Physics, Volume 3, Issue 4 (December 2021) – 30 articles

Studies that use magnetic resonance velocimetry (MRV) to assess flows through porous media require a sufficiently small voxel size to determine the velocity field at a sub-pore scale. The smaller the voxel size, the less information is lost through the discretization. However, the measurement uncertainty and the measurement time are increased. Knowing the relationship between voxel size and measurement accuracy would help researchers select a voxel size that is not too small in order to avoid unnecessary measurement effort. This study presents a systematic parameter study with a low-Reynolds-number flow of a glycerol–water mixture sent through a regularly periodic porous matrix with a pore size of 5 mm. The matrix was a 3-dimensional polymer print, and velocity-encoded MRV measurements were made at 15 different voxel sizes between 0.42 mm and 4.48 mm. The baseline accuracy of the MRV velocity data was examined through a comparison with a computational fluid dynamics (CFD) simulation. The experiment and simulation show very good agreement, indicating a low measurement error. Starting from the smallest examined voxel size, the influence of the voxel size on the accuracy of the velocity data was then examined. This experiment enables us to conclude that a voxel size of 0.96 mm, which corresponds to 20% of the pore size, is sufficient. The volume-averaged results do not change below a voxel size of 20% of the pore size, whereas systematic deviations occur with larger voxels. The same trend is observed with the local velocity data. The streamlines calculated from the MRV velocity data are not influenced by the voxel size for voxels of up to 20% of the pore size, and even slightly larger voxels still show good agreement. In summary, this study shows that even with a relatively low measurement resolution, quantitative 3-dimensional velocity fields can be obtained through porous flow systems with short measurement times and low measurement uncertainty. Full article

Low-energy Coulomb excitation is capable of providing unique information on static electromagnetic moments of short-lived excited nuclear states, including non-yrast states. The process selectively populates low-lying collective states and is, therefore, ideally suited to study phenomena such as shape coexistence and the development of exotic deformation (triaxial or octupole shapes). Historically, these experiments were restricted to stable isotopes. However, the advent of new facilities providing intense beams of short-lived radioactive species has opened the possibility to apply this powerful technique to a much wider range of nuclei. The paper discusses the observables that can be measured in a Coulomb-excitation experiment and their relation to the nuclear structure parameters with an emphasis on the nuclear shape. Recent examples of Coulomb-excitation studies that provided outcomes relevant for the Shell Model are also presented. Full article

One ambitious goal of nuclear physics is a predictive model of all nuclei, including the ones at the fringes of the nuclear chart which may remain out of experimental reach. Certain regions of the chart are providing formidable testing grounds for nuclear models in this quest as they display rapid structural evolution from one nucleus to another or phenomena such as shape coexistence. Observables measured for such nuclei can confirm or refute our understanding of the driving forces of the evolution of nuclear structure away from stability where textbook nuclear physics has been proven to not apply anymore. This paper briefly reviews the emerging picture for the very neutron-rich Fe, Cr, and Ti isotopes within the so-called $N=40$ island of inversion as obtained with nucleon knockout reactions. These have provided some of the most detailed nuclear spectroscopy in very neutron-rich nuclei produced at rare-isotope facilities. The results indicate that our current understanding, as encoded in large-scale shell-model calculations, appears correct with exciting predictions for the $N=40$ island of inversion left to be proven in the experiment. A bright future emerges with predictions of continued shell evolution and shape coexistence out to neutron number $N=50$, below ${}^{78}$Ni on the chart of nuclei. Full article

Global modulation studies with comprehensive numerical models contribute meaningfully to the refinement of very local interstellar spectra (VLISs) for cosmic rays. Modulation of positrons and anti-protons are investigated to establish how the ratio of their intensity, and with respect to electrons and protons, are changing with solar activity. This includes the polarity reversal of the solar magnetic field which creates a 22-year modulation cycle. Modeling illustrates how they are modulated over time and the particle drift they experience which is significant at lower kinetic energy. The VLIS for anti-protons has a peculiar spectral shape in contrast to protons so that the total modulation of anti-protons is awkwardly different to that for protons. We find that the proton-to-anti-proton ratio between 1–2 GeV may change by a factor of 1.5 over a solar cycle and that the intensity for anti-protons may decrease by a factor of ~2 at 100 MeV during this cycle. A composition is presented of VLIS for protons, deuteron, helium isotopes, electrons, and particularly for positrons and anti-protons. Gaining knowledge of their respective 11 and 22 year modulation is useful to interpret observations of low-energy anti-nuclei at the Earth as tests of dark matter annihilation. Full article

