On the Locality of the No Hair Conjecture and the Measure of the Universe

We reanalize the recently proposed proof by Jensen and Stein-Schabes [1] of the No Hair Theorem for inhomogeneous spacetimes, putting a special emphasis on the asymptotic behaviour of the shear and curvature. We conclude that the theorem only holds locally and estimate the minimum size a region should be in order for it to inflate. We discuss in some detail the assumptions used in the theorem. In the last section we speculate about the possible measure of the set of spacetimes that would undergo inflation.     

Analysis of the effects of the global financial crisis on the Turkish economy, using hierarchical methods

We have analyzed the topology of 50 important Turkish companies for the period 2006-2010 using the concept of hierarchical methods (the minimal spanning tree (MST) and hierarchical tree (HT)). We investigated the statistical reliability of links between companies in the MST by using the bootstrap technique. We also used the average linkage cluster analysis (ALCA) technique to observe the cluster structures much better. The MST and HT are known as useful tools to perceive and detect global structure, taxonomy, and hierarchy in financial data. We obtained four clusters of companies according to their proximity. We also observed that the Banks and Holdings cluster always forms in the centre of the MSTs for the periods 2006-2007, 2008, and 2009-2010. The clusters match nicely with their common production activities or their strong interrelationship. The effects of the Automobile sector increased after the global financial crisis due to the temporary incentives provided by the Turkish government. We find that Turkish companies were not very affected by the global financial crisis.     

On the propagation of a fissioning system across the barrier towards scission

We describe the motion of a fissioning nuclear system from the potential minimum across the saddle region to scission by means of a Fokker-Planck type equation. We pay particular attention to the problems associated with the motion of broad distributions in phase space. We introduce propagators to obtain global solutions. The results are compared with Kramers' stationary solution for all friction and with simplified dynamical calculations which start behind or on top of the barriers. We are able to find stationary solutions numerically for all finite friction values. We compare the corresponding decay rates with Kramers' formulae for large and small friction.     

Identifying the community structure of the international-trade multi-network

We study the community structure of the multi-network of commodity-specific trade relations among world countries over the 1992-2003 period. We compare structures across commodities and time by means of the normalized mutual information index (NMI). We also compare them with exogenous community structures induced by geography and regional trade agreements. We find that commodity-specific community structures are very heterogeneous and much more fragmented than that characterizing the aggregate ITN. This shows that the aggregate properties of the ITN may result (and be very different) from the aggregation of very diverse commodity-specific layers of the multi-network. We also show that commodity-specific community structures, especially those related to the chemical sector, are becoming more and more similar to the aggregate one. Finally, our findings suggest that geography-induced partitions of our set of countries are much more correlated with observed community structures than partitions induced by regional-trade agreements. This result strengthens previous findings from the empirical literature on trade.     

Constraining the topology of the universe

The first year data from the Wilkinson Microwave Anisotropy Probe are used to place stringent constraints on the topology of the Universe. We search for pairs of circles on the sky with similar temperature patterns along each circle. We restrict the search to back-to-back circle pairs, and to nearly back-to-back circle pairs, as this covers the majority of the topologies that one might hope to detect in a nearly flat universe. We do not find any matched circles with radius greater than 25 degrees. For a wide class of models, the nondetection rules out the possibility that we live in a universe with topology scale smaller than 24 Gpc.     

On the logarithmic solutions of the WDVV equations

We consider restrictions and subsystems in the ∨-systems corresponding to the logarithmic solutions of the WDVV equations. We present certain solutions through restrictions of the Coxeter systems.     

Barriers in the p-spin interacting spin-glass model: the dynamical approach

We investigate the barriers separating metastable states in the spherical p-spin glass model using the instanton method. We show that the problem of finding the barrier heights can be reduced to the causal two-real-replica dynamics. We find the probability for the system to escape one of the highest energy metastable states and the energy barrier corresponding to this process.     

Symanzik's improved actions from the viewpoint of the renormalization group

We investigate Symanzik's improvement program in a four-dimensional Euclidean scalar field theory with smooth momentum space cutoff. We use Wilson's renormalization group transformation to define the improved actions as a sequence of initial data for the effective action at the fundamental cutoff. This leads to a sequence of solutions to the renormalization group equation. We define the parameters of the improved actions implicitly by conditions on the effective action at a renormalization scale. The improved actions are close approximations to the continuum effective action. We prove their existence to every order of improvement and to every order of renormalized perturbation theory.Supported in part by a German National Scholarship Foundation fellowship, and by the National Science Foundation under Grant DMS/PHY 86-45122     

Extrema of the twisted Eguchi-Kawai action and the finite Heisenberg group

We show that representations of the finite Heisenberg group are related to fluxons, which are special configurations of the field in the twisted Eguchi-Kawai model. Fluxons correspond to extrema of the action and in particular to the ground state of this model. We construct and classify these configurations in an even-dimensional space using standard methods of group theory. We also derive the necessary and sufficient conditions for the existence and uniqueness of such configurations.     

