In this paper, we consider an infinite system of functional equations for the Potts model with competing interactions of radius r = 2 and countable spin values 0, 1, ..., and non-zero-filled, on a Cayley tree of order two. We describe conditions on hx guaranteeing compatibility of distributions µ(n)(σn).

We consider the problem of reconstructing the time-dependent history of the viscoelasticity medium from the viscoelasticity system of equations for an homogeneous anisotropic medium. As additional information, the Fourier image of the displacement vector for values ν = ν0 6= 0 of transformation parameter is given. It is shown that if the given functions satisfy some conditions of agreement and smoothness, the solution for the posed problem is uniquely defined in the class of a continuous functions and it continuously depends on given functions.

The basic ideas of the AdS/CFT correspondence in physics of strongly correlated systems are briefly discussed. The application of the AdS/CFT correspondence for the Green’s functions derivation are shown.

In this paper we, study the response of a Fermi liquid under the influence of an external magnetic field applied to the external electric field. The dispersion law of the Fermi liquid is obtained via AdS/CFT correspondence. The regions of the negative differential conductivity on the current-voltage characteristic were observed. The possibility of terahertz pulse generation in such systems was shown for a wide range of magnetic field strengths.

On the example of the three-atomic clusters Al₃, Si₃, and C₃, it is shown that an orbital-free version of the density functional theory may be used for finding equilibrium configurations of multi-atomic systems with both metallic and covalent bonding. The equilibrium interatomic distances, interbonding angles and binding energies are found to be in good agreement with known data.

The available experimental material relating to the patterns of formation and properties of functional nanostructured transition metal oxide (Mo, Co, Mn, Ni, Fe, V) composite materials is reviewed. Advanced coatings are considered those whose formation method are simple and do not require high energy costs, expensive equipment and permit the creation of materials with desired physical and chemical properties in a specified manner. In this review, the priority of oxide composite nanostructured materials technology is given to a transient electrolysis method based on the analysis of a data set that demonstrates its advantages. The results are presented for a number of studies aimed at identifying and analyzing the nature and regularities of processes that take place when obtaining oxide composite nanostructured materials using transient electrolysis methods.

The effect of hydrothermal synthetic conditions on the obtaining of lanthanide orthophosphates LnPO₄ (Ln = La, Pr, Nd, Sm) with different structure, size and shape of particles was revealed. The optimum conditions for preparation of anhydrous nanoscale lanthanide orthophosphates with monoclinic structure were determined. The prepared nanowhiskers had lengths ranging from 0.4 µm (for LaPO₄) to 5 µm (for SmPO₄), and the diameter – from 30 nm (for LaPO4) to 200 nm (for SmPO₄). The size of particles synthesized under similar conditions increased with decreased of lanthanide ion radius.

The nanosized ZnFe₂O₄ material was synthesized using the coprecipitation method from Zn₂+ and Fe₃+ cations in a boiling aqueous medium. The results of TG/DSC, XRD, SEM, TEM and VSM analysis show that the ZnFe₂O₄ material prepared after annealing at 600 ◦C had tetragonal structure, a size of 20 – 50 nm, Hc < 70 Oe, Mr < 0.5 emu/g and Ms ∼ 2.5 emu/g.

Nanocomposite polyurethane (PU) foams filled with different loadings (0.1 – 0.7 wt.%) of nanosized silica (average grain size of ∼ 7 and 12 nm) and organonanoclay were prepared by the prepolymer method, and their mechanical properties were investigated. A statistical analysis of the size distribution for foam cells was successfully applied in order to characterize their morphology. The developed approach was shown to provide a detailed analysis of the morphology development in PU foams, including the primary cell formation and their subsequent break-up and coalescence. The degree of phase separation in nanocomposite polyurethane foams, which is dependent on the nanofiller, was calculated from the IR spectra. The presence of silica nanoparticles and organoclays gives rise to significant differences in the mechanical (stress-strain) properties of the nanocomposite polyurethane foams relative to the pure polymer.

