Diffusion in Phase Space as a Tool to Assess Variability of Vertical Centre-of-Mass Motion during Long-Range Walking
The Impact of Radio Frequency Waves on the Plasma Density in the Tokamak Edge
Resonant Fast-Alfvén Wave Coupling in a 3D Coronal Arcade
Advances in the Implementation of the Exactly Energy Conserving Semi-Implicit (ECsim) Particle-in-Cell Method
Thermosolutal Marangoni Convection for Hybrid Nanofluid Models: An Analytical Approach

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Physics

Physics is an international, peer-reviewed, open access journal which presents latest researches on all aspects of physics. It publishes original research articles, review articles, communications with no restriction on the length of the papers. Physics is published quarterly online by MDPI.

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Latest Articles

Open AccessArticle

Fluctuations-Induced Quantum Radiation and Reaction from an Atom in a Squeezed Quantum Field

Matthew Bravo

Jen-Tsung Hsiang

and

Bei-Lok Hu

Physics 2023, 5(2), 554-589; https://doi.org/10.3390/physics5020040 - 24 May 2023

Abstract

In this third of a series on quantum radiation, we further explore the feasibility of using the memories (non-Markovianity) kept in a quantum field to decipher certain information about the early universe. As a model study, we let a massless quantum field be subjected to a parametric process for a finite time interval such that the mode frequency of the field transits from one constant value to another. This configuration thus mimics a statically-bounded universe, where there is an ‘in’ and an ‘out’ state with the scale factor approaching constants, not a continuously evolving one. The field subjected to squeezing by this process should contain some information of the process itself. If an atom is coupled to the field after the parametric process, its response will depend on the squeezing, and any quantum radiation emitted by the atom will carry this information away so that an observer at a much later time may still identify it. Our analyses show that (1) a remote observer cannot measure the generated squeezing via the radiation energy flux from the atom because the net radiation energy flux is canceled due to the correlation between the radiation field from the atom and the free field at the observer’s location. However, (2) there is a chance to identify squeezing by measuring the constant radiation energy density at late times. The only restriction is that this energy density is of the near-field nature and only an observer close to the atom can use it to unravel the information of squeezing. The second part of this paper focuses on (3) the dependence of squeezing on the functional form of the parametric process. By explicitly working out several examples, we demonstrate that the behavior of squeezing does reflect essential properties of the parametric process. Actually, striking features may show up in more complicated processes involving various scales. These analyses allow us to establish the connection between properties of a squeezed quantum field and details of the parametric process which performs the squeezing. Therefore, (4) one can construct templates to reconstitute the unknown parametric processes from the data of measurable quantities subjected to squeezing. In a sequel paper these results will be applied to a study of quantum radiations in cosmology. Full article

(This article belongs to the Special Issue Vacuum Fluctuations)

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Open AccessCommunication

Photons as a Signal of Deconfinement in Hadronic Matter under Extreme Conditions

Sergei Nedelko

and

Aleksei Nikolskii

Physics 2023, 5(2), 547-553; https://doi.org/10.3390/physics5020039 - 16 May 2023

Abstract

The photon production by conversion of gluons

g g \to γ

The photon production by conversion of gluons

g g \to γ

via quark loop in the framework of the mean-field approach to the QCD (quantunm chromodynamics) vacuum is studied here. According to the domain model of QCD vacuum, the confinement phase is dominated by Abelian (anti-)self-dual gluon fields, while the deconfinement phase is characterized by a strong chromomagnetic field. In the confinement phase, photon production is impossible due to the random spacial orientation of the statistical ensemble of vacuum fields. However, the conditions of Furry theorem are not satisfied in the deconfinement phase, the conversion of gluons is nonzero and, in addition, photon distribution has a strong angular anisotropy. Thus, the photon production in the discussed process acts as one of the important features of transition in quark-gluon plasma to the deconfinement phase. Full article

(This article belongs to the Special Issue From Heavy Ions to Astroparticle Physics)

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Open AccessReview

Fractal Entropy of Nuclear Medium Probed by

K_{S}^{0}

Mesons Produced in AuAu Collisions at RHIC

Mikhail Tokarev

and

Imrich Zborovský

Physics 2023, 5(2), 537-546; https://doi.org/10.3390/physics5020038 - 09 May 2023

Abstract

In this paper, we review our findings concerning fractal entropy of microscopic configurations corresponding to the production of

K_{S}^{0}

mesons in AuAu collisions in the z-scaling approach. The entropy is expressed via structural and fragmentation fractal dimensions, and model parameter [...] Read more.

