MULTIPLE SOLUTIONS TO CRITICAL MAGNETIC SCHRODINGER EQUATIONS

In this paper,we are concerned with the existence of multiple solutions to the critical magnetic Schrödinger equation(-i▽-a(x))^(2)u+⒂λV(x)u=p|u|^(p-2)u+(∫R(n)|u(y)|^(2)_(a)^(*)/|x-y|^(a)dy)|u|2_(a)^(*)-2_(u)in R^(N),(0.1)where N≥4,2≤p<2^(*),2_α^(*)=(2N-α)/(N-2)with 0<α<4,λ>0,μ∈R,A(x)=(A_(1)(x),A_(2)(x),…,A_(N)(x))is a real local Hölder continuous vector function,i is the imaginary unit,and V(x)is a real valued potential function on R^(N).Supposing thatΩ=int V^(-1)(0)■R^(N)is bounded,we show that problem(0.1)possesses at least cat_(Ω)(Ω)nontrivial solutions ifλis large.

An Explanation of the Temperature-Dependent Upper Critical Field Data of H3S on the Basis of the Thermodynamics of a Superconductor in a Magnetic Field

Excellent fits to a couple of the data-sets on the temperature (T)-dependent upper critical field (Hc2) of H3S (critical temperature, Tc ≈ 200 K at pressure ≈ 150 GPa) reported by Mozaffari, et al. (2019) were obtained by Talantsev (2019) in an approach based on an ingenious mix of the Ginzberg-Landau (GL), the Werthamer, Helfand and Hohenberg (WHH), and the Gor’kov, etc., theories which have individually been employed for the same purpose for a long time. Up to the lowest temperature (TL) in each of these data-sets, similarly accurate fits have also been obtained by Malik and Varma (2023) in a radically different approach based on the Bethe-Salpeter equation (BSE) supplemented by the Matsubara and the Landau quantization prescriptions. For T TL, however, while the (GL, WHH, etc.)-based approach leads to Hc2(0) ≈ 100 T, the BSE-based approach leads to about twice this value even at 1 K. In this paper, a fit to one of the said data-sets is obtained for the first time via a thermodynamic approach which, up to TL, is as good as those obtained via the earlier approaches. While this is interesting per se, another significant result of this paper is that for T TL it corroborates the result of the BSE-based approach.

On the magnetic anomaly at Easter Island during the 2010 Chile tsunami

A magnetic anomaly was recorded at Easter Island on 27 February 2010 during the Chile tsunami event. The physics of the magnetic anomaly is analyzed using kinematic dynamo theory. Using a single wave model, the space and time behavior of the magnetic field is given. By joint analysis of the magnetic observations, tide gauge data and numerical results of the global tsunami propagation, we show the close resemblance between the predicted spatial and temporal magnetic distributions and the field data, indicating the magnetic anomaly at Easter Island was actually induced by the motion of seawater under tsunami waves. Similarity between the field magnetic data at Easter Island during 2010 Chile tsunami and sea surface level is verified with realistic tsunami propagating model.

Maximum mass of magnetic white dwarfs

We revisit the problem of the maximum masses of magnetized white dwarfs （WDs）. The impact of a strong magnetic field on the structure equations is addressed. The pressures become anisotropic due to the presence of the magnetic field and split into parallel and perpendicular components. We first construct stable solutions of the Tolman-Oppenheimer-Volkoff equations for parallel pressures and find that physical solutions vanish for the perpendicular pressure whenB ≥ 10^13 G. This fact estab- lishes an upper bound for a magnetic field and the stability of the configurations in the （quasi） spherical approximation. Our findings also indicate that it is not possible to obtain stable magnetized WDs with super-Chandrasekhar masses because the val- ues of the magnetic field needed for them are higher than this bound. To proceed into the anisotropic regime, we can apply results for structure equations appropriate for a cylindrical metric with anisotropic pressures that were derived in our previous work. From the solutions of the structure equations in cylindrical symmetry we have con- firmed the same bound for B- 10^13 G, since beyond this value no physical solutions are possible. Our tentative conclusion is that massive WDs with masses well beyond the Chandrasekhar limit do not constitute stable solutions and should not exist.

