Bothe, Thorsten; Li Wansong; Schulte, Michael; von Kopylow, Christoph; Bergmann, Ralf B.; Jueptner, Werner P. O.
2010-10-20
Exact geometric calibration of optical devices like projectors or cameras is the basis for utilizing them in quantitative metrological applications. The common state-of-the-art photogrammetric pinhole-imaging-based models with supplemental polynomial corrections fail in the presence of nonsymmetric or high-spatial-frequency distortions and in describing caustics efficiently. These problems are solved by our vision ray calibration (VRC), which is proposed in this paper. The VRC takes an optical mapping system modeled as a black box and directly delivers corresponding vision rays for each mapped pixel. The underlying model, the calibration process, and examples are visualized and reviewed, demonstrating the potential of the VRC.
Descriptive Geometry and Geometric Modeling.
ERIC Educational Resources Information Center
Adams, J. Alan
1988-01-01
Describes experiences for engineering students to develop spatial awareness and reasoning capability. Describes geometric modeling, basic geometric concepts, operations, surface modeling, and conclusions. (YP)
Geometric moments for gait description
NASA Astrophysics Data System (ADS)
Toxqui-Quitl, C.; Morales-Batalla, V.; Padilla-Vivanco, A.; Camacho-Bello, C.
2013-09-01
The optical flow associated with a set of digital images of a moving individual is analyzed in order to extract a gait signature. For this, invariant Hu moments are obtained for image description. A Hu Moment History (HMH) is obtained from K frames to describe the gait signature of individuals in a video. The gait descriptors are subsequences of the HMH of variable width. Each subsequence is generated by means of genetic algorithms and used for classification in a neuronal network. The database for algorithm evaluation is MoBo, and the gait classification results are above 90% for the cases of slow and fast walking and 100% for the cases of walking with a ball and inclined walking. An optical processor is also implemented in order to obtain the descriptors of the human gait.
Geometric descriptions of entangled states by auxiliary varieties
Holweck, Frederic; Luque, Jean-Gabriel; Thibon, Jean-Yves
2012-10-15
The aim of the paper is to propose geometric descriptions of multipartite entangled states using algebraic geometry. In the context of this paper, geometric means each stratum of the Hilbert space, corresponding to an entangled state, is an open subset of an algebraic variety built by classical geometric constructions (tangent lines, secant lines) from the set of separable states. In this setting, we describe well-known classifications of multipartite entanglement such as 2 Multiplication-Sign 2 Multiplication-Sign (n+ 1), for n Greater-Than-Or-Slanted-Equal-To 1, quantum systems and a new description with the 2 Multiplication-Sign 3 Multiplication-Sign 3 quantum system. Our results complete the approach of Miyake and make stronger connections with recent work of algebraic geometers. Moreover, for the quantum systems detailed in this paper, we propose an algorithm, based on the classical theory of invariants, to decide to which subvariety of the Hilbert space a given state belongs.
A Geometric Description of Raman Fingerprints on Spinor BECs
NASA Astrophysics Data System (ADS)
Schultz, Justin T.; Hansen, Azure; Murphree, Joseph D.; Jayaseelan, Maitreyi; Bigelow, Nicholas P.
2016-05-01
We employ a geometric description of a coherent, diabatic two-photon Raman interaction as a rotation on the Bloch sphere of a spin-1/2 system. The spin state of the system is described by a point on the sphere and the time evolution is described by a trajectory of the sphere's surface. The axis of rotation is determined by properties of the optical Raman beams: the pulse area, the relative intensities, relative phase, and relative frequencies. The two-photon detuning gives fine control over the sizes and phases of the imprinted features. This interpretation allows us not only to precisely engineer complex, spatially varying spin textures, but also to characterize these textures with a form of atomic polarimetry as we demonstrate on a coreless vortex in a spinor BEC.
Cooper, W. James; Albertson, R Craig; Jacob, Rick E.; Westneat, Mark W.
2014-12-01
Here we present a re-description of Abudefduf luridus and reassign it to the genus Similiparma. We supplement traditional diagnoses and descriptions of this species with quantitative anatomical data collected from a family-wide geometric morphometric analysis of head morphology (44 species representing all 30 damselfish genera) and data from cranial micro-CT scans of fishes in the genus Similiparma. The use of geometric morphometric analyses (and other methods of shape analysis) permits detailed comparisons between the morphology of specific taxa and the anatomical diversity that has arisen in an entire lineage. This provides a particularly useful supplement to traditional description methods and we recommend the use of such techniques by systematists. Similiparma and its close relatives constitute a branch of the damselfish phylogenetic tree that predominantly inhabits rocky reefs in the Atlantic and Eastern Pacific, as opposed to the more commonly studied damselfishes that constitute a large portion of the ichthyofauna on all coral-reef communities.
ERIC Educational Resources Information Center
Richards, Lynn V.; Coventry, Kenny R.; Clibbens, John
2004-01-01
The effect of both geometric and extra-geometric factors on children's production of "in" is reported (free-response paradigm). Eighty children across four age groups (means 4;1, 5;5, 6;1, and 7;1) were shown video scenes of puppets placing real objects in various positions with reference to a bowl and a plate. Located objects were placed at three…
A geometric description of Maxwell field in a Kerr spacetime
NASA Astrophysics Data System (ADS)
Jezierski, Jacek; Smołka, Tomasz
2016-06-01
We consider the Maxwell field in the exterior of a Kerr black hole. For this system, we propose a geometric construction of generalized Klein–Gordon equation called Fackerell–Ipser equation. Our model is based on conformal Yano–Killing tensor (CYK tensor). We present non-standard properties of CYK tensors in the Kerr spacetime which are useful in electrodynamics.
Random geometric graph description of connectedness percolation in rod systems
NASA Astrophysics Data System (ADS)
Chatterjee, Avik P.; Grimaldi, Claudio
2015-09-01
The problem of continuum percolation in dispersions of rods is reformulated in terms of weighted random geometric graphs. Nodes (or sites or vertices) in the graph represent spatial locations occupied by the centers of the rods. The probability that an edge (or link) connects any randomly selected pair of nodes depends upon the rod volume fraction as well as the distribution over their sizes and shapes, and also upon quantities that characterize their state of dispersion (such as the orientational distribution function). We employ the observation that contributions from closed loops of connected rods are negligible in the limit of large aspect ratios to obtain percolation thresholds that are fully equivalent to those calculated within the second-virial approximation of the connectedness Ornstein-Zernike equation. Our formulation can account for effects due to interactions between the rods, and many-body features can be partially addressed by suitable choices for the edge probabilities.
Application of geometric algebra for the description of polymer conformations.
Chys, Pieter
2008-03-14
In this paper a Clifford algebra-based method is applied to calculate polymer chain conformations. The approach enables the calculation of the position of an atom in space with the knowledge of the bond length (l), valence angle (theta), and rotation angle (phi) of each of the preceding bonds in the chain. Hence, the set of geometrical parameters {l(i),theta(i),phi(i)} yields all the position coordinates p(i) of the main chain atoms. Moreover, the method allows the calculation of side chain conformations and the computation of rotations of chain segments. With these features it is, in principle, possible to generate conformations of any type of chemical structure. This method is proposed as an alternative for the classical approach by matrix algebra. It is more straightforward and its final symbolic representation considerably simpler than that of matrix algebra. Approaches for realistic modeling by means of incorporation of energetic considerations can be combined with it. This article, however, is entirely focused at showing the suitable mathematical framework on which further developments and applications can be built.
[Quantitative interpretation of graphs from Stuart pantography. II. Geometrical bases].
Ott, K
1977-05-01
In an experimental investigation, Stuart pantographic records are geometrically analyzed. The influence of the parameters' inclination and curving of condylar guidance, intercondylar distance, Bennett angle, distance of the plate, and position of the recording pencil are studied. Further quanitative analysis was not performed, as Stuart pantography is only meant for transmission to the respective articulator and is nto suitable for metric recording. PMID:266456
Generalization of the geometric description of a light beam in radiometry and photometry.
Simonot, Lionel; Boulenguez, Pierre
2013-04-01
Radiometric and photometric quantities rely on a geometric description of the beam subtended by a source and a receptor. In this paper, a generalization of this description is proposed as the product of the apparent size of the source times the receptor angular extent, whatever the natures of these elements: point, line, surface, or volume. The obtained flux density per geometric extent expressions are then applied to the determination of the irradiances induced in the near field and far field by a rectilinear source represented as a point source, a line source, and a surface source.
A Quantitative Description of FBI Public Relations.
ERIC Educational Resources Information Center
Gibson, Dirk C.
1997-01-01
States that the Federal Bureau of Investigation (FBI) had the most successful media relations program of all government agencies from the 1930s to the 1980s. Uses quantitative analysis to show why those media efforts were successful. Identifies themes that typified the verbal component of FBI publicity and the broad spectrum of mass communication…
A quantitative description for efficient financial markets
NASA Astrophysics Data System (ADS)
Immonen, Eero
2015-09-01
In this article we develop a control system model for describing efficient financial markets. We define the efficiency of a financial market in quantitative terms by robust asymptotic price-value equality in this model. By invoking the Internal Model Principle of robust output regulation theory we then show that under No Bubble Conditions, in the proposed model, the market is efficient if and only if the following conditions hold true: (1) the traders, as a group, can identify any mispricing in asset value (even if no one single trader can do it accurately), and (2) the traders, as a group, incorporate an internal model of the value process (again, even if no one single trader knows it). This main result of the article, which deliberately avoids the requirement for investor rationality, demonstrates, in quantitative terms, that the more transparent the markets are, the more efficient they are. An extensive example is provided to illustrate the theoretical development.
NASA Astrophysics Data System (ADS)
Lüdde, Hans Jürgen; Achenbach, Alexander; Kalkbrenner, Thilo; Jankowiak, Hans-Christian; Kirchner, Tom
2016-04-01
A new model to account for geometric screening corrections in an independent-atom-model description of ion-molecule collisions is introduced. The ion-molecule cross sections for net capture and net ionization are represented as weighted sums of atomic cross sections with weight factors that are determined from a geometric model of overlapping cross section areas. Results are presented for proton collisions with targets ranging from diatomic to complex polyatomic molecules. Significant improvement compared to simple additivity rule results and in general good agreement with experimental data are found. The flexibility of the approach opens up the possibility to study more detailed observables such as orientation-dependent and charge-state-correlated cross sections for a large class of complex targets ranging from biomolecules to atomic clusters.
A geometric Hamiltonian description of composite quantum systems and quantum entanglement
NASA Astrophysics Data System (ADS)
Pastorello, Davide
2015-05-01
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is discussed in this paper. As summarized in the first part of this work, in the Hamiltonian formulation the phase space of a quantum system is the Kähler manifold given by the complex projective space P(H) of the Hilbert space H of the considered quantum theory. However the phase space of a bipartite system must be P(H1 ⊗ H2) and not simply P(H1) × P(H2) as suggested by the analogy with Classical Mechanics. A part of this paper is devoted to manage this problem. In the second part of the work, a definition of quantum entanglement and a proposal of entanglement measure are given in terms of a geometrical point of view (a rather studied topic in recent literature). Finally two known separability criteria are implemented in the Hamiltonian formalism.
From information theory to quantitative description of steric effects.
Alipour, Mojtaba; Safari, Zahra
2016-07-21
Immense efforts have been made in the literature to apply the information theory descriptors for investigating the electronic structure theory of various systems. In the present study, the information theoretic quantities, such as Fisher information, Shannon entropy, Onicescu information energy, and Ghosh-Berkowitz-Parr entropy, have been used to present a quantitative description for one of the most widely used concepts in chemistry, namely the steric effects. Taking the experimental steric scales for the different compounds as benchmark sets, there are reasonable linear relationships between the experimental scales of the steric effects and theoretical values of steric energies calculated from information theory functionals. Perusing the results obtained from the information theoretic quantities with the two representations of electron density and shape function, the Shannon entropy has the best performance for the purpose. On the one hand, the usefulness of considering the contributions of functional groups steric energies and geometries, and on the other hand, dissecting the effects of both global and local information measures simultaneously have also been explored. Furthermore, the utility of the information functionals for the description of steric effects in several chemical transformations, such as electrophilic and nucleophilic reactions and host-guest chemistry, has been analyzed. The functionals of information theory correlate remarkably with the stability of systems and experimental scales. Overall, these findings show that the information theoretic quantities can be introduced as quantitative measures of steric effects and provide further evidences of the quality of information theory toward helping theoreticians and experimentalists to interpret different problems in real systems.
Houssaye, Alexandra; Herrel, Anthony; Fabre, Anne-Claire; Cornette, Raphael
2015-01-01
The challenging complexity of biological structures has led to the development of several methods for quantitative analyses of form. Bones are shaped by the interaction of historical (phylogenetic), structural, and functional constrains. Consequently, bone shape has been investigated intensively in an evolutionary context. Geometric morphometric approaches allow the description of the shape of an object in all of its biological complexity. However, when biological objects present only few anatomical landmarks, sliding semi-landmarks may provide good descriptors of shape. The sliding procedure, mandatory for sliding semi-landmarks, requires several steps that may be time-consuming. We here compare the time required by two different software packages (‘Edgewarp’ and ‘Morpho’) for the same sliding task, and investigate potential differences in the results and biological interpretation. ‘Morpho’ is much faster than ‘Edgewarp,’ notably as a result of the greater computational power of the ‘Morpho’ software routines and the complexity of the ‘Edgewarp’ workflow. Morphospaces obtained using both software packages are similar and provide a consistent description of the biological variability. The principal differences between the two software packages are observed in areas characterized by abrupt changes in the bone topography. In summary, both software packages perform equally well in terms of the description of biological structures, yet differ in the simplicity of the workflow and time needed to perform the analyses. PMID:26618086
Descriptive Quantitative Analysis of Rearfoot Alignment Radiographic Parameters.
Meyr, Andrew J; Wagoner, Matthew R
2015-01-01
Although the radiographic parameters of the transverse talocalcaneal angle (tTCA), calcaneocuboid angle (CCA), talar head uncovering (THU), calcaneal inclination angle (CIA), talar declination angle (TDA), lateral talar-first metatarsal angle (lTFA), and lateral talocalcaneal angle (lTCA) form the basis of the preoperative evaluation and procedure selection for pes planovalgus deformity, the so-called normal values of these measurements are not well-established. The objectives of the present study were to retrospectively evaluate the descriptive statistics of these radiographic parameters (tTCA, CCA, THU, CIA, TDA, lTFA, and lTCA) in a large population, and, second, to determine an objective basis for defining "normal" versus "abnormal" measurements. As a secondary outcome, the relationship of these variables to the body mass index was assessed. Anteroposterior and lateral foot radiographs from 250 consecutive patients without a history of previous foot and ankle surgery and/or trauma were evaluated. The results revealed a mean measurement of 24.12°, 13.20°, 74.32%, 16.41°, 26.64°, 8.37°, and 43.41° for the tTCA, CCA, THU, CIA, TDA, lTFA, and lTCA, respectively. These were generally in line with the reported historical normal values. Descriptive statistical analysis demonstrated that the tTCA, THU, and TDA met the standards to be considered normally distributed but that the CCA, CIA, lTFA, and lTCA demonstrated data characteristics of both parametric and nonparametric distributions. Furthermore, only the CIA (R = -0.2428) and lTCA (R = -0.2449) demonstrated substantial correlation with the body mass index. No differentiations in deformity progression were observed when the radiographic parameters were plotted against each other to lead to a quantitative basis for defining "normal" versus "abnormal" measurements. PMID:26002682
NASA Astrophysics Data System (ADS)
Checefsky, Walter A.; Abidin, Anas Z.; Nagarajan, Mahesh B.; Bauer, Jan S.; Baum, Thomas; Wismüller, Axel
2016-03-01
The current clinical standard for measuring Bone Mineral Density (BMD) is dual X-ray absorptiometry, however more recently BMD derived from volumetric quantitative computed tomography has been shown to demonstrate a high association with spinal fracture susceptibility. In this study, we propose a method of fracture risk assessment using structural properties of trabecular bone in spinal vertebrae. Experimental data was acquired via axial multi-detector CT (MDCT) from 12 spinal vertebrae specimens using a whole-body 256-row CT scanner with a dedicated calibration phantom. Common image processing methods were used to annotate the trabecular compartment in the vertebral slices creating a circular region of interest (ROI) that excluded cortical bone for each slice. The pixels inside the ROI were converted to values indicative of BMD. High dimensional geometrical features were derived using the scaling index method (SIM) at different radii and scaling factors (SF). The mean BMD values within the ROI were then extracted and used in conjunction with a support vector machine to predict the failure load of the specimens. Prediction performance was measured using the root-mean-square error (RMSE) metric and determined that SIM combined with mean BMD features (RMSE = 0.82 +/- 0.37) outperformed MDCT-measured mean BMD (RMSE = 1.11 +/- 0.33) (p < 10-4). These results demonstrate that biomechanical strength prediction in vertebrae can be significantly improved through the use of SIM-derived texture features from trabecular bone.
NASA Astrophysics Data System (ADS)
Wang, Quanzeng; Cheng, Wei-Chung; Suresh, Nitin; Hua, Hong
2016-05-01
With improved diagnostic capabilities and complex optical designs, endoscopic technologies are advancing. As one of the several important optical performance characteristics, geometric distortion can negatively affect size estimation and feature identification related diagnosis. Therefore, a quantitative and simple distortion evaluation method is imperative for both the endoscopic industry and the medical device regulatory agent. However, no such method is available yet. While the image correction techniques are rather mature, they heavily depend on computational power to process multidimensional image data based on complex mathematical model, i.e., difficult to understand. Some commonly used distortion evaluation methods, such as the picture height distortion (DPH) or radial distortion (DRAD), are either too simple to accurately describe the distortion or subject to the error of deriving a reference image. We developed the basic local magnification (ML) method to evaluate endoscope distortion. Based on the method, we also developed ways to calculate DPH and DRAD. The method overcomes the aforementioned limitations, has clear physical meaning in the whole field of view, and can facilitate lesion size estimation during diagnosis. Most importantly, the method can facilitate endoscopic technology to market and potentially be adopted in an international endoscope standard.
Toward a quantitative description of the neurodynamic organizations of teams.
Stevens, Ronald H; Galloway, Trysha L
2014-01-01
The goal was to develop quantitative models of the neurodynamic organizations of teams that could be used for comparing performance within and across teams and sessions. A symbolic modeling system was developed, where raw electroencephalography (EEG) signals from dyads were first transformed into second-by-second estimates of the cognitive Workload or Engagement of each person and transformed again into symbols representing the aggregated levels of the team. The resulting neurodynamic symbol streams had a persistent structure and contained segments of differential symbol expression. The quantitative Shannon entropy changes during these periods were related to speech, performance, and team responses to task changes. The dyads in an unscripted map navigation task (Human Communication Research Centre (HCRC) Map Task (MT)) developed fluctuating dynamics for Workload and Engagement, as they established their teamwork rhythms, and these were disrupted by external changes to the task. The entropy fluctuations during these disruptions differed in frequency, magnitude, and duration, and were associated with qualitative and quantitative changes in team organization and performance. These results indicate that neurodynamic models may be reliable, sensitive, and valid indicators of the changing neurodynamics of teams around which standardized quantitative models can begin to be developed.
Soliman, George; Yevick, David; Jessop, Paul
2014-09-01
This paper demonstrates that numerous calculations involving polarization transformations can be condensed by employing suitable geometric algebra formalism. For example, to describe polarization mode dispersion and polarization-dependent loss, both the material birefringence and differential loss enter as bivectors and can be combined into a single symmetric quantity. Their frequency and distance evolution, as well as that of the Stokes vector through an optical system, can then each be expressed as a single compact expression, in contrast to the corresponding Mueller matrix formulations. The intrinsic advantage of the geometric algebra framework is further demonstrated by presenting a simplified derivation of generalized Stokes parameters that include the electric field phase. This procedure simultaneously establishes the tensor transformation properties of these parameters.
Quantitative Luminescence Imaging System description and user's manual
Stahl, K.A.; Batishko, C.R.
1988-06-01
A Quantitative Luminescence Imaging System (QLIS) was designed and constructed. The system was developed for use in imaging and quantitative analysis of very low light level chemiluminescent phenomena. The luminescent reactions are imaged via microchannel plate image intensifier coupled to a newvicon video camera. The video record of the reaction can be stored on video tape or digitally captured by an image processing system which is integral to a host computer controller. Since the particular experimental conditions for which the QLIS was designed necessitate that the chemiluminescent reaction take place in an rf flux within a waveguide, the system includes a coherent fiber optic image transfer system which allows the video hardware to be mounted externally to the rf waveguide.
Quantitative prediction and molar description of the environment
Baum, William M.
1989-01-01
Molecular explanations of behavior, based on momentary events and variables that can be measured each time an event occurs, can be contrasted with molar explanations, based on aggregates of events and variables that can be measured only over substantial periods of time. Molecular analyses cannot suffice for quantitative accounts of behavior, because the historical variables that determine behavior are inevitably molar. When molecular explanations are attempted, they always depend on hypothetical constructs that stand as surrogates for molar environmental variables. These constructs allow no quantitative predictions when they are vague, and when they are made precise, they become superfluous, because they can be replaced with molar measures. In contrast to molecular accounts of phenomena like higher responding on ratio schedules than interval schedules and free-operant avoidance, molar accounts tend to be simple and straightforward. Molar theory incorporates the notion that behavior produces consequences that in turn affect the behavior, the notion that behavior and environment together constitute a feedback system. A feedback function specifies the dependence of consequences on behavior, thereby describing properties of the environment. Feedback functions can be derived for simple schedules, complex schedules, and natural resources. A complete theory of behavior requires describing the environment's feedback functions and the organism's functional relations. Molar thinking, both in the laboratory and in the field, can allow quantitative prediction, the mark of a mature science. PMID:22478030
NASA Astrophysics Data System (ADS)
Nagarajan, Mahesh B.; Coan, Paola; Huber, Markus B.; Diemoz, Paul C.; Wismüller, Axel
2014-03-01
Current assessment of cartilage is primarily based on identification of indirect markers such as joint space narrowing and increased subchondral bone density on x-ray images. In this context, phase contrast CT imaging (PCI-CT) has recently emerged as a novel imaging technique that allows a direct examination of chondrocyte patterns and their correlation to osteoarthritis through visualization of cartilage soft tissue. This study investigates the use of topological and geometrical approaches for characterizing chondrocyte patterns in the radial zone of the knee cartilage matrix in the presence and absence of osteoarthritic damage. For this purpose, topological features derived from Minkowski Functionals and geometric features derived from the Scaling Index Method (SIM) were extracted from 842 regions of interest (ROI) annotated on PCI-CT images of healthy and osteoarthritic specimens of human patellar cartilage. The extracted features were then used in a machine learning task involving support vector regression to classify ROIs as healthy or osteoarthritic. Classification performance was evaluated using the area under the receiver operating characteristic (ROC) curve (AUC). The best classification performance was observed with high-dimensional geometrical feature vectors derived from SIM (0.95 ± 0.06) which outperformed all Minkowski Functionals (p < 0.001). These results suggest that such quantitative analysis of chondrocyte patterns in human patellar cartilage matrix involving SIM-derived geometrical features can distinguish between healthy and osteoarthritic tissue with high accuracy.
Stochastic description of geometric phase for polarized waves in random media
NASA Astrophysics Data System (ADS)
Boulanger, Jérémie; Le Bihan, Nicolas; Rossetto, Vincent
2013-01-01
We present a stochastic description of multiple scattering of polarized waves in the regime of forward scattering. In this regime, if the source is polarized, polarization survives along a few transport mean free paths, making it possible to measure an outgoing polarization distribution. We consider thin scattering media illuminated by a polarized source and compute the probability distribution function of the polarization on the exit surface. We solve the direct problem using compound Poisson processes on the rotation group SO(3) and non-commutative harmonic analysis. We obtain an exact expression for the polarization distribution which generalizes previous works and design an algorithm solving the inverse problem of estimating the scattering properties of the medium from the measured polarization distribution. This technique applies to thin disordered layers, spatially fluctuating media and multiple scattering systems and is based on the polarization but not on the signal amplitude. We suggest that it can be used as a non-invasive testing method.
