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Agniva Datta ◽  
Muktish Acharyya

The results of Kermack–McKendrick SIR model are planned to be reproduced by cellular automata (CA) lattice model. The CA algorithms are proposed to study the model of an epidemic, systematically. The basic goal is to capture the effects of spreading of infection over a scale of length. This CA model can provide the rate of growth of the infection over the space which was lacking in the mean-field like susceptible-infected-removed (SIR) model. The motion of the circular front of an infected cluster shows a linear behavior in time. The correlation of a particular site to be infected with respect to the central site is also studied. The outcomes of the CA model are in good agreement with those obtained from SIR model. The results of vaccination have been also incorporated in the CA algorithm with a satisfactory degree of success. The advantage of the present model is that it can shed a considerable amount of light on the physical properties of the spread of a typical epidemic in a simple, yet robust way.

2022 ◽  
Vol 43 (1) ◽  
pp. 1-20
Binying Wang ◽  
Jinxing Liu ◽  
A. K. Soh ◽  
Naigang Liang

AbstractWe have proposed an “exact” strain gradient (SG) continuum model to properly predict the dispersive characteristics of diatomic lattice metamaterials with local and nonlocal interactions. The key enhancement is proposing a wavelength-dependent Taylor expansion to obtain a satisfactory accuracy when the wavelength gets close to the lattice spacing. Such a wavelength-dependent Taylor expansion is applied to the displacement field of the diatomic lattice, resulting in a novel SG model. For various kinds of diatomic lattices, the dispersion diagrams given by the proposed SG model always agree well with those given by the discrete model throughout the first Brillouin zone, manifesting the robustness of the present model. Based on this SG model, we have conducted the following discussions. (I) Both mass and stiffness ratios affect the band gap structures of diatomic lattice metamaterials, which is very helpful for the design of metamaterials. (II) The increase in the SG order can enhance the model performance if the modified Taylor expansion is adopted. Without doing so, the higher-order continuum model can suffer from a stronger instability issue and does not necessarily have a better accuracy. The proposed SG continuum model with the eighth-order truncation is found to be enough to capture the dispersion behaviors all over the first Brillouin zone. (III) The effects of the nonlocal interactions are analyzed. The nonlocal interactions reduce the workable range of the well-known long-wave approximation, causing more local extrema in the dispersive diagrams. The present model can serve as a satisfactory continuum theory when the wavelength gets close to the lattice spacing, i.e., when the long-wave approximation is no longer valid. For the convenience of band gap designs, we have also provided the design space from which one can easily obtain the proper mass and stiffness ratios corresponding to a requested band gap width.

Mathematics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 121
Aatef Hobiny ◽  
Ibrahim Abbas ◽  
Marin Marin

This article focuses on the study of redial displacement, the carrier density, the conductive and thermodynamic temperatures and the stresses in a semiconductor medium with a spherical hole. This study deals with photo-thermoelastic interactions in a semiconductor material containing a spherical cavity. The new hyperbolic theory of two temperatures with one-time delay is used. The internal surface of the cavity is constrained and the density of carriers is photogenerated by a heat flux at the exponentially decreasing pulse boundaries. The analytical solutions by the eigenvalues approach under the Laplace transformation approaches are used to obtain the solution of the problem and the inversion of the Laplace transformations is performed numerically. Numerical results for semiconductor materials are presented graphically and discussed to show the variations of physical quantities under the present model.

2021 ◽  
Vol Volume 32 - 2019 - 2021 ◽  
Issouf Abdou ◽  
Philibert Andriamanantena ◽  
Rivo Rakotozafy

This article, which is part of the general framework of mathematics applied to economics, is a decision-making model in total ignorance. Such an environment is characterized by the absence of a law of distribution of the states of nature allowing having good forecasts or anticipations. Based primarily on the integral of Choquet, this model allows aggregating the different states of nature in order to make a better decision. This integral of Choquet imposes itself with respect to the complexity of the environment and also by its relevance of aggregation of the interactive or conflicting criteria. The present model is a combination of the Schmeidler model and the Brice Mayag algorithm for the determination of Choquet 2-additive capacity. It fits into the framework of subjective models and provides an appropriate response to the Ellsberg paradox. Cet article qui s'inscrit dans le cadre général des mathématiques appliquées à l'économie est un modèle de prise de décision dans l'ignorance totale. Un tel environnement est caractérisé par l'absence d'une loi de distribution des états de la nature permettant d'avoir des bonnes prévisions ou anticipations. Se basant principalement sur l'intégrale de Choquet, ce modèle permet d'agréger les différents états de la nature afin de prendre une meilleure décision. Cette intégrale de Choquet s'impose par rapport à la complexité de l'environnement et aussi par son caractère pertinent d'agrégation des critères interactifs ou conflictuels. Le présent modèle est une combinaison du modèle de Schmeidler et de l'algorithme de Brice Mayag pour la détermination de la capacité 2-additive de Choquet. Il s'inscrit dans le cadre des modèles subjectifs et apporte une réponse appropriée au paradoxe d'Ellsberg.