The ability of space plasmas to self-regulate through mechanisms involving self-generated fluctuations is a topic of high interest. This paper presents the results of a new advanced quasilinear (QL) approach for the instability of electromagnetic ion-cyclotron modes driven by the relative alpha-proton drift observed in solar wind. For an extended parametric analysis, the present QL approach includes also the effects of intrinsic anisotropic temperatures of these populations. The enhanced fluctuations contribute to an exchange of energy between proton and alpha particles, leading to important variations of the anisotropies, the proton-alpha drift and the temperature contrast. The results presented here can help understand the observational data, in particular, those revealing the local variations associated with the properties of protons and alpha particles as well as the spatial profiles in the expanding solar wind. Full article

In the present paper, the process of inverse double-Compton (IDC) scattering is considered in the context of astrophysical applications. It is assumed that the two hard X-ray photons emitted from an astrophysical source are scattered on a free electron and converted into a single soft photon of optical range. Using the QED S-matrix formalism for the derivation of a cross-section of direct double-Compton (DDC) scattering and assuming detailed balance conditions, an analytical expression for the cross-section of the IDC process is presented. It is shown that at fixed energies of incident photons, the inverse cross-section has no infrared divergences, and its behavior is completely defined by the spectral characteristics of the photon source itself, in particular by the finite interaction time of radiation with an electron. Thus, even for the direct process, the problem of resolving infrared divergence actually refers to a real physical source of radiation in which photons are never actually plane waves. As a result, the physical frequency profile of the scattered radiation for DDC as well as for IDC processes is a function of both the intensity and line shape of the incident photon field. Full article

In this paper, in the scope of a non-extensive statistical model for the nucleon’s structure function, the volume of the gluons in the nucleons and the relations among the temperature, T, the parameter “q” of Tsallis statistics, and the scattering energies, $Q^2$, are studied. A system of equations with the usual sum rules are solved for the valence quarks, the experimental results for the polarized structure function, and the estimated carried moments for gluons and quarks. Each state of T and q leads to a set of chemical potentials and different radii for gluons and quarks. We conclude that gluons must occupy a larger volume than the quarks to fit the fraction of the total momentum. A linear function of the temperature with $Q^2$ is obtained as an approach. The obtained range of temperatures is different from the previous models. Full article

The scientific novelty of this work is determined by the rationale for the participation in transformations, along with the kinetic energy of particles, of four types of elastic energy, identified by the peculiarities of their phase changes in the oscillation process. Two types are converted into kinetic energy, while the other two types change the deformed state of particles in accordance with the equations of motion due to internal sources. The result is obtained based on the use of the superposition principle in the space of Lagrange variables with the imposition of forced and free oscillations, as well as a new model of mechanics based on the concepts of space, time, and energy with a new scale of average stresses that takes into account the energy of particles in the initial state. In such a model of mechanics, a generalized measure of the elastic energy of particles is a quadratic invariant of asymmetric tensor whose components are partial derivatives of Euler variables with respect to Lagrange variables. The concept of kinematic energy parameters is introduced, which differ from the corresponding volumetric energy densities by a multiplier equal to the modulus of elasticity, which is directly proportional to the density and heat capacity of the material, and inversely proportional to the volumetric compression coefficient. Comparison of the values of kinematic parameters shows that most of the energy required for oscillations is associated with the deformation of particles and comes from internal sources. The mechanisms of transformation of forced vibrations into their own for transverse, torsional, and longitudinal vibrations are considered, as well as the occurrence of resonance when free and forced vibrations are superimposed with the same or a similar frequency. The formation of a new free wave after each cycle of external influences with an increase in amplitude, which occurs mainly due to internal, and not external, energy sources is justified. Full article

