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Problems can be handled properly in game theory as long as a countable number of players are considered, whereas, in real life, we have a large number of players. Hence, games at the thermodynamic limit are analyzed in general. There is a one-to-one correspondence between classical games and the modeled Hamiltonian at a particular equilibrium condition, usually the Nash equilibrium. Such a correspondence is arrived for symmetric games, namely the Prisoner’s Dilemma using the Ising Hamiltonian. In this work, we have shown that another class of games known as potential games can be analyzed with the Ising Hamiltonian. Analysis of this work brings out very close observation with real-world scenarios. In other words, the model of a potential game studied using Ising Hamiltonian predicts behavioral aspects of a large population precisely.

We report the meticulous study of freshly synthesized rare earth element substituted R-FeO3 (R-Gd) orthoferrite via co-precipitation route and subsequent sintering. The R-FeO3 powder sample is characterized by X-ray Diffractometer (XRD) for the investigation of crystal structure and is confirmed as orthorhombic with space group Pbnm structure. Nanoparticle dimension is captured by Scanning Electron microscope (SEM). Magnetic character of the sample is examined using vibrating sample magnetometer (VSM), it discloses a nearly linear magnetisation behaviour (paramagnetic behaviour). Dielectric studies and electric Polarization (PE loop) are investigated. A shift is observed in the dielectric constant er from 250 °C to 300 °C. The Rietveld refinement of the crystal structure from the powder XRD confirms GdFeO3 is distorted at octahedral site of FeO6. This distortion is ascertained as weak Jahn -Teller's distortion leads to the unsaturated electric polarization. The electronic properties, total and partial density of states of GdFeO3 are studied and calculated using Tight - Binding Linear Muffin-Tin Orbital (TBLMTO) method with the Atomic Sphere Approximation (ASA). The band gap of the GdFeO3 is found to be 0.32 eV.

First-principles calculation for anti-fluorite type cubic V2Se compound has been performed to study its structural, electronic and magnetic properties using WIEN2k. We used LDA and GGA as exchange-correlation energy functional for our calculation. For the calculation of ground state electronic properties, we implemented DFT + U method with the Hubbard parameter of 5.5 eV. Geometry optimization for the ferromagnetic, anti-ferromagnetic and non-magnetic states were done and results indicate that the material is more stable in ferromagnetic state. The equilibrium lattice constant and bulk modulus were found for both LDA and GGA exchange correlation energy functional which is in agreement with the experimental lattice constant. Electronic band structure and density of states have been studied. The electronic properties indicate that the material exhibit metallic behavior.

The synthesis of a nano-dimensional cluster of PrFeO3 orthoferrite with interesting tunable characteristics is the principal objective of this work. We document a very simple and improved co-precipitation method to synthesize nanoparticles of the desired dimension of rare earth substituted orthoferrite PrFeO3. The structural distortion is analyzed with Powder X-ray diffraction, which explores a distorted perovskite crystallized ferrite with space group Pbnm (62). The electrical behaviour of the prepared sample is investigated in a frequency range of 50 Hz to 5 MHz at different temperatures. A shift in the dielectric behaviour is noticed at about 250 °C. The morphological structure of the sample explored with High Resolution Transmission Electron Microscope (HRTEM), portraits a nano clustered structure. The magnetic properties of PrFeO3 are observed with Vibrating Sample Magnetometer (VSM) at 20 K and 300 K. A Very interesting change in magnetization is noticed at about 172 K–200 K. The effect of temperature on magnetic properties of PrFeO3 is reportedly due to the spin reorientation transition from Γ2 →Γ4 at TSR ≈ 172 K–200 K temperature range. The electronic band structure of nanoscale PrFeO3 with spin up and spin down states of antiferromagnetic nature is reported. PrFeO3 also exhibit multiferroic properties.

Lithium oxide (Li2O) has been suggested as a suitable breeder blanket material for fusion reactors. Li+ vacancies are created by neutron irradiation, forming bulk defect complex whose extra character is experimentally unclear. We present a theoretical study of Li2O using density functional theory (DFT) with a plane-wave basis set. The generalized gradient approximation (GGA) and local-density approximation (LDA) were used for exchange and correlation. Here we address the total energy for defect free, cation defect, cation vacancy and vacancy formation energy in Li2O crystal in anti-fluorite structure.Lithium oxide (Li2O) has been suggested as a suitable breeder blanket material for fusion reactors. Li+ vacancies are created by neutron irradiation, forming bulk defect complex whose extra character is experimentally unclear. We present a theoretical study of Li2O using density functional theory (DFT) with a plane-wave basis set. The generalized gradient approximation (GGA) and local-density approximation (LDA) were used for exchange and correlation. Here we address the total energy for defect free, cation defect, cation vacancy and vacancy formation energy in Li2O crystal in anti-fluorite structure.

