Relationship between (2 + 1) and (3 + 1)-Friedmann–Robertson–Walker cosmologies; linear,non-linear,and polytropic state equations

It is shown that Friedmann–Robertson–Walker (FRW) cosmological models coupled to a single scalar field and to a perfect fluid fitting a wide class of matter perfect fluid state equations, determined in (3+1) dimensional gravity can be related to their (2+1) cosmological counterparts, and vice-versa, by using simple algebraic rules relating gravitational constants, state parameters, perfect fluid and scalar field characteristics. It should be pointed out that the demonstration of these relations for the scalar fields and potentials does not require the fulfilment of any state equation for the scalar field energy density and pressure. As far as to the perfect fluid is concerned, one has to demand the fulfilment of state equations of the form p+ = f(). If the considered cosmologies contain the inflation field alone, then any (3+1) scalar field cosmology possesses a (2+1) counterpart, and vice-versa. Various families of solutions are derived, and we exhibited their correspondence; for instance, solutions for pure matter perfect fluids and single scalar field fulfilling linear state equations, solutions for scalar fields coupled to matter perfect fluids, a general class of solutions for scalar fields subjected to a state equation of the form p + = are reported, in particular Barrow–Saich, and Barrow–Burd–Lancaster–Madsen solutions are exhibited explicitly, and finally perfect fluid solutions for polytropic state equations are given.     

Radial conformal killing vectors in spherically symmetric shear-free space-times

The existence of “radial” conformai Killing (RCK) vector fields is discussed for metrics describing spherically symmetric, shear-free, perfect fluids. It is shown that conformally flat metrics admit three RCK fields, while nonconformally flat metrics might admit, at most, one such field. An RCK vector parallel to the 4-velocity of the fluid occurs in a subclass of conformally flat metrics containing the Friedmann-Robertson-Walker space-times as particular cases. A new class of nonconformally flat, self-similarity solutions is found. The necessary conditions for the existence of an RCK field in other nonconformally flat metrics are given in full.     

Stationary axisymmetric solutions of the Einstein equations with rigidly rotating perfect fluid and nonlinear charged sources

A class of stationary, rigidly rotating perfect fluids coupled with nonlinear electromagnetic fields was investigated. An exact solution of the Einstein equations with sources for the Carter B(+) branch was found for the equation of state 3p+=const. We use a structure function for the Born-Infeld nonlinear electrodynamics which is invariant under duality rotations and a metric possessing a four-parameter group of motions. The solution is of Petrov type D and the eigenvectors of the electromagnetic field are aligned to the Debever-Penrose vectors.     

What is a mean gravitational field?

The equations of General Relativity are non-linear. This makes their averaging non-trivial. The notion of mean gravitational field is defined and it is proven that this field obeys the equations of General Relativity if the unaveraged field does. The workings of the averaging procedure on Maxwells field and on perfect fluids in curved space-times are also discussed. It is found that Maxwells equations are still verified by the averaged quantities but that the equation of state for other kinds of matter generally changes upon average. In particular, it is proven that the separation between matter and gravitational field is not scale-independent. The same result can be interpreted by introducing a stress-energy tensor for a mean-vacuum. Possible applications to cosmology are discussed. Finally, the work presented in this article also suggests that the signature of the metric might be scale-dependent too.Received: 16 October 2003, Published online: 15 March 2004PACS: 04.20.Cv Fundamental problems and general formalism 04.40.Nr Einstein-Maxwell spacetimes, spacetimes with fluids, radiation or classical fields - 95.35. + d Dark matter (stellar, interstellar, galactic, and cosmological)     

Effect of an electric field on the surface tension of a dipolar-quadrupolar fluid and its implication for sign preference in droplet nucleation

The effect of a uniform electric field on interfacial properties of dipolar-quadrupolar fluids is investigated by using the density-functional theory. As in the case of purely dipolar fluids the (thermodynamic) surface tension is always altered by the external field, regardless of the direction of the field. However, unlike the purely dipolar fluids, for two given external fields with the same strength but exactly opposite direction the magnitude of variation in the surface tension is different. This apparent symmetry breaking by reversing the field direction suggests a new molecular mechanism to explain the phenomenon of sign preference in droplet formation on charged condensation centers.     

