Special Issue "On Interdisciplinary Modelling and Numerical Simulation in the Realm of Physics & Engineering"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: 28 February 2021.

Special Issue Editors

Prof. Dr. Pedro José Fernández de Córdoba Castellá
Website
Guest Editor
Institute for Pure and Applied Mathematics, Interdisciplinary Modeling Group (InterTech), Universitat Politècnica de València, E-46022, Valencia, Spain
Interests: Mathematical modeling; numerical simulation
Special Issues and Collections in MDPI journals
Dr. Juan Carlos Castro Palacio
Website
Co-Guest Editor
Institute of Nuclear Fusion, ETSII, Universidad Politécnica de Madrid, c/José Gutiérrez Abascal, 2, 28006 Madrid, Spain
Interests: computational physics, machine learning, intra e intermolecular potential energy surface calculation, molecular dynamics, reaction dynamics, plasmonic nanoparticles
Dr. Miguel Ángel García-March
Website
Co-Guest Editor
ICFO – The Institute of Photonic Sciences, Av. C.F. Gauss 3, SP-08860 Castelldefels, Barcelona, Spain
Interests: ultra-cold atoms; open classical and quantum systems; complex quantum dynamics; strongly correlated quantum systems; anomalous diffusion in complex classical environments; few-atom systems; nonlinear and singular optics; quantum simulators and sensors; quantum thermodynamics and relaxation in closed quantum systems
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

In interdisciplinary approaches, which necessarily combine concepts and tools from different fields, mathematics is commonly the language used to smartly merge all the different concepts into a unique model. Cross-border modeling and numerical simulation works within the subfields of Physics and Engineering are particularly welcome in this special issue.

The scope includes (but is not limited to) original research works providing characterizations, explanations, predictions of systems, and phenomena supporting the emergence of potentially novel, useful applications which can even be at a very early stage of conception.

Some examples are the discovery of materials with new properties, key aspects of fusion energy, sensors, complex systems, and anomalous diffusion with applications in, e.g., biology (diffusion in systems with interactions, diverse geometries, etc.) and active matter (also applications of machine learning in the context of diffusion in biology and active matter), optical tweezers, (nonlinear) singular optics, interplay between condense matter and photonics (classical analogs of quantum systems), nanodevices (motors, wires, tubes, etc.), techniques to manipulate biomolecules, new applications of electromagnetic radiation, and renewable energies, among others.

Prof. Dr. Pedro José Fernández de Córdoba Castellá
Dr. Juan Carlos Castro Palacio
Dr. Miguel Ángel García-March
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Interdisciplinary modeling
  • Numerical simulation
  • Cutting-edge applications

Published Papers (10 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

Open AccessArticle
Study of the Vibrational Predissociation of the NeBr2 Complex by Computational Simulation Using the Trajectory Surface Hopping Method
Mathematics 2020, 8(11), 2029; https://doi.org/10.3390/math8112029 - 14 Nov 2020
Abstract
The vibrational predissociation of NeBr2 has been studied using a variety of theoretical and experimental methods, producing a large number of results. It is therefore a useful system for comparing different theoretical methods. Here, we apply the trajectory surface hopping (TSH) method [...] Read more.
The vibrational predissociation of NeBr2 has been studied using a variety of theoretical and experimental methods, producing a large number of results. It is therefore a useful system for comparing different theoretical methods. Here, we apply the trajectory surface hopping (TSH) method that consists of propagating the dynamics of the system on a potential energy surface (PES) corresponding to quantum molecular vibrational states with possibility of hopping towards other surfaces until the van der Waals bond dissociates. This allows quantum vibrational effects to be added to a classical dynamics approach. We have also incorporated the kinetic mechanism for a better compression of the evolution of the complex. The novelty of this work is that it allows us to incorporate all the surfaces for (v=16,17,,29) into the dynamics of the system. The calculated lifetimes are similar to those previously reported experimentally and theoretically. The rotational distribution, the rotational energy and jmax are in agreement with other works, providing new information for this complex. Full article
Show Figures

