ALBERT

Description: In this paper, we study limit cycle bifurcation near a cuspidal loop for a general near-Hamiltonian system by using expansions of the first order Melnikov functions. We give a method to compute more coefficients of the expansions to find more limit cycles near the cuspidal loop. As an application example, we considered a polynomial near-Hamiltonian system and found 12 limit cycles near the cuspidal loop and the center.

Description: The aim of the present paper is to analyze the viability of using Lorentz Force (LF) acting on a charged spacecraft to neutralize the effects of Solar Radiation Pressure (SRP) on the longitude of the ascending node and the argument of perigee of the spacecraft’s orbit. In this setting, the Gauss planetary equations for LF and SRP are presented and averaged over the true anomaly. The averaged variations for the longitude of the ascending node (h) and the argument of perigee (g) are invariant under the symmetry (i,g)⟶(−i,−g) due to Lorentz Force. The sum of change rates due to both perturbing forces of LF and SRP is assigned by zero to estimate the charge amount to balance the variation for the argument of perigee and longitude of ascending. Numerical investigations have been developed to show the evolution of the charge quantity for different orbital parameters at both Low Earth and Geosynchronous Orbits.

Description: This research article aims to investigate the consequences of binary chemical reaction, thermal radiation, and Soret–Dufour effects on a steady incompressible Darcy–Forchheimer flow of nanofluids. Stretching surface is assumed to drive the fluid along positive horizontal direction. Brownian motion, and the Thermophoresis are accounted in particular. The governing highly nonlinear system of problems which are advanced version of Navier–Stokes equations are transformed into ordinary differential equations (ODEs) using appropriately adjusted transformations invoking symmetric property of the independent variables. The numerical approach using RK45 in connection with shooting technique is adopted to solve the final equations. Graphical approach is used to interpret the results and the values of important physical quantities are given in tabular data form. Velocity field, temperature distribution and concentration distribution are graphically analyzed for variation in respective fluid parameters. Furthermore, density graphs and stream lines are sketched for the present model. The outputs indicate a rise of temperature field in connection with thermal radiation parameter. A clear decline is noticed in velocity field for elevated values of Forchheimer number and porosity factor. The Dufour effect anticipates a rising factor for temperature distribution and the same is noticed for concentration distribution in lieu of Soret effect. Thermal radiation and binary chemical reaction has strong impact on heat transport mechanism. The results for physical quantities such as skin friction, heat and mass flux rates are given in tabular data form in last section of this study.

Description: In industrial pollutants, phenol is a kind of degradation-resistant hazardous compound. It is generated during industrial processes in factories and treatment at sewage plants. In this study, we analyse the photocatalytic activity of TiO2 and rGO as a composite for the degradation of phenol. Hybridised titanium dioxide/reduced graphene oxide (TiO2/rGO) nanocomposites were synthesised by a simple hydrothermal method using flake graphite and tetrabutyl titanate as raw materials. Scanning electron microscopy (SEM), transmission electron microscopy (TEM), X-ray diffraction (XRD), Brunauer–Emmet–Teller (BET) specific area analysis, Fourier transform infrared spectroscopy (FTIR), Raman, X-ray photoelectron spectroscopy (XPS), photoelectrochemical analysis, and UV–vis diffuse reflectance spectra (DRS) were employed to characterise the physicochemical properties of the as-prepared nanocomposites. The results showed the TiO2/rGO nanocomposites’ significant anatase phase and a small fraction of the rutile phase the same as that of the as-prepared TiO2 nanoparticles. The spherical TiO2 nanoparticles (diameter 20–50 nm) were agglomerated slightly and the agglomerates were anchored on the rGO sheets and dispersed symmetrically. The specific surface area of TiO2/rGO-4% nanocomposites was 156.4 m2/g, revealing a high specific surface area. Oxygen-containing functional groups that existed in TiO2/rGO-4% nanocomposites were almost removed during hydrothermal processing. The photocurrent response of TiO2/rGO-4% was strongest among the TiO2/rGO nanocomposites, and the bandgap of TiO2/rGO-4% was 2.91 eV, showing a redshift of absorption into the visible region, which was in favour of the high photocatalytic activity of TiO2/rGO nanocomposites under visible light (λ 〉 420 nm). Moreover, the samples were employed to photodegrade phenol solution under visible light irradiation. TiO2/rGO-4% nanocomposite degraded the phenol solution up to 97.9%, and its degradation rate constant was 0.0190 h−1, which had higher degradation activity than that of other TiO2/rGO nanocomposites. This is a promising candidate catalyst material for organic wastewater treatment.

