Emergence of power-law in a market with mixed models

We investigate the problem of wealth distribution from the viewpoint of asset exchange. Robust nature of Pareto's law across economies, ideologies and nations suggests that this could be an outcome of trading strategies. However, the simple asset exchange models fail to reproduce this feature. A Yardsale (YS) model in which amount put on the bet is a fraction of minimum of the two players leads to condensation of wealth in hands of some agent while theft and fraud (TF) model in which the amount to be exchanged is a fraction of loser's wealth leads to an exponential distribution of wealth. We show that if we allow few agents to follow a different model than others, i.e., there are some agents following TF model while rest follow YS model, it leads to distribution with power-law tails. Similar effect is observed when one carries out transactions for a fraction of one's wealth using TF model and for the rest YS model is used. We also observe a power-law tail in wealth distribution if we allow the agents to follow either of the models with some probability.     

Scattering problem with nonlocal separable potential of rank-two: Application to statistical mechanics

In this paper, we present a formulation of statistical mechanics of a thermodynamic system consisting of free particles and independent correlated pairs interacting via nonlocal potential in terms of the scattering properties. Some quantum statistical properties such as energy, heat capacity, second virial coefficient, virial pressure and quantum correction of kinetic energy are described analytically. The difference between the resolvents of the interacting and free Hamiltonians, represented as , that is associated with particle correlations is used for the evaluation of the properties. The statistical properties are related to correlated states, when making a pole expansion of the analytically continued momentum matrix element of . The present work illustrates these relations for a three-dimensional nonlocal separable potential of rank-two.     

Evaluation the pozzolanic reactivity of sonochemically fabricated nano natural pozzolan

Natural pozzolans are appropriate supplementary cementitious materials in cement and concrete industry. A simple sonochemical method was developed to synthesize nanostructures of natural pozzolan. Chemical composition, crystallinity, morphology and reactivity of the natural pozzolan samples were compared before and after the sonochemical process, by using powder X-ray diffraction (XRD), Scanning Electron Microscopy (SEM), Thermal Gravimetry and Differential Thermal Analysis (TG/DTA). Compressive strength tests were performed to evaluate the properties of blended cements incorporating nano natural pozzolan. Under optimized conditions, the nano natural pozzolans showed a superior reactivity as compared with the bulk natural pozzolan. Also higher compressive strength was obtained for the cement specimen incorporating nano natural pozzolan.     

Alkali-metal-induced topological nodal line semimetalin layered XN2 (X= Cr,Mo, W)

Based on first principles calculations and the K·p effective model, we propose that alkali metal deposition on the surface of hexagonal XN₂ (X= Cr, Mo, W) nanosheets induces topologically nontrivial phases in these systems. When spin orbit coupling (SOC) is disregarded, the electron-like conduction band from N-p_z orbitals can be considered to cross the hole-like valence band from X-d²_z orbitals, thereby giving rise to a topological nodal line state in lithium-functionalized XN₂ sheets (Li₂MoN₂ and Li₂WN₂). Such band crossing is protected by the existence of mirror reflection and time reversal symmetry. More interestingly, the bands cross exactly at the Fermi level, and the linear dispersion regions of such band crossings extend to as high as 0.9 eV above the crossing. For Li₂CrN₂, the results reveal the emergence of a Dirac cone at the Fermi level. Our calculations show that lattice compression decreases the thickness of a Li₂CrN₂ nanosheet, leading to phase transition to a nodal line semimetal. The evolution of the band gap of Li₂XN₂ at the Γ point indicates that the nontrivial topological character of Li₂XN₂ nanolayers is stable over a large strain range. When SOC is included, the band crossing point is gapped out giving rise to quantum spin Hall states in Li₂CrN₂ nanosheets, while for Li₂MoN₂, the SOC-induced gap at the crossing points is negligible.     

