arXiv subjects

Daniel Onofrei

Publications and source records attributed to Daniel Onofrei.

17 recordsLinked to original sources

arXiv2025

On the Detection of Internal Defects in Structured Media

A critical issue that affects engineers trying to assess the structural integrity of various infrastructures, such as metal rods or acoustic ducts, is the challenge of detecting internal fractures (defects). Traditionally, engineers depend on audible and visual aids to identify these fractures, as they do not physically dissect the object in question into multiple pieces to check for inconsistencies. This research introduces ideas towards the development of a robust strategy to image such defects using only a small set of minimal, non-invasive measurements. Assuming a one dimensional model (e.g. longitudinal waves in long and thin rods/acoustic ducts or transverse vibrations of strings), we make use of the continuous one-dimensional wave equation to model these physical phenomena and then employ specialized mathematical analysis tools (the Laplace transform and optimization) to introduce our defect imaging ideas. In particular, we will focus on the case of a long bar which is homogeneous throughout except in a small area where a defect in its Young's modulus is present. We will first demonstrate how the problem is equivalent to a spring-mass vibrational system, and then show how our imaging strategy makes use of the Laplace domain analytic map between the characteristics of the respective defect and the measurement data. More explicitly, we will utilize MATLAB (a platform for numerical computations) to collect synthetic data (computational alternative to real world measurements) for several scenarios with one defect of arbitrary location and stiffness. Subsequently, we will use this data along with our analytically developed map (between defect characteristics and measurements) to construct a residual function which, once optimized, will reveal the location and magnitude of the stiffness defect.

cs.CE↗

arXiv2024

Personal Sound Zones and Shielded Localized Communication through Active Acoustic Control

In this paper, we present a time domain extension of our strategy on manipulating radiated scalar Helmholtz fields and discuss two important applied scenarios, namely (1) creating personal sound zones inside a bounded domain and (2) shielded localized communication. Our strategy is based on the authors' previous works establishing the possibility and stability of controlling acoustic fields using an array of almost non-radiating coupling sources and presents a detailed Fourier synthesis approach towards a time-domain effect. We require that the array of acoustic sources creates the desired fields on the control regions while maintaining a zero field beyond a larger circumscribed sphere. This paper recalls the main theoretical results then presents the underlying Fourier synthesis paradigm and show, through relevant simulations, the performance of our strategy.

cs.SD↗

arXiv2020

Feasibility Analysis for the Problem of Active Near Field/Far Field Acoustic Pattern Synthesis in Free Space and Shallow Water Environments

In this paper, a detailed sensitivity analysis of the active manipulation scheme for scalar Helmholtz fields proposed in our previous works, in both free space and constant-depth homogeneous ocean environments, is presented. We apply the method of moments (MoM) together with Tikhonov regularization with Morozov discrepancy principle to investigate the effects of problem parameters variations on the accuracy and feasibility of the proposed active field control strategy. We discuss the feasibility of the active scheme (power budget and control accuracy) as a function of the frequency, the distance between the control region and the active source, the mutual distance between the control regions, and the size of the control region. Process error is considered as well to investigate the possibility of an accurate active control in the presence of manufacturing noise. The numerical simulations show the accuracy of the active field control scheme and indicate some challenges and limitations for its physical implementations.

physics.comp-ph↗

arXiv2020

Active manipulation of Helmholtz scalar fields: Near field synthesis with directional far field control

In this article, we propose a strategy for the active manipulation of scalar Helmholtz fields in bounded near field regions of an active source while maintaining desired radiation patterns in prescribed far field directions. This control problem is considered in two environments: free space and respectively, homogeneous ocean of constant depth. In both media, we proved the existence of and characterized the surface input, modeled as Neumann data (normal velocity) or Dirichlet data (surface pressure) such that the radiated field satisfies the control constraints. We also provide a numerical strategy to construct this predicted surface input by using a method of moments-approach with a Morozov discrepancy principle-based Tikhonov regularization. Several numerical simulations are presented to demonstrate the proposed scheme in scenarios relevant to practical applications.

eess.SY↗

arXiv2018

Exact relations for Green's functions in linear PDE and boundary field equalities: a generalization of conservation laws

