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Volume 26, September

Math. Comput. Appl., Volume 26, Issue 4 (December 2021) – 8 articles

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Article
Mathematical Models with Nonlocal Initial Conditions: An Exemplification from Quantum Mechanics
Math. Comput. Appl. 2021, 26(4), 73; https://doi.org/10.3390/mca26040073 - 23 Oct 2021
Viewed by 167
Abstract
Nonlocal models are ubiquitous in all branches of science and engineering, with a rapidly expanding range of mathematical and computational applications due to the ability of such models to capture effects and phenomena that traditional models cannot. While spatial nonlocalities have received considerable [...] Read more.
Nonlocal models are ubiquitous in all branches of science and engineering, with a rapidly expanding range of mathematical and computational applications due to the ability of such models to capture effects and phenomena that traditional models cannot. While spatial nonlocalities have received considerable attention in the research community, the same cannot be said about nonlocality in time, in particular when nonlocal initial conditions are present. This paper aims at filling this gap, providing an overview of the current status of nonlocal models and focusing on the mathematical treatment of such models when nonlocal initial conditions are at the heart of the problem. Specifically, our representative example is given for a nonlocal-in-time problem for the abstract Schrödinger equation. By exploiting the linear nature of nonlocal conditions, we derive an exact representation of the solution operator under assumptions that the spectrum of Hamiltonian is contained in the horizontal strip of the complex plane. The derived representation permits us to establish the necessary and sufficient conditions for the problem’s well-posedness and the existence of its solution under different regularities. Furthermore, we present new sufficient conditions for the existence of the solution that extend the existing results in this field to the case when some nonlocal parameters are unbounded. Two further examples demonstrate the developed methodology and highlight the importance of its computer algebra component in the reduction procedures and parameter estimations for nonlocal models. Finally, a connection of the considered models and developed analysis is discussed in the context of other reduction techniques, concentrating on the most promising from the viewpoint of data-driven modelling environments, and providing directions for further generalizations. Full article
Article
Predicting Rice Production in Central Thailand Using the WOFOST Model with ENSO Impact
Math. Comput. Appl. 2021, 26(4), 72; https://doi.org/10.3390/mca26040072 - 20 Oct 2021
Viewed by 152
Abstract
The World Food Studies Simulation Model (WOFOST) model is a daily crop growth and yield forecast model with interactions with the environment, including soil, agricultural management, and especially climate conditions. An El Niño–Southern Oscillation (ENSO) phenomenon directly affected climate change and indirectly affected [...] Read more.
The World Food Studies Simulation Model (WOFOST) model is a daily crop growth and yield forecast model with interactions with the environment, including soil, agricultural management, and especially climate conditions. An El Niño–Southern Oscillation (ENSO) phenomenon directly affected climate change and indirectly affected the rice yield in Thailand. This study aims to simulate rice production in central Thailand using the WOFOST model and to find the relationship between rice yield and ENSO. The meteorological data and information on rice yields of Suphan Buri 1 variety from 2011 to 2018 in central Thailand were used to study the rice yields. The study of rice yield found that the WOFOST model was able to simulate rice yield with a Root Mean Square Error (RMSE) value of 752 kg ha1, with approximately 16% discrepancy. The WOFOST model was able to simulate the growth of Suphan Buri 1 rice, with an average discrepancy of 16.205%, and Suphan Buri province had the least discrepancy at 6.99%. Most rice yield simulations in the central region were overestimated (except Suphan Buri) because the model did not cover crop damage factors such as rice disease or insect damage. The WOFOST model had good relative accuracy and could respond to estimates of rice yields. When an El Niño phenomenon occurs at Niño 3.4, it results in lower-than-normal yields of Suphan Buri 1 rice in the next 8 months. On the other hand, when a La Niña phenomenon occurs at Niño 3.4, Suphan Buri 1 rice yields are higher than normal in the next 8 months. An analysis of the rice yield data confirms the significant impact of ENSO on rice yields in Thailand. This study shows that climate change leads to impacts on rice production, especially during ENSO years. Full article
Article
Well-Posedness and Stability Results for a Nonlinear Damped Porous–Elastic System With Infinite Memory and Distributed Delay Terms
Math. Comput. Appl. 2021, 26(4), 71; https://doi.org/10.3390/mca26040071 - 16 Oct 2021
Viewed by 217
Abstract
In the present paper, we consider an important problem from the application perspective in science and engineering, namely, one-dimensional porous–elastic systems with nonlinear damping, infinite memory and distributed delay terms. A new minimal conditions, placed on the nonlinear term and the relationship between [...] Read more.
In the present paper, we consider an important problem from the application perspective in science and engineering, namely, one-dimensional porous–elastic systems with nonlinear damping, infinite memory and distributed delay terms. A new minimal conditions, placed on the nonlinear term and the relationship between the weights of the different damping mechanisms, are used to show the well-posedness of the solution using the semigroup theory. The solution energy has an explicit and optimal decay for the cases of equal and nonequal speeds of wave propagation. Full article
Article
Time to Critical Condition in Emergency Services
Math. Comput. Appl. 2021, 26(4), 70; https://doi.org/10.3390/mca26040070 - 30 Sep 2021
Viewed by 280
Abstract
Providing uninterrupted response service is of paramount importance for emergency medical services, regardless of the operating scenario. Thus, reliable estimates of the time to the critical condition, under which there will be no available servers to respond to the next incoming call, become [...] Read more.