A Newtonian-like theory inspired by the Brans–Dicke gravitational Lagrangian has been recently proposed by us. For static configurations, the gravitational coupling acquires an intrinsic spatial dependence within the matter distribution. Therefore, the interior of astrophysical configurations may provide a testable environment for this approach as long as no screening mechanism is evoked. In this work, we focus on the stellar hydrostatic equilibrium structure in such a varying Newtonian gravitational coupling G scenario. A modified Lane–Emden equation is presented and its solutions for various values of the polytropic index are discussed. The role played by the theory parameter $\omega$, the analogue of the Brans–Dicke parameter, in the physical properties of stars is discussed. Full article

Reinhard Schlickeiser has made groundbreaking contributions to various aspects of blazar physics, including diffusive shock acceleration, the theory of synchrotron radiation, the production of gamma-rays through Compton scattering in various astrophysical sources, etc. This paper, describing the development of a self-consistent shock-in-jet model for blazars with a synchrotron mirror feature, is therefore an appropriate contribution to a Special Issue in honor of Reinhard Schlickeiser’s 70th birthday. The model is based on our previous development of a self-consistent shock-in-jet model with relativistic thermal and non-thermal particle distributions evaluated via Monte-Carlo simulations of diffusive shock acceleration, and time-dependent radiative transport. This model has been very successful in modeling spectral variability patterns of several blazars, but has difficulties describing orphan flares, i.e., high-energy flares without a significant counterpart in the low-frequency (synchrotron) radiation component. As a solution, this paper investigates the possibility of a synchrotron mirror component within the shock-in-jet model. It is demonstrated that orphan flares result naturally in this scenario. The model’s applicability to a recently observed orphan gamma-ray flare in the blazar 3C279 is discussed and it is found that only orphan flares with mild (≲ a factor of 2–3) enhancements of the Compton dominance can be reproduced in a synchrotron-mirror scenario, if no additional parameter changes are invoked. Full article

The recent associations of neutrinos with blazars require the efficient interaction of relativistic protons with ambient soft photon fields. However, along side the neutrinos, $\gamma$-ray photons are produced, which interact with the same soft photon fields producing electron-positron pairs. The strength of this cascade has significant consequences on the photon spectrum in various energy bands and puts severe constraints on the pion and neutrino production. In this study, we discuss the influence of the external thermal photon fields (accretion disk, broad-line region, and dusty torus) on the proton-photon interactions, employing a newly developed time-dependent one-zone hadro-leptonic code OneHaLe. We present steady-state cases, as well as a time-dependent case, where the emission region moves through the jet. Within the limits of this toy study, the external fields can disrupt the “usual” double-humped blazar spectrum. Similarly, a moving region would cross significant portions of the jet without reaching the previously-found steady states. Full article

The basic characteristics of cylindrical as well as spherical solitary and shock waves in degenerate electron-nucleus plasmas are theoretically investigated. The electron species is assumed to be cold, ultra-relativistically degenerate, negatively charged gas, whereas the nucleus species is considered a cold, non-degenerate, positively charged, viscous fluid. The reductive perturbation technique is utilized in order to reduce the basic equations (governing the degenerate electron-nucleus plasmas under consideration) to the modified Korteweg-de Vries and Burgers equations. The latter are numerically solved and analyzed to detect the basic characteristics of solitary and shock waves in such electron-nucleus plasmas. The nonlinear nucleus-acoustic waves are found to be propagated in the form of solitary as well as shock waves in such degenerate electron-nucleus plasmas. Their basic properties as well as their time evolution are significantly modified by the effects of cylindrical as well as spherical geometries. The results of this study is expected to be applicable not only to astrophysical compact objects, but also to ultra-cold dense plasmas produced in laboratory. Full article

