arXiv subjects

Fabio Semperlotti

Publications and source records attributed to Fabio Semperlotti.

49 records · Page 3Linked to original sources

arXiv2018

Tomographic imaging of inhomogeneous non-local media using fractional order models

We investigate a generalized tomographic imaging framework applicable to a class of inhomogeneous media characterized by non-local diffusive energy transport. Under these conditions, the transport mechanism is well described by fractional-order continuum models capable of capturing anomalous diffusion that would otherwise remain undetected when using traditional integer-order models. Although the underlying idea of the proposed framework is applicable to any transport mechanism, the case of fractional heat conduction is presented as a specific example to illustrate the methodology. By using numerical simulations, we show how complex inhomogeneous media involving non-local transport, can be successfully imaged if fractional order models are used. In particular, results will show that by properly recognizing and accounting for the fractional character of the host medium not only allows achieving increased resolution but, in case of strong and spatially distributed non-locality, it represents the only viable approach to achieve a successful reconstruction.

physics.app-ph↗

arXiv2018

Occurrence of anomalous diffusion and non-local response in highly-scattering acoustic periodic media

We investigate the occurrence of anomalous diffusive transport associated with acoustic wave fields propagating through highly-scattering periodic media. Previous studies had correlated the occurrence of anomalous diffusion to either the random properties of the scattering medium or to the presence of localized disorder. In this study, we show that anomalous diffusive transport can occur also in perfectly periodic media and in the absence of disorder. The analysis of the fundamental physical mechanism leading to this unexpected behavior is performed via a combination of deterministic, stochastic, and fractional-order models in order to capture the different elements contributing to this phenomenon. Results indicate that this anomalous transport can indeed occur in perfectly periodic media when the dispersion behavior is characterized by anisotropic (partial) bandgaps. In selected frequency ranges, the propagation of acoustic waves not only becomes diffusive but its intensity distribution acquires a distinctive Lévy alpha-stable profile having pronounced heavy-tails. In these ranges, the acoustic transport in the medium occurs according to a hybrid transport mechanism which is simultaneously propagating and anomalously diffusive. We show that such behavior is well captured by a fractional diffusive transport model whose order can be obtained by the analysis of the heavy tails.

cond-mat.dis-nn↗

arXiv2017

Design and Experimental Observation of Valley-Hall Edge States in Diatomic-Graphene-like Elastic Waveguides

We report on the design and experimental validation of a two-dimensional phononic elastic waveguide exhibiting topological Valley-Hall edge states. The lattice structure of the waveguide is inspired by the diatomic graphene and it is imprinted in an initially flat plate by means of geometric indentations. The indentations are distributed according to a hexagonal lattice structure which guarantees the existence of Dirac dispersion at the boundary of the Brillouin zone. Starting from this basic material, domain walls capable of supporting edge states can be obtained by contrasting waveguides having broken space inversion symmetry (SIS) achieved by using local resonant elements. Our theoretical study shows that such material maps into the acoustic analog of the quantum valley Hall effect (QVHE) while numerical and experimental results confirm the existence of protected edge states traveling along the walls of topologically distinct domains.

cond-mat.mes-hall↗

arXiv2017

Tunable Acoustic Valley-Hall Edge States in Reconfigurable Phononic Elastic Waveguides

This study investigates the occurrence of acoustic topological edge states in a 2D phononic elastic waveguide due to a phenomenon that is the acoustic analogue of the quantum valley Hall effect. We show that a topological transition takes place between two lattices having broken space inversion symmetry due to the application of a tunable strain field. This condition leads to the formation of gapless edge states at the domain walls, as further illustrated by the analysis of the bulk-edge correspondence and of the associated topological invariants. Although time reversal symmetry is still intact in these systems, the edge states are topologically protected when inter-valley mixing is either weak or negligible. Interestingly, topological edge states can also be triggered at the boundary of a single domain if boundary conditions are properly selected. We also show that the static modulation of the strain field allows tuning the response of the material between the different supported edge states.

cond-mat.mes-hall↗

arXiv2017

Thermoacoustics of solids: a pathway to solid state engines and refrigerators

Thermoacoustic oscillations have been one of the most exciting discoveries of the physics of fluids in the 19th century. Since its inception, scientists have formulated a comprehensive theoretical explanation of the basic phenomenon which has later found several practical applications to engineering devices. To-date, all studies have concentrated on the thermoacoustics of fluid media where this fascinating mechanism was exclusively believed to exist. Our study shows theoretical and numerical evidence of the existence of thermoacoustic instabilities in solid media. Although the underlying physical mechanism is analogous to its counterpart in fluids, the theoretical framework highlights relevant differences that have important implications on the ability to trigger and sustain the thermoacoustic response. This mechanism could pave the way to the development of highly robust and reliable solid-state thermoacoustic engines and refrigerators.

physics.app-ph↗

arXiv2017

Double-zero-index structural waveguides

We report on the theoretical and experimental realization of a double-zero-index elastic waveguide and on the corresponding acoustic cloacking and supercoupling effects. The proposed waveguide uses geometric tapers in order to induce Dirac-like cones at $\vec{k} = 0$ due to accidental degeneracy. The nature of the degeneracy is explored by a $k\cdot p$ perturbation method adapted to thin structural waveguides. Results confirm the linear nature of the dispersion around the degeneracy and the possibility to map the material to effective medium properties. Effective parameters, numerically extracted using boundary medium theory, confirm that the phononic waveguide maps into a double zero index material. Numerical and experimental results confirm the expected cloacking and supecoupling effects typical of zero index materials.

cond-mat.mtrl-sci↗

arXiv2017

Two-Dimensional Structure-Embedded Acoustic Lenses based on Periodic Acoustic Black Holes

