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Mathematical and Computational Applications, Volume 24, Issue 2

2019 June - 33 articles

Cover Story: In the following paper, we consider the problem of constructing a time-stable, reduced-order model of the 3D turbulent and incompressible Navier–Stokes equations. The main idea is to be able to do an a priori analysis of different modes in order to arrange a POD basis in a different way, which is defined by the enforcement of the energetic dissipative modes within the first orders of the reduced order basis. This enables us to model the production and the dissipation of turbulent kinetic energy (TKE) in a separate fashion within the highly ranked new velocity modes, and hence ensure good stability of the reduced-order model. We show the importance of this a priori enrichment of the reduced basis on a typical aeronautical injector with Reynolds number of 45,000. We demonstrate the capacity of this order reduction technique to recover large-scale features for very long integration times (25 ms in our case). View this paper.
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Articles (33)

  • Article
  • Open Access
3,423 Views
9 Pages

Exact Evaluation of Statistical Moments in Superradiant Emission

  • Gilberto M. Nakamura,
  • Brenno Cabella and
  • Alexandre S. Martinez

Superradiance describes the coherent collective radiation caused by the interaction between many emitters, mediated by a shared electromagnetic field. Recent experiments involving Bose–Einstein condensates coupled to high-finesse cavities and i...

(This article belongs to the Special Issue Dynamics Days Latin America and the Caribbean 2018)
  • Article
  • Open Access
11 Citations
5,651 Views
16 Pages

Mathematical Models for Simulation and Optimization of High-Flux Solar Furnaces

  • José Carlos Garcia Pereira,
  • Jorge Cruz Fernandes and
  • Luís Guerra Rosa

High-flux solar furnaces distributed throughout the world have been designed and constructed individually, i.e., on a one-by-one basis because there are several possible optical configurations that must take into account the geographical location and...

  • Article
  • Open Access
6 Citations
4,183 Views
17 Pages

Preserving the confidentiality of information is a growing concern in software development. Secure information flow is intended to maintain the confidentiality of sensitive information by preventing them from flowing to attackers. This paper discusse...

  • Article
  • Open Access
5 Citations
3,551 Views
16 Pages

There are several types of deterministic compartmental models for disease epidemiology such as SIR, SIS, SEIS, SEIR, etc. The exposed population group in, for example SEIS or SEIR, usually represents individuals in the incubation class. Time delays (...

(This article belongs to the Section Natural Sciences)
  • Article
  • Open Access
2 Citations
2,909 Views
14 Pages

The specificity and universality of intracellular Ca 2 + signals rely on the variety of spatio-temporal patterns that the Ca 2 + concentration can display. Ca 2 + release into the cytosol through inositol 1,4,5-trisphospha...

(This article belongs to the Special Issue Dynamics Days Latin America and the Caribbean 2018)
  • Article
  • Open Access
6 Citations
6,648 Views
13 Pages

A Fast Factorisation of Semi-Primes Using Sum of Squares

  • Anthony Overmars and
  • Sitalakshmi Venkatraman

For several centuries, prime factorisation of large numbers has drawn much attention due its practical applications and the associated challenges. In computing applications, encryption algorithms such as the Rivest–Shamir–Adleman (RSA) cr...

  • Feature Paper
  • Article
  • Open Access
10 Citations
5,284 Views
22 Pages

In this paper, a hybrid model in Cartesian coordinates combining a two-dimensional (2-D) generic magnetic equivalent circuit (MEC) with a 2-D analytical model based on the Maxwell–Fourier method (i.e., the formal resolution of Maxwell’s equations by...

(This article belongs to the Special Issue Mathematical Models for the Design of Electrical Machines)
  • Article
  • Open Access
22 Citations
4,118 Views
16 Pages

Three new iterative methods for solving scalar nonlinear equations using weight function technique are presented. The first one is a two-step fifth order method with four function evaluations which is improved from a two-step Newton’s method ha...

  • Communication
  • Open Access
4 Citations
3,376 Views
7 Pages

We study the properties of solutions of the mixed Dirichlet–Robin and Neumann–Robin problems for the linear system of elasticity theory in the exterior of a compact set and the asymptotic behavior of solutions of these problems at infinit...

(This article belongs to the Special Issue Related Problems of Continuum Mechanics)
  • Feature Paper
  • Article
  • Open Access
15 Citations
5,186 Views
27 Pages

Data-Driven Microstructure Property Relations

  • Julian Lißner and
  • Felix Fritzen

An image based prediction of the effective heat conductivity for highly heterogeneous microstructured materials is presented. The synthetic materials under consideration show different inclusion morphology, orientation, volume fraction and topology....

(This article belongs to the Special Issue Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics)
  • Feature Paper
  • Article
  • Open Access
30 Citations
5,051 Views
28 Pages

The computational homogenization of hyperelastic solids in the geometrically nonlinear context has yet to be treated with sufficient efficiency in order to allow for real-world applications in true multiscale settings. This problem is addressed by a...

