The Modulation of Multiple Phases Leading to the Modified KdV Equation

This paper seeks to derive the modified KdV (mKdV) equation using a novel approach from systems generated from abstract Lagrangians that possess a two-parameter symmetry group. The method to do uses a modified modulation approach, which results in the mKdV emerging with coefficients related to the conservation laws possessed by the original Lagrangian system. Alongside this, an adaptation of the method of Kuramoto is developed, providing a simpler mechanism to determine the coefficients of the nonlinear term. The theory is illustrated using two examples of physical interest, one in stratified hydrodynamics and another using a coupled Nonlinear Schr\"odinger model, to illustrate how the criterion for the mKdV equation to emerge may be assessed and its coefficients generated.Comment: 35 pages, 5 figure

Numerical analysis of flow non-uniformity in the hot gas manifold of the Space Shuttle main engine

Three-dimensional viscous flow in a conceptual hot gas manifold (HGM) for the Space Shuttle Main Engine High Pressure Fuel Turbopump (SSME HPFTP) was numerically analyzed. A finite difference scheme was used to solve the Navier-Stokes equations. The exact geometry of the SSME HGM was modeled using boundary fitted curvilinear coordinates and the General Interpolants Method (GIM) code. Slight compressibility of the subsonic flow was modeled using a linearized equation of state with artificial compressibility. A time relaxation method was used to obtain a steady state solution. The feasibility and potential usefulness of computational methods in assisting the design of SSME components which involves the flow of fluids within complex geometrical shapes is demonstrated

Low thrust orbit determination program

Logical flow and guidelines are provided for the construction of a low thrust orbit determination computer program. The program, tentatively called FRACAS (filter response analysis for continuously accelerating spacecraft), is capable of generating a reference low thrust trajectory, performing a linear covariance analysis of guidance and navigation processes, and analyzing trajectory nonlinearities in Monte Carlo fashion. The choice of trajectory, guidance and navigation models has been made after extensive literature surveys and investigation of previous software. A key part of program design relied upon experience gained in developing and using Martin Marietta Aerospace programs: TOPSEP (Targeting/Optimization for Solar Electric Propulsion), GODSEP (Guidance and Orbit Determination for SEP) and SIMSEP (Simulation of SEP)

Protection and Enforcement of New Intellectual Property

The desirability of new forms of intellectual property protection for databases and domain names is beyond the scope of this Article. Instead, this Article focuses on the protection and enforcement of intellectual property rights in databases and domain names under existing law. Because of the increased value of these assets, owners should increasingly pay attention to their protection

Simulations of stable compact proton beam acceleration from a two-ion-species ultrathin foil

We report stable laser-driven proton beam acceleration from ultrathin foils consisting of two ion species: heavier carbon ions and lighter protons. Multi-dimensional particle-in-cell (PIC) simulations show that the radiation pressure leads to very fast and complete spatial separation of the species. The laser pulse does not penetrate the carbon ion layer, avoiding the proton Rayleigh-Taylor-like (RT) instability. Ultimately, the carbon ions are heated and spread extensively in space. In contrast, protons always ride on the front of the carbon ion cloud, forming a compact high quality bunch. We introduce a simple three-interface model to interpret the instability suppression in the proton layer. The model is backed by simulations of various compound foils such as carbon-deuterium (C-D) and carbon-tritium (C-T) foils. The effects of the carbon ions' charge state on proton acceleration are also investigated. It is shown that with the decrease of the carbon ion charge state, both the RT-like instability and the Coulomb explosion degrade the energy spectrum of the protons. Finally, full 3D simulations are performed to demonstrate the robustness of the stable two-ion-species regime.Comment: 14 pages, 10figures, to be published in PO

Positive and Negative Experiences With Supportive Services and Programming: Gaps and Recommendations From Youth Experiencing Homelessness

Services for youth experiencing homelessness (YEH) are designed with limited input from the youth themselves. This study explored the experiences and recommendations for services aimed at mitigating the negative effects of homelessness among youth. A total of 45 interviews were conducted with YEH (ages 15 to 24, M = 21.5 years) who experienced at least one night of homelessness. Transcripts were coded by using a modified constructivist grounded theory approach. YEH reported myriad challenges to navigating disjointed programming and misguided policies. Recommendations from YEH for policy and programmatic change include peacekeeping and diffusion training for program staff, trauma-informed approaches, and conflict resolution among agency staff; and integrate creative outlets and transitional services into existing programs. Programming supporting YEH must extend beyond meeting only basic needs to creating opportunities for safety, autonomy, and growth. Programs targeting youth homelessness need input from YEH in their design and implementation

Optimization And Learning For Rough Terrain Legged Locomotion

We present a novel approach to legged locomotion over rough terrain that is thoroughly rooted in optimization. This approach relies on a hierarchy of fast, anytime algorithms to plan a set of footholds, along with the dynamic body motions required to execute them. Components within the planning framework coordinate to exchange plans, cost-to-go estimates, and \u27certificates\u27 that ensure the output of an abstract high-level planner can be realized by lower layers of the hierarchy. The burden of careful engineering of cost functions to achieve desired performance is substantially mitigated by a simple inverse optimal control technique. Robustness is achieved by real-time re-planning of the full trajectory, augmented by reflexes and feedback control. We demonstrate the successful application of our approach in guiding the LittleDog quadruped robot over a variety of types of rough terrain. Other novel aspects of our past research efforts include a variety of pioneering inverse optimal control techniques as well as a system for planning using arbitrary pre-recorded robot behavior

Hemorrhage into an Occult Spinal Ependymoma after Epidural Anesthesia

Summary of Background Data: Five cases of hemorrhage into a spinal neoplasm after spinal or epidural anesthesia are reported in the literature. Presentation ranges from severe low back pain to acute cauda equina syndrome. Methods: A case study of a patient who hemorrhaged into an intradural, extramedullary spinal cord mass was performed. A detailed literature review is also provided. Results: A 27 year old female underwent epidural anesthesia for Cesarean section delivery. She presented with a 3 week history of increasing low back pain with bilateral radiculopathy. Imaging studies revealed a large hemorrhagic intradural mass compressing the lower conus medullaris and cauda equina, which operatively was confirmed to be a myxopapillary ependymoma. Conclusions: We report a case of hemorrhage into a previously unrecognized ependymoma after epidural anesthesia. Underlying tumors may rarely complicate regional anesthesia in the lumbar spine