arXiv subjects

Fabio Semperlotti

Publications and source records attributed to Fabio Semperlotti.

At least 19 recordsLinked to original sources

arXiv2026

Nonabelian elastic metamaterials using holonomies acquired by crossing degeneracies

Embedding nonabelian features into elastic metamaterials promises remarkable opportunities for wave control in many practical applications such as surface acoustic wave devices, mode multiplexers, and on-material computation. Nevertheless, current realizations are limited to arrangements of coupled resonators with fine-tuned interactions, limiting their applicability to continuous media. This theoretical and numerical study introduces a design principle for continuous nonabelian elastic metamaterial waveguides. The basic configuration consists of a composite waveguide made of multiple cylindrical waveguides coupled by spatially varying elements. These elements are engineered to follow geometrically-controlled parameter variations that cross selected degeneracies and produce a targeted nonabelian holonomy. The strategy based on crossing degeneracies fundamentally differs from abelian geometric phases, where parameters avoid and encircle degeneracies, or nonabelian Wilczek-Zee phases, where parameters are fine-tuned to maintain degeneracies throughout their cycle. The resulting holonomy transfers an input longitudinal excitation in one rod to an output response in another rod. When two such waveguides are concatenated, their ordering dictates the output response, thereby revealing the emergence of nonabelian dynamics. The nonabelian behavior persists across a broad range of frequencies and under perturbations to the geometry of coupling elements or cylinder diameters. These results establish a robust, effective, and practical route to leverage nonabelian physics in elastic metamaterials.

physics.app-ph↗

arXiv2025

Embedding 1D BDI topological dynamics into continuous elastic plates

This study presents an approach that leverages the existing knowledge acquired in one-dimensional BDI class discrete metamaterials, such as mass-spring systems or acoustic resonators, and exploits it to realize fully continuous elastic two-dimensional topological waveguides. The design relies on the concept of evanescently coupled waveguides and defect resonances in order to reproduce the equivalent dynamics of prototypical BDI discrete systems, such as the Su-Schrieffer-Heeger (SSH) model. Starting with a continuous plate waveguide based on a periodic distribution of pillars, local resonators and waveguides are created by eliminating selected pillars and by exploiting the concept of point and line defects. The height of selected pillars is adjusted to tune the coupling strength between different resonators. The approach is validated by designing fully continuous elastic analogs of both the SSH chain and ladder systems. Numerical simulations and experimental results confirm the validity of the design by showing the emergence of topological edge modes at the interface of topologically distinct systems. In addition, the edge modes obtained in the elastic analog of the SSH ladder are shown to be Majorana-like modes.

physics.app-ph↗

arXiv2025

A Spectral Quantum Algorithm for Numerical Differentiation and Integration

Numerical calculus algorithms which estimate derivatives and integrals from data series acquired either via measurements or by sampling functions are essential in scientific computing. To date, a few quantum algorithms have been developed to perform calculus operations based on closed form functional inputs; yet, in many practical applications, field variables are numerically described via series of samples rather than closed form expressions. This paper presents the theoretical development and the gate-level circuit implementation of novel quantum algorithms for numerical differentiation and indefinite integration with a prescribed integration constant. The methodology relies on a spectral approach that leverages the computational efficiency of the quantum Fourier transform and the parallel computing capability afforded by quantum superposition to evaluate outputs at all domain points simultaneously. The differentiation approach is also extended to enable gradient estimation, and post-processing procedures are presented to recover sign information. The primary output of the proposed algorithms are quantum state vectors directly proportional to the numerical derivative or integral of the given data; therefore, the correctly signed results are made available to proceeding quantum computations. This result lays the foundation for the proposed algorithms to serve as core subroutines in applied quantum computing operations such as image processing, data analysis, and machine learning.

quant-ph↗

arXiv2025

On the one-dimensional SPH approximation of fractional-order operators

This work presents a theoretical formalism and the corresponding numerical techniques to obtain the approximation of fractional-order operators over a 1D domain via the smoothed particle hydrodynamics (SPH) method. The method is presented for both constant- and variable-order operators, in either integral or differential forms. Several numerical examples are presented in order to validate the theory against analytical results and to evaluate the performance of the methodology. This formalism paves the way for the solution of fractional-order continuum mechanics models via the SPH method.