ERIC Educational Resources Information Center
Rodriguez-Falces, Javier
2013-01-01
In electrophysiology studies, it is becoming increasingly common to explain experimental observations using both descriptive methods and quantitative approaches. However, some electrophysiological phenomena, such as the generation of extracellular potentials that results from the propagation of the excitation source along the muscle fiber, are…
ERIC Educational Resources Information Center
Berksteiner, Earl J.
2013-01-01
The purpose of this quantitative descriptive correlational study was to determine if associations existed between middle- and early-college (MEC) principals' leadership styles, teacher motivation, and teacher satisfaction. MEC programs were programs designed to assist high school students who were not served well in a traditional setting (Middle…
Jaferzadeh, Keyvan; Moon, Inkyu
2015-11-01
Quantitative phase information obtained by digital holographic microscopy (DHM) can provide new insight into the functions and morphology of single red blood cells (RBCs). Since the functionality of a RBC is related to its three-dimensional (3-D) shape, quantitative 3-D geometric changes induced by storage time can help hematologists realize its optimal functionality period. We quantitatively investigate RBC 3-D geometric changes in the storage lesion using DHM. Our experimental results show that the substantial geometric transformation of the biconcave-shaped RBCs to the spherocyte occurs due to RBC storage lesion. This transformation leads to progressive loss of cell surface area, surface-to-volume ratio, and functionality of RBCs. Furthermore, our quantitative analysis shows that there are significant correlations between chemical and morphological properties of RBCs.
Jaferzadeh, Keyvan; Moon, Inkyu
2015-11-01
Quantitative phase information obtained by digital holographic microscopy (DHM) can provide new insight into the functions and morphology of single red blood cells (RBCs). Since the functionality of a RBC is related to its three-dimensional (3-D) shape, quantitative 3-D geometric changes induced by storage time can help hematologists realize its optimal functionality period. We quantitatively investigate RBC 3-D geometric changes in the storage lesion using DHM. Our experimental results show that the substantial geometric transformation of the biconcave-shaped RBCs to the spherocyte occurs due to RBC storage lesion. This transformation leads to progressive loss of cell surface area, surface-to-volume ratio, and functionality of RBCs. Furthermore, our quantitative analysis shows that there are significant correlations between chemical and morphological properties of RBCs. PMID:26502322
Reilly, Matthew A
2014-10-01
This study expands on a geometric model of ocular accommodation (Reilly and Ravi, Vision Res. 50:330-336; 2010) by relaxing assumptions regarding lens symmetry about the equator. A method for predicting stretching force was derived. Two models were then developed: Model 1 held the equatorial geometry constant at all stages of accommodation, while Model 2 allowed localized deformation at the equator. Both models were compared to recent data for axial thickness, anterior and posterior radii of curvature, surface area, cross-sectional area, volume, and stretching force for the 29-year-old lens. Age-related changes in accommodation were also simulated. Model 1 gave predictions which agreed with the Helmholtz theory of accommodation, while Model 2's predictions agreed with the Schachar mechanism of accommodation. Trends predicted by Model 1 agreed with all available experimental data, while Model 2 disagreed with recent surface area measurements. Further analysis indicated that Model 1 was fundamentally more efficient in that it required less force per diopter change in optical power than Model 2. Model 1 more accurately predicted age-related changes in accommodation amplitude. This implies that the zero-force (fully accommodated) state geometry changes with age due to a shifting balance in residual stresses between the lens and capsule.
Qualitative and quantitative description of microstructure of alloys from the Fe-Al system
NASA Astrophysics Data System (ADS)
Jabłońska, M.; Mikuśkiewicz, M.; Tomaszewska, A.
2012-05-01
The paper presents the test results of qualitative and quantitative analysis of the structure of alloys from Fe-Al system after casting and heat treatment. The analysis were carried out for three alloys, with different content of Al at.%: 36, 38, 48 at %, which were produced by melting and gravity casting. A quantitative evaluation of the structure was made with use of "MET-ILO" application on the basis of images acquired from a light microscope. Moreover the influence of the chemical composition and results of quantitative description of microstructure on the hardness of alloys from the aluminium - iron system were analysed. The obtained research will be used for the development of mathematical models determining the influence of primary structure on the opportunities for plastic deformation of alloys. Structural examination was carried out using scanning electron microscopy (SEM) and scanning transmission electron microscopy (STEM). X-ray diffraction measurements were performed on this alloys.
Quantitative methods for three-dimensional comparison and petrographic description of chondrites
Friedrich, J.M.
2008-10-20
X-ray computed tomography can be used to generate three-dimensional (3D) volumetric representations of chondritic meteorites. One of the challenges of using collected X-ray tomographic data is the extraction of useful data for 3D petrographic analysis or description. Here, I examine computer-aided quantitative 3D texture metrics that can be used for the classification of chondritic meteorites. These quantitative techniques are extremely useful for discriminating between chondritic materials, but yield little information on the 3D morphology of chondrite components. To investigate the morphology of chondrite minerals such as Fe(Ni) metal and related sulfides, the homology descriptors known as Betti numbers, are examined. Both methodologies are illustrated with theoretical discussion and examples. Betti numbers may be valuable for examining the nature of metal-silicate structural changes within chondrites with increasing degrees of metamorphism.
NASA Astrophysics Data System (ADS)
Klump, J. F.; Huber, R.; Robertson, J.; Cox, S. J. D.; Woodcock, R.
2014-12-01
Despite the recent explosion of quantitative geological data, geology remains a fundamentally qualitative science. Numerical data only constitute a certain part of data collection in the geosciences. In many cases, geological observations are compiled as text into reports and annotations on drill cores, thin sections or drawings of outcrops. The observations are classified into concepts such as lithology, stratigraphy, geological structure, etc. These descriptions are semantically rich and are generally supported by more quantitative observations using geochemical analyses, XRD, hyperspectral scanning, etc, but the goal is geological semantics. In practice it has been difficult to bring the different observations together due to differing perception or granularity of classification in human observation, or the partial observation of only some characteristics using quantitative sensors. In the past years many geological classification schemas have been transferred into ontologies and vocabularies, formalized using RDF and OWL, and published through SPARQL endpoints. Several lithological ontologies were compiled by stratigraphy.net and published through a SPARQL endpoint. This work is complemented by the development of a Python API to integrate this vocabulary into Python-based text mining applications. The applications for the lithological vocabulary and Python API are automated semantic tagging of geochemical data and descriptions of drill cores, machine learning of geochemical compositions that are diagnostic for lithological classifications, and text mining for lithological concepts in reports and geological literature. This combination of applications can be used to identify anomalies in databases, where composition and lithological classification do not match. It can also be used to identify lithological concepts in the literature and infer quantitative values. The resulting semantic tagging opens new possibilities for linking these diverse sources of data.
Lee, Won-Joon; Wilkinson, Caroline M; Hwang, Hyeon-Shik; Lee, Sang-Mi
2015-05-01
Accuracy is the most important factor supporting the reliability of forensic facial reconstruction (FFR) comparing to the corresponding actual face. A number of methods have been employed to evaluate objective accuracy of FFR. Recently, it has been attempted that the degree of resemblance between computer-generated FFR and actual face is measured by geometric surface comparison method. In this study, three FFRs were produced employing live adult Korean subjects and three-dimensional computerized modeling software. The deviations of the facial surfaces between the FFR and the head scan CT of the corresponding subject were analyzed in reverse modeling software. The results were compared with those from a previous study which applied the same methodology as this study except average facial soft tissue depth dataset. Three FFRs of this study that applied updated dataset demonstrated lesser deviation errors between the facial surfaces of the FFR and corresponding subject than those from the previous study. The results proposed that appropriate average tissue depth data are important to increase quantitative accuracy of FFR. PMID:25739646
Lee, Won-Joon; Wilkinson, Caroline M; Hwang, Hyeon-Shik; Lee, Sang-Mi
2015-05-01
Accuracy is the most important factor supporting the reliability of forensic facial reconstruction (FFR) comparing to the corresponding actual face. A number of methods have been employed to evaluate objective accuracy of FFR. Recently, it has been attempted that the degree of resemblance between computer-generated FFR and actual face is measured by geometric surface comparison method. In this study, three FFRs were produced employing live adult Korean subjects and three-dimensional computerized modeling software. The deviations of the facial surfaces between the FFR and the head scan CT of the corresponding subject were analyzed in reverse modeling software. The results were compared with those from a previous study which applied the same methodology as this study except average facial soft tissue depth dataset. Three FFRs of this study that applied updated dataset demonstrated lesser deviation errors between the facial surfaces of the FFR and corresponding subject than those from the previous study. The results proposed that appropriate average tissue depth data are important to increase quantitative accuracy of FFR.
Ievlev, Anton V; Jesse, Stephen; Cochell, Thomas J; Unocic, Raymond R; Protopopescu, Vladimir A; Kalinin, Sergei V
2015-12-22
Recent advances in liquid cell (scanning) transmission electron microscopy (S)TEM has enabled in situ nanoscale investigations of controlled nanocrystal growth mechanisms. Here, we experimentally and quantitatively investigated the nucleation and growth mechanisms of Pt nanostructures from an aqueous solution of K2PtCl6. Averaged statistical, network, and local approaches have been used for the data analysis and the description of both collective particles dynamics and local growth features. In particular, interaction between neighboring particles has been revealed and attributed to reduction of the platinum concentration in the vicinity of the particle boundary. The local approach for solving the inverse problem showed that particles dynamics can be simulated by a stationary diffusional model. The obtained results are important for understanding nanocrystal formation and growth processes and for optimization of synthesis conditions.
Harden, J.W.
1982-01-01
A soil development index has been developed in order to quantitatively measure the degree of soil profile development. This index, which combines eight soil field properties with soil thickness, is designed from field descriptions of the Merced River chronosequence in central California. These eight properties are: clay films, texture plus wet consistence, rubification (color hue and chroma), structure, dry consistence, moist consistence, color value, and pH. Other properties described in the field can be added when more soils are studied. Most of the properties change systematically within the 3 m.y. age span of the Merced River chronosequence. The absence of properties on occasion does not significantly affect the index. Individual quantified field properties, as well as the integrated index, are examined and compared as functions of soil depth and age. ?? 1982.
Yan, Yuan; Shan, Hangyong; Li, Min; Chen, Shu; Liu, Jianyu; Cheng, Yanfang; Ye, Cui; Yang, Zhilin; Lai, Xuandi; Hu, Jianqiang
2015-01-01
In this work, a hierarchical DNA–directed self–assembly strategy to construct structure–controlled Au nanoassemblies (NAs) has been demonstrated by conjugating Au nanoparticles (NPs) with internal–modified dithiol single-strand DNA (ssDNA) (Au–B–A or A–B–Au–B–A). It is found that the dithiol–ssDNA–modified Au NPs and molecule quantity of thiol–modified ssDNA grafted to Au NPs play critical roles in the assembly of geometrically controlled Au NAs. Through matching Au–DNA self–assembly units, geometrical structures of the Au NAs can be tailored from one–dimensional (1D) to quasi–2D and 2D. Au–B–A conjugates readily give 1D and quasi–2D Au NAs while 2D Au NAs can be formed by A–B–Au–B–A building blocks. Surface-enhanced Raman scattering (SERS) measurements and 3D finite–difference time domain (3D-FDTD) calculation results indicate that the geometrically controllable Au NAs have regular and linearly “hot spots”–number–depended SERS properties. For a certain number of NPs, the number of “hot spots” and accordingly enhancement factor of Au NAs can be quantitatively evaluated, which open a new avenue for quantitative analysis based on SERS technique. PMID:26581251
NASA Astrophysics Data System (ADS)
Yan, Yuan; Shan, Hangyong; Li, Min; Chen, Shu; Liu, Jianyu; Cheng, Yanfang; Ye, Cui; Yang, Zhilin; Lai, Xuandi; Hu, Jianqiang
2015-11-01
In this work, a hierarchical DNA-directed self-assembly strategy to construct structure-controlled Au nanoassemblies (NAs) has been demonstrated by conjugating Au nanoparticles (NPs) with internal-modified dithiol single-strand DNA (ssDNA) (Au-B-A or A-B-Au-B-A). It is found that the dithiol-ssDNA-modified Au NPs and molecule quantity of thiol-modified ssDNA grafted to Au NPs play critical roles in the assembly of geometrically controlled Au NAs. Through matching Au-DNA self-assembly units, geometrical structures of the Au NAs can be tailored from one-dimensional (1D) to quasi-2D and 2D. Au-B-A conjugates readily give 1D and quasi-2D Au NAs while 2D Au NAs can be formed by A-B-Au-B-A building blocks. Surface-enhanced Raman scattering (SERS) measurements and 3D finite-difference time domain (3D-FDTD) calculation results indicate that the geometrically controllable Au NAs have regular and linearly “hot spots”-number-depended SERS properties. For a certain number of NPs, the number of “hot spots” and accordingly enhancement factor of Au NAs can be quantitatively evaluated, which open a new avenue for quantitative analysis based on SERS technique.
Quantitative Description of a Protein Fitness Landscape Based on Molecular Features.
Meini, María-Rocío; Tomatis, Pablo E; Weinreich, Daniel M; Vila, Alejandro J
2015-07-01
Understanding the driving forces behind protein evolution requires the ability to correlate the molecular impact of mutations with organismal fitness. To address this issue, we employ here metallo-β-lactamases as a model system, which are Zn(II) dependent enzymes that mediate antibiotic resistance. We present a study of all the possible evolutionary pathways leading to a metallo-β-lactamase variant optimized by directed evolution. By studying the activity, stability and Zn(II) binding capabilities of all mutants in the preferred evolutionary pathways, we show that this local fitness landscape is strongly conditioned by epistatic interactions arising from the pleiotropic effect of mutations in the different molecular features of the enzyme. Activity and stability assays in purified enzymes do not provide explanatory power. Instead, measurement of these molecular features in an environment resembling the native one provides an accurate description of the observed antibiotic resistance profile. We report that optimization of Zn(II) binding abilities of metallo-β-lactamases during evolution is more critical than stabilization of the protein to enhance fitness. A global analysis of these parameters allows us to connect genotype with fitness based on quantitative biochemical and biophysical parameters.
Quantitative Description of a Protein Fitness Landscape Based on Molecular Features
Meini, María-Rocío; Tomatis, Pablo E.; Weinreich, Daniel M.; Vila, Alejandro J.
2015-01-01
Understanding the driving forces behind protein evolution requires the ability to correlate the molecular impact of mutations with organismal fitness. To address this issue, we employ here metallo-β-lactamases as a model system, which are Zn(II) dependent enzymes that mediate antibiotic resistance. We present a study of all the possible evolutionary pathways leading to a metallo-β-lactamase variant optimized by directed evolution. By studying the activity, stability and Zn(II) binding capabilities of all mutants in the preferred evolutionary pathways, we show that this local fitness landscape is strongly conditioned by epistatic interactions arising from the pleiotropic effect of mutations in the different molecular features of the enzyme. Activity and stability assays in purified enzymes do not provide explanatory power. Instead, measurement of these molecular features in an environment resembling the native one provides an accurate description of the observed antibiotic resistance profile. We report that optimization of Zn(II) binding abilities of metallo-β-lactamases during evolution is more critical than stabilization of the protein to enhance fitness. A global analysis of these parameters allows us to connect genotype with fitness based on quantitative biochemical and biophysical parameters. PMID:25767204
Quantitative Description of a Protein Fitness Landscape Based on Molecular Features.
Meini, María-Rocío; Tomatis, Pablo E; Weinreich, Daniel M; Vila, Alejandro J
2015-07-01
Understanding the driving forces behind protein evolution requires the ability to correlate the molecular impact of mutations with organismal fitness. To address this issue, we employ here metallo-β-lactamases as a model system, which are Zn(II) dependent enzymes that mediate antibiotic resistance. We present a study of all the possible evolutionary pathways leading to a metallo-β-lactamase variant optimized by directed evolution. By studying the activity, stability and Zn(II) binding capabilities of all mutants in the preferred evolutionary pathways, we show that this local fitness landscape is strongly conditioned by epistatic interactions arising from the pleiotropic effect of mutations in the different molecular features of the enzyme. Activity and stability assays in purified enzymes do not provide explanatory power. Instead, measurement of these molecular features in an environment resembling the native one provides an accurate description of the observed antibiotic resistance profile. We report that optimization of Zn(II) binding abilities of metallo-β-lactamases during evolution is more critical than stabilization of the protein to enhance fitness. A global analysis of these parameters allows us to connect genotype with fitness based on quantitative biochemical and biophysical parameters. PMID:25767204
A geometric description of the non-Gaussianity generated at the end of multi-field inflation
NASA Astrophysics Data System (ADS)
Huang, Qing-Guo
2009-06-01
In this paper we mainly focus on the curvature perturbation generated at the end of multi-field inflation, such as the multi-brid inflation. Since the curvature perturbation is produced on the super-horizon scale, the bispectrum and trispectrum have a local shape. The size of bispectrum is measured by fNL and the trispectrum is characterized by two parameters τNL and gNL. For simplicity, the trajectory of inflaton is assumed to be a straight line in the field space and then the entropic perturbations do not contribute to the curvature perturbation during inflation. As long as the background inflaton path is not orthogonal to the hyper-surface for inflation to end, the entropic perturbation can make a contribution to the curvature perturbation at the end of inflation and a large local-type non-Gaussiantiy is expected. An interesting thing is that the non-Gaussianity parameters are completely determined by the geometric properties of the hyper-surface of the end of inflation. For example, fNL is proportional to the curvature of the curve on this hyper-surface along the adiabatic direction and gNL is related to the change of the curvature radius per unit arc-length of this curve. Both fNL and gNL can be positive or negative respectively, but τNL must be positive and not less than ((6/5)fNL)2.
A geometric description of the non-Gaussianity generated at the end of multi-field inflation
Huang, Qing-Guo
2009-06-01
In this paper we mainly focus on the curvature perturbation generated at the end of multi-field inflation, such as the multi-brid inflation. Since the curvature perturbation is produced on the super-horizon scale, the bispectrum and trispectrum have a local shape. The size of bispectrum is measured by f{sub NL} and the trispectrum is characterized by two parameters τ{sub NL} and g{sub NL}. For simplicity, the trajectory of inflaton is assumed to be a straight line in the field space and then the entropic perturbations do not contribute to the curvature perturbation during inflation. As long as the background inflaton path is not orthogonal to the hyper-surface for inflation to end, the entropic perturbation can make a contribution to the curvature perturbation at the end of inflation and a large local-type non-Gaussiantiy is expected. An interesting thing is that the non-Gaussianity parameters are completely determined by the geometric properties of the hyper-surface of the end of inflation. For example, f{sub NL} is proportional to the curvature of the curve on this hyper-surface along the adiabatic direction and g{sub NL} is related to the change of the curvature radius per unit arc-length of this curve. Both f{sub NL} and g{sub NL} can be positive or negative respectively, but τ{sub NL} must be positive and not less than ((6/5)f{sub NL}){sup 2}.
Belka, Mariusz; Hewelt-Belka, Weronika; Sławiński, Jarosław; Bączek, Tomasz
2014-01-01
A set of 15 new sulphonamide derivatives, presenting antitumor activity have been subjected to a metabolic stability study. The results showed that besides products of biotransformation, some additional peaks occurred in chromatograms. Tandem mass spectrometry revealed the same mass and fragmentation pathway, suggesting that geometric isomerization occurred. Thus, to support this hypothesis, quantitative structure-retention relationships were applied. Human liver microsomes were used as an in vitro model of metabolism. The biotransformation reactions were tracked by liquid chromatography assay and additionally, fragmentation mass spectra were recorded. In silico molecular modeling at a semi-empirical level was conducted as a starting point for molecular descriptor calculations. A quantitative structure-retention relationship model was built applying multiple linear regression based on selected three-dimensional descriptors. The studied compounds revealed high metabolic stability, with a tendency to form hydroxylated biotransformation products. However, significant chemical instability in conditions simulating human body fluids was noticed. According to literature and MS data geometrical isomerization was suggested. The developed in sillico model was able to describe the relationship between the geometry of isomer pairs and their chromatographic retention properties, thus it supported the hypothesis that the observed pairs of peaks are most likely geometric isomers. However, extensive structural investigations are needed to fully identify isomers’ geometry. An effort to describe MS fragmentation pathways of novel chemical structures is often not enough to propose structures of potent metabolites and products of other chemical reactions that can be observed in compound solutions at early drug discovery studies. The results indicate that the relatively non-expensive and not time- and labor-consuming in sillico approach could be a good supportive tool assisting the
NASA Astrophysics Data System (ADS)
Schnedler, M.; Portz, V.; Weidlich, P. H.; Dunin-Borkowski, R. E.; Ebert, Ph.
2015-06-01
A quantitative description of photoexcited scanning tunneling spectra is developed and applied to photoexcited spectra measured on p -doped nonpolar GaAs(110) surfaces. Under illumination, the experimental spectra exhibit an increase of the tunnel current at negative sample voltages only. In order to analyze the experimental data quantitatively, the potential and charge-carrier distributions of the photoexcited tip-vacuum-semiconductor system are calculated by solving the Poisson as well as the hole and electron continuity equations by a finite-difference algorithm. On this basis, the different contributions to the tunnel current are calculated using an extension of the model of Feenstra and Stroscio to include the light-excited carrier concentrations. The best fit of the calculated tunnel currents to the experimental data is obtained for a tip-induced band bending, which is limited by the partial occupation of the C3 surface state by light-excited electrons. The tunnel current at negative voltages is then composed of a valence band contribution and a photoinduced tunnel current of excited electrons in the conduction band. The quantitative description of the tunnel current developed here is generally applicable and provides a solid foundation for the quantitative interpretation of photoexcited scanning tunneling spectroscopy.
ERIC Educational Resources Information Center
Marrus, Natasha; Faughn, Carley; Shuman, Jeremy; Petersen, Steve E.; Constantino, John N.; Povinelli, Daniel J.; Pruett, John R., Jr.
2011-01-01
Objective: Comparative studies of social responsiveness, an ability that is impaired in autism spectrum disorders, can inform our understanding of both autism and the cognitive architecture of social behavior. Because there is no existing quantitative measure of social responsiveness in chimpanzees, we generated a quantitative, cross-species…
Karanovic, Tomislav; Djurakic, Marko; Eberhard, Stefan M
2016-03-01
Discovery of cryptic species using molecular tools has become common in many animal groups but it is rarely accompanied by morphological revision, creating ongoing problems in taxonomy and conservation. In copepods, cryptic species have been discovered in most groups where fast-evolving molecular markers were employed. In this study at Yeelirrie in Western Australia we investigate a subterranean species complex belonging to the harpacticoid genus Schizopera Sars, 1905, using both the barcoding mitochondrial COI gene and landmark-based two-dimensional geometric morphometrics. Integumental organs (sensilla and pores) are used as landmarks for the first time in any crustacean group. Complete congruence between DNA-based species delimitation and relative position of integumental organs in two independent morphological structures suggests the existence of three distinct evolutionary units. We describe two of them as new species, employing a condensed taxonomic format appropriate for cryptic species. We argue that many supposedly cryptic species might not be cryptic if researchers focus on analyzing morphological structures with multivariate tools that explicitly take into account geometry of the phenotype. A perceived supremacy of molecular methods in detecting cryptic species is in our view a consequence of disparity of investment and unexploited recent advancements in morphometrics among taxonomists. Our study shows that morphometric data alone could be used to find diagnostic morphological traits and gives hope to anyone studying small animals with a hard integument or shell, especially opening the door to assessing fossil diversity and rich museum collections. We expect that simultaneous use of molecular tools with geometry-oriented morphometrics may yield faster formal description of species. Decrypted species in this study are a good example for urgency of formal descriptions, as they display short-range endemism in small groundwater calcrete aquifers in a
1500 System Geometric Dictionary.
ERIC Educational Resources Information Center
Peloquin, Paul V.
A general description is provided of the "geometric dictionary," a graphic display aid, used by the Computer-Assisted Instruction Laboratory at the Pennsylvania State University. The purpose of the description is to enable the reader to duplicate and use the dictionary on any cathode ray tube terminal of the IBM 1500 system. The major advantages…
Microscope-Quantitative Luminescence Imaging System (M-Qlis) Description and User's Manual
Stahl, K. A.