In this paper, we review our findings concerning fractal entropy of microscopic configurations corresponding to the production of

K_{S}^{0}

mesons in AuAu collisions in the z-scaling approach. The entropy is expressed via structural and fragmentation fractal dimensions, and model parameter

c_{AuAu}

is interpreted as a specific heat of produced medium. These parameters are related to the respective momentum fractions of the colliding nuclei, the momentum fractions of the scattered constituents that fragment into the produced hadrons, and the multiplicity density of negative particles in the central interaction region. The dependence of the entropy on the collision energy over the range of 7.7–200 GeV for most central and most peripheral events is studied as a function of the transverse momentum of the produced

K_{S}^{0}

mesons. A non-trivial dependence of the entropy on the collision energy with decreasing transverse momentum is found. This reflects the irregularity of the behavior of the specific heat,

c_{AuAu}

, and can point to a manifestation of phase transition in nuclear matter. Full article

(This article belongs to the Special Issue From Heavy Ions to Astroparticle Physics)

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Open AccessArticle

Polarization and Consensus in a Voter Model under Time-Fluctuating Influences

Mauro Mobilia

Physics 2023, 5(2), 517-536; https://doi.org/10.3390/physics5020037 - 08 May 2023

Abstract

We study the effect of time-fluctuating social influences on the formation of polarization and consensus in a three-party community consisting of two types of voters (“leftists” and “rightists”) holding extreme opinions, and moderate agents acting as “centrists”. The former are incompatible and do not interact, while centrists hold an intermediate opinion and can interact with extreme voters. When a centrist and a leftist/rightist interact, they can become either both centrists or both leftists/rightists. The population eventually either reaches consensus with one of the three opinions, or a polarization state consisting of a frozen mixture of leftists and rightists. As a main novelty, here agents interact subject to time-fluctuating external influences favouring in turn the spread of leftist and rightist opinions, or the rise of centrism. The fate of the population is determined under various scenarios, and it is shown how the rate of change of external influences can drastically affect the polarization and consensus probabilities, as well as the mean time to reach the final state. Full article

(This article belongs to the Special Issue In Honor of Professor Serge Galam for His 70th Birthday and Forty Years of Sociophysics)

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Open AccessCommunication

MPD TPC Alignment

Valentin Kuzmin

Physics 2023, 5(2), 508-516; https://doi.org/10.3390/physics5020036 - 23 Apr 2023

Abstract

A method of determining the position of the readout sectors of a time projection chamber using experimental data is proposed. Considering the results of modeling the response of sensitive elements of the time projection chamber of the multipurpose detector, three types of tracks were reconstructed: cosmic muons, beams of the laser detector system, and muons from the interaction of nuclei. Employing data from the experiment simulation and the proposed method of finding the position and orientation of sectors of the time projection chamber, the accuracy of the chamber alignment is investigated. For cosmic and laser rays, the accuracy is approximately the same. It is about 750 microns for the shift of the origin of the sector and 7 arc minutes for Euler angles. The accuracy in the case of muons born in collisions of nuclei is several times worse. Full article

(This article belongs to the Special Issue From Heavy Ions to Astroparticle Physics)

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Open AccessCommunication

The Scattering and Neutrino Detector at the Large Hadron Collider in CERN

Natalia Polukhina

Nina Konovalova

and

Tatiana Shchedrina

Physics 2023, 5(2), 499-507; https://doi.org/10.3390/physics5020035 - 20 Apr 2023

Abstract

[email protected] (Scattering Neutrino Detector at the Large Hadron Collider) is a compact and stand-alone experiment to perform measurements with neutrinos produced in the LHC in a hitherto unexplored pseudorapidity region of 7.2 < η < 8.6. The experiment is located in the Tl18 (Target line 18) LHC tunnel, 480 m downstream of the ATLAS detector interaction point. The [email protected] detector is composed of a hybrid system based on an 800 kg target mass of tungsten plates, interleaved with emulsion and electronic trackers, followed downstream by a muon system. This configuration allows us to distinguish all three neutrino flavors, opening a unique opportunity to probe the physics of heavy flavor production in the LHC in a region that is not accessible to the ATLAS, CMS, LHCb and FASER experiments. The detector concept is also well suited to searching for feebly interacting particles via signatures of scattering in the detector target. The first phase of the experiment has been carried out during the ongoing LHC Run 3, and the first data of the LHC Run3 commissioning period are being processed and analyzed. Full article

