Black hole formation from massive scalar field collapse in the Einstein-de Sitter universe

We study the spherically symmetric collapse of a real, minimally coupled, massive scalar field in an asymptotically Einstein-de Sitter spacetime background. By means of an eikonal approximation for the field and metric functions, we obtain a simple analytical criterion---involving the physical size and mass scales (the field's inverse Compton wavelength and the spacetime gravitational mass) of the initial matter configuration---for generic (non-time-symmetric) initial data to collapse to a black hole. This analytical condition can then be used to place constraints on the initial primordial black hole spectrum, by considering spherical density perturbations that re-entered the horizon during an early matter-dominated phase that immediately followed inflation.Comment: 9 pages, RevTeX, 3 eps figures; to appear in Phys. Rev.

The cerebellum could solve the motor error problem through error increase prediction

We present a cerebellar architecture with two main characteristics. The first one is that complex spikes respond to increases in sensory errors. The second one is that cerebellar modules associate particular contexts where errors have increased in the past with corrective commands that stop the increase in error. We analyze our architecture formally and computationally for the case of reaching in a 3D environment. In the case of motor control, we show that there are synergies of this architecture with the Equilibrium-Point hypothesis, leading to novel ways to solve the motor error problem. In particular, the presence of desired equilibrium lengths for muscles provides a way to know when the error is increasing, and which corrections to apply. In the context of Threshold Control Theory and Perceptual Control Theory we show how to extend our model so it implements anticipative corrections in cascade control systems that span from muscle contractions to cognitive operations.Comment: 34 pages (without bibliography), 13 figure

Block co-polyMOFs: morphology control of polymer-MOF hybrid materials.

The hybridization of block copolymers and metal-organic frameworks (MOFs) to create novel materials (block co-polyMOFs, BCPMOFs) with controlled morphologies is reported. In this study, block copolymers containing poly(1,4-benzenedicarboxylic acid, H2bdc) and morphology directing poly(ethylene glycol) (PEG) or poly(cyclooctadiene) (poly(COD)) blocks were synthesized for the preparation of BCPMOFs. Block copolymer architecture and weight fractions were found to have a significant impact on the resulting morphology, mediated through the assembly of polymer precursors prior to MOF formation, as determined through dynamic light scattering. Simple modification of block copolymer weight fraction allowed for tuning of particle size and morphology with either faceted and spherical features. Modification of polymer block architecture represents a simple and powerful method to direct morphology in highly crystalline polyMOF materials. Furthermore, the BCPMOFs could be prepared from both Zr4+ and Zn2+ MOFs, yielding hybrid materials with appreciable surface areas and tuneable porosities. The resulting Zn2+ BCPMOF yielded materials with very narrow size distributions and uniform cubic morphologies. The use of topology in BCPMOFs to direct morphology in block copolymer assemblies may open new methodologies to access complex materials far from thermodynamic equilibrium