math.NA↗

arXiv2025

Reinforcement learning framework for the mechanical design of microelectronic components under multiphysics constraints

This study focuses on the development of reinforcement learning based techniques for the design of microelectronic components under multiphysics constraints. While traditional design approaches based on global optimization approaches are effective when dealing with a small number of design parameters, as the complexity of the solution space and of the constraints increases different techniques are needed. This is an important reason that makes the design and optimization of microelectronic components (characterized by large solution space and multiphysics constraints) very challenging for traditional methods. By taking as prototypical elements an application-specific integrated circuit (ASIC) and a heterogeneously integrated (HI) interposer, we develop and numerically test an optimization framework based on reinforcement learning (RL). More specifically, we consider the optimization of the bonded interconnect geometry for an ASIC chip as well as the placement of components on a HI interposer while satisfying thermoelastic and design constraints. This placement problem is particularly interesting because it features a high-dimensional solution space.

physics.comp-ph↗

arXiv2025

On the role of geometric phase in the dynamics of elastic waveguides

The geometric phase provides important mathematical insights to understand the fundamental nature and evolution of the dynamic response in a wide spectrum of systems ranging from quantum to classical mechanics. While the concept of geometric phase, which is an additional phase factor occurring in dynamical systems, holds the same meaning across different fields of application, its use and interpretation can acquire important nuances specific to the system of interest. In recent years, the development of quantum topological materials and its extension to classical mechanical systems have renewed the interest in the concept of geometric phase. This review revisits the concept of geometric phase and discusses, by means of either established or original results, its critical role in the design and dynamic behavior of elastic waveguides. Concepts of differential geometry and topology are put forward to provide a theoretical understanding of the geometric phase and its connection to the physical properties of the system. Then, the concept of geometric phase is applied to different types of elastic waveguides to explain how either topologically trivial or non-trivial behavior can emerge based on the geometric features of the waveguide.

physics.app-ph↗

arXiv2024

Physics and geometry informed neural operator network with application to acoustic scattering

In this paper, we introduce a physics and geometry informed neural operator network with application to the forward simulation of acoustic scattering. The development of geometry informed deep learning models capable of learning a solution operator for different computational domains is a problem of general importance for a variety of engineering applications. To this end, we propose a physics-informed deep operator network (DeepONet) capable of predicting the scattered pressure field for arbitrarily shaped scatterers using a geometric parameterization approach based on non-uniform rational B-splines (NURBS). This approach also results in parsimonious representations of non-trivial scatterer geometries. In contrast to existing physics-based approaches that require model re-evaluation when changing the computational domains, our trained model is capable of learning solution operator that can approximate physically-consistent scattered pressure field in just a few seconds for arbitrary rigid scatterer shapes; it follows that the computational time for forward simulations can improve (i.e. be reduced) by orders of magnitude in comparison to the traditional forward solvers. In addition, this approach can evaluate the scattered pressure field without the need for labeled training data. After presenting the theoretical approach, a comprehensive numerical study is also provided to illustrate the remarkable ability of this approach to simulate the acoustic pressure fields resulting from arbitrary combinations of arbitrary scatterer geometries. These results highlight the unique generalization capability of the proposed operator learning approach.

cs.LG↗

arXiv2024

Time transient Simulations via Finite Element Network Analysis: Theoretical Formulation and Numerical Validation

This paper extends the finite element network analysis (FENA) to include a dynamic time-transient formulation. FENA was initially formulated in the context of the linear static analysis of 1D and 2D elastic structures. By introducing the concept of super finite network element, this paper provides the necessary foundation to extend FENA to linear time-transient simulations for both homogeneous and inhomogeneous domains. The concept of neural network concatenation, originally formulated to combine networks representative of different structural components in space, is extended to the time domain. Network concatenation in time enables training neural network models based on data available in a limited time frame and then using the trained networks to simulate the system evolution beyond the initial time window characteristic of the training data set. The proposed methodology is validated by applying FENA to the transient simulation of one-dimensional structural elements (such as rods and beams) and by comparing the results with either analytical or finite element solutions. Results confirm that FENA accurately predicts the dynamic response of the physical system and, while introducing an error on the order of 1% (compared to analytical or computational solutions of the governing differential equations), it is capable of delivering extreme computational efficiency.

