Geometry, Student's Text, Part II, Unit 14.
ERIC Educational Resources Information Center
Allen, Frank B.; And Others
Unit 14 in the SMSG secondary school mathematics series is a student text covering the following topics in geometry: areas of polygonal regions, similarity, circles and spheres, characterization of sets, constructions, areas of circles and sectors, volumes of solids, and plane coordinate geometry. Appendices cover Eratosthenes' measurement of the…
Self-biased converse magnetoelectric effect
NASA Astrophysics Data System (ADS)
Chul Yang, Su; Cho, Kyung-Hoon; Park, Chee-Sung; Priya, Shashank
2011-11-01
In this letter, we investigate the direct magnetoelectric (DME) and converse magnetoelectric (CME) effects in three-phase metal-ceramic laminate composites. Longitudinally poled and transversely magnetized (L-T) laminate was fabricated by bonding nickel plates between the two particulate magnetoelectric (ME) composite layers of composition 0.8 (0.948 K0.5Na0.5NbO3 - 0.052 LiSbO3) - 0.2 (Ni0.8Zn0.2Fe2O4) (KNNLS-NZF). Under off-resonance condition, the laminates exhibited hysteretic DME and CME responses as a function of applied bias field (Hbias). Self-biased effect characterized by non-zero ME response at zero Hbias was observed. The self-biased DME and CME properties were found to be enhanced under resonance conditions. Without external Hbias, magnetic induction switching was possible by applying AC voltage. These results provide the possibility of using self-biased CME effect in electrically controlled memory devices and magnetic flux control devices.
A Self-Biasing Pulsed Depressed Collector
Kemp, Mark A.; Jensen, Aaron; Neilson, Jeff; /SLAC
2014-05-29
Depressed collectors have been utilized successfully for many years to improve the electrical efficiency of vacuum electron devices. Increasingly, pulsed, high-peak power accelerator applications are placing a premium on electrical efficiency. As RF systems are responsible for a large percentage of the overall energy usage at accelerator laboratories, methods to improve upon the state-of-the-art in pulsed high-power sources are desired. This paper presents a technique for self-biasing the stages in a multistage depressed collector. With this technique, the energy lost during the rise and fall times of the pulse can be recovered, separate power supplies are not needed, and existing modulators can be retrofitted. Calculations show that significant cost savings can be realized with the implementation of this device in high-power systems. In this paper, the technique is described along with experimental demonstration. (auth)
Unified Field Theoretical Models from Generalized Affine Geometries II
NASA Astrophysics Data System (ADS)
Cirilo-Lombardo, Diego Julio
2011-06-01
The space-time structure of the new Unified Field Theory presented in previous reference (Int. J. Theor. Phys. 49:1288-1301, 2010) is analyzed from its SL(2C) underlying structure in order to make precise the notion of minimal coupling. To this end, the framework is the language of tensors and particularly differential forms and the condition a priory of the existence of a potential for the torsion is relaxed. We shown trough exact cosmological solutions from this model, where the geometry is Euclidean R⊗ O 3˜ R⊗ SU(2), the relation between the space-time geometry and the structure of the gauge group. Precisely this relation is directly connected with the relation of the spin and torsion fields. The solution of this model is explicitly compared with our previous ones and we find that: (i) the torsion is not identified directly with the Yang Mills type strength field, (ii) there exists a compatibility condition connected with the identification of the gauge group with the geometric structure of the space-time: this fact lead the identification between derivatives of the scale factor a( τ) with the components of the torsion in order to allows the Hosoya-Ogura ansatz (namely, the alignment of the isospin with the frame geometry of the space-time), (iii) this compatibility condition precisely mark the fact that local gauge covariance, coordinate independence and arbitrary space time geometries are harmonious concepts and (iv) of two possible structures of the torsion the "tratorial" form (the only one studied here) forbids wormhole configurations, leading only, cosmological instanton space-time in eternal expansion.
Self-biased circulators for high power applications
NASA Astrophysics Data System (ADS)
Sokolov, Alexander S.
Self-biased circulators exploit the properties of high anisotropy magnetic field in hexagonal ferrites, thus allowing operation without biasing magnets and a significant size and weight reduction. Although first self-biased circulators were demonstrated more than 20 years ago, all the prototypes constructed so far are unsuitable for practical applications. An attempt to design a self-biased circulator from scratch was made. Novel exceptionally low dielectric loss and high heat conductivity ceramic materials were developed and innovative substrate synthesis techniques were employed. Low temperature cofiring of green body ferrite compacts and dielectric ceramic slurries were mastered, resulting in solid composite substrates. Original device design was developed. Key features (including wide coupling angles, wide microstriplines, thick substrate, and absence of impedance transformers) enable low insertion loss, broadband operation, high power handling, and compact size. Fabrication and testing of Ka band Y-junction self-biased circulator are reported herein. Furthermore, design approach and fabrication techniques developed here can be readily applied for the construction of X-band self-biased circulators, provided that suitable ferrite materials are available. Low temperature cofiring of ferrite and dielectric materials is especially beneficial for various RF and high-frequency applications. Multiple devices can be readily fabricated on a single wafer using conventional lithographic techniques, resulting in true microwave monolithic integrated circuit.
Super-size me: self biases increase to larger stimuli.
Sui, Jie; Humphreys, Glyn W
2015-04-01
Prior work has shown that simple perceptual match responses to pairings of shapes and labels are more efficient if the pairing is associated with the participant (e.g., circle-you) than if it is associated with another familiar person (e.g., square-friend). There is a similar advantage for matching associations with high-value rewards (circle-£9) versus low-value rewards (square-£1) (Sui, He, & Humphreys Journal of Experimental Psychology: Human Perception and Performance, 38, 1105-1117, 2012). Here we evaluated the relations between the self- and reward-bias effects by introducing occasional trials in which the size of a shape was varied unexpectedly (large or small vs. a standard medium). Participants favored stimuli that were larger than the standard when stimuli were associated with the self, and this enhancement of self bias was predicted by the degree of self bias that participants showed to standard (medium) sized stimuli. Although we observed a correlation between the magnitudes of the self and reward biases over participants, reward-bias effects were not increased to large stimuli. The data suggest both overlapping and independent components of the self and reward biases, and that self biases are uniquely enhanced when stimuli increase in size, consistent with previously reported motivational biases favoring large stimuli.
Differential geometry based solvation model II: Lagrangian formulation.
Chen, Zhan; Baker, Nathan A; Wei, G W
2011-12-01
Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation models. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The optimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and PB equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for the purpose of
Differential geometry based solvation model II: Lagrangian formulation
Chen, Zhan; Baker, Nathan A.; Wei, G. W.
2010-01-01
Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a Lagrangian formulation of our differential geometry based solvation model. The Lagrangian representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the Lagrangian representation does not need to resort to artificially enlarged van der Waals radii as often required by the Eulerian representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the Eulerian and Lagrangian formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory (SPT) of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The minimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and Poisson-Boltzmann equations. Due to the development of singularities and nonsmooth manifolds in the Lagrangian representation, the resulting potential-driven geometric flow equation is embedded into the Eulerian representation for
Electrical Characteristics of Self-Biased Channel Diode
NASA Astrophysics Data System (ADS)
Sugawara, Fumihiko; Yoshida, Tatsuya; Hoshi, Hideaki; Yamaguchi, Hideo; Ohnuma, Koichi
A new low-loss diode, a self-biased channel diode, is described. In order to achieve a two-terminal operation by using a self-bias, the shunt electrode of the source and gate of the conventional DMOSFET with a floating body is adopted in this diode. By utilizing a DMOSFET, this proposed diode attains a high breakdown voltage compared with a lateral MOSFET. In this device, forward conduction is caused by the self-gate bias created by applying a positive voltage to the shunt electrode of the source and gate with respect to the drain. The direction of forward conduction is opposite to that of forward conduction in a conventional DMOSFET. In the reverse-bias state, the reverse current is very small without any bias owing to the shunt of the source and the gate electrode. In this report, the operational mechanism and electrical characteristics of the device fabricated for the proposed diode are discussed. From the experimental results, it is clear that at room temperature, the on-state voltage of the proposed diode is between that of the Ti-SBD and Cr-SBD. The simulated I-V characteristics are consistent with the measured values. From the simulation results, the proposed diode, in which a thin gate oxide layer and a high integration density of the DMOSFET cell are used, shows lower power loss in the temperature range 25-75°C than does the Cr-SBD. At high temperatures the power loss in the proposed diode is lower than that observed in the Ti-SBD and Cr-SBD which easily fall into thermal runaway.
Plasma acceleration using a radio frequency self-bias effect
NASA Astrophysics Data System (ADS)
Rafalskyi, D.; Aanesland, A.
2015-06-01
In this work plasma acceleration using a RF self-bias effect is experimentally studied. The experiments are conducted using a novel plasma accelerator system, called Neptune, consisting of an inductively coupled plasma source and a RF-biased set of grids. The plasma accelerator can operate in a steady state mode, producing a plasma flow with separately controlled plasma flux and velocity without any magnetic configuration. The operating pressure at the source output is as low as 0.2 mTorr and can further be decreased. The ion and electron flows are investigated by measuring the ion and electron energy distribution functions both space resolved and with different orientations with respect to the flow direction. It is found that the flow of electrons from the source is highly anisotropic and directed along the ion flow and this global flow of accelerated plasma is well localized in the plasma transport chamber. The maximum flux is about 7.5.1015 ions s-1 m-2 (at standard conditions) on the axis and decreasing to almost zero at a radial distances of more than 15 cm from the flow axis. Varying the RF acceleration voltage in the range 20-350 V, the plasma flow velocity can be changed between 10 and 35 km/s. The system is prospective for different technology such as space propulsion and surface modification and also interesting for fundamental studies for space-related plasma simulations and investigation of the dynamo effect using accelerated rotating plasmas.
THREE-DIMENSIONAL GEOMETRIES AND THE ANALYSIS OF H II REGIONS
Wood, Kenneth; Barnes, J. E.; Ercolano, Barbara; Haffner, L. M.; Reynolds, R. J.; Dale, J.
2013-06-20
We compare emission line intensities from photoionization models of smooth and fractal shell geometries for low density H II regions, with particular focus on the low-ionization diagnostic diagram [N II]/H{alpha} versus H{alpha}. Building on previously published models and observations of Barnard's Loop, we show that the observed range of intensities and variations in the line intensity ratios may be reproduced with a three-dimensional shell geometry. Our models adopt solar abundances throughout the model nebula, in contrast with previous one-dimensional modeling which suggested the variations in line intensity ratios could only be reproduced if the heavy element abundances were increased by a factor of {approx}1.4. For spatially resolved H II regions, the multiple sightlines that pierce and sample different ionization and temperature conditions within smooth and fractal shells produce a range of line intensities that are easily overlooked if only the total integrated intensities from the entire nebula model are computed. Our conclusion is that inference of H II region properties, such as elemental abundances, via photoionization models of one-dimensional geometries must be treated with caution and further tested through three-dimensional modeling.
Plasma acceleration using a radio frequency self-bias effect
Rafalskyi, D.; Aanesland, A.
2015-06-15
In this work plasma acceleration using a RF self-bias effect is experimentally studied. The experiments are conducted using a novel plasma accelerator system, called Neptune, consisting of an inductively coupled plasma source and a RF-biased set of grids. The plasma accelerator can operate in a steady state mode, producing a plasma flow with separately controlled plasma flux and velocity without any magnetic configuration. The operating pressure at the source output is as low as 0.2 mTorr and can further be decreased. The ion and electron flows are investigated by measuring the ion and electron energy distribution functions both space resolved and with different orientations with respect to the flow direction. It is found that the flow of electrons from the source is highly anisotropic and directed along the ion flow and this global flow of accelerated plasma is well localized in the plasma transport chamber. The maximum flux is about 7.5·10{sup 15} ions s{sup −1} m{sup −2} (at standard conditions) on the axis and decreasing to almost zero at a radial distances of more than 15 cm from the flow axis. Varying the RF acceleration voltage in the range 20–350 V, the plasma flow velocity can be changed between 10 and 35 km/s. The system is prospective for different technology such as space propulsion and surface modification and also interesting for fundamental studies for space-related plasma simulations and investigation of the dynamo effect using accelerated rotating plasmas.
Measurements of heat transfer to helium II at atmospheric pressure in a confined geometry
Warren, R.P.; Caspi, S.
1981-08-01
Recently the enhanced heat removal capability of unsaturated superfluid helium II has been exploited in fusion and accelerator dipole magnets. In superfluid the internal convection mechanism dominates the heat removal process and orientation with respect to gravity becomes of secondary importance. Heat transfer, however, can be influenced by the thermodynamic state of the liquid, especially with regard to possible phase transformations. The transformation from non-saturated He II must involve an He I state before the film boiling transition is experienced. Some steady state measurements of heat transfer to non-saturated He II have been previously reported. In typical magnet designs, cooling passages between turns result from gaps between the electrical insulation, and are typically on the order of a fraction of a millimeter. The purpose of the work reported here is to measure the attenuation of the heat transfer within such a restrictive geometry.
Type II InAs/GaAsSb quantum dots: Highly tunable exciton geometry and topology
Llorens, J. M.; Wewior, L.; Cardozo de Oliveira, E. R.; Alén, B.; Ulloa, J. M.; Utrilla, A. D.; Guzmán, A.; Hierro, A.
2015-11-02
External control over the electron and hole wavefunctions geometry and topology is investigated in a p-i-n diode embedding a dot-in-a-well InAs/GaAsSb quantum structure with type II band alignment. We find highly tunable exciton dipole moments and largely decoupled exciton recombination and ionization dynamics. We also predicted a bias regime where the hole wavefunction topology changes continuously from quantum dot-like to quantum ring-like as a function of the external bias. All these properties have great potential in advanced electro-optical applications and in the investigation of fundamental spin-orbit phenomena.
Naga Babu, Chatla; Suresh, Paladugu; Srinivas, Katam; Sathyanarayana, Arruri; Sampath, Natarajan; Prabusankar, Ganesan
2016-05-10
Five Pb(ii)-imidazolium carboxylate coordination assemblies with novel structural motifs were derived from the reaction between the corresponding flexible, semi flexible or rigid imidazolium carboxylic acid ligands and lead nitrate. The imidazolium linker present in these molecules likely plays a triple role such as the counter ion to balance the metal charge, the ligand being an integral part of the final product and the catalyst facilitating carbon-carbon bond formation reaction. These lead-imidazolium coordination assemblies exhibit, variable chemical and thermal stabilities, as well as catalytic activity. These newly prepared catalysts are highly active towards benzoin condensation reactions with good functional group tolerance.
NASA Astrophysics Data System (ADS)
Kramer, S. L.; Ghosh, V. J.; Breitfeller, M.; Wahl, W.
2016-11-01
Third generation high brightness light sources are designed to have low emittance and high current beams, which contribute to higher beam loss rates that will be compensated by Top-Off injection. Shielding for these higher loss rates will be critical to protect the projected higher occupancy factors for the users. Top-Off injection requires a full energy injector, which will demand greater consideration of the potential abnormal beam miss-steering and localized losses that could occur. The high energy electron injection beam produces significantly higher neutron component dose to the experimental floor than a lower energy beam injection and ramped operations. Minimizing this dose will require adequate knowledge of where the miss-steered beam can occur and sufficient EM shielding close to the loss point, in order to attenuate the energy of the particles in the EM shower below the neutron production threshold (<10 MeV), which will spread the incident energy on the bulk shield walls and thereby the dose penetrating the shield walls. Designing supplemental shielding near the loss point using the analytic shielding model is shown to be inadequate because of its lack of geometry specification for the EM shower process. To predict the dose rates outside the tunnel requires detailed description of the geometry and materials that the beam losses will encounter inside the tunnel. Modern radiation shielding Monte-Carlo codes, like FLUKA, can handle this geometric description of the radiation transport process in sufficient detail, allowing accurate predictions of the dose rates expected and the ability to show weaknesses in the design before a high radiation incident occurs. The effort required to adequately define the accelerator geometry for these codes has been greatly reduced with the implementation of the graphical interface of FLAIR to FLUKA. This made the effective shielding process for NSLS-II quite accurate and reliable. The principles used to provide supplemental
XAFS study of copper(II) complexes with square planar and square pyramidal coordination geometries
NASA Astrophysics Data System (ADS)
Gaur, A.; Klysubun, W.; Nitin Nair, N.; Shrivastava, B. D.; Prasad, J.; Srivastava, K.
2016-08-01
X-ray absorption fine structure of six Cu(II) complexes, Cu2(Clna)4 2H2O (1), Cu2(ac)4 2H2O (2), Cu2(phac)4 (pyz) (3), Cu2(bpy)2(na)2 H2O (ClO4) (4), Cu2(teen)4(OH)2(ClO4)2 (5) and Cu2(tmen)4(OH)2(ClO4)2 (6) (where ac, phac, pyz, bpy, na, teen, tmen = acetate, phenyl acetate, pyrazole, bipyridine, nicotinic acid, tetraethyethylenediamine, tetramethylethylenediamine, respectively), which were supposed to have square pyramidal and square planar coordination geometries have been investigated. The differences observed in the X-ray absorption near edge structure (XANES) features of the standard compounds having four, five and six coordination geometry points towards presence of square planar and square pyramidal geometry around Cu centre in the studied complexes. The presence of intense pre-edge feature in the spectra of four complexes, 1-4, indicates square pyramidal coordination. Another important XANES feature, present in complexes 5 and 6, is prominent shoulder in the rising part of edge whose intensity decreases in the presence of axial ligands and thus indicates four coordination in these complexes. Ab initio calculations were carried out for square planar and square pyramidal Cu centres to observe the variation of 4p density of states in the presence and absence of axial ligands. To determine the number and distance of scattering atoms around Cu centre in the complexes, EXAFS analysis has been done using the paths obtained from Cu(II) oxide model and an axial Cu-O path from model of a square pyramidal complex. The results obtained from EXAFS analysis have been reported which confirmed the inference drawn from XANES features. Thus, it has been shown that these paths from model of a standard compound can be used to determine the structural parameters for complexes having unknown structure.
NASA Astrophysics Data System (ADS)
Gaur, A.; Klysubun, W.; Soni, Balram; Shrivastava, B. D.; Prasad, J.; Srivastava, K.
2016-10-01
X-ray absorption spectroscopy (XAS) is very useful in revealing the information about geometric and electronic structure of a transition-metal absorber and thus commonly used for determination of metal-ligand coordination. But XAFS analysis becomes difficult if differently coordinated metal centers are present in a system. In the present investigation, existence of distinct coordination geometries around metal centres have been studied by XAFS in a series of trimesic acid Cu(II) complexes. The complexes studied are: Cu3(tma)2(im)6 8H2O (1), Cu3(tma)2(mim)6 17H2O (2), Cu3(tma)2(tmen)3 8.5H2O (3), Cu3(tma) (pmd)3 6H2O (ClO4)3 (4) and Cu3(tma)2 3H2O (5). These complexes have not only Cu metal centres with different coordination but in complexes 1-3, there are multiple coordination geometries present around Cu centres. Using XANES spectra, different coordination geometries present in these complexes have been identified. The variation observed in the pre-edge features and edge features have been correlated with the distortion of the specific coordination environment around Cu centres in the complexes. XANES spectra have been calculated for the distinct metal centres present in the complexes by employing ab-initio calculations. These individual spectra have been used to resolve the spectral contribution of the Cu centres to the particular XANES features exhibited by the experimental spectra of the multinuclear complexes. Also, the variation in the 4p density of states have been calculated for the different Cu centres and then correlated with the features originated from corresponding coordination of Cu. Thus, these spectral features have been successfully utilized to detect the presence of the discrete metal centres in a system. The inferences about the coordination geometry have been supported by EXAFS analysis which has been used to determine the structural parameters for these complexes.
A stabilized, high stress self-biasing shape memory alloy actuator
NASA Astrophysics Data System (ADS)
Panton, B.; Zhou, Y. N.; Khan, M. I.
2016-09-01
A shape memory alloy (SMA) actuator that is biased internally would not need an external bias to achieve multiple actuation cycles. This would reduce cost, complexity and weight compared to standard one-way SMAs. The self-biasing actuators that have been developed to date have a lack of geometric and actuation stability. The current study developed a self-biasing NiTi actuator using a laser based vaporization process to alter the bulk composition of different regions. The martensitic laser processed NiTi region was the actuator, and un-processed austenitic base metal region was the internal bias. It was discovered that the laser processed region of the self-biasing actuator was unstable during high stress thermomechanical cycling due to the coarse grained microstructure. Cold-working of the half martensitic and half austenitic component resulted in similar deformation characteristics to single phase NiTi, which enabled the formation of a uniform nanocrystalline microstructure in both regions. When thermomechanically cycled 6000 times under stresses ranging from 180 to 400 MPa, it was discovered that this treated self-biasing actuator exhibited the stabilization behavior of traditional one-way actuators. This behavior was due to the uniform nanocrystalline microstructure, which impeded dislocation activity and ensured minimal plastic deformation.
Radiation tolerance of CMOS monolithic active pixel sensors with self-biased pixels
NASA Astrophysics Data System (ADS)
Deveaux, M.; Amar-Youcef, S.; Besson, A.; Claus, G.; Colledani, C.; Dorokhov, M.; Dritsa, C.; Dulinski, W.; Fröhlich, I.; Goffe, M.; Grandjean, D.; Heini, S.; Himmi, A.; Hu, C.; Jaaskelainen, K.; Müntz, C.; Shabetai, A.; Stroth, J.; Szelezniak, M.; Valin, I.; Winter, M.
2010-12-01
CMOS monolithic active pixel sensors (MAPS) are proposed as a technology for various vertex detectors in nuclear and particle physics. We discuss the mechanisms of ionizing radiation damage on MAPS hosting the dead time free, so-called self bias pixel. Moreover, we introduce radiation hardened sensor designs which allow operating detectors after exposing them to irradiation doses above 1 Mrad.
Kramer, S. L.; Ghosh, V. J.; Breitfeller, M.; Wahl, W.
2016-08-10
We present that third generation high brightness light sources are designed to have low emittance and high current beams, which contribute to higher beam loss rates that will be compensated by Top-Off injection. Shielding for these higher loss rates will be critical to protect the projected higher occupancy factors for the users. Top-Off injection requires a full energy injector, which will demand greater consideration of the potential abnormal beam miss-steering and localized losses that could occur. The high energy electron injection beam produces significantly higher neutron component dose to the experimental floor than a lower energy beam injection and ramped operations. Minimizing this dose will require adequate knowledge of where the miss-steered beam can occur and sufficient EM shielding close to the loss point, in order to attenuate the energy of the particles in the EM shower below the neutron production threshold (<10 MeV), which will spread the incident energy on the bulk shield walls and thereby the dose penetrating the shield walls. Designing supplemental shielding near the loss point using the analytic shielding model is shown to be inadequate because of its lack of geometry specification for the EM shower process. To predict the dose rates outside the tunnel requires detailed description of the geometry and materials that the beam losses will encounter inside the tunnel. Modern radiation shielding Monte-Carlo codes, like FLUKA, can handle this geometric description of the radiation transport process in sufficient detail, allowing accurate predictions of the dose rates expected and the ability to show weaknesses in the design before a high radiation incident occurs. The effort required to adequately define the accelerator geometry for these codes has been greatly reduced with the implementation of the graphical interface of FLAIR to FLUKA. In conclusion, this made the effective shielding process for NSLS-II quite accurate and reliable. The principles
Kramer, S. L.; Ghosh, V. J.; Breitfeller, M.; ...
2016-08-10
We present that third generation high brightness light sources are designed to have low emittance and high current beams, which contribute to higher beam loss rates that will be compensated by Top-Off injection. Shielding for these higher loss rates will be critical to protect the projected higher occupancy factors for the users. Top-Off injection requires a full energy injector, which will demand greater consideration of the potential abnormal beam miss-steering and localized losses that could occur. The high energy electron injection beam produces significantly higher neutron component dose to the experimental floor than a lower energy beam injection and rampedmore » operations. Minimizing this dose will require adequate knowledge of where the miss-steered beam can occur and sufficient EM shielding close to the loss point, in order to attenuate the energy of the particles in the EM shower below the neutron production threshold (<10 MeV), which will spread the incident energy on the bulk shield walls and thereby the dose penetrating the shield walls. Designing supplemental shielding near the loss point using the analytic shielding model is shown to be inadequate because of its lack of geometry specification for the EM shower process. To predict the dose rates outside the tunnel requires detailed description of the geometry and materials that the beam losses will encounter inside the tunnel. Modern radiation shielding Monte-Carlo codes, like FLUKA, can handle this geometric description of the radiation transport process in sufficient detail, allowing accurate predictions of the dose rates expected and the ability to show weaknesses in the design before a high radiation incident occurs. The effort required to adequately define the accelerator geometry for these codes has been greatly reduced with the implementation of the graphical interface of FLAIR to FLUKA. In conclusion, this made the effective shielding process for NSLS-II quite accurate and reliable. The
Black holes in the Einstein-Gauss-Bonnet theory and the geometry of their thermodynamics—II
NASA Astrophysics Data System (ADS)
Biswas, Ritabrata; Chakraborty, Subenoy
2010-03-01
In the present work we study (i) the charged black hole in Einstein-Gauss-Bonnet (EGB) theory, known as the Einstein-Maxwell-Gauss-Bonnet (EMGB) black hole and (ii) the black hole in EGB gravity with a Yang-Mills field. The thermodynamic geometry of these two black hole solutions has been investigated, using the modified entropy in Gauss-Bonnet theory.
Barber, Jessica A; Palmese, Laura; Reutenauer, Erin L; Grilo, Carlos M; Tek, Cenk
2011-07-01
Obesity has been associated with significant stigma and weight-related self-bias in community and clinical studies, but these issues have not been studied among individuals with schizophrenia. A consecutive series of 70 obese individuals with schizophrenia or schizoaffective disorder underwent assessment for perceptions of weight-based stigmatization, self-directed weight bias, negative affect, medication compliance, and quality of life. The levels of weight-based stigmatization and self-bias were compared with levels reported for nonpsychiatric overweight/obese samples. Weight measures were unrelated to stigma, self-bias, affect, and quality of life. Weight-based stigmatization was lower than published levels for nonpsychiatric samples, whereas levels of weight-based self-bias did not differ. After controlling for negative affect, weight-based self-bias predicted an additional 11% of the variance in the quality of life measure. Individuals with schizophrenia and schizoaffective disorder reported weight-based self-bias to the same extent as nonpsychiatric samples despite reporting less weight stigma. Weight-based self-bias was associated with poorer quality of life after controlling for negative affect.
Barber, Jessica; Palmese, Laura; Reutenauer, Erin L.; Grilo, Carlos; Tek, Cenk
2011-01-01
Obesity has been associated with significant stigma and weight-related self-bias in community and clinical studies, but these issues have not been studied among individuals with schizophrenia. A consecutive series of 70 obese individuals with schizophrenia or schizoaffective disorder underwent assessment for perceptions of weight-based stigmatization, self-directed weight-bias, negative affect, medication compliance, and quality of life. Levels of weight-based stigmatization and self-bias were compared to levels reported for non-psychiatric overweight/obese samples. Weight measures were unrelated to stigma, self-bias, affect, and quality of life. Weight-based stigmatization was lower than published levels for non-psychiatric samples, whereas levels of weight-based self-bias did not differ. After controlling for negative affect, weight-based self-bias predicted an additional 11% of the variance in the quality of life measure. Individuals with schizophrenia and schizoaffective disorder reported weight-based self-bias to the same extent as non-psychiatric samples despite reporting less weight stigma. Weight-based self-bias was associated with poorer quality of life after controlling for negative affect. PMID:21716053
Geometry with Coordinates, Student's Text, Part II, Unit 48. Revised Edition.
ERIC Educational Resources Information Center
Allen, Frank B.; And Others
This is part two of a two-part SMSG geometry text for high school students. One of the goals of the text is the development of analytic geometry hand-in-hand with synthetic geometry. The authors emphasize that both are deductive systems and that it is useful to have more than one mode of attack in solving problems. The text begins the development…
Ni, Chengbao; Fettinger, James C; Long, Gary J; Power, Philip P
2010-11-28
Reaction of {Li(THF)Ar'MnI(2)}(2) (Ar' = C(6)H(3)-2,6-(C(6)H(2)-2,6-(i)Pr(3))(2)) with LiAr', LiC≡CR (R = (t)Bu or Ph), or (C(6)H(2)-2,4,6-(i)Pr(3))MgBr(THF)(2) afforded the diaryl MnAr'(2) (1), the alkynyl salts Ar'Mn(C≡C(t)Bu)(4){Li(THF)}(3) (2) and Ar'Mn(C≡CPh)(3)Li(3)(THF)(Et(2)O)(2)(μ(3)-I) (3), and the manganate salt {Li(THF)}Ar'Mn(μ-I)(C(6)H(2)-2,4,6-(i)Pr(3)) (4), respectively. Complex 4 reacted with one equivalent of (C(6)H(2)-2,4,6-(i)Pr(3))MgBr(THF)(2) to afford the homoleptic dimer {Mn(C(6)H(2)-2,4,6-(i)Pr(3))(μ-C(6)H(2)-2,4,6-(i)Pr(3))}(2) (5), which resulted from the displacement of the bulkier Ar' ligand in preference to the halogen. The reaction of the more crowded {Li(THF)Ar*MnI(2)}(2) (Ar* = C(6)H(3)-2,6-(C(6)H(2)-2,4,6-(i)Pr(3))(2)) with Li(t)Bu gave complex Ar*Mn(t)Bu (6). Complex 1 is a rare monomeric homoleptic two-coordinate diaryl Mn(II) complex; while 6 displays no tendency to eliminate β-hydrogens from the (t)Bu group because of the stabilization supplied by Ar*. Compounds 2 and 3 have cubane frameworks, which are constructed from a manganese, three carbons from three acetylide ligands, three lithiums, each coordinated by a donor, plus either a carbon from a further acetylide ligand (2) or an iodide (3). The Mn(II) atom in 4 has an unusual distorted T-shaped geometry while the dimeric 5 features trigonal planar manganese coordination. The chloride substituted complex Li(2)(THF)(3){Ar'MnCl(2)}(2) (7), which has a structure very similar to that of {Li(THF)Ar'MnI(2)}(2), was also prepared for use as a possible starting material. However, its generally lower solubility rendered it less useful than the iodo salt. Complexes 1-7 were characterized by X-ray crystallography and UV-vis spectroscopy. Magnetic studies of 2-4 and 6 showed that they have 3d(5) high-spin configurations.
Peng, Yan; Mereacre, Valeriu; Anson, Christopher E; Zhang, Yiquan; Bodenstein, Tilmann; Fink, Karin; Powell, Annie K
2017-06-05
Three air-stable Co(II) mononuclear complexes with different aromatic substituents have been prepared and structurally characterized by single-crystal X-ray diffraction. The mononuclear complexes [Co(H2L1)2]·2THF (1), [Co(HL2)2] (2), and [Co(H2L3)2]·CH2Cl2 (3) (where H3L1, H2L2, and H3L3 represent 3-hydroxy-naphthalene-2-carboxylic acid (6-hydroxymethyl-pyridin-2-ylmethylene) hydrazide, nicotinic acid (6-hydroxymethyl-pyridin-2-ylmethylene) hydrazide, and 2-hydroxy-benzoic acid (6-hydroxymethyl-pyridin-2-ylmethylene) hydrazide, respectively) feature a distorted mer octahedral coordination geometry. Detailed magnetic studies of 1-3 have been conducted using direct and alternating current magnetic susceptibility data. Field-induced slow magnetic relaxation was observed for these three complexes. There are few examples of such behavior in (distorted) octahedral coordination geometry (OC) Co(II) mononuclear complexes with uniaxial anisotropy. Analysis of the six-coordinate Co(II) mononuclear single-ion magnets (SIMs) in the literature using the SHAPE program revealed that they all show what is best described as distorted trigonal prismatic (TRP) coordination geometry, and in general, these show negative D zero-field splitting (ZFS) values. On the other hand, all the Co(II) mononuclear complexes displaying what is best approximated as distorted octahedral (OC) coordination geometry show positive D values. In the new Co(II) mononuclear complexes we describe here, there is an ambiguity, since the rigid tridentate ligands confer what is best described for an octahedral complex as a mer coordination geometry, but the actual shape of the first coordination sphere is between octahedral and trigonal prismatic. The negative D values observed experimentally and supported by high-level electronic structure calculations are thus in line with a trigonal prismatic geometry. However, a consideration of the rhombicity as indicated by the E value of the ZFS in conjunction with the
Designing a Self-Biased CPW Circulator Based on Strontium Hexaferrite Thick Film
NASA Astrophysics Data System (ADS)
Kiani, E.; poorbafrani, A.
2017-08-01
A 400 μm strontium hexaferrite thick film was prepared through a two-step sintering method; with the grain size diameter of the film about 0.7 μm, the relative density about ρ_{{relative}} = 0.9 , and the remanent magnetization ( M r ) 3940 G. Based on this thick film, a self-biased coplanar waveguide circulator was proposed. The calculated S-parameters indicate that by proper optimization of the structure, an isolation of 19 dB and insertion loss of 1.53 dB is attained. The effects of film porosity and thickness on the insertion losses are discussed.
Ion acceleration in a helicon source due to the self-bias effect
Wiebold, Matt; Sung, Yung-Ta; Scharer, John E.
2012-05-15
Time-averaged plasma potential differences up to 165 V over several hundred Debye lengths are observed in low pressure (p{sub n} < 1 mTorr) expanding argon plasmas in the Madison Helicon eXperiment (MadHeX). The potential gradient leads to ion acceleration greater than that predicted by ambipolar expansion, exceeding E{sub i} Almost-Equal-To 7 kT{sub e} in some cases. RF power up to 500 W at 13.56 MHz is supplied to a half-turn, double-helix antenna in the presence of a nozzle magnetic field, adjustable up to 1 kG. A retarding potential analyzer (RPA) measures the ion energy distribution function (IEDF) and a swept emissive probe measures the plasma potential. Single and double probes measure the electron density and temperature. Two distinct mode hops, the capacitive-inductive (E-H) and inductive-helicon (H-W) transitions, are identified by jumps in density as RF power is increased. In the capacitive (E) mode, large fluctuations of the plasma potential (V{sub p-p} Greater-Than-Or-Equivalent-To 140V, V{sub p-p}/V{sub p} Almost-Equal-To 150%) exist at the RF frequency and its harmonics. The more mobile electrons can easily respond to RF-timescale gradients in the plasma potential whereas the inertially constrained ions cannot, leading to an initial flux imbalance and formation of a self-bias voltage between the source and expansion chambers. In the capacitive mode, the ion acceleration is not well described by an ambipolar relation, while in the inductive and helicon modes the ion acceleration more closely follows an ambipolar relation. The scaling of the potential gradient with the argon flow rate and RF power are investigated, with the largest potential gradients observed for the lowest flow rates in the capacitive mode. The magnitude of the self-bias voltage agrees with that predicted for RF self-bias at a wall. Rapid fluctuations in the plasma potential result in a time-dependent axial electron flux that acts to 'neutralize' the accelerated ion population
ERIC Educational Resources Information Center
Curtis, Charles W.; And Others
These materials were developed to help high school teachers to become familiar with the approach to tenth-grade Euclidean geometry which was adopted by the School Mathematics Study Group (SMSG). It is emphasized that the materials are unsuitable as a high school textbook. Each document contains material too difficult for most high school students.…
Waychunas, G.A.; Fuller, C.C.; Davis, J.A.; Rehr, J.J.
2003-01-01
X-ray absorption near-edge spectroscopy (XANES) analysis of sorption complexes has the advantages of high sensitivity (10- to 20-fold greater than extended X-ray absorption fine structure [EXAFS] analysis) and relative ease and speed of data collection (because of the short k-space range). It is thus a potentially powerful tool for characterization of environmentally significant surface complexes and precipitates at very low surface coverages. However, quantitative analysis has been limited largely to "fingerprint" comparison with model spectra because of the difficulty of obtaining accurate multiple-scattering amplitudes for small clusters with high confidence. In the present work, calculations of the XANES for 50- to 200-atom clusters of structure from Zn model compounds using the full multiple-scattering code Feff 8.0 accurately replicate experimental spectra and display features characteristic of specific first-neighbor anion coordination geometry and second-neighbor cation geometry and number. Analogous calculations of the XANES for small molecular clusters indicative of precipitation and sorption geometries for aqueous Zn on ferrihydrite, and suggested by EXAFS analysis, are in good agreement with observed spectral trends with sample composition, with Zn-oxygen coordination and with changes in second-neighbor cation coordination as a function of sorption coverage. Empirical analysis of experimental XANES features further verifies the validity of the calculations. The findings agree well with a complete EXAFS analysis previously reported for the same sample set, namely, that octahedrally coordinated aqueous Zn2+ species sorb as a tetrahedral complex on ferrihydrite with varying local geometry depending on sorption density. At significantly higher densities but below those at which Zn hydroxide is expected to precipitate, a mainly octahedral coordinated Zn2+ precipitate is observed. An analysis of the multiple scattering paths contributing to the XANES
Dahake, G; Gracewski, S M
1997-10-01
To understand better direct stress wave contributions to stone fragmentation during extracorporeal shock wave lithotripsy (ESWL), the numerical formulation developed in part I is applied to study the time evolution of stress wave fields produced inside submerged isotropic elastic solids having irregular geometries. Cut spheres are used to model stones that have already had an initial fracture. Ellipses are used to approximate other deviations from a spherical geometry. The propagation and focusing of the longitudinal (P) and shear (S) wave fronts are visualized by presenting internal strain contours. Internal strain measurements are obtained from strain gauges embedded inside plaster specimens to confirm the focusing effect obtained from the concave back surfaces of the stones. Fragmentation experiments indicate damage caused by spalling and direct stress wave focusing as well as a front surface pit presumably created by cavitation activity.
The Influence of Environment Geometry on Injury Outcome: II. Lumbosacral Spine
NASA Astrophysics Data System (ADS)
Shaibani, Saami J.
2006-03-01
It is widely agreed that the type of motor vehicle in which an occupant is situated can sometimes make a noticeable difference in injury potential even when the insult suffered is the same. A simple example might be the same occupant being in a sports car as opposed to a minivan, but such anecdotal experience does not usually help to distinguish the effect of particular features within the same category of vehicle. Other research has addressed the role of environment geometry in neck injury,[1] and this paper adopts the same methodology for the low back. The heights, lengths and angles of the seat cushion and seat back (including head rest) are all examined as descriptors of passenger compartment geometry, and any changes caused by these are determined. Useful results are feasible with the large patient population available even if clear patterns in these are not always present. As in earlier work, there is still the option of finding individual outcomes on a case-by-case basis. [1] The influence of environment geometry on injury outcome: I. Cervical spine, Bull Am Phys Soc, in press (2006).
Multisource inverse-geometry CT. Part II. X-ray source design and prototype
Neculaes, V. Bogdan; Caiafa, Antonio; Cao, Yang; De Man, Bruno; Edic, Peter M.; Frutschy, Kristopher; Gunturi, Satish; Inzinna, Lou; Reynolds, Joseph; Vermilyea, Mark; Wagner, David; Zhang, Xi; Zou, Yun; Pelc, Norbert J.; Lounsberry, Brian
2016-01-01
Purpose: This paper summarizes the development of a high-power distributed x-ray source, or “multisource,” designed for inverse-geometry computed tomography (CT) applications [see B. De Man et al., “Multisource inverse-geometry CT. Part I. System concept and development,” Med. Phys. 43, 4607–4616 (2016)]. The paper presents the evolution of the source architecture, component design (anode, emitter, beam optics, control electronics, high voltage insulator), and experimental validation. Methods: Dispenser cathode emitters were chosen as electron sources. A modular design was adopted, with eight electron emitters (two rows of four emitters) per module, wherein tungsten targets were brazed onto copper anode blocks—one anode block per module. A specialized ceramic connector provided high voltage standoff capability and cooling oil flow to the anode. A matrix topology and low-noise electronic controls provided switching of the emitters. Results: Four modules (32 x-ray sources in two rows of 16) have been successfully integrated into a single vacuum vessel and operated on an inverse-geometry computed tomography system. Dispenser cathodes provided high beam current (>1000 mA) in pulse mode, and the electrostatic lenses focused the current beam to a small optical focal spot size (0.5 × 1.4 mm). Controlled emitter grid voltage allowed the beam current to be varied for each source, providing the ability to modulate beam current across the fan of the x-ray beam, denoted as a virtual bowtie filter. The custom designed controls achieved x-ray source switching in <1 μs. The cathode-grounded source was operated successfully up to 120 kV. Conclusions: A high-power, distributed x-ray source for inverse-geometry CT applications was successfully designed, fabricated, and operated. Future embodiments may increase the number of spots and utilize fast read out detectors to increase the x-ray flux magnitude further, while still staying within the stationary target inherent
Junctionless Diode Enabled by Self-Bias Effect of Ion Gel in Single-Layer MoS2 Device.
Khan, Muhammad Atif; Rathi, Servin; Park, Jinwoo; Lim, Dongsuk; Lee, Yoontae; Yun, Sun Jin; Youn, Doo-Hyeb; Kim, Gil-Ho
2017-08-16
The self-biasing effects of ion gel from source and drain electrodes on electrical characteristics of single layer and few layer molybdenum disulfide (MoS2) field-effect transistor (FET) have been studied. The self-biasing effect of ion gel is tested for two different configurations, covered and open, where ion gel is in contact with either one or both, source and drain electrodes, respectively. In open configuration, the linear output characteristics of the pristine device becomes nonlinear and on-off ratio drops by 3 orders of magnitude due to the increase in "off" current for both single and few layer MoS2 FETs. However, the covered configuration results in a highly asymmetric output characteristics with a rectification of around 10(3) and an ideality factor of 1.9. This diode like behavior has been attributed to the reduction of Schottky barrier width by the electric field of self-biased ion gel, which enables an efficient injection of electrons by tunneling at metal-MoS2 interface. Finally, finite element method based simulations are carried out and the simulated results matches well in principle with the experimental analysis. These self-biased diodes can perform a crucial role in the development of high-frequency optoelectronic and valleytronic devices.
Geometry of river networks. II. Distributions of component size and number
Dodds, Peter Sheridan; Rothman, Daniel H.
2001-01-01
The structure of a river network may be seen as a discrete set of nested subnetworks built out of individual stream segments. These network components are assigned an integral stream order via a hierarchical and discrete ordering method. Exponential relationships, known as Horton's laws, between stream order and ensemble-averaged quantities pertaining to network components are observed. We extend these observations to incorporate fluctuations and all higher moments by developing functional relationships between distributions. The relationships determined are drawn from a combination of theoretical analysis, analysis of real river networks including the Mississippi, Amazon, and Nile, and numerical simulations on a model of directed, random networks. Underlying distributions of stream segment lengths are identified as exponential. Combinations of these distributions form single-humped distributions with exponential tails, the sums of which are in turn shown to give power-law distributions of stream lengths. Distributions of basin area and stream segment frequency are also addressed. The calculations identify a single length scale as a measure of size fluctuations in network components. This article is the second in a series of three addressing the geometry of river networks.
Geometry of deformed black holes. II. Schwarzschild hole surrounded by a Bach-Weyl ring
NASA Astrophysics Data System (ADS)
Basovník, M.; Semerák, O.
2016-08-01
We continue to study the response of black-hole space-times on the presence of additional strong sources of gravity. Restricting ourselves to static and axially symmetric (electro)vacuum exact solutions of Einstein's equations, we first considered the Majumdar-Papapetrou solution for a binary of extreme black holes in a previous paper, while here we deal with a Schwarzschild black hole surrounded by a concentric thin ring described by the Bach-Weyl solution. The geometry is again revealed on the simplest invariants determined by the metric (lapse function) and its gradient (gravitational acceleration), and by curvature (Kretschmann scalar). Extending the metric inside the black hole along null geodesics tangent to the horizon, we mainly focus on the black-hole interior (specifically, on its sections at constant Killing time) where the quantities behave in a way indicating a surprisingly strong influence of the external source. Being already distinct on the level of potential and acceleration, this is still more pronounced on the level of curvature: for a sufficiently massive and/or nearby (small) ring, the Kretschmann scalar even becomes negative in certain toroidal regions mostly touching the horizon from inside. Such regions have been interpreted as those where magnetic-type curvature dominates, but here we deal with space-times which do not involve rotation and the negative value is achieved due to the electric-type components of the Riemann/Weyl tensor. The Kretschmann scalar also shapes rather nontrivial landscapes outside the horizon.
Twisted versus braided magnetic flux ropes in coronal geometry. II. Comparative behaviour
NASA Astrophysics Data System (ADS)
Prior, C.; Yeates, A. R.
2016-06-01
Aims: Sigmoidal structures in the solar corona are commonly associated with magnetic flux ropes whose magnetic field lines are twisted about a mutual axis. Their dynamical evolution is well studied, with sufficient twisting leading to large-scale rotation (writhing) and vertical expansion, possibly leading to ejection. Here, we investigate the behaviour of flux ropes whose field lines have more complex entangled/braided configurations. Our hypothesis is that this internal structure will inhibit the large-scale morphological changes. Additionally, we investigate the influence of the background field within which the rope is embedded. Methods: A technique for generating tubular magnetic fields with arbitrary axial geometry and internal structure, introduced in part I of this study, provides the initial conditions for resistive-MHD simulations. The tubular fields are embedded in a linear force-free background, and we consider various internal structures for the tubular field, including both twisted and braided topologies. These embedded flux ropes are then evolved using a 3D MHD code. Results: Firstly, in a background where twisted flux ropes evolve through the expected non-linear writhing and vertical expansion, we find that flux ropes with sufficiently braided/entangled interiors show no such large-scale changes. Secondly, embedding a twisted flux rope in a background field with a sigmoidal inversion line leads to eventual reversal of the large-scale rotation. Thirdly, in some cases a braided flux rope splits due to reconnection into two twisted flux ropes of opposing chirality - a phenomenon previously observed in cylindrical configurations. Conclusions: Sufficiently complex entanglement of the magnetic field lines within a flux rope can suppress large-scale morphological changes of its axis, with magnetic energy reduced instead through reconnection and expansion. The structure of the background magnetic field can significantly affect the changing morphology of a
Bias and self-bias of magnetic macroparticle filters for cathodic arc plasmas
Byon, Eungsun; Anders, Andre
2002-12-01
Curved magnetic filters are often used for the removal of macroparticles from cathodic arc plasmas. This study addresses the need to further reduce losses and improving plasma throughput. The central figure of merit is the system coefficient Kappa defined as filtered ion current normalized by the plasma-producing arc current. The coefficient Kappa is investigated as a function of DC and pulsed magnetic field operation, magnetic field strength, external electric bias, and arc amplitude. It increases with positive filter bias but saturates at about 15 V for relatively low magnetic field ({approx}10 mT), whereas stronger magnetic fields lead to higher Kappa with saturation at about 25 V. Further increase of positive bias reduces Kappa. These findings are true for both pulsed and DC filters. Bias of pulsed filters has been realized using the voltage drop across a self-bias resistor, eliminating the need for a separate bias circuit. Almost 100 A of filtered copper ions have been obtained in pulse d mode, corresponding to Kappa approximately equal to 0.04. The results are interpreted by a simplified potential trough model.
Application of Molded Interconnect Device technology to the realization of a self-biased circulator
NASA Astrophysics Data System (ADS)
Laur, Vincent; Mattei, Jean-Luc; Vérissimo, Grégory; Queffelec, Patrick; Lebourgeois, Richard; Ganne, Jean-Pierre
2016-04-01
This paper describes the first electromagnetic characterization of a self-biased circulator in molded interconnect device (MID) technology. The circulator was designed using a 3D full-wave commercial simulator. It consists of microstrip access lines connected to a Y-junction in Substrate Integrated Waveguide (SIW) technology. Unlike classical technologies, the SIW Y-junction was not fabricated using metallic vias but by a Laser Direct Structuring (LDS) technique. A molded Cyclo-Olefin Polymer (COP) was used as a substrate and 3D metallized. The microwave properties of LDS-compatible COP are not well known so we investigated them through the use of cavity-perturbation and rectangular waveguide characterization methods. The device was then machined to insert a pre-oriented strontium hexaferrite puck doped with cobalt and lanthanum (Sr0,7La0,3Fe11,7Co0,3O19). The characteristics of the MID circulator were assessed between 28 and 32 GHz. Without magnets, insertion losses of 3.32 dB were measured at 30.7 GHz. At the same frequency, an isolation level of 13.89 dB and return losses of 19.89 dB were observed. These measurements demonstrate for the first time the high potential of MID technology for the realization of low-cost non-reciprocal devices.
NASA Astrophysics Data System (ADS)
Ma, J. N.; Xin, C. Z.; Ma, J.; Lin, Y. H.; Nan, C. W.
2017-03-01
Magnetoelectric (ME) composites with self-biased and wide resonance frequency band properties are promising candidates for magnetic field sensor and energy harvester. Here, we present a ME cantilever by in-series connecting a few SrFe12O19/Metglas/Pb(Zr,Ti)O3 components. Due to the in-built magnetic bias of SrFe12O19, the ME cantilever shows self-biased property. Meanwhile, by merging the resonance responses of the in-series ME components together, the ME cantilever presents multi-wide resonance bands (i.e., 500 Hz ˜ 700 Hz, 3.3 kHz ˜ 4.4 kHz and 44 kHz ˜ 70 kHz). In these three wide frequency windows, the ME voltage coefficients (α V) of the ME cantilever are higher than 40 mV/Oe, 115 mV/Oe and 400 mV/Oe, respectively.
NASA Astrophysics Data System (ADS)
Li, Jie; Lu, Caijiang
2016-11-01
This paper develops a self-biased magnetoelectric (ME) heterostructure FeCuNbSiB/terfenol-d/ultrasonic-horn/PZT by sandwiching a piezoelectric Pb(Zr,Ti)O3 (PZT) plate and a magnetization-graded FeCuNbSiB/terfenol-d layer on a rectangular-stepped ultrasonic horn substrate. The rectangular-stepped ultrasonic horn substrate severs as the resonance frequency determining element of the ME heterostructure, converges and amplifies the vibration excited by the magnetization-graded FeCuNbSiB/terfenol-d layer. The experiments show that fifteen large peaks of ME response with magnitudes of 0.2-7.5 V/(cm·Oe) in 0.5-50 kHz range are observed at zero-biased magnetic field. This demonstrates that the proposed multi-peak self-biased heterostructure may be useful for multifunctional devices for multi-frequency operation.
Culture modulates implicit ownership-induced self-bias in memory.
