Issue of time in generally covariant theories and the Komar-Bergmann approach to observables in general relativity

Diffeomorphism-induced symmetry transformations and time evolution are distinct operations in generally covariant theories formulated in phase space. Time is not frozen. Diffeomorphism invariants are consequently not necessarily constants of the motion. Time-dependent invariants arise through the choice of an intrinsic time, or equivalently through the imposition of time-dependent gauge fixation conditions. One example of such a time-dependent gauge fixing is the Komar-Bergmann use of Weyl curvature scalars in general relativity. An analogous gauge fixing is also imposed for the relativistic free particle and the resulting complete set time-dependent invariants for this exactly solvable model are displayed. In contrast with the free particle case, we show that gauge invariants that are simultaneously constants of motion cannot exist in general relativity. They vary with intrinsic time.

Dual-Regge approach to high-energy, low-mass diffraction dissociation

A dual-Regge model with a nonlinear proton Regge trajectory in the missing mass (MX2) channel, describing the experimental data on low-mass single diffraction dissociation (SDD), is constructed. Predictions for the LHC energies are given.

Phase-field approach to spatial perturbations in normal Saffman-Taylor fingers

We make a numerical study of the effect that spatial perturbations have in normal Saffman-Taylor fingers driven at constant pressure gradients. We use a phase field model that allows for spatial variations in the Hele-Shaw cell. We find that, regardless of the specific way in which spatial perturbations are introduced, a lateral instability develops on the sides of the propagating Saffman-Taylor finger. Moreover, the instability exists regardless of the intensity of spatial perturbations in the cell as long as the perturbations are felt by the finger tip. If, as the finger propagates, the spatial perturbations felt by the tip change, the instability is nonperiodic. If, as the finger propagates, the spatial perturbations felt by the tip are persistent, the instability developed is periodic. In the later case, the instability is symmetrical or asymmetrical depending on the intensity of the perturbation.

An analytical approach to sorting in periodic and random potentials

There has been a recent revolution in the ability to manipulate micrometer-sized objects on surfaces patterned by traps or obstacles of controllable configurations and shapes. One application of this technology is to separate particles driven across such a surface by an external force according to some particle characteristic such as size or index of refraction. The surface features cause the trajectories of particles driven across the surface to deviate from the direction of the force by an amount that depends on the particular characteristic, thus leading to sorting. While models of this behavior have provided a good understanding of these observations, the solutions have so far been primarily numerical. In this paper we provide analytic predictions for the dependence of the angle between the direction of motion and the external force on a number of model parameters for periodic as well as random surfaces. We test these predictions against exact numerical simulations.

Dynamical Systems approach to Saffman-Taylor fingering. A Dynamical Solvability Scenario

A dynamical systems approach to competition of Saffman-Taylor fingers in a Hele-Shaw channel is developed. This is based on global analysis of the phase space flow of the low-dimensional ordinary-differential-equation sets associated with the classes of exact solutions of the problem without surface tension. Some simple examples are studied in detail. A general proof of the existence of finite-time singularities for broad classes of solutions is given. Solutions leading to finite-time interface pinchoff are also identified. The existence of a continuum of multifinger fixed points and its dynamical implications are discussed. We conclude that exact zero-surface tension solutions taken in a global sense as families of trajectories in phase space are unphysical because the multifinger fixed points are nonhyperbolic, and an unfolding does not exist within the same class of solutions. Hyperbolicity (saddle-point structure) of the multifinger fixed points is argued to be essential to the physically correct qualitative description of finger competition. The restoring of hyperbolicity by surface tension is proposed as the key point to formulate a generic dynamical solvability scenario for interfacial pattern selection.

