Wong, Hong; Kapila, Vikram
2004-01-01
In this paper, we present a method for trajectory generation and adaptive full-state feedback control to facilitate spacecraft formation flying near the Sun-Earth L2 Lagrange point. Specifically, the dynamics of a spacecraft in the neighborhood of a Halo orbit reveals that there exist quasi-periodic orbits surrounding the Halo orbit. Thus, a spacecraft formation is created by placing a leader spacecraft on a desired Halo orbit and placing follower spacecraft on desired quasi-periodic orbits. To produce a formation maintenance controller, we first develop the nonlinear dynamics of a follower spacecraft relative to the leader spacecraft. We assume that the leader spacecraft is on a desired Halo orbit trajectory and the follower spacecraft is to track a desired quasi-periodic orbit surrounding the Halo orbit. Then, we design an adaptive, full-state feedback position tracking controller for the follower spacecraft providing an adaptive compensation for the unknown mass of the follower spacecraft. The proposed control law is simulated for the case of the leader and follower spacecraft pair and is shown to yield global, asymptotic convergence of the relative position tracking errors.
Capturing small asteroids into a Sun-Earth Lagrangian point
Lladó, Neus; Ren, Yuan; Masdemont, Josep J.; Gómez, Gerard
2014-02-01
In this paper we address the feasibility of capturing small Near-Earth Asteroids (NEAs) into the vicinity of the Sun-Earth L2 libration point using a continuous-thrust propulsion system assumed to be attached to the asteroid. The vicinity of this libration point is a gateway to the Earth-Moon neighborhood and using it for capture, or for transit, small NEAs could be interesting for mining or science purposes.
Orbital mechanics near Lagrange's points
Utashima, Masayoshi; 歌島 昌由
1997-01-01
The first libration-point satellite ISEE-3 (International Sun-Earth Explorer-3) was launched in 1978. Though, no libration-point satellites were realized after the launch of the ISEE-3, NASA launched the ESA's Solar and Heliospheric Observatory (SOHO) spacecraft into the halo orbit in the sun-earth system in late 1995. The halo orbit in the sun-earth system is adequate for missions such as solar observation, astronomical observation, NEO (Near Earth Objects) observation, communications with t...
Optimal Sunshade Configurations for Space-Based Geoengineering near the Sun-Earth L1 Point.
Directory of Open Access Journals (Sweden)
Joan-Pau Sánchez
Full Text Available Within the context of anthropogenic climate change, but also considering the Earth's natural climate variability, this paper explores the speculative possibility of large-scale active control of the Earth's radiative forcing. In particular, the paper revisits the concept of deploying a large sunshade or occulting disk at a static position near the Sun-Earth L1 Lagrange equilibrium point. Among the solar radiation management methods that have been proposed thus far, space-based concepts are generally seen as the least timely, albeit also as one of the most efficient. Large occulting structures could potentially offset all of the global mean temperature increase due to greenhouse gas emissions. This paper investigates optimal configurations of orbiting occulting disks that not only offset a global temperature increase, but also mitigate regional differences such as latitudinal and seasonal difference of monthly mean temperature. A globally resolved energy balance model is used to provide insights into the coupling between the motion of the occulting disks and the Earth's climate. This allows us to revise previous studies, but also, for the first time, to search for families of orbits that improve the efficiency of occulting disks at offsetting climate change on both global and regional scales. Although natural orbits exist near the L1 equilibrium point, their period does not match that required for geoengineering purposes, thus forced orbits were designed that require small changes to the disk attitude in order to control its motion. Finally, configurations of two occulting disks are presented which provide the same shading area as previously published studies, but achieve reductions of residual latitudinal and seasonal temperature changes.
Optimal Sunshade Configurations for Space-Based Geoengineering near the Sun-Earth L1 Point.
Sánchez, Joan-Pau; McInnes, Colin R
2015-01-01
Within the context of anthropogenic climate change, but also considering the Earth's natural climate variability, this paper explores the speculative possibility of large-scale active control of the Earth's radiative forcing. In particular, the paper revisits the concept of deploying a large sunshade or occulting disk at a static position near the Sun-Earth L1 Lagrange equilibrium point. Among the solar radiation management methods that have been proposed thus far, space-based concepts are generally seen as the least timely, albeit also as one of the most efficient. Large occulting structures could potentially offset all of the global mean temperature increase due to greenhouse gas emissions. This paper investigates optimal configurations of orbiting occulting disks that not only offset a global temperature increase, but also mitigate regional differences such as latitudinal and seasonal difference of monthly mean temperature. A globally resolved energy balance model is used to provide insights into the coupling between the motion of the occulting disks and the Earth's climate. This allows us to revise previous studies, but also, for the first time, to search for families of orbits that improve the efficiency of occulting disks at offsetting climate change on both global and regional scales. Although natural orbits exist near the L1 equilibrium point, their period does not match that required for geoengineering purposes, thus forced orbits were designed that require small changes to the disk attitude in order to control its motion. Finally, configurations of two occulting disks are presented which provide the same shading area as previously published studies, but achieve reductions of residual latitudinal and seasonal temperature changes.
Orbit Determination Error Analysis Results for the Triana Sun-Earth L2 Libration Point Mission
Marr, G.
2003-01-01
Using the NASA Goddard Space Flight Center's Orbit Determination Error Analysis System (ODEAS), orbit determination error analysis results are presented for all phases of the Triana Sun-Earth L1 libration point mission and for the science data collection phase of a future Sun-Earth L2 libration point mission. The Triana spacecraft was nominally to be released by the Space Shuttle in a low Earth orbit, and this analysis focuses on that scenario. From the release orbit a transfer trajectory insertion (TTI) maneuver performed using a solid stage would increase the velocity be approximately 3.1 km/sec sending Triana on a direct trajectory to its mission orbit. The Triana mission orbit is a Sun-Earth L1 Lissajous orbit with a Sun-Earth-vehicle (SEV) angle between 4.0 and 15.0 degrees, which would be achieved after a Lissajous orbit insertion (LOI) maneuver at approximately launch plus 6 months. Because Triana was to be launched by the Space Shuttle, TTI could potentially occur over a 16 orbit range from low Earth orbit. This analysis was performed assuming TTI was performed from a low Earth orbit with an inclination of 28.5 degrees and assuming support from a combination of three Deep Space Network (DSN) stations, Goldstone, Canberra, and Madrid and four commercial Universal Space Network (USN) stations, Alaska, Hawaii, Perth, and Santiago. These ground stations would provide coherent two-way range and range rate tracking data usable for orbit determination. Larger range and range rate errors were assumed for the USN stations. Nominally, DSN support would end at TTI+144 hours assuming there were no USN problems. Post-TTI coverage for a range of TTI longitudes for a given nominal trajectory case were analyzed. The orbit determination error analysis after the first correction maneuver would be generally applicable to any libration point mission utilizing a direct trajectory.
Capturing small asteroids into Sun-Earth Lagrangian points for mining purposes
Lladó, Neus; Ren, Yuan; Masdemont Soler, Josep; Gomez Muntaner, Gerard
2012-01-01
The aim of this paper is to study the capture of small Near Earth Objects (NEOs) into the Sun-Earth L2 using low-thrust propulsion for mining or science purposes. As it is well known, the vicinity of these points is inside a net of dynamical channels suitable for the transport in the Earth-Moon neighborhood, so different final destinations from here could be easily considered. Asteroids with very small mass and not representing a potential hazard are analyzed. An initial pruning o...
Minimum time solar sailing from geosynchronous orbit to the sun-earth L2 point
Hur, Sun H.; Bryson, Arthur E., Jr.
1992-08-01
An approximate time-optimal of a solar sail from a geosynchronous orbit to the sun-earth L2 libration point is found using a combined method of local optimization and single shooting. The local optimization strategy is based on maximizing the time rate of change of an energy variable at each time. This strategy overcomes the numerical difficulties associated with solving optimal control problems of long duration like the solar sail transfer problem. The single shooting portion of the method is employed to meet the terminal constraints. The combined method can be applied to other optimal low thrust transfer problems of long duration.
Solar radiation pressure used for formation flying control around the Sun-Earth libration point
Institute of Scientific and Technical Information of China (English)
Sheng-ping GONG; Jun-feng LI; He-xi BAOYIN
2009-01-01
Solar radiation pressure is used to control the formation flying around the L2 libration point in the Sun-Earth system. Formation flying control around a halo orbit requires a very small thrust that cannot be satisfied by the latest thrusters. The key contribution of this paper is that the continuous low thrust is produced by solar radiation pressure to achieve the tight formation flying around the libration point. However, only certain families of formation types can be controlled by solar radiation pressure since the direction of solar radiation pressure is restricted to a certain range. Two types of feasible formations using solar radiation pressure control are designed. The conditions of feasible formations are given analytically. Simulations are presented for each case, and the results show that the formations are well controlled by solar radiation pressure.
Marr, Greg C.
2003-01-01
The Triana spacecraft was designed to be launched by the Space Shuttle. The nominal Triana mission orbit will be a Sun-Earth L1 libration point orbit. Using the NASA Goddard Space Flight Center's Orbit Determination Error Analysis System (ODEAS), orbit determination (OD) error analysis results are presented for all phases of the Triana mission from the first correction maneuver through approximately launch plus 6 months. Results are also presented for the science data collection phase of the Fourier Kelvin Stellar Interferometer Sun-Earth L2 libration point mission concept with momentum unloading thrust perturbations during the tracking arc. The Triana analysis includes extensive analysis of an initial short arc orbit determination solution and results using both Deep Space Network (DSN) and commercial Universal Space Network (USN) statistics. These results could be utilized in support of future Sun-Earth libration point missions.
Webster, Cassandra M.; Folta, David C.
2017-01-01
In order to fly an occulter in formation with a telescope at the Sun-Earth L2 (SEL2) Libration Point, one must have a detailed understanding of the dy-namics that govern the restricted three body system. For initial purposes, a linear approximation is satisfactory, but operations will require a high-fidelity modeling tool along with strategic targeting methods in order to be successful. This paper focuses on the challenging dynamics of the transfer trajectories to achieve the relative positioning of two spacecraft to fly in formation at SEL2, in our case, the Wide-Field Infrared Survey Telescope (WFIRST) and a proposed Starshade. By modeling the formation transfers using a high fidelity tool, an accurate V approximation can be made to as-sist with the development of the subsystem design required for a WFIRST and Starshade formation flight mission.
Formation Flying Satellite Control Around the L2 Sun-Earth Libration Point
Hamilton, Nicholas H.
2001-12-01
A growing interest in formation flying satellites demands development and analysis of control and estimation algorithms for station-keeping and formation maneuvering. This thesis discusses the development of a discrete linear-quadratic- regulator control algorithm for formations in the vicinity of the L2 sun-earth libration point. The development of an appropriate Kalman filter is included as well. Simulations are created for the analysis of the station-keeping and various formation maneuvers of the Stellar Imager mission. The simulations provide tracking error, estimation error, and control effort results. From the control effort, useful design parameters such as AV and propellant mass are determined. For formation maneuvering, the drone spacecraft track to within 4 meters of their desired position and within 1.3 millimeters per second of their desired zero velocity. The filter, with few exceptions, keeps the estimation errors within their three-sigma values. Without noise, the controller performs extremely well, with the drones tracking to within several micrometers. Bach drone uses around 1 to 2 grams of propellant per maneuver, depending on the circumstances.
Long Term Missions at the Sun-Earth Libration Point L1: ACE, SOHO, and WIND
Roberts, Craig E.
2011-01-01
Three heliophysics missions -- the Advanced Composition Explorer (ACE), Solar Heliospheric Observatory (SOHO), and the Global Geoscience WIND -- have been orbiting the Sun-Earth interior libration point L1 continuously since 1997, 1996, and 2004, respectively. ACE and WIND (both NASA missions) and SOHO (an ESA-NASA joint mission) are all operated from the NASA Goddard Space Flight Center (GSFC). While ACE and SOHO have been dedicated libration point orbiters since their launches, WIND has had also a remarkable 10-year career flying a deep-space, multiple lunar-flyby trajectory prior to 2004. That era featured 36 targeted lunar flybys with excursions to both L1 and L2 before its final insertion in L1 orbit. A figure depicts the orbits of the three spacecraft, showing projections of the orbits onto the orthographic planes of a solar rotating ecliptic frame of reference. The SOHO orbit is a quasi-periodic halo orbit, where the frequencies of the in-plane and out-of-plane motions are practically equal. Such an orbit is seen to repeat itself with a period of approximately 178 days. For ACE and WIND, the frequencies of the in-plane and out-of-plane motions are unequal, giving rise to the characteristic Lissajous motion. ACE's orbit is of moderately small amplitude, whereas WIND's orbit is a large-amplitude Lissajous of dimensions close to those of the SOHO halo orbit. As motion about the collinear points is inherently unstable, stationkeeping maneuvers are necessary to prevent orbital decay and eventual escape from the L1 region. Though the three spacecraft are dissimilar (SOHO is a 3-axis stabilized Sun pointer, WIND is a spin-stabilized ecliptic pole pointer, and ACE is also spin-stabilized with its spin axis maintained between 4 and 20 degrees of the Sun), the stationkeeping technique for the three is fundamentally the same. The technique consists of correcting the energy of the orbit via a delta-V directed parallel or anti-parallel to the Spacecraft-to-Sun line. SOHO
Roberts, Craig; Case, Sara; Reagoso, John; Webster, Cassandra
2015-01-01
The Deep Space Climate Observatory mission launched on February 11, 2015, and inserted onto a transfer trajectory toward a Lissajous orbit around the Sun-Earth L1 libration point. This paper presents an overview of the baseline transfer orbit and early mission maneuver operations leading up to the start of nominal science orbit operations. In particular, the analysis and performance of the spacecraft insertion, mid-course correction maneuvers, and the deep-space Lissajous orbit insertion maneuvers are discussed, com-paring the baseline orbit with actual mission results and highlighting mission and operations constraints..
Mission to the Sun-Earth L5 Lagrangian Point: An Optimal Platform for Space Weather Research
Vourlidas, Angelos
2015-04-01
The Sun-Earth Lagrangian L5 point is a uniquely advantageous location for space weather research and monitoring. It covers the "birth-to-impact" travel of solar transients; it enables imaging of solar activity at least 3 days prior to a terrestrial viewpoint and measures the solar wind conditions 4-5 days ahead of Earth impact. These observations, especially behind east limb magnetograms, will be a boon for background solar wind models, which are essential for coronal mass ejection (CME) and shock propagation forecasting. From an operational perspective, the L5 orbit is the space weather equivalent to the geosynchronous orbit for weather satellites. Optimal for both research and monitoring, an L5 mission is ideal for developing a Research-to-Operations capability in Heliophysics.
CHANG'E-2 lunar escape maneuvers to the Sun-Earth L2 libration point mission
Liu, Lei; Liu, Yong; Cao, Jianfeng; Hu, Songjie; Tang, Geshi; Xie, Jianfeng
2014-01-01
This paper addresses lunar escape maneuvers of the first Chinese Sun-Earth L2 libration point mission by the CHANG'E-2 satellite, which is also the world's first satellite to reach the L2 point from a lunar orbit. The lunar escape maneuvers are heavily constrained by the remaining propellant and the condition of telemetry, track and command, among others. First, these constraints are analyzed and summarized to design a target L2 Lissajous orbit and an initial transfer trajectory. Second, the maneuver mathematical models are studied. The multilevel maneuver schemes which consist of phasing maneuvers and a final lunar escape maneuver are designed for actual operations. Based on the scheme analysis and comparison, the 2-maneuver scheme with a 5.3-h-period phasing orbit is ultimately selected. Finally, the mission status based on the scheme is presented and the control operation results are discussed in detail. The methodology in this paper is especially beneficial and applicable to a future multi-mission instance in the deep space exploration.
Directory of Open Access Journals (Sweden)
He Zhenqi
2017-01-01
Full Text Available Keeping the flying formation of spacecraft is a key problem which needs to be solved in deep space exploration missions. In this paper, the nonlinear dynamic model of formation flying is established and a series of transformations are carried out on this model equation. By using SDRE (State-Dependent Riccati Equation algorithm, the optimal control of flying formation is realized. Compared with the traditional control method based on the average orbit elements and LQR (Linear Quadratic Regulator control method, the SDRE control method has higher control precision and is more suitable for the advantages of continuous control in practical engineering. Finally, the parameter values of the sun-earth libration point L2 are substituted in the equation and simulation is performed. The simulation curves of SDRE controller are compared with LQR controller. The results show that the SDRE controllers time cost is less than the LQR controllers and the former’s fuel consumption is less than the latter’s in the system transition process.
Lavraud, B.; Liu, Y.; Segura, K.; He, J.; Qin, G.; Temmer, M.; Vial, J.-C.; Xiong, M.; Davies, J. A.; Rouillard, A. P.; Pinto, R.; Auchère, F.; Harrison, R. A.; Eyles, C.; Gan, W.; Lamy, P.; Xia, L.; Eastwood, J. P.; Kong, L.; Wang, J.; Wimmer-Schweingruber, R. F.; Zhang, S.; Zong, Q.; Soucek, J.; An, J.; Prech, L.; Zhang, A.; Rochus, P.; Bothmer, V.; Janvier, M.; Maksimovic, M.; Escoubet, C. P.; Kilpua, E. K. J.; Tappin, J.; Vainio, R.; Poedts, S.; Dunlop, M. W.; Savani, N.; Gopalswamy, N.; Bale, S. D.; Li, G.; Howard, T.; DeForest, C.; Webb, D.; Lugaz, N.; Fuselier, S. A.; Dalmasse, K.; Tallineau, J.; Vranken, D.; Fernández, J. G.
2016-08-01
We present a concept for a small mission to the Sun-Earth Lagrangian L5 point for innovative solar, heliospheric and space weather science. The proposed INvestigation of Solar-Terrestrial Activity aNd Transients (INSTANT) mission is designed to identify how solar coronal magnetic fields drive eruptions, mass transport and particle acceleration that impact the Earth and the heliosphere. INSTANT is the first mission designed to (1) obtain measurements of coronal magnetic fields from space and (2) determine coronal mass ejection (CME) kinematics with unparalleled accuracy. Thanks to innovative instrumentation at a vantage point that provides the most suitable perspective view of the Sun-Earth system, INSTANT would uniquely track the whole chain of fundamental processes driving space weather at Earth. We present the science requirements, payload and mission profile that fulfill ambitious science objectives within small mission programmatic boundary conditions.
Thieman, J.; Ng, C.; Lewis, E.; Cline, T.
2010-08-01
Sun-Earth Day is a well-coordinated series of programs, resources and events under a unique yearly theme highlighting the fundamentals of heliophysics research and missions. A menu of activities, conducted throughout the year, inspire and educate participants. Sun-Earth Day itself can vary in date, but usually is identified by a celebration on or near the spring equinox. Through the Sun-Earth Day framework we have been able to offer a series of coordinated events that promote and highlight the Sun, its connection to Earth and the other planets. Sun-Earth Day events are hosted by educators, museums, amateur astronomers and scientists and occur at schools, community groups, parks, planetaria and science centers around the globe. Sun-Earth Day raises the awareness and knowledge of formal and informal education audiences concerning space weather and heliophysics. By building on the success of Sun-Earth Day yearly celebrations, we seek to affect people of all backgrounds and ages with the wonders of heliophysics science, discovery, and exploration in ways that are both tangible and meaningful to their lives.
Lang, Kenneth R
2006-01-01
This Second Edition of Sun, Earth and Sky updates the popular text by providing comprehensive accounts of the most recent discoveries made by five modern solar spacecraft during the past decade. Their instruments have used sound waves to peer deep into the Sun’s inner regions and measure the temperature of its central nuclear reactor, and extended our gaze far from the visible Sun to record energetic outbursts that threaten Earth. Breakthrough observations with the underground Sudbury Neutrino Observatory are also included, which explain the new physics of ghostly neutrinos and solve the problematic mismatch between the predicted and observed amounts of solar neutrinos. This new edition of Sun, Earth and Sky also describes our recent understanding of how the Sun’s outer atmosphere is heated to a million degrees, and just where the Sun’s continuous winds come from. As humans we are more intimately linked with our life-sustaining Sun than with any other astronomical object, and the new edition therefore p...
LAGRANGE: LAser GRavitational-wave ANtenna at GEo-lunar Lagrange points
Conklin, J W; Aguero, V; Alfauwaz, A; Aljadaan, A; Almajed, M; Altwaijry, H; Al-Saud, T; Balakrishnan, K; Byer, R L; Bower, K; Costello, B; Cutler, G D; DeBra, D B; Faied, D M; Foster, C; Genova, A L; Hanson, J; Hooper, K; Hultgren, E; Jaroux, B; Klavins, A; Lantz, B; Lipa, J A; Palmer, A; Plante, B; Sanchez, H S; Saraf, S; Schaechter, D; Sherrill, T; Smith, E; Shu, K -L; Tenerelli, D; Vanbezooijen, R; Vasudevan, G; Williams, S D; Worden, S P; Zhou, J; Zoellner, A
2011-01-01
We describe a new space gravitational wave observatory design called LAGRANGE that maintains all important LISA science at about half the cost and with reduced technical risk. It consists of three drag-free spacecraft in the most stable geocentric formation, the Earth-Moon L3, L4, and L5 Lagrange points. Fixed antennas allow continuous contact with the Earth, solving the problem of communications bandwidth and latency. A 70 mm diameter AuPt sphere with a 35 mm gap to its enclosure serves as a single inertial reference per spacecraft, which is operated in "true" drag-free mode (no test mass forcing). This is the core of the Modular Gravitational Reference Sensor whose other advantages are: a simple caging design based on the DISCOS 1972 drag-free mission, an all optical read-out with pm fine and nm coarse sensors, and the extensive technology heritage from the Honeywell gyroscopes, and the DISCOS and Gravity Probe B drag-free sensors. An Interferometric Measurement System, designed with reflective optics and a...
On the Transfer and Control of Space Probes Around the L1 Point of the Sun-Earth+Moon System
Hou, Xi-Yun; Liu, Lin
2008-01-01
The motion around the collinear libration points in the restricted three body problem is unstable. But there exist conditionally stable periodic orbits around these points. Special-purpose space probes located in the vicinity of these points (e.g., ISEE-3, SOHO) can benefit from this dynamical property, in regard to maintaining the orbit in position and the energy required of placing the probe in position. As an example, we study in this paper the launch and orbital control of a space probe around the L1 libration point in the system consisting of the Sun and the Earth-Moon. We present some theoretical and numerical simulations' results, which may serve as a basis for the realization of such a space probe in future.
Lissajous Orbit Control for the Deep Space Climate Observatory Sun-Earth L1 Libration Point Mission
Roberts, Craig; Case, Sarah; Reagoso, John
2015-01-01
DSCOVR Lissajous Orbit sized such that orbit track never extends beyond 15 degrees from Earth-Sun line (as seen from Earth). Requiring delta-V maneuvers, control orbit to obey a Solar Exclusion Zone (SEZ) cone of half-angle 4 degrees about the Earth-Sun line. Spacecraft should never be less than 4 degrees from solar center as seen from Earth. Following Lissajous Orbit Insertion (LOI), DSCOVR should be in an opening phase that just skirts the 4-degree SEZ. Maximizes time to the point where a closing Lissajous will require avoidance maneuvers to keep it out of the SEZ. Station keeping maneuvers should take no more than 15 minutes.
Lang, Kenneth R.
1995-01-01
The Sun is enveloped by a hot, tenuous million-degree corona that expands to create a continuous solar wind that sweeps past all the planets and fills the heliosphere. The solar wind is modulated by strong gusts that are initiated by powerful explosions on the Sun, including solar flares and coronal mass ejections. This dynamic, invisible outer atmosphere of the Sun is currently under observation with the soft X-ray telescope aboard the Yohkoh spacecraft, whose results are presented. We also show observations from the Ulysses spacecraft that is now passing over the solar pole, sampling the solar wind in this region for the first time. Two other spacecraft, Voyager 1 and 2, have recently detected the outer edge of the invisible heliosphere, roughly halfway to the nearest star. Magnetic solar activity, the total radiative output from the Sun, and the Earth's mean global surface temperature all vary with the 11-year sunspot cycle in which the total number of sunspots varies from a maximum to a minimum and back to a maximum again in about 11 years. The terrestrial magnetic field hollows out a protective magnetic cavity, called the magnetosphere, within the solar wind. This protection is incomplete, however, so the Sun feeds an unseen world of high-speed particles and magnetic fields that encircle the Earth in space. These particles endanger spacecraft and astronauts, and also produce terrestrial aurorae. An international flotilla of spacecraft is now sampling the weak points in this magnetic defense. Similar spacecraft have also discovered a new radiation belt, in addition to the familiar Van Allen belts, except fed by interstellar ions instead of electrons and protons from the Sun.
On the Microwave Signal at the Second Lagrange Point.
Robitaille, Pierre-Marie; Borissova, Larissa; Rabounski, Dmitri
2007-11-01
It has been proposed that the 2.7 K Penzias-Wilson monopole is of oceanic origin. Under this scenario, the signal should be powerful near the Earth and rapidly fall in power away from our planet. As a result, the Penzias and Wilson signal is not expected to have any significant intensity at the second Lagrange point. In July 2008, the ESA will launch the PLANCK mission to this location. The low Frequency Instrument (LFI) on PLANCK is operating as a group of pseudo-correlation receivers. Since the 2.7 K signal will not be found at L2, an analytical analysis of the PLANCK LFI reveals that the knee frequency of the radiometers will rise to ˜50 mHz, well above the 3-7 mHz levels expected by the PLANCK team and substantially above the satellite spin frequency of ˜17 mHz. This will result in the production of significant stripes in the raw maps generated, potentially impacting the harvest from PLANCK. Calculations reveal that little difference exists in the intensity of the 2.7 K field, either at the position of a U2 plane (25 km), or in the COBE orbit (900 km). However, the density of the energy of the field drops to ˜10-7 of these near Earth values at the L2 point, rendering detection improbable. Since the LFI on PLANCK can operate either in absolute or difference mode and since the HFI operate as bolometers, PLANCK should unequivocally ascertain the origin of the 2.7K monopole.
Institute of Scientific and Technical Information of China (English)
Liu Chang; Mei Feng-Xiang; Guo Yong-Xin
2009-01-01
This paper studies the conformal invariance by infinitesimal point transformations of non-conservative Lagrange systems. It gives the necessary and sufficient conditions of conformal invariance by the action of infinitesimal point transformations being Lie symmetric simultaneously. Then the Noether conserved quantities of conformal invariance are obtained. Finally an illustrative example is given to verify the results.
Trivailo, Olga
2007-04-01
In view of the importance of Lagrange points to the exploration and development of space, the dynamics and stability of a satellite were studied under multiple Trojan asteroids influence. Through the use of a numerical simulator developed in MATLAB, consideration was given to the effects of gravitational forces exerted by the asteroids themselves, simulating the resulting insignificant influence of the Trojan asteroids on a satellite placed at the triangular Lagrange points. The study of optimized satellite transfers between triangular Lagrange points allowed the enforcement of multiple, specific, non-linear constraints on critical mission parameters of maximum thrust, mission duration, propellant consumption and accelerations. The optimized transfer trajectory between the two triangular Lagrange points was direction sensitive. That is, the minimum thrust optimized transfer trajectory for a satellite from L4 to L5 was unique and vastly different to that from L5 to L4. A further exciting discovery highlighted that superposition of the latter trajectories formed a perfectly smooth, uninterrupted kidney-shaped loop, fused at the two relevant points of connection. Implications for this phenomenon extend directly to future mission planning.
Conformal Invariance of Higher-Order Lagrange Systems by Lie Point Transformation
Institute of Scientific and Technical Information of China (English)
HUANG Wei-Li; CAI Jian-Le
2011-01-01
Conformal invariance and conserved quantities for a higher-order Lagrange system by Lie point transformation of groups are studied. The differential equation of motion for the higher-order Lagrange system is introduced. The definition of conformal invariance for the system together with its determining equations and conformal factor are provided. The necessary and sufficient condition that the system's conformal invariance would be Lie symmetry by the infinitesimal one-parameter point transformation group is deduced. The conserved quantity of the system is derived using the structural equation satisfied by the gauge function. An example of a higher-order mechanical system is offered to illustrate the application of the result.%Conformal invariance and conserved quantities for a higher-order Lagrange system by Lie point transformation of groups are studied.The differential equation of motion for the higher-order Lagrange system is introduced.The definition of conformal invariance for the system together with its determining equations and conformal factor are provided.The necessary and sufficient condition that the system's conformal invariance would be Lie symmetry by the infinitesimal one-parameter point transformation group is deduced.The conserved quantity of the system is derived using the structural equation satisfied by the gauge function.An example of a higher-order mechanical system is offered to illustrate the application of the result.Since the Noether theorem was published in 1918,[1] the symmetry and conserved quantity for a dynamical system play important roles in the fields of modern science and technology,and some important results have been gained so far.[2-21] Conformal invariance is a modern method for finding conserved quantities.In 1997,Galiullin etal.[22] studied conformal invariance of Birkhoff systems under special infinitesimal transformations.In recent years,we have discussed the conformal invariance of Lie symmetry for Lagrange systems
Institute of Scientific and Technical Information of China (English)
王亚敏; 乔栋; 崔平远
2015-01-01
对从环月轨道飞往日-地动平衡点轨道的转移轨道初始误差敏感度进行了数值仿真与分析。介绍了两种类型的转移轨道：长转移与短转移。建立初始速度误差与轨道末端偏差之间的数学关系式，采用数值计算获得了初始速度误差与轨道末端偏差量之间的线性关系曲线。通过建立轨道初始状态与末端状态量的一阶变分表达式，来说明始末偏差量呈线性关系的原因以及适用范围。研究表明，长转移轨道相较于短转移，对初始速度误差更为敏感，其始末偏差的线性关系适用范围更小。%The sensitivity of initial error for the transfer trajectory from lunar orbit to the Sun-Earth libration point orbit was calculated and analyzed.First,the short and long transfer trajectories for this kind of transfer issue were proposed.Then,the mathematical relation between initial error and terminal derivation was built.The relation is found to be linear by numerical calculation.Finally,the reason why the linear relation existed and its applicable conditions were explored by the first-order variation expression of initial error and terminal derivation.The result indicated that the long transfer is more sensitive to initial error than short transfer and that the applicable conditions for long transfer is stricter.
日地平动点卫星两脉冲转移轨道设计%Two impulses transfer trajectory design for Sun-Earth libration point missions
Institute of Scientific and Technical Information of China (English)
李明涛; 郑建华; 于锡峥; 高东
2009-01-01
Two impulses transfer trajectory design based on the least differential corrections method was studied, differential correction equation with the altitude and the flight path angle constraints was concluded, and the convergence of the method was discussed. Halo orbit around the L_1 libration point of the Sun-Earth system was taken as the objective orbit, two impulses transfer trajectory was designed in the framework of the circular restricted three-body problem. Effect of Halo orbit insertion (HOI) point and amplitude was studied in a systematic way, a strategy for the selection of HOI point was given, and the fast transfer trajectory for e-mergency was also studied. Numerical simulation shows that the proposed method is very effective, and transfer trajectory with moderate flight time can be obtained by choosing points on the near Earth side of Halo orbit as HOI point.%研究基于最小二乘微分修正方法的平动点卫星两脉冲转移轨道设计,推导了考虑高度和航迹角约束的微分修正公式,讨论了该方法的收敛性.以日地L_1点附近的Halo轨道为目标轨道,在圆型限制性三体问题模型下设计了其转移轨道,系统地研究了HOI(Halo Orbit Insertion)点和Halo轨道幅值对转移轨道的影响,给出了HOI点的选择策略,并讨论了应急情况下快速转移轨道设计.数值仿真验证了方法的有效性,选择Halo轨道靠近地球侧的点作HOI点可以获得飞行时间适中的转移轨道.
Institute of Scientific and Technical Information of China (English)
Fu Jing-Li; Nie Ning-Ming; Huang Jian-Fei; Jiménez Salvador; Tang Yi-Fa; Vázquez Luis; Zhao Wei-Jia
2009-01-01
This paper presents a method to find Noether-type conserved quantities and Lie point symmetries for discrete mechanico-electrical dynamical systems, which leave invariant the set of solutions of the corresponding difference scheme.This approach makes it possible to devise techniques for solving the Lagrange-Maxwell equations in differences which correspond to mechanico-electrical systems, by adapting existing differential equations. In particular, it obtains a new systematic method to determine both the one-parameter Lie groups and the discrete Noether conserved quantities of Lie point symmetries for mechanico-electrical systems. As an application, it obtains the Lie point symmetries and the conserved quantities for the difference equation of a model that represents a capacitor microphone.
The Feasibility of Shading the Greenhouse with Dust Clouds at the Stable Lunar Lagrange Points
Struck, C
2007-01-01
There are many indications that anthropogenic global warming poses a serious threat to our civilization and its ecological support systems. Ideally this problem will be overcome by reducing greenhouse gas emissions. Various space-based methods, including large-scale solar shades, diffusers or atmospheric pollutants, have been considered to reduce the solar constant (input flux) and the warming in case emissions reductions are not achieved in a timely way. Here it is pointed out that proposed technologies for near-Earth orbiting comet deflection, suggest a different kind of space-based solar shade. This shade would be made up of micron-sized dust particles derived from comet fragments or lunar mining, and positioned in orbits near the triangular Lagrange points of the Earth-Moon system. Solar radiation pressure can render such orbits unstable, but a class of nearly resonant, and long-lived orbits is shown to exist, though the phase space volume of such orbits depends on dust grain size. Advantages and disadvan...
Transit detection of a `starshade' at the inner lagrange point of an exoplanet
Gaidos, E.
2017-08-01
All water-covered rocky planets in the inner habitable zones of solar-type stars will inevitably experience a catastrophic runaway climate due to increasing stellar luminosity and limits to outgoing infrared radiation from wet greenhouse atmospheres. Reflectors or scatterers placed near Earth's inner Lagrange point (L_1) have been proposed as a "geoengineering' solution to anthropogenic climate change and an advanced version of this could modulate incident irradiation over many Gyr or `rescue' a planet from the interior of the habitable zone. The distance of the starshade from the planet that minimizes its mass is 1.6 times the Earth-L_1 distance. Such a starshade would have to be similar in size to the planet and the mutual occultations during planetary transits could produce a characteristic maximum at mid-transit in the light curve. Because of a fortuitous ratio of densities, Earth-size planets around G dwarf stars present the best opportunity to detect such an artefact. The signal would be persistent and is potentially detectable by a future space photometry mission to characterize transiting planets. The signal could be distinguished from natural phenomenon, i.e. starspots or cometary dust clouds, by its shape, persistence and transmission spectrum.
Impact of a Binary System Common Envelope on Mass Transfer through the Inner Lagrange Point
Bisikalo, D V; Kuznetsov, O A; Chechetkin, V M
1997-01-01
Results of numerical simulations of the impact of a common envelope on the matter flow pattern near the outflowing component in a semidetached binary system are presented. Three-dimensional modeling of the matter transfer gas dynamics in a low-mass X-ray binary X1822-371 enable investigation of the structure of flows in the vicinity of the inner Lagrange point L1. Taking into account the common envelope of the system substantially changes the flow pattern near the Roche surface of the outflowing component. In a stationary regime, accretion of common envelope gas is observed over a significant fraction of the donor star's surface, which inhibits the flow of gas along the Roche surface to L1. The change in the flow pattern is particularly significant near L1, where the stream of common envelope gas strips matter off the stellar surface. This, in turn, significantly increases (by an order of magnitude) the gas flow from the donor surface in comparison with the estimates of standard models.
Mass-loss through the L2 Lagrange point - application to main-sequence EMRI
Linial, Itai; Sari, Re'em
2017-08-01
We consider stable mass transfer from the secondary to the primary of an extreme mass ratio binary system. We show that when the mass transfer is sufficiently fast, mass leakage occurs through the outer Lagrange point L2, in addition to the usual transfer through L1. We provide an analytical estimate for the mass leakage rate through L2 and find the conditions in which it is comparable to the mass transfer rate through L1. Focusing on a binary system of a main-sequence star and a supermassive black hole, driven by the emission of gravitational radiation, we show that it may sustain stable mass transfer, along with mass-loss through L2. If such a mass transferring system occurs at our Galactic Centre, it produces a gravitational wave signal detectable by future detectors, such as Laser Interferometer Space Antenna (LISA). The signal evolves according to the star's adiabatic index and cooling time. For low-mass stars, the evolution is faster than the Kelvin-Helmholtz cooling rate driving the star out of the main-sequence. In some cases, the frequency and amplitude of the signal may both decrease with time, contrary to the standard chirp of a coalescing binary. Mass-loss through L2, when occurs, decreases the evolution time-scale of the emitted gravitational wave signal by up to a few tens of per cent. We conclude that L2 mass ejection is a crucial factor in analysing gravitational waves signals produced by such systems.
Sun-Earth Day Connects History, Culture and Science
Cline, T.; Thieman, J.
2003-12-01
The NASA Sun-Earth Connection Education forum annually promotes and event called Sun-Earth Day: a national celebration of the Sun, the space around the Earth (geospace), and how all of it affects life on our planet. For the past 3 years this event has provided a venue by which classrooms, museums, planetaria, and at NASA centers have had a sensational time sharing stories, images, and activities related to the Sun-Earth connections and the views o fthe Sun from Earth. Each year we select a different theme by which NASA Space Science can be further related to cross-curricular activities. Sun-Earth Day 2002, "Celebrate the Equinox", drew parallels between Native American Cultures and NASA's Sun-Earth Connection research via cultural stories, interviews, web links, activities and Native American participation. Sun-Earth Day 2003, "Live From the Aurora", shared the beauty of the Aurora through a variety of activities and stories related to perspectives of Northern Peoples. Sun-Earth Day 2004 will share the excitement of the transit of Venus through comparisons of Venus with Earth and Mars, calculations of the distances to nearby stars, and the use of transits to identify extra-solar planets. Finally, Sun-Earth Day 2005 will bring several of these themes together by turning our focus to the history and culture surrounding ancient observatories such as Chaco Canyon, Machu Picchu, and Chichen Itza.
On the Nature of the Microwave Background at the Lagrange 2 Point. Part II
Directory of Open Access Journals (Sweden)
Borissova L.
2007-10-01
Full Text Available In this work the mathematical methods of General Relativity are used to answer the following questions: if a microwave background originates from the Earth, what would be its density and associated dipole measured at the altitude of a U2 aeroplane (25 km, the COBE satellite (900 km, and the 2nd Lagrange point (1.5 million km, the position of the WMAP and PLANCK satellites? The first problem is solved via Einstein’s equations for the electromagnetic field of the Earth. The second problem is solved using the geodesic equations for light-like particles (photons which are mediators for electromagnetic radiation. We have determined that a microwave background that originates at the Earth (the Earth microwave background decreases with altitude so that the density of the energy of such a background at the altitude of the COBE orbit (900 km is 0.68 times less than that at the altitude of a U2 aeroplane. The density of the energy of the background at the L2 point is only ~1E-7 of the value detected by a U2 aeroplane or at the COBE orbit. The dipole anisotropy of the Earth microwave background, due to the rapid motion of the Earth relative to the source of another field which isn’t connected to the Earth but is located in depths of the cosmos, doesn’t depend on altitute from the surface of the Earth. Such a dipole will be the same irrespective of the position at which measurements are taken.
Sun-Earth Day 2005: Ancient Observatories: Timeless Knowledge
Thieman, J. R.; Cline, T.; Lewis, E.; Hawkins, I.; Odenwald, S.; Mayo, L.
2005-05-01
The NASA Sun-Earth Connection Education Forum (SECEF) annually promotes an event called Sun-Earth Day. For Sun-Earth Day 2005 SECEF has selected a theme called "Ancient Observatories: Timeless Knowledge. This year's Sun-Earth Day theme is your ticket to a fascinating journey through time as we explore centuries of sun watching by a great variety of cultures. From ancient solar motion tracking to modern solar activity monitoring the Sun has always occupied an important spot in mankind's quest to understand the Universe. Sun-Earth Day events usually are centered on the spring equinox around March 21, but this year there has already been a webcast from the San Francisco Exploratorium and the Native American ruins at Chaco Canyon, New Mexico on the day of winter solstice 2004. There will be another webcast on March 20 live from Chichen Itza, Mexico highlighting the solar alignment that makes a serpent appear on one of the ancient pyramids. The website http://sunearthday.nasa.gov has been developed to provide the necessary resources and opportunities for participation by scientists and educators in giving school or general public programs about Sun-Earth Day. The goal is to involve as much of the student population and the public in this event as possible and to help them understand the importance of the Sun for ancient and modern peoples. Through engaging activities available on the website, classrooms and museums can create their own event or participate in one of the opportunities we make available. Scientists, educators, amateur astronomers, and museums are invited to register on the website to receive a free packet of materials about Sun-Earth Day for use in making presentations or programs about the event. Past and future Sun-Earth Days will be discussed as well.
Sun-Earth Connection EPO's with Multiple Uses and Audiences
Foster, S. Q.; Johnson, R. M.; Russell, R.; Lu, G.; Richmond, A.; Maute, A.; Haller, D.; Conery, C.; Bintner, G.; Kiessling, D.; Hughes, W. J.
2005-05-01
The three-year life of an EPO grant can be a journey guided by clear goals and enriched by collaborative and outreach opportunities connecting Space sciences to Earth sciences for both K-12 and public audiences. This point is illustrated by two EPO projects funded by NASA Sun-Earth Connection research grants to the High Altitude Observatory (HAO) at the National Center for Atmospheric Research. They are entering their final year coordinated by the Office of Education and Outreach at University Corporation for Atmospheric Research. The content focus of both projects is well aligned with HAO's research mission and the expertise of our scientists, addressing solar dynamics, space weather, and the impacts of solar events on the magnetosphere, as well as societies inhabiting Earth's surface. The first project (Gang Lu, PI) develops presentation resources, inquiry activities, and tips that will help HAO scientists be better prepared to visit K-12 classrooms. Unexpectedly, the simultaneous development of a Teachers' Guide to NCAR's new Climate Discovery exhibit, which takes an Earth system approach to climate and global change, has created a niche for this EPO resource to be revised and repurposed for a needed unit in the guide about the exhibit's graphic panels on Sun-Earth connections. The second project (Art Richmond, PI) engages two high school "Teachers in Residence" to develop resources they can utilize with their students. Excited by exceptional educational graphics and animations in the new Physics of the Aurora: Earth Systems module co-produced by HAO and the COMET Program for advanced undergraduate courses, they chose to adapt appropriate sections of the module to enrich Earth science and math concepts addressed in their 9th and 10th grade astronomy and general physics classes. Simultaneously, the Windows to the Universe web site, which continuously updates space science content and is now developing a new Space Weather section with support from the Center for
Sun-Earth Day - Teaching Heliophysics Through Education Technology
Thieman, J.; Cline, T.; Lewis, E.
2010-01-01
Sun-Earth Day (SED) is an Education and Outreach program supported by the U.S, National Aeronautics and Space Administration (NASA). The intent of the program is to teach students and the general public about Heliophysics (the science of the study of the Sun, how it varies, and how solar dynamics affect the rest of the solar system, especially the Earth). The program was begun ten years ago. Each year since that time a particular day has been designated as "Sun-Earth Day ,,. Usually the day of the spring equinox (March 20 or 21) is Sun-Earth Day, but other days have been used as well. Each year a theme is chosen relating to Heliophysics and events reflecting that theme are planned not only for Sun-Earth Day, but for the entire year. From the very beginning educational technology was emphasized in the events in order to effectively reach wide audiences with the SED message. The main approach has been to have a "webcast" related to each year's theme, often from a location that supports the theme as well. For example, a webcast took place from the Mayan pyramids at Chichen Itza, Mexico to highlight the theme of "Ancient Observatories, Timeless Knowledge". Webcasts were not the only technology employed, however. Many of the themes centered on the dynamic nature of the Sun and the effects that solar storms can have on interplanetary space and in our day-to-day life on Earth. Activities for tracking when solar storms happen and how they affect the Earth were developed and brought together in an educational package called Space Weather Action Centers. This project is explained in more detail in another presentation in this session being given by Norma Teresinha Oliveira Reis. Recent Sun-Earth Days have utilized "social networking" technologies to reach widespread groups on the internet. Podcasts, Vodcasts, Facebook, Twitter, and Second Life are the types of network technologies being employed now. The NASA Distance learning Network is another method for bringing Sun-Earth
International Sun-Earth Explorer (ISEE)
Murdin, P.
2000-11-01
Series of three US satellites designed to study the solar wind and its interaction with the Earth's magnetosphere. ISEE-1 and 2 were placed into highly elliptical Earth orbits. ISEE-3 was placed in a halo orbit at the L1 Lagrangian point between the Sun and Earth. It gave advance warning of solar storms heading towards Earth. (See also INTERNATIONAL COMETARY EXPLORER and EXPLORER.)...
CUNY Sun-Earth Research, Space Climate
Cotten, D. E.; Cheung, T. D.; Marchese, P. J.; Johnson, L. P.; Austin, S.; Tremberger, G.
2007-05-01
Faculty and students at Queensborough Community College and Medgar Evers College of the City University of New York (CUNY) have, over several years now, employed simple software familiar to most undergraduate students to perform useful calculations, including statistical analyses, regarding various geophysical phenomena. Topics have included Space Weather, Interplanetary Magnetic Field (IMF) direction and strength fluctuations, geomagnetic and ionospheric responses to solar flares, and Coronal Mass Ejection (CME) events. Our statistical analyses have utilized second-order measures of fluctuation of the IMF strength, especially what we now call the Cheung number: the number of times that the value of Sigma-B, as provided by the ACE (Advanced Composition Explorer) data, has exceeded 0.5nT during a 6 hour interval. We have also utilized the Higuchi fractal dimension of various somewhat random fluctuations, including Sigma-B and the brightness or strength of adjacent pixels or data points in somewhat random data sequences in time or spatial dimension, including IMF fluctuations and SOHO (Solar Heliographic Observer) images of the Sun. These we have correlated with each other and with such variables as SEP (Solar Energetic Particle) peak flux, TEC (Total Electron Content) of the ionosphere, and Dst (Disturbance storm-time) in the geomagnetic field. Recent results indicate that the IMF fluctuation measures are well correlated with the SEP peak flux, the Dst, and TEC. Higuchi fractal analysis of SOHO photospheric ultraviolet brightness indicates, consistent with concomitant increased chaos or randomness of photospheric brightness, an increased likelihood of solar flare events or CME affecting interplanetary space and the earth's magnetosphere/ionosphere/atmosphere.
Thermal design of solar observer at L1 Lagrangian point in Sun-Earth system%日-地系拉格朗日 L1点太阳观测器热设计
Institute of Scientific and Technical Information of China (English)
王祥; 李义; 杨献伟
2013-01-01
对将运行于日-地L1点的太阳观测器进行了热设计，重点论述了日-地L1点的轨道外热流计算和Lyman α日冕仪（LACI）反射镜M2光阱、Lyman α日冕成像仪（LADI）滤光片组件、CCD组件、电箱、观测器主体等部分的热设计方案。通过在探测器对日面设置集热板，将观测器的主动加热功耗降低了73％；选用预埋热管的设计方案解决了对日定向观测导致的框架温差问题。仿真分析结果表明，在对日高温工作、对日低温工作、低温存储、轨道转移等4个极端工况下，观测器各组件温度均满足指标要求。该热设计方案以较低的加热功耗，解决了太阳观测器在轨工作阶段的散热、轨道转移阶段的保温等问题，满足CCD焦面工作温度＜-50℃的要求。%To ensure the temperature requirements of the solar observer working at L 1 Lagrangian point , the thermal design for Lyman αCoronagraphy Imager(LACI) and Lyman αDisk Image(LADI) was carried out, and the heat flux of the orbit was calculated .The thermal designs of light trap , filter components , detector com-ponents, electric box, and entirety of the observer were discussed in details .By using collector panels settled in the side facing to the Sun , the active heating power could be reduced by 73%.In order to reduce the tem-perature gradient caused by long-term observation facing to the sun , a heat pipe was embedded in the frame . Simulation results show that all conditions meet the temperature indicator in 4 typical cases .The thermal de-sign system with a low active power solves many problems , such as the cooling of the observer in orbit , insula-tion during orbital transfer phase , and meets the working temperature requirement of below -50℃for a CCD plane .
Institute of Scientific and Technical Information of China (English)
李冬辉
2016-01-01
Studies the asymptotic properties for median point in Taylor theorem with Lagrange remainder term as in-terval length goes to infinity.%研究当区间长度趋于无穷时，具有Lagrange型余项的Taylor定理中值点的渐近性。
Lagrange L4/L5 points and the origin of our Moon and Saturn's moons and rings.