Sparks, Samuel; Cunningham, Sheila J; Kritikos, Ada
2016-08-01
The relation of incoming stimuli to the self implicitly determines the allocation of cognitive resources. Cultural variations in the self-concept shape cognition, but the extent is unclear because the majority of studies sample only Western participants. We report cultural differences (Asian versus Western) in ownership-induced self-bias in recognition memory for objects. In two experiments, participants allocated a series of images depicting household objects to self-owned or other-owned virtual baskets based on colour cues before completing a surprise recognition memory test for the objects. The 'other' was either a stranger or a close other. In both experiments, Western participants showed greater recognition memory accuracy for self-owned compared with other-owned objects, consistent with an independent self-construal. In Experiment 1, which required minimal attention to the owned objects, Asian participants showed no such ownership-related bias in recognition accuracy. In Experiment 2, which required attention to owned objects to move them along the screen, Asian participants again showed no overall memory advantage for self-owned items and actually exhibited higher recognition accuracy for mother-owned than self-owned objects, reversing the pattern observed for Westerners. This is consistent with an interdependent self-construal which is sensitive to the particular relationship between the self and other. Overall, our results suggest that the self acts as an organising principle for allocating cognitive resources, but that the way it is constructed depends upon cultural experience. Additionally, the manifestation of these cultural differences in self-representation depends on the allocation of attentional resources to self- and other-associated stimuli. Crown Copyright © 2016. Published by Elsevier B.V. All rights reserved.
Chen, Quanpeng; Li, Jinhua; Li, Xuejin; Huang, Ke; Zhou, Baoxue; Shangguan, Wenfeng
2013-07-01
A self-biasing photoelectrochemical (PEC) cell that could work for spontaneous overall water splitting in a neutral solution was established based on the mismatched Fermi levels between the photoelectrodes. A Pt-catalyst-decorated crystalline silicon photovoltaic cell (Pt/PVC) was prepared and employed as an effective photocathode. This was coupled with a poly(ethylene glycol)-directed WO3/W photoanode prepared by a hydrothermal process. Both of the photoelectrodes showed a response to visible light. The WO3/W photoanode had a positively located valence band edge, the energy level of which was enough for water oxidation, and the Pt/PVC photocathode possessed a negatively located conduction band edge, which was capable of water reduction. More importantly, the Fermi level of the WO3/W photoanode was more positive than that of the Pt/PVC photocathode because of the p-n junction of the PVC that decoupled the band bending and enlarged the photovoltage. Under visible-light irradiation, the WO3/W photoanode provided a negative bias for the Pt/PVC photocathode, and the Pt/PVC photocathode provided a positive bias for the WO3/W photoanode. An interior bias was generated that could relax the strict criteria of overall water splitting by cooperatively separating the hole-electron pairs at both photoelectrodes. In this system, the short-circuit current and the open-circuit voltage increased with increasing light intensity (AM 1.5 illumination) to reach 121 μA cm(-2) and 0.541 V, respectively, at a light intensity of 100 mW cm(-2). Such a combination provides a promising method for the fabrication of self-driven devices for solar-energy storage. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
NASA Astrophysics Data System (ADS)
Huang, Dongyan; Lu, Caijiang; Bing, Han
2015-04-01
This letter develops a self-biased magnetoelectric (ME) structure Metglas/Terfenol-D/Be-bronze/PMN-PT (MTBP) consisting of a magnetization-graded Metglas/Terfenol-D layer, a elastic Be-bronze plate, and a piezoelectric 0.67Pb(Mg1/3Nb2/3)O3-0.33PbTiO3 (PMN-PT) plate. By using the magnetization-graded Metglas/Terfenol-D layer and the elastic Be-bronze plate, multi-peak self-biased ME responses are obtained in MTBP structure. The experimental results show that the MTBP structure with two layers of Metglas foil has maximum zero-biased ME voltage coefficient (MEVC). As frequency increases from 0.5 to 90 kHz, eleven large peaks of MEVC with magnitudes of 0.75-33 V/(cm Oe) are observed at zero-biased magnetic field. The results demonstrate that the proposed multi-peak self-biased ME structure may be useful for multifunctional devices such as multi-frequency energy harvesters or low-frequency ac magnetic field sensors.
NASA Astrophysics Data System (ADS)
Balokovic, Mislav; Harrison, Fiona; Brightman, Murray
2017-08-01
The obscuring torus is one of the main components of the basic unified model of active galactic nuclei (AGN), needed to create anisotropy in obscuration as a function of the viewing angle. We present the first study of the geometrical properties of the AGN torus in a large and representative sample of type II Seyfert nuclei. The sample consists of 124 AGN selected in the hard X-ray band from the Swift/BAT 70-month catalog and observed simultaneously with NuSTAR and Swift/XRT. These data enable us to explore the constraints that observed spectra place on the properties of the obscuring torus in individual AGN and in the local population of Seyfert II nuclei. We make use of empirically motivated spectral models for X-ray reprocessing in approximately toroidal geometry for constraining the distribution of the average column density of the torus, and the distribution of the torus covering factor within this sample. We find that the torus-averaged column density is independent of the line-of-sight column density, with typical column density that is borderline Compton-thick, i.e., around the unity optical depth for Compton scattering. The distribution of torus covering factors is broad but shows a preference for high covering, peaking around the covering factor of 90%, with the median at 70%, in agreement with recent sample studies in the infrared band. We also examine the dependence of the covering factor on intrinsic luminosity, finding that the median covering factor peaks around the intrinsic X-ray luminosity of 10^42.5 erg/s and decreases toward both lower and higher luminosities.
EXTINCTION AND DUST GEOMETRY IN M83 H II REGIONS: AN HUBBLE SPACE TELESCOPE/WFC3 STUDY
Liu, Guilin; Calzetti, Daniela; Hong, Sungryong; Whitmore, Bradley; Chandar, Rupali; O'Connell, Robert W.; Blair, William P.; Cohen, Seth H.; Kim, Hwihyun; Frogel, Jay A.
2013-12-01
We present Hubble Space Telescope/WFC3 narrow-band imaging of the starburst galaxy M83 targeting the hydrogen recombination lines (Hβ, Hα, and Paβ), which we use to investigate the dust extinction in the H II regions. We derive extinction maps with 6 pc spatial resolution from two combinations of hydrogen lines (Hα/Hβ and Hα/Paβ), and show that the longer wavelengths probe larger optical depths, with A{sub V} values larger by ≳1 mag than those derived from the shorter wavelengths. This difference leads to a factor ≳2 discrepancy in the extinction-corrected Hα luminosity, a significant effect when studying extragalactic H II regions. By comparing these observations to a series of simple models, we conclude that a large diversity of absorber/emitter geometric configurations can account for the data, implying a more complex physical structure than the classical foreground ''dust screen'' assumption. However, most data points are bracketed by the foreground screen and a model where dust and emitters are uniformly mixed. When averaged over large (≳100-200 pc) scales, the extinction becomes consistent with a ''dust screen'', suggesting that other geometries tend to be restricted to more local scales. Moreover, the extinction in any region can be described by a combination of the foreground screen and the uniform mixture model with weights of 1/3 and 2/3 in the center (≲2 kpc), respectively, and 2/3 and 1/3 for the rest of the disk. This simple prescription significantly improves the accuracy of the dust extinction corrections and can be especially useful for pixel-based analyses of galaxies similar to M83.
NASA Astrophysics Data System (ADS)
Wiebold, Matthew D.
Time-averaged plasma potential differences up to ˜ 165 V over several hundred Debye lengths are observed in low pressure (pn < 1 mTorr) expanding argon plasmas in the Madison Helicon Experiment. The potential gradient leads to ion acceleration exceeding Ei ≈ 7 kTe in some cases. Up to 1 kW of 13.56 MHz RF power is supplied to a half-turn, double-helix antenna in the presence of a nozzle magnetic field up to 1 kG. An RPA measures the IEDF and an emissive probe measures the plasma potential. Single and double probes measure the electron density and temperature. Two distinct mode hops, the capacitive-inductive (E-H) and inductive-helicon (H-W) transitions, are identified by jumps in electron density as RF power is increased. In the capacitive mode, large fluctuations of the plasma potential (Vp--p ≳ 140 V, Vp--p/Vp ≈ 150%) exist at the RF frequency, leading to formation of a self-bias voltage. The mobile electrons can flow from the upstream region during an RF cycle whereas ions cannot, leading to an initial imbalance of flux, and the self-bias voltage builds as a result. The plasma potential in the expansion chamber is held near the floating potential for argon (Vp ≈ 5kTe/e). In the capacitive mode, the ion acceleration is not well described by an ambipolar relation. The accelerated population decay is consistent with that predicted by charge-exchange collisions. Grounding the upstream endplate increases the self-bias voltage compared to a floating endplate. In the inductive and helicon modes, the ion acceleration more closely follows an ambipolar relation, a result of decreased capacitive coupling due to the decreased RF skin depth. The scaling of the potential gradient with the argon flow rate, magnetic field and RF power are investigated, with the highest potential gradients observed for the lowest flow rates in the capacitive mode. The magnitude of the self-bias voltage agrees well with that predicted for RF sheaths. Use of the self-bias effect in a
The interaction between self-bias and reward: Evidence for common and distinct processes.
Sui, Jie; Humphreys, Glyn W
2015-01-01
The perceptual matching of shapes and labels can be affected by both self- and reward-biases when shapes are linked either to labels referring to particular individuals (you, friend, stranger) or to different reward values (£8, £2, £0). We investigated the relations between these biases by varying the reward value associated with particular shape-label pairs (circle-you, square-friend, triangle-stranger). Self shape-label pairs (circle-you) always received no reward, while friend shape-label pairs (square-friend) received high reward and stranger shape-label pairs low reward (triangle-stranger), or the reverse (friend-low reward; stranger-high reward). Despite receiving no reward, responses to self-related pairs were advantaged relative to those to low-reward stimuli and did not differ from those to high-reward items. There was also an advantage for responses to high-reward friend pairs relative to low-reward stranger stimuli, and for high-reward stranger stimuli compared to low-reward friends. Correlations across individuals were found across trial blocks for both the self-advantage and the high-reward advantage, but the self- and reward-advantages were uncorrelated. This suggests that the self- and reward-advantage effects have different origins. In addition, the magnitude of the self-advantage varied according to the rated personal distance between a participant and a stranger. For individuals manifesting a close personal distance to strangers, the self-advantage was smaller, and sensitivity to reward influenced the difference between the self- and high-reward conditions. For individuals manifesting a large personal distance to strangers, sensitivity to reward did not affect self-matching. We suggest that self-advantages on perceptual matching arise independent of reward for individuals with a large personal distance to strangers. On the other hand, in individuals with a weak self-bias, high reward and the self modulate a common subjective value system.
Solar proton exposure of an ICRU sphere within a complex structure part II: Ray-trace geometry
NASA Astrophysics Data System (ADS)
Slaba, Tony C.; Wilson, John W.; Badavi, Francis F.; Reddell, Brandon D.; Bahadori, Amir A.
2016-06-01
A computationally efficient 3DHZETRN code with enhanced neutron and light ion (Z ≤ 2) propagation was recently developed for complex, inhomogeneous shield geometry described by combinatorial objects. Comparisons were made between 3DHZETRN results and Monte Carlo (MC) simulations at locations within the combinatorial geometry, and it was shown that 3DHZETRN agrees with the MC codes to the extent they agree with each other. In the present report, the 3DHZETRN code is extended to enable analysis in ray-trace geometry. This latest extension enables the code to be used within current engineering design practices utilizing fully detailed vehicle and habitat geometries. Through convergence testing, it is shown that fidelity in an actual shield geometry can be maintained in the discrete ray-trace description by systematically increasing the number of discrete rays used. It is also shown that this fidelity is carried into transport procedures and resulting exposure quantities without sacrificing computational efficiency.
Chatterjee, Ruchira; Milikisiyants, Sergey; Lakshmi, K V
2012-05-21
We use two-dimensional hyperfine sublevel correlation (HYSCORE) spectroscopy to investigate the coordination geometry of the nitrogen ligands of biomimetic models of the oxygen-evolving complex of photosystem II. In the 2D HYSCORE spectroscopy study, [(bpy)2Mn(III)(μ-O)2Mn(IV)(bpy)2](ClO4)3 (bpy, 2,2'-bipyridine) (1) and [H2O(terpy)Mn(III)(μ-O)2Mn(IV)(terpy)OH2](NO3)3 (terpy = 2,2':6',2″-terpyridine) (2) exhibit electron-nuclear hyperfine interactions that depend on both the oxidation state of the manganese ion and the geometry of the nitrogen ligand. We observe four types of (14)N hyperfine interactions corresponding to the Mn(iii) and Mn(iv) ion of each mixed-valence complex and the equatorial and axial geometry of the ligand, respectively. The strongest and the weakest hyperfine interactions arise from the axial and equatorial ligands of the Mn(iii) ion, respectively. The hyperfine interactions of intermediate strength are due to the axial and equatorial ligands of the Mn(iv) ion. Based on the results of this study, we assign the location and ligand geometry of the Mn(iii) ion of the tetranuclear manganese-calcium-oxo cluster in the S2 state of photosystem II.
2016-01-01
2-Alkenylphenols react with allenes, upon treatment with catalytic amounts of Pd(II) and Cu(II), to give benzoxepine products in high yields and with very good regio- and diastereoselectivities. This contrasts with the results obtained with Rh catalysts, which provided chromene-like products through a pathway involving a β-hydrogen elimination step. Computational studies suggest that the square planar geometry of the palladium is critical to favor the reductive elimination process required for the formation of the oxepine products. PMID:27807509
Kramer, S. L.; Ghosh, V. J.; Breitfeller, M.; Wahl, W.
2016-08-10
Third generation high brightness light sources are designed to have low emittance and high current beams, which contribute to higher beam loss rates that will be compensated by Top-Off injection. Shielding for these higher loss rates will be critical to protect the projected higher occupancy factors for the users. Top-Off injection requires a full energy injector, which will demand greater consideration of the potential abnormal beam miss-steering and localized losses that could occur. The high energy electron injection beam produces significantly higher neutron component dose to the experimental floor than a lower energy beam injection and ramped operations. Minimizing this dose will require adequate knowledge of where the miss-steered beam can occur and sufficient EM shielding close to the loss point, in order to attenuate the energy of the particles in the EM shower below the neutron production threshold (<10 MeV), which will spread the incident energy on the bulk shield walls and thereby the dose penetrating the shield walls. Designing supplemental shielding near the loss point using the analytic shielding model is shown to be inadequate because of its lack of geometry specification for the EM shower process. To predict the dose rates outside the tunnel requires detailed description of the geometry and materials that the beam losses will encounter inside the tunnel. Modern radiation shielding Monte-Carlo codes, like FLUKA, can handle this geometric description of the radiation transport process in sufficient detail, allowing accurate predictions of the dose rates expected and the ability to show weaknesses in the design before a high radiation incident occurs. The effort required to adequately define the accelerator geometry for these codes has been greatly reduced with the implementation of the graphical interface of FLAIR to FLUKA. This made the effective shielding process for NSLS-II quite accurate and reliable. Lastly, the principles used to provide
NASA Astrophysics Data System (ADS)
Gao, Zhongmei; Shao, Xinyu; Jiang, Ping; Wang, Chunming; Zhou, Qi; Cao, Longchao; Wang, Yilin
2016-06-01
An integrated multi-objective optimization approach combining Kriging model and non-dominated sorting genetic algorithm-II (NSGA-II) is proposed to predict and optimize weld geometry in hybrid fiber laser-arc welding on 316L stainless steel in this paper. A four-factor, five-level experiment using Taguchi L25 orthogonal array is conducted considering laser power ( P), welding current ( I), distance between laser and arc ( D) and traveling speed ( V). Kriging models are adopted to approximate the relationship between process parameters and weld geometry, namely depth of penetration (DP), bead width (BW) and bead reinforcement (BR). NSGA-II is used for multi-objective optimization taking the constructed Kriging models as objective functions and generates a set of optimal solutions with pareto-optimal front for outputs. Meanwhile, the main effects and the first-order interactions between process parameters are analyzed. Microstructure is also discussed. Verification experiments demonstrate that the optimum values obtained by the proposed integrated Kriging model and NSGA-II approach are in good agreement with experimental results.
NASA Astrophysics Data System (ADS)
Golbedaghi, Reza; Azimi, Saeid; Molaei, Atefeh; Hatami, Masoud; Notash, Behrouz
2017-10-01
A new Schiff base ligand HL, 1,3-bis(2-((Z)-(2-aminoethylimino)methyl)phenoxy)ethylene di amine, has been synthesized from the reaction of a new aldehyde and ethylenediamine. After preparation the Schiff base, a new dinuclear Cu(II) complex with two different geometry for each metal ion was synthesized. Single crystal X-ray structure analysis of the complex Cu(II) showed that the complex is binuclear and all nitrogen and oxygen atoms of ligand (N4O3) are coordinated to two Cu(II) center ions. The crystal structure studying shows, a perchlorate ion has been coordinated to the two Cu(II) metal centers as bridged and another perchlorate coordinated to the one of Cu(II) ion as terminal. However, two interesting structures square pyramidal and distorted octahedral Cu(II) ions are bridged asymmetrically by a perchlorate ion and oxygen of hydroxyl group of Schiff base ligand. In addition, we had a theoretical study to have a comparison of experimental and theoretical results we determined the HOMO and LUMO orbitals.
Generation of pure spin currents via spin Seebeck effect in self-biased hexagonal ferrite thin films
Li, Peng; Ellsworth, David; Chang, Houchen; Janantha, Praveen; Richardson, Daniel; Phillips, Preston; Vijayasarathy, Tarah; Wu, Mingzhong; Shah, Faisal
2014-12-15
Light-induced generation of pure spin currents in a Pt(2.5 nm)/BaFe{sub 12}O{sub 19}(1.2 μm)/sapphire(0.5 mm) structure is reported. The BaFe{sub 12}O{sub 19} film had strong in-plane uniaxial anisotropy and was therefore self-biased. Upon exposure to light, a temperature difference (ΔT) was established across the BaFe{sub 12}O{sub 19} thickness that gave rise to a pure spin current in the Pt via the spin Seebeck effect. Via the inverse spin Hall effect, the spin current produced an electric voltage across one of the Pt lateral dimensions. The voltage varied with time in the same manner as ΔT and flipped its sign when the magnetization in BaFe{sub 12}O{sub 19} was reversed.
NASA Astrophysics Data System (ADS)
Zhang, Jitao; Li, Ping; Wen, Yumei; He, Wei; Yang, Aichao; Lu, Caijiang
2014-09-01
A packaged current sensor consisting of a SmFe2/PZT/SmFe2 self-biased magnetoelectric (ME) laminate and a Fe73.5Cu1Nb3Si13.5B9 nanocrystalline flux concentrator for weak-current detection at the power-line frequency is fabricated and characterized. The giant magnetostrictive material of the SmFe2 plate with its large anisotropic constant provides a huge internal anisotropic field to bias the ME transducer in a closed magnetic loop. Consequently, the additional magnetomotive force induced by the internal field and the corresponding increased effective permeability contribute to an improvement in sensitivity. Experimental results demonstrate that the presented sensor has a higher sensitivity of 152 mV A-1 at 50 Hz with a slight nonlinearity of ˜0.01% FS and matches well with the predicted value. This current-sensing device exhibits approximately 2.3 times higher sensitivity than does conventional ME composite with PZT and Terfenol-D plates serving as the key sensitive component. In addition, the packaged sensor is evaluated for a long period of 72 h to determine stability over time, and the results are analyzed by means of a mathematical statistics method; favorable stability with an uncertainty of 0.5 μV is obtained in continuous 1 h testing. These results represent a significant advancement in the development of promising applications of tri-layer self-biased ME laminate for monitoring power-line electric cords.
NASA Astrophysics Data System (ADS)
Zhang, Xiaozhi; Meng, Siqin; Song, Dongsheng; Zhang, Yao; Yue, Zhenxing; Harris, Vincent G.
2017-03-01
Barium hexaferrite (BaM) films with in-plane c-axis orientation are promising and technically important materials for self-biased magnetic microwave devices. In this work, highly oriented BaM films with different thickness and an in-plane easy axis (c-axis) of magnetization were grown on a-plane single-crystal sapphire substrates by direct current magnetron sputtering. A procedure involving seed layers, layer-by-layer annealing was adopted to reduce the substrate-induced strains and allow for the growth of thick (~3.44 μm) films. The epitaxial growth of the BaM film on sapphire was revealed by high-resolution transmission electron microscopy with dislocations being observed at the film-substrate interface. The orientation was also verified by X-ray diffraction and more notably, polarized Raman scattering. The magnetic properties and ferromagnetic resonant frequencies were experimentally characterized by a vibrating sample magnetometry and a frequency-swept ferromagnetic resonant flip-chip technique, respectively. The micron-thick BaM films exhibited a large remanence ratio of 0.92 along in-plane easy axis and a small one of 0.09 for the in-plane hard axis loop measurement. The FMR frequency was 50.3 GHz at zero field and reached 57.9 GHz under a magnetic field of 3 kOe, indicating that the epitaxial BaM films with strong self-biased behaviors have good electromagnetic properties in millimeter-wave range.
Zhang, Xiaozhi; Meng, Siqin; Song, Dongsheng; Zhang, Yao; Yue, Zhenxing; Harris, Vincent G.
2017-01-01
Barium hexaferrite (BaM) films with in-plane c-axis orientation are promising and technically important materials for self-biased magnetic microwave devices. In this work, highly oriented BaM films with different thickness and an in-plane easy axis (c-axis) of magnetization were grown on a-plane single-crystal sapphire substrates by direct current magnetron sputtering. A procedure involving seed layers, layer-by-layer annealing was adopted to reduce the substrate-induced strains and allow for the growth of thick (~3.44 μm) films. The epitaxial growth of the BaM film on sapphire was revealed by high-resolution transmission electron microscopy with dislocations being observed at the film-substrate interface. The orientation was also verified by X-ray diffraction and more notably, polarized Raman scattering. The magnetic properties and ferromagnetic resonant frequencies were experimentally characterized by a vibrating sample magnetometry and a frequency-swept ferromagnetic resonant flip-chip technique, respectively. The micron-thick BaM films exhibited a large remanence ratio of 0.92 along in-plane easy axis and a small one of 0.09 for the in-plane hard axis loop measurement. The FMR frequency was 50.3 GHz at zero field and reached 57.9 GHz under a magnetic field of 3 kOe, indicating that the epitaxial BaM films with strong self-biased behaviors have good electromagnetic properties in millimeter-wave range. PMID:28276492
Wachter, Erin; Zamora, Ana; Heidary, David K; Ruiz, José; Glazer, Edith C
2016-08-09
Two thermally activated ruthenium(ii) polypyridyl complexes, cis-Ru(bpy)2Cl2 and trans-Ru(qpy)Cl2 were investigated to determine the impact of the geometric arrangement of the exchangable ligands on the potential of the compounds to act as chemotherapeutics. In contrast to the geometry requirements for cisplatin, trans-Ru(qpy)Cl2 was 7.1-9.5× more cytotoxic than cis-Ru(bpy)2Cl2. This discovery could open up a new area of metal-based chemotherapeutic research.
Pandey, Sharmila; Das, Partha Pratim; Singh, Akhilesh Kumar; Mukherjee, Rabindranath
2011-10-28
Using an acyclic hexadentate pyridine amide ligand, containing a -OCH(2)CH(2)O- spacer between two pyridine-2-carboxamide units (1,4-bis[o-(pyrydine-2-carboxamidophenyl)]-1,4-dioxabutane (H(2)L(9)), in its deprotonated form), four new complexes, [Co(II)(L(9))] (1) and its one-electron oxidized counterpart [Co(III)(L(9))][NO(3)]·2H(2)O (2), [Ni(II)(L(9))] (3) and [Cu(II)(L(9))] (4), have been synthesized. Structural analyses revealed that the Co(II) centre in 1 and the Ni(II) centre in 3 are six-coordinate, utilizing all the available donor sites and the Cu(II) centre in 4 is effectively five-coordinated (one of the ether O atoms does not participate in coordination). The structural parameters associated with the change in the metal coordination environment have been compared with corresponding complexes of thioether-containing hexadentate ligands. The μ(eff) values at 298 K of 1-4 correspond to S = 3/2, S = 0, S = 1 and S = 1/2, respectively. Absorption spectra for all the complexes have been investigated. EPR spectral properties of the copper(II) complex 4 have been investigated, simulated and analyzed. Cyclic voltammetric experiments in CH(2)Cl(2) reveal quasireversible Co(III)-Co(II), Ni(III)-Ni(II) and Cu(II)-Cu(I) redox processes. In going from ether O to thioether S coordination, the effect of the metal coordination environment on the redox potential values of Co(III)-Co(II) (here the effect of spin-state as well), Ni(III)-Ni(II) and Cu(II)-Cu(I) processes have been systematically analyzed.
Kramer, S. L.; Ghosh, V. J.; Breitfeller, M.; ...
2016-08-10
Third generation high brightness light sources are designed to have low emittance and high current beams, which contribute to higher beam loss rates that will be compensated by Top-Off injection. Shielding for these higher loss rates will be critical to protect the projected higher occupancy factors for the users. Top-Off injection requires a full energy injector, which will demand greater consideration of the potential abnormal beam miss-steering and localized losses that could occur. The high energy electron injection beam produces significantly higher neutron component dose to the experimental floor than a lower energy beam injection and ramped operations. Minimizing thismore » dose will require adequate knowledge of where the miss-steered beam can occur and sufficient EM shielding close to the loss point, in order to attenuate the energy of the particles in the EM shower below the neutron production threshold (<10 MeV), which will spread the incident energy on the bulk shield walls and thereby the dose penetrating the shield walls. Designing supplemental shielding near the loss point using the analytic shielding model is shown to be inadequate because of its lack of geometry specification for the EM shower process. To predict the dose rates outside the tunnel requires detailed description of the geometry and materials that the beam losses will encounter inside the tunnel. Modern radiation shielding Monte-Carlo codes, like FLUKA, can handle this geometric description of the radiation transport process in sufficient detail, allowing accurate predictions of the dose rates expected and the ability to show weaknesses in the design before a high radiation incident occurs. The effort required to adequately define the accelerator geometry for these codes has been greatly reduced with the implementation of the graphical interface of FLAIR to FLUKA. This made the effective shielding process for NSLS-II quite accurate and reliable. Lastly, the principles used to provide
Gil-Hernández, B; Calahorro, A J; Gili, P; Sanchiz, J
2017-04-05
Three new heterometallic metal-organic frameworks, namely, {(Ph4P)2[MnCu3(Hmesox)3Br(H2O)]·H2O}n (1), {(Ph4P)2[CoCu3(Hmesox)3Br]}n (2) and {(Ph4P)2[ZnCu3(Hmesox)3Br]·2.5H2O}n (3) were prepared and their structure and magnetic properties were investigated (H4mesox = mesoxalic acid, Ph4P(+) = tetraphenylphosphonium). The structure of all the compounds consist of two interpenetrating opposite-chirality supramolecular cationic and polymeric anionic 3-D (10,3)-a networks, which results in chiral compounds. The anionic network is formed from the polymerization of [Cu3(Hmesox)3Br](4-) units, working as three connectors, and M(ii) cations, working as three-connecting nodes, M = Mn(ii), Co(ii) and Zn(ii). The Ph4P(+) cations build the cationic chiral supramolecular network opposite to the anionic one. Compounds 1 and 2 exhibit long-range magnetic ordering with critical temperatures of 7.2 K and 6.9 K, respectively. However, compound 3 does not display long-range order, but shows ferromagnetic and antiferromagnetic coupling among the Cu(ii) ions. The magnetic interactions are studied by DFT calculations and compared with related Cu(ii)-mesoxalate compounds previously reported.
NASA Astrophysics Data System (ADS)
Tanaka, Masaomi; Maeda, Keiichi; Mazzali, Paolo A.; Kawabata, Koji S.; Nomoto, Ken’ichi
2017-03-01
We present modeling of line polarization to study the multidimensional geometry of stripped-envelope core-collapse supernovae (SNe). We demonstrate that a purely axisymmetric, two-dimensional (2D) geometry cannot reproduce a loop in the Stokes Q ‑ U diagram, that is, a variation of the polarization angles along the velocities associated with the absorption lines. On the contrary, three-dimensional (3D) clumpy structures naturally reproduce the loop. The fact that the loop is commonly observed in stripped-envelope SNe suggests that SN ejecta generally have a 3D structure. We study the degree of line polarization as a function of the absorption depth for various 3D clumpy models with different clump sizes and covering factors. A comparison between the calculated and observed degree of line polarization indicates that a typical size of the clump is relatively large, ≳25% of the photospheric radius. Such large-scale clumps are similar to those observed in the SN remnant Cassiopeia A. Given the small size of the observed sample, the covering factor of the clumps is only weakly constrained (∼5%–80%). The presence of a large-scale clumpy structure suggests that the large-scale convection or standing accretion shock instability takes place at the onset of the explosion.
Mondal, Amit Kumar; Goswami, Tamal; Misra, Anirban; Konar, Sanjit
2017-06-19
In this work, the effects of ligand field strength as well as the metal coordination geometry on magnetic anisotropy of pentacoordinated Co(II) complexes have been investigated using a combined experimental and theoretical approach. For that, a strategic design and synthesis of three pentacoordinate Co(II) complexes [Co(bbp)Cl2]·(MeOH) (1), [Co(bbp)Br2]·(MeOH) (2), and [Co(bbp)(NCS)2] (3) has been achieved by using the tridentate coordination environment of the ligand in conjunction with the accommodating terminal ligands (i.e., chloride, bromide, and thiocyanate). Detailed magnetic studies disclose the occurrence of slow magnetic relaxation behavior of Co(II) centers with an easy-plane magnetic anisotropy. A quantitative estimation of ZFS parameters has been successfully performed by density functional theory (DFT) calculations. Both the sign and magnitude of ZFS parameters are prophesied well by this DFT method. The theoretical results also reveal that the α → β (SOMO-SOMO) excitation contributes almost entirely to the total ZFS values for all complexes. It is worth noting that the excitation pertaining to the most positive contribution to the ZFS parameter is the dxy → dx(2)-y(2) excitation for complexes 1 and 2, whereas for complex 3 it is the dz(2) → dx(2)-y(2) excitation.
Hilimire, Matthew R.; Mayberg, Helen S.; Holtzheimer, Paul E.; Broadway, James M.; Parks, Nathan A.; DeVylder, Jordan E.; Corballis, Paul M.
2014-01-01
Background The cognitive neuropsychological model states that antidepressant treatment alters emotional biases early in treatment, and after this initial change in emotional processing, environmental and social interactions allow for long-term/sustained changes in mood and behavior. Objective Changes in negative self-bias after chronic subcallosal cingulate (SCC) deep brain stimulation (DBS) were investigated with the hypothesis that treatment would lead to changes in emotional biases followed by changes in symptom severity. Methods Patients (N = 7) with treatment-resistant depression were assessed at three time points: pre-treatment; after one month stimulation; and after six months stimulation. The P1, P2, P3, and LPP (late positive potential) components of the event-related potential elicited by positive and negative trait adjectives were recorded in both a self-referential task and a general emotion recognition task. Results Results indicate that DBS reduced automatic attentional bias towards negative words early in treatment, as indexed by the P1 component, and controlled processing of negative words later in treatment, as indexed by the P3 component. Reduction in negative words endorsed as self-descriptive after six months DBS was associated with reduced depression severity after six months DBS. Change in emotional processing may be restricted to the self-referential task. Conclusions Together, these results suggest that the cognitive neuropsychological model, developed to explain the time-course of monoamine antidepressant treatment, may also be used as a framework to interpret the antidepressant effects of SCC DBS. PMID:25499035
NASA Astrophysics Data System (ADS)
Ding, Zhenfeng; Sun, Jingchao; Wang, Younian
2005-12-01
The tuned substrate self-bias in an rf inductively coupled plasma source is controlled by means of varying the impedance of an external LC network inserted between the substrate and the ground. The influencing parameters such as the substrate axial position, different coupling coils and inserted resistance are experimentally studied. To get a better understanding of the experimental results, the axial distributions of the plasma density, electron temperature and plasma potential are measured with an rf compensated Langmuir probe; the coil rf peak-to-peak voltage is measured with a high voltage probe. As in the case of changing discharge power, it is found that continuity, instability and bi-stability of the tuned substrate bias can be obtained by means of changing the substrate axial position in the plasma source or the inserted resistance. Additionally, continuity can not transit directly into bi-stability, but evolves via instability. The inductance of the coupling coil has a substantial effect on the magnitude and the property of the tuned substrate bias.
Hilimire, Matthew R; Mayberg, Helen S; Holtzheimer, Paul E; Broadway, James M; Parks, Nathan A; DeVylder, Jordan E; Corballis, Paul M
2015-01-01
The cognitive neuropsychological model states that antidepressant treatment alters emotional biases early in treatment, and after this initial change in emotional processing, environmental and social interactions allow for long-term/sustained changes in mood and behavior. Changes in negative self-bias after chronic subcallosal cingulate (SCC) deep brain stimulation (DBS) were investigated with the hypothesis that treatment would lead to changes in emotional biases followed by changes in symptom severity. Patients (N = 7) with treatment-resistant depression were assessed at three time points: pre-treatment; after one month stimulation; and after six months stimulation. The P1, P2, P3, and LPP (late positive potential) components of the event-related potential elicited by positive and negative trait adjectives were recorded in both a self-referential task and a general emotion recognition task. Results indicate that DBS reduced automatic attentional bias toward negative words early in treatment, as indexed by the P1 component, and controlled processing of negative words later in treatment, as indexed by the P3 component. Reduction in negative words endorsed as self-descriptive after six months DBS was associated with reduced depression severity after six months DBS. Change in emotional processing may be restricted to the self-referential task. Together, these results suggest that the cognitive neuropsychological model, developed to explain the time-course of monoamine antidepressant treatment, may also be used as a framework to interpret the antidepressant effects of SCC DBS. Copyright © 2015 Elsevier Inc. All rights reserved.
NASA Astrophysics Data System (ADS)
Shoji, Mitsuo; Isobe, Hiroshi; Nakajima, Takahito; Yamaguchi, Kizashi
2015-11-01
Full geometry optimizations of ([CaMn4O4(CH3COO)8(py)(CH3COOH)2], (py: pyridine) (1)) were performed at the UB3LYP theoretical level. 1 is a theoretical model for the synthetic model ([CaMn4O4(ButCOO)8(py)(ButCOOH)2], (But: t-butyl) (2)) which closely mimicks the native oxygen evolving complex (OEC) in photosystem II. It was shown that the X-ray structure of 2 was well reproduced by 1 in the (Mn1(III), Mn2(IV), Mn3(IV), Mn4(III)) valence state with the unprotonated O5 (O5 = O2-), and two different valence states were obtained in the one-electron oxidized state. Importance of the Jahn-Teller effect of the Mn(III) site for the structural deformations was presented.
NASA Astrophysics Data System (ADS)
Gilbert, D. C.; Dikanov, S. A.; Doetschman, D. C.; Smeija, J. A.
1999-12-01
Spin coupling with pyrrole nitrogens and NO geometry in pyridyl-NO-Fe(II) tetraphenyl- 15N4-porphyrin, examined with hyperfine sublevel correlation spectroscopy (HYSCORE), was studied because of renewed interest in diatomic molecule bound ferrous hemes, e.g. the physiologically important NO synthase. Dipolar coupling locates the effective electron spin position (0.109±0.008 nm from the ring center, 0.106±0.006 nm above the ring plane and projecting 37±2° from the nearest pyrrole nitrogen). The NO projection in an X-ray study of the 4-methyl piperidine complex is 38.6°. The negative pyrrole nitrogen spin densities induced by the NO obey a sinusoidal angular relationship.
NASA Astrophysics Data System (ADS)
Jana, Subrata; Santra, Ramesh Chandra; Das, Saurabh; Chattopadhyay, Shouvik
2014-09-01
Two new copper(II) complexes, [Cu(L)(OCN)] (1) and [CuL(dca)]n (2), where HL = 2-(-(2-(diethylamino)ethylimino)methyl)naphthalen-1-ol, dca = N(CN)2-, have been synthesized and characterized by elemental analysis, IR, UV-VIS spectroscopy and single crystal X-ray diffraction studies. Complex 1 has square planar and complex 2 square pyramidal geometries in solid state around metal centre. Interactions of the complexes with calf thymus DNA (CT DNA) were studied by UV-VIS spectroscopy. Binding constant and site size of interaction were determined. Binding site size and intrinsic binding constant K revealed complex 1 interacted with calf thymus DNA better than complex 2.
NASA Astrophysics Data System (ADS)
Terzis, Petros A.; Christodoulakis, T.
2012-12-01
Lie-group symmetry analysis for systems of coupled, nonlinear ordinary differential equations is performed in order to obtain the entire solution space to Einstein’s field equations for vacuum Bianchi spacetime geometries. The symmetries used are the automorphisms of the Lie algebra of the corresponding three-dimensional isometry group acting on the hyper-surfaces of simultaneity for each Bianchi type, as well as the scaling and the time reparametrization symmetry. A detailed application of the method is presented for Bianchi type IV. The result is the acquisition of the general solution of type IV in terms of sixth Painlevé transcendent PVI, along with the known pp-wave solution. For Bianchi types I, II, V the known entire solution space is attained and very briefly listed, along with two new type V solutions of Euclidean and neutral signature and a type I pp-wave metric.
Peyrin, E; Guillaume, Y C; Guinchard, C
1999-01-01
Chiral recognition mechanism relationships for binding at site II on human serum albumin (HSA) were investigated using D, L dansyl amino acids. Sodium phosphate salt was used as a solute-HSA interaction modifier. A new model was developed using a biochromatographic approach to describe the variation in the transfer equilibrium constant with the salt concentration, i.e., the nature of the interactions. The solute binding was divided into two salt concentration ranges c. For the low c values, below 0.03 M, the nonstereoselective interactions constituted the preponderant contribution to the variation in the solute binding with the salt concentration. For the high c values, above 0.03 M, the solute binding was governed by the hydrophobic effect and the stereoselective interactions. The different contributions implied in the binding process provided an estimation of both the surface charge density (sigma/F) and the surface area of the site II binding cavity accessible to solvent, which were found to be equal to around 10.10(-7) mol/m(2) and 2 nm(2). As well, the excess of sodium ions excluded by the solute transfer from the surface area of the pocket were about(-0.7) for dansyl norvaline and (-0.8) for dansyl tryptophan. PMID:10465735
NASA Astrophysics Data System (ADS)
Romero-Salazar, C.
2016-04-01
A critical-state model is postulated that incorporates, for the first time, the structural anisotropy and flux-line cutting effect in a type-II superconductor. The model is constructed starting from the theoretical scheme of Romero-Salazar and Pérez-Rodríguez to study the anisotropy induced by flux cutting. Here, numerical calculations of the magnetic induction and static magnetization are presented for samples under an alternating magnetic field, orthogonal to a static dc-bias one. The interplay of the two anisotropies is analysed by comparing the numerical results with available experimental data for an yttrium barium copper oxide (YBCO) plate, and a vanadium-titanium (VTi) strip, subjected to a slowly oscillating field {H}y({H}z) in the presence of a static field {H}z({H}y).
NASA Astrophysics Data System (ADS)
Ma, J. N.; Xin, C. Z.; Ma, J.; Lin, Y. H.; Nan, C. W.
2016-12-01
Self-biased and wide resonance band magnetoelectric (ME) response is realized in the series-connected SrFe12O19/Metglas/ Pb(Zr, Ti)O3 composites. Both ME composites fabrication and series-connecting method are optimized in this paper. It is found that 2/5—length ratio between SFO ribbon and PZT plate is proposed to maintain the ME resonance property in the ME composites, and that series-connecting the ME components by opposite polarizations with each other is the proposal method to achieve wide resonance band ME response. Without external magnetic field, the self-biased ME composites show a resonance enhanced ME response of over 117 mV Oe-1 in a 30 kHz bandwidth frequency window. Our ME composites present a good potential for application in broadband magnetic field sensors and energy harvesters.
NASA Astrophysics Data System (ADS)
Nbili, W.; Soudani, S.; Kaabi, K.; Wojtaś, M.; Ferretti, V.; Lefebvre, F.; Jelsch, C.; Ben Nasr, C.
2017-10-01
The crystal structure of the new complex [Co(C5H7N3O)2(H2O)4](NO3)2ṡ4H2O synthesized in aqueous solution has been determined by single crystal X-ray diffraction. The compound crystallizes in the triclinic space group P 1 bar with lattice parameters: a = 7.3056(2), b = 8.4065(2), c = 10.4724(3) Å, α = 103.9470(19), β = 105.6600(14), γ = 91.1350(18)°, V = 598.54(3) Å3 and Z = 1. The Co(II) central ion is in a slightly distorted octahedral coordination geometry formed by two nitrogen atoms of two 2-amino-6-methoxypyrimidine ligands and four oxygen atoms of coordinated water molecules. The crystal packing is stabilized by intermolecular Osbnd H⋯O, Nsbnd H⋯O and Csbnd H⋯O hydrogen bonds which link the molecules into a three-dimensional network. Intermolecular interactions were investigated by Hirshfeld surfaces. Electronic properties such as HOMO and LUMO energies were derived. The vibrational absorption bands were identified by infrared spectroscopy. The compound was characterized by thermal analysis to determine its thermal behavior with respect to temperature.
NASA Astrophysics Data System (ADS)
Rasmussen, N. G.; Simeoni, G. G.; Lefmann, K.
2016-04-01
A dedicated beam-focusing device has been designed for the direct geometry thermal-cold neutron time-of-flight spectrometer TOFTOF at the neutron facility FRM II (Garching, Germany). The prototype, based on the compressed Archimedes' mirror concept, benefits from the adaptive-optics technology (adjustable supermirror curvature) and the compact size (only 0.5 m long). We have simulated the neutron transport across the entire guide system. We present a detailed computer characterization of the existing device, along with the study of the factors mostly influencing the future improvement. We have optimized the simulated prototype as a function of the neutron wavelength, accounting also for all relevant features of a real instrument like the non-reflecting side edges. The results confirm the ;chromatic; displacement of the focal point (flux density maximum) at fixed supermirror curvature, and the ability of a variable curvature to keep the focal point at the sample position. Our simulations are in excellent agreement with theoretical predictions and the experimentally measured beam profile. With respect to the possibility of a further upgrade, we find that supermirror coatings with m-values higher than 3.5 would have only marginal influence on the optimal behaviour, whereas comparable spectrometers could take advantage of longer focusing segments, with particular impact for the thermal region of the neutron spectrum.
NASA Astrophysics Data System (ADS)
Saleem, Zain Hamid
In this thesis we study a special class of black hole geometries called subtracted geometries. Subtracted geometry black holes are obtained when one omits certain terms from the warp factor of the metric of general charged rotating black holes. The omission of these terms allows one to write the wave equation of the black hole in a completely separable way and one can explicitly see that the wave equation of a massless scalar field in this slightly altered background of a general multi-charged rotating black hole acquires an SL(2, R) x SL(2, R) x SO(3) symmetry. The "subtracted limit" is considered an appropriate limit for studying the internal structure of the non-subtracted black holes because new 'subtracted' black holes have the same horizon area and periodicity of the angular and time coordinates in the near horizon regions as the original black hole geometry it was constructed from. The new geometry is asymptotically conical and is physically similar to that of a black hole in an asymptotically confining box. We use the different nice properties of these geometries to understand various classically and quantum mechanically important features of general charged rotating black holes.
NASA Astrophysics Data System (ADS)
Ozaki, Toshihiro; Hirose, Tetsuya; Asano, Hiroki; Kuroki, Nobutaka; Numa, Masahiro
2017-04-01
In this paper, we present a 151 nA quiescent and 6.8 mA maximum-output-current low-dropout (LDO) linear regulator for micropower battery management. The LDO regulator employs self-biasing and multiple-stacked cascode techniques to achieve efficient, accurate, and high-voltage-input-tolerant operation. Measurement results demonstrated that the proposed LDO regulator operates with an ultralow quiescent current of 151 nA. The maximum output currents with a 4.16 V output were 1.0 and 6.8 mA when the input voltages were 4.25 and 5.0 V, respectively.
Hadjadj, A.; Pham, N.; Roca i Cabarrocas, P.; Jbara, O.
2010-03-15
The authors demonstrate the possibility of using self-bias voltage on the radio-frequency electrode of a capacitively coupled deposition system as a diagnostic tool to detect the amorphous-to-microcrystalline silicon transition during the exposure of a-Si:H thin films to a hydrogen plasma. This is achieved by combining self-bias voltage (V{sub dc}) and kinetic-ellipsometry measurements, which provide real-time information on the film properties. On intrinsic and n-type a-Si:H films, the hydrogen-plasma exposure results in the formation of a hydrogen-modified layer, which is accompanied with a decrease in the absolute values of V{sub dc}, until a plateau corresponding to the nucleation and the growth of the microcrystalline layer occurs. On p-type a-Si:H, the amorphous-to-microcrystalline transition is characterized by a rapid increase in the absolute values of V{sub dc}. This particular trend is ascribed to the effects of boron on both the solid and plasma phases.
NASA Astrophysics Data System (ADS)
Gendron, A.; Renaud, P.; Bafleur, M.; Nolhier, N.
2008-05-01
This paper proposes a 1D-analytical description of the injection ratio of a self-biased bipolar transistor under very high current injection conditions. Starting from an expression of the current gain based on the stored charge into the emitter and base regions, we derive a new analytical expression of the current injection ratio. This analytical description demonstrates the presence of an asymptotic limit for the injection ratio at very high current densities, as the ratio of electron/hole mobilities in the case of an NPN transistor and to the ratio of hole/electron saturation velocities for a PNP. Moreover, for the first time, a base narrowing effect is demonstrated and explained in the case of a self-biased PNP, in contrast with the base widening effect (Kirk effect [Kirk CT, A theory of transistor cutoff frequency (fT) falloff at high current densities, IRE Trans Electr Dev 1961: p. 164-73]) reported for lower current density. These results are validated by numerical simulation and show a good agreement with experimental characterizations of transistors especially designed to operate under extreme condition such as electrostatic discharge (ESD) events.
ERIC Educational Resources Information Center
Desseyn, H. O.; And Others
1985-01-01
Compares linear-nonlinear and planar-nonplanar geometry through the valence-shell electron pairs repulsion (V.S.E.P.R.), Mulliken-Walsh, and electrostatic force theories. Indicates that although the V.S.E.P.R. theory has more advantages for elementary courses, an explanation of the best features of the different theories offers students a better…
ERIC Educational Resources Information Center
Desseyn, H. O.; And Others
1985-01-01
Compares linear-nonlinear and planar-nonplanar geometry through the valence-shell electron pairs repulsion (V.S.E.P.R.), Mulliken-Walsh, and electrostatic force theories. Indicates that although the V.S.E.P.R. theory has more advantages for elementary courses, an explanation of the best features of the different theories offers students a better…
NASA Astrophysics Data System (ADS)
Prástaro, Agostino
2008-02-01
Following our previous results on this subject [R.P. Agarwal, A. Prástaro, Geometry of PDE's. III(I): Webs on PDE's and integral bordism groups. The general theory, Adv. Math. Sci. Appl. 17 (2007) 239-266; R.P. Agarwal, A. Prástaro, Geometry of PDE's. III(II): Webs on PDE's and integral bordism groups. Applications to Riemannian geometry PDE's, Adv. Math. Sci. Appl. 17 (2007) 267-285; A. Prástaro, Geometry of PDE's and Mechanics, World Scientific, Singapore, 1996; A. Prástaro, Quantum and integral (co)bordism in partial differential equations, Acta Appl. Math. (5) (3) (1998) 243-302; A. Prástaro, (Co)bordism groups in PDE's, Acta Appl. Math. 59 (2) (1999) 111-201; A. Prástaro, Quantized Partial Differential Equations, World Scientific Publishing Co, Singapore, 2004, 500 pp.; A. Prástaro, Geometry of PDE's. I: Integral bordism groups in PDE's, J. Math. Anal. Appl. 319 (2006) 547-566; A. Prástaro, Geometry of PDE's. II: Variational PDE's and integral bordism groups, J. Math. Anal. Appl. 321 (2006) 930-948; A. Prástaro, Th.M. Rassias, Ulam stability in geometry of PDE's, Nonlinear Funct. Anal. Appl. 8 (2) (2003) 259-278; I. Stakgold, Boundary Value Problems of Mathematical Physics, I, The MacMillan Company, New York, 1967; I. Stakgold, Boundary Value Problems of Mathematical Physics, II, Collier-MacMillan, Canada, Ltd, Toronto, Ontario, 1968], integral bordism groups of the Navier-Stokes equation are calculated for smooth, singular and weak solutions, respectively. Then a characterization of global solutions is made on this ground. Enough conditions to assure existence of global smooth solutions are given and related to nullity of integral characteristic numbers of the boundaries. Stability of global solutions are related to some characteristic numbers of the space-like Cauchy dataE Global solutions of variational problems constrained by (NS) are classified by means of suitable integral bordism groups too.
Yang, Z; Li, X; Li, J; Long, J D; Lan, C H; Wang, T; Dong, P; He, J L
2017-03-01
A large amount of back streaming electrons will bring about a part of current drain on power supply, cause sparking or high-voltage breakdowns, and affect the neutron yield and waveform for a compact sealed-tube pulsed neutron generator. A novel idea which uses a ZnO varistor to provide a constant self-biased voltage to suppress the secondary electrons is introduced. The I-V curve for the ZnO varistor was measured in the experiment. The effects of suppressing the secondary electrons were investigated using a ZnO varistor, linear resistors, and an independent power supply, respectively. The results show that the secondary electrons are suppressed effectively by the compact ZnO varistor, while not increasing the size and the component of the device. It is a promising design for compact sealed-tube neutron generators.
NASA Astrophysics Data System (ADS)
Zhang, Jitao; Li, Ping; Wen, Yumei; He, Wei; Yang, Aichao; Lu, Caijiang
2013-11-01
Giant self-biased magnetoelectric (ME) response and obvious hysteresis are observed in trilayer homogenous ME laminate composite consisting of negative magnetostrictive Samfenol (SmFe2) plates and piezoelectric ceramic PZT (Pb(Zr,Ti)O3) plates. The large anisotropic field of SmFe2 oriented the direction [111] of easy magnetization results in an enhanced internal bias due to its huge intrinsic anisotropic constant. The experimental results demonstrate that this composite exhibits ˜30 times higher ME voltage coefficient than that of composite FeNi/PZT/FeNi with weak ME coupling at zero bias. These results provide the possibility of this homogeneous ME composite for ultra-sensitive magnetic field sensing without bias.
NASA Astrophysics Data System (ADS)
Yang, Z.; Li, X.; Li, J.; Long, J. D.; Lan, C. H.; Wang, T.; Dong, P.; He, J. L.