Many physics problems have $J(x)=L(x)E(x)+h(x)$, source $h(x)$, fields $E$,$J$ satisfying differential constraints, symbolized by $E\in\cal E$,$J\in\cal J$ where $\cal E$,$\cal J$ are orthogonal spaces. If $L(x)$ takes values in certain nonlinear manifolds $\cal M$, and coercivity, boundedness hold, then the Green's function satisfies exact identities. We also link Green's functions of different problems. The analysis, based on the theory of exact relations for composites, does not assume microscale variations in $L(x)$, and allows for other equations, such as for waves in lossy media. For bodies $Ω$, in which $L(x)\in{\cal M}$, the Dirichlet-to-Neumann map satisfies boundary field equalities. These generalize the notion of conservation laws: the constraints on the fields inside $Ω$ give identities satisfied by the boundary fields, and provide extra constraints on the interior fields. A consequence is this: if a matrix valued field $Q(x)$ with $\nabla\cdot Q=0$ takes values in a set $\cal B$ (independent of $x$) that lies on a nonlinear manifold, we find conditions on the manifold, and on $\cal B$, that with appropriate conditions on the boundary fluxes $q(x)=n(x)\cdot Q(x)$ (where $n(x)$ is the outwards normal to $\partialΩ$) force $Q(x)$ within $Ω$ to take values in a subspace $\cal D$. This forces $q(x)$ to take values in $n(x)\cdot\cal D$. We find there are additional divergence free fields inside $Ω$ that in turn generate additional boundary field equalities. There exist partial Null-Lagrangians, functionals $F(w,\nabla w)$ of a vector potential $w$ and its gradient, that act as null-Lagrangians when $\nabla w$ is constrained for $x\inΩ$ to take values in certain sets $\cal A$, of appropriate non-linear manifolds, and when $w$ satisfies appropriate boundary conditions. The extension to certain non-linear minimization problems is also sketched.

math.AP↗

arXiv2018

Sensitivity analysis for the active manipulation of Helmholtz fields in 3D

In this paper we continue to study the feasibility of active manipulation of Helmholtz fields and by using an improved and more robust numerical strategy we present a detailed sensitivity analysis for the method proposed in our previous works. In this regard, we study the behavior of physically relevant parameters (i.e. source power, control accuracy, stability) with respect to variations in: the type of control regions (bounded or unbounded), relative position of the control regions, distances between the control regions and the source, frequency range and fields to be approximated. We produce strong numerical evidence indicating the accuracy of our scheme and in the same time develop a better understanding of several important challenges for its physical implementation.

math.OC↗

arXiv2017

On the synthesis of acoustic sources with controllable near fields

In this paper we present a strategy for the the synthesis of acoustic sources with controllable near fields in free space and finite depth homogeneous ocean environments. We first present the theoretical results at the basis of our discussion and then, to illustrate our findings we focus on the following three particular examples: 1. acoustic source approximating a prescribed field pattern in a given bounded sub- region of its near field. 2. acoustic source approximating different prescribed field patterns in given disjoint bounded near field sub-regions. 3. acoustic source approximating a prescribed back-propagating field in a given bounded near field sub-region while maintaining a very low far field signature. For each of these three examples, we discuss the optimization scheme used to approx- imate their solutions and support our claims through relevant numerical simulations.

math.OC↗

arXiv2016

Anomalous localized resonance phenomena in the nonmagnetic, finite-frequency regime

The phenomenon of anomalous localized resonance (ALR) is observed at the interface between materials with positive and negative material parameters and is characterized by the fact that, when a given source is placed near the interface, the electric and magnetic fields start to have very fast and large oscillations around the interface as the absorption in the materials becomes very small while they remain smooth and regular away from the interface. In this paper, we discuss the phenomenon of anomalous localized resonance (ALR) in the context of an infinite slab of homogeneous, nonmagnetic material ($μ=1$) with permittivity $ε_s=-1-\mathrm{i}δ$ for some small loss $δ\ll 1$ surrounded by positive, nonmagnetic, homogeneous media. We explicitly characterize the limit value of the product between frequency and the width of slab beyond which the ALR phenomenon does not occur and analyze the situation when the phenomenon is observed. In addition, we also construct sources for which the ALR phenomenon never appears.

math-ph↗

arXiv2015

Sensitivity analysis for active control of the Helmholtz equation

The results in \cite{O2} (see \cite{O1} for the quasistatics regime) consider the Helmholtz equation with fixed frequency $k$ and, in particular imply that, for $k$ outside a discrete set of resonant frequencies and given a source region $D_a\subset \mathbb{R}^{d}$ ($d=\overline{2,3}$) and $u_0$, a solution of the homogeneous scalar Helmholtz equation in a set containing the control region $D_c\subset \mathbb{R}^{d}$, there exists an infinite class of boundary data on $\partial D_a$ so that the radiating solution to the corresponding exterior scalar Helmholtz problem in $\mathbb{R}^{d} \setminus D_a$ will closely approximate $u_0$ in $D_c$. Moreover, it will have vanishingly small values beyond a certain large enough "far-field" radius $R$. In this paper we study the minimal energy solution of the above problem (e.g. the solution obtained by using Tikhonov regularization with the Morozov discrepancy principle) and perform a detailed sensitivity analysis. In this regard we discuss the stability of the the minimal energy solution with respect to measurement errors as well as the feasibility of the active scheme (power budget and accuracy) depending on: the mutual distances between the antenna, control region and far field radius $R$, value of regularization parameter, frequency, location of the source.

math.AP↗

arXiv2014

Sensitivity of anomalous localized resonance phenomena with respect to dissipation

We analyze cloaking due to anomalous localized resonance in the quasistatic regime in the case when a general charge density distribution is brought near a slab superlens. If the charge density distribution is within a critical distance of the slab, then the power dissipation within the slab blows up as certain electrical dissipation parameters go to zero. The potential remains bounded far away from the slab in this limit, which leads to cloaking due to anomalous localized resonance. On the other hand, if the charge density distribution is further than this critical distance from the slab, then the power dissipation within the slab remains bounded and cloaking due to anomalous localized resonance does not occur. The critical distance is shown to strongly depend on the the rate at which the dissipation outside of the slab goes to zero.

