Cohomology Groups of Deformations of Line Bundles on Complex Tori

The cohomology groups of line bundles over complex tori (or abelian varieties) are classically studied invariants of these spaces. In this article, we compute the cohomology groups of line bundles over various holomorphic, non-commutative deformations of complex tori. Our analysis interpolates between two extreme cases. The first case is a calculation of the space of (cohomological) theta functions for line bundles over constant, commutative deformations. The second case is a calculation of the cohomologies of non-commutative deformations of degree-zero line bundles.Comment: 24 pages, exposition improved, typos fixe

Comparison between three-dimensional linear and nonlinear tsunami generation models

The modeling of tsunami generation is an essential phase in understanding tsunamis. For tsunamis generated by underwater earthquakes, it involves the modeling of the sea bottom motion as well as the resulting motion of the water above it. A comparison between various models for three-dimensional water motion, ranging from linear theory to fully nonlinear theory, is performed. It is found that for most events the linear theory is sufficient. However, in some cases, more sophisticated theories are needed. Moreover, it is shown that the passive approach in which the seafloor deformation is simply translated to the ocean surface is not always equivalent to the active approach in which the bottom motion is taken into account, even if the deformation is supposed to be instantaneous.Comment: 39 pages, 16 figures; Accepted to Theoretical and Computational Fluid Dynamics. Several references have been adde

Tachyon Condensation on Noncommutative Torus

We discuss noncommutative solitons on a noncommutative torus and their application to tachyon condensation. In the large B limit, they can be exactly described by the Powers-Rieffel projection operators known in the mathematical literature. The resulting soliton spectrum is consistent with T-duality and is surprisingly interesting. It is shown that an instability arises for any D-branes, leading to the decay into many smaller D-branes. This phenomenon is the consequence of the fact that K-homology for type II von Neumann factor is labeled by R.Comment: LaTeX, 17 pages, 1 figur

Water waves generated by a moving bottom

Tsunamis are often generated by a moving sea bottom. This paper deals with the case where the tsunami source is an earthquake. The linearized water-wave equations are solved analytically for various sea bottom motions. Numerical results based on the analytical solutions are shown for the free-surface profiles, the horizontal and vertical velocities as well as the bottom pressure.Comment: 41 pages, 13 figures. Accepted for publication in a book: "Tsunami and Nonlinear Waves", Kundu, Anjan (Editor), Springer 2007, Approx. 325 p., 170 illus., Hardcover, ISBN: 978-3-540-71255-8, available: May 200

Triangle-generation in topological D-brane categories

Tachyon condensation in topological Landau-Ginzburg models can generally be studied using methods of commutative algebra and properties of triangulated categories. The efficiency of this approach is demonstrated by explicitly proving that every D-brane system in all minimal models of type ADE can be generated from only one or two fundamental branes.Comment: 34 page

Noncommutative homotopy algebras associated with open strings

We discuss general properties of $A_\infty$-algebras and their applications to the theory of open strings. The properties of cyclicity for $A_\infty$-algebras are examined in detail. We prove the decomposition theorem, which is a stronger version of the minimal model theorem, for $A_\infty$-algebras and cyclic $A_\infty$-algebras and discuss various consequences of it. In particular it is applied to classical open string field theories and it is shown that all classical open string field theories on a fixed conformal background are cyclic $A_\infty$-isomorphic to each other. The same results hold for classical closed string field theories, whose algebraic structure is governed by cyclic $L_\infty$-algebras.Comment: 92 pages, 16 figuers; based on Ph.D thesis submitted to Graduate School of Mathematical Sciences, Univ. of Tokyo on January, 2003; v2: explanation improved, references added, published versio

Beta-gamma systems and the deformations of the BRST operator

We describe the relation between simple logarithmic CFTs associated with closed and open strings, and their "infinite metric" limits, corresponding to the beta-gamma systems. This relation is studied on the level of the BRST complex: we show that the consideration of metric as a perturbation leads to a certain deformation of the algebraic operations of the Lian-Zuckerman type on the vertex algebra, associated with the beta-gamma systems. The Maurer-Cartan equations corresponding to this deformed structure in the quasiclassical approximation lead to the nonlinear field equations. As an explicit example, we demonstrate, that using this construction, Yang-Mills equations can be derived. This gives rise to a nontrivial relation between the Courant-Dorfman algebroid and homotopy algebras emerging from the gauge theory. We also discuss possible algebraic approach to the study of beta-functions in sigma-models.Comment: LaTeX2e, 15 pages; minor revision, typos corrected, Journal of Physics A, in pres

Linear and nonlinear computations of the 1992 Nicaragua earthquake tsunami

Numerical computations of tsunamis are made for the 1992 Nicaragua earthquake using different governing equations, bottom frictional values and bathymetry data. The results are compared with each other as well as with the observations, both tide gauge records and runup heights. Comparison of the observed and computed tsunami waveforms indicates that the use of detailed bathymetry data with a small grid size is more effective than to include nonlinear terms in tsunami computation. Linear computation overestimates the amplitude for the later phase than the first arrival, particularly when the amplitude becomes large. The computed amplitudes along the coast from nonlinear computation are much smaller than the observed tsunami runup heights; the average ratio, or the amplification factor, is estimated to be 3 in the present case when the grid size of 1 minute is used. The factor however may depend on the grid size for the computation.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43193/1/24_2004_Article_BF00874378.pd

The Molecular Signature Underlying the Thymic Migration and Maturation of TCRαβ+CD4+CD8- Thymocytes

BACKGROUND: After positive selection, the newly generated single positive (SP) thymocytes migrate to the thymic medulla, where they undergo negative selection to eliminate autoreactive T cells and functional maturation to acquire immune competence and egress capability. METHODOLOGY/PRINCIPAL FINDINGS: To elucidate the genetic program underlying this process, we analyzed changes in gene expression in four subsets of mouse TCRαβ(+)CD4(+)CD8(-) thymocytes (SP1 to SP4) representative of sequential stages in a previously defined differentiation program. A genetic signature of the migration of thymocytes was thus revealed. CCR7 and PlexinD1 are believed to be important for the medullary positioning of SP thymocytes. Intriguingly, their expression remains at low levels in the newly generated thymocytes, suggesting that the cortex-medulla migration may not occur until the SP2 stage. SP2 and SP3 cells gradually up-regulate transcripts involved in T cell functions and the Foxo1-KLF2-S1P(1) axis, but a number of immune function-associated genes are not highly expressed until cells reach the SP4 stage. Consistent with their critical role in thymic emigration, the expression of S1P(1) and CD62L are much enhanced in SP4 cells. CONCLUSIONS: These results support at the molecular level that single positive thymocytes undergo a differentiation program and further demonstrate that SP4 is the stage at which thymocytes acquire the immunocompetence and the capability of emigration from the thymus