(This article belongs to the Special Issue From Heavy Ions to Astroparticle Physics)

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Open AccessCommunication

Using the Two-Phase Emission Detector RED-100 at NPP to Study Coherent Elastic Neutrinos Scattering off Nuclei

RED-100 Collaboration

Physics 2023, 5(2), 492-498; https://doi.org/10.3390/physics5020034 - 20 Apr 2023

Abstract

The two-phase emission detector RED-100 with 130 kg of liquid xenon as a working medium has been exhibited at a distance of 19 m from the core of the VVER-1000/320 nuclear power reactor at the fourth power unit of the Kalinin Nuclear Plant Power in 2021–2022. Due to the high sensitivity of the detector for weak ionization signals (down to single electrons), the detector has been used to search for the elastic coherent scattering of reactor electron antineutrinos off xenon nuclei. However, the observation of ~30 kHz single-electron noise did not quite allow for an effective selection of the useful events. The next experiment with the RED-100 detector is considered to be arranged with 62 kg of liquid argon as a working medium. The advantages of this approach are discussed in this paper. Full article

(This article belongs to the Special Issue From Heavy Ions to Astroparticle Physics)

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Open AccessCommunication

Machine Learning Approach for Event Position Reconstruction in the DEAP-3600 Dark Matter Search Experiment

DEAP Collaboration

Physics 2023, 5(2), 483-491; https://doi.org/10.3390/physics5020033 - 19 Apr 2023

Abstract

In addition to classical analytical data processing methods, machine learning methods are widely used for data analysis in elementary particle physics. Most often, such techniques are used to identify a particular class of events (the classification problem) or to predict a certain event parameter (the regression problem). Here, we present the result of using a machine learning model to solve the regression problem of event position reconstruction in the DEAP-3600 dark matter search detector. A neural network was used as a machine learning model. Improving the position resolution will improve the reduction in background events, while increasing the signal acceptance for weakly interacting massive particles. Full article

(This article belongs to the Special Issue From Heavy Ions to Astroparticle Physics)

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Open AccessArticle

p-Mode Oscillations in Highly Gravitationally Stratified Magnetic Solar Atmospheres

and

Physics 2023, 5(2), 461-482; https://doi.org/10.3390/physics5020032 - 18 Apr 2023

Cited by 1

Abstract

The aim of the study reported in this paper is to gain understanding of solar global oscillations and the propagation characteristics of p-mode oscillations in the highly gravitationally stratified magnetic solar atmosphere. The paper presents the results of 3D (3-dimensional) numerical magnetohydrodynamic (MHD) simulations of a model solar atmosphere with a uniform, vertical and cylindrically symmetric magnetic field. We use simulation drivers which result in oscillations mimicking the behaviour of p-mode oscillations. The paper reports the variation of the energy flux and oscillation frequency of the magnetosonic modes and examines their dependence on the magnetic field strength. We report results for the temporal analysis of observational data for the quiet Sun and for a region containing a small sunspot (solar pore). We compare the temporal analysis of results from observations of these ubiquitous intensity oscillations with numerical simulations of potential signatures of global oscillations of the solar atmosphere. We conclude that magnetic regions of the solar atmosphere are favourable regions for the propagation of a small leakage of energy by slow magnetosonic modes. The results also exhibit a variation in the frequency of the oscillations at different heights in the low-to-mid solar atmosphere and for different values of the magnetic field. The numerically obtained periodic behaviour and variation in frequency, even in this simplified model atmosphere, is consistent with the observational data. We find frequencies and frequency variations that are similar to measurements obtained from the intensity time series of images taken by the Solar Dynamics Observatory. Full article

(This article belongs to the Special Issue A Themed Issue in Honor of Professor Marcel Goossens on the Occasion of His 75th Birthday)

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Open AccessReview

An Introduction to Noncommutative Physics

Shi-Dong Liang

and

Matthew J. Lake

Physics 2023, 5(2), 436-460; https://doi.org/10.3390/physics5020031 - 18 Apr 2023

