Petrou types D and II perfect-fluid solutions in generalized Kerr-Schild form.

Petrov types D and II perfect-fluid solutions are obtained starting from conformally flat perfect-fluid metrics and by using a generalized KerrSchild ansatz. Most of the Petrov type D metrics obtained have the property that the velocity of the fluid does not lie in the two-space defined by the principal null directions of the Weyl tensor. The properties of the perfect-fluid sources are studied. Finally, a detailed analysis of a new class of spherically symmetric static perfect-fluid metrics is given.

The problem of physical coordinates in predictive Hamiltonian systems

In the Hamiltonian formulation of predictive relativistic systems, the canonical coordinates cannot be the physical positions. The relation between them is given by the individuality differential equations. However, due to the arbitrariness in the choice of Cauchy data, there is a wide family of solutions for these equations. In general, those solutions do not satisfy the condition of constancy of velocities moduli, and therefore we have to reparametrize the world lines into the proper time. We derive here a condition on the Cauchy data for the individuality equations which ensures the constancy of the velocities moduli and makes the reparametrization unnecessary.

Anisotropic fluid with SU(2) type structure in general relativity: A model of localized matter

A model of anisotropic fluid with three perfect fluid components in interaction is studied. Each fluid component obeys the stiff matter equation of state and is irrotational. The interaction is chosen to reproduce an integrable system of equations similar to the one associated to self-dual SU(2) gauge fields. An extension of the BelinskyZakharov version of the inverse scattering transform is presented and used to find soliton solutions to the coupled Einstein equations. A particular class of solutions that can be interpreted as lumps of matter propagating in empty space-time is examined.

A family of inhomogeneous cosmological Einstein - Rosen metrics

Some generalized soliton solutions of the cosmological EinsteinRosen type defined in the space-time region t2=z2 in terms of canonical coordinates are considered. Vacuum solutions are studied and interpreted as cosmological models. Fluid solutions are also considered and are seen to represent inhomogeneous cosmological models that become homogeneous at t?8. A subset of them evolve toward isotropic FriedmannRobertsonWalker metrics.

On the spinning axis representation

A new spinning axis representation is introduced. It allows us to calculate the evolution operator of a system with slowly varying time dependent Hamiltonian with the desired degree of approximation in the parameter used for describing its dynamical evolution. The procedure is compared with a previously existing one and applied to a simple example.

Strong coupling solution to Schrödinger Equation: the mixing of states

In this paper we give some ideas that can be useful to solve Schrödinger equations in the case when the Hamiltonian contains a large term. We obtain an expansion of the solution in reciprocal powers of the large coupling constant. The procedure followed consists in considering that the small part of the Hamiltonian engenders a motion adiabatic to the motion generated by the large part of the same.

Three-dimensional aspects of fluid flows in channels. II. Effects of meniscus and thin film regimes on viscous fingers

We perform a three-dimensional study of steady state viscous fingers that develop in linear channels. By means of a three-dimensional lattice-Boltzmann scheme that mimics the full macroscopic equations of motion of the fluid momentum and order parameter, we study the effect of the thickness of the channel in two cases. First, for total displacement of the fluids in the channel thickness direction, we find that the steady state finger is effectively two-dimensional and that previous two-dimensional results can be recovered by taking into account the effect of a curved meniscus across the channel thickness as a contribution to surface stresses. Second, when a thin film develops in the channel thickness direction, the finger narrows with increasing channel aspect ratio in agreement with experimental results. The effect of the thin film renders the problem three-dimensional and results deviate from the two-dimensional prediction.

Three-dimensional aspects of fluid flows in channels. I. Meniscus and thin film regimes

We study the forced displacement of a fluid-fluid interface in a three-dimensional channel formed by two parallel solid plates. Using a lattice-Boltzmann method, we study situations in which a slip velocity arises from diffusion effects near the contact line. The difference between the slip and channel velocities determines whether the interface advances as a meniscus or a thin film of fluid is left adhered to the plates. We find that this effect is controlled by the capillary and Péclet numbers. We estimate the crossover from a meniscus to a thin film and find good agreement with numerical results. The penetration regime is examined in the steady state. We find that the occupation fraction of the advancing finger relative to the channel thickness is controlled by the capillary number and the viscosity contrast between the fluids. For high viscosity contrast, lattice-Boltzmann results agree with previous results. For zero viscosity contrast, we observe remarkably narrow fingers. The shape of the finger is found to be universal.

The Nonequilibrium thermodynamics of small systems

The interactions of tiny objects with their environments are dominated by thermal fluctuations. Guided by theory and assisted by new micromanipulation tools, scientists have begun to study such interactions in detail.