Broadband dielectric spectroscopy was employed to study polymer nanocomposites based on PA12 filled with different loading (0.1 – 10 wt.%) of nanosized (average grain size of about 1 – 5 nm) chromium (III) oxide. The experimental dielectric data were analyzed within the formalisms of complex permittivity and electric modulus. Three relaxation processes and Maxwell–Wagner–Sillars (MWS) interfacial polarizations were observed. It was found that all the relaxations were sensitive to filler contents. The presence of nanosized amphoteric chromium (III) oxide was shown to lead to the softening of the polyamide matrix that manifested in decrease of the activation energy of the αand β-relaxation processes and glass transition temperatures. The softening of polymer matrix is the reason for the decrease in the mechanical properties of the polymer nanocomposites as compared to that of neat PA12.

The anisotropy factor is a parameter from which one can determine preferential forward and backward light scattering. In the present study, we have calculated anisotropy factor hcos θi as a function of magnetic field for magnetic spheres in a magnetic medium. We have noticed resonances in hcos θi which indicate preferential enhanced scattering in forward and backward directions. Anisotropy factor is analyzed for various size parameters. The study clearly indicates that scattering can be modulated by means of size parameter of magnetic spheres as well as magnetic field. We have further confirmed the result by studying forward and backward intensity as a function of magnetic field. Resonances noticed in the intensity are in good agreement with the previous argument. This observation can be useful for the magnetic field dependent directional scattering and novel magneto-photonic devices.

Copper oxide (CuO) nanostructures with different concentrations of sodium hydroxide for electrochemical applications such as supercapacitors have been synthesized using a simple and low-cost precipitation method. X-ray diffraction pattern confirmed the formation of CuO nanostructures without any impurities and further confirmed its highly crystalline, single phase, monoclinic nature. UV-diffuse reflectance spectral (UV-DRS) studies provided the absorption edge of the material and the estimated band gap value for the nanostructures were calculated using Kubelka-Munk (KM) absorbance plot that are determined to be around 4.74 – 4.84 eV. Field emission scanning electron microscopy (FESEM) investigations revealed the morphology of the copper oxide nanocrystals and showed the increment of diameter of the CuO nanostructures. The electrochemical behavior of the CuO nanostructures were investigated using electrochemical impedance spectroscopy (EIS) and cyclic voltammetry (CV) techniques which showed the stability, reversibility, symmetric and capacitive nature of the nanostructures.

Zero valent iron impregnated silica nanoparticles (Fe⁰/n-SiO₂) were synthesized using sol-gel process followed by supercritical drying, wet impregnation and hydrogen reduction. The synthesized nanoparticles were characterized by nitrogen Brunauer–Emmett–Teller (N₂-BET), Scanning Electron Microscopy, Transmission Electron Microscopy, Scanning Electron Microscopy with Energy-Dispersive X-ray spectroscopy, Vibrating Sample Magnetometer and X-ray diffraction techniques. Prepared samples were found to be magnetic with ultra-low density (0.048 g/mL) and high surface area (422 m²/g). Prepared samples were evaluated for adsorptive removal of Pb⁺² (5, 10, 25 and 50 ppm) from contaminated water. Results indicated that the adsorption of Pb⁺² was faster at lower concentrations (5 and 10 ppm) as > 80 % of Pb⁺² was removed within 480 minutes. At higher concentrations, the adsorption was slower, and the removal efficiency of 51.24 and 21.78 % were observed for 25 and 50 ppm Pb⁺² respectively, whereas for bare SiO₂ nanoparticles, it was 39.64 and 14.04 %.

In this study, Multi-Walled Carbon Nanotubes (MWCNTs) were chemically treated in order to investigate the structural and chemical changes in them and to use them for sensor applications. Raman spectroscopic analysis reveals that the chemically treated MWCNTs are useful for chemical and gas sensor applications.

