Biframe bundle geometry and an extension of RMW theory: Application to a charged perfect fluid

An extension of the original Rainich-Misner-Wheeler (RMW) theorem to include Einstein-Maxwell spacetimes with geometrical sources has recently been accomplished by generalizing the geometrical arena from the linear frame bundleLM to the bundle of biframesL ² M. The assumptions of a Riemannian connection one-form onLM and a general connection one-form onL ² M necessarily implies the existence of a difference formK. We provide new algebraic and differential conditions on an arbitrary triple (M, g, K), in addition to those already imposed by the generalization of the RMW theorem, which guarantee the form of the coupled Einstein-Maxwell field equations associated with a charged perfect fluid spacetime. All physical quantities associated with these field equations, namely the Maxwell field strength, the mass-energy density, the pressure, the electric and magnetic charge to mass ratios, and the unit four velocity of the fluid, can be recovered from the geometry as they are constructible entirely from the metricg, the difference formK, and their derivatives.     

Ricci flat rotating black branes with a conformally invariant Maxwell source

We consider Einstein gravity coupled to an U(1) gauge field for which the density is given by a power of the Maxwell Lagrangian. In d-dimensions the action of Maxwell field is shown to enjoy the conformal invariance if the power is chosen as d/4. We present a class of charge rotating solutions in Einstein-conformally invariant Maxwell gravity in the presence of a cosmological constant. These solutions may be interpreted as black brane solutions with inner and outer event horizons or an extreme black brane depending on the value of the mass parameter. Since we are considering power of the Maxwell density, the black brane solutions exist only for dimensions which are multiples of four. We compute conserved and thermodynamics quantities of the black brane solutions and show that the expression of the electric field does not depend on the dimension. Also, we obtain a Smarr-type formula and show that these conserved and thermodynamic quantities of black branes satisfy the first law of thermodynamics. Finally, we study the phase behavior of the rotating black branes and show that there is no Hawking–Page phase transition in spite of conformally invariant Maxwell field.     

Electromagnetic waves in a plane wave background

Source-free Maxwell equations are equivalent to the scalar wave equation. Most of its solutions are singular at infinity. If the nail eigenvector of the background metric is an eigenvector of the Maxwell field, too, the e.m. field is not changed by the plane wave.     

Measured mixer noise temperature and conversion loss of a cryogenic Schottky diode mixer near 800 GHz

We accurately measured the noise temperature and conversion loss of a cryogenically cooled Schottky diode operating near 800 GHz, using the UCB/MPE Submillimeter Receiver at the James Clerk Maxwell Telescope. The receiver temperature was in the range of the best we now routinely measure, 3150 K (DSB). Without correcting for optical loss or IF mismatch, the raw measurements set upper limits ofT _M=2850 K andL _M=9.1 dB (DSB), constant over at least a 1 GHz IF band centered at 6.4 GHz with an LO frequency of 803 GHz. Correction for estimated optical coupling and mismatch effects yieldsT _M=1600 K andL _M=5.5 dB (DSB) for the mixer diode itself. These values indicate that our receiver noise temperature is dominated by the corner cube antenna's optical efficiency and by mixer noise, but not by conversion loss or IF mismatch. The small fractional IF bandwidth, measured mixer IF band flatness from 2 to 8 GHz, and similarly good receiver temperatures at other IF frequencies imply that these values are representative over a range of frequencies near 800 GHz.     

The conservation of source strength in linear field theories and the superpotentials

In linear field theories for vector potentialsAi and tensor potentialsgik=gki, the Maxwell and the linearized Einstein equations are the only field equations from which true conservation laws result for each gauge of the field equations.     

Estimation of the magnetic entropy change by means of Landau theory and phenomenological model in La0.6Ca0.2 Sr0.2MnO3/Sb2O3 ceramic composites

In this paper, magnetocaloric properties of La_0.6Ca_0.2Sr_0.2MnO₃/Sb₂O₃ oxides have been investigated. The composite samples were prepared using the conventional solid-state reaction method. The second-order phase transition can be testified with the positive slope in Arrott plots. An excellent agreement has been found between the ?ΔS_M values estimated by Landau theory and those obtained using the classical Maxwell relation. The field dependence of the magnetic entropy change analysis shows a power law dependence,|ΔS_M|≈Hⁿ , with n(T_C) = 0.65. Moreover, the scaling analysis of magnetic entropy change exhibits that ΔS_M(T) curves collapse into a single universal curve, indicating that the observed paramagnetic to ferromagnetic phase transition is an authentic second-order phase transition. The maximum value of magnetic entropy change of composites is found to decrease slightly with the further increasing of Sb₂O₃ concentration. A phenomenological model was used to predict magnetocaloric properties of La_0.6Ca_0.2Sr_0.2MnO₃/Sb₂O₃ composites. The theoretical calculations are compared with the available experimental data.     