A high-sensitivity differential scanning calorimeter with magnetic field for magnetostructural transitions

We have developed a differential scanning calorimeter capable of working under applied magnetic fields of up to 5 T. The calorimeter is highly sensitive and operates over the temperature range 10¿300 K. It is shown that, after a proper calibration, the system enables determination of the latent heat and entropy changes in first-order solid¿solid phase transitions. The system is particularly useful for investigating materials that exhibit the giant magnetocaloric effect arising from a magnetostructural phase transition. Data for Gd5(Si0.1Ge0.9)4 are presented.

Dynamics of driven three-dimensional thin films: from hdrophilic to superhydrophobic substrates

We study the forced displacement of a thin film of fluid in contact with vertical and inclined substrates of different wetting properties, that range from hydrophilic to hydrophobic, using the lattice-Boltzmann method. We study the stability and pattern formation of the contact line in the hydrophilic and superhydrophobic regimes, which correspond to wedge-shaped and nose-shaped fronts, respectively. We find that contact lines are considerably more stable for hydrophilic substrates and small inclination angles. The qualitative behavior of the front in the linear regime remains independent of the wetting properties of the substrate as a single dispersion relation describes the stability of both wedges and noses. Nonlinear patterns show a clear dependence on wetting properties and substrate inclination angle. The effect is quantified in terms of the pattern growth rate, which vanishes for the sawtooth pattern and is finite for the finger pattern. Sawtooth shaped patterns are observed for hydrophilic substrates and low inclination angles, while finger-shaped patterns arise for hydrophobic substrates and large inclination angles. Finger dynamics show a transient in which neighboring fingers interact, followed by a steady state where each finger grows independently.

Cation distribution and magnetization of BaFe12-2xCoxSnxO19 (x=0.9,1.28) single crystals

The distribution of Sn4+ cations within the five crystallographic sites of the magnetoplumbite (M) ‐like compound BaFe12−2xCoxSnxO19 has been analyzed using single‐crystal x‐ray‐diffraction data. The species Fe3+ and Co2+ cannot be distinguished using x rays because of their very similar atomic numbers; however, the calculation of the apparent valencies for the different sites allows an insight into the Co2+ cation segregation. The use of previous data from neutron powder diffraction allows a precise picture of the cation distribution, which indicates a pronounced site selectivity for both Sn4+ and Co2+ cations. The Sn4+ cations prefer the 4f2 sites and to a much lower extent the 12k sites, while they do not enter the octahedral 2a sites at all. Co2+ cations are distributed among tetrahedral and octahedral sites displaying a clear preference for the tetrahedral 4f1 sites. Magnetic measurements indicate that the compound still exhibits uniaxial anisotropy with the easy direction parallel to the c axis. Nevertheless, the magnetic structure shows a considerable degree of noncolinearity. A strong reduction of the magnetic anisotropy regarding that of the undoped compound is also detected.

Structural and magnetic characterization of the lithiated iron oxide LixFe3O4

The Rietveld profile‐analysis method is used to investigate the x‐ray diffraction pattern of lithiated Fe3O4. It is shown that, after exposure to air, pure magnetite coexists with a lithium‐inserted LixFe3O4 phase. The Mössbauer spectra at 300 and 4.2 K have been used to estimate the lithium content of the sample, the pure magnetite concentration, and the iron distribution over the available 16c and 16d sites of the spinel structure. Magnetization measurements from 4.2 to 120 K with an external magnetic field up to 150 kOe have been used to obtain the saturation magnetic moment, the magnetic anisotropy constants, and the susceptibility. It is concluded that a noncollinear spin structure should be present in Li0.5Fe3O4. These results indicate that there is no room‐temperature extrusion of iron even for x→2.0, but that on exposure to air LixFe3O4 samples with x>0.5 are oxidized at room temperature by delithiation.

Magnetic properties of amorphous Fe-Si compositionally modulated thin films

The present paper reports on a magnetometric study of Fe‐Si compositionally modulated thin films. The low‐temperature dependence of the magnetization exhibit Bloch's T3/2 dependence with a minor T5/2 correction term. The spin‐wave stiffness constant deduced from the temperature coefficient depends on the characteristic modulation length and its values are much lower that in glassy alloys.

Spin-glass behaviour in mixed metal oxides with a rutile-type structure

We report here on the magnetic properties of compounds of composition Fe1−xCrxSbO4 and Fe1−xGaxSbO4. The introduction of paramagnetic Cr3+ and diamagnetic Ga3+ into the rutile‐related iron antimonate lattice does not destroy the antisite atomic ordering which exists in iron antimonate of composition FeSbO4. The initial slope of the Curie temperature dependence on x is similar in both series, indicating that Fe3+‐Cr3+ interactions are very small. The magnetic susceptibility measurements recorded from the compounds of composition Fe1−xCrxSbO4, x<0.4, and Fe0.9Ga0.1SbO4 show them to behave as spin glasses at low temperatures. The inhibition of compounds of the type Fe1−xCrxSbO4, x>0.4, and Fe1−xGaxSbO4, x>0.1 to undergo a spin‐glass transition above 4.2 K is associated with a dilution effect.