Geometry of N = 1 dualities in four dimensions

We discuss how N = 1 dualities in four dimensions are geometrically realized by wrapping D-branes about 3-cycles of Calabi-Yau threefolds. In this setup the N = 1 dualities for SU, SO and USp gauge groups with fundamental fields get mapped to statements about the monodromy and relations among 3-cycles of Calabi-Yau threefolds. The connection between the theory and its dual requires passing through configurations which are T-dual to the well-known phenomenon of decay of BPS states in N = 2 field theories in four dimensions. We compare our approach to recent works based on configurations of D-branes in the presence of NS 5-branes and give simple classical geometric derivations of various exotic dynamics involving D-branes ending on NS branes.     

A multistep collocation method for solving advection equations with delay

Advection equations with delay are appeared in the modeling of the dynamics of structured cell populations. In this article, we construct an efficient two-dimensional multistep collocation method for the numerical solution of a class of advection equations with delay. Equations with aftereffect and equations with both aftereffect and retardation of a state variable are considered. Computability of the algorithm and convergence properties of the proposed numerical method are analyzed for solutions in appropriate Sobolev spaces, and it is shown that the proposed scheme enjoys the spectral accuracy. Numerical examples are given and comparison with other existing methods in the literature is made to demonstrate the efficiency, superiority and high accuracy of the presented method.     

Highly tunable elastic dielectric metasurface lenses

Dielectric metasurfaces are two‐dimensional structures composed of nano‐scatterers that manipulate the phase and polarization of optical waves with subwavelength spatial resolution, thus enabling ultra‐thin components for free‐space optics. While high performance devices with various functionalities, including some that are difficult to achieve using conventional optical setups have been shown, most demonstrated components have fixed parameters. Here, we demonstrate highly tunable dielectric metasurface devices based on subwavelength thick silicon nano‐posts encapsulated in a thin transparent elastic polymer. As proof of concept, we demonstrate a metasurface microlens operating at 915 nm, with focal distance tuning from 600 μm to 1400 μm (over 952 diopters change in optical power) through radial strain, while maintaining a diffraction limited focus and a focusing efficiency above 50%. The demonstrated tunable metasurface concept is highly versatile for developing ultra‐slim, multi‐functional and tunable optical devices with widespread applications ranging from consumer electronics to medical devices and optical communications.

     

Cyclicity of the adjoint of weighted composition operators on the hilbert space of analytic functions

In this paper, we discuss the hypercyclicity, supercyclicity and cyclicity of the adjoint of a weighted composition operator on a Hilbert space of analytic functions.     

Large N Duality, Lagrangian Cycles, and Algebraic Knots

We consider knot invariants in the context of large N transitions of topological strings. In particular we consider aspects of Lagrangian cycles associated to knots in the conifold geometry. We show how these can be explicitly constructed in the case of algebraic knots. We use this explicit construction to explain a recent conjecture relating study of stable pairs on algebraic curves with HOMFLY polynomials. Furthermore, for torus knots, using the explicit construction of the Lagrangian cycle, we also give a direct A-model computation and recover the HOMFLY polynomial for this case.     

On classification ofN=2 supersymmetric theories

We find a relation between the spectrum of solitons of massiveN=2 quantum field theories ind=2 and the scaling dimensions of chiral fields at the conformal point. The condition that the scaling dimensions be real imposes restrictions on the soliton numbers and leads to a classification program for symmetricN=2 conformal theories and their massive deformations in terms of a suitable generalization of Dynkin diagrams (which coincides with the A-D-E Dynkin diagrams for minimal models). The Landau-Ginzburg theories are a proper subset of this classification. In the particular case of LG theories we relate the soliton numbers with intersection of vanishing cycles of the corresponding singularity; the relation between soliton numbers and the scaling dimensions in this particular case is a well known application of Picard-Lefschetz theory.     

Global anomalies on orbifolds

Communicated by A. Jaffe     

Curved bridge response to a moving vehicle

An algorithm is developed for the solution of the dynamic displacement and rotation of a horizontal curved guideway (bridge) as it interacts with a traversing vehicle. The algorithm is validated against experimental results, and a parametric study is presented.     

Producing a scale-invariant spectrum of perturbations in a Hagedorn phase of string cosmology

We study the generation of cosmological perturbations during the Hagedorn phase of string gas cosmology. Using tools of string thermodynamics we provide indications that it may be possible to obtain a nearly scale-invariant spectrum of cosmological fluctuations on scales which are of cosmological interest today. In our cosmological scenario, the early Hagedorn phase of string gas cosmology goes over smoothly into the radiation-dominated phase of standard cosmology, without having a period of cosmological inflation.