Dirac and Maxwell equations in the Clifford and spin-Clifford bundles

We show how to write the Dirac and the generalized Maxwell equations (including monopoles) in the Clifford and spin-Clifford bundles (of differential forms) over space-time (either of signaturep=1,q=3 orp=3,q=1). In our approach Dirac and Maxwell fields are represented by objects of the same mathematical nature and the Dirac and Maxwell equations can then be directly compared. We show also that all presentations of the Maxwell equations in (matrix) Dirac-like spinor form appearing in the literature can be obtained by choosing particular global idempotents in the bundles referred to above. We investigate also the transformation laws under the action of the Lorentz group of Dirac and Maxwell fields (defined as algebraic spinor sections of the Clifford or spin-Clifford bundles), clearing up several misunderstandings and misconceptions found in the literature. Among the many new results, we exhibit a factorization of the Maxwell field into two-component spinor fields (Weyl spinors), which is important.     

哈斯勒合金Ni-Mn-Sn的马氏体相变与反磁热性质

通过结构以及磁性测量,研究了哈斯勒合金Ni₅₀Mn_25+xSn_25-x (x=11,12)的马氏体相变和磁热性质.结果表明,与样品在奥氏体相的磁性不同,由于在马氏体相中反铁磁交换作用的增强,导致铁磁和反铁磁在马氏体状态下共存.此外,通过Maxwell方程,研究了两样品在不同磁场变化下马氏体相变温度附近的反磁热性质,并阐明了该系列合金产生大的正磁熵变(ΔS_M)不仅与其在降温过程中发生马氏体相变所导致的磁跃变(ΔM)有关,而且与发生马氏体相变所经历的温度区间有密切的联系. 关键词： 哈斯勒合金 Ni-Mn-Sn 马氏体相变 正磁熵变     

Implementing 2→<Emphasis Type="Italic">M</Emphasis> Phase-covariant Cloning in Spin Networks

We propose a scheme to implement 2→M phase-covariant quantum cloning machine by using a M+2 spin star network in which the two central spins interact with the M outer spins respectively. The effect of the magnetic field on the fidelity of the cloning is also investigated. By applying an external magnetic field on the spin system, the fidelity of the cloning machine can be largely improved.     

Free electron gas spectrum parameters of noble gases in dc electric field

Free electron gas is present in every gas, whether it is of atomic or molecular structure. Since the Maxwell spectrum type is the consequence of only thermal motion of constitutive gas particles; therefore, the presence of electric field leads to change the spectrum of charged particles due to their directed motion. However, it has been shown that in the case of occurrence only of elastic interactions between electrons and neutral gas particles (a condition that has been met in the case of weakly ionized noble gases of a relatively huge volume) the deviation of the gas spectrum of free electrons in the electric field from the Maxwell type is negligible. In such a case, the gas spectrum of free electrons is either of Maxwell type (if the frequency collision value is energy-independent) or of Druyvesteyn type (if the mean free electron path value is energy-independent). The Maxwell and Druyvesteyn distribution types are very similar. The only noticeable difference is that the tail of the Maxwell distribution decreases with the energy exponent to the first degree of energy, and the tail of Druyvesteyn distribution with the energy exponent to the second degree of energy. The aim of this paper is to determine whether the gas spectrum of free electrons in weakly ionized noble gases at small values of the product pd (pressure and inter-electrode distance) follows either the Maxwell's or Druyvesteyn's type, as well as to determine the dependence of spectrum parameters on the product pd. It has been established that better results are obtained on the assumption that the mean value of collision frequency is energy-independent.     

Electromagnetic test fields around a Schwarzschild singularity

If the two invariants of an arbitrary non-static electromagnetic vacuum field are finite at the Schwarzschild radiusr=M, the field behaves atr=M ₊ either as a purely ingoing or as a purely outgoing wave.     

The electromagnetic string with spin

The relations betweeb a field F_μν^M satisfying the usual Maxwell equations and a field F_μν^D satisfying the symmetric Maxwell-Dirac equations, and the singular potential solving both of these is given. The action principle is formulated in both forms and the reality of the string is shown. A string with spin is constructed by placing electric charges at its end-points. The motion and interactions of the string, the relation between flux and angular momentum quantization and the passage to two-body Hamiltonians are examined.     

Spin-1/2 Maxwell Fields

Requiring covariance of Maxwell's equations without a priori imposing charge invariance allows for both spin-1 and spin-1/2 transformations of the complete Maxwell field and current. The spin-1/2 case yields new transformation rules, with new invariants, for all traditional Maxwell field and source quantities. The accompanying spin-1/2 representations of the Lorentz group employ the Minkowski metric, and consequently the primary spin-1/2 Maxwell invariants are also spin-1 invariants; for example, ²–A ², E ²–B ²+2i EB–(₀ +A)². The associated Maxwell Lagrangian density is also the same for both spin-1 and spin-1/2 fields. However, in the spin-1/2 case, standard field and source quantities are complex and both charge and gauge invariance are lost. Requiring the potentials to satisfy the Klein–Gordon equation equates the Maxwell and field-potential equations with two Dirac equations of the Klein–Gordon mass, and thus one complex Klein–Gordon Maxwell field describes either two real vector fields or two Dirac fields, all of the same mass.     

