Ballistic and diffusive corrections to front propagation in the presence of multiplicative noise

We study the dynamics of reaction-diffusion fronts under the influence of multiplicative noise. An approximate theoretical scheme is introduced to compute the velocity of the front and its diffusive wandering due to the presence of noise. The theoretical approach is based on a multiple scale analysis rather than on a small noise expansion and is confirmed with numerical simulations for a wide range of the noise intensity. We report on the possibility of noise sustained solutions with a continuum of possible velocities, in situations where only a single velocity is allowed without noise.

Numerical algorithm for spectroscopic ellipsometry of thick transparent films

We present a numerical method for spectroscopic ellipsometry of thick transparent films. When an analytical expression for the dispersion of the refractive index (which contains several unknown coefficients) is assumed, the procedure is based on fitting the coefficients at a fixed thickness. Then the thickness is varied within a range (according to its approximate value). The final result given by our method is as follows: The sample thickness is considered to be the one that gives the best fitting. The refractive index is defined by the coefficients obtained for this thickness.

Using numerical classification of profiles based on Vis-NIR spectra to distinguish soils from the Piracicaba Region, Brazil

Considering that information from soil reflectance spectra is underutilized in soil classification, this paper aimed to evaluate the relationship of soil physical, chemical properties and their spectra, to identify spectral patterns for soil classes, evaluate the use of numerical classification of profiles combined with spectral data for soil classification. We studied 20 soil profiles from the municipality of Piracicaba, State of São Paulo, Brazil, which were morphologically described and classified up to the 3rd category level of the Brazilian Soil Classification System (SiBCS). Subsequently, soil samples were collected from pedogenetic horizons and subjected to soil particle size and chemical analyses. Their Vis-NIR spectra were measured, followed by principal component analysis. Pearson's linear correlation coefficients were determined among the four principal components and the following soil properties: pH, organic matter, P, K, Ca, Mg, Al, CEC, base saturation, and Al saturation. We also carried out interpretation of the first three principal components and their relationships with soil classes defined by SiBCS. In addition, numerical classification of the profiles based on the OSACA algorithm was performed using spectral data as a basis. We determined the Normalized Mutual Information (NMI) and Uncertainty Coefficient (U). These coefficients represent the similarity between the numerical classification and the soil classes from SiBCS. Pearson's correlation coefficients were significant for the principal components when compared to sand, clay, Al content and soil color. Visual analysis of the principal component scores showed differences in the spectral behavior of the soil classes, mainly among Argissolos and the others soils. The NMI and U similarity coefficients showed values of 0.74 and 0.64, respectively, suggesting good similarity between the numerical and SiBCS classes. For example, numerical classification correctly distinguished Argissolos from Latossolos and Nitossolos. However, this mathematical technique was not able to distinguish Latossolos from Nitossolos Vermelho férricos, but the Cambissolos were well differentiated from other soil classes. The numerical technique proved to be effective and applicable to the soil classification process.

Can extreme black Holes have (long) Abelian Higgs hair?

It has been argued that a black hole horizon can support the long-range fields of a Nielsen-Olesen string and that one can think of such a vortex as black hole "hair." In this paper, we examine the properties of an Abelian Higgs vortex in the presence of a charged black hole as we allow the hole to approach extremality. Using both analytical and numerical techniques, we show that the magnetic field lines (as well as the scalar field) of the vortex are completely expelled from the black hole in the extreme limit. This was to be expected, since extreme black holes in Einstein-Maxwell theory are known to exhibit such a "Meissner effect" in general. This would seem to imply that a vortex does not want to be attached to an extreme black hole. We calculate the total energy of the vortex fields in the presence of an extreme black hole. When the hole is small relative to the size of the vortex, it is energetically favored for the hole to remain inside the vortex region, contrary to the intuition that the hole should be expelled. However, as we allow the extreme horizon radius to become very large compared to the radius of the vortex, we do find evidence of an instability. This proves that it is energetically unfavorable for a thin vortex to interact with a large extreme black hole. This would seem to dispel the notion that a black hole can support "long" Abelian Higgs hair in the extreme limit. We show that these considerations do not go through in the near-extreme limit. Finally, we discuss the implications for strings that end at black holes, as in the processes where a string snaps by nucleating black holes.