Quark stars with strong magnetic fields: considering different magnetic field geometries

We calculate the mass-radius relationship of quark stars with the magnetized density- dependent quark mass model in this work, considering two magnetic field geometries： a statistically isotropic, tangled field and a force-free configuration. In both cases, magnetic field production decreases in the case of maximum quark star mass. Furthermore, a tangled, isotropic magnetic field has a relatively smaller impact on the mass and radius, compared to the force-free configuration, which implies that the geometry of the interior magnetic field is at least as important as the field strength itself when the influ- ence of the strong magnetic field on the mass and radius is assessed.

CALCULATION OF THE MAGNETIZATION AND MAGNETOCALORIC EFFECT IN THE MnFeP_(0.45)As_(0.55) COMPOUND

A magnetic state equation of the MnFeP0.45As0.55 compound has been obtained by minimizing the Gibbs free energy with respect to the volume and the magnetization based on the Bean-Rodbell model. The isothermal magnetization of the compound has been calculated using this equation. The magnetic entropy change of the compound was determined from the surface area between the two adjacent isothermal magnetization curves divided by the average temperature. A comparison and an error analysis of the calculated magnetic entropy change and the one determined from the experimental data were given.

Computation of the structure of a magnetized strange quark star

We have calculated some properties of spin polarized strange quark matter（SQM） in a strong magnetic field at zero temperature using the MIT bag model.We showed that the equation of state of spin polarized SQM is stiffer than that for unpolarized cases.We have also computed the structural properties of a spin polarized strange quark star（SQS） and found that the presence of a magnetic field leads to a more stable SQS when compared to the structural properties of an unpolarized SQS.

GLOBAL WELL-POSEDNESSOF A PRANDTL MODEL FROM MHD IN GEVREY FUNCTION SPACES

We consider a Prandtl model derived from MHD in the Prandtl-Hartmann regime that has a damping term due to the effect of the Hartmann boundary layer.A global-in-time well-posedness is obtained in the Gevrey function space with the optimal index 2.The proof is based on a cancellation mechanism through some auxiliary functions from the study of the Prandtl equation and an observation about the structure of the loss of one order tangential derivatives through twice operations of the Prandtl operator.

Anisotropic stellar structure equations for magnetized strange stars

The fact that a fermion system in an external magnetic field breaks the spherical symmetry suggests that its intrinsic geometry is axisymmetric rather than spherical. In this work we analyze the impact of anisotropic pressures, due to the presence of a magnetic field, in the structure equations of a magnetized quark star.We assume a cylindrical metric and an anisotropic energy momentum tensor for the source. We found that there is a maximum magnetic field that a strange star can sustain, closely related to the violation of the virial relations.

Magnetic-structure coupling dynamic model of a ferromagnetic plate parallel moving in air-gap magnetic field

Aiming at the air-gap magnetic field excited by wall armatures,Laplace’s partial differential equation of air-gap magnetic potential is achieved by means of the electromagnetic field theory.According to the magnetic boundary conditions and the method of separation of variables,the magnetic potential of the air-gap magnetic field is obtained.Based on the magnetization force model and Lorentz force of ferromagnetic thin-walled structures,and introducing the electromagnetic constitutive relations and boundary conditions,the calculation model of electromagnetic force of the soft ferromagnetic thin plate moving in air-gap magnetic field is established.Considering geometric nonlinearity,expressions of strain energy and kinetic energy of the elastic thin plate and the work of forces are given,respectively.The magnetic-structure coupling nonlinear vibration equations of ferromagnetic thin plate parallel moving in the air-gap magnetic field excited by armatures are obtained by using the Hamilton principle,which can be of the characterization of the system dynamics model with electro-magneto-velocity-mechanical interaction.Through numerical examples,primary resonance characteristics of the strip thin plate under the action of air-gap magnetic force are obtained.The results show that the two stable amplitude values will increase as amplitude of magnetic potential increases and thickness of air-gap decreases,and the amplitude’s multi-valued region will change due to the varieties of magnetic potential,air-gap and velocity.The model established in this paper is a theoretical reference for investigation on the multi-field coupling dynamic behaviors of structures moving in complex electromagnetic fields.