Description: Long-span prestressed double-layer composite torsional reticulated shells have beautiful shapes, which make them a solution widely applied in public buildings requiring long-span structures, such as airports and stadiums. However, once the progressive collapse occurs, this will cause serious issues. There are few studies on the damage assessment of long-span spatial structures under accidental loads. This paper proposes a new dynamic damage evaluation index that takes into account the displacement and the cumulative plastic energy dissipation to evaluate the damage of the long-span prestressed double-layer composite torsional reticulated shell. Sleeve structures were applied to the long-span space structures to study their control effect on structural damage. The equivalent load transient unloading method was used to analyze the dynamic time history of the structure. Results show that the structure suffered severe damage and progressive collapse failure after removing four nodes at different positions near the supports. In the position where the plastic hinges first appear and the position with the maximum displacement, the sleeve structures have a poor damage control effect on the structure. Arranging the two sleeve structures in the position of maximum stress, the damage of the structure can be controlled, thus reducing the severe damage and progressive collapse failure to basic intact damage.

Description: The authors wish to make the following corrections to their paper: [...]

Description: In this article we present an ordinary differential equation based technique to study the quadratic stability of non-linear dynamical systems. The non-linear dynamical systems are modeled with norm bounded linear differential inclusions. The proposed methodology reformulate non-linear differential inclusion to an equivalent non-linear system. Lyapunov function demonstrate the existence of a symmetric positive definite matrix to analyze the stability of non-linear dynamical systems. The proposed method allows us to construct a system of ordinary differential equations to localize the spectrum of perturbed system which guarantees the stability of non-linear dynamical system.

Description: Symmetry plays the central role in the structure of quantum states of bipartite (or many-body) fermionic systems. Typically, symmetry leads to the phenomenon of quantum coherence and correlations (entanglement) inherent to quantum systems only. In the present work, we study the role of symmetry (i.e., quantum correlations) in invasive quantum measurements. We consider the influence of a direct or indirect measurement process on a composite quantum system. We derive explicit analytical expressions for the case of two quantum spins positioned on both sides of the quantum cantilever. The spins are coupled indirectly to each others via their interaction with a magnetic tip deposited on the cantilever. Two types of quantum witnesses can be considered, which quantify the invasiveness of a measurement on the systems’ quantum states: (i) A local quantum witness stands for the consequence on the quantum spin states of a measurement done on the cantilever, meaning we first perform a measurement on the cantilever, and subsequently a measurement on a spin. (ii) The non-local quantum witness signifies the response of one spin if a measurement is done on the other spin. In both cases the disturbance must involve the cantilever. However, in the first case, the spin-cantilever interaction is linear in the coupling constant Ω , where as in the second case, the spin-spin interaction is quadratic in Ω . For both cases, we find and discuss analytical results for the witness.

Description: The famous Toms effect (1948) consists of a substantial increase of the critical Reynolds number when a small amount of soluble polymer is introduced into water. The most noticeable influence of polymer additives is manifested in the boundary layer near solid surfaces. The task includes the ratio of two characteristic length scales, one of which is the Prandtl scale, and the other is defined as the square root of the normalized coefficient of relaxation viscosity (Frolovskaya and Pukhnachev, 2018) and does not depend on the characteristics of the motion. In the limit case, when the ratio of these two scales tends to zero, the equations of the boundary layer are exactly integrated. One of the goals of the present paper is group analysis of the boundary layer equations in two mathematical models of the flow of aqueous polymer solutions: the second grade fluid (Rivlin and Ericksen, 1955) and the Pavlovskii model (1971). The equations of the plane non-stationary boundary layer in the Pavlovskii model are studied in more details. The equations contain an arbitrary function depending on the longitudinal coordinate and time. This function sets the pressure gradient of the external flow. The problem of group classification with respect to this function is analyzed. All functions for which there is an extension of the kernels of admitted Lie groups are found. Among the invariant solutions of the new model of the boundary layer, a special place is taken by the solution of the stationary problem of flow around a rectilinear plate.

Description: This paper reports a numerical study on heat transfer improvement in a double backward-facing expanding channel using different convectional fluids. A finite volume method with the k-ε standard model is used to investigate the effects of step, Reynolds number and type of liquid on heat transfer enhancement. Three types of conventional fluids (water, ammonia liquid and ethylene glycol) with Reynolds numbers varying from 98.5 to 512 and three cases for different step heights at a constant heat flux (q = 2000 W/m2) are examined. The top wall of the passage and the bottom wall of the upstream section are adiabatic, while the walls of both the first and second steps downstream are heated. The results show that the local Nusselt number rises with the augmentation of the Reynolds number, and the critical effects are seen in the entrance area of the first and second steps. The maximum average Nusselt number, which represents the thermal performance, can be seen clearly in case 1 for EG in comparison to water and ammonia. Due to the expanding of the passage, separation flow is generated, which causes a rapid increment in the local skin friction coefficient, especially at the first and second steps of the downstream section for water, ammonia liquid and EG. The maximum skin friction coefficient is detected in case 1 for water with Re = 512. Trends of velocities for positions (X/H1 = 2.01, X/H2 = 2.51) at the first and second steps for all the studied cases with different types of convectional fluids are indicated in this paper. The presented findings also include the contour of velocity, which shows the recirculation zones at the first and second steps to demonstrate the improvement in the thermal performance.