Fractional governing equations of transient groundwater flow in unconfined aquifers with multi-fractional dimensions in fractional time

In this study, a dimensionally consistent governing equation of transient unconfined groundwater flow in fractional time and multi-fractional space is developed. First, a fractional continuity equation for transient unconfined groundwater flow is developed in fractional time and space. For the equation of groundwater motion within a multi-fractional multidimensional unconfined aquifer, a previously developed dimensionally consistent equation for water flux in unsaturated/saturated porous media is combined with the Dupuit approximation to obtain an equation for groundwater motion in multi-fractional space in unconfined aquifers. Combining the fractional continuity and groundwater motion equations, the fractional governing equation of transient unconfined aquifer flow is then obtained. Finally, two numerical applications to unconfined aquifer groundwater flow are presented to show the skills of the proposed fractional governing equation. As shown in one of the numerical applications, the newly developed governing equation can produce heavy-tailed recession behavior in unconfined aquifer discharges.

Crystallization process and nucleation kinetics of Mg2+//SO42−, NO3−-H2O system

In order to achieve efficient recovery of ions from the simultaneous desulfurization and denitrification wastewater, the effects of various factors (i.e. the saturation temperature, the cooling termination temperature, the stirring rate and the cooling rate) on crystallization yield, metastable zone width and crystal morphology were investigated to determine the optimal crystallization conditions of Mg2+//SO42−, NO3–-H2O system. According to the results of experiments, the nucleation kinetics were also speculated by Nývlt self-consistent equation and classical 3D nucleation theory. Also, the crystallization products were characterized by X-ray diffraction and scanning electron microscopy. Under the determined optimal conditions, the yield of the crystal can reach 78%, and the crystal products were verified as pure MgSO4· 7H2O, whose morphology is complete without defects.

Fractional governing equations of transient groundwater flow in unconfined aquifers with multi-fractional dimensions in fractional time

In this study, a dimensionally-consistent governing equation of transient unconfined groundwater flow in fractional time and multi-fractional space is developed. First, a fractional continuity equation for transient unconfined groundwater flow is developed in fractional time and space. For the equation of groundwater motion within a multi-fractional multi-dimensional unconfined aquifer, a previously-developed dimensionally consistent equation for water flux in unsaturated/saturated porous media is combined with the Dupuit approximation to obtain an equation for groundwater motion in multi-fractional space in unconfined aquifers. Combining the fractional continuity and groundwater motion equations, the fractional governing equation of transient unconfined aquifer flow is then obtained. Finally, a numerical application to an unconfined aquifer groundwater flow problem is presented to show the skills of the proposed fractional governing equation.

Impact of Weak Nanoparticle Induced Disorder on Nematic Ordering

Dilute mixtures of nanoparticles (NPs) and nematic liquid crystals (LCs) are considered. We focus on cases where NPs enforce a relatively weak disorder to the LC host. We use a Lebwohl-Lasher semi-microscopic-type modeling where we assume that NPs effectively act as a spatially-dependent external field on nematic spins. The orientational distribution of locally favoured “easy” orientations is described by a probabilistic distribution function P. By means of a mean field-type approach, we derive a self-consistent equation for the average degree of nematic uniaxial order parameter S as a function of the concentration p of NPs, NP-LC coupling strength and P. Using a simple step-like probability distribution shape, we obtain the S(p) dependence displaying a crossover behaviour between two different regimes which is in line with recent experimental observations. We also discuss a possible origin of commonly observed non-monotonous variations of the nematic-isotropic phase temperature coexistence width on varying p.

Численное моделирование термодинамических параметров высокопористой меди

The modified equation of state is proposed for the calculation of thermodynamically equilibrium model TEС2 to improve the reliability of the description of thermodynamic parameters of shock-wave loading of pure materials and heterogeneous mixtures of different porosity. The parameters of the thermally consistent equation of state are determined for copper. A reliable description of the shock-wave loading of copper is obtained for a small number of fitting parameters determined by the experimental data. The thermodynamic parameters for copper of different porosity are modeled, the compression and temperature values along the shock adiabate are determined; the heat capacity value along the normal isobar is calculated. The results of calculations are compared with the known experimental results of different authors.

The self-consistent model of the anomalously slow relaxation of the systems nonwetting liquid–nanoporous medium

This paper provides information on a self-consistent model of an anomalously slow relaxation of nonwetting liquid–nanoporous medium systems with a random size distribution of pores, which introduces changes in interaction between local liquid cluster configurations in the process of liquid outflow from the porous medium. A self-consistent equation was deduced, the solution of which determines a functional connection of porous medium filling degree or time [Formula: see text]. It is shown that the anomalously slow relaxation is presented as a process of decay of interacting local metastable configurations, initialized by thermal fluctuations. As time increments, relaxation acceleration takes place with subsequent avalanche fluid outflow from the porous medium, which is connected with interaction decrease between local configurations. The dependence of the fraction of volume of liquid remaining in a porous medium changes by the power law [Formula: see text]. It is shown that for a system of water–L23 at the initial stage in the time range of [Formula: see text], an index assumes a constant value [Formula: see text], while at the following stage the acceleration of relaxation and the increase of parameter [Formula: see text] are observed.

Fractional governing equations of transient groundwater flow in confined aquifers with multi-fractional dimensions in fractional time

Using fractional calculus, a dimensionally consistent governing equation of transient, saturated groundwater flow in fractional time in a multi-fractional confined aquifer is developed. First, a dimensionally consistent continuity equation for transient saturated groundwater flow in fractional time and in a multi-fractional, multidimensional confined aquifer is developed. For the equation of water flux within a multi-fractional multidimensional confined aquifer, a dimensionally consistent equation is also developed. The governing equation of transient saturated groundwater flow in a multi-fractional, multidimensional confined aquifer in fractional time is then obtained by combining the fractional continuity and water flux equations. To illustrate the capability of the proposed governing equation of groundwater flow in a confined aquifer, a numerical application of the fractional governing equation to a confined aquifer groundwater flow problem was also performed.