Current Perspective to Physical Science Research Vol. 7

Fe-doped ZnO Dilute Magnetic Semiconductor (DMS) thin film prepared by R F magnetron sputtering on a glass substrate and the Influence of Fe-doping at 3% on structural, morphological, and optical properties has been studied. The X-ray Diffraction (XRD) analysis shows that Fe doping has a significant effect on crystalline structure, grain size, and strain in the thin film. Crystalline structure is obtained for 3% Fe doping as observed from Atomic Force Microscopy (AFM) and X-ray Diffraction (XRD). UV-visible spectroscopy was used to study the optical behavior of the thin films.

Stagger-period sequences are a kind of discrete-time sequences, but the Fourier analysis of the uniform-period, discrete-time sequences does not apply to a stagger-period sequence; this means that the uniform-period analytical conclusions would be misleading. In this chapter we first define the essential concepts related to the stagger-period sequence and the stagger-lag autocorrelation matrix; we propose the Fourier transform pair of the stagger-period deterministic sequence and its spectrum, and discuss properties related to the transform pair, such as the orthogonality of a complex staggered exponential sequence, extension of the spectral period, Toeplitz of the circularly stagger-lag matrix, the staggered Parseval’s theorem, etc.; we verify inverses of each other of this transform pair and derive the convergence condition of this Fourier transform. Then, another Fourier transform pair of the stagger-lag autocorrelation matrix and its power spectrum density, properties related to this transform pair, inverses of each other of this transform pair, and the convergence condition of this Fourier transform of power spectrum are also studied. During illustrating examples, the similarities and differences of the equations and properties between the uniform-period and stagger-period analyses are described. Two applications of the Fourier analysis: search of the best stagger periods and spectrum estimation of the stagger-period sequence, are also discussed in details later. In the end, the advantages and methodologies of this study are summarized. This chapter “The Fourier Analysis for Stagger-Period Sequences, its Applications” will open the first page of the stagger-period signal processing.    

This chapter is the second part in a series of publications on the Compact Muon Solenoid (CMS) detector magnetic field map creation. The CMS detector at the Large Hadron Collider has a heterogeneous solenoid magnet where the created magnetic flux penetrates both nonmagnetic and ferromagnetic materials of the experimental setup. The chapter describes the performance of the magnetic field measuring and monitoring systems for the CMS detector. To cross-check the magnetic flux distribution obtained with the CMS magnet model, four systems for measuring the magnetic flux density in the detector volume were used. The magnetic induction inside the 6 m diameter superconducting solenoid was measured and is currently monitored by four nuclear magnetic resonance (NMR) probes installed using special tubes at a radius of 2.9148 m outside the barrel hadron calorimeter at ±0.006 m from the coil median XY-plane. Two more NMR probes were installed at the faces of the tracking system at Z-coordinates of -2.835 and +2.831 m and a radius of 0.651 m from the solenoid axis. The field inside the superconducting solenoid was precisely measured in 2006 in a cylindrical volume of 3.448 m in diameter and 7 m in length using ten three-dimensional (3D) B-sensors based on the Hall effect (Hall probes). These B-sensors were installed on each of the two propeller arms of an automated field-mapping machine. In addition to these measurement systems, a system for monitoring the magnetic field during the CMS detector operation has been developed. Inside the solenoid in the horizontal plane, four 3D B-sensors were installed at the faces of the tracking detector at distances X = ±0.959 m and Z-coordinates of -2.899 and +2.895 m. Twelve 3D B-sensors were installed on the surfaces of the flux-return yoke nose disks. Seventy 3D B-sensors were installed in the air gaps of the CMS magnet yoke in 11 XY-planes of the azimuthal sector at 270°. A specially developed flux loop technique was used for the most complex measurements of the magnetic flux density inside the steel blocks of the CMS magnet yoke. The flux loops are installed in 22 sections of the flux-return yoke blocks in grooves of 30 mm wide and 12–13mm deep and consist of 7–10 turns of 45-wire flat ribbon cable. The areas enclosed by these coils varied from 0.3 to 1.59 m² in the blocks of the barrel wheels and from 0.5 to 1.12 m² in the blocks of the yoke endcap disks. Measurement of the magnetic flux density in the steel blocks of the magnet yoke using flux loops and three-dimensional B-sensors confirmed the correctness of the magnetic flux distribution modelling in the muon momenta measuring system, which provided a high muon momentum resolution and a reliable muon identification. The development of the magnetic field measurement and monitoring systems and the results of the magnetic flux density measurements across the CMS magnet are presented and discussed in this chapter.

We are researching how compact stars are affected by the sudden shift in their properties caused by the quark deconfinement phase transition. The hadronic phase is explained using the relativistic mean-field theory, which includes a scalar-isovector \(\delta\)-meson effective field. To describe the quark phase, we use the MIT bag model, which considers the interactions between u, d and s quarks within the bag in the one-gluon exchange approximation. We analyze the drastic changes in the parameters of the near-critical configuration of the compact star and calculate the amount of energy released by the corequake in the two extreme cases of deconfinement phase transition scenarios. These scenarios correspond to the ordinary first-order phase transition (Maxwell scenario) and the phase transition calculated by using the bulk Gibbs equilibrium conditions and global charge neutrality (Gibbs scenario).