1991-10-01
A Microscope Quantitative Luminescence Imaging System (M-QLIS} has been designed and constructed. The M-QLIS is designed for use in studies of chemiluminescent phenomena associated with absorption of radio-frequency radiation. The system consists of a radio-frequency waveguide/sample holder, microscope, intensified video camera, radiometric calibration source and optics, and computer-based image processor with radiometric analysis software. The system operation, hardware, software, and radiometric procedures are described.
Puri, Ritika; Khamrui, Kaushik; Khetra, Yogesh; Malhotra, Ravinder; Devraja, H C
2016-02-01
Promising development and expansion in the market of cham-cham, a traditional Indian dairy product is expected in the coming future with the organized production of this milk product by some large dairies. The objective of this study was to document the extent of variation in sensory properties of market samples of cham-cham collected from four different locations known for their excellence in cham-cham production and to find out the attributes that govern much of variation in sensory scores of this product using quantitative descriptive analysis (QDA) and principal component analysis (PCA). QDA revealed significant (p < 0.05) difference in sensory attributes of cham-cham among the market samples. PCA identified four significant principal components that accounted for 72.4 % of the variation in the sensory data. Factor scores of each of the four principal components which primarily correspond to sweetness/shape/dryness of interior, surface appearance/surface dryness, rancid and firmness attributes specify the location of each market sample along each of the axes in 3-D graphs. These findings demonstrate the utility of quantitative descriptive analysis for identifying and measuring attributes of cham-cham that contribute most to its sensory acceptability.
MAYHEW, TERRY M.
1999-01-01
Previous quantitative descriptions of cellular ultrastructure have focused on spatial content (volume, surface area and number of organelles and membrane domains). It is possible to complement such descriptions by also quantifying spatial arrangements. Hitherto, applications of stereological methods for achieving this (notably, estimation of covariance and pair correlation functions) have been confined to organ and tissue levels. This study explores 3-dimensional subcellular arrangements of key organelles within acinar cells of rabbit parotid salivary glands, highly polarised epithelial cells specialised for exocrine secretion of α-amylase. It focuses on spatial arrangements of secretion product stores (zymogen granules), rough endoplasmic reticulum (RER) and mitochondria. Systematic random samples of electron microscopical fields of view from 3 rabbits were analysed using test grids bearing linear dipole probes of different sizes. Unbiased estimates of organelle volume densities were obtained by point counting and estimates of covariance and pair correlation functions by dipole counting. Plots of pair correlation functions against dipole length identified spatial arrangement differences between organelle types. Volumes within RER and mitochondrial compartments were positively correlated with themselves at distances below 4 μm and 2 μm respectively but were essentially randomly arranged at longer distances. In sharp contrast, zymogen granules were not randomly arranged. They were clustered at distances below 6–7 μm and more widely scattered at greater distances. These findings provide quantitative confirmation of the polarised arrangement of zymogen granules within acinar cells and further support for the relative invariance of biological organisation between subjects. PMID:10337960
A quantitative description in three dimensions of oxygen uptake by human red blood cells.
Vandegriff, K D; Olson, J S
1984-01-01
Oxygen uptake by human erythrocytes has been examined both experimentally and theoretically in terms of the influence of unstirred solvent layers that are adjacent to the cell surface. A one-dimensional plane sheet model has been compared with more complex spherical and cylindrical coordinate schemes. Although simpler and faster, the plane sheet algorithm is an inadequate representation when unstirred solvent layers are considered. The cylindrical disk model most closely represents the physical geometry of human red cells and is required for a quantitative analysis. In our stopped-flow rapid mixing experiments, the thickness of the unstirred solvent layer expands with time as the residual turbulence decays. This phenomenon has been quantified using a formulation based on previously developed hydrodynamic theories. An initial 10(-4) cm unstirred layer is postulated to occur during mixing and expand rapidly with time by a (t)0.5 function when flow stops. This formula, in combination with the three-dimensional cylinder scheme, has been used to describe quantitatively uptake time courses at various oxygen concentrations, two different external solvent viscosities, and two different internal heme concentrations. PMID:6722268
Marrus, Natasha; Faughn, Carley; Shuman, Jeremy; Petersen, Steve; Constantino, John; Povinelli, Daniel; Pruett, John R.
2011-01-01
Objective Comparative studies of social responsiveness, an ability that is impaired in autistic spectrum disorders, can inform our understanding of both autism and the cognitive architecture of social behavior. Because there is no existing quantitative measure of social responsiveness in chimpanzees, we generated a quantitative, cross-species (human-chimpanzee) social responsiveness measure. Method We translated the Social Responsiveness Scale (SRS), an instrument that quantifies human social responsiveness, into an analogous instrument for chimpanzees. We then retranslated this "Chimp SRS" into a human "Cross-Species SRS" (XSRS). We evaluated three groups of chimpanzees (n=29) with the Chimp SRS and typical and autistic spectrum disorder (ASD) human children (n=20) with the XSRS. Results The Chimp SRS demonstrated strong inter-rater reliability at the three sites (ranges for individual ICCs: .534–.866 and mean ICCs: .851–.970). As has been observed in humans, exploratory principal components analysis of Chimp SRS scores supports a single factor underlying chimpanzee social responsiveness. Human subjects' XSRS scores were fully concordant with their SRS scores (r=.976, p=.001) and distinguished appropriately between typical and ASD subjects. One chimpanzee known for inappropriate social behavior displayed a significantly higher score than all other chimpanzees at its site, demonstrating the scale's ability to detect impaired social responsiveness in chimpanzees. Conclusion Our initial cross-species social responsiveness scale proved reliable and discriminated differences in social responsiveness across (in a relative sense) and within (in a more objectively quantifiable manner) humans and chimpanzees. PMID:21515200
Quantitative description of ion transport via plasma membrane of yeast and small cells
Volkov, Vadim
2015-01-01
Modeling of ion transport via plasma membrane needs identification and quantitative understanding of the involved processes. Brief characterization of main ion transport systems of a yeast cell (Pma1, Ena1, TOK1, Nha1, Trk1, Trk2, non-selective cation conductance) and determining the exact number of molecules of each transporter per a typical cell allow us to predict the corresponding ion flows. In this review a comparison of ion transport in small yeast cell and several animal cell types is provided. The importance of cell volume to surface ratio is emphasized. The role of cell wall and lipid rafts is discussed in respect to required increase in spatial and temporary resolution of measurements. Conclusions are formulated to describe specific features of ion transport in a yeast cell. Potential directions of future research are outlined based on the assumptions. PMID:26113853
Quantitative Description of Glycan-Receptor Binding of Influenza A Virus H7 Hemagglutinin
Srinivasan, Karunya; Raman, Rahul; Jayaraman, Akila; Viswanathan, Karthik; Sasisekharan, Ram
2013-01-01
In the context of recently emerged novel influenza strains through reassortment, avian influenza subtypes such as H5N1, H7N7, H7N2, H7N3 and H9N2 pose a constant threat in terms of their adaptation to the human host. Among these subtypes, it was recently demonstrated that mutations in H5 and H9 hemagglutinin (HA) in the context of lab-generated reassorted viruses conferred aerosol transmissibility in ferrets (a property shared by human adapted viruses). We previously demonstrated that the quantitative binding affinity of HA to α2→6 sialylated glycans (human receptors) is one of the important factors governing human adaptation of HA. Although the H7 subtype has infected humans causing varied clinical outcomes from mild conjunctivitis to severe respiratory illnesses, it is not clear where the HA of these subtypes stand in regard to human adaptation since its binding affinity to glycan receptors has not yet been quantified. In this study, we have quantitatively characterized the glycan receptor-binding specificity of HAs from representative strains of Eurasian (H7N7) and North American (H7N2) lineages that have caused human infection. Furthermore, we have demonstrated for the first time that two specific mutations; Gln226→Leu and Gly228→Ser in glycan receptor-binding site of H7 HA substantially increase its binding affinity to human receptor. Our findings contribute to a framework for monitoring the evolution of H7 HA to be able to adapt to human host. PMID:23437033
A quantitative description of Ndc80 complex linkage to human kinetochores
Suzuki, Aussie; Badger, Benjamin L.; Salmon, Edward D.
2015-01-01
The Ndc80 complex, which mediates end-on attachment of spindle microtubules, is linked to centromeric chromatin in human cells by two inner kinetochore proteins, CENP-T and CENP-C. Here to quantify their relative contributions to Ndc80 recruitment, we combine measurements of kinetochore protein copy number with selective protein depletion assays. This approach reveals about 244 Ndc80 complexes per human kinetochore (∼14 per kinetochore microtubule), 215 CENP-C, 72 CENP-T and only 151 Ndc80s as part of the KMN protein network (1:1:1 Knl1, Mis12 and Ndc80 complexes). Each CENP-T molecule recruits ∼2 Ndc80 complexes; one as part of a KMN network. In contrast, ∼40% of CENP-C recruits only a KMN network. Replacing the CENP-C domain that binds KMN with the CENP-T domain that recruits both an Ndc80 complex and KMN network yielded functional kinetochores. These results provide a quantitative picture of the linkages between centromeric chromatin and the microtubule-binding Ndc80 complex at the human kinetochore. PMID:26345214
Quantitative description of fluid flows produced by left-right cilia in zebrafish.
Fox, Craig; Manning, M Lisa; Amack, Jeffrey D
2015-01-01
Motile cilia generate directional flows that move mucus through airways, cerebrospinal fluid through brain ventricles, and oocytes through fallopian tubes. In addition, specialized monocilia beat in a rotational pattern to create asymmetric flows that are involved in establishing the left-right (LR) body axis during embryogenesis. These monocilia, which we refer to as "left-right cilia," produce a leftward flow of extraembryonic fluid in a transient "organ of asymmetry" that directs asymmetric signaling and development of LR asymmetries in the cardiovascular system and gastrointestinal tract. The asymmetric flows are thought to establish a chemical gradient and/or activate mechanosensitive cilia to initiate calcium ion signals and a conserved Nodal (TGFβ) pathway on the left side of the embryo, but the mechanisms underlying this process remain unclear. The zebrafish organ of asymmetry, called Kupffer's vesicle, provides a useful model system for investigating LR cilia and cilia-powered fluid flows. Here, we describe methods to visualize flows in Kupffer's vesicle using fluorescent microspheres and introduce a new and freely available MATLAB particle tracking code to quantitatively describe these flows. Analysis of normal and aberrant flows indicates this approach is useful for characterizing flow properties that impact LR asymmetry and may be more broadly applicable for quantifying other cilia flows. PMID:25837391
da Silva, Paula Porrelli Moreira; Casemiro, Renata Cristina; Zillo, Rafaela Rebessi; de Camargo, Adriano Costa; Prospero, Evanilda Teresinha Perissinotto; Spoto, Marta Helena Fillet
2014-01-01
This study evaluated the effect of pasteurization followed by storage under different conditions on the sensory attributes of frozen juçara pulp using quantitative descriptive analysis (QDA). Pasteurization of packed frozen pulp was performed by its immersion in stainless steel tank containing water (80°C) for 5 min, followed by storage under refrigerated and frozen conditions. A trained sensory panel evaluated the samples (6°C) on day 1, 15, 30, 45, 60, 75, and 90. Sensory attributes were separated as follows: appearance (foamy, heterogeneous, purple, brown, oily, and creamy), aroma (sweet and fermented), taste (astringent, bitter, and sweet), and texture (oily and consistent), and compared to a reference material. In general, unpasteurized frozen pulp showed the highest score for foamy appearance, and pasteurized samples showed highest scores to creamy appearance. Pasteurized samples remained stable regarding brown color development while unpasteurized counterparts presented increase. Color is an important attribute related to the product identity. All attributes related to taste and texture remained constant during storage for all samples. Pasteurization followed by storage under frozen conditions has shown to be the best conservation method as samples submitted to such process received the best sensory evaluation, described as foamy, slightly heterogeneous, slightly bitter, and slightly astringent. PMID:25473489
NASA Astrophysics Data System (ADS)
Lindlein, Norbert; Leuchs, Gerd
This chapter shall discuss the basics and the applications of geometrical optical methods in modern optics. Geometrical optics has a long tradition and some ideas are many centuries old. Nevertheless, the invention of modern personal computers which can perform several million floating-point operations in a second also revolutionized the methods of geometrical optics and so several analytical methods lost importance whereas numerical methods such as ray tracing became very important. Therefore, the emphasis in this chapter is also on modern numerical methods such as ray tracing and some other systematic methods such as the paraxial matrix theory.
Geometrical deployment for braided stent.
Bouillot, Pierre; Brina, Olivier; Ouared, Rafik; Yilmaz, Hasan; Farhat, Mohamed; Erceg, Gorislav; Lovblad, Karl-Olof; Vargas, Maria Isabel; Kulcsar, Zsolt; Pereira, Vitor Mendes
2016-05-01
The prediction of flow diverter stent (FDS) implantation for the treatment of intracranial aneurysms (IAs) is being increasingly required for hemodynamic simulations and procedural planning. In this paper, a deployment model was developed based on geometrical properties of braided stents. The proposed mathematical description is first applied on idealized toroidal vessels demonstrating the stent shortening in curved vessels. It is subsequently generalized to patient specific vasculature predicting the position of the filaments along with the length and local porosity of the stent. In parallel, in-vitro and in-vivo FDS deployments were measured by contrast-enhanced cone beam CT (CBCT) in idealized and patient-specific geometries. These measurements showed a very good qualitative and quantitative agreement with the virtual deployments and provided experimental validations of the underlying geometrical assumptions. In particular, they highlighted the importance of the stent radius assessment in the accuracy of the deployment prediction. Thanks to its low computational cost, the proposed model is potentially implementable in clinical practice providing critical information for patient safety and treatment outcome assessment. PMID:26891065
NASA Astrophysics Data System (ADS)
Talman, Richard
1999-10-01
Mechanics for the nonmathematician-a modern approach For physicists, mechanics is quite obviously geometric, yet the classical approach typically emphasizes abstract, mathematical formalism. Setting out to make mechanics both accessible and interesting for nonmathematicians, Richard Talman uses geometric methods to reveal qualitative aspects of the theory. He introduces concepts from differential geometry, differential forms, and tensor analysis, then applies them to areas of classical mechanics as well as other areas of physics, including optics, crystal diffraction, electromagnetism, relativity, and quantum mechanics. For easy reference, Dr. Talman treats separately Lagrangian, Hamiltonian, and Newtonian mechanics-exploring their geometric structure through vector fields, symplectic geometry, and gauge invariance respectively. Practical perturbative methods of approximation are also developed. Geometric Mechanics features illustrative examples and assumes only basic knowledge of Lagrangian mechanics. Of related interest . . . APPLIED DYNAMICS With Applications to Multibody and Mechatronic Systems Francis C. Moon A contemporary look at dynamics at an intermediate level, including nonlinear and chaotic dynamics. 1998 (0-471-13828-2) 504 pp. MATHEMATICAL PHYSICS Applied Mathematics for Scientists and Engineers Bruce Kusse and Erik Westwig A comprehensive treatment of the mathematical methods used to solve practical problems in physics and engineering. 1998 (0-471-15431-8) 680 pp.
NASA Astrophysics Data System (ADS)
Baker, David M. H.; Head, James W.; Neumann, Gregory A.; Smith, David E.; Zuber, Maria T.
2012-03-01
The morphologic transition from complex impact craters, to peak-ring basins, and to multi-ring basins has been well-documented for decades. Less clear has been the morphometric characteristics of these landforms due to their large size and the lack of global high-resolution topography data. We use data from the Lunar Orbiter Laser Altimeter (LOLA) instrument onboard the Lunar Reconnaissance Orbiter (LRO) spacecraft to derive the morphometric characteristics of impact basins on the Moon, assess the trends, and interpret the processes involved in the observed morphologic transitions. We first developed a new technique for measuring and calculating the geometric/morphometric properties of impact basins on the Moon. This new method meets a number of criteria that are important for consideration in any topographic analysis of crater landforms (e.g., multiple data points, complete range of azimuths, systematic, reproducible analysis techniques, avoiding effects of post-event processes, robustness with respect to the statistical techniques). The resulting data more completely capture the azimuthal variation in topography that is characteristic of large impact structures. These new calculations extend the well-defined geometric trends for simple and complex craters out to basin-sized structures. Several new geometric trends for peak-ring basins are observed. Basin depth: A factor of two reduction in the depth to diameter (d/Dr) ratio in the transition from complex craters to peak-ring basins may be characterized by a steeper trend than known previously. The d/Dr ratio for peak-ring basins decreases with rim-crest diameter, which may be due to a non-proportional change in excavation cavity growth or scaling, as may occur in the simple to complex transition, or increased magnitude of floor uplift associated with peak-ring formation. Wall height, width, and slope: Wall height and width increase with increasing rim-crest diameter, while wall slope decreases; decreasing ratios
NASA Technical Reports Server (NTRS)
Grebowsky, G. J.
1982-01-01
Present LANDSAT data formats are reviewed to clarify how the geodetic location and registration capabilities were defined for P-tape products and RBV data. Since there is only one geometric model used in the master data processor, geometric location accuracy of P-tape products depends on the absolute accuracy of the model and registration accuracy is determined by the stability of the model. Due primarily to inaccuracies in data provided by the LANDSAT attitude management system, desired accuracies are obtained only by using ground control points and a correlation process. The verification of system performance with regards to geodetic location requires the capability to determine pixel positions of map points in a P-tape array. Verification of registration performance requires the capability to determine pixel positions of common points (not necessarily map points) in 2 or more P-tape arrays for a given world reference system scene. Techniques for registration verification can be more varied and automated since map data are not required. The verification of LACIE extractions is used as an example.
Ogawa, Junji; Yokota, Azusa; Araki, Takuya; Aomori, Tohru; Nakamura, Tomonori; Yamamoto, Koujirou; Koshiishi, Ichiro
2014-09-01
Gadoxetate, a magnetic resonance imaging contrast agent, is eliminated into bile. Gadoxetate geometrical isomers are chromatographically classified into two groups by differences between their ionic states (GIs-I and GIs-II; 65:35 w/w); however, the elimination mechanism of each isomer in vivo remains controversial. Thus, the contribution of carrier-mediated transport systems on the biliary elimination of gadoxetate was examined. Gadoxetate was injected intravenously into rats, and the time courses of the plasma concentrations and biliary elimination of GIs-I and GIs-II were examined by high-performance liquid chromatography techniques. The results showed that 34.7% of GIs-I (GIs-I(s); 22.6% of gadoxetate) was quickly eliminated into bile within 30 min after injection. The contents of the residual GIs-I (GIs-I(r)) and GIs-II in plasma similarly decreased according to a first-order elimination process (t1/2=23-27 min), and 64.0% of GIs-I(r) and GIs-II (49.6% of gadoxetate) was eliminated into the bile within 2 h after injection. There was no significant difference between the elimination half-lives of GIs-I(r) and GIs-II in rats. In conclusion, the geometrical isomer with specific conformation corresponding to 22.6% of gadoxetate was eliminated into bile in rats via a carrier-mediated transport system no later than 30 min after intravenous injection.
Geometric classification of open-cell metal foams using X-ray micro-computed tomography
Bock, Jessica Jacobi, Anthony M.
2013-01-15
The geometry of foams has long been an area of interest, and a number of idealized geometric descriptions have been proposed. In order to acquire detailed, quantitative, geometric data for aluminum open-cell metal foams, X-ray {mu}CT is employed. The X-ray {mu}CT images are analyzed using specialized software, FoamView Registered-Sign , from which geometric information including strut length and pore shapes are extracted. The X-ray {mu}CT analysis allows comparison of the ideal geometric models to the actual geometric characteristics of the metal foam samples. The results reveal a high variability in ligament length, as well as features supporting the ideal geometry known as the Weaire-Phelan unit cell. The geometric findings provide information useful for improving current models of open-cell metal foam. Applications can range from predicting heat transfer or load failure to predicting liquid retention. Highlights: Black-Right-Pointing-Pointer Aluminum open-cell metal foams are geometrically classified Black-Right-Pointing-Pointer X-ray micro-computed tomography and specialized software are used to gather geometric data Black-Right-Pointing-Pointer The foams are shown to have a high variability in strut length Black-Right-Pointing-Pointer The Weaire-Phelan unit cell is shown to be a better representative of these foams.
Pragmatic geometric model evaluation
NASA Astrophysics Data System (ADS)
Pamer, Robert
2015-04-01
Quantification of subsurface model reliability is mathematically and technically demanding as there are many different sources of uncertainty and some of the factors can be assessed merely in a subjective way. For many practical applications in industry or risk assessment (e. g. geothermal drilling) a quantitative estimation of possible geometric variations in depth unit is preferred over relative numbers because of cost calculations for different scenarios. The talk gives an overview of several factors that affect the geometry of structural subsurface models that are based upon typical geological survey organization (GSO) data like geological maps, borehole data and conceptually driven construction of subsurface elements (e. g. fault network). Within the context of the trans-European project "GeoMol" uncertainty analysis has to be very pragmatic also because of different data rights, data policies and modelling software between the project partners. In a case study a two-step evaluation methodology for geometric subsurface model uncertainty is being developed. In a first step several models of the same volume of interest have been calculated by omitting successively more and more input data types (seismic constraints, fault network, outcrop data). The positions of the various horizon surfaces are then compared. The procedure is equivalent to comparing data of various levels of detail and therefore structural complexity. This gives a measure of the structural significance of each data set in space and as a consequence areas of geometric complexity are identified. These areas are usually very data sensitive hence geometric variability in between individual data points in these areas is higher than in areas of low structural complexity. Instead of calculating a multitude of different models by varying some input data or parameters as it is done by Monte-Carlo-simulations, the aim of the second step of the evaluation procedure (which is part of the ongoing work) is to
Zhou, Lixia; Zhu, Dunxue; Zhang, Shujuan; Pan, Bingcai
2015-03-01
Understanding the aggregation and deposition behavior of carbon nanotubes (CNTs) is of great significance in terms of their fate and transport in the environment. Attachment efficiency is a widely used index for well-dispersed CNT solutions. However, in natural waters, CNTs are usually heterogeneous in particle size. The attachment efficiency method is not applicable to such systems. Describing the dispersion stability of CNTs in natural aquatic systems is still a challenge. In this work, a settling curve modeling (SCM) method was developed for the description of the aggregation and deposition behavior of CNTs in aqueous solutions. The effects of water chemistry (natural organic matter, pH, and ionic strength) on the aggregation and deposition behavior of pristine and surface-functionalized multi-walled carbon nanotubes (MWCNTs) were systematically studied to evaluate the reliability of the SCM method. The results showed that, as compared to particle size and optical density, the centrifugal sedimentation rate constant (ks) from the settling curve profile is a practical, useful and reliable index for the description of heterogeneous CNT suspensions. The SCM method was successfully applied to MWCNT in three natural waters. The constituents in water, especially organic matter, determine the dispersion stability of MWCNTs in natural water bodies.
Shabelnikova, Ya. L. Yakimov, E. B.; Nikolaev, D. P.; Chukalina, M. V.
2015-06-15
A solar cell on a wafer of multicrystalline silicon containing grain boundaries was studied by the induced-current method. The sample was scanned by an electron beam and by a laser beam at two wavelengths (980 and 635 nm). The recorded induced-current maps were aligned by means of a specially developed code, that enabled to analyze the same part of the grain boundary for three types of measurements. Optimization of the residual between simulated induced-current profiles and those obtained experimentally yielded quantitative estimates of the characteristics of a sample and its defects: the diffusion length of minority carriers and recombination velocity at the grain boundary.
Markey, C M; Meyer, G T
1992-01-01
The morphology of the epididymal duct and, in particular, the epididymal microvasculature was examined at the light microscope level in young sexually-mature rats (3-5 months) and aged rats (18 months) to investigate the structural changes that may occur within the organ as a result of ageing, and which may predispose the organ to pathological changes. Quantitative data on the microvascular network of the epididymis (percentage of capillaries in the interstitial region, average area and surface density of the capillary lumen) were collected in 4 regions of the epididymis: the initial segment, caput, corpus and cauda. Epithelial cell height, epididymal lumen diameter, number of smooth muscle cells and percentage of smooth muscle surrounding the duct were also assessed within the same 4 regions. The data for both young and aged groups revealed a trend of decreasing capillary size from the initial segment of the epididymis to the cauda by 23%. Further, the percentage of capillaries within the interstitial region of the epididymis decreases dramatically (52%) in the same direction. The possible contribution of lymphatic capillaries to the data is discussed. The data revealed that none of the parameters assessed changed significantly up to 18 months of age. The quantitative data on the microvascular morphology of the epididymis presented in this study provide the basis for subsequent studies directed at the blood flow dynamics of the organ. Images Fig. 1 Fig. 2 PMID:1506280
NASA Astrophysics Data System (ADS)
Mostaço-Guidolin, Leila B.; C-T Ko, Alex; Popescu, Dan P.; Smith, Michael S. D.; Kohlenberg, Elicia K.; Shiomi, Masashi; Major, Arkady; Sowa, Michael G.