The generalized radiation gauge for a simply connected space-time

In the following we shall make some remarks on the existence of the generalized radiation gauge if space-timeM is topologically non trivial (M R ⁴). This specialU(1)-gauge generalizes in a sense the wellknown Coulomb gauge and if it is possible to use that gauge the Maxwell equations reduce to a well defined elliptical eigenvalue problem. This can be discussed using, for example, the Hodge theory and the theory of the spectrum of elliptic differential operators.     

峰值电流达几千安量级的闪电M分量放电特征及机理探讨

利用2009年山东人工触发闪电实验获取的实测雷电流资料、近距离电场和高速摄像资料,分析了6次峰值电流达几千安量级的M分量.6次M分量均对应闪电通道中明显的发光亮度的脉冲式变化,持续时间小于1 ms.M分量的电流波形和近距离电场波形均呈较为对称的V形,且波形的上升时间均为几十微秒,同步记录结果显示,电场先于通道底部电流发生变化且先达到峰值.这些M分量在发生前,闪电通道中存在一定的连续电流,通道的导电性优于先导-回击过程.M分量发生前的闪电 关键词： 闪电 M分量')" href="#">M分量 先导-回击 通道电流     

Conformal Vector Fields and Eigenvectors of Laplacian Operator

In this paper, we consider an n-dimensional compact Riemannian manifold (M,g) of constant scalar curvature and show that the presence of a non-Killing conformal vector field ξ on M that is also an eigenvector of the Laplacian operator acting on smooth vector fields with eigenvalue λ together with a condition on Ricci curvature of M, that the Ricci curvature in the direction of a certain vector field is greater than or equal to (n − 1)λ, forces M to be isometric to the n-sphere S ⁿ (λ).     

A Quantum Mechanical Gauge Model and a Possible Dynamical Solution of the StrongCPProblem

A model describing a quantum mechanical particle on a circle with minimal electromagnetic interaction with a space independent vector potential, and with a potential −M cos(?−θ_M) so that it mimics the massive Schwinger model, is discussed as a prototype of mechanisms and infrared structures which characterize gauge quantum field theories in positive gauges and QCD in particular. The functional integral representation in terms of the field variables which enter in the Lagrangean displays non-standard features, like a complex functional measure (failure of Nelson positivity), a crucial rôle of the boundary conditions, and the decomposition intoθsectors already in finite volume. In the infinite volume limit, one essentially recovers the standard picture whenM=0 (“massless fermions”), but one meets substantial differences forM≠0: for generic boundary conditions, independently of the Lagrangean angle of the topological term, the infinite volume limit selects the sector withθ=θ_Mand provides a natural “dynamical” solution of the strong CP problem. In comparison with previous approaches, the strategy discussed here allows us to exploit the consequences of theθdependence of the free energy density, with a unique minimum atθ=θ_M.     

梯度颗粒复合介质的光学双稳

重点研究了组分的梯度构形对带壳球形颗粒复合介质的光学双稳特性的影响.其中球形颗粒是由非线性核和介电函数具有梯度分布的线性壳组成.对于壳层介电函数具有幂指数分布的情况,通过求解麦克斯韦方程,得到各区域的势能分布函数,从而求得核内电场的数学表达式.数值研究发现,该复合介质的光学双稳阈值和区域与壳层的厚度及壳层的介电幂指数有关,随着壳层厚度增大或幂指数增大,双稳阈值将变宽.此外,还研究了正入射情况下复合材料体系的反射系数随外电场的变化情况, 发现其关系曲线是一条回线. 关键词： 梯度颗粒 复合介质 光学双稳     

Solution of collinear cracks in an electrostrictive solid

A general treatment is presented of the two-dimensional problem of N collinear cracks in an infinite electrostrictive material subjected to remote electric loads based on the complex variable method combined with analytical extension of the complex variable functions. First, for the case of permeable cracks, general solutions for the electric potentials, Maxwell stresses, electroelastic stresses and stress intensity factors are derived. As specific examples, explicit and concise results are obtained for the cases of one crack and two collinear cracks. Then, these results are extended to the cases of impermeable and conducting collinear cracks, respectively. It is found that, in general, the total stresses always have the classical singularity of the r ^{- 1/2} type at the crack tips, whereas the Maxwell stresses have an r ^{- 1} singularity for the above three crack models. Finally, it is concluded that the applied electric field may either enhance or retard crack growth depending on the electric boundary conditions adopted on the crack faces, and the Maxwell stresses on the crack faces and at infinity.     

A topological theory of the electromagnetic field

It is shown that Maxwell equations in vacuum derive from an underlying topological structure given by a scalar field which represents a map S ³×RS ² and determines the electromagnetic field through a certain transformation, which also linearizes the highly nonlinear field equations to the Maxwell equations. As a consequence, Maxwell equations in vacuum have topological solutions, characterized by a Hopf index equal to the linking number of any pair of magnetic lines. This allows the classification of the electromagnetic fields into homotopy classes, labeled by the value of the helicity. Although the model makes use of only c-number fields, the helicity always verifies A·Bd³ r=n, n being an integer and an action constant, which necessarily appears in the theory, because of reasons of dimensionality.