Two-perfect fluid interpretation of an energy tensor

The paper contains the necessary and sufficient conditions for a given energy tensor to be interpreted as a sum of two perfect fluids. Given a tensor of this class, the decomposition in two perfect fluids (which is determined up to a couple of real functions) is obtained.     

Friedmann universes containing wave fields

In this paper the Friedmann universes containing(i) a massless real scalar field,(ii) a massive real scalar field,(iii) electromagnetic fields,(iv) the combined massive complex scalar and electromagnetic fields are investigated. In(i) the field has to be either purely spatial or else purely temporal and the latter case is completely solved. Similarly in(ii) the purely time-dependent case has been reduced to a single fourth order ordinary differential equation. In this case graphs of the numerical solutions have been exhibited. In(iii) as expected, no non-trivial solution exists. In(iv) all possible cases are studied. In case the complex wave function is a product of two non-constant functions, i.e. ψ=ξ(r)τ(t), there exists no solution. In the subcase gx(r)=ξ^*(r)=constant, ¦τ(t)¦=constant the problem is completely solved. In the subcase ξ(r)=ξ^*(r)=constant and ¦τ(t)¦ is non-constant, the system of equations boil down to the same fourth order ordinary differential equation as mentioned before. In the last two sub-cases, the time-dependent wave field carries electric charge density which, strangely enough, is decoupled from the electromagnetic fields.     

二维电磁感应光子带隙的动态生成与调控

研究了由两个垂直传播的强驻波激光场共同耦合的一个四能级Tripod型冷⁸⁷Rb原子介质的稳态光学响应特性. 结果发现, 当两驻波场满足双光失谐条件时, 可在这两驻波场的传播方向上同时获得反射率高达95%以上的电磁感应光子带隙结构; 通过适当调节强激光场, 还可实现一个方向为光子带隙而另一个方向为透明窗口或者两个方向均为透明窗口的结构. 并且光子带隙和透明窗口的频宽和位置是可调谐的. 这种全光控制的二维的信号光禁闭和导通机制可用于实现全光开关和全光路由, 有利于复杂的全光通讯网络的开发. 关键词： 相干诱导光子带隙 电磁感应透明 周期调制原子相干     

Anisotropic field dependence of the magnetic transition in Cu2Te2O5Br2

In this paper, we present the results of measurements of the thermal conductivity of Cu2Te2O5Br2, a compound where tetrahedra of Cu2+ ions carrying S=1/2 spins form chains along the c-axis of the tetragonal crystal structure. The thermal conductivity was measured along both the c- and the a-direction as a function of temperature between 3 and 300 K and in external magnetic fields H up to 69 kOe, oriented both parallel and perpendicular to the c-axis. Distinct features of (T) were observed in the vicinity of TN=11.4 K in zero magnetic field. These features are unaltered in external fields which are parallel to the c-axis, but are more pronounced when a field is applied perpendicularly to the c-axis. The transition temperature increases upon enhancing the external field, but only if the field is oriented along the a-axis.     

Living fluids

One of the major emerging fields of research of the beginning of this century concerns living fluids. By “living fluids”, we mean two major categories of complex fluids: (i) fluids which are essential to life, like blood, and (ii) active fluids made of particles that are able to propel themselves in the suspending fluid by converting a form of their energy into mechanical motion. Studies on active fluids have known a considerable interest since the last decade. Blood might be viewed as an old topic, but the progresses in experimental techniques, analytical concepts and numerics, have contributed nowadays to a dramatic renewal of the interest in this field, with a great potential towards understanding physical and mechanical factors in cardiovascular diseases. These fields have considerably strengthened interdisciplinary research. The series of reviews of this dossier focus on the tremendous recent progress achieved in research on living fluids both from the experimental and theoretical points of views. These reviews present also the major open issues, making of this dossier a unique guide for future research in these fields. This project grew up thanks to the international summer school that we organized on the topic “living fluids” at the IES (Institut dʼétudes scientifiques) of Cargèse (Corsica) in 2012.     