Abstract

Noncommutativity in physics has a long history, tracing back to classical mechanics. In recent years, many new developments in theoretical physics, and in practical applications rely on different techniques of noncommutative algebras. In this review, we introduce the basic concepts and techniques of noncommutative physics in a range of areas, including classical physics, condensed matter systems, statistical mechanics, and quantum mechanics, and we present some important examples of noncommutative algebras, including the classical Poisson brackets, the Heisenberg algebra, Lie and Clifford algebras, the Dirac algebra, and the Snyder and Nambu algebras. Potential applications of noncommutative structures in high-energy physics and gravitational theory are also discussed. In particular, we review the formalism of noncommutative quantum mechanics based on the Seiberg–Witten map and propose a parameterization scheme to associate the noncommutative parameters with the Planck length and the cosmological constant. We show that noncommutativity gives rise to an effective gauge field, in the Schrödinger and Pauli equations. This term breaks translation and rotational symmetries in the noncommutative phase space, generating intrinsic quantum fluctuations of the velocity and acceleration, even for free particles. This review is intended as an introduction to noncommutative phenomenology for physicists, as well as a basic introduction to the mathematical formalisms underlying these effects. Full article

(This article belongs to the Special Issue New Advances in Quantum Geometry)

Open AccessArticle

Genetic Algorithm for Determination of the Event Collision Time and Particle Identification by Time-of-Flight at NICA SPD

Semyon Yurchenko

and

Mikhail Zhabitsky

Physics 2023, 5(2), 423-435; https://doi.org/10.3390/physics5020030 - 17 Apr 2023

Abstract

Particle identification is an important feature of the future SPD (Spin Physics Detector) experiment at the NICA (Nuclotron-based Ion Collider fAcility) collider. In particular, the identification of particles with momenta up to a few

GeV / c

(with c the speed of light) [...] Read more.

GeV / c

(with c the speed of light) by their time-of-flight facilitates the reconstruction of events of interest. The high time resolution of modern TOF (Time-Of-Flight) detectors demands the need to obtain the event collision time,

t_{0}

, with comparable accuracy. While the determination of the collision time is feasible through the use of TOF signals supplemented by track reconstruction, it proves to be computationally expensive. In the presented study, a dedicated Genetic Algorithm is developed as a fast and accurate method to determine the proton–proton collision time by the measurements of the TOF detector at the SPD experiment. By using this reliable method for the

t_{0}

determination we compare different approaches for the particle identification procedure based on TOF signals. Full article

(This article belongs to the Special Issue From Heavy Ions to Astroparticle Physics)

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Open AccessArticle

The Asymmetric Dynamical Casimir Effect

Matthew J. Gorban

William D. Julius

and

Gerald B. Cleaver

Physics 2023, 5(2), 398-422; https://doi.org/10.3390/physics5020029 - 11 Apr 2023

Abstract

A mirror with time-dependent boundary conditions will interact with the quantum vacuum to produce real particles via a phenomenon called the dynamical Casimir effect (DCE). When asymmetric boundary conditions are imposed on the fluctuating mirror, the DCE produces an asymmetric spectrum of particles. We call this the asymmetric dynamical Casimir effect (ADCE). Here, we investigate the necessary conditions and general structure of the ADCE through both a waves-based and a particles-based perspective. We review the current state of the ADCE literature and expand upon previous studies to generate new asymmetric solutions. The physical consequences of the ADCE are examined, as the imbalance of particles produced must be balanced with the subsequent motion of the mirror. The transfer of momentum from the vacuum to macroscopic objects is discussed. Full article

(This article belongs to the Special Issue Vacuum Fluctuations)

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Open AccessCommunication

Feasibility Study of Hypernucleus Production at NICA/MPD

and

Physics 2023, 5(2), 391-397; https://doi.org/10.3390/physics5020028 - 11 Apr 2023

Abstract

The NICA (Nuclotron-based Ion Collider fAcility) project at the Joint Institute for Nuclear Research (JINR, Dubna, Russia) is aimed at the construction of a new accelerator complex for heavy ions and polarized particles. Heavy-ion collisions at NICA are planned to be studied in the region of the highest net-baryon density, which favors the formation of bound nuclear systems with strangeness hypernuclei. The multipurpose detector (MPD) at NICA is designed to reconstruct interactions of relativistic nuclei in a high-multiplicity environment. In this paper, we report the feasibility study results for the reconstruction of

_{Λ}^{3}

_{Λ}^{4}

H and

_{Λ}^{4}

He in Bi+Bi collisions at the nucleon-nucleon center-of-mass energy,

\sqrt{s_{N N}} =

9.2 GeV. Full article

(This article belongs to the Special Issue From Heavy Ions to Astroparticle Physics)