Gott, J Richard
2005-12-01
The current standard theory of the origin of the Moon is that the Earth was hit by a giant impactor the size of Mars causing ejection of debris from its mantle that coalesced to form the moon; but where did this Mars-sized impactor come from? Isotopic evidence suggests that it came from 1 AU radius in the solar nebula, and computer simulations are consistent with its approaching Earth on a zero-energy parabolic trajectory. How could such a large object form at 1 AU in a quiescent disk of planetesimals without having already collided with the Earth at an earlier epoch before having the chance to grow large? Belbruno and Gott propose that the giant impactor could have formed in a stable orbit from debris at the Earth's Lagrange point L(5) (or L(4)). It would grow quietly by accretion at L(5) (or L(4)), but eventually gravitational perturbations by other growing planetesimals would kick it out into a horseshoe orbit and finally into a chaotic creeping orbit, which Belbruno and Gott show would, with high probability, hit the Earth on a near zero-energy parabolic trajectory. We can see other examples of this phenomenon occurring in the solar system. Asteroid 2002AA29 is in a horseshoe orbit relative to the Earth that looks exactly like the horseshoe orbits that Belbruno and Gott found for objects that had been perturbed from L(4)/L(5). The regular moons of Saturn are made of ice and have the same albedo as the ring particles (ice chunks, plus some dust). We (J. R. Gott, R. Vanderbei, and E. Belbruno) propose that the regular icy moons of Saturn (out to the orbit of Titan), which are all in nearly circular orbits, formed out of a thin disk of planetesimals (ice chunks) rather like the rings of Saturn today only larger in extent. In such a situation formation of objects at L(4)/L(5) might be expected. Indeed, Saturn's moon Dione is accompanied by moons (Helene and Polydeuces) at both L(4) and L(5) Lagrange points, and Saturn's moon Tethys is also accompanied by moons
Sun-earth connection education through modern views of ancient
Thieman, J. R.
The NASA Sun-Earth Connection Education Forum (SECEF) has the responsibility of using the latest science results from the study of solar physics, space physics, and aeronomy to inspire students in the classroom and to inform the public in general. SECEF works with NASA's Sun-Earth Connection spaceflight missions to accomplish this goal. Each year the missions and SECEF combine to promote their science through a major event designed to attract the attention of all. In late 2004 and 2005 the event will be the study of solar observatories created by ancient peoples and a comparison of their knowledge and culture to present understanding. Two solar observatory sites will be featured, Chaco Canyon in the U.S. and Chichen Itza in Mexico. There are many other places throughout the world that could also be featured as solar observatories and some of these may be described on the SECEF web site or used in future occurrences. Special emphasis is placed on events associated with the solstice and equinox dates. It is hoped that there will be happenings around the world on these days and SECEF will work with many museums, science centers, and other groups to help make this happen. Plans for the 2005 Ancient Observatories event and possible future events on the same subject will be described.
High-Performance Data Analysis Tools for Sun-Earth Connection Missions Project
National Aeronautics and Space Administration — The Interactive Data Language (IDL) is a standard tool used by many researchers in observational fields. Present day Sun-Earth Connection missions like SOHO, or...
Phasing Delta-V for transfers from Sun-Earth halo orbits to the Moon
Chen, Hongru; Kawakatsu, Yasuhiro; Hanada, Toshiya
2016-10-01
Inspired by successful extended missions such as the ISEE-3, an investigation for the extended mission that involves a lunar encounter following a Sun-Earth halo orbit mission is considered valuable. Most previous studies present the orbit-to-orbit transfers where the lunar phase is not considered. Intended for extended missions, the present work aims to solve for the minimum phasing ∆V for various initial lunar phases. Due to the solution multiplicity of the two-point boundary value problem, the general constrained optimization algorithm that does not identify multiple feasible solutions is shown to miss minima. A two-step differential corrector with a two-body Lambert solver is developed for identifying multiple solutions. The minimum ∆V associated with the short-way and long-way approaches can be recovered. It is acquired that the required ∆V to cover all initial lunar phases is around 45 m/s for the halo orbit with out-of-plane amplitude Az greater than 3.5×105 km, and 14 m/s for a small halo orbit with Az=1×105 km. In addition, the paper discusses the phasing planning based on the ∆V result and the shift of lunar phase with halo orbit revolution.
Sun-Earth Day: Growth and Impact of NASA E/PO Program
Hawkins, I.; Thieman, J.
2004-12-01
Over the past six years, the NASA Sun-Earth Connection Education Forum has sponsored and coordinated education public outreach events to highlight NASA Sun-Earth Connection research and discoveries. Our strategy involves using celestial phenomena, such as total solar eclipses and the Transit of Venus to celebrate Sun-Earth Day, a popular Education and Public Outreach international program. Sun-Earth Day also focuses attention on Equinoxes and Solstices to engage K-12 schools and the general public in space science activities, demonstrations, and interactions with space scientists. In collaboration with partners that include the Exploratorium, Maryland Science Center, NASA Connect, Sun-Earth Connection missions, Ideum, and others, we produce webcasts, other multi-media, and print resources for use by school and informal educators nation-wide. We provide training and professional development to K-12 educators, museum personnel, amateur astronomers, Girl Scout leaders, etc., so they can implement their own outreach programs taking advantage of our resources. A coordinated approach promotes multiple programs occurring each year under a common theme. We will report lessons learned from several years of experience, and strategies for growth and sustainability. We will also share our plans for "Ancient Observatories - Timeless Knowledge" our theme for Sun-Earth Day 2005, which will feature solar alignments at ancient sites that mark the equinoxes and/or solstices. The video and webcast programming will feature several sites including: Chaco Canyon (New Mexico), Hovenweep (Utah), and Chichen Itza (Mexico). Many of these sites present unique opportunities to develop authentic cultural connections to Native Americans, highlighting the importance of the Sun across the ages.
Earth-Affecting Solar Causes Observatory (EASCO): a mission at the Sun-Earth L5
DEFF Research Database (Denmark)
Gopalswamy, Nat; Davila, Joseph M.; Auchère, Frédéric
2011-01-01
. The Earth-Affecting Solar Causes Observatory (EASCO) is a proposed mission to be located at the Sun-Earth L5 that overcomes these deficiencies. The mission concept was recently studied at the Mission Design Laboratory (MDL), NASA Goddard Space Flight Center, to see how the mission can be implemented...
Extension Of Lagrange Interpolation
Directory of Open Access Journals (Sweden)
Mousa Makey Krady
2015-01-01
Full Text Available Abstract In this paper is to present generalization of Lagrange interpolation polynomials in higher dimensions by using Gramers formula .The aim of this paper is to construct a polynomials in space with error tends to zero.
Extension Of Lagrange Interpolation
Mousa Makey Krady
2015-01-01
Abstract In this paper is to present generalization of Lagrange interpolation polynomials in higher dimensions by using Gramers formula .The aim of this paper is to construct a polynomials in space with error tends to zero.
Noncommutative Lagrange Mechanics
Directory of Open Access Journals (Sweden)
Denis Kochan
2008-02-01
Full Text Available It is proposed how to impose a general type of ''noncommutativity'' within classical mechanics from first principles. Formulation is performed in completely alternative way, i.e. without any resort to fuzzy and/or star product philosophy, which are extensively applied within noncommutative quantum theories. Newton-Lagrange noncommutative equations of motion are formulated and their properties are analyzed from the pure geometrical point of view. It is argued that the dynamical quintessence of the system consists in its kinetic energy (Riemannian metric specifying Riemann-Levi-Civita connection and thus the inertia geodesics of the free motion. Throughout the paper, ''noncommutativity'' is considered as an internal geometric structure of the configuration space, which can not be ''observed'' per se. Manifestation of the noncommutative phenomena is mediated by the interaction of the system with noncommutative background under the consideration. The simplest model of the interaction (minimal coupling is proposed and it is shown that guiding affine connection is modified by the quadratic analog of the Lorentz electromagnetic force (contortion term.
Sun-Earth Day: Reaching the Education Audience by Informal Means
Thieman, J.; Lewis, E.; Cline, T.
2010-01-01
For ten years the Sun-Earth Day program has promoted Heliophysics education to ever larger audiences through events centered on attractive annual themes. What originally started out as a one day event quickly evolved into a series of programs and events that occur throughout the year culminating with a celebration on or near the Spring Equinox. The events are often formal broadcasts or webcasts seeking to convey the science behind the latest solar-terrestrial mission discoveries. This has been quite successful, but it is clear that the younger generation increasingly depends on social networking approaches and informal news transmission for learning what is happening in the world around them. For 2010, the Sun-Earth Day team put emphasis on using informal approaches to bring the theme to the audience. The main event, a webcast from the NASA booth at the National Science Teachers Association (NSTA) annual meeting by the NASA EDGE group, took a lighthearted and offbeat approach to interviewing scientists and educators about Heliophysics news. NASA EDGE programs are unscripted and unpredictable, and that represents a different approach to getting the message across. The webcast was supplemented by a number of social networking avenues. The Sun-Earth Day program explored a wide range of social media applications including Facebook, Twitter, NING, podcasting, iPhone apps, etc. Each of these offers unique and effective methods to promote Heliophysics content and mission related highlights. The facebook site was quite popular and message posting there told the Sun-Earth Day story piece by piece. The same could be said of twittering and the tweetup held at the NSTA site. Has all of this been effective? Results are still being gathered, but anecdotal responses from the world seem very positive. What other methods might be used in the future to bring the science to a personal hands-on, interactive experience? Outcomes: Participants will: (1) Be introduced to the Sun-Earth
Lagrange Theorem for polygroups
Directory of Open Access Journals (Sweden)
alireza sedighi
2014-12-01
Full Text Available So far?, ?isomorphism theorems in hyperstructure were proved for different structures of polygroups?, ?hyperrings and etc?. ?In this paper?, ?the polygroups properties is studied with the introduction of a suitable equivalence relation?. ?We show that the above relation is strongly regular?. ?Our main purpose in the paper is investigating Lagrang theorem and other expressing of isomorphism theorems for polygroups?.
Climate and weather of the Sun-Earth system (CAWSES) highlights from a priority program
Lübken, Franz-Josef
2012-01-01
CAWSES (Climate and Weather of the Sun-Earth System) is the most important scientific program of SCOSTEP (Scientific Committee on Solar-Terrestrial Physics). CAWSES has triggered a scientific priority program within the German Research Foundation for a period of 6 years. Approximately 30 scientific institutes and 120 scientists were involved in Germany with strong links to international partners. The priority program focuses on solar influence on climate, atmospheric coupling processes, and space climatology. This book summarizes the most important results from this program covering some impor
-Dimensional Fractional Lagrange's Inversion Theorem
Directory of Open Access Journals (Sweden)
F. A. Abd El-Salam
2013-01-01
Full Text Available Using Riemann-Liouville fractional differential operator, a fractional extension of the Lagrange inversion theorem and related formulas are developed. The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for one implicitly defined independent variable is obtained. Then, a fractional version of Lagrange's expansion in more than one unknown function is generalized. For extending the treatment in higher dimensions, some relevant vectors and tensors definitions and notations are presented. A fractional Taylor expansion of a function of -dimensional polyadics is derived. A fractional -dimensional Lagrange inversion theorem is proved.
Lagrange structure and quantization
Energy Technology Data Exchange (ETDEWEB)
Kazinski, Peter O. [Department of Quantum Field Theory, Tomsk State University, Tomsk 634050 (Russian Federation); Lyakhovich, Simon L. [Department of Quantum Field Theory, Tomsk State University, Tomsk 634050 (Russian Federation); Sharapov, Alexey A. [Department of Quantum Field Theory, Tomsk State University, Tomsk 634050 (Russian Federation)
2005-07-01
A path-integral quantization method is proposed for dynamical systems whose classical equations of motion do not necessarily follow from the action principle. The key new notion behind this quantization scheme is the Lagrange structure which is more general than the lagrangian formalism in the same sense as Poisson geometry is more general than the symplectic one. The Lagrange structure is shown to admit a natural BRST description which is used to construct an AKSZ-type topological sigma-model. The dynamics of this sigma-model in d+1 dimensions, being localized on the boundary, are proved to be equivalent to the original theory in d dimensions. As the topological sigma-model has a well defined action, it is path-integral quantized in the usual way that results in quantization of the original (not necessarily lagrangian) theory. When the original equations of motion come from the action principle, the standard BV path-integral is explicitly deduced from the proposed quantization scheme. The general quantization scheme is exemplified by several models including the ones whose classical dynamics are not variational.
Lagrange structure and quantization
Kazinski, P O; Sharapov, A A
2005-01-01
A path-integral quantization method is proposed for dynamical systems whose classical equations of motion do \\textit{not} necessarily follow from the action principle. The key new notion behind this quantization scheme is the Lagrange structure which is more general than the Lagrangian formalism in the same sense as Poisson geometry is more general than the symplectic one. The Lagrange structure is shown to admit a natural BRST description which is used to construct an AKSZ-type topological sigma-model. The dynamics of this sigma-model in $d+1$ dimensions, being localized on the boundary, are proved to be equivalent to the original theory in $d$ dimensions. As the topological sigma-model has a well defined action, it is path-integral quantized in the usual way that results in quantization of the original (not necessarily Lagrangian) theory. When the original equations of motion come from the action principle, the standard BV path-integral is explicitly deduced from the proposed quantization scheme. The genera...
THE DIVERGENCE OF LAGRANGE INTERPOLATION IN EQUIDISTANT NODES
Institute of Scientific and Technical Information of China (English)
Lu Zhikang; Xia Mao
2003-01-01
It is a classical result of Bernstein that the sequence of Lagrange interpolation polynomials to | x | at equally spaced nodes in [- 1,1] diverges everywhere, except at zero and the end-points. In this paper we show that the sequence of Lagrange interpolation polynomials corresponding to the functions which possess better smoothness on equidistant nodes in [-1,1] still diverges every where in the interval except at zero and the end-points.
Larsen, Kristine
2014-01-01
One of the current trends in pedagogy at all levels(K-college) is the so-called ‘flipped classroom’, in which students prepare for a class meeting through self-study of the material. It is based on a rejection of the classic model of the faculty member as the ‘sage on the stage’ instead, responsibility for learning shifts to the individual student. The faculty member takes on the role of learning facilitator or mentor, and focuses the students’ learning by crafting and administering timely formative assessments (in multiple formats and applied multiple times) that aid both students and the faculty member in tracking the students’ mastery of the learning outcomes. In a flipped, freshman-only, section of SCI 111 Elementary Earth-Physical Sciences (a required introductory science course for pre-service elementary school teachers) the students learned through a combination of individual and group hands-on in-class activities, technology (including PowerPoint presentations and short videos viewed prior to attending class), in-class worksheets, and in-class discussions. Students self-differentiated in how they interacted with the available teaching materials, deciding which activities to spend the most time on based on their individual needs (based on an online quiz taken the night before the class period, and their personal self-confidence with the material). Available in-class activities and worksheets were developed by the faculty member based on student scores on the online quiz as well as personal messages submitted through the course management system the night before the class meeting. While this placed a significant burden on the faculty member in terms of course preparation, it allowed for just-in-time teaching to take place. This poster describes the results of student mastery of content centered on the sun-earth-moon system (specifically seasons, moon phases, and eclipses) as compared to traditional classroom sections.
Visualizing Sun-Earth-Moon Relationships through Hands-On Modeling
Morton, Abby
2013-04-01
"Tell me and I forget, teach me and I may remember, involve me and I learn." -Benjamin Franklin Understanding the spatial relationships between the sun, Earth and Moon is fundamental to any basic earth science education. Since both of the following concepts involve shadows on three-dimensional spheres, seeing them on paper is not often conducive to understanding. In the first activity, students use five Styrofoam balls painted to look like the sun and the four positions of the earth in each season. Students position the Earth-balls in their correct order around the sun and translate what they are seeing onto paper. In the second activity, students hold up a Styrofoam ball painted half white, half black. A picture of the sun is projected at the front of the classroom. They move the ball around their heads as if they were the Earth, keeping the lit side of the moon always facing the sun. They then draw the phases of the moon as they see them.
Institute of Scientific and Technical Information of China (English)
龚建新
2014-01-01
在Excel中可以用“宏”工具自定义函数解决水文资料中水位流量关系曲线插值问题。文章定义了一个一元三点拉格朗日插值公式的函数过程，简单实用，可以将它直接应用到河流断面水位流量观测数据上，一经调入，使用方法和效率同Excel中内置函数基本上没有区别。%Macro tool in Excellcan be applied to self-define function for handling the interpolation of the rating curve in the hydrological data.In this paper, a unary three point function process of Lagrange interpolation formula is successfully defined.It, simple and prac-tical, can be directly applied to the observed stage-discharge data of the river cross section.Once it is introduced, its usage and effi-ciency are similar to the built-in functions in Excel.
Perspective on the Lagrange-Jacobi mesh
Rampho, Gaotsiwe J.
2016-07-01
This paper presents a unified treatment of the kinetic energy matrix elements related to a number of Lagrange functions associated with the Lagrange-Jacobi mesh. The matrix elements can be readily modified for application to problems requiring eigenfunction expansion with Lagrange-Legendre, Lagrange-Chebyshev, Lagrange-Gegenbauer, as well as the Lagrange-Jacobi functions. The applicability of and the accuracy attainable with the matrix elements is demonstrated with the solution to the Schrödinger equation for confining trigonometric Pöschl-Teller potentials. The results obtained are within machine accuracy when appropriate choices of the basis functions are used.
ITM-Related Data and Model Services at the Sun Earth Connection Active Archive (SECAA)
McGuire, R.; Bilitza, D.; Kovalick, T.; Papitashvili, N.; Candey, R.; Han, D.
2004-12-01
NASA's Sun Earth Connection Active Archive (SECAA) provides access to a large volume of data and models that are of relevance to Ionospheric, Thermospheric and Mesospheric (ITM) physics. SECAA has developed a number of web systems to facilitate user access to this important data source and is making these services available through Web Services (or Application Programming Interfaces, API) directly to applications such as VxOs. The Coordinated Data Analysis web (CDAWeb) lets user plot data using a wide range of parameter display options including mapped images and movies. Capabilities also include parameter listings and data downloads in CDF and ASCII format. CDAWeb provides access to data from most of NASA's currently operating space science satellites and many of the earlier missions; of special ITM interest are DE-2, ISIS, FAST, Equator-S, and TIMED. SECAA maintains and supports the Common Data Format (CDF) including software to read and write CDF files. Most recently translator services have been added for CDF translations to/from netCDF, FITS, CDFXML, and ASCII. The SSCWeb interface enables users to plot orbits for the majority of space physics satellites (including TIMED, UARS, DMSP, NOAA, LANL etc.) and to query for magnetic field line conjunctions between multiple spacecraft and ground stations and for magnetic region occupancy. Recently an Interactive 3-D orbit viewer was added to SSCWeb. Access to legacy data from older ITM satellite missions is provided through the ATMOWeb system with the ability to generate plots and download data subsets in ASCII format. Recently added capabilities include the option to filter the data using an upper and lower boundary for any one of the data set parameters. We will also present the newest version of the web portal to SECAA's models catalog, ftp archive, and web interfaces. The web interfaces (Fortran, C, Java) let users compute, list, plot, and download model parameters for selected models (IRI, IGRF, MSIS/CIRA, AE
High-Performance Data Analysis Tools for Sun-Earth Connection Missions
Messmer, Peter
2011-01-01
The data analysis tool of choice for many Sun-Earth Connection missions is the Interactive Data Language (IDL) by ITT VIS. The increasing amount of data produced by these missions and the increasing complexity of image processing algorithms requires access to higher computing power. Parallel computing is a cost-effective way to increase the speed of computation, but algorithms oftentimes have to be modified to take advantage of parallel systems. Enhancing IDL to work on clusters gives scientists access to increased performance in a familiar programming environment. The goal of this project was to enable IDL applications to benefit from both computing clusters as well as graphics processing units (GPUs) for accelerating data analysis tasks. The tool suite developed in this project enables scientists now to solve demanding data analysis problems in IDL that previously required specialized software, and it allows them to be solved orders of magnitude faster than on conventional PCs. The tool suite consists of three components: (1) TaskDL, a software tool that simplifies the creation and management of task farms, collections of tasks that can be processed independently and require only small amounts of data communication; (2) mpiDL, a tool that allows IDL developers to use the Message Passing Interface (MPI) inside IDL for problems that require large amounts of data to be exchanged among multiple processors; and (3) GPULib, a tool that simplifies the use of GPUs as mathematical coprocessors from within IDL. mpiDL is unique in its support for the full MPI standard and its support of a broad range of MPI implementations. GPULib is unique in enabling users to take advantage of an inexpensive piece of hardware, possibly already installed in their computer, and achieve orders of magnitude faster execution time for numerically complex algorithms. TaskDL enables the simple setup and management of task farms on compute clusters. The products developed in this project have the
Lagrange Spaces with (γ,β-Metric
Directory of Open Access Journals (Sweden)
Suresh K. Shukla
2013-01-01
Full Text Available We study Lagrange spaces with (γ,β-metric, where γ is a cubic metric and β is a 1-form. We obtain fundamental metric tensor, its inverse, Euler-Lagrange equations, semispray coefficients, and canonical nonlinear connection for a Lagrange space endowed with a (γ,β-metric. Several other properties of such space are also discussed.
Mikic, Zoran; Grebowsky, Joseph M. (Technical Monitor)
2001-01-01
This report covers technical progress during the fourth quarter of the second year of NASA Sun-Earth Connections Theory Program (SECTP) contract 'The Structure and Dynamics of the Solar Corona and Inner Heliosphere,' NAS5-99188, between NASA and Science Applications International Corporation, and covers the period May 16,2001 to August 15, 2001. Under this contract SAIC and the University of California, Irvine (UCI) have conducted research into theoretical modeling of active regions, the solar corona, and the inner heliosphere, using the MHD model.
THE DIVERGENCE OF LAGRANGE INTERPOLATION FOR |x|α
Institute of Scientific and Technical Information of China (English)
Zhikang Lu; Xifang Ge
2005-01-01
This paper shows that the sequence of Lagrange interpolation polynomials corresponding to the function f(x) = |x|α(1 ＜α＜ 2) on [-1, 1] can diverge everywhere in the interval except at zero and the end-points.
Near-Earth asteroid flyby trajectories from the Sun-Earth L2 for Chang'e-2's extended flight
Gao, Yang
2013-02-01
Driven by curiosity about possible flight options for the Chang'e-2 spacecraft after it remains at the Sun-Earth L2 point, effective approaches were developed for designing preliminary fuel-optimal near-Earth asteroid flyby trajectories. The approaches include the use of modified unstable manifolds, grid search of the manifolds' parameters, and a two-impulse maneuver for orbital phase matching and z-axis bias change, and are demonstrated to be effective in asteroid target screening and trajectory optimization. Asteroid flybys are expected to be within a distance of 2 × 107 km from the Earth owing to the constrained Earth-spacecraft communication range. In this case, the spacecraft's orbital motion is significantly affected by the gravities of both the Sun and the Earth, and therefore, the concept of the "heliocentric oscillating-Kepler orbit" is proposed, because the classical orbital elements of the flyby trajectories referenced in the heliocentric inertial frame oscillate significantly with respect to time. The analysis and results presented in this study show that, among the asteroids whose orbits are the most accurately predicted, "Toutatis", "2005 NZ6", or "2010 CL19" might be encountered by Chang'e-2 in late 2012 or 2013 with total impulses less than 100m/s.
Gopalswamy, N.; Davila, J. M.; St Cyr, O. C.; Sittler, E. C.; Auchere, F.; Duvall, Jr. T. L.; Hoeksema, J. T.; Maksimovic, M.; MacDowall, R. J.; Szabo, A.; Collier, M. R.
2011-01-01
This paper describes the scientific rationale for an L5 mission and a partial list of key scientific instruments the mission should carry. The L5 vantage point provides an unprecedented view of the solar disturbances and their solar sources that can greatly advance the science behind space weather. A coronagraph and a heliospheric imager at L5 will be able to view CMEs broadsided, so space speed of the Earth-directed CMEs can be measured accurately and their radial structure discerned. In addition, an inner coronal imager and a magnetograph from L5 can give advance information on active regions and coronal holes that will soon rotate on to the solar disk. Radio remote sensing at low frequencies can provide information on shock-driving CMEs, the most dangerous of all CMEs. Coordinated helioseismic measurements from the Sun Earth line and L5 provide information on the physical conditions at the base of the convection zone, where solar magnetism originates. Finally, in situ measurements at L5 can provide information on the large-scale solar wind structures (corotating interaction regions (CIRs)) heading towards Earth that potentially result in adverse space weather.
Near-Earth asteroid flyby trajectories from the Sun-Earth L2 for Chang'e-2's extended flight
Institute of Scientific and Technical Information of China (English)
Yang Gao
2013-01-01
Driven by curiosity about possible flight options for the Chang'e-2 spacecraft after it remains at the Sun-Earth L2 point,effective approaches were developed for designing preliminary fuel-optimal near-Earth asteroid flyby trajectories.The approaches include the use of modified unstable manifolds,grid search of the manifolds' parameters,and a two-impulse maneuver for orbital phase matching and z-axis bias change,and are demonstrated to be effective in asteroid target screening and trajectory optimization.Asteroid flybys are expected to be within a distance of 2 × 107 km from the Earth owing to the constrained Earth-spacecraft communication range.In this case,the spacecraft's orbital motion is significantly affected by the gravities of both the Sun and the Earth,and therefore,the concept of the“heliocentric oscillating-Kepler orbit” is proposed,because the classical orbital elements of the flyby trajectories referenced in the heliocentric inertial frame oscillate significantly with respect to time.The analysis and results presented in this study show that,among the asteroids whose orbits are the most accurately predicted,“Toutatis”,“2005 NZ6”,or “2010CL19” might be encountered by Chang'e-2 in late 2012 or 2013 with total impulses less than 100 m/s.
日地系统多物理耦合机制的设计与实现%Design and Implementation of Multi-physics Coupling Mechanism of Sun-Earth System
Institute of Scientific and Technical Information of China (English)
李姗姗; 王群
2011-01-01
以日地系统活动规律研究为背景,通过对SCIRUN提出的PRMI进行4点改进,提出一种高效的日地系统多物理耦合交互机制PRMI,能够在物理模型组件进行并行远程方法调用实现耦合交互的同时,自动实现网格重映射和数据并行分布重映射.实验结果证明PRMI具有较好的性能.%In the background of study on activity regularity of the sun-earth system, this paper proposes an efficient multi-physics coupling interaction mechanism PRMI++ for sun-earth system based on SCIRUN group's PRMI with four-point improvement. It can automatically accomplish gird re-mapping and parallel distribution re-mapping of data when the physical model components on the parallel remote method invocation to achieve coupling interactions. Experimental results prove PRMI++ has better performance.
Energy Technology Data Exchange (ETDEWEB)
Suescun D, D.; Figueroa J, J. H. [Pontificia Universidad Javeriana Cali, Departamento de Ciencias Naturales y Matematicas, Calle 18 No. 118-250, Cali, Valle del Cauca (Colombia); Rodriguez R, K. C.; Villada P, J. P., E-mail: dsuescun@javerianacali.edu.co [Universidad del Valle, Departamento de Fisica, Calle 13 No. 100-00, Cali, Valle del Cauca (Colombia)
2015-09-15
A new method to solve numerically the inverse equation of punctual kinetics without using Lagrange interpolating polynomial is formulated; this method uses a polynomial approximation with N points based on a process of recurrence for simulating different forms of nuclear power. The results show a reliable accuracy. Furthermore, the method proposed here is suitable for real-time measurements of reactivity, with step sizes of calculations greater that Δt = 0.3 s; due to its precision can be used to implement a digital meter of reactivity in real time. (Author)
Analysis of Lagrange's original derivation of the Euler-Lagrange Differential Equation
Laughlin, Ryan; Close, Hunter
2012-03-01
The Euler-Lagrange differential equation provides the Lagrangian equations of motion, and thus allows the exact trajectory of an object in a potential to be found. We analyze the original derivation of the Euler-Lagrange differential equation via a translation of the third edition of Lagrange's Mecanique Analytique (1811). We compare and contrast this derivation with the derivation commonly done in a junior-level classical mechanics course. Lagrange uses several founding concepts to produce a generalized equation of motion for all dynamics. These concepts are, in the order addressed by Lagrange, the Principle of Virtual Velocities, the Conservation des Forces Vives, and the Principle of Least Action. Lagrange then employs what he calls the Method of Variations to the general equation of motion for dynamics to ultimately resolve something similar to the Euler-Lagrange Differential equation we use today. We also compare modern notation with Lagrange's notation.
Confined helium on Lagrange meshes
Baye, Daniel
2015-01-01
The Lagrange-mesh method has the simplicity of a calculation on a mesh and can have the accuracy of a variational method. It is applied to the study of a confined helium atom. Two types of confinement are considered. Soft confinements by potentials are studied in perimetric coordinates. Hard confinement in impenetrable spherical cavities is studied in a system of rescaled perimetric coordinates varying in [0,1] intervals. Energies and mean values of the distances between electrons and between an electron and the helium nucleus are calculated. A high accuracy of 11 to 15 significant figures is obtained with small computing times. Pressures acting on the confined atom are also computed. For sphere radii smaller than 1, their relative accuracies are better than $10^{-10}$. For larger radii up to 10, they progressively decrease to $10^{-3}$, still improving the best literature results.
Gould, Alan; Willard, Carolyn; Pompea, Stephen
This guide is aimed at helping students arrive at a clear understanding of seasons as they investigate the connections between the sun and the earth. Activities include: (1) "Name the Season"; (2) "Sun-Earth Survey"; (3) "Trip to the Sun"; (4) "What Shape is Earth's Orbit?"; (5) "Temperatures around the…
Integrals of Lagrange functions and sum rules
Energy Technology Data Exchange (ETDEWEB)
Baye, Daniel, E-mail: dbaye@ulb.ac.be [Physique Quantique, CP 165/82, Universite Libre de Bruxelles, B 1050 Bruxelles (Belgium); Physique Nucleaire Theorique et Physique Mathematique, CP 229, Universite Libre de Bruxelles, B 1050 Bruxelles (Belgium)
2011-09-30
Exact values are derived for some matrix elements of Lagrange functions, i.e. orthonormal cardinal functions, constructed from orthogonal polynomials. They are obtained with exact Gauss quadratures supplemented by corrections. In the particular case of Lagrange-Laguerre and shifted Lagrange-Jacobi functions, sum rules provide exact values for matrix elements of 1/x and 1/x{sup 2} as well as for the kinetic energy. From these expressions, new sum rules involving Laguerre and shifted Jacobi zeros and weights are derived. (paper)
Leiva, A. M.; Briozzo, C. B.
In a previous work we successfully implemented a control algorithm to stabilize unstable periodic orbits in the Sun-Earth-Moon Quasi-Bicircular Problem (QBCP). Applying the same techniques, in this work we stabilize an unstable trajectory performing fast transfers between the Earth and the Moon in a dynamical system similar to the QBCP but incorporating the gravitational perturbation of the planets Mercury, Venus, Mars, Jupiter, Saturn, Uranus, and Neptune, assumed to move on circular coplanar heliocentric orbits. In the control stage we used as a reference trajectory an unstable periodic orbit from the unperturbed QBCP. We performed 400 numerical experiments integrating the trajectories over time spans of ~40 years, taking for each one random values for the initial positions of the planets. In all cases the control impulses applied were larger than 20 cm/s, consistently with realistic implementations. The minimal and maximal yearly mean consumptions were ~10 m/s and ~71 m/s, respectively. FULL TEXT IN SPANISH
Optimal design of near-Earth asteroid sample-return trajectories in the Sun-Earth-Moon system
He, Shengmao; Zhu, Zhengfan; Peng, Chao; Ma, Jian; Zhu, Xiaolong; Gao, Yang
2016-08-01
In the 6th edition of the Chinese Space Trajectory Design Competition held in 2014, a near-Earth asteroid sample-return trajectory design problem was released, in which the motion of the spacecraft is modeled in multi-body dynamics, considering the gravitational forces of the Sun, Earth, and Moon. It is proposed that an electric-propulsion spacecraft initially parking in a circular 200-km-altitude low Earth orbit is expected to rendezvous with an asteroid and carry as much sample as possible back to the Earth in a 10-year time frame. The team from the Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences has reported a solution with an asteroid sample mass of 328 tons, which is ranked first in the competition. In this article, we will present our design and optimization methods, primarily including overall analysis, target selection, escape from and capture by the Earth-Moon system, and optimization of impulsive and low-thrust trajectories that are modeled in multi-body dynamics. The orbital resonance concept and lunar gravity assists are considered key techniques employed for trajectory design. The reported solution, preliminarily revealing the feasibility of returning a hundreds-of-tons asteroid or asteroid sample, envisions future space missions relating to near-Earth asteroid exploration.
Optimal design of near-Earth asteroid sample-return trajectories in the Sun-Earth-Moon system
Institute of Scientific and Technical Information of China (English)
Shengmao He; Zhengfan Zhu; Chao Peng; Jian Ma; Xiaolong Zhu; Yang Gao
2016-01-01
In the 6th edition of the Chinese Space Trajec-tory Design Competition held in 2014, a near-Earth asteroid sample-return trajectory design problem was released, in which the motion of the spacecraft is modeled in multi-body dynamics, considering the gravitational forces of the Sun, Earth, and Moon. It is proposed that an electric-propulsion spacecraft initially parking in a circular 200-km-altitude low Earth orbit is expected to rendezvous with an asteroid and carry as much sample as possible back to the Earth in a 10-year time frame. The team from the Technology and Engi-neering Center for Space Utilization, Chinese Academy of Sciences has reported a solution with an asteroid sample mass of 328 tons, which is ranked first in the competition. In this article, we will present our design and optimization methods, primarily including overall analysis, target selec-tion, escape from and capture by the Earth–Moon system, and optimization of impulsive and low-thrust trajectories that are modeled in multi-body dynamics. The orbital res-onance concept and lunar gravity assists are considered key techniques employed for trajectory design. The reported solution, preliminarily revealing the feasibility of returning a hundreds-of-tons asteroid or asteroid sample, envisions future space missions relating to near-Earth asteroid explo-ration.
The Spanish Space Weather Service SeNMEs. A Case Study on the Sun-Earth Chain
Palacios, J.; Cid, C.; Guerrero, A.; Saiz, E.; Cerrato, Y.; Rodríguez-Bouza, M.; Rodríguez-Bilbao, I.; Herraiz, M.; Rodríguez-Caderot, G.
2016-04-01
The Spanish Space Weather Service SeNMEs, www.senmes.es, is a portal created by the SRG-SW of the Universidad de Alcalá, Spain, to meet societal needs of near real-time space weather services. This webpage-portal is divided in different sections to fulfill users needs about space weather effects: radio blackouts, solar energetic particle events, geomagnetic storms and presence of geomagnetically induced currents. In less than one year of activity, this service has released a daily report concerning the solar current status and interplanetary medium, informing about the chances of a solar perturbation to hit the Earth's environment. There are also two different forecasting tools for geomagnetic storms, and a daily ionospheric map. These tools allow us to nowcast a variety of solar eruptive events and forecast geomagnetic storms and their recovery, including a new local geomagnetic index, LDiñ, along with some specific new scaling. In this paper we also include a case study analysed by SeNMEs. Using different high resolution and cadence data from space-borne solar telescopes SDO, SOHO and GOES, along with ionospheric and geomagnetic data, we describe the Sun-Earth feature chain for the event.
Institute of Scientific and Technical Information of China (English)
何胜茂; 彭超; 高扬
2016-01-01
There are several flight options for the Chang’E-2 spacecraft after its remaining at the Sun-Earth L2 point, for example, impacting the Moon or recapture into lunar orbit, returning to Earth orbit or atmospheric reentry, heading for halo orbits of the Earth-Moon L1 or L2 or the Sun-Earth L1 point, as well as flying by near-Earth asteroids in interplanetary space (Finally, Chang’E-2 successfully implemented a close flyby of Toutatis, a potentially hazardous near-Earth asteroid, on Dec.13, 2012). The analyses of these flight options require designing preliminary transfer trajectories with total velocity impulses no more than 100 m/s in four-body dynamics, in which the motion of the spacecraft is influenced by the gravities of the Sun, Earth, and Moon. In this study, we shall present low-energy Toutatis flyby trajectories from a Sun-Earth L2 quasi-periodic orbit, specifically, via a single lunar gravity assist that is intentionally utilized for exploring potential benefits, compared with the direct transfer manner that is adopted in the practical mission. Compared with the direct transfer trajectories to the asteroid, lunar gravity assist is demonstrated to be capable of saving propellant for the Toutatis flyby mission, and the equivalent velocity impulses are 58.46 m/s.%对于停留在日地系统L2的“嫦娥2号”探测器，其后续飞行方案有多个选项，例如主动撞月或重返月球轨道、返回地球轨道或再入大气、飞往地月系统L1/L2或日地系统L1、进入深空飞越近地小行星(最终，“嫦娥2号”于2012年12月13日成功地实现了对Toutatis小行星的近距离飞越)。探讨上述的飞行方案需要对飞行轨道进行初步设计，总的速度脉冲限制在100 m/s以内并且需要考虑探测器同时受到太阳、地球、月球的引力作用。本研究设计了探测器从日地系统L2出发借力月球实现Toutatis小行星飞越的飞行方案，与直接飞越方案相比
Lagrange relaxation and Dantzig-Wolfe decomposition
DEFF Research Database (Denmark)
Vidal, Rene Victor Valqui
1989-01-01
The paper concerns a large-scale linear programming problem having a block-diagonal structure with coupling constraints. It is shown that there are deep connections between the Lagrange relaxation techniques and the Dantzig-Wolfe decomposition methods......The paper concerns a large-scale linear programming problem having a block-diagonal structure with coupling constraints. It is shown that there are deep connections between the Lagrange relaxation techniques and the Dantzig-Wolfe decomposition methods...
Lagrange relaxation and Dantzig-Wolfe decomposition
DEFF Research Database (Denmark)
Vidal, Rene Victor Valqui
1989-01-01
The paper concerns a large-scale linear programming problem having a block-diagonal structure with coupling constraints. It is shown that there are deep connections between the Lagrange relaxation techniques and the Dantzig-Wolfe decomposition methods......The paper concerns a large-scale linear programming problem having a block-diagonal structure with coupling constraints. It is shown that there are deep connections between the Lagrange relaxation techniques and the Dantzig-Wolfe decomposition methods...
Lennartsson, O. W.
1997-01-01
The objective of this project has been to complete the archiving of energetic (10 eV/epsilon - 18 keV/epsilon) ion composition data from the Lockheed Plasma Composition Experiment on the International Sun-Earth Explorer One (ISEE 1) satellite, using a particular data format that had previously been approved by NASA and the NSSDC. That same format, a combination of ion velocity moments and differential flux spectra, had been used in 1991 to archive, at the NSSDC, the first 28 months (the "Prime" period of ISEE investigations) of data from the Lockheed instrument under NASA Contract NAS5-33047. With the completion of this project, the almost 4 1/2-year time span of these unique data is now covered by a very compact set, approximately 1 gigabyte in total, of electronic files with physical quantities, all in ASCII. The files are organized by data type and time of data acquisition, in Universal Time, and named according to year and day of year. Each calendar day has five separate files (five types of data), the lengths of which vary from day to day, depending on the instrument mode of operation. The data format and file structure are described in detail in appendices 1 and 2. The physical medium consists of high-density (6250 cpi) 9-track magnetic tapes, complemented by a set of hardcopy line plots of certain plasma parameters. In this case there are five tapes, to be added to the six previous ones from 1991, and 25 booklets of plots, one per month, to be added to the previous 28. The tapes, including an extra standard-density (1600 cpi) tape with electronic versions of the Data User's Guide and self-guiding VAX/VMS command files, and the hardcopy plots are being boxed for shipment to the NSSDC.
Lennartsson, O. W.
1997-08-01
The objective of this project has been to complete the archiving of energetic (10 eV/epsilon - 18 keV/epsilon) ion composition data from the Lockheed Plasma Composition Experiment on the International Sun-Earth Explorer One (ISEE 1) satellite, using a particular data format that had previously been approved by NASA and the NSSDC. That same format, a combination of ion velocity moments and differential flux spectra, had been used in 1991 to archive, at the NSSDC, the first 28 months (the "Prime" period of ISEE investigations) of data from the Lockheed instrument under NASA Contract NAS5-33047. With the completion of this project, the almost 4 1/2-year time span of these unique data is now covered by a very compact set, approximately 1 gigabyte in total, of electronic files with physical quantities, all in ASCII. The files are organized by data type and time of data acquisition, in Universal Time, and named according to year and day of year. Each calendar day has five separate files (five types of data), the lengths of which vary from day to day, depending on the instrument mode of operation. The data format and file structure are described in detail in appendices 1 and 2. The physical medium consists of high-density (6250 cpi) 9-track magnetic tapes, complemented by a set of hardcopy line plots of certain plasma parameters. In this case there are five tapes, to be added to the six previous ones from 1991, and 25 booklets of plots, one per month, to be added to the previous 28. The tapes, including an extra standard-density (1600 cpi) tape with electronic versions of the Data User's Guide and self-guiding VAX/VMS command files, and the hardcopy plots are being boxed for shipment to the NSSDC.
THE DIVERGENCE OF LAGRANGE INTERPOLATION FOR |x|α (2＜α＜4) AT EQUIDISTANT NODES
Institute of Scientific and Technical Information of China (English)
Hui Su; Shusheng Xu
2006-01-01
It is a classical result of Bernstein that the sequence of Lagrange interpolation polynomials to |x| at equally spaced nodes in [-1, 1] diverges everywhere, except at zero and the end-points. In the present paper, we prove that the sequence of Lagrange interpolation polynomials corresponding to |x|α(2 ＜α＜ 4) on equidistant nodes in [-1,1] diverges everywhere, except at zero and the end-points.
BIVARIATE LAGRANGE-TYPE VECTOR VALUED RATIONAL INTERPOLANTS
Institute of Scientific and Technical Information of China (English)
Chuan-qing Gu; Gong-qing Zhu
2002-01-01
An axiomatic definition to bivariate vector valued rational interpolation on distinct plane interpolation points is at first presented in this paper. A two-variable vector valued rational interpolation formula is explicitly constructed in the following form: the determinantal formulas for denominator scalar polynomials and for numerator vector polynomials,which possess Lagrange-type basic function expressions. A practical criterion of existence and uniqueness for interpolation is obtained. In contrast to the underlying method, the method of bivariate Thiele-type vector valued rational interpolation is reviewed.
On Subspaces of an Almost -Lagrange Space
Directory of Open Access Journals (Sweden)
P. N. Pandey
2012-01-01
Full Text Available We discuss the subspaces of an almost -Lagrange space (APL space in short. We obtain the induced nonlinear connection, coefficients of coupling, coefficients of induced tangent and induced normal connections, the Gauss-Weingarten formulae, and the Gauss-Codazzi equations for a subspace of an APL-space. Some consequences of the Gauss-Weingarten formulae have also been discussed.
A new Remesh-Lagrange technique for advecting temperature that minimizes numerical diffusion
Hasenclever, J.; Phipps Morgan, J.; Shi, C.
2007-12-01
The proper treatment of heat-advection is a generally underappreciated problem within CFD, yet particularly critical for calculating physically sound erosion in plume-lithosphere interactions and temperature sensitive melting processes. Typically, Eulerian (fixed-mesh) codes have been preferred to solve for fluid flow and they are almost essential for finite-difference-based algorithms. Unfortunately, the Eulerian approach introduces numerical artifacts into the solution of the advection-diffusion heat transport problem that can only be suppressed by adding 'too-diffusive' artificial diffusion to the equations, as for example in the Smolarkiewicz formulation for heat advection. We have developed a 'Remesh-Lagrange' method using a partly deforming finite element mesh and find it to be significantly more accurate than our previous methods. In several test scenarios we show the large improvement in accuracy that can be obtained by using a Lagrangian approach for 10-30 time steps (depending upon the distortion of the finite elements in the deformed Lagrangian mesh) and then regridding to the initial mesh. When an element becomes too distorted the nodes connected to it become fixed and we switch from Lagrange to a Semi-Lagrange formulation for these nodes. Instead of the standard 'linear backward' Semi-Lagrange we are also experimenting with a more accurate interpolation scheme for an unstructured mesh that additionally includes the nodal derivatives of the temperature field when calculating the value at the Semi-Lagrange traceback point. The same bicubic interpolation method for an unstructured grid is used to remesh the 'too-distorted' Lagrange grid back to the initial undistorted mesh. We compare the Remesh-Lagrange technique against the following Eulerian methods in a series of 2-D numerical experiments advecting stripes and Gaussian peaks in steady circulating flow: linear back-interpolation Semi-Lagrange method; bicubic back-interpolation Semi-Lagrange method
Euler-Lagrange Forms and Cohomology Groups on Jet Bundles
Institute of Scientific and Technical Information of China (English)
CHEN Jing-Bo
2005-01-01
@@ Using the language of jet bundles, we generalize the definitions of Euler-Lagrange one-form and the associated cohomology which were introduced by Guo et al. [Commun. Theor. Phys. 37(2002)1]. Continuous and discreteLagrange mechanics and field theory are presented. Higher order Euler-Lagrange cohomology groups are also introduced.
Lagrange interpolation for the radiation shielding calculation
Isozumi, Y; Miyatake, H; Kato, T; Tosaki, M
2002-01-01
Basing on some formulas of Lagrange interpolation derived in this paper, a computer program for table calculations has been prepared. Main features of the program are as follows; 1) maximum degree of polynomial in Lagrange interpolation is 10, 2) tables with both one variable and two variables can be applied, 3) logarithmic transformations of function and/or variable values can be included and 4) tables with discontinuities and cusps can be applied. The program has been carefully tested by using the data tables in the manual of shielding calculation for radiation facilities. For all available tables in the manual, calculations with the program have been reasonably performed under conditions of 1) logarithmic transformation of both function and variable values and 2) degree 4 or 5 of the polynomial.
Lagrange, central norms, and quadratic Diophantine equations
Directory of Open Access Journals (Sweden)
R. A. Mollin
2005-01-01
Full Text Available We consider the Diophantine equation of the form x2−Dy2=c, where c=±1,±2, and provide a generalization of results of Lagrange with elementary proofs using only basic properties of simple continued fractions. As a consequence, we achieve a completely general, simple, and elegant criterion for the central norm to be 2 in the simple continued fraction expansion of D.
Optimization of Wireless Optical Communication System Based on Augmented Lagrange Algorithm
Energy Technology Data Exchange (ETDEWEB)
He Suxiang; Meng Hongchao; Wang Hui [School of Science, Wuhan University of Technology, Wuhan 430070 (China); Zhao Yanli, E-mail: yanlizhao@mail.hust.edu.cn [Wuhan National Laboratory for Optoelectronics, School of Optoelectronics Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074 (China)
2011-02-01
The optimal model for wireless optical communication system with Gaussian pointing loss factor is studied, in which the value of bit error probability (BEP) is prespecified and the optimal system parameters is to be found. For the superiority of augmented Lagrange method, the model considered is solved by using a classical quadratic augmented Lagrange algorithm. The detailed numerical results are reported. Accordingly, the optimal system parameters such as transmitter power, transmitter wavelength, transmitter telescope gain and receiver telescope gain can be established, which provide a scheme for efficient operation of the wireless optical communication system.
Non-Noether symmetries and conserved quantities of the Lagrange mechano-electrical systems
Institute of Scientific and Technical Information of China (English)
Fu Jing-Li; Chen Li-Qun; Liu Rong-Wan
2004-01-01
This paper focuses on studying non-Noether symmetries and conserved quantities of Lagrange mechano-electrical dynamical systems. Based on the relationships between the motion and Lagrangian, we present conservation laws on non-Noether symmetries for Lagrange mechano-electrical dynamical systems. A criterion is obtained on which non-Noether symmetry leads to Noether symmetry of the systems. The work also gives connections between the nonNoether symmetries and Lie point symmetries, and further obtains Lie invariants to form a complete set of non-Noether conserved quantity. Finally, an example is discussed to illustrate these results.
Principal symbol of Euler-Lagrange operators
Fatibene, L.; Garruto, S.
2016-07-01
We shall introduce the principal symbol for quite a general class of (quasi linear) Euler-Lagrange operators and use them to characterise well-posed initial value problems in gauge covariant field theories. We shall clarify how constraints can arise in covariant Lagrangian theories by extending the standard treatment in GR and without resorting to Hamiltonian formalism. Finally as an example of application, we sketch a quantisation procedure based on what is done in LQG by framing it in a more general context which applies to general gauge covariant field theories.