In this paper, the improved and the new analytical and semi-analytical expressions for calculating the magnetic vector potential, magnetic field, magnetic force, mutual inductance, torque, and stiffness between two inclined current-carrying arc segments in air are given. The expressions are obtained either in the analytical form over the incomplete elliptic integrals of the first and the second kind or by the single numerical integration of some elliptical integrals of the first and the second kind. The validity of the presented formulas is proved from the particular cases when the inclined circular loops are addressed. We mention that all formulas are obtained by the integral approach, except the stiffness, which is found by the derivative of the magnetic force. The novelty of this paper is the treatment of the inclined circular carting-current arc segments for which the calculations of the previously mentioned electromagnetic quantities are given. Full article

In 1979, I arrived back at the University of Chicago from a two-year stint in Australia to find a very large German post-doc eagerly awaiting me, so we could work together on transport of cosmic ray electrons perpendicular to the galactic plane [...] Full article

Electromagnetic expulsion acts on a body suspended in a conducting fluid or plasma, which is subject to the influence of electric and magnetic fields. Physically, the effect is a magnetohydrodynamic analogue of the buoyancy (Archimedean) force, which is caused by the nonequal electric conductivities inside and outside the body. It is suggested that electromagnetic expulsion can drive the observed plasma counter-streaming flows in solar filaments. Exact analytical solutions and scaling arguments for a characteristic plasma flow speed are reviewed, and their applicability in the limit of large magnetic Reynolds numbers, relevant in the solar corona, is discussed. Full article

A condensed review is presented for two basic topics in the theory of pattern formation in nonlinear dissipative media: (i) domain walls (DWs, alias grain boundaries), which appear as transient layers between different states occupying semi-infinite regions, and (ii) two- and three-dimensional (2D and 3D) quasiperiodic (QP) patterns, which are built as a superposition of plane–wave modes with incommensurate spatial periodicities. These topics are selected for the present review, dedicated to the 70th birthday of Professor Michael I. Tribelsky, due to the impact made on them by papers of Prof. Tribelsky and his coauthors. Although some findings revealed in those works may now seem “old”, they keep their significance as fundamentally important results in the theory of nonlinear DW and QP patterns. Adding to the findings revealed in the original papers by M.I. Tribelsky et al., the present review also reports several new analytical results, obtained as exact solutions to systems of coupled real Ginzburg–Landau (GL) equations. These are a new solution for symmetric DWs in the bimodal system including linear mixing between its components; a solution for a strongly asymmetric DWs in the case when the diffusion (second-derivative) term is present only in one GL equation; a solution for a system of three real GL equations, for the symmetric DW with a trapped bright soliton in the third component; and an exact solution for DWs between counter-propagating waves governed by the GL equations with group-velocity terms. The significance of the “old” and new results, collected in this review, is enhanced by the fact that the systems of coupled equations for two- and multicomponent order parameters, addressed in this review, apply equally well to modeling thermal convection, multimode light propagation in nonlinear optics, and binary Bose–Einstein condensates. Full article

Experimentally observed complex networks are often scale-free, small-world and have an unexpectedly large number of small cycles. An Apollonian network is one notable example of a model network simultaneously having all three of these properties. This network is constructed by a deterministic procedure of consequentially splitting a triangle into smaller and smaller triangles. In this paper, a similar construction based on the consequential splitting of tetragons and other polygons with an even number of edges is presented. The suggested procedure is stochastic and results in the ensemble of planar scale-free graphs. In the limit of a large number of splittings, the degree distribution of the graph converges to a true power law with an exponent, which is smaller than three in the case of tetragons and larger than three for polygons with a larger number of edges. It is shown that it is possible to stochastically mix tetragon-based and hexagon-based constructions to obtain an ensemble of graphs with a tunable exponent of degree distribution. Other possible planar generalizations of the Apollonian procedure are also briefly discussed. Full article

The Gamow shell model (GSM) is a powerful method for the description of the exotic properties of drip line nuclei. Internucleon correlations are included via a configuration interaction framework. Continuum coupling is directly included at basis level by using the Berggren basis, in which, bound, resonance, and continuum single-particle states are treated on an equal footing in the complex momentum plane. Two different types of Gamow shell models have been developed: its first embodiment is that of the GSM defined with phenomenological nuclear interactions, whereas the GSM using realistic nuclear interactions, called the realistic Gamow shell model, was introduced later. The present review focuses on the recent applications of the GSM to drip line nuclei. Full article