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Open AccessCommunication

Clustering in Oxygen Nuclei and Spectator Fragments in ¹⁶O–¹⁶O Collisions at the LHC

Aleksandr Svetlichnyi

Savva Savenkov

Roman Nepeivoda

and

Igor Pshenichnov

Physics 2023, 5(2), 381-390; https://doi.org/10.3390/physics5020027 - 04 Apr 2023

Abstract

A new version of the Abrasion–Ablation Monte Carlo for Colliders model with the Minimum Spanning Tree clusterization algorithm (AAMCC-MST) is used to simulate

^{16}

O–

^{16}

O collisions at the LHC, accounting for the presence of alpha-clustered states in

^{16}

O. The yields [...] Read more.

A new version of the Abrasion–Ablation Monte Carlo for Colliders model with the Minimum Spanning Tree clusterization algorithm (AAMCC-MST) is used to simulate

^{16}

O–

^{16}

O collisions at the LHC, accounting for the presence of alpha-clustered states in

^{16}

O. The yields of He, Li, Be, B, C and N spectator nuclei are calculated taking into account the pre-equilibrium clusterization of spectator matter and short-range correlations (SRC) between nucleons in

^{16}

O. The impact of

α

-clustering and SRC on the production of spectator neutrons and deuterons is investigated. The results on the production of spectator nucleons and fragments can help in evaluating the performance of Zero Degree Calorimeters in future studies of

^{16}

O–

^{16}

O collisions at the LHC. Full article

(This article belongs to the Special Issue From Heavy Ions to Astroparticle Physics)

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Open AccessReview

Isospin-Symmetry Breaking within the Nuclear Shell Model: Present Status and Developments

Nadezda A. Smirnova

Physics 2023, 5(2), 352-380; https://doi.org/10.3390/physics5020026 - 31 Mar 2023

Abstract

The paper reviews the recent progress in the description of isospin-symmetry breaking within the nuclear shell model and applications to actual problems related to the structure and decay of exotic neutron-deficient nuclei and nuclei along the

N = Z

line, where N is [...] Read more.

N = Z

line, where N is the neutron number and Z the atomic number. The review recalls the fundamentals of the isospin formalism for two-nucleon and many-nucleon systems, including quantum numbers, the spectrum’s structure and selection rules for weak and electromagnetic transitions; and at the end, summarizes experimental signatures of isospin-symmetry breaking effects, which motivated efforts towards the creation of a relevant theoretical framework to describe those phenomena. The main approaches to construct accurate isospin-nonconserving Hamiltonians within the shell model are briefly described and recent advances in the description of the structure and (isospin-forbidden) decay modes of neutron-deficient nuclei are highlighted. The paper reviews major implications of the developed theoretical tools to (i) the fundamental interaction studies on nuclear decays and (ii) the estimation of the rates of nuclear reactions that are important for nuclear astrophysics. The shell model is shown to be one of the most suitable approaches to describing isospin-symmetry breaking in nuclear states at low energies. Further efforts in extending and refining the description to larger model spaces, and in developing first-principle theories to deal with isospin-symmetry breaking in many-nucleon systems, seem to be indispensable steps towards our better understanding of nuclear properties in the precision era. Full article

(This article belongs to the Special Issue The Nuclear Shell Model 70 Years after Its Advent: Achievements and Prospects)

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Open AccessArticle

Nonlinear Coupling of Alfvén and Slow Magnetoacoustic Waves in Partially Ionized Solar Plasmas: The Effect of Thermal Misbalance

José Luis Ballester

Physics 2023, 5(2), 331-351; https://doi.org/10.3390/physics5020025 - 30 Mar 2023

Cited by 1

Abstract

Solar chromosphere and photosphere, as well as solar atmospheric structures, such as prominences and spicules, are made of partially ionized plasmas. Observations have reported the presence of damped or amplified oscillations in these solar plasmas, which have been interpreted in terms of magnetohydrodynamic (MHD) waves. Slow magnetoacoustic waves could be responsible for these oscillations. The present study investigates the temporal behavior of the field-aligned motions that represent slow magnetoacoustic waves excited in a partially ionized prominence plasma by the ponderomotive force. Starting from single-fluid MHD equations, including radiative losses, a heating mechanism and ambipolar diffusion, and using a regular perturbation method, first- and second-order partial differential equations have been derived. By numerically solving second-order equations describing field-aligned motions, the temporal behavior of the longitudinal velocity perturbations is obtained. The damping or amplification of these perturbations can be explained in terms of heating–cooling misbalance, the damping effect due to ambipolar diffusion and the variation of the first adiabatic exponent with temperature and ionization degree. Full article