The quantum effects of the spin and the Bohm potential in the oblique propagation of magnetosonic waves

We study the quantum corrections to the oblique propagation of the magnetosonic waves in a warm quantum magnetoplasma composed by mobile ions and electrons. We use a fluid formalism to include quantum corrections due to the Bohm potential and to the spin magnetization energy of electrons. The effects of both quantum corrections are shown in the dispersion relation for perpendicular, parallel and oblique propagation. We find that the quantum contributions to the low frequency depend on the type in the oblique propagation with respect to the background magnetic field. The relevance in astrophysical scenarios is exemplified.     

Primordial superstrings and the origin of the universe

We discuss some of the cosmological implications of superstring theories. We pay particular attention to the issue of the initial state and its relationship withR-duality.     

Ab initio simulations of the K-edge shift along the aluminum Hugoniot

We develop a first-principles approach to calculate the near-edge absorption spectrum of dense plasmas based on density functional electronic structure calculations and molecular dynamics simulations. We apply the method to the calculation of the K-edge shift along the aluminum shock compressed Hugoniot. We obtain a good agreement with measurements performed at moderate compression and find that the variation of the XANES spectra could be used as a signature for melting along the Hugoniot. We also show that the calculation of the K-edge shift along the Hugoniot formally requires a fully self-consistent calculation beyond the frozen-core approximation and provides an opportunity to test the accuracy of first principle simulation methods in the high-pressure high-temperature regime.     

Influence of the size,geometry and temporal response of the finite piezoelectric sensor on the photoacoustic signal: the case of the point-like source

Most photoacoustic (PA) work assumes a point-like detection of generated pressure waves; this assumption results in important differences between predicted and experimental signals, as shown in this paper. We used the geometry of a real sensor in the theoretical signal generation through the discretization of the sensing surface, considering each element as a point-like sensor. We modeled the interaction between the wavefront and the real sensor, starting from a well-known PA pressure relation for a point-like source and punctual detection. We obtained the electrical response of the real sensor experimentally and modeled it as a summation of Gaussian functions. The impulse response was convolved with the total PA pressure to obtain the theoretical PA signal. We analyzed the dependence of the source-sensor distance on the discretization size. Then the predicted signal and experimental data were compared for two different frequency response transducers. We found differences in shape and temporal width of simulated PA signals for point-like-source/punctual-detection model and for point-like-source/finite-sensor model.     

Calculations of the propagator within the tomographic-probability framework

We show that the ambiguity in choosing the tomographic propagator for an evolving linear quantum system is related to the homogeneity properties of the system symplectic tomogram. We study in detail an example of the driven harmonic oscillator. We prove that two formally different propagators of the quantum kinetic equation for the oscillator are identical on the domain of homogeneous tomographic probability distributions.     

Fluctuations of the Increment of the Argument for the Gaussian Entire Function

The Gaussian entire function is a random entire function, characterised by a certain invariance with respect to isometries of the plane. We study the fluctuations of the increment of the argument of the Gaussian entire function along planar curves. We introduce an inner product on finite formal linear combinations of curves (with real coefficients), that we call the signed length, which describes the limiting covariance of the increment. We also establish asymptotic normality of fluctuations.     

On the validity of the Fokker-Planck equation for the Heisenberg magnet

We assume an explicit stochastic dynamics for the microscopic variables in the Heisenberg magnet based on experimental data. We obtain additional terms to the Fokker-Planck Equation and also explicit expressions for the numerical coefficients in the Master Equation, near T_c.     

On the interbasis expansion for the Kaluza-Klein monopole system

We study the interbasis expansion of the wave-functions of the Kaluza-Klein monopole system in the parabolic coordinate system with respect to the spherical coordinate system, and vice versa. We show that the coefficients of the expansion are proportional to Clebsch-Gordan coefficients. We analyse the discrete and continuous spectrum as well, briefly discuss the feature that the (reduced) Kaluza-Klein monopole system is separable in three coordinate systems, and the fact that there are five functionally independent integrals of motion, respectively observables, a property which characterizes this system as super-integrable.     

On the calculation of the Berry phase in a solvable model

We study fermions defined on a one-dimensional interval, for which the interaction is given by a four-parameter family of boundary conditions. We compare the full solution to the adiabatic approximation and determine the Berry phase for a number of typical orbits in parameter space. We observe the occurrence of a non-trivial fundamental group and discuss the possibilities of avoided crossings and apparent crossings.     

Observers in Kerr spacetimes: the ergoregion on the equatorial plane

We perform a detailed analysis of the properties of stationary observers located on the equatorial plane of the ergosphere in a Kerr spacetime, including light-surfaces. This study highlights crucial differences between black hole and the super-spinner sources. In the case of Kerr naked singularities, the results allow us to distinguish between “weak” and “strong ” singularities, corresponding to spin values close to or distant from the limiting case of extreme black holes, respectively. We derive important limiting angular frequencies for naked singularities. We especially study very weak singularities as resulting from the spin variation of black holes. We also explore the main properties of zero angular momentum observers for different classes of black hole and naked singularity spacetimes.