Evidence for static magnetism in the vortex cores of ortho-II YBa2Cu3O6.50

Evidence for static alternating magnetic fields in the vortex cores of underdoped YBa2Cu3O6+x is reported. Muon spin rotation measurements of the internal magnetic field distribution of the vortex state of YBa2Cu3O6.50 in applied fields of H = 1 T and H = 4 T reveal a feature in the high-field tail of the field distribution which is not present in optimally doped YBa2Cu3O6.95 and which fits well to a model with static magnetic fields in the vortex cores. The magnitude of the fields is estimated to be 18(2) G and decreases above T = 10 K. We discuss possible origins of the additional vortex core magnetism within the context of existing theories.     

Space-times with spherically symmetric hypersurfaces

When discussing spherically symmetric gravitational fields one usually assumes that the whole space-time is invariant under theO(3) group of transformations. In this paper, the Einstein field equations are investigated under the weaker assumption that only the 3-spacest=const areO(3) symmetric. The following further assumptions are made: (1) Thet lines are orthogonal to the spacest=const. (2) The source in the field equations in a perfect fluid, or dust, or the term, or the empty space. (3) With respect to the center of symmetry the fluid source may move only radially if at all. Under these assumptions one solution with a perfect fluid source, found previously by Stephani, is recovered and interpreted geometrically, and it is shown that it is the sole solution which is not spherically symmetric in the traditional sense. The paper ends with a general discussion of cosmological models whose 3-spacest=const are the same as in the Robertson-Walker models. No new solutions were explicitly found, but it is shown that such models exist in which the sign of curvature is not fixed in time.     

Field-dependent diamagnetic transition in magnetic superconductor Sm1.85Ce0.15CuO4-y

The magnetic penetration depth of single crystal Sm(1.85)Ce(0.15)CuO(4-y) was measured down to 0.4 K in dc fields up to 7 kOe. For insulating Sm2CuO4, Sm3+ spins order at the Ne el temperature, T(N)=6 K, independent of the applied field. Superconducting Sm(1.85)Ce(0.15)CuO(4-y) (T(c) approximately 23 K) shows a sharp increase in diamagnetic screening below T(*)(H) which varied from 4.0 K (H=0) to 0.5 K (H=7 kOe) for a field along the c axis. If the field was aligned parallel to the conducting planes, T(*) remained unchanged. The unusual field dependence of T(*) indicates a spin-freezing transition that dramatically increases the superfluid density.     

Magnetic fluid behavior in uniform DC,AC, and rotating magnetic fields

New flows and instabilities are demonstrated for magnetic fluids and by dual analogy to dielectric fluids. If a fluid drop is contained in a thin gap between two glass plates (Hele–Shaw cell) with a simultaneously applied in-plane rotating field and a DC axial field, smooth spirals or an abrupt transformation to many small droplets can occur. A preliminary minimum magnetization and surface energy analysis is presented to model the abrupt transformation in ferrofluids. An analysis of effective DC magnetoviscosity is also presented for planar Couette flow with an applied uniform DC field transverse to a duct axis with the effective magnetoviscosity and flow spin velocity calculated as a function of field strength. Related Couette viscometer measurements of ferrofluid viscosity show zero and negative magnetoviscosity values for rotating magnetic fields.     

Dynamical mass and geodesic motion

We show that even though particles with dynamically generated masses do not have the standard point test particle energy-momentum tensor associated with them, their motion in an external gravitational field is nonetheless geodesic. We discuss dynamically massive conformal perfect fluids and construct conformal invariant particle trajectories for them, and show that such fluids behave just like standard kinematically massive perfect fluids in the particular conformal gauge in which the symmetry breaking field is taken to have a constant, spacetime independent vacuum expectation value.     