About Nodal Systems for Lagrange Interpolation on the Circle
Directory of Open Access Journals (Sweden)
E. Berriochoa
2012-01-01
Full Text Available We study the convergence of the Laurent polynomials of Lagrange interpolation on the unit circle for continuous functions satisfying a condition about their modulus of continuity. The novelty of the result is that now the nodal systems are more general than those constituted by the n roots of complex unimodular numbers and the class of functions is different from the usually studied. Moreover, some consequences for the Lagrange interpolation on [-1,1] and the Lagrange trigonometric interpolation are obtained.
Exact invariants and adiabatic invariants of the singular Lagrange system
Institute of Scientific and Technical Information of China (English)
陈向炜; 李彦敏
2003-01-01
Based on the theory of symmetries and conserved quantities of the singular Lagrange system,the perturbations to the symmetries and adiabatic invariants of the singular Lagrange systems are discussed.Firstly,the concept of higher-order adiabatic invariants of the singular Lagrange system is proposed.Then,the conditions for the existence of the exact invariants and adiabatic invariants are proved,and their forms are given.Finally,an example is presented to illustrate these results.
EXACT AND ADIABATIC INVARIANTS OF FIRST-ORDER LAGRANGE SYSTEMS
Institute of Scientific and Technical Information of China (English)
陈向炜; 尚玫; 梅凤翔
2001-01-01
A system of first-order differential equations is expressed in the form of first-order Lagrange equations. Based on the theory of symmetries and conserved quantities of first-order Lagrange systems, the perturbation to the symmetries and adiabatic invariants of first-order Lagrange systems are discussed. Firstly, the concept of higher-order adiabatic invariants of the first-order Lagrange system is proposed. Then, conditions for the existence of the exact and adiabatic invariants are proved, and their forms are given. Finally, an example is presented to illustrate these results.
New covariant Lagrange formulation for field theories
Ootsuka, T
2012-01-01
A novel approach for Lagrange formulation for field theories is proposed in terms of Kawaguchi geometry (areal metric space). On the extended configuration space M for classical field theory composed of spacetime and field configuration space, one can define a geometrical structure called Kawaguchi areal metric K from the field Lagrangian and (M,K) can be regarded as Kawaguchi manifold. The geometrical action functional is given by K and the dynamics of field is determined by covariant Euler-Lagrange equation derived from the variational principle of the action. The solution to the equation becomes a minimal hypersurface on (M,K) which has the same dimension as spacetime. We propose that this hypersurface is what we should regard as our real spacetime manifold, while the usual way to understand spacetime is to consider it as the parameter spacetime (base manifold) of a fibre bundle. In this way, the dynamics of field and spacetime structure is unified by Kawaguchi geometry. The theory has the property of stro...
A new proof of the Lagrange multiplier rule
J. Brinkhuis (Jan); V. Protassov (Vladimir)
2015-01-01
textabstractWe present an elementary self-contained proof for the Lagrange multiplier rule. It does not refer to any substantial preparations and it is only based on the observation that a certain limit is positive. At the end of this note, the power of the Lagrange multiplier rule is analyzed.
Extended Lagrange interpolation in L1 spaces
Occorsio, Donatella; Russo, Maria Grazia
2016-10-01
Let w (x )=e-xβxα , w ¯(x )=x w (x ) and denote by {pm(w)}m,{pn(w¯)}n the corresponding sequences of orthonormal polynomials. The zeros of the polynomial Q2 m +1=pm +1(w )pm(w ¯) are simple and are sufficiently far among them. Therefore it is possible to construct an interpolation process essentially based on the zeros of Q2m+1, which is called "Extended Lagrange Interpolation". Here we study the convergence of this interpolation process in suitable weighted L1 spaces. This study completes the results given by the authors in previous papers in weighted Lup((0 ,+∞ )) , for 1≤p≤∞. Moreover an application of the proposed interpolation process in order to construct an e cient product quadrature scheme for weakly singular integrals is given.
Srivastava, Vineet K.; Kumar, Jai; Kushvah, Badam Singh
2016-12-01
In this paper, we construct a third-order analytic approximate solution using the Lindstedt-Poincare method in the photogravitational circular restricted three body problem considering the Sun as a radiating source and the Earth as an oblate spheroid for computing halo orbits around the collinear Lagrangian points L1 and L2. Further, the well-known differential correction and continuation schemes are used to compute halo orbits and their families numerically. The effects of solar radiation pressure and oblateness on the orbit are studied around both Lagrangian points. From the study, it is noticed that time period of the halo orbit increases around L1 and L2 accounting oblateness of the Earth and solar radiation pressure of the Sun. It is also found that stability of halo orbits is a weak function of the out-of-plane amplitude and mass reduction factor.
Kohutova, Petra; Bocquet, François-Xavier; Henley, Edmund M.; Owens, Matthew J.
2016-10-01
This study demonstrates two significant ways of improving persistence forecasts of the solar wind, which exploit the relatively unchanging nature of the ambient solar wind to provide 27 day forecasts, when using data from the Lagrangian L1 point. Such forecasts are useful as a prediction tool for the ambient wind, and for benchmarking of solar wind models. We show that solar wind persistence forecasts can be improved by removing transient solar wind features such as coronal mass ejections (CMEs). Using CME indicators to automatically identify CME-contaminated periods in ACE data from 1998 to 2011, and replacing these with solar wind from a previous synodic rotation, persistence forecasts improve (relative to a baseline): skill scores for Bz, a crucial parameter for determining solar wind geoeffectiveness, improve by 7.7 percentage points when using a proton temperature-based indicator with good operational potential. We also show that persistence forecasts can be improved by using measurements away from L1, to reduce the requirement on coronal stability for an entire synodic period, at the cost of reduced lead time. Using STEREO-B data from 2007 to 2013 to create such a reduced lead time persistence forecast, we show that Bz skill scores improve by 17.1 percentage points relative to ACE. Finally, we report on implications for persistence forecasts from any future missions to the L5 Lagrangian point and on the successful operational implementation (in spring 2015) of the normal (ACE-based) and reduced lead time (STEREO-based) persistence forecasts in the Met Office's Space Weather Operations Centre, as well as plans for future improvements.
A Full Study on the Sun-Earth Connection of an Earth-Directed CME Magnetic Flux Rope
Vemareddy, P
2015-01-01
We present an investigation of an eruption event of coronal mass ejection (CME) magnetic flux rope (MFR) from source active region (AR) NOAA 11719 on 11 April 2013 utilizing observations from SDO, STEREO, SOHO, and WIND spacecraft. The source AR consists of pre-existing sigmoidal structure stacked over a filament channel which is regarded as MFR system. EUV observations of low corona suggest a further development of this MFR system by added axial flux through tether-cutting reconnection of loops at the middle of sigmoid under the influence of continuous slow flux motions during past two days. Our study implies that the MFR system in the AR is initiated to upward motion by kink-instability and further driven by torus-instability. The CME morphology, captured in simultaneous three-point coronagraph observations, is fitted with Graduated Cylindrical Shell (GCS) model and discerns an MFR topology with orientation aligning with magnetic neutral line in the source AR. This MFR expands self-similarly and is found to...
Dynamic constitutive equation of GFRP obtained by Lagrange experiment
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The note presents a method of constructing dynamic constitutive equations of material by means of Lagrange experiment and analysis. Tests were carried out by a light gas gun and the stress history profiles were recorded on multiple Lagrange positions. The dynamic constitutive equations were deduced from the regression of a series of data which was obtained by Lagrange analysis based upon recorded multiple stress histories. Here constitutive equations of glass fibre reinforced phenolic resin composite(GFRP) in uniaxil strain state under dynamic loading are given. The proposed equations of the material agree well with experimental results.
CDCC calculations with the Lagrange-mesh technique
Energy Technology Data Exchange (ETDEWEB)
Druet, T., E-mail: tdruet@ulb.ac.b [Physique Quantique, C.P. 165/82, Universite Libre de Bruxelles (ULB), B 1050 Brussels (Belgium); Physique Nucleaire Theorique et Physique Mathematique, C.P. 229, Universite Libre de Bruxelles (ULB), B 1050 Brussels (Belgium); Baye, D., E-mail: dbaye@ulb.ac.b [Physique Quantique, C.P. 165/82, Universite Libre de Bruxelles (ULB), B 1050 Brussels (Belgium); Physique Nucleaire Theorique et Physique Mathematique, C.P. 229, Universite Libre de Bruxelles (ULB), B 1050 Brussels (Belgium); Descouvemont, P., E-mail: pdesc@ulb.ac.b [Physique Nucleaire Theorique et Physique Mathematique, C.P. 229, Universite Libre de Bruxelles (ULB), B 1050 Brussels (Belgium); Sparenberg, J.-M., E-mail: jmspar@ulb.ac.b [Physique Quantique, C.P. 165/82, Universite Libre de Bruxelles (ULB), B 1050 Brussels (Belgium); Physique Nucleaire Theorique et Physique Mathematique, C.P. 229, Universite Libre de Bruxelles (ULB), B 1050 Brussels (Belgium)
2010-11-15
We apply the Lagrange-mesh technique to the Continuum Discretized Coupled Channel (CDCC) theory. The CDCC equations are solved with the R-matrix method, using Lagrange functions as variational basis. The choice of Lagrange functions is shown to be efficient and accurate for elastic scattering as well as for breakup reactions. We describe the general formalism for two-body projectiles, and apply it to the d+{sup 58}Ni collision at E{sub d}=80 MeV. Various numerical and physical aspects are discussed. Benchmark calculations on elastic scattering and breakup are presented.
LAGRANGE STABILITY IN MEAN SQUARE OF STOCHASTIC REACTION DIFFUSION EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This work is devoted to the discussion of stochastic reaction diffusion equations and some new theorems on Lagrange stability in mean square of the solution are established via Lyapunov method which is nothing to be done in the past.
Gauss-Bonnet dark energy by Lagrange multipliers
Capozziello, Salvatore; Odintsov, Sergei D
2013-01-01
A string-inspired effective theory of gravity, containing Gauss-Bonnet invariant interacting with a scalar field, is considered in view of obtaining cosmological dark energy solutions. A Lagrange multiplier is inserted into the action in order to achieve the cosmological reconstruction by selecting suitable forms of couplings and potentials. Several cosmological exact solutions (including dark energy of quintessence, phantom or Little Rip type) are derived in presence and in absence of the Lagrange multiplier showing the difference in the two dynamical approaches. In the models that we consider, the Lagrange multiplier behaves as a sort of dust fluid that realizes the transitions between matter dominated and dark energy epochs. The relation between Lagrange multipliers and Noether symmetries is discussed.
Rayleigh-Lagrange formalism for classical dissipative systems.
Virga, Epifanio G
2015-01-01
It is often believed that the Rayleigh-Lagrange formalism for classical dissipative systems is unable to encompass forces described by nonlinear functions of the velocities. Here we show that this is indeed a misconception.
Lagrange Multipliers and Third Order Scalar-Tensor Field Theories
Horndeski, Gregory W.
2016-01-01
In a space of 4-dimensions, I will examine constrained variational problems in which the Lagrangian, and constraint scalar density, are concomitants of a (pseudo-Riemannian) metric tensor and its first two derivatives. The Lagrange multiplier for these constrained extremal problems will be a scalar field. For suitable choices of the Lagrangian, and constraint, we can obtain Euler-Lagrange equations which are second order in the scalar field and third order in the metric tensor. The effect of ...
The Mortar Element Method with Lagrange Multipliers for Stokes Problem
Institute of Scientific and Technical Information of China (English)
Yaqin Jiang
2007-01-01
In this paper, we propose a mortar element method with Lagrange multiplier for incompressible Stokes problem, i.e., the matching constraints of velocity on mortar edges are expressed in terms of Lagrange multipliers. We also present P1 nonconforming element attached to the subdomains. By proving inf-sup condition, we derive optimal error estimates for velocity and pressure. Moreover, we obtain satisfactory approximation for normal derivatives of the velocity across the interfaces.
A Note on Dynamics About the Coherent Sun–Earth–Moon Collinear Libration Points
Olikara, Zubin P.; Gómez, Gerard; Masdemont, Josep J.
Orbits about the Sun-Earth libration points are perturbed by the Moon, and orbits about the Earth-Moon libration points are perturbed by the Sun. We study both situations in the framework of a single, coherent model, the Hill restricted four-body problem. This model is presented in a Sun-Earth rotating reference frame to complement its earlier Earth-Moon frame formulation. We provide an overview of the planar quasi-periodic orbits that originate from the L 1 and L 2 Lyapunov periodic orbits in Hill's problem and the circular restricted three-body problem. The role of resonances is also discussed.
Directory of Open Access Journals (Sweden)
Héctor Torres-Silva
2008-11-01
Full Text Available This work deals with the problem of the construction of the Lagrange functional for an electromagnetic field. The generalised Maxwell equations for an electromagnetic field in free space are introduced. The main idea relies on the change of Lagrange function under the integral action. Usually, the Lagrange functional which describes the electromagnetic field is built with the quadrate of the electromagnetic field tensor . Such a quadrate term is the reason, from a mathematical point of view, for the linear form of the Maxwell equations in free space. The author does not make this assumption and nonlinear Maxwell equations are obtained. New material parameters of free space are established. The equations obtained are quite similar to the well-known Maxwell equations. The energy tensor of the electromagnetic field from a chiral approach to the Born Infeld Lagrangian is discussed in connection with the cosmological constant.Se aborda el problema de la construcción de la funcional de Lagrange de un campo electromagnético. Se introducen las ecuaciones generalizadas de Maxwell de un campo electromagnético en el espacio libre. La idea principal se basa en el cambio de función de Lagrange en virtud de la acción integral. Por lo general, la funcional de lagrange, que describe el campo electromagnético, se construye con el cuadrado del tensor de campo electromagnético. Ese término cuadrático es la razón, desde un punto de vista matemático, de la forma lineal de las ecuaciones de Maxwell en el espacio libre. Se obtienen las ecuaciones no lineales de Maxwell sin considerar esta suposición. Las ecuaciones de Maxwell obtenidas son bastante similares a las conocidas ecuaciones de Maxwell. Se analiza el tensor de energía del campo electromagnético en un enfoque quiral de la Lagrangiana de Born Infeld en relación con la constante cosmológica.
Euler-Lagrange Elasticity: elasticity without stress or strain
Hardy, Humphrey
2014-03-01
A Euler-Lagrange (E-L) approach to elasticity is proposed that produces differential equations of elasticity without the need to define stress or strain tensors. The positions of the points within the body are the independent parameters instead of strain. Force replaces stress. The advantage of this approach is that the E-L differential equations are the same for both infinitesimal and finite deformations. Material properties are expressed in terms of the energy of deformation. The energy is expressed as a function of the principal invariants of the deformation gradient tensor. This scalar invariant representation of the energy of deformation enters directly into the E-L differential equations so that there is no need to define fourth order tensor material properties. By experimentally measuring the force and displacement of materials the functional form of the energy of deformation can be determined. The E-L differential equations can be input directly into finite element, finite difference, or other numerical models. If desired, stress and stain can be calculated as dependent parameters.
Maximilien Brice
2012-01-01
20 fevrier 2012 - Le Vice-Président du Gouvernement Wallon et Ministre du Développement durable et de la Fonction Publique en charge de l’Energie du Logement et de la Recherche J.-M. Nollet, Royaume de Belgique, visite la salle de contrôle de CMS au Point 5, la caverne expérimentale CMS et le hall de tests des aimants supraconducteurs du LHC. Les chefs de département T. Lagrange et F. Hemmer accompagnent la délégation. L. Walckiers guide la visite SM18.
Lagrange Multipliers and Third Order Scalar-Tensor Field Theories
Horndeski, Gregory W
2016-01-01
In a space of 4-dimensions, I will examine constrained variational problems in which the Lagrangian, and constraint scalar density, are concomitants of a (pseudo-Riemannian) metric tensor and its first two derivatives. The Lagrange multiplier for these constrained extremal problems will be a scalar field. For suitable choices of the Lagrangian, and constraint, we can obtain Euler-Lagrange equations which are second order in the scalar field and third order in the metric tensor. The effect of disformal transformations on the constraint Lagrangians, and their generalizations, is examined. This will yield other second order scalar-tensor Lagrangians which yield field equations which are at most of third order. No attempt is made to construct all possible third order scalar-tensor Euler-Lagrange equations in a 4-space, although nine classes of such field equations are presented. Two of these classes admit subclasses which yield conformally invariant field equations. A few remarks on scalar-tensor-connection theor...
Dark energy from modified gravity with Lagrange multipliers
Energy Technology Data Exchange (ETDEWEB)
Capozziello, Salvatore [Dipartimento di Scienze Fisiche, Universita ' Federico II' di Napoli (Italy)] [INFN Sezione di Napoli, Complesso Universitario di Monte S. Angelo, Ed. N, via Cintia, I-80126 Napoli (Italy); Matsumoto, Jiro [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); Nojiri, Shin' ichi, E-mail: nojiri@phys.nagoya-u.ac.j [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan)] [Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya 464-8602 (Japan); Odintsov, Sergei D. [Institucio Catalana de Recerca i Estudis Avancats (ICREA) and Institut de Ciencies de l' Espai (IEEC-CSIC), Campus UAB, Facultat de Ciencies, Torre C5-Par-2a pl, E-08193 Bellaterra, Barcelona (Spain)
2010-09-27
We study scalar-tensor theory, k-essence and modified gravity with Lagrange multiplier constraint which role is to reduce the number of degrees of freedom. Dark Energy cosmology of different types ({Lambda}CDM, unified inflation with DE, smooth non-phantom/phantom transition epoch) is reconstructed in such models. It is demonstrated that presence of Lagrange multiplier simplifies the reconstruction scenario. It is shown that mathematical equivalence between scalar theory and F(R) gravity is broken due to presence of constraint. The cosmological evolution is defined by the second F{sub 2}(R) function dictated by the constraint. The convenient F(R) gravity sector is relevant for local tests. This opens the possibility to make originally non-realistic theory to be viable by adding the corresponding constraint. A general discussion on the role of Lagrange multipliers to make higher-derivative gravity canonical is developed.
Trivariate Local Lagrange Interpolation and Macro Elements of Arbitrary Smoothness
Matt, Michael Andreas
2012-01-01
Michael A. Matt constructs two trivariate local Lagrange interpolation methods which yield optimal approximation order and Cr macro-elements based on the Alfeld and the Worsey-Farin split of a tetrahedral partition. The first interpolation method is based on cubic C1 splines over type-4 cube partitions, for which numerical tests are given. The second is the first trivariate Lagrange interpolation method using C2 splines. It is based on arbitrary tetrahedral partitions using splines of degree nine. The author constructs trivariate macro-elements based on the Alfeld split, where each tetrahedron
Noether's theory of Lagrange systems in discrete case
Institute of Scientific and Technical Information of China (English)
Lu Hong-Sheng; Zhang-Hong-Bin; Gu Shu-Long
2011-01-01
In this paper, Noether theory of Lagrange systems in discrete case are studied. First, we briefly overview the wellknown Noether theory of Lagrange system in the continuous case. Then, we introduce some definitions and notations,such as the operators of discrete translation to the right and the left and the operators of discrete differentiation to the right and the left, and give the conditions for the invariance of the difference functional on the uniform lattice and the non-uniform one, respectively. We also deduce the discrete analog of the Noether-type identity. Finally, the discrete analog of Noether's theorem is presented. An example was discussed to illustrate these results.
Institute of Scientific and Technical Information of China (English)
GUO Han-Ying; LI Yu-Qi; WU Ke; WANG Shi-Kun
2002-01-01
In this second papcr of a scries of papers, we explore the differcnce discrete versions for the Euler-Lagrange cohomology and apply them to the symplectic or multisymplectic geometry and their preserving propertiesin both the Lagrangian and Hamiltonian formalisms for discrete mechanics and field theory in the framework of multi-parameter differential approach. In terns of the difference discrete Euler-Lagrange cohomological concepts, we show thatthe symplcctic or multisymplectic geometry and their difference discrete structure-preserving properties can always beestablished not only in thc solution spaces of the discrete Euler-Lagrange or canonical equations derived by the differencediscrete variational principle but also in the function space in each case if and only if the relevant closed Euler-Lagrangecohomological conditions are satisfied.
LEBESGUE CONSTANT FOR LAGRANGE INTERPOLATION ON EQUIDISTANT NODES
Institute of Scientific and Technical Information of China (English)
A. Eisinberg; G. Fedele; G. Franzè
2004-01-01
Properties of Lebesgue function for Lagrange interpolation on equidistant nodes are investigated.It is proved that Lebesgue function can be formulated both in terms of a hypergeometric function 2F1 and Jacobi polynomials. Moreover, an integral expression of Lebesgue function is also obtained and the asymptotic behavior of Lebesgue constant is studied.
Visualizing and Understanding the Components of Lagrange and Newton Interpolation
Yang, Yajun; Gordon, Sheldon P.
2016-01-01
This article takes a close look at Lagrange and Newton interpolation by graphically examining the component functions of each of these formulas. Although interpolation methods are often considered simply to be computational procedures, we demonstrate how the components of the polynomial terms in these formulas provide insight into where these…
A Method for Deriving Transverse Masses Using Lagrange Multipliers
Gross, Eilam; Vitells, Ofer
2008-01-01
We use Lagrange multipliers to extend the traditional definition of Transverse Mass used in experimental high energy physics. We demonstrate the method by implementing it to derive a new Transverse Mass that can be used as a discriminator to distinguish between top decays via a charged W or a charged Higgs Boson.
Lagrange mesh, relativistic flux tube, and rotating string
Buisseret, F.; Semay, C.
2004-01-01
The Lagrange mesh method is a very accurate and simple procedure to compute eigenvalues and eigenfunctions of nonrelativistic and semirelativistic Hamiltonians. We show here that it can be used successfully to solve the equations of both the relativistic flux tube model and the rotating string model, in the symmetric case. Verifications of the convergence of the method are given.
Lagrange mesh, relativistic flux tube, and rotating string.
Buisseret, Fabien; Semay, Claude
2005-02-01
The Lagrange mesh method is a very accurate and simple procedure to compute eigenvalues and eigenfunctions of nonrelativistic and semirelativistic Hamiltonians. We show here that it can be used successfully to solve the equations of both the relativistic flux tube model and the rotating string model, in the symmetric case. Verifications of the convergence of the method are given.
ON LAGRANGE INTERPOLATION TO |x|α(1 ＜α＜ 2) WITH EQUALLY SPACED NODES
Institute of Scientific and Technical Information of China (English)
Xia Mao
2004-01-01
S.M. Lozinskii proved the exact convergence rate at the zero of Lagrange interpolation polynomials to |x| based on equidistant nodes in [-1, 1]. In 2000, M. Rever generalized S.M. Lozinskii's result to |x|α(0 ≤α≤ 1). In this paper we will present the exact rate of convergence at the point zero for the interpolants of |x|α(1 ＜α＜ 2)..
Weyl-Euler-Lagrange Equations of Motion on Flat Manifold
Directory of Open Access Journals (Sweden)
Zeki Kasap
2015-01-01
Full Text Available This paper deals with Weyl-Euler-Lagrange equations of motion on flat manifold. It is well known that a Riemannian manifold is said to be flat if its curvature is everywhere zero. Furthermore, a flat manifold is one Euclidean space in terms of distances. Weyl introduced a metric with a conformal transformation for unified theory in 1918. Classical mechanics is one of the major subfields of mechanics. Also, one way of solving problems in classical mechanics occurs with the help of the Euler-Lagrange equations. In this study, partial differential equations have been obtained for movement of objects in space and solutions of these equations have been generated by using the symbolic Algebra software. Additionally, the improvements, obtained in this study, will be presented.
Lagrange multiplier for perishable inventory model considering warehouse capacity planning
Amran, Tiena Gustina; Fatima, Zenny
2017-06-01
This paper presented Lagrange Muktiplier approach for solving perishable raw material inventory planning considering warehouse capacity. A food company faced an issue of managing perishable raw materials and marinades which have limited shelf life. Another constraint to be considered was the capacity of the warehouse. Therefore, an inventory model considering shelf life and raw material warehouse capacity are needed in order to minimize the company's inventory cost. The inventory model implemented in this study was the adapted economic order quantity (EOQ) model which is optimized using Lagrange multiplier. The model and solution approach were applied to solve a case industry in a food manufacturer. The result showed that the total inventory cost decreased 2.42% after applying the proposed approach.
Thierry Lagrange: A transparent, service-oriented approach to finance
2009-01-01
The motto for the new Finance and Purchasing Department Head, Thierry Lagrange, is "strengthening services for users". With a head-count of around sixty, the Finance and Purchasing Department is small compared to the large technical departments. But its work is crucial and supports all the Laboratory’s activities. The FP Department manages the Organization’s financial resources and commitments, checking that resources match expenses, that sufficient cash is available, that contracts are concluded on the best possible terms - in short, that monies are available and properly managed. In these lean times, this delicate balancing act requires the skills of an insider, someone who knows the Organization like the back of his hand. Thierry Lagrange, recently appointed Head of Finance and Purchasing, has spent most of his career at CERN, and the past five years as Deputy Head of the Finance Department. Nobody knows the subtleties and p...
Dark energy from modified gravity with Lagrange multipliers
Capozziello, Salvatore; Nojiri, Shin'ichi; Odintsov, Sergei D
2010-01-01
We study scalar-tensor theory, k-essence and modified gravity with Lagrange multiplier constraint which role is to reduce the number of degrees of freedom. Dark Energy cosmology of different types ($\\Lambda$CDM, unified inflation with DE, smooth non-phantom/phantom transition epoch) is reconstructed in such models. It is shown that mathematical equivalence between scalar theory and $F(R)$ gravity is broken due to presence of constraint. The cosmological dynamics of $F(R)$ gravity is modified by the second $F_2(R)$ function dictated by the constraint. Dark Energy cosmology is defined by this function while standard $F_1(R)$ function is relevant for local tests (modification of newton regime). A general discussion on the role of Lagrange multipliers to make higher-derivative gravity canonical is developed.
Analyzing modified unimodular gravity via Lagrange multipliers
Sáez-Gómez, Diego
2016-06-01
The so-called unimodular version of general relativity is revisited. Unimodular gravity is constructed by fixing the determinant of the metric, which leads to the trace-free part of the equations instead of the usual Einstein field equations. Then a cosmological constant naturally arises as an integration constant. While unimodular gravity turns out to be equivalent to general relativity (GR) at the classical level, it provides important differences at the quantum level. Here we extend the unimodular constraint to some extensions of general relativity that have drawn a lot of attention over the last years—f (R ) gravity (or its scalar-tensor picture) and Gauss-Bonnet gravity. The corresponding unimodular version of such theories is constructed as well as the conformal transformation that relates the Einstein and Jordan frames for these nonminimally coupled theories. From the classical point of view, the unimodular versions of such extensions are completely equivalent to their originals, but an effective cosmological constant arises naturally, which may provide a richer description of the evolution of the Universe. Here we analyze the case of Starobisnky inflation and compare it with the original one.
On the Equivalence of Euler-Lagrange and Noether Equations
Energy Technology Data Exchange (ETDEWEB)
Faliagas, A. C., E-mail: apostol.faliagas@gmail.com [University of Athens, Department of Mathematics (Greece)
2016-03-15
We prove that, under the condition of nontriviality, the Euler-Lagrange and Noether equations are equivalent for a general class of scalar variational problems. Examples are position independent Lagrangians, Lagrangians of p-Laplacian type, and Lagrangians leading to nonlinear Poisson equations. As applications we prove certain propositions concerning the nonlinear Poisson equation and its generalisations, and the equivalence of admissible and inner variations for the systems under consideration.
Volumetric Displacement Effects In Euler-Lagrange Simulations of Sediment-Laden Oscillatory Flows
Apte, S.; Finn, J. R.; Cihonski, A.
2013-12-01
An improved, three-dimensional approach for Euler-Lagrange simulation of sediment-laden oscillatory turbulent flows is developed. In this approach, the sediment particles are unresolved and subgrid similar to a discrete element model (DEM), however, the fluid volume (mass) displaced by the particle is accounted for in the conservation equations. Recent Euler-Lagrange modeling of a few microbubbles entrained in a traveling vortex ring (Cihonski et al., JFM, 2013) has shown that extension of the standard point-particle DEM method to include local volume displacement effects is critical in capturing vortex distortion effects due to microbubbles, even in a very dilute suspension. We extend this approach to investigate particle-laden oscillatory boundary layers representative of coastal sediment environments. A wall bounded, doubly periodic domain is considered laden with a layer of sediment particles in laminar as well as turbulent oscillatory boundary layers corresponding to the experiments of Keiller and Sleath (1987) and Jensen et al. (1987). Inter-particle and particle-wall collisions are modeled using a soft-sphere model which uses a nested collision grid to minimize computational effort. The effects of fluid mass displaced by the particles on the flow statistics are quantified by comparing a standard two-way coupling approach (without volume displacement effects) with volume displacement effects to show that the latter models are important for cases with low specific gravity.
Two Lagrange-like optical invariants and some applications.
Corrente, Fabio; Onorato, Pasquale
2011-05-01
Geometric optics can be completely derived from Fermat's principle, as classical mechanics can be obtained by the application of the Hamilton principle. In Lagrangian optics, for optical systems with rotational symmetry, is known the invariant L₃, the Lagrange optical invariant. For systems built only with spherical lenses, we demonstrate there are two other optical invariants, L₁ and L₂, analogous to L₃. A proof based on Snell's law, the Weierstrass-Erdman jump condition, and the expression of the ray between two optical surfaces in the Hamiltonian formalism is reported. The presence of a conserved vector, L, allows us to write the equation of an emerging ray without any approximation.
Euler-Lagrange formulas for pseudo-Kähler manifolds
Park, JeongHyeong
2016-01-01
Let c be a characteristic form of degree k which is defined on a Kähler manifold of real dimension m > 2 k. Taking the inner product with the Kähler form Ωk gives a scalar invariant which can be considered as a generalized Lovelock functional. The associated Euler-Lagrange equations are a generalized Einstein-Gauss-Bonnet gravity theory; this theory restricts to the canonical formalism if c =c2 is the second Chern form. We extend previous work studying these equations from the Kähler to the pseudo-Kähler setting.
Lagrange-Noether method for solving second-order differential equations
Institute of Scientific and Technical Information of China (English)
Wu Hui-Bin; Wu Run-Heng
2009-01-01
The purpose of this paper is to provide a new method called the Lagrange-Noether method for solving second-order differential equations. The method is,firstly,to write the second-order differential equations completely or partially in the form of Lagrange equations,and secondly,to obtain the integrals of the equations by using the Noether theory of the Lagrange system. An example is given to illustrate the application of the result.
Error estimates of Lagrange interpolation and orthonormal expansions for Freud weights
Kwon, K. H.; Lee, D. W.
2001-08-01
Let Sn[f] be the nth partial sum of the orthonormal polynomials expansion with respect to a Freud weight. Then we obtain sufficient conditions for the boundedness of Sn[f] and discuss the speed of the convergence of Sn[f] in weighted Lp space. We also find sufficient conditions for the boundedness of the Lagrange interpolation polynomial Ln[f], whose nodal points are the zeros of orthonormal polynomials with respect to a Freud weight. In particular, if W(x)=e-(1/2)x2 is the Hermite weight function, then we obtain sufficient conditions for the inequalities to hold:andwhere and k=0,1,2...,r.
Einstein Gravity, Lagrange-Finsler Geometry, and Nonsymmetric Metrics
Directory of Open Access Journals (Sweden)
Sergiu I. Vacaru
2008-10-01
Full Text Available We formulate an approach to the geometry of Riemann-Cartan spaces provided with nonholonomic distributions defined by generic off-diagonal and nonsymmetric metrics inducing effective nonlinear and affine connections. Such geometries can be modelled by moving nonholonomic frames on (pseudo Riemannian manifolds and describe various types of nonholonomic Einstein, Eisenhart-Moffat and Finsler-Lagrange spaces with connections compatible to a general nonsymmetric metric structure. Elaborating a metrization procedure for arbitrary distinguished connections, we define the class of distinguished linear connections which are compatible with the nonlinear connection and general nonsymmetric metric structures. The nonsymmetric gravity theory is formulated in terms of metric compatible connections. Finally, there are constructed such nonholonomic deformations of geometric structures when the Einstein and/or Lagrange-Finsler manifolds are transformed equivalently into spaces with generic local anisotropy induced by nonsymmetric metrics and generalized connections. We speculate on possible applications of such geometric methods in Einstein and generalized theories of gravity, analogous gravity and geometric mechanics.
Finding critical points whose polarization is also a critical point
Squassina, Marco; Van Schaftingen, Jean
2011-01-01
We show that near any given minimizing sequence of paths for the mountain pass lemma, there exists a critical point whose polarization is also a critical point. This is motivated by the fact that if any polarization of a critical point is also a critical point and the Euler-Lagrange equation is a second-order semi-linear elliptic problem, T. Bartsch, T. Weth and M. Willem (J. Anal. Math., 2005) have proved that the critical point is axially symmetric.
Lagrange's early contributions to the theory of first-order partial differential equations
Engelsman, S.B.
1980-01-01
In 1776, J. L. Lagrange gave a definition of the concept of a “complete solution” of a first-order partial differential equation. This definition was entirely different from the one given earlier by Euler. One of the sources for Lagrange's reformulation of this concept can be found in his attempt to
Euler-Lagrange Equations of Networks with Higher-Order Elements
Directory of Open Access Journals (Sweden)
Z. Biolek
2017-06-01
Full Text Available The paper suggests a generalization of the classic Euler-Lagrange equation for circuits compounded of arbitrary elements from Chua’s periodic table. Newly defined potential functions for general (α, β elements are used for the construction of generalized Lagrangians and generalized dissipative functions. Also procedures of drawing the Euler-Lagrange equations are demonstrated.
The third-order Lagrange equation for mechanical systems of variable mass
Institute of Scientific and Technical Information of China (English)
Ma Shan-Jun; Ge Wei-Guo; Huang Pei-Tian
2005-01-01
In this paper, based on the third-order D'Alembert-Lagrange principle for mechanical systems of variable mass,the third-order Lagrange equations of mechanical systems of variable mass are obtained From the equations the motion of mechanical systems of variable mass can be studied. In addition, the equations may enrich the theory of third-order differential equation.
Analytical Solution of Nonlinear Problems in Classical Dynamics by Means of Lagrange-Ham
DEFF Research Database (Denmark)
Kimiaeifar, Amin; Mahdavi, S. H; Rabbani, A.
2011-01-01
In this work, a powerful analytical method, called Homotopy Analysis Methods (HAM) is coupled with Lagrange method to obtain the exact solution for nonlinear problems in classic dynamics. In this work, the governing equations are obtained by using Lagrange method, and then the nonlinear governing...
A Lagrange multiplier based divide and conquer finite element algorithm
Farhat, C.
1991-01-01
A novel domain decomposition method based on a hybrid variational principle is presented. Prior to any computation, a given finite element mesh is torn into a set of totally disconnected submeshes. First, an incomplete solution is computed in each subdomain. Next, the compatibility of the displacement field at the interface nodes is enforced via discrete, polynomial and/or piecewise polynomial Lagrange multipliers. In the static case, each floating subdomain induces a local singularity that is resolved very efficiently. The interface problem associated with this domain decomposition method is, in general, indefinite and of variable size. A dedicated conjugate projected gradient algorithm is developed for solving the latter problem when it is not feasible to explicitly assemble the interface operator. When implemented on local memory multiprocessors, the proposed methodology requires less interprocessor communication than the classical method of substructuring. It is also suitable for parallel/vector computers with shared memory and compares favorably with factorization based parallel direct methods.
On Lagrange Multipliers in Work with Quality and Reliability Assurance
DEFF Research Database (Denmark)
Vidal, Rene Victor Valqui; Becker, P.
1986-01-01
In optimizing some property of a system, reliability say, a designer usually has to accept certain constraints regarding cost, completion time, volume, weight, etc. The solution of optimization problems with boundary constraints can be helped substantially by the use of Lagrange multipliers techn...... in the areas of sales promotion and teaching. These maps illuminate the logic structure of solution sequences. One such map is shown, illustrating the application of LMT in one of the examples....... techniques (LMT). With representative examples of increasing complexity, the wide applicability of LMT is illustrated. Two particular features are put in focus. First, an easy to follow yet powerful new graphical approach is presented, Second, the concept of Fuller-Polya maps is shown to be helpful...
Perdomo, Oscar M
2016-01-01
It is well known that, from the Newtonian point of view, the Lagrangian point $L_4$ in the circular restricted three body is stable if $\\mu< \\frac{1}{18}(9-\\sqrt{19})\\approx 0.03852$. In this paper we will provide a formula that allows us to compute the eigenvalues of the matrix that determines the stability of the equilibrium points of a family of ordinary differential equations. As an application we will show that, under the relativistic framework, the Lagrangian point $L_4$ is also stable for the Sun-Earth system. Similar arguments show the stability for $L_4$ not only for the Sun-Earth system but for systems coming from a range of values for $\\mu$ similar to those in the Newtonian restricted three body problem.
Feng, Ruibin; Leung, Chi-Sing; Constantinides, Anthony G; Zeng, Wen-Jun
2016-07-27
The major limitation of the Lagrange programming neural network (LPNN) approach is that the objective function and the constraints should be twice differentiable. Since sparse approximation involves nondifferentiable functions, the original LPNN approach is not suitable for recovering sparse signals. This paper proposes a new formulation of the LPNN approach based on the concept of the locally competitive algorithm (LCA). Unlike the classical LCA approach which is able to solve unconstrained optimization problems only, the proposed LPNN approach is able to solve the constrained optimization problems. Two problems in sparse approximation are considered. They are basis pursuit (BP) and constrained BP denoise (CBPDN). We propose two LPNN models, namely, BP-LPNN and CBPDN-LPNN, to solve these two problems. For these two models, we show that the equilibrium points of the models are the optimal solutions of the two problems, and that the optimal solutions of the two problems are the equilibrium points of the two models. Besides, the equilibrium points are stable. Simulations are carried out to verify the effectiveness of these two LPNN models.
Improved Faddeev-Jackiw quantization of the electromagnetic field and Lagrange multiplier fields
Institute of Scientific and Technical Information of China (English)
YANG Jin-Long; HUANG Yong-Chang
2008-01-01
We use the improved Faddeev-Jackiw quantization method to quantize the electromagnetic field and its Lagrange multiplier fields.The method's comparison with the usual Faddeev-Jackiw method and the Dirac method is given.We show that this method is equivalent to the Dirac method and also retains all the merits of the usual Faddeev-Jackiw method.Moreover,it is simpler than the usual one if one needs to obtain new secondary constraints.Therefore,the improved Faddeev-Jackiw method is essential.Meanwhile,we find the new meaning of the Lagrange multipliers and explain the Faddeev-Jackiw generalized brackets concerning the Lagrange multipliers.
Directory of Open Access Journals (Sweden)
Suxiang He
2014-01-01
Full Text Available An implementable nonlinear Lagrange algorithm for stochastic minimax problems is presented based on sample average approximation method in this paper, in which the second step minimizes a nonlinear Lagrange function with sample average approximation functions of original functions and the sample average approximation of the Lagrange multiplier is adopted. Under a set of mild assumptions, it is proven that the sequences of solution and multiplier obtained by the proposed algorithm converge to the Kuhn-Tucker pair of the original problem with probability one as the sample size increases. At last, the numerical experiments for five test examples are performed and the numerical results indicate that the algorithm is promising.
基于最小二乘法的 Lagrange 方法在衰减冲击波中的研究%Study on Lagrange Analysis with Least Squares in Attenuating Waves
Institute of Scientific and Technical Information of China (English)
陶为俊; 浣石
2014-01-01
The existing reactive flow Lagrange analysis methods are still inadequate to solve the particle velocity history from a series of gauges embedded in material.Based on this point,a new Lagrange analysis method combined the inverse analysis with self-consistent examination was presented.The theoretical accuracy of this method can achieve that the M-order partial derivative of the stress equals zero,and the self-consistent examination is satisfied.Besides,this method is applied to process the experimental data of the light gas gun.Comparing results of this method,experimental data and the traditional inverse analysis results,it turns out that this method not only makes the particle-line function reflecting the behavior of various physical quantities along the particle-line,but also reduces the accidental error of the particle-line.%在已知粒子速度的情况下，采用现有 Lagrange 分析方法求解动力学方程仍有不足。针对这一情况，将反解法和自洽检验法相结合，提出了基于最小二乘法的 Lagrange 反解法。该方法的理论精度能够实现应力沿路径线的 M（M 为迹线数）阶导数恒为零，并且能够满足自洽检验法。通过对一组混凝土的实验数据进行处理，并将处理结果与实验结果以及传统Lagrange反解法进行对比，比较结果表明，该方法不仅使得迹线函数能够很好地反应各物理量沿迹线的变化性态，而且还能够适当减小偶然误差。
Odintsov, S D
2015-01-01
We study mimetic $F(R)$ gravity with potential and Lagrange multiplier constraint. In the context of these theories, we introduce a reconstruction technique which enables us to realize arbitrary cosmologies, given the Hubble rate and an arbitrarily chosen $F(R)$ gravity. We exemplify our method by realizing cosmologies that are in concordance with current observations (Planck data) and also well known bouncing cosmologies. The attribute of our method is that the $F(R)$ gravity can be arbitrarily chosen, so we can have the appealing features of the mimetic approach combined with the known features of some $F(R)$ gravities, which unify early-time with late-time acceleration. Moreover, we study the existence and the stability of de Sitter points in the context of mimetic $F(R)$ gravity. In the case of unstable de Sitter points, it is demonstrated that graceful exit from inflation occurs. We also study the Einstein frame counterpart theory of the Jordan frame mimetic $F(R)$ gravity, we discuss the general propert...
Access to Mars from Earth-Moon Libration Point Orbits:. [Manifold and Direct Options
Kakoi, Masaki; Howell, Kathleen C.; Folta, David
2014-01-01
This investigation is focused specifically on transfers from Earth-Moon L(sub 1)/L(sub 2) libration point orbits to Mars. Initially, the analysis is based in the circular restricted three-body problem to utilize the framework of the invariant manifolds. Various departure scenarios are compared, including arcs that leverage manifolds associated with the Sun-Earth L(sub 2) orbits as well as non-manifold trajectories. For the manifold options, ballistic transfers from Earth-Moon L(sub 2) libration point orbits to Sun-Earth L(sub 1)/L(sub 2) halo orbits are first computed. This autonomous procedure applies to both departure and arrival between the Earth-Moon and Sun-Earth systems. Departure times in the lunar cycle, amplitudes and types of libration point orbits, manifold selection, and the orientation/location of the surface of section all contribute to produce a variety of options. As the destination planet, the ephemeris position for Mars is employed throughout the analysis. The complete transfer is transitioned to the ephemeris model after the initial design phase. Results for multiple departure/arrival scenarios are compared.
Transfer Trajectories to L3 Libration Point of Sun-Earth System%基于准流形方法日地系L3点转移轨道设计
Institute of Scientific and Technical Information of China (English)
潘迅; 泮斌峰
2015-01-01
针对深空探测中轨道转移时间长且能量消耗较大的问题,提出基于准流形实现从地球停泊轨道到日地系L3点转移轨道的设计方法.在日地限制性三体问题模型下,在L1点或L2点Halo轨道上施加扰动推力,构造准流形,利用其非线性三体动力学特性,通过霍曼转移轨道与近地轨道进行拼接,使航天器进入准流形后能够无动力滑行到L3点附近区域.在准流形与L3点周期轨道交点,施加速度脉冲,使航天器进入相应周期轨道,从而完成轨道转移.仿真结果表明,利用该方法所得结果与基于不变流形的转移轨道相比,能将速度增量从4 398 m/s减少为4 014 m/s,并将转移时间从9年以上缩短到7.3年以内,有效地提高了航天器的工作效率.
Institute of Scientific and Technical Information of China (English)
周天帅; 李东; 陈新民; 杨虎军
2004-01-01
圆形限制性三体问题中存在5个动平衡点.其中日-地系统中共线平衡点L1和L2是近十几年来国外研究热点.首先介绍了5个平衡点的位置关系及卫星应用,接着从理论上简单比较了Halo轨道和Lissajous轨道的区别,指出Halo轨道和Lissajous轨道是线性化偏差方程的特解.介绍国外日-地动平衡点卫星应用情况,分析了转移轨道的两种可行方式.
Some generalized Lagrange-based Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials
Srivastava, H. M.; Özarslan, M. A.; Kaanoğlu, C.
2013-03-01
In this paper, we introduce a general family of Lagrange-based Apostol-type polynomials thereby unifying the Lagrange-based Apostol-Bernoulli and the Lagrange-based Apostol-Genocchi polynomials. We also define Lagrange-based Apostol-Euler polynomials via the generating function. In terms of these generalizations, we find new and useful relations between the unified family and the Apostol-Euler polynomials. We also derive their explicit representations and list some basic properties of each of them. Further relations between the above-mentioned polynomials, including a family of bilinear and bilateral generating functions, are given. Moreover, a generating relation involving the Stirling numbers of the second kind is derived.
球面上的Lagrange插值%Lagrange Interpolation on a Sphere
Institute of Scientific and Technical Information of China (English)
周恒; 王仁宏
2006-01-01
In this paper, we obtain a properly posed set of nodes for interpolation on a sphere. Moreover it is applied to construct properly posed set of nodes for Lagrange interpolation on the trivariate polynomial space of total degree n.
ON LAGRANGE INTERPOLATION FOR [X|a (0＜a＜1)
Institute of Scientific and Technical Information of China (English)
Laiyi Zhu; Zhiyong Huang
2009-01-01
We study the optimal order of approximation for |x|a (0 ＜ a ＜ 1) by Lagrange interpolation polynomials based on Chebyshev nodes of the first kind. It is proved that the Jackson order of approximation is attained.
Directory of Open Access Journals (Sweden)
Heejeong Koh
2013-01-01
Full Text Available We obtain the general solution of Euler-Lagrange-Rassias quartic functional equation of the following . We also prove the Hyers-Ulam-Rassias stability in various quasinormed spaces when .
Stable iterative Lagrange principle in convex programming as a tool for solving unstable problems
Kuterin, F. A.; Sumin, M. I.
2017-01-01
A convex programming problem in a Hilbert space with an operator equality constraint and a finite number of functional inequality constraints is considered. All constraints involve parameters. The close relation of the instability of this problem and, hence, the instability of the classical Lagrange principle for it to its regularity properties and the subdifferentiability of the value function in the problem is discussed. An iterative nondifferential Lagrange principle with a stopping rule is proved for the indicated problem. The principle is stable with respect to errors in the initial data and covers the normal, regular, and abnormal cases of the problem and the case where the classical Lagrange principle does not hold. The possibility of using the stable sequential Lagrange principle for directly solving unstable optimization problems is discussed. The capabilities of this principle are illustrated by numerically solving the classical ill-posed problem of finding the normal solution of a Fredholm integral equation of the first kind.
The symplectic structure of Euler-Lagrange superequations and Batalin-Vilkoviski formalism
Energy Technology Data Exchange (ETDEWEB)
Monterde, J; Vallejo, J A [Departament de Geometria i Topologia, Universitat de Valencia, Avda V A Estelles 1, 46100, Burjassot (Spain)
2003-05-09
We study the graded Euler-Lagrange equations from the viewpoint of graded Poincare-Cartan forms. An application to a certain class of solutions of the Batalin-Vilkoviski master equation is also given.
Integración automatizada de las ecuaciones de Lagrange en el movimiento orbital.
Abad, A.; San Juan, J. F.
The new techniques of algebraic manipulation, especially the Poisson Series Processor, permit the analytical integration of the more and more complex problems of celestial mechanics. The authors are developing a new Poisson Series Processor, PSPC, and they use it to solve the Lagrange equation of the orbital motion. They integrate the Lagrange equation by using the stroboscopic method, and apply it to the main problem of the artificial satellite theory.
A New Type of Conserved Quantity of Mei Symmetry for Lagrange Systems
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A new type of conserved quantity, which is induced from the Mei symmetry of Lagrange systems, is studied.The conditions for that the new type of conserved quantity exists and the form of the new type of conserved quantity are obtained. An illustrated example is given. The Noether conserved quantity induced from the Mei symmetry of Lagrange systems is a special case of the new type of conserved quantity given in this paper.
Solution of second order linear fuzzy difference equation by Lagrange's multiplier method
Directory of Open Access Journals (Sweden)
Sankar Prasad Mondal
2016-06-01
Full Text Available In this paper we execute the solution procedure for second order linear fuzzy difference equation by Lagrange's multiplier method. In crisp sense the difference equation are easy to solve, but when we take in fuzzy sense it forms a system of difference equation which is not so easy to solve. By the help of Lagrange's multiplier we can solved it easily. The results are illustrated by two different numerical examples and followed by two applications.
