Shape differentiability of the eigenvalues of elliptic systems

We consider second order elliptic systems of partial differential equations subject to Dirichlet and Neumann boundary conditions. We prove analyticity of the elementary symmetric functions of the eigenvalues, and compute Hadamard-type formulas for such functions. Then we provide a characterization of criticality of the domain under volume constraint, and prove that if the system is rotation invariant, then balls are critical domains for all those functions.Comment: Submitted for the IMSE 2014 Conference Proceeding

Health and safety at work: the prevention model in Italy. WP C.S.D.L.E. “Massimo D’Antona”.IT – 408/2020

A research itinerary aimed at clarifying the substantive content and the type of prevention that shapes the rules for the protection of health and safety of workers in the Italian legal system. The focus will be on the difference between primary and secondary prevention in the warranty of fundamental right

On the eigenvalues of a biharmonic Steklov problem

We consider an eigenvalue problem for the biharmonic operator with Steklov-type boundary conditions. We obtain it as a limiting Neumann problem for the biharmonic operator in a process of mass concentration at the boundary. We study the dependence of the spectrum upon the domain. We show analyticity of the symmetric functions of the eigenvalues under isovolumetric perturbations and prove that balls are critical points for such functions under measure constraint. Moreover, we show that the ball is a maximizer for the first positive eigenvalue among those domains with a prescribed fixed measure.Comment: This paper will appear in the proceedings of the IMSE 2014 Conferenc

On-demand Aerodynamics in Integrally Actuated Membranes with Feedback Control

This paper is a numerical investigation on model reduction and control system design of integrally actuated membrane wings. A high-fidelity electro-aeromechanical model is used for the simulation of the dynamic fluid-structure interaction between a low-Reynolds-number flow and a dielectric elastomeric wing. Two reduced-order models with different levels of complexity are then derived. They are based on the projection of the fullorder discretisation of fluid and structure on modal shapes obtained from eigenvalue analysis and Proper Orthogonal Decomposition. The low-order systems are then used for the design of Proportional-Integral-Derivative and Linear Quadratic Gaussian feedback schemes to control wing lift. When implemented in the full-order model, closed-loop dynamics are in very good agreement with the reduced-order model for both tracking and gust rejection, demonstrating the suitability of the approach. The control laws selected in this work were found to be effective only for low-frequency disturbances due to the large phase delay introduced by the fluid convective time-scales, but results demonstrate the potential for the aerodynamic control of membrane wings in outdoor flight using dielectric elastomers

Alasdair MacIntyre’s Contribution to Marxism: A Road not Taken

This essay questions, through a critique of his reading of classical Marxism, the path taken by Alasdair MacIntyre since his break with the Marxist Left in the 1960s. It argues that MacIntyre was uncharitable in his criticisms of Marxism, or at least in his conflation of the most powerful aspects of the classical Marxist tradition with the crudities of Kautskyian and Stalinist materialism. Contra MacIntyre, this essay locates in the writings of the revolutionary Left which briefly flourished up to and just after the Russian Revolution a rich source of dialectical thinking on the relationship between structure and agency that escapes the twin errors of crude materialism or political voluntarism. Moreover, it suggests that by reaching back to themes reminiscent of the young Marx this tradition laid the basis for a renewed ethical Marxism, and that in his youth MacIntyre pointed to the realisation of this project

Semiclassical bounds for spectra of biharmonic operators

We provide complementary semiclassical bounds for the Riesz means $R_1(z)$ of the eigenvalues of various biharmonic operators, with a second term in the expected power of $z$. The method we discuss makes use of the averaged variational principle (AVP), and yields two-sided bounds for individual eigenvalues, which are semiclassically sharp. The AVP also yields comparisons with Riesz means of different operators, in particular Laplacians

On the behavior of clamped plates under large compression

We determine the asymptotic behavior of eigenvalues of clamped plates under large compression by relating this problem to eigenvalues of the Laplacian with Robin boundary conditions. Using the method of fundamental solutions, we then carry out a numerical study of the extremal domains for the first eigenvalue, from which we see that these depend on the value of the compression, and start developing a boundary structure as this parameter is increased. The corresponding number of nodal domains of the first eigenfunction of the extremal domain also increases with the compression.This work was partially supported by the Funda ̧c ̃ao para a Ciˆencia e a Tecnologia(Portugal) through the program “Investigador FCT” with reference IF/00177/2013 and the projectExtremal spectral quantities and related problems(PTDC/MAT-CAL/4334/2014).info:eu-repo/semantics/publishedVersio

A Minimaxmax Problem for Improving the Torsional Stability of Rectangular Plates

We use a gap function in order to compare the torsional performances of different reinforced plates under the action of external forces. Then, we address a shape optimization problem, whose target is to minimize the torsional displacements of the plate: this leads us to set up a minimaxmax problem, which includes a new kind of worst-case optimization. Two kinds of reinforcements are considered: one aims at strengthening the plate, the other aims at weakening the action of the external forces. For both of them, we study the existence of optima within suitable classes of external forces and reinforcements. Our results are complemented with numerical experiments and with a number of open problems and conjectures

Primo e secondo welfare: il contrasto della debolezza sociale oggi = First and second welfare: the contrast of social weakness today. WP C.S.D.L.E. “Massimo D’Antona”.IT – 342/2017

The essay takes into consideration contractual and legal welfare schemes, considered instruments to improve solidarity in social security system. The Author suggests to go beyond the context and to face nowadays challenges (in particular as regards work digitalization and fragmentation) strengthening solidarity between workers and widening the target’s extension of legal social protection