A Dimension-Adaptive Multi-Index Monte Carlo Method Applied to a Model of a Heat Exchanger

We present an adaptive version of the Multi-Index Monte Carlo method, introduced by Haji-Ali, Nobile and Tempone (2016), for simulating PDEs with coefficients that are random fields. A classical technique for sampling from these random fields is the Karhunen-Lo\`eve expansion. Our adaptive algorithm is based on the adaptive algorithm used in sparse grid cubature as introduced by Gerstner and Griebel (2003), and automatically chooses the number of terms needed in this expansion, as well as the required spatial discretizations of the PDE model. We apply the method to a simplified model of a heat exchanger with random insulator material, where the stochastic characteristics are modeled as a lognormal random field, and we show consistent computational savings

On quantifying uncertainties for the linearized BGK kinetic equation

We consider the linearized BGK equation and want to quantify uncertainties in the case of modelling errors. More specifically, we want to quantify the error produced if the pre-determined equilibrium function is chosen inaccurately. In this paper we consider perturbations in the velocity and in the temperature of the equilibrium function and consider how much the error is amplified in the solution

Approaches in biotechnological applications of natural polymers

Natural polymers, such as gums and mucilage, are biocompatible, cheap, easily available and non-toxic materials of native origin. These polymers are increasingly preferred over synthetic materials for industrial applications due to their intrinsic properties, as well as they are considered alternative sources of raw materials since they present characteristics of sustainability, biodegradability and biosafety. As definition, gums and mucilages are polysaccharides or complex carbohydrates consisting of one or more monosaccharides or their derivatives linked in bewildering variety of linkages and structures. Natural gums are considered polysaccharides naturally occurring in varieties of plant seeds and exudates, tree or shrub exudates, seaweed extracts, fungi, bacteria, and animal sources. Water-soluble gums, also known as hydrocolloids, are considered exudates and are pathological products; therefore, they do not form a part of cell wall. On the other hand, mucilages are part of cell and physiological products. It is important to highlight that gums represent the largest amounts of polymer materials derived from plants. Gums have enormously large and broad applications in both food and non-food industries, being commonly used as thickening, binding, emulsifying, suspending, stabilizing agents and matrices for drug release in pharmaceutical and cosmetic industries. In the food industry, their gelling properties and the ability to mold edible films and coatings are extensively studied. The use of gums depends on the intrinsic properties that they provide, often at costs below those of synthetic polymers. For upgrading the value of gums, they are being processed into various forms, including the most recent nanomaterials, for various biotechnological applications. Thus, the main natural polymers including galactomannans, cellulose, chitin, agar, carrageenan, alginate, cashew gum, pectin and starch, in addition to the current researches about them are reviewed in this article.. }To the Conselho Nacional de Desenvolvimento Cientfíico e Tecnológico (CNPq) for fellowships (LCBBC and MGCC) and the Coordenação de Aperfeiçoamento de Pessoal de Nvíel Superior (CAPES) (PBSA). This study was supported by the Portuguese Foundation for Science and Technology (FCT) under the scope of the strategic funding of UID/BIO/04469/2013 unit, the Project RECI/BBB-EBI/0179/2012 (FCOMP-01-0124-FEDER-027462) and COMPETE 2020 (POCI-01-0145-FEDER-006684) (JAT)

Brain metastases as primary manifestation of a melanocytic malignant peripheral nerve sheath tumor in a 60-year-old man

BACKGROUND: Malignant peripheral nerve sheath tumors are rare tumor entities that originate from peripheral nerve sheaths and have an unfavorable prognosis. Metastatic spread to the cerebral parenchyma is absolutely rare. This case report describes the clinical course in a 60-year-old man whose tumor came to medical attention because of a seizure. CASE PRESENTATION: Magnetic resonance imaging demonstrated two intracerebral lesions. The symptomatic lesion was removed microneurosurgically and histology demonstrated a metastasis from a malignant peripheral nerve sheath tumor. Postoperatively, whole-brain irradiation was performed. The primary tumor was identified in the area of the sciatic nerve on the right. Follow-up 14 months after resection showed that there was no progression of the intracerebral lesions but an increase in size and number of distant metastases. CONCLUSION: There are no generally accepted guidelines for the treatment of malignant peripheral nerve sheath tumors with cerebral metastases. This case report presents and discusses one possible therapeutic approach. Due to the poor overall prognosis, the least invasive therapy should be chosen

Image decomposition and uncertainty quantification for the assessment of manufacturing tolerances in stress analysis

This article presents a methodology for the treatment of uncertainty in nonlinear, interference-fit, stress analysis problems arising from manufacturing tolerances. Image decomposition is applied to the uncertain stress field to produce a small number of shape descriptors that allow for variability in the location of high-stress points when geometric parameters (dimensions) are changed within tolerance ranges. A meta-model, in this case based on the polynomial chaos expansion, is trained using a full finite element model to provide a mapping from input geometric parameters to output shape descriptors. Global sensitivity analysis using Sobol’s indices provides a design tool that enables the influence of each input parameter on the observed variances of the outputs to be quantified. The methodology is illustrated by a simplified practical design problem in the manufacture of automotive wheels

Non-intrusive polynomial chaos method applied to full-order and reduced problems in computational fluid dynamics: A comparison and perspectives

In this work, Uncertainty Quantification (UQ) based on non-intrusive Polynomial Chaos Expansion (PCE) is applied to the CFD problem of the flow past an airfoil with parameterized angle of attack and inflow velocity. To limit the computational cost associated with each of the simulations required by the non-intrusive UQ algorithm used, we resort to a Reduced Order Model (ROM) based on Proper Orthogonal Decomposition (POD)-Galerkin approach. A first set of results is presented to characterize the accuracy of the POD-Galerkin ROM developed approach with respect to the Full Order Model (FOM) solver (OpenFOAM). A further analysis is then presented to assess how the UQ results are affected by substituting the FOM predictions with the surrogate ROM ones

Targeted Inactivation of Cerberus Like-2 Leads to Left Ventricular Cardiac Hyperplasia and Systolic Dysfunction in the Mouse

Previous analysis of the Cerberus like 2 knockout (Cerl2(-/-)) mouse revealed a significant mortality during the first day after birth, mostly due to cardiac defects apparently associated with randomization of the left-right axis. We have however, identified Cerl2-associated cardiac defects, particularly a large increase in the left ventricular myocardial wall in neonates that cannot be explained by laterality abnormalities. Therefore, in order to access the endogenous role of Cerl2 in cardiogenesis, we analyzed the embryonic and neonatal hearts of Cerl2 null mutants that did not display a laterality phenotype. Neonatal mutants obtained from the compound mouse line Cer2(-/-)Fundacao para a Ciencia e Tecnologia (FCT); IBB/CBME [PEst-OE/EQB/LA0023/2011]; FCT [SFRH/BD/62081/2009]info:eu-repo/semantics/publishedVersio