The postulations á la D'Alembert and á la Cauchy for higher gradient continuum theories are equivalent. A review of existing results

In order to found continuum mechanics, two different postulations have been used. The first, introduced by Lagrange and Piola, starts by postulating how the work expended by internal interactions in a body depends on the virtual velocity field and its gradients. Then, by using the divergence theorem, a representation theorem is found for the volume and contact interactions which can be exerted at the boundary of the considered body. This method assumes an a priori notion of internal work, regards stress tensors as dual of virtual displacements and their gradients, deduces the concept of contact interactions and produces their representation in terms of stresses using integration by parts. The second method, conceived by Cauchy and based on the celebrated tetrahedron argument, starts by postulating the type of contact interactions which can be exerted on the boundary of every (suitably) regular part of a body. Then it proceeds by proving the existence of stress tensors from a balance-type postulate. In this paper, we review some relevant literature on the subject, discussing how the two postulations can be reconciled in the case of higher gradient theories. Finally, we underline the importance of the concept of contact surface, edge and wedge s-order forces

Bias extension test for pantographic sheets: numerical simulations based on second gradient shear energies

We consider a bi-dimensional sheet consisting of two orthogonal families of inextensible fibres. Using the representation due to Rivlin and Pipkin for admissible placements, i.e. placements preserving the lengths of the inextensible fibres, we numerically simulate a standard bias extension test on the sheet, solving a non-linear constrained optimization problem. Several first and second gradient deformation energy models are considered, depending on the shear angle between the fibres and on its gradient, and the results obtained are compared. The proposed numerical simulations will be helpful in designing a systematic experimental campaign aimed at characterizing the internal energy for physical realizations of the ideal pantographic structure presented in this paper

On-Chip Integrated Antenna Structures for Biomedical Implantable Sensors

AbstractThis paper explores some different geometries of integrated antennas in a 0.35 μm CMOS technology for devices operating in theinternationally available unlicensed 2.4 GHz band. At this frequency, the wavelength is short enough to implement smallantennas with dimensions economically feasible for silicon integration.Two are the considered different families of structures: spiral and dipole antennas, and some different antenna structures (singleloop,4-loop, double-4-loop, dipole, bent-dipole, meander-dipole) are examined, all modeled and simulated in Ansoft HFSS.Their inductive and radiation characteristics are compared. Chip dimensions of the order of one square millimetre are considered

Referential description of the evolution of a 2D swarm of robots interacting with the closer neighbors. Perspectives of continuum modeling via higher gradient continua

In the present paper a discrete robotic system model whose elements interact via a simple geometric law is presented and some numerical simulations are provided and discussed. The main idea of the work is to show the resemblance between the cases of first and second neighbors interaction with (respectively) first and second gradient continuous deformable bodies. Our numerical results showed indeed that the interaction and the evolution process described is suitable to closely reproduce some basic characteristics of the behavior of bodies whose deformation energy depends on first or on higher gradients of the displacement. Moreover, some specific qualitative characteristics of the continuous deformation are also reproduced. The model introduced here will need further investigation and generalization in both theoretical and numerical directions

A Discrete Risk-Theory Approach to Manage Equity-Linked Policies in an Incomplete Market

We construct a model where, at each time instance, risky securities can only take a limited number of values and the equity-linked policy sold by the insurer to policyholders pays benefits linked to these securities. Since the number of states in the model exceeds the number of securities in the (incomplete) market, the martingale measure is not unique, posing a problem in pricing insurance instruments. In this framework, we consider how a super-replicating strategy violates the assumption of absence of arbitrage, yet simultaneously allows the insurance company to fully hedge against financial risk. Since the super-replicating strategy, when considered alone, would be too costly for any rational insured, through the definition of the safety loading, we demonstrate how the insurer can still hedge against financial risk, albeit at the expense of increasing its exposure to demographic risk. This approach does not aim to show how the pricing of the index-linked policy can actually be performed, but rather highlights how risk theory-based approaches (via the definition of the profit and loss random variable) enable the management of the trade-off between financial risk and demographic risk

A cohort-based Partial Internal Model for demographic risk

We investigate the quantification of demographic risk in a framework consistent with the market-consistent valuation imposed by Solvency II. We provide compact formulas for evaluating inflows and outflows of a portfolio of insurance policies based on a cohort approach. In this context, we maintain the highest level of generality in order to consider both traditional policies and equity-linked policies: therefore, we propose a market-consistent valuation of the liabilities. In the second step we evaluate the Solvency Capital Requirement of the idiosyncratic risk, linked to accidental mortality, and the systematic risk one, also known as trend risk, proposing a formal closed formula for the former and an algorithm for the latter. We show that accidental volatility depends on the intrinsic characteristics of the policies of the cohort (Sums-at-Risk), on the age of the policyholders and on the variability of the sums insured; trend risk depends both on accidental volatility and on the longevity forecasting model used

Modeling Deformable Bodies Using Discrete Systems with Centroid-Based Propagating Interaction: Fracture and Crack Evolution

International audienceWe use a simple discrete system in order to model deformation and fracture within the same theoretical and numerical framework. The model displays a rich behavior, accounting for different fracture phenomena, and in particular for crack formation and growth. A comparison with standard Finite Element simulations and with the basic Griffith theory of fracture is provided. Moreover, an ‘almost steady’ state, i.e. a long apparent equilibrium followed by an abrupt crack growth, is obtained by suitably parameterizing the system. The model can be easily generalized to higher order interactions corresponding, in the homogenized limit, to higher gradient continuum theories

Electro-optical modulation at 1550 nm in an as-deposited hydrogenated amorphous silicon p-i-n waveguiding device.

Hydrogenated amorphous silicon (a-Si:H) has been already considered for the objective of passive optical elements, like waveguides and ring resonators, within photonic integrated circuits at λ = 1.55 μm. However the study of its electro-optical properties is still at an early stage, therefore this semiconductor in practice is not considered for light modulation as yet. We demonstrated, for the first time, effective electrooptical modulation in a reverse biased a-Si:H p-i-n waveguiding structure. In particular, phase modulation was studied in a waveguide integrated Fabry-Perot resonator in which the Vπ·Lπ product was determined to be 63 V·cm. Characteristic switch-on and switch-off times of 14 ns were measured. The device employed a wider gap amorphous silicon carbide (a-SiC:H) film for the lower cladding layer instead of silicon oxide. In this way the highest temperature involved in the fabrication process was 170°C, which ensured the desired technological compatibility with CMOS processes. © 2011 Optical Society of America