Homogenization of spectral problem for locally periodic elliptic operators with sign-changing density function

The paper deals with homogenization of a spectral problem for a second order self-adjoint elliptic operator stated in a thin cylinder with homogeneous Neumann boundary condition on the lateral boundary and Dirichlet condition on the bases of the cylinder. We assume that the operator coefficients and the spectral density function are locally periodic in the axial direction of the cylinder, and that the spectral density function changes sign. We show that the behavior of the spectrum depends essentially on whether the average of the density function is zero or not. In both cases we construct the effective 1-dimensional spectral problem and prove the convergence of spectra.     

Homogenization of boundary value problems for monotone operators in perforated domains with rapidly oscillating boundary conditions of fourier type

We deal with homogenization problem for nonlinear elliptic and parabolic equations in a periodically perforated domain, a nonlinear Fourier boundary conditions being imposed on the perforation border. Under the assumptions that the studied differential equation satisfies monotonicity and 2-growth conditions and that the coefficient of the boundary operator is centered at each level set of unknown function, we show that the problem under consideration admits homogenization and derive the effective model. Bibliography: 24 titles.     

Singular Double Porosity Model

We consider the linear parabolic equation describing the transport of a contaminant in a porous media crossed by a net of infinitely thin fractures. The permeability is very high in the fractures but very low in the porous blocks. We derive the homogenized model corresponding to a net of infinitely thin fractures, by means of the singular measures technique. We assume that these singular measures are supported by hyperplanes of codimension one. We prove in a second step that this homogenized model could be obtained indistinctly either by letting the fracture thickness, in the standard double porosity model, tend to zero, or by homogenizing a model with infinitely thin fractures.     

内埋炸药下超高韧性水泥基复合材料的抗爆性能

为研究超高韧性水泥基复合材料(ultra-high toughness cementitious composites, UHTCC)在内埋炸药爆炸下的抗爆性能和损伤破坏规律,对不同炸药埋深下的UHTCC和高强混凝土(high-strength concrete, HSC)进行了内埋炸药抗爆实验。得到了两种材料靶体的破坏状态,并利用接触爆炸的实验结果计算出了两种材料的抗爆性能参数。结果表明,在相同条件下,UHTCC抗爆性能优于高强混凝土。为了进一步探究UHTCC的抗压强度、抗拉强度以及拉伸韧性对靶体在内埋炸药下抗爆性能的影响,首先,采用改进的K&C模型对炸药埋深为40 mm的超高韧性水泥基复合材料靶体进行数值模拟,模拟结果与实验结果基本吻合,并根据数值模拟的结果得到了爆炸冲击波沿靶体径向衰减速度大于轴向衰减速度这一规律,验证了数值模型的有效性;然后,通过调整改进K&C模型中与抗压强度、抗拉强度以及拉伸韧性相关的参数,数值预测了不同抗压强度、抗拉强度以及拉伸韧性下UHTCC靶体的破坏状态,发现增强UHTCC的韧性可以有效防止靶体发生整体性破坏,增大UHTCC的抗拉强度可以减小靶体迎爆面的开坑直径,增大UHTCC的抗压强度对减小开坑直径效果不明显。     

Investigation of structural and electronic properties of β- HgS: Molecular dynamics simulations

The pressure induced phase transition of β-HgS is studied using an ab initio molecular dynamics simulation. The structural phase transformation from the zinc-blende structure to the NaCl-type structure (space group $Fm\overline{3}m$) and from this structure to CsCl-type structure ($Pm\overline{3}m$) with the application of hydrostatic pressure is predicted. Additionally, the electronic properties of HgS and various physical properties such as the lattice constants, the bulk modulus and the pressure derivative of the bulk modulus are revealed. Furthermore, these phase transitions are obtained using the total energy and enthalpy calculations. According to these calculations these transformations are occurring at about 20?GPa and 28?GPa for $F\overline{4}3m$ →$Fm\overline{3}m$ and $Fm\overline{3}m$ →$Pm\overline{3}m$, respectively.     

An existence result for nonisothermal immiscible incompressible 2‐phase flow in heterogeneous porous media

In the present article, we study the temperature effects on two‐phase immiscible incompressible flow through a porous medium. The mathematical model is given by a coupled system of 2‐phase flow equations and an energy balance equation. The model consists of the usual equations derived from the mass conservation of both fluids along with the Darcy‐Muskat and the capillary pressure laws. The problem is written in terms of the phase formulation; ie, the saturation of one phase, the pressure of the second phase, and the temperature are primary unknowns. The major difficulties related to this model are in the nonlinear degenerate structure of the equations, as well as in the coupling in the system. Under some realistic assumptions on the data, we show the existence of weak solutions with the help of an appropriate regularization and a time discretization. We use suitable test functions to obtain a priori estimates. We prove a new compactness result to pass to the limit in nonlinear terms.     

Post-Harvest Operations to Generate High-Quality Medicinal Cannabis Products: A Systemic Review

The traditional Cannabis plant as a medicinal crop has been explored for many thousands of years. The Cannabis industry is rapidly growing; therefore, optimising drying methods and producing high-quality medical products have been a hot topic in recent years. We systemically analysed the current literature and drew a critical summary of the drying methods implemented thus far to preserve the quality of bioactive compounds from medicinal Cannabis. Different drying techniques have been one of the focal points during the post-harvesting operations, as drying preserves these Cannabis products with increased shelf life. We followed or even highlighted the most popular methods used. Drying methods have advanced from traditional hot air and oven drying methods to microwave-assisted hot air drying or freeze-drying. In this review, traditional and modern drying technologies are reviewed. Each technology will have different pros and cons of its own. Moreover, this review outlines the quality of the Cannabis plant component harvested plays a major role in drying efficiency and preserving the chemical constituents. The emergence of medical Cannabis, and cannabinoid research requires optimal post-harvesting processes for different Cannabis strains. We proposed the most suitable method for drying medicinal Cannabis to produce consistent, reliable and potent medicinal Cannabis. In addition, drying temperature, rate of drying, mode and storage conditions after drying influenced the Cannabis component retention and quality.     

On boundary value problem with singular inhomogeneity concentrated on the boundary

We study the asymptotic behavior of solutions to a boundary value problem for the Poisson equation with a singular right-hand side, singular potential and with alternating type of the boundary condition. Assuming that the boundary microstructure is periodic, we construct the limit problem and prove the homogenization theorem by means of the unfolding method. The proof requires that the dimension be larger than two.