Physics

The understanding of factors that affect the dissemination of a viral infection is fundamental to help combat it. For instance, during the COVID-19 pandemic that changed the lives of people all over the world, one observes regions with different incidences of cases. One can speculate that population density might be one of the variables that affect the incidence of cases. In populous areas, such as big cities or congested urban areas, higher COVID-19 incidences could be observed than in rural regions. It is natural to think that if population density is such an important factor, then a gradient or difference in population density might lead to a diffusion process that will proceed until equilibrium is reached. The aim of this paper consists of the inclusion of a diffusion concept into the COVID-19 modeling. With this concept, one covers a gradient-driven transfer of the infection next to epidemic growth models (SIR-type models). This is discussed for a certain period of the German situation based on the quite different incidence data for the different federal states of Germany. With this ansatz, some phenomena of the actual development of the pandemic are found to be confirmed. The model provides a possibility to investigate certain scenarios, such as border-crossings or local spreading events, and their influence on the COVID-19 propagation. The resulting information can be a basis for the decisions of politicians and medical persons in charge of managing a pandemic. Full article

Inorganic crystal scintillators play a crucial role in particle detection for various applications in fundamental physics and applied science. The use of such materials as scintillating bolometers, which operate at temperatures as low as 10 mK and detect both heat (phonon) and scintillation signals, significantly extends detectors performance compared to the conventional scintillation counters. In particular, such low-temperature devices offer a high energy resolution in a wide energy interval thanks to a phonon signal detection, while a simultaneous registration of scintillation emitted provides an efficient particle identification tool. This feature is of great importance for a background identification and rejection. Combined with a large variety of elements of interest, which can be embedded in crystal scintillators, scintillating bolometers represent powerful particle detectors for rare-event searches (e.g., rare alpha and beta decays, double-beta decay, dark matter particles, neutrino detection). Here, we review the features and results of low-temperature scintillation detection achieved over a 30-year history of developments of scintillating bolometers and their use in rare-event search experiments. Full article

Ongoing social restrictions, including social distancing and lockdown, adopted by many countries to inhibit spread of the the COVID-19 epidemic, must attempt to find a trade-off between induced economic damage, healthcare system collapse, and the costs in terms of human lives. Applying and removing restrictions on a system with a given latency as represented by an epidemic outbreak (and formally comparable with mechanical inertia), may create critical instabilities, overshoots, and strong oscillations in the number of infected people around the desirable set-point, defined in a practical way as the maximum number of hospitalizations acceptable by a given healthcare system. A good understanding of the system reaction to any change of the input control variable can be reasonably achieved using a proportional–integral–derivative controller (PID), which is a widely used technique in various physics and technological applications. In this paper, this control theory to is proposed to be applied epidemiology, to understand the reaction of COVID-19 propagation to social restrictions and to reduce epidemic damages through the correct tuning of the containment policy. Regarding the synthesis of this interdisciplinary approach, the extended to the susceptible–infectious–recovered (SIR) model name “SIR-PID” is suggested. Full article

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

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

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