2011-08-01
The composition and structure of atherosclerotic lesions can be directly related to the risk they pose to the patient. Multimodal nonlinear optical (NLO) microscopy provides a powerful means to visualize the major extracellular components of the plaque that critically determine its structure. Textural features extracted from NLO images were investigated for their utility in providing quantitative descriptors of structural and compositional changes associated with plaque development. Ten texture parameters derived from the image histogram and gray level co-occurrence matrix were examined that highlight specific structural and compositional motifs that distinguish early and late stage plaques. Tonal-texture parameters could be linked to key histological features that characterize vulnerable plaque: the thickness and density of the fibrous cap, size of the atheroma, and the level of inflammation indicated through lipid deposition. Tonal and texture parameters from NLO images provide objective metrics that correspond to structural and biochemical changes that occur within the vessel wall in early and late stage atherosclerosis.
Godelmann, Rolf; Kost, Christian; Patz, Claus-Dieter; Ristow, Reinhard; Wachter, Helmut
2016-09-01
To examine whether NMR analysis is a suitable method for the quantitative determination of wine components, an international collaborative trial was organized to evaluate the method according to the international regulations and guidelines of the German Institute for Standardization/International Organization for Standardization, AOAC INTERNATIONAL, the International Union of Pure and Applied Chemistry, and the International Organization of Vine and Wine. Sugars such as glucose; acids such as malic, acetic, fumaric, and shikimic acids (the latter two as minor components); and sorbic acid, a preservative, were selected for the exemplary quantitative determination of substances in wine. Selection criteria for the examination of sample material included different NMR spectral signal types (singlet and multiplet), as well as the suitability of the proposed substances for manual integration at different levels of challenge (e.g., interference as a result of the necessary suppression of a water signal or the coverage of different typical wine concentration ranges for a selection of major components, minor components, and additives). To show that this method can be universally applied, NMR measurement and the method of evaluation were not strictly elucidated. Fifteen international laboratories participated in the collaborative trial and determined six parameters in 10 samples. The values, in particular the reproducibility SD (SR), were compared with the expected Horwitz SD (SH) by forming the quotient SR/SH (i.e., the HorRat value). The resulting HorRat values of most parameters were predominantly between 0.6 and 1.5, and thus of an acceptable range. PMID:27436715
He, Hong-Gu; Vehviläinen-Julkunen, Katri; Qian, Xiao-Fang; Sapountzi-Krepia, Despina; Gong, Yuhua; Wang, Wenru
2015-05-01
This study examined Chinese fathers' feelings about their partners' delivery and views on their presence during labour and birth. A questionnaire survey was conducted with 403 fathers whose partners gave birth in one provincial hospital in China. Data were analysed by descriptive statistics, χ(2)-test and content analysis. The results indicated that more than 80% of fathers experienced feelings of pride related to fatherhood and of love towards their partners and newborns. Significant differences in fathers' feelings were found between subgroups with regard to age, education, employment, presence in the delivery room, method of birth and whether preparatory visits had been made to the hospital. The majority who answered an open-ended question on the meaning of fathers' presence in the delivery room held a positive attitude towards fathers' presence at labour and birth, as their presence could empower their partners and provide psychological support. This study indicates fathers' presence at delivery and birth is important and that younger fathers need more support. It also provides evidence for clinical practice and future interventions to improve fathers' psychological health and experiences.
Quantitative description of the lie-to-sit-to-stand-to-walk transfer by a single body-fixed sensor.
Bagalà, Fabio; Klenk, Jochen; Cappello, Angelo; Chiari, Lorenzo; Becker, Clemens; Lindemann, Ulrich
2013-07-01
Sufficient capacity and quality of performance of complex movement patterns during daily activity, such as standing up from a bed, is a prerequisite for independent living and also may be an indicator of fall risk. Until now, the transfer from lying-to-sit-to-stand-to-walk (LSSW) was investigated by functional testing, subjective rating or for activity classification of subtasks. The aim of this study was to use a single body-fixed inertial sensor to describe the complex movement of the LSSW transfer. Fifteen older patients of a geriatric rehabilitation clinic (median age 81 years) and ten young, healthy persons (median age 37 years) were instructed to stand up from bed in a continuous movement and to start walking. Data acquisition was performed using an inertial measurement unit worn on the lower back. Parameters extracted from the sensor outputs were able to correctly classify the subjects into a correct group with sensitivity and specificity between 90% and 100%. ICCs 3,1 of the descriptive parameters ranged between 0.85 and 0.95 in the cohort of older patients. The different strategies adopted to transfer from lying to standing up were estimated through an extended Kalman filter. The results obtained in this study suggest the usability of the instrumented LSSW test in clinical settings.
Nevin, John A.
1984-01-01
Quantitative analysis permits the isolation of invariant relations in the study of behavior. The parameters of these relations can serve as higher-order dependent variables in more extensive analyses. These points are illustrated by reference to quantitative descriptions of performance maintained by concurrent schedules, multiple schedules, and signal-detection procedures. Such quantitative descriptions of empirical data may be derived from mathematical theories, which in turn can lead to novel empirical analyses so long as their terms refer to behavioral and environmental events. Thus, quantitative analysis is an integral aspect of the experimental analysis of behavior. PMID:16812400
Brunskill, Jeffrey C
2010-03-01
This paper presents a study of the relationship between quantitative and qualitative descriptions of temperature. Online weather forecast narratives produced by local television forecasters were collected from affiliates in 23 cities throughout the northeastern, central and southern portions of the United States from August 2007 to July 2008. The narratives were collected to study the terminology and reference frames that local forecasters use to describe predicted temperatures for the following day. The main objectives were to explore the adjectives used to describe thermal conditions and the impact that geographical and seasonal variations in thermal conditions have on these descriptions. The results of this empirical study offer some insights into the structure of weather narratives and suggest that spatiotemporal variations in the weather impact how forecasters describe the temperature to their local audiences. In a broader sense, this investigation builds upon research in biometeorology, urban planning and linguistics that has explored the physiological and psychological factors that influence subjective assessments of thermal sensation and comfort. The results of this study provide a basis to reason about how thermal comfort is conveyed in meteorological communications and how experiential knowledge derived from daily observations of the weather influence how we think about and discuss the weather.
Braghieri, Ada; Piazzolla, Nicoletta; Galgano, Fernanda; Condelli, Nicola; De Rosa, Giuseppe; Napolitano, Fabio
2016-12-01
The quantitative descriptive analysis (QDA) was combined with temporal dominance of sensations (TDS) to assess the sensory properties of Lucanian dry-sausages either added with nitrate, nitrite and l-ascorbic acid (NS), or not (NNS). Both QDA and TDS differentiated the two groups of sausages. NNS products were perceived with higher intensity of hardness (P<0.05) and tended to be perceived with higher intensities of flavor (P<0.10), pepper (P<0.20), and oiliness (P<0.20), while resulting lower in chewiness (P<0.20). TDS showed that in all the sausages hardness was the first dominant attribute; then, in NNS products flavor remained dominant until the end of tasting, whereas in NS products oiliness prevailed. In conclusion, TDS showed that the perception of some textural parameters, such as oiliness, during mastication was more dominant in NS products, whereas using conventional QDA this attribute appeared higher in sausages manufactured without preservatives. Therefore, TDS provided additional information for the description and differentiation of Lucanian sausages. PMID:27486959
Brunskill, Jeffrey C
2010-03-01
This paper presents a study of the relationship between quantitative and qualitative descriptions of temperature. Online weather forecast narratives produced by local television forecasters were collected from affiliates in 23 cities throughout the northeastern, central and southern portions of the United States from August 2007 to July 2008. The narratives were collected to study the terminology and reference frames that local forecasters use to describe predicted temperatures for the following day. The main objectives were to explore the adjectives used to describe thermal conditions and the impact that geographical and seasonal variations in thermal conditions have on these descriptions. The results of this empirical study offer some insights into the structure of weather narratives and suggest that spatiotemporal variations in the weather impact how forecasters describe the temperature to their local audiences. In a broader sense, this investigation builds upon research in biometeorology, urban planning and linguistics that has explored the physiological and psychological factors that influence subjective assessments of thermal sensation and comfort. The results of this study provide a basis to reason about how thermal comfort is conveyed in meteorological communications and how experiential knowledge derived from daily observations of the weather influence how we think about and discuss the weather. PMID:19876657
Representing geometrical knowledge.
Anderson, J A
1997-01-01
This paper introduces perspex algebra which is being developed as a common representation of geometrical knowledge. A perspex can currently be interpreted in one of four ways. First, the algebraic perspex is a generalization of matrices, it provides the most general representation for all of the interpretations of a perspex. The algebraic perspex can be used to describe arbitrary sets of coordinates. The remaining three interpretations of the perspex are all related to square matrices and operate in a Euclidean model of projective space-time, called perspex space. Perspex space differs from the usual Euclidean model of projective space in that it contains the point at nullity. It is argued that the point at nullity is necessary for a consistent account of perspective in top-down vision. Second, the geometric perspex is a simplex in perspex space. It can be used as a primitive building block for shapes, or as a way of recording landmarks on shapes. Third, the transformational perspex describes linear transformations in perspex space that provide the affine and perspective transformations in space-time. It can be used to match a prototype shape to an image, even in so called 'accidental' views where the depth of an object disappears from view, or an object stays in the same place across time. Fourth, the parametric perspex describes the geometric and transformational perspexes in terms of parameters that are related to everyday English descriptions. The parametric perspex can be used to obtain both continuous and categorical perception of objects. The paper ends with a discussion of issues related to using a perspex to describe logic. PMID:9304680
Spudeit, William Anderson; Sulzbach, Natalia Saretta; Bittencourt, Myla de A; Duarte, Anita Maurício Camillo; Liang, Hua; Lino-de-Oliveira, Cilene; Marino-Neto, José
2013-10-01
resembled that observed in rodents and primates. This pattern can be quantitatively described and compared using different suitable and coordinated behavioral measures, enabling further studies on the comparative and evolutionary aspects of the mechanisms that shape the post-consummatory behavioral flux in amniotes.
Identifying and Fostering Higher Levels of Geometric Thinking
ERIC Educational Resources Information Center
Škrbec, Maja; Cadež, Tatjana Hodnik
2015-01-01
Pierre M. Van Hiele created five levels of geometric thinking. We decided to identify the level of geometric thinking in the students in Slovenia, aged 9 to 11 years. The majority of students (60.7%) are at the transition between the zero (visual) level and the first (descriptive) level of geometric thinking. Nearly a third (31.7%) of students is…
Yamamoto, Shinya; Bamba, Takeshi; Sano, Atsushi; Kodama, Yukako; Imamura, Miho; Obata, Akio; Fukusaki, Eiichiro
2012-08-01
Soy sauces, produced from different ingredients and brewing processes, have variations in components and quality. Therefore, it is extremely important to comprehend the relationship between components and the sensory attributes of soy sauces. The current study sought to perform metabolite profiling in order to devise a method of assessing the attributes of soy sauces. Quantitative descriptive analysis (QDA) data for 24 soy sauce samples were obtained from well selected sensory panelists. Metabolite profiles primarily concerning low-molecular-weight hydrophilic components were based on gas chromatography with time-of-flightmass spectrometry (GC/TOFMS). QDA data for soy sauces were accurately predicted by projection to latent structure (PLS), with metabolite profiles serving as explanatory variables and QDA data set serving as a response variable. Moreover, analysis of correlation between matrices of metabolite profiles and QDA data indicated contributing compounds that were highly correlated with QDA data. Especially, it was indicated that sugars are important components of the tastes of soy sauces. This new approach which combines metabolite profiling with QDA is applicable to analysis of sensory attributes of food as a result of the complex interaction between its components. This approach is effective to search important compounds that contribute to the attributes.
Geometric methods in computational fluid dynamics. [turbomachinery
NASA Technical Reports Server (NTRS)
Eiseman, P. R.
1980-01-01
General methods for the construction of geometric computational fluid dynamic algorithms are presented which simulate a variety of flow fields in various nontrivial regions. Included are: basic developments with tensors; various forms for the equations of motion; generalized numerical methods and boundary conditions; and methods for mesh generation to meet the strong geometric constraints of turbomachines. Coordinate generation is shown generally to yield mesh descriptions from one or more transformations that are smoothly joined together to form a composite mesh.
NASA Astrophysics Data System (ADS)
Hensleigh, J.; Buscombe, D.; Wheaton, J. M.; Brasington, J.; Welcker, C. W.; Anderson, K.
2015-12-01
The increasing use of high-resolution topography (HRT) constructed from point clouds obtained from technology such as LiDAR, SoNAR, SAR, SfM and a variety of range-imaging techniques, has created a demand for custom analytical tools and software for point cloud decimation (data thinning and gridding) and spatially explicit statistical analysis of terrestrial surfaces. We will present on a number of analytical and computational tools designed to quantify surface roughness and texture, directly from point clouds in a variety of ways (using spatial- and frequency-domain statistics). TopCAT (Topographic Point Cloud Analysis Toolkit; Brasington et al., 2012) and PySESA (Python program for Spatially Explicit Spectral Analysis) both work by applying a small moving window to (x,y,z) data to calculate a suite of (spatial and spectral domain) statistics, which are then spatially-referenced on a regular (x,y) grid at a user-defined resolution. Collectively, these tools facilitate quantitative description of surfaces and may allow, for example, fully automated texture characterization and segmentation, roughness and grain size calculation, and feature detection and classification, on very large point clouds with great computational efficiency. Using tools such as these, it may be possible to detect geomorphic change in surfaces which have undergone minimal elevation difference, for example deflation surfaces which have coarsened but undergone no net elevation change, or surfaces which have eroded and accreted, leaving behind a different textural surface expression than before. The functionalities of the two toolboxes are illustrated with example high-resolution bathymetric point cloud data collected with multibeam echosounder, and topographic data collected with LiDAR.
Geometric Algebra for Physicists
NASA Astrophysics Data System (ADS)
Doran, Chris; Lasenby, Anthony
2007-11-01
Preface; Notation; 1. Introduction; 2. Geometric algebra in two and three dimensions; 3. Classical mechanics; 4. Foundations of geometric algebra; 5. Relativity and spacetime; 6. Geometric calculus; 7. Classical electrodynamics; 8. Quantum theory and spinors; 9. Multiparticle states and quantum entanglement; 10. Geometry; 11. Further topics in calculus and group theory; 12. Lagrangian and Hamiltonian techniques; 13. Symmetry and gauge theory; 14. Gravitation; Bibliography; Index.
Geometrizing the Quantum - A Toy Model
Koch, Benjamin
2009-12-15
It is shown that the equations of relativistic Bohmian mechanics for multiple bosonic particles have a dual description in terms of a classical theory of conformally 'curved' space-time. This shows that it is possible to formulate quantum mechanics as a purely classical geometrical theory. The results are further generalized to interactions with an external electromagnetic field.
Geometric approach to dislocation and disclination theory
Nesterov, A.I.; Ovchinnikov, S.G.
1988-05-01
Cartan structure equations are used to create a four-dimensional geometric description of dislocations in continuum theory. It is shown that the dislocation distribution is determined by the torsion tensor, while the disclination distribution is determined by the curvature tensor. An analogy to electrodynamics is offered.
Exploring New Geometric Worlds
ERIC Educational Resources Information Center
Nirode, Wayne
2015-01-01
When students work with a non-Euclidean distance formula, geometric objects such as circles and segment bisectors can look very different from their Euclidean counterparts. Students and even teachers can experience the thrill of creative discovery when investigating these differences among geometric worlds. In this article, the author describes a…
A geometric approach to quantum vortices
NASA Astrophysics Data System (ADS)
Penna, Vittorio; Spera, Mauro
1989-12-01
In this paper a geometrical description is given of the theory of quantum vortices first developed by Rasetti and Regge [Physica A 80, 217 (1975)] relying on the symplectic techniques of Marsden and Weinstein [J. Phys. D 7, 305 (1983)], and Kirillov-Kostant-Souriau geometric quantization. The RR-current algebra is interpreted as the natural Hamiltonian algebra associated to a certain coadjoint orbit of the group G=SDiff(R3), the KKS prequantization condition of which is related to the Feynman-Onsager relation. This orbit is also shown to possess a G-invariant Kaehler structure, whence, in principle, it is possible to quantize it in a natural way.
Geometric intrinsic symmetries
Gozdz, A. Szulerecka, A.; Pedrak, A.
2013-08-15
The problem of geometric symmetries in the intrinsic frame of a many-body system (nucleus) is considered. An importance of symmetrization group notion is discussed. Ageneral structure of the intrinsic symmetry group structure is determined.
NASA Technical Reports Server (NTRS)
Lada, Charles J.
2004-01-01
This grant funds a research program to use infrared extinction measurements to probe the detailed structure of dark molecular cloud cores and investigate the physical conditions which give rise to star and planet formation. The goals of this program are to acquire, reduce and analyze deep infrared and molecular-line observations of a carefully selected sample of nearby dark clouds in order to determine the detailed initial conditions for star formation from quantitative measurements of the internal structure of starless cloud cores and to quantitatively investigate the evolution of such structure through the star and planet formation process.
Preservation of the geometric quantum discord in noisy environments
Hu, Ming-Liang; Tian, Dong-Ping
2014-04-15
Geometric description of quantum correlations is favored for their distinct physical significance. Geometric discords based on the trace distance and the Bures distance are shown to be well-defined quantum correlation measures. Here, we examine their particular dynamical behaviors under independent as well as common structured reservoirs and reveal their robustness against decoherence. We showed that the two well-defined geometric discords may be preserved well or even be improved and generated by the noisy process of the common reservoir. Moreover, we also provided a strategy for the long-time preservation of these two geometric discords in independent reservoirs. -- Highlights: •Inherent robustness of the trace distance and the Bures distance discord. •Generating geometric discord from classical states by the noisy process. •Improvement of the geometric discord in common reservoir. •The robust pathway for preserving discord in independent reservoirs.
Toroidal Precession as a Geometric Phase
J.W. Burby and H. Qin
2012-09-26
Toroidal precession is commonly understood as the orbit-averaged toroidal drift of guiding centers in axisymmetric and quasisymmetric configurations. We give a new, more natural description of precession as a geometric phase effect. In particular, we show that the precession angle arises as the holonomy of a guiding center's poloidal trajectory relative to a principal connection. The fact that this description is physically appropriate is borne out with new, manifestly coordinate-independent expressions for the precession angle that apply to all types of orbits in tokamaks and quasisymmetric stellarators alike. We then describe how these expressions may be fruitfully employed in numerical calculations of precession.
Geometrical optical illusionists.
Wade, Nicholas J
2014-01-01
Geometrical optical illusions were given this title by Oppel in 1855. Variants on such small distortions of visual space were illustrated thereafter, many of which bear the names of those who first described them. Some original forms of the geometrical optical illusions are shown together with 'perceptual portraits' of those who described them. These include: Roget, Chevreul, Fick, Zöllner, Poggendorff, Hering, Kundt, Delboeuf Mach, Helmholtz, Hermann, von Bezold, Müller-Lyer, Lipps, Thiéry, Wundt, Münsterberg, Ebbinghaus, Titchener, Ponzo, Luckiesh, Sander, Ehrenstein, Gregory, Heard, White, Shepard, and. Lingelbach. The illusions are grouped under the headings of orientation, size, the combination of size and orientation, and contrast. Early theories of illusions, before geometrical optical illusions were so named, are mentioned briefly.
Inflation from geometrical tachyons
Thomas, Steven; Ward, John
2005-10-15
We propose an alternative formulation of tachyon inflation using the geometrical tachyon arising from the time dependent motion of a BPS D3-brane in the background geometry due to k parallel NS5-branes arranged around a ring of radius R. Because of the fact that the mass of this geometrical tachyon field is {radical}(2/k) times smaller than the corresponding open-string tachyon mass, we find that the slow-roll conditions for inflation and the number of e-foldings can be satisfied in a manner that is consistent with an effective 4-dimensional model and with a perturbative string coupling. We also show that the metric perturbations produced at the end of inflation can be sufficiently small and do not lead to the inconsistencies that plague the open-string tachyon models. Finally we argue for the existence of a minimum of the geometrical tachyon potential which could give rise to a traditional reheating mechanism.
Geometrical optical illusionists.
Wade, Nicholas J
2014-01-01
Geometrical optical illusions were given this title by Oppel in 1855. Variants on such small distortions of visual space were illustrated thereafter, many of which bear the names of those who first described them. Some original forms of the geometrical optical illusions are shown together with 'perceptual portraits' of those who described them. These include: Roget, Chevreul, Fick, Zöllner, Poggendorff, Hering, Kundt, Delboeuf Mach, Helmholtz, Hermann, von Bezold, Müller-Lyer, Lipps, Thiéry, Wundt, Münsterberg, Ebbinghaus, Titchener, Ponzo, Luckiesh, Sander, Ehrenstein, Gregory, Heard, White, Shepard, and. Lingelbach. The illusions are grouped under the headings of orientation, size, the combination of size and orientation, and contrast. Early theories of illusions, before geometrical optical illusions were so named, are mentioned briefly. PMID:25507310
Geometrical optical illusionists.
Wade, Nicholas J
2014-01-01
Geometrical optical illusions were given this title by Oppel in 1855. Variants on such small distortions of visual space were illustrated thereafter, many of which bear the names of those who first described them. Some original forms of the geometrical optical illusions are shown together with 'perceptual portraits' of those who described them. These include: Roget, Chevreul, Fick, Zöllner, Poggendorff, Hering, Kundt, Delboeuf Mach, Helmholtz, Hermann, von Bezold, Müller-Lyer, Lipps, Thiéry, Wundt, Münsterberg, Ebbinghaus, Titchener, Ponzo, Luckiesh, Sander, Ehrenstein, Gregory, Heard, White, Shepard, and. Lingelbach. The illusions are grouped under the headings of orientation, size, the combination of size and orientation, and contrast. Early theories of illusions, before geometrical optical illusions were so named, are mentioned briefly. PMID:25420326
PREFACE: Geometrically frustrated magnetism Geometrically frustrated magnetism
NASA Astrophysics Data System (ADS)
Gardner, Jason S.
2011-04-01
Frustrated magnetism is an exciting and diverse field in condensed matter physics that has grown tremendously over the past 20 years. This special issue aims to capture some of that excitement in the field of geometrically frustrated magnets and is inspired by the 2010 Highly Frustrated Magnetism (HFM 2010) meeting in Baltimore, MD, USA. Geometric frustration is a broad phenomenon that results from an intrinsic incompatibility between some fundamental interactions and the underlying lattice geometry based on triangles and tetrahedra. Most studies have centred around the kagomé and pyrochlore based magnets but recent work has looked at other structures including the delafossite, langasites, hyper-kagomé, garnets and Laves phase materials to name a few. Personally, I hope this issue serves as a great reference to scientist both new and old to this field, and that we all continue to have fun in this very frustrated playground. Finally, I want to thank the HFM 2010 organizers and all the sponsors whose contributions were an essential part of the success of the meeting in Baltimore. Geometrically frustrated magnetism contents Spangolite: an s = 1/2 maple leaf lattice antiferromagnet? T Fennell, J O Piatek, R A Stephenson, G J Nilsen and H M Rønnow Two-dimensional magnetism and spin-size effect in the S = 1 triangular antiferromagnet NiGa2S4 Yusuke Nambu and Satoru Nakatsuji Short range ordering in the modified honeycomb lattice compound SrHo2O4 S Ghosh, H D Zhou, L Balicas, S Hill, J S Gardner, Y Qi and C R Wiebe Heavy fermion compounds on the geometrically frustrated Shastry-Sutherland lattice M S Kim and M C Aronson A neutron polarization analysis study of moment correlations in (Dy0.4Y0.6)T2 (T = Mn, Al) J R Stewart, J M Hillier, P Manuel and R Cywinski Elemental analysis and magnetism of hydronium jarosites—model kagome antiferromagnets and topological spin glasses A S Wills and W G Bisson The Herbertsmithite Hamiltonian: μSR measurements on single crystals
Geometric Series via Probability
ERIC Educational Resources Information Center
Tesman, Barry
2012-01-01
Infinite series is a challenging topic in the undergraduate mathematics curriculum for many students. In fact, there is a vast literature in mathematics education research on convergence issues. One of the most important types of infinite series is the geometric series. Their beauty lies in the fact that they can be evaluated explicitly and that…
NASA Technical Reports Server (NTRS)
Ives, David
1995-01-01
This paper presents a highly automated hexahedral grid generator based on extensive geometrical and solid modeling operations developed in response to a vision of a designer-driven one day turnaround CFD process which implies a designer-driven one hour grid generation process.
