conditions allows for a continuous set of equilibrium points. We prove an exponential rate of convergence for the solution towards a (uniquely determined) equilibrium point.

math.AP

A Numerical Framework For Nonlinear Peridynamics On Two-dimensional Manifolds Based On Implicit P-(Ec)k Schemes

In this manuscript, an original numerical procedure for the nonlinear peridynamics on arbitrarily--shaped two-dimensional (2D) closed manifolds is proposed. When dealing with non parameterized 2D manifolds at the discrete scale, the problem of computing geodesic distances between two non-adjacent points arise. Here, a routing procedure is implemented for computing geodesic distances by re-interpreting the triangular computational mesh as a non-oriented graph; thus returning a suitable and general method. Moreover, the time integration of the peridynamics equation is demanded to a P-(EC)$^k$ formulation of the implicit $β$-Newmark scheme. The convergence of the overall proposed procedure is questioned and rigorously proved. Its abilities and limitations are analyzed by simulating the evolution of a two-dimensional sphere. The performed numerical investigations are mainly motivated by the issues related to the insurgence of singularities in the evolution problem. The obtained results return an interesting picture of the role played by the nonlocal character of the integrodifferential equation in the intricate processes leading to the spontaneous formation of singularities in real materials.

math.NA

The Nanoplasmonic Purcell Effect in Ultrafast and High-Light-Yield Perovskite Scintillators

The development of X-ray scintillators with ultrahigh light yields and ultrafast response times is a long sought-after goal. In this work, we theoretically predict and experimentally demonstrate a fundamental mechanism that pushes the frontiers of ultrafast X-ray scintillator performance: the use of nanoscale-confined surface plasmon polariton modes to tailor the scintillator response time via the Purcell effect. By incorporating nanoplasmonic materials in scintillator devices, this work predicts over 10-fold enhancement in decay rate and 38% reduction in time resolution even with only a simple planar design. We experimentally demonstrate the nanoplasmonic Purcell effect using perovskite scintillators, enhancing the light yield by over 120% to 88 $\pm$ 11 ph/keV, and the decay rate by over 60% to 2.0 $\pm$ 0.2 ns for the average decay time, and 0.7 $\pm$ 0.1 ns for the ultrafast decay component, in good agreement with the predictions of our theoretical framework. We perform proof-of-concept X-ray imaging experiments using nanoplasmonic scintillators, demonstrating 182% enhancement in the modulation transfer function at 4 line pairs per millimeter spatial frequency. This work highlights the enormous potential of nanoplasmonics in optimizing ultrafast scintillator devices for applications including time-of-flight X-ray imaging and photon-counting computed tomography.

physics.optics

Dispersive effects in two- and three-dimensional peridynamics

In this paper we study the dispersive properties related to a model of peridynamic evolution, governed by a non local initial value problem, in the cases of two and three spatial dimensions. The features of the wave propagation characterized by the nontrivial interactions between nonlocality and the regimes of low and high frequencies are studied and suitable numerical investigations are exposed.

math.AP

Dispersive effects in a scalar nonlocal wave equation inspired by peridynamics

We study the dispersive properties of a linear equation in one spatial dimension which is inspired by models in peridynamics. The interplay between nonlocality and dispersion is analyzed in detail through the study of the asymptotics at low and high frequencies, revealing new features ruling the wave propagation in continua where nonlocal characteristics must be taken into account. Global dispersive estimates and existence of conserved functionals are proved. A comparison between these new effects and the classical local {\it scenario} is deepened also through a numerical analysis.

math.AP

Qualitative aspects in nonlocal dynamics

In this paper we investigate, through numerical studies, the dynamical evolutions encoded in a linear one-dimensional nonlocal equation arising in peridynamcs. The different propagation regimes ranging from the hyperbolic to the dispersive, induced by the nonlocal feature of the equation, are carefully analyzed. The study of an initial value Riemann-like problem suggests the formation of a singularity.

nlin.PS

Waves in flexural beams\with nonlinear adhesive interaction

The paper studies the initial boundary value problem related to the dynamic evolution of an elastic beam interacting with a substrate through an elastic-breakable forcing term. This discontinuous interaction is aimed to model the phenomenon of attachement-detachement of the beam occurring in adhesion phenomena. We prove existence of solutions in energy space and exhibit various counterexamples to uniqueness. Furthermore we characterize some relavant features of the solutions, ruling the main effectes of the nonlinearity due to the elasic-breakable term on the dynamical evolution, by proving the linearization property according to \cite{G96} and an asymtotic result pertaining the long time behavior.

