Improved Poincare inequalities with weights

In this paper we prove that if $\Omega\in\mathbb{R}^n$ is a bounded John domain, the following weighted Poincare-type inequality holds: $$\inf_{a\in \mathbb{R}}\| (f(x)-a) w_1(x) \|_{L^q(\Omega)} \le C \|\nabla f(x) d(x)^\alpha w_2(x) \|_{L^p(\Omega)}$$ where $f$ is a locally Lipschitz function on $\Omega$, $d(x)$ denotes the distance of $x$ to the boundary of $\Omega$, the weights $w_1, w_2$ satisfy certain cube conditions, and $\alpha \in [0,1]$ depends on $p,q$ and $n$. This result generalizes previously known weighted inequalities, which can also be obtained with our approach

Athena: Advanced air launched space booster

The infrastructure for routine, reliable, and inexpensive access of space is a goal that has been actively pursued over the past 50 years, but has yet not been realized. Current launch systems utilize ground launching facilities which require the booster vehicle to plow up through the dense lower atmosphere before reaching space. An air launched system on the other hand has the advantage of being launched from a carrier aircraft above this dense portion of the atmosphere and hence can be smaller and lighter compared to its ground based counterpart. The goal of last year's Aerospace Engineering Course 483 (AE 483) was to design a 227,272 kg (500,000 lb.) air launched space booster which would beat the customer's launch cost on existing launch vehicles by at least 50 percent. While the cost analysis conducted by the class showed that this goal could be met, the cost and size of the carrier aircraft make it appear dubious that any private company would be willing to invest in such a project. To avoid this potential pitfall, this year's AE 483 class was to design as large an air launched space booster as possible which can be launched from an existing or modification to an existing aircraft. An initial estimate of the weight of the booster is 136,363 kg (300,000 lb.) to 159,091 kg (350,000 lb.)

Technology Development Roadmap: A Technology Development Roadmap for a Future Gravitational Wave Mission

Humankind will detect the first gravitational wave (GW) signals from the Universe in the current decade using ground-based detectors. But the richest trove of astrophysical information lies at lower frequencies in the spectrum only accessible from space. Signals are expected from merging massive black holes throughout cosmic history, from compact stellar remnants orbiting central galactic engines from thousands of close contact binary systems in the Milky Way, and possibly from exotic sources, some not yet imagined. These signals carry essential information not available from electromagnetic observations, and which can be extracted with extraordinary accuracy. For 20 years, NASA, the European Space Agency (ESA), and an international research community have put considerable effort into developing concepts and technologies for a GW mission. Both the 2000 and 2010 decadal surveys endorsed the science and mission concept of the Laser Interferometer Space Antenna (LISA). A partnership of the two agencies defined and analyzed the concept for a decade. The agencies partnered on LISA Pathfinder (LPF), and ESA-led technology demonstration mission, now preparing for a 2015 launch. Extensive technology development has been carried out on the ground. Currently, the evolved Laser Interferometer Space Antenna (eLISA) concept, a LISA-like concept with only two measurement arms, is competing for ESA's L2 opportunity. NASA's Astrophysics Division seeks to be a junior partner if eLISA is selected. If eLISA is not selected, then a LISA-like mission will be a strong contender in the 2020 decadal survey. This Technology Development Roadmap (TDR) builds on the LISA concept development, the LPF technology development, and the U.S. and European ground-based technology development. The eLISA architecture and the architecture of the Mid-sized Space-based Gravitational-wave Observatory (SGO Mid)-a competitive design with three measurement arms from the recent design study for a NASA-led mission after 2020-both use the same technologies. Further, NASA participation in an ESA-led mission would likely augment the eLISA architecture with a third arm to become the SGO Mid architecture. For these reasons, this TDR for a future GW mission applies to both designs and both programmatic paths forward. It is adaptable to the different timelines and roles for an ESA-led or a NASA-led mission, and it is adaptable to available resources. Based on a mature understanding of the interaction between technology and risk, the authors of this TDR have chosen a set of objectives that are more expansive than is usual. The objectives for this roadmap are: (1) reduce technical and development risks and costs; (2) understand and, where possible, relieve system requirements and consequences; (3) increase technical insight into critical technologies; and (4) validate the design at the subsystem level. The emphasis on these objectives, particularly the latter two, is driven by outstanding programmatic decisions, namely whether a future GW mission is ESA-led or NASA-led, and availability of resources. The relative emphasis is best understood in the context of prioritization