The structural, elastic, electronic, optical and thermodynamic properties of the sodium polonide Na2Po compound have been studied through the full potential linearized augmented plane wave plus local orbitals (FP-LAPW + lo) and tight-binding linear muffin-tin orbital (TB-LMTO) methods. The exchange–correlation potential was treated within the local density approximation for the TB-LMTO calculations and within the generalized gradient approximation for the FP-LAPW + lo calculations. In addition, Tran and Blaha-modified Becke–Johnson (TB-mBJ) potential and Engel–Vosko generalized gradient approximation were used for the electronic and optical properties. Ground state properties such as the equilibrium lattice constant, bulk modulus and its pressure derivative were calculated and compared with available data. The single-crystal and polycrystalline elastic constants of the considered compound were calculated via the total energy versus strain in the framework of the FP-LAPW + lo approach. The calculated electronic structure reveals that Na2Po is a direct band gap semiconductor. The frequency-dependent dielectric function, refractive index, extinction coefficient, reflectivity coefficient and electron energy loss function spectra are calculated for a wide energy range. The variations of the lattice constant, bulk modulus, heat capacity, volume expansion coefficient and Debye temperature with temperature and pressure were calculated successfully using the FP-LAPW + lo method in combination with the quasi-harmonic Debye model.

Jute fibers are an environmental friendly natural fiber which can be used as good alternatives in the reinforcement of composite materials. The physical and mechanical properties of jute fiber are studied. The humidification cum heat treatment is carried out for the jute fiber. The tensile strength measurement was made for the untreated and humidification cum heat treated bundle jute fiber. The tensile strength of untreated and treated bundle jute fibers are 71.7 ± 9.5 MPa and 104.9 ± 8.8MPa respectively. A 45% increase in tensile strength is noticed. The structural organisation in the untreated and treated jute fiber is studied by X-ray fibre diffraction. The tensile strength measurement is carried out for the composite of Paper-Tamarind seed gum and Paper-Tamarind seed gum - Jute fiber and their measured tensile strength are 4.3 ± 0.5 MPa and 6.1 ± 1.2 MPa respectively. The enhancement in tensile strength for Paper-Tamarind seed gum - Jute fiber composite is observed. The environmental friendly biocomposite bags prepared are: Paper-Tamarind seed gum - Jute fiber and Paper-Tamarind seed gum, which can withstand load of 9.0 kg and 6.0 kg respectively. An increase of 50% in the load bearing capacity is achieved by reinforcing jute fibre.

Ab-initio calculations of nano-sized (∼1 nm) amorphous-TiO2 cluster and dye molecules (N3 and N719) have been carried out. Optimized structures of amorphous cluster and dye molecules have been obtained via molecular dynamics (MD) and density functional theory (DFT) calculations, respectively. The lowest excited state energies of the TiO2 cluster and the dye molecules have been obtained using time-dependent DFT. The calculations show that HOMO-LUMO gap and singlet-singlet excited state energies for amorphous cluster are very similar to that of a crystalline TiO2 cluster. Our calculations also show that the energy levels of the molecular dyes are well aligned with those of the amorphous cluster. © 2013 Elsevier B.V. All rights reserved., K.R.G acknowledges the following support (a) CSIC under JAE-DOC program ‘Junta para la Ampliación de Estudios’ cofinanciada por el FSE, (b) the Basque Departamento de Educación, Universidades e Investigación, the University of the Basque Country UPV/EHU (Grant No. IT-366-07) and (c) the Spanish Ministerio de Ciencia e Innovación (Grant No. FIS2010-19609-C02-02).

First-principles calculations based on the tight-binding linear muffin-tin orbital (TB-LMTO) method are performed to investigate the occurrence of spin polarization in the alkali-metal oxides (M2O) [M: Li, Na, K, Rb] in antifluorite (anti-CaF2-type) structure with non-magnetic sp (F, Cl, Br and I) dopants. The calculations reveal that non-magnetic substitutional doping at cation site can induce stable half-metallic ferromagnetic ground state in I2-VI compounds. Total energy calculations show that the antifluorite ferromagnetic state is energetically more stable than the antifluorite non-magnetic state at equilibrium volume. Ground state properties such as equilibrium lattice constant and bulk modulus were calculated. The calculated magnetic moment is found to be 2.00 μB per dopant atom.

