Isomorphic chain complexes of Hamiltonian dynamics on tori

In this work we construct for a given smooth, generic Hamiltonian $H : \mathbb{S}^1\times\mathbb{T}^n \longrightarrow \mathbb{R}$ on the torus a chain isomorphism $\Phi_* : \big(C_*(H),\partial^M_*\big) \longrightarrow \big(C_*(H),\partial^F_*\big)$ between the Morse complex of the Hamiltonian action $A_H$ on the free loop space of the torus $\Lambda_0(\mathbb{T}^n)$ and the Floer complex. Though both complexes are generated by the critical points of $A_H$, their boundary operators differ. Therefore the construction of $\Phi$ is based on counting the moduli spaces of hybrid type solutions which involves stating a new non-Lagrangian boundary value problem for Cauchy-Riemann type operators not yet studied in Floer theory

Exact Localisations of Feedback Sets

The feedback arc (vertex) set problem, shortened FASP (FVSP), is to transform a given multi digraph $G=(V,E)$ into an acyclic graph by deleting as few arcs (vertices) as possible. Due to the results of Richard M. Karp in 1972 it is one of the classic NP-complete problems. An important contribution of this paper is that the subgraphs $G_{\mathrm{el}}(e)$, $G_{\mathrm{si}}(e)$ of all elementary cycles or simple cycles running through some arc $e \in E$, can be computed in $\mathcal{O}\big(|E|^2\big)$ and $\mathcal{O}(|E|^4)$, respectively. We use this fact and introduce the notion of the essential minor and isolated cycles, which yield a priori problem size reductions and in the special case of so called resolvable graphs an exact solution in $\mathcal{O}(|V||E|^3)$. We show that weighted versions of the FASP and FVSP possess a Bellman decomposition, which yields exact solutions using a dynamic programming technique in times $\mathcal{O}\big(2^{m}|E|^4\log(|V|)\big)$ and $\mathcal{O}\big(2^{n}\Delta(G)^4|V|^4\log(|E|)\big)$, where $m \leq |E|-|V| +1$, $n \leq (\Delta(G)-1)|V|-|E| +1$, respectively. The parameters $m,n$ can be computed in $\mathcal{O}(|E|^3)$, $\mathcal{O}(\Delta(G)^3|V|^3)$, respectively and denote the maximal dimension of the cycle space of all appearing meta graphs, decoding the intersection behavior of the cycles. Consequently, $m,n$ equal zero if all meta graphs are trees. Moreover, we deliver several heuristics and discuss how to control their variation from the optimum. Summarizing, the presented results allow us to suggest a strategy for an implementation of a fast and accurate FASP/FVSP-SOLVER

Numerical approximation of phase field based shape and topology optimization for fluids

We consider the problem of finding optimal shapes of fluid domains. The fluid obeys the Navier--Stokes equations. Inside a holdall container we use a phase field approach using diffuse interfaces to describe the domain of free flow. We formulate a corresponding optimization problem where flow outside the fluid domain is penalized. The resulting formulation of the shape optimization problem is shown to be well-posed, hence there exists a minimizer, and first order optimality conditions are derived. For the numerical realization we introduce a mass conserving gradient flow and obtain a Cahn--Hilliard type system, which is integrated numerically using the finite element method. An adaptive concept using reliable, residual based error estimation is exploited for the resolution of the spatial mesh. The overall concept is numerically investigated and comparison values are provided

The Nutria that Roared: How Building Coalitions Can Empower the Small to Drive Great Change

Hurricane Katrina saved the New Orleans economy. To be clear, Hurricane Katrina was not “good”—it was a devastating event, the most destructive storm in American history, costing thousands of lives and billions of dollars in damage. But when the books are written, and the story is told, the conclusion will be inescapable: Hurricane Katrina marked a profoundly positive inflection point in the New Orleans economy

Light Transmission Through Metallic-Mean Quasiperiodic Stacks with Oblique Incidence

