Boundary breathers in the sinh-Gordon model

We present an investigation of the boundary breather states of the sinh-Gordon model restricted to a half-line. The classical boundary breathers are presented for a two parameter family of integrable boundary conditions. Restricting to the case of boundary conditions which preserve the \phi --> -\phi symmetry of the bulk theory, the energy spectrum of the boundary states is computed in two ways: firstly, by using the bootstrap technique and subsequently, by using a WKB approximation. Requiring that the two descriptions of the spectrum agree with each other allows a determination of the relationship between the boundary parameter, the bulk coupling constant, and the parameter appearing in the reflection factor derived by Ghoshal to describe the scattering of the sinh-Gordon particle from the boundary.Comment: 16 pages amslate

Yang-Mills connections over manifolds with Grassmann structure

Let M be a manifold with Grassmann structure, i.e. with an isomorphism of the cotangent bundle T^*M\cong E\otimes H with the tensor product of two vector bundles E and H. We define the notion of a half-flat connection \nabla^W in a vector bundle W\to M as a connection whose curvature F\in S^2E\otimes\wedge^2 H\otimes W \subset\wedge^2 T^*M\otimes W. Under appropriate assumptions, for example, when the Grassmann structure is associated with a quaternionic Kaehler structure on M, half-flatness implies the Yang-Mills equations. Inspired by the harmonic space approach, we develop a local construction of (holomorphic) half-flat connections \nabla^W over a complex manifold with (holomorphic) Grassmann structure equipped with a suitable linear connection. Any such connection \nabla^W can be obtained from a prepotential by solving a system of linear first order ODEs. The construction can be applied, for instance, to the complexification of hyper-Kaehler manifolds or more generally to hyper-Kaehler manifolds with admissible torsion and to their higher-spin analogues. It yields solutions of the Yang-Mills equations.Comment: 41 pages; very minor changes, version to appear in JM

The sine-Gordon model with integrable defects revisited

Application of our algebraic approach to Liouville integrable defects is proposed for the sine-Gordon model. Integrability of the model is ensured by the underlying classical r-matrix algebra. The first local integrals of motion are identified together with the corresponding Lax pairs. Continuity conditions imposed on the time components of the entailed Lax pairs give rise to the sewing conditions on the defect point consistent with Liouville integrability.Comment: 24 pages Latex. Minor modifications, added comment

Free Field Realization of Vertex Operators for Level Two Modules of Uq(sl(2)^)U_q(\hat{sl(2)})

Free field relization of vertex operators for lvel two modules of $U_q(\hat{sl(2)})$ is shown through the free field relization of the modules given by Idzumi in Ref.[4,5]. We constructed types I and II vertex operators when the spin of the addociated evaluation modules is 1/2 and typ II's for the spin 1.Comment: 15 pages, to appear in J.Phys.A:Math and Genera

Multisymplectic approach to integrable defects in the sine-Gordon model

Ideas from the theory of multisymplectic systems, introduced recently in integrable systems by the author and Kundu to discuss Liouville integrability in classical field theories with a defect, are applied to the sine-Gordon model. The key ingredient is the introduction of a second Poisson bracket in the theory that allows for a Hamiltonian description of the model that is completely equivalent to the standard one, in the absence of a defect. In the presence of a defect described by frozen Bäcklund transformations, our approach based on the new bracket unifies the various tools used so far to attack the problem. It also gets rid of the known issues related to the evaluation of the Poisson brackets of the defect matrix which involve fields at coinciding space point (the location of the defect). The original Lagrangian approach also finds a nice reinterpretation in terms of the canonical transformation representing the defect conditions

Progress in classically solving ten dimensional supersymmetric reduced Yang-Mills theories