ERIC Educational Resources Information Center
Smart, Julie; Marshall, Jeff
2007-01-01
Children possess a genuine curiosity for exploring the natural world around them. One third grade teacher capitalized on this inherent trait by leading her students on "A Geometric Scavenger Hunt." The four-lesson inquiry investigation described in this article integrates mathematics and science. Among the students' discoveries was the fact that…
Morphing of geometric composites via residual swelling.
Pezzulla, Matteo; Shillig, Steven A; Nardinocchi, Paola; Holmes, Douglas P
2015-08-01
Understanding and controlling the shape of thin, soft objects has been the focus of significant research efforts among physicists, biologists, and engineers in the last decade. These studies aim to utilize advanced materials in novel, adaptive ways such as fabricating smart actuators or mimicking living tissues. Here, we present the controlled growth-like morphing of 2D sheets into 3D shapes by preparing geometric composite structures that deform by residual swelling. The morphing of these geometric composites is dictated by both swelling and geometry, with diffusion controlling the swelling-induced actuation, and geometric confinement dictating the structure's deformed shape. Building on a simple mechanical analog, we present an analytical model that quantitatively describes how the Gaussian and mean curvatures of a thin disk are affected by the interplay among geometry, mechanics, and swelling. This model is in excellent agreement with our experiments and numerics. We show that the dynamics of residual swelling is dictated by a competition between two characteristic diffusive length scales governed by geometry. Our results provide the first 2D analog of Timoshenko's classical formula for the thermal bending of bimetallic beams - our generalization explains how the Gaussian curvature of a 2D geometric composite is affected by geometry and elasticity. The understanding conferred by these results suggests that the controlled shaping of geometric composites may provide a simple complement to traditional manufacturing techniques. PMID:26076671
NASA Technical Reports Server (NTRS)
Lada, Charles J.
2005-01-01
This grant funds a research program to use infrared extinction measurements to probe the detailed structure of dark molecular cloud cores and investigate the physical conditions which give rise to star and planet formation. The goals of this program are to acquire, reduce and analyze deep infrared and molecular-line observations of a carefully selected sample of nearby dark clouds in order to internal structure of starless cloud cores and to quantitatively investigate the evolution of such structure through the star and planet formation process. During the second year of this grant, progress toward these goals is discussed.
The geometrical structure of quantum theory as a natural generalization of information geometry
Reginatto, Marcel
2015-01-13
Quantum mechanics has a rich geometrical structure which allows for a geometrical formulation of the theory. This formalism was introduced by Kibble and later developed by a number of other authors. The usual approach has been to start from the standard description of quantum mechanics and identify the relevant geometrical features that can be used for the reformulation of the theory. Here this procedure is inverted: the geometrical structure of quantum theory is derived from information geometry, a geometrical structure that may be considered more fundamental, and the Hilbert space of the standard formulation of quantum mechanics is constructed using geometrical quantities. This suggests that quantum theory has its roots in information geometry.
Geometric Brownian Motion with Tempered Stable Waiting Times
NASA Astrophysics Data System (ADS)
Gajda, Janusz; Wyłomańska, Agnieszka
2012-08-01
One of the earliest system that was used to asset prices description is Black-Scholes model. It is based on geometric Brownian motion and was used as a tool for pricing various financial instruments. However, when it comes to data description, geometric Brownian motion is not capable to capture many properties of present financial markets. One can name here for instance periods of constant values. Therefore we propose an alternative approach based on subordinated tempered stable geometric Brownian motion which is a combination of the popular geometric Brownian motion and inverse tempered stable subordinator. In this paper we introduce the mentioned process and present its main properties. We propose also the estimation procedure and calibrate the analyzed system to real data.
Hühn, Jonas; Fedeli, Chiara; Zhang, Qian; Masood, Atif; Del Pino, Pablo; Khashab, Niveen M; Papini, Emanuele; Parak, Wolfgang J
2016-06-01
Protein adsorption to nanoparticles is described as a chemical reaction in which proteins attach to binding sites on the nanoparticle surface. This process is defined by a dissociation coefficient, which tells how many proteins are adsorbed per nanoparticle in dependence of the protein concentration. Different techniques to experimentally determine dissociation coefficients of protein adsorption to nanoparticles are reviewed. Results of more than 130 experiments in which dissociation coefficients have been determined are compared. Data show that different methods, nanoparticle systems, and proteins can lead to significantly different dissociation coefficients. However, we observed a clear tendency of smaller dissociation coefficients upon less negative towards more positive zeta potentials of the nanoparticles. The zeta potential thus is a key parameter influencing protein adsorption to the surface of nanoparticles. Our analysis highlights the importance of the characterization of the parameters governing protein-nanoparticle interaction for quantitative evaluation and objective literature comparison. PMID:26748245
Special generalized densities and propagators: A geometric account
NASA Astrophysics Data System (ADS)
Canarutto, Daniel
2016-11-01
Starting from a short review of spaces of generalized sections of vector bundles, we give a concise systematic description, in precise geometric terms, of Leray densities, principal value densities, propagators and elementary solutions of field equations in flat spacetime. We then sketch a partly original geometric presentation of free quantum fields and show how propagators arise from their graded commutators in the boson and fermion cases.
NASA Astrophysics Data System (ADS)
Le Pape, Olivier; Baulier, Loîc; Cloarec, Aurélie; Martin, Jocelyne; Le Loc'h, François; Désaunay, Yves
2007-02-01
This study describes the spatial distribution of young-of-the-year common sole based on beam trawl surveys conducted in late summer in the coastal and estuarine parts of the Bay of Biscay (France). Previous studies showed that habitat suitability for juvenile common sole varies according to physical factors and notably bathymetry and sediment structure. Nevertheless, the use of these descriptors alone to model habitat suitability led to considerable unexplained variability in juvenile common sole distribution. Hence, the epibenthic macro- and megafauna collected during beam trawl surveys was taken into account to improve models of habitat suitability for these juvenile flatfish. Ecotrophic guilds based on life traits (behaviour, mobility and feeding) were used to develop generic indicators of trawled benthic fauna. These synthetic descriptors were used in generalized linear models of habitat suitability in order to characterize the distribution of juvenile common sole. This approach significantly improved the description based on physical descriptors and allowed demonstrating that young common sole distribution is related to the density of trawled deposit and suspension feeders and also of carnivorous organisms. These models provide a reliable method to develop indicators of nursery habitat suitability from trawl survey data with the aim of assessing and surveying their quality.
NASA Astrophysics Data System (ADS)
Chapoullié, Cédric; Da Costa, Jean-Pierre; Cataldi, Michel; Vignoles, Gérard L.; Germain, Christian
2015-11-01
This paper proposes a two-scale approach for the description of fibrous materials from tomographic data. It operates at two scales: coarse scale to describe weaving patterns and fine scale to depict fiber layout within yarns. At both scales, the proposed approach starts with the segmentation of yarns and fibers. Then, the fibrous structure (fiber diameters, fiber and yarn orientations, fiber density within yarns) is described. The segmentation algorithms are applied to a chunk of a woven ceramic-matrix composite observed at yarn and fiber scales using tomographic data from the European synchrotron radiation facility. The fiber and yarn segmentation results allow investigation of intrayarn fiber layout. The analysis of intrayarn fiber density and orientations shows the effects of the weaving process on fiber organization, in particular fiber compaction or yarn shearing. These results pave the way toward a deeper analysis of such materials. Indeed, the data collected with the proposed methods are a key starting point for realistic image synthesis. Such images may in turn be used to validate the fiber and yarn segmentation algorithms. Besides, and above all, they will allow material behavior simulation, aiming at the evaluation of the material's strengths and weaknesses inferred from its fibrous architecture.
Perspective: Geometrically frustrated assemblies
NASA Astrophysics Data System (ADS)
Grason, Gregory M.
2016-09-01
This perspective will overview an emerging paradigm for self-organized soft materials, geometrically frustrated assemblies, where interactions between self-assembling elements (e.g., particles, macromolecules, proteins) favor local packing motifs that are incompatible with uniform global order in the assembly. This classification applies to a broad range of material assemblies including self-twisting protein filament bundles, amyloid fibers, chiral smectics and membranes, particle-coated droplets, curved protein shells, and phase-separated lipid vesicles. In assemblies, geometric frustration leads to a host of anomalous structural and thermodynamic properties, including heterogeneous and internally stressed equilibrium structures, self-limiting assembly, and topological defects in the equilibrium assembly structures. The purpose of this perspective is to (1) highlight the unifying principles and consequences of geometric frustration in soft matter assemblies; (2) classify the known distinct modes of frustration and review corresponding experimental examples; and (3) describe outstanding questions not yet addressed about the unique properties and behaviors of this broad class of systems.
Geometrically representing spin correlations
NASA Astrophysics Data System (ADS)
White, Ian G.; Mirasola, Anthony; Hollingsworth, Jacob; Mukherjee, Rick; Hazzard, Kaden R. A.
2016-05-01
We develop a general method to visualize spin correlations, and we demonstrate its usefulness in ultracold matter from fermions in lattices to trapped ions and ultracold molecules. Correlations are of fundamental interest in many-body physics: they characterize phases in condensed matter and AMO, and are required for quantum sensing and computing. However, it is often difficult to understand even the simplest correlations - for example between two spin-1/2's - directly from the components Cab =
Fang, B; Zhang, M; Fan, X; Ren, F Z
2016-08-01
An α-lactalbumin-oleic acid (α-LA-OA) complex has exhibited selective antitumor activity in animal models and clinical trials. Although apoptosis and autophagy are activated and the functions of several organelles are disrupted in response to α-LA-OA, the detailed antitumor mechanism remains unclear. In this study, we used a novel technique, isobaric tags for relative and absolute quantitation, to analyze the proteome of tumor cells treated with α-LA-OA. We identified 112 differentially expressed proteins: 95 were upregulated to satisfy the metabolism of tumor cells; 17 were downregulated and targets of α-LA-OA. According to the differentially expressed proteins, α-LA-OA exerted its antitumor activity by disrupting cytoskeleton stability and cell motility, and by inhibiting DNA, lipid, and ATP synthesis, leading to cellular stress and activation of programmed cell death. This study provides a systematic evaluation of the antitumor activity of α-LA-OA, identifying its interacting targets and establishing the theoretical basis of α-LA-OA for use in cancer therapy. PMID:27236751
Geometric diffusion of quantum trajectories.
Yang, Fan; Liu, Ren-Bao
2015-07-16
A quantum object can acquire a geometric phase (such as Berry phases and Aharonov-Bohm phases) when evolving along a path in a parameter space with non-trivial gauge structures. Inherent to quantum evolutions of wavepackets, quantum diffusion occurs along quantum trajectories. Here we show that quantum diffusion can also be geometric as characterized by the imaginary part of a geometric phase. The geometric quantum diffusion results from interference between different instantaneous eigenstate pathways which have different geometric phases during the adiabatic evolution. As a specific example, we study the quantum trajectories of optically excited electron-hole pairs in time-reversal symmetric insulators, driven by an elliptically polarized terahertz field. The imaginary geometric phase manifests itself as elliptical polarization in the terahertz sideband generation. The geometric quantum diffusion adds a new dimension to geometric phases and may have applications in many fields of physics, e.g., transport in topological insulators and novel electro-optical effects.
Combining appearance and geometric features for facial expression recognition
NASA Astrophysics Data System (ADS)
Yu, Hui; Liu, Honghai
2015-03-01
This paper introduces a method for facial expression recognition combining appearance and geometric facial features. The proposed framework consistently combines multiple facial representations at both global and local levels. First, covariance descriptors are computed to represent regional features combining various feature information with a low dimensionality. Then geometric features are detected to provide a general facial movement description of the facial expression. These appearance and geometric features are combined to form a vector representation of the facial expression. The proposed method is tested on the CK+ database and shows encouraging performance.
Decaestecker, C; Lopes, B S; Gordower, L; Camby, I; Cras, P; Martin, J J; Kiss, R; VandenBerg, S R; Salmon, I
1997-04-01
The oligoastrocytoma, as a mixed glioma, represents a nosologic dilemma with respect to precisely defining the oligodendroglial and astroglial phenotypes that constitute the neoplastic cell lineages of these tumors. In this study, cell image analysis with Feulgen-stained nuclei was used to distinguish between oligodendroglial and astrocytic phenotypes in oligodendrogliomas and astrocytomas and then applied to mixed oligoastrocytomas. Quantitative features with respect to chromatin pattern (30 variables) and DNA ploidy (8 variables) were evaluated on Feulgen-stained nuclei in a series of 71 gliomas using computer-assisted microscopy. These included 32 oligodendrogliomas (OLG group: 24 grade II and 8 grade III tumors according to the WHO classification), 32 astrocytomas (AST group: 13 grade II and 19 grade III tumors), and 7 oligoastrocytomas (OLGAST group). Initially, image analysis with multivariate statistical analyses (Discriminant Analysis) could identify each glial tumor group. Highly significant statistical differences were obtained distinguishing the morphonuclear features of oligodendrogliomas from those of astrocytomas, regardless of their histological grade. When compared with the 7 mixed oligoastrocytomas under study, 5 exhibited DNA ploidy and chromatin pattern characteristics similar to grade II oligodendrogliomas, I to grade III oligodendrogliomas, and I to grade II astrocytomas. Using multifactorial statistical analyses (Discriminant Analysis combined with Principal Component Analysis). It was possible to quantify the proportion of "typical" glial cell phenotypes that compose grade II and III oligodendrogliomas and grade II and III astrocytomas in each mixed glioma. Cytometric image analysis may be an important adjunct to routine histopathology for the reproducible identification of neoplasms containing a mixture of oligodendroglial and astrocytic phenotypes. PMID:9100670
Geometric Heat Engines Featuring Power that Grows with Efficiency.
Raz, O; Subaşı, Y; Pugatch, R
2016-04-22
Thermodynamics places a limit on the efficiency of heat engines, but not on their output power or on how the power and efficiency change with the engine's cycle time. In this Letter, we develop a geometrical description of the power and efficiency as a function of the cycle time, applicable to an important class of heat engine models. This geometrical description is used to design engine protocols that attain both the maximal power and maximal efficiency at the fast driving limit. Furthermore, using this method, we also prove that no protocol can exactly attain the Carnot efficiency at nonzero power.
Geometric Heat Engines Featuring Power that Grows with Efficiency
NASA Astrophysics Data System (ADS)
Raz, O.; Subaşı, Y.; Pugatch, R.
2016-04-01
Thermodynamics places a limit on the efficiency of heat engines, but not on their output power or on how the power and efficiency change with the engine's cycle time. In this Letter, we develop a geometrical description of the power and efficiency as a function of the cycle time, applicable to an important class of heat engine models. This geometrical description is used to design engine protocols that attain both the maximal power and maximal efficiency at the fast driving limit. Furthermore, using this method, we also prove that no protocol can exactly attain the Carnot efficiency at nonzero power.
Sudden change of geometric quantum discord in finite temperature reservoirs
Hu, Ming-Liang Sun, Jian
2015-03-15
We investigate sudden change (SC) behaviors of the distance-based measures of geometric quantum discords (GQDs) for two non-interacting qubits subject to the two-sided and the one-sided thermal reservoirs. We found that the GQDs defined by different distances exhibit different SCs, and thus the SCs are the combined result of the chosen discord measure and the property of a state. We also found that the thermal reservoir may generate states having different orderings related to different GQDs. These inherent differences of the GQDs reveal that they are incompatible in characterizing quantum correlations both quantitatively and qualitatively. - Highlights: • Comparable study of different distance-based geometric quantum discords. • Evolution of the geometric quantum discords in finite temperature reservoirs. • Different geometric quantum discords exhibit distinct sudden changes. • Nonunique states ordering imposed by different geometric quantum discords.
Howarth, P A
2011-02-23
Two aspects of the geometric horopter, which here is based on the criterion of equality of angle, are clarified. The first is that in the fixation plane (containing the nodal points and the fixation point) the locus of points lying on the horopter is the larger arc of a circle, and not a full circle as has been previously accepted. The second is that elsewhere, the locus of these points is a straight line perpendicular to this plane and midway between the eyes. These rules hold for both symmetric and asymmetric convergence, and for fixation elevated or depressed from the horizontal.
Geometric phase in Bohmian mechanics
Chou, Chia-Chun; Wyatt, Robert E.
2010-10-15
Using the quantum kinematic approach of Mukunda and Simon, we propose a geometric phase in Bohmian mechanics. A reparametrization and gauge invariant geometric phase is derived along an arbitrary path in configuration space. The single valuedness of the wave function implies that the geometric phase along a path must be equal to an integer multiple of 2{pi}. The nonzero geometric phase indicates that we go through the branch cut of the action function from one Riemann sheet to another when we locally travel along the path. For stationary states, quantum vortices exhibiting the quantized circulation integral can be regarded as a manifestation of the geometric phase. The bound-state Aharonov-Bohm effect demonstrates that the geometric phase along a closed path contains not only the circulation integral term but also an additional term associated with the magnetic flux. In addition, it is shown that the geometric phase proposed previously from the ensemble theory is not gauge invariant.
Matalas, N.C.
1991-01-01
What constitutes a comprehensive description of drought, a description forming a basis for answering why a drought occurred is outlined. The description entails two aspects that are "naturally" coupled, named physical and economic, and treats the set of hydrologic measures of droughts in terms of their multivariate distribution, rather than in terms of a collection of the marginal distributions. ?? 1991 Springer-Verlag.
Geometric time delay interferometry
NASA Astrophysics Data System (ADS)
Vallisneri, Michele
2005-08-01
The space-based gravitational-wave observatory LISA, a NASA-ESA mission to be launched after 2012, will achieve its optimal sensitivity using time delay interferometry (TDI), a LISA-specific technique needed to cancel the otherwise overwhelming laser noise in the interspacecraft phase measurements. The TDI observables of the Michelson and Sagnac types have been interpreted physically as the virtual measurements of a synthesized interferometer. In this paper, I present Geometric TDI, a new and intuitive approach to extend this interpretation to all TDI observables. Unlike the standard algebraic formalism, Geometric TDI provides a combinatorial algorithm to explore exhaustively the space of second-generation TDI observables (i.e., those that cancel laser noise in LISA-like interferometers with time-dependent arm lengths). Using this algorithm, I survey the space of second-generation TDI observables of length (i.e., number of component phase measurements) up to 24, and I identify alternative, improved forms of the standard second-generation TDI observables. The alternative forms have improved high-frequency gravitational-wave sensitivity in realistic noise conditions (because they have fewer nulls in the gravitational-wave and noise response functions), and are less susceptible to instrumental gaps and glitches (because their component phase measurements span shorter time periods).
Geometric precipices in string cosmology
Kaloper, Nemanja; Watson, Scott
2008-03-15
We consider the effects of graviton multiplet fields on transitions between string gas phases. Focusing on the dilaton field, we show that it may obstruct transitions between different thermodynamic phases of the string gas, because the sign of its dimensionally reduced, T-duality invariant, part is conserved when the energy density of the Universe is positive. Thus, many interesting solutions for which this sign is positive end up in a future curvature singularity. Because of this, some of the thermodynamic phases of the usual gravitating string gases behave like superselection sectors. For example, a past-regular Hagedorn phase and an expanding Friedmann-Robertson-Walker (FRW) phase dominated by string momentum modes cannot be smoothly connected in the framework of string cosmology with positive sources. The singularity separates them like a geometric precipice in the moduli space, preventing the dynamics of the theory from bridging across. Sources which simultaneously violate the positivity of energy and null energy condition (NEC) could modify these conclusions. We provide a quantitative measure of positivity of energy and NEC violations that would be necessary for such transitions. These effects must dominate the Universe at the moment of transition, altering the standard gas pictures. At present, it is not known how to construct such sources from first principles in string theory.
The relationship between strain geometry and geometrically necessary dislocations
NASA Astrophysics Data System (ADS)
Hansen, Lars; Wallis, David
2016-04-01
The kinematics of past deformations are often a primary goal in structural analyses of strained rocks. Details of the strain geometry, in particular, can help distinguish hypotheses about large-scale tectonic phenomena. Microstructural indicators of strain geometry have been heavily utilized to investigate large-scale kinematics. However, many of the existing techniques require structures for which the initial morphology is known, and those structures must undergo the same deformation as imposed macroscopically. Many deformed rocks do not exhibit such convenient features, and therefore the strain geometry is often difficult (if not impossible) to ascertain. Alternatively, crystallographic textures contain information about the strain geometry, but the influence of strain geometry can be difficult to separate from other environmental factors that might affect slip system activity and therefore the textural evolution. Here we explore the ability for geometrically necessary dislocations to record information about the deformation geometry. It is well known that crystallographic slip due to the motion of dislocations yields macroscopic plastic strain, and the mathematics are established to relate dislocation glide on multiple slip systems to the strain tensor of a crystal. This theoretical description generally assumes that dislocations propagate across the entire crystal. However, at any point during the deformation, dislocations are present that have not fully transected the crystal, existing either as free dislocations or as dislocations organized into substructures like subgrain boundaries. These dislocations can remain in the lattice after deformation if the crystal is quenched sufficiently fast, and we hypothesize that this residual dislocation population can be linked to the plastic strain geometry in a quantitative manner. To test this hypothesis, we use high-resolution electron backscatter diffraction to measure lattice curvatures in experimentally deformed
Geometrical Destabilization of Inflation
NASA Astrophysics Data System (ADS)
Renaux-Petel, Sébastien; Turzyński, Krzysztof
2016-09-01
We show the existence of a general mechanism by which heavy scalar fields can be destabilized during inflation, relying on the fact that the curvature of the field space manifold can dominate the stabilizing force from the potential and destabilize inflationary trajectories. We describe a simple and rather universal setup in which higher-order operators suppressed by a large energy scale trigger this instability. This phenomenon can prematurely end inflation, thereby leading to important observational consequences and sometimes excluding models that would otherwise perfectly fit the data. More generally, it modifies the interpretation of cosmological constraints in terms of fundamental physics. We also explain how the geometrical destabilization can lead to powerful selection criteria on the field space curvature of inflationary models.
Geometrical aspects of entanglement
Leinaas, Jon Magne; Myrheim, Jan; Ovrum, Eirik
2006-07-15
We study geometrical aspects of entanglement, with the Hilbert-Schmidt norm defining the metric on the set of density matrices. We focus first on the simplest case of two two-level systems and show that a 'relativistic' formulation leads to a complete analysis of the question of separability. Our approach is based on Schmidt decomposition of density matrices for a composite system and nonunitary transformations to a standard form. The positivity of the density matrices is crucial for the method to work. A similar approach works to some extent in higher dimensions, but is a less powerful tool. We further present a numerical method for examining separability and illustrate the method by a numerical study of bound entanglement in a composite system of two three-level systems.
Goldberg, P.W.
1993-04-01
In this paper we consider the problem of learning the positions of spheres in metric spaces, given as data randomly drawn points classified according to whether they are internal or external to an unknown sphere. The particular metrics under consideration are geometrical shape metrics, and the results are intended to be applicable to the problem of learning to identify a shape from related shapes classified according to whether they resemble it visually. While it is typically NP-hard to locate a central point for a hypothesis sphere, we find that it is however often possible to obtain a non-spherical hypothesis which can accurately predict whether further random points lie within the unknown sphere. We exhibit algorithms which achieve this, and in the process indicate useful general techniques for computational learning. Finally we exhibit a natural shape metric and show that it defines a class of spheres not predictable in this sense, subject to standard cryptographic assumptions.