Providing uninterrupted response service is of paramount importance for emergency medical services, regardless of the operating scenario. Thus, reliable estimates of the time to the critical condition, under which there will be no available servers to respond to the next incoming call, become very useful measures of the system’s performance. In this contribution, we develop a key performance indicator by providing an explicit formula for the average time to the shortage condition. Our analytical expression for this average time is a function of the number of parallel servers and the inter-arrival and service times. We assume exponential distributions of times in our analytical expression, but for evaluating the mean first-passage time to the critical condition under more realistic scenarios, we validate our result through exhaustive simulations with lognormal service time distributions. For this task, we have implemented a simulator in R. Our results indicate that our analytical formula is an acceptable approximation under any situation of practical interest. Full article
(This article belongs to the Special Issue Numerical and Evolutionary Optimization 2021)
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Article
Modified Representations for the Close Evaluation Problem
Math. Comput. Appl. 2021, 26(4), 69; https://doi.org/10.3390/mca26040069 - 28 Sep 2021
Viewed by 203
Abstract
When using boundary integral equation methods, we represent solutions of a linear partial differential equation as layer potentials. It is well-known that the approximation of layer potentials using quadrature rules suffer from poor resolution when evaluated closed to (but not on) the boundary. [...] Read more.
When using boundary integral equation methods, we represent solutions of a linear partial differential equation as layer potentials. It is well-known that the approximation of layer potentials using quadrature rules suffer from poor resolution when evaluated closed to (but not on) the boundary. To address this challenge, we provide modified representations of the problem’s solution. Similar to Gauss’s law used to modify Laplace’s double-layer potential, we use modified representations of Laplace’s single-layer potential and Helmholtz layer potentials that avoid the close evaluation problem. Some techniques have been developed in the context of the representation formula or using interpolation techniques. We provide alternative modified representations of the layer potentials directly (or when only one density is at stake). Several numerical examples illustrate the efficiency of the technique in two and three dimensions. Full article
(This article belongs to the Special Issue Computational Methods for Coupled Problems in Science and Engineering)
Article
Modelling Forest Fires Using Complex Networks
Math. Comput. Appl. 2021, 26(4), 68; https://doi.org/10.3390/mca26040068 - 28 Sep 2021
Viewed by 202
Abstract
Forest fires have been a major threat to the environment throughout history. In order to mitigate its consequences, we present, in a first of a series of works, a mathematical model with the purpose of predicting fire spreading in a given land portion [...] Read more.
Forest fires have been a major threat to the environment throughout history. In order to mitigate its consequences, we present, in a first of a series of works, a mathematical model with the purpose of predicting fire spreading in a given land portion divided into patches, considering the area and the rate of spread of each patch as inputs. The rate of spread can be estimated from previous knowledge on fuel availability, weather and terrain conditions. We compute the time duration of the spreading process in a land patch in order to construct and parametrize a landscape network, using cellular automata simulations. We use the multilayer network model to propose a network of networks at the landscape scale, where the nodes are the local patches, each with their own spreading dynamics. We compute some respective network measures and aim, in further work, for the establishment of a fire-break structure according to increasing accuracy simulation results. Full article
Article
Towards Building the OP-Mapped WENO Schemes: A General Methodology
by and
Math. Comput. Appl. 2021, 26(4), 67; https://doi.org/10.3390/mca26040067 - 23 Sep 2021
Viewed by 240
Abstract
A serious and ubiquitous issue in existing mapped WENO schemes is that most of them can hardly preserve high resolutions, but in the meantime prevent spurious oscillations in the solving of hyperbolic conservation laws with long output times. Our goal for this article [...] Read more.
A serious and ubiquitous issue in existing mapped WENO schemes is that most of them can hardly preserve high resolutions, but in the meantime prevent spurious oscillations in the solving of hyperbolic conservation laws with long output times. Our goal for this article was to address this widely known problem. In our previous work, the order-preserving (OP) criterion was originally introduced and carefully used to devise a new mapped WENO scheme that performs satisfactorily in long simulations, and hence it was indicated that the OP criterion plays a critical role in the maintenance of low-dissipation and robustness for mapped WENO schemes. Thus, in our present work, we firstly defined the family of mapped WENO schemes, whose mappings meet the OP criterion, as OP-Mapped WENO. Next, we attentively took a closer look at the mappings of various existing mapped WENO schemes and devised a general formula for them. That helped us to extend the OP criterion to the design of improved mappings. Then, we created a generalized implementation of obtaining a group of OP-Mapped WENO schemes, named MOP-WENO-X, as they are developed from the existing mapped WENO-X schemes, where the notation “X” is used to identify the version of the existing mapped WENO scheme. Finally, extensive numerical experiments and comparisons with competing schemes were conducted to demonstrate the enhanced performances of the MOP-WENO-X schemes. Full article
(This article belongs to the Special Issue Computational Methods for Coupled Problems in Science and Engineering)
Article
The Limited Validity of the Conformable Euler Finite Difference Method and an Alternate Definition of the Conformable Fractional Derivative to Justify Modification of the Method
Math. Comput. Appl. 2021, 26(4), 66; https://doi.org/10.3390/mca26040066 - 23 Sep 2021
Viewed by 210
Abstract
A method recently advanced as the conformable Euler method (CEM) for the finite difference discretization of fractional initial value problem [...] Read more.
A method recently advanced as the conformable Euler method (CEM) for the finite difference discretization of fractional initial value problem Dtαyt = ft;yt, yt0 = y0, atb, and used to describe hyperchaos in a financial market model, is shown to be valid only for α=1. The property of the conformable fractional derivative (CFD) used to show this limitation of the method is used, together with the integer definition of the derivative, to derive a modified conformable Euler method for the initial value problem considered. A method of constructing generalized derivatives from the solution of the non-integer relaxation equation is used to motivate an alternate definition of the CFD and justify alternative generalizations of the Euler method to the CFD. The conformable relaxation equation is used in numerical experiments to assess the performance of the CEM in comparison to that of the alternative methods. Full article
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