Pure and (Co, Al) co-doped (Co=1, 3, 5 mol %, and Al = 5 mol % as constant) SnO₂ nanoparticles were synthesized in aqueous solution by the chemical co-precipitation method using polyethylene glycol (PEG) as a stabilizer. The effects of structural and photoluminescence of (Co, Al) co-doped SnO₂ nanoparticles are investigated. The XRD pattern reveals that the samples are in a single phase rutile type tetragonal crystalline structure of SnO₂. The peak positions with Co concentration are slightly shifted to lower 2θ values and size of particles from XRD calculations are in between 20–30 nm. The Raman studies of the samples reveal that the Raman peaks are shifted towards lower wave numbers, when compared to those of pure SnO₂ at 150 cm⁻¹, 303 cm⁻¹, 476 cm⁻¹, 630 cm⁻¹, and 765 cm⁻¹ respectively. Photoluminescence studies show that pure SnO₂ has an emission peak at 444 nm and (Co, Al) co-doped samples show emission peaks at 417 nm, 433 nm and 485 nm with exciting wave length 320 nm. The PL intensity increases and broadening of peaks for co-doped samples with increase of Co concentration indicates the decrease of size of the crystallinity. The UV absorption spectrum exhibits absorption at 310 nm, and is in agreement with the emission spectra.

In the current status, we have successfully synthesized lead sulfide (PbS) thin films using a modified successive ionic layer absorption and reaction (SILAR) method. The synthesized film was characterized using UV-Vis-NIR spectrophotometer, X-ray diffraction (XRD) and field emission scanning electron microscopy (FESEM) techniques for optical, structural and morphological properties. Opto-structural study demonstrates that synthesized thin film has a pure crystal structure. The surface morphology study indicates a nanospherical surface morphology without pinhole on the substrate surfaces. Overall study clearly demonstrates that the synthesized PbS thin film by SILAR method have great potential for sensitization of oxide microstructure.

This work reports the possibility of mixing metal oxides along with graphene and polymer to form Metal Oxide-Graphene-Polymer films. The metal oxides used in this work were lead Oxide (PbO) and tungsten oxide (WO3). Polyvinylidene fluoride (PVDF) is the polymer, which is used as matrix in preparation of these metal oxide and graphene mixed nanocomposite films. Metal Oxide-Graphene-PVDF films were developed using a chemical technique called solvent casting. The prepared films were characterized using techniques like FE-SEM, XRD and FT-IR to understand its morphological, crystalline and functional properties. I-V characteristics were analyzed using four-probe techniques. The developed Metal Oxide-Graphene-PVDF films have potential applications in a wide range of fields and particularly for electronic applications. The ability of these films to be used as electronic components in devices was explored.

ZnO nanostructured thin films are synthesized by a simple spray pyrolysis technique using zinc acetyl acetonate precursor on Si substrates. The morphology control is achieved by varying the substrate temperature during deposition between 350 and 450 ◦C. The microstructural changes accompanying the changes in growth conditions are observed under the transmission electron microscopy. The vibrational properties of these films are studied using Raman spectroscopy and the differences in crystallinity are explained. The electrical properties are determined from I–V measurements.

Copper zinc tin sulfide/selenide Cu₂ZnSn(S, Se)₄ (CZTSSe) is an alternative promising material for solar cell applications. It exhibits a high optical absorbance and tunable band gap. We have investigated the effect of excess selenium on the formation of CZTSSe phase which was prepared by the thermal melt method. The CZTSSe alloys were characterized by X-ray diffraction (XRD), Raman spectroscopy and UV-VIS spectroscopy. The crystallographic structure and phase were confirmed by X-ray diffraction and Raman spectroscopic techniques. In Raman spectroscopy, we found that the phase shifts from 327 cm⁻¹ to 338 cm⁻¹ when the selenium content excess is 5 %. In optical studies, a band gap for the CZTSSe alloys of about 1.43 eV to 1.44 eV was observed.

Ru metal doped TiO₂ nanoparticles were synthesized using a sol gel method with and without ionic liquid. Ru metal is well dispersed while utilizing ionic liquid as reaction medium for catalyst synthesis with respect to Ru–TiO₂ catalyst. A TEM image for Ru–TiO₂–IL catalyst reveals, stable, well dispersed and agglomeration free Ru metal doped TiO₂ nanoparticles. CO₂ Hydrogenation reaction on task specific ionic liquid medium, offered the formic acid in high TON/TOF value with added advantage of 5 times catalyst recycling.

Densities, viscosities, surface tension and Ultrasonic speeds of nano composite 5Methyl Salicylaldehyde (5MS) with Aniline (A) were measured over the entire composition range at temperature 303 K. The adiabatic compressibility (β), free length (Lf ), free volume (Vf ) and viscous relaxation time (T ) have been calculated from the experimental data. The experimental results have been correlated using Fuzzy Evidence Theory and the results are interpreted on the basis of possible hydrogen bonding between unlike molecules and changes in molecular association equilibria as well as structural effects for these systems. A good agreement among experimental data and the values estimated by theoretical procedure was obtained.

