Physics, Volume 3, Issue 2 (June 2021) – 18 articles

The Lagrange formalism is developed for Bateman oscillators, which includes both damped and amplified systems, and a novel method to derive the Caldirola-Kanai and null Lagrangians is presented. For the null Lagrangians, the corresponding gauge functions are obtained. It is shown that the gauge functions can be used to convert the undriven Bateman oscillators into the driven ones. Applications of the obtained results to quantizatation of the Bateman oscillators are briefly discussed. Full article

In this paper, a current that is called spin current and corresponds to the variation of the matter action in BF theory with respect to the spin connection A which takes values in Lie algebra $\mathfrak{so}(3,\mathbb{C})$, in self-dual formalism is introduced. For keeping the 2-form $B^i$ constraint (covariant derivation) $D{B}^i=0$ satisfied, it is suggested adding a new term to the BF Lagrangian using a new field ${\psi }^i$, which can be used for calculating the spin current. The equations of motion are derived and the solutions are dicussed. It is shown that the solutions of the equations do not require a specific metric on the 4-manifold M, and one just needs to know the symmetry of the system and the information about the spin current. Finally, the solutions for spherically and cylindrically symmetric systems are found. Full article

With the vaccination against Covid-19 now available, how vaccination campaigns influence the mathematical modeling of epidemics is quantitatively explored. In this paper, the standard susceptible-infectious-recovered/removed (SIR) epidemic model is extended to a fourth compartment, V, of vaccinated persons. This extension involves the time t-dependent effective vaccination rate, $v\left(t\right)$, that regulates the relationship between susceptible and vaccinated persons. The rate $v\left(t\right)$ competes with the usual infection, $a\left(t\right)$, and recovery, $\mu \left(t\right)$, rates in determining the time evolution of epidemics. The occurrence of a pandemic outburst with rising rates of new infections requires $k+b<1-2\eta$, where $k=\mu \left(0\right)/a\left(0\right)$ and $b=v\left(0\right)/a\left(0\right)$ denote the initial values for the ratios of the three rates, respectively, and $\eta \ll 1$ is the initial fraction of infected persons. Exact analytical inverse solutions $t\left(Q\right)$ for all relevant quantities $Q=[S,I,R,V]$ of the resulting SIRV model in terms of Lambert functions are derived for the semi-time case with time-independent ratios k and b between the recovery and vaccination rates to the infection rate, respectively. These inverse solutions can be approximated with high accuracy, yielding the explicit time-dependences $Q\left(t\right)$ by inverting the Lambert functions. The values of the three parameters k, b and $\eta$ completely determine the reduced time evolution of the SIRV-quantities $Q\left(\tau \right)$. The influence of vaccinations on the total cumulative number and the maximum rate of new infections in different countries is calculated by comparing with monitored real time Covid-19 data. The reduction in the final cumulative fraction of infected persons and in the maximum daily rate of new infections is quantitatively determined by using the actual pandemic parameters in different countries. Moreover, a new criterion is developed that decides on the occurrence of future Covid-19 waves in these countries. Apart from in Israel, this can happen in all countries considered. Full article

The possible ways of dynamics of a homogeneous and isotropic space described by the Friedmann–Lemaitre–Robertson–Walker metric in the framework of cubic in the Ricci scalar $f\left(R\right)$ gravity in the absence of matter are considered. This paper points towards an effective method for limiting the parameters of extended gravity models. A method for $f\left(R\right)$-gravity models, based on the metric dynamics of various model parameters in the simplest example is proposed. The influence of the parameters and initial conditions on further dynamics are discussed. The parameters can be limited by (i) slow growth of space, (ii) instability and (iii) divergence with the inflationary scenario. Full article