Apte, Sourabh; Finn, Justin; Cihonski, Andrew
2013-11-01
Recent Euler-Lagrange discrete element modeling of a few microbubbles entrained in a traveling vortex ring (Cihonski et al., JFM, 2013) has shown that extension of the point-particle method to include local volume displacement effects is critical for capturing vortex distortion effects due to microbubbles, even in a very dilute suspension. We extend this approach to investigate particle-laden oscillatory boundary layers representative of coastal sediment environments. A wall bounded, doubly periodic domain is considered laden with a layer of sediment particles in laminar as well as turbulent oscillatory boundary layers corresponding to the experiments of Keiller and Sleath (1987) and Jensen et al. (1987). Inter-particle and particle-wall collisions are modeled using a soft-sphere model which uses a nested collision grid to minimize computational effort. The effects of fluid mass displaced by the particles on the flow statistics are quantified by comparing a standard two-way coupling approach (without volume displacement effects) with volume displacement effects to show that the latter models are important for low cases with low particle-fluid density ratios. NSF project #1133363, Sediment-Bed-Turbulence Coupling in Oscillatory Flows. EPSRC Project # EP/J00507X/1, EP/J005541/1 Sand Transport under Irregular and Breaking Waves Conditions (SINBAD).
Weyl-Euler-Lagrange equations on twistor space for tangent structure
Kasap, Zeki
2016-06-01
Twistor spaces are certain complex three-manifolds, which are associated with special conformal Riemannian geometries on four-manifolds. Also, classical mechanic is one of the major subfields for mechanics of dynamical system. A dynamical system has a state determined by a collection of real numbers, or more generally by a set of points in an appropriate state space for classical mechanic. Euler-Lagrange equations are an efficient use of classical mechanics to solve problems using mathematical modeling. On the other hand, Weyl submitted a metric with a conformal transformation for unified theory of classical mechanic. This paper aims to introduce Euler-Lagrage partial differential equations (mathematical modeling, the equations of motion according to the time) for the movement of objects on twistor space and also to offer a general solution of differential equation system using the Maple software. Additionally, the implicit solution of the equation will be obtained as a result of a special selection of graphics to be drawn.
The Lagrange reduction of the N-body problem, a survey
Chenciner, Alain
2011-01-01
In his fondamental "Essay on the 3-body problem", Lagrange, well before Jacobi's "reduction of the node", carries out the first complete reduction of symetries. Discovering the so-called homographic motions, he shows that they necessarily take place in a fixed plane. The true nature of this reduction is revealed if one considers the n-body problem in an euclidean space of arbitrary dimension. The actual dimension of the ambiant space then appears as a constraint, namely the angular momentum bivector's degeneracy. The main part of this survey is a detailed description of the results obtained in a joint paper with Alain Albouy published in french (Inventiones 1998): for a non homothetic homographic motion to exist, it is necessary that the space of motion be even dimensional. Two cases are possible: either the configuration is "central" (that is a critical point of the potential among configurations with a given moment of inertia) and the space where the motion takes place is endowed with an hermitian structure...
Orbital Maneuvers for Spacecrafts Travelling to/from the Lagrangian Points
Bertachini, A.
The well-known Lagrangian points that appear in the planar restricted three-body problem (Szebehely, 1967) are very important for astronautical applications. They are five points of equilibrium in the equations of motion, what means that a particle located at one of those points with zero velocity will remain there indefinitely. The collinear points (L1, L2 and L3) are always unstable and the triangular points (L4 and L5) are stable in the present case studied (Sun-Earth system). They are all very good points to locate a space-station, since they require a small amount of V (and fuel), the control to be used for station-keeping. The triangular points are specially good for this purpose, since they are stable equilibrium points. In this paper, the planar restricted three-body problem is regularized (using Lemaître regularization) and combined with numerical integration and gradient methods to solve the two point boundary value problem (the Lambert's three-body problem). This combination is applied to the search of families of transfer orbits between the Lagrangian points and the Earth, in the Sun-Earth system, with the minimum possible cost of the control used. So, the final goal of this paper is to find the magnitude and direction of the two impulses to be applied in the spacecraft to complete the transfer: the first one when leaving/arriving at the Lagrangian point and the second one when arriving/living at the Earth. This paper is a continuation of two previous papers that studied transfers in the Earth-Moon system: Broucke (1979), that studied transfer orbits between the Lagrangian points and the Moon and Prado (1996), that studied transfer orbits between the Lagrangian points and the Earth. So, the equations of motion are: whereis the pseudo-potential given by: To solve the TPBVP in the regularized variables the following steps are used: i) Guess a initial velocity Vi, so together with the initial prescribed position ri the complete initial state is known; ii
Beichman, C.; Gomez, G.; Lo, M.; Masdemont, J.; Romans, L.
2002-01-01
In this paper, we describe the mission design for TPF assuming a distributed spacecraft concept using formation flight around both a halo orbit around L2 as well as a heliocentric orbit. Although the mission architecture is still under study, the next two years will include study of four design cncepts and a downselect to two concepts around 2005.
Comparison of Direct Eulerian Godunov and Lagrange Plus Remap, Artificial Viscosity Schemes
Energy Technology Data Exchange (ETDEWEB)
Pember, R B; Anderson, R W
2001-03-30
The authors compare two algorithms for solving the equations of unsteady inviscid compressible flow in an Eulerian frame: a staggered grid, Lagrange plus remap artificial viscosity scheme and a cell-centered, direct Eulerian higher-order Godunov scheme. They use the two methods to compute solutions to a number of one- and two-dimensional problems. The results show the accuracy of the two schemes to be generally equivalent. In a 1984 survey paper by Woodward and Colella, the Lagrange plus remap approach did not compare favorably with the higher-order Godunov methodology. They examine, therefore, how certain features of the staggered grid scheme considered here contribute to its improved accuracy. The critical features are shown to be the use of a monotonic artificial viscosity in the Lagrange step and, in the remap step, the use of a corner transport upwind scheme with van Leer limiters in conjunction with separate advection of internal and kinetic energies.
Co op erative Tracking Control for Networked Lagrange Systems：Algorithms and Exp eriments
Institute of Scientific and Technical Information of China (English)
CHEN Gang; YUE Yuan-Long; LIN Qing
2014-01-01
This paper considers the coordinated tracking problem for a group of Lagrange systems in the presence of parametric uncertainties. Distributed adaptive controllers are proposed with the aid of Lyapunov techniques. Compared with the previous work in the context of networked Lagrange systems control, the results in this paper are suitable for the general digraph communication topologies. Under the condition that the desired trajectory is only available to a portion of Lagrange systems, we discuss the cooperative tracking problem with general digraph communication topology, which contains a spanning tree with the root node being the active target system. Under the case where the neighbor0s velocity is unavailable, a distributed filter is introduced to overcome this deficiency. Experimental results on networked robot-arms are provided to show the effectiveness of the proposed control algorithms.
Directory of Open Access Journals (Sweden)
FEMY AYU ASTITI
2013-03-01
Full Text Available Optimization problems can be solved by various methods, such as Lagrange Method. This method can be used to find the solution. Using Lagrange method, the extreme value can be obtained, so that the optimal solution can be found. In this research, the maximum revenue of UD. Sari Madu is a limited by several constraints. After the objective function and constraint function being model, than maximum revenue is found. From first until fourth quarterly, the maximum revenue is found Rp. 9.701.333, Rp. 10.064.148, 9.793.272 and Rp. 9.397.730 respectively.
Directory of Open Access Journals (Sweden)
FEMY AYU ASTITI
2013-01-01
Full Text Available Optimization problems can be solved by various methods, such as Lagrange Method. This method can be used to find the solution. Using Lagrange method, the extreme value can be obtained, so that the optimal solution can be found. In this research, the maximum revenue of UD. Sari Madu is a limited by several constraints. After the objective function and constraint function being model, than maximum revenue is found. From first until fourth quarterly, the maximum revenue is found Rp. 9.701.333, Rp. 10.064.148, 9.793.272 and Rp. 9.397.730 respectively.
Modified Augmented Lagrange Multiplier Methods for Large-Scale Chemical Process Optimization
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Chemical process optimization can be described as large-scale nonlinear constrained minimization. The modified augmented Lagrange multiplier methods (MALMM) for large-scale nonlinear constrained minimization are studied in this paper. The Lagrange function contains the penalty terms on equality and inequality constraints and the methods can be applied to solve a series of bound constrained sub-problems instead of a series of unconstrained sub-problems. The steps of the methods are examined in full detail. Numerical experiments are made for a variety of problems, from small to very large-scale, which show the stability and effectiveness of the methods in large-scale problems.
Discrete variational principle and first integrals for Lagrange-Maxwell mechanico-electrical systems
Institute of Scientific and Technical Information of China (English)
Fu Jing-Li; Dai Gui-Dong; Salvador Jiménez; Tang Yi-Fa
2007-01-01
This paper presents a discrete variational principle and a method to build first-integrals for finite dimensional Lagrange-Maxwell mechanico-electrical systems with nonconservative forces and a dissipation function.The discrete variational principle and the corresponding Euler-Lagrange equations are derived from a discrete action associated to these systems.The first-integrals are obtained by introducing the infinitesimal transformation with respect to the generalized coordinates and electric quantities of the systems.This work also extends discrete Noether symmetries to mechanico-electrical dynamical systerns.A practical example iS presented to illustrate the results.
Resolution of the Gross-Pitaevskii equation with the imaginary-time method on a Lagrange mesh.
Baye, D; Sparenberg, J-M
2010-11-01
The Lagrange-mesh method is an approximate variational calculation which has the simplicity of a mesh calculation. Combined with the imaginary-time method, it is applied to the iterative resolution of the Gross-Pitaevskii equation. Two variants of a fourth-order factorization of the exponential of the Hamiltonian and two types of mesh (Lagrange-Hermite and Lagrange-sinc) are employed and compared. The accuracy is checked with the help of these comparisons and of the virial theorem. The Lagrange-Hermite mesh provides very accurate results with short computing times for values of the dimensionless parameter of the nonlinear term up to 10⁴. For higher values up to 10⁷, the Lagrange-sinc mesh is more efficient. Examples are given for anisotropic and nonseparable trapping potentials.
THE EXACT CONVERGENCE RATE AT ZERO OF LAGRANGE INTERPOLATION POLYNOMIAL TO |x|α
Institute of Scientific and Technical Information of China (English)
Zhikang Lu; Xifang Ge
2006-01-01
In this paper we present a generalized quantitative version of a result due to M. Revers concerning the exact convergence rate at zero of Lagrange interpolation polynomial to f(x) = |x|α with on equally spaced nodes in [-1, 1].
Simulation of free surfaces in 3-D with the arbitrary Lagrange-Euler method
DEFF Research Database (Denmark)
Szabo, Peter; Hassager, Ole
1995-01-01
The arbitrary Lagrange-Euler (ALE) kinematic description has been implemented in a 3-D transient finite element program so as to simulate multiple fluid flows with Surfaces and interfaces of general shapes. The description of fluid interfaces includes continuity of velocity and a discontinuous...
Field theory and weak Euler-Lagrange equation for classical particle-field systems.
Qin, Hong; Burby, Joshua W; Davidson, Ronald C
2014-10-01
It is commonly believed as a fundamental principle that energy-momentum conservation of a physical system is the result of space-time symmetry. However, for classical particle-field systems, e.g., charged particles interacting through self-consistent electromagnetic or electrostatic fields, such a connection has only been cautiously suggested. It has not been formally established. The difficulty is due to the fact that the dynamics of particles and the electromagnetic fields reside on different manifolds. We show how to overcome this difficulty and establish the connection by generalizing the Euler-Lagrange equation, the central component of a field theory, to a so-called weak form. The weak Euler-Lagrange equation induces a new type of flux, called the weak Euler-Lagrange current, which enters conservation laws. Using field theory together with the weak Euler-Lagrange equation developed here, energy-momentum conservation laws that are difficult to find otherwise can be systematically derived from the underlying space-time symmetry.
The First-Order Euler-Lagrange equations and some of their uses
Adam, C
2016-01-01
In many nonlinear field theories, relevant solutions may be found by reducing the order of the original Euler-Lagrange equations, e.g., to first order equations (Bogomolnyi equations, self-duality equations, etc.). Here we generalise, further develop and apply one particular method for the order reduction of nonlinear field equations which, despite its systematic and versatile character, is not widely known.
Dynamic Modeling and Simulation of Marine Satellite Tracking Antenna Using Lagrange Method
DEFF Research Database (Denmark)
Wang, Yunlong; Nourbakhsh, S. M; Hussain, Dil muhammed Akbar
2016-01-01
Marine Satellite Tracking Antenna (MSTA) is a necessary device in ships for receiving satellite signals when they are sailing on the sea. This paper presents a simple methodology to obtain the dynamic equations of MSTA through Lagrange method, which is fundamental in design of modelbased...
Euler-Lagrange Equations for the Gribov Reggeon Calculus in QCD and in Gravity
Lipatov, L. N.
The theory of the high energy scattering in QCD and gravity is based on the reggeization of gluons and gravitons, respectively. We discuss the corresponding effective actions for reggeized particle interactions. The Euler-Lagrange equations in these theories are constructed with a variational approach for the effective actions and by using their invariance under the gauge and general coordinate transformations.
Perturbation to Lie Symmetry and Lutzky Adiabatic Invariants for Lagrange Systems
Institute of Scientific and Technical Information of China (English)
REN Ji-Rong; DING Ning; LI Ran; FANG Jian-Hui; DUAN Yi-Shi; WANG Peng; ZHANG Xiao-Ni
2008-01-01
Based on the concept of adiabatic invariant, perturbation to Lie symmetry and Lutzky adiabatic invariants for Lagrange systems are studied by using different methods from those of previous works. Exact invariants induced from Lie symmetry of the system without perturbation are given. Perturbation to Lie symmetry is discussed and Lutzky adiabatic invariants of the system subject to perturbation are obtained.
Scherpen, Jacquelien M.A.; Ortega, Romeo; Escobar, Gerardo
1997-01-01
In this paper we analyse and experimentally verify the (local) disturbance attenuation properties of some asymptotically stabilizing nonlinear controllers for Euler-Lagrange systems reported in the literature. Our objective with this study is twofold: first, to compare the performance of these schem
TRANSMISSION MOMENTARY EFFICIENCY BASED ON THE D'ALEMBERT-LAGRANGE EQUATION FOR INVOLUTES GEARS
Institute of Scientific and Technical Information of China (English)
Liang Yi; Lai Changying
2004-01-01
The D'Alembert-Lagrange equation is introduced and used to derive the formulas of momentary efficiency for external gearing of standard involutes spur gears.The gearings with correct and increased center distance are discussed.The momentary efficiency formula is calculated and analyzed using software Matlab.The derived formula of momentary efficiency is also compared with the traditional formula.
DEFF Research Database (Denmark)
Catani, Paul; Teräsvirta, Timo; Yin, Meiqun
A Lagrange multiplier test for testing the parametric structure of a constant conditional correlation generalized autoregressive conditional heteroskedasticity (CCC-GARCH) model is proposed. The test is based on decomposing the CCC-GARCH model multiplicatively into two components, one of which...
Formation control of multiple Euler-Lagrange systems via null-space-based behavioral control
Chen, Jie; Huang, Jie; Dou, Lihua; Fang, Hao
2016-01-01
This paper addresses the formation control problem of multiple Euler-Lagrange systems with model uncertainties in the environment containing obstacles. Utilizing the null-space-based (NSB) behavioral control architecture, the proposed problem can be decomposed into elementary missions (behaviors) wi
The first-order Euler-Lagrange equations and some of their uses
Energy Technology Data Exchange (ETDEWEB)
Adam, C.; Santamaria, F. [Departamento de Física de Partículas and Instituto Galego de Física de Altas Enerxias (IGFAE),Campus Vida, E-15782 Santiago de Compostela (Spain)
2016-12-13
In many nonlinear field theories, relevant solutions may be found by reducing the order of the original Euler-Lagrange equations, e.g., to first order equations (Bogomolnyi equations, self-duality equations, etc.). Here we generalise, further develop and apply one particular method for the order reduction of nonlinear field equations which, despite its systematic and versatile character, is not widely known.
Energy Technology Data Exchange (ETDEWEB)
Olivares Pilón, Horacio, E-mail: holivare@ulb.ac.be [Physique Quantique, CP 165/82, Université Libre de Bruxelles, B 1050 Brussels (Belgium)
2012-04-09
Accurate calculations for the ground state of the molecular ions He{sup 3+}{sub 2} and HeH{sup 2+} placed in a strong magnetic field B≳10{sup 2} a.u. (≈2.35×10{sup 11} G) using the Lagrange-mesh method are presented. The Born–Oppenheimer approximation of zero order (infinitely massive centers) and the parallel configuration (molecular axis parallel to the magnetic field) are considered. Total energies are found with 9–10 s.d. The obtained results show that the molecular ions He{sup 3+}{sub 2} and HeH{sup 2+} exist at B>100 a.u. and B>1000 a.u., respectively, as predicted in Turbiner and López Vieyra (2007) while a saddle point in the potential curve appears for the first time at B∼80 a.u. and B∼740 a.u., respectively. -- Highlights: ► Application of the Lagrange-mesh method to two exotic molecular systems. ► He{sup 3+}{sub 2} and HeH{sup 2+} exist at B>100 a.u. and B>1000 a.u., respectively. ► Accurate results for the total energy. ► A saddle point in the potential appears at B∼80 a.u. and B∼740 a.u., respectively.
Directory of Open Access Journals (Sweden)
Leonardo Solanilla Ch
2009-07-01
Full Text Available En este artículo se muestra que el modelo esférico de Lagrange para las integrales elípticas es interpretable como un computador analógico. Además del lema fundamental que sustenta la analogía, se presentan ejemplos de cálculo para las amplitudes de la suma y la diferencia de dos amplitudes elípticas dadas. En el computador analógico, estas operaciones se materializan por medio de construcciones con regla y compás esféricos. A lo largo de la presentación, se discuten las ventajas y desventajas del procedimiento propuesto. Al final, se esbozan algunas conclusiones sobre los métodos usados y sobre un posible método híbrido para la aproximación numérica de las amplitudes elípticas.In this paper, we show that Lagrange's spherical model for elliptic integrals can be understood as an actual analog computer. In addition to proving the fundamental lemma establishing analogy, we provide examples which show a way to compute the amplitude of the addition (and subtraction of two elliptic integrals. In our computer, these operations are performed by using a spherical compass and a spherical straightedge. We also discuss the pros and cons of our procedure. At the end, we draw some conclusions concerning the possibility of alternative hybrid numerical solutions to the elliptic amplitudes
On reflection symmetry and its application to the Euler-Lagrange equations in fractional mechanics.
Klimek, Małgorzata
2013-05-13
We study the properties of fractional differentiation with respect to the reflection symmetry in a finite interval. The representation and integration formulae are derived for symmetric and anti-symmetric fractional derivatives, both of the Riemann-Liouville and Caputo type. The action dependent on the left-sided Caputo derivatives of orders in the range (1,2) is considered and we derive the Euler-Lagrange equations for the symmetric and anti-symmetric part of the trajectory. The procedure is illustrated with an example of the action dependent linearly on fractional velocities. For the obtained Euler-Lagrange system, we discuss its localization resulting from the subsequent symmetrization of the action.
Almost Kaehler Ricci Flows and Einstein and Lagrange-Finsler Structures on Lie Algebroids
Vacaru, Sergiu I
2015-01-01
In this work we investigate Ricci flows of almost Kaehler structures on Lie algebroids when the fundamental geometric objects are completely determined by (semi) Riemannian metrics, or effective) regular generating Lagrange/ Finsler, functions. There are constructed canonical almost symplectic connections for which the geometric flows can be represented as gradient ones and characterized by nonholonomic deformations of Grigory Perelman's functionals. The first goal of this paper is to define such thermodynamical type values and derive almost K\\"ahler - Ricci geometric evolution equations. The second goal is to study how fixed Lie algebroid, i.e. Ricci soliton, configurations can be constructed for Riemannian manifolds and/or (co) tangent bundles endowed with nonholonomic distributions modelling (generalized) Einstein or Finsler - Cartan spaces. Finally, there are provided some examples of generic off-diagonal solutions for Lie algebroid type Ricci solitons and (effective) Einstein and Lagrange-Finsler algebro...
Multivariable Lagrange expansion and generalization of Carlitz-Srivastava mixed generating functions
Energy Technology Data Exchange (ETDEWEB)
Dattoli, G. [ENEA, Centro Ricerche Frascati, Rome (Italy). Dipt. Innovazione; Lorenzutta, S. [ENEA, Centro Ricerche Ezio Clementel, Bologna (Italy). Dipt. Innovazione; Sacchetti, D. [Rome Univ. La Sapienza, Rome (Italy). Dipt. di Statistica, Probabilita' e Stat. Applicate
1999-07-01
Families of mixed generating functions, generalizing those of the Carlitz-Srivastava type, are derived by exploiting methods based on the multivariable extension of the Lagrange expansion. It is also shown that the combination with techniques of operational nature offers a wide flexibility to explore a wealth of mixed bilateral generating functions for special functions with many variables. [Italian] In questo lavoro si derivano famiglie di funzioni generatrici che generalizzano quelle del tipo Carlitz-Srivastava. I metodi utilizzati sono basati su una estensione a piu' variabili della espansione di Lagrange. Si dimostra anche che una opportuna combinazione con tecniche di natura operatoriale offre un'ampia flessibilita' per lo studio di funzioni generatrici viste per funzioni speciali con piu' variabili.
Institute of Scientific and Technical Information of China (English)
Luo Shao-Kai; Chen Xiang-Wei; Guo Yong-Xin
2007-01-01
Based on the invariance of differential equations under infinitesimal transformations of group, Lie symmetries,exact invariants, perturbation to the symmetries and adiabatic invariants in form of non-Noether for a Lagrange system are presented. Firstly, the exact invariants of generalized Hojman type led directly by Lie symmetries for a Lagrange system without perturbations are given. Then, on the basis of the concepts of Lie symmetries and higher order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for the system with the action of small disturbance is investigated, the adiabatic invariants of generalized Hojman type for the system are directly obtained, the conditions for existence of the adiabatic invariants and their forms are proved. Finally an example is presented to illustrate these results.
A mixed element based on Lagrange multiplier method for modified couple stress theory
Kwon, Young-Rok; Lee, Byung-Chai
2017-01-01
A 2D mixed element is proposed for the modified couple stress theory. The C1 continuity for the displacement field is required because of the second derivatives of displacement in the energy form of the theory. The C1 continuity is satisfied in a weak sense with the Lagrange multiplier method. A supplementary rotation is introduced as an independent variable and the kinematic relation between the physical rotation and the supplementary rotation is constrained with Lagrange multipliers. Convergence criteria and a stability condition are derived, and the number and the positions of nodes for each independent variable are determined. Internal degrees of freedom are condensed out, so the element has only 21 degrees of freedom. The proposed element passes the C^{0-1} patch test. Numerical results show that the principle of limitation is applied to the element and the element is robust to mesh distortion. Furthermore, the size effects are captured well with the element.
Reduced projection augmented Lagrange bi-conjugate gradient method for contact and impact problems
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Based on the numerical governing formulation and non-linear complementary conditions of contact and impact problems, a reduced projection augmented Lagrange biconjugate gradient method is proposed for contact and impact problems by translating non-linear complementary conditions into equivalent formulation of non-linear programming. For contact-impact problems, a larger time-step can be adopted arriving at numerical convergence compared with penalty method. By establishment of the impact-contact formulations which are equivalent with original non-linear complementary conditions, a reduced projection augmented Lagrange bi-conjugate gradient method is deduced to improve precision and efficiency of numerical solutions. A numerical example shows that the algorithm we suggested is valid and exact.
Regularization of a discrete backward problem using coefficients of truncated Lagrange polynomials
Directory of Open Access Journals (Sweden)
Duc Trong Dang
2007-04-01
Full Text Available We consider the problem of finding the initial temperature $u(x,0$, from a countable set of measured values ${ u(x_j,1}$. The problem is severely ill-posed and a regularization is in order. Using the Hermite polynomials and coefficients of truncated Lagrange polynomials, we shall change the problem into an analytic interpolation problem and give explicitly a stable approximation. Error estimates and some numerical examples are given.
Application of "interpolation polynomial of lagrange" for functions with many variables
Directory of Open Access Journals (Sweden)
Валерий Анатольевич Тараник
2015-08-01
Full Text Available The interpolation polynomial of Lagrange is used for the functions of one variable. In this article it is considered a possibility of its application for a function with a few variables. Thus, a method does not suffer large changes. It will remain the same simple, and can serve as a good alternative at the decision of tasks, for that before were used more difficult methods
Institute of Scientific and Technical Information of China (English)
Laiyi Zhu
2006-01-01
We study some approximation properties of Lagrange interpolation polynomial based on the zeros of (1 -x2)cosnarccosx. By using a decomposition for f(x) ∈ CrCr+1 we obtain an estimate of ||f(x)-Ln+2(f,x)|| which reflects the influence of the position of the x's and ω(f(r+1),δ)j,j = 0, 1,... ,s,on the error of approximation.
FLAG: A multi-dimensional adaptive free-Lagrange code for fully unstructured grids
Energy Technology Data Exchange (ETDEWEB)
Burton, D.E.; Miller, D.S.; Palmer, T. [Lawrence Livermore National Lab., CA (United States)
1995-07-01
The authors describe FLAG, a 3D adaptive free-Lagrange method for unstructured grids. The grid elements were 3D polygons, which move with the flow, and are refined or reconnected as necessary to achieve uniform accuracy. The authors stressed that they were able to construct a 3D hydro version of this code in 3 months, using an object-oriented FORTRAN approach.
Conformal invariance and Hojman conserved quantities of first order Lagrange systems
Institute of Scientific and Technical Information of China (English)
Chen Xiang-Wei; Liu Chang; Mei Feng-Xiang
2008-01-01
In this paper the conformal invaxiance by infinitesimal transformations of first order Lagrange systems is discussed in detail.The necessary and sufficient conditions of conformal invariance and Lie symmetry simultaneously by the action of infinitesimal transformations are given.Then it gets the Hojman conserved quantities of conformal invariance by the infinitesimal transformations.Finally an example is given to illustrate the application of the results.
Jet Riemann-Lagrange Geometry Applied to Evolution DEs Systems from Economy
Neagu, Mircea
2007-01-01
The aim of this paper is to construct a natural Riemann-Lagrange differential geometry on 1-jet spaces, in the sense of nonlinear connections, generalized Cartan connections, d-torsions, d-curvatures, jet electromagnetic fields and jet Yang-Mills energies, starting from some given non-linear evolution DEs systems modelling economic phenomena, like the Kaldor model of the bussines cycle or the Tobin-Benhabib-Miyao model regarding the role of money on economic growth.
Hojman conserved quantity deduced by weak Noether symmetry for Lagrange systems
Institute of Scientific and Technical Information of China (English)
Xie Jia-Fang; Gang Tie-Qiang; Mei Feng-Xiang
2008-01-01
This paper studies the Hojman conserved quantity,a non-Noether conserved quantity,deduced by special weak Noether symmetry for Lagrange systems.Under special infinitesimal transformations in which the time is not variable,its criterion is given and a method of how to seek the Hojman conserved quantity is presented.A Hojman conserved quantity can be found by using the special weak Noether symmetry.
On generalizations of the series of Taylor, Lagrange, Laurent and Teixeira
Directory of Open Access Journals (Sweden)
L. M. B. C. Campos
1990-01-01
Full Text Available The classical theorems of Taylor, Lagrange, Laurent and Teixeira, are extended from the representation of a complex function F(z, to its derivative F(ν(z of complex order ν, understood as either a Liouville (1832 or a Rieman (1847 differintegration (Campos 1984, 1985; these results are distinct from, and alternative to, other extensions of Taylor's series using differintegrations (Osler 1972, Lavoie & Osler & Tremblay 1976. We consider a complex function F(z, which is analytic (has an isolated singularity at ζ, and expand its derivative of complex order F(ν(z, in an ascending (ascending-descending series of powers of an auxiliary function f(z, yielding the generalized Teixeira (Lagrange series, which includes, for f(z=z−ζ, the generalized Taylor (Laurent series. The generalized series involve non-integral powers and/or coefficients evaluated by fractional derivatives or integrals, except in the case ν=0, when the classical theorems of Taylor (1715, Lagrange (1770, Laurent (1843 and Teixeira (1900 are regained. As an application, these generalized series can be used to generate special functions with complex parameters (Campos 1986, e.g., the Hermite and Bessel types.
An effective Euler-Lagrange model for suspended sediment transport by open channel flows
Institute of Scientific and Technical Information of China (English)
Huabin Shi; Xiping Yu n
2015-01-01
An Euler–Lagrange two-phase flow model is developed to study suspended sediment transport by open-channel flows with an Eddy Interaction Model (EIM) applied to consider the effect of fluid turbulence on sediment diffusion. For the continuous phase, the mean fluid velocity, the turbulent kinetic energy and its dissipation rate are directly estimated by well-established empirical formulas. For the dispersed phase, sediment particles are tracked by solving the equation of motion. The EIM is applied to compute the particle fluctuation velocity. Neglecting the effect of particles on flow turbulence as usually suggested for dilute cases in the literature, the Euler–Lagrange model is applied to simulate suspended sediment transport in open channels. Although the numerical results agree well with those by the well-known random walk particle tracking model (RWM) and with the laboratory data for fine sediment cases, it is clearly shown that such an Euler–Lagrange model underestimates the sediment concentration for the medium-sized and coarse sediment cases. To improve the model, a formula is proposed to consider the local fluid turbulence enhancement around a particle due to vortex shedding in the wake. Numerical results of the modified model then agree very well with laboratory data for not only the fine but also the coarse sediment cases.
Directory of Open Access Journals (Sweden)
M. Eshaghi Gordji
2011-01-01
Full Text Available We prove the generalized Hyers-Ulam-Rassias stability of a general system of Euler-Lagrange-type quadratic functional equations in non-Archimedean 2-normed spaces and Menger probabilistic non-Archimedean-normed spaces.
Haringa, Cees; Tang, Wenjun; Deshmukh, Amit T; Xia, Jianye; Reuss, Matthias; Heijnen, Joseph J; Mudde, Robert F; Noorman, Henk J
2016-10-01
The trajectories, referred to as lifelines, of individual microorganisms in an industrial scale fermentor under substrate limiting conditions were studied using an Euler-Lagrange computational fluid dynamics approach. The metabolic response to substrate concentration variations along these lifelines provides deep insight in the dynamic environment inside a large-scale fermentor, from the point of view of the microorganisms themselves. We present a novel methodology to evaluate this metabolic response, based on transitions between metabolic "regimes" that can provide a comprehensive statistical insight in the environmental fluctuations experienced by microorganisms inside an industrial bioreactor. These statistics provide the groundwork for the design of representative scale-down simulators, mimicking substrate variations experimentally. To focus on the methodology we use an industrial fermentation of Penicillium chrysogenum in a simplified representation, dealing with only glucose gradients, single-phase hydrodynamics, and assuming no limitation in oxygen supply, but reasonably capturing the relevant timescales. Nevertheless, the methodology provides useful insight in the relation between flow and component fluctuation timescales that are expected to hold in physically more thorough simulations. Microorganisms experience substrate fluctuations at timescales of seconds, in the order of magnitude of the global circulation time. Such rapid fluctuations should be replicated in truly industrially representative scale-down simulators.
Directory of Open Access Journals (Sweden)
Mahdi M. M. El-Arini
2013-01-01
Full Text Available In recent years, the solar energy has become one of the most important alternative sources of electric energy, so it is important to operate photovoltaic (PV panel at the optimal point to obtain the possible maximum efficiency. This paper presents a new optimization approach to maximize the electrical power of a PV panel. The technique which is based on objective function represents the output power of the PV panel and constraints, equality and inequality. First the dummy variables that have effect on the output power are classified into two categories: dependent and independent. The proposed approach is a multistage one as the genetic algorithm, GA, is used to obtain the best initial population at optimal solution and this initial population is fed to Lagrange multiplier algorithm (LM, then a comparison between the two algorithms, GA and LM, is performed. The proposed technique is applied to solar radiation measured at Helwan city at latitude 29.87°, Egypt. The results showed that the proposed technique is applicable.
Yang, Taiseung; Spilker, Robert L
2007-06-01
A three-dimensional (3D) contact finite element formulation has been developed for biological soft tissue-to-tissue contact analysis. The linear biphasic theory of Mow, Holmes, and Lai (1984, J. Biomech., 17(5), pp. 377-394) based on continuum mixture theory, is adopted to describe the hydrated soft tissue as a continuum of solid and fluid phases. Four contact continuity conditions derived for biphasic mixtures by Hou et al. (1989, ASME J. Biomech. Eng., 111(1), pp. 78-87) are introduced on the assumed contact surface, and a weighted residual method has been used to derive a mixed velocity-pressure finite element contact formulation. The Lagrange multiplier method is used to enforce two of the four contact continuity conditions, while the other two conditions are introduced directly into the weighted residual statement. Alternate formulations are possible, which differ in the choice of continuity conditions that are enforced with Lagrange multipliers. Primary attention is focused on a formulation that enforces the normal solid traction and relative fluid flow continuity conditions on the contact surface using Lagrange multipliers. An alternate approach, in which the multipliers enforce normal solid traction and pressure continuity conditions, is also discussed. The contact nonlinearity is treated with an iterative algorithm, where the assumed area is either extended or reduced based on the validity of the solution relative to contact conditions. The resulting first-order system of equations is solved in time using the generalized finite difference scheme. The formulation is validated by a series of increasingly complex canonical problems, including the confined and unconfined compression, the Hertz contact problem, and two biphasic indentation tests. As a clinical demonstration of the capability of the contact analysis, the gleno-humeral joint contact of human shoulders is analyzed using an idealized 3D geometry. In the joint, both glenoid and humeral head
Klotz, Justin R; Obuz, Serhat; Kan, Zhen; Dixon, Warren E
2017-02-07
A decentralized controller is designed for leader-based synchronization of communication-delayed networked agents. The agents have heterogeneous dynamics modeled by uncertain, nonlinear Euler-Lagrange equations of motion affected by heterogeneous, unknown, exogenous disturbances. The developed controller requires only one-hop (delayed) communication from network neighbors and the communication delays are assumed to be heterogeneous, uncertain, and time-varying. Each agent uses an estimate of communication delay to provide feedback of estimated recent tracking error. Simulation results are provided to demonstrate the improved performance of the developed controller over other popular control designs.
Algebraic equations an introduction to the theories of Lagrange and Galois
Dehn, Edgar
2004-01-01
Meticulous and complete, this presentation of Galois' theory of algebraic equations is geared toward upper-level undergraduate and graduate students. The theories of both Lagrange and Galois are developed in logical rather than historical form. And they are given a more thorough exposition than is customary. For this reason, and also because the author concentrates on concrete applications of algebraic theory, Algebraic Equations is an excellent supplementary text, offering students a concrete introduction to the abstract principles of Galois theory. Of further value are the many numerical ex
AN INEXACT LAGRANGE-NEWTON METHOD FOR STOCHASTIC QUADRATIC PROGRAMS WITH RECOURSE
Institute of Scientific and Technical Information of China (English)
ZhouChangyin; HeGuoping
2004-01-01
In this paper, two-stage stochastic quadratic programming problems with equality constraints are considered. By Monte Carlo simulation-based approximations of the objective function and its first (second)derivative,an inexact Lagrange-Newton type method is proposed.It is showed that this method is globally convergent with probability one. In particular, the convergence is local superlinear under an integral approximation error bound condition.Moreover, this method can be easily extended to solve stochastic quadratic programming problems with inequality constraints.
Guermond, Jean-Luc
2014-01-01
© 2014 Society for Industrial and Applied Mathematics. This paper proposes an explicit, (at least) second-order, maximum principle satisfying, Lagrange finite element method for solving nonlinear scalar conservation equations. The technique is based on a new viscous bilinear form introduced in Guermond and Nazarov [Comput. Methods Appl. Mech. Engrg., 272 (2014), pp. 198-213], a high-order entropy viscosity method, and the Boris-Book-Zalesak flux correction technique. The algorithm works for arbitrary meshes in any space dimension and for all Lipschitz fluxes. The formal second-order accuracy of the method and its convergence properties are tested on a series of linear and nonlinear benchmark problems.
Field theory and weak Euler-Lagrange equation for classical particle-field systems
Energy Technology Data Exchange (ETDEWEB)
Qin, Hong [PPPL; Burby, Joshua W [PPPL; Davidson, Ronald C [PPPL
2014-10-01
It is commonly believed that energy-momentum conservation is the result of space-time symmetry. However, for classical particle-field systems, e.g., Klimontovich-Maxwell and Klimontovich- Poisson systems, such a connection hasn't been formally established. The difficulty is due to the fact that particles and the electromagnetic fields reside on different manifolds. To establish the connection, the standard Euler-Lagrange equation needs to be generalized to a weak form. Using this technique, energy-momentum conservation laws that are difficult to find otherwise can be systematically derived.
The role of Lagrange multiplier in Gauss-Bonnet dark energy
Makarenko, Andrey N.
2016-04-01
We review accelerating cosmology in Gauss-Bonnet gravity with Lagrange multiplier constraint studied in [S. Capozziello, A. N. Makarenko and S. D. Odintsov, Phys. Rev. D 87 (2013) 084037, arXiv: 1302.0093 [gr-qc], S. Capozziello, M. Francaviglia and A. N. Makarenko, Astrophys. Space Sci. 349 (2014) 603-609, arXiv: 1304.5440 [gr-qc]. Several examples of dark energy universes are presented. We can get new dark energy solutions (with additional scalar) as well as certain limits to earlier found accelerating solutions.
An extension of the immersed boundary method based on the distributed Lagrange multiplier approach
Feldman, Yuri; Gulberg, Yosef
2016-10-01
An extended formulation of the immersed boundary method, which facilitates simulation of incompressible isothermal and natural convection flows around immersed bodies and which may be applied for linear stability analysis of the flows, is presented. The Lagrangian forces and heat sources are distributed on the fluid-structure interface. The method treats pressure, the Lagrangian forces, and heat sources as distributed Lagrange multipliers, thereby implicitly providing the kinematic constraints of no-slip and the corresponding thermal boundary conditions for immersed surfaces. Extensive verification of the developed method for both isothermal and natural convection 2D flows is provided. Strategies for adapting the developed approach to realistic 3D configurations are discussed.
A multi-mesh finite element method for Lagrange elements of arbitrary degree
Witkowski, Thomas
2010-01-01
We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviours of these variables, the meshes can be independently adapted. The resulting linear systems are usually much smaller, when compared to the usage of a single mesh, and the overall computational runtime can be more than halved in such cases. Our multi-mesh method works for Lagrange finite elements of arbitrary degree and is independent of the spatial dimension. The approach is well defined, and can be implemented in existing adaptive finite element codes with minimal effort. We show computational examples in 2D and 3D ranging from dendritic growth to solid-solid phase-transitions. A further application comes from fluid dynamics where we demonstrate the applicability of the approach for solving the incompressible Navier-Stokes equations with Lagrange finite elements of the same order for velocity and pressure. The...
Zhao, Quanyu; Kurata, Hiroyuki
2010-08-01
Elementary mode (EM) analysis is potentially effective in integrating transcriptome or proteome data into metabolic network analyses and in exploring the mechanism of how phenotypic or metabolic flux distribution is changed with respect to environmental and genetic perturbations. The EM coefficients (EMCs) indicate the quantitative contribution of their associated EMs and can be estimated by maximizing Shannon's entropy as a general objective function in our previous study, but the use of EMCs is still restricted to a relatively small-scale networks. We propose a fast and universal method that optimizes hundreds of thousands of EMCs under the constraint of the Maximum entropy principle (MEP). Lagrange multipliers (LMs) are applied to maximize the Shannon's entropy-based objective function, analytically solving each EMC as the function of LMs. Consequently, the number of such search variables, the EMC number, is dramatically reduced to the reaction number. To demonstrate the feasibility of the MEP with Lagrange multipliers (MEPLM), it is coupled with enzyme control flux (ECF) to predict the flux distributions of Escherichia coli and Saccharomycescerevisiae for different conditions (gene deletion, adaptive evolution, temperature, and dilution rate) and to provide a quantitative understanding of how metabolic or physiological states are changed in response to these genetic or environmental perturbations at the elementary mode level. It is shown that the ECF-based method is a feasible framework for the prediction of metabolic flux distribution by integrating enzyme activity data into EMs to genetic and environmental perturbations.
Chen, Gang; Song, Yongduan; Lewis, Frank L
2016-05-03
This paper investigates the distributed fault-tolerant control problem of networked Euler-Lagrange systems with actuator and communication link faults. An adaptive fault-tolerant cooperative control scheme is proposed to achieve the coordinated tracking control of networked uncertain Lagrange systems on a general directed communication topology, which contains a spanning tree with the root node being the active target system. The proposed algorithm is capable of compensating for the actuator bias fault, the partial loss of effectiveness actuation fault, the communication link fault, the model uncertainty, and the external disturbance simultaneously. The control scheme does not use any fault detection and isolation mechanism to detect, separate, and identify the actuator faults online, which largely reduces the online computation and expedites the responsiveness of the controller. To validate the effectiveness of the proposed method, a test-bed of multiple robot-arm cooperative control system is developed for real-time verification. Experiments on the networked robot-arms are conduced and the results confirm the benefits and the effectiveness of the proposed distributed fault-tolerant control algorithms.
De la representación de sistemas Euler - Lagrange a la Hamiltoniana generalizada
Directory of Open Access Journals (Sweden)
L. H. Rodríguez - Alfaro
2015-01-01
Full Text Available La representación Hamiltoniana generalizada de sistemas brinda una estructura que puede ser utilizada con ventaja en muchas áreas, entre las cuales se puede mencionar el diseño de observadores y el diagnóstico de fallas basado en modelos. Muchos de los trabajos en estos te mas tienen como punto de partida al sistema en forma Hamiltoniana generalizada y, en general, se omite la explicación de cómo llegar a esta representación, por ejemplo, a partir de un modelo no lineal basado en las ecuaciones de Euler - Lagrange. En este tra bajo se presenta un análisis detallado de cómo es que se obtiene la representación Hamiltoniana generalizada de un sistema a partir de las n ecuaciones diferenciales de segundo orden obtenidas con el formalismo Euler - Lagrange. Con la finalidad de mostrar e n lo particular, después del caso general, cómo se obtiene la representación Hamiltoniana generalizada, se presentan algunos casos de estudio.
Institute of Scientific and Technical Information of China (English)
ZHOU Yang,ZHENG Zhe; WU Siliang
2015-01-01
This paper presents a large-range, high-precision and continuously variable delay reconstruction method for wideband and arbitrary bandlimited signal, which combines dynamic index technique with complex-coefficient Lagrange interpolation technique. The method samples time-continuous bandlimited signal and stores samples in sequence. It manages to obtain the high-precision delay parameters of every sampling period from desired delay to compute the so-called index position variable and interpolator parameters. It dynamically in-dexes and chooses a set of samples to implement piecewise complex-coefficient Lagrange interpolation for reconstruct-ing the delayed sequences. The time-continuous delay re-construction signal can be simply accomplished through digital-to-analog conversion. The mathematical model of the method and its transformed form is given, and the arithmetic of dynamic index and complex-coefficient La-grange interpolation is derived. Simulation and test results show the validity and performance of the method.
Poenaru, D. N.; Plonski, I. H.; Greiner, W.
2007-04-01
Very general reflection asymmetrical saddle point nuclear shapes are obtained by solving an integro-differential equation without being necessary to specify a certain parametrization. This equation is derived as an Euler-Lagrange relationship associated to the variational problem of minimizing the potential energy with constraints (constant volume and given deformation parameter). The mass asymmetry in binary cold fission of Th and U isotopes is explained as the result of adding a phenomenological shell correction to the liquid drop model deformation energy. Applications to ternary fission are outlined.
A low diffusive Lagrange-remap scheme for the simulation of violent ai-water free-surface flows
Bernard-Champmartin, Aude; De Vuyst, Florian
2014-10-01
In 2002, Després and Lagoutière [17] proposed a low-diffusive advection scheme for pure transport equation problems, which is particularly accurate for step-shaped solutions, and thus suited for interface tracking procedure by a color function. This has been extended by Kokh and Lagoutière [28] in the context of compressible multifluid flows using a five-equation model. In this paper, we explore a simplified variant approach for gas-liquid three-equation models. The Eulerian numerical scheme has two ingredients: a robust remapped Lagrange solver for the solution of the volume-averaged equations, and a low diffusive compressive scheme for the advection of the gas mass fraction. Numerical experiments show the performance of the computational approach on various flow reference problems: dam break, sloshing of a tank filled with water, wate-water impact and finally a case of Rayleigh-Taylor instability. One of the advantages of the present interface capturing solver is its natural implementation on parallel processors or computers. wave formation and wave breaking; wall wave impacts, local pressure peaks and pressure loadings; formation of air pockets; ejection, fragmentation of liquid droplets; Archimedes buoyancy effect with rising of bubbles and fall of droplets; effects of gas compressibility inducing a gas-to-liquid response by a pressure wave, etc. In this paper, we consider immiscible gas-liquid two-phase flow problems. The strong ratio of mass density between gas and liquid (typically 1:1000) is known to be a source of numerical stiffness and numerical instability. Therefore robust computational approaches supporting high density ratio have to be considered. Among the family of conservative Finite Volume methods (FVM), the Lagrange-remapped solvers (see e.g. [42,45,6,4,25,2]) provide both robustness and stability with achievement of mathematical properties of positiveness and entropy compatibility.Lagrange-remap numerical schemes (also referred to as Eule-Lagrange
Chen, Liang-Ming; Lv, Yue-Yong; Li, Chuan-Jiang; Ma, Guang-Fu
2016-12-01
In this paper, we investigate cooperatively surrounding control (CSC) of multi-agent systems modeled by Euler-Lagrange (EL) equations under a directed graph. With the consideration of the uncertain dynamics in an EL system, a backstepping CSC algorithm combined with neural-networks is proposed first such that the agents can move cooperatively to surround the stationary target. Then, a command filtered backstepping CSC algorithm is further proposed to deal with the constraints on control input and the absence of neighbors’ velocity information. Numerical examples of eight satellites surrounding one space target illustrate the effectiveness of the theoretical results. Project supported by the National Basic Research Program of China (Grant No. 2012CB720000) and the National Natural Science Foundation of China (Grant Nos. 61304005 and 61403103).
Quantifying statistical uncertainties in ab initio nuclear physics using Lagrange multipliers
Carlsson, B D
2016-01-01
Theoretical predictions need quantified uncertainties for a meaningful comparison to experimental results. This is an idea which presently permeates the field of theoretical nuclear physics. In light of the recent progress in estimating theoretical uncertainties in ab initio nuclear physics, we here present and compare methods for evaluating the statistical part of the uncertainties. A special focus is put on the (for the field) novel method of Lagrange multipliers (LM). Uncertainties from the fit of the nuclear interaction to experimental data are propagated to a few observables in light-mass nuclei to highlight any differences between the presented methods. The main conclusion is that the LM method is more robust, while covariance based methods are less demanding in their evaluation.
Ma, Chao; Shi, Peng; Zhao, Xudong; Zeng, Qingshuang
2015-06-01
This paper investigates the consensus problem of multiple Euler-Lagrange systems under directed topology. Unlike the common assumptions on continuous-time information exchanges, a more realistic sampled-data communication strategy is proposed with probabilistic occurrence of time-varying delays. Both of the sampling period and the delays are assumed to be time-varying, which is more general in some practical situations. In addition, the relative coordinate derivative information is not required in the distributed controllers such that the communication network burden can be further reduced. In particular, a distinct feature of the proposed scheme lies in the fact that it can effectively reduce the energy consumption. By employing the stochastic analysis techniques, sufficient conditions are established to guarantee that the consensus can be achieved. Finally, a numerical example is provided to illustrate the applicability and benefits of the theoretical results.
How to Zoom: Bias, Contamination, and Lagrange Volumes in Multimass Cosmological Simulations
Onorbe, Jose; Maller, Ariyeh H; Bullock, James S; Rocha, Miguel; Hahn, Oliver
2013-01-01
We perform a suite of multimass cosmological zoom simulations of individual dark matter halos and explore how to best select Lagrangian regions for resimulation without contaminating the halo of interest with low-resolution particles. Such contamination can lead to significant errors in the gas distribution of hydrodynamical simulations, as we show. For a fixed Lagrange volume, we find that the chance of contamination increases systematically with the level of zoom. In order to avoid contamination, the Lagrangian volume selected for resimulation must increase monotonically with the resolution difference between parent box and the zoom region. We provide a simple formula for selecting Lagrangian regions (in units of the halo virial volume) as a function of the level of zoom required. We also explore the degree to which a halo's Lagrangian volume correlates with other halo properties (concentration, spin, formation time, shape, etc.) and find no significant correlation. There is a mild correlation between Lagra...