(This article belongs to the Special Issue Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics)
  • Article
  • Open Access
3,213 Views
18 Pages

Component commonality is a well-known approach in manufacturing, where the same components are used for multiple products. It has been implemented by many established companies such as Airbus, Kodak, Toyota, etc. We consider a standard two-product in...

  • Article
  • Open Access
7 Citations
3,220 Views
11 Pages

A localized radial basis function meshless method is applied to approximate a nonlinear biological population model with highly satisfactory results. The method approximates the derivatives at every point corresponding to their local support domain....

(This article belongs to the Special Issue Computational Methods in Interdisciplinary Applications of Nonlinear Dynamics)
  • Article
  • Open Access
2 Citations
3,174 Views
20 Pages

In this paper, we introduce the ρ , q -analog of the p-adic factorial function. By utilizing some properties of ρ , q -numbers, we obtain several new and interesting identities and formulas. We then construct the p-adic &rho...

(This article belongs to the Section Natural Sciences)
  • Feature Paper
  • Article
  • Open Access
20 Citations
4,445 Views
21 Pages

This paper aims to present a finite element (FE) formulation for the study of the natural frequencies of functionally graded orthotropic laminated plates characterized by cross-ply layups. A nine-node Lagrange element is considered for this purpose....

(This article belongs to the Special Issue Mesh-Free and Finite Element-Based Methods for Structural Mechanics Applications)
  • Feature Paper
  • Article
  • Open Access
3,207 Views
16 Pages

Density gradients across reaction fronts propagating vertically can lead to Rayleigh–Taylor instabilities. Reaction fronts can also become unstable due to diffusive instabilities, regardless the presence of a mass density gradient. In this pape...

(This article belongs to the Special Issue Dynamics Days Latin America and the Caribbean 2018)
  • Article
  • Open Access
12 Citations
5,448 Views
16 Pages

In the paper, the authors introduce a unified generalization of the Catalan numbers, the Fuss numbers, the Fuss–Catalan numbers, and the Catalan–Qi function, and discover some properties of the unified generalization, including a product-...

  • Article
  • Open Access
3 Citations
3,858 Views
16 Pages

Time Recurrence Analysis of a Near Singular Billiard

  • Rodrigo Simile Baroni,
  • Ricardo Egydio de Carvalho,
  • Bruno Castaldi and
  • Bruno Furlanetto

Billiards exhibit rich dynamical behavior, typical of Hamiltonian systems. In the present study, we investigate the classical dynamics of particles in the eccentric annular billiard, which has a mixed phase space, in the limit that the scatterer is p...

(This article belongs to the Special Issue Dynamics Days Latin America and the Caribbean 2018)
  • Feature Paper
  • Article
  • Open Access
5 Citations
4,612 Views
7 Pages

Cycles in population dynamics are abundant in nature and are understood as emerging from the interaction among coupled species. When sampling is conducted at a slow rate compared to the population cycle period (aliasing effect), one is prone to misin...

(This article belongs to the Special Issue Dynamics Days Latin America and the Caribbean 2018)
  • Article
  • Open Access
7 Citations
5,050 Views
20 Pages

A Transdisciplinary Approach for Analyzing Stress Flow Patterns in Biostructures

  • Reena Patel,
  • Guillermo Riveros,
  • David Thompson,
  • Edward Perkins and ,
  • Jan Jeffery Hoover,
  • John Peters and
  • Antoinette Tordesillas
  • + 2 authors+ 0 author

This work presents a transdisciplinary, integrated approach that uses computational mechanics experiments with a flow network strategy to gain fundamental insights into the stress flow of high-performance, lightweight, structured composites by invest...

(This article belongs to the Special Issue Mesh-Free and Finite Element-Based Methods for Structural Mechanics Applications)
  • Feature Paper
  • Article
  • Open Access
16 Citations
5,457 Views
21 Pages

In the following paper, we consider the problem of constructing a time stable reduced order model of the 3D turbulent and incompressible Navier–Stokes equations. The lack of stability associated with the order reduction methods of the Navier&nd...

(This article belongs to the Special Issue Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics)
  • Article
  • Open Access
3 Citations
3,708 Views
12 Pages

Suppression of Phase Synchronization in Scale-Free Neural Networks Using External Pulsed Current Protocols

  • Bruno Rafael Reichert Boaretto,
  • Roberto C. Budzinski,
  • Thiago L. Prado and
  • Sergio Roberto Lopes

The synchronization of neurons is fundamental for the functioning of the brain since its lack or excess may be related to neurological disorders, such as autism, Parkinson’s and neuropathies such as epilepsy. In this way, the study of synchroni...

(This article belongs to the Special Issue Dynamics Days Latin America and the Caribbean 2018)
  • Article
  • Open Access
4 Citations
3,865 Views
17 Pages

Finite Symmetries in Agent-Based Epidemic Models

  • Gilberto M. Nakamura,
  • Ana Carolina P. Monteiro,
  • George C. Cardoso and
  • Alexandre S. Martinez

Predictive analysis of epidemics often depends on the initial conditions of the outbreak, the structure of the afflicted population, and population size. However, disease outbreaks are subjected to fluctuations that may shape the spreading process. A...