Geometric Frustration with Disorder
NASA Astrophysics Data System (ADS)
Woo, Nayoon; Silevitch, Daniel M.; Rosenbaum, Thomas F.
2014-03-01
We study the effects of Nd doping on the geometrically-frustrated Heisenberg antiferromagnet Gadolinium Gallium Garnet (GGG), using linear and nonlinear ac magnetic susceptibility. Doping levels from 0.1 to 1 percent Nd alleviate the intrinsic frustration of pure GGG and elevate the ordering temperature compared to the pure material. We use nonlinear pump-probe magnetic susceptometry to examine cluster dynamics for both the pure and the doped series. At low frequency (~10 Hz), spectral hole burning is possible, indicating the presence of spin clusters with discrete energy levels largely decoupled from the overall spin bath. At kHz, we find a Fano resonance, revealing scattering pathways between spin cluster excitations and the bath. We trace the evolution of this resonance behavior as a function of dopant concentration.
Salt Bridges: Geometrically Specific, Designable Interactions
Donald, Jason E.; Kulp, Daniel W.; DeGrado, William F.
2010-01-01
Salt bridges occur frequently in proteins, providing conformational specificity and contributing to molecular recognition and catalysis. We present a comprehensive analysis of these interactions in protein structures by surveying a large database of protein structures. Salt bridges between Asp or Glu and His, Arg, or Lys display extremely well-defined geometric preferences. Several previously observed preferences are confirmed and others that were previously unrecognized are discovered. Salt bridges are explored for their preferences for different separations in sequence and in space, geometric preferences within proteins and at protein-protein interfaces, cooperativity in networked salt bridges, inclusion within metal-binding sites, preference for acidic electrons, apparent conformational side chain entropy reduction upon formation, and degree of burial. Salt bridges occur far more frequently between residues at close than distant sequence separations, but at close distances there remain strong preferences for salt bridges at specific separations. Specific types of complex salt bridges, involving three or more members, are also discovered. As we observe a strong relationship between the propensity to form a salt bridge and the placement of salt-bridging residues in protein sequences, we discuss the role that salt bridges might play in kinetically influencing protein folding and thermodynamically stabilizing the native conformation. We also develop a quantitative method to select appropriate crystal structure resolution and B-factor cutoffs. Detailed knowledge of these geometric and sequence dependences should aid de novo design and prediction algorithms. PMID:21287621
Salt bridges: geometrically specific, designable interactions.
Donald, Jason E; Kulp, Daniel W; DeGrado, William F
2011-03-01
Salt bridges occur frequently in proteins, providing conformational specificity and contributing to molecular recognition and catalysis. We present a comprehensive analysis of these interactions in protein structures by surveying a large database of protein structures. Salt bridges between Asp or Glu and His, Arg, or Lys display extremely well-defined geometric preferences. Several previously observed preferences are confirmed, and others that were previously unrecognized are discovered. Salt bridges are explored for their preferences for different separations in sequence and in space, geometric preferences within proteins and at protein-protein interfaces, co-operativity in networked salt bridges, inclusion within metal-binding sites, preference for acidic electrons, apparent conformational side chain entropy reduction on formation, and degree of burial. Salt bridges occur far more frequently between residues at close than distant sequence separations, but, at close distances, there remain strong preferences for salt bridges at specific separations. Specific types of complex salt bridges, involving three or more members, are also discovered. As we observe a strong relationship between the propensity to form a salt bridge and the placement of salt-bridging residues in protein sequences, we discuss the role that salt bridges might play in kinetically influencing protein folding and thermodynamically stabilizing the native conformation. We also develop a quantitative method to select appropriate crystal structure resolution and B-factor cutoffs. Detailed knowledge of these geometric and sequence dependences should aid de novo design and prediction algorithms.
Geometric Reasoning in an Active-Engagement Upper-Division E&M Classroom
ERIC Educational Resources Information Center
Cerny, Leonard Thomas
2012-01-01
A combination of theoretical perspectives is used to create a rich description of student reasoning when facing a highly-geometric electricity and magnetism problem in an upper-division active-engagement physics classroom at Oregon State University. Geometric reasoning as students encounter problem situations ranging from familiar to novel is…
Geometrical method of decoupling
NASA Astrophysics Data System (ADS)
Baumgarten, C.
2012-12-01
The computation of tunes and matched beam distributions are essential steps in the analysis of circular accelerators. If certain symmetries—like midplane symmetry—are present, then it is possible to treat the betatron motion in the horizontal, the vertical plane, and (under certain circumstances) the longitudinal motion separately using the well-known Courant-Snyder theory, or to apply transformations that have been described previously as, for instance, the method of Teng and Edwards. In a preceding paper, it has been shown that this method requires a modification for the treatment of isochronous cyclotrons with non-negligible space charge forces. Unfortunately, the modification was numerically not as stable as desired and it was still unclear, if the extension would work for all conceivable cases. Hence, a systematic derivation of a more general treatment seemed advisable. In a second paper, the author suggested the use of real Dirac matrices as basic tools for coupled linear optics and gave a straightforward recipe to decouple positive definite Hamiltonians with imaginary eigenvalues. In this article this method is generalized and simplified in order to formulate a straightforward method to decouple Hamiltonian matrices with eigenvalues on the real and the imaginary axis. The decoupling of symplectic matrices which are exponentials of such Hamiltonian matrices can be deduced from this in a few steps. It is shown that this algebraic decoupling is closely related to a geometric “decoupling” by the orthogonalization of the vectors E→, B→, and P→, which were introduced with the so-called “electromechanical equivalence.” A mathematical analysis of the problem can be traced down to the task of finding a structure-preserving block diagonalization of symplectic or Hamiltonian matrices. Structure preservation means in this context that the (sequence of) transformations must be symplectic and hence canonical. When used iteratively, the decoupling
Geometric Effects on Electron Cloud
Wang, L
2007-07-06
The development of an electron cloud in the vacuum chambers of high intensity positron and proton storage rings may limit the machine performances by inducing beam instabilities, beam emittance increase, beam loss, vacuum pressure increases and increased heat load on the vacuum chamber wall. The electron multipacting is a kind of geometric resonance phenomenon and thus is sensitive to the geometric parameters such as the aperture of the beam pipe, beam shape and beam bunch fill pattern, etc. This paper discusses the geometric effects on the electron cloud build-up in a beam chamber and examples are given for different beams and accelerators.
Geometric derivations of minimal sets of sufficient multiview constraints
Thomas, Orrin H.; Oshel, Edward R.
2012-01-01
Geometric interpretations of four of the most common determinant formulations of multiview constraints are given, showing that they all enforce the same geometry and that all of the forms commonly in use in the machine vision community are a subset of a more general form. Generalising the work of Yi Ma yields a new general 2 x 2 determinant trilinear and 3 x 3 determinant quadlinear. Geometric descriptions of degenerate multiview constraints are given, showing that it is necessary, but insufficient, that the determinant equals zero. Understanding the degeneracies leads naturally into proofs for minimum sufficient sets of bilinear, trilinear and quadlinear constraints for arbitrary numbers of conjugate observations.
Guitars, Violins, and Geometric Sequences
ERIC Educational Resources Information Center
Barger, Rita; Haehl, Martha
2007-01-01
This article describes middle school mathematics activities that relate measurement, ratios, and geometric sequences to finger positions or the placement of frets on stringed musical instruments. (Contains 2 figures and 2 tables.)
Antenna with Dielectric Having Geometric Patterns
NASA Technical Reports Server (NTRS)
Dudley, Kenneth L. (Inventor); Elliott, Holly A. (Inventor); Cravey, Robin L. (Inventor); Connell, John W. (Inventor); Ghose, Sayata (Inventor); Watson, Kent A. (Inventor); Smith, Jr., Joseph G. (Inventor)
2013-01-01
An antenna includes a ground plane, a dielectric disposed on the ground plane, and an electrically-conductive radiator disposed on the dielectric. The dielectric includes at least one layer of a first dielectric material and a second dielectric material that collectively define a dielectric geometric pattern, which may comprise a fractal geometry. The radiator defines a radiator geometric pattern, and the dielectric geometric pattern is geometrically identical, or substantially geometrically identical, to the radiator geometric pattern.
Leaf Morphology, Taxonomy and Geometric Morphometrics: A Simplified Protocol for Beginners
Viscosi, Vincenzo; Cardini, Andrea
2011-01-01
Taxonomy relies greatly on morphology to discriminate groups. Computerized geometric morphometric methods for quantitative shape analysis measure, test and visualize differences in form in a highly effective, reproducible, accurate and statistically powerful way. Plant leaves are commonly used in taxonomic analyses and are particularly suitable to landmark based geometric morphometrics. However, botanists do not yet seem to have taken advantage of this set of methods in their studies as much as zoologists have done. Using free software and an example dataset from two geographical populations of sessile oak leaves, we describe in detailed but simple terms how to: a) compute size and shape variables using Procrustes methods; b) test measurement error and the main levels of variation (population and trees) using a hierachical design; c) estimate the accuracy of group discrimination; d) repeat this estimate after controlling for the effect of size differences on shape (i.e., allometry). Measurement error was completely negligible; individual variation in leaf morphology was large and differences between trees were generally bigger than within trees; differences between the two geographic populations were small in both size and shape; despite a weak allometric trend, controlling for the effect of size on shape slighly increased discrimination accuracy. Procrustes based methods for the analysis of landmarks were highly efficient in measuring the hierarchical structure of differences in leaves and in revealing very small-scale variation. In taxonomy and many other fields of botany and biology, the application of geometric morphometrics contributes to increase scientific rigour in the description of important aspects of the phenotypic dimension of biodiversity. Easy to follow but detailed step by step example studies can promote a more extensive use of these numerical methods, as they provide an introduction to the discipline which, for many biologists, is less
Gaussian geometric discord in terms of Hellinger distance
Suciu, Serban Isar, Aurelian
2015-12-07
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we address the quantification of general non-classical correlations in Gaussian states of continuous variable systems from a geometric perspective. We give a description of the Gaussian geometric discord by using the Hellinger distance as a measure for quantum correlations between two non-interacting non-resonant bosonic modes embedded in a thermal environment. We evaluate the Gaussian geometric discord by taking two-mode squeezed thermal states as initial states of the system and show that it has finite values between 0 and 1 and that it decays asymptotically to zero in time under the effect of the thermal bath.
Geometric transitions and D-term SUSY breaking
Aganagic, Mina; Aganagic, Mina; Beem, Christopher
2007-11-05
We propose a new way of using geometric transitions to study metastable vacua in string theory and certain confining gauge theories. The gauge theories in question are N=2 supersymmetric theories deformed to N=1 by superpotential terms. We first geometrically engineer supersymmetry-breaking vacua by wrapping D5 branes on rigid 2-cycles in noncompact Calabi-Yau geometries, such that the central charges of the branes are misaligned. In a limit of slightly misaligned charges, this has a gauge theory description, where supersymmetry is broken by Fayet-Iliopoulos D-terms. Geometric transitions relate these configurations to dual Calabi-Yaus with fluxes, where H_RR, H_NS and dJ are all nonvanishing. We argue that the dual geometry can be effectively used to study the resulting non-supersymmetric, confining vacua
ERIC Educational Resources Information Center
Beller, Charley
2013-01-01
The study of definite descriptions has been a central part of research in linguistics and philosophy of language since Russell's seminal work "On Denoting" (Russell 1905). In that work Russell quickly dispatches analyses of denoting expressions with forms like "no man," "some man," "a man," and "every…
Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.
Arrieta, Jorge; Cartwright, Julyan H E; Gouillart, Emmanuelle; Piro, Nicolas; Piro, Oreste; Tuval, Idan
2015-01-01
Mixing fluid in a container at low Reynolds number--in an inertialess environment--is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing. PMID:26154384
Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach
Arrieta, Jorge; Cartwright, Julyan H. E.; Gouillart, Emmanuelle; Piro, Nicolas; Piro, Oreste; Tuval, Idan
2015-01-01
Mixing fluid in a container at low Reynolds number— in an inertialess environment—is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the “belly phase,” peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing. PMID:26154384
Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.
Arrieta, Jorge; Cartwright, Julyan H E; Gouillart, Emmanuelle; Piro, Nicolas; Piro, Oreste; Tuval, Idan
2015-01-01
Mixing fluid in a container at low Reynolds number--in an inertialess environment--is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.
Geometrically nonlinear behavior of piezoelectric laminated plates
NASA Astrophysics Data System (ADS)
Rabinovitch, Oded
2005-08-01
The geometrically nonlinear behavior of piezo-laminated plates actuated with isotropic or anisotropic piezoelectric layers is analytically investigated. The analytical model is derived using the variational principle of virtual work along with the lamination and plate theories, the von Karman large displacement and moderate rotation kinematic relations, and the anisotropic piezoelectric constitutive laws. A solution strategy that combines the approach of the method of lines, the advantages of the finite element concept, and the variational formulation is developed. This approach yields a set of nonlinear ordinary differential equations with nonlinear boundary conditions, which are solved using the multiple-shooting method. Convergence and verification of the model are examined through comparison with linear and nonlinear results of other approximation methods. The nonlinear response of two active plate structures is investigated numerically. The first plate is actuated in bending using monolithic piezoceramic layers and the second one is actuated in twist using macro-fiber composites. The results quantitatively reveal the complicated in-plane stress state associated with the piezoelectric actuation and the geometrically nonlinear coupling of the in-plane and out-of-plane responses of the plate. The influence of the nonlinear effects ranges from significant stiffening in certain combinations of electrical loads and boundary conditions to amplifications of the induced deflections in others. The paper closes with a summary and conclusions.
Dietary ecology of Murinae (Muridae, Rodentia): a geometric morphometric approach.
Gómez Cano, Ana Rosa; Hernández Fernández, Manuel; Alvarez-Sierra, M Ángeles
2013-01-01
Murine rodents represent a highly diverse group, which displays great ecological versatility. In the present paper we analyse the relationship between dental morphology, on one hand, using geometric morphometrics based upon the outline of first upper molar and the dietary preference of extant murine genera, on the other. This ecomorphological study of extant murine rodents demonstrates that dietary groups can be distinguished with the use of a quantitative geometric morphometric approach based on first upper molar outline. A discriminant analysis of the geometric morphometric variables of the first upper molars enables us to infer the dietary preferences of extinct murine genera from the Iberian Peninsula. Most of the extinct genera were omnivore; only Stephanomys showed a pattern of dental morphology alike that of the herbivore genera. PMID:24236090
Dietary Ecology of Murinae (Muridae, Rodentia): A Geometric Morphometric Approach
Gómez Cano, Ana Rosa; Hernández Fernández, Manuel; Álvarez-Sierra, M. Ángeles
2013-01-01
Murine rodents represent a highly diverse group, which displays great ecological versatility. In the present paper we analyse the relationship between dental morphology, on one hand, using geometric morphometrics based upon the outline of first upper molar and the dietary preference of extant murine genera, on the other. This ecomorphological study of extant murine rodents demonstrates that dietary groups can be distinguished with the use of a quantitative geometric morphometric approach based on first upper molar outline. A discriminant analysis of the geometric morphometric variables of the first upper molars enables us to infer the dietary preferences of extinct murine genera from the Iberian Peninsula. Most of the extinct genera were omnivore; only Stephanomys showed a pattern of dental morphology alike that of the herbivore genera. PMID:24236090
Dietary ecology of Murinae (Muridae, Rodentia): a geometric morphometric approach.
Gómez Cano, Ana Rosa; Hernández Fernández, Manuel; Alvarez-Sierra, M Ángeles
2013-01-01
Murine rodents represent a highly diverse group, which displays great ecological versatility. In the present paper we analyse the relationship between dental morphology, on one hand, using geometric morphometrics based upon the outline of first upper molar and the dietary preference of extant murine genera, on the other. This ecomorphological study of extant murine rodents demonstrates that dietary groups can be distinguished with the use of a quantitative geometric morphometric approach based on first upper molar outline. A discriminant analysis of the geometric morphometric variables of the first upper molars enables us to infer the dietary preferences of extinct murine genera from the Iberian Peninsula. Most of the extinct genera were omnivore; only Stephanomys showed a pattern of dental morphology alike that of the herbivore genera.
Geometrical modelling of textile reinforcements
NASA Technical Reports Server (NTRS)
Pastore, Christopher M.; Birger, Alexander B.; Clyburn, Eugene
1995-01-01
The mechanical properties of textile composites are dictated by the arrangement of yarns contained with the material. Thus to develop a comprehensive understanding of the performance of these materials, it is necessary to develop a geometrical model of the fabric structure. This task is quite complex, as the fabric is made form highly flexible yarn systems which experience a certain degree of compressability. Furthermore there are tremendous forces acting on the fabric during densification typically resulting in yarn displacement and misorientation. The objective of this work is to develop a methodology for characterizing the geometry of yarns within a fabric structure including experimental techniques for evaluating these models. Furthermore, some applications of these geometric results to mechanical prediction models are demonstrated. Although more costly than its predecessors, the present analysis is based on the detailed architecture developed by one of the authors and his colleagues and accounts for many of the geometric complexities that other analyses ignore.
Guiding light via geometric phases
NASA Astrophysics Data System (ADS)
Slussarenko, Sergei; Alberucci, Alessandro; Jisha, Chandroth P.; Piccirillo, Bruno; Santamato, Enrico; Assanto, Gaetano; Marrucci, Lorenzo
2016-09-01
All known methods for transverse confinement and guidance of light rely on modification of the refractive index, that is, on the scalar properties of electromagnetic radiation. Here, we disclose the concept of a dielectric waveguide that exploits vectorial spin-orbit interactions of light and the resulting geometric phases. The approach relies on the use of anisotropic media with an optic axis that lies orthogonal to the propagation direction but is spatially modulated, so that the refractive index remains constant everywhere. A spin-controlled cumulative phase distortion is imposed on the beam, balancing diffraction for a specific polarization. As well as theoretical analysis, we present an experimental demonstration of the guidance using a series of discrete geometric-phase lenses made from liquid crystal. Our findings show that geometric phases may determine the optical guiding behaviour well beyond a Rayleigh length, paving the way to a new class of photonic devices. The concept is applicable to the whole electromagnetic spectrum.
Geometric scalar theory of gravity
Novello, M.; Bittencourt, E.; Goulart, E.; Salim, J.M.; Toniato, J.D.; Moschella, U. E-mail: eduhsb@cbpf.br E-mail: egoulart@cbpf.br E-mail: toniato@cbpf.br
2013-06-01
We present a geometric scalar theory of gravity. Our proposal will be described using the ''background field method'' introduced by Gupta, Feynman, Deser and others as a field theory formulation of general relativity. We analyze previous criticisms against scalar gravity and show how the present proposal avoids these difficulties. This concerns not only the theoretical complaints but also those related to observations. In particular, we show that the widespread belief of the conjecture that the source of scalar gravity must be the trace of the energy-momentum tensor — which is one of the main difficulties to couple gravity with electromagnetic phenomenon in previous models — does not apply to our geometric scalar theory. From the very beginning this is not a special relativistic scalar gravity. The adjective ''geometric'' pinpoints its similarity with general relativity: this is a metric theory of gravity. Some consequences of this new scalar theory are explored.
Guiding light via geometric phases
NASA Astrophysics Data System (ADS)
Slussarenko, Sergei; Alberucci, Alessandro; Jisha, Chandroth P.; Piccirillo, Bruno; Santamato, Enrico; Assanto, Gaetano; Marrucci, Lorenzo
2016-09-01
All known methods for transverse confinement and guidance of light rely on modification of the refractive index, that is, on the scalar properties of electromagnetic radiation. Here, we disclose the concept of a dielectric waveguide that exploits vectorial spin–orbit interactions of light and the resulting geometric phases. The approach relies on the use of anisotropic media with an optic axis that lies orthogonal to the propagation direction but is spatially modulated, so that the refractive index remains constant everywhere. A spin-controlled cumulative phase distortion is imposed on the beam, balancing diffraction for a specific polarization. As well as theoretical analysis, we present an experimental demonstration of the guidance using a series of discrete geometric-phase lenses made from liquid crystal. Our findings show that geometric phases may determine the optical guiding behaviour well beyond a Rayleigh length, paving the way to a new class of photonic devices. The concept is applicable to the whole electromagnetic spectrum.
Geometrical Optics of Dense Aerosols
Hay, Michael J.; Valeo, Ernest J.; Fisch, Nathaniel J.
2013-04-24
Assembling a free-standing, sharp-edged slab of homogeneous material that is much denser than gas, but much more rare ed than a solid, is an outstanding technological challenge. The solution may lie in focusing a dense aerosol to assume this geometry. However, whereas the geometrical optics of dilute aerosols is a well-developed fi eld, the dense aerosol limit is mostly unexplored. Yet controlling the geometrical optics of dense aerosols is necessary in preparing such a material slab. Focusing dense aerosols is shown here to be possible, but the nite particle density reduces the eff ective Stokes number of the flow, a critical result for controlled focusing. __________________________________________________
Geometrical spin symmetry and spin
Pestov, I. B.
2011-07-15
Unification of General Theory of Relativity and Quantum Mechanics leads to General Quantum Mechanics which includes into itself spindynamics as a theory of spin phenomena. The key concepts of spindynamics are geometrical spin symmetry and the spin field (space of defining representation of spin symmetry). The essence of spin is the bipolar structure of geometrical spin symmetry induced by the gravitational potential. The bipolar structure provides a natural derivation of the equations of spindynamics. Spindynamics involves all phenomena connected with spin and provides new understanding of the strong interaction.
Geometric validation plan for ASTER
NASA Astrophysics Data System (ADS)
Iwasaki, Akira; Matsumoto, Ken; Fujisada, Hiroyuki
1998-12-01
The ASTER system is a multispectral imager which covers a spectral range from visible to thermal infrared light by combining three subsystems composed of four telescopes. To ensure the high-quality data products concerning to the geolocation and band-to-band matching performance, the geometric registration is needed. This paper describes the geometric validation procedure for a multi-telescope imager with a cross-track pointing function. The strategy for the maintenance of database files and the preparation a GCP library is also shown.
Geometric phases in astigmatic optical modes of arbitrary order
Habraken, Steven J. M.; Nienhuis, Gerard
2010-08-15
The transverse spatial structure of a paraxial beam of light is fully characterized by a set of parameters that vary only slowly under free propagation. They specify bosonic ladder operators that connect modes of different orders, in analogy to the ladder operators connecting harmonic-oscillator wave functions. The parameter spaces underlying sets of higher-order modes are isomorphic to the parameter space of the ladder operators. We study the geometry of this space and the geometric phase that arises from it. This phase constitutes the ultimate generalization of the Gouy phase in paraxial wave optics. It reduces to the ordinary Gouy phase and the geometric phase of nonastigmatic optical modes with orbital angular momentum in limiting cases. We briefly discuss the well-known analogy between geometric phases and the Aharonov-Bohm effect, which provides some complementary insights into the geometric nature and origin of the generalized Gouy phase shift. Our method also applies to the quantum-mechanical description of wave packets. It allows for obtaining complete sets of normalized solutions of the Schroedinger equation. Cyclic transformations of such wave packets give rise to a phase shift, which has a geometric interpretation in terms of the other degrees of freedom involved.
Teleportation of geometric structures in 3D
NASA Astrophysics Data System (ADS)
Aerts, Diederik; Czachor, Marek; Orłowski, Łukasz
2009-04-01
The simplest quantum teleportation algorithms can be represented in geometric terms in spaces of dimensions 3 (for real state vectors) and 4 (for complex state vectors). The geometric representation is based on geometric-algebra coding, a geometric alternative to the tensor-product coding typical of quantum mechanics. We discuss all the elementary ingredients of the geometric version of the algorithm: geometric analogs of states and controlled Pauli gates. A fully geometric presentation is possible if one employs a nonstandard representation of directed magnitudes, formulated in terms of colors defined via stereographic projection of a color wheel, and not by means of directed volumes.
Vergence, Vision, and Geometric Optics
ERIC Educational Resources Information Center
Keating, Michael P.
1975-01-01
Provides a definition of vergence in terms of the curvature of the wave fronts, and gives examples to illustrate the advantages of this approach. The vergence treatment of geometrical optics provides both conceptual and algebraic advantages, particularly for the life science student, over the traditional object distance-image distance-focal length…
Geometric quantum noise of spin.