2017-03-01
A large amount of back streaming electrons will bring about a part of current drain on power supply, cause sparking or high-voltage breakdowns, and affect the neutron yield and waveform for a compact sealed-tube pulsed neutron generator. A novel idea which uses a ZnO varistor to provide a constant self-biased voltage to suppress the secondary electrons is introduced. The I-V curve for the ZnO varistor was measured in the experiment. The effects of suppressing the secondary electrons were investigated using a ZnO varistor, linear resistors, and an independent power supply, respectively. The results show that the secondary electrons are suppressed effectively by the compact ZnO varistor, while not increasing the size and the component of the device. It is a promising design for compact sealed-tube neutron generators.
Simmons, Charles J; Stratemeier, Horst; Hitchman, Michael A; Reinen, Dirk; Masters, Vanessa M; Riley, Mark J
2011-06-06
The crystal structures of trans-diaquabis(methoxyacetato)copper(II) and the isostructural nickel(II) complex have been determined over a wide temperature range. In conjunction with the reported behavior of the g-values, the structural data suggest that the copper(II) compound exhibits a thermal equilibrium between three structural forms, two having orthorhombically distorted, tetragonally elongated geometries but with the long and intermediate bonds to different atoms, and the third with a tetragonally compressed geometry. This is apparently the first reported example of a copper(II) complex undergoing an equilibrium between tetragonally elongated and compressed forms. The optical spectrum of single crystals of the copper(II) compound is used to obtain metal-ligand bonding parameters which yield the g-values of the compressed form of the complex and hence the proportions of the complex in each structural form at every temperature. When combined with estimates of the Jahn-Teller distortions of the different forms, the latter produce excellent agreement with the observed temperature dependence of the bond lengths. The behavior of an infrared combination band is consistent with such a thermal equilibrium, as is the temperature dependence of the thermal ellipsoid parameters and the XAFS. The potential surfaces of the different forms of the copper(II) complex have been calculated by a model based upon Jahn-Teller coupling. It is suggested that cooperative effects may cause the development of the population of tetragonally compressed complexes, and the crystal packing is consistent with this hypothesis, though the present model may oversimplify the diversity of structural forms present at high temperature. © 2011 American Chemical Society
RF plasma MOCVD of Y2O3 thin films: Effect of RF self-bias on the substrates during deposition
NASA Astrophysics Data System (ADS)
Chopade, S. S.; Barve, S. A.; Thulasi Raman, K. H.; Chand, N.; Deo, M. N.; Biswas, A.; Rai, Sanjay; Lodha, G. S.; Rao, G. M.; Patil, D. S.
2013-11-01
Yttrium oxide (Y2O3) thin films have been deposited by radio frequency plasma assisted metal organic chemical vapor deposition (MOCVD) process using (2,2,6,6-tetramethyl-3,5-heptanedionate) yttrium (commonly known as Y(thd)3) precursor in a plasma of argon and oxygen gases at a substrate temperature of 350 °C. The films have been deposited under influence of varying RF self-bias (-50 V to -175 V) on silicon, quartz, stainless steel and tantalum substrates. The deposited coatings are characterized by glancing angle X-ray diffraction (GIXRD), Fourier transform infrared spectroscopy (FTIR), X-ray photoelectron spectroscopy (XPS), spectroscopic ellipsometry and scanning electron microscopy (SEM). GIXRD and FTIR results indicate deposition of Y2O3 (BCC structure) in all cases. However, XPS results indicate nonstoichiometric cubic phase deposition on the surface of deposited films. The degree of nonstoichiometry varies with bias during deposition. Ellipsometry results indicate that the refractive index for the deposited films is varying from 1.70 to 1.83 that is typical for Y2O3. All films are transparent in the investigated wavelength range 300-1200 nm. SEM results indicate that the microstructure of the films is changing with applied bias. Results indicate that it is possible to deposit single phase cubic Y2O3 thin films at low substrate temperature by RF plasma MOCVD process. RF self-bias that decides about the energy of impinging ions on the substrates plays an important role in controlling the texture of deposited Y2O3 films on the substrates. Results indicate that to control the structure of films and its texture, it is important to control the bias on the substrate during deposition. The films deposited at high bias level show degradation in the crystallinity and reduction of thickness.
Enrichment Activities for Geometry.
ERIC Educational Resources Information Center
Usiskin, Zalman
1983-01-01
Enrichment activities that teach about geometry as they instruct in geometry are given for some significant topics. The facets of geometry included are tessellations, round robin tournaments, geometric theorems on triangles, and connections between geometry and complex numbers. (MNS)
Tanase, Stéfania; Tuna, Floriana; Guionneau, Philippe; Maris, Thierry; Rombaut, Guillaume; Mathonière, Corine; Andruh, Marius; Kahn, Olivier; Sutter, Jean-Pascal
2003-03-10
Two molecule-based magnets, [Mn(2)(tea)Mo(CN)(7)].H(2)O, 1, and [Mn(2)(tea)Mo(CN)(7)], 2 (tea stands for triethanolamine), formed with the 4d ion building block, [Mo(CN)(7)](4)(-), Mn(II) ions, and an additional ligand, tea, have been prepared and structurally characterized by single-crystal X-ray analyses. Whereas 1 is obtained by a self-assembling process in solution, compound 2 is quantitatively formed through a smooth thermal treatment of 1. Their magnetic properties revealed that these compounds exhibit magnetic ordering at T(c) = 75 and 106 K respectively for compounds 1 and 2. The difference for their critical temperature is attributed to the geometry of the coordination sphere of a Mn(II) site found to be square-pyramidal for 1 and tetrahedral for 2.
NASA Astrophysics Data System (ADS)
Gmerek, Felix; Stuhlmann, Benjamin; Álvarez-Valtierra, Leonardo; Pratt, David W.; Schmitt, Michael
2016-02-01
We determined the changes of the geometries of 2- and 3-tolunitrile upon excitation to the lowest excited singlet states from Franck-Condon fits of the vibronic intensities in several fluorescence emission spectra and of the rotational constant changes upon excitation. These structural changes can be connected to the altered electron distribution in the molecules and are compared to the results of ab initio calculations. We show how the torsional barriers of the methyl groups in both components are used as probe of the molecular changes upon electronic excitation.
NASA Astrophysics Data System (ADS)
Potter, William J.; Cotter, Garret
2013-02-01
In this paper we develop the jet model of Potter & Cotter to include a magnetically dominated accelerating parabolic base transitioning to a slowly decelerating conical jet with a geometry set by recent radio observations of M87. We conserve relativistic energy-momentum and particle number along the jet and calculate the observed synchrotron emission from the jet by calculating the integrated line-of-sight synchrotron opacity through the jet in the rest frame of each section of plasma. We calculate the inverse-Compton emission from synchrotron, cosmic microwave background (CMB), accretion disc, starlight, broad-line region (BLR), dusty torus and narrow-line region photons by transforming into the rest frame of the plasma along the jet. We fit our model to simultaneous multi-wavelength observations of the Compton-dominant FSRQ type blazar PKS 0227-369, with a jet geometry set by M87 and an accelerating bulk Lorentz factor consistent with simulations and theory. We investigate models in which the jet comes into equipartition at different distances along the jet and equipartition is maintained via the conversion of jet bulk kinetic energy into particle acceleration. We find that the jet must still be magnetically dominated within the BLR and cannot be in equipartition due to the severe radiative energy losses. The model fits the observations, including radio data, very well if the jet comes into equipartition outside the BLR within the dusty torus (1.5 pc) or at further distances (34 pc). The fits require a high-power jet with a large bulk Lorentz factor observed close to the line of sight, consistent with our expectations for a Compton-dominant blazar. We find that our fit in which the jet comes into equipartition furthest along the jet, which has a jet with the geometry of M87 scaled linearly with black hole mass, has an inferred black hole mass close to previous estimates. This implies that the jet of PKS 0227 might be well described by the same jet geometry as M87.
Gmerek, Felix; Stuhlmann, Benjamin; Álvarez-Valtierra, Leonardo; Pratt, David W; Schmitt, Michael
2016-02-28
We determined the changes of the geometries of 2- and 3-tolunitrile upon excitation to the lowest excited singlet states from Franck-Condon fits of the vibronic intensities in several fluorescence emission spectra and of the rotational constant changes upon excitation. These structural changes can be connected to the altered electron distribution in the molecules and are compared to the results of ab initio calculations. We show how the torsional barriers of the methyl groups in both components are used as probe of the molecular changes upon electronic excitation.
NASA Astrophysics Data System (ADS)
Kumari, Mukesh; Prakash, Chandra; Chatterjee, Ratnamala
2017-05-01
In this work, room temperature magnetoelectric properties of (0-3) particulate composites of non lead based piezoelectric BNTKNNLTS [0.97(Bi0.5Na0.5TiO3)-0.03(K0.47Na0.47Li0.06Nb0.74Sb0.06Ta0.2O3) and magnetostrictive CZFMO (Co0.6Zn0.4Fe1.7Mn0.3O4) are presented. Composite samples of (1-x)(BNTKNNLTS)-x(CZFMO), with x=0.1 and 0.5, are synthesized by solid state reaction route. X-ray diffraction confirms the single phase formation of parent phases and the presence of two phases in the composites. Similar sintering conditions of the two individual components lead to optimal ferroelectric and ferromagnetic properties in the composites. A large self-biased magnetoelectric (ME) coupling 74 mV/cm.Oe for the sample with x=0.1 (measured in longitudinally magnetized-transversely polarized configuration) is observed at room temperature.
ERIC Educational Resources Information Center
Scott, Paul
1988-01-01
Discusses the use of computer graphics in the teaching of geometry. Describes five types of geometry: Euclidean geometry, transformation geometry, coordinate geometry, three-dimensional geometry, and geometry of convex sets. (YP)
Boeuf, J. P.; Claustre, J.; Chaudhury, B.; Fubiani, G.
2012-11-15
The physics of a magnetic filter under conditions similar to those of the negative ion source for the ITER neutral beam injector is analyzed with the help of a two-dimensional particle-in-cell Monte Carlo Collisions model. A detailed analysis of the different terms of the electron momentum equations shows how diamagnetic and drift currents can be dominant in different regions of the filter. Electron transport through the filter is due to an E Multiplication-Sign B drift current on one side of the chamber induced by the presence of the chamber walls perpendicular to the electron diamagnetic current. The filter design of the ITER negative ion source, which does not allow a closed electron diamagnetic current, induces an asymmetry of the plasma that is analyzed with the particle model. It is shown that electron transport through the filter in this geometry is very different from the transport in an ideal, one-dimensional magnetic filter often considered in the literature and described in detail in the companion paper [Boeuf et al., Phys. Plasmas 19, 113509 (2012)].
NASA Astrophysics Data System (ADS)
Yoo, S.; Zeng, X. C.
2006-05-01
We performed a constrained search for the geometries of low-lying neutral germanium clusters GeN in the size range of 21⩽N⩽29. The basin-hopping global optimization method is employed for the search. The potential-energy surface is computed based on the plane-wave pseudopotential density functional theory. A new series of low-lying clusters is found on the basis of several generic structural motifs identified previously for silicon clusters [S. Yoo and X. C. Zeng, J. Chem. Phys. 124, 054304 (2006)] as well as for smaller-sized germanium clusters [S. Bulusu et al., J. Chem. Phys. 122, 164305 (2005)]. Among the generic motifs examined, we found that two motifs stand out in producing most low-lying clusters, namely, the six/nine motif, a puckered-hexagonal-ring Ge6 unit attached to a tricapped trigonal prism Ge9, and the six/ten motif, a puckered-hexagonal-ring Ge6 unit attached to a bicapped antiprism Ge10. The low-lying clusters obtained are all prolate in shape and their energies are appreciably lower than the near-spherical low-energy clusters. This result is consistent with the ion-mobility measurement in that medium-sized germanium clusters detected are all prolate in shape until the size N ˜65.
Gainsford, Graeme J; Bhuiyan, M Delower H; Kay, Andrew J
2008-04-01
The compounds N-[2-(4-cyano-5-dicyanomethylene-2,2-dimethyl-2,5-dihydrofuran-3-yl)vinyl]-N-phenylacetamide, C(20)H(16)N(4)O(2), (I), and 2-{3-cyano-5,5-dimethyl-4-[2-(piperidin-1-yl)vinyl]-2,5-dihydrofuran-2-ylidene}malononitrile 0.376-hydrate, C(17)H(18)N(4)O x 0.376 H(2)O, (II), are novel push-pull molecules. The significant bonding changes in the polyene chain compared with the parent molecule 2-dicyanomethylene-4,5,5-trimethyl-2,5-dihyrofuran-3-carbonitrile are consistent with the relative electron-donating properties of the acetanilido and piperidine groups. The packing of (I) utilizes one phenyl-cyano C-H...N and two phenyl-carbonyl C-H...O hydrogen bonds. Compound (II) crystallizes with a partial water molecule (0.376H(2)O), consistent with cell packing that is dominated by attractive C-H...N(cyano) interactions. These compounds are precursors to novel nonlinear optical chromophores, studied to assess the impact of donor strength and the extent of conjugation on bond-length alternation, crystal packing and aggregation.
Linder, Douglas P; Rodgers, Kenton R
2015-09-17
Zn(II) is used in nature as a biocatalyst in hundreds of enzymes, and the structure and dynamics of its catalytic activity are subjects of considerable interest. Many of the Zn(II)-based enzymes are classified as hydrolytic enzymes, in which the Lewis acidic Zn(II) center facilitates proton transfer(s) to a Lewis base, from proton donors such as water or thiol. This report presents the results of a quantum computational study quantifying the dynamic relationship between the zinc coordination number (CN), its coordination geometry, and the thermodynamic driving force behind these proton transfers originating from a charge-neutral methylthiol ligand. Specifically, density functional theory (DFT) and second-order perturbation theory (MP2) calculations have been performed on a series of [(imidazole)nZn-S(H)CH3](2+) and [(imidazole)nZn-SCH3](+) complexes with the CN varied from 1 to 6, n = 0-5. As the number of imidazole ligands coordinated to zinc increases, the S-H proton dissociation energy also increases, (i.e., -S(H)CH3 becomes less acidic), and the Zn-S bond energy decreases. Furthermore, at a constant CN, the S-H proton dissociation energy decreases as the S-Zn-(ImH)n angles increase about their equilibrium position. The zinc-coordinated thiol can become more or less acidic depending upon the position of the coordinated imidazole ligands. The bonding and thermodynamic relationships discussed may apply to larger systems that utilize the [(His)3Zn(II)-L] complex as the catalytic site, including carbonic anhydrase, carboxypeptidase, β-lactamase, the tumor necrosis factor-α-converting enzyme, and the matrix metalloproteinases.
Waychunas, G.A.; Fuller, C.C.; Davis, J.A.
2002-01-01
"Two-line" ferrihydrite samples precipitated and then exposed to a range of aqueous Zn solutions (10-5 to 10-3 M), and also coprecipitated in similar Zn solutions (pH 6.5), have been examined by Zn and Fe K-edge X-ray absorption spectroscopy. Typical Zn complexes on the surface have Zn-O distances of 1.97(0.2) A?? and coordination numbers of about 4.0(0.5), consistent with tetrahedral oxygen coordination. This contrasts with Zn-O distances of 2.11(.02) A?? and coordination numbers of 6 to 7 in the aqueous Zn solutions used in sample preparation. X-ray absorption extended fine structure spectroscopy (EXAFS) fits to the second shell of cation neighbors indicate as many as 4 Zn-Fe neighbors at 3.44(.04) A?? in coprecipitated samples, and about two Zn-Fe neighbors at the same distance in adsorption samples. In both sets of samples, the fitted coordination number of second shell cations decreases as sorption density increases, indicating changes in the number and type of available complexing sites or the onset of competitive precipitation processes. Comparison of our results with the possible geometries for surface complexes and precipitates suggests that the Zn sorption complexes are inner sphere and at lowest adsorption densities are bidentate, sharing apical oxygens with adjacent edge-sharing Fe(O,OH)6 octahedra. Coprecipitation samples have complexes with similar geometry, but these are polydentate, sharing apices with more than two adjacent edge-sharing Fe(O,OH)6 polyhedra. The results are inconsistent with Zn entering the ferrihydrite structure (i.e., solid solution formation) or formation of other Zn-Fe precipitates. The fitted Zn-Fe coordination numbers drop with increasing Zn density with a minimum of about 0.8(.2) at Zn/(Zn + Fe) of 0.08 or more. This change appears to be attributable to the onset of precipitation of zinc hydroxide polymers with mainly tetrahedral Zn coordination. At the highest loadings studied, the nature of the complexes changes further
Li, X; Suzuki, K; Kanaori, K; Tajima, K; Kashiwada, A; Hiroaki, H; Kohda, D; Tanaka, T
2000-07-01
We previously reported the de novo design of an amphiphilic peptide [YGG(IEKKIEA)4] that forms a native-like, parallel triple-stranded coiled coil. Starting from this peptide, we sought to regulate the assembly of the peptide by a metal ion. The replacement of the Ile18 and Ile22 residues with Ala and Cys residues, respectively, in the hydrophobic positions disrupted of the triple-stranded alpha-helix structure. The addition of Cd(II), however, resulted in the reconstitution of the triple-stranded alpha-helix bundle, as revealed by circular dichroism (CD) spectroscopy and sedimentation equilibrium analysis. By titration with metal ions and monitoring the change in the intensity of the CD spectra at 222 nm, the dissociation constant Kd was determined to be 1.5 +/- 0.8 microM for Cd(II). The triple-stranded complex formed by the 113Cd(II) ion showed a single 113Cd NMR resonance at 572 ppm whose chemical shift was not affected by the presence of Cl- ions. The 113Cd NMR resonance was connected with the betaH protons of the cysteine residue by 1H-113Cd heteronuclear multiple quantum correlation spectroscopy. These NMR results indicate that the three cysteine residues are coordinated to the cadmium ion in a trigonal-planar complex. Hg(II) also induced the assembly of the peptide into a triple-stranded alpha-helical bundle below the Hg(II)/peptide ratio of 1/3. With excess Hg(II), however, the alpha-helicity of the peptide was decreased, with the change of the Hg(II) coordination state from three to two. Combining this construct with other functional domains should facilitate the production of artificial proteins with functions controlled by metal ions.
Li, X.; Suzuki, K.; Kanaori, K.; Tajima, K.; Kashiwada, A.; Hiroaki, H.; Kohda, D.; Tanaka, T.
2000-01-01
We previously reported the de novo design of an amphiphilic peptide [YGG(IEKKIEA)4] that forms a native-like, parallel triple-stranded coiled coil. Starting from this peptide, we sought to regulate the assembly of the peptide by a metal ion. The replacement of the Ile18 and Ile22 residues with Ala and Cys residues, respectively, in the hydrophobic positions disrupted of the triple-stranded alpha-helix structure. The addition of Cd(II), however, resulted in the reconstitution of the triple-stranded alpha-helix bundle, as revealed by circular dichroism (CD) spectroscopy and sedimentation equilibrium analysis. By titration with metal ions and monitoring the change in the intensity of the CD spectra at 222 nm, the dissociation constant Kd was determined to be 1.5 +/- 0.8 microM for Cd(II). The triple-stranded complex formed by the 113Cd(II) ion showed a single 113Cd NMR resonance at 572 ppm whose chemical shift was not affected by the presence of Cl- ions. The 113Cd NMR resonance was connected with the betaH protons of the cysteine residue by 1H-113Cd heteronuclear multiple quantum correlation spectroscopy. These NMR results indicate that the three cysteine residues are coordinated to the cadmium ion in a trigonal-planar complex. Hg(II) also induced the assembly of the peptide into a triple-stranded alpha-helical bundle below the Hg(II)/peptide ratio of 1/3. With excess Hg(II), however, the alpha-helicity of the peptide was decreased, with the change of the Hg(II) coordination state from three to two. Combining this construct with other functional domains should facilitate the production of artificial proteins with functions controlled by metal ions. PMID:10933497
Ju, Dehao; Shrimpton, John; Bowdrey, Moira; Hearn, Alex
2012-08-01
A breath activated, pressurized metered dose inhaler (pMDI) device (Oxette(®)) has been developed to replace the traditional cigarette. In this paper, internal and external spray characters are measured by high speed imaging along with sizing the residual droplets at the distance from the discharge orifice where the human oropharynx locates. Two different formulations with 95% and 98% mass fraction of HFA 134a and two prototype cigarette alternatives with different expansion chamber volumes have been analyzed. The internal and external flows issuing from early stage prototype Oxette(®) are discussed along with boiling and evaporation phenomena. The expansion and entrainment regions of the jet are observed and discussed with comparison to the turbulent round jet of a single phase. From the visualizations of internal flows in the earlier design, a small expansion chamber can hardly generate small bubbles, which is difficult to produce fine sprays. The larger the expansion chamber volume, the more room for the propellant evaporation, recirculation, bubble generation and growth, all of which produces finer sprays. Therefore the later prototype of Oxette(®) 2 made a significant improvement to produce fine sprays and facilitated development of the cigarette alternative. Furthermore, the characters of the spray generated by Oxette(®) are compared to that issuing from a pMDI by previous researchers, where the residual MMD is larger than that of a pMDI, because the Oxette(®) has a smaller expansion chamber and the geometry provides less opportunity for the recirculation due to restrictions of the design space. Although the formulation with higher mass fraction of HFA 134a can generate smaller droplets, it cannot produce steady puffs with relatively low mass flow rate. Copyright © 2012 Elsevier B.V. All rights reserved.
Gronski, P; Bauer, R; Bodenbender, L; Boland, P; Diderrich, G; Harthus, H P; Kanzy, E J; Kühn, K; Schmidt, K H; Walter, G
1988-04-01
Electron micrographs of a fraction containing dimers isolated from pooled human polyclonal immunoglobulin G (IgG) suggest essentially a cyclic geometry compatible with bivalently associated monomers. It is obvious that such a structure can be produced by idiotype (Id)--anti-idiotype (anti-Id) interactions where the latter are able to neutralize certain combining site related Id functions. Accordingly, antibody (ab) activities against tetanus toxoid (tt) and rubella antigen (ag) were found to be almost exclusively confined to the monomeric molecules in preparations composed of monomers and dimers only. Moreover, electron micrographs of complexes prepared from a murine monoclonal Id as well as anti-Id reveal the presence of ring complexes, especially of cyclic tetramers. Gel filtration patterns of mixtures containing equimolar concentrations (concns) of such abs (1.6 x 10(-6) M) show, correspondingly for 9 different Id--anti-Id pairs and therefore probably representing a more common feature, mainly the formation of even-numbered complexes, especially tetramers. That is basically in accordance to an equilibrium model developed by Archer and Krakauer but not from a quantitative point of view because non-ideality terms had not been originally included. Despite taking strain energies determined by Schumaker et al. for cyclic complexes of polyclonal rabbit abs and a bivalent hapten into account for computation of size distribution patterns, the predominant formation of dimers was, nevertheless, again predicted by the modified theory in contrast to the experimental results. Fundamental conformity could only be achieved by further decreasing one of the statistical factors, namely the ring closing factor, which theoretically influences the generation of cyclic dimers. Therefore, referring to the experimental results of Schumaker et al., we postulate a strain energy well above 700 cal/mol for cyclic dimers produced by interacting Ids and anti-Ids. In general, the findings
Hancock, Robert D; Reibenspies, Joseph H; Maumela, Hulisani
2004-05-03
The synthesis and structures of [Pb(DOTAM)](ClO4)2.4.5H2O (1) and [Hg(DOTAM)](ClO4)2.0.5CH3OH.1.5H2O (2) are reported, where DOTAM is 1,4,7,10-tetrakis(carbamoylmethyl)-1,4,7,10-tetraazacyclododecane. Compound 1 is triclinic, space group P, a = 12.767(3) A, b = 13.528(2) A, c = 18.385(3) A, alpha = 101.45(2) degrees, beta = 93.32(2) degrees, gamma = 90.53(2) degrees, Z = 4, R = 0.0500. Compound 2 is monoclinic, space group Cc, a = 12.767(3) A, b = 13.528(2) A, c = 18.385(3) A, beta = 101.91(2) degrees, Z = 4, R = 0.0381. The Pb(II) ion in 1 has an average Pb-N = 2.63 A to four N-donors from the macrocyclic ring, and four O-donors (average Pb-O = 2.77 A) from the amide pendant donors of the macrocycle, with a water molecule placed with Pb-O = 3.52 A above the proposed site of the lone pair (Lp) on Pb. The Hg(II) in 2 appears to be only six-coordinate, with four Hg-N bond lengths averaging 2.44 A, and two Hg-O from pendant amide donors at 2.41 A. The other two amide donors appear to be noncoordinating, with Hg-O distances of 2.74 and 2.82 A. A water situated 3.52 A above the proposed site of the lone pair on Pb(II) in 1 is oriented in such a way that it might be thought to be forming a Pb-Lp.H-O-H hydrogen bond. It is concluded that that this is not an H-bond, but that the presence of the lone pair allows a closer approach of the hydrogens to Pb than would be true otherwise. The structural analogy in the VSEPR sense between Pb(II), which has the 5d(10)6s(2) outer electron structure, and the Hg(II) ion, which has the 5d10 structure, is examined. The tendency of Hg(II) toward linear coordination, with two short Hg-L bonds (L = ligand) at 180 degrees to each other, and other donor groups at roughly 90 degrees to this and at much longer bond distances, is paralleled by Pb(II). One of the short Hg-L bonds is replaced in the Pb(II) structures by the lone pair (Lp), which is opposite the short Pb-L bond, or in some cases 2-4 shorter Pb-L bonds.
ERIC Educational Resources Information Center
Cukier, Mimi; Asdourian, Tony; Thakker, Anand
2012-01-01
Geometry provides a natural window into what it is like to do mathematics. In the world of geometry, playful experimentation is often more fruitful than following a procedure, and logic plus a few axioms can open new worlds. Nonetheless, teaching a geometry course in a way that combines both rigor and play can be difficult. Many geometry courses…
ERIC Educational Resources Information Center
Cukier, Mimi; Asdourian, Tony; Thakker, Anand
2012-01-01
Geometry provides a natural window into what it is like to do mathematics. In the world of geometry, playful experimentation is often more fruitful than following a procedure, and logic plus a few axioms can open new worlds. Nonetheless, teaching a geometry course in a way that combines both rigor and play can be difficult. Many geometry courses…
Gainsford, Graeme J; Bhuiyan, M Delower H; Kay, Andrew J
2008-11-01
The planar component of 2-{3-cyano-4-[3-(1-decyl-1,4-dihydroquinolin-4-ylidene)prop-1-enyl]-5,5-dimethyl-2,5-dihydrofuran-2-ylidene}malononitrile, C(32)H(46)N(4)O, (I), forms into layers parallel to the (\\overline{1}01) plane. The larger of the two spaces between layers is filled by the alkyl chains, giving a ;sandwich stack' appearance. The packing of 2-{3-cyano-4-[5-(1-decyl-1,4-dihydroquinolin-4-ylidene)penta-1,3-dienyl]-5,5-dimethyl-2,5-dihydrofuran-2-ylidene}malononitrile, C(34)H(38)N(4)O, (II), which has partial disorder in the 1-decyl group, utilizes weak C-H...N, C-H...O and C-N...pi interactions in a three-dimensional ;herring-bone' array with molecular segments parallel to the (111) and (\\overline{1}1\\overline{1}) planes. Different rotational isomers with respect to the polyene chain and the 5,5-dimethyl-2,5-dihydrofuran-2-ylidene link are observed in the two structures. The significance of the study lies in the delocalization of charge along the polyene chain and the supramolecular aggregation present, which highlight the difficulty in obtaining the noncentrosymmetric alignment required for high nonlinear optical (NLO) responses in zwitterionic chromophores.
Hsieh, Ping-Yen; Lee, Chi-Young; Tai, Nyan-Hwa
2016-02-01
We developed an innovative approach of self-biased sputtering solid doping source process to synthesize doped crystalline Si film on flexible polyimide (PI) substrate via microwave-plasma-enhanced chemical vapor deposition (MWPECVD) using SiCl4/H2 mixture. In this process, P dopants or B dopants were introduced by sputtering the solid doping target through charged-ion bombardment in situ during high-density microwave plasma deposition. A strong correlation between the number of solid doping targets and the characteristics of doped Si films was investigated in detail. The results show that both P- and B-doped crystalline Si films possessed a dense columnar structure, and the crystallinity of these structures decreased with increasing the number of solid doping targets. The films also exhibited a high growth rate (>4.0 nm/s). Under optimal conditions, the maximum conductivity and corresponding carrier concentration were, respectively, 9.48 S/cm and 1.2 × 10(20) cm(-3) for P-doped Si film and 7.83 S/cm and 1.5 × 10(20) cm(-3) for B-doped Si film. Such high values indicate that the incorporation of dopant with high doping efficiency (around 40%) into the Si films was achieved regardless of solid doping sources used. Furthermore, a flexible crystalline Si film solar cell with substrate configuration was fabricated by using the structure of PI/Mo film/n-type Si film/i-type Si film/p-type Si film/ITO film/Al grid film. The best solar cell performance was obtained with an open-circuit voltage of 0.54 V, short-circuit current density of 19.18 mA/cm(2), fill factor of 0.65, and high energy conversion of 6.75%. According to the results of bending tests, the critical radius of curvature (RC) was 12.4 mm, and the loss of efficiency was less than 1% after the cyclic bending test for 100 cycles at RC, indicating superior flexibility and bending durability. These results represent important steps toward a low-cost approach to high-performance flexible crystalline Si film
Learning Geometry through Dynamic Geometry Software
ERIC Educational Resources Information Center
Forsythe, Sue
2007-01-01
In this article, the author investigates effective teaching and learning of geometrical concepts using dynamic geometry software (DGS). Based from her students' reactions to her project, the author found that her students' understanding of the concepts was better than if they had learned geometry through paper-based tasks. However, mixing computer…
Learning Geometry through Dynamic Geometry Software
ERIC Educational Resources Information Center
Forsythe, Sue
2007-01-01
In this article, the author investigates effective teaching and learning of geometrical concepts using dynamic geometry software (DGS). Based from her students' reactions to her project, the author found that her students' understanding of the concepts was better than if they had learned geometry through paper-based tasks. However, mixing computer…
Gong, Lindan; Jang, Yoon Jung; Kim, Jinheung; Kim, Seog K
2012-08-16
Zn(II) meso-tetrakis(N-methylpyridinium-4-yl)porphyrin (ZnTMPyP) produced a unique linear dichroism (LD) spectrum when forming a complex with Z-form poly[d(G-C)(2)]. The spectrum was characterized by a large positive wavelength-dependent LD signal in the Soret absorption region. The magnitudes of LD in both the DNA and Soret band increased as the [porphyrin]/[DNA base] ratio increased and were larger by 20-40 times compared to the negative LD of the ZnTMPyP bound to B-form poly[d(G-C)(2)] and poly[d(A-T)(2)]. The angles calculated from LD were respectively 49° and 42° for B(x) and B(y) transitions of the porphyrin with respect to the local helix axis of Z-form poly[d(G-C)(2)]. The appearance of the unique LD spectrum for the Z-form poly[d(G-C)(2)] complex was accompanied by a bisignate circular dichroism spectrum in the Soret region, whose magnitude was proportional to the square of the porphyrin concentration, suggesting a stacking interaction between Z-form poly[d(G-C)(2)]-bound ZnTMPyP with other bound ZnTMPyP. From these observations, a conceivable binding mode of ZnTMPyP to Z-form poly[d(G-C)(2)] complex was proposed, in which ZnTMPyP binds at the major groove or across the groove. In contrast with Z-form poly[d(G-C)(2)], ZnTMPyP binds to poly[d(A-T)(2)] in a monomeric manner with the angles of 57° and 59° for the two porphyrin's transition moments with respect to the local polynucleotide helix axis. The polarized spectral properties of ZnTMPyP bound to B-form poly[d(G-C)(2)] coincide with the intercalated nonmetallic TMPyP, namely, a negative CD signal in the Soret band and a negative wavelength-dependent reduced LD signal, with a magnitude larger than that in the DNA absorption region in spite of its axial ligands.
ERIC Educational Resources Information Center
Yilmaz, Gül Kaleli
2015-01-01
This study aims to investigate the effects of using Dynamic Geometry Software (DGS) Cabri II Plus and physical manipulatives on the transformational geometry achievement of candidate teachers. In this study, the semi-experimental method was used, consisting of two experimental and one control groups. The samples of this study were 117 students. A…
Krishnamoorthy, Paramasivam; Sathyadevi, Palanisamy; Butorac, Rachel R; Cowley, Alan H; Bhuvanesh, Nattamai S P; Dharmaraj, Nallasamy
2012-04-21
A new series of geometrically different complexes containing ferrocenyl hydrazone ligands were synthesised by reacting suitable precursor complex [MCl(2)(PPh(3))(2)] with the ligands HL(1) or HL(2) (where M = Cu(II) or Ni(II); HL(1) = [Cp(2)Fe(CH=N-NH-CO-C(6)H(5))] (1) and HL(2) = [Cp(2)Fe(CH=N-NH-CO-C(5)H(4)N)]) (2). The new complexes of the composition [Cu(L(1))(PPh(3))(2)], (3) [Cu(L(2))(PPh(3))(2)] (4), [Ni(L(1))(2)] (5) and [Ni(L(2))(2)] (6) were characterised by various spectral studies. Among them, complexes 3 and 5 characterised by single crystal X-ray diffraction showed a distorted tetrahedral structure for the former with 1:1 metal-ligand stoichiometry, but a distorted square planar geometry with 1:2 metal-ligand stoichiometry in the case of the latter. Systematic biological investigations like DNA binding, DNA cleavage, protein binding, free radical scavenging and cytotoxicity activities were carried out using all the synthesised compounds and the results obtained were explained on the basis of structure-activity relationships. The binding constant (K(b)) values of the synthesised compounds are found to be in the order of magnitude 10(3)-10(5) M(-1) and also they exhibit significant cleavage of supercoiled (SC) pUC19 DNA in the presence of H(2)O(2) as co-oxidant. The conformational changes of bovine serum albumin (BSA) upon binding with the above complexes were also studied. In addition, concentration dependent free radical scavenging potential of all the synthesised compounds (1-6) was also carried out under in vitro conditions. Assays on the cytotoxicity of the above complexes against HeLa and A431 tumor cells and NIH 3T3 normal cells were also carried out.
ERIC Educational Resources Information Center
McDonald, Nathaniel J.
2001-01-01
Chronicles a teacher's first year teaching geometry at the Hershey Montessori Farm School in Huntsburg, Ohio. Instructional methods relied on Euclid primary readings and combined pure abstract logic with practical applications of geometry on the land. The course included geometry background imparted by Montessori elementary materials as well as…
ERIC Educational Resources Information Center
McDonald, Nathaniel J.
2001-01-01
Chronicles a teacher's first year teaching geometry at the Hershey Montessori Farm School in Huntsburg, Ohio. Instructional methods relied on Euclid primary readings and combined pure abstract logic with practical applications of geometry on the land. The course included geometry background imparted by Montessori elementary materials as well as…
Venkatakrishnan, Thengarai S; Sahoo, Shaon; Bréfuel, Nicolas; Duhayon, Carine; Paulsen, Carley; Barra, Anne-Laure; Ramasesha, S; Sutter, Jean-Pascal
2010-05-05
Nonconventional heptacoordination in combination with efficient magnetic exchange coupling is shown to yield a 1-D heteronuclear {Fe(II)Nb(IV)} compound with remarkable magnetic features when compared to other Fe(II)-based single chain magnets (SCM). Cyano-bridged heterometallic {3d-4d} and {3d-5d} chains are formed upon assembling Fe(II) bearing a pentadentate macrocycle as the blocking ligand with octacyano metallates, [M(CN)(8)](4-) (M = Nb(IV), Mo(IV), W(IV)). X-ray diffraction (single-crystal and powder) measurements reveal that the [{(H(2)O)Fe(L(1))}{M(CN)(8)}{Fe(L(1))}](infinity) architectures consist of isomorphous 1-D polymeric structures based on the alternation of {Fe(L(1))}(2+) and {M(CN)(8)}(4-) units (L(1) stands for the pentadentate macrocycle). Analysis of the magnetic susceptibility behavior revealed cyano-bridged {Fe-Nb} exchange interaction to be antiferromagnetic with J = -20 cm(-1) deduced from fitting an Ising model taking into account the noncollinear spin arrangement. For this ferrimagnetic chain a slow relaxation of its magnetization is observed at low temperature revealing a SCM behavior with Delta/k(B) = 74 K and tau(0) = 4.6 x 10(-11) s. The M versus H behavior exhibits a hysteresis loop with a coercive field of 4 kOe at 1 K and reveals at 380 mK magnetic avalanche processes, i.e., abrupt reversals in magnetization as H is varied. The origin of these characteristics is attributed to the combination of efficient {Fe-Nb} exchange interaction and significant anisotropy of the {Fe(L(1))} unit. High field EPR and magnetization experiments have revealed for the parent compound [Fe(L(1))(H(2)O)(2)]Cl(2) a negative zero field splitting parameter of D approximately = -17 cm(-1). The crystal structure, magnetic behavior, and Mossbauer data for [Fe(L(1))(H(2)O)(2)]Cl(2) are also reported.
Developments in special geometry
NASA Astrophysics Data System (ADS)
Mohaupt, Thomas; Vaughan, Owen
2012-02-01
We review the special geometry of Script N = 2 supersymmetric vector and hypermultiplets with emphasis on recent developments and applications. A new formulation of the local c-map based on the Hesse potential and special real coordinates is presented. Other recent developments include the Euclidean version of special geometry, and generalizations of special geometry to non-supersymmetric theories. As applications we disucss the proof that the local r-map and c-map preserve geodesic completeness, and the construction of four- and five-dimensional static solutions through dimensional reduction over time. The shared features of the real, complex and quaternionic version of special geometry are stressed throughout.
ERIC Educational Resources Information Center
Morris, Barbara H.
2004-01-01
This article describes a geometry project that used the beauty of stained-glass-window designs to teach middle school students about geometric figures and concepts. Three honors prealgebra teachers and a middle school mathematics gifted intervention specialist created a geometry project that covered the curriculum and also assessed students'…
Twistors to twisted geometries
Freidel, Laurent; Speziale, Simone
2010-10-15
In a previous paper we showed that the phase space of loop quantum gravity on a fixed graph can be parametrized in terms of twisted geometries, quantities describing the intrinsic and extrinsic discrete geometry of a cellular decomposition dual to the graph. Here we unravel the origin of the phase space from a geometric interpretation of twistors.
ERIC Educational Resources Information Center
Lyublinskaya, Irina; Funsch, Dan
2012-01-01
Several interactive geometry software packages are available today to secondary school teachers. An example is The Geometer's Sketchpad[R] (GSP), also known as Dynamic Geometry[R] software, developed by Key Curriculum Press. This numeric based technology has been widely adopted in the last twenty years, and a vast amount of creativity has been…
Euclidean Geometry via Programming.
ERIC Educational Resources Information Center
Filimonov, Rossen; Kreith, Kurt
1992-01-01
Describes the Plane Geometry System computer software developed at the Educational Computer Systems laboratory in Sofia, Bulgaria. The system enables students to use the concept of "algorithm" to correspond to the process of "deductive proof" in the development of plane geometry. Provides an example of the software's capability…
Geometry of multihadron production
Bjorken, J.D.
1994-10-01
This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions.
ERIC Educational Resources Information Center
Lyublinskaya, Irina; Funsch, Dan
2012-01-01
Several interactive geometry software packages are available today to secondary school teachers. An example is The Geometer's Sketchpad[R] (GSP), also known as Dynamic Geometry[R] software, developed by Key Curriculum Press. This numeric based technology has been widely adopted in the last twenty years, and a vast amount of creativity has been…
On the granular stress-geometry equation
NASA Astrophysics Data System (ADS)
DeGiuli, Eric; Schoof, Christian
2014-01-01
Using discrete calculus, we derive the missing stress-geometry equation for rigid granular materials in two dimensions, in the mean-field approximation. We show that i) the equation imposes that the voids cannot carry stress, ii) stress transmission is generically elliptic and has a quantitative relation to anisotropic elasticity, and iii) the packing fabric plays an essential role.
NASA Astrophysics Data System (ADS)
Aiken, Brenda L.
The Commonwealth of Virginia requires high school students to receive a passing grade in core courses and a passing score on End-of-Course Standards of Learning (EOC SOL) tests to receive verified credits that lead to a Virginia high school diploma. These tests are believed to accurately reflect what students should know and be able to do in order to experience success in their endeavors beyond high school. For some students remediation is required to experience success on EOC SOL tests. This study sought to determine the effect of a County's public high school summer remediation program on student gains on EOC SOL tests in Algebra I, Biology, Chemistry, Geometry, and World History and Geography II. Specifically, the purpose of the study sought to determine the following: (a) If significant gains were made by students who attended the summer remediation program; (b) If significant gains were made by students who did not attend the summer remediation program; (c) If there were differences in gain scores of students who attended and those who did not attend the summer remediation program; and (d) If there were differences in gain scores among students who attended the summer remediation program related to school site, gender, ethnicity, learning ability group, socioeconomic status, and level of English proficiency. The results of the study indicate that students who attended and those who did not attend the summer remediation program made significant gains. However, the gains for students who attended the summer remediation program were significantly greater than the gains made by students who did not attend. The study also found that there were no significant differences in gain scores among students who attended the summer remediation program related to gender, ethnicity, learning ability group, socioeconomic status, and level of English proficiency. There were significant differences in Algebra I gain scores related to school site. Recommendations for
NASA Technical Reports Server (NTRS)
Robertshaw, H. H.; Reinholtz, C. F.
1989-01-01
Vibration control and kinematic control with variable-geometry trusses are covered. The analytical approach taken is to model each actuator with lumped masses and model a beam with finite elements, including in each model the generalized reaction forces from the beam on the actuator or vice versa. It is concluded that, from an operational standpoint, the variable-geometry truss actuator is more favorable than the inertia-type actuator. A spatial variable-geometry truss is used to test out rudimentary robotic tasks.
Proof in Transformation Geometry
ERIC Educational Resources Information Center
Bell, A. W.
1971-01-01
The first of three articles showing how inductively-obtained results in transformation geometry may be organized into a deductive system. This article discusses two approaches to enlargement (dilatation), one using coordinates and the other using synthetic methods. (MM)
ERIC Educational Resources Information Center
Chern, Shiing-Shen
1990-01-01
Discussed are the major historical developments of geometry. Euclid, Descartes, Klein's Erlanger Program, Gaus and Riemann, globalization, topology, Elie Cartan, and an application to molecular biology are included as topics. (KR)
ERIC Educational Resources Information Center
Emenaker, Charles E.
1999-01-01
Describes a sixth-grade interdisciplinary geometry unit based on Charles Dickens's "A Christmas Carol". Focuses on finding area, volume, and perimeter, and working with estimation, decimals, and fractions in the context of making gingerbread houses. (ASK)
Flyby Geometry Optimization Tool
NASA Technical Reports Server (NTRS)
Karlgaard, Christopher D.
2007-01-01
The Flyby Geometry Optimization Tool is a computer program for computing trajectories and trajectory-altering impulsive maneuvers for spacecraft used in radio relay of scientific data to Earth from an exploratory airplane flying in the atmosphere of Mars.
Proof in Transformation Geometry
ERIC Educational Resources Information Center
Bell, A. W.
1971-01-01
The first of three articles showing how inductively-obtained results in transformation geometry may be organized into a deductive system. This article discusses two approaches to enlargement (dilatation), one using coordinates and the other using synthetic methods. (MM)
ERIC Educational Resources Information Center
Chern, Shiing-Shen
1990-01-01
Discussed are the major historical developments of geometry. Euclid, Descartes, Klein's Erlanger Program, Gaus and Riemann, globalization, topology, Elie Cartan, and an application to molecular biology are included as topics. (KR)
Facilitating Understandings of Geometry.
ERIC Educational Resources Information Center
Pappas, Christine C.; Bush, Sara
1989-01-01
Illustrates some learning encounters for facilitating first graders' understanding of geometry. Describes some of children's approaches using Cuisenaire rods and teacher's intervening. Presents six problems involving various combinations of Cuisenaire rods and cubes. (YP)
ERIC Educational Resources Information Center
Emenaker, Charles E.
1999-01-01
Describes a sixth-grade interdisciplinary geometry unit based on Charles Dickens's "A Christmas Carol". Focuses on finding area, volume, and perimeter, and working with estimation, decimals, and fractions in the context of making gingerbread houses. (ASK)
Software Geometry in Simulations
NASA Astrophysics Data System (ADS)
Alion, Tyler; Viren, Brett; Junk, Tom
2015-04-01
The Long Baseline Neutrino Experiment (LBNE) involves many detectors. The experiment's near detector (ND) facility, may ultimately involve several detectors. The far detector (FD) will be significantly larger than any other Liquid Argon (LAr) detector yet constructed; many prototype detectors are being constructed and studied to motivate a plethora of proposed FD designs. Whether it be a constructed prototype or a proposed ND/FD design, every design must be simulated and analyzed. This presents a considerable challenge to LBNE software experts; each detector geometry must be described to the simulation software in an efficient way which allows for multiple authors to easily collaborate. Furthermore, different geometry versions must be tracked throughout their use. We present a framework called General Geometry Description (GGD), written and developed by LBNE software collaborators for managing software to generate geometries. Though GGD is flexible enough to be used by any experiment working with detectors, we present it's first use in generating Geometry Description Markup Language (GDML) files to interface with LArSoft, a framework of detector simulations, event reconstruction, and data analyses written for all LAr technology users at Fermilab. Brett is the other of the framework discussed here, the General Geometry Description (GGD).
NASA Astrophysics Data System (ADS)
McAteer, R. T. J.
2013-06-01
When Mandelbrot, the father of modern fractal geometry, made this seemingly obvious statement he was trying to show that we should move out of our comfortable Euclidean space and adopt a fractal approach to geometry. The concepts and mathematical tools of fractal geometry provides insight into natural physical systems that Euclidean tools cannot do. The benet from applying fractal geometry to studies of Self-Organized Criticality (SOC) are even greater. SOC and fractal geometry share concepts of dynamic n-body interactions, apparent non-predictability, self-similarity, and an approach to global statistics in space and time that make these two areas into naturally paired research techniques. Further, the iterative generation techniques used in both SOC models and in fractals mean they share common features and common problems. This chapter explores the strong historical connections between fractal geometry and SOC from both a mathematical and conceptual understanding, explores modern day interactions between these two topics, and discusses how this is likely to evolve into an even stronger link in the near future.
Tautges, Timothy J.
2005-01-01
The Common Geometry Module (CGM) is a code library which provides geometry functionality used for mesh generation and other applications. This functionality includes that commonly found in solid modeling engines, like geometry creation, query and modification; CGM also includes capabilities not commonly found in solid modeling engines, like geometry decomposition tools and support for shared material interfaces. CGM is built upon the ACIS solid modeling engine, but also includes geometry capability developed beside and on top of ACIS. CGM can be used as-is to provide geometry functionality for codes needing this capability. However, CGM can also be extended using derived classes in C++, allowing the geometric model to serve as the basis for other applications, for example mesh generation. CGM is supported on Sun Solaris, SGI, HP, IBM, DEC, Linux and Windows NT platforms. CGM also indudes support for loading ACIS models on parallel computers, using MPI-based communication. Future plans for CGM are to port it to different solid modeling engines, including Pro/Engineer or SolidWorks. CGM is being released into the public domain under an LGPL license; the ACIS-based engine is available to ACIS licensees on request.
Integrable Background Geometries
NASA Astrophysics Data System (ADS)
Calderbank, David M. J.
2014-03-01
This work has its origins in an attempt to describe systematically the integrable geometries and gauge theories in dimensions one to four related to twistor theory. In each such dimension, there is a nondegenerate integrable geometric structure, governed by a nonlinear integrable differential equation, and each solution of this equation determines a background geometry on which, for any Lie group G, an integrable gauge theory is defined. In four dimensions, the geometry is selfdual conformal geometry and the gauge theory is selfdual Yang-Mills theory, while the lower-dimensional structures are nondegenerate (i.e., non-null) reductions of this. Any solution of the gauge theory on a k-dimensional geometry, such that the gauge group H acts transitively on an ℓ-manifold, determines a (k+ℓ)-dimensional geometry (k+ℓ≤4) fibering over the k-dimensional geometry with H as a structure group. In the case of an ℓ-dimensional group H acting on itself by the regular representation, all (k+ℓ)-dimensional geometries with symmetry group H are locally obtained in this way. This framework unifies and extends known results about dimensional reductions of selfdual conformal geometry and the selfdual Yang-Mills equation, and provides a rich supply of constructive methods. In one dimension, generalized Nahm equations provide a uniform description of four pole isomonodromic deformation problems, and may be related to the {SU}(∞) Toda and dKP equations via a hodograph transformation. In two dimensions, the {Diff}(S^1) Hitchin equation is shown to be equivalent to the hyperCR Einstein-Weyl equation, while the {SDiff}(Σ^2) Hitchin equation leads to a Euclidean analogue of Plebanski's heavenly equations. In three and four dimensions, the constructions of this paper help to organize the huge range of examples of Einstein-Weyl and selfdual spaces in the literature, as well as providing some new ! ones. The nondegenerate reductions have a long ancestry. More ! recently
NASA Astrophysics Data System (ADS)
Vassiliou, Peter J.
2009-10-01
Cartan's method of moving frames is briefly recalled in the context of immersed curves in the homogeneous space of a Lie group G. The contact geometry of curves in low dimensional equi-affine geometry is then made explicit. This delivers the complete set of invariant data which solves the G-equivalence problem via a straightforward procedure, and which is, in some sense a supplement to the equivariant method of Fels and Olver. Next, the contact geometry of curves in general Riemannian manifolds (M,g) is described. For the special case in which the isometries of (M,g) act transitively, it is shown that the contact geometry provides an explicit algorithmic construction of the differential invariants for curves in M. The inputs required for the construction consist only of the metric g and a parametrisation of structure group SO(n); the group action is not required and no integration is involved. To illustrate the algorithm we explicitly construct complete sets of differential invariants for curves in the Poincaré half-space H3 and in a family of constant curvature 3-metrics. It is conjectured that similar results are possible in other Cartan geometries.
Frolov, Vadim A; Escalada, Artur; Akimov, Sergey A; Shnyrova, Anna V
2015-01-01
Cellular membranes define the functional geometry of intracellular space. Formation of new membrane compartments and maintenance of complex organelles require division and disconnection of cellular membranes, a process termed membrane fission. Peripheral membrane proteins generally control membrane remodeling during fission. Local membrane stresses, reflecting molecular geometry of membrane-interacting parts of these proteins, sum up to produce the key membrane geometries of fission: the saddle-shaped neck and hour-glass hemifission intermediate. Here, we review the fundamental principles behind the translation of molecular geometry into membrane shape and topology during fission. We emphasize the central role the membrane insertion of specialized protein domains plays in orchestrating fission in vitro and in cells. We further compare individual to synergistic action of the membrane insertion during fission mediated by individual protein species, proteins complexes or membrane domains. Finally, we describe how local geometry of fission intermediates defines the functional design of the protein complexes catalyzing fission of cellular membranes. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.