Laser surface alloying of an electroless Ni–P coating with Al-356 substrate

Laser surface alloying of an electroless plating Ni–P coatings on an Al-356 aluminium alloy was carried out using a 1-kW pulsed Nd:YAG laser. The microstructure, chemical composition and phase identification of the alloyed layer were determined using scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDX) and X-ray diffractometry (XRD), respectively. It was shown that laser surface treatment produced a relatively smooth, crack-free and hard surface layer. The hardness of the surface significantly increased due to the formation of the uniformly distributed fine Ni–Al intermetallic phases. The corrosion behaviour of the surface alloyed specimens in 3.5% NaCl solution at 23 °C was also determined by electrochemical techniques. The laser-alloyed surface showed an improved corrosion and pitting potential compared to the substrate as well as the plated Ni–P coating.     

Current-voltage characteristics of Au/GaN/GaAs structure

Au/GaN/n-GaAs structure has been fabricated by the electrochemically anodic nitridation method for providing an evidence of achievement of stable electronic passivation of n-doped GaAs surface. The change of the electronic properties of the GaAs surface induced by the nitridation process has been studied by means of current-voltage (I-V) characterizations on Schottky barrier diodes (SBDs) shaped on gallium nitride/gallium arsenide structure. Au/GaN/n-GaAs Schottky diode that showed rectifying behavior with an ideality factor value of 2.06 and barrier height value of 0.73 eV obeys a metal-interfacial layer-semiconductor (MIS) configuration rather than an ideal Schottky diode due to the existence of GaN at the Au/GaAs interfacial layer. The formation of the GaN interfacial layer for the stable passivation of gallium arsenide surface is investigated through calculation of the interface state density N_ss with and without taking into account the series resistance R_s. While the interface state density calculated without taking into account R_s has increased exponentially with bias from 2.2×10¹² cm⁻² eV⁻¹ in (E_c−0.48) eV to 3.85×10¹² cm⁻² eV⁻¹ in (E_c−0.32) eV of n-GaAs, the N_ss obtained taking into account the series resistance has remained constant with a value of 2.2×10¹² cm⁻² eV⁻¹ in the same interval. This has been attributed to the passivation of the n-doped GaAs surface with the formation of the GaN interfacial layer.     

Influence of frequency, temperature and composition on electrical properties of polycrystalline Co0.5CdxFe2.5−xO4 ferrites

Polycrystalline ferrites with general formula Co_0.5Cd_xFe_2.5−xO₄ (0.0?x?0.5) were prepared by sol-gel method. The dielectric properties ε′, ε″, loss tangent tan δ and ac conductivity σ_ac have been studied as a function of frequency, temperature and composition. The experimental results indicate that ε′, ε″, tan δ and σ_ac decrease as the frequency increases; whereas they increase as the temperature increases. These parameters are found to increase by increasing the concentration of Cd content up to x=0.2, after which they start to decrease with further increase in concentration of Cd ion. The dielectric properties and ac conductivity in studied samples have been explained on the basis of space charge polarization according to Maxwell and Wagner's two-layer model and the hoping between adjacent Fe²⁺ and Fe³⁺ as well as the hole hopping between Co³⁺and Co²⁺ ions at B-sites. The values of activation energies E_f for conduction process are determined from Arrhenius plots, and the variations in these activation energies as a function of Cd content are discussed. The complex impedance analysis is used to separate the grain and grain boundary of the system Co_0.5Cd_xFe_2.5−xO₄. The variations of both grain boundary and grain resistances with temperature and composition are evaluated in the frequency range 42 Hz-5 MHz.     

Nonclassical Symmetries for Nonlinear Partial Differential Equations via Compatibility

The determining equations for the nonclassical symmetry reductions of nonlinear partial differential equations with arbitrary order can be obtained by requiring the compatibility between the original equations and the invariant surface conditions. The (2+1)-dimensional shallow water wave equation,
Boussinesq equation, and the dispersive wave equations in shallow water serve as examples illustrating how compatibility leads quickly and easily to the determining equations for their nonclassical symmetries.