Shnirman, Alexander; Gefen, Yuval; Saha, Arijit; Burmistrov, Igor S; Kiselev, Mikhail N; Altland, Alexander
2015-05-01
The presence of geometric phases is known to affect the dynamics of the systems involved. Here, we consider a quantum degree of freedom, moving in a dissipative environment, whose dynamics is described by a Langevin equation with quantum noise. We show that geometric phases enter the stochastic noise terms. Specifically, we consider small ferromagnetic particles (nanomagnets) or quantum dots close to Stoner instability, and investigate the dynamics of the total magnetization in the presence of tunneling coupling to the metallic leads. We generalize the Ambegaokar-Eckern-Schön effective action and the corresponding semiclassical equations of motion from the U(1) case of the charge degree of freedom to the SU(2) case of the magnetization. The Langevin forces (torques) in these equations are strongly influenced by the geometric phase. As a first but nontrivial application, we predict low temperature quantum diffusion of the magnetization on the Bloch sphere, which is governed by the geometric phase. We propose a protocol for experimental observation of this phenomenon.
Celestial mechanics with geometric algebra
NASA Technical Reports Server (NTRS)
Hestenes, D.
1983-01-01
Geometric algebra is introduced as a general tool for Celestial Mechanics. A general method for handling finite rotations and rotational kinematics is presented. The constants of Kepler motion are derived and manipulated in a new way. A new spinor formulation of perturbation theory is developed.
The geometric oblateness of Uranus
NASA Technical Reports Server (NTRS)
Franklin, F. A.; Avis, C. C.; Colombo, G.; Shapiro, I. I.
1980-01-01
The paper considers photographs of Uranus obtained by the Stratoscope II balloon-borne telescope in 1970. These data have been redigitized and reanalyzed, and the geometric oblateness of Uranus was determined from the isophotes near the limb using an expression in terms of the equatorial and polar radii.
Platonic Symmetry and Geometric Thinking
ERIC Educational Resources Information Center
Zsombor-Murray, Paul
2007-01-01
Cubic symmetry is used to build the other four Platonic solids and some formalism from classical geometry is introduced. Initially, the approach is via geometric construction, e.g., the "golden ratio" is necessary to construct an icosahedron with pentagonal faces. Then conventional elementary vector algebra is used to extract quantitative…
Linear patterning of mesenchymal condensations is modulated by geometric constraints
Klumpers, Darinka D.; Mao, Angelo S.; Smit, Theo H.; Mooney, David J.
2014-01-01
The development of the vertebral column starts with the formation of a linear array of mesenchymal condensations, forming the blueprint for the eventual alternating pattern of bone and cartilage. Despite growing insight into the molecular mechanisms of morphogenesis, the impact of the physical aspects of the environment is not well understood. We hypothesized that geometric boundary conditions may play a pivotal role in the linear patterning of condensations, as neighbouring tissues provide physical constraints to the cell population. To study the process of condensation and the patterning thereof under tightly controlled geometric constraints, we developed a novel in vitro model that combines micropatterning with the established micromass assay. The spacing and alignment of condensations changed with the width of the cell adhesive patterns, a phenomenon that could not be explained by cell availability alone. Moreover, the extent of chondrogenic commitment was increased on substrates with tighter geometric constraints. When the in vivo pattern of condensations was investigated in the developing vertebral column of chicken embryos, the measurements closely fit into the quantitative relation between geometric constraints and inter-condensation distance found in vitro. Together, these findings suggest a potential role of geometric constraints in skeletal patterning in a cellular process of self-organization. PMID:24718453
Multiscale geometric modeling of macromolecules II: Lagrangian representation
Feng, Xin; Xia, Kelin; Chen, Zhan; Tong, Yiying; Wei, Guo-Wei
2013-01-01
Geometric modeling of biomolecules plays an essential role in the conceptualization of biolmolecular structure, function, dynamics and transport. Qualitatively, geometric modeling offers a basis for molecular visualization, which is crucial for the understanding of molecular structure and interactions. Quantitatively, geometric modeling bridges the gap between molecular information, such as that from X-ray, NMR and cryo-EM, and theoretical/mathematical models, such as molecular dynamics, the Poisson-Boltzmann equation and the Nernst-Planck equation. In this work, we present a family of variational multiscale geometric models for macromolecular systems. Our models are able to combine multiresolution geometric modeling with multiscale electrostatic modeling in a unified variational framework. We discuss a suite of techniques for molecular surface generation, molecular surface meshing, molecular volumetric meshing, and the estimation of Hadwiger’s functionals. Emphasis is given to the multiresolution representations of biomolecules and the associated multiscale electrostatic analyses as well as multiresolution curvature characterizations. The resulting fine resolution representations of a biomolecular system enable the detailed analysis of solvent-solute interaction, and ion channel dynamics, while our coarse resolution representations highlight the compatibility of protein-ligand bindings and possibility of protein-protein interactions. PMID:23813599
Geometric hashing and object recognition
NASA Astrophysics Data System (ADS)
Stiller, Peter F.; Huber, Birkett
1999-09-01
We discuss a new geometric hashing method for searching large databases of 2D images (or 3D objects) to match a query built from geometric information presented by a single 3D object (or single 2D image). The goal is to rapidly determine a small subset of the images that potentially contain a view of the given object (or a small set of objects that potentially match the item in the image). Since this must be accomplished independent of the pose of the object, the objects and images, which are characterized by configurations of geometric features such as points, lines and/or conics, must be treated using a viewpoint invariant formulation. We are therefore forced to characterize these configurations in terms of their 3D and 2D geometric invariants. The crucial relationship between the 3D geometry and its 'residual' in 2D is expressible as a correspondence (in the sense of algebraic geometry). Computing a set of generating equations for the ideal of this correspondence gives a complete characterization of the view of independent relationships between an object and all of its possible images. Once a set of generators is in hand, it can be used to devise efficient recognition algorithms and to give an efficient geometric hashing scheme. This requires exploiting the form and symmetry of the equations. The result is a multidimensional access scheme whose efficiency we examine. Several potential directions for improving this scheme are also discussed. Finally, in a brief appendix, we discuss an alternative approach to invariants for generalized perspective that replaces the standard invariants by a subvariety of a Grassmannian. The advantage of this is that one can circumvent many annoying general position assumptions and arrive at invariant equations (in the Plucker coordinates) that are more numerically robust in applications.
Geometrical modelling of textile reinforcements
NASA Technical Reports Server (NTRS)
Pastore, Christopher M.; Birger, Alexander B.; Clyburn, Eugene
1995-01-01
The mechanical properties of textile composites are dictated by the arrangement of yarns contained within the material. Thus, to develop a comprehensive understanding of the performance of these materials, it is necessary to develop a geometrical model of the fabric structure. This task is quite complex, as the fabric is made from highly flexible yarn systems which experience a certain degree of compressibility. Furthermore there are tremendous forces acting on the fabric during densification typically resulting in yarn displacement and misorientation. The objective of this work is to develop a methodology for characterizing the geometry of yarns within a fabric structure including experimental techniques for evaluating these models. Furthermore, some applications of these geometric results to mechanical property predictions models are demonstrated.
The verdict geometric quality library.
Knupp, Patrick Michael; Ernst, C.D. (Elemental Technologies, Inc., American Fork, UT); Thompson, David C.; Stimpson, C.J.; Pebay, Philippe Pierre
2006-03-01
Verdict is a collection of subroutines for evaluating the geometric qualities of triangles, quadrilaterals, tetrahedra, and hexahedra using a variety of metrics. A metric is a real number assigned to one of these shapes depending on its particular vertex coordinates. These metrics are used to evaluate the input to finite element, finite volume, boundary element, and other types of solvers that approximate the solution to partial differential equations defined over regions of space. The geometric qualities of these regions is usually strongly tied to the accuracy these solvers are able to obtain in their approximations. The subroutines are written in C++ and have a simple C interface. Each metric may be evaluated individually or in combination. When multiple metrics are evaluated at once, they share common calculations to lower the cost of the evaluation.
Automated landmarking and geometric characterization of the carotid siphon.
Bogunović, Hrvoje; Pozo, José María; Cárdenes, Rubén; Villa-Uriol, María Cruz; Blanc, Raphaël; Piotin, Michel; Frangi, Alejandro F
2012-05-01
based on geometric features. The proposed characterization provides a rich description of geometry and is ready to be applied in the search for geometric risk factors of the carotid siphon.
Polar metals by geometric design.
Kim, T H; Puggioni, D; Yuan, Y; Xie, L; Zhou, H; Campbell, N; Ryan, P J; Choi, Y; Kim, J-W; Patzner, J R; Ryu, S; Podkaminer, J P; Irwin, J; Ma, Y; Fennie, C J; Rzchowski, M S; Pan, X Q; Gopalan, V; Rondinelli, J M; Eom, C B
2016-05-01
Gauss's law dictates that the net electric field inside a conductor in electrostatic equilibrium is zero by effective charge screening; free carriers within a metal eliminate internal dipoles that may arise owing to asymmetric charge distributions. Quantum physics supports this view, demonstrating that delocalized electrons make a static macroscopic polarization, an ill-defined quantity in metals--it is exceedingly unusual to find a polar metal that exhibits long-range ordered dipoles owing to cooperative atomic displacements aligned from dipolar interactions as in insulating phases. Here we describe the quantum mechanical design and experimental realization of room-temperature polar metals in thin-film ANiO3 perovskite nickelates using a strategy based on atomic-scale control of inversion-preserving (centric) displacements. We predict with ab initio calculations that cooperative polar A cation displacements are geometrically stabilized with a non-equilibrium amplitude and tilt pattern of the corner-connected NiO6 octahedral--the structural signatures of perovskites--owing to geometric constraints imposed by the underlying substrate. Heteroepitaxial thin-films grown on LaAlO3 (111) substrates fulfil the design principles. We achieve both a conducting polar monoclinic oxide that is inaccessible in compositionally identical films grown on (001) substrates, and observe a hidden, previously unreported, non-equilibrium structure in thin-film geometries. We expect that the geometric stabilization approach will provide novel avenues for realizing new multifunctional materials with unusual coexisting properties. PMID:27096369
Polar metals by geometric design
NASA Astrophysics Data System (ADS)
Kim, T. H.; Puggioni, D.; Yuan, Y.; Xie, L.; Zhou, H.; Campbell, N.; Ryan, P. J.; Choi, Y.; Kim, J.-W.; Patzner, J. R.; Ryu, S.; Podkaminer, J. P.; Irwin, J.; Ma, Y.; Fennie, C. J.; Rzchowski, M. S.; Pan, X. Q.; Gopalan, V.; Rondinelli, J. M.; Eom, C. B.
2016-05-01
Gauss’s law dictates that the net electric field inside a conductor in electrostatic equilibrium is zero by effective charge screening; free carriers within a metal eliminate internal dipoles that may arise owing to asymmetric charge distributions. Quantum physics supports this view, demonstrating that delocalized electrons make a static macroscopic polarization, an ill-defined quantity in metals—it is exceedingly unusual to find a polar metal that exhibits long-range ordered dipoles owing to cooperative atomic displacements aligned from dipolar interactions as in insulating phases. Here we describe the quantum mechanical design and experimental realization of room-temperature polar metals in thin-film ANiO3 perovskite nickelates using a strategy based on atomic-scale control of inversion-preserving (centric) displacements. We predict with ab initio calculations that cooperative polar A cation displacements are geometrically stabilized with a non-equilibrium amplitude and tilt pattern of the corner-connected NiO6 octahedra—the structural signatures of perovskites—owing to geometric constraints imposed by the underlying substrate. Heteroepitaxial thin-films grown on LaAlO3 (111) substrates fulfil the design principles. We achieve both a conducting polar monoclinic oxide that is inaccessible in compositionally identical films grown on (001) substrates, and observe a hidden, previously unreported, non-equilibrium structure in thin-film geometries. We expect that the geometric stabilization approach will provide novel avenues for realizing new multifunctional materials with unusual coexisting properties.
Polar metals by geometric design.
Kim, T H; Puggioni, D; Yuan, Y; Xie, L; Zhou, H; Campbell, N; Ryan, P J; Choi, Y; Kim, J-W; Patzner, J R; Ryu, S; Podkaminer, J P; Irwin, J; Ma, Y; Fennie, C J; Rzchowski, M S; Pan, X Q; Gopalan, V; Rondinelli, J M; Eom, C B
2016-05-01
Gauss's law dictates that the net electric field inside a conductor in electrostatic equilibrium is zero by effective charge screening; free carriers within a metal eliminate internal dipoles that may arise owing to asymmetric charge distributions. Quantum physics supports this view, demonstrating that delocalized electrons make a static macroscopic polarization, an ill-defined quantity in metals--it is exceedingly unusual to find a polar metal that exhibits long-range ordered dipoles owing to cooperative atomic displacements aligned from dipolar interactions as in insulating phases. Here we describe the quantum mechanical design and experimental realization of room-temperature polar metals in thin-film ANiO3 perovskite nickelates using a strategy based on atomic-scale control of inversion-preserving (centric) displacements. We predict with ab initio calculations that cooperative polar A cation displacements are geometrically stabilized with a non-equilibrium amplitude and tilt pattern of the corner-connected NiO6 octahedral--the structural signatures of perovskites--owing to geometric constraints imposed by the underlying substrate. Heteroepitaxial thin-films grown on LaAlO3 (111) substrates fulfil the design principles. We achieve both a conducting polar monoclinic oxide that is inaccessible in compositionally identical films grown on (001) substrates, and observe a hidden, previously unreported, non-equilibrium structure in thin-film geometries. We expect that the geometric stabilization approach will provide novel avenues for realizing new multifunctional materials with unusual coexisting properties.
Geometric mean for subspace selection.
Tao, Dacheng; Li, Xuelong; Wu, Xindong; Maybank, Stephen J
2009-02-01
Subspace selection approaches are powerful tools in pattern classification and data visualization. One of the most important subspace approaches is the linear dimensionality reduction step in the Fisher's linear discriminant analysis (FLDA), which has been successfully employed in many fields such as biometrics, bioinformatics, and multimedia information management. However, the linear dimensionality reduction step in FLDA has a critical drawback: for a classification task with c classes, if the dimension of the projected subspace is strictly lower than c - 1, the projection to a subspace tends to merge those classes, which are close together in the original feature space. If separate classes are sampled from Gaussian distributions, all with identical covariance matrices, then the linear dimensionality reduction step in FLDA maximizes the mean value of the Kullback-Leibler (KL) divergences between different classes. Based on this viewpoint, the geometric mean for subspace selection is studied in this paper. Three criteria are analyzed: 1) maximization of the geometric mean of the KL divergences, 2) maximization of the geometric mean of the normalized KL divergences, and 3) the combination of 1 and 2. Preliminary experimental results based on synthetic data, UCI Machine Learning Repository, and handwriting digits show that the third criterion is a potential discriminative subspace selection method, which significantly reduces the class separation problem in comparing with the linear dimensionality reduction step in FLDA and its several representative extensions. PMID:19110492
Geometric mean for subspace selection.
Tao, Dacheng; Li, Xuelong; Wu, Xindong; Maybank, Stephen J
2009-02-01
Subspace selection approaches are powerful tools in pattern classification and data visualization. One of the most important subspace approaches is the linear dimensionality reduction step in the Fisher's linear discriminant analysis (FLDA), which has been successfully employed in many fields such as biometrics, bioinformatics, and multimedia information management. However, the linear dimensionality reduction step in FLDA has a critical drawback: for a classification task with c classes, if the dimension of the projected subspace is strictly lower than c - 1, the projection to a subspace tends to merge those classes, which are close together in the original feature space. If separate classes are sampled from Gaussian distributions, all with identical covariance matrices, then the linear dimensionality reduction step in FLDA maximizes the mean value of the Kullback-Leibler (KL) divergences between different classes. Based on this viewpoint, the geometric mean for subspace selection is studied in this paper. Three criteria are analyzed: 1) maximization of the geometric mean of the KL divergences, 2) maximization of the geometric mean of the normalized KL divergences, and 3) the combination of 1 and 2. Preliminary experimental results based on synthetic data, UCI Machine Learning Repository, and handwriting digits show that the third criterion is a potential discriminative subspace selection method, which significantly reduces the class separation problem in comparing with the linear dimensionality reduction step in FLDA and its several representative extensions.
NASA Astrophysics Data System (ADS)
Weidlich, W.
1987-03-01
General concepts for the quantitative description of the dynamics of social processes are introduced. They allow for embedding social science into the conceptual framework of synergetics. Equations of motion for the socioconfiguration are derived on the stochastic and quasideterministic level. As an application the migration of interacting human populations is treated. The solutions of the nonlinear migratory equations include limit cycles and strange attractors. The empiric evaluation of interregional migratory dynamics is exemplified in the case of Germany.
NASA Astrophysics Data System (ADS)
Ford, David; Huntsman, Steven
2006-06-01
Thermodynamics (in concert with its sister discipline, statistical physics) can be regarded as a data reduction scheme based on partitioning a total system into a subsystem and a bath that weakly interact with each other. Whereas conventionally, the systems investigated require this form of data reduction in order to facilitate prediction, a different problem also occurs, in the context of communication networks, markets, etc. Such “empirically accessible” systems typically overwhelm observers with the sort of information that in the case of (say) a gas is effectively unobtainable. What is required for such complex interacting systems is not prediction (this may be impossible when humans besides the observer are responsible for the interactions) but rather, description as a route to understanding. Still, the need for a thermodynamical data reduction scheme remains. In this paper, we show how an empirical temperature can be computed for finite, empirically accessible systems, and further outline how this construction allows the age-old science of thermodynamics to be fruitfully applied to them.
Geometrical Visualisation--Epistemic and Emotional
ERIC Educational Resources Information Center
Rodd, Melissa
2010-01-01
A well-documented experience of students of elementary Euclidean geometry is "seeing" a geometric result and being sure about its truth; this sort of experience gives rise to the notion of geometrical visualisation that is developed here. In this essay a philosophical argument for the epistemic potential of geometrical visualisation is reviewed,…
Development of a Geometric Spatial Visualization Tool
ERIC Educational Resources Information Center
Ganesh, Bibi; Wilhelm, Jennifer; Sherrod, Sonya
2009-01-01
This paper documents the development of the Geometric Spatial Assessment. We detail the development of this instrument which was designed to identify middle school students' strategies and advancement in understanding of four geometric concept domains (geometric spatial visualization, spatial projection, cardinal directions, and periodic patterns)…
The effect of electron beam geometric deformation errors on the small-signal characteristic of ECRM
NASA Astrophysics Data System (ADS)
Yongjian, Yu
1993-08-01
In this paper is studied the effect of electron beam geometric deformation errors on the small — signal characteristics of the TE{mn/o} mode Electron Cyclotron Resonance Maser (ECRM), based on the elliptically cross—sectional e—beam deformation model. As an example, the effect of small geometric deformation errors on the TE{01/o} mode fundamental ECRM coupling coefficient is quantitatively shown.
A geometric approach for quadrotor trajectory tracking control
NASA Astrophysics Data System (ADS)
Shi, Xiao-Ning; Zhang, Yong-An; Zhou, Di
2015-11-01
This paper investigates the trajectory tracking problem for quadrotor with attitude finite-time convergence via geometric approach. First, a global geometric dynamic description is presented on the special Euclidean group (SE(3)), and the trajectory tracking control is decomposed into two cascaded tracking control loops: the position tracking control loop and the attitude tracking control loop. Then, based on the fact that the attitude tracking loop is a fast loop, a finite-time controller based on the exponential coordinate is proposed to speed up the response rate of the attitude control loop, so that the artificial singularity and redundancy can be avoided. In addition, a backstepping controller is designed for the position tracking loop to construct the thrust magnitude control input for the position dynamics and the reference rotation matrix for the attitude tracking loop. Finally, the numerical simulation results are presented to demonstrate the effectiveness of this trajectory tracking strategy.
Birkhoff's equations and geometrical theory of rotational relativistic system
NASA Astrophysics Data System (ADS)
Luo, Shao-kai; Chen, Xiang-wei; Fu, Jing-li
2001-04-01
The Birkhoffian and Birkhoff's functions of a rotational relativistic system are constructed, the Pfaff action of rotational relativistic system is defined, the Pfaff-Birkhoff principle of a rotational relativistic system is given and the Pfaff-Birkhoff-D'Alembert principles and Birkhoff's equations of rotational relativistic system are constructed. The geometrical description of a rotational relativistic system is studied and the exact properties of Birkhoff's equations and their forms on R×T*M for a rotational relativistic system are obtained. The global analysis of Birkhoff's equations for a rotational relativistic system is studied, the global properties of autonomous, semi-autonomous and non-autonomous rotational relativistic Birkhoff's equations and the geometrical properties of energy change for rotational relativistic Birkhoff's equations are given.
Geometric foundations of Cartan gauge gravity
NASA Astrophysics Data System (ADS)
Catren, Gabriel
2015-03-01
We use the theory of Cartan connections to analyze the geometrical structures underpinning the gauge-theoretical descriptions of the gravitational interaction. According to the theory of Cartan connections, the spin connection ω and the soldering form θ that define the fundamental variables of the Palatini formulation of general relativity can be understood as different components of a single field, namely a Cartan connection A = ω + θ. In order to stress both the similarities and the differences between the notions of Ehresmann connection and Cartan connection, we explain in detail how a Cartan geometry (PH → M, A) can be obtained from a G-principal bundle PG → M endowed with an Ehresmann connection (being the Lorentz group H a subgroup of G) by means of a bundle reduction mechanism. We claim that this reduction must be understood as a partial gauge fixing of the local gauge symmetries of PG, i.e. as a gauge fixing that leaves "unbroken" the local Lorentz invariance. We then argue that the "broken" part of the symmetry — that is the internal local translational invariance — is implicitly preserved by the invariance under the external diffeomorphisms of M.
SQCD Vacua and Geometrical Engineering
Tatar, Radu; Wetenhall, Ben
2008-11-23
We consider the geometrical engineering constructions for the N = 1 SQCD vacua. After one T-duality, these geometries with wrapped D5 branes become N = 1 brane configurations with NS-branes and D4-branes. After performing a flop, the geometries contain branes, antibranes and branes wrapped on non-holomorphic cycles. The various tachyon condensations between pairs of wrapped D5 branes and anti-D5 branes together with deformations of the cycles give rise to a variety of supersymmetric and metastable non-supersymmetric vacua.
Moving walls and geometric phases
NASA Astrophysics Data System (ADS)
Facchi, Paolo; Garnero, Giancarlo; Marmo, Giuseppe; Samuel, Joseph
2016-09-01
We unveil the existence of a non-trivial Berry phase associated to the dynamics of a quantum particle in a one dimensional box with moving walls. It is shown that a suitable choice of boundary conditions has to be made in order to preserve unitarity. For these boundary conditions we compute explicitly the geometric phase two-form on the parameter space. The unboundedness of the Hamiltonian describing the system leads to a natural prescription of renormalization for divergent contributions arising from the boundary.
Quantitative Pedagogy: A Digital Two Player Game to Examine Communicative Competence.
Lopez-Rosenfeld, Matías; Carrillo, Facundo; Garbulsky, Gerry; Fernandez Slezak, Diego; Sigman, Mariano
2015-01-01
Inner concepts are much richer than the words that describe them. Our general objective is to inquire what are the best procedures to communicate conceptual knowledge. We construct a simplified and controlled setup emulating important variables of pedagogy amenable to quantitative analysis. To this aim, we designed a game inspired in Chinese Whispers, to investigate which attributes of a description affect its capacity to faithfully convey an image. This is a two player game: an emitter and a receiver. The emitter was shown a simple geometric figure and was asked to describe it in words. He was informed that this description would be passed to the receiver who had to replicate the drawing from this description. We capitalized on vast data obtained from an android app to quantify the effect of different aspects of a description on communication precision. We show that descriptions more effectively communicate an image when they are coherent and when they are procedural. Instead, the creativity, the use of metaphors and the use of mathematical concepts do not affect its fidelity. PMID:26554833
Quantitative Pedagogy: A Digital Two Player Game to Examine Communicative Competence
Lopez-Rosenfeld, Matías; Carrillo, Facundo; Garbulsky, Gerry; Fernandez Slezak, Diego; Sigman, Mariano
2015-01-01
Inner concepts are much richer than the words that describe them. Our general objective is to inquire what are the best procedures to communicate conceptual knowledge. We construct a simplified and controlled setup emulating important variables of pedagogy amenable to quantitative analysis. To this aim, we designed a game inspired in Chinese Whispers, to investigate which attributes of a description affect its capacity to faithfully convey an image. This is a two player game: an emitter and a receiver. The emitter was shown a simple geometric figure and was asked to describe it in words. He was informed that this description would be passed to the receiver who had to replicate the drawing from this description. We capitalized on vast data obtained from an android app to quantify the effect of different aspects of a description on communication precision. We show that descriptions more effectively communicate an image when they are coherent and when they are procedural. Instead, the creativity, the use of metaphors and the use of mathematical concepts do not affect its fidelity. PMID:26554833
Quantitative Pedagogy: A Digital Two Player Game to Examine Communicative Competence.
