Monopoles and the Emergence of Black Hole Entropy

One of the remarkable features of black holes is that they possess a thermodynamic description, even though they do not appear to be statistical systems. We use self-gravitating magnetic monopole solutions as tools for understanding the emergence of this description as one goes from an ordinary spacetime to one containing a black hole. We describe how causally distinct regions emerge as a monopole solution develops a horizon. We define an entropy that is naturally associated with these regions and that has a clear connection with the Hawking-Bekenstein entropy in the critical black hole limit.Comment: 6 pages, one figure RevTe

Structure and stability of helices in square-well homopolymers

Recently, it has been demonstrated [Magee et al., Phys. Rev. Lett. 96, 207802 (2006)] that isolated, square-well homopolymers can spontaneously break chiral symmetry and freeze into helical structures at sufficiently low temperatures. This behavior is interesting because the square-well homopolymer is itself achiral. In this work, we use event-driven molecular dynamics, combined with an optimized parallel tempering scheme, to study this polymer model over a wide range of parameters. We examine the conditions where the helix structure is stable and determine how the interaction parameters of the polymer govern the details of the helix structure. The width of the square well (proportional to lambda) is found to control the radius of the helix, which decreases with increasing well width until the polymer forms a coiled sphere for sufficiently large wells. The helices are found to be stable for only a window of molecular weights. If the polymer is too short, the helix will not form. If the polymer is too long, the helix is no longer the minimum energy structure, and other folded structures will form. The size of this window is governed by the chain stiffness, which in this model is a function of the ratio of the monomer size to the bond length. Outside this window, the polymer still freezes into a locked structure at low temperature, however, unless the chain is sufficiently stiff, this structure will not be unique and is similar to a glassy state.Comment: Submitted to Physical Review

Spin gap behavior in Cu2_2Sc2_2Ge4_4O13_{13} by 45^{45}Sc nuclear magnetic resonance

We report the results of a $^{45}$Sc nuclear magnetic resonance (NMR) study on the quasi-one-dimensional compound Cu$_2$Sc$_2$Ge$_4$O$_{13}$ at temperatures between 4 and 300 K. This material has been a subject of current interest due to indications of spin gap behavior. The temperature-dependent NMR shift exhibits a character of low-dimensional magnetism with a negative broad maximum at $T_{max}$ $\simeq$ 170 K. Below $$, the NMR shifts and spin lattice relaxation rates clearly indicate activated responses, confirming the existence of a spin gap in Cu$_2$Sc$_2$Ge% $_4$O$_{13}$. The experimental NMR data can be well fitted to the spin dimer model, yielding a spin gap value of about 275 K which is close to the 25 meV peak found in the inelastic neutron scattering measurement. A detailed analysis further points out that the nearly isolated dimer picture is proper for the understanding of spin gap nature in Cu$_2$Sc$_2$Ge$_4$O$_{13}$.Comment: 4 pages, 6 figures, submitted to Phys. Rev.

Quasi-Black Holes from Extremal Charged Dust

One can construct families of static solutions that can be viewed as interpolating between nonsingular spacetimes and those containing black holes. Although everywhere nonsingular, these solutions come arbitrarily close to having a horizon. To an observer in the exterior region, it becomes increasingly difficulty to distinguish these from a true black hole as the critical limiting solution is approached. In this paper we use the Majumdar-Papapetrou formalism to construct such quasi-black hole solutions from extremal charged dust. We study the gravitational properties of these solutions, comparing them with the the quasi-black hole solutions based on magnetic monopoles. As in the latter case, we find that solutions can be constructed with or without hair.Comment: 18 page

Preparing Preservice Teachers to Address the Disproportionality of ELLs in Exceptional Education Programs

As our nation’s classrooms become more diverse, how to best educate all of our students is of paramount importance. The educational placement of students of racial, cultural, ethnic, and linguistic diversity in classes for students with special needs at a disproportionate level is well documented. This paper addresses the issue of disproportionate representation of English Language Learners (ELLs) in special education programs. Teacher beliefs, cultural bias, lack of culturally responsive professional development opportunities, and assessments contribute to inappropriate referrals and identification. Preparing preservice teachers to understand disproportionality and why it exists can help reduce the inappropriate referrals and placement of ELLs in special education programs

Gravitational Properties of Monopole Spacetimes Near the Black Hole Threshold

Although nonsingular spacetimes and those containing black holes are qualitatively quite different, there are continuous families of configurations that connect the two. In this paper we use self-gravitating monopole solutions as tools for investigating the transition between these two types of spacetimes. We show how causally distinct regions emerge as the black hole limit is achieved, even though the measurements made by an external observer vary continuously. We find that near-critical solutions have a naturally defined entropy, despite the absence of a true horizon, and that this has a clear connection with the Hawking-Bekenstein entropy. We find that certain classes of near-critical solutions display naked black hole behavior, although they are not truly black holes at all. Finally, we present a numerical simulation illustrating how an incident pulse of matter can induce the dynamical collapse of a monopole into an extremal black hole. We discuss the implications of this process for the third law of black hole thermodynamics.Comment: 23 pages, 4 figures RevTe