Students Discovering Spherical Geometry Using Dynamic Geometry Software
ERIC Educational Resources Information Center
Guven, Bulent; Karatas, Ilhan
2009-01-01
Dynamic geometry software (DGS) such as Cabri and Geometers' Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to…
Students Discovering Spherical Geometry Using Dynamic Geometry Software
ERIC Educational Resources Information Center
Guven, Bulent; Karatas, Ilhan
2009-01-01
Dynamic geometry software (DGS) such as Cabri and Geometers' Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to…
NASA Astrophysics Data System (ADS)
Ochiai, T.; Nacher, J. C.
2011-09-01
Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.
Geometry of spinor regularization
NASA Technical Reports Server (NTRS)
Hestenes, D.; Lounesto, P.
1983-01-01
The Kustaanheimo theory of spinor regularization is given a new formulation in terms of geometric algebra. The Kustaanheimo-Stiefel matrix and its subsidiary condition are put in a spinor form directly related to the geometry of the orbit in physical space. A physically significant alternative to the KS subsidiary condition is discussed. Derivations are carried out without using coordinates.
Sliding vane geometry turbines
Sun, Harold Huimin; Zhang, Jizhong; Hu, Liangjun; Hanna, Dave R
2014-12-30
Various systems and methods are described for a variable geometry turbine. In one example, a turbine nozzle comprises a central axis and a nozzle vane. The nozzle vane includes a stationary vane and a sliding vane. The sliding vane is positioned to slide in a direction substantially tangent to an inner circumference of the turbine nozzle and in contact with the stationary vane.
ERIC Educational Resources Information Center
Cooper, Brett D.; Barger, Rita
2009-01-01
The many connections between music and mathematics are well known. The length of a plucked string determines its tone, the time signature of a piece of music is a ratio, and note durations are measured in fractions. One connection commonly overlooked is that between music and geometry--specifically, geometric transformations, including…
ERIC Educational Resources Information Center
KLIER, KATHERINE M.
PRESENTED IS A FUSED COURSE IN PLANE, SOLID, AND COORDINATE GEOMETRY. ELEMENTARY SET THEORY, LOGIC, AND THE PRINCIPLE OF SEPARATION PROVIDE UNIFYING THREADS THROUGHOUT THE TEXT. THE TWO CURRICULUM GUIDES HAVE BEEN PREPARED FOR USE WITH TWO DIFFERENT TEXTS. EITHER CURRICULUM GUIDE MAY BE USED DEPENDING UPON THE CHOICE OF THE TEACHER AND THE NEEDS…
ERIC Educational Resources Information Center
Martin, John
2010-01-01
The cycloid has been called the Helen of Geometry, not only because of its beautiful properties but also because of the quarrels it provoked between famous mathematicians of the 17th century. This article surveys the history of the cycloid and its importance in the development of the calculus.
ERIC Educational Resources Information Center
Hirata, Li Ann
Core Geometry is a course offered in the Option Y sequence of the high school mathematics program described by the Hawaii State Department of Education's guidelines. The emphasis of this course is on the general awareness and use of the relationships among points, lines, and figures in planes and space. This sample course is based on the…
Emergent Hyperbolic Network Geometry
NASA Astrophysics Data System (ADS)
Bianconi, Ginestra; Rahmede, Christoph
2017-02-01
A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links, triangles, tetrahedra etc.) that have a natural geometric interpretation. As such simplicial complexes are widely used in quantum gravity approaches that involve a discretization of spacetime. Here, by extending our knowledge of growing complex networks to growing simplicial complexes we investigate the nature of the emergent geometry of complex networks and explore whether this geometry is hyperbolic. Specifically we show that an hyperbolic network geometry emerges spontaneously from models of growing simplicial complexes that are purely combinatorial. The statistical and geometrical properties of the growing simplicial complexes strongly depend on their dimensionality and display the major universal properties of real complex networks (scale-free degree distribution, small-world and communities) at the same time. Interestingly, when the network dynamics includes an heterogeneous fitness of the faces, the growing simplicial complex can undergo phase transitions that are reflected by relevant changes in the network geometry.
Emergent Hyperbolic Network Geometry.
Bianconi, Ginestra; Rahmede, Christoph
2017-02-07
A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links, triangles, tetrahedra etc.) that have a natural geometric interpretation. As such simplicial complexes are widely used in quantum gravity approaches that involve a discretization of spacetime. Here, by extending our knowledge of growing complex networks to growing simplicial complexes we investigate the nature of the emergent geometry of complex networks and explore whether this geometry is hyperbolic. Specifically we show that an hyperbolic network geometry emerges spontaneously from models of growing simplicial complexes that are purely combinatorial. The statistical and geometrical properties of the growing simplicial complexes strongly depend on their dimensionality and display the major universal properties of real complex networks (scale-free degree distribution, small-world and communities) at the same time. Interestingly, when the network dynamics includes an heterogeneous fitness of the faces, the growing simplicial complex can undergo phase transitions that are reflected by relevant changes in the network geometry.
ERIC Educational Resources Information Center
Case, Christine L.
1991-01-01
Presented is an activity in which students make models of viruses, which allows them to visualize the shape of these microorganisms. Included are some background on viruses, the biology and geometry of viruses, directions for building viruses, a comparison of cells and viruses, and questions for students. (KR)
ERIC Educational Resources Information Center
Wares, Arsalan; Elstak, Iwan
2017-01-01
The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra…
ERIC Educational Resources Information Center
Hartz, Viggo
1981-01-01
Allowing students to use a polystyrene cutter to fashion their own three-dimensional models is suggested as a means of allowing individuals to experience problems and develop ideas related to solid geometry. A list of ideas that can lead to mathematical discovery is provided. (MP)
Emergent Hyperbolic Network Geometry
Bianconi, Ginestra; Rahmede, Christoph
2017-01-01
A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links, triangles, tetrahedra etc.) that have a natural geometric interpretation. As such simplicial complexes are widely used in quantum gravity approaches that involve a discretization of spacetime. Here, by extending our knowledge of growing complex networks to growing simplicial complexes we investigate the nature of the emergent geometry of complex networks and explore whether this geometry is hyperbolic. Specifically we show that an hyperbolic network geometry emerges spontaneously from models of growing simplicial complexes that are purely combinatorial. The statistical and geometrical properties of the growing simplicial complexes strongly depend on their dimensionality and display the major universal properties of real complex networks (scale-free degree distribution, small-world and communities) at the same time. Interestingly, when the network dynamics includes an heterogeneous fitness of the faces, the growing simplicial complex can undergo phase transitions that are reflected by relevant changes in the network geometry. PMID:28167818
ERIC Educational Resources Information Center
Hartz, Viggo
1981-01-01
Allowing students to use a polystyrene cutter to fashion their own three-dimensional models is suggested as a means of allowing individuals to experience problems and develop ideas related to solid geometry. A list of ideas that can lead to mathematical discovery is provided. (MP)
ERIC Educational Resources Information Center
Cooper, Brett D.; Barger, Rita
2009-01-01
The many connections between music and mathematics are well known. The length of a plucked string determines its tone, the time signature of a piece of music is a ratio, and note durations are measured in fractions. One connection commonly overlooked is that between music and geometry--specifically, geometric transformations, including…
Hsü, K J; Hsü, A J
1990-01-01
Music critics have compared Bach's music to the precision of mathematics. What "mathematics" and what "precision" are the questions for a curious scientist. The purpose of this short note is to suggest that the mathematics is, at least in part, Mandelbrot's fractal geometry and the precision is the deviation from a log-log linear plot. PMID:11607061
Teaching Geometry with Tangrams.
ERIC Educational Resources Information Center
Russell, Dorothy S.; Bologna, Elaine M.
1982-01-01
Geometry is viewed as the most neglected area of the elementary school mathematics curriculum. Tangram activities provide numerous worthwhile mathematical experiences for children. A method of constructing tangrams through paper folding is followed by suggested spatial visualization, measurement, and additional activities. (MP)
ERIC Educational Resources Information Center
Fielker, David
2007-01-01
Geoff Giles died suddenly in 2005. He was a highly original thinker in the field of geometry teaching. As early as 1964, when teaching at Strathallen School in Perth, he was writing in "MT27" about constructing tessellations by modifying the sides of triangles and (irregular) quadrilaterals to produce what he called "trisides" and "quadrisides".…
ERIC Educational Resources Information Center
Wares, Arsalan; Elstak, Iwan
2017-01-01
The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra…
ERIC Educational Resources Information Center
Case, Christine L.
1991-01-01
Presented is an activity in which students make models of viruses, which allows them to visualize the shape of these microorganisms. Included are some background on viruses, the biology and geometry of viruses, directions for building viruses, a comparison of cells and viruses, and questions for students. (KR)
ERIC Educational Resources Information Center
MacKeown, P. K.
1984-01-01
Clarifies two concepts of gravity--those of a fictitious force and those of how space and time may have geometry. Reviews the position of Newton's theory of gravity in the context of special relativity and considers why gravity (as distinct from electromagnetics) lends itself to Einstein's revolutionary interpretation. (JN)
Atiyah, Michael; Dijkgraaf, Robbert; Hitchin, Nigel
2010-01-01
We review the remarkably fruitful interactions between mathematics and quantum physics in the past decades, pointing out some general trends and highlighting several examples, such as the counting of curves in algebraic geometry, invariants of knots and four-dimensional topology. PMID:20123740
ERIC Educational Resources Information Center
Fielker, David
2007-01-01
Geoff Giles died suddenly in 2005. He was a highly original thinker in the field of geometry teaching. As early as 1964, when teaching at Strathallen School in Perth, he was writing in "MT27" about constructing tessellations by modifying the sides of triangles and (irregular) quadrilaterals to produce what he called "trisides" and "quadrisides".…
ERIC Educational Resources Information Center
MacKeown, P. K.
1984-01-01
Clarifies two concepts of gravity--those of a fictitious force and those of how space and time may have geometry. Reviews the position of Newton's theory of gravity in the context of special relativity and considers why gravity (as distinct from electromagnetics) lends itself to Einstein's revolutionary interpretation. (JN)
Advanced geometries and regimes
Bulanov, S. S.; Bulanov, S. V.; Turchetti, G.; Limpouch, J.; Klimo, O.; Psikal, J.; Margarone, D.; Korn, G.
2013-07-26
We review and discuss different schemes of laser ion acceleration as well as advanced target geometries in connection with the development of the laser-driven proton source for hadron therapy of oncological diseases, which is a part of the ELIMED project.
NASA Astrophysics Data System (ADS)
Zhang, Zhao; Liu, Liyuan; Feng, Peng; Liu, Jian; Wu, Nanjian
2016-04-01
In this paper, we propose a compact ring-oscillator-based self-biased phase-locked loop (SBPLL) for system-on-chip (SoC) clock generation. It adopts the proposed triple-well NMOS source degeneration voltage-to-current (V-I) converter instead of the operational amplifier (OPAMP) based V-I converter and a proposed simple start-up circuit with a negligible area to save power and area. The SBPLL is implemented in the 0.18 µm CMOS process, and it occupies 0.048 mm2 active core. The measurement results show the SBPLL can generate output frequency in a wide range from 300 MHz to 1.125 GHz with a constant loop bandwidth that is around 5 MHz and a relatively low jitter performance that is less than 4.9 mUI over the entire covered frequency range. From -20 to 70 °C the rms jitter variation and loop bandwidth variation at 1.125 GHz are 0.2 ps and 350 kHz, respectively. The rms jitter performance variation of all covered frequency points is less than 10% in the supply range from 1.5 to 1.7 V. Such SBPLL shows robustness over environmental variation. The maximum power consumption is 5.6 mW with 1.6 V supply at an output frequency of 1.125 GHz.
Geometry of thermodynamic control.
Zulkowski, Patrick R; Sivak, David A; Crooks, Gavin E; DeWeese, Michael R
2012-10-01
A deeper understanding of nonequilibrium phenomena is needed to reveal the principles governing natural and synthetic molecular machines. Recent work has shown that when a thermodynamic system is driven from equilibrium then, in the linear response regime, the space of controllable parameters has a Riemannian geometry induced by a generalized friction tensor. We exploit this geometric insight to construct closed-form expressions for minimal-dissipation protocols for a particle diffusing in a one-dimensional harmonic potential, where the spring constant, inverse temperature, and trap location are adjusted simultaneously. These optimal protocols are geodesics on the Riemannian manifold and reveal that this simple model has a surprisingly rich geometry. We test these optimal protocols via a numerical implementation of the Fokker-Planck equation and demonstrate that the friction tensor arises naturally from a first-order expansion in temporal derivatives of the control parameters, without appealing directly to linear response theory.
Cylindrical geometry hall thruster
Raitses, Yevgeny; Fisch, Nathaniel J.
2002-01-01
An apparatus and method for thrusting plasma, utilizing a Hall thruster with a cylindrical geometry, wherein ions are accelerated in substantially the axial direction. The apparatus is suitable for operation at low power. It employs small size thruster components, including a ceramic channel, with the center pole piece of the conventional annular design thruster eliminated or greatly reduced. Efficient operation is accomplished through magnetic fields with a substantial radial component. The propellant gas is ionized at an optimal location in the thruster. A further improvement is accomplished by segmented electrodes, which produce localized voltage drops within the thruster at optimally prescribed locations. The apparatus differs from a conventional Hall thruster, which has an annular geometry, not well suited to scaling to small size, because the small size for an annular design has a great deal of surface area relative to the volume.
NASA Astrophysics Data System (ADS)
Cederwall, Martin; Rosabal, J. A.
2015-07-01
We investigate exceptional generalised diffeomorphisms based on E 8(8) in a geometric setting. The transformations include gauge transformations for the dual gravity field. The surprising key result, which allows for a development of a tensor formalism, is that it is possible to define field-dependent transformations containing connection, which are covariant. We solve for the spin connection and construct a curvature tensor. A geometry for the Ehlers symmetry SL( n + 1) is sketched. Some related issues are discussed.
Emergent geometry, emergent forces
NASA Astrophysics Data System (ADS)
Selesnick, S. A.
2017-10-01
We give a brief account of some aspects of Finkelstein’s quantum relativity, namely an extension of it that derives elements of macroscopic geometry and the Lagrangians of the standard model including gravity from a presumed quantum version of spacetime. These emerge as collective effects in this quantal substrate. Our treatment, which is largely self-contained, differs mathematically from that originally given by Finkelstein. Dedicated to the memory of David Ritz Finkelstein
Freezing in confined geometries
NASA Technical Reports Server (NTRS)
Sokol, P. E.; Ma, W. J.; Herwig, K. W.; Snow, W. M.; Wang, Y.; Koplik, Joel; Banavar, Jayanth R.
1992-01-01
Results of detailed structural studies, using elastic neutron scattering, of the freezing of liquid O2 and D2 in porous vycor glass, are presented. The experimental studies have been complemented by computer simulations of the dynamics of freezing of a Lennard-Jones liquid in narrow channels bounded by molecular walls. Results point to a new simple physical interpretation of freezing in confined geometries.
Freezing in confined geometries
NASA Technical Reports Server (NTRS)
Sokol, P. E.; Ma, W. J.; Herwig, K. W.; Snow, W. M.; Wang, Y.; Koplik, Joel; Banavar, Jayanth R.
1992-01-01
Results of detailed structural studies, using elastic neutron scattering, of the freezing of liquid O2 and D2 in porous vycor glass, are presented. The experimental studies have been complemented by computer simulations of the dynamics of freezing of a Lennard-Jones liquid in narrow channels bounded by molecular walls. Results point to a new simple physical interpretation of freezing in confined geometries.
Integral geometry and holography
Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; Sully, James
2015-10-27
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS_{3}/CFT_{2} correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS_{3} whose kinematic space is two-dimensional de Sitter space.
Noncommutative geometry and arithmetics
NASA Astrophysics Data System (ADS)
Almeida, P.
2009-09-01
We intend to illustrate how the methods of noncommutative geometry are currently used to tackle problems in class field theory. Noncommutative geometry enables one to think geometrically in situations in which the classical notion of space formed of points is no longer adequate, and thus a “noncommutative space” is needed; a full account of this approach is given in [3] by its main contributor, Alain Connes. The class field theory, i.e., number theory within the realm of Galois theory, is undoubtedly one of the main achievements in arithmetics, leading to an important algebraic machinery; for a modern overview, see [23]. The relationship between noncommutative geometry and number theory is one of the many themes treated in [22, 7-9, 11], a small part of which we will try to put in a more down-to-earth perspective, illustrating through an example what should be called an “application of physics to mathematics,” and our only purpose is to introduce nonspecialists to this beautiful area.
NASA Astrophysics Data System (ADS)
Beggs, Edwin J.; Majid, Shahn
2017-04-01
We study noncommutative bundles and Riemannian geometry at the semiclassical level of first order in a deformation parameter λ, using a functorial approach. This leads us to field equations of 'Poisson-Riemannian geometry' between the classical metric, the Poisson bracket and a certain Poisson-compatible connection needed as initial data for the quantisation of the differential structure. We use such data to define a functor Q to O(λ2) from the monoidal category of all classical vector bundles equipped with connections to the monoidal category of bimodules equipped with bimodule connections over the quantised algebra. This is used to 'semiquantise' the wedge product of the exterior algebra and in the Riemannian case, the metric and the Levi-Civita connection in the sense of constructing a noncommutative geometry to O(λ2) . We solve our field equations for the Schwarzschild black-hole metric under the assumption of spherical symmetry and classical dimension, finding a unique solution and the necessity of nonassociativity at order λ2, which is similar to previous results for quantum groups. The paper also includes a nonassociative hyperboloid, nonassociative fuzzy sphere and our previously algebraic bicrossproduct model.
Emergent Complex Network Geometry
Wu, Zhihao; Menichetti, Giulia; Rahmede, Christoph; Bianconi, Ginestra
2015-01-01
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant for routing problems, inference and data mining. In real growing networks, topological, structural and geometrical properties emerge spontaneously from their dynamical rules. Nevertheless we still miss a model in which networks develop an emergent complex geometry. Here we show that a single two parameter network model, the growing geometrical network, can generate complex network geometries with non-trivial distribution of curvatures, combining exponential growth and small-world properties with finite spectral dimensionality. In one limit, the non-equilibrium dynamical rules of these networks can generate scale-free networks with clustering and communities, in another limit planar random geometries with non-trivial modularity. Finally we find that these properties of the geometrical growing networks are present in a large set of real networks describing biological, social and technological systems. PMID:25985280
Integral geometry and holography
Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; ...
2015-10-27
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS3/CFT2 correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulkmore » curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS3 whose kinematic space is two-dimensional de Sitter space.« less
Graded geometry and Poisson reduction
Cattaneo, A. S.; Zambon, M.
2009-02-02
The main result extends the Marsden-Ratiu reduction theorem in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof. Further, we provide an alternative algebraic proof for the main result.
Computer-Aided Geometry Modeling
NASA Technical Reports Server (NTRS)
Shoosmith, J. N. (Compiler); Fulton, R. E. (Compiler)
1984-01-01
Techniques in computer-aided geometry modeling and their application are addressed. Mathematical modeling, solid geometry models, management of geometric data, development of geometry standards, and interactive and graphic procedures are discussed. The applications include aeronautical and aerospace structures design, fluid flow modeling, and gas turbine design.
Teaching of Geometry in Bulgaria
ERIC Educational Resources Information Center
Bankov, Kiril
2013-01-01
Geometry plays an important role in the school mathematics curriculum all around the world. Teaching of geometry varies a lot (Hoyls, Foxman, & Kuchemann, 2001). Many countries revise the objectives, the content, and the approaches to the geometry in school. Studies of the processes show that there are not common trends of these changes…
Geometrie verstehen: statisch - kinematisch
NASA Astrophysics Data System (ADS)
Kroll, Ekkehard
Dem Allgemeinen steht begrifflich das Besondere gegenüber. In diesem Sinne sind allgemeine Überlegungen zum Verstehen von Mathematik zu ergänzen durch Untersuchungen hinsichtlich des Verstehens der einzelnen mathematischen Disziplinen, insbesondere der Geometrie. Hier haben viele Schülerinnen und Schüler Probleme. Diese rühren hauptsächlich daher, dass eine fertige geometrische Konstruktion in ihrer statischen Präsentation auf Papier nicht mehr die einzelnen Konstruktionsschritte erkennen lässt; zum Nachvollzug müssen sie daher ergänzend in einer Konstruktionsbeschreibung festgehalten werden.
Gillespie, Ronald J; Robinson, Edward A
2005-05-01
Although the structure of almost any molecule can now be obtained by ab initio calculations chemists still look for simple answers to the question "What determines the geometry of a given molecule?" For this purpose they make use of various models such as the VSEPR model and qualitative quantum mechanical models such as those based on the valence bond theory. The present state of such models, and the support for them provided by recently developed methods for analyzing calculated electron densities, are reviewed and discussed in this tutorial review.
NASA Astrophysics Data System (ADS)
Calcagni, Gianluca
2012-08-01
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is controlled by a multiscale fractional diffusion equation, and physically interpreted as a composite stochastic process. The simplest example is a fractional telegraph process, describing quantum spacetimes with a spectral dimension equal to 2 in the ultraviolet and monotonically rising to 4 towards the infrared. The general profile of the spectral dimension of the recently introduced multifractional spaces is constructed for the first time.
Dillon, Moira R.; Spelke, Elizabeth S.
2015-01-01
Research on animals, infants, children, and adults provides evidence that distinct cognitive systems underlie navigation and object recognition. Here we examine whether and how these systems interact when children interpret 2D edge-based perspectival line drawings of scenes and objects. Such drawings serve as symbols early in development, and they preserve scene and object geometry from canonical points of view. Young children show limits when using geometry both in non-symbolic tasks and in symbolic map tasks that present 3D contexts from unusual, unfamiliar points of view. When presented with the familiar viewpoints in perspectival line drawings, however, do children engage more integrated geometric representations? In three experiments, children successfully interpreted line drawings with respect to their depicted scene or object. Nevertheless, children recruited distinct processes when navigating based on the information in these drawings, and these processes depended on the context in which the drawings were presented. These results suggest that children are flexible but limited in using geometric information to form integrated representations of scenes and objects, even when interpreting spatial symbols that are highly familiar and faithful renditions of the visual world. PMID:25441089
Proterozoic Geomagnetic Field Geometry
NASA Astrophysics Data System (ADS)
Panzik, J. E.; Evans, D. A.
2011-12-01
Pre-Mesozoic continental reconstructions and paleoclimatic inferences from paleomagnetism rely critically upon the assumption of a time-averaged geocentric axial dipole (GAD) magnetic field. We have been testing the GAD assumption and localized non-dipole components in a different manner, by observing directional variations within the Matachewan, Mackenzie and Franklin dyke swarms. Large dyke swarms, commonly emplaced within a few million years, provide the necessary broad areal coverage to perform a test of global geomagnetic field geometry. Our analysis varies the quadrupole and octupole values of the generalized paleolatitude equation to determine a minimal angular dispersion and maximum precision of paleopoles from each dyke swarm. As a control, paleomagnetic data from the central Atlantic magmatic province (CAMP) show the sensitivities of our method to non-GAD contributions to the ancient geomagnetic field. Within the uncertainties, CAMP data are consistent with independent estimates of non-GAD contributions derived from global tectonic reconstructions (Torsvik & Van der Voo, 2002). Current results from the three Proterozoic dyke swarms all have best fits that are non-dipolar, but they differ in their optimal quadrupole/ octupole components. Treated together under the hypothesis of a static Proterozoic field geometry, the data allow a pure GAD geodynamo within the uncertainty of the method. Current results were performed using Fisherian statistics, but Bingham statistics will be included to account for the ellipticity of data.
NASA Astrophysics Data System (ADS)
Marmo, G.; Morandi, G.
The following sections are included: * INTRODUCTION * HOMOTOPY AND TOPOLOGICAL INVARIANTS * THE DUALITY BETWEEN 𝕄 AND F({{M}}) * DIFFERENTIAL CALCULUS ON LIE GROUPS AND COSET SPACES * FIBER SPACES AND PARALLEL TRANSPORT * DIFFERENTIAL CALCULUS ON FIBER BUNDLES * SEQUENCES ON PRINCIPAL BUNDLES. CHERN-SIMONS TERMS * CONCLUSIONS * ACKNOWLEDGEMENTS * APPENDIX * GLOSSARIES. I. TOPOLOGICAL TERMS * GLOSSARIES. II. ALGEBRAIC TERMS * REFERENCES
Critique of information geometry
Skilling, John
2014-12-05
As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to destination p. Because the only compatible connective H is from≠to asymmetric, H(p;q)≠H(q;p), there can be no compatible geometrical distance (which would necessarily be from=to symmetric). Hence there is no distance relationship compatible with the structure of probability theory. Metrics g and densities sqrt(det(g)) interpreted as prior probabilities follow from the definition of distance, and must fail likewise. Various metrics and corresponding priors have been proposed, Fisher's being the most popular, but all must behave unacceptably. This is illustrated with simple counter-examples.
Noncommutative geometry of Zitterbewegung
NASA Astrophysics Data System (ADS)
Eckstein, Michał; Franco, Nicolas; Miller, Tomasz
2017-03-01
Drawing from the advanced mathematics of noncommutative geometry, we model a "classical" Dirac fermion propagating in a curved spacetime. We demonstrate that the inherent causal structure of the model encodes the possibility of Zitterbewegung—the "trembling motion" of the fermion. We recover the well-known frequency of Zitterbewegung as the highest possible speed of change in the fermion's "internal space." Furthermore, we show that the bound does not change in the presence of an external electromagnetic field and derive its explicit analogue when the mass parameter is promoted to a Yukawa field. We explain the universal character of the model and discuss a table-top experiment in the domain of quantum simulation to test its predictions.
Correa, Diego H.; Silva, Guillermo A.
2008-07-28
We discuss how geometrical and topological aspects of certain (1/2)-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents.
Magnetism in curved geometries
Streubel, Robert; Fischer, Peter; Kronast, Florian; ...
2016-08-17
Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisymmetric exchange, i.e. Dzyaloshinskii–Moriya-like interaction. Asmore » a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topologically induced magnetization patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered physical properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addition to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. Finally, these recent developments ranging from theoretical predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomography approaches are in the focus of this review.« less
Magnetism in curved geometries
Streubel, Robert; Fischer, Peter; Kronast, Florian; Kravchuk, Volodymyr P.; Sheka, Denis D.; Gaididei, Yuri; Schmidt, Oliver G.; Makarov, Denys
2016-08-17
Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisymmetric exchange, i.e. Dzyaloshinskii–Moriya-like interaction. As a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topologically induced magnetization patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered physical properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addition to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. Finally, these recent developments ranging from theoretical predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomography approaches are in the focus of this review.
Magnetism in curved geometries
NASA Astrophysics Data System (ADS)
Streubel, Robert; Fischer, Peter; Kronast, Florian; Kravchuk, Volodymyr P.; Sheka, Denis D.; Gaididei, Yuri; Schmidt, Oliver G.; Makarov, Denys
2016-09-01
Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisymmetric exchange, i.e. Dzyaloshinskii-Moriya-like interaction. As a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topologically induced magnetization patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered physical properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addition to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. These recent developments ranging from theoretical predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomography approaches are in the focus of this review.
NASA Astrophysics Data System (ADS)
Gualtieri, Marco
2014-10-01
Generalized Kähler geometry is the natural analogue of Kähler geometry, in the context of generalized complex geometry. Just as we may require a complex structure to be compatible with a Riemannian metric in a way which gives rise to a symplectic form, we may require a generalized complex structure to be compatible with a metric so that it defines a second generalized complex structure. We prove that generalized Kähler geometry is equivalent to the bi-Hermitian geometry on the target of a 2-dimensional sigma model with (2, 2) supersymmetry. We also prove the existence of natural holomorphic Courant algebroids for each of the underlying complex structures, and that these split into a sum of transverse holomorphic Dirac structures. Finally, we explore the analogy between pre-quantum line bundles and gerbes in the context of generalized Kähler geometry.
Thermodynamics of Asymptotically Conical Geometries.
Cvetič, Mirjam; Gibbons, Gary W; Saleem, Zain H
2015-06-12
We study the thermodynamical properties of a class of asymptotically conical geometries known as "subtracted geometries." We derive the mass and angular momentum from the regulated Komar integral and the Hawking-Horowitz prescription and show that they are equivalent. By deriving the asymptotic charges, we show that the Smarr formula and the first law of thermodynamics hold. We also propose an analog of Christodulou-Ruffini inequality. The analysis can be generalized to other asymptotically conical geometries.
Planetary Image Geometry Library
NASA Technical Reports Server (NTRS)
Deen, Robert C.; Pariser, Oleg
2010-01-01
The Planetary Image Geometry (PIG) library is a multi-mission library used for projecting images (EDRs, or Experiment Data Records) and managing their geometry for in-situ missions. A collection of models describes cameras and their articulation, allowing application programs such as mosaickers, terrain generators, and pointing correction tools to be written in a multi-mission manner, without any knowledge of parameters specific to the supported missions. Camera model objects allow transformation of image coordinates to and from view vectors in XYZ space. Pointing models, specific to each mission, describe how to orient the camera models based on telemetry or other information. Surface models describe the surface in general terms. Coordinate system objects manage the various coordinate systems involved in most missions. File objects manage access to metadata (labels, including telemetry information) in the input EDRs and RDRs (Reduced Data Records). Label models manage metadata information in output files. Site objects keep track of different locations where the spacecraft might be at a given time. Radiometry models allow correction of radiometry for an image. Mission objects contain basic mission parameters. Pointing adjustment ("nav") files allow pointing to be corrected. The object-oriented structure (C++) makes it easy to subclass just the pieces of the library that are truly mission-specific. Typically, this involves just the pointing model and coordinate systems, and parts of the file model. Once the library was developed (initially for Mars Polar Lander, MPL), adding new missions ranged from two days to a few months, resulting in significant cost savings as compared to rewriting all the application programs for each mission. Currently supported missions include Mars Pathfinder (MPF), MPL, Mars Exploration Rover (MER), Phoenix, and Mars Science Lab (MSL). Applications based on this library create the majority of operational image RDRs for those missions. A
Investigating Fractal Geometry Using LOGO.
ERIC Educational Resources Information Center
Thomas, David A.
1989-01-01
Discusses dimensionality in Euclidean geometry. Presents methods to produce fractals using LOGO. Uses the idea of self-similarity. Included are program listings and suggested extension activities. (MVL)
TIPS geometry influences patency.
Klasen-Sansone, J; Bode, J; Lanzman, R S; Kubitz, R; Immig, S; Heusch, P; Antoch, G; Häussinger, D; Blondin, D
2015-01-01
The purpose of this study was to evaluate potential causes of Transjugular intrahepatic portosystemic shunt (TIPS) dysfunction. We retrospectively evaluated 26 patients who required TIPS revision (group I) and 24 patients who did not require any further intervention (group II) within the first two years following TIPS implantation. The distance of the distal end of the stent to the hepatocaval junction was measured. Furthermore, the angle between the stent and the portal vein (inflow) and the angle between the stent and the hepatic vein (outflow) were measured. Furthermore, the following data were evaluated: pre- and postinterventional portal pressure gradients, maximal postinterventional flow and blood values [C-reactive protein (CRP), bilirubin, glutamic-oxaloacetic transaminase (GOT), glutamic-pyruvic transaminase (GPT)]. Compared with control subjects, patients who required TIPS revision showed a significantly longer distance from the distal end of the stent to the hepatocaval junction (I: 17.3 ± 10 mm, II: 6.7 ± 5.7 mm, p < 0.001). There was a statistically significant correlation between the above named distance and the time to revision (Pearson's correlation coefficient, r = 0.5, p = 0.01). In addition, patients with TIPS revision had a significantly larger angle of portalvenous inflow (alpha angle) than the control group (I: 100.5 ± 31.5°, II: 64.5 ± 31.6°, p < 0.001). Our results show that the distance from the end of the stent to the hepatocaval junction and the angle of portalvenous inflow are technical factors that may influence the shunt's patency rate. Of these two, the distance to the hepatocaval junction can be influenced easily by the interventionalist. © Georg Thieme Verlag KG Stuttgart · New York.
Kligfield, R.; Geiser, P.; Geiser, J.
1985-01-01
Blind thrusts are structures which at no time in their history broke the erosion surface and along which displacement progressively changes upwards. Faults of the stiff layer along which displacement progressively decreases to zero (tip) are one prominent type of blind thrust structure. Shortening above such tips is accommodated entirely by folding whereas shortening below the tip is partitioned between folding and faulting. For these types of faults it is possible to determine the original length of the stiff layer for balancing purposes. A systematic methodology for line length and area restoration is outlined for determining blind thrust geometry. Application of the methodology is particularly suitable for use with microcomputers. If the folded form of the cover is known along with the position of the fault and its tip, then it is possible to locate hanging and footwall cutoffs. If the fault trajectory, tip, and a single hanging wall footwall cutoff pair are known, then the folded form of the cover layer can be determined. In these constructions it is necessary to specify pin lines for balancing purposes. These pin lines may or may not have a zero displacement gradient, depending upon the amount of simple shear deformation. Examples are given from both Laramide structures of the western USA and the Appalachians.
Conformal Lorentz geometry revisited
NASA Astrophysics Data System (ADS)
Teleman, Kostake
1996-02-01
. We also show that Mach's principle on inertial motions receives an explanation in our theory by considering the particular geodesic paths, for which one of the partners of an interacting pair is fixed and sent to infinity. In fact we study a dynamical system (W,L) which presents some formal and topological similarities with a system of two particles interacting gravitationally. (W,L) is the only conformally invariant relativistic two-point dynamical system. At the end we show that W can be naturally regarded as the base of a principal GL(2,C)-bundle which comes with a natural connection. We study this bundle from differential geometric point of view. Physical interpretations will be discussed in a future paper. This text is an improvement of a previous version, which was submitted under the title ``Hypertwistor Geometry.'' [See, K. Teleman, ``Hypertwistor Geometry (abstract),'' 14th International Conference on General Relativity and Gravitation, Florence, Italy, 1995.] The change of the title and many other improvements are due to the valuable comments of the referee, who also suggested the author to avoid hazardous interpretations.
GPS: Geometry, Probability, and Statistics
ERIC Educational Resources Information Center
Field, Mike
2012-01-01
It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…
Sex Differences in Geometry Achievement.
ERIC Educational Resources Information Center
Dees, Roberta L.
The following questions are addressed: (1) Are there sex differences in achievement, either in entering knowledge of geometry in the fall, or in achievement in acquiring standard geometry content by year's end? (2) Are there sex differences in the performance of students on the van Hiele test, either at the beginning or end of the year? and (3)…
GPS: Geometry, Probability, and Statistics
ERIC Educational Resources Information Center
Field, Mike
2012-01-01
It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…
Linguistic geometry for autonomous navigation
Stilman, B.
1995-09-01
To discover the inner properties of human expert heuristics, which were successful in a certain class of complex control systems, we develop a formal theory, the Linguistic Geometry. This paper reports two examples of application of Linguistic Geometry to autonomous navigation of aerospace vehicles that demonstrate dramatic search reduction.
The Application of Mechanics to Geometry. Popular Lectures in Mathematics.
ERIC Educational Resources Information Center
Kogan, B. Yu
Presented in this translation are three chapters. Chapter I discusses the composition of forces and several theorems of geometry are proved using the fundamental concepts and certain laws of statics. Chapter II discusses the perpetual motion postulate; several geometric theorems are proved using the postulate that perpetual motion is impossible.…
NASA Astrophysics Data System (ADS)
Belogurov, S.; Berchun, Yu; Chernogorov, A.; Malzacher, P.; Ovcharenko, E.; Semennikov, A.
2011-12-01
Due to conceptual difference between geometry descriptions in Computer-Aided Design (CAD) systems and particle transport Monte Carlo (MC) codes direct conversion of detector geometry in either direction is not feasible. An original set of tools has been developed for building a GEANT4/ROOT compatible geometry in the CATIA CAD system and exchanging it with mentioned MC packages using GDML file format. A Special structure of a CATIA product tree, a wide range of primitives, different types of multiple volume instantiation, and supporting macros have been implemented.
An improved combinatorial geometry model for arbitrary geometry in DSMC
NASA Astrophysics Data System (ADS)
Kargaran, H.; Minuchehr, A.; Zolfaghari, A.
2017-03-01
This paper focuses on a new direct simulation Monte Carlo (DSMC) code based on combinatorial geometry (CG) for simulation of any rarefied gas flow. The developed code, called DgSMC-A, has been supplied with an improved CG modeling able to significantly optimize the particle-tracking process, resulting in a highly reduced runtime compared to the conventional codes. The improved algorithm inserts a grid over the geometry and saves those grid elements containing some part of the geometry border. Since only a small part of a grid is engaged with the geometry border, significant time can be saved using the proposed algorithm. Embedding the modified algorithm in the DgSMC-A resulted in a fast, robust and self-governing code needless to any mesh generator. The code completely handles complex geometries created with first-and second-order surfaces. In addition, we developed a new surface area calculator in the CG methodology for complex geometries based on the Monte Carlo method with acceptable accuracy. Several well-known test cases are examined to indicate the code ability to deal with a wide range of realistic problems. Results are also found to be in good agreement with references and experimental data.
Isobe, H; Shoji, M; Yamanaka, S; Umena, Y; Kawakami, K; Kamiya, N; Shen, J-R; Yamaguchi, K
2012-11-28
Full geometry optimizations of several inorganic model clusters, CaMn(4)O(4)XYZ(H(2)O)(2) (X, Y, Z = H(2)O, OH(-) or O(2-)), by the use of the B3LYP hybrid density functional theory (DFT) have been performed to illuminate plausible molecular structures of the catalytic site for water oxidation in the S(0), S(1), S(2) and S(3) states of the Kok cycle for the oxygen-evolving complex (OEC) of photosystem II (PSII). Optimized geometries obtained by the energy gradient method have revealed the degree of symmetry breaking of the unstable three-center Mn(a)-X-Mn(d) bond in CaMn(4)O(4)XYZ(H(2)O)(2). The right-elongated (R) Mn(a)-X···Mn(d) and left-elongated (L) Mn(a)···X-Mn(d) structures appear to occupy local minima on a double-well potential for several key intermediates in these states. The effects of insertion of one extra water molecule to the vacant coordination site, Mn(d) (Mn(a)), for R (L) structures have also been examined in detail. The greater stability of the L-type structure over the R-type has been concluded for key intermediates in the S(2) and S(3) states. Implications of the present DFT structures are discussed in relation to previous DFT and related results, together with recent X-ray diffraction results for model compounds of cubane-like OEC cluster of PSII.
Chandra, Sulekh; Kumar, Anil
2007-11-01
Mn(II), Co(II), Ni(II) and Cu(II) complexes are synthesized with thiosemicarbazone (L) derived from pyrrole-2-carboxyaldehyde. These complexes are characterized by elemental analysis, molar conductance, magnetic susceptibility measurement, mass, IR, electronic and EPR spectral studies. The molar conductance measurement of the complexes in DMSO indicates that the complexes are non-electrolyte except Co(L)2(NO3)2 and Ni(L)2(NO3)2 complexes which are 1:2 electrolyte. All the complexes are of high-spin type. On the basis of spectral studies an octahedral geometry may be assigned for Mn(II), Co(II) and Ni(II) complexes except Co(L)2(NO3)2 and Ni(L)2(NO3)2 which are of tetrahedral geometry. A tetragonal geometry may be suggested for Cu(II) complexes.
NASA Astrophysics Data System (ADS)
Lotay, Jason
2017-04-01
Jason Lotay explains how mathematicians studying special geometries are collaborating with physicists to explore M-theory, an 11-dimensional description of the world that unifies the various string theories
Emergent geometry from quantized spacetime
Yang, Hyun Seok; Sivakumar, M.
2010-08-15
We examine the picture of emergent geometry arising from a mass-deformed matrix model. Because of the mass deformation, a vacuum geometry turns out to be a constant curvature spacetime such as d-dimensional sphere and (anti-)de Sitter spaces. We show that the mass-deformed matrix model giving rise to the constant curvature spacetime can be derived from the d-dimensional Snyder algebra. The emergent geometry beautifully confirms all the rationale inferred from the algebraic point of view that the d-dimensional Snyder algebra is equivalent to the Lorentz algebra in (d+1)-dimensional flat spacetime. For example, a vacuum geometry of the mass-deformed matrix model is completely described by a G-invariant metric of coset manifolds G/H defined by the Snyder algebra. We also discuss a nonlinear deformation of the Snyder algebra.
Drift waves in stellarator geometry
Persson, M.; Nadeem, M.; Lewandowski, J.L.V.; Gardner, H.J.
2000-02-07
Drift waves are investigated in a real three-dimensional stellarator geometry. A linear system, based on the cold ion fluid model and a ballooning mode formalism, is solved numerically in the geometry of the stellarator H1-NF. The spectra of stable and unstable modes, as well as localization, are discussed. The dependence of the spectrum of the unstable modes on the wavevector, plasma density variation, and the location in the plasma is presented.
Casimir effects for classical and quantum liquids in slab geometry: A brief review
NASA Astrophysics Data System (ADS)
Biswas, Shyamal
2015-05-01
We analytically explore Casimir effects for confinement of classical and quantum fluctuations in slab (film) geometry (i) for classical (critical) fluctuations over 4He liquid around the λ point, and (ii) for quantum (phonon) fluctuations of Bogoliubov excitations over an interacting Bose-Einstein condensate. We also briefly review Casimir effects for confinement of quantum vacuum fluctuations confined to two plates of different geometries.
The Common Geometry Module (CGM).
Tautges, Timothy James
2004-12-01
The Common Geometry Module (CGM) is a code library which provides geometry functionality used for mesh generation and other applications. This functionality includes that commonly found in solid modeling engines, like geometry creation, query and modification; CGM also includes capabilities not commonly found in solid modeling engines, like geometry decomposition tools and support for shared material interfaces. CGM is built upon the ACIS solid modeling engine, but also includes geometry capability developed beside and on top of ACIS. CGM can be used as-is to provide geometry functionality for codes needing this capability. However, CGM can also be extended using derived classes in C++, allowing the geometric model to serve as the basis for other applications, for example mesh generation. CGM is supported on Sun Solaris, SGI, HP, IBM, DEC, Linux and Windows NT platforms. CGM also includes support for loading ACIS models on parallel computers, using MPI-based communication. Future plans for CGM are to port it to different solid modeling engines, including Pro/Engineer or SolidWorks. CGM is being released into the public domain under an LGPL license; the ACIS-based engine is available to ACIS licensees on request.
Emergent Geometry from Entropy and Causality
NASA Astrophysics Data System (ADS)
Engelhardt, Netta
generalizations are discussed, both at the classical and perturbatively quantum limits. In particular, several No Go Theorems are proven, indicative of a conclusion that supplementary approaches or information may be necessary to recover the full spacetime geometry. Part II of this thesis involves the relation between geometry and causality, the property that information cannot travel faster than light. Requiring this of any quantum field theory results in constraints on string theory setups that are dual to quantum field theories via the AdS/CFT correspondence. At the level of perturbative quantum gravity, it is shown that causality in the field theory constraints the causal structure in the bulk. At the level of nonperturbative quantum string theory, we find that constraints on causal signals restrict the possible ways in which curvature singularities can be resolved in string theory. Finally, a new program of research is proposed for the construction of bulk geometry from the divergences of correlation functions in the dual field theory. This divergence structure is linked to the causal structure of the bulk and of the field theory.
On The Explosion Geometry of Red Supergiant Stars
NASA Astrophysics Data System (ADS)
Leonard, Douglas C.; Supernova Spectropolarimetry Project (SNSPOL)
2016-06-01
From progenitor studies, type II-Plateau supernovae (SNe II-P) have been decisively and uniquely determined to arise from isolated red supergiant (RSG) stars, establishing the most homogeneous --- and well understood --- progenitor class of any type of core-collapse supernova. The physical process by which these stars explode, however, remains a mystery. A fundamental clue to the nature of the explosion mechanism is explosion geometry: In short, are supernovae round? Because young supernova atmospheres are electron-scattering dominated, their net linear polarization provides a direct probe of early-time supernova geometry, with higher degrees of polarization generally indicating greater departures from spherical symmetry. This presentation will describe the ongoing work being carried out on RSG explosion geometry by the SuperNova SpectroPOLarimetry project (SNSPOL), with a particular focus on SN 2013ej -- an SN II-P that exhibited remarkably high polarization just days after the explosion, and for which twelve epochs of spectropolarimetry trace an intriguing tale about its geometry deep into the nebular phase.We acknowledge support from NSF grants AST-1009571 and AST-1210311, under which part of this research was carried out.
Cell geometry dictates TNFα-induced genome response.
Mitra, Aninda; Venkatachalapathy, Saradha; Ratna, Prasuna; Wang, Yejun; Jokhun, Doorgesh Sharma; Shivashankar, G V
2017-05-16
Cells in physiology integrate local soluble and mechanical signals to regulate genomic programs. Whereas the individual roles of these signals are well studied, the cellular responses to the combined chemical and physical signals are less explored. Here, we investigated the cross-talk between cellular geometry and TNFα signaling. We stabilized NIH 3T3 fibroblasts into rectangular anisotropic or circular isotropic geometries and stimulated them with TNFα and analyzed nuclear translocation of transcription regulators -NFκB (p65) and MKL and downstream gene-expression patterns. We found that TNFα induces geometry-dependent actin depolymerization, which enhances IκB degradation, p65 nuclear translocation, nuclear exit of MKL, and sequestration of p65 at the RNA-polymerase-II foci. Further, global transcription profile of cells under matrix-TNFα interplay reveals a geometry-dependent gene-expression pattern. At a functional level, we find cell geometry affects TNFα-induced cell proliferation. Our results provide compelling evidence that fibroblasts, depending on their geometries, elicit distinct cellular responses for the same cytokine.
Cell geometry dictates TNFα-induced genome response
Mitra, Aninda; Venkatachalapathy, Saradha; Ratna, Prasuna; Wang, Yejun; Jokhun, Doorgesh Sharma; Shivashankar, G. V.
2017-01-01
Cells in physiology integrate local soluble and mechanical signals to regulate genomic programs. Whereas the individual roles of these signals are well studied, the cellular responses to the combined chemical and physical signals are less explored. Here, we investigated the cross-talk between cellular geometry and TNFα signaling. We stabilized NIH 3T3 fibroblasts into rectangular anisotropic or circular isotropic geometries and stimulated them with TNFα and analyzed nuclear translocation of transcription regulators –NFκB (p65) and MKL and downstream gene-expression patterns. We found that TNFα induces geometry-dependent actin depolymerization, which enhances IκB degradation, p65 nuclear translocation, nuclear exit of MKL, and sequestration of p65 at the RNA-polymerase-II foci. Further, global transcription profile of cells under matrix-TNFα interplay reveals a geometry-dependent gene-expression pattern. At a functional level, we find cell geometry affects TNFα-induced cell proliferation. Our results provide compelling evidence that fibroblasts, depending on their geometries, elicit distinct cellular responses for the same cytokine. PMID:28461498
A Comment on Molecular Geometry
NASA Astrophysics Data System (ADS)
Gomba, Frank J.
1999-12-01
A method of determining the correct molecular geometry of simple molecules and ions with one central atom is proposed. While the usual method of determining the molecular geometry involves first drawing the Lewis structure, this method can be used without doing so. In fact, the Lewis structure need not be drawn at all. The Lewis structure may be drawn as the final step, with the geometry of the simple molecule or ion already established. In the case of diatomic molecules, any atom may be used as the central atom. When hydrogen is present in a multiatom molecule or ion, this method "naturally" eliminates choosing hydrogen; but, any other atom may be used as the central atom to determine the correct geometry. The Lewis structure can then be used to determine the formal charges on the atoms. In this way there is a check on the selection of the central atom, should the correct Lewis structure be desired. Thus, it assumes that one is familiar with both Lewis structures and the valence shell electron pair repulsion (VSEPR) approach to bonding. The approach suggested in this paper will give rapid and accurate molecular geometries, and it is fun !!!
Black holes and large order quantum geometry
Huang Minxin; Klemm, Albrecht; Marino, Marcos; Tavanfar, Alireza
2009-03-15
We study five-dimensional black holes obtained by compactifying M theory on Calabi-Yau threefolds. Recent progress in solving topological string theory on compact, one-parameter models allows us to test numerically various conjectures about these black holes. We give convincing evidence that a microscopic description based on Gopakumar-Vafa invariants accounts correctly for their macroscopic entropy, and we check that highly nontrivial cancellations--which seem necessary to resolve the so-called entropy enigma in the Ooguri-Strominger-Vafa conjecture--do in fact occur. We also study analytically small 5d black holes obtained by wrapping M2 branes in the fiber of K3 fibrations. By using heterotic/type II duality we obtain exact formulae for the microscopic degeneracies in various geometries, and we compute their asymptotic expansion for large charges.
Advanced geometries for ballistic neutron guides
NASA Astrophysics Data System (ADS)
Schanzer, Christian; Böni, Peter; Filges, Uwe; Hils, Thomas
2004-08-01
Sophisticated neutron guide systems take advantage of supermirrors being used to increase the neutron flux. However, the finite reflectivity of supermirrors becomes a major loss mechanism when many reflections occur, e.g. in long neutron guides and for long wavelengths. In order to reduce the number of reflections, ballistic neutron guides have been proposed. Usually linear tapered sections are used to enlarge the cross-section and finally, focus the beam to the sample. The disadvantages of linear tapering are (i) an inhomogeneous phase space at the sample position and (ii) a decreasing flux with increasing distance from the exit of the guide. We investigate the properties of parabolic and elliptic tapering for ballistic neutron guides, using the Monte Carlo program McStas with a new guide component dedicated for such geometries. We show that the maximum flux can indeed be shifted away from the exit of the guide. In addition we explore the possibilities of parabolic and elliptic geometries to create point like sources for dedicated experimental demands.
Thermodynamic geometry: Evolution, correlation and phase transition
NASA Astrophysics Data System (ADS)
Bellucci, S.; Tiwari, B. N.
2011-06-01
Under the fluctuation of the electric charge and atomic mass, this paper considers the theory of the thin film depletion layer formation of an ensemble of finitely excited, non-empty d/f-orbital heavy materials, from the thermodynamic geometric perspective. At each state of the local adiabatic evolutions, we examine the nature of the thermodynamic parameters, viz., electric charge and mass, changing at each respective embedding. The definition of the intrinsic Riemannian geometry and differential topology offers the properties of (i) local heat capacities, (ii) global stability criterion and (iv) global correlation length. Under the Gaussian fluctuations, such an intrinsic geometric consideration is anticipated to be useful in the statistical coating of the thin film layer of a desired quality-fine high cost material on a low cost durable coatant. From the perspective of everyday applications, thermodynamic geometry is thus intrinsically self-consistent with the theory of local and global economic optimizations. Following the above procedure, the quality of the thin layer depletion could self-consistently be examined to produce quality products economically.