Quantum measurements of physical quantities are often described as ideal measurements. However, only a few measurements fulfil the conditions of ideal measurements. The aim of the present work is to describe real position measurements with detectors that are able to detect single particles. For this purpose, a detector model is developed that can describe the time dependence of the interaction between a non-relativistic particle and a detector. The example of a position measurement shows that this interaction can be described with the methods of quantum mechanics. At the beginning of a position measurement, the detector behaves as a target consisting of a large number of quantum mechanical systems. In the first reaction, the incident particle interacts with a single atom, electron or nucleus, but not with the whole detector. This reaction and all following reactions are quantum mechanical processes. At the end of the measurement, the detector can be considered as a classical apparatus. A detector is neither a quantum mechanical system nor a classical apparatus. The detector model explains why one obtains a well-defined result for each individual position measurement. It further explains that, in general, it is impossible to predict the outcome of an individual measurement. Full article

The tunable optical pulling force on a graded plasmonic core-shell nanoparticle consisting of a gain dielectric core and graded plasmonic shell is investigated in the illumination of a plane wave. In this paper, the electrostatic polarizability and the equivalent permittivity of the core-shell sphere are derived and the plasmonic enhanced optical pulling force in the antibonding and bonding dipole modes of the graded nanoparticle are demonstrated. Additionally, the resonant pulling force occurring on the dipole mode is shown to be dependent on the aspect ratio of the core-shell particle, which is illustrated by the obtained equivalent permittivity. This shows that the gradation of the graded shell will influence the plasmonic feature of the particle, thus further shifting the resonant optical force peaks and strengthening the pulling force. The obtained results provide an additional degree of freedom to manipulate nanoparticles and give a deep insight into light–matter interaction. Full article

In this paper, a discussion of the Landau damping of Langmuir waves is presented together with a simple derivation which does not require the application of methods of complex analysis. A general dispersion relation is derived systematically which corresponds to a nonlinear equation. The latter equation is solved numerically but asymptotic limits are also discussed. Full article

The purpose of this paper is to study and analyze the concept of fractional-order complex-valued chaotic networks with external bounded disturbances and uncertainties. The synchronization problem and parameter identification of fractional-order complex-valued chaotic neural networks (FOCVCNNs) with time-delay and unknown parameters are investigated. Synchronization between a driving FOCVCNN and a response FOCVCNN, as well as the identification of unknown parameters are implemented. Based on fractional complex-valued inequalities and stability theory of fractional-order chaotic complex-valued systems, the paper designs suitable adaptive controllers and complex update laws. Moreover, it scientifically estimates the uncertainties and external disturbances to establish the stability of controlled systems. The computer simulation results verify the correctness of the proposed method. Not only a new method for analyzing FOCVCNNs with time-delay and unknown complex parameters is provided, but also a sensitive decrease of the computational and analytical complexity. Full article

Examining the evolution of the maximum of valence quark distribution, $q_V$, weighted by Bjorken x, $h(x,t)\equiv x{q}_V(x,t)$, it is observed that $h(x,t)$ at the peak becomes a one-parameter function; $h(x_p,t)=\Phi \left(x_p\left(t\right)\right)$, where $x_p$ is the position of the peak, $t=log{Q}^2$, and $Q^2$ is the resolution scale. This observation is used to derive a new model-independent relation which connects the partial derivative of the valence parton distribution functions (PDFs) in $x_p$ to the quantum chromodynamics (QCD) evolution equation through the $x_p$ derivative of the logarithm of the function $\Phi \left(x_p\left(t\right)\right)$. A numerical analysis of this relation using empirical PDFs results in an observation of the exponential form of the $\Phi \left(x_p\left(t\right)\right)=h(x_p,t)=C{e}^{D{x}_p\left(t\right)}$ for leading to next-to-next leading order approximations of PDFs for the range of $Q^2$, covering four orders in magnitude. The exponent, D, of the observed “height-position” correlation function converges with the increase in the order of approximation. This result holds for all the PDF sets considered. A similar relation is observed also for the pion valence quark distribution, indicating that the obtained relation may be universal for any non-singlet partonic distribution. The observed “height-position” correlation is used also to indicate that no finite number of exchanges can describe the analytic behavior of the valence quark distribution at the position of the peak at fixed $Q^2$. Full article