First-principles calculations based on the tight-binding linear muffin-tin orbital (TB-LMTO) method were performed to investigate the occurrence of spin polarization in the alkali metal oxides (M2O) [M: Li, Na, K, Rb] in antifluorite (anti- CaF2-type) structure with non-magnetic (N, P, As, Sb and Bi) dopants. The calculations reveal that non-magnetic substitutional doping at anion site can induce stable half-metallic ferromagnetic ground state in I2–VI compounds. Total energy calculations show that the antifluorite ferromagnetic state is energetically more stable than the antifluorite non-magnetic state at equilibrium volume. Ground state properties such as equilibrium lattice constant and bulk modulus were calculated. The calculated magnetic moment is found to be 1.00 μB per dopant atom. The magnetic moment is mainly contributed by p orbitals of dopant atom.

First-principles calculations were performed to investigate the stability, electronic structure and magnetism in Group IV elements-doped alkali-metal oxides (M 2 O) [M: Li, Na, K, Rb] in antifluorite structure using the linear muffin-tin orbital method in its tight-binding representation (TB-LMTO). The calculations reveal that non-magnetic dopants can induce stable half-metallic ferromagnetic ground state in I 2 –VI compounds. Total energy calculations show that the ferromagnetic state is energetically more stable than the non-magnetic state at equilibrium volume. Ground state properties such as equilibrium lattice constant and bulk modulus were calculated. The magnetic moment is found to be 2.00 μ B per dopant atom.

Magnetic and electronic structure calculations were carried out for WC-, MnP-, NaCl- and zinc blende (ZB)-type Mo and W based group V compounds, TMX (TM = Mo and W; X = N, P, As, Sb and Bi), using the tight-binding linear muffin-tin orbital (TB-LMTO) method. For these compounds in these four structures, the total energy has been calculated as a function of volume in spin-polarization and non-spin-polarization calculations. From the total energy calculations, it is observed that these compounds favour the structures for which there is octahedral co-ordination for the anion rather than tetrahedral co-ordination. For the large volume expansion, these compounds prefer tetrahedral co-ordination compared to octahedral co-ordination. Moreover, these compounds in the ZB-type structure are found to exhibit half-metallic property with a magnetic moment of 3.00 μB per formula unit under expansion of volume. The equilibrium lattice constant, bulk modulus, heat of formation, magnetic moment, spin-flip-gap and minority spin bandgap are calculated and compared with available results. The band structure and density of states are presented.

First-principles calculations have been performed to investigate the electronic structure and ground-state properties of alkali-metal Selenides (M2Se) and Tellurides (M2Te) [ M: Li, Na, K ] using the Tight-Binding Linear Muffin-Tin Orbital (TB-LMTO) method. The exchange correlation energy is described within the local density approximation (LDA) using the von Barth and Hedin parameterization scheme. At ambient conditions, these compounds are found to crystallize in the face center cubic antifluorite (anti- CaF 2-type) structure. Ground-state properties such as total energy, equilibrium lattice parameter, and bulk modulus are calculated for these compounds. The calculated equilibrium lattice parameter is in agreement with experimental result. From the electronic structure calculations, we find that Li 2 Se , Li 2 Te , K 2 Se , and K 2 Te are indirect bandgap semiconductors, whereas Na 2 Se and Na 2 Te are direct bandgap semiconductors. The present results are compared with the earlier results of series of alkali-metal sulfides (M2S) and alkali-metal oxides ( M 2 O ), allowing us to make predictions about the total energy, bulk modulus, valence-band width, and bandgap behavior of the rest of the alkali-chalcogenide crystals.

Ab initio electronic structure calculations of hypothetical zinc-blende CaX (X =P , As, Sb) were performed using tight-binding linear muffin-tin orbital method. It was found that, these compounds are ferromagnets exhibiting half-metallicity. Total energy calculations show that the zinc blende ferromagnetic phase is more stable than the zinc-blende non-magnetic phase at equilibrium volume. Ground state properties such as equilibrium lattice constant, bulk modulus and cohesive energy were calculated. The calculated magnetic moment is found to be 1µB per formula unit for all these materials, which agrees well with the other theoretical results. On reducing the cell volume all these compounds are found to undergo a magnetic phase transition from zinc-blende ferromagnetic phase to zinc-blende non-magnetic phase.

Self-consistent scalar-relativistic band structure calculations have been performed to investigate the electronic structure and groundstate properties of alkali-metal oxides Li2O, Na2O, K2O and Rb2O in cubic antifluorite (anti-CaF2-type) structure using the linear muffin-tin orbital in its tight-binding representation (TB-LMTO) method. The calculated ground-state properties of these compounds such as equilibrium lattice parameter and bulk modulus are in agreement with the other theoretical calculations and experimental results. The results of the electronic structure calculations show that Li2O, K2O and Rb2O are indirect band gap semiconductors, whereas Na2O is found to be a direct band gap semiconductor. r 2007 Elsevier B.V. All rights reserved.