In this paper, the merger rate of black holes in a cluster of primordial black holes (PBHs) is investigated. The clusters have characteristics close to those of typical globular star clusters. A cluster that has a wide mass spectrum ranging from ${10}^{-2}$ to $10M_{\odot }$ (Solar mass) and contains a massive central black hole of the mass $M_{•}={10}^3{M}_{\odot }$ is considered. It is shown that in the process of the evolution of cluster, the merger rate changed significantly, and by now, the PBH clusters have passed the stage of active merging of the black holes inside them. Full article

In this paper, a simple example to illustrate what is basically known from the Gauss’ times interplay between geometry and mechanics in thin shells is presented. Specifically, the eigen-mode spectrum in spontaneously curved (i.e., up-down asymmetric) extensible polymerized or elastic membranes is studied. It is found that in the spontaneously curved crystalline membrane, the flexural mode is coupled to the acoustic longitudinal mode, even in the harmonic approximation. If the coupling (proportional to the membrane spontaneous curvature) is strong enough, the coupled modes dispersions acquire the imaginary part, i.e., effective damping. The damping is not related to the entropy production (dissipation); it comes from the redistribution of the energy between the modes. The curvature-induced mode coupling makes the flexural mode more rigid, and the acoustic mode becomes softer. As it concerns the transverse acoustical mode, it remains uncoupled in the harmonic approximation, keeping its standard dispersion law. We anticipate that the basic ideas inspiring this study can be applied to a large variety of interesting systems, ranging from still fashionable graphene films, both in the freely suspended and on a substrate states, to the not yet fully understood lipid membranes in the so-called gel and rippled phases. Full article

In this paper, Lorentz boosts and Wigner rotations are considered from a (complexified) quaternionic point of view. It is demonstrated that, for a suitably defined self-adjoint complex quaternionic 4-velocity, pure Lorentz boosts can be phrased in terms of the quaternion square root of the relative 4-velocity connecting the two inertial frames. Straightforward computations then lead to quite explicit and relatively simple algebraic formulae for the composition of 4-velocities and the Wigner angle. The Wigner rotation is subsequently related to the generic non-associativity of the composition of three 4-velocities, and a necessary and sufficient condition is developed for the associativity to hold. Finally, the authors relate the composition of 4-velocities to a specific implementation of the Baker–Campbell–Hausdorff theorem. As compared to ordinary $4\times 4$ Lorentz transformations, the use of self-adjoint complexified quaternions leads, from a computational view, to storage savings and more rapid computations, and from a pedagogical view to to relatively simple and explicit formulae. Full article

Recent progress in Cs₂HfCl₆ (CHC) crystal production achieved within the last five years is presented. Various aspects have been analyzed, including the chemical purity of raw materials, purification methods, optimization of the growth and thermal conditions, crystal characterization, defect structure, and internal radioactive background. Large volume, crack-free, and high quality CHC crystals with an ultimate scintillating performance were produced as a result of such extensive research and development (R & D) program. For example, the CHC crystal sample with dimensions ∅23 × 30 mm³ demonstrates energy resolution of 3.2% FWHM at 662 keV, the relative light output at the level of 30,000 ph/MeV and excellent linearity down to 20 keV. Additionally, this material exhibits excellent pulse shape discrimination ability and low internal background of less than 1 Bq/kg. Furthermore, attempts to produce a high quality CHC crystal resulted in research on this material optimization by constitution of either alkali ions (Cs to Tl), or main element (Hf to Zr), or halogen ions (Cl to Br, I, or their mixture in different ratio), as well as doping with various active ions (Te⁴⁺, Ce³⁺, Eu³⁺, etc.). This leads to a range of new established scintillating materials, such as Tl₂HfCl₆, Tl₂ZrCl₆, Cs₂HfCl₄Br₂, Cs₂HfCl₃Br₃, Cs₂ZrCl₆, and Cs₂HfI₆. To exploit the whole potential of these compounds, detailed studies of the material’s fundamental properties, and understanding of the variety of the luminescence mechanisms are required. This will help to understand the origin of the high light yield and possible paths to further extend it. Perspectives of CHC crystals and related materials as detectors for rare nuclear processes are also discussed. Full article

