A Codazzi-like equation and the singular set for C1C^{1} smooth surfaces in the Heisenberg group

In this paper, we study the structure of the singular set for a $C^{1}$ smooth surface in the $3$-dimensional Heisenberg group $\boldsymbol{H}_{1}$. We discover a Codazzi-like equation for the $p$-area element along the characteristic curves on the surface. Information obtained from this ordinary differential equation helps us to analyze the local configuration of the singular set and the characteristic curves. In particular, we can estimate the size and obtain the regularity of the singular set. We understand the global structure of the singular set through a Hopf-type index theorem. We also justify that Codazzi-like equation by proving a fundamental theorem for local surfaces in $\boldsymbol{H}_{1}$.Comment: 64 pages, 17 figure

Co-operative Versus Independent Transport of Different Cargoes by Kinesin-1

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72137/1/j.1600-0854.2008.00722.x.pd

Hysteresis and the dynamic phase transition in thin ferromagnetic films

Hysteresis and the non-equilibrium dynamic phase transition in thin magnetic films subject to an oscillatory external field have been studied by Monte Carlo simulation. The model under investigation is a classical Heisenberg spin system with a bilinear exchange anisotropy in a planar thin film geometry with competing surface fields. The film exhibits a non-equilibrium phase transition between dynamically ordered and dynamically disordered phases characterized by a critical temperature Tcd, whose location of is determined by the amplitude H0 and frequency w of the applied oscillatory field. In the presence of competing surface fields the critical temperature of the ferromagnetic-paramagnetic transition for the film is suppressed from the bulk system value, Tc, to the interface localization-delocalization temperature Tci. The simulations show that in general Tcd < Tci for the model film. The profile of the time-dependent layer magnetization across the film shows that the dynamically ordered and dynamically disordered phases coexist within the film for T < Tcd. In the presence of competing surface fields, the dynamically ordered phase is localized at one surface of the film.Comment: PDF file, 21 pages including 8 figure pages; added references,typos added; to be published in PR

Two binding partners cooperate to activate the molecular motor Kinesin-1

The regulation of molecular motors is an important cellular problem, as motility in the absence of cargo results in futile adenosine triphosphate hydrolysis. When not transporting cargo, the microtubule (MT)-based motor Kinesin-1 is kept inactive as a result of a folded conformation that allows autoinhibition of the N-terminal motor by the C-terminal tail. The simplest model of Kinesin-1 activation posits that cargo binding to nonmotor regions relieves autoinhibition. In this study, we show that binding of the c-Jun N-terminal kinase–interacting protein 1 (JIP1) cargo protein is not sufficient to activate Kinesin-1. Because two regions of the Kinesin-1 tail are required for autoinhibition, we searched for a second molecule that contributes to activation of the motor. We identified fasciculation and elongation protein ζ1 (FEZ1) as a binding partner of kinesin heavy chain. We show that binding of JIP1 and FEZ1 to Kinesin-1 is sufficient to activate the motor for MT binding and motility. These results provide the first demonstration of the activation of a MT-based motor by cellular binding partners

A multilevel voltage-source converter system with balanced dc voltages

A multilevel voltage-source converter system is proposed for high-voltage, high-power applications such as large induction motor drives, back-to-back interconnected power systems, and electrical traction drives. Multilevel voltage-source converters have a voltage unbalance problem in the dc capacitors. The problem may be solved by use of additional voltage regulators or separate dc sources. However, these solutions are found not to be practicable for most applications. The proposed converter system can solve the voltage unbalance problem of the conventional multilevel voltage-source converters, without using any additional voltage balance circuits or separate voltage sources. Mechanism of the voltage unbalance problem is analyzed theoretically in this paper. The validity of the new converter system is demonstrated by simulation and experiment

Free and smooth boundaries in 2-D finite-difference schemes for transient elastic waves

A method is proposed for accurately describing arbitrary-shaped free boundaries in single-grid finite-difference schemes for elastodynamics, in a time-domain velocity-stress framework. The basic idea is as follows: fictitious values of the solution are built in vacuum, and injected into the numerical integration scheme near boundaries. The most original feature of this method is the way in which these fictitious values are calculated. They are based on boundary conditions and compatibility conditions satisfied by the successive spatial derivatives of the solution, up to a given order that depends on the spatial accuracy of the integration scheme adopted. Since the work is mostly done during the preprocessing step, the extra computational cost is negligible. Stress-free conditions can be designed at any arbitrary order without any numerical instability, as numerically checked. Using 10 grid nodes per minimal S-wavelength with a propagation distance of 50 wavelengths yields highly accurate results. With 5 grid nodes per minimal S-wavelength, the solution is less accurate but still acceptable. A subcell resolution of the boundary inside the Cartesian meshing is obtained, and the spurious diffractions induced by staircase descriptions of boundaries are avoided. Contrary to what occurs with the vacuum method, the quality of the numerical solution obtained with this method is almost independent of the angle between the free boundary and the Cartesian meshing.Comment: accepted and to be published in Geophys. J. In

