Search Results (8)

This study aims to solve the problem of the recovery efficiency of natural gas hydrate being affected by a large amount of mud and sand in the solid fluidization mining of natural gas hydrate. Therefore, a new method for the separation of in situ sediment and natural gas hydrate in a spiral-swirling downhole is proposed, and the corresponding numerical simulation model is established to realize the analysis and verification of key flow field parameters such as flow velocity, pressure, sediment, and natural gas hydrate phase distribution. The results show that the flow velocity field of the mixed slurry presents an ‘M’-shaped symmetrical distribution, and the slurry near the wall of the separator can obtain a larger flow velocity, which is beneficial to the separation of mud–sand and natural gas hydrate. The static pressure field shows an axisymmetric distribution that decreases first and then increases, indicating that the pressure of the mixed slurry increases with the increase in the radial position, and the closer to the wall, the greater the static pressure of the mixed slurry. Near the wall of the separator, the volume fraction of the sediment phase reaches the maximum. In contrast, the volume fraction of the natural gas hydrate phase reaches the minimum, which confirms the separation effect of the sediment and the natural gas hydrate. The results show that the separation of sediments and natural gas hydrate can be realized, thereby improving the exploitation efficiency of natural gas hydrate. The designed spiral cyclone coupling separator provides a new solution to solving the problem of sand removal in natural gas hydrate exploitation. Full article

We consider the p-Laplace boundary value problem with the Dirichlet boundary condition. A new lower estimate for positive solutions of the problem is obtained. As an application of this new lower estimate, some sufficient conditions for the existence and nonexistence of positive solutions for the p-Laplace problem are obtained. Full article

This paper discusses the existence of positive radial symmetric solutions of the nonlinear biharmonic equation ${▵}^{2}u=f(u,▵u)$ on an annular domain $\Omega$ in ${\mathbb{R}}^N$ with the Navier boundary conditions ${u|}_{\partial \Omega }=0$ and ${▵u|}_{\partial \Omega }=0$, where $f:{\mathbb{R}}^{+}\times {\mathbb{R}}^{-}\to {\mathbb{R}}^{+}$ is a continuous function. We present some some inequality conditions of f to obtain the existence results of positive radial symmetric solutions. These inequality conditions allow $f(\xi ,\eta )$ to have superlinear or sublinear growth on $\xi ,\eta$ as $\left|\right(\xi ,\eta \left)\right|\to 0$ and ∞. Our discussion is mainly based on the fixed-point index theory in cones. Full article

The many problems faced by the theory of general relativity (GR) have always motivated us to explore the modified theory of GR. Considering the importance of studying the black hole (BH) entropy and its correction in gravity physics, we study the correction of thermodynamic entropy for a kind of spherically symmetric black hole under the generalized Brans–Dicke (GBD) theory of modified gravity. We derive and calculate the entropy and heat capacity. It is found that when the value of event horizon radius $r_{+}$ is small, the effect of the entropy-correction term on the entropy is very obvious, while for larger values $r_{+}$, the contribution of the correction term on entropy can be almost ignored. In addition, we can observe that as the radius of the event horizon increases, the heat capacity of BH in GBD theory will change from a negative value to a positive value, indicating that there is a phase transition in black holes. Given that studying the structure of geodesic lines is important for exploring the physical characteristics of a strong gravitational field, we also investigate the stability of particles’ circular orbits in static spherically symmetric BHs within the framework of GBD theory. Concretely, we analyze the dependence of the innermost stable circular orbit on model parameters. In addition, the geodesic deviation equation is also applied to investigate the stable circular orbit of particles in GBD theory. The conditions for the stability of the BH solution and the limited range of radial coordinates required to achieve stable circular orbit motion are given. Finally, we show the locations of stable circular orbits, and obtain the angular velocity, specific energy, and angular momentum of the particles which move in circular orbits. Full article