2021 ◽  
pp. 1-41
Syamak Pazireh ◽  
Jeff Defoe

Abstract Despite advances in computational power, the cost of time-accurate flows in axial compressor and fan stages with spatially non-uniform inflow is still too high for design-stage use in industry. Body force modeling reduces the computation time to practical levels, mainly by reducing the problem to a steady one. These computations are important to determine efficiency penalties associated with non-uniform inflows. Previous studies of body force methods have, in most cases, relied on computations with the presence of the blades to calibrate loss models. In some recent studies, uncalibrated models have been used, but such models can drop off in accuracy at conditions where separation would occur on the blade surfaces. In this paper, a neural network-based loss model introduced in a recent paper by the authors is implemented for NASA rotor 67 for both uniform and non-uniform inflow conditions. For uniform inflow, the spanwise trend of entropy variation is generally captured with the new body force model. Although there are discrepancies at some span fractions, the present model generally predicts the compressor's isentropic efficiency to within 3% compared to bladed RANS simulations. For non-uniform inflow, we consider a stagnation pressure profile representative of boundary layer ingestion. The results show that the region of maximum entropy generation is captured by the present model and the prediction of isentropic efficiency penalty due to the non-uniform inflow is only 0.2 points less than that determined from bladed computations.

2021 ◽  
Vol 2 (3) ◽  
pp. 41-61
Muhammad Imran Asjad ◽  
Maryam Aleem ◽  
Waqas Ali ◽  
Muhammad Abubakar ◽  
Fahd Jarad

In this paper, we use a model of non-Newtonian second grade fluid which having three partial differentialequations of momentum, heat and mass transfer with initial condition and boundary condition. Wedevelop the modified Laplace transform of this model with fractional order generalized Caputo fractional operator.We find out the solutions for temperature, concentration and velocity fields by using modified Laplacetransform and investigated the impact of the order α and ρ on temperature, concentration and velocity fieldsrespectively. From the graphical results, we have seen that both the α and ρ have reverse effect on the fluidflow properties. In consequence, it is observed that flow properties of present model can be enhanced nearthe plate for smaller and larger values of ρ. Furthermore, we have compared the present results with theexisting literature for the validation and found that they are in good agreement.

2021 ◽  
Vol 11 (2) ◽  
pp. 107-112
H. Kemer ◽  
R. Bouras ◽  
M. Sonebi ◽  
N. Mesboua ◽  
A. Benmounah

Abstract In order to decrease the fitting deviation between rheometrical measurements and empirical parameters using slump test, this paper proposes a new analytical method to evaluate the high yield stress of materials (cement pastes).In doing so, an experimental study was performed for measuring the empirical characteristics by cylindrical mold with different water to binder ratios (w/b) by aiming to increase the yield stress. Parallelly, experimental observations showed clearly the unyielded zone at flow stoppage of high yield stress samples. Based on these results, an idea was formed to applied metallic element at inlet of mold in order to push the spreading of paste. The obtained results of the model proposed in this paper were compared with the yield stress evaluated from shear flow curves using AR2000-rheometer with plate-plate geometry at rate-controlled. In fact, this study demonstrates the applicability and novelty of the present model in the process of relating the empirical parameters to yield stress.

Evgeniya Giricheva

The model of a three-trophic community with intraguild predation is considered. The system consists of three coupled ordinary differential equations describing the dynamics of resource, prey and predator. Models with intraguild predation are characterized by predators that feed on resource of its own prey. A number of similar models with different functional responses have been proposed. In contrast to previous works, in the present model, the predator functional response to the resource is differed from that to the prey. The model takes into account an intraspecific competition of prey to stabilize the system in resource-rich environment. Conditions of existence and local stability of non-negative solutions are established. The possibility of Hopf bifurcation around positive equilibrium with consumption rate as bifurcation parameter is studied. For the model, in the plane of the consumption and predation rates, the regions of existence and stability of boundary and internal equilibria are constructed. Numerical simulations show that the region of equilibrium coexistence of populations is increased due to the inclusion of prey self-limitation in the model. Bifurcation diagrams confirm the stabilizing effect of intraspecific competition of prey on the system dynamics in resource-rich environment.

2021 ◽  
Vol 2133 (1) ◽  
pp. 012043
Jun Zhang ◽  
Fang-qian He ◽  
Yu-chen Jiang

Abstract With loads on prefabricated bridges becoming more and more heavier, their dynamic behaviors should be paid more attention to. A virtual prototyping model with the object-oriented technology and the mode synthesis method is presented in MATLAB to analyze dynamic behaviors of prefabricated bridges. Using structural characteristics of the bridges properly, substructures can be looked on as objects which can be encapsulated with the mode synthesis method. The compatibility conditions on interfaces, the Lagrange’s equation and Ritz’s variational principle play the role of messages transmitting among objects. Simulation results indicate that the present model can easily study dynamic behaviors of bridges in the same model.

2021 ◽  
Vol 2101 (1) ◽  
pp. 012075
Haolong Liu ◽  
Xuming Su ◽  
Hongtae Kang

Abstract In this article, experimental tests under static tensile loadings and tension-tension cyclic loadings were conducted for T300/924 unidirectional laminated composites at different porosity levels. On the basis of the experimental tests, a physical-based residual stiffness model for porous CFRP composites was put forward. The present model describes the deterioration of composites under cyclic loading in perspective of the initiation and propagation of cracks in the matrix, and is capable of capturing the effect of voids on fatigue behaviors of the composites. Lastly, the stiffness degradations of laminates with different void contents under various stress levels were predicted, and the predicted stiffness reduction as well as fatigue life of the material agreed well with the experimental data.

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