It is shown that there exists an on-shell light cone gauge where half of the fermionic components of the super vector potential vanish, so that part of the superspace flatness conditions becomes linear. After reduction to $(1+1)$ space-time dimensions, the general solution of this subset of equations is derived. The remaining non-linear equations are written in a form which is analogous to Yang equations, albeit with superderivatives involving sixteen fermionic coordinates. It is shown that this non-linear part may, nevertheless, be solved by methods similar to powerful technics previously developed for the (purely bosonic) self-dual Yang Mills equations in four dimensions.Comment: 17 pages Latex non figure

Generation of Single-Cell Transcript Variability by Repression

Gene expression levels vary greatly within similar cells, even within clonal cell populations [1]. These spontaneous expression differences underlie cell fate diversity in both differentiation and disease [2]. The mechanisms responsible for generating expression variability are poorly understood. Using single-cell transcriptomics, we show that transcript variability emerging during Dictyostelium differentiation is driven predominantly by repression rather than activation. The increased variability of repressed genes was observed over a broad range of expression levels, indicating that variability is actively imposed and not a passive statistical effect of the reduced numbers of molecules accompanying repression. These findings can be explained by a simple model of transcript production, with expression controlled by the frequency, rather than the magnitude, of transcriptional firing events. Our study reveals that the generation of differences between cells can be a direct consequence of the basic mechanisms of transcriptional regulation

Boundary Reflection Matrix for D4(1)D_4^{(1)} Affine Toda Field Theory

We present one loop boundary reflection matrix for $d_4^{(1)}$ Toda field theory defined on a half line with the Neumann boundary condition. This result demonstrates a nontrivial cancellation of non-meromorphic terms which are present when the model has a particle spectrum with more than one mass. Using this result, we determine uniquely the exact boundary reflection matrix which turns out to be \lq non-minimal' if we assume the strong-weak coupling \lq duality'.Comment: 14 pages, Late

Interplay between Zamolodchikov-Faddeev and Reflection-Transmission algebras

We show that a suitable coset algebra, constructed in terms of an extension of the Zamolodchikov-Faddeev algebra, is homomorphic to the Reflection-Transmission algebra, as it appears in the study of integrable systems with impurity.Comment: 8 pages; a misprint in eq. (2.14) and (2.15) has been correcte

Capturing vertical profiles of aerosols and black carbon over the Indian Ocean using autonomous unmanned aerial vehicles

International audienceMeasurements of the vertical distribution of aerosol properties provide essential information for generating more accurate model estimates of radiative forcing and atmospheric heating rates compared with employing remotely sensed column averaged properties. A month long campaign over the Indian Ocean during March 2006 investigated the interaction of aerosol, clouds, and radiative effects. Routine vertical profiles of aerosol and water vapor were determined using autonomous unmanned aerial vehicles equipped with miniaturized instruments. Comparisons of these airborne instruments with established ground-based instruments and in aircraft-to-aircraft comparisons demonstrated an agreement within 10%. Aerosol absorption optical depths measured directly using the unmanned aircraft differed from columnar AERONET sun-photometer results by only 20%. Measurements of total particle concentration, particle size distributions, aerosol absorption and black carbon concentrations are presented along with the trade wind thermodynamic structure from the surface to 3000 m above sea level. Early March revealed a well-mixed layer up to the cloud base at 500 m above mean seal level (m a.s.l.), followed by a decrease of aerosol concentrations with altitude. The second half of March saw the arrival of a high altitude plume existing above the mixed layer that originated from a continental source and increased aerosol concentrations by more than tenfold, yet the surface air mass showed little change in aerosol concentrations and was still predominantly influenced by marine sources. Black carbon concentrations at 1500 m above sea level increased from 70 ng/m³ to more than 800 ng/m³ with the arrival of this polluted plume. The absorption aerosol optical depth increased from as low as 0.005 to as much as 0.035 over the same period. The spectral dependence of the aerosol absorption revealed an absorption Angstrom exponent of 1.0, which is typical of an aerosol with most of its absorption attributed to black carbon and generally indicates the absorbing component originated from fossil fuel sources and other high-temperature combustion sources. The results indicate that surface measurements do not represent the aerosol properties within the elevated layers, especially if these layers are influenced by long range transport