Boundary integral formulation for interfacial cracks in thermodiffusive bimaterials

An original boundary integral formulation is proposed for the problem of a semi-infinite crack at the interface between two dissimilar elastic materials in the presence of heat flows and mass diffusion. Symmetric and skew-symmetric weight function matrices are used together with a generalized Betti's reciprocity theorem in order to derive a system of integral equations that relate the applied loading, the temperature and mass concentration fields, the heat and mass fluxes on the fracture surfaces and the resulting crack opening. The obtained integral identities can have many relevant applications, such as for the modelling of crack and damage processes at the interface between different components in electrochemical energy devices characterized by multi-layered structures (solid oxide fuel cells and lithium ions batteries).Comment: 43 pages, 9 figure

Effective elastic properties of planar SOFCs: A non-local dynamic homogenization approach

The focus of the article is on the analysis of effective elastic properties of planar Solid Oxide Fuell Cell (SOFC) devices. An ideal periodic multi-layered composite (SOFC-like) reproducing the overall properties of multi-layer SOFC devices is defined. Adopting a non-local dynamic homogenization method, explicit expressions for overall elastic moduli and inertial terms of this material are derived in terms of micro-fluctuation functions. These micro-fluctuation function are then obtained solving the cell problems by means of finite element techniques. The effects of the temperature variation on overall elastic and inertial properties of the fuel cells are studied. Dispersion relations for acoustic waves in SOFC-like multilayered materials are derived as functions of the overall constants, and the results obtained by the proposed computational homogenization approach are compared with those provided by rigorous Floquet-Boch theory. Finally, the influence of the temperature and of the elastic properties variation on the Bloch spectrum is investigated

Multiscale asymptotic homogenization analysis of thermo-diffusive composite materials

In this paper an asymptotic homogenization method for the analysis of composite materials with periodic microstructure in presence of thermodiffusion is described. Appropriate down-scaling relations correlating the microscopic fields to the macroscopic displacements, temperature and mass concentration are introduced. The effects of the material inhomogeneities are described by perturbation functions derived from the solution of recursive cell problems. Exact expressions for the overall elastic and thermodiffusive constants of the equivalent first order thermodiffusive continuum are derived. The proposed approach is applied to the case of a two-dimensional bi-phase orthotropic layered material, where the effective elastic and thermodiffusive properties can be determined analytically. Considering this illustrative example and assuming periodic body forces, heat and mass sources acting on the medium, the solution performed by the first order homogenization approach is compared with the numerical results obtained by the heterogeneous model.Comment: 40 pages, 13 figure

Adaptive Regularization for Nonconvex Optimization Using Inexact Function Values and Randomly Perturbed Derivatives

A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function with Lipschitz continuous $p$-th derivative and given an arbitrary optimality order $q \leq p$, it is shown that this algorithm will, in expectation, compute such a point in at most $O\left(\left(\min_{j\in\{1,\ldots,q\}}\epsilon_j\right)^{-\frac{p+1}{p-q+1}}\right)$ inexact evaluations of $f$ and its derivatives whenever $q\in\{1,2\}$, where $\epsilon_j$ is the tolerance for $j$th order accuracy. This bound becomes at most $O\left(\left(\min_{j\in\{1,\ldots,q\}}\epsilon_j\right)^{-\frac{q(p+1)}{p}}\right)$ inexact evaluations if $q>2$ and all derivatives are Lipschitz continuous. Moreover these bounds are sharp in the order of the accuracy tolerances. An extension to convexly constrained problems is also outlined.Comment: 22 page

Adaptive Regularization Algorithms with Inexact Evaluations for Nonconvex Optimization

A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that is constraints whose evaluation and enforcement has negligible cost) under the assumption that the derivative of highest degree is $\beta$-H\"{o}lder continuous. It features a very flexible adaptive mechanism for determining the inexactness which is allowed, at each iteration, when computing objective function values and derivatives. The complexity analysis covers arbitrary optimality order and arbitrary degree of available approximate derivatives. It extends results of Cartis, Gould and Toint (2018) on the evaluation complexity to the inexact case: if a $q$th order minimizer is sought using approximations to the first $p$ derivatives, it is proved that a suitable approximate minimizer within $\epsilon$ is computed by the proposed algorithm in at most $O(\epsilon^{-\frac{p+\beta}{p-q+\beta}})$ iterations and at most $O(|\log(\epsilon)|\epsilon^{-\frac{p+\beta}{p-q+\beta}})$ approximate evaluations. An algorithmic variant, although more rigid in practice, can be proved to find such an approximate minimizer in $O(|\log(\epsilon)|+\epsilon^{-\frac{p+\beta}{p-q+\beta}})$ evaluations.While the proposed framework remains so far conceptual for high degrees and orders, it is shown to yield simple and computationally realistic inexact methods when specialized to the unconstrained and bound-constrained first- and second-order cases. The deterministic complexity results are finally extended to the stochastic context, yielding adaptive sample-size rules for subsampling methods typical of machine learning.Comment: 32 page

