Stability estimate for an inverse problem for the magnetic Schrödinger equation from the Dirichlet-to-Neumann map

We consider the problem of stability estimate of the inverse problem of determining the magnetic field entering the magnetic Schrödinger equation in a bounded smooth domain of Rn with input Dirichlet data, from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated to the solutions of the magnetic Schrödinger equation. We prove in dimension n?2 that the knowledge of the Dirichlet-to-Neumann map for the magnetic Schrödinger equation measured on the boundary determines uniquely the magnetic field and we prove a Hölder-type stability in determining the magnetic field induced by the magnetic potential.     

Two-dimensional magnetic solitons and thermodynamics of quasi-two-dimensional magnets

The article reviews two-dimensional magnetic solitons in a classical weakly-anisotropic Heisenberg magnets. Topological classification, structure, dynamical properties and thermodynamical contribution of 2D solitons to response functions of the magnet are discussed. Based on effective equations of motion we calculated the soliton contribution to the dynamical structure factor of ferromagnets and antiferromagnets both for localized topological solitons and magnetic vortices.     

The Theory of Closed 1-Forms,Levels of Quasiperiodic Functions and Transport Phenomena in Electron Systems

The paper is devoted to the applications of the theory of dynamical systems to the theory of transport phenomena in metals in the presence of strong magnetic fields. More precisely, we consider the connection between the geometry of the trajectories of dynamical systems arising at the Fermi surface in the presence of an external magnetic field and the behavior of the conductivity tensor in a metal in the limit ω_Bτ →∞. We describe the history of the question and investigate special features of such behavior in the case of the appearance of trajectories of the most complex type on the Fermi surface of a metal.     

低频交变磁场对于刚性直圆管中脉动流的影响*

本文通过求解灾变磁场作用下刚性直圆管脉动流的运动方程,得到了它的分析解.计算了流速分布及阻抗.计算结果对于深入了解低频磁场对于血液动力学的影响以及它的临床应用具有一定参考价值.     

Magnetic Catalysis of the P-Parity-Breaking Phase Transition of the First Order and High-Temperature Superconductivity

In the framework of a (2+1)-dimensional P-even gauge theory based on the massive Gross–Neveu model, we show that an external magnetic field induces the P-parity-breaking phase transition of the first order. A dynamical generation of the Chern–Simons term and fractional particle spin and statistics occurs at the critical point. The results in the paper can be interesting in connection with recently discovered phase transitions in high-temperature superconductors.     

Long-Time Stabilization of Solutions to the Ginzburg–Landau Equations of Superconductivity

 The long-time dynamical properties of solutions (φ,A) to the time-dependent Ginzburg–Landau (TDGL) equations of superconductivity are investigated. The applied magnetic field varies with time, but it is assumed to approach a long-time asymptotic limit. Sufficient conditions (in terms of the time rate of change of the applied magnetic field) are given which guarantee that the dynamical process defined by the TDGL equations is asymptotically autonomous, i.e., it approaches a dynamical system as time goes to infinity. Analyticity of an energy functional is used to show that every solution of the TDGL equations asymptotically approaches a (single) stationary solution of the (time-independent) Ginzburg–Landau equations. The standard “φ = − ∇ · A” gauge is chosen. (Received 30 June 2000; in revised form 30 December 2000)     

Long-Time Stabilization of Solutions to the Ginzburg–Landau Equations of Superconductivity

 The long-time dynamical properties of solutions (φ,A) to the time-dependent Ginzburg–Landau (TDGL) equations of superconductivity are investigated. The applied magnetic field varies with time, but it is assumed to approach a long-time asymptotic limit. Sufficient conditions (in terms of the time rate of change of the applied magnetic field) are given which guarantee that the dynamical process defined by the TDGL equations is asymptotically autonomous, i.e., it approaches a dynamical system as time goes to infinity. Analyticity of an energy functional is used to show that every solution of the TDGL equations asymptotically approaches a (single) stationary solution of the (time-independent) Ginzburg–Landau equations. The standard “φ = − ∇ · A” gauge is chosen.     

