We establish nonexistence of nontrivial solutions (including sign-changing ones) for some partial differential inequalities of elliptic and parabolic type containing nonlinear terms that depend on the positive and negative part of the sought function in different ways. Systems of elliptic inequalities with similar structure are also considered. The proofs are based on the test function method.
Nanofluid as a special thermal transporting medium has recently received unprecedented attention due to its improved heat transfer performance compared to conventional fluids. Numerous researches have been conducted on the natural convection characteristics of different nanofluids in various configurations of cavities due to the important applications of natural convection in environmental, petrochemical, medical, aviation and space technology, industrial and many more areas. The emergence of a magnetic field as a tool for the manipulation of convective flow and heat transfer behaviours of nanofluids in non-square enclosures has been extensively reviewed. The influence of several variables such as controlling parameters, heat distribution methods, thermal and concentration boundary conditions, magnetic field types, numerical methods, correlation types, nanofluid types, heaters types, numbers and length, and slip conditions, etc., on the magnetohydrodynamic (MHD) natural convection flow and heat transfer behaviours of nanofluid in non-square cavities has been given great attention and brought to the spotlight for discussion. The concepts of bioconvection, micro-polar nanofluid, bio-nanofluid (green nanofluid), ionic nanofluid, and hybrid nanofluid have also been discussed for the first time in relation to natural convection. Special cases of MHD natural convection in non-square cavities involving hybrid nanofluids and micro-polar nanofluids are also presented herein. The application of several numerical methods (which is the major approach studied so far) to investigate the hydromagnetic behaviours of nanofluids in non-square cavities is the focus of this work.
In this study, the viscosity of MgO-Water nanofluid in a different volume fraction of nanoparticles, temperatures, and shear rates has been predicted by Artificial Neural Networks (ANNs) and surface methods. In the ANN method, an algorithm is proposed to select the best neuron number for the hidden layer. In the fitting method, a surface is proposed for each volume fraction of nanoparticles, and finally, the results of ANN and surface fitting method have been compared. It can be observed that, increasing the volume fraction from 0.07% to 1.25% at temperatures of 25, 30, 40, 50, and 60 °C resulted in about two-fold increase in viscosity. Also, the best network has 24 neurons in the hidden layer. It can be seen that for a network with 24 neurons in the hidden layer has the best overall correlation, and this coefficient is 0.999035. The mean absolute value of errors in ANN and fitting method are 0.0118 and 0.0206, respectively.
In this letter, two time delay dynamic models, TDD-NCP model and Fudan-CCDC model, are introduced to track the data of COVID-19. The TDD-NCP model is developed recently by Cheng's group group in Fudan and SUFE. The TDD-NCP model introduced the time delay process into the differential equations to describe the latent period of the epidemic. The Fudan-CDCC model is established when Wenbin Chen suggested to determine the kernel functions in the TDD-NCP model by the public data from CDCC. By the public data of the cumulative confirmed cases in different regions in China and different countries, these models can clearly illustrate that the containment of the epidemic highly depends on early and effective isolations.
The turbulent characteristics of heat transfer and flow have been determined by applying the Van Driest model of the eddy diffusivity for water and ethylene glycol-based nanofluids. The properties of CuO, Al2O3 and SiO2 nanofluids in two base liquids viz., water and EG-water mixture with the ratio of 60:40 are considered for various concentrations and bulk temperature ranges. Based on the observations, it is concluded that numerical outcomes are validated with experimental measurements for heat transfer properties. It is monitored that SiO2 reaches a higher temperature gradient in comparison to CuO at a similar temperature and concentration in EG-water with the mixture of 60: 40. The gradients are greater for the EGW mixture compared to water-based nanofluids. However, the water-based nanofluids have higher heat transfer coefficients compared to EG-water nanofluid at identical flow velocities.
Fangzhu, which has been lost for thousands of years, is an ancient device for water collection from air, its mechanism is unknown yet. Here we elucidate its possible surface-geometric and related physical properties by the oldest the Yin-Yang contradiction. In view of modern nanotechnology, we reveal that Fangzhu’s water-harvesting ability is obtained through a hydrophilic-hydrophobic hierarchy of the surface, mimicking spider web’s water collection, lotus or desert beetle’s water intake. The convex-concave hierarchy of Fangzhu’s textured surface enables it to have low wettability(high geometric potential) to attract water molecules from air through the nano-scale convex surface and transfer the attracted water along the concave surface to the collector. A mathematical model is established to reveal three main factors affecting its effectiveness, i.e., the air velocity, the surface temperature and surface structure. The lost technology can play an extremely important role in modern architecture, ocean engineering, transportation and others to catch water from air for everyday use.
The newly generalized energy storage component namely memristor is a fundamental circuit element so called universal charge-controlled mem-element is proposed for controlling the analysis and coexisting attractors. The governing differential equations of memristor are highly non-linear for mathematical relationships. The mathematical model of memristor is established in terms of newly defined fractal-fractional differential operators so called Atangana-Baleanu, Caputo-Fabrizio and Caputo fractal-fractional differential operator. A novel numerical approach is developed for the governing differential equations of memristor on the basis of Atangana-Baleanu, Caputo-Fabrizio and Caputo fractal-fractional differential operator. We discussed chaotic behavior of memristor under three criteria as (i) varying fractal order, we fixed fractional order, (ii) varying fractional order, we fixed fractal order and (ii) varying fractal and fractional orders simultaneously. Our investigated graphical illustrations and simulated results via MATLAB for the chaotic behaviors of memristor suggest that newly presented Atangana-Baleanu, Caputo-Fabrizio and Caputo fractal-fractional differential operator has generates significant results as compared with classical approach.
The paper is devoted to the Stackelberg control of a linear parabolic equation with missing initial conditions. The strategy involves two controls called follower and leader. The objective of the follower is to bring the state to a desired state while the leader has to bring the system to rest at the final time. The results are obtained by means of Fenchel-Legendre transform and appropriate Carleman inequalities.
The existence and occurrence, especially by a backward bifurcation, of endemic equilibria is of utmost importance in determining the spread and persistence of a disease. In many epidemiological models, the equation for the endemic equilibria is quadratic, with the coefficients determined by the parameters of the model. Despite its apparent simplicity, such an equation can describe an amazing number of dynamical behaviours. In this paper, we shall provide a comprehensive survey of possible bifurcation patterns, deriving explicit conditions on the equation's parameters for the occurrence of each of them, and discuss illustrative examples.