Chiral unitary approach to eta'N scattering at low energies

We study the eta'N interaction within a chiral unitary approach which includes piN , etaN and related pseudoscalar meson-baryon coupled channels. Since the SU(3) singlet does not contribute to the standard interaction and the eta' is mostly a singlet, the resulting scattering amplitude is very small and inconsistent with experimental estimations of the eta' N scattering length. The additional consideration of vector meson-baryon states into the coupled channel scheme, via normal and anomalous couplings of pseudoscalar to vector mesons, enhances substantially the eta' N amplitude. We also exploit the freedom of adding to the Lagrangian a new term, allowed by the symmetries of QCD, which couples baryons to the singlet meson of SU(3). Adjusting the unknown strength to the eta' N scattering length, we obtain predictions for the elastic eta'N -> etaN and inelastic eta' N -> etaN , piN , KLambda, KEpsilon cross sections at low eta' energies, and discuss their significance.

Langevin approach to generate synthetic turbulent flows

We present an analytical scheme, easily implemented numerically, to generate synthetic Gaussian turbulent flows by using a linear Langevin equation, where the noise term acts as a stochastic stirring force. The characteristic parameters of the velocity field are well introduced, in particular the kinematic viscosity and the spectrum of energy. As an application, the diffusion of a passive scalar is studied for two different energy spectra. Numerical results are compared favorably with analytical calculations.

Design of Optical Systems With Extended Depth of Field: an Educational Approach to Wavefront Coding Techniques

A practical activity designed to introduce wavefront coding techniques as a method to extend the depth of field in optical systems is presented. The activity is suitable for advanced undergraduate students since it combines different topics in optical engineering such as optical system design, aberration theory, Fourier optics, and digital image processing. This paper provides the theoretical background and technical information for performing the experiment. The proposed activity requires students able to develop a wide range of skills since they are expected to deal with optical components, including spatial light modulators, and develop scripts to perform some calculations.

Phenomenological approach to nonlinear Langevin equations

In this paper we address the problem of consistently constructing Langevin equations to describe fluctuations in nonlinear systems. Detailed balance severely restricts the choice of the random force, but we prove that this property, together with the macroscopic knowledge of the system, is not enough to determine all the properties of the random force. If the cause of the fluctuations is weakly coupled to the fluctuating variable, then the statistical properties of the random force can be completely specified. For variables odd under time reversal, microscopic reversibility and weak coupling impose symmetry relations on the variable-dependent Onsager coefficients. We then analyze the fluctuations in two cases: Brownian motion in position space and an asymmetric diode, for which the analysis based in the master equation approach is known. We find that, to the order of validity of the Langevin equation proposed here, the phenomenological theory is in agreement with the results predicted by more microscopic models

A proteomics approach to decipher the molecular nature of planarian stem cells.

Background In recent years, planaria have emerged as an important model system for research into stem cells and regeneration. Attention is focused on their unique stem cells, the neoblasts, which can differentiate into any cell type present in the adult organism. Sequencing of the Schmidtea mediterranea genome and some expressed sequence tag projects have generated extensive data on the genetic profile of these cells. However, little information is available on their protein dynamics. Results We developed a proteomic strategy to identify neoblast-specific proteins. Here we describe the method and discuss the results in comparison to the genomic high-throughput analyses carried out in planaria and to proteomic studies using other stem cell systems. We also show functional data for some of the candidate genes selected in our proteomic approach. Conclusions We have developed an accurate and reliable mass-spectra-based proteomics approach to complement previous genomic studies and to further achieve a more accurate understanding and description of the molecular and cellular processes related to the neoblasts.

Langevin approach to generate synthetic turbulent flows

We present an analytical scheme, easily implemented numerically, to generate synthetic Gaussian turbulent flows by using a linear Langevin equation, where the noise term acts as a stochastic stirring force. The characteristic parameters of the velocity field are well introduced, in particular the kinematic viscosity and the spectrum of energy. As an application, the diffusion of a passive scalar is studied for two different energy spectra. Numerical results are compared favorably with analytical calculations.

Theoretical approach to the magnetostructural correlations in spin-Peierls compound CuGeO3

A theoretical density-functional study has been carried out to analyze the exchange coupling in the chains of CuGeO3 using discrete models. The results show a good agreement with the experimental exchange coupling constant (J) together with a strong dependence of J with the Cu-O-Cu angle. The calculation of the J values for a distorted model indicates a larger degree of dimerization than those reported previously.