A product estimate for Ginzburg–Landau and application to the gradient-flow

We prove a new inequality for the Jacobian (or vorticity) associated to the Ginzburg–Landau energy in any dimension, and give static and dynamical corollaries. We then present a method to prove convergence of gradient-flows of families of energies which Gamma-converge to a limiting energy, which we apply to establish, thanks to the previous dynamical estimate, the limiting dynamical law of a finite number of vortices for the heat-flow of Ginzburg–Landau in dimension 2, with and without magnetic field. To cite this article: E. Sandier, S. Serfaty, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Magnetic Susceptibility of the Random One- Dimensional Transverse Ising Model

We study the 1- dimensional Ising model with random coupling constants in the presence of a transverse magnetic field h. In the nonrandom (translationally invariant) case it is known that there is a value of h for which the magnetic susceptibility diverges logarithmically. We demonstrate that in the random case this logarithmic divergence is smoothed out into an infinitely differentiable essential singularity.     

磁性刚体航天器的混沌姿态运动

研究在地球万有引力场和磁场中的磁性刚体航天器在圆轨道上的混沌姿态运动。利用动量矩原理建立了系统的动力学模型。应用Melnikov方法证明了存在复杂非游荡Cantor集。分别采用时间历程、功率谱、Poincaré映射和Liapunov指数对系统动力学行为进行了数值研究。数值仿真表明,随着磁场力矩的增强,系统准周期环面破裂而出现混沌。     

On the refined modeling of the force distribution in a bistable magnetoelastic energy harvesting system due to a magnetic field

Abstract: The problem of a bistable magnetoelastic beam under base excitation was discussed in [1] under the aspect of chaotic behaviour in mechanical systems. Three decades later the system was used in [2] to design an energy harvesting system which performs well under harmonic excitation for a broad range of excitation frequencies due to its bistability. The initial modeling was tailored to obtain a model with one degree of freedom based on the assumption that the magnetic force acts on the beam tip only. A more appropriate model can be found when considering a distributed force along the beam. The authors present the force distribution on a ferromagnetic beam due to the magnetic field of two permanent magnets. A semi-analytic method is used to compute the magnetic field. The force distribution can in future be used to derive a refined nonlinear dynamical model for the ferromagnetic elastic beam. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamical Spin Susceptibility in the <Emphasis Type="Italic">t-J</Emphasis> Model: The Memory Function Method

Based on the method of the equations of motion for the relaxation function in terms of Hubbard operators, we evaluate the dynamical spin susceptibility for the t-J model in the paramagnetic phase. Using a Mori-type projection technique, we express the relaxation function in terms of the second-order memory function, which is evaluated in the approximation of coupled modes for hole excitations and spin fluctuations in the fourth order in the hopping parameter t and the exchange interaction J. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 2, pp. 240–255, November, 2005.     

Algebra with polynomial commutation relations for the Zeeman-Stark effect in the hydrogen atom

We study the Zeeman-Stark effect for the hydrogen atom in crossed homogeneous electric and magnetic fields. A nonhomogeneous perturbing potential can also be present. If the crossed fields satisfy some resonance relation, then the degeneration in the resonance spectral cluster is removed only in the second-order term of the perturbation theory. The averaged Hamiltonian in this cluster is expressed in terms of generators of some dynamical algebra with polynomial commutation relations; the structure of these relations is determined by a pair of coprime integers contained in the resonance ratio. We construct the irreducible hypergeometric representations of this algebra. The averaged spectral problem in the irreducible representation is reduced to a second-or third-order ordinary differential equation whose solutions are model polynomials. The asymptotic behavior of the solution of the original problem concerning the Zeeman-Stark effect in the resonance cluster is constructed using the coherent states of the dynamical algebra. We also describe the asymptotic behavior of the spectrum in nonresonance clusters, where the degeneration is already removed in the first-order term of the perturbation theory.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 3, pp. 530–555, March, 2005.     