Background gradient suppression in stimulated echo NMR diffusion studies using magic pulsed field gradient ratios

By evaluating the spin echo attenuation for a generalized 13-interval PFG NMR sequence consisting of pulsed field gradients with four different effective intensities (F(p/r) and G(p/r)), magic pulsed field gradient (MPFG) ratios for the prepare (G(p)/F(p)) and the read (G(r)/F(r)) interval are derived, which suppress the cross term between background field gradients and the pulsed field gradients even in the cases where the background field gradients may change during the z-store interval of the pulse sequence. These MPFG ratios depend only on the timing of the pulsed gradients in the pulse sequence and allow a convenient experimental approach to background gradient suppression in NMR diffusion studies with heterogeneous systems, where the local properties of the (internal) background gradients are often unknown. If the pulsed field gradients are centered in the tau-intervals between the pi and pi/2 rf pulses, these two MPFG ratios coincide to eta=G(p/r)/F(p/r)=1-8/[1+(1/3)(delta/tau)(2)]. Since the width of the pulsed field gradients (delta) is bounded by 0< or =delta< or =tau, eta can only be in the range of 5< or =-eta< or =7. The predicted suppression of the unwanted cross terms is demonstrated experimentally using time-dependent external gradients which are controlled in the NMR experiment as well as spatially dependent internal background gradients generated by the magnetic properties of the sample itself. The theoretical and experimental results confirm and extend the approach of Sun et al. (J. Magn. Reson. 161 (2003) 168), who recently introduced a 13-interval type PFG NMR sequence with two asymmetric pulsed magnetic field gradients suitable to suppress unwanted cross terms with spatially dependent background field gradients.     

Theoretical Optimization of Stellarators

Net current free toroidal ("stellarator") confinement is studied with a combination of several methods: a complete set of analytical vacuum fields for finding favorable vacuum field configurations; three-dimensional MHD codes for finite-?, equilibrium computations; the expansion of a general toroidal equilibrium around its magnetic axis as guideline for the computational search in configurational space and for finite-?, MHD stability; Monte Carlo simulations for particle containment; continuous modular coil systems generating the configurations considered. Results are: vacuum field configurations with sizeable Q = 0, 1, 2, 3 helical fields, substantial twist number (? 1/2), significant reduction of the parallel current density, and vacuum magnetic well exist for a toroidal aspect ratio of 15-20 and can be generated by modular coils whose excursions from meridional planes are small compared to the toroidal period length. In these configurations, the finite-? toroidal shift is strongly reduced, so that a larger ? value (factor 2-4) than in the equivalent Q = 2 stellarator can be achieved. Stability calculations do not exclude the possibility of stable equilibria of this kind with (?) ? 0.05-0.1; transport calculations without electrical field show improvement-as compared to the Q = 2 stellarator-in the collisional and plateau regimes.     

Effect of the direction of the electric field on the interfacial instability between a passive fluid and a viscoelastic polymer

In this paper, we study the linear stability of the interface between an Upper Convective Maxwell fluid and a hydrodynamically passive fluid subject to an electric field applied either parallel or normal to the flat interface between the two fluids. The fluids are leaky-dielectric and we apply surface-coupled model. We solve the model equations analytically and study the dispersion and neutral curves for various parameters representing the applied potential, the fluid’s elasticity, the physical and the electrical properties of the fluids, and the heights of the fluids in the presence of both normal and parallel electric fields. It is found that the critical wavenumber is independent of the Weissenberg number. However, increasing the Weissenberg number increases the maximum growth rate for both the normal and the parallel fields. The critical wavenumber increases with the dimensionless applied voltage for the normal field. Lastly for the normal field, for some values of the dimensionless parameters, the growth rate reached very large values representing some type of singularity as has been observed in the literature. However, for the same values of the parameters no singularity is observed for the parallel field.