New null Lagrangians and gauge functions are derived and they are called nonstandard because their forms are different than those previously found. The invariance of the action is used to make the Lagrangians and gauge functions exact. The first exact nonstandard null Lagrangian and its gauge function for the law of inertia are obtained, and their physical implications are discussed. Full article

In this paper, the fluctuation properties of the number of energy levels (mode fluctuation) are studied in the mixed-type lemon billiards at high lying energies. The boundary of the lemon billiards is defined by the intersection of two circles of equal unit radius with the distance $2B$ between the centers, as introduced by Heller and Tomsovic. In this paper, the case of two billiards, defined by $B=0.1953,0.083$, is studied. It is shown that the fluctuation of the number of energy levels follows the Gaussian distribution quite accurately, even though the relative fraction of the chaotic part of the phase space is only 0.28 and 0.16, respectively. The theoretical description of spectral fluctuations in the Berry–Robnik picture is discussed. Also, the (golden mean) integrable rectangular billiard is studied and an almost Gaussian distribution is obtained, in contrast to theory expectations. However, the variance as a function of energy, E, behaves as $\sqrt{E}$, in agreement with the theoretical prediction by Steiner. Full article

Almost 70 years ago, the Fermi–Pasta–Ulam–Tsingou (FPUT) paradox was formulated in, observed in, and reported using normal modes of a nonlinear, one-dimensional, non-integrable string. Let us recap the paradox. One normal mode is excited, which drives three or four more normal modes in the core. Then, that is it for quite a long time. So why are many normal modes staying weakly excited in the tail? Furthermore, how many? A quantitative, analytical answer to the latter question is given here using resonances and secular avalanches A comparison with the previous numerical data is made and extremely good agreement is found. Full article

The review presents the development of an approach of constructing approximate solutions to complicated physics problems, starting from asymptotic series, through optimized perturbation theory, to self-similar approximation theory. The close interrelation of underlying ideas of these theories is emphasized. Applications of the developed approach are illustrated by typical examples demonstrating that it combines simplicity with good accuracy. Full article

In this paper, the instability of a vertical fluid motion, or throughflow, is investigated in a horizontal bidisperse porous layer that is uniformly heated from below. By means of the order-1 Galerkin approximation method, the critical Darcy–Rayleigh number for the onset of steady instability is determined in closed form. The coincidence between the linear instability threshold and the global nonlinear stability threshold, in the energy norm, is shown. Full article

In this paper, conformal invariant gravitation, based on Weyl geometry, is considered. In addition to the gravitational and matter action integrals, the interaction between the Weyl vector (entered in Weyl geometry) and the vector, representing the world line of the independent observer, are introduced. It is shown that the very existence of such an interaction selects the exponentially growing scale factor solutions among the cosmological vacua. Full article

As it was shown earlier, a wide class of nonlinear 3-dimensional (3D) fluid flows of incompressible viscous fluid can be described by only one scalar function dubbed the quasi-potential. This class of fluid flows is characterized by a three-component velocity field having a two-component vorticity field. Both these fields may, in general, depend on all three spatial variables and time. In this paper, the governing equations for the quasi-potential are derived and simple illustrative examples of 3D flows in the Cartesian coordinates are presented. The generalisation of the developed approach to the fluid flows in the cylindrical and spherical coordinate frames represents a nontrivial problem that has not been solved yet. In this paper, this gap is filled and the concept of a quasi-potential to the cylindrical and spherical coordinate frames is further developed. A few illustrative examples are presented which can be of interest for practical applications. Full article