In this paper, we discuss the existence of positive radially symmetric entire solutions of the p-k-Hessian equation ${\sigma }_k^{\frac{1}{k}}\left(\lambda \left(D_i\left({\left|Du\right|}^{p-2}{D}_{j}u\right)\right)\right)={\alpha }^{\frac{1}{k}}\left(\right|x\left|\right)f\left(u\right),$ and the general p-k-Hessian system ${\sigma }_k^{\frac{1}{k}}\left(\lambda \left(D_i\left({\left|Du\right|}^{p-2}{D}_{j}u\right)\right)\right)={\alpha }^{\frac{1}{k}}\left(\right|x\left|\right)f_1\left(v\right)f_2\left(u\right)$, ${\sigma }_k^{\frac{1}{k}}\left(\lambda \left(D_i\left({\left|Dv\right|}^{p-2}{D}_{j}v\right)\right)\right)={\beta }^{\frac{1}{k}}\left(\right|x\left|\right)g_1\left(u\right)g_2\left(v\right)$. Full article

Two generalized mathematical models with memory for the concentration of tumor cells have been analytically studied using the cylindrical coordinate and the integral transform methods. The generalization consists of the formulating of two mathematical models with Caputo-time fractional derivative, models that are suitable to highlight the influence of the history of tumor evolution on the present behavior of the concentration of cancer cells. The time-oscillating concentration of cancer cells has been considered on the boundary of the domain. Analytical solutions of the fractional differential equations of the mathematical models have been determined using the Laplace transform with respect to the time variable and the finite Hankel transform with respect to the radial coordinate. The positive roots of the transcendental equation with Bessel function $J_0(r)=0$, which are needed in our study, have been determined with the subroutine $r_n=root(J_0(r),r,(2n-1)\pi /4,(2n+3)\pi /4),n=1,2,\dots$ of the Mathcad 15 software. It is found that the memory effects are stronger at small values of the time, t. This aspect is highlighted in the graphical illustrations that analyze the behavior of the concentration of tumor cells. Additionally, the concentration of cancer cells is symmetric with respect to radial angle, and its values tend to be zero for large values of the time, t. Full article

The disclosing of new diffusion frontiers for wind energy, like deep-water offshore applications or installations in urban environments, is putting new focus on Darrieus vertical-axis wind turbines (VAWTs). To partially fill the efficiency gap of these turbines, aerodynamic developments are still needed. This work in particular focuses on the development of a mathematical model that allows predicting the possible performance improvements enabled in a VAWT by application of the Gurney flaps (GFs) as a function of the blade thickness, the rotor solidity and geometry of the Gurney flap itself. The performance of airfoil with GFs was evaluated by means of detailed simulations making use of computational fluid dynamics (CFD). The accuracy of the CFD model was assessed against the results of a dedicated experimental study. In the simulations, a dedicated method to simulate cycles of variation of the angle of attack similar to those taking place in a cycloidal motion (rather than purely sinusoidal ones) was also developed. Based on the results from CFD, a multidimensional interpolation based on the radial basis functions was conducted in order to find the GF design solution that provides the highest efficiency for a given turbine in terms of airfoil and solidity. The results showed that, for the selected study cases based on symmetric airfoils, the GF positioned facing outwards from the turbine, which provides the upwind part of the revolution, can lead to power increments ranging from approximately 30% for the lower-solidity turbine up to 90% for the higher-solidity turbine. It was also shown that the introduction of a GF should be coupled with a re-optimization of the airfoil thickness to maximize the performance. Full article

This paper suggests an innovative approach for the ideal placement and categorization of capacitors in radial distribution networks (RDNs) by applying symmetric fuzzy and improved bacterial foraging optimization algorithm (IBFOA) solutions. The reactive power reimbursement significantly enhances the function of the power system, and capacitor placement is an impressive technique used to reduce loss of the system. The capacitor allocation for distribution system problems involves determining the ideal location and size of the capacitor. In this work, load flow is performed at first to compute actual losses and voltages at different nodes without compensation. In the planned technique, the loss sensitivity factor (VSF) and voltage stability index (VSI) are utilized to determine the optimal location of capacitors in RDNs. Here, the IBFOA is used to determine the proper rating of the capacitor. The suggested scheme is applied on three different types of RDNs. Full article