Modeling Complex Systems by Structural Invariants Approach

When modeling complex systems, we usually encounter the following difficulties: partiality, large amount of data, and uncertainty of conclusions. It can be said that none of the known approaches solves these difficulties perfectly, especially in cases where we expect emergences in the complex system. The most common is the physical approach, sometimes reinforced by statistical procedures. The physical approach to modeling leads to a complicated description of phenomena associated with a relatively simple geometry. If we assume emergences in the complex system, the physical approach is not appropriate at all. In this article, we apply the approach of structural invariants, which has the opposite properties: a simple description of phenomena associated with a more complicated geometry (in our case pregeometry). It does not require as much data and the calculations are simple. The price paid for the apparent simplicity is a qualitative interpretation of the results, which carries a special type of uncertainty. Attention is mainly focused (in this article) on the invariant matroid and bases of matroid (M, BM) in combination with the Ramsey graph theory. In addition, this article introduces a calculus that describes the emergent phenomenon using two quantities-the power of the emergent phenomenon and the complexity of the structure that is associated with this phenomenon. The developed method is used in the paper for modeling and detecting emergent situations in cases of water floods, traffic jams, and phase transition in chemistry

Effect of p-d hybridization and structural distortion on the electronic properties of AgAlM2 (M = S, Se, Te) chalcopyrite semiconductors

We have carried out ab-initio calculation and study of structural and electronic properties of AgAlM2 (M = S, Se, Te) chalcopyrite semiconductors using Density Functional Theory (DFT) based self consistent Tight binding Linear Muffin Tin orbital (TB-LMTO) method. Calculated equlibrium values of lattice constants, anion displacement parameter (u), tetragonal distortion ({\eta} = c/2a) and bond lengths have good agreement with experimental values. Our study suggests these semiconductors to be direct band gap semiconductors with band gaps 1.98 eV, 1.59 eV and 1.36 eV respectively. These are in good agreement with experimental value within the limitation of local density approximation (LDA). Our explicit study of the effects of anion displacement and p-d hybridization show that band gap increases by 9.8%, 8.2% and 5.1% respectively for AgAlM2 (M = S, Se, Te) due to former effect and decreases by 51%, 47% and 42% respectively due to later effect.Comment: 15 pages, 17 figures, This article has been communicated to Solid State Communication

The influence of oxygen vacancies on the linear and nonlinear optical properties of Pb7O(OH)(3)(CO3)(3)(BO3)

We have investigated the influence of the oxygen vacancy on the linear and nonlinear optical properties and the microscopic first hyperpol of asymmetric Pb7O(OH)(3)(CO3)(3)(BO3). The O-vacancy reduces the energy gap and changes the energy band gap from indirect to direct. The calculated indirect energy band gap of Pb7O(OH)(3)(CO3)(3)(BO3) (I) of 3.56 eV is in good agreement with the experimental gap of 3.65 eV. The direct gap in O-deficient Pb7O(OH)(3)(CO3)(3)(BO3)) (II) is 1.61 eV. The oxygen vacancy results in a red-shifted energy band gap, making the material useful in the visible region. Calculations show that I exhibits a negative uniaxial anisotropy and birefringence, whereas II exhibits positive uniaxial anisotropy and birefringence. This shows that the O-vacancy has a significant influence on the uniaxial anisotropy and birefringence. We have calculated the second harmonic generation (SHG) for I and II at zero energy limit and at wavelength lambda = 1064 nm. The calculated SHG for I at lambda = 1064 nm is close to the experimental value of the well known compound KTiOPO4 (KTP), whereas for II it is about a quarter of the experimental value of the KTP. In addition, the microscopic first hyperpolarizability for I and II is calculated at the static limit and at wavelength 1064 nm

Facile synthesis of nanosized sodium magnesium hydride, NaMgH₃

The ternary magnesium hydride NaMgH3 has been synthesised via reactive milling techniques. The method employed neither a reactive H2 atmosphere nor high pressure sintering or other post-treatment processes. The formation of the ternary hydride was studied as a function of milling time and ball:powder ratio. High purity NaMgH3 powder (orthorhombic space group Pnma, a=5.437(2) Å, b=7.705(5) Å, c=5.477(2) Å; Z=4) was prepared in 5 h at high ball:powder ratios and characterised by powder X-ray diffraction (PXD), Raman spectroscopy and scanning electron microscopy/energy dispersive X-ray spectroscopy (SEM/EDX). The products formed sub-micron scale (typically 200–400 nm in size) crystallites that were approximately isotropic in shape. The dehydrogenation behaviour of the ternary hydride was investigated by temperature programmed desorption (TPD). The nanostructured hydride releases hydrogen in two steps with an onset temperature for the first step of 513 K

Optical second harmonic generation in Yttrium Aluminum Borate single crystals (theoretical simulation and experiment)

Experimental measurements of the second order susceptibilities for the second harmonic generation are reported for YAl3(BO3)4 (YAB) single crystals for the two principal tensor components xyz and yyy. First principles calculation of the linear and nonlinear optical susceptibilities for Yttrium Aluminum Borate YAl3(BO3)4 (YAB) crystal have been carried out within a framework of the full-potential linear augmented plane wave (FP-LAPW) method. Our calculations show a large anisotropy of the linear and nonlinear optical susceptibilities. The observed dependences of the second order susceptibilities for the static frequency limit and for the frequency may be a consequence of different contribution of electron-phonon interactions. The imaginary parts of the second order SHG susceptibility chi_{123}^{(2)}(omega), chi_{112}^{(2)}(omega), chi_{222}^{(2)}(omega), and chi_{213}^{(2)}(omega) are evaluated. We find that the 2(omega) inter-band and intra-band contributions to the real and imaginary parts of chi_{ijk}^{(2)}\l(omega) show opposite signs. The calculated second order susceptibilities are in reasonably good agreement with the experimental measurements.Comment: 16 pages, 11 figure

Electronic structure, linear, nonlinear optical susceptibilities and birefringence of CuInX2 (X = S, Se, Te) chalcopyrite-structure compounds

The electronic structure, linear and nonlinear optical properties have been calculated for CuInX2 (X=S, Se, Te) chalcopyrite-structure single crystals using the state-of-the-art full potential linear augmented plane wave (FP-LAPW) method. We present results for band structure, density of states, and imaginary part of the frequency-dependent linear and nonlinear optical susceptibilities. We find that these crystals are semiconductors with direct band gaps. We have calculated the birefringence of these crystals. The birefringence is negative for CuInS2 and CuInSe2 while it is positive for CuInTe2 in agreement with the experimental data. Calculations are reported for the frequency-dependent complex second-order non-linear optical susceptibilities . The intra-band and inter-band contributions to the second harmonic generation increase when we replace S by Se and decrease when we replace Se by Te. We find that smaller energy band gap compounds have larger values of in agreement with the experimental data and previous theoretical calculations.Comment: 17 pages, 6 figure

Electronic and magnetic properties of the Fe-doped CuInS2

The Fe-doped CuInS2 could have important applications for photovoltaic or spintronic applications. This material has been analyzed from first principles with the local density and the generalized gradient approximation, as well as with a Hubbard term. The effect on the electronic and magnetic structure has been carried out for both ferromagnetic and antiferromagnetic spin alignments. The results compare well with the experimental ones