First-principles calculations have been performed to investigate the electronic structure and ground-state properties of alkali-metal sulfides Li2S, Na2S, K2S and Rb2S using the tight-binding linear muffin-tin orbital (TB-LMTO) method. At ambient conditions these compounds are found to crystallize in the cubic antifluorite (anti-CaF2-type) structure. The exchange correlation energy is described in the local density approximation (LDA) using the von-Barth and Hedin parameterization scheme. The calculated ground-state properties of these compounds such as equilibrium lattice parameter and bulk modulus are in agreement with the other theoretical calculations and experiment results. From the results of the electronic-structure calculations, we find that Li2S, K2S and Rb2S are indirect bandgap semiconductors, whereas Na2S is found to be a direct bandgap semiconductor. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Self-consistent scalar-relativistic band structure calculations have been performed to investigate the electronic structure and ground-state properties of Na2Po in cubic antifluorite (anti-CaF2-type) structure using the linear muffin-tin orbital in its tight-binding representation (TB-LMTO) method. Ground state properties such as equilibrium lattice constant and bulk modulus were calculated. The results of the electronic structure calculations show that Na2Po is direct bandgap semiconductor.

A combined experimental and theoretical study of the local chemistry of cerium oxide films and islands on Ru(0001) is presented. Based on intensity-voltage low-energy electron microscopy [$I(V)$-LEEM] and resonant x-ray photoemission spectroscopy, we establish a one-to-one correspondence between the local oxidation state of ${\mathrm{Ce}}^{3+}$ [cubic Ce${}_{2}$O${}_{3}$(111)] and ${\mathrm{Ce}}^{4+}$ [cubic CeO${}_{2}$(111)] and their respective spatially resolved $I(V)$ curves. Ab initio scattering theory explains the difference between the $I(V)$ curves in the low-energy range in terms of the ${k}_{\ensuremath{\parallel}}=0$ projected band structure arising from the different structure of the Ce 5d states in fully oxidized and reduced ceria. The theoretical analysis unambiguously attributes the LEEM contrast observed for chemically reduced cerium oxide to a variation in oxidation state on the nanometer scale, which is not present for the as-grown islands.

The structural, magnetic and optical properties of Rh2MnAl and Rh2MnBi Heusler alloys have been studied through the full potential linearized augmented plane wave (FP-LAPW) method. The exchange-correlation potential was treated within the generalized gradient approximation (GGA). The effect of the magnetic ordering, i.e. ferromagnetic (FM) and antiferromangnetic (AFM) along [001] and [111] crystal axis on the dielectric functions is revealed. Our calculations show that the Kerr rotation and elipticity is enhanced within 0-8 eV energy range by the substitution of Al by semimet al. (© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

First‐principles calculations were performed to investigate the occurrence of spin polarization in the Lithium metal oxide (Li2O) in its ground state antifluorite structure with non‐magnetic (M: F, Cl, Br and I) dopants. Total energy calculations show that the antifluorite ferromagnetic state is more stable than the antifluorite non‐magnetic state at equilibrium volume. The calculations reveal that non‐magnetic substitutional doping at cation site can induce stable half‐metallic ferromagnetic ground state in Li2O host. Ground state properties such as equilibrium lattice constant and bulk modulus were calculated. The calculated magnetic moment is found to be 2.00 μB per dopant atom.

The first-principles tight-binding linear muffin-tin orbital method within the local density approximation (LDA) has been used to calculate the ground-state properties, structural phase stability and pressure dependence of the band gap of NaZnX (X = P, As, Sb). All three compounds are found to crystallize in the tetragonal Cu2Sb-type (C38) structure. NaZnAs is also found to crystallize in the zinc-blende-type related structure, i.e. the MgAgAs (order CaF2)-type structure. By interchanging the position of the atoms in the zinc-blende structure, three phases (α, β and γ) are formed. The energy–volume relations for these compounds have been obtained in the Cu2Sb-type and cubic α, β and γ phases of the zinc-blende-type related structure. Under ambient conditions these compounds are more stable in the Cu2Sb-type structure and are in agreement with experimental observations. At high pressure, these compounds undergo a structural phase transition from the tetragonal Cu2Sb-type to cubic α (or β) phase, and the transition pressures were calculated. The equilibrium lattice parameter, bulk modulus and the cohesive energy for these compounds have also been calculated and are compared with the available results. In the Cu2Sb-type structure, NaZnP is found to be a direct-band-gap semiconductor, NaZnAs shows a very small direct band gap and NaZnSb is found to be a metal. In the α and β phases, NaZnP is found to be a direct-band-gap semiconductor, whereas NaZnAs and NaZnSb are found to be semi-metallic. In the γ-phase, all three compounds are found to exhibit metallic behaviour. However, this phase is energetically unfavourable.