Dynamics and optimal control of a spatial diffusion HIV/AIDS model with ART and PrEP treatments

In this paper, to investigate the synthetic effect of PrEP (pre-exposure prophylaxis) and ART (antiretrovial therapy) on HIV transmission among MSM (men who have sex with men) in heterogenous environment, an realistic HIV epidemic model with spatial diffusion is established. Here, HIV infectious people are divided into three immunity based compartments, i.e., CD4+ T cell count less than 350, between 350 and 500, and more than 500, respectively. The basic reproduction number $R_0$ is established and proved as a threshold parameter: The global asymptotic stability of the disease-free steady state holds for $R_0<1$, and the disease will be present if $R_0>1$. Considering the substantial advantages of PrEP and ART in controlling HIV transmissions among MSM, the optimal control problem is presented for the case of positive constant diffusion coefficients, which minimize the total population of susceptible individual and HIV infected individual, the cost of PrEP and ART thearpy. As an illustration of our theoretical results, we conduct numerical simulations. We also conduct an optimal control case study where model parameters are estimated from the demographic and epidemiological data from China. This work suggests: (1) Spatial factors cannot be ignored during the HIV intervention; (2)Taking the PrEP intervention measure for HIV transmissions among MSM as early as possible will help to improve the control efficiency and reduces its cost; (3) Reducing the PrEP drug costs will promote the efficiency of PrEP treatment in preventing the spread of HIV among MSM.

Effect of Amount of Fibre and Damage Level on Service Life of SFR Recycled Concrete in Aggressive Environment

The paper presents a numerical calculation of the service life of concrete structures considering the effect of chlorides in the case of the material properties of structural lightweight waste aggregate concrete. Different amounts of fibres (0.0%, 1.0%, and 1.5%) and different values of compressive preloading (0%, 50%, and 100% of the ultimate strength capacity-USC) were considered. The subject of the research was the comparison of the influence of the constant diffusion coefficient and the time-dependent diffusion coefficient regarding the service life of the selected structure. Nine groups of material characteristics in combination with two numerical models are compared. A time-dependent diffusion coefficient and maturation coefficient, which were determined based on long-term monitoring (up to 461 days), were accepted for the numerical modelling. Thanks to time-dependent parameters, it is possible to observe the results of the theoretical service life of the structure and the influence of the mentioned factors. The analysed structure can be considered as the upper layer of an industrial floor in a chemical plant. It is important to determine the theoretical service life at which the structure shall be inspected or replaced. The results, in general, show that a higher amount of fibres reduces the service life as well as the preloading of the structure. An exception was a mixture with 1% of fibre loaded to 50% USC, which shows a lower diffusion coefficient than the specimens without preloading.

All-at-once multigrid approaches for one-dimensional space-fractional diffusion equations

We focus on a time-dependent one-dimensional space-fractional diffusion equation with constant diffusion coefficients. An all-at-once rephrasing of the discretized problem, obtained by considering the time as an additional dimension, yields a large block linear system and paves the way for parallelization. In particular, in case of uniform space–time meshes, the coefficient matrix shows a two-level Toeplitz structure, and such structure can be leveraged to build ad-hoc iterative solvers that aim at ensuring an overall computational cost independent of time. In this direction, we study the behavior of certain multigrid strategies with both semi- and full-coarsening that properly take into account the sources of anisotropy of the problem caused by the grid choice and the diffusion coefficients. The performances of the aforementioned multigrid methods reveal sensitive to the choice of the time discretization scheme. Many tests show that Crank–Nicolson prevents the multigrid to yield good convergence results, while second-order backward-difference scheme is shown to be unconditionally stable and that it allows good convergence under certain conditions on the grid and the diffusion coefficients. The effectiveness of our proposal is numerically confirmed in the case of variable coefficients too and a two-dimensional example is given.

