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.     

Maxwell fields onH-space

It is shown that theH space associated with a solutionM of the Einstein-Maxwell equations can be endowed with a self-dual Maxwell field which arises from the radiation component ofM's Maxwell field.     

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.     

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.     

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.     

Approximate vacuums in (:φ2m :g(x))2 field theories and perturbation series

A class of perturbation problems is considered, in which the Rayleigh-Schrödinger perturbation series for the ground state eigenvalue and eigenvector are presumed to diverge. This class includes the (:^2m :g(x))₂, (m=2, 3) quantum field theory models and the quantum mechanical anharmonic oscillator. It is shown that, using matrix elements and vectors which occur in the series coefficients, one may construct convergent approximants to the eigenvalue and eigenvector. Results of a calculation of the ground state energy of thex ⁴ anharmonic oscillator are given.Supported in part by the National Research Council of Canada.     

Some duct flows of a fractional Maxwell fluid

The aim of this paper is to establish the analytical solutions corresponding to two types of unsteady flows of fractional Maxwell fluid in a duct of rectangular cross-section. The fractional calculus approach is used in solving the problems. With the help of the methods of separation of variables and Laplace transforms, the expressions for the velocity field and the volume flux are presented under series forms in terms of the generalized G functions. Similar solutions for Newtonian and ordinary Maxwell fluids, performing the same motions, are also obtained as the limiting cases of our solutions. Furthermore, the influence of pertinent parameters on the flows is delineated and appropriate conclusions are drawn.     

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.     

Surface plasmon-polaritons on ultrathin metal films

We discuss the surface plasmon-polaritons used for ultrathin metal films with the aid of linear response theory and make comparisons with the known result given by Economou E N. In this paper we consider transverse electromagnetic fields and assume that the electromagnetic field in the linear response formula is the induced field due to the current of the electrons. It satisfies the Maxwell equation and thus we replace the current (charge) term in the Maxwell equation with the linear response expectation value. Finally,taking the external field to be zero,we obtain the dispersion relation of the surface plasmons from the eigenvalue equation. In addition,the charge-density and current-density in the z direction on the surface of ultrathin metal films are also calculated. The results may be helpful to the fundamental understanding of the complex phenomenon of surface plasmon-polaritons.     

On the Robinson,Schild, and Strauss solution of the Einstein-Maxwell equations

The Robinson, Schild, and Strauss explicit solution of the Einstein-Maxwell equations is considered. Two subclasses of this solution are determined: (i) the class of metrics for which both eigenvectors of the Maxwell field are eigenvectors of the Weyl tensor, and (ii) the class of metrics of Petrov typeD.     

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.     

A new theorem relating quantum tomogram to the Fresnel operator

According to Fan-Hu's formalism (Fan Hong-Yi and Hu Li-Yun 2009 Opt. Commun. bf282 3734) that the tomogram of quantum states can be considered as the module-square of the state wave function in the intermediate coordinate-momentum representation which is just the eigenvector of the Fresnel quadrature phase, we derive a new theorem for calculating quantum tomogram of density operator, i.e., the tomogram of a density operator ρ is equal to the marginal integration of the classical Weyl correspondence function of F⁺ρF, where F is the Fresnel operator. Applications of this theorem to evaluating the tomogram of optical chaotic field and squeezed chaotic optical field are presented.     

相控阵超声热疗场共轭直接合成的模式优化研究

对多阵元超声热疗声场进行模式优化研究.在对空间声场提出合理的优化目标函数后,提出了两种优化算法进行全局寻优:一种是遗传算法构造的声场模式控制算法;另一种是特征向量算法.用遗传算法和特征向量算法对声场控制模式控制的仿真研究表明:能达到声场控制模式优化的目标,而遗传算法比特征向量算法具有更多特征优势. 关键词： 优化 遗传算法 超声相控阵 热疗     

On potentials for several classes of spinor and tensor fields in curved spacetimes

Already known results with respect to the existence of a vector potential for the Maxwell field tensor and a tensor potential for Weyl's conformal curvature tensor in four-dimensional spacetimes are generalized. It is shown that there exists a spinor potential of type (n–1,1) for any totally symmetric spinor field of rankn. From this theorem we deduce a series of corollaries, for example, that every antisymmetric tensor of second rank admits a linear representation in terms of the first derivatives of two vector fields. Further, some investigations are made on the existence of potentials for arbitrary symmetric spinors of type (n, m).     