Generalized Weyl solutions

It was shown by Weyl that the general static axisymmetric solution of the vacuum Einstein equations in four dimensions is given in terms of a single axisymmetric solution of the Laplace equation in three-dimensional flat space. Weyls construction is generalized here to arbitrary dimension D>~4. The general solution of the D-dimensional vacuum Einstein equations that admits D-2 orthogonal commuting non-null Killing vector fields is given either in terms of D-3 independent axisymmetric solutions of Laplaces equation in three-dimensional flat space or by D-4 independent solutions of Laplaces equation in two-dimensional flat space. Explicit examples of new solutions are given. These include a five-dimensional asymptotically flat black ring with an event horizon of topology S1S2 held in equilibrium by a conical singularity in the form of a disk.

Singularity-free space-time

We show that the solution published in the paper by Senovilla [Phys. Rev. Lett. 64, 2219 (1990)] is geodesically complete and singularity-free. We also prove that the solution satisfies the stronger energy and causality conditions, such as global hyperbolicity, the strong energy condition, causal symmetry, and causal stability. A detailed discussion about which assumptions in the singularity theorems are not satisfied is performed, and we show explicitly that the solution is in accordance with those theorems. A brief discussion of the results is given.

Soliton solutions and cosmological gravitational waves

We examine plane-symmetric cosmological solutions to Einstein's equations which can be generated by the "soliton" technique, using the homogeneous Bianchi solutions as seeds and arbitrary numbers of real or complex poles. In some circumstances, these solutions can be interpreted as "incipient" gravitational waves on the Bianchi background. At early times they look like nonlinear inhomogeneities propagating at nearly the speed of light ("gravisolitons"), while at late times they look like cosmological gravitational waves.

Multisoliton solutions to Einstein's equations

We discuss a multisoliton solution to Einsteins equations in vacuum. The solution is interpreted as many gravitational solitons propagating and colliding on a homogeneous cosmological background. Following a previous letter, we characterize the solitons by their localizability and by their peculiar properties under collisions. Furthermore, we define an associated frame-dependent velocity field which illustrates the solitonic character of these gravitational solitons in the classical sense.

Radiative isotropic cosmologies with extra dimensions

We solve Einsteins equations in an n-dimensional vacuum with the simplest ansatz leading to a Friedmann-Robertson-Walker (FRW) four-dimensional space time. We show that the FRW model must be of radiation. For the open models the extra dimensions contract as a result of cosmological evolution. For flat and closed models they contract only when there is one extra dimension.

Cosmic strings and Einstein-Rosen soliton waves

We consider all generalized soliton solutions of the Einstein-Rosen form in the cylindrical context. They are Petrov type-I solutions which describe solitonlike waves interacting with a line source placed on the symmetry axis. Some of the solutions develop a curvature singularity on the axis which is typical of massive line sources, whereas others just have the conical singularity revealing the presence of a static cosmic string. The analysis is based on the asymptotic behavior of the Riemann and metric tensors, the deficit angle, and a C-velocity associated to Thornes C-energy. The C-energy is found to be radiated along the null directions.

Particle creation in a colliding plane wave spacetime: Wave packet quantization

We use wave packet mode quantization to compute the creation of massless scalar quantum particles in a colliding plane wave spacetime. The background spacetime represents the collision of two gravitational shock waves followed by trailing gravitational radiation which focus into a Killing-Cauchy horizon. The use of wave packet modes simplifies the problem of mode propagation through the different spacetime regions which was previously studied with the use of monochromatic modes. It is found that the number of particles created in a given wave packet mode has a thermal spectrum with a temperature which is inversely proportional to the focusing time of the plane waves and which depends on the mode trajectory.

Soliton collision in general relativity

An exact solution of the Einstein equations in vacuum representing two pairs of gravitational solitons propagating on an expanding universe is given and studied. It is suggested that the solitons evolve from quasiparticles to pure gravitational waves. Two of the four solitons collide and the focusing produced on null rays is studied. Although the spacetime following the collision is highly distorted, null rays do not focus to a singularity.