Fractionalization in a square-lattice model with time-reversal symmetry

We propose a two-dimensional time-reversal invariant system of essentially non-interacting electrons on a square lattice that exhibits configurations with fractional charges e/2. These are vortex-like topological defects in the dimerization order parameter describing spatial modulation in the electron hopping amplitudes. Charge fractionalization is established by a simple counting argument, analytical calculation within the effective low-energy theory, and by an exact numerical diagonalization of the lattice Hamiltonian. We comment on the exchange statistics of fractional charges and possible realizations of the system.Comment: 4 pages, 3 figures, RevTex 4. (v2) improved discussion of lattice effects and confinement; clearer figure

Dodecahedral topology fails to explain quadrupole-octupole alignment

The CMB quadrupole and octupole, as well as being weaker than expected, align suspiciously well with each other. Non-trivial spatial topology can explain the weakness. Might it also explain the alignment? The answer, at least in the case of the Poincare dodecahedral space, is a resounding no.Comment: 5 pages, 1 figur

Invariance of Structure in an Aging Colloidal Glass

We study concentrated colloidal suspensions, a model system which has a glass transition. The non-equilibrium nature of the glassy state is most clearly highlighted by aging -- the dependence of the system's properties on the time elapsed since vitrification. Fast laser scanning confocal microscopy allows us to image a colloidal glass and track the particles in three dimensions. We analyze the static structure in terms of tetrahedral packing. We find that while the aging of the suspension clearly affects its dynamics, none of the geometrical quantities associated with tetrahedra change with age.Comment: Submitted to the proceedings of "The 3rd International Workshop on Complex Systems" in Sendai, Japa

Ice storm effects on the canopy structure of a northern hardwood forest after 8 years

Ice storms can cause severe damage to forest canopies, resulting in differential mortality among tree species and size classes and leading to long-lasting changes in the vertical structure and composition of the forest. An intense ice storm in 1998 damaged large areas of the northern hardwood forest, including much of the Hubbard Brook Experimental Forest, New Hampshire (USA). Following up on detailed poststorm assessments, we measured changes in the vertical structure of the forest canopy 8 years poststorm. We focused on how the presence of disease-induced advance regeneration of American beech (Fagus grandifolia Ehrh.) has affected canopy structure in the recovering forest. We measured foliage-height profiles using a point-quadrat approach and a pole-mounted leaf area index (LAI) sensor. Although the total LAIs of damaged and undamaged areas were similar, areas damaged in 1998 showed an increased proportion of total leaf area between 6 and 10 m above the ground. The foliage at this height is largely (54%) beech. To the extent that this heavily beech-dominated understory layer suppresses regeneration of other species, these findings suggest that rare disturbances of mature northern hardwood forests affected by beech bark disease will increase the importance of damage-prone and economically marginal beech

Polynomial Interpretation of Multipole Vectors

Copi, Huterer, Starkman and Schwarz introduced multipole vectors in a tensor context and used them to demonstrate that the first-year WMAP quadrupole and octopole planes align at roughly the 99.9% confidence level. In the present article the language of polynomials provides a new and independent derivation of the multipole vector concept. Bezout's Theorem supports an elementary proof that the multipole vectors exist and are unique (up to rescaling). The constructive nature of the proof leads to a fast, practical algorithm for computing multipole vectors. We illustrate the algorithm by finding exact solutions for some simple toy examples, and numerical solutions for the first-year WMAP quadrupole and octopole. We then apply our algorithm to Monte Carlo skies to independently re-confirm the estimate that the WMAP quadrupole and octopole planes align at the 99.9% level.Comment: Version 1: 6 pages. Version 2: added uniqueness proof to Corollary 2; added proper citation (to Starkman et al.) for Open Question; other minor improvement