In this paper, an investigation of the role of nuclear saturation parameters on f-mode oscillations in neutron stars is performed within the Cowling approximation. It is found that the uncertainty in the effective nucleon mass plays a dominant role in controlling the f-mode frequencies. The effect of the uncertainties in saturation parameters on previously-proposed empirical relations of the frequencies with astrophysical observables relevant for asteroseismology are also investigated. These results can serve as an important tool for constraining the nuclear parameter space and understand the behaviour of dense nuclear matter from the future detection of f-modes. Full article

Non-additive entropy is obtained through the thermodynamic description of a system with a fractal structure in its energy-momentum space, called a thermofractal. The entropic parameter, q, is determined in terms of the fractal structure parameters. The characteristics of the thermofractals are determined by two parameters associated with the number of degrees of freedom of the fractal structure and the scale. The parameter q, of non-extensive thermodynamics, has a physical meaning related to the number of degrees of freedom of the thermofractal. The two types of thermofractals are distinguished by the value of $q>1$ or $q<1$. Studying the group of transformations of the fractal system, we identify three different classes of transformations and their mathematical expressions. For one class of transformations of thermofractals, the group is isomorphic with q-calculus. Another class of transformations led to new mathematical expressions that extended the deformed q-algebra. Finally, we comment regarding the applications of the results obtained here for different areas such as QCD and scale-free networks. Full article

We revisit the possibility of first order electroweak phase transition (EWPT) in one of the simplest extensions of the Standard Model scalar sector, namely the two-Higgs-doublet model (2HDM). We take into account the ensuing constraints from the electroweak precision tests, Higgs signal strengths and the recent LHC bounds from direct scalar searches. By studying the vacuum transition in 2HDM, we discuss in detail the entropy released in the first order EWPT in various parameter planes of a 2HDM. Full article

Amorphous chalcogenide glasses are intrinsically metastable, highly photosensitive, and therefore exhibit numerous light-induced effects upon bandgap and sub-bandgap illumination. Depending on the pulse duration of the excitation laser, ChGs exhibit a series of light-induced effects spanning over femtosecond to seconds time domain. For continuous wave (CW) illumination, the effects are dominantly metastable in terms of photodarkening (PD) and photobleaching (PB) that take place via homopolar to heteropolar bond conversion. On the other hand, under nanosecond and ultrafast pulsed illumination, ChGs exhibit transient absorption (TA) that is instigated from the transient bonding rearrangements through self-trapped exciton recombination. In the first part of the review, we pay special attention to continuous wave light-induced PD and PB, while in the second part we will focus on the TA and controlling such effects via internal and external parameters, e.g., chemical composition, temperature, sample history, etc. Full article

In this paper, analytical and semi-analytical formulas are presented for the self- and mutual inductance of thin ordinary disk coils and thin Bitter disk coils. The coils lie concentrically in a plane. The ordinary coils are coils with constant current density. The current density of a current carrying Bitter disc is not uniform across its cross-sectional area, but it is a function of the ratio of the inner diameter of the disk to an arbitrary radius within the disk. In this paper, we show the possibility to calculate the mutual and self-inductance of thin disk coils from the real coils of the cross-sections using some valuable conditions. The formulas for the mutual inductance and the self-inductance were obtained in the semi-analytic form as the combination of the elliptic integral of the second kind and a simple integral for the ordinary disk coils. The mutual inductance and self-inductance were obtained in the analytical form as the elliptic integral of the second kind for the Bitter disk coils. The formula for the self-inductance of the ordinary full disk was obtained in the close form. All formulas are given in remarkably simple form and give perfectly accurate results with a significantly small computational time. All cases of either regular or singular (disks in contact or overlapping) are covered. Many presented examples show the excellent numerical agreement with previously published methods. Full article