The propagation of s- and p-polarized light through quasiperiodic multilayers, consisting of layers with different refractive indices, is studied by the transfer matrix method. In particular, we focus on the transmission coefficient of the systems in dependency on the incidence angle and on the ratio of the refractive indices. We obtain additional bands with almost complete transmission in the quasiperiodic systems at frequencies in the range of the photonic band gap of a system with a periodic alignment of the two materials for both types of light polarization. With increasing incidence angle these bands bend towards higher frequencies, where the curvature of the transmission bands in the quasiperiodic stack depends on the metallic mean of the construction rule. Additionally, in the quasiperiodic systems for p-polarized light the bands show almost complete transmission near the Brewster's angle in contrast to the results for s-polarized light. Further, we present results for the influence of the refractive indices at the midgap frequency of the periodic stack, where the quasiperiodicity was found to be most effective.Comment: 10 pages, 7 figure

The Return of Lost Property According to Jewish & Common Law: A Comparison

This article compares the legal rules and jurisprudence of the American common law and Jewish law in the area of finding and returning lost or abandoned property, illustrating the interplay between the purely legal and ethical components of the respective legal systems. Surprisingly enough, the differences between the two systems are not usually significant; they follow the same basic legal principles, and typically lead to the same results. There are, however, two major exceptions: Jewish law imposes a duty to rescue the lost property of one\u27s neighbor, while the common law does not require that one initiate the process by retrieving the article. Thus according to Jewish law, when one happens to stumble across lost property, one must intervene to retrieve it; according to the common law one need not. Second, Jewish law imposes ethical duties as part of its legal mandate, a practice the common law does not follow. This article approaches the issues raised in returning lost property in the order they are encountered as property is lost or found. The first two sections discuss the issue of defining lost property ; the next four sections discuss the obligations of the finder; the subsequent two sections discuss the legal relationship between the finder and the original owner; and the last section discusses miscellaneous issues related to lost property

Shape optimization for surface functionals in Navier--Stokes flow using a phase field approach

We consider shape and topology optimization for fluids which are governed by the Navier--Stokes equations. Shapes are modelled with the help of a phase field approach and the solid body is relaxed to be a porous medium. The phase field method uses a Ginzburg--Landau functional in order to approximate a perimeter penalization. We focus on surface functionals and carefully introduce a new modelling variant, show existence of minimizers and derive first order necessary conditions. These conditions are related to classical shape derivatives by identifying the sharp interface limit with the help of formally matched asymptotic expansions. Finally, we present numerical computations based on a Cahn--Hilliard type gradient descent which demonstrate that the method can be used to solve shape optimization problems for fluids with the help of the new approach

Type II/F-theory Superpotentials with Several Deformations and N=1 Mirror Symmetry

We present a detailed study of D-brane superpotentials depending on several open and closed-string deformations. The relative cohomology group associated with the brane defines a generalized hypergeometric GKZ system which determines the off-shell superpotential and its analytic properties under deformation. Explicit expressions for the N=1 superpotential for families of type II/F-theory compactifications are obtained for a list of multi-parameter examples. Using the Hodge theoretic approach to open-string mirror symmetry, we obtain new predictions for integral disc invariants in the A model instanton expansion. We study the behavior of the brane vacua under extremal transitions between different Calabi-Yau spaces and observe that the web of Calabi-Yau vacua remains connected for a particular class of branes.Comment: 62 pages; v2: typos corrected and references adde

Subsurface Ice Probe

The subsurface ice probe (SIPR) is a proposed apparatus that would bore into ice to depths as great as hundreds of meters by melting the ice and pumping the samples of meltwater to the surface. Originally intended for use in exploration of subsurface ice on Mars and other remote planets, the SIPR could also be used on Earth as an alternative to coring, drilling, and melting apparatuses heretofore used to sample Arctic and Antarctic ice sheets. The SIPR would include an assembly of instrumentation and electronic control equipment at the surface, connected via a tether to a compact assembly of boring, sampling, and sensor equipment in the borehole (see figure). Placing as much equipment as possible at the surface would help to attain primary objectives of minimizing power consumption, sampling with high depth resolution, and unobstructed imaging of the borehole wall. To the degree to which these requirements would be satisfied, the SIPR would offer advantages over the aforementioned ice-probing systems

Delta-doped CCD's as low-energy particle detectors and imagers

The back surface of a thinned charged-coupled device (CCD) is treated to eliminate the backside potential well that appears in a conventional thinned CCD during backside illumination. The backside of the CCD includes a delta layer of high-concentration dopant confined to less than one monolayer of the crystal semiconductor. The thinned, delta-doped CCD is used to detect very low-energy particles that penetrate less than 1.0 nm into the CCD, including electrons having energies less than 1000 eV and protons having energies less than 10 keV