Exact ground state of the generalized three-dimensional Shastry-Sutherland model

We generalize the Shastry-Sutherland model to three dimensions. By representing the model as a sum of the semidefinite positive projection operators, we exactly prove that the model has exact dimer ground state. Several schemes for constructing the three-dimensional Shastry-Sutherland model are proposed.Comment: Latex, 3 pages, 5 eps figure

Summary of symposium: Low luminosity sources

The author summarized certain aspects of the conference. He shares this task with another colleague thereby breaking the task into more manageable proportions. The author covers the low luminosity sources. He begins his review with a summary of some major themes of the conference and ends with a few speculations on possible theoretical mechanisms

Stabilization over power-constrained parallel Gaussian channels

This technical note is concerned with state-feedback stabilization of multi-input systems over parallel Gaussian channels subject to a total power constraint. Both continuous-time and discrete-time systems are treated under the framework of H2 control, and necessary/sufficient conditions for stabilizability are established in terms of inequalities involving unstable plant poles, transmitted power, and noise variances. These results are further used to clarify the relationship between channel capacity and stabilizability. Compared to single-input systems, a range of technical issues arise. In particular, in the multi-input case, the optimal controller has a separation structure, and the lower bound on channel capacity for some discrete-time systems is unachievable by linear time-invariant (LTI) encoders/decoder

On the dynamical and arithmetic degrees of rational self-maps of algebraic varieties

Let f : X --> X be a dominant rational map of a projective variety defined over a global field, let d_f be the dynamical degree of f, and let h_X be a Weil height on X relative to an ample divisor. We prove that h_X(f^n(P)) << (d_f + e)^n h_X(P), where the implied constant depends only on X, h_X, f, and e. As applications, we prove a fundamental inequality a_f(P) \le d_f for the upper arithmetic degree and we construct canonical heights for (nef) divisors. We conjecture that a_f(P) = d_f whenever the orbit of P is Zariski dense, and we describe some cases for which we can prove our conjecture.Comment: 32 page

Magnetocentrifugally Driven Flows from Young Stars and Disks. VI. Accretion with a Multipole Stellar Field

Previous analyses of magnetospheric accretion and outflow in classical T Tauri stars (CTTSs), within the context of both the X-wind model and other theoretical scenarios, have assumed a dipolar geometry for the stellar magnetic field if it were not perturbed by the presence of an accreting, electrically conducting disk. However, CTTS surveys reveal that accretion hot spots cover a small fraction of the stellar surface, and that the net field polarization on the stellar surface is small. Both facts imply that the magnetic field generated by the star has a complex non-dipolar structure. To address this discrepancy between theory and observations, we re-examine X-wind theory without the dipole constraint. Using simple physical arguments based on the concept of trapped flux, we show that a dipole configuration is in fact not essential. Independent of the precise geometry of the stellar magnetosphere, the requirement for a certain level of trapped flux predicts a definite relationship among various CTTS observables. Moreover, superposition of multipole stellar fields naturally yield small observed hot-spot covering fractions and small net surface polarizations. The generalized X-wind picture remains viable under these conditions, with the outflow from a small annulus near the inner disk edge little affected by the modified geometry, but with inflow highly dependent on the details of how the emergent stellar flux is linked and trapped by the inner disk regions. Our model is consistent with data, including recent spectropolarimetric measurements of the hot spot sizes and field strengths in V2129 Oph and BP Tau.Comment: ApJ accepted; 47 pages (submission format), 7 figure