Initial Conditions of Planet Formation: Lifetimes of Primordial Disks

The statistical properties of circumstellar disks around young stars are important for constraining theoretical models for the formation and early evolution of planetary systems. In this brief review, I survey the literature related to ground-based and Spitzer-based infrared (IR) studies of young stellar clusters, with particular emphasis on tracing the evolution of primordial (``protoplanetary'') disks through spectroscopic and photometric diagnostics. The available data demonstrate that the fraction of young stars with optically thick primordial disks and/or those which show spectroscopic evidence for accretion appears to approximately follow an exponential decay with characteristic time ~2.5 Myr (half-life = 1.7 Myr). Large IR surveys of ~2-5 Myr-old stellar samples show that there is real cluster-by-cluster scatter in the observed disk fractions as a function of age. Recent Spitzer surveys have found convincing evidence that disk evolution varies by stellar mass and environment (binarity, proximity to massive stars, and cluster density). Perhaps most significantly for understanding the planeticity of stars, the disk fraction decay timescale appears to vary by stellar mass, ranging from ~1 Myr for >1.3 Msun stars to ~3 Myr for <0.08 Msun brown dwarfs. The exponential decay function may provide a useful empirical formalism for estimating very rough ages for YSO populations and for modeling the effects of disk-locking on the angular momentum of young stars.Comment: 8 pages, 1 figure, invited review, Proceedings of the 2nd Subaru International Conference "Exoplanets and Disks: Their Formation and Diversity", Keauhou - Hawaii - USA, 9-12 March 200

Inverse scattering method for square matrix nonlinear Schr\"odinger equation under nonvanishing boundary conditions

Matrix generalization of the inverse scattering method is developed to solve the multicomponent nonlinear Schr\"odinger equation with nonvanishing boundary conditions. It is shown that the initial value problem can be solved exactly. The multi-soliton solution is obtained from the Gel'fand--Levitan--Marchenko equation.Comment: 25 pages, 2 figures; (v2) title changed, typos in equations corrected, sec.3.1 modified and extende

Functional variants of DOG1 control seed chilling responses and variation in seasonal life-history strategies in Arabidopsis thaliana.

The seasonal timing of seed germination determines a plant's realized environmental niche, and is important for adaptation to climate. The timing of seasonal germination depends on patterns of seed dormancy release or induction by cold and interacts with flowering-time variation to construct different seasonal life histories. To characterize the genetic basis and climatic associations of natural variation in seed chilling responses and associated life-history syndromes, we selected 559 fully sequenced accessions of the model annual species Arabidopsis thaliana from across a wide climate range and scored each for seed germination across a range of 13 cold stratification treatments, as well as the timing of flowering and senescence. Germination strategies varied continuously along 2 major axes: 1) Overall germination fraction and 2) induction vs. release of dormancy by cold. Natural variation in seed responses to chilling was correlated with flowering time and senescence to create a range of seasonal life-history syndromes. Genome-wide association identified several loci associated with natural variation in seed chilling responses, including a known functional polymorphism in the self-binding domain of the candidate gene DOG1. A phylogeny of DOG1 haplotypes revealed ancient divergence of these functional variants associated with periods of Pleistocene climate change, and Gradient Forest analysis showed that allele turnover of candidate SNPs was significantly associated with climate gradients. These results provide evidence that A. thaliana's germination niche and correlated life-history syndromes are shaped by past climate cycles, as well as local adaptation to contemporary climate

Valuing Adjuncts as Liaisons for University Excellence (VALUE) Program

Adjuncts are increasingly becoming more important in higher education and make up nearly onethird of VCU’s teaching faculty. While VCU has made strides in increasing the number of tenuretrack and term professors, the size and needs of certain departments will always make adjunct instructors necessary. A number of schools on both the Monroe Park and MCV campuses utilize professionals from the Richmond community to enhance experiential learning, thereby making a university investment in adjunct faculty a means by which to elevate VCU’s strategic mission. Adjuncts often provide a community perspective that comes from the professional work they do outside of the university setting and as a whole are reflective of VCU’s diverse student population. As a result, they serve a critical role in student success and diversity initiatives. Keeping adjuncts connected with campus resources and engaged with the larger VCU community is also an important step in making the university more inclusive. This project will study opportunities associated with the orientation and support of adjunct faculty at VCU on both Monroe Park and MCV campuses. This project is research-oriented and will serve as an important foundation for developing and implementing a plan for institutionalized adjunct support. To develop a detailed proposal for implementation, our team consulted with several key stakeholders including: academic leaders who hire and support adjuncts in the current decentralized process students who have taken classes with adjunct instructors adjunct faculty who have recently taught at VCU Through a combination of methods, we aim to determine how adjuncts are utilized across the university, identify resources currently provided, and assess additional resource needs in an effort to inform a new orientation and support program for adjunct faculty at VCU

An Algebraic Model for the Multiple Meixner Polynomials of the First Kind

An interpretation of the multiple Meixner polynomials of the first kind is provided through an infinite Lie algebra realized in terms of the creation and annihilation operators of a set of independent oscillators. The model is used to derive properties of these orthogonal polynomials

A superintegrable finite oscillator in two dimensions with SU(2) symmetry

A superintegrable finite model of the quantum isotropic oscillator in two dimensions is introduced. It is defined on a uniform lattice of triangular shape. The constants of the motion for the model form an SU(2) symmetry algebra. It is found that the dynamical difference eigenvalue equation can be written in terms of creation and annihilation operators. The wavefunctions of the Hamiltonian are expressed in terms of two known families of bivariate Krawtchouk polynomials; those of Rahman and those of Tratnik. These polynomials form bases for SU(2) irreducible representations. It is further shown that the pair of eigenvalue equations for each of these families are related to each other by an SU(2) automorphism. A finite model of the anisotropic oscillator that has wavefunctions expressed in terms of the same Rahman polynomials is also introduced. In the continuum limit, when the number of grid points goes to infinity, standard two-dimensional harmonic oscillators are obtained. The analysis provides the $N\rightarrow \infty$ limit of the bivariate Krawtchouk polynomials as a product of one-variable Hermite polynomials

Stability of Bose-Einstein Condensates Confined in Traps

Bose-Einstein condensation has been realized in dilute atomic vapors. This achievement has generated immerse interest in this field. Presented is a review of recent theoretical research into the properties of trapped dilute-gas Bose-Einstein condensates. Among them, stability of Bose-Einstein condensates confined in traps is mainly discussed. Static properties of the ground state are investigated by use of the variational method. The anlysis is extended to the stability of two-component condensates. Time-development of the condensate is well-described by the Gross-Pitaevskii equation which is known in nonlinear physics as the nonlinear Schr\"odinger equation. For the case that the inter-atomic potential is effectively attractive, a singularity of the solution emerges in a finite time. This phenomenon which we call collapse explains the upper bound for the number of atoms in such condensates under traps.Comment: 74 pages with 12 figures, submitted to the review section of International Journal of Modern Physics

Extended SL(2,R)/U(1) characters, or modular properties of a simple non-rational conformal field theory

We define extended SL(2,R)/U(1) characters which include a sum over winding sectors. By embedding these characters into similarly extended characters of N=2 algebras, we show that they have nice modular transformation properties. We calculate the modular matrices of this simple but non-trivial non-rational conformal field theory explicitly . As a result, we show that discrete SL(2,R) representations mix with continuous SL(2,R) representations under modular transformations in the coset conformal field theory. We comment upon the significance of our results for a general theory of non-rational conformal field theories.Comment: JHEP style, 25 pages, 2 figures, v2: minor corrections, reference added, version to appear in JHE