Multi-dimensional Simulation of Phase Change by a 0D-2D Model Coupling via Stefan Condition

Considering phase changes associated with a high-temperature molten material cooled down from the outside,this work presents an improvement of the modelling and the numerical simulation of such processes for an application pertaining to the safety of light water nuclear reactors.Postulating a core meltdown accident,the behaviour of the core melt(aka corium)into a steel vessel is of tremendous importance when evaluating the vessel integrity.Evaluating correctly the heat fluxes requires the numerical simulation of the interaction between the liquid material and its solid counterpart which forms during the solidification process,but also may melt back.To simulate this configuration,encoun-tered in various industrial applications,one considers a bi-phase model constituted by a liquid phase in contact and interaction with its solid phase.The liquid phase may solidify in presence of low energetic source,while the solid phase may melt due to an intense heat flux from the high-temperature liquid.In the frame of the in-house legacy code,several simplifying assumptions(0D multi-layer discretization,instantaneous heat transfer via a quadratic temperature profile in solids)are made for the modelling of such phase changes.In the present work,these shortcomings are illustrated and further overcome by solving a 2D heat conduction model in the solid by a mixed Raviart-Thomas finite element method coupled to the liquid phase due to heat and mass exchanges through Stefan condition.The liquid phase is modeled with a 0D multi-layer approach.The 0D-liquid and 2D-solid mod-els are coupled by a Stefan like phase change interface model.Several sanity checks are performed to assess the validity of the approach on 1D and 2D academical configurations for which exact or reference solutions are available.Then more advanced situations(genu-ine multi-dimensional phase changes and an"industrial-like scenario")are simulated to verify the appropriate behavior of the obtained coupled simulation scheme.

A Posteriori Stabilized Sixth-Order Finite Volume Scheme with Adaptive Stencil Construction:Basics for the 1D Steady-State Hyperbolic Equations

We propose an adaptive stencil construction for high-order accurate finite volume schemes a posteriori stabilized devoted to solve one-dimensional steady-state hyperbolic equations.High accuracy(up to the sixth-order presently)is achieved,thanks to polynomial recon-structions while stability is provided with an a posteriori MOOD method which controls the cell polynomial degree for eliminating non-physical oscillations in the vicinity of dis-continuities.We supplemented this scheme with a stencil construction allowing to reduce even further the numerical dissipation.The stencil is shifted away from troubles(shocks,discontinuities,etc.)leading to less oscillating polynomial reconstructions.Experimented on linear,Burgers',and Euler equations,we demonstrate that the adaptive stencil technique manages to retrieve smooth solutions with optimal order of accuracy but also irregular ones without spurious oscillations.Moreover,we numerically show that the approach allows to reduce the dissipation still maintaining the essentially non-oscillatory behavior.

Implementation of Network Intrusion Detection System Using Soft Computing Algorithms (Self Organizing Feature Map and Genetic Algorithm)

In today’s world, computer network is evolving very rapidly. Most public or/and private companies set up their own local networks system for the purpose of promoting communication and data sharing within the companies. Unfortunately, their data and local networks system are under risks. With the advanced computer networks, the unauthorized users attempt to access their local networks system so as to compromise the integrity, confidentiality and availability of resources. Multiple methods and approaches have to be applied to protect their data and local networks system against malicious attacks. The main aim of our paper is to provide an intrusion detection system based on soft computing algorithms such as Self Organizing Feature Map Artificial Neural Network and Genetic Algorithm to network intrusion detection system. KDD Cup 99 and 1998 DARPA dataset were employed for training and testing the intrusion detection rules. However, GA’s traditional Fitness Function was improved in order to evaluate the efficiency and effectiveness of the algorithm in classifying network attacks from KDD Cup 99 and 1998 DARPA dataset. SOFM ANN and GA training parameters were discussed and implemented for performance evaluation. The experimental results demonstrated that SOFM ANN achieved better performance than GA, where in SOFM ANN high attack detection rate is 99.98%, 99.89%, 100%, 100%, 100% and low false positive rate is 0.01%, 0.1%, 0%, 0%, 0% for DoS, R2L, Probe, U2R attacks, and Normal traffic respectively.