cs.CE↗

arXiv2024

Multiple scattering simulation via physics-informed neural networks

This work presents a physics-driven machine learning framework for the simulation of acoustic scattering problems. The proposed framework relies on a physics-informed neural network (PINN) architecture that leverages prior knowledge based on the physics of the scattering problem as well as a tailored network structure that embodies the concept of the superposition principle of linear wave interaction. The framework can also simulate the scattered field due to rigid scatterers having arbitrary shape as well as high-frequency problems. Unlike conventional data-driven neural networks, the PINN is trained by directly enforcing the governing equations describing the underlying physics, hence without relying on any labeled training dataset. Remarkably, the network model has significantly lower discretization dependence and offers simulation capabilities akin to parallel computation. This feature is particularly beneficial to address computational challenges typically associated with conventional mesh-dependent simulation methods. The performance of the network is investigated via a comprehensive numerical study that explores different application scenarios based on acoustic scattering.

physics.comp-ph↗

arXiv2023

Classical analogue to the Kitaev model and Majorana-like topological bound states

This study explores the possibility and presents a methodology to synthesize a classical mechanical analogue to the quantum mechanical 1D Kitaev model. While being fundamentally different, we will identify significant conceptual similarities between the two models that culminate in the occurrence, in the classical analogue system, of topologically non-trivial bound states that are akin to Majorana zero modes. By reformulating the Hamiltonian of the classical system in a form reminiscent of second quantization, we show that a 1D staggered classical mechanical chain can exhibit dynamic characteristics analogous to the Kitaev's 1D superconducting model, as well as its characteristic bound states. The non-trivial topological nature of the bound states is further confirmed by the topological band structure analysis and by the topological invariant. While the non-Abelian nature of these states remains an open question, these results allow envisioning the possibility to achieve topological braiding in classical mechanical systems.

cond-mat.mes-hall↗

arXiv2023

GRIDS-Net: Inverse shape design and identification of scatterers via geometric regularization and physics-embedded deep learning

This study presents a deep learning based methodology for both remote sensing and design of acoustic scatterers. The ability to determine the shape of a scatterer, either in the context of material design or sensing, plays a critical role in many practical engineering problems. This class of inverse problems is extremely challenging due to their high-dimensional, nonlinear, and ill-posed nature. To overcome these technical hurdles, we introduce a geometric regularization approach for deep neural networks (DNN) based on non-uniform rational B-splines (NURBS) and capable of predicting complex 2D scatterer geometries in a parsimonious dimensional representation. Then, this geometric regularization is combined with physics-embedded learning and integrated within a robust convolutional autoencoder (CAE) architecture to accurately predict the shape of 2D scatterers in the context of identification and inverse design problems. An extensive numerical study is presented in order to showcase the remarkable ability of this approach to handle complex scatterer geometries while generating physically-consistent acoustic fields. The study also assesses and contrasts the role played by the (weakly) embedded physics in the convergence of the DNN predictions to a physically consistent inverse design.

physics.comp-ph↗

arXiv2022

Multiscale multimesh finite element method | $\text{M}^2$-FEM: Hierarchical mesh-decoupling for integral structural theories