Thermo-physcial Properties and Characterization of TiO2 based Nanofluid Blended with Moringa Oleifera Oil

Nanoparticle TiO2 was synthesized by the co-precipitate method and was dispersed in palm oil blended with Moringa oleifera seed oil (Enriched palm oil-EPO). Structural and compositional analysis of TiO2 nanoparticles was carried out using SEM (Scanning Electron Microscope), XRD (X-Ray Diffraction) and FTIR analysis (Fourier Transform Infrared Spectroscopy). Using the analytical method, particle dimension, crystallite size by Debye Scherrer’s equation and vibrational energy of the molecule was investigated. Palm oil was blended with synthesised Moring oil to enhance its oxidative stability. TiO2 nanoparticles were dispersed at different volume fraction in EPO to analyse the temperature dependent physical properties. Bio-degradable lubricant nature of TiO2 based nanofluid was investigated by the variation of viscosity and density with temperature (30 to 60˚C). The amphiphilic properties of fatty acids in blended oils can contribute better lubrication compared to mineral oils. Experimented viscosity and density values with temperature was fitted to a non-linear equations, and was pragmatic that quadratic equation exhibits a best fit R2 > 0.999. Theoretical value of the viscosity was predicted using Einstein, Batchelor, and Wang mathematical model and was compared with the experimental value. Brownian motion of the particle in the oil was studied through the diffusion constant, diffusion time, and Brownian velocity. The present study could be used to synthesis nanofluid with desired volume fraction, viscosities and densities, so as work as a suitable bio degradable lubricant in many industrial applications.

Comparative Study of Solvation Behaviour of Oxidising Agents Like Kclo3, Kbro3 and KIO3 in Aqueous Solvent Systems at Different Temperatures

The investigation of the solvationtrend of oxidizing agents like KClO3, KBrO3 and KIO3as electrolytes in aqueous salt solution rendersthe datasuited to interpret ion–ion, solute–solvent, ion-solvent and solvent–solvent interactions and synergy. Apparent molar volumes (∅_V) and viscosity B-coefficients for KClO3, KBrO3 and KIO3solutions in aqueous 0.5 % KCl ,system have been calculated from density (ρ) and viscosity (η) measurements at 298.15 to 313.15 K using a calibrated bicapillary pycnometer and the simple, yet accurate apparatus known as Ubbelohde viscometer respectively. Jones-Dole equation,Masson’s equation, Roots equation and Moulik’s equations are implemented to analyse various interactions inter and intra ionic attractions among the ion–ion, ion–solvent, and solute–solvent. Additionallythe apparent molar volumes of transfer Δ ∅(tr) and Rate constant diffusion controlled reaction (kd)are valuated.

Analysis of the Influence of the Cathodic Polarization Value on the Amount of Hydrogen Sorption of Al-Sm with the Alloy of Electrochemical Measurements

The effect of cathodic polarization on the rate of hydrogen sorption from an aqueous organic electrolyte on an Al-Sm alloy using the potentiostatic and potentiodynamic methods were studied. The obtained data allowed us to calculate the diffusion-kinetic characteristics of this process, such as the interstitial constant, diffusion constant CН √ D, constant current iconst, diffusion coefficient D and adsorption of hydrogen atoms G. The number of nuclei decreases, but their mass and radius increase in the potential range from –2.0 V to –2.4 V. The adsorption of hydrogen on the surface increases; which confirms that predominance of the discharge of hydrogen atoms occurs at more negative potentials according to the recombination mechanism.

Exact simulation for multivariate Itô diffusions

We provide the first generic exact simulation algorithm for multivariate diffusions. Current exact sampling algorithms for diffusions require the existence of a transformation which can be used to reduce the sampling problem to the case of a constant diffusion matrix and a drift which is the gradient of some function. Such a transformation, called the Lamperti transformation, can be applied in general only in one dimension. So, completely different ideas are required for the exact sampling of generic multivariate diffusions. The development of these ideas is the main contribution of this paper. Our strategy combines techniques borrowed from the theory of rough paths, on the one hand, and multilevel Monte Carlo on the other.