Realism, positivism, instrumentalism, and quantum geometry
NASA Astrophysics Data System (ADS)
Prugovečki, Eduard
1992-02-01
The roles of classical realism, logical positivism, and pragmatic instrumentalism in the shaping of fundamental ideas in quantum physics are examined in the light of some recent historical and sociological studies of the factors that influenced their development. It is shown that those studies indicate that the conventionalistic form of instrumentalism that has dominated all the major post-World War II developments in quantum physics is not an outgrowth of the Copenhagen school, and that despite the “schism” in twentieth century physics created by the Bohr-Einstein “disagreements” on foundational issues in quantum theory, both their philosophical stands were very much opposed to those of conventionalistic instrumentalism. Quotations from the writings of Dirac, Heisenberg, Popper, Russell, and other influential thinkers, are provided, illustrating the fact that, despite the various divergencies in their opinions, they all either opposed the instrumentalist concept of “truth” in general, or its conventionalistic version in post-World War II quantum physics in particular. The basic epistemic ideas of a quantum geometry approach to quantum physics are reviewed and discussed from the point of view of a quantum realism that seeks to reconcile Bohr's “positivism” with Einstein's “realism” by emphasizing the existence of an underlying quantum reality, in which they both believed. This quantum geometry framework seeks to introduce geometro-stochastic concepts that are specifically designed for the systematic description of that underlying quantum reality, by developing the conceptual and mathematical tools that are most appropriate for such a use.
Electrodynamics and Spacetime Geometry: Foundations
NASA Astrophysics Data System (ADS)
Cabral, Francisco; Lobo, Francisco S. N.
2016-11-01
We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.
Conventionalism and integrable Weyl geometry
NASA Astrophysics Data System (ADS)
Pucheu, M. L.
2015-03-01
Since the appearance of Einstein's general relativity, gravitation has been associated to the space-time curvature. This theory introduced a geometrodynamic language which became a convenient tool to predict matter behaviour. However, the properties of space-time itself cannot be measurable by experiments. Taking Poincaré idea that the geometry of space-time is merely a convention, we show that the general theory of relativity can be completely reformulated in a more general setting, a generalization of Riemannian geometry, namely, the Weyl integrable geometry. The choice of this new mathematical language implies, among other things, that the path of particles and light rays should now correspond to Weylian geodesies. Such modification in the dynamic of bodies brings a new perception of physical phenomena that we will explore.
DOGBONE GEOMETRY FOR RECIRCULATING ACCELERATORS.
BERG,J.S.; JOHNSTONE,C.; SUMMERS,D.
2001-06-18
Most scenarios for accelerating muons require recirculating acceleration. A racetrack shape for the accelerator requires particles with lower energy in early passes to traverse almost the same length of arc as particles with the highest energy. This extra arc length may lead to excess decays and excess cost. Changing the geometry to a dogbone shape, where there is a single linac and the beam turns completely around at the end of the linac, returning to the same end of the linac from which it exited, addresses this problem. In this design, the arc lengths can be proportional to the particle's momentum. This paper proposes an approximate cost model for a recirculating accelerator, attempts to make cost-optimized designs for both racetrack and dogbone geometries, and demonstrates that the dogbone geometry does appear to be more cost effective.
Quantum geometry and gravitational entropy
Simon, Joan; Balasubramanian, Vijay; Czech, Bart Iomiej; Larjo, Klaus; Marolf, Donald; Simon, Joan
2007-05-29
Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S5 universes. In this sector we devise a"coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.
Nernst branes from special geometry
NASA Astrophysics Data System (ADS)
Dempster, P.; Errington, D.; Mohaupt, T.
2015-05-01
We construct new black brane solutions in U(1) gauged N = 2 supergravity with a general cubic prepotential, which have entropy density s ˜ T 1/3 as T → 0 and thus satisfy the Nernst Law. By using the real formulation of special geometry, we are able to obtain analytical solutions in closed form as functions of two parameters, the temperature T and the chemical potential μ. Our solutions interpolate between hyperscaling violating Lifshitz geometries with ( z, θ) = (0 , 2) at the horizon and ( z, θ) = (1 , -1) at infinity. In the zero temperature limit, where the entropy density goes to zero, we recover the extremal Nernst branes of Barisch et al, and the parameters of the near horizon geometry change to ( z, θ) = (3 , 1).
Electrodynamics and Spacetime Geometry: Foundations
NASA Astrophysics Data System (ADS)
Cabral, Francisco; Lobo, Francisco S. N.
2017-02-01
We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.
Individualized Geometry: A Geometry Unit for the Intermediate Grades.
ERIC Educational Resources Information Center
Geissler, Dennis; Larson, Richard
This geometry unit for the intermediate grades is based on the Holt Mathematics Series (levels 3-6), using the concepts of Individually Guided Education (IGE). It is divided into seven levels, one for grade 3 and two each for grades 4-6. Each is designed for both individual and group learning. A vocabulary list is used as a key for activities; a…
Geometry, topology, and string theory
Varadarajan, Uday
2003-01-01
A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.
Geometry of generalized depolarizing channels
Burrell, Christian K.
2009-10-15
A generalized depolarizing channel acts on an N-dimensional quantum system to compress the 'Bloch ball' in N{sup 2}-1 directions; it has a corresponding compression vector. We investigate the geometry of these compression vectors and prove a conjecture of Dixit and Sudarshan [Phys. Rev. A 78, 032308 (2008)], namely, that when N=2{sup d} (i.e., the system consists of d qubits), and we work in the Pauli basis then the set of all compression vectors forms a simplex. We extend this result by investigating the geometry in other bases; in particular we find precisely when the set of all compression vectors forms a simplex.
RSRM Propellant Grain Geometry Modification
NASA Technical Reports Server (NTRS)
Schorr, Andrew A.; Endicott, Joni B.; McCool, Alex (Technical Monitor)
2000-01-01
This document is composed of viewgraphs about the RSRM propellant grain geometry modification project, which hopes to improve personnel and system safety by modifying propellant grain geometry to improve structural factors of safety. Using techniques such as Finite Element Analysis to determine blend radii required to reduce localized stresses, and ballistic predictions to ensure that the ballistics, ignition transient and Block Model have not been adversely affected, the project hopes to build and test FSM-10 with a new design, and determine flight effectivity pending successful test evaluation.
Teaching Activity-Based Taxicab Geometry
ERIC Educational Resources Information Center
Ada, Tuba
2013-01-01
This study aimed on the process of teaching taxicab geometry, a non-Euclidean geometry that is easy to understand and similar to Euclidean geometry with its axiomatic structure. In this regard, several teaching activities were designed such as measuring taxicab distance, defining a taxicab circle, finding a geometric locus in taxicab geometry, and…
Teaching Activity-Based Taxicab Geometry
ERIC Educational Resources Information Center
Ada, Tuba
2013-01-01
This study aimed on the process of teaching taxicab geometry, a non-Euclidean geometry that is easy to understand and similar to Euclidean geometry with its axiomatic structure. In this regard, several teaching activities were designed such as measuring taxicab distance, defining a taxicab circle, finding a geometric locus in taxicab geometry, and…
Exploring Fractal Geometry with Children.
ERIC Educational Resources Information Center
Vacc, Nancy Nesbitt
1999-01-01
Heightens the awareness of elementary school teachers, teacher educators, and teacher-education researchers of possible applications of fractal geometry with children and, subsequently, initiates discussion about the appropriateness of including this new mathematics in the elementary curriculum. Presents activities for exploring children's…
Teaching Geometry According to Euclid.
ERIC Educational Resources Information Center
Hartshorne, Robin
2000-01-01
This essay contains some reflections and questions arising from encounters with the text of Euclid's Elements. The reflections arise out of the teaching of a course in Euclidean and non-Euclidean geometry to undergraduates. It is concluded that teachers of such courses should read Euclid and ask questions, then teach a course on Euclid and later…
Generative CAI in Analytical Geometry.
ERIC Educational Resources Information Center
Uttal, William R.; And Others
A generative computer-assisted instruction system is being developed to tutor students in analytical geometry. The basis of this development is the thesis that a generative teaching system can be developed by establishing and then stimulating a simplified, explicit model of the human tutor. The goal attempted is that of a computer environment…
3DHZETRN: Inhomogeneous Geometry Issues
NASA Technical Reports Server (NTRS)
Wilson, John W.; Slaba, Tony C.; Badavi, Francis F.
2017-01-01
Historical methods for assessing radiation exposure inside complicated geometries for space applications were limited by computational constraints and lack of knowledge associated with nuclear processes occurring over a broad range of particles and energies. Various methods were developed and utilized to simplify geometric representations and enable coupling with simplified but efficient particle transport codes. Recent transport code development efforts, leading to 3DHZETRN, now enable such approximate methods to be carefully assessed to determine if past exposure analyses and validation efforts based on those approximate methods need to be revisited. In this work, historical methods of representing inhomogeneous spacecraft geometry for radiation protection analysis are first reviewed. Two inhomogeneous geometry cases, previously studied with 3DHZETRN and Monte Carlo codes, are considered with various levels of geometric approximation. Fluence, dose, and dose equivalent values are computed in all cases and compared. It is found that although these historical geometry approximations can induce large errors in neutron fluences up to 100 MeV, errors on dose and dose equivalent are modest (<10%) for the cases studied here.
Foucault pendulum through basic geometry
NASA Astrophysics Data System (ADS)
von Bergmann, Jens; von Bergmann, HsingChi
2007-10-01
We provide a thorough explanation of the Foucault pendulum that utilizes its underlying geometry on a level suitable for science students not necessarily familiar with calculus. We also explain how the geometrically understood Foucault pendulum can serve as a prototype for more advanced phenomena in physics known as Berry's phase or geometric phases.
Analogical Reasoning in Geometry Education
ERIC Educational Resources Information Center
Magdas, Ioana
2015-01-01
The analogical reasoning isn't used only in mathematics but also in everyday life. In this article we approach the analogical reasoning in Geometry Education. The novelty of this article is a classification of geometrical analogies by reasoning type and their exemplification. Our classification includes: analogies for understanding and setting a…
Exploring Bundling Theory with Geometry
ERIC Educational Resources Information Center
Eckalbar, John C.
2006-01-01
The author shows how instructors might successfully introduce students in principles and intermediate microeconomic theory classes to the topic of bundling (i.e., the selling of two or more goods as a package, rather than separately). It is surprising how much students can learn using only the tools of high school geometry. To be specific, one can…
Instructional Identities of Geometry Students
ERIC Educational Resources Information Center
Aaron, Wendy Rose; Herbst, Patricio
2012-01-01
We inspect the hypothesis that geometry students may be oriented toward how they expect that the teacher will evaluate them as students or otherwise oriented to how they expect that their work will give them opportunities to do mathematics. The results reported here are based on a mixed-methods analysis of twenty-two interviews with high school…
General Relativity: Geometry Meets Physics
ERIC Educational Resources Information Center
Thomsen, Dietrick E.
1975-01-01
Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…
Exploring Fractal Geometry with Children.
ERIC Educational Resources Information Center
Vacc, Nancy Nesbitt
1999-01-01
Heightens the awareness of elementary school teachers, teacher educators, and teacher-education researchers of possible applications of fractal geometry with children and, subsequently, initiates discussion about the appropriateness of including this new mathematics in the elementary curriculum. Presents activities for exploring children's…
Generative CAI in Analytical Geometry.
ERIC Educational Resources Information Center
Uttal, William R.; And Others
A generative computer-assisted instruction system is being developed to tutor students in analytical geometry. The basis of this development is the thesis that a generative teaching system can be developed by establishing and then stimulating a simplified, explicit model of the human tutor. The goal attempted is that of a computer environment…
Teaching Geometry According to Euclid.
ERIC Educational Resources Information Center
Hartshorne, Robin
2000-01-01
This essay contains some reflections and questions arising from encounters with the text of Euclid's Elements. The reflections arise out of the teaching of a course in Euclidean and non-Euclidean geometry to undergraduates. It is concluded that teachers of such courses should read Euclid and ask questions, then teach a course on Euclid and later…
General Relativity: Geometry Meets Physics
ERIC Educational Resources Information Center
Thomsen, Dietrick E.
1975-01-01
Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…
Improving Student Reasoning in Geometry
ERIC Educational Resources Information Center
Wong, Bobson; Bukalov, Larisa
2013-01-01
In their years of teaching geometry, Wong and Bukalov realized that the greatest challenge has been getting students to improve their reasoning. Many students have difficulty writing formal proofs--a task that requires a good deal of reasoning. Wong and Bukalov reasoned that the solution was to divide the lessons into parallel tasks, allowing…
Signature geometry and quantum engineering
NASA Astrophysics Data System (ADS)
Samociuk, Stefan
2013-09-01
As the operating frequency of electromagnetic based devices increase, physical design geometry is playing an ever more important role. Evidence is considered in support of a relationship between the dimensionality of primitive geometric forms, such as transistors, and corresponding electromagnetic coupling efficiency. The industry of electronics is defined as the construction of devices by the patterning of primitive forms to physical materials. Examples are given to show the evolution of these primitives, down to nano scales, are requiring exacting geometry and three dimensional content. Consideration of microwave monolithic integrated circuits,(MMIC), photonics and metamaterials,(MM), support this trend and also add new requirements of strict geometric periodicity and multiplicity. Signature geometries,(SG), are characterized by distinctive attributes and examples are given. The transcendent form transcode algorithm, (TTA) is introduced as a multi dimensional SG and its use in designing photonic integrated circuits and metamaterials is discussed . A creative commons licensed research database, TRANSFORM, containing TTA geometries in OASIS file formats is described. An experimental methodology for using the database is given. Multidimensional SG and extraction of three dimensional cross sections as primitive forms is discussed as a foundation for quantum engineering and the exploitation of phenomena other than the electromagnetic.
Math Sense: Algebra and Geometry.
ERIC Educational Resources Information Center
Howett, Jerry
This book is designed to help students gain the range of math skills they need to succeed in life, work, and on standardized tests; overcome math anxiety; discover math as interesting and purposeful; and develop good number sense. Topics covered in this book include algebra and geometry. Lessons are organized around four strands: (1) skill lessons…
Geometry in transition: a model of emergent geometry.
Delgadillo-Blando, Rodrigo; O'Connor, Denjoe; Ydri, Badis
2008-05-23
We study a three matrix model with global SO(3) symmetry containing at most quartic powers of the matrices. We find an exotic line of discontinuous transitions with a jump in the entropy, characteristic of a 1st order transition, yet with divergent critical fluctuations and a divergent specific heat with critical exponent alpha=1/2. The low temperature phase is a geometrical one with gauge fields fluctuating on a round sphere. As the temperature increased the sphere evaporates in a transition to a pure matrix phase with no background geometrical structure. Both the geometry and gauge fields are determined dynamically. It is not difficult to invent higher dimensional models with essentially similar phenomenology. The model presents an appealing picture of a geometrical phase emerging as the system cools and suggests a scenario for the emergence of geometry in the early Universe.
Adaptive Geometry Shader Tessellation for Massive Geometry Display
2015-03-01
necessary to prepare complex models for use in analysis and visualization tasks. We investigated several avenues for high-speed visualization and worked to...geometry, visualization 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18. NUMBER OF PAGES 22 19a. NAME OF RESPONSIBLE...Introduction and Background 1 2. Approach 2 3. Speed Improvements in the Visual Simulation Laboratory 2 4. Ray Tracing 4 5. Sharing Display Technologies
Beyond core knowledge: Natural geometry
Spelke, Elizabeth; Lee, Sang Ah; Izard, Véronique
2010-01-01
For many centuries, philosophers and scientists have pondered the origins and nature of human intuitions about the properties of points, lines, and figures on the Euclidean plane, with most hypothesizing that a system of Euclidean concepts either is innate or is assembled by general learning processes. Recent research from cognitive and developmental psychology, cognitive anthropology, animal cognition, and cognitive neuroscience suggests a different view. Knowledge of geometry may be founded on at least two distinct, evolutionarily ancient, core cognitive systems for representing the shapes of large-scale, navigable surface layouts and of small-scale, movable forms and objects. Each of these systems applies to some but not all perceptible arrays and captures some but not all of the three fundamental Euclidean relationships of distance (or length), angle, and direction (or sense). Like natural number (Carey, 2009), Euclidean geometry may be constructed through the productive combination of representations from these core systems, through the use of uniquely human symbolic systems. PMID:20625445
Geometry-invariant resonant cavities
NASA Astrophysics Data System (ADS)
Liberal, I.; Mahmoud, A. M.; Engheta, N.
2016-03-01
Resonant cavities are one of the basic building blocks in various disciplines of science and technology, with numerous applications ranging from abstract theoretical modelling to everyday life devices. The eigenfrequencies of conventional cavities are a function of their geometry, and, thus, the size and shape of a resonant cavity is selected to operate at a specific frequency. Here we demonstrate theoretically the existence of geometry-invariant resonant cavities, that is, resonators whose eigenfrequencies are invariant with respect to geometrical deformations of their external boundaries. This effect is obtained by exploiting the unusual properties of zero-index metamaterials, such as epsilon-near-zero media, which enable decoupling of the temporal and spatial field variations in the lossless limit. This new class of resonators may inspire alternative design concepts, and it might lead to the first generation of deformable resonant devices.
Tin clusters adopt prolate geometries
NASA Astrophysics Data System (ADS)
Shvartsburg, Alexandre A.; Jarrold, Martin F.
1999-08-01
We have characterized the structures of Snn cations up to n=68 using ion mobility measurements. Up to n~35, tin clusters track the prolate growth pattern previously found for Sin and Gen. However, the detailed size-dependent variations start deviating from those observed for Sin above n=14 and Gen above n=21. Over the n~35-65 size range, tin clusters gradually rearrange towards near-spherical geometries, passing through several intermediate structural families. Two or three isomers are resolved for some sizes in the n=18-49 range. The observed geometries are independent of the He buffer gas temperature between 78 and 378 K and are not affected by collisional annealing.
Geometry-invariant resonant cavities
Liberal, I.; Mahmoud, A. M.; Engheta, N.
2016-01-01
Resonant cavities are one of the basic building blocks in various disciplines of science and technology, with numerous applications ranging from abstract theoretical modelling to everyday life devices. The eigenfrequencies of conventional cavities are a function of their geometry, and, thus, the size and shape of a resonant cavity is selected to operate at a specific frequency. Here we demonstrate theoretically the existence of geometry-invariant resonant cavities, that is, resonators whose eigenfrequencies are invariant with respect to geometrical deformations of their external boundaries. This effect is obtained by exploiting the unusual properties of zero-index metamaterials, such as epsilon-near-zero media, which enable decoupling of the temporal and spatial field variations in the lossless limit. This new class of resonators may inspire alternative design concepts, and it might lead to the first generation of deformable resonant devices. PMID:27010103
Experimental Probes of Spacetime Geometries
Hewett, JoAnne
2009-07-10
A novel approach which exploits the geometry of extra spacetime dimensions has been recently proposed as a means to resolving the hierarchy problem, i.e., the large energy gap that separates the electroweak scale and the scale where gravity becomes strong. I will describe two models of this type: one where the apparent hierarchy is generated by a large volume for the extra dimensions, and a second where the observed hierarchy is created by an exponential warp factor which arises from a non-factorizable geometry. Both scenarios have concrete and distinctive phenomenological tests at the TeV scale. I will describe the classes of low-energy and collider signatures for both models, summarize the present constraints from experiment, and examine the ability of future accelerators to probe their parameter space.
Information geometry of Boltzmann machines.
Amari, S; Kurata, K; Nagaoka, H
1992-01-01
A Boltzmann machine is a network of stochastic neurons. The set of all the Boltzmann machines with a fixed topology forms a geometric manifold of high dimension, where modifiable synaptic weights of connections play the role of a coordinate system to specify networks. A learning trajectory, for example, is a curve in this manifold. It is important to study the geometry of the neural manifold, rather than the behavior of a single network, in order to know the capabilities and limitations of neural networks of a fixed topology. Using the new theory of information geometry, a natural invariant Riemannian metric and a dual pair of affine connections on the Boltzmann neural network manifold are established. The meaning of geometrical structures is elucidated from the stochastic and the statistical point of view. This leads to a natural modification of the Boltzmann machine learning rule.
Dynamics, Spectral Geometry and Topology
Burghelea, Dan
2011-02-10
The paper is an informal report on joint work with Stefan Haller on Dynamics in relation with Topology and Spectral Geometry. By dynamics one means a smooth vector field on a closed smooth manifold; the elements of dynamics of concern are the rest points, instantons and closed trajectories. One discusses their counting in the case of a generic vector field which has some additional properties satisfied by a still very large class of vector fields.
Extending dark optical trapping geometries.
Arnold, Aidan S
2012-07-01
New counterpropagating geometries are presented for localizing ultracold atoms in the dark regions created by the interference of Laguerre-Gaussian laser beams. In particular dark helices, an "optical revolver," axial lattices of rings, and axial lattices of ring lattices of rings are considered and a realistic scheme for achieving phase stability is explored. The dark nature of these traps will enable their use as versatile tools for low-decoherence atom interferometry with zero differential light shifts.
Core foundations of abstract geometry.
Dillon, Moira R; Huang, Yi; Spelke, Elizabeth S
2013-08-27
Human adults from diverse cultures share intuitions about the points, lines, and figures of Euclidean geometry. Do children develop these intuitions by drawing on phylogenetically ancient and developmentally precocious geometric representations that guide their navigation and their analysis of object shape? In what way might these early-arising representations support later-developing Euclidean intuitions? To approach these questions, we investigated the relations among young children's use of geometry in tasks assessing: navigation; visual form analysis; and the interpretation of symbolic, purely geometric maps. Children's navigation depended on the distance and directional relations of the surface layout and predicted their use of a symbolic map with targets designated by surface distances. In contrast, children's analysis of visual forms depended on the size-invariant shape relations of objects and predicted their use of the same map but with targets designated by corner angles. Even though the two map tasks used identical instructions and map displays, children's performance on these tasks showed no evidence of integrated representations of distance and angle. Instead, young children flexibly recruited geometric representations of either navigable layouts or objects to interpret the same spatial symbols. These findings reveal a link between the early-arising geometric representations that humans share with diverse animals and the flexible geometric intuitions that give rise to human knowledge at its highest reaches. Although young children do not appear to integrate core geometric representations, children's use of the abstract geometry in spatial symbols such as maps may provide the earliest clues to the later construction of Euclidean geometry.
On the Explosion Geometry of Red Supergiant Stars
NASA Astrophysics Data System (ADS)
Leonard, Douglas Christopher; Dessart, Luc; Pignata, Giuliano; Hillier, D. John; Williams, George Grant; Smith, Paul S.; Khandrika, Harish; Bilinski, Christopher; Duong, Nhieu; Flatland, Kelsi; Gonzalez, Luis; Hoffman, Jennifer L.; Horst, Chuck; Huk, Leah; Milne, Peter; Rachubo, Alisa A.; Smith, Nathan
2015-08-01
From progenitor studies, type II-Plateau supernovae (SNe II-P) have been decisively and uniquely determined to arise from isolated red supergiant (RSG) stars with initial masses ranging from 8 to 16 solar masses (Smartt 2009), establishing the most homogeneous -- and well understood -- progenitor class of any type of core-collapse supernova. However, we must admit a fundamental truth: We do not know how these stars explode. A basic discriminant among proposed explosion models is explosion geometry, since some models predict severe distortions from spherical symmetry. A primary method to gain such geometric information is through spectropolarimetry of the expanding (but, unresolved) atmosphere, with higher degrees of linear polarization generally demanding larger departures from spherical symmetry. Initially, as a class, SNe II-P were found to be only weakly polarized at the early epochs observed, suggesting a nearly spherical explosion for RSG stars. However, late-time observations of SN 2004dj captured a dramatic spike in polarization at just the moment the "inner core" of the ejecta was first revealed in this SN II-P (i.e., at the "drop" off of the photometric plateau; Leonard et al. 2006). This raised the possibility that the explosion of RSGs might be driven by a strongly non-spherical mechanism, with the evidence for the asphericity cloaked at early times by the massive, opaque, quasi-spherical hydrogen envelope. In this presentation we shall describe the continuing work on the explosion geometry of RSGs being carried out by the SuperNova SpectroPOLarimetry project (SNSPOL), with a particular focus on SN 2013ej -- an SN II-P that exhibited remarkably high polarization just days after the explosion (Leonard et al. 2013), and for which twelve epochs of spectropolarimetry trace an intriguing tale about its geometry deep into the nebular phase. We acknowledge support from NSF grants AST-1009571 and AST-1210311, under which part of this research was carried out.
On the Explosion Geometry of Red Supergiant Stars
NASA Astrophysics Data System (ADS)
Leonard, Douglas C.; Dessart, L.; Hillier, D.; Pignata, G.
2012-01-01
From progenitor studies, type II-Plateau supernovae (SNe II-P) have been decisively and uniquely determined to arise from isolated red supergiant stars, establishing the most homogeneous --- and well understood --- progenitor class of any type of core-collapse supernova. The precise nature of the mechanism responsible for the stellar explosion, however, remains the subject of considerable debate. A fundamental clue to the nature of the explosion mechanism is explosion geometry: In short, are supernovae round? Because young supernova atmospheres are electron-scattering dominated, their net linear polarization provides a direct probe of early-time supernova geometry, with higher degrees of polarization generally indicating greater departures from spherical symmetry. Here we present spectropolarimetry data for the most well-sampled SN II-P to date, SN 2008bk, and compare (and contrast) the results with those obtained for SN 2004dj, the only other SN II-P for which spectropolarimetry data were obtained with similar fine temporal sampling before, during, and after the fall off of the photometric plateau (Leonard et al. 2006). Both objects are polarized, indicating departures from spherical symmetry, although the timing of the onset -- as well as the persistence -- of the polarization differ between the two objects. Curiously, the detailed spectropolarimetric characteristics of the two objects at the epochs of recorded maximum polarization are extremely similar, feature by feature, suggesting a common cause --- or, at least, geometry. We interpret the data in light of non-Local-Thermodynamic Equilibrium, time-dependent radiative-transfer simulations specifically crafted for SN II-P ejecta. DCL acknowledges support from NSF grant AST-1009571, under which part of this research was carried out. Based on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere, Chile, under observing programs 081.D-0128, 082.D-0151, and 085.D
The unassigned distance geometry problem
Duxbury, P. M.; Granlund, L.; Gujarathi, S. R.; ...
2015-11-19
Studies of distance geometry problems (DGP) have focused on cases where the vertices at the ends of all or most of the given distances are known or assigned, which we call assigned distance geometry problems (aDGPs). In this contribution we consider the unassigned distance geometry problem (uDGP) where the vertices associated with a given distance are unknown, so the graph structure has to be discovered. uDGPs arises when attempting to find the atomic structure of molecules and nanoparticles using X-ray or neutron diffraction data from non-crystalline materials. Rigidity theory provides a useful foundation for both aDGPs and uDGPs, though itmore » is restricted to generic realizations of graphs, and key results are summarized. Conditions for unique realization are discussed for aDGP and uDGP cases, build-up algorithms for both cases are described and experimental results for uDGP are presented.« less
Geometry of statistical target detection
NASA Astrophysics Data System (ADS)
Basener, William F.; Allen, Brian; Bretney, Kristen
2017-01-01
This paper presents an investigation into the underlying geometry and performance of various statistical target detection algorithms for hyperspectral imagery, presents results from algorithm testing, and investigates general trends and observable principles for understanding performance. Over the variety of detection algorithms, there is no universally best performing algorithm. In our test, often top performing algorithms on one class of targets obtain mediocre results on another class of targets. However, there are two clear trends: quadratic detectors such as ACE generally performed better than linear ones especially for subpixel targets (our top 15 scoring algorithms were quadratic detectors), and using anomaly detection to prescreen image spectra improved the performance of the quadratic detectors (8 of our top 9 scoring algorithms using anomaly prescreening). We also demonstrate that simple combinations of detection algorithms can outperform single algorithms in practice. In our derivation of detection algorithms, we provide exposition on the underlying mathematical geometry of the algorithms. That geometry is then used to investigate differences in algorithm performance. Tests are conducted using imagery and targets freely available online. The imagery was acquired over Cooke City, Montana, a small town near Yellowstone National Park, using the HyMap V/NIR/SWIR sensor with 126 spectral bands. There are three vehicle and four fabric targets located in the town and surrounding area.
Hyperbolic geometry of complex networks.
Krioukov, Dmitri; Papadopoulos, Fragkiskos; Kitsak, Maksim; Vahdat, Amin; Boguñá, Marián
2010-09-01
We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong clustering in complex networks emerge naturally as simple reflections of the negative curvature and metric property of the underlying hyperbolic geometry. Conversely, we show that if a network has some metric structure, and if the network degree distribution is heterogeneous, then the network has an effective hyperbolic geometry underneath. We then establish a mapping between our geometric framework and statistical mechanics of complex networks. This mapping interprets edges in a network as noninteracting fermions whose energies are hyperbolic distances between nodes, while the auxiliary fields coupled to edges are linear functions of these energies or distances. The geometric network ensemble subsumes the standard configuration model and classical random graphs as two limiting cases with degenerate geometric structures. Finally, we show that targeted transport processes without global topology knowledge, made possible by our geometric framework, are maximally efficient, according to all efficiency measures, in networks with strongest heterogeneity and clustering, and that this efficiency is remarkably robust with respect to even catastrophic disturbances and damages to the network structure.
Spectroscopic studies on Co(II), Ni(II), Cu(II) and Zn(II) complexes with a N4-macrocylic ligands.
Swamy, S J; Pola, Someshwar
2008-09-01
Complexes of cobalt(II), nickel(II), copper(II) and zinc(II) with a new tetraaza macrocyclic ligand have been synthesized and characterized by microanalyses, molar conductance, magnetic susceptibility, mass, thermogravimetric (TGA), IR, 1H and 13C NMR, electronic and ESR spectral studies. All the complexes are found to have the formula [MLX2]x nH2O and are six-coordinated with distorted octahedral geometry.
Network geometry with flavor: From complexity to quantum geometry.
Bianconi, Ginestra; Rahmede, Christoph
2016-03-01
Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d-dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s=-1,0,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d. In d=1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d>1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t. Interestingly the NGF remains fully classical but its
Network geometry with flavor: From complexity to quantum geometry
NASA Astrophysics Data System (ADS)
Bianconi, Ginestra; Rahmede, Christoph
2016-03-01
Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d -dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s =-1 ,0 ,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d . In d =1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d >1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t . Interestingly the NGF remains fully classical but
ERIC Educational Resources Information Center
Kutluca, Tamer
2013-01-01
The aim of this study is to investigate the effect of dynamic geometry software GeoGebra on Van Hiele geometry understanding level of students at 11th grade geometry course. The study was conducted with pre and posttest control group quasi-experimental method. The sample of the study was 42 eleventh grade students studying in the spring term of…
A Whirlwind Tour of Computational Geometry.
ERIC Educational Resources Information Center
Graham, Ron; Yao, Frances
1990-01-01
Described is computational geometry which used concepts and results from classical geometry, topology, combinatorics, as well as standard algorithmic techniques such as sorting and searching, graph manipulations, and linear programing. Also included are special techniques and paradigms. (KR)
The Geometry of Quasar Outflows
NASA Astrophysics Data System (ADS)
Ganguly, Rajib
2012-10-01
Quasar outflows are important for understanding the accretion and growth processes of the central black hole, but also potentially play a role in feedback to the galaxy, halting star formation and infall of gas. A big uncertainty lies in the geometry and density of these outflows, especially as a function of ionization and velocity. We aim to tackle this using the archival COS M grating spectra of 266 quasars. We separate the geometry of outflows into two parts: the solid angle subtended around the black hole, and the distance of the outflow from the central engine. Large numbers of quasars with high resolution spectra are required for each aspect of this statistical investigation. First, we will determine which/how many absorption-line systems are intrinsic through both partial covering methods and statistical assessments. Second, we will consider the incidence of intrinsic absorbers as a function of quasar property {e.g., radio-loudness, SED shape, black hole mass, bolometric luminosity}. This will reveal what determines the solid angle. This can only be done at moderate redshifts where quasars with a larger range of properties are observable, and hence requires HST/COS. Third, we will use the wide range of diagnostic lines to constrain the physical conditions of the absorbers. We will target the CIII*1175 complex and apply photoionization models to constrain the densities and ionization parameters. This will provide the largest set yet of intrinsic absorbers with systematic distance constraints. In tandem with the solid angles, this work will inform models regarding the geometry of quasar outflows.
Cable equation for general geometry.
López-Sánchez, Erick J; Romero, Juan M
2017-02-01
The cable equation describes the voltage in a straight cylindrical cable, and this model has been employed to model electrical potential in dendrites and axons. However, sometimes this equation might give incorrect predictions for some realistic geometries, in particular when the radius of the cable changes significantly. Cables with a nonconstant radius are important for some phenomena, for example, discrete swellings along the axons appear in neurodegenerative diseases such as Alzheimers, Parkinsons, human immunodeficiency virus associated dementia, and multiple sclerosis. In this paper, using the Frenet-Serret frame, we propose a generalized cable equation for a general cable geometry. This generalized equation depends on geometric quantities such as the curvature and torsion of the cable. We show that when the cable has a constant circular cross section, the first fundamental form of the cable can be simplified and the generalized cable equation depends on neither the curvature nor the torsion of the cable. Additionally, we find an exact solution for an ideal cable which has a particular variable circular cross section and zero curvature. For this case we show that when the cross section of the cable increases the voltage decreases. Inspired by this ideal case, we rewrite the generalized cable equation as a diffusion equation with a source term generated by the cable geometry. This source term depends on the cable cross-sectional area and its derivates. In addition, we study different cables with swelling and provide their numerical solutions. The numerical solutions show that when the cross section of the cable has abrupt changes, its voltage is smaller than the voltage in the cylindrical cable. Furthermore, these numerical solutions show that the voltage can be affected by geometrical inhomogeneities on the cable.
Losa, Gabriele A
2009-01-01
The extension of the concepts of Fractal Geometry (Mandelbrot [1983]) toward the life sciences has led to significant progress in understanding complex functional properties and architectural / morphological / structural features characterising cells and tissues during ontogenesis and both normal and pathological development processes. It has even been argued that fractal geometry could provide a coherent description of the design principles underlying living organisms (Weibel [1991]). Fractals fulfil a certain number of theoretical and methodological criteria including a high level of organization, shape irregularity, functional and morphological self-similarity, scale invariance, iterative pathways and a peculiar non-integer fractal dimension [FD]. Whereas mathematical objects are deterministic invariant or self-similar over an unlimited range of scales, biological components are statistically self-similar only within a fractal domain defined by upper and lower limits, called scaling window, in which the relationship between the scale of observation and the measured size or length of the object can be established (Losa and Nonnenmacher [1996]). Selected examples will contribute to depict complex biological shapes and structures as fractal entities, and also to show why the application of the fractal principle is valuable for measuring dimensional, geometrical and functional parameters of cells, tissues and organs occurring within the vegetal and animal realms. If the criteria for a strict description of natural fractals are met, then it follows that a Fractal Geometry of Life may be envisaged and all natural objects and biological systems exhibiting self-similar patterns and scaling properties may be considered as belonging to the new subdiscipline of "fractalomics".
Cable equation for general geometry
NASA Astrophysics Data System (ADS)
López-Sánchez, Erick J.; Romero, Juan M.
2017-02-01
The cable equation describes the voltage in a straight cylindrical cable, and this model has been employed to model electrical potential in dendrites and axons. However, sometimes this equation might give incorrect predictions for some realistic geometries, in particular when the radius of the cable changes significantly. Cables with a nonconstant radius are important for some phenomena, for example, discrete swellings along the axons appear in neurodegenerative diseases such as Alzheimers, Parkinsons, human immunodeficiency virus associated dementia, and multiple sclerosis. In this paper, using the Frenet-Serret frame, we propose a generalized cable equation for a general cable geometry. This generalized equation depends on geometric quantities such as the curvature and torsion of the cable. We show that when the cable has a constant circular cross section, the first fundamental form of the cable can be simplified and the generalized cable equation depends on neither the curvature nor the torsion of the cable. Additionally, we find an exact solution for an ideal cable which has a particular variable circular cross section and zero curvature. For this case we show that when the cross section of the cable increases the voltage decreases. Inspired by this ideal case, we rewrite the generalized cable equation as a diffusion equation with a source term generated by the cable geometry. This source term depends on the cable cross-sectional area and its derivates. In addition, we study different cables with swelling and provide their numerical solutions. The numerical solutions show that when the cross section of the cable has abrupt changes, its voltage is smaller than the voltage in the cylindrical cable. Furthermore, these numerical solutions show that the voltage can be affected by geometrical inhomogeneities on the cable.
NASA Astrophysics Data System (ADS)
Sharma, Amit Kumar; Chandra, Sulekh
2011-10-01
Complexes of the type [M(L)X 2], where M = Co(II), Ni(II) and Cu(II), have been synthesized with novel NO-donor Schiff's base ligand, 1,4-diformylpiperazine bis(4-imino-2,3-dimethyl-1-phenyl-3-pyrazolin-5-one) which is obtained by the acid catalyzed condensation of 1,4-diformylpiperazine with 4-aminoantipyrine. The elemental analyses, molar conductance measurements, magnetic susceptibility measurements, IR, UV, NMR, mass and EPR studies of the compounds led to the conclusion that the ligand acts as tetradentate chelate. The Schiff's base ligand forms hexacoordinated complexes having octahedral geometry for Ni(II) and tetragonal geometry for Co(II) and Cu(II) complexes. The mycological studies of the compounds were examined against the several opportunistic pathogens, i.e., Alternaria brassicae, Aspergillus niger and Fusarium oxysporum. The Cu(II) complexes were found to have most fungicidal behavior.
Geometry in the Early Years: A Commentary
ERIC Educational Resources Information Center
Dindyal, Jaguthsing
2015-01-01
The primary goal of this paper is to provide a commentary on the teaching and learning of geometry in the early years of schooling with the set of papers in this issue as a guiding factor. It is structured around issues about geometry education of young learners, such as: what should we teach in geometry and why; representation of geometrical…
Preservice Primary School Teachers' Elementary Geometry Knowledge
ERIC Educational Resources Information Center
Marchis, Iuliana
2012-01-01
Geometrical notions and properties occur in real-world problems, thus Geometry has an important place in school Mathematics curricula. Primary school curricula lays the foundation of Geometry knowledge, pupils learn Geometry notions and properties by exploring their environment. Thus it is very important that primary school teachers have a good…
Teaching Geometry: An Experiential and Artistic Approach.
ERIC Educational Resources Information Center
Ogletree, Earl J.
The view that geometry should be taught at every grade level is promoted. Primary and elementary school children are thought to rarely have any direct experience with geometry, except on an incidental basis. Children are supposed to be able to learn geometry rather easily, so long as the method and content are adapted to their development and…
Geometry: Career Related Units. Teacher's Edition.
ERIC Educational Resources Information Center
Pierro, Mike; And Others
Using six geometry units as resource units, the document explores 22 math-related careers. The authors intend the document to provide senior high school students with career orientation and exploration experiences while they learn geometry skills. The units are to be considered as a part of a geometry course, not a course by themselves. The six…
Students' Misconceptions and Errors in Transformation Geometry
ERIC Educational Resources Information Center
Ada, Tuba; Kurtulus, Aytac
2010-01-01
This study analyses the students' performances in two-dimensional transformation geometry and explores the mistakes made by the students taking the analytic geometry course given by researchers. An examination was given to students of Education Faculties who have taken the analytic geometry course at Eskisehir Osmangazi University in Turkey. The…
Geometry in the Early Years: A Commentary
ERIC Educational Resources Information Center
Dindyal, Jaguthsing
2015-01-01
The primary goal of this paper is to provide a commentary on the teaching and learning of geometry in the early years of schooling with the set of papers in this issue as a guiding factor. It is structured around issues about geometry education of young learners, such as: what should we teach in geometry and why; representation of geometrical…
Engaging All Students with "Impossible Geometry"
ERIC Educational Resources Information Center
Wiest, Lynda R.; Ayebo, Abraham; Dornoo, Michael D.
2010-01-01
Geometry is an area in which Australian students performed particularly poorly on the 2007 Trends in International Mathematics and Science Study (TIMSS). One innovative area of recreational geometry that has rich potential to engage and challenge a wide variety of students is "impossible geometry." An impossible geometric object is a…
Worldsheet geometries of ambitwistor string
NASA Astrophysics Data System (ADS)
Ohmori, Kantaro
2015-06-01
Mason and Skinner proposed the ambitwistor string theory which directly reproduces the formulas for the amplitudes of massless particles proposed by Cachazo, He and Yuan. In this paper we discuss geometries of the moduli space of worldsheets associated to the bosonic or the RNS ambitwistor string. Further, we investigate the factorization properties of the amplitudes when an internal momentum is near on-shell in the abstract CFT language. Along the way, we propose the existence of the ambitwistor strings with three or four fermionic worldsheet currents.
Complex geometry and string theory
NASA Astrophysics Data System (ADS)
Morozov, A. Y.; Perelomov, A. M.
1990-06-01
The analytic properties of string theory are reviewed. It is demonstrated that the theory of strings is connected with contemporary fields of complex geometry. A massless classical point-like particle which moves in Minkowski space of D dimensions is considered. The formulation used to develop string theory is based on the Polyakov approach. In order to find the quantum scattering amplitude in the Polyakov approach, the functional integral over all Riemannian surfaces is calculated. The simplest case of the amplitude of vacuum-vacuum transitions Z of a closed string is considered. The description of linear bundles in the divisor terms is given.
Quanta of geometry and unification
NASA Astrophysics Data System (ADS)
Chamseddine, Ali H.
2016-11-01
This is a tribute to Abdus Salam’s memory whose insight and creative thinking set for me a role model to follow. In this contribution I show that the simple requirement of volume quantization in spacetime (with Euclidean signature) uniquely determines the geometry to be that of a noncommutative space whose finite part is based on an algebra that leads to Pati-Salam grand unified models. The Standard Model corresponds to a special case where a mathematical constraint (order one condition) is satisfied. This provides evidence that Salam was a visionary who was generations ahead of his time.
Bondi accretion in trumpet geometries
NASA Astrophysics Data System (ADS)
Miller, August J.; Baumgarte, Thomas W.
2017-02-01
The Bondi solution, which describes the radial inflow of a gas onto a non-rotating black hole, provides a powerful test for numerical relativistic codes. However, the Bondi solution is usually derived in Schwarzschild coordinates, which are not well suited for dynamical spacetime evolutions. Instead, many current numerical relativistic codes adopt moving-puncture coordinates, which render black holes in trumpet geometries. Here we transform the Bondi solution into trumpet coordinates, which result in regular expressions for the fluid flow extending into the black-hole interior. We also evolve these solutions numerically and demonstrate their usefulness for testing and calibrating numerical codes.
Quanta of Geometry and Unification
NASA Astrophysics Data System (ADS)
Chamseddine, Ali H.
This is a tribute to Abdus Salam's memory whose insight and creative thinking set for me a role model to follow. In this contribution I show that the simple requirement of volume quantization in space-time (with Euclidean signature) uniquely determines the geometry to be that of a noncommutative space whose finite part is based on an algebra that leads to Pati-Salam grand unified models. The Standard Model corresponds to a special case where a mathematical constraint (order one condition) is satisfied. This provides evidence that Salam was a visionary who was generations ahead of his time.
Regular polygons in taxicab geometry
NASA Astrophysics Data System (ADS)
Hanson, J. R.
2014-10-01
A polygon of n sides will be called regular in taxicab geometry if it has n equal angles and n sides of equal taxicab length. This paper will show that there are no regular taxicab triangles and no regular taxicab pentagons. The sets of taxicab rectangles and taxicab squares will be shown to be the same, respectively, as the sets of Euclidean rectangles and Euclidean squares. A method of construction for a regular taxicab 2n-gon for any n will be demonstrated.
Geometry of physical dispersion relations
NASA Astrophysics Data System (ADS)
Rätzel, Dennis; Rivera, Sergio; Schuller, Frederic P.
2011-02-01
To serve as a dispersion relation, a cotangent bundle function must satisfy three simple algebraic properties. These conditions are derived from the inescapable physical requirements that local matter field dynamics must be predictive and allow for an observer-independent notion of positive energy. Possible modifications of the standard relativistic dispersion relation are thereby severely restricted. For instance, the dispersion relations associated with popular deformations of Maxwell theory by Gambini-Pullin or Myers-Pospelov are not admissible. Dispersion relations passing the simple algebraic checks derived here correspond to physically admissible Finslerian refinements of Lorentzian geometry.
Geometry-dependent distributed polarizability models for the water molecule
Loboda, Oleksandr; Ingrosso, Francesca; Ruiz-López, Manuel F.; Millot, Claude; Szalewicz, Krzysztof
2016-01-21
Geometry-dependent distributed polarizability models have been constructed by fits to ab initio calculations at the coupled cluster level of theory with up to noniterative triple excitations in an augmented triple-zeta quality basis set for the water molecule in the field of a point charge. The investigated models include (i) charge-flow polarizabilities between chemically bonded atoms, (ii) isotropic or anisotropic dipolar polarizabilities on oxygen atom or on all atoms, and (iii) combinations of models (i) and (ii). For each model, the polarizability parameters have been optimized to reproduce the induction energy of a water molecule polarized by a point charge successively occupying a grid of points surrounding the molecule. The quality of the models is ascertained by examining their ability to reproduce these induction energies as well as the molecular dipolar and quadrupolar polarizabilities. The geometry dependence of the distributed polarizability models has been explored by changing bond lengths and HOH angle to generate 125 molecular structures (reduced to 75 symmetry-unique ones). For each considered model, the distributed polarizability components have been fitted as a function of the geometry by a Taylor expansion in monomer coordinate displacements up to the sum of powers equal to 4.
Three-dimensional representation of complex muscle architectures and geometries.
Blemker, Silvia S; Delp, Scott L
2005-05-01
Almost all computer models of the musculoskeletal system represent muscle geometry using a series of line segments. This simplification (i) limits the ability of models to accurately represent the paths of muscles with complex geometry and (ii) assumes that moment arms are equivalent for all fibers within a muscle (or muscle compartment). The goal of this work was to develop and evaluate a new method for creating three-dimensional (3D) finite-element models that represent complex muscle geometry and the variation in moment arms across fibers within a muscle. We created 3D models of the psoas, iliacus, gluteus maximus, and gluteus medius muscles from magnetic resonance (MR) images. Peak fiber moment arms varied substantially among fibers within each muscle (e.g., for the psoas the peak fiber hip flexion moment arms varied from 2 to 3 cm, and for the gluteus maximus the peak fiber hip extension moment arms varied from 1 to 7 cm). Moment arms from the literature were generally within the range of fiber moment arms predicted by the 3D models. The models accurately predicted changes in muscle surface geometry over a 55 degrees range of hip flexion, as compared to changes in shape predicted from MR images (average errors between the model and measured surfaces were between 1.7 and 5.2 mm). This new framework for representing muscle will enhance the accuracy of computer models of the musculoskeletal system.
Geometry-induced rigidity in pressurized elastic shells
NASA Astrophysics Data System (ADS)
Reis, Pedro; Florijn, Bastiaan; Lazarus, Arnaud
2012-02-01
We study the indentation of pressurized thin elastic shells, with positive Gauss curvature. In our precision desktop-scale experiments, the geometry of the shells and their material properties are custom-controlled using rapid prototyping and digital fabrication techniques. The mechanical response is quantified through load-displacement compression tests and the differential pressure is set by a syringe-pump system under feedback control. Focus is given to the linear regime of the response towards quantifying the geometry-induced rigidity of pressurized shells with different shapes. We find that this effective stiffness is proportional to the local mean curvature in the neighborhood of the locus of indentation. Combining classic theory of shells with recent developments by D. Vella et al. (2011), we rationalize the dependence of the geometry-induced rigidity on: i) the mean curvature at the point of indentation, ii) the material properties of the shell and iii) the in-out differential pressure. The proposed predictive framework is in excellent agreement with our experiments, over a wide range of control parameters. The prominence of geometry in this class of problems points to the relevance and applicability of our results over a wide range of lengthscales.
Automated, Parametric Geometry Modeling and Grid Generation for Turbomachinery Applications
NASA Technical Reports Server (NTRS)
Harrand, Vincent J.; Uchitel, Vadim G.; Whitmire, John B.
2000-01-01
The objective of this Phase I project is to develop a highly automated software system for rapid geometry modeling and grid generation for turbomachinery applications. The proposed system features a graphical user interface for interactive control, a direct interface to commercial CAD/PDM systems, support for IGES geometry output, and a scripting capability for obtaining a high level of automation and end-user customization of the tool. The developed system is fully parametric and highly automated, and, therefore, significantly reduces the turnaround time for 3D geometry modeling, grid generation and model setup. This facilitates design environments in which a large number of cases need to be generated, such as for parametric analysis and design optimization of turbomachinery equipment. In Phase I we have successfully demonstrated the feasibility of the approach. The system has been tested on a wide variety of turbomachinery geometries, including several impellers and a multi stage rotor-stator combination. In Phase II, we plan to integrate the developed system with turbomachinery design software and with commercial CAD/PDM software.
Casimir effects for classical and quantum liquids in slab geometry: A brief review
Biswas, Shyamal
2015-05-15
We analytically explore Casimir effects for confinement of classical and quantum fluctuations in slab (film) geometry (i) for classical (critical) fluctuations over {sup 4}He liquid around the λ point, and (ii) for quantum (phonon) fluctuations of Bogoliubov excitations over an interacting Bose-Einstein condensate. We also briefly review Casimir effects for confinement of quantum vacuum fluctuations confined to two plates of different geometries.
Fuzzy Logic for Incidence Geometry
2016-01-01
The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly used names of landmarks, water areas, and so forth. Unlike single points that are given in Cartesian coordinates, these geographic entities are extended in space and often loosely defined, but people easily perform spatial reasoning with extended geographic objects “as if they were points.” Unfortunately, up to date, geographic information systems (GIS) miss the capability of geometric reasoning with extended objects. The aim of the paper is to present a mathematical apparatus for approximate geometric reasoning with extended objects that is usable in GIS. In the paper we discuss the fuzzy logic (Aliev and Tserkovny, 2011) as a reasoning system for geometry of extended objects, as well as a basis for fuzzification of the axioms of incidence geometry. The same fuzzy logic was used for fuzzification of Euclid's first postulate. Fuzzy equivalence relation “extended lines sameness” is introduced. For its approximation we also utilize a fuzzy conditional inference, which is based on proposed fuzzy “degree of indiscernibility” and “discernibility measure” of extended points. PMID:27689133
Entanglement classification with algebraic geometry
NASA Astrophysics Data System (ADS)
Sanz, M.; Braak, D.; Solano, E.; Egusquiza, I. L.
