Representations of reductive normal algebraic monoids

The rational representation theory of a reductive normal algebraic monoid (with one-dimensional center) forms a highest weight category, in the sense of Cline, Parshall, and Scott. This is a fundamental fact about the representation theory of reductive normal algebraic monoids. We survey how this result was obtained, and treat some natural examples coming from classical groups.Comment: 10 pages. To appear in a volume of the Fields Communications Series: "Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics," edited by Mahir Can, Zhenheng Li, Benjamin Steinberg, and Qiang Wan

Hole Spin Mixing in InAs Quantum Dot Molecules

Holes confined in single InAs quantum dots have recently emerged as a promising system for the storage or manipulation of quantum information. These holes are often assumed to have only heavy-hole character and further assumed to have no mixing between orthogonal heavy hole spin projections (in the absence of a transverse magnetic field). The same assumption has been applied to InAs quantum dot molecules formed by two stacked InAs quantum dots that are coupled by coherent tunneling of the hole between the two dots. We present experimental evidence of the existence of a hole spin mixing term obtained with magneto-photoluminescence spectroscopy on such InAs quantum dot molecules. We use a Luttinger spinor model to explain the physical origin of this hole spin mixing term: misalignment of the dots along the stacking direction breaks the angular symmetry and allows mixing through the light-hole component of the spinor. We discuss how this novel spin mixing mechanism may offer new spin manipulation opportunities that are unique to holes.Comment: 13 pages, 9 figure

Photoluminescence Spectroscopy of the Molecular Biexciton in Vertically Stacked Quantum Dot Pairs

We present photoluminescence studies of the molecular neutral biexciton-exciton spectra of individual vertically stacked InAs/GaAs quantum dot pairs. We tune either the hole or the electron levels of the two dots into tunneling resonances. The spectra are described well within a few-level, few-particle molecular model. Their properties can be modified broadly by an electric field and by structural design, which makes them highly attractive for controlling nonlinear optical properties.Comment: 4 pages, 5 figures, (v2, revision based on reviewers comments, published

Experiment K-6-03. Gravity and skeletal growth, part 1. Part 2: Morphology and histochemistry of bone cells and vasculature of the tibia; Part 3: Nuclear volume analysis of osteoblast histogenesis in periodontal ligament cells; Part 4: Intervertebral disc swelling pressure associated with microgravity

Bone area, bone electrophysiology, bone vascularity, osteoblast morphology, and osteoblast histogenesis were studied in rats associated with Cosmos 1887. The results suggest that the synchronous animals were the only group with a significantly larger bone area than the basal group, that the bone electrical potential was more negative in flight than in the synchronous rats, that the endosteal osteoblasts from flight rats had greater numbers of transitional Golgi vesicles but no difference in the large Golgi saccules or the alkaline phosphatase activity, that the perioteal vasculature in the shaft of flight rats often showed very dense intraluminal deposits with adjacent degenerating osteocytes as well as lipid accumulations within the lumen of the vessels and sometimes degeneration of the vascular wall (this change was not present in the metaphyseal region of flight animals), and that the progenitor cells decreased in flight rats while the preosteoblasts increased compared to controls. Many of the results suggest that the animals were beginning to recover from the effects of spaceflight during the two day interval between landing and euthanasia; flight effects, such as the vascular changes, did not appear to recover

Electrically tunable g-factors in quantum dot molecular spin states

We present a magneto-photoluminescence study of individual vertically stacked InAs/GaAs quantum dot pairs separated by thin tunnel barriers. As an applied electric field tunes the relative energies of the two dots, we observe a strong resonant increase or decrease in the g-factors of different spin states that have molecular wavefunctions distributed over both quantum dots. We propose a phenomenological model for the change in g-factor based on resonant changes in the amplitude of the wavefunction in the barrier due to the formation of bonding and antibonding orbitals.Comment: 5 pages, 5 figures, Accepted by Phys. Rev. Lett. New version reflects response to referee comment

Effects of clumping on temperature I: externally heated clouds

We present a study of radiative transfer in dusty, clumpy star-forming regions. A series of self-consistent, 3-D, continuum radiative transfer models are constructed for a grid of models parameterized by central luminosity, filling factor, clump radius, and face-averaged optical depth. The temperature distribution within the clouds is studied as a function of this parameterization. Among our results, we find that: (a) the effective optical depth is smaller in clumpy regions than in equivalent homogeneous regions; (b) penetration of radiation is drive by the fraction of open sky (FOS) -- which measures the fraction of solid angle which is devoid of clumps; (c) FOS increases as clump radius increases and filling factor decreases; (d) for FOS > 0.6-0.8 the sky is sufficiently open that the temperature is relatively insensitive to FOS; (e) the physical process by which radiation penetrates is streaming between clumps; (f) filling factor dominates the temperature distribution for large optical depths, and at small clump radii for small optical depths; (g) at lower optical depths, the temperature distribution is most sensitive to filling factors of 1-10 per cent, in accordance with many observations; (h) direct shadowing can be important approximately one clump radius behind a clump.Comment: 12 pages, 17 figures, accepted by MNRA

The Complexity of Fixed-Height Patterned Tile Self-Assembly

We characterize the complexity of the PATS problem for patterns of fixed height and color count in variants of the model where seed glues are either chosen or fixed and identical (so-called non-uniform and uniform variants). We prove that both variants are NP-complete for patterns of height 2 or more and admit O(n)-time algorithms for patterns of height 1. We also prove that if the height and number of colors in the pattern is fixed, the non-uniform variant admits a O(n)-time algorithm while the uniform variant remains NP-complete. The NP-completeness results use a new reduction from a constrained version of a problem on finite state transducers.Comment: An abstract version appears in the proceedings of CIAA 201

Spin Fine Structure in Optically Excited Quantum Dot Molecules

The interaction between spins in coupled quantum dots is revealed in distinct fine structure patterns in the measured optical spectra of InAs/GaAs double quantum dot molecules containing zero, one, or two excess holes. The fine structure is explained well in terms of a uniquely molecular interplay of spin exchange interactions, Pauli exclusion and orbital tunneling. This knowledge is critical for converting quantum dot molecule tunneling into a means of optically coupling not just orbitals, but spins.Comment: 10 pages, 7 figures, added material, (published

Physical-chemical modeling of the low-mass protostar IRAS 16293-2422

We present detailed gas-phase chemical models for the envelope of the low-mass star-forming region IRAS 16293-2422. By considering both time- and space-dependent chemistry, these models are used to study both the physical structure proposed by Schoier et al. (2002), as well as the chemical evolution of this region. A new feature of our study is the use of a detailed, self-consistent radiative transfer model to translate the model abundances into line strengths and compare them directly with observations of a total of 76 transitions for 18 chemical species, and their isotopes. The model can reproduce many of the line strengths observed within 50%. The best fit is for times in the range of 3e3 - 3e4 yrs, and requires only minor modifications to our model for the high-mass star-forming region AFGL 2591. The ionization rate for the source may be higher than previously expected -- either due to an enhanced cosmic-ray ionization rate, or, more probably, to the presence of X-ray induced ionization from the center. A significant fraction of the CO is found to desorb in the temperature range of 15-40 K; below this temperature, \~90% or more of the CO is frozen out. The inability of the model to explain the HCS+, C2H, and OCS abundances suggests the importance of further laboratory studies of basic reaction rates. Finally, predictions of the abundances and spatial distributions of other species which could be observed by future facilities (e.g., Herschel-HIFI, SOFIA, millimeter arrays) are provided.Comment: 15 pages, 11 Figures, accepted for publication by A&