Maharishi Vyasa based on a Patanjali Yog sutra defined a universal, natural, indivisible, exceedingly small quanta of time known as kshana or moment. According to him time kshana is not a particle. It is a creation of the mind without mass. It is the time taken by an elementary particle to change its direction from east to north. For the elementary particle such as a spinning electron, the calculated value of a kshana in sec with different models of electron is of the same order magnitude as calculated for zitterbewegung which is equal to ten to the power minus twenty-one sec and is a constant. We found that the number of kshana in a second is inversely proportional to the radius of the spinning electron and independent of mass of the electron. Smaller the radius, small is the value of a kshana. Based on this definition of kshana, calculated value of the radius of an electron is equal to the reduced Compton wavelength.

This article discusses the dielectric properties of poly (9-vinylcarbazole) (PVK) and ferrocene-doped PVK thin films. The article discusses the preparation of the thin films and the measurement of their dielectric properties as a function of ferrocene concentration, frequency, and temperature. The poly (N-vinyl carbazole) (PVK) is a well-known hole transport polymer; therefore, this material is suitable for clarifying the effect of the injected holes on the breakdown process in polymer thin film. The thin films were grown by the isothermal solution casting technique. Dielectric properties of grown films were studied as function of ferrocene concentration, frequency, and temperature. The relative permittivity  (\( \varepsilon\)')  is increased with increasing ferrocene percentage (~1%) due to the free charge carriers. The relative permittivity decreases for higher ferrocene percentage (~2%). However, the relative permittivity of PVK and ferrocene-doped PVK samples remains almost constant for studied temperature range (313–413 K).  The frequency dependence of tan \(\sigma\) for all samples is studied. The frequency dependence of dielectric parameter exhibits frequency dispersion behavior, which suggests all types of polarization present in the lower frequency range. The loss tangent (tan \(\sigma\) ) values are larger at higher temperatures in the low frequency region. However, the tan \(\sigma\) values at different temperatures are almost similar in the high frequency region. It is observed that the relative permittivity is maximum, dielectric loss is minimum, and AC conductivity is minimum for 1% ferrocene doped PVK as compared to pure PVK and 2% ferrocene doped PVK samples. The temperature effect is more pronounced in the low-frequency region. The conductivity of PVK is increased as the ferrocene dopant concentration of increases up to 2%. The higher conductivity is related to the additional hopping sites for the charge carriers.

This chapter is the third part in a series of publications on the Compact Muon Solenoid (CMS) detector magnetic field map creation. The chapter focuses on pioneering work on the performance of the three-dimensional (3D) magnetic field map in the entire volume of the CMS detector at the Large Hadron Collider at CERN. In the CMS detector the magnetic field deflects the charged particles produced in the proton–proton collisions at the center-of-mass energy of 13.6 TeV. The curvatures of the charged particles allow the measurements of the particle momenta with help of the silicon tracking detectors located in the solenoidal magnetic flux density of 3.81 T. The magnetic system of the CMS detector is of a heterogeneous type, where the magnetic flux is created by a superconducting solenoid coil enclosed in a steel flux-return yoke. The 10,000-ton steel yoke of the magnet is used as a series of magnetized layers up to 620 mm thick which are penetrated only by muons, making it possible to identify them and measure their momenta in a muon spectrometer.  The programs for simulation and reconstruction of the momenta of the charged particles emerging from collision events require the knowledge of the value of the magnetic flux density components at the coordinates of space points along the trajectories of the particles. To describe the CMS magnetic flux distribution in the entire CMS detector volume, a system of the primitive 3D volumes containing the values of the magnetic flux density measured inside the superconducting coil inner volume and modelled outside the coil across a special mesh of reference nodes was developed. This system, called the CMS magnetic field map, follows the geometric features of the yoke and allows the interpolation of the magnetic flux density between the nodes to obtain the magnetic field values at any spatial point inside a cylinder of 18 m in diameter and 48 m in length, where all the CMS sub-detectors are located. The geometry of the volumes is described inside one 30° azimuthal sector of the CMS magnet. To obtain the values of the magnetic flux density components across the entire azimuth angle of the CMS detector, rotational symmetry is applied. Volumes are organized in a hierarchical structure optimized for fast global searching, and caching techniques allow simulation and track extrapolation algorithms to minimize the number of global volume searches.

In this paper we give approximations to the Mittag-Leffler functions in terms of elementary functions using different methods. This allowed us to establish a practical method we called integerization principle. This principle states that many fractional nonlinear oscillators may be solved by means of the solution to some integer-order Duffing oscillator equation. The accuracy of the obtained results is illustrated in concrete examples. Formulas for estimating the errors in the approximations are also provided.

In this article we give a new analytical solution to the Duffing-Helmholtz oscillator equation in terms of elementary functions. The solution obtained is compared with the numerical solution and with the exact analytical solution obtained using elliptic functions. We apply the obtained results to some physics problems. The proposed methodology may be of great interest to researchers in the field of nonlinear oscillators.