In the present work, we have used simple, cost effective arrested precipitation technique (APT) to deposit CdZn(SSe)₂ thin films. Preparative conditions were optimized during the initial stage of experimentation to obtain good quality CdZn(SSe)₂ thin films. The as-deposited film was studied for its structural, morphological, optical, and compositional analysis by XRD, SEM, UV-Vis-NIR spectrophotometer and EDSanalysis techniques respectively. XRD analysis revealed that the film was polycrystalline in nature and exhibit hexagonal crystal structure. The SEM micrograph shows the formation of spherical surface morphology. EDS results confirm the presence of Cd, Zn, S and Se elements in the synthesized thin film. The band gap value of thin film was calculated from the absorption spectra which is found to be 1.8 eV. From J–V measurements, photo-conversion efficiency is found to be 0.07%.

The physical phenomena of rewetting and quenching are of prime importance in nuclear reactor safety in the event of Loss of Coolant Accident (LOCA). In such a case, the fuel pins become dry hot. Under this condition, cold water is injected from emergency core cooling system (ECCS). The quenching behavior of such heated rod bundle (re-flood heat transfer behavior) is quite complex. It is well known that Nanofluids have better heat removal capability and a high heat transfer coefficient owing to their enhanced thermal properties. Recent investigations have shown that the addition of the Al₂O₃ nanoparticles result in better cooling capabilities as compared to the traditionally used quenching media. In this context, the authors have carried out experiments on quenching behavior of hot zircalloy tube with water and nanofluids as stated above. Quenching of the tube was observed to occur within few seconds in both the cases in the presence of decay heat. It was also observed that the nanofluids showed slightly reduced quenching time as compared to water.

Nanoparticles of Yb:Y₂O₃ have been synthesized by co-precipitation synthesis routes. The (NH₄)₂SO₄ surfactant was added to Y(OH)₃ precipitate during synthesis to control the size, morphology, agglomeration and phase of nanoparticles. The dried precipitates were calcined at 900 ◦C to obtain the desired cubic phase Yb:Y₂O₃ nano particles. In the present study we reported the effects of surfactant concentration on size, morphology, agglomeration and phase of Yb:Y₂O₃ nanoparticles. However the addition of surfactant is not enough to get nonagglomerated nanoparticles. The extracted precipitate should be washed in proper solvent to avoid formation of hard agglomerate during drying. Hence the effects of washing solvent (i.e. water and methanol) on agglomeration and transparency were also reported. The transparency of the sintered pellets, prepared by varying the surfactant concentration and washing solvent, was evaluated. A transparency of ∼ 80 % at 1500 nm was achieved in 1 mm thick Yb:Y₂O₃ ceramic pellet by optimization of the surfactant and washing solvent.

Recently, the accelerometer has taken on a vital role in health monitoring system. The monitoring of patients disease has been aided by the use of different diagnostics. These devices exist at the macro level and also in micro level for condition monitoring. Capacitive Micro-accelerometer is a wearable sensor for monitoring of scoliosis disease in patients by analyzing their sitting posture, asymmetrical balance of patients. A new approach for accelerometer , using an L-shaped cantilever parallel plate MEMS accelerometer design is proposed. This micro accelerometer is designed using INTELLISUITE 8.6. Static analysis is done using Thermo Electro Mechanical module to examine the performance. Proposed design is compared with the existing design. In the future , this can also be applied in NANO level applications with respect to its design and fabrication.

A novel reduced graphene oxide (rGO) decorated organic binol based receptor ((S)-1) has been designed and synthesized. The resulting nanocomposite (rGO–(S)-1) material was then utilized as a selective fluorescent chemosensor for Ag⁺ ion in aqueous media at physiological pH. In addition, the nanocomposite showed no cross-reaction with any of the potential interfering metal ions. The reduced graphene oxideorganic nanocomposite was characterized using various spectroscopic, microscopic and analytical studies.

