In this paper, an equilibrium problem for 2D non-homogeneous anisotropic elastic body is considered. It is assumed that the body has a thin elastic inclusion and a thin rigid inclusion. A connection ...between the inclusions at a given point is characterized by a junction stiffness parameter. The elastic inclusion is delaminated, thus forming an interfacial crack with the matrix. Inequality-type boundary conditions are imposed at the crack faces to prevent interpenetration. Existence of solutions is proved; different equivalent formulations of the problem are discussed; junction conditions at the connection point are found. A convergence of solutions as the junction stiffness parameter tends to zero and to infinity as well as the rigidity parameter of the elastic inclusion tends to infinity is investigated. An analysis of limit models is provided. An optimal control problem is analyzed with the cost functional equal to the derivative of the energy functional with respect to the crack length. A solution existence of an inverse problem for finding the junction stiffness and rigidity parameters is proved.
Abstract
In this paper, we deal with an inverse electrical conductivity problem which considers the reconstruction of nonlinear electrical conductivity in steady currents operations using boundary ...measurements. In the current set up, we establish a monotonic relation between the unknown material property to the (measured) Dirichlet-to-Neumann operator (DtN). It is in fact the Monotonicity Principle which is the base of a class of non-iterative and real-time imaging methods and algorithms. To be more precise, we indicate the issues appear in our nonlinear case to transfer this Monotonicity result from the Dirichlet Energy to the DtN operator which is the fundamental huddle in comparison to linear and p-Laplacian cases. Finally, we introduce a new Average DtN operator which is different from the existing ones and resolves complications produced by non-linearity in our problem.
Abstract This paper deals with the Monotonicity Principle (MP) for nonlinear materials with piecewise growth exponent. The results obtained are relevant because they enable the use of a fast imaging ...method based on MP, applied to a wide class of problems with two or more materials, at least one of which is nonlinear. The treatment is very general and makes it possible to model a wide range of practical configurations such as superconducting (SC), perfect electrical conducting (PEC) or perfect electrical insulating (PEI) materials. A key role is played by the average Dirichlet-to-Neumann operator, introduced in Corbo Esposito et al (2021 Inverse Problems 37 045012), where the MP for a single type of nonlinearity was treated. Realistic numerical examples confirm the theoretical findings.
In this paper, we present OliVier a new Public Key Exchange cryptosystem that is based on a multivariate quadratic polynomial system: Oil & Vinegar polynomials together with fully quadratic ones. We ...describe its designing process, usage, complexity
This article deals with two funerary epigraphs found after the fall in the level of the river Calore, near the remains of an ancient Roman bridge. The epigraphs are above an ara and a cupa, the ...latter being outstanding for its singular form, probably set along one of the two sides of a secondary branch of the via Latina way in ancient times. Perfectly preserved, today they are in the abbey of Sant'Anastasia a Ponte.
In this paper, we analyze the algebraic invariants for two classes of multivariate quadratic systems: systems made by OV quadratic polynomials and systems made by both OV polynomials and fully ...quadratic ones. For such systems, we explicitly compute the Hilbert series, and we give bounds on the degree of regularity, solving degree and first fall degree that are useful in cryptographic applications.
The data clustering problem consists in dividing a data set into prescribed groups of homogeneous data. This is an NP-hard problem that can be relaxed in the spectral graph theory, where the optimal ...cuts of a graph are related to the eigenvalues of graph 1-Laplacian. In this paper, we first give new notations to describe the paths, among critical eigenvectors of the graph 1-Laplacian, realizing sets with prescribed genus. We introduce the pseudo-orthogonality to characterize
m
3
(
G
), a special eigenvalue for the graph 1-Laplacian. Furthermore, we use it to give an upper bound for the third graph Cheeger constant
h
3
(
G
), that is,
h
3
(
G
) ⩽
m
3
(
G
). This is a first step for proving that the
k
-th Cheeger constant is the minimum of the 1-Laplacian Raylegh quotient among vectors that are pseudo-orthogonal to the vectors realizing the previous
k
− 1 Cheeger constants. Eventually, we apply these results to give a method and a numerical algorithm to compute
m
3
(
G
), based on a generalized inverse power method.
In this paper we present a first non-iterative imaging method for nonlinear materials, based on Monotonicity Principle. Specifically, we deal with the inverse obstacle problem, where the aim is to ...retrieve a nonlinear anomaly embedded in linear known background. The Monotonicity Principle (MP) is a general property for various class of PDEs, that has recently generalized to nonlinear elliptic PDEs. Basically, it states a monotone relation between the point-wise value of the unknown material property and the boundary measurements. It is at the foundation of a class of non-iterative imaging methods, characterized by a very low execution time that makes them ideal candidates for real-time applications. In this work, we develop an inversion method that overcomes some of the peculiar difficulties in practical application of MP to imaging of nonlinear materials, preserving the feasibility for real-time applications. For the sake of clarity, we focus on a specific application, i.e. the Magnetostatic Permeability Tomography where the goal is retrieving the unknown (nonlinear) permeability by boundary measurements in DC operations. This choice is motivated by applications in the inspection of boxes and containers for security. Reconstructions from simulated data prove the effectiveness of the presented method.
Inverse problems, which are related to Maxwell's equations, in the presence of nonlinear materials is a quite new topic in the literature. The lack of contributions in this area can be ascribed to ...the significant challenges that such problems pose. Retrieving the spatial behaviour of some unknown physical property, from boundary measurements, is a nonlinear and highly ill-posed problem even in the presence of linear materials. Furthermore, this complexity grows exponentially in the presence of nonlinear materials. In the tomography of linear materials, the Monotonicity Principle (MP) is the foundation of a class of non-iterative algorithms able to guarantee excellent performances and compatibility with real-time applications. Recently, the MP has been extended to nonlinear materials under very general assumptions. Starting from the theoretical background for this extension, we develop a first real-time inversion method for the inverse obstacle problem in the presence of nonlinear materials. The proposed method is intendend for all problems governed by the quasilinear Laplace equation, i.e. static problems involving nonlinear materials. In this paper, we provide some preliminary results which give the foundation of our method and some extended numerical examples.
Ultrasonic motors have been exploited mainly in low power and low duty cycle applications. In aerospace and automotive applications, there is also the need for motors able to provide high torque but ...employed at very low duty cycle. In this work numerical simulations and experimental measurements carried out on a high power ultrasonic motor are presented. The proposed motor is composed of a annular shaped stator and two light cone shaped rotors. The rotors are pressed in contact to the borders of the inner surface of the stator by means of an opportune pre-stress system. A travelling rotating wave is generated in the stator by two and four Bolted Langevin Transducers, opportunely placed on the lateral surface of the stator. Each transducer is designed to excite in the ring radial nonaxisymmetric modes. The effective generation of the travelling wave in the stator, with both two and four driving transducers, has been accurately simulated with a FEM software. A prototype of the motor has been constructed and experimentally characterized. Comparisons between simulation and measurements have shown a satisfactory agreement. The improvement of motor performances achieved by increasing the number of driving transducers is analyzed and discussed.