Figure 1

Open AccessArticle
Fast Switch and Spline Function Inversion Algorithm with Multistep Optimization and k-Vector Search for Solving Kepler’s Equation in Celestial Mechanics
Mathematics 2020, 8(11), 2017; https://doi.org/10.3390/math8112017 - 12 Nov 2020
Abstract
Obtaining the inverse of a nonlinear monotonic function f(x) over a given interval is a common problem in pure and applied mathematics, the most famous example being Kepler’s description of orbital motion in the two-body approximation. In traditional numerical approaches, [...] Read more.
Obtaining the inverse of a nonlinear monotonic function f(x) over a given interval is a common problem in pure and applied mathematics, the most famous example being Kepler’s description of orbital motion in the two-body approximation. In traditional numerical approaches, this problem is reduced to solving the nonlinear equation f(x)y=0 in each point y of the co-domain. However, modern applications of orbital mechanics for Kepler’s equation, especially in many-body problems, require highly optimized numerical performance. Ongoing efforts continually attempt to improve such performance. Recently, we introduced a novel method for computing the inverse of a one-dimensional function, called the fast switch and spline inversion (FSSI) algorithm. It works by obtaining an accurate interpolation of the inverse function f1(y) over an entire interval with a very small generation time. Here, we describe two significant improvements with respect to the performance of the original algorithm. First, the indices of the intervals for building the spline are obtained by k-vector search combined with bisection, thereby making the generation time even smaller. Second, in the case of Kepler’s equation, a multistep method for the optimized calculation of the breakpoints of the spline polynomial was designed and implemented in Cython. We demonstrate results that accurately solve Kepler’s equation for any value of the eccentricity e[0,1ϵ], with ϵ=2.22×1016, which is the limiting error in double precision. Even with modest current hardware, the CPU generation time for obtaining the solution with high accuracy in a large number of points of the co-domain can be kept to around a few nanoseconds per point. Full article
Show Figures

Figure 1

Open AccessArticle
Mathematical Modeling and Simulation of a Gas Emission Source Using the Network Simulation Method
Mathematics 2020, 8(11), 1996; https://doi.org/10.3390/math8111996 - 09 Nov 2020
Abstract
A mathematical model for the simulation of the diffusion of the pollutants released from a point source is presented. All phenomena have been included, such as thermal and wind gradients, turbulence, fumigation, convective and diffusive effects, and atmospheric stabilities. To better understand the [...] Read more.
A mathematical model for the simulation of the diffusion of the pollutants released from a point source is presented. All phenomena have been included, such as thermal and wind gradients, turbulence, fumigation, convective and diffusive effects, and atmospheric stabilities. To better understand the dynamics of these occurrences, the Network Simulation Method was used to provide the concentration of pollutants in three spatial coordinates. The model was simulated in open source software and validated with experimental data, satisfying the Hanna criteria. Additionally, this model selects for the appropriate expressions based on the physical phenomena that govern each case and allows for time-dependent data entry. The cases studied show the great coupling that exists between the variables of wind velocity and atmospheric stability for the pollutant diffusion. The model can be used for two important aims, to identify the behavior of the emission of pollutants, and to determine the concentration of a pollutant at various points, through an inverse problem, locating the source of the emission. Full article
Show Figures

Figure 1

Open AccessArticle
Machinery Failure Approach and Spectral Analysis to Study the Reaction Time Dynamics over Consecutive Visual Stimuli: An Entropy-Based Model
Mathematics 2020, 8(11), 1979; https://doi.org/10.3390/math8111979 - 06 Nov 2020
Abstract
The reaction times of individuals over consecutive visual stimuli have been studied using an entropy-based model and a failure machinery approach. The used tools include the fast Fourier transform and a spectral entropy analysis. The results indicate that the reaction times produced by [...] Read more.
The reaction times of individuals over consecutive visual stimuli have been studied using an entropy-based model and a failure machinery approach. The used tools include the fast Fourier transform and a spectral entropy analysis. The results indicate that the reaction times produced by the independently responding individuals to visual stimuli appear to be correlated. The spectral analysis and the entropy of the spectrum yield that there are features of similarity in the response times of each participant and among them. Furthermore, the analysis of the mistakes made by the participants during the reaction time experiments concluded that they follow a behavior which is consistent with the MTBF (Mean Time Between Failures) model, widely used in industry for the predictive diagnosis of electrical machines and equipment. Full article
Show Figures