纵向磁场激励下简支输流微梁的动力学行为研究

受磁场驱动的微机电系统在工作中存在着力、磁、流-固耦合等非线性特征，其力学行为非常复杂，并将影响系统运行的安全性与可靠性.该文采用非局部Euler梁模型研究磁场激励下简支输流微梁（一种微机电系统）的动力学行为，通过动力系统分支理论和谐波平衡法来考察系统的稳定性和幅频特性曲线.结果表明，可以采用改变磁场强度、流速和阻尼的三重方式调节微机电系统的频率.研究中还发现，小尺度效应和磁场强度可以影响临界流速，阻尼的存在可以改变临界流速的个数和系统的分岔类型.     

具有结构内阻尼磁性刚体航天器姿态动力学稳定性分析

在地球引力场和磁场中,在考虑了航天器结构内阻尼及气体阻力的影响条件下,研究磁性刚体航天器在绕地球圆轨道运行时可能出现的混沌问题.根据动量矩定理建立动力学模型,应用Melnikov方法证明了动力系统在一定条件下会发生混沌行为,并且给出了解析判据.最后利用数值仿真分析了系统的动力学行为,理论结果与数值仿真结果相一致.     

Exact solution for the thermodynamics of the one-dimensional Hubbard model with infinite repulsion in a magnetic field

We demonstrate that in the limit of infinite repulsion in a magnetic field, the canonical partition function of the one-dimensional Hubbard model in the nearest-neighbor approximation factors into the product of partition functions of holons and spinons, which can be calculated exactly. We thus obtain exact numerical dependences of the free energy, entropy, internal energy, specific heat, chemical potential, and magnetic susceptibility on the hole concentration, temperature, and magnetic field induction.     

Static Theory for Planar Ferromagnets and Antiferromagnets

Here we generalize the “BBH”-asymptotic analysis to a simplified mathematical model for the planar ferromagnets and antiferromagnets. To develop such a static theory is a necessary step for a rigorous mathematical justification of dynamical laws for the magnetic vortices formally derived in [1] and [2]. Received March 15, 2001, Accepted May 16, 2001     

Simulating the effect of external helical magnetic fields on MHD stability of tokamak plasma

The effect of external helical magnetic fields on the stability of a rotating plasma in an axially symmetric tokamak machine is simulated numerically. Threshold amplitude effects are investigated using the NFTC code for the complete nonlinear dynamical 3-D system of MHD equations. The research was partially funded by Russian Foundation of Basic Research (grant 96-07-89110) and Ministry of Science grants 201.03.002 and 0201.03.003. Translated from Chislennye Metody i Vychislitel'nyi Eksperiment, Moscow State University, pp. 4–14, 1998.     

Gamma‐convergence of gradient flows with applications to Ginzburg‐Landau

We present a method to prove convergence of gradient flows of families of energies that Γ‐converge to a limiting energy. It provides lower‐bound criteria to obtain the convergence that correspond to a sort of C¹‐order Γ‐convergence of functionals. We then apply this method to establish the limiting dynamical law of a finite number of vortices for the heat flow of the Ginzburg‐Landau energy in dimension 2, retrieving in a different way the existing results for the case without magnetic field and obtaining new results for the case with magnetic field. © 2004 Wiley Periodicals, Inc.     

Study of the size-flux relation of pores and spots

Using the vector magnetic field data from the Huairou Solar Observing Station of National Astronomical Observatories, a statistical study on the size-flux relation of photospheric magnetic features without any assumption is given. The selected data here include mature sunspots, as well as protosunspot (with a partial penumbra) and pore. We studied not only their size-flux relations of pore, protosunspot and mature sunspot, but also that of umbra and penumbra of the mature sunspots. The size-flux relationship of mature sunspots and their umbra and penumbra is found to be in different indexes of power-law. No evident relations are found between size and flux of the pores and protosunspots. We found that there is a threshold of 1×10¹² Wb or (3–4.03) × 10⁷ km² for the transition from a pore to a protospot. Such results may be useful for understanding the physical conditions and dynamical processes of magnetic flux tubes in solar plasma during sunspot’s formation. In addition, their characteristic size is also given.