Modelling of sediment movement in the surf and swash zones

Under the action of marine currents,non-cohesive sediments evolve by bed-load,by saltation or suspension depending on their granulometry.Several authors have considered that the movement of sediment is bidimensional and modelized the effects of swell by a constant velocitynear the seabed.Here we have studied the velocity profile of fluctuating currents near the seabed and studied the movement of sediment in 3D.The results show that in the areas of study（surf and swash）the movement of sediment occurs in a volume,and the evolution of sediment varies from an areato another.The obtained theoretical profiles of the position and velocity vectors confirm the observations of several authors.

HANDEL'S FIXED POINT THEOREM:A MORSE THEORETICAL POINT OF VIEW

Michael Handel has proved in [10] a fixed point theorem for an orientation preserving homeomorphism of the open unit disk, that turned out to be an efficient tool in the study of the dynamics of surface homeomorphisms. The present article fits into a series of articles by the author [13] and by Juliana Xavier [21, 22], where proofs were given, related to the classical Brouwer Theory, instead of the Homotopical Brouwer Theory used in the original article. Like in [13, 21] and [22], we will use “free brick decompositions” but will present a more conceptual Morse theoretical argument. It is based on a new preliminary lemma, that gives a nice “condition at infinity” for our problem.

Finslerian Ricci Deformation and Conformal Metrics

In this paper, a new Ricci flow is canonically introduced in Finsler Geometry and, under the variance of Finsler-Ehresmann form, conformal changes of Finsler metrics are studied. Some existence conditions of this Finslerian Ricci flow on a compact manifold which preserves the conformal class of the initial metric are obtained as an application.

Aggregating Density Estimators: An Empirical Study

Density estimation methods based on aggregating several estimators are described and compared over several simulation models. We show that aggregation gives rise in general to better estimators than simple methods like histograms or kernel density estimators. We suggest three new simple algorithms which aggregate histograms and compare very well to all the existing methods.

Functional Kernel Estimation of the Conditional Extreme Quantile under Random Right Censoring

The study of estimation of conditional extreme quantile in incomplete data frameworks is of growing interest. Specially, the estimation of the extreme value index in a censorship framework has been the purpose of many investigations when finite dimension covariate information has been considered. In this paper, the estimation of the conditional extreme quantile of a heavy-tailed distribution is discussed when some functional random covariate (i.e. valued in some infinite-dimensional space) information is available and the scalar response variable is right-censored. A Weissman-type estimator of conditional extreme quantiles is proposed and its asymptotic normality is established under mild assumptions. A simulation study is conducted to assess the finite-sample behavior of the proposed estimator and a comparison with two simple estimations strategies is provided.

Leveraging Pima Dataset to Diabetes Prediction: Case Study of Deep Neural Network

Diabetes is a chronic disease. In 2019, it was the ninth leading cause of death with an estimated 1.5 million deaths. Poorly controlled, diabetes can lead to serious health problems. That explains why early diagnosis of diabetes is very important. Several approaches that use Artificial Intelligence, specifically Deep Learning, have been widely used with promising results. The contribution of this paper is in two-folds: 1) Deep Neural Network (DNN) approach is used on Pima Indian dataset to predict diabetes using 10 k-fold cross validation and 89% accuracy is obtained;2) comparative analysis of previous work is provided on diabetes prediction using DNN with the tested model. The results showed that 10 k-fold cross-validation could decrease the efficiency of diabetes prediction models using DNN.

An Hybrid Model for Rectal Tumour Response Prediction during Radiotherapy

A hybrid model is proposed in this study to predict rectal tumour response during radiotherapy treatment. As the oxygen partial pressure distribution (pO2) is a data which is naturally represented at the microscopic scale, we firstly estimate the optimal pO2 distribution using both a diffusion equation and a discrete multi-scale model (that we proposed in a previous study). The aim is to use the effectiveness in algorithmic complexity of the discrete model and its multi-scale aspect in this work to estimate biological information at cellular scale and then construct them at macroscopic scale. Secondly, the obtained pO2 distribution results are used as an input of a biomechanical model in order to simulate tumour volume evolution during radiotherapy. FDG PET images of 21 rectal cancer patients undergoing radiotherapy are used to simulate the tumour evolution during the treatment. The simulated results using the proposed hybride model, allow the interpretation of tumour aggressiveness.