math.AP

Elastic-brittle reinforcement of flexural structures

This note provides a variational description of the mechanical effects of flexural stiffening of a 2D plate glued to an elastic-brittle or an elastic-plastic reinforcement. The reinforcement is assumed to be linear elastic outside possible free plastic yield lines or free crack. Explicit Euler equations and a compliance identity are shown for the reinforcement of a 1D beam.

math.OC

Regularity and energy transfer for a nonlinear beam equation

In this paper we study some key effects of a discontinuous forcing term in a fourth order wave equation on a bounded domain, modeling the adhesion of an elastic beam with a substrate through an elastic-breakable interaction. By using a spectral decomposition method we show that the main effects induced by the nonlinearity at the transition from attached to detached states can be traced in a loss of regularity of the solution and in a migration of the total energy through the scales.

math.AP

Euler's optimal profile problem

We study an old variational problem formulated by Euler as Proposition 53 of his `Scientia Navalis' by means of the direct method of the calculus of variations. Precisely, through relaxation arguments, we prove the existence of minimizers. We fully investigate the analytical structure of the minimizers in dependence of the geometric parameters and we identify the ranges of uniqueness and non-uniqueness.

math.OC

Singularity formation in fractional Burgers' equations

The formation of singularities in finite time in non-local Burgers' equations, with time-fractional derivative, is studied in detail. The occurrence of finite time singularity is proved, revealing the underlying mechanism, and precise estimates on the blow-up time are provided. The employment of the present equation to model a problem arising in job market is also analyzed.

math.AP

The gap in Pure Traction Problems between Linear Elasticity and Variational Limit of Finite Elasticity

A limit elastic energy for pure traction problem is derived from re-scaled nonlinear energy of an hyperelastic material body subject to an equilibrated force field. We show that the strains of minimizing sequences associated to re-scaled non linear energies weakly converge, up to subsequences, to the strains of minimizers of a limit energy, provided an additional compatibility condition is fulfilled by the force field. The limit energy is different from classical energy of linear elasticity; nevertheless the compatibility condition entails the coincidence of related minima and minimizers. A strong violation of this condition provides a limit energy which is unbounded from below, while a mild violation may produce a limit energy with infinitely many extra minimizers which are not minimizers of standard linear elastic energy and whose strains are not uniformly bounded. A relevant consequence of this analysis is that a rigorous validation of linear elasticity fails for compressive force fields that do not fulfil such compatibility condition.

math.AP

A new variational approach to linearization of traction problems in elasticity

A new energy functional for pure traction problems in elasticity has been deduced in [23] as the variational limit of nonlinear elastic energy functional for a material body subject to an equilibrated force field: a sort of Gamma limit with respect to the weak convergence of strains when a suitable small parameter tends to zero. This functional exhibits a gap that makes it different from the classical linear elasticity functional. Nevertheless a suitable compatibility condition on the force field ensures coincidence of related minima and minimizers. Here we show some relevant properties of the new functional and prove stronger convergence of minimizing sequences for suitable choices of nonlinear elastic energies.

math.OC

Numerical Methods for the Nonlocal Wave Equation of the Peridynamics

In this paper we will consider the peridynamic equation of motion which is described by a second order in time partial integro-differential equation. This equation has recently received great attention in several fields of Engineering because seems to provide an effective approach to modeling mechanical systems avoiding spatial discontinuous derivatives and body singularities. In particular, we will consider the linear model of peridynamics in a one-dimensional spatial domain. Here we will review some numerical techniques to solve this equation and propose some new computational methods of higher order in space; moreover we will see how to apply the methods studied for the linear model to the nonlinear one. Also a spectral method for the spatial discretization of the linear problem will be discussed. Several numerical tests will be given in order to validate our results.

math.NA

Wellposedness of a nonlinear peridynamic model

We consider an evolution equation inspired by a model in peridynamics, with a singular pairwise interaction force term, and we give global in time existence, uniqueness and stability results for the Cauchy problem.

math.AP