Search results for "Numerical Analysis"

Singularity tracking for Camassa-Holm and Prandtl's equations

2006

In this paper we consider the phenomenon of singularity formation for the Camassa-Holm equation and for Prandtl's equations. We solve these equations using spectral methods. Then we track the singularity in the complex plane estimating the rate of decay of the Fourier spectrum. This method allows us to follow the process of the singularity formation as the singularity approaches the real axis.

Some inequalities involving the euclidean condition of a matrix

1960

MAST solution of advection problems in irrotational flow fields

2007

Abstract A new numerical–analytical Eulerian procedure is proposed for the solution of convection-dominated problems in the case of existing scalar potential of the flow field. The methodology is based on the conservation inside each computational elements of the 0th and 1st order effective spatial moments of the advected variable. This leads to a set of small ODE systems solved sequentially, one element after the other over all the computational domain, according to a MArching in Space and Time technique. The proposed procedure shows the following advantages: (1) it guarantees the local and global mass balance; (2) it is unconditionally stable with respect to the Courant number, (3) the so…

Multi-directional vs. mono-directional multi-step strategies for single point incremental forming of non-axisymmetric components

2020

Abstract Multi Stage approach is used in Single Point Incremental Forming (SPIF) to overcome one of the main forming limitations, namely the maximum wall angle, characterizing the single stage process. In this paper, different multi-path strategies for the production of parts with flat edges are considered in order to evaluate the best solution in terms of feasibility and geometrical accuracy of the final part: A) mono-directional incremental draw angle; B) mono-directional incremental draw angle with increasing part side; C) Multi-directional approach with non-horizontal path planes. Strain evaluation by means of CGA (Circular Grid Analysis) and defect analysis have been carried out in ord…

Material Flow in FSW of T-joints: Experimental and Numerical Analysis

2008

In the paper the authors present the results of both an experimental and a numerical campaign focused on the analysis of the occurring material flow in the FSW of T joints of aluminum alloys. In particular to investigate the metal flow experimental tests and observations has been developed utilizing a thin foil of copper as marker placed between the skin and the stringer. In this way, the actual metal flow occurring during the FSW of T-joints has been highlighted together with the real bonding surface. The acquired information is definitively useful in order to choose effective set of process parameters, improving the process mechanics and avoiding the insurgence of defects.

Deep Learning Based Cardiac MRI Segmentation: Do We Need Experts?

2021

Deep learning methods are the de facto solutions to a multitude of medical image analysis tasks. Cardiac MRI segmentation is one such application, which, like many others, requires a large number of annotated data so that a trained network can generalize well. Unfortunately, the process of having a large number of manually curated images by medical experts is both slow and utterly expensive. In this paper, we set out to explore whether expert knowledge is a strict requirement for the creation of annotated data sets on which machine learning can successfully be trained. To do so, we gauged the performance of three segmentation models, namely U-Net, Attention U-Net, and ENet, trained with dif…

Neural Networks, Inside Out: Solving for Inputs Given Parameters (A Preliminary Investigation)

2021

Artificial neural network (ANN) is a supervised learning algorithm, where parameters are learned by several back-and-forth iterations of passing the inputs through the network, comparing the output with the expected labels, and correcting the parameters. Inspired by a recent work of Boer and Kramer (2020), we investigate a different problem: Suppose an observer can view how the ANN parameters evolve over many iterations, but the dataset is oblivious to him. For instance, this can be an adversary eavesdropping on a multi-party computation of an ANN parameters (where intermediate parameters are leaked). Can he form a system of equations, and solve it to recover the dataset?

Deep neural networks to recover unknown physical parameters from oscillating time series.

2022

PLOS ONE 17(5), e0268439 (2022). doi:10.1371/journal.pone.0268439

Fast MATLAB assembly of FEM matrices in 2D and 3D: Edge elements

2014

We propose an effective and flexible way to assemble finite element stiffness and mass matrices in MATLAB. We apply this for problems discretized by edge finite elements. Typical edge finite elements are Raviart-Thomas elements used in discretizations of H(div) spaces and Nedelec elements in discretizations of H(curl) spaces. We explain vectorization ideas and comment on a freely available MATLAB code which is fast and scalable with respect to time.

Fractional generalized cumulative entropy and its dynamic version

2021

Following the theory of information measures based on the cumulative distribution function, we propose the fractional generalized cumulative entropy, and its dynamic version. These entropies are particularly suitable to deal with distributions satisfying the proportional reversed hazard model. We study the connection with fractional integrals, and some bounds and comparisons based on stochastic orderings, that allow to show that the proposed measure is actually a variability measure. The investigation also involves various notions of reliability theory, since the considered dynamic measure is a suitable extension of the mean inactivity time. We also introduce the empirical generalized fract…