(This article belongs to the Special Issue A Themed Issue in Honor of Professor Marcel Goossens on the Occasion of His 75th Birthday)

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Open AccessCommunication

Finite-Size Effects of Casimir–van der Waals Forces in the Self-Assembly of Nanoparticles

Raul Esquivel-Sirvent

Physics 2023, 5(1), 322-330; https://doi.org/10.3390/physics5010024 - 21 Mar 2023

Abstract

Casimir–van der Waals forces are important in the self-assembly processes of nanoparticles. In this paper, using a hybrid approach based on Lifshitz theory of Casimir–van der Waals interactions and corrections due to the shape of the nanoparticles, it is shown that for non-spherical nanoparticles, the usual Hamaker approach overestimates the magnitude of the interaction. In particular, the study considers nanoplates of different thicknesses, nanocubes assembled with their faces parallel to each other, and tilted nanocubes, where the main interaction is between edges. Full article

(This article belongs to the Special Issue Vacuum Fluctuations)

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Open AccessArticle

Resonant Fast-Alfvén Wave Coupling in a 3D Coronal Arcade

Andrew Wright

and

Thomas Elsden

Physics 2023, 5(1), 310-321; https://doi.org/10.3390/physics5010023 - 17 Mar 2023

Abstract

The resonant excitation of Alfvén waves using the fast magnetosonic mode is important in space plasmas. In this paper, we consider a simple model of a three-dimensional (3D) coronal arcade. A numerical approach is used to produce a driven normal mode. We find that resonant coupling can occur in 3D, but there are new features that are absent in 2D. In particular, the polarisation of the Alfvén waves can vary with position throughout the Resonant Zone. Moreover, there are an infinite number of possible paths the resonant waves can exist on. Full article

(This article belongs to the Special Issue A Themed Issue in Honor of Professor Marcel Goossens on the Occasion of His 75th Birthday)

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Open AccessArticle

On the Use and Misuse of the Oberbeck–Boussinesq Approximation

Antonio Barletta

Michele Celli

and

D. Andrew S. Rees

Physics 2023, 5(1), 298-309; https://doi.org/10.3390/physics5010022 - 17 Mar 2023

Cited by 1

Abstract

The Oberbeck–Boussinesq approximation is the most commonly employed theoretical scheme for the study of natural or mixed convection flows. However, the misunderstanding of this approximated framework is a possibility that may cause the emergence of paradoxes or, at least, incorrect conclusions. In this paper, the basic features of the Oberbeck–Boussinesq approximation are briefly recalled and three simple examples where this theoretical scheme may be misused are provided. Such misuses of the approximation lead to erroneous conclusions that, in the examples presented in this note, entail violations of the principle of mass conservation. A discussion about the Oberbeck–Boussinesq approximation as an asymptotic theory obtained by letting the product of the thermal expansion coefficient and the reference temperature difference tend to zero is also presented. Full article

(This article belongs to the Section Statistical Physics and Nonlinear Phenomena)

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Open AccessArticle

The Interplay between Coronal Holes and Solar Active Regions from Magnetohydrostatic Models

Jaume Terradas

Physics 2023, 5(1), 276-297; https://doi.org/10.3390/physics5010021 - 28 Feb 2023

Abstract

Coronal holes (CHs) and active regions (ARs) are typical magnetic structures found in the solar corona. The interaction of these two structures was investigated mainly from the observational point of view, but a basic theoretical understanding of how they are connected is missing. To address this problem, in this paper, magnetohydrostatic models are constructed by numerically solving a Grad–Shafranov equation in two dimensions. A common functional form for the pressure and temperature in the CH and in the AR are assumed throught the study. Keeping the parameters of the CH constant and modifying the parameters of the nearby bipolar AR, one finds essentially three types of solutions depending on the magnitude and sign of the magnetic field at the closest foot of the AR to the CH. Two of the three solutions match well with the observation, but the third solution predicts the existence of closed magnetic field lines with quite low density and temperature with opposite characteristics to those in typical ARs. Simple analytical expressions are obtained for the pressure, temperature and density at the core of the AR and their dependence upon several major physical parameters are studied. The results obtained in this paper need to be contrasted with observations. Full article

(This article belongs to the Special Issue A Themed Issue in Honor of Professor Marcel Goossens on the Occasion of His 75th Birthday)

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