Noncommutative Deformation of Spinor Zero Mode and ADHM Construction

A method to construct noncommutative instantons as deformations from commutative instantons was provided in arXiv:0805.3373. Using this noncommutative deformed instanton, we investigate the spinor zero modes of the Dirac operator in a noncommutative instanton background on noncommutative R^4, and we modify the index of the Dirac operator on the noncommutative space slightly and show that the number of the zero mode of the Dirac operator is preserved under the noncommutative deformation. We prove the existence of the Green's function associated with instantons on noncommutative R^4, as a smooth deformation of the commutative case. The feature of the zero modes of the Dirac operator and the Green's function derives noncommutative ADHM equations which coincide with the ones introduced by Nekrasov and Schwarz. We show a one-to-one correspondence between the instantons on noncommutative R^4 and ADHM data. An example of a noncommutative instanton and a spinor zero mode are also given.Comment: 34 pages, no figures, v3: an appendix and some definitions added,typos correcte

On non commutative sinh-Gordon Equation

We give a noncommutative extension of sinh-Gordon equation. We generalize a linear system and Lax representation of the sinh-Gordon equation in noncommutative space. This generalization gives a noncommutative version of the sinh-Gordon equation with extra constraints, which can be expressed as global conserved currents.Comment: 7 Page

Polar relaxation by dynein-mediated removal of cortical myosin II

Nearly 6 decades ago, Lewis Wolpert proposed the relaxation of the polar cell cortex by the radial arrays of astral microtubules as a mechanism for cleavage furrow induction (White and Borisy, 1983; Wolpert, 1960). While this mechanism has remained controversial (Rappaport, 1996), recent work has provided evidence for polar relaxation by astral microtubules (Chen et al., 2008; Dechant and Glotzer, 2003; Foe and Dassow, 2008; Murthy and Wadsworth, 2008; Werner et al., 2007), although its molecular mechanisms remain elusive. Here, using C. elegans embryos, we show that polar relaxation is achieved through dynein-mediated removal of myosin II from the polar cortexes. Mutants that position centrosomes closer to the polar cortex accelerated furrow induction whereas suppression of dynein activity delayed furrowing. We provide evidence that dynein-mediated removal of myosin II from the polar cortexes triggers cortical flow towards the cell equator, which induces the assembly of the actomyosin contractile ring. These studies for the first time provide a molecular basis for the aster-dependent polar relaxation, which works in parallel with equatorial stimulation to promote robust cytokinesis

Notes on Exact Multi-Soliton Solutions of Noncommutative Integrable Hierarchies

We study exact multi-soliton solutions of integrable hierarchies on noncommutative space-times which are represented in terms of quasi-determinants of Wronski matrices by Etingof, Gelfand and Retakh. We analyze the asymptotic behavior of the multi-soliton solutions and found that the asymptotic configurations in soliton scattering process can be all the same as commutative ones, that is, the configuration of N-soliton solution has N isolated localized energy densities and the each solitary wave-packet preserves its shape and velocity in the scattering process. The phase shifts are also the same as commutative ones. Furthermore noncommutative toroidal Gelfand-Dickey hierarchy is introduced and the exact multi-soliton solutions are given.Comment: 18 pages, v3: references added, version to appear in JHE

Factorization methods for Noncommutative KP and Toda hierarchy

We show that the solution space of the noncommutative KP hierarchy is the same as that of the commutative KP hierarchy owing to the Birkhoff decomposition of groups over the noncommutative algebra. The noncommutative Toda hierarchy is introduced. We derive the bilinear identities for the Baker--Akhiezer functions and calculate the $N$-soliton solutions of the noncommutative Toda hierarchy.Comment: 7 pages, no figures, AMS-LaTeX, minor corrections, final version to appear in Journal of Physics

Molecular Dynamics Simulation of Heat-Conducting Near-Critical Fluids

Using molecular dynamics simulations, we study supercritical fluids near the gas-liquid critical point under heat flow in two dimensions. We calculate the steady-state temperature and density profiles. The resultant thermal conductivity exhibits critical singularity in agreement with the mode-coupling theory in two dimensions. We also calculate distributions of the momentum and heat fluxes at fixed density. They indicate that liquid-like (entropy-poor) clusters move toward the warmer boundary and gas-like (entropy-rich) regions move toward the cooler boundary in a temperature gradient. This counterflow results in critical enhancement of the thermal conductivity

New BPS Solitons in 2+1 Dimensional Noncommutative CP^1 Model

Investigating the solitons in the non-commutative $CP^{1}$ model, we have found a new set of BPS solitons which does not have counterparts in the commutative model.Comment: 8 pages, LaTeX2e, references added, improvements to discussions, Version to be published in JHE

On a direct approach to quasideterminant solutions of a noncommutative KP equation

A noncommutative version of the KP equation and two families of its solutions expressed as quasideterminants are discussed. The origin of these solutions is explained by means of Darboux and binary Darboux transformations. Additionally, it is shown that these solutions may also be verified directly. This approach is reminiscent of the wronskian technique used for the Hirota bilinear form of the regular, commutative KP equation but, in the noncommutative case, no bilinearising transformation is available.Comment: 11 page

Daily life support : building a collective neighborhood

Thesis (M. Arch.)--Massachusetts Institute of Technology, Dept. of Architecture, 1990.Includes bibliographical references (p. 69).Do the house forms and residential neighborhoods commonly found in the U.S. accommodate the present needs and lifestyles of the people who live in them? The single-family detached house and multi-family units like the triple-decker originated in an era quite unlike the one in which we now find ourselves. I intend to explore the possibility that we may not have to adapt to a dwelling sensibility that is restrictive and inappropriate for the late 20th and early 21st centuries. Perhaps the result will not look radically different than the models we already know but will only function in a subtly different manner, for very specific reasons of use and daily life. I will design a piece of a residential neighborhood in Newton Upper Falls, Massachusetts based on the premise that the physical, organizational, and functional aspects of housing design do affect and can contribute to the quality of people's lives. Some questions that I find valid for exploration in the context of housing are: 1) can a mix of uses animate a neighborhood by providing commonly needed services and by reducing the isolation of the home from everything else in life: work, shopping, child care, entertainment?; 2) have we been perpetuating outdated Victorian ideals about the separation of work and home based on roles related to gender? If so, couldn't housing design be more progressive in supporting the way women and men actually live today rather than the way one's great-grandparents lived?;(cont.) 3) if women still perform most of the household chores and child-rearing in the U.S. (whether married, single, or divorced), with the majority of American women also working full-time and getting paid two-thirds the salary of men, couldn't there exist a type of housing that considers the enormous demands on a person's time, energy, and resources necessary to accomplish all of this? I intend to research selected examples of feminist and experimental housing designs prior to starting my own. The Danish precedent of cohousing and Dolores Hayden's historical research and interpretive stance will establish my basic approach to the design project and its program. The design will be further informed by my own rethinking of domestic life and the architectural implications of it, recorded in "patterns" similar in intention to those of Alexander, et al.by Leslie K. Hamanaka.M.Arch