math.AP↗

arXiv2014

On the active manipulation of EM fields in open waveguides

In this paper we present the extension of the results proposed in \cite{Onofrei-S} and study the problem of active control of TM waves propagating in a waveguide. The main goal is to cancel, in a prescribed near field region, the longitudinal component of the electric field of an incoming TM wave while having vanishingly small fields near the waveguide boundary. The main analytical challenge is to design appropriate source functions for the scalar Helmholtz equation so that the desired cancellation effect will be obtained. We show the existence of a class of solutions to the problem and provide numerical support of the results. Discussion on the feasibility of the proposed approach as well as possible design strategies are offered.

math.AP↗

arXiv2012

On the active manipulation of quasistatic fields and its applications

Following the ideas proposed in \cite{OMV1} and \cite{OMV2} on active exterior cloaking, we present here a systematic integral equation method to generate suitable quasistatic fields for cloaking, illusions and energy focusing (with given accuracy) in multiple regions of interests. In the quasistatic regime, the central issue is to design appropriate source functions for the Laplace equation so that the resulting solution will satisfy the required properties. We show the existence and non-uniqueness of solutions to the problem and study the physically relevant unique $L^2$-minimal energy solution. We also provide some numerical evidences on the feasibility of the proposed approach.

math.AP↗

arXiv2011

Mathematical analysis of the two dimensional active exterior cloaking in the quasistatic regime

We design a device that generates fields canceling out a known probing field inside a region to be cloaked while generating very small fields far away from the device. The fields we consider satisfy the Laplace equation, but the approach remains valid in the quasistatic regime in a homogeneous medium. We start by relating the problem of designing an exterior cloak in the quasistatic regime to the classic problem of approximating a harmonic function with harmonic polynomials. An explicit polynomial solution to the problem was given earlier in [Phys. Rev. Lett. 103 (2009), 073901]. Here we show convergence of the device field to the field needed to perfectly cloak an object. The convergence region limits the size of the cloaked region, and the size and position of the device.

math-ph↗

arXiv2011

Transformation elastodynamics and active exterior acoustic cloaking

This chapter consists of three parts. In the first part we recall the elastodynamic equations under coordinate transformations. The idea is to use coordinate transformations to manipulate waves propagating in an elastic material. Then we study the effect of transformations on a mass-spring network model. The transformed networks can be realized with "torque springs", which are introduced here and are springs with a force proportional to the displacement in a direction other than the direction of the spring terminals. Possible homogenizations of the transformed networks are presented, with potential applications to cloaking. In the second and third parts we present cloaking methods that are based on cancelling an incident field using active devices which are exterior to the cloaked region and that do not generate significant fields far away from the devices. In the second part, the exterior cloaking problem for the Laplace equation is reformulated as the problem of polynomial approximation of analytic functions. An explicit solution is given that allows to cloak larger objects at a fixed distance from the cloaking device, compared to previous explicit solutions. In the third part we consider the active exterior cloaking problem for the Helmholtz equation in 3D. Our method uses the Green's formula and an addition theorem for spherical outgoing waves to design devices that mimic the effect of the single and double layer potentials in Green's formula.

math-ph↗

arXiv2009

Complete characterization and synthesis of the response function of elastodynamic networks

The response function of a network of springs and masses, an elastodynamic network, is the matrix valued function $W(ω)$, depending on the frequency $ω$, mapping the displacements of some accessible or terminal nodes to the net forces at the terminals. We give necessary and sufficient conditions for a given function $W(ω)$ to be the response function of an elastodynamic network, assuming there is no damping. In particular we construct an elastodynamic network that can mimic a suitable response in the frequency or time domain. Our characterization is valid for networks in three dimensions and also for planar networks, which are networks where all the elements, displacements and forces are in a plane. The network we design can fit within an arbitrarily small neighborhood of the convex hull of the terminal nodes, provided the springs and masses occupy an arbitrarily small volume. Additionally, we prove stability of the network response to small changes in the spring constants and/or addition of springs with small spring constants.

math-ph↗

arXiv2009

Broadband Exterior Cloaking

It is shown how a recently proposed method of cloaking is effective over a broad range of frequencies. The method is based on three or more active devices. The devices, while not radiating significantly, create a ``quiet zone'' between the devices where the wave amplitude is small. Objects placed within this region are virtually invisible. The cloaking is demonstrated by simulations with a broadband incident pulse.

math-ph↗

arXiv2009

Active Exterior Cloaking

A new method of cloaking is presented. For two-dimensional quasistatics it is proven how a single active exterior cloaking device can be used to shield an object from surrounding fields, yet produce very small scattered fields. The problem is reduced to finding a polynomial which is approximately one within one disk and zero within a second disk, and such a polynomial is constructed. For the two-dimensional Helmholtz equation, it is numerically shown that three active exterior devices placed around the object suffice to produce very good cloaking.

math-ph↗