Figure 1

Open AccessArticle
Modelling of Alumina Splat Solidification on Preheated Steel Substrate Using the Network Simulation Method
Mathematics 2020, 8(9), 1568; https://doi.org/10.3390/math8091568 - 11 Sep 2020
Abstract
A mathematical model, consisting of a set of differential equations, for the simulation of the alumina splat solidification on steel substrate is presented. The network simulation method is used to solve the problem, which provides the temperatures and the cooling rate in the [...] Read more.
A mathematical model, consisting of a set of differential equations, for the simulation of the alumina splat solidification on steel substrate is presented. The network simulation method is used to solve the problem, which provides the temperatures and the cooling rate in the splat and substrate with a high temporal and spatial resolution for different values of the preheated substrate temperature. The results of this calculation provide important information for the design of ceramic coatings. The model design is explained in depth and simulated in open source software. As expected, the temperature evolutions in several points of the splat, an important variable to know the type of phases and the effect of the manufacturing parameters on this process, coincide with the experimental results. The model is also checked by another experimental test with tin and a bigger splat, which enables the temperature to be measured during solidification. It is worth highlighting the study of the cooling rate, a fundamental parameter to determine the phase, whether amorphous, gamma or alpha. Furthermore, a sensitive study of the mesh was included in order to optimize the computational time. Full article
Show Figures

Figure 1

Open AccessArticle
Stability Assessment of Stochastic Differential-Algebraic Systems via Lyapunov Exponents with an Application to Power Systems
Mathematics 2020, 8(9), 1393; https://doi.org/10.3390/math8091393 - 20 Aug 2020
Abstract
In this paper, we discuss stochastic differential-algebraic equations (SDAEs) and the asymptotic stability assessment for such systems via Lyapunov exponents (LEs). We focus on index-1 SDAEs and their reformulation as ordinary stochastic differential equations (SDEs). Via ergodic theory, it is then feasible to [...] Read more.
In this paper, we discuss stochastic differential-algebraic equations (SDAEs) and the asymptotic stability assessment for such systems via Lyapunov exponents (LEs). We focus on index-1 SDAEs and their reformulation as ordinary stochastic differential equations (SDEs). Via ergodic theory, it is then feasible to analyze the LEs via the random dynamical system generated by the underlying SDEs. Once the existence of well-defined LEs is guaranteed, we proceed to the use of numerical simulation techniques to determine the LEs numerically. Discrete and continuous QR decomposition-based numerical methods are implemented to compute the fundamental solution matrix and use it in the computation of the LEs. Important computational features of both methods are illustrated via numerical tests. Finally, the methods are applied to two applications from power systems engineering, including the single-machine infinite-bus (SMIB) power system model. Full article
Show Figures

Figure 1

Open AccessArticle
Predictive Power of Adaptive Candlestick Patterns in Forex Market. Eurusd Case
Mathematics 2020, 8(5), 802; https://doi.org/10.3390/math8050802 - 14 May 2020
Abstract
The Efficient Market Hypothesis (EMH) states that all available information is immediately reflected in the price of any asset or financial instrument, so that it is impossible to predict its future values, making it follow a pure stochastic process. Among all financial markets, [...] Read more.
The Efficient Market Hypothesis (EMH) states that all available information is immediately reflected in the price of any asset or financial instrument, so that it is impossible to predict its future values, making it follow a pure stochastic process. Among all financial markets, FOREX is usually addressed as one of the most efficient. This paper tests the efficiency of the EURUSD pair taking only into consideration the price itself. A novel categorical classification, based on adaptive criteria, of all possible single candlestick patterns is presented. The predictive power of candlestick patterns is evaluated from a statistical inference approach, where the mean of the average returns of the strategies in out-of-sample historical data is taken as sample statistic. No net positive average returns are found in any case after taking into account transaction costs. More complex candlestick patterns are considered feeding supervised learning systems with the information of past bars. No edge is found even in the case of considering the information of up to 24 preceding candlesticks. Full article
Show Figures