On the limit behavior of the magnetic Zakharov system

In this paper,we prove that the solutions of magnetic Zakharov system converge to those of generalized Zakharov system in Sobolev space H s,s > 3/2,when parameter β→∞.Further,when parameter (α,β) →∞ together,we prove that the solutions of magnetic Zakharov system converge to those of Schro¨dinger equation with magnetic effect in Sobolev space H s,s > 3/2.Moreover,the convergence rate is also obtained.

Global Well-posedness for the Non-viscous MHD Equations with Magnetic Diffusion in Critical Besov Spaces

In this paper,we mainly investigate the Cauchy problem of the non-viscous MHD equations with magnetic diffusion.We first establish the local well-posedness(existence,uniqueness and continuous dependence)with initial data(u_(0),b_(0))in critical Besov spaces B_(p,1)^(d/p+1)×B_(p,1)^(d/p)with 1≤p≤∞,and give a lifespan T of the solution which depends on the norm of the Littlewood–Paley decomposition(profile)of the initial data.Then,we prove the global existence in critical Besov spaces.In particular,the results of global existence also hold in Sobolev space C([0,∞);H~s(S~2))×(C([0,∞);H^(s-1)(S~2))∩L~2([0,∞);H~s(S~2)))with s>2,when the initial data satisfies∫_(S~2)b_(0)dx=0 and||u_(0)||B_(()∞,1~((S~2)))~1+||b_(0)||B_(()∞,1^(S~2))~0≤ε.It’s worth noting that our results imply some large and low regularity initial data for the global existence.

On the Asymptotic Behavior of Nonlinear Schrodinger Equations with Magnetic Effect

The purpose of this paper is to study the long time asymptotic behavior for a nonlinear Schrdinger equations with magnetic effect. Under certain conditions, we prove the existence and nonexistence of the non-trivial free asymptotic solutions. In addition, the decay estimates of the solutions are also obtained.

Microscopic calculation of the magnetic field of neutron stars

Based on the Dirac equation describing an electron moving in a uniform and cylindrically symmetric magnetic field which may be the result of the self-consistent mean field of the electrons themselves in a neutron star, we have obtained the eigen solutions and the orbital magnetic moments of electrons in which each eigen orbital can be calculated. From the eigen energy spectrum we find that the lowest energy level is the highly degenerate orbitals with the quantum numbers pz = 0, n = 0, and m ≥0. At the ground state, the electrons fill the lowest eigen states to form many Landau magnetic cells and each cell is a circular disk with the radius λfree and the thickness λe, where λfree is the electron mean free path determined by Coulomb cross section and electron density and λe is the electron Compton wavelength. The magnetic moment of each cell and the number of cells in the neutron star are calculated, from which the total magnetic moment and magnetic field of the neutron star can be calculated. The results are compared with the observational data and the agreement is reasonable.

The Grad-Shafranov reconstruction in twenty years: 1996–2016

We review and summarize the applications of the Grad-Shafranov(GS) reconstruction technique to space plasma structures in the Earth's magnetosphere and in the interplanetary space. We organize our presentations following the branches of the "academic family tree" rooted on Prof. Bengt U. ? Sonnerup, the inventor of the GS method. Special attentions are paid to validations of the GS reconstruction results via(1) the direct validation by co-spatial in-situ measurements among multiple spacecraft, and(2) indirect validation by implications and interpretations of the physical connection between the structures reconstructed and other related processes. For the latter, the inter-comparison and interconnection between the large-scale magnetic flux ropes(i.e., Magnetic Clouds) in the solar wind and their solar source properties are presented. In addition, we also summarize various GS-type(or-like) reconstruction and an extension of the GS technique to toroidal geometry. In particular,we point to a possible advancement with added complexity of "helical symmetry" and mixed helicity, in the hope of stimulating interest in future development. We close by offering some thoughts on appreciating the scientific merit of GS reconstruction in general.

Stellar structure of magnetars

Magnetars are strong magnetized neutron stars which could emit quiescent X-ray, repeating burst of soft gamma ray, and even the giant flares. We investigate the effects of magnetic fields on the structure of isolated magnetars. The stellar structure together with the magnetic field configuration can be obtained at the same time within a self-consistent procedure. The magnetar mass and radius are found to be weakly enhanced by the strong magnetic fields. Unlike other previous investigations, the magnetic field is unable to violate the mass limit of the neutron stars.