A Lagrange multiplier-based formulation to model sliding and rolling friction problems in ANSYS
Phadke, Rahul A.
Friction is a very complex phenomenon that occurs between bodies in contact. Friction and its effects have been studied by researchers for hundreds of years. Most mechanical systems look to reduce friction because it hampers system performance. However, friction is desired in certain important applications such as turbine blades, built-up structures and transportation systems. Dry friction is used in such cases as a damping or isolation technique. The inexpensive, environmentally robust nature of friction make it a popular choice as a passive damping technique. However, due to its inherently complex nature, friction modeling presents considerable challenges to designers. This dissertation presents a Lagrange multiplier-based approach called the Microslip Superelement (MSE) approach to model partial slip at the interface. The formulation has been implemented in the ANSYS framework and studies sliding and rolling contact problems. A particular application to turbine blade clamping is presented and comparisons are made with experimental benchmark data.
Adaptive Synchronization of Networked Euler-Lagrange Systems with Directed Switching Top ology
Institute of Scientific and Technical Information of China (English)
GUO Hai-Bo; LI Hua-Yi; ZHONG Wei-Chao; ZHANG Shi-Jie; CAO Xi-Bin
2014-01-01
In this paper, the cooperative control problem of networked Euler-Lagrange systems with parametric uncertainties and unidirectional interaction is addressed under dynamically changing topology. As the communication graph evolves over time, a distributed control law via local effective interactions is designed. Adaptive techniques are used to deal with parametric uncertainties in the dynamics. With a continuous Lyapunov function, it is obtained that synchronization can still be achieved asymptotically as long as the union graph of the switching topologies has a directed spanning tree frequently enough. Extensions to disturbance rejection problems are also addressed using simple disturbance-observer or sliding mode control scheme. Illustrative examples with comparing simulation in the context of attitude synchronization of five non-identical spacecraft are further presented to show the effectiveness of the proposed cooperative control strategy.
The two faces of mimetic Horndeski gravity: disformal transformations and Lagrange multiplier
Arroja, Frederico; Karmakar, Purnendu; Matarrese, Sabino
2015-01-01
We show that very general scalar-tensor theories of gravity (including, e.g., Horndeski models) are generically invariant under disformal transformations. However there is a special subset, when the transformation is not invertible, that yields new equations of motion which are a generalization of the so-called "mimetic" dark matter theory recently introduced by Chamsedinne and Mukhanov. These new equations of motion can also be derived from an action containing an additional Lagrange multiplier field. The general mimetic scalar-tensor theory has the same number of derivatives in the equations of motion as the original scalar-tensor theory. As an application we show that the simplest mimetic scalar-tensor model is able to mimic the cosmological background of a flat FLRW model with an irrotational barotropic perfect fluid with any constant equation of state.
Coordination Control of Networked Euler-Lagrange Systems with Possible Switching Topology
Institute of Scientific and Technical Information of China (English)
MINHai-Bo; LIUZhi-Guo; LIUYuan; WANGShi-Cheng; YANGYan-Li
2013-01-01
This paper studies adaptive coordination control of Euler-Lagrange (EL) systems with unknown parameters in system dynamics and possible switching topology.By introducing a novel adaptive control architecture,decentralized controllers are developed,which allow for parametric uncertainties.Based upon graph theory,Lyapunov theory and switching control theory,the stability of the proposed algorithms are demonstrated.A distinctive feature of this work is to address the coordination control of EL systems with unknown parameters and switching topology in a unified theoretical framework.It is shown that both static and dynamic coordinations can be reached even when the communication is switching.Simulation results are provided to demonstrate the effectiveness of the obtained results.
Robust Observer Based Disturbance Rejection Control for Euler-Lagrange Systems
Directory of Open Access Journals (Sweden)
Yanjun Zhang
2016-01-01
Full Text Available Robust disturbance rejection control methodology is proposed for Euler-Lagrange systems, and parameters optimization strategy for the observer is explored. First, the observer based disturbance rejection methodology is analyzed, based on which the disturbance rejection paradigm is proposed. Thus, a disturbance observer (DOB with partial feedback linearization and a low-pass filter is proposed for nonlinear dynamic model under relaxed restrictions of the generalized disturbance. Then, the outer-loop backstepping controller is designed for desired tracking performance. Considering that the parameters of DOB cannot be obtained directly based on Lyapunov stability analysis, parameter of DOB is optimized under standard H∞ control framework. By analyzing the influence of outer-loop controller on the inner-loop observer parameter, robust stability constraint is proposed to guarantee the robust stability of the closed-loop system. Experiment on attitude tracking of an aircraft is carried out to show the effectiveness of the proposed control strategy.
A stabilized explicit Lagrange multiplier based domain decomposition method for parabolic problems
Zheng, Zheming; Simeon, Bernd; Petzold, Linda
2008-05-01
A fully explicit, stabilized domain decomposition method for solving moderately stiff parabolic partial differential equations (PDEs) is presented. Writing the semi-discretized equations as a differential-algebraic equation (DAE) system where the interface continuity constraints between subdomains are enforced by Lagrange multipliers, the method uses the Runge-Kutta-Chebyshev projection scheme to integrate the DAE explicitly and to enforce the constraints by a projection. With mass lumping techniques and node-to-node matching grids, the method is fully explicit without solving any linear system. A stability analysis is presented to show the extended stability property of the method. The method is straightforward to implement and to parallelize. Numerical results demonstrate that it has excellent performance.
Si, Weijian; Qu, Xinggen; Liu, Lutao
2014-01-01
A novel direction of arrival (DOA) estimation method in compressed sensing (CS) is presented, in which DOA estimation is considered as the joint sparse recovery from multiple measurement vectors (MMV). The proposed method is obtained by minimizing the modified-based covariance matching criterion, which is acquired by adding penalties according to the regularization method. This minimization problem is shown to be a semidefinite program (SDP) and transformed into a constrained quadratic programming problem for reducing computational complexity which can be solved by the augmented Lagrange method. The proposed method can significantly improve the performance especially in the scenarios with low signal to noise ratio (SNR), small number of snapshots, and closely spaced correlated sources. In addition, the Cramér-Rao bound (CRB) of the proposed method is developed and the performance guarantee is given according to a version of the restricted isometry property (RIP). The effectiveness and satisfactory performance of the proposed method are illustrated by simulation results.
Distributed tracking for networked Euler-Lagrange systems without velocity measurements
Institute of Scientific and Technical Information of China (English)
Qingkai Yang; Hao Fang; Yutian Mao; Jie Huang
2014-01-01
The problem of distributed coordinated tracking control for networked Euler-Lagrange systems without velocity measure-ments is investigated. Under the condition that only a portion of the fol owers have access to the leader, sliding mode estimators are developed to estimate the states of the dynamic leader in fi-nite time. To cope with the absence of velocity measurements, the distributed observers which only use position information are designed. Based on the outputs of the estimators and observers, distributed tracking control laws are proposed such that al the fol-lowers with parameter uncertainties can track the dynamic leader under a directed graph containing a spanning tree. It is shown that the distributed observer-control er guarantees asymptotical stabil-ity of the closed-loop system. Numerical simulations are worked out to il ustrate the effectiveness of the control laws.
On a Lagrange-Hamilton formalism describing position and momentum uncertainties
Schuch, Dieter
1993-01-01
According to Heisenberg's uncertainty relation, in quantum mechanics it is not possible to determine, simultaneously, exact values for the position and the momentum of a material system. Calculating the mean value of the Hamiltonian operator with the aid of exact analytic Gaussian wave packet solutions, these uncertainties cause an energy contribution additional to the classical energy of the system. For the harmonic oscillator, e.g., this nonclassical energy represents the ground state energy. It will be shown that this additional energy contribution can be considered as a Hamiltonian function, if it is written in appropriate variables. With the help of the usual Lagrange-Hamilton formalism known from classical particle mechanics, but now considering this new Hamiltonian function, it is possible to obtain the equations of motion for position and momentum uncertainties.
Euler-Lagrange models with complex currents of three-phase electrical machines
Basic, Duro; Rouchon, Pierre
2008-01-01
A Lagrangian formulation with complex currents is developed and yields a direct and simple method for modeling three-phases permanent-magnet and induction machines. The Lagrangian is the sum of the mechanical kinetic energy and of the magnetic energy. This magnetic energy is expressed in terms of rotor angle, complex stator and rotor currents. Such Lagrangian setting is a precious guide for modeling space-harmonics and saturation effects. A complexification procedure is applied here in order to derive the Euler-Lagrange equations with complex stator and rotor currents. Such complexification process avoids the usual separation into real and imaginary parts and simplifies notably the calculations. Via simple modification of magnetic energies we derive non-trivial dynamical models describing permanent-magnet machines with both saturation and saliency, and induction machines with both saturation and space harmonics.
Critical Point Theory for Lagrangian Systems
Mazzucchelli, Marco
2012-01-01
Lagrangian systems constitute a very important and old class in dynamics. Their origin dates back to the end of the eighteenth century, with Joseph-Louis Lagrange's reformulation of classical mechanics. The main feature of Lagrangian dynamics is its variational flavor: orbits are extremal points of an action functional. The development of critical point theory in the twentieth century provided a powerful machinery to investigate existence and multiplicity questions for orbits of Lagrangian systems. This monograph gives a modern account of the application of critical point theory, and more spec
A second order anti-diffusive Lagrange-remap scheme for two-component flows
Directory of Open Access Journals (Sweden)
Lagoutière Frédéric
2011-11-01
Full Text Available We build a non-dissipative second order algorithm for the approximate resolution of the one-dimensional Euler system of compressible gas dynamics with two components. The considered model was proposed in [1]. The algorithm is based on [8] which deals with a non-dissipative first order resolution in Lagrange-remap formalism. In the present paper we describe, in the same framework, an algorithm that is second order accurate in time and space, and that preserves sharp interfaces. Numerical results reported at the end of the paper are very encouraging, showing the interest of the second order accuracy for genuinely non-linear waves. Nous construisons un algorithme d’ordre deux et non dissipatif pour la résolution approchée des équations d’Euler de la dynamique des gaz compressibles à deux constituants en dimension un. Le modèle que nous considérons est celui à cinq équations proposé et analysé dans [1]. L’algorithme est basé sur [8] qui proposait une résolution approchée à l’ordre un et non dissipative au moyen d’un splitting de type Lagrange-projection. Dans le présent article, nous décrivons, dans le même formalisme, un algorithme d’ordre deux en temps et en espace, qui préserve des interfaces « parfaites » entre les constituants. Les résultats numériques rapportés à la fin de l’article sont très encourageants ; ils montrent clairement les avantages d’un schéma d’ordre deux pour les ondes vraiment non linéaires.
Drag reduction in numerical two-phase Taylor–Couette turbulence using an Euler–Lagrange approach
Arza, Vamsi Spandan; Ostilla-Monico, Rodolfo; Verzicco, Roberto; Lohse, Detlef
2016-01-01
Two-phase turbulent Taylor–Couette (TC) flow is simulated using an Euler–Lagrange approach to study the effects of a secondary phase dispersed into a turbulent carrier phase (here bubbles dispersed into water). The dynamics of the carrier phase is computed using direct numerical simulations (DNS) in
Directory of Open Access Journals (Sweden)
Cheng Xu
2015-01-01
Full Text Available In this manuscript, the local fractional arbitrary Euler-Lagrange formula are utilized to address the diffusion model of fractal heat and mass transfer in a fluidized bed based on the Fick's law with local fractional vector calculus. This article has been corrected. Link to the correction 10.2298/TSCI150923149E
Sun-earth environment study to understand earthquake prediction
Mukherjee, S.
2007-05-01
Earthquake prediction is possible by looking into the location of active sunspots before it harbours energy towards earth. Earth is a restless planet the restlessness turns deadly occasionally. Of all natural hazards, earthquakes are the most feared. For centuries scientists working in seismically active regions have noted premonitory signals. Changes in thermosphere, Ionosphere, atmosphere and hydrosphere are noted before the changes in geosphere. The historical records talk of changes of the water level in wells, of strange weather, of ground-hugging fog, of unusual behaviour of animals (due to change in magnetic field of the earth) that seem to feel the approach of a major earthquake. With the advent of modern science and technology the understanding of these pre-earthquake signals has become stronger enough to develop a methodology of earthquake prediction. A correlation of earth directed coronal mass ejection (CME) from the active sunspots has been possible to develop as a precursor of the earthquake. Occasional local magnetic field and planetary indices (Kp values) changes in the lower atmosphere that is accompanied by the formation of haze and a reduction of moisture in the air. Large patches, often tens to hundreds of thousands of square kilometres in size, seen in night-time infrared satellite images where the land surface temperature seems to fluctuate rapidly. Perturbations in the ionosphere at 90 - 120 km altitude have been observed before the occurrence of earthquakes. These changes affect the transmission of radio waves and a radio black out has been observed due to CME. Another heliophysical parameter Electron flux (Eflux) has been monitored before the occurrence of the earthquakes. More than hundreds of case studies show that before the occurrence of the earthquakes the atmospheric temperature increases and suddenly drops before the occurrence of the earthquakes. These changes are being monitored by using Sun Observatory Heliospheric observatory (SOHO) satellite data. Whatever the manifestations in the environment of the atmosphere or geosphere may be, there is a positive correlation of CMEs with change in magnetic field followed by aurora borealis or sudden spark of light from the sky before an earthquake. Any change in geomorphology in the pixel level, changes in groundwater level, geochemical anomalies of soils surrounding active faults and vegetation anomalies should be monitored in the mirror image position of sunspots on the earth facing side in reference to CME from the sun.
The Maunder minimum and the variable sun-earth connection
Wei Hock Soon, Willie
2003-01-01
This book takes an excursion through solar science, science history, and geoclimate with a husband and wife team who revealed some of our sun's most stubborn secrets. E Walter and Annie S D Maunder's work helped in understanding our sun's chemical, electromagnetic and plasma properties. They knew the sun's sunspot migration patterns and its variable, climate-affecting, inactive and active states in short and long time frames. An inactive solar period starting in the mid-seventeenth century lasted approximately seventy years, one that E Walter Maunder worked hard to make us understand: the Maun
CarbonTracker-Lagrange: A model-data assimilation system for North American carbon flux estimates
He, Wei; Chen, Huilin; van der Velde, Ivar; Andrews, Arlyn; Sweeney, Colm; Baker, Ian; Ju, Weimin; van der Laan-Luijkx, Ingrid; Tans, Pieter; Peters, Wouter
2016-04-01
, and then compared this result with similar recent inversion results. Our results suggest that: (1) The CarbonTracker-Lagrange system involving BC optimization makes mole fraction simulations more consistent with observations over all available sites, especially better fitting the aircraft sites; (2) This system is mostly insensitive to the choice of prior lateral BC products; (3) Our new Lagrangian inverse system (without continuous in-situ data) places the North American Carbon sink for the year 2010 at -0.43 to -0.69 PgC/yr, comparable to the TM5 based estimates of CarbonTracker North America (-0.41 PgC/yr) and CarbonTracker Europe (-0.62 PgC/yr). We conclude that CarbonTracker-Lagrange is a viable, credible, and efficient new tool to understand regional carbon fluxes from an atmospheric perspective.
WEIGHTED LEAST SQUARE CONVERGENCE OF LAGRANGE INTERPOLATION ON THE UNIT CIRCLE
Institute of Scientific and Technical Information of China (English)
Xie Siqing
2001-01-01
In the paper, a result of Walsh and Sharma on least squareconvergence of Lagrange interpolation polynomials based on the n-th roots of unity is extended to Lagrange interpolation on the sets obtained by pro-jecting vertically the zeros of (1-x)2P.β (x),α＞0,β＞0, (1-x)p β (x),α＞0,β＞-1, (1+x)p ,(x) ,α＞-1 ,β＞0, and P (x ) ,α＞ - 1 ,β＞ - 1, respectively, onto the unit circle, where p ( ,β) (x ) ,α＞ - 1 , β＞ - 1, stands for the n-th Jacobi polynomial. Moreover, a result of Saff and Walsh is also extended.CLC Number：O17 Document ID：AFoundation Item：Project supported by NSFC under grant 10071039, and by Education Committee of Jiangsu Province under grant 00KJB110005.References：[1]Walsh,J.L. and Sharma,A.,Least Square Approximation and Interpolation in Roots of Unity,Pacific J. Math. ,14(1964),727-730.[2]Erdos,P. and Turán,P. ,On Interpolation I ,Ann. Math. ,38(1937),142-155.[3]Lozinsi,S.M.,Uber Interpolation (in Russian),Math. Sbornik (N.S.),8(1940),57-68.[4]Saff,E.B. and Walsh,J.L. ,On the Convergence of Rational Functions which Interpolate in the Roots of Unity,Pacific J. Math. 45(1973),639-641.[5]Sharma,A. and Vertesi,P. ,Mean Convergence and Interpolation in Roots of Unity,SIAM J.Math. Anal. ,14(1983),800-806.[6]Natason,I.P. ,Constructive Theory of Functions,Gostekhizdat,Moscow,1949.[7]Szego,G. ,Orthogoral Polynomials,Math. Soc. Colloq. Publ. ,Vol.[2]3 4th ed. Math. Soc. ,Providence,RI. ,1975.Manuscript Received：1999年9月13日Manuscript Revised：2001年5月8日Published：2001年9月1日
Numerical simulations of two-phase Taylor-Couette turbulence using an Euler-Lagrange approach
Spandan, Vamsi; Verzicco, Roberto; Lohse, Detlef
2015-01-01
Two-phase turbulent Taylor-Couette (TC) flow is simulated using an Euler-Lagrange approach to study the effects of a secondary phase dispersed into a turbulent carrier phase (here bubbles dispersed into water). The dynamics of the carrier phase is computed using Direct Numerical Simulations (DNS) in an Eulerian framework, while the bubbles are tracked in a Lagrangian manner by modelling the effective drag, lift, added mass and buoyancy force acting on them. Two-way coupling is implemented between the dispersed phase and the carrier phase which allows for momentum exchange among both phases and to study the effect of the dispersed phase on the carrier phase dynamics. The radius ratio of the TC setup is fixed to $\\eta=0.833$, and a maximum inner cylinder Reynolds number of $Re_i=8000$ is reached. We vary the Froude number ($Fr$), which is the ratio of the centripetal to the gravitational acceleration of the dispersed phase and study its effect on the net torque required to drive the TC system. In a two-phase TC...
An Euler-Lagrange method considering bubble radial dynamics for modeling sonochemical reactors.
Jamshidi, Rashid; Brenner, Gunther
2014-01-01
Unsteady numerical computations are performed to investigate the flow field, wave propagation and the structure of bubbles in sonochemical reactors. The turbulent flow field is simulated using a two-equation Reynolds-Averaged Navier-Stokes (RANS) model. The distribution of the acoustic pressure is solved based on the Helmholtz equation using a finite volume method (FVM). The radial dynamics of a single bubble are considered by applying the Keller-Miksis equation to consider the compressibility of the liquid to the first order of acoustical Mach number. To investigate the structure of bubbles, a one-way coupling Euler-Lagrange approach is used to simulate the bulk medium and the bubbles as the dispersed phase. Drag, gravity, buoyancy, added mass, volume change and first Bjerknes forces are considered and their orders of magnitude are compared. To verify the implemented numerical algorithms, results for one- and two-dimensional simplified test cases are compared with analytical solutions. The results show good agreement with experimental results for the relationship between the acoustic pressure amplitude and the volume fraction of the bubbles. The two-dimensional axi-symmetric results are in good agreement with experimentally observed structure of bubbles close to sonotrode.
Fan, Peifeng; Liu, Jian; Xiang, Nong; Yu, Zhi
2016-01-01
A manifestly covariant, or geometric, field theory for relativistic classical particle-field system is developed. The connection between space-time symmetry and energy-momentum conservation laws for the system is established geometrically without splitting the space and time coordinates, i.e., space-time is treated as one identity without choosing a coordinate system. To achieve this goal, we need to overcome two difficulties. The first difficulty arises from the fact that particles and field reside on different manifold. As a result, the geometric Lagrangian density of the system is a function of the 4-potential of electromagnetic fields and also a functional of particles' world-lines. The other difficulty associated with the geometric setting is due to the mass-shell condition. The standard Euler-Lagrange (EL) equation for a particle is generalized into the geometric EL equation when the mass-shell condition is imposed. For the particle-field system, the geometric EL equation is further generalized into a w...
Directory of Open Access Journals (Sweden)
Weijian Si
2014-01-01
Full Text Available A novel direction of arrival (DOA estimation method in compressed sensing (CS is presented, in which DOA estimation is considered as the joint sparse recovery from multiple measurement vectors (MMV. The proposed method is obtained by minimizing the modified-based covariance matching criterion, which is acquired by adding penalties according to the regularization method. This minimization problem is shown to be a semidefinite program (SDP and transformed into a constrained quadratic programming problem for reducing computational complexity which can be solved by the augmented Lagrange method. The proposed method can significantly improve the performance especially in the scenarios with low signal to noise ratio (SNR, small number of snapshots, and closely spaced correlated sources. In addition, the Cramér-Rao bound (CRB of the proposed method is developed and the performance guarantee is given according to a version of the restricted isometry property (RIP. The effectiveness and satisfactory performance of the proposed method are illustrated by simulation results.
Optimal control of two coupled spinning particles in the Euler-Lagrange picture
Delgado-Téllez, M.; Ibort, A.; Rodríguez de la Peña, T.; Salmoni, R.
2016-01-01
A family of optimal control problems for a single and two coupled spinning particles in the Euler-Lagrange formalism is discussed. A characteristic of such problems is that the equations controlling the system are implicit and a reduction procedure to deal with them must be carried out. The reduction of the implicit control equations arising in these problems will be discussed in the slightly more general setting of implicit equations defined by invariant one-forms on Lie groups. As an example the first order differential equations describing the extremal solutions of an optimal control problem for a single spinning particle, obtained by using Pontryagin’s Maximum Principle (PMP), will be found and shown to be completely integrable. Then, again using PMP, solutions for the problem of two coupled spinning particles will be characterized as solutions of a system of coupled non-linear matrix differential equations. The reduction of the implicit system will show that the reduced space for them is the product of the space of states for the independent systems, implying the absence of ‘entanglement’ in this instance. Finally, it will be shown that, in the case of identical systems, the degree three matrix polynomial differential equations determined by the optimal feedback law, constitute a completely integrable Hamiltonian system and some of its solutions are described explicitly.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
This paper, with a finite element method, studies the interaction of a coupled incompressible fluid-rigid structure system with a free surface subjected to external wave excitations. With this fully coupled model, the rigid structure is taken as "fictitious" fluid with zero strain rate. Both fluid and structure are described by velocity and pressure. The whole domain, including fluid region and structure region, is modeled by the incompressible Navier-Stokes equations which are discretized with fixed Eulerian mesh. However, to keep the structure's rigid body shape and behavior, a rigid body constraint is enforced on the "fictitious" fluid domain by use of the Distributed Lagrange Multiplier/Fictitious Domain (DLM/FD) method which is originally introduced to solve particulate flow problems by Glowinski et al. For the verification of the model presented herein, a 2D numerical wave tank is established to simulate small amplitude wave propagations, and then numerical results are compared with analytical solutions. Finally, a 2D example of fluid-structure interaction under wave dynamic forces provides convincing evidences for the method excellent solution quality and fidelity.
The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices
Lin, Zhouchen; Wu, Leqin; Ma, Yi
2010-01-01
This paper proposes scalable and fast algorithms for solving the Robust PCA problem, namely recovering a low-rank matrix with an unknown fraction of its entries being arbitrarily corrupted. This problem arises in many applications, such as image processing, web data ranking, and bioinformatic data analysis. It was recently shown that under surprisingly broad conditions, the Robust PCA problem can be exactly solved via convex optimization that minimizes a combination of the nuclear norm and the $\\ell^1$-norm . In this paper, we apply the method of augmented Lagrange multipliers (ALM) to solve this convex program. As the objective function is non-smooth, we show how to extend the classical analysis of ALM to such new objective functions and prove the optimality of the proposed algorithms and characterize their convergence rate. Empirically, the proposed new algorithms can be more than five times faster than the previous state-of-the-art algorithms for Robust PCA, such as the accelerated proximal gradient (APG) ...
Ahrens, Cory D
2014-01-01
The classical $S_n$ equations of Carlson and Lee have been a mainstay in multi-dimensional radiation transport calculations. In this paper, an alternative to the $S_n$ equations, the "Lagrange Discrete Ordinate" (LDO) equations are derived. These equations are based on an interpolatory framework for functions on the unit sphere in three dimensions. While the LDO equations retain the formal structure of the classical $S_n$ equations, they have a number of important differences. The LDO equations naturally allow the angular flux to be evaluated in directions other than those found in the quadrature set. To calculate the scattering source in the LDO equations, no spherical harmonic moments are needed--only values of the angular flux. Moreover, the LDO scattering source preserves the eigenstructure of the continuous scattering operator. The formal similarity of the LDO equations with the $S_n$ equations should allow easy modification of mature 3D $S_n$ codes such as PARTISN or PENTRAN to solve the LDO equations. ...
Extrasolar planetary dynamics with a generalized planar Laplace-Lagrange secular theory
Veras, D; Veras, Dimitri; Armitage, Philip J.
2007-01-01
The dynamical evolution of nearly half of the known extrasolar planets in multiple-planet systems may be dominated by secular perturbations. The commonly high eccentricities of the planetary orbits calls into question the utility of the traditional Laplace-Lagrange (LL) secular theory in analyses of the motion. We analytically generalize this theory to fourth-order in the eccentricities, compare the result with the second-order theory and octupole-level theory, and apply these theories to the likely secularly-dominated HD 12661, HD 168443, HD 38529 and Ups And multi-planet systems. The fourth-order scheme yields a multiply-branched criterion for maintaining apsidal libration, and implies that the apsidal rate of a small body is a function of its initial eccentricity, dependencies which are absent from the traditional theory. Numerical results indicate that the primary difference the second and fourth-order theories reveal is an alteration in secular periodicities, and to a smaller extent amplitudes of the pla...
Predicting the safe load on backpacker's arm using Lagrange multipliers method
Abdalla, Faisal Saleh; Rambely, Azmin Sham
2014-09-01
In this study, a technique has been suggested to reduce a backpack load by transmitting determined loads to the children arm. The purpose of this paper is to estimate school children arm muscles while load carriage as well as to determine the safe load can be carried at wrist while walking with backpack. A mathematical model, as three DOFs model, was investigated in the sagittal plane and Lagrange multipliers method (LMM) was utilized to minimize a quadratic objective function of muscle forces. The muscle forces were minimized with three different load conditions which are termed as 0-L=0 N, 1-L=21.95 N, and 2-L=43.9 N. The investigated muscles were estimated and compared to their maximum forces throughout the load conditions. Flexor and extensor muscles were estimated and the results showed that flexor muscles were active while extensor muscles showed inactivity. The estimated muscle forces were didn't exceed their maximum forces with 0-L and 1-L conditions whereas biceps and FCR muscles exceeded their maximum forces with 2-L condition. Consequently, 1-L condition is quiet safe to be carried by hand whereas 2-L condition is not. Thus to reduce the load in the backpack the transmitted load shouldn't exceed 1-L condition.
Directory of Open Access Journals (Sweden)
B. Kuldeep
2015-06-01
Full Text Available Fractional calculus has recently been identified as a very important mathematical tool in the field of signal processing. Digital filters designed by fractional derivatives give more accurate frequency response in the prescribed frequency region. Digital filters are most important part of multi-rate filter bank systems. In this paper, an improved method based on fractional derivative constraints is presented for the design of two-channel quadrature mirror filter (QMF bank. The design problem is formulated as minimization of L2 error of filter bank transfer function in passband, stopband interval and at quadrature frequency, and then Lagrange multiplier method with fractional derivative constraints is applied to solve it. The proposed method is then successfully applied for the design of two-channel QMF bank with higher order filter taps. Performance of the QMF bank design is then examined through study of various parameters such as passband error, stopband error, transition band error, peak reconstruction error (PRE, stopband attenuation (As. It is found that, the good design can be obtained with the change of number and value of fractional derivative constraint coefficients.
Institute of Scientific and Technical Information of China (English)
JIAErhui; LINQun
2002-01-01
In this paper which is motivated by computation on parallel machine,we show that the superconvergence results of the finite element method(FEM) with Lagrange multipliers based on domain decomposition method(DDM) with nonmatching grids can be carried over to parabolic problems.The main idea of this paper is to achieve the combination of parallel computational method with the higher accuracy technique by interpolation finite element postprocessing.
Institute of Scientific and Technical Information of China (English)
JIA Erhui; LIN Qun
2002-01-01
In this paper which is motivated by computation on parallel machine, we show that the superconvergence results of the finite element method(FEM) with Lagrange mul-tipliers based on domain decomposition method (DDM) with nonmatching grids can be carried over to parabolic problems. The main idea of this paper is to achieve the combina-tion of parallel computational method with the higher accuracy technique by interpolation finite element postprocessing.
Sun, Yuxin; Xiong, Zhenhua
2017-01-01
In turning processes, chatter is an unstable vibration which adversely affects surface finish and machine tool components. Stiffness variation (SV) is an effective strategy for chatter suppression by periodically modulating the stiffness around a nominal value. The dynamics of SV turning is governed by a time periodic delay differential equation (DDE) where the time-period/time-delay ratio (TPTDR) can be arbitrary. Recently, first-, second- and higher-order full-discretization methods (FDMs) have been reported as a popular class of methods for milling stability prediction. However, these FDMs can only deal with time periodic DDE where the TPTDR equals one. In this paper, two high-order FDMs using Lagrange interpolation (HLFDMs) are proposed for stability analysis of SV turning. On each discrete time interval, the time delay term is interpolated by the second-degree Lagrange polynomial, and the time periodic term is linearly interpolated. The state term is approximated using linear interpolation and second-degree Lagrange polynomial interpolation, achieving the first- and second-order HLFDM, respectively. Finally, the transition matrix over a single period is deduced for stability analysis via the Floquet theory. Benchmark examples of damped delay Mathieu equations are used to verify the proposed algorithm, which demonstrates that HLFDMs are highly efficient and accurate. In addition, the second-order HLFDM is used to investigate the effects of SV amplitude and frequency parameters. These results provide theoretical insights for the selection of SV parameters.
Institute of Scientific and Technical Information of China (English)
GUO HanYing; LI YuQi; WU Ke; WANG ShiKun
2002-01-01
In the previous papers I and H, we have studied the difference discrete variational principle and the EulerLagrange cohomology in the framework of multi-parameter differential approach. W5 have gotten the difference discreteEulcr-Lagrangc equations and canonical ones for the difference discrete versions of classical mechanics and tield theoryas well as the difference discrete versions for the Euler-Lagrange cohomology and applied them to get the necessaryand sufficient condition for the symplectic or multisymplectic geometry preserving properties in both the Lagrangianand Hamiltonian formalisms. In this paper, we apply the difference discrete variational principle and Euler-Lagrangecohomological approach directly to the symplectic and multisymplectic algorithms. We will show that either Hamiltonianschemes or Lagrangian ones in both the symplectic and multisymplectic algorithms arc variational integrators and theirdifference discrete symplectic structure-preserving properties can always be established not only in the solution spacebut also in the function space if and only if the related closed Euler Lagrange cohomological conditions are satisfied.
三种耦合 RLC 电路的 Lagrange 函数和 Hamilton 函数%LAGRANGIANS AND HAMILTONIANS OF THREE COUPLED RLC CIRCUITS
Institute of Scientific and Technical Information of China (English)
丁光涛
2014-01-01
利用 Lagrange 力学逆问题理论和方法，构造电感、电容和电阻三种耦合 RLC 电路的 Lagrange 函数和Hamilton 函数。%The Lagrangians and the Hamiltonians of inductively coupled RLC circuit,capacitive coupling RLC circuit and resistance coupled RLC circuit were constructed by using theory and methods of inverse problem of La-grangian mechanics.
Directory of Open Access Journals (Sweden)
Debra Lewis
2013-05-01
Full Text Available Relative equilibria of Lagrangian and Hamiltonian systems with symmetry are critical points of appropriate scalar functions parametrized by the Lie algebra (or its dual of the symmetry group. Setting aside the structures – symplectic, Poisson, or variational – generating dynamical systems from such functions highlights the common features of their construction and analysis, and supports the construction of analogous functions in non-Hamiltonian settings. If the symmetry group is nonabelian, the functions are invariant only with respect to the isotropy subgroup of the given parameter value. Replacing the parametrized family of functions with a single function on the product manifold and extending the action using the (coadjoint action on the algebra or its dual yields a fully invariant function. An invariant map can be used to reverse the usual perspective: rather than selecting a parametrized family of functions and finding their critical points, conditions under which functions will be critical on specific orbits, typically distinguished by isotropy class, can be derived. This strategy is illustrated using several well-known mechanical systems – the Lagrange top, the double spherical pendulum, the free rigid body, and the Riemann ellipsoids – and generalizations of these systems.
Lewis, Debra
2013-05-01
Relative equilibria of Lagrangian and Hamiltonian systems with symmetry are critical points of appropriate scalar functions parametrized by the Lie algebra (or its dual) of the symmetry group. Setting aside the structures - symplectic, Poisson, or variational - generating dynamical systems from such functions highlights the common features of their construction and analysis, and supports the construction of analogous functions in non-Hamiltonian settings. If the symmetry group is nonabelian, the functions are invariant only with respect to the isotropy subgroup of the given parameter value. Replacing the parametrized family of functions with a single function on the product manifold and extending the action using the (co)adjoint action on the algebra or its dual yields a fully invariant function. An invariant map can be used to reverse the usual perspective: rather than selecting a parametrized family of functions and finding their critical points, conditions under which functions will be critical on specific orbits, typically distinguished by isotropy class, can be derived. This strategy is illustrated using several well-known mechanical systems - the Lagrange top, the double spherical pendulum, the free rigid body, and the Riemann ellipsoids - and generalizations of these systems.
Institute of Scientific and Technical Information of China (English)
邹乐; 李昌文
2011-01-01
In this paper, the Lagrange interpolation polynomial in power exponent form is improved and two new interpolation polynomials in power exponent form are derived, I. E. a modified Lagrange form and a barycentric Lagrange form. The advantages of the barycentric Lagrange form lie in its less computation and good numerical stability. Besides, when adding a new data pair, the barycentric form needs no recomputation of all the basis functions. The conversion algorithm of the Lagrange interpolation polynomial in power exponent form into the Newton interpolation polynomial in power exponent form, and the conversion algorithm of the Newton interpolation polynomial in power exponent form into the Lagrange interpolation polynomial in power exponent form are both discussed.%文章对Lagrange插指多项式进行了改进,得到了改进的Lagrange插指多项式和重心型Lagrange插指多项式.重心型Lagrange捅指多项式具有计算量小、数值计算稳定性好和增加新的插指节点不需重新计算原有插指节点基函数的优点.同时该文还讨论了Lagrange插指多项式与Newton插指多项式的相互转化,给出了与Newton插指多项式与Lagrange插指多项式相互转化的算法.
Störmer problem restricted to a spherical surface and the Euler and Lagrange tops
Piña, Eduardo; Cortés, Emilio
2016-11-01
In a recent work, Cortés and Poza (2015 Eur. J. Phys. 36 055009) analysed, in full, the dynamics of a charged particle in the field of a magnetic dipole restricted to a spherical surface with the dipole at its centre. This model can be considered as the classical non-relativistic Störmer problem on a sphere. Here, we started from a Lagrangian approach: we derived the Hamilton equations of motion and observed that in this restricted case the equations can be reduced to quadratures, and they were integrated numerically. From the Hamiltonian function we found, for the polar angle, an equivalent one-dimensional system of a particle in the presence of an effective potential. In the present work we start from a change of variable to the cosine of the polar angle. In terms of this variable we obtain an equation that turns out to be the same as the one of a particle in a quartic potential. Then, we can actually solve the equations of motion for the polar angle using Jacobi elliptic functions, and for the azimuthal angle we use the same integrals which were expressed by Jacobi in terms of theta functions, both in the Euler and Lagrange tops. In this restricted Störmer problem, the student at undergraduate or graduate level will have a good example of an integrable nonlinear physical system in which, after analysis of its complex dynamics, one can obtain an analytical solution by means of some special functions of mathematical physics. Additionally, one discovers that the equations of motion of this restricted case of a charge in a magnetic dipole field have the same mathematical structure as the corresponding equations of other well known integrable classical dynamical systems.
Institute of Scientific and Technical Information of China (English)
周长银; 贺国平
2004-01-01
In this paper, two-stage stochastic quadratic programming problems with equality constraints are considered.By Monte Carlo simulation-based approximations of the objective function and its first(second)derivative,an inexact Lagrange-Newton type method is proposed.It is showed that this method is globally convergent with probability one.In particular, the convergence is local superlinear under an integral approximation error bound condition.Moreover, this method can be easily extended to solve stochastic quadratic programming problems with inequality constraints.
Institute of Scientific and Technical Information of China (English)
侯锡云; 刘林
2007-01-01
在限制性三体问题中共线平动点附近的运动虽然是不稳定的,但可以是有条件稳定的,该动力学特征使得一些有特殊目的的探测器只需消耗较少的能量即可定点在这些点附近(如ISEE-3、SOHO).以日-地(月)系的L1点为例,根据其附近的运动特征,探讨定点探测器的发射与轨道控制问题,给出了相应的数值模拟结果,为工程上的实现提供理论依据.
Andrews, A. E.
2016-12-01
CarbonTracker-Lagrange (CT-L) is a flexible modeling framework developed to take advantage of newly available atmospheric data for CO2 and other long-lived gases such as CH4 and N2O. The North American atmospheric CO2 measurement network has grown from three sites in 2004 to >100 sites in 2015. The US network includes tall tower, mountaintop, surface, and aircraft sites in the NOAA Global Greenhouse Gas Reference Network along with sites maintained by university, government and private sector researchers. The Canadian network is operated by Environment and Climate Change Canada. This unprecedented dataset can provide spatially and temporally resolved CO2 emissions and uptake flux estimates and quantitative information about drivers of variability, such as drought and temperature. CT-L is a platform for systematic comparison of data assimilation techniques and evaluation of assumed prior, model and observation errors. A novel feature of CT-L is the optimization of boundary values along with surface fluxes, leveraging vertically resolved data available from NOAA's aircraft sampling program. CT-L uses observation footprints (influence functions) from the Weather Research and Forecasting/Stochastic Time-Inverted Lagrangian Transport (WRF-STILT) modeling system to relate atmospheric measurements to upwind fluxes and boundary values. Footprints are pre-computed and the optimization algorithms are efficient, so many variants of the calculation can be performed. Fluxes are adjusted using Bayesian or Geostatistical methods to provide optimal agreement with observations. Satellite measurements of CO2 and CH4 from GOSAT are available starting in July 2009 and from OCO-2 since September 2014. With support from the NASA Carbon Monitoring System, we are developing flux estimation strategies that use remote sensing and in situ data together, including geostatistical inversions using satellite retrievals of solar-induced chlorophyll fluorescence. CT-L enables quantitative
Invariant Manifolds, Lagrangian Trajectories and Space Mission Design
Belló, Miguel; Gómez, Gerard; Masdemont, Josep J.
The last 30 years have produced an explosion in the capabilities of designing and managing libration point missions. The starting point was the ground-breaking mission of the third International Sun-Earth Explorer spacecraft (ISEE-3). The ISEE-3 was launched August 12, 1978 to pursue studies of the Earth-Sun interactions, in a first step of what now is known as Space Weather. After a direct transfer of the ISEE-3 to the vicinity of the Sun-Earth Lagrange point, it was inserted into a nearly-periodic halo orbit, in order to monitor the solar wind about 1 h before it reached the Earth's magneto-sphere as well as the ISEE-1 and 2 spacecraft (which where in an elliptical orbit around the Earth).
Directory of Open Access Journals (Sweden)
Smith Simon J
1999-01-01
Full Text Available For a fixed integer and , let denote the th fundamental polynomial for Hermite–Fejér interpolation on the Chebyshev nodes . (So is the unique polynomial of degree at most which satisfies , and whose first derivatives vanish at each . In this paper it is established that It is also shown that is an increasing function of , and the best possible bound so that for all , and is obtained. The results generalise those for Lagrange interpolation, obtained by P. Erdős and G. Grünwald in 1938.
Institute of Scientific and Technical Information of China (English)
GUO Han-Ying,; LI Yu-Qi; WU Ke1; WANG Shi-Kun
2002-01-01
In this first paper of a series, we study the difference discrete variational principle in the framework of multi-parameter differential approach by regarding the forward difference as an entire geometric object in view of noncommutative differential geometry. Regarding the difference as an entire geometric object, the difference discrete version of Legendre transformation can be introduced. By virtue of this variational principle, we can discretely deal with the variation problems in both the Lagrangian and Hamiltonian formalisms to get difference discrete Euler-Lagrange equations and canonical ones for the difference discrete versions of the classical mechanics and classical field theory.
As origens da teoria dos invariantes na Inglaterra e o Mécanique Analytique de Lagrange (1788)
Santos, Nilson Diego de Alcantara [UNESP
2014-01-01
As origens da Teoria dos Invariantes na Inglaterra e o Mécanique Analytique de Lagrange (1788), é um trabalho voltado principalmente a entender uma possível influência que levou George Boole em 1841, a escrever o artigo Exposition of a General Theory of Linear Transformations e verificar se a motivação que o fez produzir este trabalho é igual ou diferente da motivação que ele exerceu sobre Arthur Cayley e consequentemente sobre James Joseph Sylvester. O presente trabalho apresenta um estudo d...
Análisis de gradientes en elementos singulares cuadráticos de Serendipity y de Lagrange
Michavila, Francisco; Gavete, Luis; Díez, Félix
1987-01-01
En el presente artículo se considera el tratamiento por el Metodo de Elementos Finitos de las singularidades que aparecen en la mecánica de la fractura en el caso elástico. Para ello se realiza un análisis de los gradientes de los desplazamientos para los elementos singulares cuadráticos de Serendipity y de Lagrange, que tienen su nodo en la cuarta parte del lado. De todo ello se deducen las restricciones que deben verificar para que la singularidad quede adecuadamente modelizada. Sin embargo...
Adaptation of the Euler-Lagrange equation for studying one-dimensional motions in a constant force
Dias, Clenilda F; Silva, Gislene M; Santos, Creuza A S; Barros, Pedro; Carvalho-Santos, Vagson L
2012-01-01
In this work we have shown that the Euler-Lagrange equation (ELE) can be simplified for one-dimensional motions. By using the partial derivative operators definition, we have proposed two operators, here called \\textit{mean delta operators}, which may be used to solve the ELE in a simplest way. We have applied this simplification to solve three known mechanical problems: a free fall body, the Atwood's machine and the inclinated plan. The proposed simplification may be used for introducing the lagrangian formalism for classical mechanics in introductory physics students, e.g., high school or undergraduate students in the beginning of engineering, mathematics and/or physics courses.
Institute of Scientific and Technical Information of China (English)
GUOHan－Ying; WUKe; 等
2002-01-01
In the previous papers I and II,we have studied the difference discrete variational principle and the Euler-Lagrange cohomology in the framework of multi-parameter differential approach.We have gotten the difference discrete Euler-Lagrange equations and canonical ones for the difference discrete versions of classical mechanics and field theory as well as the difference discrete versions for the Euler-Lagrange cohomology and applied them to get the necessary and sufficient condition for the symplectic or multisymplectic geometry preserving properties in both the lagrangian and Hamiltonian formalisms.In this paper,we apply the difference discrete variational principle and Euler-Lagrange cohomological approach directly to the symplectic and multisymplectic algorithms.We will show that either Hamiltonian schemes of Lagrangian ones in both the symplectic and multisymplectic algorithms are variational integrators and their difference discrete symplectic structure-preserving properties can always be established not only in the solution space but also in the function space if and only if the related closed Euler-Lagrange cohomological conditions are satisfied.
On the Construction of Low-Energy Cislunar and Trans-lunar Transfers Based on the Libration Points
Xu, Ming; Xu, Shijie
2014-01-01
There exist cislunar and trans-lunar libration points near the Moon, which are referred as the LL1 and LL2 points respectively and can generate the different types of low-energy trajectories transferring from Earth to Moon. The time-dependent analytic model including the gravitational forces from the Sun, Earth and Moon is employed to investigate the energy-minimal and practical transfer trajectories. However, different from the circular restricted three-body problem, the equivalent gravitational equilibria are defined according to the geometry of instantaneous Hill's boundary due to the gravitational perturbation from the Sun. The relationship between the altitudes of periapsis and eccentricities is achieved from the Poincar\\'e mapping for all the lunar captured trajectories, which presents the statistical feature of the fuel cost and captured orbital elements rather than generating a specified Moon-captured segment. The minimum energy required by the captured trajectory on a lunar circular orbit is deduced ...
García-Risueño, Pablo; Alonso, José Luis
2011-01-01
In order to accelerate molecular dynamics simulations, it is very common to impose holonomic constraints on their hardest degrees of freedom. In this way, the time step used to integrate the equations of motion can be increased, thus allowing, in principle, to reach longer total simulation times. The imposition of such constraints results in an aditional set of Nc equations (the equations of constraint) and unknowns (their associated Lagrange multipliers), that must be solved in one way or another at each time step of the dynamics. In this work it is shown that, due to the essentially linear structure of typical biological polymers, such as nucleic acids or proteins, the algebraic equations that need to be solved involve a matrix which is banded if the constraints are indexed in a clever way. This allows to obtain the Lagrange multipliers through a non-iterative procedure, which can be considered exact up to machine precision, and which takes O(Nc) operations, instead of the usual O(Nc3) for generic molecular...
Yang, Zi-Jiang; Qin, Pan
2016-07-01
This paper considers the problem of distributed synchronisation tracking control of multiple Euler-Lagrange systems on a directed graph which contains a spanning tree with the leader node being the root. To design the high performance distributed controllers, a virtual double-integrator is introduced in each agent and is controlled by a virtual distributed linear high-gain synchronisation tracking controller, so that the position and velocity of each agent track those of the reference trajectory with arbitrarily short transient time and small ultimate tracking error. Then taking the double-integrator's position and velocity as the estimates of those of the reference trajectory, in each generalised coordinate of each Euler-Lagrange agent, a local controller with a disturbance observer and a sliding mode control term is designed, to suppress the mutual interactions among the agents and the modelling uncertainties. The boundedness of the overall signals and the synchronisation tracking control performance are analysed, and the conditions for guaranteed control performance are clarified. Simulation examples are provided to demonstrate the performance of the distributed controllers.
Control of asteroid retrieval trajectories to libration point orbits
Ceriotti, Matteo; Sanchez, Joan Pau
2016-09-01
The fascinating idea of shepherding asteroids for science and resource utilization is being considered as a credible concept in a not too distant future. Past studies identified asteroids which could be efficiently injected into manifolds which wind onto periodic orbits around collinear Lagrangian points of the Sun-Earth system. However, the trajectories are unstable, and errors in the capture maneuver would lead to complete mission failure, with potential danger of collision with the Earth, if uncontrolled. This paper investigates the controllability of some asteroids along the transfers and the periodic orbits, assuming the use of a solar-electric low-thrust system shepherding the asteroid. Firstly, an analytical approach is introduced to estimate the stability of the trajectories from a dynamical point of view; then, a numerical control scheme based on a linear quadratic regulator is proposed, where the gains are optimized for each trajectory through a genetic algorithm. A stochastic simulation with a Monte Carlo approach is used to account for different perturbed initial conditions and the epistemic uncertainty on the asteroid mass. Results show that only a small subset of the considered combinations of trajectories/asteroids are reliably controllable, and therefore controllability must be taken into account in the selection of potential targets.
Lukyanov, S. S.
1983-01-01
This paper is dedicated to the possible investigation of the utilization of the solar radiation pressure for the spacecraft motion control in the vicinity of collinear libration point of planar restricted ring problem of three bodies. The control is realized by changing the solar sail area at its permanent orientation. In this problem the influence of the trajectory errors and the errors of the execution control is accounted. It is worked out, the estimation method of the solar sail sizes, which are necessary for spacecraft keeping in the vicinity of collinear libration point during the certain time with given probability. The main control parameters were calculated for some examples in case of libration points of the Sun-Earth and Earth-Moon systems.
Directory of Open Access Journals (Sweden)
Erik Kyrkjebø
2015-04-01
Full Text Available This paper compares a dynamic and a kinematic observer approach for output coordination control of mechanical systems formulated in the Euler-Lagrange framework. The observers are designed to estimate missing velocity and acceleration information based on position/attitude measurements to provide a full state vector to the coordination control algorithm. The kinematic observer approach utilizes a virtual system designed to mimic the kinematic behaviour of the leader in order to estimate unknown states of the state vector with a minimum of information available. The dynamic observer approach is based on utilizing the full dynamic model of the follower system when estimating the missing states. The two observers are compared in terms of estimation principles and practical performance, and applied to two practical examples; leader-follower robot manipulator synchronization control, and underway replenishment operations for surface ships.
