A PDE-constrained optimization formulation for discrete fracture network flows

We investigate a new numerical approach for the computation of the 3D flow in a discrete fracture network that does not require a conforming discretization of partial differential equations on complex 3D systems of planar fractures. The discretization within each fracture is performed independently of the discretization of the other fractures and of their intersections. Independent meshing process within each fracture is a very important issue for practical large scale simulations making easier mesh generation. Some numerical simulations are given to show the viability of the method. The resulting approach can be naturally parallelized for dealing with systems with a huge number of fractures

Repositioning template for mandibular reconstruction with fibular free flap: an alternative technique to pre-plating and virtual surgical planning

Oral malignancies involving the mandibular bone require a complex reconstructive plan. Mandibular reconstruction with a fibular free flap is currently considered the best choice for functional and aesthetic rehabilitation after oncological surgery. This flap can be modelled with multiple osteotomies and can provide bone, muscle and skin for composite reconstruction. One of the most delicate aspects of mandibular reconstruction is the technique of bone modelling; the risk of prolonging the period of ischaemia and not restoring the correct maxillomandibular and occlusal relationships can ultimately lead to a higher rate of complications as well as poor aesthetic and functional results. Recently, there has been rising interest in virtual surgical planning and computer-assisted mandibular reconstruction in pre-operative planning; however, this is not always possible because of the costs involved and the set-up time for the entire procedure. In this paper, we present a simple and inexpensive technique for fibular free flap modelling and repositioning after segmental resection of the mandible; the technique entails the pre-operative preparation of a resin repositioning template on a stereolithographic model. This technique has been successfully applied in four cases: two cases underwent resection involving only the mandibular body, one case involving the mandibular body and symphysis and one case in which a ramus to ramus resection was performed. In this preliminary report, we show that the resin repositioning template is an easy, safe and useful tool for mandibular reconstruction with a fibular free flap

A globally conforming method for solving flow in discrete fracture networks using the Virtual Element Method

A new approach for solving flow in Discrete Fracture Networks (DFN) is developed in this work by means of the Virtual Element Method. Taking advantage of the features of the VEM, we obtain global conformity of all fracture meshes while preserving a fracture-independent meshing process. This new approach is based on a generalization of globally conforming Finite Elements for polygonal meshes that avoids complications arising from the meshing process. The approach is robust enough to treat many DFNs with a large number of fractures with arbitrary positions and orientations, as shown by the simulations. Higher order Virtual Element spaces are also included in the implementation with the corresponding convergence results and accuracy aspects

Enforcing Dirichlet boundary conditions in physics-informed neural networks and variational physics-informed neural networks

In this paper, we present and compare four methods to enforce Dirichlet boundary conditions in Physics-Informed Neural Networks (PINNs) and Variational Physics-Informed Neural Networks (VPINNs). Such conditions are usually imposed by adding penalization terms in the loss function and properly choosing the corresponding scaling coefficients; however, in practice, this requires an expensive tuning phase. We show through several numerical tests that modifying the output of the neural network to exactly match the prescribed values leads to more efficient and accurate solvers. The best results are achieved by exactly enforcing the Dirichlet boundary conditions by means of an approximate distance function. We also show that variationally imposing the Dirichlet boundary conditions via Nitsche's method leads to suboptimal solvers.Comment: 22 pages, 45 figure

The Impact of Symbolic and Substantive Actions on Environmental Legitimacy

Drawing on institutional theory and insights from stakeholder theory and impression management, we empirically analyze the impact of both environmental symbolic polices (participation in voluntary environmental programs, green trademarks, environmental-dedicated board committees, environmental pay policies and community communication) and substantive actions (environmental patents and pollution prevention practices) on environmental legitimacy. We show that (1) symbolic actions have a weaker positive effect on legitimacy than substantive actions, (2) that the impact of symbolic actions is greater when they are combined with substantive actions, (3) that this impact is only short-term while substantive actions have both short- and long-term effects

Coupling traffic models on networks and urban dispersion models for simulating sustainable mobility strategies

The aim of the present paper is to investigate the viability of macroscopic traffic models for modeling and testing different traffic scenarios, in order to define the impact on air quality of different strategies for the reduction of traffic emissions. To this aim, we complement a well assessed traffic model on networks (Garavello, Piccoli, 2006) with a strategy for estimating data needed from the model and we couple it with the urban dispersion model Sirane (Soulhac, 2000)

A hybrid mortar virtual element method for discrete fracture network simulations

The most challenging issue in performing underground flow simulations in Discrete Fracture Networks (DFN), is to effectively tackle the geometrical difficulties of the problem. In this work we put forward a new application of the Virtual Element Method combined with the Mortar method for domain decomposition: we exploit the flexibility of the VEM in handling polygonal meshes in order to easily construct meshes conforming to the traces on each fracture, and we resort to the mortar approach in order to ``weakly'' impose continuity of the solution on intersecting fractures. The resulting method replaces the need for matching grids between fractures, so that the meshing process can be performed independently for each fracture. Numerical results show optimal convergence and robustness in handling very complex geometries

Family involvement and firms’ establishment mode choice in foreign markets

Extant literature on foreign entry increasingly recognizes firms’ heterogeneity as a potential reason for inconsistency in results on the establishment mode choice, i.e. whether and under which conditions firms should choose to enter a new country through a greenfield investment or an acquisition. Our study contributes to this debate by identifying family ownership and family involvement in management as potential powerful sources of such heterogeneity. Integrating international business studies with both corporate finance literature on family firms and recent contributions from the Socio Emotional Wealth perspective on family ownership, we claim that, due to greater risk aversion and lower access to information, the family involvement either in the firm ownership and management leads to a higher propensity towards greenfield initiatives (vs. acquisitions). However, we also find that such a propensity decreases with international experience especially in family-owned firms given the greater ability of professionalized management to overcome family-related concerns on making acquisitions. Our analysis on 1,045 foreign initiatives undertaken by 311 Italian family and non-family firms between 2003 and 2013 confirms our expectations – indicating family ownership as a significant driver of international business choices