2017-05-01
We approach multipartite entanglement classification in the symmetric subspace in terms of algebraic geometry, its natural language. We show that the class of symmetric separable states has the structure of a Veronese variety and that its k-secant varieties are SLOCC invariants. Thus SLOCC classes gather naturally into families. This classification presents useful properties such as a linear growth of the number of families with the number of particles, and nesting, i.e. upward consistency of the classification. We attach physical meaning to this classification through the required interaction length of parent Hamiltonians. We show that the states W N and GHZ N are in the same secant family and that, effectively, the former can be obtained in a limit from the latter. This limit is understood in terms of tangents, leading to a refinement of the previous families. We compute explicitly the classification of symmetric states with N≤slant4 qubits in terms of both secant families and its refinement using tangents. This paves the way to further use of projective varieties in algebraic geometry to solve open problems in entanglement theory.
Weyl gravity and Cartan geometry
NASA Astrophysics Data System (ADS)
Attard, J.; François, J.; Lazzarini, S.
2016-04-01
We point out that the Cartan geometry known as the second-order conformal structure provides a natural differential geometric framework underlying gauge theories of conformal gravity. We are concerned with two theories: the first one is the associated Yang-Mills-like Lagrangian, while the second, inspired by [1], is a slightly more general one that relaxes the conformal Cartan geometry. The corresponding gauge symmetry is treated within the Becchi-Rouet-Stora-Tyutin language. We show that the Weyl gauge potential is a spurious degree of freedom, analogous to a Stueckelberg field, that can be eliminated through the dressing field method. We derive sets of field equations for both the studied Lagrangians. For the second one, they constrain the gauge field to be the "normal conformal Cartan connection.''Finally, we provide in a Lagrangian framework a justification of the identification, in dimension 4, of the Bach tensor with the Yang-Mills current of the normal conformal Cartan connection, as proved in [2].
Turbine engine variable geometry device
NASA Technical Reports Server (NTRS)
Rogo, Casimir (Inventor); Lenz, Herman N. (Inventor)
1985-01-01
A variable geometry device for use with the turbine nozzle of a turbine engine of the type having a support housing and a combustion chamber contained within the support housing. A pair of spaced walls in the support housing define an annular and radially extending nozzle passageway. The outer end of the nozzle passageway is open to the combustion chamber while the inner end of the nozzle passageway is open to one or more turbine stages. A plurality of circumferentially spaced nozzle vanes are mounted to one of the spaced walls and protrude across the nozzle passageway. An annular opening is formed around the opposite spaced wall and an annular ring is axially slidably mounted within the opening. A motor is operatively connected to this ring and, upon actuation, axially displaces the ring within the nozzle passageway. In addition, the ring includes a plurality of circumferentially spaced slots which register with the nozzle vanes so that the vane geometry remains the same despite axial displacement of the ring.
Target Detection Using Fractal Geometry
NASA Technical Reports Server (NTRS)
Fuller, J. Joseph
1991-01-01
The concepts and theory of fractal geometry were applied to the problem of segmenting a 256 x 256 pixel image so that manmade objects could be extracted from natural backgrounds. The two most important measurements necessary to extract these manmade objects were fractal dimension and lacunarity. Provision was made to pass the manmade portion to a lookup table for subsequent identification. A computer program was written to construct cloud backgrounds of fractal dimensions which were allowed to vary between 2.2 and 2.8. Images of three model space targets were combined with these backgrounds to provide a data set for testing the validity of the approach. Once the data set was constructed, computer programs were written to extract estimates of the fractal dimension and lacunarity on 4 x 4 pixel subsets of the image. It was shown that for clouds of fractal dimension 2.7 or less, appropriate thresholding on fractal dimension and lacunarity yielded a 64 x 64 edge-detected image with all or most of the cloud background removed. These images were enhanced by an erosion and dilation to provide the final image passed to the lookup table. While the ultimate goal was to pass the final image to a neural network for identification, this work shows the applicability of fractal geometry to the problems of image segmentation, edge detection and separating a target of interest from a natural background.
Geometry and the quantum: basics
NASA Astrophysics Data System (ADS)
Chamseddine, Ali H.; Connes, Alain; Mukhanov, Viatcheslav
2014-12-01
Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. This commutation relation appears in two versions, one sided and two sided. It implies the quantization of the volume. In the one-sided case it implies that the manifold decomposes into a disconnected sum of spheres which will represent quanta of geometry. The two sided version in dimension 4 predicts the two algebras M 2(ℍ) and M 4(ℂ) which are the algebraic constituents of the Standard Model of particle physics. This taken together with the non-commutative algebra of functions allows one to reconstruct, using the spectral action, the Lagrangian of gravity coupled with the Standard Model. We show that any connected Riemannian Spin 4-manifold with quantized volume > 4 (in suitable units) appears as an irreducible representation of the two-sided commutation relations in dimension 4 and that these representations give a seductive model of the "particle picture" for a theory of quantum gravity in which both the Einstein geometric standpoint and the Standard Model emerge from Quantum Mechanics. Physical applications of this quantization scheme will follow in a separate publication.
Quanta of geometry: noncommutative aspects.
Chamseddine, Ali H; Connes, Alain; Mukhanov, Viatcheslav
2015-03-06
In the construction of spectral manifolds in noncommutative geometry, a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of real scalar fields naturally appears and implies, by equality with the index formula, the quantization of the volume. We first show that this condition implies that the manifold decomposes into disconnected spheres, which will represent quanta of geometry. We then refine the condition by involving the real structure and two types of geometric quanta, and show that connected spin manifolds with large quantized volume are then obtained as solutions. The two algebras M_{2}(H) and M_{4}(C) are obtained, which are the exact constituents of the standard model. Using the two maps from M_{4} to S^{4} the four-manifold is built out of a very large number of the two kinds of spheres of Planckian volume. We give several physical applications of this scheme such as quantization of the cosmological constant, mimetic dark matter, and area quantization of black holes.
Fuzzy Logic for Incidence Geometry.
Tserkovny, Alex
The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly used names of landmarks, water areas, and so forth. Unlike single points that are given in Cartesian coordinates, these geographic entities are extended in space and often loosely defined, but people easily perform spatial reasoning with extended geographic objects "as if they were points." Unfortunately, up to date, geographic information systems (GIS) miss the capability of geometric reasoning with extended objects. The aim of the paper is to present a mathematical apparatus for approximate geometric reasoning with extended objects that is usable in GIS. In the paper we discuss the fuzzy logic (Aliev and Tserkovny, 2011) as a reasoning system for geometry of extended objects, as well as a basis for fuzzification of the axioms of incidence geometry. The same fuzzy logic was used for fuzzification of Euclid's first postulate. Fuzzy equivalence relation "extended lines sameness" is introduced. For its approximation we also utilize a fuzzy conditional inference, which is based on proposed fuzzy "degree of indiscernibility" and "discernibility measure" of extended points.
Quanta of Geometry: Noncommutative Aspects
NASA Astrophysics Data System (ADS)
Chamseddine, Ali H.; Connes, Alain; Mukhanov, Viatcheslav
2015-03-01
In the construction of spectral manifolds in noncommutative geometry, a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of real scalar fields naturally appears and implies, by equality with the index formula, the quantization of the volume. We first show that this condition implies that the manifold decomposes into disconnected spheres, which will represent quanta of geometry. We then refine the condition by involving the real structure and two types of geometric quanta, and show that connected spin manifolds with large quantized volume are then obtained as solutions. The two algebras M2(H ) and M4(C ) are obtained, which are the exact constituents of the standard model. Using the two maps from M4 to S4 the four-manifold is built out of a very large number of the two kinds of spheres of Planckian volume. We give several physical applications of this scheme such as quantization of the cosmological constant, mimetic dark matter, and area quantization of black holes.
Differential Geometry Based Multiscale Models
Wei, Guo-Wei
2010-01-01
Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atom-istic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier–Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson–Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson–Nernst–Planck equations that
Differential geometry based multiscale models.
Wei, Guo-Wei
2010-08-01
Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atomistic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier-Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson-Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson-Nernst-Planck equations that are
From Special Geometry to Black Hole Partition Functions
NASA Astrophysics Data System (ADS)
Mohaupt, Thomas
These notes are based on lectures given at the Erwin-Schrödinger Institute in Vienna in 2006/2007 and at the 2007 School on Attractor Mechanism in Frascati. Lecture I reviews special geometry from the superconformal point of view. Lecture II discusses the black hole attractor mechanism, the underlying variational principle and black hole partition functions. Lecture III applies the formalism introduced in the previous lectures to large and small BPS black holes in N = 4 supergravity. Lecture IV is devoted to the microscopic description of these black holes in N = 4 string compactifications. The lecture notes include problems which allow the readers to develop some of the key ideas by themselves. Appendix A reviews special geometry from the mathematical point of view. Appendix B provides the necessary background in modular forms needed for understanding S-duality and string state counting.
From Special Geometry to Black Hole Partition Functions
NASA Astrophysics Data System (ADS)
Mohaupt, Thomas
These notes are based on lectures given at the Erwin-Schrödinger Institute in Vienna in 2006/2007 and at the 2007 School on Attractor Mechanism in Frascati. Lecture I reviews special geometry from the superconformal point of view. Lecture II discusses the black hole attractor mechanism, the underlying variational principle and black hole partition functions. Lecture III applies the formalism introduced in the previous lectures to large and small BPS black holes in N = 4 supergravity. Lecture IV is devoted to the microscopic description of these black holes in N = 4 string compactifications. The lecture notes include problems which allow the readers to develop some of the key ideas by themselves. Appendix A reviews special geometry from the mathematical point of view. Appendix B provides the necessary background in modular forms needed for understanding S-duality and string state counting.
Chandra, Sulekh; Kumar, Anil
2007-04-01
Co(II), Ni(II) and Cu(II) complexes are synthesized with thiosemicarbazone (L1) and semicarbazone (L2) derived from 2-acetyl furan. These complexes are characterized by elemental analysis, molar conductance, magnetic susceptibility measurements, mass, IR, electronic and EPR spectral studies. The molar conductance measurements of the complexes in DMSO correspond to non-electrolytic nature except Ni(L)2(NO3)2, which is 1:2 electrolyte. All the complexes are of high-spin type. On the basis of spectral studies an octahedral geometry may be assigned for Co(II) and Ni(II) complexes except nitrato complexes of Ni(II) which is of tetrahedral geometry, whereas tetragonal geometry for Cu(II) complexes.
Geometry-induced capillary emptying.
Rascón, Carlos; Parry, Andrew O; Aarts, Dirk G A L
2016-10-24
When a capillary is half-filled with liquid and turned to the horizontal, the liquid may flow out of the capillary or remain in it. For lack of a better criterion, the standard assumption is that the liquid will remain in a capillary of narrow cross-section, and will flow out otherwise. Here, we present a precise mathematical criterion that determines which of the two outcomes occurs for capillaries of arbitrary cross-sectional shape, and show that the standard assumption fails for certain simple geometries, leading to very rich and counterintuitive behavior. This opens the possibility of creating very sensitive microfluidic devices that respond readily to small physical changes, for instance, by triggering the sudden displacement of fluid along a capillary without the need of any external pumping.
Kinematic dynamos in spheroidal geometries
NASA Astrophysics Data System (ADS)
Ivers, D. J.
2017-10-01
The kinematic dynamo problem is solved numerically for a spheroidal conducting fluid of possibly large aspect ratio with an insulating exterior. The solution method uses solenoidal representations of the magnetic field and the velocity by spheroidal toroidal and poloidal fields in a non-orthogonal coordinate system. Scaling of coordinates and fields to a spherical geometry leads to a modified form of the kinematic dynamo problem with a geometric anisotropic diffusion and an anisotropic current-free condition in the exterior, which is solved explicitly. The scaling allows the use of well-developed spherical harmonic techniques in angle. Dynamo solutions are found for three axisymmetric flows in oblate spheroids with semi-axis ratios 1≤a/c≤25. For larger aspect ratios strong magnetic fields may occur in any region of the spheroid, depending on the flow, but the external fields for all three flows are weak and concentrated near the axis or periphery of the spheroid.
Geometry of minisuperspace in examples
NASA Astrophysics Data System (ADS)
Kerbrat, Yvan; Kerbrat-Lunc, Hélène; Śniatycki, Jȩdrzej
1992-04-01
Minisuperspace, interpreted as the configuration space for homogeneous cosmologies, has a naturally defined pseudo-Riemannian metric (supermetric) such that solutions of the ADM equations correspond to geodesics of the supermetric parametrized by arc-length (supertime). The supermetric is used to analyse the geometry of minisuperspace. In particular, if the supermetric is incomplete, its prolongations relate different components of minisuperspace. For Robertson-Walker universes with a homogeneous scalar field there exists a C1 prolongation of supermetric relating the positive and the negative curvature models. If the potential vanishes, then this prolongation is C∞. There is no prolongation of supermetric through generic boundary points between the Bianchi VIII and Bianchi IX models.
Geometry of spinning Ellis wormholes
NASA Astrophysics Data System (ADS)
Chew, Xiao Yan; Kleihaus, Burkhard; Kunz, Jutta
2016-11-01
We give a detailed account of the properties of spinning Ellis wormholes, supported by a phantom field. The general set of solutions depends on three parameters, associated with the size of the throat, the rotation, and the symmetry of the solutions. For symmetric wormholes the global charges possess the same values in both asymptotic regions, while this is no longer the case for nonsymmetric wormholes. We present mass formulas for these wormholes, study their quadrupole moments, and discuss the geometry of their throat and their ergoregion. We demonstrate, that these wormholes possess limiting configurations corresponding to an extremal Kerr black hole. Moreover, we analyze the geodesics of these wormholes, and show that they possess bound orbits.
Geometry-induced capillary emptying
Parry, Andrew O.; Aarts, Dirk G. A. L.
2016-01-01
When a capillary is half-filled with liquid and turned to the horizontal, the liquid may flow out of the capillary or remain in it. For lack of a better criterion, the standard assumption is that the liquid will remain in a capillary of narrow cross-section, and will flow out otherwise. Here, we present a precise mathematical criterion that determines which of the two outcomes occurs for capillaries of arbitrary cross-sectional shape, and show that the standard assumption fails for certain simple geometries, leading to very rich and counterintuitive behavior. This opens the possibility of creating very sensitive microfluidic devices that respond readily to small physical changes, for instance, by triggering the sudden displacement of fluid along a capillary without the need of any external pumping. PMID:27791079
Geometry dependence of stellarator turbulence
NASA Astrophysics Data System (ADS)
Mynick, H. E.; Xanthopoulos, P.; Boozer, A. H.
2009-11-01
Using the nonlinear gyrokinetic code package GENE/GIST [F. Jenko, W. Dorland, M. Kotschenreuther, and B. N. Rogers, Phys. Plasmas 7, 1904 (2000); P. Xanthopoulos, W. A. Cooper, F. Jenko, Yu. Turkin, A. Runov, and J. Geiger, Phys. Plasmas 16, 082303 (2009)], we study the turbulent transport in a broad family of stellarator designs, to understand the geometry dependence of the microturbulence. By using a set of flux tubes on a given flux surface, we construct a picture of the two-dimensional structure of the microturbulence over that surface and relate this to relevant geometric quantities, such as the curvature, local shear, and effective potential in the Schrödinger-like equation governing linear drift modes.
Spinors in Physics and Geometry
NASA Astrophysics Data System (ADS)
Trautman, A.; Furlan, G.
1988-11-01
The Table of Contents for the full book PDF is as follows: * Preface * Killing Spinors According to O. Hijazi and Applications * Self-Duality Conditions Satisfied by the Spin Connections on Spheres * Maslov Index and Half - Forms * Spin - 3/2 Fields on Black Hole Spacetimes * Indecomposable Conformal Spinors and Operator Product Expansions in a Massless QED Model * Nonlinear Spinor Representations * Nonlinear Wave Equations for Intrinsic Spinor Coordinates * Twistors - "Spinors" of SU(2,2), Their Generalizations and Achievements * Spinors, Reflections and Clifford Algebras: A Review * overline {SL}(n, R) Spinors for Particles, Gravity and Superstrings * Spinors on Compact Riemann Surfaces * Simple Spinors as Urfelder * Applications of Cartan Spinors to Differential Geometry in Higher Dimensions * Killing Spinors on Spheres and Projective Spaces * Spinor Structures on Homogeneous Riemannian Spaces * Classical Strings and Minimal Surfaces * Representing Spinors with Differential Forms * Inequalities for Spinors Norms in Clifford Algebras * The Importance of Spin * The Theory of World Spinors * Final List of Participants
Changing the Structure Boundary Geometry
Karasev, Viktor; Dzlieva, Elena; Ivanov, Artyom
2008-09-07
Analysis of previously obtained results shows that hexagonal crystal lattice is the dominant type of ordering, in particular, in striated glow discharges. We explore the possibility for changing the dust distribution in horizontal cross sections of relatively highly ordered structures in a glow-discharge. Presuming that boundary geometry can affect dust distribution, we used cylindrical coolers held at 0 deg. C and placed against a striation containing a structure, to change the geometry of its outer boundary. By varying the number of coolers, their positions, and their separations from the tube wall, azimuthally asymmetric thermophoretic forces can be used to form polygonal boundaries and vary the angles between their segments (in a horizontal cross section). The corner in the structure's boundary of 60 deg. stimulates formation of hexagonal cells. The structure between the supported parallel boundaries is also characterized by stable hexagonal ordering. We found that a single linear boundary segment does not give rise to any sizable domain, but generates a lattice extending from the boundary (without edge defects). A square lattice can be formed by setting the angle equal to 90 deg. . However, angles of 45 deg. and 135 deg. turned out easier to form. Square lattice was created by forming a near-135 deg. corner with four coolers. It was noted that no grain ordering is observed in the region adjacent to corners of angles smaller than 30 deg. , which do not promote ordering into cells of any shape. Thus, manipulation of a structure boundary can be used to change dust distribution, create structures free of the ubiquitous edge defects that destroy orientation order, and probably change the crystal lattice type.
Local geometry of isoscalar surfaces.
Dopazo, César; Martín, Jesús; Hierro, Juan
2007-11-01
An inert dynamically passive scalar in a constant density fluid forced by a statistically homogeneous field of turbulence has been investigated using the results of a 256(3) grid direct numerical simulation. Mixing characteristics are characterized in terms of either principal curvatures or mean and Gauss curvatures. The most probable small-scale scalar geometries are flat and tilelike isosurfaces. Preliminary correlations between flow and scalar small-scale structures associate highly curved saddle points with large-strain regions and elliptic points with vorticity-dominated zones. The concavity of the scalar profiles along the isosurface normal coordinate xn correlates well with negative mean curvatures, Gauss curvatures displaying any sign, which correspond to scalar minima, tiles, or saddle points; on the other hand, convexity along xn is associated with positive mean curvatures, Gauss curvatures ranging from negative to positive signs, featuring maxima, tiles, or saddle points; inflection points along xn correlate well with small values of the mean curvature and zero or negative values of kg, corresponding to plane isosurfaces or saddle points with curvatures of equal and opposite signs. Small values of the scalar gradient are associated with elliptic points, either concave or convex (kg>0) , for both concave and convex scalar profiles along xn. Large values of the scalar gradient (or, equivalently, scalar fluctuation dissipation rates) are generally connected with small values of the Gauss curvature (either flat or moderate-curvature tilelike local geometries), with both concave and convex scalar profiles along xn equally probable. Vortical local flow structures correlate well with small and moderate values of the scalar gradient, while strain-dominated regions are associated with large values.
Convection in Slab and Spheroidal Geometries
NASA Technical Reports Server (NTRS)
Porter, David H.; Woodward, Paul R.; Jacobs, Michael L.
2000-01-01
Three-dimensional numerical simulations of compressible turbulent thermally driven convection, in both slab and spheroidal geometries, are reviewed and analyzed in terms of velocity spectra and mixing-length theory. The same ideal gas model is used in both geometries, and resulting flows are compared. The piecewise-parabolic method (PPM), with either thermal conductivity or photospheric boundary conditions, is used to solve the fluid equations of motion. Fluid motions in both geometries exhibit a Kolmogorov-like k(sup -5/3) range in their velocity spectra. The longest wavelength modes are energetically dominant in both geometries, typically leading to one convection cell dominating the flow. In spheroidal geometry, a dipolar flow dominates the largest scale convective motions. Downflows are intensely turbulent and up drafts are relatively laminar in both geometries. In slab geometry, correlations between temperature and velocity fluctuations, which lead to the enthalpy flux, are fairly independent of depth. In spheroidal geometry this same correlation increases linearly with radius over the inner 70 percent by radius, in which the local pressure scale heights are a sizable fraction of the radius. The effects from the impenetrable boundary conditions in the slab geometry models are confused with the effects from non-local convection. In spheroidal geometry nonlocal effects, due to coherent plumes, are seen as far as several pressure scale heights from the lower boundary and are clearly distinguishable from boundary effects.
Convection in Slab and Spheroidal Geometries
NASA Technical Reports Server (NTRS)
Porter, David H.; Woodward, Paul R.; Jacobs, Michael L.
2000-01-01
Three-dimensional numerical simulations of compressible turbulent thermally driven convection, in both slab and spheroidal geometries, are reviewed and analyzed in terms of velocity spectra and mixing-length theory. The same ideal gas model is used in both geometries, and resulting flows are compared. The piecewise-parabolic method (PPM), with either thermal conductivity or photospheric boundary conditions, is used to solve the fluid equations of motion. Fluid motions in both geometries exhibit a Kolmogorov-like k(sup -5/3) range in their velocity spectra. The longest wavelength modes are energetically dominant in both geometries, typically leading to one convection cell dominating the flow. In spheroidal geometry, a dipolar flow dominates the largest scale convective motions. Downflows are intensely turbulent and up drafts are relatively laminar in both geometries. In slab geometry, correlations between temperature and velocity fluctuations, which lead to the enthalpy flux, are fairly independent of depth. In spheroidal geometry this same correlation increases linearly with radius over the inner 70 percent by radius, in which the local pressure scale heights are a sizable fraction of the radius. The effects from the impenetrable boundary conditions in the slab geometry models are confused with the effects from non-local convection. In spheroidal geometry nonlocal effects, due to coherent plumes, are seen as far as several pressure scale heights from the lower boundary and are clearly distinguishable from boundary effects.
Subsectors, Dynkin diagrams and new generalised geometries
NASA Astrophysics Data System (ADS)
Strickland-Constable, Charles
2017-08-01
We examine how generalised geometries can be associated with a labelled Dynkin diagram built around a gravity line. We present a series of new generalised geometries based on the groups Spin( d, d) × ℝ + for which the generalised tangent space transforms in a spinor representation of the group. In low dimensions these all appear in subsectors of maximal supergravity theories. The case d = 8 provides a geometry for eight-dimensional backgrounds of M theory with only seven-form flux, which have not been included in any previous geometric construction. This geometry is also one of a series of "half-exceptional" geometries, which "geometrise" a six-form gauge field. In the appendix, we consider exam-ples of other algebras appearing in gravitational theories and give a method to derive the Dynkin labels for the "section condition" in general. We argue that generalised geometry can describe restrictions and subsectors of many gravitational theories.
Riemannian geometry of fluctuation theory: An introduction
NASA Astrophysics Data System (ADS)
Velazquez, Luisberis
2016-05-01
Fluctuation geometry was recently proposed as a counterpart approach of Riemannian geometry of inference theory (information geometry), which describes the geometric features of the statistical manifold M of random events that are described by a family of continuous distributions dpξ(x|θ). This theory states a connection among geometry notions and statistical properties: separation distance as a measure of relative probabilities, curvature as a measure about the existence of irreducible statistical correlations, among others. In statistical mechanics, fluctuation geometry arises as the mathematical apparatus of a Riemannian extension of Einstein fluctuation theory, which is also closely related to Ruppeiner geometry of thermodynamics. Moreover, the curvature tensor allows to express some asymptotic formulae that account for the system fluctuating behavior beyond the gaussian approximation, while curvature scalar appears as a second-order correction of Legendre transformation between thermodynamic potentials.
Serpentine Geometry Plasma Actuators for Flow Control
2013-08-23
Serpentine geometry plasma actuators for flow control Mark Riherd and Subrata Roy Citation: J. Appl. Phys. 114, 083303 (2013); doi: 10.1063...DATES COVERED 00-00-2013 to 00-00-2013 4. TITLE AND SUBTITLE Serpentine geometry plasma actuators for flow control 5a. CONTRACT NUMBER 5b...unclassified c. THIS PAGE unclassified Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18 Serpentine geometry plasma actuators for flow
NASA Technical Reports Server (NTRS)
Samareh, Jamshid A.
1996-01-01
The purpose of this paper is to discuss the use of Computer-Aided Design (CAD) geometry in a Multi-Disciplinary Design Optimization (MDO) environment. Two techniques are presented to facilitate the use of CAD geometry by different disciplines, such as Computational Fluid Dynamics (CFD) and Computational Structural Mechanics (CSM). One method is to transfer the load from a CFD grid to a CSM grid. The second method is to update the CAD geometry for CSM deflection.
Geometry of solar coronal rays
NASA Astrophysics Data System (ADS)
Filippov, B. P.; Martsenyuk, O. V.; Platov, Yu. V.; Den, O. E.
2016-02-01
Coronal helmet streamers are the most prominent large-scale elements of the solar corona observed in white light during total solar eclipses. The base of the streamer is an arcade of loops located above a global polarity inversion line. At an altitude of 1-2 solar radii above the limb, the apices of the arches sharpen, forming cusp structures, above which narrow coronal rays are observed. Lyot coronagraphs, especially those on-board spacecrafts flying beyond the Earth's atmosphere, enable us to observe the corona continuously and at large distances. At distances of several solar radii, the streamers take the form of fairly narrow spokes that diverge radially from the Sun. This radial direction displays a continuous expansion of the corona into the surrounding space, and the formation of the solar wind. However, the solar magnetic field and solar rotation complicate the situation. The rotation curves radial streams into spiral ones, similar to water streams flowing from rotating tubes. The influence of the magnetic field is more complex and multifarious. A thorough study of coronal ray geometries shows that rays are frequently not radial and not straight. Coronal streamers frequently display a curvature whose direction in the meridional plane depends on the phase of the solar cycle. It is evident that this curvature is related to the geometry of the global solar magnetic field, which depends on the cycle phase. Equatorward deviations of coronal streamers at solar minima and poleward deviations at solar maxima can be interpreted as the effects of changes in the general topology of the global solar magnetic field. There are sporadic temporal changes in the coronal rays shape caused by remote coronal mass ejections (CMEs) propagating through the corona. This is also a manifestation of the influence of the magnetic field on plasma flows. The motion of a large-scale flux rope associated with a CME away from the Sun creates changes in the structure of surrounding field
NASA Astrophysics Data System (ADS)
Anderson, Lara B.; Heckman, Jonathan J.; Katz, Sheldon
2014-05-01
T-branes are a non-abelian generalization of intersecting branes in which the matrix of normal deformations is nilpotent along some subspace. In this paper we study the geometric remnant of this open string data for six-dimensional F-theory vacua. We show that in the dual M-theory / IIA compactification on a smooth Calabi-Yau threefold X smth, the geometric remnant of T-brane data translates to periods of the three-form potential valued in the intermediate Jacobian of X smth. Starting from a smoothing of a singular Calabi-Yau, we show how to track this data in singular limits using the theory of limiting mixed Hodge structures, which in turn directly points to an emergent Hitchin-like system coupled to defects. We argue that the physical data of an F-theory compactification on a singular threefold involves specifying both a geometry as well as the remnant of three-form potential moduli and flux which is localized on the discriminant. We give examples of T-branes in compact F-theory models with heterotic duals, and comment on the extension of our results to four-dimensional vacua.
Latent geometry of bipartite networks
NASA Astrophysics Data System (ADS)
Kitsak, Maksim; Papadopoulos, Fragkiskos; Krioukov, Dmitri
2017-03-01
Despite the abundance of bipartite networked systems, their organizing principles are less studied compared to unipartite networks. Bipartite networks are often analyzed after projecting them onto one of the two sets of nodes. As a result of the projection, nodes of the same set are linked together if they have at least one neighbor in common in the bipartite network. Even though these projections allow one to study bipartite networks using tools developed for unipartite networks, one-mode projections lead to significant loss of information and artificial inflation of the projected network with fully connected subgraphs. Here we pursue a different approach for analyzing bipartite systems that is based on the observation that such systems have a latent metric structure: network nodes are points in a latent metric space, while connections are more likely to form between nodes separated by shorter distances. This approach has been developed for unipartite networks, and relatively little is known about its applicability to bipartite systems. Here, we fully analyze a simple latent-geometric model of bipartite networks and show that this model explains the peculiar structural properties of many real bipartite systems, including the distributions of common neighbors and bipartite clustering. We also analyze the geometric information loss in one-mode projections in this model and propose an efficient method to infer the latent pairwise distances between nodes. Uncovering the latent geometry underlying real bipartite networks can find applications in diverse domains, ranging from constructing efficient recommender systems to understanding cell metabolism.
Geometry-induced asymmetric diffusion
Shaw, Robert S.; Packard, Norman; Schröter, Matthias; Swinney, Harry L.
2007-01-01
Past work has shown that ions can pass through a membrane more readily in one direction than the other. We demonstrate here in a model and an experiment that for a mixture of small and large particles such asymmetric diffusion can arise solely from an asymmetry in the geometry of the pores of the membrane. Our deterministic simulation considers a two-dimensional gas of elastic disks of two sizes diffusing through a membrane, and our laboratory experiment examines the diffusion of glass beads of two sizes through a metal membrane. In both experiment and simulation, the membrane is permeable only to the smaller particles, and the asymmetric pores lead to an asymmetry in the diffusion rates of these particles. The presence of even a small percentage of large particles can clog a membrane, preventing passage of the small particles in one direction while permitting free flow of the small particles in the other direction. The purely geometric kinetic constraints may play a role in common biological contexts such as membrane ion channels. PMID:17522257
Contour matching by epipolar geometry
NASA Astrophysics Data System (ADS)
Hu, Mao-Lin; Zhang, Damin; Wei, Sui
2003-09-01
Matching features computed in images is an important process in multiview image analysis. When the motion between two images is large, the matching problem becomes very difficult. In this paper, we propose a contour matching algorithm based on geometric constraints. With the assumption that the contours are obtained from images taken from a moving camera with static scenes, we apply the epipolar constraint between two sets of contours and compute the corresponding points on the contours. From the initial epipolar constraints obtained from comer point matching, candidate contours are selected according to the epipolar geometry, the linear relation among tangent vectors of the contour. In order to reduce the possibility of false matches, the curvature of the contour of match points on a contour is also used as a selection method. The initial epipolar constraint is refined from the matched sets of contours. The algorithm can be applied to a pair or two pairs of images. All of the processes are fully automatic and successfully implemented and tested with various synthetic images.
Noncommutative Riemannian geometry on graphs
NASA Astrophysics Data System (ADS)
Majid, Shahn
2013-07-01
We show that arising out of noncommutative geometry is a natural family of edge Laplacians on the edges of a graph. The family includes a canonical edge Laplacian associated to the graph, extending the usual graph Laplacian on vertices, and we find its spectrum. We show that for a connected graph its eigenvalues are strictly positive aside from one mandatory zero mode, and include all the vertex degrees. Our edge Laplacian is not the graph Laplacian on the line graph but rather it arises as the noncommutative Laplace-Beltrami operator on differential 1-forms, where we use the language of differential algebras to functorially interpret a graph as providing a 'finite manifold structure' on the set of vertices. We equip any graph with a canonical 'Euclidean metric' and a canonical bimodule connection, and in the case of a Cayley graph we construct a metric compatible connection for the Euclidean metric. We make use of results on bimodule connections on inner calculi on algebras, which we prove, including a general relation between zero curvature and the braid relations.
Latent geometry of bipartite networks.
Kitsak, Maksim; Papadopoulos, Fragkiskos; Krioukov, Dmitri
2017-03-01
Despite the abundance of bipartite networked systems, their organizing principles are less studied compared to unipartite networks. Bipartite networks are often analyzed after projecting them onto one of the two sets of nodes. As a result of the projection, nodes of the same set are linked together if they have at least one neighbor in common in the bipartite network. Even though these projections allow one to study bipartite networks using tools developed for unipartite networks, one-mode projections lead to significant loss of information and artificial inflation of the projected network with fully connected subgraphs. Here we pursue a different approach for analyzing bipartite systems that is based on the observation that such systems have a latent metric structure: network nodes are points in a latent metric space, while connections are more likely to form between nodes separated by shorter distances. This approach has been developed for unipartite networks, and relatively little is known about its applicability to bipartite systems. Here, we fully analyze a simple latent-geometric model of bipartite networks and show that this model explains the peculiar structural properties of many real bipartite systems, including the distributions of common neighbors and bipartite clustering. We also analyze the geometric information loss in one-mode projections in this model and propose an efficient method to infer the latent pairwise distances between nodes. Uncovering the latent geometry underlying real bipartite networks can find applications in diverse domains, ranging from constructing efficient recommender systems to understanding cell metabolism.
Combinatorics, geometry, and mathematical physics
Chen, W.Y.C.; Louck, J.D.
1998-11-01
This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). Combinatorics and geometry have been among the most active areas of mathematics over the past few years because of newly discovered inter-relations between them and their potential for applications. In this project, the authors set out to identify problems in physics, chemistry, and biology where these methods could impact significantly. In particular, the experience suggested that the areas of unitary symmetry and discrete dynamical systems could be brought more strongly under the purview of combinatorial methods. Unitary symmetry deals with the detailed description of the quantum mechanics of many-particle systems, and discrete dynamical systems with chaotic systems. The depth and complexity of the mathematics in these physical areas of research suggested that not only could significant advances be made in these areas, but also that here would be a fertile feedback of concept and structure to enrich combinatorics itself by setting new directions. During the three years of this project, the goals have been realized beyond expectation, and in this report the authors set forth these advancements and justify their optimism.
Eye movements and information geometry.
Lenz, Reiner
2016-08-01
The human visual system uses eye movements to gather visual information. They act as visual scanning processes and can roughly be divided into two different types: small movements around fixation points and larger movements between fixation points. The processes are often modeled as random walks, and recent models based on heavy tail distributions, also known as Levý flights, have been used in these investigations. In contrast to these approaches we do not model the stochastic processes, but we will show that the step lengths of the movements between fixation points follow generalized Pareto distributions (GPDs). We will use general arguments from the theory of extreme value statistics to motivate the usage of the GPD and show empirically that the GPDs provide good fits for measured eye tracking data. In the framework of information geometry the GPDs with a common threshold form a two-dimensional Riemann manifold with the Fisher information matrix as a metric. We compute the Fisher information matrix for the GPDs and introduce a feature vector describing a GPD by its parameters and different geometrical properties of its Fisher information matrix. In our statistical analysis we use eye tracker measurements in a database with 15 observers viewing 1003 images under free-viewing conditions. We use Matlab functions with their standard parameter settings and show that a naive Bayes classifier using the eigenvalues of the Fisher information matrix provides a high classification rate identifying the 15 observers in the database.
Kumari, Mukesh; Singh, Amrita; Chatterjee, Ratnamala E-mail: ratnamalac@gmail.com; Gupta, Arti; Prakash, Chandra
2014-12-28
In this work, magnetoelectric properties of a co-sintered bilayered composite of non-lead based piezoelectric 0.97(Bi{sub 0.5}Na{sub 0.5}TiO{sub 3})–0.03(K{sub 0.47}Na{sub 0.47}Li{sub 0.06}Nb{sub 0.74}Sb{sub 0.06}Ta{sub 0.2}O{sub 3}) and magnetostrictive Co{sub 0.6}Zn{sub 0.4}Fe{sub 1.7}Mn{sub 0.3}O{sub 4} are presented. Similar optimal sintering conditions of the individual components lead to a very clean interface as evidenced in the scanning electron microscopy, angle dispersive X-ray diffraction, and energy-dispersive X-ray (EDX) results. Clean interface results in strong intimate mechanical coupling between both components and causes a maximum transfer of induced strain, leading to a large magnetoelectric coupling ∼142 mV/cm·Oe measured in longitudinally magnetized-transversely polarized configuration (L-T mode). Remnant polarization ∼32 μC/cm{sup 2}, remnant magnetization ∼0.50 emu/g, and sufficiently high self biased magnetoelectricity ∼135 mV/cm Oe (L-T mode) were observed for this composite.
PREFACE: Water in confined geometries
NASA Astrophysics Data System (ADS)
Rovere, Mauro
2004-11-01
The study of water confined in complex systems in solid or gel phases and/or in contact with macromolecules is relevant to many important processes ranging from industrial applications such as catalysis and soil chemistry, to biological processes such as protein folding or ionic transport in membranes. Thermodynamics, phase behaviour and the molecular mobility of water have been observed to change upon confinement depending on the properties of the substrate. In particular, polar substrates perturb the hydrogen bond network of water, inducing large changes in the properties upon freezing. Understanding how the connected random hydrogen bond network of bulk water is modified when water is confined in small cavities inside a substrate material is very important for studies of stability and the enzymatic activity of proteins, oil recovery or heterogeneous catalysis, where water-substrate interactions play a fundamental role. The modifications of the short-range order in the liquid depend on the nature of the water-substrate interaction, hydrophilic or hydrophobic, as well as on its spatial range and on the geometry of the substrate. Despite extensive study, both experimentally and by computer simulation, there remain a number of open problems. In the many experimental studies of confined water, those performed on water in Vycor are of particular interest for computer simulation and theoretical studies since Vycor is a porous silica glass characterized by a quite sharp distribution of pore sizes and a strong capability to absorb water. It can be considered as a good candidate for studying the general behaviour of water in hydrophilic nanopores. But there there have been a number of studies of water confined in more complex substrates, where the interpretation of experiments and computer simulation is more difficult, such as in zeolites or in aerogels or in contact with membranes. Of the many problems to consider we can mention the study of supercooled water. It is
Quantum groups: Geometry and applications
Chu, Chong -Sun
1996-05-13
The main theme of this thesis is a study of the geometry of quantum groups and quantum spaces, with the hope that they will be useful for the construction of quantum field theory with quantum group symmetry. The main tool used is the Faddeev-Reshetikhin-Takhtajan description of quantum groups. A few content-rich examples of quantum complex spaces with quantum group symmetry are treated in details. In chapter 1, the author reviews some of the basic concepts and notions for Hopf algebras and other background materials. In chapter 2, he studies the vector fields of quantum groups. A compact realization of these vector fields as pseudodifferential operators acting on the linear quantum spaces is given. In chapter 3, he describes the quantum sphere as a complex quantum manifold by means of a quantum stereographic projection. A covariant calculus is introduced. An interesting property of this calculus is the existence of a one-form realization of the exterior differential operator. The concept of a braided comodule is introduced and a braided algebra of quantum spheres is constructed. In chapter 4, the author considers the more general higher dimensional quantum complex projective spaces and the quantum Grassman manifolds. Differential calculus, integration and braiding can be introduced as in the one dimensional case. Finally, in chapter 5, he studies the framework of quantum principal bundle and construct the q-deformed Dirac monopole as a quantum principal bundle with a quantum sphere as the base and a U(1) with non-commutative calculus as the fiber. The first Chern class can be introduced and integrated to give the monopole charge.
Teaching Geometry to Visually Impaired Students
ERIC Educational Resources Information Center
Pritchard, Christine K.; Lamb, John H.
2012-01-01
NCTM (2000) described geometry as "a means of describing, analyzing, and understanding the world and seeing beauty in its structures" (p. 309). Dossey et al. (2002) captured the essence of this aspect of visualization by stating that geometry fosters in students an ability to "visualize and mentally manipulate geometric objects." (p. 200).…
Trigonometry and Analytic Geometry: Curriculum Guide.
ERIC Educational Resources Information Center
Harlandale Independent School District, San Antonio, TX. Career Education Center.
The guide (one-quarter trigonometry course; two-quarter analytic geometry course) provides both subject matter and career preparation assistance for advanced mathematics teachers. It is arranged in vertical columns relating curriculum concepts in trigonometry and analytic geometry to curriculum performance objectives, career concepts and teaching…
A Multivariate Model of Achievement in Geometry
ERIC Educational Resources Information Center
Bailey, MarLynn; Taasoobshirazi, Gita; Carr, Martha
2014-01-01
Previous studies have shown that several key variables influence student achievement in geometry, but no research has been conducted to determine how these variables interact. A model of achievement in geometry was tested on a sample of 102 high school students. Structural equation modeling was used to test hypothesized relationships among…
Making Euclidean Geometry Compulsory: Are We Prepared?
ERIC Educational Resources Information Center
Van Putten, Sonja; Howie, Sarah; Stols, Gerrit
2010-01-01
This study investigated the attitude towards, as well as the level of understanding of Euclidean geometry in pre-service mathematics education (PME) students. In order to do so, a case study was undertaken within which a one group pre-post-test procedure was conducted around a geometry module, and a representative group of students was interviewed…
Improving African American Achievement in Geometry Honors
ERIC Educational Resources Information Center
Mims, Adrian B.
2010-01-01
This case study evaluated the significance of implementing an enrichment mathematics course during the summer to rising African American ninth graders entitled, "Geometry Honors Preview." In the past, 60 to 70 percent of African American students in this school district had withdrawn from Geometry Honors by the second academic quarter. This study…
Cognitive Styles, Dynamic Geometry and Measurement Performance
ERIC Educational Resources Information Center
Pitta-Pantazi, Demetra; Christou, Constantinos
2009-01-01
This paper reports the outcomes of an empirical study undertaken to investigate the effect of students' cognitive styles on achievement in measurement tasks in a dynamic geometry learning environment, and to explore the ability of dynamic geometry learning in accommodating different cognitive styles and enhancing students' learning. A total of 49…
Visual and Analytic Strategies in Geometry
ERIC Educational Resources Information Center
Kospentaris, George; Vosniadou, Stella; Kazic, Smaragda; Thanou, Emilian
2016-01-01
We argue that there is an increasing reliance on analytic strategies compared to visuospatial strategies, which is related to geometry expertise and not on individual differences in cognitive style. A Visual/Analytic Strategy Test (VAST) was developed to investigate the use of visuo-spatial and analytic strategies in geometry in 30 mathematics…
Computing Bisectors in a Dynamic Geometry Environment
ERIC Educational Resources Information Center
Botana, Francisco
2013-01-01
In this note, an approach combining dynamic geometry and automated deduction techniques is used to study the bisectors between points and curves. Usual teacher constructions for bisectors are discussed, showing that inherent limitations in dynamic geometry software impede their thorough study. We show that the interactive sketching of bisectors…
The slab geometry laser. I - Theory
NASA Technical Reports Server (NTRS)
Eggleston, J. M.; Kane, T. J.; Kuhn, K.; Byer, R. L.; Unternahrer, J.
1984-01-01
Slab geometry solid-state lasers offer significant performance improvements over conventional rod-geometry lasers. A detailed theoretical description of the thermal, stress, and beam-propagation characteristics of a slab laser is presented. The analysis includes consideration of the effects of the zig-zag optical path, which eliminates thermal and stress focusing and reduces residual birefringence.
An approach for management of geometry data
NASA Technical Reports Server (NTRS)
Dube, R. P.; Herron, G. J.; Schweitzer, J. E.; Warkentine, E. R.
1980-01-01
The strategies for managing Integrated Programs for Aerospace Design (IPAD) computer-based geometry are described. The computer model of geometry is the basis for communication, manipulation, and analysis of shape information. IPAD's data base system makes this information available to all authorized departments in a company. A discussion of the data structures and algorithms required to support geometry in IPIP (IPAD's data base management system) is presented. Through the use of IPIP's data definition language, the structure of the geometry components is defined. The data manipulation language is the vehicle by which a user defines an instance of the geometry. The manipulation language also allows a user to edit, query, and manage the geometry. The selection of canonical forms is a very important part of the IPAD geometry. IPAD has a canonical form for each entity and provides transformations to alternate forms; in particular, IPAD will provide a transformation to the ANSI standard. The DBMS schemas required to support IPAD geometry are explained.
Stop Teaching and Let Students Learn Geometry
ERIC Educational Resources Information Center
Bosse, Michael J.; Adu-Gyamfi, Kwaku
2011-01-01
For many high school students as well as preservice teachers, geometry can be difficult to learn without experiences that allow them to build their own understanding. The authors' approach to geometry instruction--with its integration of content, multiple representations, real-world examples, reading and writing, communication and collaboration as…
A Multivariate Model of Achievement in Geometry
ERIC Educational Resources Information Center
Bailey, MarLynn; Taasoobshirazi, Gita; Carr, Martha
2014-01-01
Previous studies have shown that several key variables influence student achievement in geometry, but no research has been conducted to determine how these variables interact. A model of achievement in geometry was tested on a sample of 102 high school students. Structural equation modeling was used to test hypothesized relationships among…
Reasoning by Contradiction in Dynamic Geometry
ERIC Educational Resources Information Center
Baccaglini-Frank, Anna; Antonini, Samuele; Leung, Allen; Mariotti, Maria Alessandra
2013-01-01
This paper addresses contributions that dynamic geometry systems (DGSs) may give in reasoning by contradiction in geometry. We present analyses of three excerpts of students' work and use the notion of pseudo object, elaborated from previous research, to show some specificities of DGS in constructing proof by contradiction. In particular, we…
Making Euclidean Geometry Compulsory: Are We Prepared?
ERIC Educational Resources Information Center
Van Putten, Sonja; Howie, Sarah; Stols, Gerrit
2010-01-01
This study investigated the attitude towards, as well as the level of understanding of Euclidean geometry in pre-service mathematics education (PME) students. In order to do so, a case study was undertaken within which a one group pre-post-test procedure was conducted around a geometry module, and a representative group of students was interviewed…
Geometry and Education in the Internet Age.
ERIC Educational Resources Information Center
Kortenkamp, Ulrich H.; Richter-Gebert, Jurgen
This paper discusses the requirements of Interactive Geometry Systems (IGSs) and how they can be fulfilled, explains how a geometry tool can benefit from the Internet, and presents Cinderella's Cafe. Cinderella's Cafe is a new IGS with a high mathematical background that uses the most general mathematical models whenever possible, is highly…
The Geometry of the Universe: Part 2
ERIC Educational Resources Information Center
Francis, Stephanie
2009-01-01
Hyperbolic geometry occurs on hyperbolic planes--the most commonly cited one being a saddle shape. In this article, the author explores negative hyperbolic curvature, and provides a detailed description of how she constructed two hyperbolic paraboloids. Hyperbolic geometry occurs on surfaces that have negative curvature. (Contains 11 figures and 4…
An approach for management of geometry data
NASA Technical Reports Server (NTRS)
Dube, R. P.; Herron, G. J.; Schweitzer, J. E.; Warkentine, E. R.
1980-01-01
The strategies for managing Integrated Programs for Aerospace Design (IPAD) computer-based geometry are described. The computer model of geometry is the basis for communication, manipulation, and analysis of shape information. IPAD's data base system makes this information available to all authorized departments in a company. A discussion of the data structures and algorithms required to support geometry in IPIP (IPAD's data base management system) is presented. Through the use of IPIP's data definition language, the structure of the geometry components is defined. The data manipulation language is the vehicle by which a user defines an instance of the geometry. The manipulation language also allows a user to edit, query, and manage the geometry. The selection of canonical forms is a very important part of the IPAD geometry. IPAD has a canonical form for each entity and provides transformations to alternate forms; in particular, IPAD will provide a transformation to the ANSI standard. The DBMS schemas required to support IPAD geometry are explained.
Teaching Molecular Geometry with the VSEPR Model
ERIC Educational Resources Information Center
Gillespie, Ronald J.
2004-01-01
The first introduction to molecular geometry should be through the simple and easily understood VSEPR model, as the Valence Bond Theory and MO Theory suffer from limitations as far as understanding molecular geometry is concerned. The VSEPR model gives a perfectly satisfactory description of the bonding that follows directly from the Lewis model…
Exact geometries from quantum chemical calculations
NASA Astrophysics Data System (ADS)
Cremer, Dieter; Kraka, Elfi; He, Yuan
2001-06-01
For seventeen molecules, complete basis set (CBS) geometries are obtained for Møller-Plesset perturbation methods at second (MP2), fourth (MP4), and sixth order (MP6) as well as for the Coupled Cluster methods CCD, CCSD, and CCSD( T). The correlation consistent basis sets cc-pVDZ, cc-pVTZ, and cc-pVQZ were systematically applied and calculated geometries extrapolated to the limit of an infinitely large basis set. MP6 equilibrium geometries are more accurate than MP2 or MP4 geometries at the CBS limit and provide AH bond lengths with an accuracy of 0.001 Å. However, AB bonds are always predicted too long because of the lack of sufficient coupling effects between p-electron correlation at MP6. CCSD( T) provides reasonable AB bond lengths although these are in general too short by 0.003 Å. Due to error cancellation very accurate geometries are obtained at the CCSD( T)/cc-pVTZ and CCSD( T)/cc-pVQZ level of theory. With the help of the accurate equilibrium geometries obtained in this work, several experimentally based geometries could be corrected. The effects of HF-optimized basis sets, diffuse functions or the frozen core approximation on geometry optimizations are discussed. It is emphasized that the use of the cc-pVDZ or any other VDZ+P basis set should be avoided in correlation corrected ab initio calculations.
Reflection: Its Concepts and Applications in Geometry
ERIC Educational Resources Information Center
Man, Yiu Kwong
2004-01-01
This paper discusses the basic concepts of reflection and its related concepts in optics. It aims at providing examples on how to apply the principle of reflection in geometry. Explorations of the concepts involved via dynamic geometry software are also included.
Reflection: Its Concepts and Applications in Geometry
ERIC Educational Resources Information Center
Man, Yiu Kwong
2004-01-01
This paper discusses the basic concepts of reflection and its related concepts in optics. It aims at providing examples on how to apply the principle of reflection in geometry. Explorations of the concepts involved via dynamic geometry software are also included.
Geometry, Senior High School Curriculum Guide.
ERIC Educational Resources Information Center
Klier, Katherine M., Ed.
This syllabus presents a fused course in plane, solid, and coordinate geometry for secondary school students. Elementary set theory, logic, and the principles of separation provide unifying threads throughout this approach to geometry. There are actually two curriculum guides included; one for each of two different texts--Henderson, Pingry, and…
Fractal Geometry in Elementary School Mathematics.
ERIC Educational Resources Information Center
Vacc, Nancy Nesbitt
1992-01-01
Reports a case study to evaluate whether basic concepts of fractal geometry are teachable to elementary school children and to determine the effectiveness of having an elementary school student present a lesson to inservice and preservice teachers. Concludes that simple concepts of fractal geometry appear appropriate for the elementary school…
Historical Digressions in Greek Geometry Lessons.
ERIC Educational Resources Information Center
Thomaidis, Yannis
1991-01-01
Presents an attempt to combine the history of mathematics of ancient Greece with the course on theoretical geometry taught in Greek secondary schools. Three sections present the history of ancient Greek geometry, geometrical constructions using straightedges and compasses, and an application of Ptolemy's theorem in solving ancient astronomy…
Historical Digressions in Greek Geometry Lessons.