This study presents a generalized multiscale multimesh finite element method ($\text{M}^2$-FEM) that addresses several long-standing challenges in the numerical simulation of integral structural theories, often used to model multiscale and nonlocal effects. The major challenges in the numerical simulation of integral boundary value problems are primarily rooted in the coupling of the spatial discretization of the global (parent) and integral (child) domains which severely restricts the computational efficiency of existing algorithms by imposing an implicit trade-off in the accuracy achieved by the child domain and in the resources dedicated to the simulation of the overall parent domain. One of the most defining contributions of this study consists in the development of a mesh-decoupling technique that generates isolated sets of meshes such that the parent and child domains can be discretized and approximated independently. This mesh-decoupling has a multi-fold impact on the simulation of integral theories such that, when compared to existing state-of-the-art techniques, the proposed algorithm achieves simultaneously better numerical accuracy and efficiency (hence allowing a greater flexibility in both mesh size and computational cost trade-off decisions), greater ability to adopt generalized integral kernel functions, and the ability to handle non-regular (non-rectangular) domains via unstructured meshing. In this study, we choose a benchmark problem based on an extended version of the Eringen's nonlocal elasticity theory (implicitly, a multiscale theory) that leverages the use of generalized attenuation kernels and non-constant horizons of nonlocality. Nonetheless, the proposed $\text{M}^2$-FEM algorithm is very general and it can be applied to a variety of integral theories, even beyond structural elasticity.

math.NA↗

arXiv2022

On the role of the microstructure in the deformation of porous solids

This study explores the role that the microstructure plays in determining the macroscopic static response of porous elastic continua and exposes the occurrence of position-dependent nonlocal effects that are strictly correlated to the configuration of the microstructure. Then, a nonlocal continuum theory based on variable-order fractional calculus is developed in order to accurately capture the complex spatially distributed nonlocal response. The remarkable potential of the fractional approach is illustrated by simulating the nonlinear thermoelastic response of porous beams. The performance, evaluated both in terms of accuracy and computational efficiency, is directly contrasted with high-fidelity finite element models that fully resolve the pores' geometry. Results indicate that the reduced-order representation of the porous microstructure, captured by the synthetic variable-order parameter, offers a robust and accurate representation of the multiscale material architecture that largely outperforms classical approaches based on the concept of average porosity.

cond-mat.mtrl-sci↗

arXiv2022

Multiscale nonlocal beam theory: An application of distributed-order fractional operators

This study presents a comprehensive theoretical framework to simulate the response of multiscale nonlocal elastic beams. By employing distributed-order (DO) fractional operators with a fourth-order tensor as the strength-function, the framework can accurately capture anisotropic behavior of 2D heterogeneous beams with nonlocal effects localized across multiple scales. Building upon this general continuum theory and on the multiscale character of DO operators, a one-dimensional (1D) multiscale nonlocal Timoshenko model is also presented. This approach enables a significant model-order reduction without compromising the heterogeneous nonlocal description of the material, hence leading to an efficient and accurate multiscale nonlocal modeling approach. Both 1D and 2D approaches are applied to simulate the mechanical responses of nonlocal beams. The direct comparison of numerical simulations produced by either the DO or an integer-order fully-resolved model (used as ground truth) clearly illustrates the ability of the DO formulation to capture the effect of the microstructure on the macroscopic response. The assessment of the computational cost also indicates the superior efficiency of the proposed approach.

cs.CE↗

arXiv2022

On the instabilities of intrinsic thermoacoustic modes in a thermoacoustic waveguide with anechoic terminations

A recent study [H. Hao and F. Semperlotti, Phys. Rev. B 104, 104303 (2021)] investigated the dynamic behavior of an infinite one-dimensional (1D) thermoacoustic waveguide (TAWG) and illustrated its ability to sustain nonreciprocal and near zero-index sound propagation behavior; these properties can be very beneficial in the design of acoustic devices, including acoustic diodes, amplifiers, and cloaks. Nevertheless, it is critical to realize that when this concept is implemented in a finite-length waveguide, dynamic instabilities may occur and either drastically reduce or completely hinder the ability of the TAWG to control and manipulate sound. In this work, we uncover and investigate the occurrence of either evanescent or intrinsic thermoacoustic (ITA) modes in a 1D TAWG with anechoic terminations. The stability analysis clearly distinguishes these two types of evanescent modes and highlights their different origin rooted in either acoustic or thermoviscous effects. Numerical results reveal that ITA modes in anechoic-terminated TAWG are strictly connected to the acoustic-driven evanescent modes, and evolve towards unstable modes as the TA coupling strength is increased. This study may have important implications for the practical design of novel acoustic manipulating devices enabled by TA coupling elements. The conclusions drawn in this study may also shed lights on the effective suppression of instabilities in TAWGs.