Recent studies have introduced a new class of two-dimensional acoustic metamaterials whose dispersion and propagation properties results from the use of geometric inhomogeneities in the form of Acoustic Black Holes (ABH). The ABH is an element able to smoothly bend and slow down elastic waves, therefore providing a variety of unconventional dispersion and propagation properties typically observed in more complex multi-material and locally resonant designs. This approach enables thin-walled structural elements having fully embedded acoustic lenses capable of different functionalities such as focusing, collimation, and negative refraction. Numerical simulations show that such structures exhibit broadband operating conditions that span both the metamaterial and the phononic range. Full field experimental measurements allow validating the design approach and confirm the performance of the embedded acoustic lens.

physics.class-ph↗

arXiv2016

Model-order reduction of lumped parameter systems via fractional calculus

This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach to the simulation of non-homogeneous systems dictates the use of numerical solutions and often imposes stringent compromises between accuracy and computational performance. Fractional calculus provides an alternative approach where complex dynamical systems can be modeled with compact fractional equations that not only can still guarantee analytical solutions, but can also enable high levels of order reduction without compromising on accuracy. Different approaches are explored in order to transform the integer order model into a reduced order fractional model able to match the dynamic response of the initial system. Analytical and numerical results show that, under certain conditions, an exact match is possible and the resulting fractional differential models have both a complex and frequency-dependent order of the differential operator. The implications of this type of approach for both model order reduction and model synthesis are discussed.

math.NA↗

arXiv2016

Implicit operators for networked mechanical and thermal systems with integer-order components

Complex systems are composed of a large number of simple components connected to each other in the form of a network. It is shown that, for some network configurations, the equivalent dynamic behavior of the system is governed by an implicit integro-differential operator even though the individual components themselves satisfy equations that use explicit operators of integer order. The networks considered here are infinite trees and ladders, and each is composed only of two types of integer-order components with potential-driven flows that are repeated ad infinitum. In special cases the equivalent operator for the system is a fractional-order derivative, but in general it is implicit and can only be expressed as a solution of an operator equation. These implicit operators, which are a generalization of fractional-order derivatives, play an important role in the analysis and modeling of complex systems.

math-ph↗

arXiv2016

Anomalous refraction of acoustic guided waves in solids with geometrically tapered metasurfaces

The concept of metasurface has recently opened new exciting directions to engineer the refraction properties in both optical and acoustic media. Metasurfaces are typically designed by assembling arrays of sub-wavelength anisotropic scatterers able to mold incoming wavefronts in rather unconventional ways. The concept of metasurface was pioneered in photonics and later extended to acoustics while its application to the propagation of elastic waves in solids is relatively unexplored. We investigate the design of acoustic metasurfaces to control elastic guided waves in thin-walled structural elements. These engineered discontinuities enable anomalous refraction of guided wave modes consistently with the generalized Snell's law. The metasurfaces are made out of locally-resonant torus-like tapers enabling accurate phase shift of the incoming wave which ultimately affects the refraction properties. We show that anomalous refraction can be achieved on transmitted antisymmetric modes ($A_0$) either when using a symmetric ($S_0$) or antisymmetric ($A_0$) incident wave, the former clearly involving mode conversion. The same metasurface design also allows achieving structure embedded planar focal lenses and phase masks for non-paraxial propagation.

cond-mat.mtrl-sci↗

arXiv2014

Phononic Thin Plates with Embedded Acoustic Black Holes

We introduce a class of two-dimensional non-resonant single-phase phononic materials and investigate its peculiar dispersion characteristics. The material consists of a thin plate-like structure with an embedded periodic lattice of Acoustic Black Holes. The use of these periodic tapers allows achieving remarkable dispersion properties such as Zero Group Velocity in the fundamental modes, negative group refraction index, bi-refraction, and mode anisotropy. The dispersion properties are numerically investigated using a three-dimensional supercell plane wave expansion method. The effect on the dispersion characteristics of key geometric parameters of the black hole, such as the taper profile and the residual thickness, are also explored.

cond-mat.mtrl-sci↗

arXiv2014

A passively tunable non-resonant acoustic metamaterial lens for selective ultrasonic excitation

In this paper, we present an approach to ultrasonic beam-forming and beam-steering in structures based on the concept of embedded non-resonant acoustic metamaterial lenses. The lens design exploits the principle of acoustic drop-channel which enables the dynamic coupling of multiple ultrasonic waveguides at selected frequencies. In contrast with currently available technology, the embedded lens allows generating directional excitation by means of a single ultrasonic transducer. The lens design and performance are numerically investigated by using Plane Wave Expansion and Finite Difference Time Domain techniques applied to bulk structures. Then, the design is experimentally validated on a thin aluminum plate where the lens is implemented by through-holes. The dynamic response of the embedded lens is estimated by reconstructing, via Laser Vibrometry, the velocity field induced by a piezoelectric shaker source.

physics.class-ph↗

arXiv2013

Achieving Selective Damage Interrogation and Sub-Wavelength Resolution in Thin Plates with Embedded Metamaterial Acoustic Lenses

In this study, we present an approach to ultrasonic beamforming and high resolution identification of acoustic sources having critical implications for structural health monitoring technology. The proposed concept is based on the design of dynamically tailored structural elements via embedded acoustic metamaterial lenses. This approach provides a completely new alternative to conventional phased-array technology enabling the formation of steerable and collimated (or focused) ultrasonic beams by exploiting a single transducer. The ultrasonic beams can be steered by simply tuning the frequency of the excitation. Also, the embedded lens can be designed to achieve sub-wavelength resolution to incipient clustered damage.

cond-mat.mtrl-sci↗