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

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

Decision-making in blackjack : an electrophysiological analysis

Previous studies have identified a negative potential in the event-related potential (ERP), the error-related negativity (ERN), which is claimed to be triggered by a deviation from a reward expectation. Furthermore, this negativity is related to shifts in risk taking, strategic behavioral adjustments, and inhibition. We used a computer Blackjack gambling task to further examine the process associated with the ERN. Our findings are in line with the view that the ERN process is related to the degree of reward expectation. Furthermore, increased ERN amplitude is associated with the negative evaluation of ongoing decisions, and the amplitude of the ERN is directly related to risk-taking and decision-making behavior. However, the findings suggest that an explanation exclusively based on the deviation from a reward expectation may be insufficient and that the intention of the participants and the importance of a negative event for learning and behavioral change are crucial to the understanding of ERN phenomena

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

Non-Contact Thermal Properties Measurement with Low-Power Laser and IR Camera System

As shown by the Phoenix Mars Lander's Thermal and Electrical Conductivity Probe (TECP), contact measurements of thermal conductivity and diffusivity (using a modified flux-plate or line-source heat-pulse method) are constrained by a number of factors. Robotic resources must be used to place the probe, making them unavailable for other operations for the duration of the measurement. The range of placement is also limited by mobility, particularly in the case of a lander. Placement is also subject to irregularities in contact quality, resulting in non-repeatable heat transfer to the material under test. Most important from a scientific perspective, the varieties of materials which can be measured are limited to unconsolidated or weakly-cohesive regolith materials, rocks, and ices being too hard for nominal insertion strengths. Accurately measuring thermal properties in the laboratory requires significant experimental finesse, involving sample preparation, controlled and repeatable procedures, and, practically, instrumentation much more voluminous than the sample being tested (heater plates, insulation, temperature sensors). Remote measurements (infrared images from orbiting spacecraft) can reveal composite properties like thermal inertia, but suffer both from a large footprint (low spatial resolution) and convolution of the thermal properties of a potentially layered medium. In situ measurement techniques (the Phoenix TECP is the only robotic measurement of thermal properties to date) suffer from problems of placement range, placement quality, occupation of robotic resources, and the ability to only measure materials of low mechanical strength. A spacecraft needs the ability to perform a non-contact thermal properties measurement in situ. Essential components include low power consumption, leveraging of existing or highly-developed flight technologies, and mechanical simplicity. This new in situ method, by virtue of its being non-contact, bypasses all of these problems. The use of photons to both excite and measure the thermal response of any surface material to a high resolution (estimated footprint = 10 square centimeters) is a generational leap in physical properties measurements. The proposed method consists of spot-heating the surface of a material with a low (less than 1 W) power laser. This produces a moderate (5-10 K) temperature increase in the material