A coupled theory of electromagnetism and gravitation

A coupling electromagnetism with a previously developed scalar theory of gravitation is presented. The principle features of this coupling are: (1) a slight alteration to the Maxwell equations, (2) the motion of a charged particle satisfies an equation with the Lorentz force-appearing on the right side in place of zero, and (3) the energy density of the electromagnetic field appears in the gravitational field equation in a manner similar to the mass term in the Klein-Gordonequation. The field of a static, spherically symmetric charged particle is computed. The electromagnetic field gives rise to l/r ² terms in the gravitational potential.     

Approximation and Reconstruction of the Electrostatic Field in Wire–Plate Precipitators by a Low-Order Model

The numerical computation of the ionic space charge and electric field produced by corona discharge in a wire–plate electrostatic precipitator (ESP) is considered. The electrostatic problem is defined by a reduced set of the Maxwell equations. Since self-consistent conditions at the wire and at the plate cannot be specified a priori, a time-consuming iterative numerical procedure is required. The efficiency of all numerical solvers of the reduced Maxwell equations depends in particular on the accuracy of the initial guess solution. The objectives of this work are two: first, we propose a semianalytical technique based on the Karhunen–Loève (KL) decomposition of the current density field J, which can significantly improve the performance of a numerical solver; second, we devise a procedure to reconstruct the complete electric field from a given J. The approximate solution of the current density field is based on the derivation of an analytical approximation , which, added to a linear combination of few KL basis functions, constitutes an accurate approximation of J. In the first place, this result is useful for optimization procedures of the current density field, which involve the computation of many different configurations. Second, we show that from the current density field we can obtain an accurate estimate for the complete electrostatic field which can be used to speed up the convergence of the iterative procedure of standard numerical solvers.     

Uniqueness of the physical vacuum and the Wightman functions in the infinite volume limit for some non polynomial interactions

We consider quantum field theoretical models inn dimensional space-time given by interaction densities which are bounded functions of an ultraviolet cut-off boson field. Using methods of euclidean Markov field theory and of classical statistical mechanics, we construct the infinite volume imaginary and real time Wightman functions as limits of the corresponding quantities for the space cut-off models. In the physical Hilbert space, the space-time translations are represented by strongly continuous unitary groups and the generator of time translationsH is positive and has a unique, simple lowest eigenvalue zero, with eigenvector , which is the unique state invariant under space-time translations. The imaginary time Wightman functions and the infinite volume vacuum energy density are given as analytic functions of the coupling constant. The Wightman functions have cluster properties also with respect to space translations.     

Eigenvector Localization in Real Networks and Its Implications for Epidemic Spreading

The spectral properties of the adjacency matrix, in particular its largest eigenvalue and the associated principal eigenvector, dominate many structural and dynamical properties of complex networks. Here we focus on the localization properties of the principal eigenvector in real networks. We show that in most cases it is either localized on the star defined by the node with largest degree (hub) and its nearest neighbors, or on the densely connected subgraph defined by the maximum K-core in a K-core decomposition. The localization of the principal eigenvector is often strongly correlated with the value of the largest eigenvalue, which is given by the local eigenvalue of the corresponding localization subgraph, but different scenarios sometimes occur. We additionally show that simple targeted immunization strategies for epidemic spreading are extremely sensitive to the actual localization set.

     

Generalized Hellmann-Feynman Theorem for Ensemble Average Expressed in the Formalism of Pure State Expectation

We show that the generalized Hellmann-Feynman theorem (GHFT) for ensemble average can be expressed in the formalism of pure state expectation. We employ the thermo field dynamics proposed by Umezawa and Takahash to realize this goal, the pure state |0(β)〉 is defined in doubled eigenvector space of the Hamiltonian. Relation between the GHFT and entropy-variation in the context of |0(β)〉 is also derived.     

Forms of the evans-vigier fieldB (3)

The newly inferred longitudinal magnetic field of vacuum electromagnetism is given in a number of equivalent forms derived in several different ways. It is therefore overwhelmingly likely that the Evans-Vigier fieldB ⁽³⁾ will be isolated experimentally through its characteristic square root power density dependence. It is the first classical field of vacuum electromagnetism to be inferred since Maxwell and as such fundamentally extends our understanding of the nature of electromagnetism and field-particle theory.