Shape Optimization for Thermal Insulation Problems

[EN] In this work we consider two domains: an external domain whose geometry varies, and an internal fixed one. From the thermal insulation viewpoint, we are considering a body to be insulated, enveloped in a layer of insulator, and we want to find the best shape for the thermal insulator, in terms of heat dispersion. Mathematically, our problem is described by an elliptic partial differential equation with Dirichlet-Robin boundary conditions.This research has been carried on within the PON R&I 2014-2020 - “AIM: Attraction and International Mobility” (Linea 2.1, project AIM1834118 - 2, CUP: E61G19000050001). The authors are members of the INdAM Research Group GNCS.Tozza, S.; Toraldo, G. (2022). Shape Optimization for Thermal Insulation Problems. En Proceedings of the YIC 2021 - VI ECCOMAS Young Investigators Conference. Editorial Universitat Politècnica de València. 11-15. https://doi.org/10.4995/YIC2021.2021.12288OCS111

A two-phase gradient method for quadratic programming problems with a single linear constraint and bounds on the variables

We propose a gradient-based method for quadratic programming problems with a single linear constraint and bounds on the variables. Inspired by the GPCG algorithm for bound-constrained convex quadratic programming [J.J. Mor\'e and G. Toraldo, SIAM J. Optim. 1, 1991], our approach alternates between two phases until convergence: an identification phase, which performs gradient projection iterations until either a candidate active set is identified or no reasonable progress is made, and an unconstrained minimization phase, which reduces the objective function in a suitable space defined by the identification phase, by applying either the conjugate gradient method or a recently proposed spectral gradient method. However, the algorithm differs from GPCG not only because it deals with a more general class of problems, but mainly for the way it stops the minimization phase. This is based on a comparison between a measure of optimality in the reduced space and a measure of bindingness of the variables that are on the bounds, defined by extending the concept of proportioning, which was proposed by some authors for box-constrained problems. If the objective function is bounded, the algorithm converges to a stationary point thanks to a suitable application of the gradient projection method in the identification phase. For strictly convex problems, the algorithm converges to the optimal solution in a finite number of steps even in case of degeneracy. Extensive numerical experiments show the effectiveness of the proposed approach.Comment: 30 pages, 17 figure

Using gradient directions to get global convergence of Newton-type methods

The renewed interest in Steepest Descent (SD) methods following the work of Barzilai and Borwein [IMA Journal of Numerical Analysis, 8 (1988)] has driven us to consider a globalization strategy based on SD, which is applicable to any line-search method. In particular, we combine Newton-type directions with scaled SD steps to have suitable descent directions. Scaling the SD directions with a suitable step length makes a significant difference with respect to similar globalization approaches, in terms of both theoretical features and computational behavior. We apply our strategy to Newton's method and the BFGS method, with computational results that appear interesting compared with the results of well-established globalization strategies devised ad hoc for those methods.Comment: 22 pages, 11 Figure

A Sequential Monte Carlo Approach for the pricing of barrier option in a Stochastic Volatility Model

In this paper we propose a numerical scheme to estimate the price of a barrier option in a general framework. More precisely, we extend a classical Sequential Monte Carlo approach, developed under the hypothesis of deterministic volatility, to Stochastic Volatility models, in order to improve the efficiency of Standard Monte Carlo techniques in the case of barrier options whose underlying approaches the barriers. The paper concludes with the application of our procedure to two case studies in a SABR model

Modelling Lobbying Behaviour and Interdisciplinarity Dynamics in Academia

Disciplinary diversity is being recognized today as the key to establish a vibrant academic environment with bigger potential for breakthroughs in research and technology. However, the interaction of several factors including policies, and behavioral attitudes put significant barriers on advancing interdisciplinarity. A "cognitive rigidity" may rise due to reactive academic lobbying favouring inbreeding. Here, we address, analyse and discuss a mathematical model of lobbying and interdisciplinarity dynamics in Academia. The model consists of four coupled non-linear Ordinary Differential Equations simulating the interaction between three types of academic individuals and a state reflecting the rate of knowledge advancement which is related to the level of disciplinary diversity. Our model predicts a rich nonlinear behaviour including multiplicity of states and sustained periodic oscillations resembling the everlasting struggle between the "new" and the "old". The effect of a control policy that inhibits lobbying is also studied. By appropriate adjustment of the model parameters we approximated the jump/phase transitions in breakthroughs in mathematical and molecular biological sciences resulted by the increased flow of Russian scientists in the USA after the dissolution of the Soviet Union starting in 1989, the launch of the Human Genome Project in 1992 and the Internet diffusion starting in 2000

A Semi-Automatic Numerical Algorithm for Turing Patterns Formation in a Reaction-Diffusion Model

The Turing pattern formation is modeled by reaction - diffusion (RD) type partial differential equations , and it plays a crucial role in ecological studies. Big data analytics and suitable frameworks to manage and predict structures and configurations are mandatory. The processing and resolution procedures of mathematical models relies upon numerical schemes, and concurrently upon the related automated algorithms. Starting from a RD model for vegetation patterns, we propose a semi-automatic algorithm based on a smart numerical criterion for observing ecological reliable results. Numerical experiments are carried out in the case of spot's formations

An Individual Based Model of Wound Closure in Plant Stems

Wound closure in plant stems (after either fire or mechanical damage) is a complex, multi-scale process that involves the formation of a callous tissue (callus lips) responsible for cell proliferation and overgrowth at the injury edges, resulting in coverage of the scarred tissue. Investigating such phenomena, it is difficult to discriminate between cell-specific growth responses, associated with physiological adaptations, and cell proliferation reactions emerging from specific cambium dynamics due to changes in mechanical constrains. In particular, the effects of cell–cell mechanical interactions on the wound closure process have never been investigated. To understand to what extent callus lip formation depends on the intra-tissue mechanical balance of forces, we built a simplified individual-based model (IBM) of cell division and differentiation in a generic woody tissue. Despite its simplified physiological assumptions, the model was capable to simulate callus hyperproliferation and wound healing as an emergent property of the mechanical interactions between individual cells. The model output suggests that the existence of a scar alone does constrain the growth trajectories of the remaining proliferating cells around the injury, thus resulting in the wound closure, ultimately engulfing the damaged tissue in the growing stem

Uncertainty quantification of unsteady source flows in heterogeneous porous media

Unsteady flow generated by a point-like source takes place into a -dimensional porous formation where the spatial variability of the hydraulic conductivity is modelled within a stochastic framework that regards as a stationary, normally distributed random space function (rsf). As a consequence, the hydraulic head becomes also stochastic, and we aim at quantifying its uncertainty. Towards this aim, we have derived the head covariance by means of a perturbation expansion which regards the variance of the zero mean rsf (hereafter being the ensemble average operator) as a small parameter. The analytical results are expressed in terms of multiple quadratures which are markedly reduced after adopting specific autocorrelation for . This enables one to obtain simple results providing straightforward physical insight into the spatial distribution of as a consequence of the heterogeneity of . In view of those applications (pumping tests) aiming at the identification of the hydraulic properties of geological formations, we have focused on a flow generated by a source of instantaneous and constant strength. The attainment of the large time (steady-state) regime is studied in detail