Machine Learning With Data Assimilation and Uncertainty Quantification for Dynamical Systems:A Review

Data assimilation(DA)and uncertainty quantification(UQ)are extensively used in analysing and reducing error propagation in high-dimensional spatial-temporal dynamics.Typical applications span from computational fluid dynamics(CFD)to geoscience and climate systems.Recently,much effort has been given in combining DA,UQ and machine learning(ML)techniques.These research efforts seek to address some critical challenges in high-dimensional dynamical systems,including but not limited to dynamical system identification,reduced order surrogate modelling,error covariance specification and model error correction.A large number of developed techniques and methodologies exhibit a broad applicability across numerous domains,resulting in the necessity for a comprehensive guide.This paper provides the first overview of state-of-the-art researches in this interdisciplinary field,covering a wide range of applications.This review is aimed at ML scientists who attempt to apply DA and UQ techniques to improve the accuracy and the interpretability of their models,but also at DA and UQ experts who intend to integrate cutting-edge ML approaches to their systems.Therefore,this article has a special focus on how ML methods can overcome the existing limits of DA and UQ,and vice versa.Some exciting perspectives of this rapidly developing research field are also discussed.Index Terms-Data assimilation(DA),deep learning,machine learning(ML),reduced-order-modelling,uncertainty quantification(UQ).

Simple and Pseudo Quadratic Leibniz Superalgebras

Compactness of subspaces of a Z2-graded vector space is introduced and used to study simple Leibniz superalgebras. We introduce left and right super-invariance of bilinear forms over superalgebras. Pseudo-quadratic Leibniz superalgebras are Leibniz superalgebras endowed with a non degenerate, supersymmetric and super-invariant bilinear form. In this paper, we show that every nondegenerate, supersymmetric and super-invariant bilinear form over a Leibniz superalgebra induce a Lie superalgebra over the underlying vector space. Then by using double extension extended to Leibniz superalgebras, we study pseudo-quadratic Leibniz superalgebras and the induced Lie superalgebras. In particular, we generalize some results on Leibniz algebras to Leibniz superalgebras.

High Order ADER-IPDG Methods for the Unsteady Advection-Diffusion Equation

We present a high-order Galerkin method in both space and time for the 1D unsteady linear advection-diffusion equation. Three Interior Penalty Discontinuous Galerkin (IPDG) schemes are detailed for the space discretization, while the time integration is performed at the same order of accuracy thanks to an Arbitrary high order DERivatives (ADER) method. The orders of convergence of the three ADER-IPDG methods are carefully examined through numerical illustrations, showing that the approach is consistent, accurate, and efficient. The numerical results indicate that the symmetric version of IPDG is typically more accurate and more efficient compared to the other approaches.

An Unconventional Divergence Preserving Finite-Volume Discretization of Lagrangian Ideal MHD

We construct an unconventional divergence preserving discretization of updated Lagrangian ideal magnetohydrodynamics(MHD)over simplicial grids.The cell-centered finite-volume(FV)method employed to discretize the conservation laws of volume,momentum,and total energy is rigorously the same as the one developed to simulate hyperelasticity equations.By construction this moving mesh method ensures the compatibility between the mesh displacement and the approximation of the volume flux by means of the nodal velocity and the attached unit corner normal vector which is nothing but the partial derivative of the cell volume with respect to the node coordinate under consideration.This is precisely the definition of the compatibility with the Geometrical Conservation Law which is the cornerstone of any proper multi-dimensional moving mesh FV discretization.The momentum and the total energy fluxes are approximated utilizing the partition of cell faces into sub-faces and the concept of sub-face force which is the traction force attached to each sub-face impinging at a node.We observe that the time evolution of the magnetic field might be simply expressed in terms of the deformation gradient which characterizes the Lagrange-to-Euler mapping.In this framework,the divergence of the magnetic field is conserved with respect to time thanks to the Piola formula.Therefore,we solve the fully compatible updated Lagrangian discretization of the deformation gradient tensor for updating in a simple manner the cell-centered value of the magnetic field.Finally,the sub-face traction force is expressed in terms of the nodal velocity to ensure a semi-discrete entropy inequality within each cell.The conservation of momentum and total energy is recovered prescribing the balance of all the sub-face forces attached to the sub-faces impinging at a given node.This balance corresponds to a vectorial system satisfied by the nodal velocity.It always admits a unique solution which provides the nodal velocity.The robustness and the accuracy of this unconventional FV scheme have been demonstrated by employing various representative test cases.Finally,it is worth emphasizing that once you have an updated Lagrangian code for solving hyperelasticity you also get an almost free updated Lagrangian code for solving ideal MHD ensuring exactly the compatibility with the involution constraint for the magnetic field at the discrete level.