(This article belongs to the Special Issue Dynamics Days Latin America and the Caribbean 2018)
  • Feature Paper
  • Article
  • Open Access
39 Citations
5,773 Views
26 Pages

Symplectic Model Order Reduction with Non-Orthonormal Bases

  • Patrick Buchfink,
  • Ashish Bhatt and
  • Bernard Haasdonk

Parametric high-fidelity simulations are of interest for a wide range of applications. However, the restriction of computational resources renders such models to be inapplicable in a real-time context or in multi-query scenarios. Model order reductio...

(This article belongs to the Special Issue Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics)
  • Article
  • Open Access
3 Citations
3,655 Views
16 Pages

Investigation of Details in the Transition to Synchronization in Complex Networks by Using Recurrence Analysis

  • Roberto C. Budzinski,
  • Bruno Rafael Reichert Boaretto,
  • Thiago L. Prado and
  • Sergio Roberto Lopes

The study of synchronization in complex networks is useful for understanding a variety of systems, including neural systems. However, the properties of the transition to synchronization are still not well known. In this work, we analyze the details o...

(This article belongs to the Special Issue Dynamics Days Latin America and the Caribbean 2018)
  • Feature Paper
  • Article
  • Open Access
5 Citations
4,673 Views
28 Pages

The industrial application motivating this work is the fatigue computation of aircraft engines’ high-pressure turbine blades. The material model involves nonlinear elastoviscoplastic behavior laws, for which the parameters depend on the tempera...

(This article belongs to the Special Issue Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics)
  • Feature Paper
  • Article
  • Open Access
10 Citations
6,048 Views
28 Pages

The present work addresses a solution algorithm for homogenization problems based on an artificial neural network (ANN) discretization. The core idea is the construction of trial functions through ANNs that fulfill a priori the periodic boundary cond...

(This article belongs to the Special Issue Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics)
  • Article
  • Open Access
3 Citations
3,205 Views
17 Pages

On Determination of Wave Velocities through the Eigenvalues of Material Objects

  • Mikhail U. Nikabadze,
  • Sergey A. Lurie,
  • Hovik A. Matevossian and
  • Armine R. Ulukhanyan

The statement of the eigenvalue problem for a tensor–block matrix of any order and of any

even rank is formulated. It is known that the eigenvalues of the tensor and the tensor–block matrix

are invariant quantities. Therefore, in this work,...

(This article belongs to the Special Issue Mathematical Modeling in Physical Sciences)
  • Article
  • Open Access
4 Citations
4,120 Views
13 Pages

Observable for a Large System of Globally Coupled Excitable Units

  • Santiago Boari,
  • Gonzalo Uribarri,
  • Ana Amador and
  • Gabriel B. Mindlin

The study of large arrays of coupled excitable systems has largely benefited from a technique proposed by Ott and Antonsen, which results in a low dimensional system of equations for the system’s order parameter. In this work, we show how to ex...

(This article belongs to the Special Issue Dynamics Days Latin America and the Caribbean 2018)
  • Article
  • Open Access
36 Citations
4,037 Views
13 Pages

In this study, free vibration behaviors of various embedded nanowires made of different materials are investigated by using Eringen’s nonlocal elasticity theory. Silicon carbide nanowire (SiCNW), silver nanowire (AgNW), and gold nanowire (AuNW)...

(This article belongs to the Special Issue Mesh-Free and Finite Element-Based Methods for Structural Mechanics Applications)
  • Article
  • Open Access
18 Citations
6,701 Views
18 Pages

In this study, we investigate the existence of chaos in the global cryptocurrency market. Specifically, we analyze parameters of chaotic order, nonlinearity, sensitivity to the initial conditions, monofractality, and multifractality. For this purpose...

(This article belongs to the Section Social Sciences)
  • Feature Paper
  • Article
  • Open Access
7 Citations
5,148 Views
40 Pages

In this paper, function approximation is utilized to establish functional series approximations to integrals. The starting point is the definition of a dual Taylor series, which is a natural extension of a Taylor series, and spline based series appro...

  • Feature Paper
  • Article
  • Open Access
30 Citations
8,606 Views
27 Pages

Study of a Hybrid Excitation Synchronous Machine: Modeling and Experimental Validation

  • Salim Asfirane,
  • Sami Hlioui,
  • Yacine Amara and
  • Mohamed Gabsi

This paper deals with a parallel hybrid excitation synchronous machine (HESM). First, an expanded literature review of hybrid/double excitation machines is provided. Then, the structural topology and principles of operation of the hybrid excitation m...

(This article belongs to the Special Issue Mathematical Models for the Design of Electrical Machines)
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Math. Comput. Appl. - ISSN 2297-8747