physics.flu-dyn↗

arXiv2022

Fractional-Order Shell Theory: Formulation and Application to the Analysis of Nonlocal Cylindrical Panels

We present a theoretical and computational framework based on fractional calculus for the analysis of the nonlocal static response of cylindrical shell panels. The differ-integral nature of fractional derivatives allows an efficient and accurate methodology to account for the effect of long-range (nonlocal) interactions in curved structures. More specifically, the use of frame-invariant fractional-order kinematic relations enables a physically, mathematically, and thermodynamically consistent formulation to model the nonlocal elastic interactions. In order to evaluate the response of these nonlocal shells under practical scenarios involving generalized loads and boundary conditions, the fractional-Finite Element Method (f-FEM) is extended to incorporate shell elements based on the first-order shear-deformable displacement theory. Finally, numerical studies are performed exploring both the linear and the geometrically nonlinear static response of nonlocal cylindrical shell panels. This study is intended to provide a general foundation to investigate the nonlocal behavior of curved structures by means of fractional order models.

cs.CE↗

arXiv2021

Multiscale Nonlocal Elasticity: A Distributed Order Fractional Formulation

This study presents a generalized multiscale nonlocal elasticity theory that leverages distributed order fractional calculus to accurately capture coexisting multiscale and nonlocal effects within a macroscopic continuum. The nonlocal multiscale behavior is captured via distributed order fractional constitutive relations derived from a nonlocal thermodynamic formulation. The governing equations of the inhomogeneous continuum are obtained via the Hamilton principle. As a generalization of the constant order fractional continuum theory, the distributed order theory can model complex media characterized by inhomogeneous nonlocality and multiscale effects. In order to understand the correspondence between microscopic effects and the properties of the continuum, an equivalent mass-spring lattice model is also developed by direct discretization of the distributed order elastic continuum. Detailed theoretical arguments are provided to show the equivalence between the discrete and the continuum distributed order models in terms of internal nonlocal forces, potential energy distribution, and boundary conditions. These theoretical arguments facilitate the physical interpretation of the role played by the distributed order framework within nonlocal elasticity theories. They also highlight the outstanding potential and opportunities offered by this methodology to account for multiscale nonlocal effects. The capabilities of the methodology are also illustrated via a numerical study that highlights the excellent agreement between the displacement profiles and the total potential energy predicted by the two models under various order distributions. Remarkably, multiscale effects such as displacement distortion, material softening, and energy concentration are well captured at continuum level by the distributed order theory.

cs.CE↗

arXiv2021

Displacement-Driven Approach to Nonlocal Elasticity

This study presents a physically consistent displacement-driven reformulation of the concept of action-at-a-distance, which is at the foundation of nonlocal elasticity. In contrast to existing approaches that adopts an integral stress-strain constitutive relation, the displacement-driven approach is predicated on an integral strain-displacement relation. The most remarkable consequence of this reformulation is that the (total) strain energy is guaranteed to be convex and positive-definite without imposing any constraint on the symmetry of the kernels. This feature is critical to enable the application of nonlocal formulations to general continua exhibiting asymmetric interactions; ultimately a manifestation of material heterogeneity. Remarkably, the proposed approach also enables a strong satisfaction of the locality recovery condition and of the laws of thermodynamics, which are not foregone conclusions in most classical nonlocal elasticity theories. Additionally, the formulation is frame-invariant and the nonlocal operator remains physically consistent at boundaries. The study is complemented by a detailed analysis of the dynamic response of the nonlocal continuum and of its intrinsic dispersion leading to the consideration that the choice of nonlocal kernels should depend on the specific material. Examples of exponential or power-law kernels are presented in order to demonstrate the applicability of the method to different classes of nonlocal media. The ability to admit generalized kernels reinforces the generalized nature of the displacement-driven approach over existing integral methodologies, which typically lead to simplified differential models based on exponential kernels. The theoretical formulation is also leveraged to simulate the static response of nonlocal beams and plates illustrating the intrinsic consistency of the approach, which is free from unwanted boundary effects.

math.NA↗