ERIC Educational Resources Information Center
Thomaidis, Yannis
1991-01-01
Presents an attempt to combine the history of mathematics of ancient Greece with the course on theoretical geometry taught in Greek secondary schools. Three sections present the history of ancient Greek geometry, geometrical constructions using straightedges and compasses, and an application of Ptolemy's theorem in solving ancient astronomy…
Computing Bisectors in a Dynamic Geometry Environment
ERIC Educational Resources Information Center
Botana, Francisco
2013-01-01
In this note, an approach combining dynamic geometry and automated deduction techniques is used to study the bisectors between points and curves. Usual teacher constructions for bisectors are discussed, showing that inherent limitations in dynamic geometry software impede their thorough study. We show that the interactive sketching of bisectors…
The slab geometry laser. I - Theory
NASA Technical Reports Server (NTRS)
Eggleston, J. M.; Kane, T. J.; Kuhn, K.; Byer, R. L.; Unternahrer, J.
1984-01-01
Slab geometry solid-state lasers offer significant performance improvements over conventional rod-geometry lasers. A detailed theoretical description of the thermal, stress, and beam-propagation characteristics of a slab laser is presented. The analysis includes consideration of the effects of the zig-zag optical path, which eliminates thermal and stress focusing and reduces residual birefringence.
Improving African American Achievement in Geometry Honors
ERIC Educational Resources Information Center
Mims, Adrian B.
2010-01-01
This case study evaluated the significance of implementing an enrichment mathematics course during the summer to rising African American ninth graders entitled, "Geometry Honors Preview." In the past, 60 to 70 percent of African American students in this school district had withdrawn from Geometry Honors by the second academic quarter. This study…
Stop Teaching and Let Students Learn Geometry
ERIC Educational Resources Information Center
Bosse, Michael J.; Adu-Gyamfi, Kwaku
2011-01-01
For many high school students as well as preservice teachers, geometry can be difficult to learn without experiences that allow them to build their own understanding. The authors' approach to geometry instruction--with its integration of content, multiple representations, real-world examples, reading and writing, communication and collaboration as…
Poisson geometry from a Dirac perspective
NASA Astrophysics Data System (ADS)
Meinrenken, Eckhard
2017-07-01
We present proofs of classical results in Poisson geometry using techniques from Dirac geometry. This article is based on mini-courses at the Poisson summer school in Geneva, June 2016, and at the workshop Quantum Groups and Gravity at the University of Waterloo, April 2016.
Topics in sub-Riemannian geometry
NASA Astrophysics Data System (ADS)
Agrachev, A. A.
2016-12-01
Sub-Riemannian geometry is the geometry of spaces with non-holonomic constraints. This paper presents an informal survey of some topics in this area, starting with the construction of geodesic curves and ending with a recent definition of curvature. Bibliography: 28 titles.
Amoeboid motion in confined geometry
NASA Astrophysics Data System (ADS)
Wu, Hao; Thiébaud, M.; Hu, W.-F.; Farutin, A.; Rafaï, S.; Lai, M.-C.; Peyla, P.; Misbah, C.
2015-11-01
Many eukaryotic cells undergo frequent shape changes (described as amoeboid motion) that enable them to move forward. We investigate the effect of confinement on a minimal model of amoeboid swimmer. A complex picture emerges: (i) The swimmer's nature (i.e., either pusher or puller) can be modified by confinement, thus suggesting that this is not an intrinsic property of the swimmer. This swimming nature transition stems from intricate internal degrees of freedom of membrane deformation. (ii) The swimming speed might increase with increasing confinement before decreasing again for stronger confinements. (iii) A straight amoeoboid swimmer's trajectory in the channel can become unstable, and ample lateral excursions of the swimmer prevail. This happens for both pusher- and puller-type swimmers. For weak confinement, these excursions are symmetric, while they become asymmetric at stronger confinement, whereby the swimmer is located closer to one of the two walls. In this study, we combine numerical and theoretical analyses.
Amoeboid motion in confined geometry.
Wu, Hao; Thiébaud, M; Hu, W-F; Farutin, A; Rafaï, S; Lai, M-C; Peyla, P; Misbah, C
2015-01-01
Many eukaryotic cells undergo frequent shape changes (described as amoeboid motion) that enable them to move forward. We investigate the effect of confinement on a minimal model of amoeboid swimmer. A complex picture emerges: (i) The swimmer's nature (i.e., either pusher or puller) can be modified by confinement, thus suggesting that this is not an intrinsic property of the swimmer. This swimming nature transition stems from intricate internal degrees of freedom of membrane deformation. (ii) The swimming speed might increase with increasing confinement before decreasing again for stronger confinements. (iii) A straight amoeoboid swimmer's trajectory in the channel can become unstable, and ample lateral excursions of the swimmer prevail. This happens for both pusher- and puller-type swimmers. For weak confinement, these excursions are symmetric, while they become asymmetric at stronger confinement, whereby the swimmer is located closer to one of the two walls. In this study, we combine numerical and theoretical analyses.
FINAL REPORT: GEOMETRY AND ELEMENTARY PARTICLE PHYSICS
Singer, Isadore M.
2008-03-04
The effect on mathematics of collaborations between high-energy theoretical physics and modern mathematics has been remarkable. Mirror symmetry has revolutionized enumerative geometry, and Seiberg-Witten invariants have greatly simplified the study of four manifolds. And because of their application to string theory, physicists now need to know cohomology theory, characteristic classes, index theory, K-theory, algebraic geometry, differential geometry, and non-commutative geometry. Much more is coming. We are experiencing a deeper contact between the two sciences, which will stimulate new mathematics essential to the physicists’ quest for the unification of quantum mechanics and relativity. Our grant, supported by the Department of Energy for twelve years, has been instrumental in promoting an effective interaction between geometry and string theory, by supporting the Mathematical Physics seminar, postdoc research, collaborations, graduate students and several research papers.
ERIC Educational Resources Information Center
McAndrew, Erica M.; Morris, Wendy L.; Fennell, Francis
2017-01-01
Use of mathematics-related literature can engage students' interest and increase their understanding of mathematical concepts. A quasi-experimental study of two second-grade classrooms assessed whether daily inclusion of geometry-related literature in the classroom improved attitudes toward geometry and achievement in geometry. Consistent with the…
ERIC Educational Resources Information Center
McAndrew, Erica M.; Morris, Wendy L.; Fennell, Francis
2017-01-01
Use of mathematics-related literature can engage students' interest and increase their understanding of mathematical concepts. A quasi-experimental study of two second-grade classrooms assessed whether daily inclusion of geometry-related literature in the classroom improved attitudes toward geometry and achievement in geometry. Consistent with the…
Visuospatial Working Memory in Intuitive Geometry, and in Academic Achievement in Geometry
ERIC Educational Resources Information Center
Giofre, David; Mammarella, Irene C.; Ronconi, Lucia; Cornoldi, Cesare
2013-01-01
A study was conducted on the involvement of visuospatial working memory (VSWM) in intuitive geometry and in school performance in geometry at secondary school. A total of 166 pupils were administered: (1) six VSWM tasks, comprising simple storage and complex span tasks; and (2) the intuitive geometry task devised by Dehaene, Izard, Pica, and…
Analogy and Dynamic Geometry System Used to Introduce Three-Dimensional Geometry
ERIC Educational Resources Information Center
Mammana, M. F.; Micale, B.; Pennisi, M.
2012-01-01
We present a sequence of classroom activities on Euclidean geometry, both plane and space geometry, used to make three dimensional geometry more catchy and simple. The activity consists of a guided research activity that leads the students to discover unexpected properties of two apparently distant geometrical entities, quadrilaterals and…
Analogy and Dynamic Geometry System Used to Introduce Three-Dimensional Geometry
ERIC Educational Resources Information Center
Mammana, M. F.; Micale, B.; Pennisi, M.
2012-01-01
We present a sequence of classroom activities on Euclidean geometry, both plane and space geometry, used to make three dimensional geometry more catchy and simple. The activity consists of a guided research activity that leads the students to discover unexpected properties of two apparently distant geometrical entities, quadrilaterals and…
Drawing Dynamic Geometry Figures Online with Natural Language for Junior High School Geometry
ERIC Educational Resources Information Center
Wong, Wing-Kwong; Yin, Sheng-Kai; Yang, Chang-Zhe
2012-01-01
This paper presents a tool for drawing dynamic geometric figures by understanding the texts of geometry problems. With the tool, teachers and students can construct dynamic geometric figures on a web page by inputting a geometry problem in natural language. First we need to build the knowledge base for understanding geometry problems. With the…
Visuospatial Working Memory in Intuitive Geometry, and in Academic Achievement in Geometry
ERIC Educational Resources Information Center
Giofre, David; Mammarella, Irene C.; Ronconi, Lucia; Cornoldi, Cesare
2013-01-01
A study was conducted on the involvement of visuospatial working memory (VSWM) in intuitive geometry and in school performance in geometry at secondary school. A total of 166 pupils were administered: (1) six VSWM tasks, comprising simple storage and complex span tasks; and (2) the intuitive geometry task devised by Dehaene, Izard, Pica, and…
Comba, Peter; Haaf, Christina; Wadepohl, Hubert
2009-07-20
Four very rigid second generation bispidine-based ligands (bispidine = 3,7-diazabicyclo[3.3.1]nonane; tetra-, penta- and hexadentate; exclusively tertiary amine donors except for one of the pentadentate ligands, where one of the donors is a pyridyl group) and their Co(II), Ni(II), Cu(II), and Zn(II) complexes are reported. The experimentally determined X-ray crystal structures and computational data, based on empirical force field (MM) and approximate density functional theory (DFT) calculations, indicate that these new ligands, which are based on a modular system and therefore allow for a wide range of donor sets and coordination geometries, have rather large cavities (i.e., lead to a preference for +II over +III oxidation states and induce relatively low ligand fields), enforce trigonal geometries (pentacoordinate systems: preference for trigonal bipyramidal, hexacoordinate complexes: preference for trigonal prismatic), and lead, especially for Cu(II), to very high complex stabilities.
Stratospheric Aerosol Extinction Retrieval for SCIAMACHY Measurements in Limb Geometry
NASA Astrophysics Data System (ADS)
Dörner, S.; Pukite, J.; Penning de Vries, M.; Beirle, S.; Wagner, T.
2015-12-01
Techniques for retrieving height resolved information on stratospheric aerosol improved significantly in the past decade with the availability of satellites measurements in limb geometry. Instruments like OMPS, OSIRIS and SCIAMACHY provide height resolved radiance spectra with global coverage. Long term data sets of stratospheric aerosol extinction profiles are important for a detailed investigation of spatial and temporal variation and formation processes (e.g. after volcanic eruptions or in polar stratospheric clouds). Resulting data sets contain vital information for climate models (radiative effect) or chemistry models (reaction surface for heterogeneous chemistry). This study focuses on the SCIAMACHY instrument which measured scattered sunlight in the ultra violet, visible and near infra red spectral range between 2002 and 2012. SCIAMACHY's unique method of alternating measurements in limb and nadir geometry provides co-located profile and column information respectively that can be used to characterize plumes with small horizontal extents. The covered wavelength range potentially provides information on effective micro-physical properties of the aerosol particles. However, scattering on background aerosol constitutes only a small fraction of detected radiance and assumptions on particle characteristics (e.g., size distribution) have to be made which results in potential uncertainties especially for wavelengths below 700 nm and for measurements in backscatter geometry. Methods to reduce these uncertainties are investigated and applied to our newly developed retrieval algorithm. In addition, so called spatial straylight contamination of the measured signal was identified as a significant error source and an empirical correction scheme was developed. Comparisons with SAGE II measurement in occultation geometry and balloon borne measurements with an optical particle counter confirm the viability of our retrieval algorithm.
Stokes flow in ellipsoidal geometry
NASA Astrophysics Data System (ADS)
Vafeas, Panayiotis; Dassios, George
2006-09-01
Particle-in-cell models for Stokes flow through a relatively homogeneous swarm of particles are of substantial practical interest, because they provide a relatively simple platform for the analytical or semianalytical solution of heat and mass transport problems. Despite the fact that many practical applications involve relatively small particles (inorganic, organic, biological) with axisymmetric shapes, the general consideration consists of rigid particles of arbitrary shape. The present work is concerned with some interesting aspects of the theoretical analysis of creeping flow in ellipsoidal, hence nonaxisymmetric domains. More specifically, the low Reynolds number flow of a swarm of ellipsoidal particles in an otherwise quiescent Newtonian fluid, that move with constant uniform velocity in an arbitrary direction and rotate with an arbitrary constant angular velocity, is analyzed with an ellipsoid-in-cell model. The solid internal ellipsoid represents a particle of the swarm. The external ellipsoid contains the ellipsoidal particle and the amount of fluid required to match the fluid volume fraction of the swarm. The nonslip flow condition on the surface of the solid ellipsoid is supplemented by the boundary conditions on the external ellipsoidal surface which are similar to those of the sphere-in-cell model of Happel (self-sufficient in mechanical energy). This model requires zero normal velocity component and shear stress. The boundary value problem is solved with the aim of the potential representation theory. In particular, the Papkovich-Neuber complete differential representation of Stokes flow, valid for nonaxisymmetric geometries, is considered here, which provides the velocity and total pressure fields in terms of harmonic ellipsoidal eigenfunctions. The flexibility of the particular representation is demonstrated by imposing some conditions, which made the calculations possible. It turns out that the velocity of first degree, which represents the leading
basement reservoir geometry and properties
NASA Astrophysics Data System (ADS)
Walter, bastien; Geraud, yves; Diraison, marc
2017-04-01
Basement reservoirs are nowadays frequently investigated for deep-seated fluid resources (e.g. geothermal energy, groundwater, hydrocarbons). The term 'basement' generally refers to crystalline and metamorphic formations, where matrix porosity is negligible in fresh basement rocks. Geothermal production of such unconventional reservoirs is controlled by brittle structures and altered rock matrix, resulting of a combination of different tectonic, hydrothermal or weathering phenomena. This work aims to characterize the petro-structural and petrophysical properties of two basement surface analogue case studies in geological extensive setting (the Albert Lake rift in Uganda; the Ifni proximal margin of the South West Morocco Atlantic coast). Different datasets, using field structural study, geophysical acquisition and laboratory petrophysical measurements, were integrated to describe the multi-scale geometry of the porous network of such fractured and weathered basement formations. This study points out the multi-scale distribution of all the features constituting the reservoir, over ten orders of magnitude from the pluri-kilometric scale of the major tectonics structures to the infra-millimetric scale of the secondary micro-porosity of fractured and weathered basements units. Major fault zones, with relatively thick and impermeable fault core structures, control the 'compartmentalization' of the reservoir by dividing it into several structural blocks. The analysis of these fault zones highlights the necessity for the basement reservoirs to be characterized by a highly connected fault and fracture system, where structure intersections represent the main fluid drainage areas between and within the reservoir's structural blocks. The suitable fluid storage areas in these reservoirs correspond to the damage zone of all the fault structures developed during the tectonic evolution of the basement and the weathered units of the basement roof developed during pre
Modeling of Internal State and Performance of an Ironmaking Blast Furnace: Slot vs Sector Geometries
NASA Astrophysics Data System (ADS)
Shen, Yansong; Guo, Baoyu; Chew, Sheng; Austin, Peter; Yu, Aibing
2016-04-01
Mathematical modeling is a cost-effective method to understand internal state and predict performance of ironmaking blast furnace (BF) for improving productivity and maintaining stability. In the past studies, both slot and sector geometries were used for BF modeling. In this paper, a mathematical model is described for simulating the complex behaviors of solid, gas and liquid multiphase flow, heat and mass transfers, and chemical reactions in a BF. Then the model is used to compare different model configurations, viz. slot and sector geometries by investigating their effects on predicted behaviors, in terms of two aspects: (i) internal state including cohesive zone, velocity, temperature, components concentration, reduction degree, gas utilization, and (ii) performance indicators including liquid output at the bottom and gas utilization rate at the furnace top. The comparisons show that on one hand, predictions of internal state of the furnace such as fluid flow and thermo-chemical phenomena using the slot and sector geometries are qualitatively comparable but quantitatively different. Both sector and slot geometries give a similar cohesive zone shape but the sector geometry gives a higher cohesive zone near the wall and faster reduction. On the other hand, the two geometries can produce similar performance indicators including gas utilization at the furnace top and liquid output at the bottom. Such a study is useful in selecting geometry for numerically examining BF operation with respect to different needs.
Ekennia, Anthony C.; Onwudiwe, Damian C.; Olasunkanmi, Lukman O.; Osowole, Aderoju A.; Ebenso, Eno E.
2015-01-01
Heteroleptic complexes of zinc(II), copper(II), manganese(II), and cobalt(II) of the types [MLL′(H2O)2]·nH2O and [MLL′]·nH2O have been synthesized using sodium N-methyl-N-phenyldithiocarbamate (L) and benzoylacetone (L′). The metal complexes were characterized by elemental analysis, electrical conductance, magnetic susceptibility, infrared (IR), and UV-visible spectroscopic studies. The electrical conductance measurements revealed the nonelectrolytic nature of the synthesized complexes. The results of the elemental analyses, magnetic susceptibility measurements, and electronic spectra inferred that the Zn(II) complex adopted a four-coordinate geometry while the Co(II), Cu(II), and Mn(II) complexes assumed octahedral geometries. The IR spectra showed that the metal ions coordinated with the ligands via the S- and O-donor atoms. The geometry, electronic, and thermodynamic parameters of the complexes were obtained from density functional theory (DFT) calculations. The spin density distributions, relative strength of H–bonds, and thermodynamic parameters revealed that the order of stability of the metal complexes is Mn < Co < Cu > Zn. The agar diffusion methods were used to study the antimicrobial activity of the complexes against two Gram positive bacteria (S. aureus and S. pneumoniae), one Gram negative bacterium (E. coli), and two fungi organisms (A. niger and A. candida) and the complexes showed a broad spectrum of activities against the microbes. PMID:26681931
Moving KML geometry elements within Google Earth
NASA Astrophysics Data System (ADS)
Zhu, Liang-feng; Wang, Xi-feng; Pan, Xin
2014-11-01
During the process of modeling and visualizing geospatial information on the Google Earth virtual globe, there is an increasing demand to carry out such operations as moving geospatial objects defined by KML geometry elements horizontally or vertically. Due to the absence of the functionality and user interface for performing the moving transformation, it is either hard or impossible to interactively move multiple geospatial objects only using the existing Google Earth desktop application, especially when the data sets are in large volume. In this paper, we present a general framework and associated implementation methods for moving multiple KML geometry elements within Google Earth. In our proposed framework, we first load KML objects into the Google Earth plug-in, and then extract KML geometry elements from the imported KML objects. Subsequently, we interactively control the movement distance along a specified orientation by employing a custom user interface, calculate the transformed geographic location for each KML geometry element, and adjust geographic coordinates of the points in each KML objects. And finally, transformed KML geometry elements can be displayed in Google Earth for 3D visualization and spatial analysis. A key advantage of the proposed framework is that it provides a simple, uniform and efficient user interface for moving multiple KML geometry elements within Google Earth. More importantly, the proposed framework and associated implementations can be conveniently integrated into other customizable Google Earth applications to support interactively visualizing and analyzing geospatial objects defined by KML geometry elements.
Detection of edges using local geometry
NASA Technical Reports Server (NTRS)
Gualtieri, J. A.; Manohar, M.
1989-01-01
Researchers described a new representation, the local geometry, for early visual processing which is motivated by results from biological vision. This representation is richer than is often used in image processing. It extracts more of the local structure available at each pixel in the image by using receptive fields that can be continuously rotated and that go to third order spatial variation. Early visual processing algorithms such as edge detectors and ridge detectors can be written in terms of various local geometries and are computationally tractable. For example, Canny's edge detector has been implemented in terms of a local geometry of order two, and a ridge detector in terms of a local geometry of order three. The edge detector in local geometry was applied to synthetic and real images and it was shown using simple interpolation schemes that sufficient information is available to locate edges with sub-pixel accuracy (to a resolution increase of at least a factor of five). This is reasonable even for noisy images because the local geometry fits a smooth surface - the Taylor series - to the discrete image data. Only local processing was used in the implementation so it can readily be implemented on parallel mesh machines such as the MPP. Researchers expect that other early visual algorithms, such as region growing, inflection point detection, and segmentation can also be implemented in terms of the local geometry and will provide sufficiently rich and robust representations for subsequent visual processing.
Calculus of Elementary Functions, Part II. Teacher's Commentary. Revised Edition.
ERIC Educational Resources Information Center
Herriot, Sarah T.; And Others
This course is intended for students who have a thorough knowledge of college preparatory mathematics, including algebra, axiomatic geometry, trigonometry, and analytic geometry. This teacher's guide is for Part II of the course. It is designed to follow Part I of the text. The guide contains background information, suggested instructional…
Bonnett, R; Buckley, D G; Hamzetash, D; Hawkes, G E; Ioannou, S; Stoll, M S
1984-01-01
An improved preparation of photobilirubin II in ammoniacal methanol is described. Evidence is presented which distinguishes between the two structures proposed earlier for photobilirubin II in favour of the cycloheptadienyl structure. Nuclear-Overhauser-enhancement measurements with bilirubin IX alpha and photobilirubin II in dimethyl sulphoxide are complicated by the occurrence of negative and zero effects. The partition coefficient of photobilirubin II between chloroform and phosphate buffer (pH 7.4) is 0.67. PMID:6743241
Atmospheric Science Data Center
2016-02-16
SAGE II Data and Information The goals of the Stratospheric Aerosol and Gas Experiment ( SAGE ) II are to determine the spatial distributions of stratospheric ... profiles and calculating monthly averages of each. The SAGE II sensor (a Sun Photometer) was launched into a 57-degree inclination ...
Inverse Marx modulators for self-biasing klystron depressed collectors
Kemp, Mark A.
2014-07-31
A novel pulsed depressed collector biasing scheme is proposed. This topology feeds forward energy recovered during one RF pulse for use on the following RF pulse. The presented ''inverse'' Marx charges biasing capacitors in series, and discharges them in parallel. Simulations are shown along with experimental demonstration on a 62kW klystron.
Self-biased reconfigurable graphene stacks for terahertz plasmonics
NASA Astrophysics Data System (ADS)
Gomez-Diaz, J. S.; Moldovan, C.; Capdevila, S.; Romeu, J.; Bernard, L. S.; Magrez, A.; Ionescu, A. M.; Perruisseau-Carrier, J.
2015-03-01
The gate-controllable complex conductivity of graphene offers unprecedented opportunities for reconfigurable plasmonics at terahertz and mid-infrared frequencies. However, the requirement of a gating electrode close to graphene and the single ‘control knob’ that this approach offers limits the practical implementation and performance of these devices. Here we report on graphene stacks composed of two or more graphene monolayers separated by electrically thin dielectrics and present a simple and rigorous theoretical framework for their characterization. In a first implementation, two graphene layers gate each other, thereby behaving as a controllable single equivalent layer but without any additional gating structure. Second, we show that adding an additional gate allows independent control of the complex conductivity of each layer within the stack and provides enhanced control on the stack equivalent complex conductivity. These results are very promising for the development of THz and mid-infrared plasmonic devices with enhanced performance and reconfiguration capabilities.
Self-biased reconfigurable graphene stacks for terahertz plasmonics.
Gomez-Diaz, J S; Moldovan, C; Capdevila, S; Romeu, J; Bernard, L S; Magrez, A; Ionescu, A M; Perruisseau-Carrier, J
2015-03-02
The gate-controllable complex conductivity of graphene offers unprecedented opportunities for reconfigurable plasmonics at terahertz and mid-infrared frequencies. However, the requirement of a gating electrode close to graphene and the single 'control knob' that this approach offers limits the practical implementation and performance of these devices. Here we report on graphene stacks composed of two or more graphene monolayers separated by electrically thin dielectrics and present a simple and rigorous theoretical framework for their characterization. In a first implementation, two graphene layers gate each other, thereby behaving as a controllable single equivalent layer but without any additional gating structure. Second, we show that adding an additional gate allows independent control of the complex conductivity of each layer within the stack and provides enhanced control on the stack equivalent complex conductivity. These results are very promising for the development of THz and mid-infrared plasmonic devices with enhanced performance and reconfiguration capabilities.
Emergence of wave equations from quantum geometry
Majid, Shahn
2012-09-24
We argue that classical geometry should be viewed as a special limit of noncommutative geometry in which aspects which are inter-constrained decouple and appear arbitrary in the classical limit. In particular, the wave equation is really a partial derivative in a unified extra-dimensional noncommutative geometry and arises out of the greater rigidity of the noncommutative world not visible in the classical limit. We provide an introduction to this 'wave operator' approach to noncommutative geometry as recently used[27] to quantize any static spacetime metric admitting a spatial conformal Killing vector field, and in particular to construct the quantum Schwarzschild black hole. We also give an introduction to our related result that every classical Riemannian manifold is a shadow of a slightly noncommutative one wherein the meaning of the classical Ricci tensor becomes very natural as the square of a generalised braiding.
Structure analysis for plane geometry figures
NASA Astrophysics Data System (ADS)
Feng, Tianxiao; Lu, Xiaoqing; Liu, Lu; Li, Keqiang; Tang, Zhi
2013-12-01
As there are increasing numbers of digital documents for education purpose, we realize that there is not a retrieval application for mathematic plane geometry images. In this paper, we propose a method for retrieving plane geometry figures (PGFs), which often appear in geometry books and digital documents. First, detecting algorithms are applied to detect common basic geometry shapes from a PGF image. Based on all basic shapes, we analyze the structural relationships between two basic shapes and combine some of them to a compound shape to build the PGF descriptor. Afterwards, we apply matching function to retrieve candidate PGF images with ranking. The great contribution of the paper is that we propose a structure analysis method to better describe the spatial relationships in such image composed of many overlapped shapes. Experimental results demonstrate that our analysis method and shape descriptor can obtain good retrieval results with relatively high effectiveness and efficiency.
Interactive graphics for quick-geometry modeling
NASA Technical Reports Server (NTRS)
Townsend, J. C.
1984-01-01
The QUICK-geometry system is a method for defining configuration shapes in completely analytical form. It was developed for use when the analytical definition of aircraft geometry is advantageous or necessary for the solution of the flow around it. While the QUICK-geometry system provides a convenient and flexible method for generating configurations with completely analytical definitions, experience showed that it can be difficult to match a previously defined configuration with a QUICK-geometry definition. Therefore, the National Aeronautics and Space Administration (NASA) and other users developed computer programs that aid in the generation of QUICK inputs. A NASA-developed set of such programs which recently were upgraded extensively to improve its usability and portability are described.
The Oak Leaf: Connecting Geometry and Biology.
ERIC Educational Resources Information Center
Snyder, Judy
1999-01-01
Presents an activity that integrates biology and mathematics. Involves students in actual biological research and uses geometry, statistics, and computers to interpret data about the leaves of a tree. (ASK)
Fractal Geometry in the High School Classroom.
ERIC Educational Resources Information Center
Camp, Dane R.
1995-01-01
Discusses classroom activities that involve applications of fractal geometry. Includes an activity sheet that explores Pascal's triangle, Sierpinsky's gasket, and modular arithmetic in two and three dimensions. (Author/MKR)
Designing Phoxonic Metamaterials with Fractal Geometry
NASA Astrophysics Data System (ADS)
Ni, Sisi; Koh, Cheong Yang; Kooi, Steve; Thomas, Edwin
2012-02-01
Recently, the concepts of fractal geometry have been introduced into electromagnetic and plasmonic metamaterials. With their self-similarity, structures based on fractal geometry should exhibit multi-band character with high Q factors due to the scaling law. However, there exist few studies of phononic metamaterials based on fractal geometry. We use COMSOL to investigate the wave propagation in two dimensional systems possessing fractal geometries. The simulations of these systems, guided by our recently developed general design framework, help to understand the role of design in determining the phononic properties of the structures. Proposed structures are being fabricated via standard lithographic or 3D printing techniques. The wave behavior of the structures can be characterized using Brillouin Light Scattering, Scanning Acoustic Microscope and Near-field Scanning Optical Microscopy. Due to their sparse spatial distribution, fractal phononic structures show potential fir ``smart skin'', where multifunctional components can be fabricated on the same platform.
Geometry of contextuality from Grothendieck's coset space
NASA Astrophysics Data System (ADS)
Planat, Michel
2015-07-01
The geometry of cosets in the subgroups of the two-generator free group nicely fits, via Grothendieck's dessins d'enfants, the geometry of commutation for quantum observables. In previous work, it was established that dessins stabilize point-line geometries whose incidence structure reflects the commutation of (generalized) Pauli operators. Now we find that the nonexistence of a dessin for which the commutator precisely corresponds to the commutator of quantum observables on all lines of the geometry is a signature of quantum contextuality. This occurs first at index : in Mermin's square and at index in Mermin's pentagram, as expected. Commuting sets of -qubit observables with are found to be contextual as well as most generalized polygons. A geometrical contextuality measure is introduced.
Geometry independence of three-string vertices
NASA Astrophysics Data System (ADS)
Maeno, Masahiro
1989-01-01
The geometry independence of three-string vertices in both HIKKO's and Witten's string field theories is examined. A careful regularization shows that the anomaly which has been reported by Morris and Mañes vanishes.
Non-Euclidean Geometry and Unreal Numbers.
ERIC Educational Resources Information Center
Thwaites, G. N.
1989-01-01
This article discusses two of the reasons for the decline of formal Euclidean geometry in recent syllabi: (1) Traditional approach; and (2) Inherent difficulties. Suggested are some reasons and examples as to why the decline should be reversed. (YP)
NASA Astrophysics Data System (ADS)
Chavan, S. S.; Sawant, V. A.
2010-02-01
Some thiazolylazo derivatives and their metal complexes of the type [M(L)(H 2O)Cl]; M = Mn(II), Co(II), Ni(II), Cu(II) and L = 6-(2'-thiazolylazo)-2-mercapto-quinazolin-4-one (HL 1), 6-(4'-phenyl-2'-thiazolylazo)-2-mercapto-quinazolin-4-one (HL 2), 6-(2'-thiazolylazo)-2-mercapto-3-( m-tolyl)-quinazolin-4-one (HL 3) and 6-(4'-phenyl-2'-thiazolylazo)-2-mercapto-3-( m-tolyl)-quinazolin-4-one (HL 4) have been prepared. All the complexes were characterized on the basis of elemental analysis, molar conductance, magnetic moment, IR, UV-vis, ESR, TG-DTA and powder X-ray diffraction studies. IR spectra of these complexes reveal that the complex formation occurred through thiazole nitrogen, azo nitrogen, imino nitrogen and sulfur atom of the ligands. On the basis of electronic spectral data and magnetic susceptibility measurement octahedral geometry has been proposed for the Mn(II), Co(II) and Ni(II) complexes and distorted octahedral geometry for the Cu(II) complexes. Electrochemical behavior of Ni(II) complexes exhibit quasireversible oxidation corresponding to Ni(III)/Ni(II) couple along with ligand reduction. X-ray diffraction study is used to elucidate the crystal structure of the complexes.
DeLucca, John F.; Peloquin, John M.; Smith, Lachlan J.; Wright, Alexander C.; Vresilovic, Edward J.; Elliott, Dawn M.
2017-01-01
Geometry is an important indicator of disc mechanical function and degeneration. While the geometry and associated degenerative changes in the nucleus pulposus and the annulus fibrosus are well-defined, the geometry of the cartilage endplate (CEP) and its relationship to disc degeneration are unknown. The objectives of this study were to quantify CEP geometry in three dimensions using an MRI FLASH imaging sequence and evaluate relationships between CEP geometry and age, degeneration, spinal level, and overall disc geometry. To do so, we assessed the MRI-based measurements for accuracy and repeatability. Next, we measured CEP geometry across a larger sample set and correlated CEP geometric parameters to age, disc degeneration, level, and disc geometry. The MRI-based measures resulted in thicknesses (0.3–1 mm) that are comparable to prior measurements of CEP thickness. CEP thickness was greatest at the anterior/posterior (A/P) margins and smallest in the center. The CEP A/P thickness, axial area, and lateral width decreased with age but were not related to disc degeneration. Age-related, but not degeneration-related, changes in geometry suggest that the CEP may not follow the progression of disc degeneration. Ultimately, if the CEP undergoes significant geometric changes with aging and if these can be related to low back pain, a clinically feasible translation of the FLASH MRI-based measurement of CEP geometry presented in this study may prove a useful diagnostic tool. PMID:27232974
Phase distribution in complex geometry conduits
Lahey, R.T. Jr.; Lopez de Bertodano, M.; Jones, O.C. Jr.
1992-12-31
Some of the most important and challenging problems in two-phase flow today have to do with the understanding and prediction of multidimensional phenomena, in particular, lateral phase distribution in both simple and complex geometry conduits. A prior review paper summarized the state-of-the-art in the understanding of phase distribution phenomena, and the ability to perform mechanistic multidimensional predictions. The purpose of this paper is to update that review, with particular emphasis on complex geometry conduit predictive capabilities.
Geometry of quantum computation with qutrits.
Li, Bin; Yu, Zu-Huan; Fei, Shao-Ming
2013-01-01
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum computation with n qutrits. We show that the optimal quantum circuits are essentially equivalent to the shortest path between two points in a certain curved geometry of SU(3(n)). As an example, three-qutrit systems are investigated in detail.
Optimum geometry selection for sensor fusion
NASA Astrophysics Data System (ADS)
Kadar, Ivan
1998-07-01
A relative sensors-to-target geometry measure-of-merit (MOM), based on the Geometric Dilution of Precision (GDOP) measure, is developed. The method of maximum likelihood estimation is introduced for the solution of the position location problem. A linearized measurement model-based error sensitivity analysis is used to derive an expression for the GDOP MOM. The GDOP MOM relates the sensor measurement errors to the target position errors as a function of sensors-to-target geometry. In order to illustrate the efficacy of GDOP MOM for fusion systems, GDOP functional relationships are computed for bearing-only measuring sensors-to-target geometries. The minimum GDOP and associated specific target-to-sensors geometries are computed and illustrated for both two and three bearing-only measuring sensors. Two and three-dimensional plots of relative error contours provide a geometric insight to sensor placement as a function of geometry induced error dilution. The results can be used to select preferred target- to-sensor(s) geometries for M sensors in this application. The GDOP MOM is general and is readily extendable to other measurement-based sensors and fusion architectures.
Orientifolded locally AdS3 geometries
NASA Astrophysics Data System (ADS)
Loran, F.; Sheikh-Jabbari, M. M.
2011-01-01
Continuing the analysis of [Loran F and Sheikh-Jabbari M M 2010 Phys. Lett. B 693 184-7], we classify all locally AdS3 stationary axi-symmetric unorientable solutions to AdS3 Einstein gravity and show that they are obtained by applying certain orientifold projection on AdS3, BTZ or AdS3 self-dual orbifold, respectively, O-AdS3, O-BTZ and O-SDO geometries. Depending on the orientifold fixed surface, the O-surface, which is either a space-like 2D plane or a cylinder, or a light-like 2D plane or a cylinder, one can distinguish four distinct cases. For the space-like orientifold plane or cylinder cases, these geometries solve AdS3 Einstein equations and are hence locally AdS3 everywhere except at the O-surface, where there is a delta-function source. For the light-like cases, the geometry is a solution to Einstein equations even at the O-surface. We discuss the causal structure for static, extremal and general rotating O-BTZ and O-SDO cases as well as the geodesic motion on these geometries. We also discuss orientifolding Poincaré patch AdS3 and AdS2 geometries as a way to geodesic completion of these spaces and comment on the 2D CFT dual to the O-geometries.
An Improvement on SSA Congruence for Geometry and Trigonometry.
ERIC Educational Resources Information Center
Yeshurun, Shraga; Kay, David C.
1983-01-01
Three ideas are explored: (1) an improvement of the SSA congruence theorem for trigonometry; (2) a discussion of the failure of SSA in spherical geometry; and (3) an extension of SSA to spherical geometry and hyperbolic geometry. (MNS)
An Improvement on SSA Congruence for Geometry and Trigonometry.
ERIC Educational Resources Information Center
Yeshurun, Shraga; Kay, David C.
1983-01-01
Three ideas are explored: (1) an improvement of the SSA congruence theorem for trigonometry; (2) a discussion of the failure of SSA in spherical geometry; and (3) an extension of SSA to spherical geometry and hyperbolic geometry. (MNS)
NASA Astrophysics Data System (ADS)
Kalanithi, M.; Kodimunthiri, D.; Rajarajan, M.; Tharmaraj, P.
2011-11-01
Coordination compounds of VO(IV), Co(II), Ni(II), Cu(II) and Zn(II) with the Schiff base obtained through the condensation of 2-aminothiazole with 3-formyl chromone were synthesized. The compounds were characterized by 1H, 13C NMR, UV-Vis, IR, Mass, EPR, molar conductance and magnetic susceptibility measurements. The Cu(II) complex possesses tetrahedrally distorted square planar geometry whereas Co(II), Ni(II), and Zn(II) show distorted tetrahedral geometry. The VO(IV) complex shows square pyramidal geometry. The cyclic voltammogram of Cu (II) complex showed a well defined redox couple Cu(II)/Cu(I) with quasireversible nature. The antimicrobial activity against the species Pseudomonas aeruginosa, Escherichia coli, Staphylococcus aureus, Bacillus subtilis, Candida albigans and Aspergillus niger was screened and compared to the activity of the ligand. Emission spectrum was recorded for the ligand and the metal(II) complexes. The second harmonic generation (SHG) efficiency was measured and found to have one fourth of the activity of urea. The SEM image of the copper(II) complex implies that the size of the particles is 2 μm.
Plasma drift-kinetic equation calculations in three-dimensional magnetic geometries
Reynolds, J. M.; Lopez-Bruna, D.
2010-07-15
A new code to simulate three-dimensional plasmas in complex toroidal geometries is presented. It solves drift-kinetic equations for the one-particle distribution function f based on their projection onto a functional basis consisting of an arbitrary number of Legendre-Laguerre polynomials. In this paper, these theoretical aspects of the code are exposed together with their relation with the standard formalism. Comparisons with neoclassical theory for the large aspect ratio case and first calculations in the geometry of the TJ-II Heliac are also presented.
Geometry-induced protein pattern formation
Thalmeier, Dominik; Halatek, Jacob; Frey, Erwin
2016-01-01
Protein patterns are known to adapt to cell shape and serve as spatial templates that choreograph downstream processes like cell polarity or cell division. However, how can pattern-forming proteins sense and respond to the geometry of a cell, and what mechanistic principles underlie pattern formation? Current models invoke mechanisms based on dynamic instabilities arising from nonlinear interactions between proteins but neglect the influence of the spatial geometry itself. Here, we show that patterns can emerge as a direct result of adaptation to cell geometry, in the absence of dynamical instability. We present a generic reaction module that allows protein densities robustly to adapt to the symmetry of the spatial geometry. The key component is an NTPase protein that cycles between nucleotide-dependent membrane-bound and cytosolic states. For elongated cells, we find that the protein dynamics generically leads to a bipolar pattern, which vanishes as the geometry becomes spherically symmetrical. We show that such a reaction module facilitates universal adaptation to cell geometry by sensing the local ratio of membrane area to cytosolic volume. This sensing mechanism is controlled by the membrane affinities of the different states. We apply the theory to explain AtMinD bipolar patterns in Δ EcMinDE Escherichia coli. Due to its generic nature, the mechanism could also serve as a hitherto-unrecognized spatial template in many other bacterial systems. Moreover, the robustness of the mechanism enables self-organized optimization of protein patterns by evolutionary processes. Finally, the proposed module can be used to establish geometry-sensitive protein gradients in synthetic biological systems. PMID:26739566
Schmidt, Taly Gilat
2011-01-01
Inverse-geometry computed tomography (IGCT) systems are being developed to provide improved volumetric imaging. In conventional multislice CT systems, x-rays are emitted from a small area and irradiate a large-area detector. In an IGCT system, x-ray sources are distributed over a large area, with each beam irradiating a small-area detector. Therefore, in the inverse geometry, a series of narrow x-ray beams are switched on and off while the gantry rotates. In conventional CT geometry, cone-beam and scatter artifacts increase with the imaged volume thickness. An inverse geometry may be less susceptible to scatter effects, because only a fraction of the field of view is irradiated at one time. The distributed source in the inverse geometry potentially improves sampling, leading to reduced cone-beam artifacts. In the inverse geometry, the tube current may be adjusted separately for each source location, which potentially reduces dose. Multiple IGCT prototypes have been constructed and tested on phantoms. A gantry-based IGCT system with one-second gantry rotation was developed, and images of phantoms and small animals were successfully acquired. Clinical feasibility with acceptable noise levels and scan times has not yet been shown. Overall, results from prototype systems suggest that the inverse geometry will enable imaging of a thick volume (∼16 cm) while potentially reducing cone-beam artifacts, scatter effects, and radiation dose. The magnitude of these benefits will depend on the specific IGCT implementation and need to be quantified relative to comparable multislice scanners. Copyright © 2011 Society of Cardiovascular Computed Tomography. Published by Elsevier Inc. All rights reserved.
Geometry-induced protein pattern formation.
Thalmeier, Dominik; Halatek, Jacob; Frey, Erwin
2016-01-19
Protein patterns are known to adapt to cell shape and serve as spatial templates that choreograph downstream processes like cell polarity or cell division. However, how can pattern-forming proteins sense and respond to the geometry of a cell, and what mechanistic principles underlie pattern formation? Current models invoke mechanisms based on dynamic instabilities arising from nonlinear interactions between proteins but neglect the influence of the spatial geometry itself. Here, we show that patterns can emerge as a direct result of adaptation to cell geometry, in the absence of dynamical instability. We present a generic reaction module that allows protein densities robustly to adapt to the symmetry of the spatial geometry. The key component is an NTPase protein that cycles between nucleotide-dependent membrane-bound and cytosolic states. For elongated cells, we find that the protein dynamics generically leads to a bipolar pattern, which vanishes as the geometry becomes spherically symmetrical. We show that such a reaction module facilitates universal adaptation to cell geometry by sensing the local ratio of membrane area to cytosolic volume. This sensing mechanism is controlled by the membrane affinities of the different states. We apply the theory to explain AtMinD bipolar patterns in [Formula: see text] EcMinDE Escherichia coli. Due to its generic nature, the mechanism could also serve as a hitherto-unrecognized spatial template in many other bacterial systems. Moreover, the robustness of the mechanism enables self-organized optimization of protein patterns by evolutionary processes. Finally, the proposed module can be used to establish geometry-sensitive protein gradients in synthetic biological systems.
Twisted geometries, twistors, and conformal transformations
NASA Astrophysics Data System (ADS)
Lângvik, Miklos; Speziale, Simone
2016-07-01
The twisted geometries of spin network states are described by simple twistors, isomorphic to null twistors with a timelike direction singled out. The isomorphism depends on the Immirzi parameter γ and reduces to the identity for γ =∞ . Using this twistorial representation, we study the action of the conformal group SU(2,2) on the classical phase space of loop quantum gravity, described by twisted geometry. The generators of translations and conformal boosts do not preserve the geometric structure, whereas the dilatation generator does. It corresponds to a one-parameter family of embeddings of T*SL(2,C) in twistor space, and its action preserves the intrinsic geometry while changing the extrinsic one—that is the boosts among polyhedra. We discuss the implication of this action from a dynamical point of view and compare it with a discretization of the dilatation generator of the continuum phase space, given by the Lie derivative of the group character. At leading order in the continuum limit, the latter reproduces the same transformation of the extrinsic geometry, while also rescaling the areas and volumes and preserving the angles associated with the intrinsic geometry. Away from the continuum limit, its action has an interesting nonlinear structure but is in general incompatible with the closure constraint needed for the geometric interpretation. As a side result, we compute the precise relation between the extrinsic geometry used in twisted geometries and the one defined in the gauge-invariant parametrization by Dittrich and Ryan and show that the secondary simplicity constraints they posited coincide with those dynamically derived in the toy model of [Classical Quantum Gravity 32, 195015 (2015)].
XAFS studies of Pb(II)-chloro and Hg(II)-chloro ternary complexes on goethite
Bargar, J.R.; Persson, Petra; Brown, Gordon E.
1997-01-01
EXAFS spectroscopy was used to study Pb(II) and Hg(II) adsorption complexes on goethite (??-FeOOH) in the presence of Cl-. At pH 7, the dominant Pb(II) species are bonded to edges of FeO6 octahedra and are similar to complexes that occur in the absence of Cl-. At pH ??? 6, Pb(II)-chloro ternary complexes predominate and are bonded to corners of FeO6 octahedra. At pH 6.5, linear Hg(OH)Cl ternary complexes predominate that are bonded to goethite through surface oxygens in a bent Hg-O-Fe geometry. In the absence of Cl-, the Hg(II) surface complexes retain this basic geometry, but an OH group replaces the chloride ion in the first coordination shell.
NASA Astrophysics Data System (ADS)
Refat, Moamen S.; El-Metwaly, Nashwa M.
2011-10-01
The reactions of the two common dyes [2TMPACT and 4PENI] with Mn(II), Co(II), Ni(II) and Cu(II) ions were done. All the isolated complexes have been characterized by physicochemical and spectroscopic techniques. The IR data reflect the bidentate mode of 2TMPACT towards the mononuclear complex [Mn(II)] even its tetradentate in binuclear complexes [Co(II) and Cu(II)]. However, the bidentate mode is the only behavior of 4PENI ligand towards each metal ion in its mononuclear complexes. The UV-vis spectral analysis beside the magnetic moment measurements are proposed different geometries concerning each metal ions with the two ligands under investigation, as the Mn(II)-2TMPACT complex is an octahedral but Mn(II)-4PENI is a tetrahedral geometry. All the synthesized compounds are thermogravimetrically investigated. The proposed thermal decomposition was discussed for each compound with each step as well as, the kinetic parameters were calculated for all preferrible decomposition steps. The mass spectroscopy tool was used to emphasis on the suitable molecular formula proposed and the fragmentation patterns were displayed. The fluorescence properties of the synthesized ligands and their complexes were studied in DMSO at room temperature.
Refat, Moamen S; el-Metwaly, Nashwa M
2011-10-15
The reactions of the two common dyes [2TMPACT and 4PENI] with Mn(II), Co(II), Ni(II) and Cu(II) ions were done. All the isolated complexes have been characterized by physicochemical and spectroscopic techniques. The IR data reflect the bidentate mode of 2TMPACT towards the mononuclear complex [Mn(II)] even its tetradentate in binuclear complexes [Co(II) and Cu(II)]. However, the bidentate mode is the only behavior of 4PENI ligand towards each metal ion in its mononuclear complexes. The UV-vis spectral analysis beside the magnetic moment measurements are proposed different geometries concerning each metal ions with the two ligands under investigation, as the Mn(II)-2TMPACT complex is an octahedral but Mn(II)-4PENI is a tetrahedral geometry. All the synthesized compounds are thermogravimetrically investigated. The proposed thermal decomposition was discussed for each compound with each step as well as, the kinetic parameters were calculated for all preferrible decomposition steps. The mass spectroscopy tool was used to emphasis on the suitable molecular formula proposed and the fragmentation patterns were displayed. The fluorescence properties of the synthesized ligands and their complexes were studied in DMSO at room temperature.
NASA Astrophysics Data System (ADS)
El-Metwally, Nashwa M.; Al-Hazmi, Gamil A. A.
2013-04-01
Some thiosemicarbazide complexes were prepared and deliberately investigated by all allowed tools. The ligand coordinates as a mono negative bidentate towards VO(II) and Ni(II) as well as a neutral bidentate towards Pd(II) and Cu(II) ions. Electronic spectral data beside the magnetic measurements facilitate the structural geometry proposal. EPR spectra of Cu(II) and VO(II) complexes were recorded in their solid state. Spin Hamiltonian parameters and molecular orbital coefficient for Cu(II) and VO(II) complexes were calculated and supporting the octahedral geometry of Cu(II) complex and a square pyramidal for VO(II) one. The biological activity investigation was studied by the use of all prepared compounds. The VO(II) and Cu(II) complexes display the susceptible biotoxicity against a gram-positive bacterium. Also, Cu(II) complex displays the same toxicity against gram-negative bacteria used. The effect of all compounds on DNA were photographed. A successive degradation for the DNA target was observed with Pd(II) and Ni(II) complexes beside their original ligand.
Beam geometry selection using sequential beam addition
Popple, Richard A. Brezovich, Ivan A.; Fiveash, John B.
2014-05-15
Purpose: The selection of optimal beam geometry has been of interest since the inception of conformal radiotherapy. The authors report on sequential beam addition, a simple beam geometry selection method, for intensity modulated radiation therapy. Methods: The sequential beam addition algorithm (SBA) requires definition of an objective function (score) and a set of candidate beam geometries (pool). In the first iteration, the optimal score is determined for each beam in the pool and the beam with the best score selected. In the next iteration, the optimal score is calculated for each beam remaining in the pool combined with the beam selected in the first iteration, and the best scoring beam is selected. The process is repeated until the desired number of beams is reached. The authors selected three treatment sites, breast, lung, and brain, and determined beam arrangements for up to 11 beams from a pool comprised of 25 equiangular transverse beams. For the brain, arrangements were additionally selected from a pool of 22 noncoplanar beams. Scores were determined for geometries comprised equiangular transverse beams (EQA), as well as two tangential beams for the breast case. Results: In all cases, SBA resulted in scores superior to EQA. The breast case had the strongest dependence on beam geometry, for which only the 7-beam EQA geometry had a score better than the two tangential beams, whereas all SBA geometries with more than two beams were superior. In the lung case, EQA and SBA scores monotonically improved with increasing number of beams; however, SBA required fewer beams to achieve scores equivalent to EQA. For the brain case, SBA with a coplanar pool was equivalent to EQA, while the noncoplanar pool resulted in slightly better scores; however, the dose-volume histograms demonstrated that the differences were not clinically significant. Conclusions: For situations in which beam geometry has a significant effect on the objective function, SBA can identify
NASA Astrophysics Data System (ADS)
Singh, Vinod P.; Singh, Pooja
2013-03-01
A series of metal complexes of Co(II), Ni(II), Cu(II) and Zn(II) with 2-amino benzoic acid thiophen-2-ylmethylene hydrazide (Habth) and 2-hydroxy benzoic acid thiophen-2-ylmethylene hydrazide (Hhbth) have been synthesized. The complexes were characterized by elemental analyses, molar conductance, magnetic susceptibility measurements, electronic, IR, NMR, ESR spectra and thermal studies (TGA and DTA). Molecular structure of the Habth ligand was determined by single crystal X-ray diffraction technique. Habth acts as a monobasic bidentate ligand in all its complexes bonding through a deprotonated Csbnd O- and lbond2 Cdbnd Nsbnd groups whereas, Hhbth acts as a monobasic bidentate in its Co(II) and Ni(II) complexes, bonding through a deprotonated Csbnd O- and lbond2 Cdbnd Nsbnd groups and as monobasic tridentate in Cu(II) and Zn(II) complexes bonding through lbond2 Cdbnd O, lbond2 Cdbnd Nsbnd and deprotonated (Csbnd O)- groups with the metal ion. Electronic spectra suggest a square planar geometry for Co(II), Ni(II) and Cu(II) complexes of Habth and Co(II) and Ni(II) complexes of Hhbth. However, the Cu(II) and Zn(II) complexes of Hhbth have octahedral geometry. The ESR spectra of Cu(II) complex of Hhbth in the solid state and in DMSO frozen solution show axial signals and suggest the presence of unpaired electron in d orbital of Cu(II). The Cu(II) complex of Habth in solid state shows isotropic signal, whereas, axial signal in DMSO frozen solution in the range of tetragonally distorted octahedral geometry due to interactions of DMSO molecules at axial positions. Thermal studies of some of the metal complexes show a multi-step decomposition pattern of bonded ligands in the complex.