Espino, Daniel M; Shepherd, Duncan E T; Hukins, David W L
2014-01-01
A transient multi-physics model of the mitral heart valve has been developed, which allows simultaneous calculation of fluid flow and structural deformation. A recently developed contact method has been applied to enable simulation of systole (the stage when blood pressure is elevated within the heart to pump blood to the body). The geometry was simplified to represent the mitral valve within the heart walls in two dimensions. Only the mitral valve undergoes deformation. A moving arbitrary Lagrange-Euler mesh is used to allow true fluid-structure interaction (FSI). The FSI model requires blood flow to induce valve closure by inducing strains in the region of 10-20%. Model predictions were found to be consistent with existing literature and will undergo further development.
Klein, L. R.
1974-01-01
The free vibrations of elastic structures of arbitrary complexity were analyzed in terms of their component modes. The method was based upon the use of the normal unconstrained modes of the components in a Rayleigh-Ritz analysis. The continuity conditions were enforced by means of Lagrange Multipliers. Examples of the structures considered are: (1) beams with nonuniform properties; (2) airplane structures with high or low aspect ratio lifting surface components; (3) the oblique wing airplane; and (4) plate structures. The method was also applied to the analysis of modal damping of linear elastic structures. Convergence of the method versus the number of modes per component and/or the number of components is discussed and compared to more conventional approaches, ad-hoc methods, and experimental results.
Energy Technology Data Exchange (ETDEWEB)
Bono, R.; Bugliosi, E.H.; Schiliro, T.; Gilli, G. [Torino Univ. (Italy). Dept. of Public Health and Microbiology
2001-01-01
Benzene, toluene and xylenes (BTX) air pollution is a very important topic for environmental health, due to the toxicity and/or mutagenic or carcinogenic properties of these aromatics and the commercialisation of the unleaded gasoline containing amount of BTX. We measured BTX in the air of Turin city, the capital of Piedmont region (north-western Italy), during 10 years, from 1989 to 1998. The sampling site selected was Lagrange Street (LS), an 'urban canyon' placed in the centre of the city. The behaviour of BTX in LS was conditioned by some local and national legislative measures enforced during 1990s for the reduction of automotive traffic and BTX air pollution, respectively. Taking into account the existence of similar measures undertaken also in several cities in the developed countries, largely described but never discussed, the aim of this study was to verify in LS the preventive effects of these regulatory actions by means of a longitudinal survey extended over 10 years. Results obtained in Lagrange Street highlight seasonal trends, typical of this kind of pollutants, and an important reduction (from 42.6 to 15.9ppbv) of aromatic hydrocarbons (sum of benzene, toluene and xylenes) in atmospheric air from 1990 to 1997. In particular, the annual level of benzene in air showed a mean from 9.2ppbv in 1990 to 2.0ppbv in 1997, almost half of the 3.1ppbv imposed by law since 31 December 1998. In conclusion, the present findings induce a consistent optimism about the usefulness and the effectiveness of these types of regulatory actions enforced to reduce the human exposure to BTX, which could be extended also to other trafficated sites where the aromatics air pollution has to be reduced. (Author)
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
This paper discusses the validity of (adaptive) Lagrange generalized plain finite element method(FEM) and plate element method for accurate analysis of acoustic waves in multi-layered piezoelectric structures with tiny interfaces between metal electrodes and surface mounted piezoelectric substrates. We have come to conclusion that the quantitative relationships between the acoustic and electric fields in a piezoelectric structure can be accurately determined through the proposed finite element methods. The higher-order Lagrange FEM proposed for dynamic piezoelectric computation is proved to be very accurate (prescribed relative error 0.02%-0.04%) and a great improvement in convergence accuracy over the higher order Mindlin plate element method for piezoelectric structural analysis due to the assumptions and corrections in the plate theories. The converged Lagrange finite element methods are compared with the plate element methods and the computed results are in good agreement with available exact and experimental data. The adaptive Lagrange finite element methods and a new FEA computer program developed for macro- and micro-scale analyses are reviewed, and recently extended with great potential to high-precision nano-scale analysis in this paper and the similarities between piezoelectric and seismic wave propagations in layered structures and plates are stressed.
Energy Technology Data Exchange (ETDEWEB)
Pember, R.B.; Anderson, R.W.
2000-11-22
We present a comparison of two algorithms for solving the equations of unsteady inviscid compressible flow in a Eulerian frame. The first algorithm is a staggered grid Lagrange plus remap scheme. The Lagrange step in this method is a time-centered version of the scheme due to Tipton, while the remap step employs a variant of the corner transport upwind scheme due to Colella. The second algorithm is a spatially operator-split version of the higher-order Godunov scheme for gas dynamics due to Colella. They use the two methods to compute solutions to a number of one- and two-dimensional problems. The results show the accuracy and performance of the two schemes to be generally equivalent. In a 1984 survey paper by Woodward and Colella, staggered grid, Lagrange plus remap, artificial viscosity schemes did not compare favorably with cell-centered direct Eulerian higher-order Godunov methods. They examine, therefore, how certain features of the staggered grid scheme discussed here contribute to its improved accuracy. They show in particular that the improved accuracy of the present scheme is due in part to the use of a monotonic artificial viscosity in the Lagrange step and the use of an improved upwind method in the remap step.
Institute of Scientific and Technical Information of China (English)
张武; 洪涛
2002-01-01
This paper discusses the validity of (adaptive) Lagrange generalized plain finite element method (FEM) and plate element method for accurate analysis of acoustic waves in multi-layered piezoelectric structures with tiny interfaces between metal electrodes and surface mounted piezoelectric substrates. We have come to conclusion that the quantitative relationships between the acoustic and electric fields in a piezoelectric structure can be accurately determined through the proposed finite element methods. The higher-order Lagrange FEM proposed for dynamic piezoelectric computation is proved to be very accurate (prescribed relative error 0.02% - 0.04% ) and a great improvement in convergence accuracy over the higher order Mindlin plate element method for piezoelectric structural analysis due to the assumptions and corrections in the plate theories.The converged lagrange finite element methods are compared with the plate element methods and the computedresults are in good agreement with available exact and experimental data. The adaptive Lagrange finite elementmethods and a new FEA computer program developed for macro- and micro-scale analyses are reviewed, and recently extended with great potential to high-precision nano-scale analysis in this paper and the similarities between piezoelectric and seismic wave propagations in layered structures and plates are stressed.
Komsiyah, S.
2014-03-01
The objective in this paper is about economic dispatch problem of electric power generation where scheduling the committed generating units outputs so as to meet the required load demand at minimum operating cost, while satisfying all units and system equality and inequality constraint. In the operating of electric power system, an economic planning problem is one of variables that its must be considered since economically planning will give more efficiency in operational cost. In this paper the economic dispatch problem which has non linear cost function solved by using swarm intelligent method is Gaussian Particle Swarm Optimization (GPSO) and Lagrange Multiplier. GPSO is a population-based stochastic algorithms which their moving inspired by swarm intelligent and probabilities theories. To analize its accuracy, the economic dispatch solution by GPSO method will be compared with Lagrange multiplier method. From the running test result the GPSO method give economically planning calculation which it better than Lagrange multiplier method and the GPSO method faster to getting error convergence. Therefore the GPSO method have better performance to getting global best solution than the Lagrange method.
Hopkins, Randall C.; Capizzo, Peter; Fincher, Sharon; Hornsby, Linda S.; Jones, David
2010-01-01
The Advanced Concepts Office at Marshall Space Flight Center completed a brief spacecraft design study for the 8-meter monolithic Advanced Technology Large Aperture Space Telescope (ATLAST-8m). This spacecraft concept provides all power, communication, telemetry, avionics, guidance and control, and thermal control for the observatory, and inserts the observatory into a halo orbit about the second Sun-Earth Lagrange point. The multidisciplinary design team created a simple spacecraft design that enables component and science instrument servicing, employs articulating solar panels for help with momentum management, and provides precise pointing control while at the same time fast slewing for the observatory.
Energy Technology Data Exchange (ETDEWEB)
Barboza, Luciano Vitoria [Sul-riograndense Federal Institute for Education, Science and Technology (IFSul), Pelotas, RS (Brazil)], E-mail: luciano@pelotas.ifsul.edu.br
2009-07-01
This paper presents an overview about the maximum load ability problem and aims to study the main factors that limit this load ability. Specifically this study focuses its attention on determining which electric system buses influence directly on the power demand supply. The proposed approach uses the conventional maximum load ability method modelled by an optimization problem. The solution of this model is performed using the Interior Point methodology. As consequence of this solution method, the Lagrange multipliers are used as parameters that identify the probable 'bottlenecks' in the electric power system. The study also shows the relationship between the Lagrange multipliers and the cost function in the Interior Point optimization interpreted like sensitivity parameters. In order to illustrate the proposed methodology, the approach was applied to an IEEE test system and to assess its performance, a real equivalent electric system from the South- Southeast region of Brazil was simulated. (author)
The d'Alembert-lagrange principle for gradient theories and boundary conditions
Gouin, Henri
2007-01-01
Motions of continuous media presenting singularities are associated with phenomena involving shocks, interfaces or material surfaces. The equations representing evolutions of these media are irregular through geometrical manifolds. A unique continuous medium is conceptually simpler than several media with surfaces of singularity. To avoid the surfaces of discontinuity in the theory, we transform the model by considering a continuous medium taking intoaccount more complete internal energies expressed in gradient developments associated with the variables of state. Nevertheless, resulting equations of motion are of an higher order than those of the classical models: they lead to non-linear models associated with more complex integration processes on the mathematical level as well as on the numerical point of view. In fact, such models allow a precise study of singular zones when they have a non negligible physical thickness. This is typically the case for capillarity phenomena in fluids or mixtures of fluids in...
Tsou, H.
2008-08-01
A new Instituto Nacional de Tecnica Aeroespacial (INTA) station, located about 70 km east of the Deep Space Network (DSN) Madrid complex (Robledo), is planned to support National Polar-orbiting Operational Environmental Satellite System (NPOESS) satellites. The 26.7-GHz NPOESS Ka-band downlink to this proposed station can potentially interfere with the DSN Madrid station that may support the future lunar and Sun-Earth Lagrange point missions operating in the 25.5- to 27.0-GHz band. A preliminary compatibility analysis has been conducted to assess the potential impact to the DSN Madrid complex from the NPOESS Ka-band downlink to the planned INTA station.
Directory of Open Access Journals (Sweden)
Yi-Tsung Lin
2016-04-01
Full Text Available Instead of obsessively emphasizing to reduce the number of time increments and reshape the models, a novel surface contact transformation to increase efficiency is presented in this study. Wear on the bearing surfaces was investigated following the coupled regions from the pressure distribution, computed by means of three-dimensional finite element method models; an approximate analytical model and formulation in three-dimensional frictional contact problems based on modified localized Lagrange multiplier method have also been developed and discussed. Understanding wear behavior patterns in mechanical components is a significant task in engineering design. The proposed approach provides a complete and effective solution to the wear problem in a quasi-dynamic manner. However, expensive computing time is needed in the incremental procedures. In this article, an alternative and efficient finite element approach is introduced to reduce the computation costs of wear prediction. Through the successful verification of wear depth and volume loss of the pin-on-plate, block-on-ring, and metal-on-plastic artificial hip joint wear behaviors, the numerical calculations are shown to be both valid and feasible. Furthermore, the results also show that the central processing unit time required by the proposed method is nearly half that of the previous methods without loss of accuracy.
Arolla, Sunil K
2014-01-01
A volume-filtered Euler-Lagrange large eddy simulation methodology is used to predict the physics of turbulent liquid-solid slurry flow through a horizontal pipe. A dynamic Smagorinsky model based on Lagrangian averaging is employed to account for the sub-filter scale effects in the liquid phase. A fully conservative immersed boundary method is used to account for the pipe geometry on a uniform cartesian grid. The liquid and solid phases are coupled through volume fraction and momentum exchange terms. Particle-particle and particle-wall collisions are modeled using a soft-sphere approach. A series of simulations have been performed by varying the superficial liquid velocity to be consistent with the experimental data by Dahl et al. (2003). Depending on the liquid flow rate, a particle bed can form and develop different patterns, which are discussed in the light of various regime diagrams proposed in the literature. The fluctuation in the height of the liquid-bed interface is characterized to understand the sp...
Hentosh, Oksana E.; Prykarpatsky, Yarema A.; Blackmore, Denis; Prykarpatski, Anatolij K.
2017-10-01
The work is devoted to recent investigations of the Lax-Sato compatible linear vector field equations, especially to the related Lie-algebraic structures and integrability properties of a very interesting class of nonlinear dynamical systems called the dispersionless heavenly type equations, which were initiated by Plebański and later analyzed in a series of articles. The AKS-algebraic and related R-structure schemes are used to study the orbits of the corresponding co-adjoint actions, which are intimately related to the classical Lie-Poisson structures on them. It is demonstrated that their compatibility condition coincides with the corresponding heavenly equation being considered. It is shown that all these equations originate in this way and can be represented as a Lax compatibility condition for specially constructed loop vector fields on the torus. The infinite hierarchy of conservations laws related to the heavenly equations is described, and its analytical structure connected with the Casimir invariants is mentioned. In addition, typical examples of such equations, demonstrating in detail their integrability via the scheme devised herein, are presented. The relationship of the very interesting Lagrange-d'Alembert type mechanical interpretation of the devised integrability scheme with the Lax-Sato equations is also discussed.
Wie, Bong; Ahn, Jaemyung
2017-03-01
This paper is concerned with a classical yet still mystifying problem regarding multiple roots of the angles-only initial orbit determination (IOD) polynomial equations of Lagrange, Laplace, and Gauss of the form: f( x) = x 8+ a x 6+ b x 3+ c=0 where a, c0 has been extensively treated in the celestial mechanics literature. However, the literature on applied astrodynamics has not treated this multiple-root issue in detail, and not many specific numerical examples with multiple roots are available in the literature. In this paper, a very simple method of determining the correct root from two or three non-spurious roots is presented, which doesn't utilize any a priori knowledge and/or additional observations of the object. The proposed method exploits a simple approximate polynomial equation of the form: g( x) = x 8+ a x 6=0. An approximate polynomial equation, either g( x) = x 8+ c=0 or g( x) = x 8+ a x 6= x 6( x 2+ a) = 0, can also be used for quickly estimating an initial guess of the correct root.
Warner, Paul
2017-09-01
For any appreciable radiation source, such as a nuclear reactor core or radiation physics accelerator, there will be the safety requirement to shield operators from the effects of the radiation from the source. Both the size and weight of the shield need to be minimised to reduce costs (and to increase the space available for the maintenance envelope on a plant). This needs to be balanced against legal radiation dose safety limits and the requirement to reduce the dose to operators As Low As Reasonably Practicable (ALARP). This paper describes a method that can be used, early in a shield design, to scope the design and provide a practical estimation of the size of the shield by optimising the shield internals. In particular, a theoretical model representative of a small reactor is used to demonstrate that the primary shielding radius, thickness of the primary shielding inner wall and the thicknesses of two steel inner walls, can be set using the Lagrange multiplier method with a constraint on the total flux on the outside of the shielding. The results from the optimisation are presented and an RZ finite element transport theory calculation is used to demonstrate that, using the optimised geometry, the constraint is achieved.
Mustafa, Omar
2013-01-01
Using a generalized coordinate along with a proper invertible coordinate transformation, we show that the Euler-Lagrange equation used by Bagchi et al. 16 is in clear violation of the Hamilton's principle. We also show that Newton's equation of motion they have used is not in a form that satisfies the dynamics of position-dependent mass (PDM) settings.. The equivalence between Euler-Lagrange's and Newton's equations is now proved and documented through the proper invertible coordinate transformation and the introduction of a new PDM byproducted reaction-type force. The total mechanical energy for the PDM is shown to be conservative (i.e., dE/dt=0, unlike Bagchi et al.'s 16 observation).
Mauricio Galán; José Godina
2011-01-01
Este artículo describe el proceso de análisis matemático de un dispositivo mecánico que se ha diseñado para ser adaptado a una silla de ruedas, las ecuaciones de movimiento en el plano del dispositivo, se formulan a partir de las ecuaciones de Euler Lagrange de la mecánica clásica, asimismo las restricciones no holonómicas del sistema son caracterizadas por multiplicadores de Lagrange, la integración de ambos conceptos matemáticos son parte de la formulación de un modelo cinemático que es el ...
Noether's theorem and Lie symmetries for time-dependent Hamilton-Lagrange systems.
Struckmeier, Jürgen; Riedel, Claus
2002-12-01
Noether and Lie symmetry analyses based on point transformations that depend on time and spatial coordinates will be reviewed for a general class of time-dependent Hamiltonian systems. The resulting symmetries are expressed in the form of generators whose time-dependent coefficients follow as solutions of sets of ordinary differential ("auxiliary") equations. The interrelation between the Noether and Lie sets of auxiliary equations will be elucidated. The auxiliary equations of the Noether approach will be shown to admit invariants for a much broader class of potentials, compared to earlier studies. As an example, we work out the Noether and Lie symmetries for the time-dependent Kepler system. The Runge-Lenz vector of the time-independent Kepler system will be shown to emerge as a Noether invariant if we adequately interpret the pertaining auxiliary equation. Furthermore, additional nonlocal invariants and symmetries of the Kepler system will be isolated by identifying further solutions of the auxiliary equations that depend on the explicitly known solution path of the equations of motion. Showing that the invariants remain unchanged under the action of different symmetry operators, we demonstrate that a unique correlation between a symmetry transformation and an invariant does not exist.
Directory of Open Access Journals (Sweden)
Hakan Kum
2012-01-01
Full Text Available This study examines the validity of the purchasing power parity (PPP in Turkey for annual data from 1953 to 2009. While results from both the ADF unit root and the DF-GLS unit root test indicate mixed results, PPP holds for Turkey with the presence of structural breaks which are obtained by Zivot and Andrews and Lagrange Multiplier unit root tests.
On the Geometrical Meaning of Lagrange Multiplier Method%关于拉格朗日乘数法的几何意义
Institute of Scientific and Technical Information of China (English)
陈建发
2016-01-01
This paper uses gradient vector and directional derivative to study the rate of change of functions on curves or surfaces. It gives a geometrical interpretation of the Lagrange multiplier method.%利用梯度和方向导数的概念讨论函数在曲线或曲面上的变化率，从而给出拉格朗日乘数法的一个直观的几何解释。
Brown, Jonathan M.; Petersen, Jeremy D.
2014-01-01
NASA's WIND mission has been operating in a large amplitude Lissajous orbit in the vicinity of the interior libration point of the Sun-Earth/Moon system since 2004. Regular stationkeeping maneuvers are required to maintain the orbit due to the instability around the collinear libration points. Historically these stationkeeping maneuvers have been performed by applying an incremental change in velocity, or (delta)v along the spacecraft-Sun vector as projected into the ecliptic plane. Previous studies have shown that the magnitude of libration point stationkeeping maneuvers can be minimized by applying the (delta)v in the direction of the local stable manifold found using dynamical systems theory. This paper presents the analysis of this new maneuver strategy which shows that the magnitude of stationkeeping maneuvers can be decreased by 5 to 25 percent, depending on the location in the orbit where the maneuver is performed. The implementation of the optimized maneuver method into operations is discussed and results are presented for the first two optimized stationkeeping maneuvers executed by WIND.
Directory of Open Access Journals (Sweden)
Fan Meng
Full Text Available This paper studies the problem of the restoration of images corrupted by mixed Gaussian-impulse noise. In recent years, low-rank matrix reconstruction has become a research hotspot in many scientific and engineering domains such as machine learning, image processing, computer vision and bioinformatics, which mainly involves the problem of matrix completion and robust principal component analysis, namely recovering a low-rank matrix from an incomplete but accurate sampling subset of its entries and from an observed data matrix with an unknown fraction of its entries being arbitrarily corrupted, respectively. Inspired by these ideas, we consider the problem of recovering a low-rank matrix from an incomplete sampling subset of its entries with an unknown fraction of the samplings contaminated by arbitrary errors, which is defined as the problem of matrix completion from corrupted samplings and modeled as a convex optimization problem that minimizes a combination of the nuclear norm and the l(1-norm in this paper. Meanwhile, we put forward a novel and effective algorithm called augmented Lagrange multipliers to exactly solve the problem. For mixed Gaussian-impulse noise removal, we regard it as the problem of matrix completion from corrupted samplings, and restore the noisy image following an impulse-detecting procedure. Compared with some existing methods for mixed noise removal, the recovery quality performance of our method is dominant if images possess low-rank features such as geometrically regular textures and similar structured contents; especially when the density of impulse noise is relatively high and the variance of Gaussian noise is small, our method can outperform the traditional methods significantly not only in the simultaneous removal of Gaussian noise and impulse noise, and the restoration ability for a low-rank image matrix, but also in the preservation of textures and details in the image.
Chobanyan, E.; Ilić, M. M.; Notaroš, B. M.
2015-05-01
A novel double-higher-order entire-domain volume integral equation (VIE) technique for efficient analysis of electromagnetic structures with continuously inhomogeneous dielectric materials is presented. The technique takes advantage of large curved hexahedral discretization elements—enabled by double-higher-order modeling (higher-order modeling of both the geometry and the current)—in applications involving highly inhomogeneous dielectric bodies. Lagrange-type modeling of an arbitrary continuous variation of the equivalent complex permittivity of the dielectric throughout each VIE geometrical element is implemented, in place of piecewise homogeneous approximate models of the inhomogeneous structures. The technique combines the features of the previous double-higher-order piecewise homogeneous VIE method and continuously inhomogeneous finite element method (FEM). This appears to be the first implementation and demonstration of a VIE method with double-higher-order discretization elements and conformal modeling of inhomogeneous dielectric materials embedded within elements that are also higher (arbitrary) order (with arbitrary material-representation orders within each curved and large VIE element). The new technique is validated and evaluated by comparisons with a continuously inhomogeneous double-higher-order FEM technique, a piecewise homogeneous version of the double-higher-order VIE technique, and a commercial piecewise homogeneous FEM code. The examples include two real-world applications involving continuously inhomogeneous permittivity profiles: scattering from an egg-shaped melting hailstone and near-field analysis of a Luneburg lens, illuminated by a corrugated horn antenna. The results show that the new technique is more efficient and ensures considerable reductions in the number of unknowns and computational time when compared to the three alternative approaches.
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Peng, Haijun; Wang, Wei
2016-10-01
An adaptive surrogate model-based multi-objective optimization strategy that combines the benefits of invariant manifolds and low-thrust control toward developing a low-computational-cost transfer trajectory between libration orbits around the L1 and L2 libration points in the Sun-Earth system has been proposed in this paper. A new structure for a multi-objective transfer trajectory optimization model that divides the transfer trajectory into several segments and gives the dominations for invariant manifolds and low-thrust control in different segments has been established. To reduce the computational cost of multi-objective transfer trajectory optimization, a mixed sampling strategy-based adaptive surrogate model has been proposed. Numerical simulations show that the results obtained from the adaptive surrogate-based multi-objective optimization are in agreement with the results obtained using direct multi-objective optimization methods, and the computational workload of the adaptive surrogate-based multi-objective optimization is only approximately 10% of that of direct multi-objective optimization. Furthermore, the generating efficiency of the Pareto points of the adaptive surrogate-based multi-objective optimization is approximately 8 times that of the direct multi-objective optimization. Therefore, the proposed adaptive surrogate-based multi-objective optimization provides obvious advantages over direct multi-objective optimization methods.
Lagrange relaxation for UAV path planning%拉格朗日松弛的无人机路径规划
Institute of Scientific and Technical Information of China (English)
刘山; 顾晔倩; 李雨石; 曹盛文; 刘轩
2012-01-01
提出了基于城市建筑物遮挡模型的无人驾驶飞行器(简称无人机)路径规划方法,主要包含两方面的内容:一是利用圆柱体虚拟城市的建筑物环境,使建筑物对无人机的遮挡面积可计算,另外,由于建筑物的相对位置会相互遮挡,不可以进行简单的面积加法.采用程序实现了无人机的遮挡总和的计算,即每个建筑物遮挡面积的并集.二是在计算出无人机飞行的水平平面上(x,y)点的遮挡曲面值的基础上,给出了无人机基于拉格朗日松弛算法的优化路径规划,即走一条遮挡面积最小的路径的方法.给出matlab仿真结果,实验结果表明该方法是十分有效的.%It proposes a path planning algorithm based on an urban building block model for Unmanned Air Vehicle (UAV for short).The proposed algorithm mainly contains two aspects. First the algorithm simulates the buildings in urban environment with cylinders, so it' s able to calculate the block area of the relative position between the buildings and UAV. In addition, the total shading area isn' t the addition of each shading area, instead it' s a union set. The algorithm calculates the union set by using a program. Second, after calculating the curved surface of UAV' s flight plane, this algorithm proposes an optimal path planning method based on Lagrange relaxation of UAV. The path is a polygonal line along the equant diagonal line on the searching area of UAV. The shading area of this path is minimal. The Matlab simulation result suggests this algorithm is efficient.
The utility of polarized heliospheric imaging for space weather monitoring.
DeForest, C E; Howard, T A; Webb, D F; Davies, J A
2016-01-01
A polarizing heliospheric imager is a critical next generation tool for space weather monitoring and prediction. Heliospheric imagers can track coronal mass ejections (CMEs) as they cross the solar system, using sunlight scattered by electrons in the CME. This tracking has been demonstrated to improve the forecasting of impact probability and arrival time for Earth-directed CMEs. Polarized imaging allows locating CMEs in three dimensions from a single vantage point. Recent advances in heliospheric imaging have demonstrated that a polarized imager is feasible with current component technology.Developing this technology to a high technology readiness level is critical for space weather relevant imaging from either a near-Earth or deep-space mission. In this primarily technical review, we developpreliminary hardware requirements for a space weather polarizing heliospheric imager system and outline possible ways to flight qualify and ultimately deploy the technology operationally on upcoming specific missions. We consider deployment as an instrument on NOAA's Deep Space Climate Observatory follow-on near the Sun-Earth L1 Lagrange point, as a stand-alone constellation of smallsats in low Earth orbit, or as an instrument located at the Sun-Earth L5 Lagrange point. The critical first step is the demonstration of the technology, in either a science or prototype operational mission context.
On Lagrange interpolation for continuous function with Φ-bounded variation%连续Φ-有界变差函数的Lagrange插值逼近
Institute of Scientific and Technical Information of China (English)
梅雪峰; 周观珍
2001-01-01
本文主要讨论连续Φ-有界变差函数借助于Jacobi多项式的根的Lagrange插值逼近问题，并给出了插值多项式在上一致收敛的速度估计。%This paper investigated Lagrange interpolation for continuous function with Φ-bounded variation on Jacobi abscissas. The main result of the paper is that author gave estimation for the order of convergence.
Stability of the fixed points of the complex Swift-Hohenberg equation
Khairudin, N. I.; Abdullah, F. A.; Hassan, Y. A.
2016-02-01
We performed an investigation of the stability of fixed points in the complex Swift- Hohenberg equation using a variational formulation. The analysis is based on fixed points Euler-Lagrange equations and analytically showed that the Jacobian eigenvalues touched the imaginary axis and in general, Hopf bifurcation arises. The eigenvalues undergo a stability criterion in order to have Hopf's stability. Trial functions and linear loss dispersion parameter ε are responsible for the existence of stable pulse solutions in this system. We study behavior of the stable soliton-like solutions as we vary a bifurcation ε.
基于Lagrange方法封闭的两相湍流场方程模型%A Field-Equation Turbulence Model Closed By Lagrange Method
Institute of Scientific and Technical Information of China (English)
王路; 徐江荣; 刘保银
2016-01-01
First⁃order moment equations of hybrid second⁃order moment model are obtained by Euler method, while second⁃order moment equations are deduced by Lagrange equations. Equations for particle fraction and momentum are provided firstly. A Lagrange model with mean Langevin equations is obtained and Reynold stress equation is deduced, so that hybrid second⁃order moment model is closed without additional approximate assumptions. Wall⁃jet⁃flow loaded with solid particles is simulated. It shows that the model is effective.%两相湍流场方程模型采用基于Euler方法的一阶矩方程，而二阶矩方程由Lagrange方法得到，新模型的封闭不需要附加其它假设。首先基于概率密度函数给出颗粒运动的连续方程和动量方程，其次由基于平均Langevin方程的Lagrange模型推导得到颗粒二阶矩方程，最终获得封闭的二阶矩模型。将新模型用于气固两相壁面射流的数值模拟，结果表明新模型合理有效。
Chalons, Christophe; Girardin, Mathieu; Kokh, Samuel
2017-04-01
We propose an all regime Lagrange-Projection like numerical scheme for 2D homogeneous models for two-phase flows. By all regime, we mean that the numerical scheme is able to compute accurate approximate solutions with an under-resolved discretization, i.e. a mesh size and time step much bigger than the Mach number M of the mixture. The key idea is to decouple acoustic, transport and phase transition phenomenon using a Lagrange-Projection decomposition in order to treat implicitly (fast) acoustic and phase transition phenomenon and explicitly the (slow) transport phenomena. Then, extending a strategy developed in the case of the usual gas dynamics equations, we alter the numerical flux in the acoustic approximation to obtain a uniform truncation error in terms of M. This modified scheme is conservative and endowed with good stability properties with respect to the positivity of the density and preserving the mass fraction within the interval (0 , 1). Numerical evidences are proposed and show the ability of the scheme to deal with cases where the flow regime may vary from low to high Mach values.
Directory of Open Access Journals (Sweden)
Min Zhu
2014-01-01
Full Text Available An active disturbance rejection station-keeping control scheme is derived and analyzed for station-keeping missions of spacecraft along a class of unstable periodic orbits near collinear libration points of the Sun-Earth system. It is an error driven, rather than model-based control law, essentially accounting for the independence of model accuracy and linearization. An extended state observer is designed to estimate the states in real time by setting an extended state, that is, the sum of unmodeled dynamic and external disturbance. This total disturbance is compensated by a nonlinear state error feedback controller based on the extended state observer. A nonlinear tracking differentiator is designed to obtain the velocity of the spacecraft since only position signals are available. In addition, the system contradiction between rapid response and overshoot can be effectively solved via arranging the transient process in tracking differentiator. Simulation results illustrate that the proposed method is adequate for station-keeping of unstable Halo orbits in the presence of system uncertainties, initial injection errors, solar radiation pressure, and perturbations of the eccentric nature of the Earth's orbit. It is also shown that the closed-loop control system performance is improved significantly using our method comparing with the general LQR method.
Congedo, Giuseppe
2016-01-01
General relativity is supported by great experimental evidence. Yet there is a lot of interest in precisely setting its limits with on going and future experiments. A question to answer is about the validity of the Strong Equivalence Principle. Ground experiments and Lunar Laser Ranging have provided the best upper limit on the Nordtvedt parameter $\\sigma[\\eta]=4.4\\times 10^{-4}$. With the future planetary mission BepiColombo, this parameter will be further improved by at least an order of magnitude. In this paper we envisage yet another possible testing environment with spacecraft ranging towards the nearby Sun-Earth collinear Lagrangian points. Neglecting errors in planetary masses and ephemerides, we forecast $\\sigma[\\eta]=6.4\\text{-}2.0\\times10^{-4}$ (5 yr integration time) via ranging towards $L_1$ in realistic and optimistic scenarios depending on current and future range capabilities and knowledge of the Earth's ephemerides. A combined measurement, $L_1$+$L_2$, gives instead $4.8\\text{-}1.7\\times10^{-4...
Jiwari, Ram
2015-08-01
In this article, the author proposed two differential quadrature methods to find the approximate solution of one and two dimensional hyperbolic partial differential equations with Dirichlet and Neumann's boundary conditions. The methods are based on Lagrange interpolation and modified cubic B-splines respectively. The proposed methods reduced the hyperbolic problem into a system of second order ordinary differential equations in time variable. Then, the obtained system is changed into a system of first order ordinary differential equations and finally, SSP-RK3 scheme is used to solve the obtained system. The well known hyperbolic equations such as telegraph, Klein-Gordon, sine-Gordon, Dissipative non-linear wave, and Vander Pol type non-linear wave equations are solved to check the accuracy and efficiency of the proposed methods. The numerical results are shown in L∞ , RMS andL2 errors form.
Kalinin, A. V.; Sumin, M. I.; Tyukhtina, A. A.
2017-02-01
An initial-boundary value problem for Maxwell's equations in the quasi-stationary magnetic approximation is investigated. Special gauge conditions are presented that make it possible to state the problem of independently determining the vector magnetic potential. The well-posedness of the problem is proved under general conditions on the coefficients. For quasi-stationary Maxwell equations, final observation problems formulated in terms of the vector magnetic potential are considered. They are treated as convex programming problems in a Hilbert space with an operator equality constraint. Stable sequential Lagrange principles are stated in the form of theorems on the existence of a minimizing approximate solution of the optimization problems under consideration. The possibility of applying algorithms of dual regularization and iterative dual regularization with a stopping rule is justified in the case of a finite observation error.
Hendzel, Z.; Rykała, Ł.
2017-02-01
The work presents the dynamic equations of motion of a wheeled mobile robot with mecanum wheels derived with the use of Lagrange equations of the second kind. Mecanum wheels are a new type of wheels used in wheeled mobile robots and they consist of freely rotating rollers attached to the circumference of the wheels. In order to derive dynamic equations of motion of a wheeled mobile robot, the kinetic energy of the system is determined, as well as the generalised forces affecting the system. The resulting mathematical model of a wheeled mobile robot was generated with the use of Maple V software. The results of a solution of inverse and forward problems of dynamics of the discussed object are also published.
Directory of Open Access Journals (Sweden)
Makkulau Makkulau
2010-01-01
Full Text Available There are several problems in industrial process for example problems associated with product quality. In statistics, observation which is significantly different to the average is called outlier. The outlier can give significant influence to the result of modeling, which can affect the decision making. This research develops the outlier detection method using the Likelihood Displacement Statistic method, called Likelihood Displacement Statistic-Lagrange (LDL method. The LDL method is applied to sugar and molasses production data of Djombang Baru Sugar Factory, Jombang, East Java. The result of this research shows that factors influenced the sugar and molasses production are sugar cane with the dirt less than 5%, sugar cane with the dirt between 5% to 7%, sugar cane with the dirt higher than 7%, and imbibition water
Institute of Scientific and Technical Information of China (English)
张孝彩; 张毅
2016-01-01
The Lie symmetry and the conserved quantity of fractional Lagrange system based on El-Nabulsi models are studied.Firstly,the D’Alembert-Lagrange principle of the El-Nabulsi models is de-duced based on the fractional action-like variational problem which is expanded by the Riemann-Liouville integral,and the differential equations of motion of the system are obtained.Secondly,the definition and the criterion of the Lie symmetry are given,the determination equations of the Lie symmetry of the system are established,and the generalized Hojman theorem is put forward.At the same time,the existence condition and the form of the generalized Hojman conserved quantity are obtained.Then,the generalized Noether theorem is established,the existence condition and the form of the Noether conserved quantity led by the Lie symmetry are given.Finally,two examples are given to illustrate the application of the re-sults.%研究基于 El-Nabulsi 模型的分数阶 Lagrange 系统的 Lie 对称性与守恒量。基于按 Riemann-Liouville 积分拓展的类分数阶变分问题导出 El-Nabulsi 模型的 D’Alembert-Lagrange 原理，得到系统的运动微分方程；给出分数阶 Lie 对称性的定义和判据，建立了 Lie 对称性确定方程，并提出广义 Hojman 定理，给出广义 Hojman 守恒量存在的条件及其形式；最后，建立了广义 Noether 定理，给出分数阶 Lie 对称性导致 Noether 守恒量的条件及其形式，并给出两个算例以说明结果的应用。
A knowledge discovery approach to explore some Sun/Earth's climate relationships
Pou, A.; Valdes, J.
2009-09-01
Recent developments in data driven modeling and analysis including computational intelligence techniques may throw new light on the exploration of possible solar activity/Earth's climate relationships. Here we present three different examples of methodologies under development and some preliminary results. a) Multivariate Time Series Model Mining (MVTSMM) analysis [1] and Genetic Programming were applied to Greenland's CRETE Site-E ice core Delta O18/16 values (1721-1983, one year interval sampling) and with sunspots activity (International Sunspots Number) during the same time span [2]. According to the results (1771 to 1933 period) indicated by the lag importance spectrum obtained with MVTSMM analysis, the sun's activity itself shows high internal variability and is inhomogeneous. The Dalton minimum, a low activity period usually considered to occur between 1790 and 1830, is shown to be a complex structure beginning about 1778 and ending in 1840. Apparently, the system entered a new state in 1912. In the joint analysis, the analytical tool uses extensively the solar activity data to explain the Delta O18/16 data, showing areas of stable patterns, lag drifts and abrupt pattern disruptions, indicating changes of state in the solar processes of several kinds at different times. b) A similar MVTSMM analysis was conducted on Central England Temperature (CET) and solar activity data using Group Sunspots Number (GSN) with a useful interpretive span of time from 1771 to 1916. The joint analysis involved large amounts of solar activity variables, except for the 1843-1862 and 1877-1889 periods where the discovered models used much less information from GSN data. As with the Crete-E/ISN analysis the lag importance spectrum of CET/GSN shows a number of clear discontinuities. A quarter of them are present in both (1778-1779, 1806, 1860-1862, 1912-1913). These experiments were designed for testing methodologies and not for specific hypothesis testing. However, it seems that Delta O18/16 data would more readily respond to solar influences. This raises the suspicion that perhaps they do not only reflect temperatures but also solar activity, as well as other possible factors not directly related to atmospheric temperatures. These methodologies may be useful as exploratory tools, directing the attention to specific areas where further research should be required. This could be the case of the Delta O18/16 data, frequently considered to be a reliable and accurate proxy of temperatures. c) Another experiment was made using daily maximum temperatures from 10 Spanish meteorological stations for the period 1901-2005 [3]. Using a hybrid procedure (Differential Evolution and Fletcher-Reeves Classical Optimization) it was found that a subset was capable of preserving the 10-dimensional similarity when nonlinearly mapped into 1D. A daily index, F1 was applied to the whole dataset and grouped by years and transformed into a Kolmogorov-Smirnov dissimilarity matrix, space optimized and clustered giving the following landmarks: 1911-12, 1919-1920, 1960, 1973 and 1989. A visual comparison with the aa geomagnetic index may suggest a certain coupling with changes in the magnetic field behavior. The complexity of the patterns suggest that the possible relationships between Earth's climate and solar activity may occur in much more complex ways than just irradiance variations and simple linear correlations. REFERENCES: [1] Valdés, J.J., Bonham-Carter, G. " Time Dependent Neural Network Models For Detecting Changes of State in Complex Processes: Applications in Earth Sciences and Astronomy”. Neural Networks, vol 19, (2), pp 196-207, 2006. [2] Valdés, J., Pou, A. "Greenland Temperatures and Solar Activity: A Computational Intelligence Approach," Proceedings of the 2007 IEEE International Joint Conference on Neural Networks (IJCNN 2007). Orlando, Florida, USA. August 12-17, 2007. [3] Valdés, J., Pou, A., Orchard, B. "Characterization of Climatic Variations in Spain at the Regional Scale: A Computational Intelligence Approach," Proceedings of the IEEE World Congress on Computational Intelligence (WCCI-2008). Hong Kong, China. June 1, 2008.
Sun, the Earth, and Near-Earth Space: A Guide to the Sun-Earth System
Eddy, John A.
2010-01-01
In a world of warmth and light and living things we soon forget that we are surrounded by a vast universe that is cold and dark and deadly dangerous, just beyond our door. On a starry night, when we look out into the darkness that lies around us, the view can be misleading in yet another way: for the brightness and sheer number of stars, and their chance groupings into familiar constellations, make them seem much nearer to each other, and to us, that in truth they are. And every one of them--each twinkling, like a diamond in the sky--is a white-hot sun, much like our own. The nearest stars in our own galaxy--the Milky Way-- are more than a million times further away from us than our star, the Sun. We could make a telephone call to the Moon and expect to wait but a few seconds between pieces of a conversation, or but a few hours in calling any planet in our solar system.
High-Performance Data Analysis Tools for Sun-Earth Connection Missions Project
National Aeronautics and Space Administration — The Interactive Data Language (IDL) is a standard tool used by many researchers in observational fields. Present day Sun-Earch Connection missions like RHESSI or...
International Symposium on Recent Observations and Simulations of the Sun-Earth System
2007-01-10
Dynamics and the Response of Geospace 14. Chertoprud V., Ioshpa B., Obridko V.: Fractal Properties of Magnetic Fields of Active and Quiet Solar...Andenes, Norway. The project is partly financed by the Bulgarian Ministry of Science and Education. OTHER RELATED TOPICS: POSTER... Fractal
Effectiveness of GeoWall Visualization Technology for Conceptualization of the Sun-Earth-Moon System
Turner, N. E.; Gray, C.; Mitchell, E. J.
2004-12-01
One persistent difficulty many introductory astronomy students face is the lack of a 3-dimensional mental model of the Earth-Moon system. Students without such a mental model can have a very hard time conceptualizing the geometric relationships that cause the cycle of lunar phases. The GeoWall is a recently developed and affordable projection mechanism for three-dimensional stereo visualization which is becoming a popular tool in classrooms and research labs. We present results from a study using a 3-D GeoWall with a simulated sunlit Earth-Moon system on undergraduate students' ability to understand the origins of lunar phases. We test students exposed to only in-class instruction, some with a laboratory exercise using the GeoWall Earth-Moon simulation, some students who were exposed to both, and some with an alternate activity involving lunar observations. Students are given pre and post tests using the a diagnostic test called the Lunar Phase Concept Inventory (LPCI). We discuss the effectiveness of this technology as a teaching tool for lunar phases.
Colorado Lights: Exploring the Sun-Earth Connection through Art and Writing
Possel, T.; Cobabe-Ammann, E.; Wood, E.; Becker, K.
2007-12-01
Over the last decade, it has become increasingly clear that science can be an important way to excite children about reading, writing and the arts. The natural beauty that science represents inspires students to both think about the world around them and strive to find the words and images that communicate their excitement. Colorado Lights is a new program that provides a set of five activities for students in Grades 3 through 5 to explore the beauty, science and mythology of the aurora creatively through art and writing. This standards-based, flexible 'plug-and-play' program is based on the latest research on bringing science into the literacy and art classroom. It can be used as a complete sequence of lessons or can be used as guidelines for teachers to develop their own activities.
2003-03-01
Mars: Express journey to Mars ASE 2003: Knocked out by meteorites Events: Sun-Earth Day ASE 2003: Fun Physics - popular as ever Appointments: Sykes to bring science to the people UK Science Education: The future's bright, the future's science ASE 2003: A grand finale for Catherine Teaching Resources: UK goes to the planets Cambridge Physics Update: Basement physics Conferences: Earth Science Teachers' Association Conference 2003 New Website: JESEI sets sail GIREP: Teacher education seminar Malaysia: Rewards for curriculum change Cambridge Physics Update: My boomerang will come back! Teaching Resources: Widening particiption through ideas and evidence with the University of Surrey Wales: First Ffiseg Events: Nuna: Solar car on tour Physics on Stage: Physics on Stage 3 embraces life Symposium: In what sense a nuclear 'debate'? Gifted and Talented: Able pupils experiencing challenging science Australia: ISS flies high Down Under
Directory of Open Access Journals (Sweden)
E. W. Grafarend
1997-06-01
Full Text Available The length of the gravitational field lines/of the orthogonal trajectories of a family of gravity equipotential surfaces/of the plumbline between a terrestrial topographic point and a point on a reference equipotential surface like the geoid í also known as the orthometric height í plays a central role in Satellite Geodesy as well as in Physical Geodesy. As soon as we determine the geometry of the Earth pointwise by means of a satellite GPS (Global Positioning System: «global problem solver» we are left with the problem of converting ellipsoidal heights (geometric heights into orthometric heights (physical heights. For the computation of the plumbline we derive its three differential equations of first order as well as the three geodesic equations of second order. The three differential equations of second order take the form of a Newton differential equation when we introduce the parameter time via the Marussi gauge on a conformally flat three-dimensional Riemann manifold and the generalized force field, the gradient of the superpotential, namely the modulus of gravity squared and taken half. In particular, we compute curvature and torsion of the plumbline and prove their functional relationship to the second and third derivatives of the gravity potential. For a spherically symmetric gravity field, curvature and torsion of the plumbline are zero, the plumbline is straight. Finally we derive the three Lagrangean as well as the six Hamiltonian differential equations of the plumbline, in particular in their star form with respect to Marussi gauge.
Battista, Emmanuele; Dell'Agnello, Simone; Esposito, Giampiero; Di Fiore, Luciano; Simo, Jules; Grado, Aniello
2015-09-01
equilibrium we find quantum corrections below a millimeter. In the latter case, for the point L1, general relativity corrects Newtonian theory by 7.61 m, comparable, as an order of magnitude, with the lunar geodesic precession of about 3 m per orbit. The latter is a cumulative effect accurately measured at the centimeter level through the lunar laser ranging positioning technique. Thus, it is possible to study a new laser ranging test of general relativity to measure the 7.61 m correction to the L1 Lagrangian point, an observable never used before in the Sun-Earth-Moon system. Performing such an experiment requires controlling the propulsion to precisely reach L1, using an instrumental accuracy comparable to the measurement of the lunar geodesic precession, and understanding systematic effects resulting from thermal radiation and multibody gravitational perturbations. This will then be the basis to consider a second-generation experiment to study deviations of effective field theories of gravity from general relativity in the Sun-Earth-Moon system.
基于Lagrange方法的单旋翼飞行器动力学建模%Dynamics modeling for monowing rotorcraft using Lagrange method
Institute of Scientific and Technical Information of China (English)
李家乐; 王正平
2016-01-01
For the dynamics modeling for the microminiature monowing rotorcraft,several coordinate systems for different parts of the vehicle were set up to reflect the relative movements.Firstly,vectors such as position,velocity and acceleration were obtained by transformation of coordinates,and substituted into Lagrange equation to get dynamic model.Then,attitude responses were obtained by numerical calculation of the model.Simulation results show that the force is zero and the energy remains constant when the rotorcraft is hovering;non-conservative force works and the energy increase when the rotorcraft is climbing or flying forward.%为了进行微小型单旋翼飞行器的动力学建模,通过建立多个坐标系来反映各部分间的相对运动.首先,利用坐标变换得到位置、速度及加速度等向量,并代入拉格朗日方程得到运动学模型;然后,对模型进行数值求解,得到飞行器的姿态响应.仿真结果表明,飞行器定点盘旋时合外力为零,能量保持不变;爬升或前飞时有非保守力做正功,能量增大.
Directory of Open Access Journals (Sweden)
Aksjonov Andrei
2015-12-01
Full Text Available The mathematical model of the three-dimensional crane using the Euler-Lagrange approach is derived. A state-space representation of the derived model is proposed and explored in the Simulink® environment and on the laboratory stand. The obtained control design was simulated, analyzed and compared with existing encoder-based system provided by the three-dimensional (3D Crane manufacturer Inteco®. As well, an anti-swing fuzzy logic control has been developed, simulated, and analyzed. Obtained control algorithm is compared with the existing anti-swing proportional-integral controller designed by the 3D crane manufacturer Inteco®. 5-degree of freedom (5DOF control schemes are designed, examined and compared with the various load masses. The topicality of the problem is due to the wide usage of gantry cranes in industry. The solution is proposed for the future research in sensorless and intelligent control of complex motor driven application.
Seichter, Felicia; Vogt, Josef; Radermacher, Peter; Mizaikoff, Boris
2017-01-25
The calibration of analytical systems is time-consuming and the effort for daily calibration routines should therefore be minimized, while maintaining the analytical accuracy and precision. The 'calibration transfer' approach proposes to combine calibration data already recorded with actual calibrations measurements. However, this strategy was developed for the multivariate, linear analysis of spectroscopic data, and thus, cannot be applied to sensors with a single response channel and/or a non-linear relationship between signal and desired analytical concentration. To fill this gap for a non-linear calibration equation, we assume that the coefficients for the equation, collected over several calibration runs, are normally distributed. Considering that coefficients of an actual calibration are a sample of this distribution, only a few standards are needed for a complete calibration data set. The resulting calibration transfer approach is demonstrated for a fluorescence oxygen sensor and implemented as a hierarchical Bayesian model, combined with a Lagrange Multipliers technique and Monte-Carlo Markov-Chain sampling. The latter provides realistic estimates for coefficients and prediction together with accurate error bounds by simulating known measurement errors and system fluctuations. Performance criteria for validation and optimal selection of a reduced set of calibration samples were developed and lead to a setup which maintains the analytical performance of a full calibration. Strategies for a rapid determination of problems occurring in a daily calibration routine, are proposed, thereby opening the possibility of correcting the problem just in time.