A Method to Predict Amino Acids at Proximity of Beta-Sheet Axes from Protein Sequences

A general and elementary protein folding step was described in a previous article. Energy conservation during this folding step yielded an equation with remarkable solutions over the field of rational numbers. Sets of sequences optimized for folding were derived. In this work, a geometrical analysis of protein beta-sheet backbone structures allows the definition of positions of topological interest. They correspond to amino acids’ alpha carbons located on a unique axis crossing all beta-sheet’s strands or at proximity of this axis defined here. These positions of topological interest are shown to be highly correlated with the absence of sequences optimized for folding. Applications in protein structure prediction for the quality assessment of structural models are envisioned.

Conventional and Enhanced Canonical Quantizations, Application to Some Simple Manifolds

It is well known that the representations over an arbitrary configuration space related to a physical system of the Heisenberg algebra allow to distinguish the simply and non simply-connected manifolds [arXiv:quant-ph/9908.014, arXiv:hep-th/0608.023]. In the light of this classification, the dynamics of a quantum particle on the line is studied in the framework of the conventional quantization scheme as well as that of the enhanced quantization recently introduced by J. R. Klauder [arXiv:quant-ph/1204.2870]. The quantum action functional restricted to the phase space coherent states is obtained from the enhanced quantization procedure, showing the coexistence of classical and quantum theories, a fundamental advantage offered by this new approach. The example of the one dimensional harmonic oscillator is given. Next, the spectrum of a free particle on the two-sphere is recognized from the covariant diffeomorphic representations of the momentum operator in the configuration space. Our results based on simple models also point out the already-known link between interaction and topology at quantum level.

Towards Post-Quantum Cryptography Using Thermal Noise Theory and True Random Numbers Generation

The advent of quantum computers and algorithms challenges the semantic security of symmetric and asymmetric cryptosystems. Thus, the implementation of new cryptographic primitives is essential. They must follow the breakthroughs and properties of quantum calculators which make vulnerable existing cryptosystems. In this paper, we propose a random number generation model based on evaluation of the thermal noise power of the volume elements of an electronic system with a volume of 58.83 cm3. We prove through the sampling of the temperature of each volume element that it is difficult for an attacker to carry out an exploit. In 12 seconds, we generate for 7 volume elements, a stream of randomly generated keys of 187 digits that will be transmitted from source to destination through the properties of quantum cryptography.

Amalgamated Geometric Structure of the Local Multiverse

We consider multiverses as time-amalgamated multiply warped products of Lorentzian (Einstein) manifolds. We define the Local Multiverse as a time-connected component associated with our physical (3 + 1)-spacetime. It is a collection of “parallel universes” with (mutually) synchronized timelines. Metaphysical considerations suggest that the Local Multiverse could be an extremely complex agglomeration with, at least, several hundred parallel universes in the Solar neighbourhood (and many thousands in galaxy bulks). In this paper we study a simplified time-almagamated globally hyperbolic model. Our picture implies the multiversality of elementary particles which are, actually, transcosmic (super)strings with multiple endpoints on parallel universes considered as D-branes.

GEOMETRY ON THE WASSERSTEIN SPACE OVER A COMPACT RIEMANNIAN MANIFOLD

We revisit the intrinsic differential geometry of the Wasserstein space over a Riemannian manifold,due to a series of papers by Otto,Otto-Villani,Lott,Ambrosio-Gigli-Savaré,etc.

QUANTIZATION COMMUTES WITH REDUCTION,A SURVEY

We review the themes relating to the proposition that“quantization commutes with reduction”([Q,R]=0),from symplectic manifolds to Cauchy-Riemann manifolds.