Topology Changing Transitions in Bubbling Geometries
Horava, Petr; Shepard, Peter G.
2005-02-15
Topological transitions in bubbling half-BPS Type IIB geometries with SO(4) x SO(4) symmetry can be decomposed into a sequence of n elementary transitions. The half-BPS solution that describes the elementary transition is seeded by a phase space distribution of fermions filling two diagonal quadrants. We study the geometry of this solution in some detail. We show that this solution can be interpreted as a time dependent geometry, interpolating between two asymptotic pp-waves in the far past and the far future. The singular solution at the transition can be resolved in two different ways, related by the particle-hole duality in the effective fermion description. Some universal features of the topology change are governed by two-dimensional Type 0B string theory, whose double scaling limit corresponds to the Penrose limit of AdS_5 x S5 at topological transition. In addition, we present the full class of geometries describing the vicinity of the most general localized classical singularity that can occur in this class of half-BPS bubbling geometries.
Topology Changing Transitions in Bubbling Geometries
Horava, Petr; Shepard, Peter G.
2005-02-15
Topological transitions in bubbling half-BPS Type IIB geometries with SO(4) x SO(4) symmetry can be decomposed into a sequence of n elementary transitions. The half-BPS solution that describes the elementary transition is seeded by a phase space distribution of fermions filling two diagonal quadrants. We study the geometry of this solution in some detail. We show that this solution can be interpreted as a time dependent geometry, interpolating between two asymptotic pp-waves in the far past and the far future. The singular solution at the transition can be resolved in two different ways, related by the particle-hole duality in the effective fermion description. Some universal features of the topology change are governed by two-dimensional Type 0B string theory, whose double scaling limit corresponds to the Penrose limit of AdS_5 x S^5 at topological transition. In addition, we present the full class of geometries describing the vicinity of the most general localized classical singularity that can occur in this class of half-BPS bubbling geometries.
Towards numerical simulation of bubbly flows in complex geometries
NASA Astrophysics Data System (ADS)
Mattson, Michael; Mahesh, Krishnan
2008-11-01
We are developing the LES capability for bubbly flows in complex geometries using unstructured grids and an Euler--Lagrangian methodology. Two Lagrangian bubble models are considered: (i) the bubbles are treated as a dispersed phase in the carrier fluid, and individual bubbles are point particles governed by an equation for bubble motion and (ii) the force coupling method by Maxey et al. [Fluid Dyn. Res., 32 (1997), 143-156]. The evolution of the bubble radius (assuming spherical bubbles) is governed by the Rayleigh--Plesset equation and integrated using a Runge--Kutta integrator with adaptive time-stepping. The talk will discuss numerical issues and contrast results between the two methodologies. Numerical results ranging from the motion of individual bubbles in channels and around bodies to drag reduction by bubbles in turbulent channel flow will be presented.
6D microstate geometries from 10D structures
NASA Astrophysics Data System (ADS)
Giusto, Stefano; Martucci, Luca; Petrini, Michela; Russo, Rodolfo
2013-11-01
We use the formalism of Generalised Geometry to characterise in general the supersymmetric backgrounds in type II supergravity that have a null Killing vector. We then specify this analysis to configurations that preserve the same supersymmetries as the D1-D5-P system compactified on a four-manifold. We give a set of equations on the forms defining the supergravity background that are equivalent to the supersymmetry constraints and the equations of motion. This study is motivated by the search of new microstate geometries for the D1-D5-P black hole. As an example, we rewrite the linearised three-charge solution of arXiv:hep-th/0311092 in our formalism and show how to extend it to a non-linear, regular and asymptotically flat configuration. The dictionary is the following: H=H, FhereIIA=-FthereIIA, FhereIIB=FthereIIB, K=-32K, χ=-32K, ΨhereIIB=32ΦthereIIB, ΨhereIIA=-32ΦthereIIA.
Using surface impedance for calculating wakefields in flat geometry
Bane, Karl; Stupakov, Gennady
2015-03-18
Beginning with Maxwell's equations and assuming only that the wall interaction can be approximated by a surface impedance, we derive formulas for the generalized longitudinal and transverse impedance in flat geometry, from which the wakefields can also be obtained. From the generalized impedances, by taking the proper limits, we obtain the normal longitudinal, dipole, and quad impedances in flat geometry. These equations can be applied to any surface impedance, such as the known dc, ac, and anomalous skin models of wall resistance, a model of wall roughness, or one for a pipe with small, periodic corrugations. We show that, formore » the particular case of dc wall resistance, the longitudinal impedance obtained here agrees with a known result in the literature, a result that was derived from a very general formula by Henke and Napoly. As an example, we apply our results to representative beam and machine parameters in the undulator region of LCLS-II and estimate the impact of the transverse wakes on the machine performance.« less
Toric geometry and string theory descriptions of qudit systems
NASA Astrophysics Data System (ADS)
Belhaj, Adil; Ez-Zahraouy, Hamid; Sedra, Moulay Brahim
2015-09-01
In this paper, we propose a new way to approach qudit systems using toric geometry and related topics including the local mirror symmetry used in the string theory compactification. We refer to such systems as (n, d) quantum systems where n and d denote the number of the qudits and the basis states respectively. Concretely, we first relate the (n, d) quantum systems to the holomorphic sections of line bundles on n dimensional projective spaces CPn with degree n(d - 1) . These sections are in one-to-one correspondence with dn integral points on a n-dimensional simplex. Then, we explore the local mirror map in the toric geometry language to establish a linkage between the (n, d) quantum systems and type II D-branes placed at singularities of local Calabi-Yau manifolds. (1, d) and (2, d) are analyzed in some details and are found to be related to the mirror of the ALE space with the Ad-1 singularity and a generalized conifold respectively.
Deformations of special geometry: in search of the topological string
NASA Astrophysics Data System (ADS)
Cardoso, G. L.; de Wit, B.; Mahapatra, S.
2014-09-01
The topological string captures certain superstring amplitudes which are also encoded in the underlying string effective action. However, unlike the topological string free energy, the effective action that comprises higher-order derivative couplings is not defined in terms of duality covariant variables. This puzzle is resolved in the context of real special geometry by introducing the so-called Hesse potential, which is defined in terms of duality covariant variables and is related by a Legendre transformation to the function that encodes the effective action. It is demonstrated that the Hesse potential contains a unique subsector that possesses all the characteristic properties of a topological string free energy. Genus g ≤ 3 contributions are constructed explicitly for a general class of effective actions associated with a special-Kähler target space and are shown to satisfy the holomorphic anomaly equation of perturbative type-II topological string theory. This identification of a topological string free energy from an effective action is primarily based on conceptual arguments and does not involve any of its more specific properties. It is fully consistent with known results. A general theorem is presented that captures some characteristic features of the equivalence, which demonstrates at the same time that non-holomorphic deformations of special geometry can be dealt with consistently.
GEMPAK: An arbitrary aircraft geometry generator
NASA Technical Reports Server (NTRS)
Stack, S. H.; Edwards, C. L. W.; Small, W. J.
1977-01-01
A computer program, GEMPAK, has been developed to aid in the generation of detailed configuration geometry. The program was written to allow the user as much flexibility as possible in his choices of configurations and the detail of description desired and at the same time keep input requirements and program turnaround and cost to a minimum. The program consists of routines that generate fuselage and planar-surface (winglike) geometry and a routine that will determine the true intersection of all components with the fuselage. This paper describes the methods by which the various geometries are generated and provides input description with sample input and output. Also included are descriptions of the primary program variables and functions performed by the various routines. The FORTRAN program GEMPAK has been used extensively in conjunction with interfaces to several aerodynamic and plotting computer programs and has proven to be an effective aid in the preliminary design phase of aircraft configurations.
Geometry optimization of branchings in vascular networks
NASA Astrophysics Data System (ADS)
Khamassi, Jamel; Bierwisch, Claas; Pelz, Peter
2016-06-01
Progress has been made in developing manufacturing technologies which enable the fabrication of artificial vascular networks for tissue cultivation. However, those networks are rudimentary designed with respect to their geometry. This restricts long-term biological functionality of vascular cells which depends on geometry-related fluid mechanical stimuli and the avoidance of vessel occlusion. In the present work, a bioinspired geometry optimization for branchings in artificial vascular networks has been conducted. The analysis could be simplified by exploiting self-similarity properties of the system. Design rules in the form of two geometrical parameters, i.e., the branching angle and the radius ratio of the daughter branches, are derived using the wall shear stress as command variable. The numerical values of these parameters are within the range of experimental observations. Those design rules are not only beneficial for tissue engineering applications. Moreover, they can be used as indicators for diagnoses of vascular diseases or for the layout of vascular grafts.
The Magnetic Field Geometry of Cool Stars
NASA Astrophysics Data System (ADS)
See, Victor; Jardine, Moira; Vidotto, Aline; Donati, Jean-Francois; Folsom, Colin; Boro Saikia, Sudeshna; Bouvier, Jerome; Fares, Rim; Gregory, Scott; Hussain, Gaitee; Jeffers, Sandra; Marsden, Stephen; Morin, Julien; Moutou, Claire; do Nascimento, Jose-Dias, Jr.; Petit, Pascal; Rosen, Lisa; Waite, Ian
2016-06-01
Zeeman-Doppler imaging has been used to map the large-scale surface magnetic fields of cool stars across a wide range of stellar masses and rotation periods. The derived field geometries are surprising, with many stars showing strong azimuthal fields that are not observed on the Sun. In this poster, using 100 magnetic maps of over 50 stars, we present results showing how the magnetic field geometry of cool stars varies as a function of fundamental parameters. The stellar mass, and hence internal structure, critically influences the field geometry, although this is modified by the stellar rotation rate. We discuss the implications of these results for dynamo theory and the nature of stellar magnetic activity.
First-order Dyson coordinates and geometry.
Hermes, Matthew R; Hirata, So
2013-08-15
The mathematical constructs of the Dyson coordinates and geometry are introduced. The former are a unitary transformation of the normal coordinates and the anharmonic vibrational counterpart of the Dyson orbitals in electronic structure theory. The first-order Dyson coordinates bring the sums of the harmonic force constants and their first-order diagrammatic perturbation corrections (the first-order Dyson self-energy) to a diagonal form. The first-order Dyson geometry has no counterpart in electronic structure theory. It is the point on the potential energy surface at which the sums of the energy gradients and their first-order diagrammatic perturbation corrections vanish. It agrees with the vibrationally averaged geometry of vibrational self-consistent field (VSCF) theory in the bulk limit. These constructs provide a unified view of the relationship of VSCF and its diagrammatically size-consistent modifications as well as the self-consistent phonon method widely used in solid-state physics.
Packing of charged chains on toroidal geometries?
NASA Astrophysics Data System (ADS)
Yao, Zhenwei; Olvera de La Cruz, Monica
2013-03-01
We study sequential Langmuir adsorption of a flexible charged polyelectrolyte chain on tori. In the regime of monomer-monomer electrostatic interaction dominating over thermal fluctuations, it becomes a generalized Thomson problem. Various patterns of adsorbed chain are found including double spirals, disclination-like structures, Janus tori and uniform wrappings, arising from the long-range electrostatic interaction and the toroidal geometry. Their broken mirror symmetry and energetics are analyzed. In particular, we find a power law for the electrostatic energy; the dependence of the power on the geometry of tori implies a geometric origin. Furthermore, in the regime of large thermal fluctuation, we systematically study random walks on tori that generate chain configurations; the features associated with the toroidal geometry are discussed. This work was funded by grants from the Office of the Director of Defense Research and Engineering (DDR&E) and the Air Force Office of Scientific Research (AFOSR) under Award No. FA9550-10-1-0167.
Novel nanophotonics geometries for sensing applications
NASA Astrophysics Data System (ADS)
Smolyaninov, Igor I.; Davis, Christopher C.
2004-10-01
We describe our latest experimental and theoretical results on two promising nanophotonics geometries for sensor applications. These geometries are based on various combinations of nanohole and/or microdroplet arrays on the surfaces of metal films which support propagation of surface plasmon-polaritons. These novel geometries exhibit large enhancements of local electromagnetic field, which can be used in various nonlinear optical sensing arrangements. For example, liquid microdroplets on the gold film surface support surface plasmon whispering gallery modes. Local field enhancement due to excitation of such modes is determined by combination of both cavity electrodynamics and surface plasmon-polariton related effects. In addition, individual microdroplets have interesting imaging properties, which may be used in high-resolution visualization of individual viruses and cells.
Remarks on Contact and Jacobi Geometry
NASA Astrophysics Data System (ADS)
Bruce, Andrew James; Grabowska, Katarzyna; Grabowski, Janusz
2017-07-01
We present an approach to Jacobi and contact geometry that makes many facts, presented in the literature in an overcomplicated way, much more natural and clear. The key concepts are Kirillov manifolds and linear Kirillov structures, i.e., homogeneous Poisson manifolds and, respectively, homogeneous linear Poisson manifolds. The difference with the existing literature is that the homogeneity of the Poisson structure is related to a principal GL(1,R)-bundle structure on the manifold and not just to a vector field. This allows for working with Jacobi bundle structures on nontrivial line bundles and drastically simplifies the picture of Jacobi and contact geometry. Our results easily reduce to various basic theorems of Jacobi and contact geometry when the principal bundle structure is trivial, while giving new insights into the theory.
Gully geometry: what are we measuring?
NASA Astrophysics Data System (ADS)
Casalí, J.; Giménez, R.; Campo-Bescós, M. A.
2015-07-01
Much of the research on (ephemeral) gully erosion comprises the determination of the geometry of these eroded channels, especially their width and depth. This is not a simple task due to uncertainty generated by the wide range of variability in gully cross section shapes found in the field. However, in the literature, this uncertainty is not recognized so that no criteria for their measurement are indicated. The aim of this work is to make researchers aware of the ambiguity that arises when characterizing the geometry of an ephemeral gully and similar eroded channels. In addition, a measurement protocol is proposed with the ultimate goal of pooling criteria in future works. It is suggested that the geometry of a gully could be characterized through its mean equivalent width and mean equivalent depth, which, together with its length, define an "equivalent prismatic gully" (EPG). The latter would facilitate the comparison between different gullies.
Pearson's Functions to Describe FSW Weld Geometry
Lacombe, D.; Coupard, D.; Tcherniaeff, S.; Girot, F.; Gutierrez-Orrantia, M. E.
2011-01-17
Friction stir welding (FSW) is a relatively new joining technique particularly for aluminium alloys that are difficult to fusion weld. In this study, the geometry of the weld has been investigated and modelled using Pearson's functions. It has been demonstrated that the Pearson's parameters (mean, standard deviation, skewness, kurtosis and geometric constant) can be used to characterize the weld geometry and the tensile strength of the weld assembly. Pearson's parameters and process parameters are strongly correlated allowing to define a control process procedure for FSW assemblies which make radiographic or ultrasonic controls unnecessary. Finally, an optimisation using a Generalized Gradient Method allows to determine the geometry of the weld which maximises the assembly tensile strength.
Geometric Monte Carlo and black Janus geometries
NASA Astrophysics Data System (ADS)
Bak, Dongsu; Kim, Chanju; Kim, Kyung Kiu; Min, Hyunsoo; Song, Jeong-Pil
2017-04-01
We describe an application of the Monte Carlo method to the Janus deformation of the black brane background. We present numerical results for three and five dimensional black Janus geometries with planar and spherical interfaces. In particular, we argue that the 5D geometry with a spherical interface has an application in understanding the finite temperature bag-like QCD model via the AdS/CFT correspondence. The accuracy and convergence of the algorithm are evaluated with respect to the grid spacing. The systematic errors of the method are determined using an exact solution of 3D black Janus. This numerical approach for solving linear problems is unaffected initial guess of a trial solution and can handle an arbitrary geometry under various boundary conditions in the presence of source fields.
Supersymmetric geometries of IIA supergravity III
NASA Astrophysics Data System (ADS)
Gran, Ulf; Papadopoulos, George; von Schultz, Christian
2016-06-01
We find that (massive) IIA backgrounds that admit a {G}_2ltimes {mathbb{R}}^8 invariant Killing spinor must exhibit a null Killing vector field which leaves the Killing spinor invariant and that the rotation of the Killing vector field satisfies a certain g2 instanton condition. This result together with those in [4] and [5] complete the classification of geometries of all (massive) IIA backgrounds that preserve one supersymmetry. We also explore the geometry of a class of backgrounds which admit a {G}_2ltimes {mathbb{R}}^8 invariant Killing spinor and where in addition an appropriate 1-form bilinear vanishes. In all cases, we express the fluxes of the theory in terms of the geometry.
Interfacial geometry dictates cancer cell tumorigenicity
NASA Astrophysics Data System (ADS)
Lee, Junmin; Abdeen, Amr A.; Wycislo, Kathryn L.; Fan, Timothy M.; Kilian, Kristopher A.
2016-08-01
Within the heterogeneous architecture of tumour tissue there exists an elusive population of stem-like cells that are implicated in both recurrence and metastasis. Here, by using engineered extracellular matrices, we show that geometric features at the perimeter of tumour tissue will prime a population of cells with a stem-cell-like phenotype. These cells show characteristics of cancer stem cells in vitro, as well as enhanced tumorigenicity in murine models of primary tumour growth and pulmonary metastases. We also show that interfacial geometry modulates cell shape, adhesion through integrin α5β1, MAPK and STAT activity, and initiation of pluripotency signalling. Our results for several human cancer cell lines suggest that interfacial geometry triggers a general mechanism for the regulation of cancer-cell state. Similar to how a growing tumour can co-opt normal soluble signalling pathways, our findings demonstrate how cancer can also exploit geometry to orchestrate oncogenesis.
ERIC Educational Resources Information Center
Guven, Bulent
2012-01-01
This study examines the effect of dynamic geometry software (DGS) on students' learning of transformation geometry. A pre- and post-test quasi-experimental design was used. Participants in the study were 68 eighth grade students (36 in the experimental group and 32 in the control group). While the experimental group students were studying the…
Coordinate Geometry. Geometry Module for Use in a Mathematics Laboratory Setting.
ERIC Educational Resources Information Center
Brotherton, Sheila; And Others
This is one of a series of geometry modules developed for use by secondary students in a laboratory setting. This module includes: (1) Pythagorean Theorem (with review of radicals); (2) Basic Coordinate Geometry (distance and midpoint, slope, slope of parallels and perpendiculars, and equation of a line); (3) Selecting Coordinates; (4) Coordinate…
ERIC Educational Resources Information Center
Guven, Bulent
2012-01-01
This study examines the effect of dynamic geometry software (DGS) on students' learning of transformation geometry. A pre- and post-test quasi-experimental design was used. Participants in the study were 68 eighth grade students (36 in the experimental group and 32 in the control group). While the experimental group students were studying the…
ERIC Educational Resources Information Center
Anderson, Karen L.; Casey, M. Beth; Thompson, William L.; Burrage, Marie S.; Pezaris, Elizabeth; Kosslyn, Stephen M.
2008-01-01
This study investigated the relationship between 3 ability-based cognitive styles (verbal deductive, spatial imagery, and object imagery) and performance on geometry problems that provided different types of clues. The purpose was to determine whether students with a specific cognitive style outperformed other students, when the geometry problems…
Aspects of electrostatics in BTZ geometries
NASA Astrophysics Data System (ADS)
Herrera, Y.; Hurovich, V.; Santillán, O.; Simeone, C.
2015-10-01
In the present paper the electrostatics of charges in nonrotating BTZ black hole and wormhole spacetimes is studied. Our attention is focused on the self-force of a point charge in the geometry, for which a regularization prescription based on the Haddamard Green function is employed. The differences between the self-force in both cases is a theoretical experiment for distinguishing both geometries, which otherwise are locally indistinguishable. This idea was applied before to four and higher-dimensional black holes by the present and other authors. However, the particularities of the BTZ geometry makes the analysis considerable more complicated than those. First, the BTZ spacetimes are not asymptotically flat but instead asymptotically AdS. In addition, the relative distance d (r ,r +1 ) between two particles located at a radius r and r +1 in the geometry tends to zero when r →∞. This behavior, which is radically different in a flat geometry, changes the analysis of the asymptotic conditions for the electrostatic field. The other problem is that there exist several regularization methods other than the one we are employing, and there does not exist a proof in three dimensions that they are equivalent. However, we focus on the Haddamard method and obtain an expression for the hypothetical self-force in series, and the resulting expansion is convergent to the real solution. We suspect that the convergence is not uniform, and furthermore there are no summation formulas at our disposal. It appears, for points that are far away from the black hole the calculation of the Haddamard self-force requires higher-order summation. These subtleties are carefully analyzed in the paper, and it is shown that they lead to severe problems when calculating the Haddamard self-force for asymptotic points in the geometry.
NASA Astrophysics Data System (ADS)
Drzewiecka-Antonik, Aleksandra; Ferenc, Wiesława; Wolska, Anna; Klepka, Marcin T.; Cristóvão, Beata; Sarzyński, Jan; Rejmak, Paweł; Osypiuk, Dariusz
2017-01-01
The Co(II), Ni(II) and Cu(II) complexes with herbicide 2,4-dichlorophenoxyacetic acid (2,4-D) were synthesized and structurally characterized. The geometry of metal-ligand interaction was refined using XAFS and DFT studies. The Co(2,4-D)2·6H2O and Ni(2,4-D)2·4H2O complexes have octahedral geometry with two carboxylate groups of 2,4-D anions and four water molecules in the coordination sphere. The square planar geometry around metal cations formed by the carboxylate groups from two monodentate ligands and two water molecules, is observed for Cu(2,4-D)2·4H2O complex. In the recrystallized Ni(II) complex dinuclear 'Chinese lantern' structures with bridging carboxylate groups of 2,4-D were observed.
Method for Determining Optimum Injector Inlet Geometry
NASA Technical Reports Server (NTRS)
Trinh, Huu P. (Inventor); Myers, W. Neill (Inventor)
2015-01-01
A method for determining the optimum inlet geometry of a liquid rocket engine swirl injector includes obtaining a throttleable level phase value, volume flow rate, chamber pressure, liquid propellant density, inlet injector pressure, desired target spray angle and desired target optimum delta pressure value between an inlet and a chamber for a plurality of engine stages. The method calculates the tangential inlet area for each throttleable stage. The method also uses correlation between the tangential inlet areas and delta pressure values to calculate the spring displacement and variable inlet geometry of a liquid rocket engine swirl injector.
Fields and Laplacians on Quantum Geometries
NASA Astrophysics Data System (ADS)
Thürigen, Johannes
2015-01-01
In fundamentally discrete approaches to quantum gravity such as loop quantum gravity, spin-foam models, group field theories or Regge calculus observables are functions on discrete geometries. We present a bra-ket formalism of function spaces and discrete calculus on abstract simplicial complexes equipped with geometry and apply it to the mentioned theories of quantum gravity. In particular we focus on the quantum geometric Laplacian and discuss as an example the expectation value of the heat kernel trace from which the spectral dimension follows.
Semiclassical geometry of charged black holes
Frolov, Andrei V.; Kristjansson, Kristjan R.; Thorlacius, Larus
2005-07-15
At the classical level, two-dimensional dilaton gravity coupled to an abelian gauge field has charged black hole solutions, which have much in common with four-dimensional Reissner-Nordstroem black holes, including multiple asymptotic regions, timelike curvature singularities, and Cauchy horizons. The black hole spacetime is, however, significantly modified by quantum effects, which can be systematically studied in this two-dimensional context. In particular, the back-reaction on the geometry due to pair-creation of charged fermions destabilizes the inner horizon and replaces it with a spacelike curvature singularity. The semiclassical geometry has the same global topology as an electrically neutral black hole.
SABRINA - an interactive geometry modeler for MCNP
West, J.T.; Murphy, J. )
1988-01-01
One of the most difficult tasks when analyzing a complex three-dimensional system with Monte Carlo is geometry model development. SABRINA attempts to make the modeling process more user-friendly and less of an obstacle. It accepts both combinatorial solid bodies and MCNP surfaces and produces MCNP cells. The model development process in SABRINA is highly interactive and gives the user immediate feedback on errors. Users can view their geometry from arbitrary perspectives while the model is under development and interactively find and correct modeling errors. An example of a SABRINA display is shown. It represents a complex three-dimensional shape.
Path Deviation Equations in AP-Geometry
NASA Astrophysics Data System (ADS)
Wanas, M. I.; Kahil, M. E.
2006-02-01
Recently, it has been shown that Absolute Parallelism (AP) geometry admits paths that are naturally quantized. These paths have been used to describe the motion of spinning particles in a background gravitational field. In case of a weak static gravitational field limits, the paths are applied successfully to interpret the discrepancy in the motion of thermal neutrons in the Earth's gravitational field (COW-experiment). The aim of the present work is to explore the properties of the deviation equations corresponding to these paths. In the present work the deviation equations are derived and compared to the geodesic deviation equation of the Riemannian geometry.
Computational fluid dynamics using CATIA created geometry
Gengler, J.E.
1989-01-01
A method has been developed to link the geometry definition residing on a CAD/CAM system with a computational fluid dynamics (CFD) tool needed to evaluate aerodynamic designs and requiring the memory capacity of a supercomputer. Requirements for surfaces suitable for CFD analysis are discussed. Techniques for developing surfaces and verifying their smoothness are compared, showing the capability of the CAD/CAM system. The utilization of a CAD/CAM system to create a computational mesh is explained, and the mesh interaction with the geometry and input file preparation for the CFD analysis is discussed.
Solc filters in a reflective geometry
NASA Astrophysics Data System (ADS)
Messaadi, Abdelghafour; Vargas, Asticio; Sánchez-López, María M.; García-Martínez, Pascuala; Kula, Przemysław; Bennis, Noureddine; Moreno, Ignacio
2017-04-01
We present the realization of a bulk optics birefringent Solc filter in a reflective geometry. This geometry reduces by half the number of required retarders, ensures the same spectral retardance function in pairs of retarders, and helps to make more compact filters. The key element is a quarter-wave Fresnel rhomb located in between the set of retarders and a mirror. Two cases are considered: the first Solc filter uses multiple-order quartz retarders, and the second one uses two liquid-crystal retarders. The latter has the advantage of being tunable via an applied voltage. Experimental results show how to filter the spectral content of a supercontinuum laser.
Holographic Geometries for Condensed Matter Applications
NASA Astrophysics Data System (ADS)
Keränen, V.; Thorlacius, L.
2015-01-01
Holographic modeling of strongly correlated many-body systems motivates the study of novel spacetime geometries where the scaling behavior of quantum critical systems is encoded into spacetime symmetries. Einstein-Dilaton-Maxwell theory has planar black brane solutions that exhibit Lifshitz scaling and in some cases hyperscaling violation. Entanglement entropy and Wilson loops in the dual field theory are studied by inserting simple geometric probes involving minimal surfaces into the black brane geometry. Coupling to background matter fields leads to interesting low-energy behavior in holographic models, such as U(1) symmetry breaking and emergent Lifshitz scaling.
Thin shells joining local cosmic string geometries
NASA Astrophysics Data System (ADS)
Eiroa, Ernesto F.; Rubín de Celis, Emilio; Simeone, Claudio
2016-10-01
In this article we present a theoretical construction of spacetimes with a thin shell that joins two different local cosmic string geometries. We study two types of global manifolds, one representing spacetimes with a thin shell surrounding a cosmic string or an empty region with Minkowski metric, and the other corresponding to wormholes which are not symmetric across the throat located at the shell. We analyze the stability of the static configurations under perturbations preserving the cylindrical symmetry. For both types of geometries we find that the static configurations can be stable for suitable values of the parameters.
Computational fluid dynamics using CATIA created geometry
NASA Astrophysics Data System (ADS)
Gengler, Jeanne E.
1989-07-01
A method has been developed to link the geometry definition residing on a CAD/CAM system with a computational fluid dynamics (CFD) tool needed to evaluate aerodynamic designs and requiring the memory capacity of a supercomputer. Requirements for surfaces suitable for CFD analysis are discussed. Techniques for developing surfaces and verifying their smoothness are compared, showing the capability of the CAD/CAM system. The utilization of a CAD/CAM system to create a computational mesh is explained, and the mesh interaction with the geometry and input file preparation for the CFD analysis is discussed.
Information geometry and the renormalization group.
Maity, Reevu; Mahapatra, Subhash; Sarkar, Tapobrata
2015-11-01
Information theoretic geometry near critical points in classical and quantum systems is well understood for exactly solvable systems. Here, we show that renormalization group flow equations can be used to construct the information metric and its associated quantities near criticality for both classical and quantum systems in a universal manner. We study this metric in various cases and establish its scaling properties in several generic examples. Scaling relations on the parameter manifold involving scalar quantities are studied, and scaling exponents are identified. The meaning of the scalar curvature and the invariant geodesic distance in information geometry is established and substantiated from a renormalization group perspective.
2014-02-14
ISS038-E-047576 (14 Feb. 2014) --- NASA astronaut Rick Mastracchio, Expedition 38 flight engineer, works with the Burning and Suppression of Solids (BASS-II) experiment in the Microgravity Science Glovebox (MSG) located in the Destiny laboratory of the International Space Station. BASS-II explores how different substances burn in microgravity with benefits for combustion on Earth and fire safety in space.
2014-02-14
ISS038-E-047582 (14 Feb. 2014) --- NASA astronaut Rick Mastracchio, Expedition 38 flight engineer, works with the Burning and Suppression of Solids (BASS-II) experiment in the Microgravity Science Glovebox (MSG) located in the Destiny laboratory of the International Space Station. BASS-II explores how different substances burn in microgravity with benefits for combustion on Earth and fire safety in space.
DeLucca, John F; Peloquin, John M; Smith, Lachlan J; Wright, Alexander C; Vresilovic, Edward J; Elliott, Dawn M
2016-08-01
Geometry is an important indicator of disc mechanical function and degeneration. While the geometry and associated degenerative changes in the nucleus pulposus and the annulus fibrosus are well-defined, the geometry of the cartilage endplate (CEP) and its relationship to disc degeneration are unknown. The objectives of this study were to quantify CEP geometry in three dimensions using an MRI FLASH imaging sequence and evaluate relationships between CEP geometry and age, degeneration, spinal level, and overall disc geometry. To do so, we assessed the MRI-based measurements for accuracy and repeatability. Next, we measured CEP geometry across a larger sample set and correlated CEP geometric parameters to age, disc degeneration, level, and disc geometry. The MRI-based measures resulted in thicknesses (0.3-1 mm) that are comparable to prior measurements of CEP thickness. CEP thickness was greatest at the anterior/posterior (A/P) margins and smallest in the center. The CEP A/P thickness, axial area, and lateral width decreased with age but were not related to disc degeneration. Age-related, but not degeneration-related, changes in geometry suggest that the CEP may not follow the progression of disc degeneration. Ultimately, if the CEP undergoes significant geometric changes with aging and if these can be related to low back pain, a clinically feasible translation of the FLASH MRI-based measurement of CEP geometry presented in this study may prove a useful diagnostic tool. © 2016 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 34:1410-1417, 2016.
NASA Astrophysics Data System (ADS)
Nair, M. Sivasankaran; Joseyphus, R. Selwin
2008-09-01
Co(II), Ni(II), Cu(II) and Zn(II) complexes of the Schiff base derived from vanillin and DL-α-aminobutyric acid were synthesized and characterized by elemental analysis, IR, electronic spectra, conductance measurements, magnetic measurements, powder XRD and biological activity. The analytical data show the composition of the metal complex to be [ML(H 2O)], where L is the Schiff base ligand. The conductance data indicate that all the complexes are non-electrolytes. IR results demonstrate the tridentate binding of the Schiff base ligand involving azomethine nitrogen, phenolic oxygen and carboxylato oxygen atoms. The IR data also indicate the coordination of a water molecule with the metal ion in the complex. The electronic spectral measurements show that Co(II) and Ni(II) complexes have tetrahedral geometry, while Cu(II) complex has square planar geometry. The powder XRD studies indicate that Co(II) and Cu(II) complexes are amorphous, whereas Ni(II) and Zn(II) complexes are crystalline in nature. Magnetic measurements show that Co(II), Ni(II) and Cu(II) complexes have paramagnetic behaviour. Antibacterial results indicated that the metal complexes are more active than the ligand.
Geometry of inferior endplates of the cervical spine.
Lou, Jigang; Liu, Hao; Rong, Xin; Li, Huibo; Wang, Beiyu; Gong, Quan
2016-03-01
Device subsidence is a well-known complication following cervical disc arthroplasty. Its occurrence has been closely tied with the endplate-implant contact interface. But current literature on the geometry of cervical endplate is very scarce. The aim of this anatomical investigation was to analyze geometry of inferior endplates of the cervical vertebrae, thereby identifying the common endplate shape patterns and providing morphological reference values consummating the design of the implant. Reformatted CT scans of 85 individuals were analyzed and endplate concave depth, endplate concave apex location, sagittal diameter of endplate, coronal concave angle, as well as transverse diameter of endplate were measured in mid-sagittal plane and specified coronal plane. According to the endplate concave apex location, the inferior endplates in mid-sagittal plane were classified into 3 types: type I with posteriorly positioned apex, type II with middle situated concave apex and type III with anteriorly positioned apex. Moreover, the inferior endplates in specified coronal plane were also classified into three types: concave, flat and irregular. Based on visual assessment, for the mid-sagittal plane, type I endplate accounted for 26.9% of all the 510 endplates of 85 individuals, while the proportion of type II and type III endplates were 53.9 and 19.2% respectively. For the specified coronal plane, 68.6% of all the 510 endplates were evaluated as concave, 26.9% as flat and the remaining 4.5% as irregular. Among all measured segments, C3 had the largest endplate concave depth values in mid-sagittal plane, while C7 the least; C5 and C6 had the largest sagittal endplate diameter values, while C2 the least. For each level, the sagittal endplate concave depth and endplate diameter of females were significantly smaller than those of males (P<0.05). Among all measured segments, C7 had the least coronal concave angle. Gender did not influence coronal concave angle significantly (P>0
Project-Based Learning to Explore Taxicab Geometry
ERIC Educational Resources Information Center
Ada, Tuba; Kurtulus, Aytac
2012-01-01
In Turkey, the content of the geometry course in the Primary School Mathematics Education, which is developed by The Council of Higher Education (YOK), comprises Euclidean and non-Euclidean types of geometry. In this study, primary mathematics teacher candidates compared these two geometries by focusing on Taxicab geometry among non-Euclidean…
SABRINA: an interactive solid geometry modeling program for Monte Carlo
West, J.T.
1985-01-01
SABRINA is a fully interactive three-dimensional geometry modeling program for MCNP. In SABRINA, a user interactively constructs either body geometry, or surface geometry models, and interactively debugs spatial descriptions for the resulting objects. This enhanced capability significantly reduces the effort in constructing and debugging complicated three-dimensional geometry models for Monte Carlo Analysis.
Alignment of Elementary Geometry Curriculum with Current Standards.
ERIC Educational Resources Information Center
Pickreign, Jamar; Capps, Lelon R.
2000-01-01
Examines geometry language used in K-6 textbooks and compares the findings to language used in modern mathematics standards documents. Finds a substantial misalignment between the geometry presented in textbooks, the geometry teaching expectations of mathematics education professionals, and the geometry being assessed in student performance…
Project-Based Learning to Explore Taxicab Geometry
ERIC Educational Resources Information Center
Ada, Tuba; Kurtulus, Aytac
2012-01-01
In Turkey, the content of the geometry course in the Primary School Mathematics Education, which is developed by The Council of Higher Education (YOK), comprises Euclidean and non-Euclidean types of geometry. In this study, primary mathematics teacher candidates compared these two geometries by focusing on Taxicab geometry among non-Euclidean…
SPICE: A Means for Determining Observation Geometry
NASA Astrophysics Data System (ADS)
Acton, C.; Bachman, N.; Diaz Del Rio, J.; Semenov, B.; Wright, E.; Yamamoto, Y.
2011-10-01
The "SPICE"1system is the NASA Planetary Science Division's method of conveniently packaging, archiving, and subsequently accessing observation geometry needed to understand science data returned from robotic spacecraft. This paper provides an overview of "SPICE"-what it is and how it's used- and then offers a glimpse into how it is being extended to better support the space science community.
From Circle to Hyperbola in Taxicab Geometry
ERIC Educational Resources Information Center
Berger, Ruth I.
2015-01-01
This "Activity for Students" article presents a taxicab geometry problem that engages students in plotting points and observing surprising shapes and underlining reasons for the appearance of figures when working with street grids. With this activity, teachers can provide an extra challenge by writing additional problems introducing a…
Fostering Spatial vs. Metric Understanding in Geometry
ERIC Educational Resources Information Center
Kinach, Barbara M.
2012-01-01
Learning to reason spatially is increasingly recognized as an essential component of geometry education. Generally taken to be the "ability to represent, generate, transform, communicate, document, and reflect on visual information," "spatial reasoning" uses the spatial relationships between objects to form ideas. Spatial thinking takes a variety…
Honeycomb Geometry: Applied Mathematics in Nature.
ERIC Educational Resources Information Center
Roberts, William J.
1984-01-01
Study and exploration of the hexagonal shapes found in honeycombs is suggested as an interesting topic for geometry classes. Students learn that the hexagonal pattern maximizes the enclosed region and minimizes the wax needed for construction, while satisfying the bees' cell-size constraint. (MNS)
The Convex Geometry of Linear Inverse Problems
2010-12-02
equator. Via elementary trigonometry , the solid angle that K subtends is given by π/2− sin−1(h). Hence, if h(β) is the largest number such that β caps of...1107–1130. [34] Harris, J., Algebraic Geometry: A First Course . Springer. [35] Haupt, J., Bajwa, W., Raz, G., and Nowak, R. (2008). Toeplitz
Environment Study with Buckminster Fuller's Geometry
ERIC Educational Resources Information Center
Cohen, Martin J.; Petrillo, Joseph
1972-01-01
Describes the teaching of geodesic-dome concepts to students in grades 3-5 through the trial use of Energetic and Synergetic Geometry as well as the undertaking of a workshop designed to prepare elementary and secondary school teachers to conduct further experiments. (CC)
Connecting Functions in Geometry and Algebra
ERIC Educational Resources Information Center
Steketee, Scott; Scher, Daniel
2016-01-01
One goal of a mathematics education is that students make significant connections among different branches of mathematics. Connections--such as those between arithmetic and algebra, between two-dimensional and three-dimensional geometry, between compass-and-straight-edge constructions and transformations, and between calculus and analytic…
Connecting Functions in Geometry and Algebra
ERIC Educational Resources Information Center
Steketee, Scott; Scher, Daniel
2016-01-01
One goal of a mathematics education is that students make significant connections among different branches of mathematics. Connections--such as those between arithmetic and algebra, between two-dimensional and three-dimensional geometry, between compass-and-straight-edge constructions and transformations, and between calculus and analytic…
On the Geometry of Constant Returns.
ERIC Educational Resources Information Center
Jehle, Geoffrey A.
2002-01-01
States that often constant returns to scale are also much more and that many important results depend on the very special properties of this class of production function. Offers a unified set of simple proofs, employing only familiar diagrams and high school geometry, for most of the crucial analytical properties of constant returns production.…
Reshaping Mathematics for Understanding Motion Geometry.
ERIC Educational Resources Information Center
Slovin, Hannah; Venenciano, Linda; Ishihara, Melanie; Beppu, Cynthia
This book introduces concepts of geometry that students use throughout middle-grade and higher-level mathematics courses. These concepts, presented through the study of transformations, provide a framework for other important topics such as number, measurement, proportional reasoning, and graphing on the coordinate plane. The book is designed for…
Honeycomb Geometry: Applied Mathematics in Nature.
ERIC Educational Resources Information Center
Roberts, William J.
1984-01-01
Study and exploration of the hexagonal shapes found in honeycombs is suggested as an interesting topic for geometry classes. Students learn that the hexagonal pattern maximizes the enclosed region and minimizes the wax needed for construction, while satisfying the bees' cell-size constraint. (MNS)
Geometry and the Design of Product Packaging
ERIC Educational Resources Information Center
Cherico, Cindy M.
2011-01-01
The most common question the author's students ask is, "When will I ever use this in real life?" To address this question in her geometry classes, the author sought to create a project that would incorporate a real-world business situation with their lesson series on the surface area and volume of three-dimensional objects--specifically, prisms,…
Fostering Spatial vs. Metric Understanding in Geometry
ERIC Educational Resources Information Center
Kinach, Barbara M.
2012-01-01
Learning to reason spatially is increasingly recognized as an essential component of geometry education. Generally taken to be the "ability to represent, generate, transform, communicate, document, and reflect on visual information," "spatial reasoning" uses the spatial relationships between objects to form ideas. Spatial thinking takes a variety…
Special Relativity as a Simple Geometry Problem
ERIC Educational Resources Information Center
de Abreu, Rodrigo; Guerra, Vasco
2009-01-01
The null result of the Michelson-Morley experiment and the constancy of the one-way speed of light in the "rest system" are used to formulate a simple problem, to be solved by elementary geometry techniques using a pair of compasses and non-graduated rulers. The solution consists of a drawing allowing a direct visualization of all the fundamental…
Discernment of Invariants in Dynamic Geometry Environments
ERIC Educational Resources Information Center
Leung, Allen; Baccaglini-Frank, Anna; Mariotti, Maria Alessandra
2013-01-01
In this paper, we discuss discernment of invariants in dynamic geometry environments (DGE) based on a combined perspective that puts together the lens of variation and the maintaining dragging strategy developed previously by the authors. We interpret and describe a model of discerning invariants in DGE through types of variation awareness and…
Meromorphic Higgs bundles and related geometries
NASA Astrophysics Data System (ADS)
Dalakov, Peter
2016-11-01
The present note is mostly a survey on the generalised Hitchin integrable system and moduli spaces of meromorphic G-Higgs bundles. We also fill minor gaps in the existing literature, outline a calculation of the infinitesimal period map and review some related geometries.
Discernment of Invariants in Dynamic Geometry Environments
ERIC Educational Resources Information Center
Leung, Allen; Baccaglini-Frank, Anna; Mariotti, Maria Alessandra
2013-01-01
In this paper, we discuss discernment of invariants in dynamic geometry environments (DGE) based on a combined perspective that puts together the lens of variation and the maintaining dragging strategy developed previously by the authors. We interpret and describe a model of discerning invariants in DGE through types of variation awareness and…
Effectivizing the geometry of the curve complex
NASA Astrophysics Data System (ADS)
Aougab, Tarik
This thesis is devoted to understanding how the geometry of the curve complex of a surface S, the Teichmuller space of S, and of the mapping class group of S explicitly depend on the underlying topology of S. Moreover, this thesis demonstrates that the geometry of the mapping class group, and the tools used to study this geometry such as Masur and Minsky's celebrated distance formula, can be used to answer basic, but surprisingly challenging questions related to the combinatorial properties of curves on surfaces. In particular, we prove that all curve graphs are uniformly hyperbolic, independent of the topology of the underlying surface. We also give effective versions of several results regarding train track splitting sequences, and the subset of the curve graph corresponding to curves which bound disks in a handlebody. Finally, we study the local geometry of a family of curve graphs all related to the same surface, and specifically we give upper and lower bounds on the maximum size of a complete subgraph for these graphs.
Applications of Differential Geometry to Cartography
ERIC Educational Resources Information Center
Benitez, Julio; Thome, Nestor
2004-01-01
This work introduces an application of differential geometry to cartography. The mathematical aspects of some geographical projections of Earth surface are revealed together with some of its more important properties. An important problem since the discovery of the 'spherical' form of the Earth is how to compose a reliable map of the surface of…
Special Relativity as a Simple Geometry Problem
ERIC Educational Resources Information Center
de Abreu, Rodrigo; Guerra, Vasco
2009-01-01
The null result of the Michelson-Morley experiment and the constancy of the one-way speed of light in the "rest system" are used to formulate a simple problem, to be solved by elementary geometry techniques using a pair of compasses and non-graduated rulers. The solution consists of a drawing allowing a direct visualization of all the fundamental…
Hydrophobicity of silver surfaces with microparticle geometry
NASA Astrophysics Data System (ADS)
Macko, Ján; Oriňaková, Renáta; Oriňak, Andrej; Kovaľ, Karol; Kupková, Miriam; Erdélyi, Branislav; Kostecká, Zuzana; Smith, Roger M.
2016-11-01
The effect of the duration of the current deposition cycle and the number of current pulses on the geometry of silver microstructured surfaces and on the free surface energy, polarizability, hydrophobicity and thus adhesion force of the silver surfaces has been investigated. The changes in surface hydrophobicity were entirely dependent on the size and density of the microparticles on the surface. The results showed that formation of the silver microparticles was related to number of current pulses, while the duration of one current pulse played only a minor effect on the final surface microparticle geometry and thus on the surface tension and hydrophobicity. The conventional geometry of the silver particles has been transformed to the fractal dimension D. The surface hydrophobicity depended predominantly on the length of the dendrites not on their width. The highest silver surface hydrophobicity was observed on a surface prepared by 30 current pulses with a pulse duration of 1 s, the lowest one when deposition was performed by 10 current pulses with a duration of 0.1 s. The partial surface tension coefficients γDS and polarizability kS of the silver surfaces were calculated. Both parameters can be applied in future applications in living cells adhesion prediction and spectral method selection. Silver films with microparticle geometry showed a lower variability in final surface hydrophobicity when compared to nanostructured surfaces. The comparisons could be used to modify surfaces and to modulate human cells and bacterial adhesion on body implants, surgery instruments and clean surfaces.
Transport Code for Regular Triangular Geometry
1993-06-09
DIAMANT2 solves the two-dimensional static multigroup neutron transport equation in planar regular triangular geometry. Both regular and adjoint, inhomogeneous and homogeneous problems subject to vacuum, reflective or input specified boundary flux conditions are solved. Anisotropy is allowed for the scattering source. Volume and surface sources are allowed for inhomogeneous problems.
Environment Study with Buckminster Fuller's Geometry
ERIC Educational Resources Information Center
Cohen, Martin J.; Petrillo, Joseph
1972-01-01
Describes the teaching of geodesic-dome concepts to students in grades 3-5 through the trial use of Energetic and Synergetic Geometry as well as the undertaking of a workshop designed to prepare elementary and secondary school teachers to conduct further experiments. (CC)
Learning Geometry by Designing Persian Mosaics
ERIC Educational Resources Information Center
Karssenberg, Goossen
2014-01-01
To encourage students to do geometry, the art of Islamic geometric ornamentation was chosen as the central theme of a lesson strand which was developed using the newly presented didactical tool called "Learning by Acting". The Dutch students who took these lessons in 2010 to 2013 were challenged to act as if they themselves were Persian…
From wave geometry to fake supergravity
NASA Astrophysics Data System (ADS)
Townsend, Paul K.
2008-08-01
The 'Wave Geometry' equation of the pre-WWII Hiroshima program is also the key equation of the current 'fake supergravity' program. I review the status of (fake) supersymmetric domain walls and (fake) pseudo-supersymmetric cosmologies. An extension of the domain-wall/cosmology correspondence to a triple correspondence with instantons shows that 'pseudo-supersymmetry' has another interpretation as the Euclidean supersymmetry.
The Valence Bond Interpretation of Molecular Geometry.
ERIC Educational Resources Information Center
Smith, Derek W.
1980-01-01
Presents ways in which the valence bond (VB) theory describes the bonding and geometry of molecules, following directly from earlier principles laid down by Pauling and others. Two other theories (molecular orbital approach and valence shell electron pair repulsion) are discussed and compared to VB. (CS)
Asynchronous event-based hebbian epipolar geometry.
Benosman, Ryad; Ieng, Sio-Hoï; Rogister, Paul; Posch, Christoph
2011-11-01
Epipolar geometry, the cornerstone of perspective stereo vision, has been studied extensively since the advent of computer vision. Establishing such a geometric constraint is of primary importance, as it allows the recovery of the 3-D structure of scenes. Estimating the epipolar constraints of nonperspective stereo is difficult, they can no longer be defined because of the complexity of the sensor geometry. This paper will show that these limitations are, to some extent, a consequence of the static image frames commonly used in vision. The conventional frame-based approach suffers from a lack of the dynamics present in natural scenes. We introduce the use of neuromorphic event-based--rather than frame-based--vision sensors for perspective stereo vision. This type of sensor uses the dimension of time as the main conveyor of information. In this paper, we present a model for asynchronous event-based vision, which is then used to derive a general new concept of epipolar geometry linked to the temporal activation of pixels. Practical experiments demonstrate the validity of the approach, solving the problem of estimating the fundamental matrix applied, in a first stage, to classic perspective vision and then to more general cameras. Furthermore, this paper shows that the properties of event-based vision sensors allow the exploration of not-yet-defined geometric relationships, finally, we provide a definition of general epipolar geometry deployable to almost any visual sensor.
Learning Geometry by Designing Persian Mosaics
ERIC Educational Resources Information Center
Karssenberg, Goossen
2014-01-01
To encourage students to do geometry, the art of Islamic geometric ornamentation was chosen as the central theme of a lesson strand which was developed using the newly presented didactical tool called "Learning by Acting". The Dutch students who took these lessons in 2010 to 2013 were challenged to act as if they themselves were Persian…
User Interface Design for Dynamic Geometry Software
ERIC Educational Resources Information Center
Kortenkamp, Ulrich; Dohrmann, Christian
2010-01-01
In this article we describe long-standing user interface issues with Dynamic Geometry Software and common approaches to address them. We describe first prototypes of multi-touch-capable DGS. We also give some hints on the educational benefits of proper user interface design.
Quilts and Tangrams: Linking Literature and Geometry.
ERIC Educational Resources Information Center
Bohning, Gerry; Williams, Rebecca
1997-01-01
Suggests that by making quilt squares with tangrams, children link geometry and children's literature. Provides background on quilts and tangrams, and provides guidelines for teachers. Points out that children gain communication and mathematical thinking skills as they manipulate and explore relationships among pieces. Contains an annotated…