How many black holes fit on the head of a pin?

The Bekenstein–Hawking entropy of certain black holes can be computed microscopically in string theory by mapping the elusive problem of counting microstates of a strongly gravitating black hole to the tractable problem of counting microstates of a weakly coupled D-brane system, which has no event horizon, and indeed comfortably fits on the head of a pin. We show here that, contrary to widely held beliefs, the entropy of spherically symmetric black holes can easily be dwarfed by that of stationary multi-black-hole “molecules” of the same total charge and energy. Thus, the corresponding pin-sized D-brane systems do not even approximately count the microstates of a single black hole, but rather those of a zoo of entropically dominant multicentered configurations. Fourth Award in the 2007 Essay Competition of the Gravity Research Foundation.     

On the Zero-Energy-Limit Solution for the Modified Gross–Pitaevskii Equation

The modified Gross–Pitaevskii equation was derived and solved to obtain the 1D solution in the zero-energy limit. This stationary solution could account for the dominated contributions due to the kinetic effect as well as the chemical potential in inhomogeneous Bose gases.     

Faddeev-Noble Versus Sasakawa-Sawada Equations for the Nuclear Three-Body Coulomb Problem

We compare the efficiency of two Faddeev-type approaches for the nuclear three-body Coulomb problem. The first one is a modification of Noble’s approach, the second one is due to Sasakawa and Sawada. In an integral-equation formulation both of these methods rely on the same Green’s operators and driving terms. The differences lie in the treatment of the long-range Coulomb potentials. Numerical examples show that the modified Faddeev-Noble approach provides for faster convergence.     

Banach spaces of distributions having two module structures

After a discussion of a space of test functions and the corresponding space of distributions, a family of Banach spaces (B, ∥ ∥_B) in standard situation is described. These are spaces of distributions having a pointwise module structure and also a module structure with respect to convolution. The main results concern relations between the different spaces associated to B established by means of well-known methods from the theory of Banach modules, among them B₀ and $\text{B}\text{?}$, the closure of the test functions in B and the weak relative completion of B, respectively. The latter is shown to be always a dual Banach space. The main diagram, given in Theorem 4.7, gives full information concerning inclusions between these spaces, showing also a complete symmetry. A great number of corresponding formulas is established. How they can be applied is indicated by selected examples, in particular by certain Segal algebras and the A_p-algebras of Herz. Various further applications are to be given elsewhere.     

Holonomy and path structures in general relativity and Yang-Mills theory

This article is about a different representation of the geometry of the gravitational field, one in which the paths of test bodies play a crucial role. The primary concept is the geometry of the motion of a test body, and the relation between different such possible motions. Space-time as a Lorentzian manifold is regarded as a secondary construct, and it is shown how to construct it from the primary data. Some technical problems remain. Yang-Mills fields are defined by their holonomy in an analogous construction. I detail the development of this idea in the literature, and give a new version of the construction of a bundle and connection from holonomy data. The field equations of general relativity are discussed briefly in this context.     

A generic view of Dantzig-Wolfe decomposition in mixed integer programming

The Dantzig-Wolfe reformulation principle is presented based on the concept of generating sets. The use of generating sets allows for an easy extension to mixed integer programming. Moreover, it provides a unifying framework for viewing various column generation practices, such as relaxing or tightening the column generation subproblem and introducing stabilization techniques.     

Spatially resolved Raman spectroscopy evaluation of residual stresses in 3C-SiC layer deposited on Si substrates with different crystallographic orientations

Raman scattering studies were performed on hot-wall chemical vapor deposited (heteroepitaxial) silicon carbide (SiC) films grown on Si substrates with orientations of (1 0 0), (1 1 1), (1 1 0) and (2 1 1), respectively. Raman spectra suggested that good quality cubic SiC single crystals could be obtained on the Si substrate, independent of its crystallographic orientation. Average residual stresses in the epitaxially grown 3C-SiC films were measured with the laser waist focused on the epilayer surface. Tensile and compressive residual stresses were found to be stored within the SiC film and in the Si substrate, respectively. The residual stress exhibited a marked dependence on the orientation of the substrate. The measured stresses were comparable to the thermal stress deduced from elastic deformation theory, which demonstrates that the large lattice mismatch between cubic SiC and Si is effectively relieved by initial carbonization. The confocal configuration of the optical probe enabled a stress evaluation along the cross-section of the sample, which showed maximum tensile stress magnitude at the SiC/Si interface from the SiC side, decreasing away from the interface in varied rate for different crystallographic orientations. Defocusing experiments were used to precisely characterize the geometry of the laser probe in 3C-SiC single crystal. Based on this knowledge, a theoretical convolution of the in-depth stress distribution could be obtained, which showed a satisfactory agreement with stress values obtained by experiments performed on the 3C-SiC surface.