We present the initial design studies and specifications for an accelerator and conveyor system to irradiate collagen samples, modifying properties such as the putrescibility and mechanical behaviours in a paradigm shift from existing, widely used technology. We show the integrated design requirements for a magnetic rastering scheme to move the beam position in order to ensure a uniform dose distribution over the full surface of the hide and discuss its dependence on factors such as the size of the hide, the beam current and conveyor speed. We also present initial energy deposition studies using beam particle interaction simulation program G4beamline, in order to determine the numerical beam parameters and angle of incidence needed to ensure a uniform depth-dose distribution throughout the hide thickness. Full article

High-multiplicity proton-proton (pp) collisions at the Large Hadron Collider (LHC) energies have created a new domain of research to look for a possible formation of quark–gluon plasma in these events. In this paper, we estimate various thermal properties of the matter formed in pp collisions at the LHC energies, such as mean free path, isobaric expansivity, thermal pressure, and heat capacity using a thermodynamically consistent Tsallis distribution function. Particle species-dependent mean free path and isobaric expansivity are studied as functions of final state charged particle multiplicity for pp collisions at the center-of-mass energy $\sqrt{s}$ = 7 TeV. The effects of degree of non-extensivity, baryochemical potential, and temperature on these thermal properties are studied. The findings are compared with the theoretical expectations. Full article

In astroparticle, nuclear and subnuclear physics, low-counting experiments play an increasingly important role in the investigation of rare processes such as dark matter, double beta decay, some neutrino processes and low-background spectrometry. Extremely low-background features are more and more required to produce detectors and apparata of suitable sensitivity. Over time, a great deal of interest and attention in developing experimental techniques suitable to improve, verify and maintain the radiopurity of these detectors has arisen. In this paper, the characterization of inorganic crystal scintillators (such as, e.g., NaI(Tl), ZnWO${}_4$ and CdWO${}_4$) using $\alpha$, $\beta$ and $\gamma$ radioactive sources and the main experimental techniques applied in the field to quantitatively identify the radioactive contaminants are highlighted; in particular, we focus on inorganic crystal scintillators, widely used in rare processes investigation, considering their applications at noncryogenic temperatures in the framework of the DAMA experiment activities at the Gran Sasso National Laboratory of the INFN (National Institute for Nuclear Physics, INFN). Full article

Recently, I have considered a multi-variable feedforward control practice in a novel way being called “considerate control”. It was shown how the considerate control is related to Bristol gains, which indicate accurately either the required increase in input scope or the reduced output scope as compared to inconsiderate control. Here, considerate control is expanded to regulating control, necessitating some feedback design. Clearly, high-gain feedback leads to considerate control results in low frequency. Considerate pre-compensation decouples loops also at higher frequencies. However, as an analysis of the included examples demonstrates, such considerate design may insert non-minimum phase-lag into loops that did not have it, thus, reducing the loop bandwidth relative to that achievable in a skillful inconsiderate design, sometimes very significantly. As is often the case, there is a trade-off between consideration and performance. Full article

We report test results searching for an effect of electrostatic charge on weight. For conducting test objects of mass of order 1 kg, we found no effect on weight, for potentials ranging from 10 V to 200 kV, corresponding to charge states ranging from ${10}^{-9}$ to over ${10}^{-5}$ coulombs, and for both polarities, to within a measurement precision of 2 g. While such a result may not be unexpected, this is the first unipolar, high-voltage, meter-scale, static test for electro-gravitic effects reported in the literature. Our investigation was motivated by the search for possible coupling to a long-range scalar field that could surround the planet, yet go otherwise undetected. The large buoyancy force predicted within the classical Kaluza theory involving a long-range scalar field is falsified by our results, and this appears to be the first such experimental test of the classical Kaluza theory in the weak field regime, where it was otherwise thought identical with known physics. A parameterization is suggested to organize the variety of electro-gravitic experiment designs. Full article