The Invalidity of the Laplace Law for Biological Vessels and of Estimating Elastic Modulus from Total Stress vs. Strain: a New Practical Method

The quantification of the stiffness of tubular biological structures is often obtained, both in vivo and in vitro, as the slope of total transmural hoop stress plotted against hoop strain. Total hoop stress is typically estimated using the "Laplace law." We show that this procedure is fundamentally flawed for two reasons: Firstly, the Laplace law predicts total stress incorrectly for biological vessels. Furthermore, because muscle and other biological tissue are closely volume-preserving, quantifications of elastic modulus require the removal of the contribution to total stress from incompressibility. We show that this hydrostatic contribution to total stress has a strong material-dependent nonlinear response to deformation that is difficult to predict or measure. To address this difficulty, we propose a new practical method to estimate a mechanically viable modulus of elasticity that can be applied both in vivo and in vitro using the same measurements as current methods, with care taken to record the reference state. To be insensitive to incompressibility, our method is based on shear stress rather than hoop stress, and provides a true measure of the elastic response without application of the Laplace law. We demonstrate the accuracy of our method using a mathematical model of tube inflation with multiple constitutive models. We also re-analyze an in vivo study from the gastro-intestinal literature that applied the standard approach and concluded that a drug-induced change in elastic modulus depended on the protocol used to distend the esophageal lumen. Our new method removes this protocol-dependent inconsistency in the previous result.Comment: 34 pages, 13 figure

Discontinua urbani. Dispositio e città nel Novecento / Urban Discontinuity. Dispositio and city in the Twentieth Century

Il contributo tende a mettere in luce i rapporti tra l’aspirazione novecentesca al discontinua urbani e la dispositio. Sulla base di una premessa centrata su tre questioni rilevanti (valore del centro, relazione ordine discontinuo/identità del manufatto, modalità di trasferimento delle condizioni di contesto nella spazialità discontinua), il testo approfondisce i contenuti del principio eteronomo e del metodo selettivo che hanno caratterizzato il contributo di alcuni maestri della scuola italiana nella seconda metà del secolo scorso. Paper tends to highlight relationships between the twentieth-century inspiration to discontinua urbani and the dispositio. On the base premise focused on three relevant issues (value of the centre, relationship discontinuous order / artefact identity, transferring modes of contextual conditions into discontinuous spatiality), text deepens heteronomous principle and selective method as contents whose have characterized contributions by some Italian School masters of the second half of the last century

Adjustment curves for binary responses associated to stochastic processes

Functional Data, Random Multiplicative Cascade, Adjustment Curve, Stochastic Process

Variational Implementation of Immersed Finite Element Methods

Dirac-delta distributions are often crucial components of the solid-fluid coupling operators in immersed solution methods for fluid-structure interaction (FSI) problems. This is certainly so for methods like the Immersed Boundary Method (IBM) or the Immersed Finite Element Method (IFEM), where Dirac-delta distributions are approximated via smooth functions. By contrast, a truly variational formulation of immersed methods does not require the use of Dirac-delta distributions, either formally or practically. This has been shown in the Finite Element Immersed Boundary Method (FEIBM), where the variational structure of the problem is exploited to avoid Dirac-delta distributions at both the continuous and the discrete level. In this paper, we generalize the FEIBM to the case where an incompressible Newtonian fluid interacts with a general hyperelastic solid. Specifically, we allow (i) the mass density to be different in the solid and the fluid, (ii) the solid to be either viscoelastic of differential type or purely elastic, and (iii) the solid to be and either compressible or incompressible. At the continuous level, our variational formulation combines the natural stability estimates of the fluid and elasticity problems. In immersed methods, such stability estimates do not transfer to the discrete level automatically due to the non- matching nature of the finite dimensional spaces involved in the discretization. After presenting our general mathematical framework for the solution of FSI problems, we focus in detail on the construction of natural interpolation operators between the fluid and the solid discrete spaces, which guarantee semi-discrete stability estimates and strong consistency of our spatial discretization.Comment: 42 pages, 5 figures, Revision

analysis of the al and ti additions influences on phases generation and damage in a hot dip galvanizing process

Abstract Cheap iron-based alloys, such as Ductile Cast Irons (DCIs) and low carbon steels, are more and more used in the mechanical field because they are characterized by good strength and good workability. However, the low value of electrochemical potential of low carbon steel leads to quick environmental corrosion that can compromise the operative life of mechanical components. Therefore, it is important to protect them against corrosion even for safety and reliability reasons. The use of a traditional protection technique, like Hot Dip Galvanizing (HDG), allows low costs too. In this work, the phase formation during HDG process is presented and discussed. In particular, the influence of Al and Ti additions on the pure Zn bath is shown in the metallographic analysis, presenting also the results of pure Zn bath

Comparative analysis of overland flow models using finite volume schemes

In this paper attention is first focused on a comparative analysis of three hydraulic models for overland flow simulations. In particular, the overland flow was considered as a 2D unsteady flow and was mathematically described using three approaches (fully dynamic, diffusive and kinematic waves). Numerical results highlighted that the differences among the simulations were not very important when the simulations referred to commonly used ideal tests found in the literature in which the topography is reduced to plane surface. Significant differences were observed in more complicated tests for which only the fully dynamic model was able to provide a good prediction of the observed discharges and water depths. Then, attention is focused on the fully dynamic model and in particular on the analysis of two numerical schemes (TVD-MacCormack and HLL) and the influence of the grid size. Numerical tests carried out on irregular topography show that, as the grid size decreases, the performance of the HLL scheme becomes closer to that of the TVD-MacCormack scheme in shorter computational times at least for high rainfall intensity

Discontinua urbani. Dispositio e città nel Novecento

Il contributo tende a mettere in luce i rapporti tra l’aspirazione novecentesca al discontinua urbani e la dispositio. Sulla base di una premessa centrata su tre questioni rilevanti (valore del centro, relazione ordine discontinuo/identità del manufatto, modalità di trasferimento delle condizioni di contesto nella spazialità discontinua), il testo approfondisce i contenuti del principio eteronomo e del metodo selettivo che hanno caratterizzato il contributo di alcuni maestri della scuola italiana nella seconda metà del secolo scorso