Trajectory refinement of three-body orbits in the real solar system model
Dei Tos, Diogene A.; Topputo, Francesco
2017-04-01
In this paper, an automatic algorithm for the correction of orbits in the real solar system model is described. The differential equations governing the dynamics of a massless particle in the n-body problem are written as perturbation of the circular restricted three-body problem in a non-uniformly rotating, pulsating frame by using a Lagrangian formalism. The refinement is carried out by means of a modified multiple shooting technique, and the problem is solved for a finite number of trajectory states at several time instants. The analysis involves computing the dynamical substitutes of the collinear points, as well as several Lagrange point orbits, for the Sun-Earth, Sun-Jupiter, and Earth-Moon gravitational systems.
一种基于Lagrange神经网络的多用户检测器%A Multiuser Detector Based on Lagrange Neural Network
Institute of Scientific and Technical Information of China (English)
唐普英; 陈永倩; 黄顺吉
2001-01-01
提出并讨论了一种基于Lagrange神经网络的多用户检测器，利用神经网络能有效地求解优化问题；推导了Lagrange神经网络多用户检测器(LNN-MUD)。理论分析和计算结果表明：在误比特性能和抗干扰性能上，该检测器均优于传统检测器和解相关检测器；在抗“远近”干扰能力方面，该检测器优于传统检测器而弱于解相关检测器，且易于实时应用和VLSI实现。%According to the optimization theory and the neural network (NN)theory, a multiuser detector (MUD) is proposed, which takes the optimum MUD problem as combinatorial optimum problem. Using the neural network which has the ability of fast optimization computing, the Lagrange neural network (LNN) MUD is derived. Theoretical analysis and numerical results show that in aspect of bit-error rate and multiple access interfernce, the LNN MUD is better than the conventional and decorrelated MUD in aspect of "near-far" resistance, the LNN MUD is better than the conventional MUD and worse than the decorrelated detector and the LNN MUD can be easily implemented by VLSI technology.
Xu, Rong-dong; Li, Heng
2005-04-01
In the light of obscure conception of Ashi points in the circle of acupuncture and moxibustion at present, this article tries to clarify the origin and definition of Ashi points by textual research of literatures. It is put forward that Ashi points are not the same with "tender spot" and "Buding point, Tianying point", but are some special responding points, including regular points and extra points, when the organism is ill. When these points are pressed the organism will be comfortable or painful. And the definition, location and clinical location method of Ashi points are proposed.
Gordon, Steven C.
1993-01-01
Spacecraft in orbit near libration point L1 in the Sun-Earth system are excellent platforms for research concerning solar effects on the terrestrial environment. One spacecraft mission launched in 1978 used an L1 orbit for nearly 4 years, and future L1 orbital missions are also being planned. Orbit determination and station-keeping are, however, required for these orbits. In particular, orbit determination error analysis may be used to compute the state uncertainty after a predetermined tracking period; the predicted state uncertainty levels then will impact the control costs computed in station-keeping simulations. Error sources, such as solar radiation pressure and planetary mass uncertainties, are also incorporated. For future missions, there may be some flexibility in the type and size of the spacecraft's nominal trajectory, but different orbits may produce varying error analysis and station-keeping results. The nominal path, for instance, can be (nearly) periodic or distinctly quasi-periodic. A periodic 'halo' orbit may be constructed to be significantly larger than a quasi-periodic 'Lissajous' path; both may meet mission requirements, but perhaps the required control costs for these orbits are probably different. Also for this spacecraft tracking and control simulation problem, experimental design methods can be used to determine the most significant uncertainties. That is, these methods can determine the error sources in the tracking and control problem that most impact the control cost (output); it also produces an equation that gives the approximate functional relationship between the error inputs and the output.
Dettagli utilizzo cluster HP "Lagrange"
2008-01-01
Dal mese di marzo il CILEA ospita e gestisce il cluster “lagrange” costituito da 208 nodi bi-processore Intel quad-core 5460. L'articolo intende presentare le problematiche relative all'utilizzo della macchina fornendo le istruzioni operative necessarie all'uso più efficace.
Stabilization and set-point regulation of underactuated mechanical systems
Loccufier, Mia
2016-09-01
Mechanical systems are referred to as underactuated if the number of independent actuators are fewer than the number of degrees of freedom, a general encountered problem in engineering applications. The considered mechanical systems belong to the class of Euler- Lagrange systems where both kinetic energy and potential energy are modeled in their most general form and energy dissipation is modeled according to the dissipation function of Rayleigh, i.e. viscous damping forces are assumed. The control objectives are stabilization and set-point regulation. The structure of the controller is a parallel combination of static output feedback with dynamic output feedback where nonlinear amplifiers are included. An energy based approach with Liapunov functions and the Kalman-Yacubovich-Popov main lemma yields alternative stability theorems. A number of conditions are introduced with respect to the controller's structure in order to guarantee stability. However, sufficient design freedom is left to choose a proper tuning principle and obtain the specified control objectives such as fast convergence to a set-point combined with disturbance rejection. A restriction on the control input energy can be incorporated as well. The applicability of the method will be illustrated with planar manipulators. The main contribution is that a methodology is developed which incorporates many controllers and tuning facilities.
Prediction of Geomagnetic Storm Strength from Inner Heliospheric In Situ Observations
Kubicka, M.; Möstl, C.; Amerstorfer, T.; Boakes, P. D.; Feng, L.; Eastwood, J. P.; Törmänen, O.
2016-12-01
Prediction of the effects of coronal mass ejections (CMEs) on Earth strongly depends on knowledge of the interplanetary magnetic field southward component, B z . Predicting the strength and duration of B z inside a CME with sufficient accuracy is currently impossible, forming the so-called B z problem. Here, we provide a proof-of-concept of a new method for predicting the CME arrival time, speed, B z , and resulting disturbance storm time (Dst) index on Earth based only on magnetic field data, measured in situ in the inner heliosphere (vector magnetic field data from a spacecraft at an artificial Lagrange point between the Sun and Earth or to data taken by any spacecraft temporarily crossing the Sun-Earth line.
Mission design for LISA Pathfinder
Landgraf, M; Kemble, S
2004-01-01
Here we describe the mission design for SMART-2/LISA Pathfinder. The best trade-off between the requirements of a low-disturbance environment and communications distance is found to be a free-insertion Lissajous orbit around the first co-linear Lagrange point of the Sun-Earth system L1, 1.5x 10^6 km from Earth. In order to transfer SMART-2/LISA Pathfinder from a low Earth orbit, where it will be placed by a small launcher, the spacecraft carries out a number of apogee-raise manoeuvres, which ultimatively place it to a parabolic escape trajectory towards L1. The challenges of the design of a small mission are met, fulfilling the very demanding technology demonstration requirements without creating excessive requirements on the launch system or the ground segment.
JWST observations of stellar occultations by solar system bodies and rings
Santos-Sanz, P; Pinilla-Alonso, N; Stansberry, J; Lin, Z-Y; Zhang, Z-W; Vilenius, E; Müller, Th; Ortiz, J L; Braga-Ribas, F; Bosh, A; Duffard, R; Lellouch, E; Tancredi, G; Young, L
2015-01-01
In this paper we investigate the opportunities provided by the James Webb Space Telescope (JWST) for significant scientific advances in the study of solar system bodies and rings using stellar occultations. The strengths and weaknesses of the stellar occultation technique are evaluated in light of JWST's unique capabilities. We identify several possible JWST occultation events by minor bodies and rings, and evaluate their potential scientific value. These predictions depend critically on accurate a priori knowledge of the orbit of JWST near the Sun-Earth Lagrange-point 2 (L2). We also explore the possibility of serendipitous stellar occultations by very small minor bodies as a by-product of other JWST observing programs. Finally, to optimize the potential scientific return of stellar occultation observations, we identify several characteristics of JWST's orbit and instrumentation that should be taken into account during JWST's development.
Datsenko, I.; Lozovenko, O.; Minaiev, Yu
2016-09-01
In their recent paper, Wang and Su (2015 Eur. J. Phys. 36 055010) acquainted readers with a solution to a problem about the optimal shape of an object for generating a maximum gravity field at a given point in space. After applying the variational principal and the Euler-Lagrange equation they obtained the shape for two-, three- and arbitrary n-dimensional cases. We are convinced that the problem is interesting enough to consider it with students. In this Comment we will try to present an easier way to solve it for the three-dimensional space.
Institute of Scientific and Technical Information of China (English)
李蔚; 黄云清; 周佳立
2012-01-01
用构造最优局部逼近空间的方法对Lagrange型四边形单位分解有限元法进行了最优误差分析.单位分解取Lagrange型四边形上的标准双线性基函数,构造了一个特殊的局部多项式逼近空间,给出了具有2阶再生性的Lagrange型四边形单位分解有限元插值格式,从而得到了高于局部逼近阶的最优插值误差.%In this paper, by constructing a optimal local approximation space,we investigate optimal error estimates for partition of unity finite element method(PUFEM) on Lagrange rectangle.Using standard base functions defined on bilinear Lagrange rectangle as partition of unity ,a special polynomial local approximation space is established,then PUFEM interpolants with reproducing property of order 2 is constructed. Thereby we derive the optimal error estimates of higher order than the local approximations for PUFEM interpolants.
Ultimate generalization of Noether's theorem in the realm of Hamiltonian point dynamics
Struckmeier, Jürgen
2012-01-01
Noether's theorem in the realm of point dynamics establishes the correlation of a constant of motion of a Hamilton-Lagrange system with a particular symmetry transformation that preserves the form of the action functional. Although usually derived in the Lagrangian formalism, the natural context for deriving Noether's theorem for first-order Lagrangian systems is the Hamiltonian formalism. The reason is that the class of transformations that leave the action functional invariant coincides with the class of canonical transformations. As a result, any invariant of a Hamiltonian system can be correlated with a symmetry transformation simply by means of the canonical transformation rules. As this holds for any invariant, we thereby obtain the most general representation of Noether's theorem. In order to allow for symmetry mappings that include a transformation of time, we must refer to the extended Hamiltonian formalism. This formalism enables us to define generating functions of canonical transformations that al...
2004-04-01
Point clouds are one of the most primitive and fundamental surface representations. A popular source of point clouds are three dimensional shape...acquisition devices such as laser range scanners. Another important field where point clouds are found is in the representation of high-dimensional...framework for comparing manifolds given by point clouds is presented in this paper. The underlying theory is based on Gromov-Hausdorff distances, leading
Space time as a continuum with a point defect
Tartaglia, A
2006-01-01
In cosmology it has become usual to try and explain observational data, such as the temperature distribution of the cosmic microwave background or the accelerated expansion of the universe, introducing new entities as dark matter and dark energy. Here we describe a different approach treating space time as a continuum endowed with properties similar to the ones of ordinary material continua, such as internal viscosity and strain distributions originated by defects in the texture. A Lagrangian modelled on the one valid for simple dissipative phenomena in fluids is build and used for empty space time. The internal "viscosity" is shown to correspond to a four-vector field. Using the known symmetry of the universe, assuming the vector field to be divergence-less and solving the Euler-Lagrange equation we obtain directly inflation and a phase of accelerated expansion of space time. The vector field is shown to be connected with the displacement vector field induced by a point defect in a four-dimensional continuum...
Point by Point: Adding up Motivation
Marchionda, Denise
2010-01-01
Students often view their course grades as a mysterious equation of teacher-given grades, teacher-given grace, and some other ethereal components based on luck. However, giving students the power to earn points based on numerous daily/weekly assignments and attendance makes the grading process objective and personal, freeing the instructor to…
Esthetics in Orthodontics: interest points, reference points and discrepancy points
Directory of Open Access Journals (Sweden)
Carlos Alexandre Câmara
2012-10-01
Full Text Available It is fundamental for orthodontists and all professionals related with facial, oral and dental esthetics to know how the individuals observe dentofacial structures. Thus, it will be the purpose of this Orthodontic Insight to present and describe the Interest, Reference and Discrepancy. Points With the knowledge and perception of these points it will be easier for orthodontists to create a convergent canal of communication with their patients.É fundamental para os ortodontistas e todos os profissionais que estão envolvidos com a estética facial, bucal e dentária conhecer a forma como os indivíduos observam as estruturas dentofaciais. Sendo assim, será o objetivo desse artigo apresentar e descrever os pontos de Interesse, de Referência e de Discrepância. Com o conhecimento e percepção desses pontos, será mais fácil para os ortodontistas criar canais convergentes de comunicação com os seu pacientes.
A maximum power point tracking algorithm for photovoltaic applications
Nelatury, Sudarshan R.; Gray, Robert
2013-05-01
The voltage and current characteristic of a photovoltaic (PV) cell is highly nonlinear and operating a PV cell for maximum power transfer has been a challenge for a long time. Several techniques have been proposed to estimate and track the maximum power point (MPP) in order to improve the overall efficiency of a PV panel. A strategic use of the mean value theorem permits obtaining an analytical expression for a point that lies in a close neighborhood of the true MPP. But hitherto, an exact solution in closed form for the MPP is not published. This problem can be formulated analytically as a constrained optimization, which can be solved using the Lagrange method. This method results in a system of simultaneous nonlinear equations. Solving them directly is quite difficult. However, we can employ a recursive algorithm to yield a reasonably good solution. In graphical terms, suppose the voltage current characteristic and the constant power contours are plotted on the same voltage current plane, the point of tangency between the device characteristic and the constant power contours is the sought for MPP. It is subject to change with the incident irradiation and temperature and hence the algorithm that attempts to maintain the MPP should be adaptive in nature and is supposed to have fast convergence and the least misadjustment. There are two parts in its implementation. First, one needs to estimate the MPP. The second task is to have a DC-DC converter to match the given load to the MPP thus obtained. Availability of power electronics circuits made it possible to design efficient converters. In this paper although we do not show the results from a real circuit, we use MATLAB to obtain the MPP and a buck-boost converter to match the load. Under varying conditions of load resistance and irradiance we demonstrate MPP tracking in case of a commercially available solar panel MSX-60. The power electronics circuit is simulated by PSIM software.
Institute of Scientific and Technical Information of China (English)
朱俊鹏; 徐江荣; 王路
2014-01-01
基于两相湍流PDF理论，颗粒矩拉格朗日方程可以通过求解颗粒PDF输运方程获得，但不同的数学方法推导获得的颗粒PDF输运方程形式是不同的，哪一种颗粒PDF输运方程的形式更可靠呢？该文先介绍不同形式的颗粒PDF输运方程，然后给出了使用颗粒PDF输运方程获得的颗粒矩拉格朗日方程。另一方面，从颗粒朗之万方程出发，用简单平均的方法推导颗粒运动一阶矩与二阶矩拉格朗日方程组，将这两种不同方法得到的结果进行比较。结果表明，基于色噪声扩维法PDF理论得到的颗粒矩方程组更为可靠。%The particle moment Lagrange equations can be obtained by solving the particle probability density function( PDF) transport equation based on PDF two-phase theory.But different mathematical methods obtain different forms of PDF transport equations.Which form is more reliable? In this paper, the different forms PDF transport equations are introduced firstly, and then the particle moment Lagrange equations are given by using PDF transport equation.On the other hand, with Langevin equation, one-order and two-order moment Lagrange equations are derived with a simple average method and the results of these two different methods are compared.It is shown that the moment equations based on PDF theory with expanding dimension method of colored noise is more reliable.
DEFF Research Database (Denmark)
Aanæs, Henrik; Dahl, Anders Lindbjerg; Pedersen, Kim Steenstrup
2012-01-01
on spatial invariance of interest points under changing acquisition parameters by measuring the spatial recall rate. The scope of this paper is to investigate the performance of a number of existing well-established interest point detection methods. Automatic performance evaluation of interest points is hard......Not all interest points are equally interesting. The most valuable interest points lead to optimal performance of the computer vision method in which they are employed. But a measure of this kind will be dependent on the chosen vision application. We propose a more general performance measure based...... position. The LED illumination provides the option for artificially relighting the scene from a range of light directions. This data set has given us the ability to systematically evaluate the performance of a number of interest point detectors. The highlights of the conclusions are that the fixed scale...
Serial floating point formatter
Energy Technology Data Exchange (ETDEWEB)
Peterson, R. D.; Penner, W. A.
1985-11-12
A floating point formatter for changing fixed point serial digital data, such as that received by a seismic data acquisition system, is disclosed wherein fixed point serial digital data is received and scaled to remove any bias added by preamplification. The scaled data is shifted a predetermined number of bits and a resulting exponent is calculated. The shifted data signal and corresponding exponent are combined and further scaled to permit stacking the data without exceeding the system capacity.
Hongchuan Yu; Zhang, Jian J.; Zheng Jiao
2014-01-01
We present a novel framework to compute geodesics on implicit surfaces and point clouds. Our framework consists of three parts, particle based approximate geodesics on implicit surfaces, Cartesian grid based approximate geodesics on point clouds, and geodesic correction. The first two parts can effectively generate approximate geodesics on implicit surfaces and point clouds, respectively. By introducing the geodesic curvature flow, the third part produces smooth and accurate geodesic solution...
The quantization of the Horava theory at the kinetic-conformal point
Bellorin, Jorge
2016-01-01
The kinetic-conformal point for the Horava theory is the point lambda = 1/3, where lambda is the independent dimensionless coupling arising in the kinetic term of the theory. At this point the kinetic term acquires conformal invariance although the full theory is not conformally invariant. For any value of lambda the nonprojectable version of the theory has second-class constraints, which play a central role in the process of quantization. Here we study the nonprojectable theory at the kinetic-conformal point. The generic counting of degrees of freedom indicates that this theory propagates the same physical degrees of freedom of general relativity. We analyze this point rigorously taking all the z=1,2,3 terms that contribute to the action of quadratic order in perturbations. We obtain an elliptic structure for all the constraints and equations for the Lagrange multipliers and show how their solutions lead to the two independent tensorial modes together with their reduced Hamiltonian. This strengthens the cons...
Linton, J. Oliver
2017-03-01
There are five unique points in a star/planet system where a satellite can be placed whose orbital period is equal to that of the planet. Simple methods for calculating the positions of these points, or at least justifying their existence, are developed.
Model Breaking Points Conceptualized
Vig, Rozy; Murray, Eileen; Star, Jon R.
2014-01-01
Current curriculum initiatives (e.g., National Governors Association Center for Best Practices and Council of Chief State School Officers 2010) advocate that models be used in the mathematics classroom. However, despite their apparent promise, there comes a point when models break, a point in the mathematical problem space where the model cannot,…
Choudhary, Debi Prasad
2010-01-01
We used the flux calibrated images through the Broad Band Filter Imager and Stokes Polarimeter data obtained with the Solar Optical Telescope onboard the Hinode spacecraft to study the properties of bright points in and around the sunspots. The well isolated bright points were selected and classified as umbral dot, peripheral umbral dot, penumbral grains and G-band bright point depending on their location. Most of the bright points are smaller than about 150 km. The larger points are mostly associated with the penumbral features. The bright points are not uniformly distributed over the umbra but preferentially located around the penumbral boundary and in the fast decaying parts of umbra. The color temperature of the bright points, derived using the continuum irradiance, are in the range of 4600 K to 6600 K with cooler ones located in the umbra. The temperature increases as a function of distance from the center to outside. The G-band, CN-band and CaII H flux of the bright points as a function of their blue ba...
Chiaverina, Chris; Lisensky, George
2014-01-01
Ferromagnetic materials such as nickel, iron, or cobalt lose the electron alignment that makes them attracted to a magnet when sufficient thermal energy is added. The temperature at which this change occurs is called the "Curie temperature," or "Curie point." Nickel has a Curie point of 627 K, so a candle flame is a sufficient…
Model Breaking Points Conceptualized
Vig, Rozy; Murray, Eileen; Star, Jon R.
2014-01-01
Current curriculum initiatives (e.g., National Governors Association Center for Best Practices and Council of Chief State School Officers 2010) advocate that models be used in the mathematics classroom. However, despite their apparent promise, there comes a point when models break, a point in the mathematical problem space where the model cannot,…
Holographic Three point Functions
DEFF Research Database (Denmark)
Bissi, Agnese
In this thesis it is addressed the problem of the computation of three point correlation functions within the AdS=CFT correspondence. In the context of the AdS 5=CFT4 correspondence we present three computations. First we compare the results of tree level three point functions of two giant...... gravitons and a point like graviton and its dual counterpart, namely two Schur polynomials and a single trace chiral primary. Secondly we compute the one loop correction to planar, non extremal three point functions of two heavy and one light operators, both from the gauge and string side in the Frolov......-Tseytlin regime. Finally we generalize the scalar product of two states belonging to the SO(6) sector of N = 4 SYM with implications on the construction of three point functions of 3 non-BPS operators from the gauge theory side. On the other hand in the AdS4=CFT3 correspondence we compare the computations...
Multispectral Image Feature Points
Directory of Open Access Journals (Sweden)
Cristhian Aguilera
2012-09-01
Full Text Available This paper presents a novel feature point descriptor for the multispectral image case: Far-Infrared and Visible Spectrum images. It allows matching interest points on images of the same scene but acquired in different spectral bands. Initially, points of interest are detected on both images through a SIFT-like based scale space representation. Then, these points are characterized using an Edge Oriented Histogram (EOH descriptor. Finally, points of interest from multispectral images are matched by finding nearest couples using the information from the descriptor. The provided experimental results and comparisons with similar methods show both the validity of the proposed approach as well as the improvements it offers with respect to the current state-of-the-art.
Holographic Three point Functions
DEFF Research Database (Denmark)
Bissi, Agnese
In this thesis it is addressed the problem of the computation of three point correlation functions within the AdS=CFT correspondence. In the context of the AdS 5=CFT4 correspondence we present three computations. First we compare the results of tree level three point functions of two giant...... gravitons and a point like graviton and its dual counterpart, namely two Schur polynomials and a single trace chiral primary. Secondly we compute the one loop correction to planar, non extremal three point functions of two heavy and one light operators, both from the gauge and string side in the Frolov......-Tseytlin regime. Finally we generalize the scalar product of two states belonging to the SO(6) sector of N = 4 SYM with implications on the construction of three point functions of 3 non-BPS operators from the gauge theory side. On the other hand in the AdS4=CFT3 correspondence we compare the computations...
DEFF Research Database (Denmark)
Elleby, Anita; Ingwersen, Peter
2010-01-01
with novel publication point indicators (PPIs) that are formalized and exemplified. Two diachronic citation windows are applied: 2006-07 and 2006-08. Web of Science (WoS) as well as Google Scholar (GS) are applied to observe the cite delay and citedness for the different document types published by DIIS......The paper presents comparative analyses of two publication point systems, The Norwegian and the in-house system from the interdiscplinary Danish Institute for International Studies (DIIS), used as case in the study for publications published 2006, and compares central citation-based indicators......; the Cumulated Publication Point Indicator (CPPI), which graphically illustrates the cumulated gain of obtained vs. ideal points, both seen as vectors; and the normalized Cumulated Publication Point Index (nCPPI) that represents the cumulated gain of publication success as index values, either graphically...
Lennartsson, O. W.
1994-01-01
The Lockheed plasma composition experiment on the ISEE 1 spacecraft has provided one of the largest and most varied sets of data on earth's energetic plasma environment, covering both the solar wind, well beyond the bow shock, and the near equatorial magnetosphere to a distance of almost 23 earth radii. This report is an overview of the last four years of data analysis and archiving. The archiving for NSSDC includes most data obtained during the initial 28-months of instrument operation, from early November 1977 through the end of February 1980. The data products are a combination of spectra (mass and energy angle) and velocity moments. A copy of the data user's guide and examples of the data products are attached as appendix A. The data analysis covers three major areas: solar wind ions upstream and downstream of the day side bowshock, especially He(++) ions; terrestrial ions flowing upward from the auroral regions, especially H(+), O(+), and He(+) ions; and ions of both solar and terrestrial origins in the tail plasma sheet and lobe regions. Copies of publications are attached.
Lennartsson, O. W.
1994-05-01
The Lockheed plasma composition experiment on the ISEE 1 spacecraft has provided one of the largest and most varied sets of data on earth's energetic plasma environment, covering both the solar wind, well beyond the bow shock, and the near equatorial magnetosphere to a distance of almost 23 earth radii. This report is an overview of the last four years of data analysis and archiving. The archiving for NSSDC includes most data obtained during the initial 28-months of instrument operation, from early November 1977 through the end of February 1980. The data products are a combination of spectra (mass and energy angle) and velocity moments. A copy of the data user's guide and examples of the data products are attached as appendix A. The data analysis covers three major areas: solar wind ions upstream and downstream of the day side bowshock, especially He(++) ions; terrestrial ions flowing upward from the auroral regions, especially H(+), O(+), and He(+) ions; and ions of both solar and terrestrial origins in the tail plasma sheet and lobe regions. Copies of publications are attached.
Sun-Earth Day:2008 Space Weather Around the World Total Solar Eclipse of 2008 August 1st in Siberia
Institute of Scientific and Technical Information of China (English)
2008-01-01
A very unique astronomical phenomenon will take place on the territory of Russia on the 1st August 2008.The total eclipse with a width of about 250 km will cross the Western Siberia from the north to the south,then will cross the Altai Mountains and will go further to the difficult to access regions of China and Mongolia.
Antiochos, S. K.
2005-05-01
A large Coronal Mass Ejection (CME) can consist of billions of tonnes of matter, along with entangled magnetic field, erupting from the Sun at speeds well over 1,000 km/s. These giant disruptions of the solar atmosphere drive the most destructive space weather at Earth and throughout the solar system. Furthermore, CMEs are the most dramatic example of how slowly-evolving processes on the Sun can conspire to produce explosive activity. Understanding their origin has long been a central objective for space physics research. This talk will present some of the latest observations and theories for CMEs and discuss the outstanding challenges to modeling and predicting their initiation. This work was supported in part by NASA and ONR.
Dankenbring, Chelsey; Capobianco, Brenda M.
2016-01-01
Current reform efforts in science education in the United States call for students to learn science through the integration of science and engineering practices. Studies have examined the effect of engineering design on students' understanding of engineering, technology, and science concepts. However, the majority of studies emphasize the accuracy…
Gopalswamy, Nat; Yan, Yihua
2015-01-01
This paper presents an overview of results obtained during the CAWSES II period on the short term variability of the Sun and how it affects the near Earth space environment. CAWSES II was planned to examine the behavior of the solar terrestrial system as the solar activity climbed to its maximum phase in solar cycle 24. After a deep minimum following cycle 23, the Sun climbed to a very weak maximum in terms of the sunspot number in cycle 24 (MiniMax24), so many of the results presented here refer to this weak activity in comparison with cycle 23. The short term variability that has immediate consequence to Earth and geospace manifests as solar eruptions from closed field regions and high speed streams from coronal holes. Both electromagnetic (flares) and mass emissions (coronal mass ejections, CMEs) are involved in solar eruptions, while coronal holes result in high speed streams that collide with slow wind forming the so called corotating interaction regions (CIRs). Fast CMEs affect Earth via leading shocks ...
A Sun-Earth-Moon Activity to Develop Student Understanding of Lunar Phases and Frames of Reference
Ashmann, Scott
2012-01-01
The Moon is an ever-present subject of observation, and it is a recurring topic in the science curriculum from kindergarten's basic observations through graduate courses' mathematical analyses of its orbit. How do students come to comprehend Earth's nearest neighbor? What is needed for them to understand the lunar phases and other phenomena and…
Kappenman, J. G.
2004-05-01
The solar flare activity of October-November 2003 reached historic intensity levels and produced several large Earth-directed CME's that had the potential to cause historically large geomagnetic storms as well. These CME's did cause various geomagnetic storm indices, particularly the regional K and Planetary Kp index, to reach maximum levels for many hours. However, the resulting geomagnetic storms, while causing isolated and important disruptions to power grids, were not of historically large size when considering the rate-of-change of regional geomagnetic fields in many locations. Impacts to power grids are caused by large dB/dt variations in regional geomagnetic fields, in most cases the peak geomagnetic disturbance intensities (in nT/min) were only a fraction of what has occurred during historically large geomagnetic storm events. A review will be provided of the CME passages and features of the passage that drove resulting geomagnetic storm events and impacts to electric power grid infrastructures on October 29-30, 2003. A brief overview of the geomagnetic storm disturbance morphologies and intensities relative to other noteworthy storms will also be provided.
Sun-Earth Connections: How the Sun Knocks Out My Cell Phone from 150 Million Kilometers Away
Ladbury, Raymond L.
2014-01-01
Large solar particle events (SPE) threaten many elements of critical infrastructure. A 2013 study by Lloyds of London and Atmospheric and Environmental Research recently found that if a worst-case solar event like the 1859 Carrington Event struck our planet now, it could result on $0.6-$2.36 trillion in damages to the economy. In March 2014, researchers Y. D. Liu et al. revealed that just such an event had narrowly missed Earth in July 2012. The event was observed by the STEREO A spacecraft. In this presentation, we examine how the sun can pack such a punch from 150 million km away, the threats such solar particle events pose, their mechanisms and the efforts NASA and other space agencies are carrying out to understand and mitigate such risks.
Energy Technology Data Exchange (ETDEWEB)
Yan Xiaohui; Zhang Xinyi [Department of Physics, Surface Physics Laboratory (State Key Laboratory), and Synchrotron Radiation Research Center of Fudan University, Shanghai 200433 (China); Liu Chenglin [Physics Department of Yancheng Teachers' College, Yancheng 224002 (China); Dang, Ruishan [Second Military Medical University, Shanghai 200433 (China); Huang Yuying; He Wei [Beijing Synchrotron Radiation Facility, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100039 (China); Ding Guanghong [Shanghai Research Center of Acupuncture and Meridian, Pudong, Shanghai 201203 (China)
2009-05-07
We used synchrotron x-ray fluorescence analysis to probe the distribution of four chemical elements in and around acupuncture points, two located in the forearm and two in the lower leg. Three of the four acupuncture points showed significantly elevated concentrations of elements Ca, Fe, Cu and Zn in relation to levels in the surrounding tissue, with similar elevation ratios for Cu and Fe. The mapped distribution of these elements implies that each acupuncture point seems to be elliptical with the long axis along the meridian. (note)
Designated Wildlife Lakes - points
Minnesota Department of Natural Resources — This is a point shapefile of Designated Wildlife Lakes in Minnesota. This shapefile was created by converting lake polygons from the Designated Wildlife Lakes...
DEFF Research Database (Denmark)
Ungar, David; Ernst, Erik
2007-01-01
Point Argument: "Dynamic Languages (in Reactive Environments) Unleash Creativity," by David Ungar. For the sake of creativity, the profession needs to concentrate more on inventing new and better dynamic languages and environments and less on improving static languages. Counterpoint Argument...
Allegheny County Address Points
Allegheny County / City of Pittsburgh / Western PA Regional Data Center — This dataset contains address points which represent physical address locations assigned by the Allegheny County addressing authority. Data is updated by County...
... medlineplus.gov/ency/article/003273.htm Point tenderness - abdomen To use the sharing features on this page, ... over a certain part of the belly area (abdomen). Considerations The abdomen is an area of the ...
National Wetlands Inventory Points
Minnesota Department of Natural Resources — Wetland point features (typically wetlands that are too small to be as area features at the data scale) mapped as part of the National Wetlands Inventory (NWI). The...
Triple Point Topological Metals
Directory of Open Access Journals (Sweden)
Ziming Zhu
2016-07-01
Full Text Available Topologically protected fermionic quasiparticles appear in metals, where band degeneracies occur at the Fermi level, dictated by the band structure topology. While in some metals these quasiparticles are direct analogues of elementary fermionic particles of the relativistic quantum field theory, other metals can have symmetries that give rise to quasiparticles, fundamentally different from those known in high-energy physics. Here, we report on a new type of topological quasiparticles—triple point fermions—realized in metals with symmorphic crystal structure, which host crossings of three bands in the vicinity of the Fermi level protected by point group symmetries. We find two topologically different types of triple point fermions, both distinct from any other topological quasiparticles reported to date. We provide examples of existing materials that host triple point fermions of both types and discuss a variety of physical phenomena associated with these quasiparticles, such as the occurrence of topological surface Fermi arcs, transport anomalies, and topological Lifshitz transitions.
Bedrock Outcrop Points Compilation
Vermont Center for Geographic Information — A compilation of bedrock outcrops as points and/or polygons from 1:62,500 and 1:24,000 geologic mapping by the Vermont Geological Survey, the United States...
Transitivity on Weierstrass points
Laing, Zoe
2010-01-01
We look for Riemann surfaces whose automorphism group acts transitively on the Weierstrass points. We concentrate on hyperelliptic surfaces, surfaces with PSL(2, q) as automorphism group, Platonic surfaces and Fermat curves.
Iowa State University GIS Support and Research Facility — Point locations of geologic samples/files in the IGS repository. Types of samples include well cuttings, outcrop samples, cores, drillers logs, measured sections,...
Allegheny County Address Points
Allegheny County / City of Pittsburgh / Western PA Regional Data Center — This dataset contains address points which represent physical address locations assigned by the Allegheny County addressing authority. Data is updated by County...
DEFF Research Database (Denmark)
Agarwal, Pankaj K.; Arge, Lars Allan; Erickson, Jeff
2003-01-01
also describe an indexing scheme in which the number of I/Os required to answer a query depends monotonically on the difference between the query time stamp t and the current time. Finally, we develop an efficient indexing scheme to answer approximate nearest-neighbor queries among moving points.......We propose three indexing schemes for storing a set S of N points in the plane, each moving along a linear trajectory, so that any query of the following form can be answered quickly: Given a rectangle R and a real value t, report all K points of S that lie inside R at time t. We first present...... an indexing structure that, for any given constant >0, uses O(N/B) disk blocks and answers a query in O((N/B)1/2+ +K/B) I/Os, where B is the block size. It can also report all the points of S that lie inside R during a given time interval. A point can be inserted or deleted, or the trajectory of a point can...
Analysis of medium-energy transfers to the Moon
Oshima, Kenta; Topputo, Francesco; Campagnola, Stefano; Yanao, Tomohiro
2017-03-01
This study analyzes a recently discovered class of exterior transfers to the Moon. These transfers terminate in retrograde ballistic capture orbits, i.e., orbits with negative Keplerian energy and angular momentum with respect to the Moon. Yet, their Jacobi constant is relatively low, for which no forbidden regions exist, and the trajectories do not appear to mimic the dynamics of the invariant manifolds of the Lagrange points. This paper shows that these orbits shadow instead lunar collision orbits. We investigate the dynamics of singular, lunar collision orbits in the Earth-Moon planar circular restricted three-body problem, and reveal their rich phase space structure in the medium-energy regime, where invariant manifolds of the Lagrange point orbits break up. We show that lunar retrograde ballistic capture trajectories lie inside the tube structure of collision orbits. We also develop a method to compute medium-energy transfers by patching together orbits inside the collision tube and those whose apogees are located in the appropriate quadrant in the Sun-Earth system. The method yields the novel family of transfers as well as those ending in direct capture orbits, under particular energetic and geometrical conditions.
DuneXpress: dust astronomy with Dune and ConeXpress
Altobelli, N.; Lera, S.; Srama, R.; Vo, X.; de Kam, J.; Gruen, E.
We present a mission scenario to implement the Cosmic Dune mission concept (Cosmic dust measurements near Earth) using the ConeXpress platform developed by Dutch Space. We discuss the different strategies for the instrument integration on-board the platform and present a preliminary mission design. Goal of the mission is to reach the Sun-Earth Lagrange point L2. As ConeXpress is propelled with ion engines, a mission design inspired from the Smart 1 mission is developed. The ConeXpress spacecraft benefits of launch opportunities as secondary payload on-board an Ariane 5 rocket and is injected into a classical geostationary transfer orbit (GTO). Starting from this parking orbit, the mission scenario is divided in 3 phases. The first phase consists in raising the orbit perigee as quick as possible up to 20000 km to minimize the spacecraft exposure to the Van Allen radiation belt. During the second phase, the perigee altitude is kept constant, while the apogee altitude is raised up to the Moon's orbit distance. The third phase consists in a Moon swing-by, which injects the spacecraft into a Halo orbit around the Lagrange point L2.
Smolkova, Valentina
2015-01-01
The Arctic is warming much faster than the entire planet, and this causes severe melting of sea ice. However, the climate of different regions of the Earth is interconnected, and changes in the amount of ice in the Arctic can dramatically affect the climate across the whole planet. Some scientists claim that a possible tipping point is the event of the ice-free Arctic Ocean in summer. Certain predictions point towards ice-free Arctic summers around the year 2050, whereas others pre- dict this...
Holographic Three point Functions
DEFF Research Database (Denmark)
Martirosyan, Ara
The main subject of this thesis is the computation of structure constants appearing in the three-point functions for certain type of states/operators in the context of the AdS/CFT correspondence, which is one of the important parts of the dynamical problem in the dual theories of the correspondence...
2012-01-01
Located next to the car park by the flag poles, a few metres from the Main CERN Reception (building 33), a new snack point catered by Novae will open to the public on Wednesday 8 August. More information will be available in the next issue of the Bulletin!
Ahmed, Syed Jamil; Heddon, Dee; Mackey, Sally
2007-01-01
This collection of three articles represents the "Points and Practices" section of this month's issue of "Research in Drama Education." The first article, "'Fitting the Bill' for 'Helping Them.' A Response to 'Integrated Popular Theatre Approach in Africa' and 'Commissioned Theatre Projects on Human Rights in…
ACCESS Pointing Control System
Brugarolas, Paul; Alexander, James; Trauger, John; Moody, Dwight; Egerman, Robert; Vallone, Phillip; Elias, Jason; Hejal, Reem; Camelo, Vanessa; Bronowicki, Allen; O'Connor, David; Partrick, Richard; Orzechowski, Pawel; Spitter, Connie; Lillie, Chuck
2010-01-01
ACCESS (Actively-Corrected Coronograph for Exoplanet System Studies) was one of four medium-class exoplanet concepts selected for the NASA Astrophysics Strategic Mission Concept Study (ASMCS) program in 2008/2009. The ACCESS study evaluated four major coronograph concepts under a common space observatory. This paper describes the high precision pointing control system (PCS) baselined for this observatory.
Decision Points in Cataloging.
Bright, Franklyn F.
Libraries are frequently faced with policy decisions which can affect the quality and cost of library services for years to come. This point can be illustrated by citing examples of decisions made at the University of Wisconsin Library in the areas of: (1) conforming to national cataloging standards; (2) producing catalog cards in-house; and (3)…
Ahmed, Syed Jamil; Heddon, Dee; Mackey, Sally
2007-01-01
This collection of three articles represents the "Points and Practices" section of this month's issue of "Research in Drama Education." The first article, "'Fitting the Bill' for 'Helping Them.' A Response to 'Integrated Popular Theatre Approach in Africa' and 'Commissioned Theatre Projects on Human Rights in…
DEFF Research Database (Denmark)
Elleby, Anita; Ingwersen, Peter
2010-01-01
with novel publication point indicators (PPIs) that are formalized and exemplified. Two diachronic citation windows are applied: 2006-07 and 2006-08. Web of Science (WoS) as well as Google Scholar (GS) are applied to observe the cite delay and citedness for the different document types published by DIIS...
DEFF Research Database (Denmark)
Jensen, Ole B.; Morelli, Nicola
2011-01-01
where the networks meet and establish contact. Thus we argue for the usefulness of the notion of Critical Point of Contact (CPC) to deepen our understanding of the actual life within networks. En route to this notion we draw upon theories within as diverse realms such as interaction design, service...
DEFF Research Database (Denmark)
2012-01-01
In this brief article, we shall illustrate the application of the analytical and interventionist concept of ‘Critical Points of Contact’ (CPC) through a number of urban design studios. The notion of CPC has been developed over a span of the last three to four years and is reported in more detail...
DEFF Research Database (Denmark)
Zhang, Xiaohong
determination’ based on the relationship between the point clouds on regular objects (e.g. flat top buildings) and the ground truth of the objects used for calibration. In order to extract the footprints on the objects, filtering was implemented before the calibration. Three example tests have been made...
Holographic Three point Functions
DEFF Research Database (Denmark)
Martirosyan, Ara
The main subject of this thesis is the computation of structure constants appearing in the three-point functions for certain type of states/operators in the context of the AdS/CFT correspondence, which is one of the important parts of the dynamical problem in the dual theories of the correspondence...
Institute of Scientific and Technical Information of China (English)
潘修强; 梅成才; 陈军杰
2013-01-01
为使机器手臂圆满地完成医疗搀扶等既定看护工作的同时能耗达到最低,针对机器手臂在医疗看护时的两个基本动作(拦截接住,对接捕获),描述并建立机器手臂的动力学方程,构建案例模型,并分别引入最优化控制技术,对最优控制问题进行离散并数字求解,得到系统的最优解；并基于上述工作基础,针对详述能耗J和各个限制方程微小异动之间关系的拉格朗日因子,深入探讨该两案例中的拉格朗日因子的不同表现.从案例结果分析,相对于传统方法求解能耗最优化问题,DCNLP法表现出了较好的鲁棒性,对初始值的估算要求较低,探讨的结果能对机器手臂如何更好地完成要求操作给出积极建议.%In order to have the manipulator arm consummately complete the established caregiving works of medical arm supporting and propping while minimising the energy consumption,aiming at two basic motions of manipulator arm' s medical caregiving,the interception catch and the docking capture,we describe and establish the dynamics equation for manipulator arm,construct case model,and introduce optimal control technology respectively,we scatter the optimal control problem and make digital solution to obtain the optimal solution； Moreover,based on the above working basis,and aiming at the Lagrange multiplier which recounting the relationship between the energy consumption J and the tiny abnormal motion of each restriction equation,we thoroughly discuss the different performances of the Lagrange multipliers in two cases.Analyses derived from the cases results demonstrate that,DCNLP method performs well in robustness in contrast to the traditional method used for solving energy consumption optimisation,it has lower requirement on initial estimation.The discuss result can provide active suggestion for manipulator arm in terms of the way to better complete the required operation.
Henig Proper Efficient Points and Generalized Henig Proper Efficient Points
Institute of Scientific and Technical Information of China (English)
Jing Hui QIU
2009-01-01
Applying the theory of locally convex spaces to vector optimization,we investigate the relationship between Henig proper efficient points and generalized Henig proper efficient points. In particular,we obtain a sufficient and necessary condition for generalized Henig proper efficient points to be Henig proper efficient points. From this,we derive several convenient criteria for judging Henig proper efficient points.
Sentís, Gael; Calsamiglia, John; Chiribella, Giulio; Munoz-Tapia, Ramon
2016-01-01
Sudden changes are ubiquitous in nature. Identifying them is of crucial importance for a number of applications in medicine, biology, geophysics, and social sciences. Here we investigate the problem in the quantum domain, considering a source that emits particles in a default state, until a point where it switches to another state. Given a sequence of particles emitted by the source, the problem is to find out where the change occurred. For large sequences, we obtain an analytical expression for the maximum probability of correctly identifying the change point when joint measurements on the whole sequence are allowed. We also construct strategies that measure the particles individually and provide an online answer as soon as a new particle is emitted by the source. We show that these strategies substantially underperform the optimal strategy, indicating that quantum sudden changes, although happening locally, are better detected globally.
Antova, Gergana; Kunchev, Ivan; Mickrenska-Cherneva, Christina
2016-10-01
The representation of physical buildings in Building Information Models (BIM) has been a subject of research since four decades in the fields of Construction Informatics and GeoInformatics. The early digital representations of buildings mainly appeared as 3D drawings constructed by CAD software, and the 3D representation of the buildings was only geometric, while semantics and topology were out of modelling focus. On the other hand, less detailed building representations, with often focus on ‘outside’ representations were also found in form of 2D /2,5D GeoInformation models. Point clouds from 3D laser scanning data give a full and exact representation of the building geometry. The article presents different aspects and the benefits of using point clouds in BIM in the different stages of a lifecycle of a building.
Sentís, Gael; Bagan, Emilio; Calsamiglia, John; Chiribella, Giulio; Muñoz-Tapia, Ramon
2016-10-01
Sudden changes are ubiquitous in nature. Identifying them is crucial for a number of applications in biology, medicine, and social sciences. Here we take the problem of detecting sudden changes to the quantum domain. We consider a source that emits quantum particles in a default state, until a point where a mutation occurs that causes the source to switch to another state. The problem is then to find out where the change occurred. We determine the maximum probability of correctly identifying the change point, allowing for collective measurements on the whole sequence of particles emitted by the source. Then, we devise online strategies where the particles are measured individually and an answer is provided as soon as a new particle is received. We show that these online strategies substantially underperform the optimal quantum measurement, indicating that quantum sudden changes, although happening locally, are better detected globally.
Floating point coprocessor upgrade
Energy Technology Data Exchange (ETDEWEB)
Weber, T.
1987-04-01
A method was developed to increase the throughput of the Hewlett Packard, 98635A floating point processor equipped, model 236C computer. The increase was carried out in three phases each with a clock and or chip change during the modification. Two programs were written to test the results and evaluate the increases in performance made to the computer. The first one shows reduction in processing times of 34.3%, while the other recorded 34.6%.
Wallace, Patrick
2016-07-01
As far as pointing is concerned, a solar telescope is merely an ordinary astronomical telescope but with enhancements for observing solar and coronal features. The paper discusses the additional coordinate systems that need to be supported, shows how to generate the required solar ephemerides (both orbital and physical), and sets out a suitable application programming interface for the telescope control system to use when making solar observations.
Building Points - MO 2012 Stoddard Structure Points (SHP)
NSGIC GIS Inventory (aka Ramona) — Missouri Structure Points are structure points generated from a two pass look over the 2007 State 2ft imagery. Unlike the structure footprints, the building point...
Building Points - MO 2012 Dunklin Structure Points (SHP)
NSGIC GIS Inventory (aka Ramona) — Missouri Structure Points are structure points generated from a two pass look over the 2007 State 2ft imagery. Unlike the structure footprints, the building point...
Building Points - MO 2012 Scott Structure Points (SHP)
NSGIC GIS Inventory (aka Ramona) — Missouri Structure Points are structure points generated from a two pass look over the 2007 State 2ft imagery. Unlike the structure footprints, the building point...
Building Points - MO 2012 Pemiscot Structure Points (SHP)
NSGIC GIS Inventory (aka Ramona) — Missouri Structure Points are structure points generated from a two pass look over the 2007 State 2ft imagery. Unlike the structure footprints, the building point...
Building Points - MO 2012 New Madrid Structure Points (SHP)
NSGIC GIS Inventory (aka Ramona) — Missouri Structure Points are structure points generated from a two pass look over the 2007 State 2ft imagery. Unlike the structure footprints, the building point...
Building Points - MO 2012 Mississippi Structure Points (SHP)
NSGIC GIS Inventory (aka Ramona) — Missouri Structure Points are structure points generated from a two pass look over the 2007 State 2ft imagery. Unlike the structure footprints, the building point...
Directory of Open Access Journals (Sweden)
Giovanni E. Reyes
2006-01-01
Full Text Available Este escrito estudia las funciones tanto de producción como de costos, no solamente en sí misma, sino lo que es más importante, en términos de sus mutas transformaciones, cuando las condiciones de cálculo pueden ser particularmente difíciles o complicadas. Es un tópico relacionado con la teoría de producción la que se presenta más allá de las formas tradicionales, de abordar las funciones de costo y producción por separado. Es un tema que pertenece a los aspectos fundamentales de gestión de cualquier empresa. En este estudio, utilicé las formas homotéticas y no homotéticas de las funciones, finalizando el escrito con aplicaciones derivadas del método de transformadas de Lagrange, con el fin de maximizar resultados a partir de factores específicos que tienen restricciones, tales como aquellas relacionadas con límites en el presupuesto.
Kim, W Chan; Mauborgne, Renée
2003-04-01
When William Bratton was appointed police commissioner of New York City in 1994, turf wars over jurisdiction and funding were rife and crime was out of control. Yet in less than two years, and without an increase in his budget, Bratton turned New York into the safest large city in the nation. And the NYPD was only the latest of five law-enforcement agencies Bratton had turned around. In each case, he succeeded in record time despite limited resources, a demotivated staff, opposition from powerful vested interests, and an organization wedded to the status quo. Bratton's turnarounds demonstrate what the authors call tipping point leadership. The theory of tipping points hinges on the insight that in any organization, fundamental changes can occur quickly when the beliefs and energies of a critical mass of people create an epidemic movement toward an idea. Bratton begins by overcoming the cognitive hurdles that block organizations from recognizing the need for change. He does this by putting managers face-to-face with operational problems. Next, he manages around limitations on funds, staff, or equipment by concentrating resources on the areas that are most in need of change and that have the biggest payoffs. He meanwhile solves the motivation problem by singling out key influencers--people with disproportionate power due to their connections or persuasive abilities. Finally, he closes off resistance from powerful opponents. Not every CEO has the personality to be a Bill Bratton, but his successes are due to much more than his personality. He relies on a remarkably consistent method that any manager looking to turn around an organization can use to overcome the forces of inertia and reach the tipping point.