Figure 1

Open AccessArticle
State Vector Identification of Hybrid Model of a Gas Turbine by Real-Time Kalman Filter
Mathematics 2020, 8(5), 659; https://doi.org/10.3390/math8050659 - 27 Apr 2020
Abstract
A model and real-time simulation of a gas turbine engine (GTE) by real-time tasks (RTT) is presented. A Kalman filter is applied to perform the state vector identification of the GTE model. The obtained algorithms are recursive and multivariable; for this reason, ANSI [...] Read more.
A model and real-time simulation of a gas turbine engine (GTE) by real-time tasks (RTT) is presented. A Kalman filter is applied to perform the state vector identification of the GTE model. The obtained algorithms are recursive and multivariable; for this reason, ANSI C libraries have been developed for (a) use of matrices and vectors, (b) dynamic memory management, (c) simulation of state-space systems, (d) approximation of systems using equations in matrix finite difference, (e) computing the mean square errors vector, and (f) state vector identification of dynamic systems through digital Kalman filter. Simulations were performed in a Single Board Computer (SBC) Raspberry Pi 2® with a real-time operating system. Execution times have been measured to justify the real-time simulation. To validate the results, multiple time plots are analyzed to verify the quality and convergence time of the mean square error obtained. Full article
Show Figures

Figure 1

Open AccessArticle
Percentile Study of χ Distribution. Application to Response Time Data
Mathematics 2020, 8(4), 514; https://doi.org/10.3390/math8040514 - 02 Apr 2020
Cited by 1
Abstract
As a continuation of our previous work, where a Maxwell–Boltzmann distribution was found to model a collective’s reaction times, in this work we will carry out a percentile study of the χ distribution for some freedom ranging from k = 2 to k [...] Read more.
As a continuation of our previous work, where a Maxwell–Boltzmann distribution was found to model a collective’s reaction times, in this work we will carry out a percentile study of the χ distribution for some freedom ranging from k = 2 to k = 10. The most commonly used percentiles in the biomedical and behavioral sciences have been included in the analysis. We seek to provide a look-up table with percentile ratios, taken symmetrically about the median, such that this distribution can be identified in practice in an easy way. We have proven that these ratios do not depend upon the variance chosen for the k generating Gaussians. In general, the χ probability density, generalized to take any value of the variance, represents an ideal gas in a k-dimensional space. We also derive an approximate expression for the median of the generalized χ distribution. In the second part of the results, we will focus on the practical case of k = 3, which represents the ideal gas in physics, and models quite well the reaction times of a human collective. Accurately, we will perform a more detailed scrutiny of the percentiles for the reaction time distribution of a sample of 50 school-aged children (7200 reaction times). Full article
Show Figures

Figure 1

Open AccessArticle
A Fractional Derivative Modeling of Heating and Cooling of LED Luminaires
Mathematics 2020, 8(3), 362; https://doi.org/10.3390/math8030362 - 06 Mar 2020
Abstract
In the context of energy efficient lighting, we present a mathematical study of the heating and cooling processes of a common type of luminaires, consisting of a single light-emitting diode source in thermal contact with an aluminum passive heat sink. First, we study [...] Read more.
In the context of energy efficient lighting, we present a mathematical study of the heating and cooling processes of a common type of luminaires, consisting of a single light-emitting diode source in thermal contact with an aluminum passive heat sink. First, we study stationary temperature distributions by addressing the appropriate system of partial differential equations with a commercial finite element solver. Then, we study the temporal evolution of the temperature of the chip and find that it is well approximated with a fractional derivative generalization of Newton’s cooling law. The mathematical results are compared and shown to largely agree with our laboratory measurements. Full article
Show Figures

Figure 1

Back to TopTop