Strong ionospheric field‐aligned currents for radial interplanetary magnetic fields

The present work has investigated the configuration of field‐aligned currents (FACs) during a long period of radial interplanetary magnetic field (IMF) on 19 May 2002 by using high‐resolution and precise vector magnetic field measurements of CHAMP satellite. During the interest period IMF B y and B z are weakly positive and B x keeps pointing to the Earth for almost 10 h. The geomagnetic indices D s t is about −40 nT and AE about 100 nT on average. The cross polar cap potential calculated from Assimilative Mapping of Ionospheric Electrodynamics and derived from DMSP observations have average values of 10–20 kV. Obvious hemispheric differences are shown in the configurations of FACs on the dayside and nightside. At the south pole FACs diminish in intensity to magnitudes of about 0.1 μA/m 2 , the plasma convection maintains two‐cell flow pattern, and the thermospheric density is quite low. However, there are obvious activities in the northern cusp region. One pair of FACs with a downward leg toward the pole and upward leg on the equatorward side emerge in the northern cusp region, exhibiting opposite polarity to FACs typical for duskward IMF orientation. An obvious sunward plasma flow channel persists during the whole period. These ionospheric features might be manifestations of an efficient magnetic reconnection process occurring in the northern magnetospheric flanks at high latitude. The enhanced ionospheric current systems might deposit large amount of Joule heating into the thermosphere. The air densities in the cusp region get enhanced and subsequently propagate equatorward on the dayside. Although geomagnetic indices during the radial IMF indicate low‐level activity, the present study demonstrates that there are prevailing energy inputs from the magnetosphere to both the ionosphere and thermosphere in the northern polar cusp region. Key Points A pair of strong FACs emerges with opposite polarity to DPY FACs Obvious sunward plasma flow channel persists during the period Enhanced air densities are found in the cusp regionPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/107563/1/jgra51028.pd

The Utility of the Abstract Relational Model and Attribute Paths in SQL

It is well-known that querying information is difficult for domain experts, for they are not familiar with querying actual relational schemata due to the notions of primary and foreign keys and the various ways of representing and storing information in a relational database. To overcome these problems, the Abstract Relational Model and the query language, SQLP, have been proposed. They are the theoretical foundations and ensure that explicit primary and foreign keys are hidden from the user's view and that queries can be expressed more compactly. In this paper we evaluate these theoretical advantages with user studies that compare SQLP to plain SQL as the baseline. The experiments show significant statistical evidence that SQLP indeed requires less time for understanding and authoring queries, with no loss in accuracy. Considering the positive results, we develop a method to reverse engineer legacy relational schemata into abstract relational ones

Liquid Flyback Booster Pre-Phase A Study Assessment

Mw concept of a flyback booster has been around since early in the Shuttle program. The original two-stage Shuttle concepts used a manned flyback booster. These boosters were eliminated from the program for funding and size reasons. The current Shuttle uses two Redesigned Solid Rocket Motors (RSRMs), which are recovered and refurbished after each flight; this is one of the major cost factors of the program. Replacement options have been studied over the past ten years. The conclusion reached by the most recent study is that the liquid flyback booster (LFBB) is the only competitive option from a life-cycle cost perspective. The purpose of this study was to assess the feasibility and practicality of LFBBs. The study provides an expansion of the recommendations made during the during the aforementioned study. The primary benefits are the potential for enhanced reusability and a reuction of recurring costs. The potential savings in vehicle turnaround could offset the up-front costs. Development of LFBBs requires a commitment to the Shuttle program for 20 to 30 years. LFBBs also offer enhanced safety and abort capabilities. Currently, any failure of an RSRM can be considered catastrophic since them we no intact abort capabilities during the burn of the RSRMS. The performance goal of the LFBBs was to lift a fully loaded Orbiter under optimal conditions, so as not to be the limiting factor of the performance capability of the Shuttle. In addition, a final benefit is the availability of growth paths for applications other than the Shuttle

Dynamic phase transitions in thin ferromagnetic films

Monte Carlo simulations have been used to investigate the dynamic phase behavior of a classical Heisenberg spin system with a bilinear exchange anisotropy in a planar thin film geometry. Studies of the field amplitude, frequency and temperature dependence show dynamic phase transitions in films subject to a pulsed oscillatory external field. Thin films with competing surface fields show separate and distinct dynamic phase transitions for the bulk and surface layers of the film. Between the two transitions, a mixed state with coexisting dynamically ordered and dynamically disordered phases is observed in the film. In contrast, the free film with no surface fields shows a single dynamic phase transition as in a bulk system.Comment: 25 pages including figures in pdf format, to be published in PR