Thin films of vanadium oxide (V₂O_5−x) were prepared by rf magnetron sputtering process and are heat treated to study the annealing effect. As-deposited thin films are amorphous in nature and crystallinity is improved by annealing the sample. Thin layers with high density and small grain size varying from 36 nm to 70 nm were seen in the FESEM images of as-deposited thin films. In the case of annealed thin films, it has been transformed to thin elongated rod like structure with 202.5 nm length and an average diameter of approximately 48 nm. Optical properties were studied by using UV-Vis-NIR spectrophotometer and the reduction in transmission in annealed thin films is due to the crystalline nature of thin films. Studies were done on the samples by taking photoluminescence and Laser Raman spectra.

Nanocrystalline (CdZn)Se thin films have been successfully synthesized via a simple and cost effective arrested precipitation technique. The deposition and synthetic strategy of (CdZn)Se thin films exert appreciable influence on the photovoltaic properties of solar cells. In this paper, systematic characterizations of optostructural, morphological, compositional and electrochemical properties have been carried out. The optical band gap was evaluated from UV-Vis-NIR spectra at wavelengths ranging from 400 – 1100 nm. X-ray diffraction (XRD) pattern reveals that the deposited film was nanocrystalline in nature and exhibited a cubic crystal structure. The dependency of microstructural parameters such as crystallite size has been studied. Scanning electron microscopy (SEM) images demonstrate that surface morphology was uniform, dense, smooth and well adhered to substrate surface. The as-deposited nanorystalline (CdZn)Se thin film exhibits 0.61 % conversion efficiency at room temperature.

Nanoferrofluids of Co_xFe_3−xO₄ were prepared by the chemical co-precipitation method by varying the value of x (0.2, 0.6 and 1.0 M). The structural and surface morphological investigations were done by X-ray diffraction (XRD) and SEM techniques respectively. The particle size calculated from the data of XRD, (3 1 1) plane revealed that the particle size increases with higher cobalt content and are in the range of 5 – 16 nm. The ultrasonic velocity of the aqueous carrier fluid and Cobalt ferrofluids was measured by varying the temperature from 30 – 70 ◦C. The ultrasonic velocities of magnetic nanoferrofluids decrease with concentration in the absence of magnetic field. The higher value for the nanoferrofluid’s velocity compared to that of the carrier liquid in the absence of a magnetic field shows the influence of dispersed particles on the velocity of ultrasonic propagation.

Nanocrystalline Ba_0.97Ca_0.03SO₄:Eu powder has been prepared by combustion method. XRD shows orthorhombic structure, the lattice parameter values are a = 8.836 Ǻ, b = 5.440 Ǻ, c = 6.859 Ǻ. The nanocrystalline powder Ba_0.97Ca_0.03SO₄:Eu having a grain size of 47 nm, and also FTIR, PL, and three dimensional structure studies of the material and the results are presented in detail.

Topological insulators are a new class of electronic materials with promising device applications. In this work, multi-layer Bi₂Se₃ field effect transistors (FETs) are prepared by standard lithography followed by mechanical exfoliation method. Electrical characterization of the FET has been studied at room temperature. We observed both insulating and metallic-type transport behavior when device was gate-biased. Electron-phonon scattering plays a vital role in observing this behavior. We assume that this sort of behavior could be raised from the inherent metallic surface and semiconducting interior bulk properties of Bi₂Se₃.

The Electrical rectification properties of an asymmetric molecule’s amine group and nitro group has been studied by placing the compound between two gold electrodes and using Extended Hu¨ ckel, Parametric and non-equilibrium Green’s function (NEGF) formalisms. The conductance of the device falls exponentially with an increased number of CH₂ moieties in the molecule. Current rectification was observed based on HOMO, LUMO gaps and potential drop across the molecules. The investigation of the spatial dispersion of frontier orbitals, the highest occupied molecular orbitals, lowest unoccupied molecular (HOMO-LUMO) of the molecule command the transmission of electrons in the molecule. The results demonstrate that, depending on the group of molecules and number of CH₂ moieties present, current shipping from left side of device to right side of device based on orbital energy gaps. Our findings demonstrate that a true molecular diode can be created, and thus miniaturize the electronic circuit’s size to the Nano scale.