**Abstract: **We investigate the behavior of the kinetic and the exchange energy densities near the nuclear cusp of atomic systems. Considering hydrogenic orbitals, we derive analytical expressions near the nucleus, for single shells, as well as in the semiclassical limit of large non-relativistic neutral atoms. We show that a model based on the helium iso-electronic series is very accurate, as also confirmed by numerical calculations on real atoms up to two thousands electrons. Based on this model, we propose non-local density-dependent ingredients that are suitable for the description of the kinetic and exchange energy densities in the region close to the nucleus. These non-local ingredients are invariant under the uniform scaling of the density, and they can be used in the construction of non-local exchange-correlation and kinetic functionals.

**Abstract: **In this paper, the Diffusion Limited Cluster Aggregation (DLCA) method is employed to reconstruct the three-dimensional network of silica aerogel. Then, simulation of nitrogen adsorption at 77 K in silica aerogel is conducted by the Grand Canonical Monte Carlo (GCMC) method. To reduce the computational cost and guarantee accuracy, a continuous-discrete hybrid potential model, as well as an adsorbed layer thickness estimation method, is employed. Four different structures are generated to investigate impacts of specific surface area and porosity on adsorptive capacity. Good agreement with experimental results is found over a wide range of relative pressures, which proves the validity of the model. Specific surface area and porosity mainly affect nitrogen uptake under low pressure and high pressure, respectively.

**Abstract: **We model the behavior of an ideal liquid junction, across a porous and possibly charged medium between two ion-containing solutions, by means of the Nernst–Planck equation for the stationary state, in conditions of local electroneutrality. An analytical solution of the equation was found long ago by Planck for the uncharged junction with only ions of valences +1 and −1. Other analytical results, which have later been obtained also for more general situations, seem impractical for performing calculations. In this paper, we obtain analytical solutions for systems with up to three valence classes, which can be applied to perform numerical calculations in a straightforward way. Our method provides a much larger amount of information on the behavior of the system than the well-known Henderson’s approximation. At the same time, it is more simple and reliable, and much less demanding in terms of computational effort, than the nowadays commonly employed numerical methods, typically based on discrete integration and trial-and-error numerical inversions. We present some examples of practical applications of our results. We study in particular the uphill transport (*i.e.*, the transport from the lower-concentration to the higher-concentration region) of a divalent cation in a liquid junction containing also other univalent anions and cations.

**Abstract: **Finite-temperature density functional theory (DFT) has become of topical interest, partly due to the increasing ability to create novel states of warm-correlated matter (WCM).Warm-dense matter (WDM), ultra-fast matter (UFM), and high-energy density matter (HEDM) may all be regarded as subclasses of WCM. Strong electron-electron, ion-ion and electron-ion correlation effects and partial degeneracies are found in these systems where the electron temperature *T*_{e} is comparable to the electron Fermi energy *E*_{F}. Thus, many electrons are in continuum states which are partially occupied. The ion subsystem may be solid, liquid or plasma, with many states of ionization with ionic charge *Z*_{j}. Quasi-equilibria with the ion temperature *T*_{i} ≠ *T*_{e} are common. The ion subsystem in WCM can no longer be treated as a passive “external potential”, as is customary in *T* = 0 DFT dominated by solid-state theory or quantum chemistry. Many basic questions arise in trying to implement DFT for WCM. Hohenberg-Kohn-Mermin theory can be adapted for treating these systems if suitable finite-*T* exchange-correlation (XC) functionals can be constructed. They are functionals of both the one-body electron density ne and the one-body ion densities *ρj*. Here, *j* counts many species of nuclei or charge states. A method of approximately but accurately mapping the quantum electrons to a classical Coulomb gas enables one to treat electron-ion systems entirely classically at any temperature and arbitrary spin polarization, using exchange-correlation effects calculated *in situ*, directly from the pair-distribution functions. This eliminates the need for any XC-functionals. This classical map has been used to calculate the equation of state of WDM systems, and construct a finite-*T* XC functional that is found to be in close agreement with recent quantum path-integral simulation data. In this review, current developments and concerns in finite-*T* DFT, especially in the context of non-relativistic warm-dense matter and ultra-fast matter will be presented.

**Abstract: **The hydro-mechanical coupling transport process of sand production is numerically investigated with special attention paid to the bonding effect between sand grains. By coupling the lattice Boltzmann method (LBM) and the discrete element method (DEM), we are able to capture particles movements and fluid flows simultaneously. In order to account for the bonding effects on sand production, a contact bond model is introduced into the LBM-DEM framework. Our simulations first examine the experimental observation of “initial sand production is evoked by localized failure” and then show that the bonding or cement plays an important role in sand production. Lower bonding strength will lead to more sand production than higher bonding strength. It is also found that the influence of flow rate on sand production depends on the bonding strength in cemented granular media, and for low bonding strength sample, the higher the flow rate is, the more severe the erosion found in localized failure zone becomes.

**Abstract: **Adsorption complexes of germanium on the reconstructed Si(001)(4 × 2) surface have been simulated by the Si_{96}Ge_{2}Н_{84} cluster. For Ge atoms located on the surface layer, DFT calculations (B3LYP/6-31G**) of their 3d semicore-level energies have shown a clear-cut correlation between the 3d_{5/2} chemical shifts and mutual arrangement of Ge atoms. Such a shift is positive when only one Ge atom penetrates into the crystalline substrate, while being negative for both penetrating Ge atoms. We interpret these results in terms of the charge distribution in clusters under consideration.