Space Based Gravitational Wave Astronomy Beyond LISA

The Laser Interferometer Space Antenna (LISA) will open three decades of gravitational wave(GW) spectrum between 0.1 and 100 mHz, the mHz band [1]. This band is expected to be the richest part of the GW spectrum, in types of sources, numbers of sources, signal-to-noise ratios and discovery potential. When LISA opens the low-frequency window of the gravitational wave spectrum,around 2034, the surge of gravitational-wave astronomy will strongly compel a subsequent mission to further explore the frequency bands of the GW spectrum that can only be accessed from space. The 2020's is the time to start developing technology and studying mission concepts for a large-scale mission to be launched in the 2040's. The mission concept would then be proposed to Astro2030. Only space-based missions can access the GW spectrum between 108 and 1 Hz because of the Earth's seismic noise. This white paper surveys the science in this band and mission concepts that could accomplish that science. The proposed small scale activity is a technology development program that would support a range of concepts and a mission concept study to choose a specific mission concept for Astro2030. In this white paper, we will refer to a generic GW mission beyond LISA as bLISA

Building a Field: The Future of Astronomy with Gravitational Waves

Harnessing the sheer discovery potential of GW Astronomy will require bold, deliberate,and sustained efforts to train and develop the requisite workforce. The next decaderequires a strategic plan to build - from the ground up - a robust, open, andwell-connected GW Astronomy community with deep participation from traditionalastronomers, physicists, data scientists, and instrumentalists. This basic infrastructure issorely needed as an enabling foundation for research. We outline a set ofrecommendations for funding agencies, universities, and professional societies to helpbuild a thriving, diverse, and inclusive new field

Micrometeoroid Events in LISA Pathfinder

The zodiacal dust complex, a population of dust and small particles that pervades the Solar System, provides important insight into the formation and dynamics of planets, comets, asteroids, and other bodies. Here we present a new set of data obtained using a novel technique: direct measurements of momentum transfer to a spacecraft from individual particle impacts. This technique is made possible by the extreme precision of the instruments flown on the LISA Pathfinder spacecraft, a technology demonstrator for a future space-based gravitational wave observatory that operated near the first Sun-Earth Lagrange point from early 2016 through Summer of 2017. Using a simple model of the impacts and knowledge of the control system, we show that it is possible to detect impacts and measure properties such as the transferred momentum (related to the particle's mass and velocity), direction of travel, and location of impact on the spacecraft. In this paper, we present the results of a systematic search for impacts during 4348 hours of Pathfinder data. We report a total of 54 candidates with momenta ranging from 0.2$\,\mu\textrm{Ns}$ to 230$\,\mu\textrm{Ns}$. We furthermore make a comparison of these candidates with models of micrometeoroid populations in the inner solar system including those resulting from Jupiter-family comets, Oort-cloud comets, Hailey-type comets, and Asteroids. We find that our measured population is consistent with a population dominated by Jupiter-family comets with some evidence for a smaller contribution from Hailey-type comets. This is in agreement with consensus models of the zodiacal dust complex in the momentum range sampled by LISA Pathfinder.Comment: 22 pages, 14 figures, accepted in Ap

Laser Interferometer Space Antenna

Following the selection of The Gravitational Universe by ESA, and the successful flight of LISA Pathfinder, the LISA Consortium now proposes a 4 year mission in response to ESA's call for missions for L3. The observatory will be based on three arms with six active laser links, between three identical spacecraft in a triangular formation separated by 2.5 million km. LISA is an all-sky monitor and will offer a wide view of a dynamic cosmos using Gravitational Waves as new and unique messengers to unveil The Gravitational Universe. It provides the closest ever view of the infant Universe at TeV energy scales, has known sources in the form of verification binaries in the Milky Way, and can probe the entire Universe, from its smallest scales near the horizons of black holes, all the way to cosmological scales. The LISA mission will scan the entire sky as it follows behind the Earth in its orbit, obtaining both polarisations of the Gravitational Waves simultaneously, and will measure source parameters with astrophysically relevant sensitivity in a band from below $10^{-4}\,$Hz to above $10^{-1}\,$Hz.Comment: Submitted to ESA on January 13th in response to the call for missions for the L3 slot in the Cosmic Vision Programm