Gross, Michael A K; Moore, Elizabeth M
2010-01-01
SOFIA is an airborne, gyroscopically stabilized 2.5m infrared telescope, mounted to a spherical bearing. Unlike its predecessors, SOFIA will work in absolute coordinates, despite its continually changing position and attitude. In order to manage this, SOFIA must relate equatorial and telescope coordinates using a combination of avionics data and star identification, manage field rotation and track sky images. We describe the algorithms and systems required to acquire and maintain the equatorial reference frame, relate it to tracking imagers and the science instrument, set up the oscillating secondary mirror, and aggregate pointings into relocatable nods and dithers.
Ubiquitous Pointing and Drawing
Directory of Open Access Journals (Sweden)
Kristian Jantz
2007-12-01
Full Text Available This paper presents a system that enables a presenter to work directly on the projection without the typical interruption of the presentation flow being caused by a mouse or keyboard activity. The lecturer simply uses his fingers as a natural and intuitive pointing device. The system consists of an LED, a standard webcam, a video projector, and a small software system running on a notebook computer. The camera is positioned such that it views the projection area. After a few calibration clicks, the mouse emulation is functional at any place of the projection area.
DEFF Research Database (Denmark)
Jensen, Ole B.; Morelli, Nicola
2011-01-01
where the networks meet and establish contact. Thus we argue for the usefulness of the notion of Critical Point of Contact (CPC) to deepen our understanding of the actual life within networks. En route to this notion we draw upon theories within as diverse realms such as interaction design, service...... design, geography, and mobility studies. After the introduction in section we develop and define the notion of CPC based upon a broad set of disciplines and theories. We illustrate the usefulness of the notion within the field of mobility in the network city and within the field of service design...
Potra, Florian A.; Wright, Stephen J.
2000-12-01
The modern era of interior-point methods dates to 1984, when Karmarkar proposed his algorithm for linear programming. In the years since then, algorithms and software for linear programming have become quite sophisticated, while extensions to more general classes of problems, such as convex quadratic programming, semi-definite programming, and nonconvex and nonlinear problems, have reached varying levels of maturity. We review some of the key developments in the area, including comments on both the complexity theory and practical algorithms for linear programming, semi-definite programming, monotone linear complementarity, and convex programming over sets that can be characterized by self-concordant barrier functions.
Pearson, Chris; North, Chris; Bendo, George; Conversi, Luca; Dowell, Darren; Griffin, Matt; Jin, Terry; Laporte, Nicolas; Papageorgiou, Andreas; Schulz, Bernhard; Shupe, Dave; Smith, Anthony J; Xu, Kevin
2014-01-01
The different algorithms appropriate for point source photometry on data from the SPIRE instrument on-board the Herschel Space Observatory, within the Herschel Interactive Processing Environment (HIPE) are compared. Point source photometry of a large ensemble of standard calibration stars and dark sky observations is carried out using the 4 major methods within HIPE: SUSSEXtractor, DAOphot, the SPIRE Timeline Fitter and simple Aperture Photometry. Colour corrections and effective beam areas as a function of the assumed source spectral index are also included to produce a large number of photometric measurements per individual target, in each of the 3 SPIRE bands (250, 350, 500um), to examine both the accuracy and repeatability of each of the 4 algorithms. It is concluded that for flux densities down to the level of 30mJy that the SPIRE Timeline Fitter is the method of choice. However, at least in the 250 and 350um bands, all 4 methods provide photometric repeatability better than a few percent down to at appr...
Directory of Open Access Journals (Sweden)
G.R. Finnie
1997-05-01
Full Text Available Accurate estimation of the size and development effort for software projects requires estimation models which can be used early enough in the development life cycle to be of practical value. Function Point Analysis (FPA has become possibly the most widely used estimation technique in practice. However the technique was developed in the data processing environment of the 1970's and, despite undergoing considerable reassessment and formalisation, still attracts criticism for the weighting scoring it employs and for the way in which the function point score is adapted for specific system characteristics. This paper reviews the validity of the weighting scheme and the value of adjusting for system characteristics by studying their effect in a sample of 299 software developments. In general the value adjustment scheme does not appear to cater for differences in productivity. The weighting scheme used to adjust system components in terms of being simple, average or complex also appears suspect and should be redesigned to provide a more realistic estimate of system functionality.
Solving Directly Two Point Non Linear Boundary Value Problems Using Direct Adams Moulton Method
Directory of Open Access Journals (Sweden)
Zanariah A. Majid
2011-01-01
Full Text Available Problem statement: In this study, a direct method of Adams Moulton type was developed for solving non linear two point Boundary Value Problems (BVPs directly. Most of the existence researches involving BVPs will reduced the problem to a system of first order Ordinary Differential Equations (ODEs. This approach is very well established but it obviously will enlarge the systems of first order equations. However, the direct method in this research will solved the second order BVPs directly without reducing it to first order ODEs. Approach: Lagrange interpolation polynomial was applied in the derivation of the proposed method. The method was implemented using constant step size via shooting technique in order to determine the approximated solutions. The shooting technique will employ the Newtons method for checking the convergent of the guessing values for the next iteration. Results: Numerical results confirmed that the direct method gave better accuracy and converged faster compared to the existing method. Conclusion: The proposed direct method is suitable for solving two point non linear boundary value problems.
Family of 2n-Point Ternary Non-Stationary Interpolating Subdivision Scheme
Directory of Open Access Journals (Sweden)
MEHWISH BARI
2017-10-01
Full Text Available This article offers 2n-point ternary non-stationary interpolating subdivision schemes, with the tension parameter, by using Lagrange identities. By choosing the suitable value of tension parameter, we can get different limit curves according to our own choice. Tightness or looseness of the limit curve depends upon the increment or decline the value of tension parameter. The proposed schemes are the counter part of some existing parametric and non-parametric stationary schemes. The main purpose of this article is to reproduce conics and the proposed schemes reproduce conics very well such that circle, ellipse, parabola and hyperbola. We also establish a deviation error formula which is useful to calculate the maximum deviation of limit curve from the original limit curve. The presentation and of the proposed schemes are verified by closed and open figures. The given table shows the less deviation of the limit curves by proposed scheme as compare to the existing scheme. Graphical representation of deviation error is also presented and it shows that as the number of control points increases, the deviation error decreases.
The general problem of the motion of coupled rigid bodies about a fixed point
Leimanis, Eugene
1965-01-01
In the theory of motion of several coupled rigid bodies about a fixed point one can distinguish three basic ramifications. 1. The first, the so-called classical direction of investigations, is concerned with particular cases of integrability ot the equations of motion of a single rigid body about a fixed point,1 and with their geo metrical interpretation. This path of thought was predominant until the beginning of the 20th century and its most illustrious represen tatives are L. EULER (1707-1783), J L. LAGRANGE (1736-1813), L. POINSOT (1777-1859), S. V. KOVALEVSKAYA (1850-1891), and others. Chapter I of the present monograph intends to reflect this branch of investigations. For collateral reading on the general questions dealt with in this chapter the reader is referred to the following textbooks and reports: A. DOMOGAROV [1J, F. KLEIN and A. SOMMERFELD [11, 1 , 1 J, A. G. 2 3 GREENHILL [10J, A. GRAY [1J, R. GRAMMEL [4 J, E. J. ROUTH [21' 2 , 1 2 31' 32J, J. B. SCARBOROUGH [1J, and V. V. GOLUBEV [1, 2J.
Energy Technology Data Exchange (ETDEWEB)
Fogt, H. [Technikum Joanneum, Fachhochschule-Studiengang Fahrzeugtechnik, Graz (Austria); Kneer, A. [Battelle Ingenieurtechnik GmbH, Eschborn (Germany); Seidel, V. [ICCM Inst. of Computational Continuum Mechanics GmbH, Hamburg (Germany)
1997-12-01
Apart from experimental and empirical methods, numerical calculations are increasingly being used for the examination and judging of two-phase flows and for the design of flow mechanics systems and components. Typical examples are injection systems, atomisers, mixers, steam-raising units and plants for smoke and exhaust gas cleaning. One frequently counteracts the long calculation times that occur in the numerical solution of two- or multi-phase equations by simplifying the assumptions. In energy and process technology, one often falls back on one-dimensional calculation procedures. This has the advantage that the behaviour of whole plants can be described by them the spatial and temporal resolution down to detecting small sale detail phenomena is only successful up to a point with these methods. Due to the constantly rising performance of the computers and by applying new mathematical/information methods, CFD methods make detailed numerical investigations of two-phase flow processes possible with reasonable computing times. The possibilities and limits are shown in the article by some examples. [Deutsch] Zur Untersuchung und Beurteilung von Zweiphasenstroemungen und fuer die Auslegung stroemungsmechanischer Systeme und Komponenten werden neben experimentellen und empirischen Methoden zunehmend numerische Rechenverfahren eingesetzt. Typische Beispiele sind Einspritzsysteme, Zerstaeuber, Mischer, Dampferzeuger und Anlagen zur Rauch- bzw. Abgasreinigung. Den hohen Rechenzeiten, die bei der numerischen Loesung der zwei- und mehrphasigen Erhaltungsgleichungen anfallen, wird haeufig durch Vereinfachung der Ansaetze entgegengewirkt. In der Enegie- und Verfahrenstechnik wird oft auf eindimensionale Rechenverfahren zurueckgegriffen. Sie bieten den Vorteil, dass mit ihnen das Verhalten ganzer Anlagen beschrieben werden kann. Die raeumliche und zeitliche Aufloesung bis hin zur Erfassung kleinskaliger Detailerscheinungen gelingt mit diesen Methoden nur bedingt. CFD Methoden
Point Source Extraction with MOPEX
Marleau, D M F R
2005-01-01
MOPEX (MOsaicking and Point source EXtraction) is a package developed at the Spitzer Science Center for astronomical image processing. We report on the point source extraction capabilities of MOPEX. Point source extraction is implemented as a two step process: point source detection and profile fitting. Non-linear matched filtering of input images can be performed optionally to increase the signal-to-noise ratio and improve detection of faint point sources. Point Response Function (PRF) fitting of point sources produces the final point source list which includes the fluxes and improved positions of the point sources, along with other parameters characterizing the fit. Passive and active deblending allows for successful fitting of confused point sources. Aperture photometry can also be computed for every extracted point source for an unlimited number of aperture sizes. PRF is estimated directly from the input images. Implementation of efficient methods of background and noise estimation, and modified Simplex a...
September 2002 Lidar Point Data of Southern California Coastline: Dana Point to Point La Jolla
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains lidar point data from a strip of Southern California coastline (including water, beach, cliffs, and top of cliffs) from Dana Point to Point La...
May 2002 Lidar Point Data of Southern California Coastline: Dana Point to Point La Jolla
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains lidar point data from a strip of Southern California coastline (including water, beach, cliffs, and top of cliffs) from Dana Point to Point La...
September 2002 Lidar Point Data of Southern California Coastline: Dana Point to Point La Jolla
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains lidar point data from a strip of Southern California coastline (including water, beach, cliffs, and top of cliffs) from Dana Point to Point...
Directory of Open Access Journals (Sweden)
Lehnert B.
2011-04-01
Full Text Available A point-mass concept has been elaborated from the equations of the gravitational field. One application of these deductions results in a black hole configuration of the Schwarzschild type, having no electric charge and no angular momentum. The critical mass of a gravitational collapse with respect to the nuclear binding energy is found to be in the range of 0.4 to 90 solar masses. A second application is connected with the spec- ulation about an extended symmetric law of gravitation, based on the options of positive and negative mass for a particle at given positive energy. This would make masses of equal polarity attract each other, while masses of opposite polarity repel each other. Matter and antimatter are further proposed to be associated with the states of positive and negative mass. Under fully symmetric conditions this could provide a mechanism for the separation of antimatter from matter at an early stage of the universe.
Honda, Naofumi; Takei, Yoshitsugu
2015-01-01
The discovery of a virtual turning point truly is a breakthrough in WKB analysis of higher order differential equations. This monograph expounds the core part of its theory together with its application to the analysis of higher order Painlevé equations of the Noumi–Yamada type and to the analysis of non-adiabatic transition probability problems in three levels. As M.V. Fedoryuk once lamented, global asymptotic analysis of higher order differential equations had been thought to be impossible to construct. In 1982, however, H.L. Berk, W.M. Nevins, and K.V. Roberts published a remarkable paper in the Journal of Mathematical Physics indicating that the traditional Stokes geometry cannot globally describe the Stokes phenomena of solutions of higher order equations; a new Stokes curve is necessary.
DEFF Research Database (Denmark)
Hermann, A. K.
2016-01-01
“Slow journalism” is a term anthropologist and sociologists sometimes use to describe their empirical work, ethnography. To journalists and media observers, meanwhile, “slow journalism” signifies a newfound dedication to serious long-form journalism. Not surprisingly, thus, “ethnographic journalism......”—a genre where reporters adopt research strategies from social science—takes “slow” to the extreme. Immersing themselves in communities for weeks, months and years, ethnographic journalists seek to gain what anthropologists call “the native's point of view”. Based on in-depth interviews with practitioners...... and analyses of their journalistic works, this paper offers a study of ethnographic journalism suggesting that slow time operates in at least three separate registers. First, in terms of regimentation, ethnographic journalism is mostly long-form pieces that demand time-consuming research and careful writing...
McGuire, J. B.
2011-12-01
There is a body of conventional wisdom that holds that a solvable quantum problem, by virtue of its solvability, is pathological and thus irrelevant. It has been difficult to refute this view owing to the paucity of theoretical constructs and experimental results. Recent experiments involving equivalent ions trapped in a spatial conformation of extreme anisotropic confinement (longitudinal extension tens, hundreds or even thousands of times transverse extension) have modified the view of relevancy, and it is now possible to consider systems previously thought pathological, in particular point Bosons that repel in one dimension. It has been difficult for the experimentalists to utilize existing theory, mainly due to long-standing theoretical misunderstanding of the relevance of the permutation group, in particular the non-commutativity of translations (periodicity) and transpositions (permutation). This misunderstanding is most easily rectified in the case of repelling Bosons.
Latent myofascial trigger points.
Ge, Hong-You; Arendt-Nielsen, Lars
2011-10-01
A latent myofascial trigger point (MTP) is defined as a focus of hyperirritability in a muscle taut band that is clinically associated with local twitch response and tenderness and/or referred pain upon manual examination. Current evidence suggests that the temporal profile of the spontaneous electrical activity at an MTP is similar to focal muscle fiber contraction and/or muscle cramp potentials, which contribute significantly to the induction of local tenderness and pain and motor dysfunctions. This review highlights the potential mechanisms underlying the sensory-motor dysfunctions associated with latent MTPs and discusses the contribution of central sensitization associated with latent MTPs and the MTP network to the spatial propagation of pain and motor dysfunctions. Treating latent MTPs in patients with musculoskeletal pain may not only decrease pain sensitivity and improve motor functions, but also prevent latent MTPs from transforming into active MTPs, and hence, prevent the development of myofascial pain syndrome.
Optimization of the Forcing Term for the Solution of Two-Point Boundary Value Problems
Directory of Open Access Journals (Sweden)
Gianni Arioli
2013-01-01
by standard methods of constrained optimization, for example, with Lagrange multipliers. We provide an application of this algorithm to the planar restricted three body problem in order to study the planning of low-thrust transfer orbits.
Inigo-Golfin, J
After 3 years of work in point 1, a number of surface buildings have already been completed and handed over to CERN (the control, the gas and the cooling and ventilation buildings) and, probably more appealing to the public, 60,000 m3 of earth have already been excavated from underground. At present, the technical cavern USA15 and its access shaft are almost finished, leaving only the main cavern and the liaison galleries to be completed in the coming year and a half. The main cavern has been excavated down to the radiation limit and its walls and vault will presently be concreted (see below the picture of the section of the vault with the impressive shell of 1.2 m thickness). The excavation of the bench (27 vertical metres to go yet!) will proceed from August, when some additional civil engineering work in the LHC tunnel will be undertaken. Needless to say many different services are necessary around the detector, both for its installation and future operation for physics. To that end much of the heavy...
Inigo-Golfin, J.
The ATLAS experimental area is located in Point 1, just across the main CERN entrance, in the commune of Meyrin. There people are ever so busy to finish the different infrastructures for ATLAS. Not only has Civil Engineering finished the construction of the USA15 technical cavern, but the excavation of the main UX15 cavern has resumed below the machine tunnel, after a brief halt to allow the construction of the UJ-caverns for the power converters of the LHC machine. The excavation work should end in August 2002. The UX15 hand-over to ATLAS is expected in April 2003. On the surface civil engineering is starting to complete the last two surface buildings (SDX1 and SH1), once the services (cooling pipes, ventilation ducts and the largest item, the lift modules and its lift of course) in the shaft PX15 have been completed. But the civil engineering is not all. A lot more is under way. The site installation of the steel structures in the caverns is to begin in Autumn, along with all the cooling pipes, airconditi...
2004-01-01
CERN - Globe of Science and Innovation 20 and 21 October Acrobatics, mime, a cappella singing, projections of images, a magical setting... a host of different tools of a grandeur matching that of the Universe they relate. A camera makes a massive zoom out to reveal the multiple dimensions of Nature. Freeze the frame: half way between the infinitesimally small and the infinitesimally large, a man suspends his everyday life (hence the title "Point de Suspension", which refers to the three dots at the end of an uncompleted sentence) to take a glimpse of the place he occupies in the great history of the Universe. An unusual perspective on what it means to be a human being... This spectacle in the Globe of Science and Innovation, specially created by the Miméscope* company for the official ceremony marking CERN's fiftieth anniversary, is a gift from the Government of the Republic and Canton of Geneva, which also wishes to share this moment of wonder with the local population. There will be three performances for...
2004-01-01
CERN - Globe of Science and Innovation 20 and 21 October Acrobatics, mime, a cappella singing, projections of images, a magical setting... a host of different tools of a grandeur matching that of the Universe they relate. A camera makes a massive zoom out to reveal the multiple dimensions of Nature. Freeze the frame: half way between the infinitesimally small and the infinitesimally large, a man suspends his everyday life (hence the title "Point de Suspension", which refers to the three dots at the end of an uncompleted sentence) to take a glimpse of the place he occupies in the great history of the Universe. An unusual perspective on what it means to be a human being... This wondrous show in the Globe of Science and Innovation, specially created by the Miméscope* company for the official ceremony marking CERN's fiftieth anniversary, is a gift from the Government of the Republic and Canton of Geneva, which also wishes to share this moment of wonder with the local population. There will be three perfo...
2004-01-01
http://www.cern.ch/cern50/ CERN - Globe of Science and Innovation 20 and 21 October Acrobatics, mime, a cappella singing, projections of images, a magical setting... a host of different tools of a grandeur matching that of the Universe they relate. A camera makes a massive zoom out to reveal the multiple dimensions of Nature. Freeze the frame: half way between the infinitesimally small and the infinitesimally large, a man suspends his everyday life (hence the title "Point de Suspension", which refers to the three dots at the end of an uncompleted sentence) to take a glimpse of the place he occupies in the great history of the Universe. An unusual perspective on what it means to be a human being... This wondrous show in the Globe of Science and Innovation, specially created by the Miméscope* company for the official ceremony marking CERN's fiftieth anniversary, is a gift from the Government of the Republic and Canton of Geneva, which also wishes to share this moment of wonder with the local pop...
The computed cranial focal point
Jong, G.A. de; Maal, T.J.J.; Delye, H.
2015-01-01
INTRODUCTION: Stereophotogrammetry is a radiation-free method for monitoring skull development after craniosynostosis repair. Lack of clear fixed reference points complicate longitudinal comparison of 3D photographs. Therefore we developed the 'computed cranial focal point' (CCFP). METHODS: The CCFP
Solving discrete zero point problems
van der Laan, G.; Talman, A.J.J.; Yang, Z.F.
2004-01-01
In this paper an algorithm is proposed to .nd a discrete zero point of a function on the collection of integral points in the n-dimensional Euclidean space IRn.Starting with a given integral point, the algorithm generates a .nite sequence of adjacent integral simplices of varying dimension and termi
Magic Pointing for Eyewear Computers
DEFF Research Database (Denmark)
Jalaliniya, Shahram; Mardanbegi, Diako; Pederson, Thomas
2015-01-01
In this paper, we propose a combination of head and eye movements for touchlessly controlling the "mouse pointer" on eyewear devices, exploiting the speed of eye pointing and accuracy of head pointing. The method is a wearable computer-targeted variation of the original MAGIC pointing approach...
Magic Pointing for Eyewear Computers
DEFF Research Database (Denmark)
Jalaliniya, Shahram; Mardanbegi, Diako; Pederson, Thomas
2015-01-01
In this paper, we propose a combination of head and eye movements for touchlessly controlling the "mouse pointer" on eyewear devices, exploiting the speed of eye pointing and accuracy of head pointing. The method is a wearable computer-targeted variation of the original MAGIC pointing approach...
Clinical Application of Point Diji
Institute of Scientific and Technical Information of China (English)
栾继萍
2004-01-01
@@ Diji (SP 8) is a cleft point of the Spleen Channel of Foot-Taiyang. Its indications include abdominal pain, diarrhea, edema, dysmenorrhea and certain other symptoms caused by incoordination between the liver and the spleen. Either taking the point alone or together with some other adjunct points in clinical practice, the author has obtained satisfactory curative effects.
Ground point filtering of UAV-based photogrammetric point clouds
Anders, Niels; Seijmonsbergen, Arie; Masselink, Rens; Keesstra, Saskia
2016-04-01
Unmanned Aerial Vehicles (UAVs) have proved invaluable for generating high-resolution and multi-temporal imagery. Based on photographic surveys, 3D surface reconstructions can be derived photogrammetrically so producing point clouds, orthophotos and surface models. For geomorphological or ecological applications it may be necessary to separate ground points from vegetation points. Existing filtering methods are designed for point clouds derived using other methods, e.g. laser scanning. The purpose of this paper is to test three filtering algorithms for the extraction of ground points from point clouds derived from low-altitude aerial photography. Three subareas were selected from a single flight which represent different scenarios: 1) low relief, sparsely vegetated area, 2) low relief, moderately vegetated area, 3) medium relief and moderately vegetated area. The three filtering methods are used to classify ground points in different ways, based on 1) RGB color values from training samples, 2) TIN densification as implemented in LAStools, and 3) an iterative surface lowering algorithm. Ground points are then interpolated into a digital terrain model using inverse distance weighting. The results suggest that different landscapes require different filtering methods for optimal ground point extraction. While iterative surface lowering and TIN densification are fully automated, color-based classification require fine-tuning in order to optimize the filtering results. Finally, we conclude that filtering photogrammetric point clouds could provide a cheap alternative to laser scan surveys for creating digital terrain models in sparsely vegetated areas.
Imaging study on acupuncture points
Energy Technology Data Exchange (ETDEWEB)
Yan, X H; Zhang, X Y [Synchrotron Radiation Research Center, Physics Department, and Surface Physics Laboratory (State Key Laboratory) of Fudan University, Shanghai 200433 (China); Liu, C L [Physics Department of Yancheng Teachers College, Yancheng 224002 (China); Dang, R S [Second Military Medical University, Shanghai 200433 (China); Ando, M [DDS center, Research Institute for Science and Technology, Tokyo University of Science, Yamasaki 2541, Noda, Chiba 278-8510 (Japan); Sugiyama, H [Photon Factory, Institute of Material Structure Science, High Energy Accelerator Research Organization, Oho 1-1, Tsukuba, Ibaraki 305-0801 (Japan); Chen, H S [Institute of Modern Physics, Fudan University, Shanghai 200433 (China); Ding, G H, E-mail: xy-zhang@fudan.edu.c [Shanghai Research Center of Acupuncture and Meridian, Shanghai 201203 (China)
2009-09-01
The topographic structures of acupuncture points were investigated by using the synchrotron radiation based Dark Field Image (DFI) method. Four following acupuncture points were studied: Sanyinjiao, Neiguan, Zusanli and Tianshu. We have found that at acupuncture point regions there exists the accumulation of micro-vessels. The images taken in the surrounding tissue out of the acupuncture points do not show such kind of structure. It is the first time to reveal directly the specific structure of acupuncture points by X-ray imaging.
Imaging study on acupuncture points
Yan, X. H.; Zhang, X. Y.; Liu, C. L.; Dang, R. S.; Ando, M.; Sugiyama, H.; Chen, H. S.; Ding, G. H.
2009-09-01
The topographic structures of acupuncture points were investigated by using the synchrotron radiation based Dark Field Image (DFI) method. Four following acupuncture points were studied: Sanyinjiao, Neiguan, Zusanli and Tianshu. We have found that at acupuncture point regions there exists the accumulation of micro-vessels. The images taken in the surrounding tissue out of the acupuncture points do not show such kind of structure. It is the first time to reveal directly the specific structure of acupuncture points by X-ray imaging.
Wempen, Faithe
2010-01-01
Master PowerPoint and improve your presentation skills-with one book!. It's no longer enough to have slide after slide of text, bullets, and charts. It's not even enough to have good speaking skills if your PowerPoint slides bore your audience. Get the very most out of all that PowerPoint 2010 has to offer while also learning priceless tips and techniques for making good presentations in this new PowerPoint 2010 Bible. Well-known PowerPoint expert and author Faithe Wempen provides formatting tips; shows you how to work with drawings, tables, and SmartArt; introduces new collaboration tools; wa
Lagrange versus symplectic algorithm for constrained systems
Energy Technology Data Exchange (ETDEWEB)
Rothe, Heinz J; Rothe, Klaus D [Institut fuer Theoretische Physik - Universitaet Heidelberg, Philosophenweg 16, D-69120 Heidelberg (Germany)
2003-02-14
The systematization of the purely Lagrangian approach to constrained systems in the form of an algorithm involves the iterative construction of a generalized Hessian matrix W taking a rectangular form. This Hessian will exhibit as many left zero modes as there are Lagrangian constraints in the theory. We apply this approach to a general Lagrangian in the first-order formulation and show how the seemingly overdetermined set of equations is solved for the velocities by suitably extending W to a rectangular matrix. As a byproduct we thereby demonstrate the equivalence of the Lagrangian approach to the traditional Dirac approach. By making use of this equivalence we show that a recently proposed symplectic algorithm does not necessarily reproduce the full constraint structure of the traditional Dirac algorithm.
DCS Terrain Submission for Lagrange County, IN
Federal Emergency Management Agency, Department of Homeland Security — Terrain data, as defined in FEMA Guidelines and Specifications, Appendix N: Data Capture Standards, describes the digital topographic data that was used to create...
DCS Terrain Submission for Lagrange County, IN
Federal Emergency Management Agency, Department of Homeland Security — Terrain data, as defined in FEMA Guidelines and Specifications, Appendix N: Data Capture Standards, describes the digital topographic data that was used to create...
View Dependent Sequential Point Trees
Institute of Scientific and Technical Information of China (English)
Wen-Cheng Wang; Feng Wei; En-Hua Wu
2006-01-01
Sequential point trees provide the state-of-the-art technique for rendering point models, by re-arranging hierarchical points sequentially according to geometric errors running on GPU for fast rendering. This paper presents a view dependent method to augment sequential point trees by embedding the hierarchical tree structures in the sequential list of hierarchical points. By the method, two kinds of indices are constructed to facilitate the points rendering in an order mostly from near to far and from coarse to fine. As a result, invisible points can be culled view-dependently in high efficiency for hardware acceleration, and at the same time, the advantage of sequential point trees could be still fully taken. Therefore, the new method can run much faster than the conventional sequential point trees, and the acceleration can be highly promoted particularly when the objects possess complex occlusion relationship and viewed closely because invisible points would be in a high percentage of the points at finer levels.
Point to point processing of digital images using parallel computing
Directory of Open Access Journals (Sweden)
Eric Olmedo
2012-05-01
Full Text Available This paper presents an approach the point to point processing of digital images using parallel computing, particularly for grayscale, brightening, darkening, thresholding and contrast change. The point to point technique applies a transformation to each pixel on image concurrently rather than sequentially. This approach used CUDA as parallel programming tool on a GPU in order to take advantage of all available cores. Preliminary results show that CUDA obtains better results in most of the used filters. Except in the negative filter with lower resolutions images OpenCV obtained better ones, but using images in high resolutions CUDA performance is better.
Graph kernels between point clouds
Bach, Francis
2007-01-01
Point clouds are sets of points in two or three dimensions. Most kernel methods for learning on sets of points have not yet dealt with the specific geometrical invariances and practical constraints associated with point clouds in computer vision and graphics. In this paper, we present extensions of graph kernels for point clouds, which allow to use kernel methods for such ob jects as shapes, line drawings, or any three-dimensional point clouds. In order to design rich and numerically efficient kernels with as few free parameters as possible, we use kernels between covariance matrices and their factorizations on graphical models. We derive polynomial time dynamic programming recursions and present applications to recognition of handwritten digits and Chinese characters from few training examples.
Collapsing floating-point operations
Defour, David
2004-01-01
This paper addresses the issue of collapsing dependent floating-point operations. The presentation focuses on studying the dataflow graph of benchmark involving a large number of floating-point instructions. In particular, it focuses on the relevance of new floating-point operators performing two dependent operations which are similar to "fused multiply and add". Finally, this paper examines the implementation cost and critical path reduction from this strategy.
Pointing Devices for Wearable Computers
Andrés A. Calvo; Saverio Perugini
2014-01-01
We present a survey of pointing devices for wearable computers, which are body-mounted devices that users can access at any time. Since traditional pointing devices (i.e., mouse, touchpad, and trackpoint) were designed to be used on a steady and flat surface they are inappropriate for wearable computers. Just as the advent of laptops resulted in the development of the touchpad and trackpoint, the emergence of wearable computers is leading to the development of pointing devices designed for th...
Energy Technology Data Exchange (ETDEWEB)
Walter, H. [Bundesamt fuer Strahlenschutz, Oberschleissheim (Germany)
2003-07-01
For the simulation of atmospheric dispersion processes, the application of Gaussian-plume-models has been a suitable method in the past. Based on further developments in meteorology, other models, especially Lagrangian-particle-models for the computation of the radiation exposure to the population within regulatory applications are available. The different aspects of the mathematical-physical derivation and the resulting possibility of the application of the Gaussian-model and in general of the Lagrangian models from the meteoro-logical point of view are presented in this comparative study. Furthermore, the result of a literature survey of the comparison of the application of dispersion models for longterm emissions based on the Gaussian- or respectively the Lagrangian algorithms are presented. Altogether, the possibilities and constraints of Gaussian-plume-models in comparison to La-grangian-models used within the computation of the radiation exposure to the population become evident. Based on the comparison the recommendation is given to examine the introduction of the La-grangian-model within decision support systems or computational procedures for regulatory purposes. (orig.)
Brocard Point and Euler Function
Sastry, K. R. S.
2007-01-01
This paper takes a known point from Brocard geometry, a known result from the geometry of the equilateral triangle, and bring in Euler's [empty set] function. It then demonstrates how to obtain new Brocard Geometric number theory results from them. Furthermore, this paper aims to determine a [triangle]ABC whose Crelle-Brocard Point [omega]…
ATLAS Civil Engineering Point 1
Jean-Claude Vialis
1999-01-01
Different phases of realisation to Point 1 : zone of the ATLAS experiment The ATLAS experimental area is located in Point 1, just across the main CERN entrance, in the commune of Meyrin. There people are ever so busy to finish the different infrastructures for ATLAS. Real underground video. The film has original working sound.
Improved Dynamic Planar Point Location
DEFF Research Database (Denmark)
Brodal, Gerth Stølting; Arge, Lars; Georgiadis, Loukas
2006-01-01
We develop the first linear-space data structures for dynamic planar point location in general subdivisions that achieve logarithmic query time and poly-logarithmic update time.......We develop the first linear-space data structures for dynamic planar point location in general subdivisions that achieve logarithmic query time and poly-logarithmic update time....
ATLAS Civil Engineering Point 1
Jean-Claude Vialis
1998-01-01
Different phases of the PX 15 realisation to Point 1: zone of the ATLAS experiment 19-11-1998 Realisation of the Walkway for PX 15 and the putting up scaffolds 15-01-1999 Film from the surface of Point 1 and descent in the well of PX 15
Mathematical points as didactical ideas
DEFF Research Database (Denmark)
Mogensen, Arne
2012-01-01
Mathematics teaching in Denmark was recently recommended better organized in sequences with clear mathematical pedagogical goals and a focus on mathematical points. In this paper I define a mathematical point and inform on coding of transcripts in a video based Danish research study on grade 8...
Building Points - MO 2014 Barton Structure Points (SHP)
NSGIC GIS Inventory (aka Ramona) — Staff at the Geographic Resources Center placed attributed points on all roofed structures visible at a scale of 1:2000 using MSDIS-DOQQ 2008 2-foot aerial imagery...
Building Points - MO 2014 Camden Structure Points (SHP)
NSGIC GIS Inventory (aka Ramona) — Staff at the Geographic Resources Center placed attributed points on all roofed structures visible at a scale of 1:2000 using MSDIS-DOQQ 2008 2-foot aerial imagery...
Building Points - MO 2014 Dade Structure Points (SHP)
NSGIC GIS Inventory (aka Ramona) — Staff at the Geographic Resources Center placed attributed points on all roofed structures visible at a scale of 1:2000 using MSDIS-DOQQ 2008 2-foot aerial imagery...
Building Points - MO 2014 Clark Structure Points (SHP)
NSGIC GIS Inventory (aka Ramona) — Staff at the Geographic Resources Center placed attributed points on all roofed structures visible at a scale of 1:2000 using MSDIS-DOQQ 2008 2-foot aerial imagery...
Building Points - MO 2014 Audrain Structure Points (SHP)
NSGIC GIS Inventory (aka Ramona) — Staff at the Geographic Resources Center placed attributed points on all roofed structures visible at a scale of 1:2000 using MSDIS-DOQQ 2008 2-foot aerial imagery...
Building Points - MO 2014 Bates Structure Points (SHP)
NSGIC GIS Inventory (aka Ramona) — Staff at the Geographic Resources Center placed attributed points on all roofed structures visible at a scale of 1:2000 using MSDIS-DOQQ 2008 2-foot aerial imagery...
Building Points - MO 2014 Benton Structure Points (SHP)
NSGIC GIS Inventory (aka Ramona) — Staff at the Geographic Resources Center placed attributed points on all roofed structures visible at a scale of 1:2000 using MSDIS-DOQQ 2008 2-foot aerial imagery...
Building Points - MO 2014 Butler Structure Points (SHP)
NSGIC GIS Inventory (aka Ramona) — Staff at the Geographic Resources Center placed attributed points on all roofed structures visible at a scale of 1:2000 using MSDIS-DOQQ 2008 2-foot aerial imagery...
Geodetic Control Points - Multi-State Control Point Database
NSGIC GIS Inventory (aka Ramona) — The Multi-State Control Point Database (MCPD) is a database of geodetic and mapping control covering Idaho and Montana. The control were submitted by registered land...
Building Points - MO 2014 Christian Structure Points (SHP)
NSGIC GIS Inventory (aka Ramona) — Staff at the Geographic Resources Center placed attributed points on all roofed structures visible at a scale of 1:2000 using MSDIS-DOQQ 2008 2-foot aerial imagery...
Building Points - MO 2012 St. Francois Structure Points (SHP)
NSGIC GIS Inventory (aka Ramona) — Staff at the Geographic Resources Center placed categorized points on all roofed structures visible at a scale of 1:2000 using MSDIS-DOQQ 2008 2-foot aerial imagery...
Building Points - MO 2012 St. Genevieve Structure Points (SHP)
NSGIC GIS Inventory (aka Ramona) — Staff at the Geographic Resources Center placed categorized points on all roofed structures visible at a scale of 1:2000 using MSDIS-DOQQ 2008 2-foot aerial imagery...
Building Points - MO 2012 Perry Structure Points (SHP)
NSGIC GIS Inventory (aka Ramona) — Staff at the Geographic Resources Center placed categorized points on all roofed structures visible at a scale of 1:2000 using MSDIS-DOQQ 2008 2-foot aerial imagery...
Building Points - MO 2012 Cape Girardeau Structure Points (SHP)
NSGIC GIS Inventory (aka Ramona) — Staff at the Geographic Resources Center placed categorized points on all roofed structures visible at a scale of 1:2000 using MSDIS-DOQQ 2008 2-foot aerial imagery...
Building Points - MO 2012 Iron Structure Points (SHP)
NSGIC GIS Inventory (aka Ramona) — Staff at the Geographic Resources Center placed categorized points on all roofed structures visible at a scale of 1:2000 using MSDIS-DOQQ 2008 2-foot aerial imagery...
Building Points - MO 2012 Madison Structure Points (SHP)
NSGIC GIS Inventory (aka Ramona) — Staff at the Geographic Resources Center placed categorized points on all roofed structures visible at a scale of 1:2000 using MSDIS-DOQQ 2008 2-foot aerial imagery...
Building Points - MO 2012 Bollinger Structure Points (SHP)
NSGIC GIS Inventory (aka Ramona) — Staff at the Geographic Resources Center placed categorized points on all roofed structures visible at a scale of 1:2000 using MSDIS-DOQQ 2008 2-foot aerial imagery...
Geodetic Control Points - Multi-State Control Point Database
NSGIC State | GIS Inventory — The Multi-State Control Point Database (MCPD) is a database of geodetic and mapping control covering Idaho and Montana. The control were submitted by registered land...
Building Points - MO 2014 Andrew Structure Points (SHP)
NSGIC GIS Inventory (aka Ramona) — Staff at the Geographic Resources Center placed attributed points on all roofed structures visible at a scale of 1:2000 using MSDIS-DOQQ 2008 2-foot aerial imagery...
Denardini, Clezio Marcos
2016-07-01
We have developed a tool for measuring the evolutional stage of the space weather regional warning centers using the approach of the innovative evolution starting from the perspective presented by Figueiredo (2009, Innovation Management: Concepts, metrics and experiences of companies in Brazil. Publisher LTC, Rio de Janeiro - RJ). It is based on measuring the stock of technological skills needed to perform a certain task that is (or should) be part of the scope of a space weather center. It also addresses the technological capacity for innovation considering the accumulation of technological and learning capabilities, instead of the usual international indices like number of registered patents. Based on this definition, we have developed a model for measuring the capabilities of the Brazilian Study and Monitoring Program Space Weather (Embrace), a program of the National Institute for Space Research (INPE), which has gone through three national stages of development and an international validation step. This program was created in 2007 encompassing competence from five divisions of INPE in order to carry out the data collection and maintenance of the observing system in space weather; to model processes of the Sun-Earth system; to provide real-time information and to forecast space weather; and provide diagnostic their effects on different technological systems. In the present work, we considered the issues related to the innovation of micro-processes inherent to the nature of the Embrace program, not the macro-economic processes, despite recognizing the importance of these. During the development phase, the model was submitted to five scientists/managers from five different countries member of the International Space Environment Service (ISES) who presented their evaluations, concerns and suggestions. It was applied to the Embrace program through an interview form developed to be answered by professional members of regional warning centers. Based on the returning
Quantization of the Hořava theory at the kinetic-conformal point
Bellorín, Jorge; Restuccia, Alvaro
2016-09-01
The Hořava theory depends on several coupling constants. The kinetic term of its Lagrangian depends on one dimensionless coupling constant λ . For the particular value λ =1 /3 the kinetic term becomes conformal invariant, although the full Lagrangian does not have this symmetry. For any value of λ the nonprojectable version of the theory has second-class constraints that play a central role in the process of quantization. Here we study the complete nonprojectable theory, including the Blas-Pujolàs-Sibiryakov interacting terms, at the kinetic-conformal point λ =1 /3 . The generic counting of degrees of freedom indicates that this theory propagates the same physical degrees of freedom of general relativity. We analyze this point rigorously, taking into account all the z =1 , 2, 3 terms that contribute to the action describing quadratic perturbations around the Minkowski spacetime. We show that the constraints of the theory and equations determining the Lagrange multipliers are strongly elliptic partial differential equations, an essential condition for a constrained phase-space structure in field theory. We show how their solutions lead to the two independent tensorial physical modes propagated by the theory. We also obtain the reduced Hamiltonian. These arguments strengthen the consistency of the theory. We find the restrictions on the space of coupling constants to ensure the positiveness of the reduced Hamiltonian. We obtain the propagator of the physical modes, showing that there are not ghosts and that the propagator effectively acquires the z =3 scaling for all physical degrees of freedom at the high-energy regime. By evaluating the superficial degree of divergence, taking into account the second-class constraints, we show that the theory is power-counting renormalizable. We analyze, in the path-integral formulation of the theory, the measure associated to the second-class constraints both in the canonical and the Lagrangian (foliation
Cleaning Massive Sonar Point Clouds
DEFF Research Database (Denmark)
Arge, Lars Allan; Larsen, Kasper Green; Mølhave, Thomas;
2010-01-01
We consider the problem of automatically cleaning massive sonar data point clouds, that is, the problem of automatically removing noisy points that for example appear as a result of scans of (shoals of) fish, multiple reflections, scanner self-reflections, refraction in gas bubbles, and so on. We...... describe a new algorithm that avoids the problems of previous local-neighbourhood based algorithms. Our algorithm is theoretically I/O-efficient, that is, it is capable of efficiently processing massive sonar point clouds that do not fit in internal memory but must reside on disk. The algorithm is also...
ATLAS: civil engineering Point 1
2000-01-01
The construction work at point one was a massive site including overground and underground work. Point 1 under construction is worth to see.Tools and machinery used during the construction and the multible scenes with people working in different parts of point1. Scenes from the 3D CAD office and some talking in english. Printing out drawings and later views of the empty tunnel were the LHC accelerator is installed 80m under the surface.The film gives the view to the close history in other words to the time before the installations.
Geometric Computations On Indecisive Points
DEFF Research Database (Denmark)
Jørgensen, Allan Grønlund; Phillips, Jeff; Loffler, Maarten
2011-01-01
We study computing with indecisive point sets. Such points have spatial uncertainty where the true location is one of a finite number of possible locations. This data arises from probing distributions a few times or when the location is one of a few locations from a known database. In particular......-hard. We generalize our polynomial-time algorithm to all LP-type problems. We also utilize our indecisive framework to deterministically and approximately compute on a more general class of uncertain data where the location of each point is given by a probability distribution....
Wempen, Faithe
2013-01-01
Master PowerPoint and improve your presentation skills with one book! In today's business climate, you need to know PowerPoint inside and out, and that's not all. You also need to be able to make a presentation that makes an impact. From using sophisticated transitions and animation in your PowerPoint presentations to interfacing in person with your audience, this information-packed book helps you succeed. Start creating professional-quality slides that captivate audiences and discover essential tips and techniques for making first-rate presentations, whether you're at a podium or
NOTE: Do acupuncture points exist?
Yan, Xiaohui; Zhang, Xinyi; Liu, Chenglin; Dang, Ruishan; Huang, Yuying; He, Wei; Ding, Guanghong
2009-05-01
We used synchrotron x-ray fluorescence analysis to probe the distribution of four chemical elements in and around acupuncture points, two located in the forearm and two in the lower leg. Three of the four acupuncture points showed significantly elevated concentrations of elements Ca, Fe, Cu and Zn in relation to levels in the surrounding tissue, with similar elevation ratios for Cu and Fe. The mapped distribution of these elements implies that each acupuncture point seems to be elliptical with the long axis along the meridian.
ATLAS Civil Engineering Point 1
Jean-Claude Vialis
1998-01-01
Different phases of realisation to Point 1 : zone of the ATLAS experiment After watching this film you can get the view of the civil engineering work at POINT1 where the ATLAS will be built. 03-11-1998 The video starts with the view of the POINT1 taken from the roof of the building 33. 04-11-1998 View of the installation of the entrance of the SDX1 18/19-11-1998 Installation of the rafters to the building PX15
Positional nystagmus showing neutral points.
Hiruma, Kiyoshi; Numata, Tsutomu
2004-01-01
We encountered patients who had their static direction-changing positional nystagmus canceled at about 20-30 degrees yaw head rotation from the supine position. This nystagmus was also canceled when the head was rotated 180 degrees from this position. We call these head positions neutral points. At the neutral points, the cupula of the horizontal semicircular canal of the affected ear is positioned vertical to the gravitational plane and no deflection of the cupula occurs. The positional nystagmus observed (except the neutral points) was thought to occur due to a "heavy cupula" or "light cupula", which may be determined by the specific gravity of its endolymph.
Allegheny County Cell Tower Points
Allegheny County / City of Pittsburgh / Western PA Regional Data Center — This dataset portrays cell tower locations as points in Allegheny County. The dataset is based on outbuilding codes in the Property Assessment Parcel Database used...
Hawaii ESI: NESTS (Nest Points)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for seabird nesting colonies in coastal Hawaii. Vector points in this data set represent locations of...
NULL Convention Floating Point Multiplier
Directory of Open Access Journals (Sweden)
Anitha Juliette Albert
2015-01-01
Full Text Available Floating point multiplication is a critical part in high dynamic range and computational intensive digital signal processing applications which require high precision and low power. This paper presents the design of an IEEE 754 single precision floating point multiplier using asynchronous NULL convention logic paradigm. Rounding has not been implemented to suit high precision applications. The novelty of the research is that it is the first ever NULL convention logic multiplier, designed to perform floating point multiplication. The proposed multiplier offers substantial decrease in power consumption when compared with its synchronous version. Performance attributes of the NULL convention logic floating point multiplier, obtained from Xilinx simulation and Cadence, are compared with its equivalent synchronous implementation.
NULL convention floating point multiplier.
Albert, Anitha Juliette; Ramachandran, Seshasayanan
2015-01-01
Floating point multiplication is a critical part in high dynamic range and computational intensive digital signal processing applications which require high precision and low power. This paper presents the design of an IEEE 754 single precision floating point multiplier using asynchronous NULL convention logic paradigm. Rounding has not been implemented to suit high precision applications. The novelty of the research is that it is the first ever NULL convention logic multiplier, designed to perform floating point multiplication. The proposed multiplier offers substantial decrease in power consumption when compared with its synchronous version. Performance attributes of the NULL convention logic floating point multiplier, obtained from Xilinx simulation and Cadence, are compared with its equivalent synchronous implementation.
Virginia ESI: REPTPT (Reptile Points)
National Oceanic and Atmospheric Administration, Department of Commerce — This data set contains sensitive biological resource data for sea turtles in Virginia. Vector points in this data set represent nesting sites. Species-specific...
Allegheny County Cell Tower Points
Allegheny County / City of Pittsburgh / Western PA Regional Data Center — This dataset portrays cell tower locations as points in Allegheny County. The dataset is based on outbuilding codes in the Property Assessment Parcel Database used...
Articulation Points in Complex Networks
Tian, Liang; Shi, Da-Ning; Liu, Yang-Yu
2016-01-01
An articulation point in a network is a node whose removal disconnects the network. Those nodes play key roles in ensuring connectivity of many real-world networks, from infrastructure networks to protein interaction networks and terrorist communication networks. Despite their fundamental importance, a general framework of studying articulation points in complex networks is lacking. Here we develop analytical tools to study key issues pertinent to articulation points, e.g. the expected number of them and the network vulnerability against their removal, in an arbitrary complex network. We find that a greedy articulation point removal process provides us a novel perspective on the organizational principles of complex networks. Moreover, this process is associated with two fundamentally different types of percolation transitions with a rich phase diagram. Our results shed light on the design of more resilient infrastructure networks and the effective destruction of terrorist communication networks.
Articulation points in complex networks
Tian, Liang; Bashan, Amir; Shi, Da-Ning; Liu, Yang-Yu
2017-01-01
An articulation point in a network is a node whose removal disconnects the network. Those nodes play key roles in ensuring connectivity of many real-world networks, from infrastructure networks to protein interaction networks and terrorist communication networks. Despite their fundamental importance, a general framework of studying articulation points in complex networks is lacking. Here we develop analytical tools to study key issues pertinent to articulation points, such as the expected number of them and the network vulnerability against their removal, in an arbitrary complex network. We find that a greedy articulation point removal process provides us a different perspective on the organizational principles of complex networks. Moreover, this process results in a rich phase diagram with two fundamentally different types of percolation transitions. Our results shed light on the design of more resilient infrastructure networks and the effective destruction of terrorist communication networks.
Calcareous Fens - Source Feature Points
Minnesota Department of Natural Resources — Pursuant to the provisions of Minnesota Statutes, section 103G.223, this database contains points that represent calcareous fens as defined in Minnesota Rules, part...