The GASMEMS network: Rationale, programme and initial results

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.GASMEMS is an Initial Training Network supported by the European Commission, which aims at training young researchers in the field of rarefied gas flows in MEMS, and at structuring research in Europe in the field of gas microflows in order to improve global fundamental knowledge and enable technological applications to an industrial and commercial level. The partners and the global objectives of this 4 year programme are detailed, and some initial results are presented. First experimental data about the flow of binary gas mixtures through rectangular microchannels are successfully compared with continuum and kinetic models, in the slip flow and early transition regimes. The behaviour of these mixtures has also been simulated in triangular microchannels, for the whole range of the Knudsen number, using a kinetic approach and the McCormack model. Heat transfer in plane microchannels has been numerically investigated, pointing out compressibility and rarefaction effects. The effect of thermal creep has been studied comparing BGK, Smodel and ellipsoidal model with the solution from the full Boltzmann equation. A semi-analytical model of the Knudsen layer has been developed and used to simulate the problem of thermal transpiration in a microchannel. Gaseous flows through rough microchannels have been simulated using kinetic theory and DSMC method, the wall roughness being simulated as a highly porous medium of variable thickness.This study is funded by the European Community's Seventh Framework Programme FP7/2007-2013 under grant agreement ITN GASMEMS n° 215504

Assessment of co-creativity in the process of game design

We consider game design as a sociocultural and knowledge modelling activity, engaging participants in the design of a scenario and a game universe based on a real or imaginary socio-historical context, where characters can introduce life narratives and interaction that display either known social realities or entirely new ones. In this research, participants of the co-creation activity are Malaysian students who were working in groups to design game-based learning resources for rural school children. After the co-creativity activity, the students were invited to answer the co-creativity scale, an adapted version of the Assessment Scale of Creative Collaboration (ASCC), combining both the co-creativity factors and learners’ experiences on their interests, and difficulties they faced during the co-creativity process. The preliminary results showed a high diversity on the participants’ attitudes towards collaboration, especially related to their preferences towards individual or collaborative work

Dynamic energy release rate in couple-stress elasticity

This paper is concerned with energy release rate for dynamic steady state crack problems in elastic materials with microstructures. A Mode III semi-infinite crack subject to loading applied on the crack surfaces is considered. The micropolar behaviour of the material is described by the theory of couple-stress elasticity developed by Koiter. A general expression for the dynamic J-integral including both traslational and micro-rotational inertial contributions is derived, and the conservation of this integral on a path surrounding the crack tip is demonstrated

Remarks on the energy release rate for an antiplane moving crack in couple stress elasticity

This paper is concerned with the steady-state propagation of an antiplane semi-infinite crack in couple stress elastic materials. A distributed loading applied at the crack faces and moving with the same velocity of the crack tip is considered, and the influence of the loading profile variations and microstructural effects on the dynamic energy release rate is investigated. The behaviour of both energy release rate and maximum total shear stress when the crack tip speed approaches the critical speed (either that of the shear waves or that of the localised surface waves) is studied. The limit case corresponding to vanishing characteristic scale lengths is addressed both numerically and analytically by means of a comparison with classical elasticity results.Comment: 37 pages, 13 figure

Association between diverticulosis and colonic neoplastic lesions in individuals with a positive faecal immunochemical test

Background The association between diverticulosis and colonic neoplastic lesions has been suggested, but data in literature are conflicting. This study aimed to investigate such a relationship in patients participating in a colorectal cancer screening program who underwent high-quality colonoscopy.Methods Data from consecutive individuals 50-75 years of age with a positive faecal immunological test were considered. Diverticulosis was categorised as present or absent. The prevalence of neoplastic lesions (adenoma, advanced adenoma, and cancer) between individuals with and those without diverticula was compared. A multivariate analysis was performed.Results Overall, data from 970 consecutive individuals were evaluated, and diverticulosis was detected in 354 (36.5%) cases. At least one adenoma was detected in 490 (50.5%) people, at least one advanced adenoma in 264 (27.2%), multiple adenoma in 71 (7.3%), whilst a cancer was diagnosed in 48 (4.9%) cases. At univariate analysis, the adenoma detection rate in patients with diverticula was significantly higher than in controls (55.9% vs 47.4%; p=0.011). At multivariate analysis, presence of diverticulosis was an independent risk factor for both adenoma detection rate (OR=1.58; 95% CI=1.14-2.18; p=0.006) and advanced adenoma (OR=1.57; 95% CI=1.10-2.24; p=0.013), but not for colorectal cancer.Conclusions In a colorectal screening setting, the adenoma detection rate was significantly higher in individuals with diverticulosis than in controls