Lopez-Rosenfeld, Matías; Carrillo, Facundo; Garbulsky, Gerry; Fernandez Slezak, Diego; Sigman, Mariano
2015-01-01
Inner concepts are much richer than the words that describe them. Our general objective is to inquire what are the best procedures to communicate conceptual knowledge. We construct a simplified and controlled setup emulating important variables of pedagogy amenable to quantitative analysis. To this aim, we designed a game inspired in Chinese Whispers, to investigate which attributes of a description affect its capacity to faithfully convey an image. This is a two player game: an emitter and a receiver. The emitter was shown a simple geometric figure and was asked to describe it in words. He was informed that this description would be passed to the receiver who had to replicate the drawing from this description. We capitalized on vast data obtained from an android app to quantify the effect of different aspects of a description on communication precision. We show that descriptions more effectively communicate an image when they are coherent and when they are procedural. Instead, the creativity, the use of metaphors and the use of mathematical concepts do not affect its fidelity.
Measurement error in geometric morphometrics.
Fruciano, Carmelo
2016-06-01
Geometric morphometrics-a set of methods for the statistical analysis of shape once saluted as a revolutionary advancement in the analysis of morphology -is now mature and routinely used in ecology and evolution. However, a factor often disregarded in empirical studies is the presence and the extent of measurement error. This is potentially a very serious issue because random measurement error can inflate the amount of variance and, since many statistical analyses are based on the amount of "explained" relative to "residual" variance, can result in loss of statistical power. On the other hand, systematic bias can affect statistical analyses by biasing the results (i.e. variation due to bias is incorporated in the analysis and treated as biologically-meaningful variation). Here, I briefly review common sources of error in geometric morphometrics. I then review the most commonly used methods to measure and account for both random and non-random measurement error, providing a worked example using a real dataset.
NPP VIIRS Geometric Performance Status
NASA Technical Reports Server (NTRS)
Lin, Guoqing; Wolfe, Robert E.; Nishihama, Masahiro
2011-01-01
Visible Infrared Imager Radiometer Suite (VIIRS) instrument on-board the National Polar-orbiting Operational Environmental Satellite System (NPOESS) Preparatory Project (NPP) satellite is scheduled for launch in October, 2011. It is to provide satellite measured radiance/reflectance data for both weather and climate applications. Along with radiometric calibration, geometric characterization and calibration of Sensor Data Records (SDRs) are crucial to the VIIRS Environmental Data Record (EDR) algorithms and products which are used in numerical weather prediction (NWP). The instrument geometric performance includes: 1) sensor (detector) spatial response, parameterized by the dynamic field of view (DFOV) in the scan direction and instantaneous FOV (IFOV) in the track direction, modulation transfer function (MTF) for the 17 moderate resolution bands (M-bands), and horizontal spatial resolution (HSR) for the five imagery bands (I-bands); 2) matrices of band-to-band co-registration (BBR) from the corresponding detectors in all band pairs; and 3) pointing knowledge and stability characteristics that includes scan plane tilt, scan rate and scan start position variations, and thermally induced variations in pointing with respect to orbital position. They have been calibrated and characterized through ground testing under ambient and thermal vacuum conditions, numerical modeling and analysis. This paper summarizes the results, which are in general compliance with specifications, along with anomaly investigations, and describes paths forward for characterizing on-orbit BBR and spatial response, and for improving instrument on-orbit performance in pointing and geolocation.
Geometric pumping in autophoretic channels
NASA Astrophysics Data System (ADS)
Michelin, Sebastien; Montenegro Johnson, Thomas; de Canio, Gabriele; Lobatto-Dauzier, Nicolas; Lauga, Eric
2015-11-01
Pumping at the microscale has important applications from biological fluid handling to lab-on-a-chip systems. It can be achieved either from a global (e.g. imposed pressure gradient) or local forcing (e.g. ciliary pumping). Phoretic slip flows generated from concentration or temperature gradients are examples of such local flow forcing. Autophoresis is currently receiving much attention for the design of self-propelled particles achieving force- and torque-free locomotion by combining two essential surface properties: (i) an activity that modifies the solute content of the particle's environment (e.g. catalytic reaction or solute release), and (ii) a mobility that generates a slip flow from the resulting local concentration gradients. Recent work showed that geometric asymmetry is sufficient for a chemically-homogeneous particle to self-propel. Here we extend this idea to micro-pumping in active channels whose walls possess both chemical activity and phoretic mobility. Using a combination of theoretical analysis and numerical simulations, we show that geometrically-asymmetric but chemically-homogeneous channels can generate pumping and analyze the resulting flow patterns.
Geometrical interpretation for the outer SU(3) outer multiplicity label
NASA Technical Reports Server (NTRS)
Draayer, Jerry P.; Troltenier, D.
1995-01-01
A geometrical interpretation for the outer multiplicity rho that occurs in a reduction of the product of two SU(3) representations, (lambda(sub pi), mu(sub pi)) x (lambda(sub nu), mu(sub nu)) approaches sigma(sub rho)(lambda, mu)(sub rho), is introduced. This coupling of proton (pi) and neutron (nu) representations arises, for example, in both boson and fermion descriptions of heavy deformed nuclei. Attributing a geometry to the coupling raises the possibility of introducing a simple interaction that provides a physically meaningful way for distinguishing multiple occurrences of (lambda, mu) values that can arise in such products.
Phenomenological description of phase inversion.
Piela, K; Ooms, G; Sengers, J V
2009-02-01
We propose an extended Ginzburg-Landau model for a description of the ambivalence region associated with the phenomenon of phase inversion observed in dispersed water-oil flow through a pipe. In analogy to the classical mean-field theory of phase transitions, it is shown that a good quantitative representation of the ambivalence region is obtained by using the injected phase volume fraction and a friction factor as the appropriate physical parameters.
Geometric optimization of thermal systems
NASA Astrophysics Data System (ADS)
Alebrahim, Asad Mansour
2000-10-01
The work in chapter 1 extends to three dimensions and to convective heat transfer the constructal method of minimizing the thermal resistance between a volume and one point. In the first part, the heat flow mechanism is conduction, and the heat generating volume is occupied by low conductivity material (k 0) and high conductivity inserts (kp) that are shaped as constant-thickness disks mounted on a common stem of kp material. In the second part the interstitial spaces once occupied by k0 material are bathed by forced convection. The internal and external geometric aspect ratios of the elemental volume and the first assembly are optimized numerically subject to volume constraints. Chapter 2 presents the constrained thermodynamic optimization of a cross-flow heat exchanger with ram air on the cold side, which is used in the environmental control systems of aircraft. Optimized geometric features such as the ratio of channel spacings and flow lengths are reported. It is found that the optimized features are relatively insensitive to changes in other physical parameters of the installation and relatively insensitive to the additional irreversibility due to discharging the ram-air stream into the atmosphere, emphasizing the robustness of the thermodynamic optimum. In chapter 3 the problem of maximizing exergy extraction from a hot stream by distributing streams over a heat transfer surface is studied. In the first part, the cold stream is compressed in an isothermal compressor, expanded in an adiabatic turbine, and discharged into the ambient. In the second part, the cold stream is compressed in an adiabatic compressor. Both designs are optimized with respect to the capacity-rate imbalance of the counter-flow and the pressure ratio maintained by the compressor. This study shows the tradeoff between simplicity and increased performance, and outlines the path for further conceptual work on the extraction of exergy from a hot stream that is being cooled gradually. The aim
Elastic scattering in geometrical model
NASA Astrophysics Data System (ADS)
Plebaniak, Zbigniew; Wibig, Tadeusz
2016-10-01
The experimental data on proton-proton elastic and inelastic scattering emerging from the measurements at the Large Hadron Collider, calls for an efficient model to fit the data. We have examined the optical, geometrical picture and we have found the simplest, linear dependence of this model parameters on the logarithm of the interaction energy with the significant change of the respective slopes at one point corresponding to the energy of about 300 GeV. The logarithmic dependence observed at high energies allows one to extrapolate the proton-proton elastic, total (and inelastic) cross sections to ultra high energies seen in cosmic rays events which makes a solid justification of the extrapolation to very high energy domain of cosmic rays and could help us to interpret the data from an astrophysical and a high energy physics point of view.
Geometrical setting of solid mechanics
Fiala, Zdenek
2011-08-15
Highlights: > Solid mechanics within the Riemannian symmetric manifold GL (3, R)/O (3, R). > Generalized logarithmic strain. > Consistent linearization. > Incremental principle of virtual power. > Time-discrete approximation. - Abstract: The starting point in the geometrical setting of solid mechanics is to represent deformation process of a solid body as a trajectory in a convenient space with Riemannian geometry, and then to use the corresponding tools for its analysis. Based on virtual power of internal stresses, we show that such a configuration space is the (globally) symmetric space of symmetric positive-definite real matrices. From this unifying point of view, we shall analyse the logarithmic strain, the stress rate, as well as linearization and intrinsic integration of corresponding evolution equation.
Geometrical characteristics of uniportal VATS
Rocco, Gaetano; Viti, Andrea; Terzi, Alberto
2013-01-01
In terms of accuracy and efficacy Uniportal Video-Assisted Thoracic Surgery (VATS) resections are comparable to standard VATS. In standard three-ports VATS, the geometric configuration of a parallelogram generates interference with the optical source, creating a plane with a torsion angle not favorable on the flat two-dimensional vision of currently available monitors. The potential advantages of single-port VATS approach include not only the one intercostal space incision (reduction of postoperative pain) but also a translational approach of VATS instruments along a sagittal plane. Accordingly, the Uniportal approach enables VATS instruments to draw two parallel lines on the plane, bringing them to approach the target lesion from a caudo-cranial perspective thus achieving a projective plane. As a consequence, taking advantage of the unique spatial features specific to uniportal VATS, the surgeon is enabled to bring the operative fulcrum inside the chest to address the target lesion in a fashion similar to open surgery. PMID:24040527
Dualities and geometrical invariants for static and spherically symmetric spacetimes
NASA Astrophysics Data System (ADS)
Seidel, Paola Terezinha; Cabral, Luís Antonio
2016-04-01
In this work, we consider spinless particles in curved spacetime and symmetries related to extended isometries. We search for solutions of a generalized Killing equation whose structure entails a general class of Killing tensors. The conserved quantities along particle’s geodesic are associated with a dual description of the spacetime metric. In the Hamiltonian formalism, some conserved quantities generate a dual description of the metric. The Killing tensors belonging to the conserved objects imply in a nontrivial class of dual metrics even for a Schwarzschild metric in the original spacetime. From these metrics, we construct geometrical invariants for classes of dual spacetimes to explore their singularity structure. A nontrivial singularity behavior is obtained in the dual sector.
Geometric solitons of Hamiltonian flows on manifolds
Song, Chong; Sun, Xiaowei; Wang, Youde
2013-12-15
It is well-known that the LIE (Locally Induction Equation) admit soliton-type solutions and same soliton solutions arise from different and apparently irrelevant physical models. By comparing the solitons of LIE and Killing magnetic geodesics, we observe that these solitons are essentially decided by two families of isometries of the domain and the target space, respectively. With this insight, we propose the new concept of geometric solitons of Hamiltonian flows on manifolds, such as geometric Schrödinger flows and KdV flows for maps. Moreover, we give several examples of geometric solitons of the Schrödinger flow and geometric KdV flow, including magnetic curves as geometric Schrödinger solitons and explicit geometric KdV solitons on surfaces of revolution.
Splitting homomorphisms and the Geometrization Conjecture
NASA Astrophysics Data System (ADS)
Myers, Robert
2000-09-01
This paper gives an algebraic conjecture which is shown to be equivalent to Thurston's Geometrization Conjecture for closed, orientable 3-manifolds. It generalizes the Stallings-Jaco theorem which established a similar result for the Poincaré Conjecture. The paper also gives two other algebraic conjectures; one is equivalent to the finite fundamental group case of the Geometrization Conjecture and the other is equivalent to the union of the Geometrization Conjecture and Thurston's Virtual Bundle Conjecture.
Geometric Mathematical Framework for Multibody System Dynamics
NASA Astrophysics Data System (ADS)
Terze, Zdravko; Vrdoljak, Milan; Zlatar, Dario
2010-09-01
The paper surveys geometric mathematical framework for computational modeling of multibody system dynamics. Starting with the configuration space of rigid body motion and analysis of it's Lie group structure, the elements of respective Lie algebra are addressed and basic relations pertinent to geometrical formulations of multibody system dynamics are surveyed. Dynamical model of multibody system on manifold introduced, along with the outline of geometric characteristics of holonomic and non-holonomic kinematical constraints.
NASA Astrophysics Data System (ADS)
Morrison, David R.; Ronen Plesser, M.
2015-09-01
For complete intersection Calabi-Yau manifolds in toric varieties, Gross and Haase-Zharkov have given a conjectural combinatorial description of the special Lagrangian torus fibrations whose existence was predicted by Strominger, Yau and Zaslow. We present a geometric version of this construction, generalizing an earlier conjecture of the first author.
A geometric approach to high resolution TVD schemes
NASA Technical Reports Server (NTRS)
Goodman, J. B.; Leveque, R. J.
1984-01-01
A geometric approach, similar to Van Leer's MUSCL schemes, is used to construct a second-order accurate generalization of Godunov's method for solving scalar conservation laws. By making suitable approximations, a scheme is obtained which is easy to implement and total variation diminishing. The entropy condition is also investigated from the standpoint of the spreading of rarefaction waves. Quantitative information is obtained for Godunov's method on the rate of spreading which explain the kinks in rarefaction waves often observed at the sonic point.
Phase-space networks of geometrically frustrated systems.
Han, Yilong
2009-11-01
We illustrate a network approach to the phase-space study by using two geometrical frustration models: antiferromagnet on triangular lattice and square ice. Their highly degenerated ground states are mapped as discrete networks such that the quantitative network analysis can be applied to phase-space studies. The resulting phase spaces share some comon features and establish a class of complex networks with unique Gaussian spectral densities. Although phase-space networks are heterogeneously connected, the systems are still ergodic due to the random Poisson processes. This network approach can be generalized to phase spaces of some other complex systems.
Phase-space networks of geometrically frustrated systems
NASA Astrophysics Data System (ADS)
Han, Yilong
2009-11-01
We illustrate a network approach to the phase-space study by using two geometrical frustration models: antiferromagnet on triangular lattice and square ice. Their highly degenerated ground states are mapped as discrete networks such that the quantitative network analysis can be applied to phase-space studies. The resulting phase spaces share some comon features and establish a class of complex networks with unique Gaussian spectral densities. Although phase-space networks are heterogeneously connected, the systems are still ergodic due to the random Poisson processes. This network approach can be generalized to phase spaces of some other complex systems.
Geometric, Kinematic and Radiometric Aspects of Image-Based Measurements
NASA Technical Reports Server (NTRS)
Liu, Tianshu
2002-01-01
This paper discusses theoretical foundations of quantitative image-based measurements for extracting and reconstructing geometric, kinematic and dynamic properties of observed objects. New results are obtained by using a combination of methods in perspective geometry, differential geometry. radiometry, kinematics and dynamics. Specific topics include perspective projection transformation. perspective developable conical surface, perspective projection under surface constraint, perspective invariants, the point correspondence problem. motion fields of curves and surfaces. and motion equations of image intensity. The methods given in this paper arc useful for determining morphology and motion fields of deformable bodies such as elastic bodies. viscoelastic mediums and fluids.
Gaussian geometric discord of two-mode systems in a thermal environment
Suciu, Serban Isar, Aurelian
2014-11-24
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the Gaussian geometric discord for a system consisting of two non-interacting non-resonant bosonic modes embedded in a thermal environment. We take as initial state of the system a two-mode squeezed thermal state and describe the time evolution of the Gaussian geometric discord under the influence of the thermal bath. By tracing the distance between the state of the considered subsystem and the closest classical-quantum Gaussian state we evaluate the Gaussian geometric discord for all times and temperatures. The geometric discord has finite values between 0 and 1 and decreases asymptotically to zero at large times and temperatures with oscillations on the time axis.
Geometric Reasoning in an Active-Engagement Upper-Division E&M Classroom
NASA Astrophysics Data System (ADS)
Cerny, Leonard Thomas
A combination of theoretical perspectives is used to create a rich description of student reasoning when facing a highly-geometric electricity and magnetism problem in an upper-division active-engagement physics classroom at Oregon State University. Geometric reasoning as students encounter problem situations ranging from familiar to novel is described using van Zee and Manogue's (2010) ethnography of communication. Bing's (2008) epistemic framing model is used to illuminate how students are framing what they are doing and whether or not they see the problem as geometric. Kuo, Hull, Gupta, and Elby's (2010) blending model and Krutetskii's (1976) model of harmonic reasoning are used to illuminate ways students show problem-solving expertise. Sayer and Wittmann's (2008) model is used to show how resource plasticity impacts students' geometric reasoning and the degree to which students accept incorrect results.
A geometric model of defensive peripersonal space.
Bufacchi, R J; Liang, M; Griffin, L D; Iannetti, G D
2016-01-01
Potentially harmful stimuli occurring within the defensive peripersonal space (DPPS), a protective area surrounding the body, elicit stronger defensive reactions. The spatial features of the DPPS are poorly defined and limited to descriptive estimates of its extent along a single dimension. Here we postulated a family of geometric models of the DPPS, to address two important questions with respect to its spatial features: What is its fine-grained topography? How does the nervous system represent the body area to be defended? As a measure of the DPPS, we used the strength of the defensive blink reflex elicited by electrical stimulation of the hand (hand-blink reflex, HBR), which is reliably modulated by the position of the stimulated hand in egocentric coordinates. We tested the goodness of fit of the postulated models to HBR data from six experiments in which we systematically explored the HBR modulation by hand position in both head-centered and body-centered coordinates. The best-fitting model indicated that 1) the nervous system's representation of the body area defended by the HBR can be approximated by a half-ellipsoid centered on the face and 2) the DPPS extending from this area has the shape of a bubble elongated along the vertical axis. Finally, the empirical observation that the HBR is modulated by hand position in head-centered coordinates indicates that the DPPS is anchored to the face. The modeling approach described in this article can be generalized to describe the spatial modulation of any defensive response. PMID:26510762
Geometric asymmetry driven Janus micromotors
NASA Astrophysics Data System (ADS)
Zhao, Guanjia; Pumera, Martin
2014-09-01
The production and application of nano-/micromotors is of great importance. In order for the motors to work, asymmetry in their chemical composition or physical geometry must be present if no external asymmetric field is applied. In this paper, we present a ``coconut'' micromotor made of platinum through the partial or complete etching of the silica templates. It was shown that although both the inner and outer surfaces are made of the same material (Pt), motion of the structure can be observed as the convex surface is capable of generating oxygen bubbles. This finding shows that not only the chemical asymmetry of the micromotor, but also its geometric asymmetry can lead to fast propulsion of the motor. Moreover, a considerably higher velocity can be seen for partially etched coconut structures than the velocities of Janus or fully etched, shell-like motors. These findings will have great importance on the design of future micromotors.The production and application of nano-/micromotors is of great importance. In order for the motors to work, asymmetry in their chemical composition or physical geometry must be present if no external asymmetric field is applied. In this paper, we present a ``coconut'' micromotor made of platinum through the partial or complete etching of the silica templates. It was shown that although both the inner and outer surfaces are made of the same material (Pt), motion of the structure can be observed as the convex surface is capable of generating oxygen bubbles. This finding shows that not only the chemical asymmetry of the micromotor, but also its geometric asymmetry can lead to fast propulsion of the motor. Moreover, a considerably higher velocity can be seen for partially etched coconut structures than the velocities of Janus or fully etched, shell-like motors. These findings will have great importance on the design of future micromotors. Electronic supplementary information (ESI) available: Additional SEM images, data analysis, Videos S
Geometric Quantization and Foliation Reduction
NASA Astrophysics Data System (ADS)
Skerritt, Paul
A standard question in the study of geometric quantization is whether symplectic reduction interacts nicely with the quantized theory, and in particular whether "quantization commutes with reduction." Guillemin and Sternberg first proposed this question, and answered it in the affirmative for the case of a free action of a compact Lie group on a compact Kahler manifold. Subsequent work has focused mainly on extending their proof to non-free actions and non-Kahler manifolds. For realistic physical examples, however, it is desirable to have a proof which also applies to non-compact symplectic manifolds. In this thesis we give a proof of the quantization-reduction problem for general symplectic manifolds. This is accomplished by working in a particular wavefunction representation, associated with a polarization that is in some sense compatible with reduction. While the polarized sections described by Guillemin and Sternberg are nonzero on a dense subset of the Kahler manifold, the ones considered here are distributional, having support only on regions of the phase space associated with certain quantized, or "admissible", values of momentum. We first propose a reduction procedure for the prequantum geometric structures that "covers" symplectic reduction, and demonstrate how both symplectic and prequantum reduction can be viewed as examples of foliation reduction. Consistency of prequantum reduction imposes the above-mentioned admissibility conditions on the quantized momenta, which can be seen as analogues of the Bohr-Wilson-Sommerfeld conditions for completely integrable systems. We then describe our reduction-compatible polarization, and demonstrate a one-to-one correspondence between polarized sections on the unreduced and reduced spaces. Finally, we describe a factorization of the reduced prequantum bundle, suggested by the structure of the underlying reduced symplectic manifold. This in turn induces a factorization of the space of polarized sections that agrees
Geometric reasoning about assembly tools
Wilson, R.H.
1997-01-01
Planning for assembly requires reasoning about various tools used by humans, robots, or other automation to manipulate, attach, and test parts and subassemblies. This paper presents a general framework to represent and reason about geometric accessibility issues for a wide variety of such assembly tools. Central to the framework is a use volume encoding a minimum space that must be free in an assembly state to apply a given tool, and placement constraints on where that volume must be placed relative to the parts on which the tool acts. Determining whether a tool can be applied in a given assembly state is then reduced to an instance of the FINDPLACE problem. In addition, the author presents more efficient methods to integrate the framework into assembly planning. For tools that are applied either before or after their target parts are mated, one method pre-processes a single tool application for all possible states of assembly of a product in polynomial time, reducing all later state-tool queries to evaluations of a simple expression. For tools applied after their target parts are mated, a complementary method guarantees polynomial-time assembly planning. The author presents a wide variety of tools that can be described adequately using the approach, and surveys tool catalogs to determine coverage of standard tools. Finally, the author describes an implementation of the approach in an assembly planning system and experiments with a library of over one hundred manual and robotic tools and several complex assemblies.
Geometric Reasoning for Automated Planning
NASA Technical Reports Server (NTRS)
Clement, Bradley J.; Knight, Russell L.; Broderick, Daniel
2012-01-01
An important aspect of mission planning for NASA s operation of the International Space Station is the allocation and management of space for supplies and equipment. The Stowage, Configuration Analysis, and Operations Planning teams collaborate to perform the bulk of that planning. A Geometric Reasoning Engine is developed in a way that can be shared by the teams to optimize item placement in the context of crew planning. The ISS crew spends (at the time of this writing) a third or more of their time moving supplies and equipment around. Better logistical support and optimized packing could make a significant impact on operational efficiency of the ISS. Currently, computational geometry and motion planning do not focus specifically on the optimized orientation and placement of 3D objects based on multiple distance and containment preferences and constraints. The software performs reasoning about the manipulation of 3D solid models in order to maximize an objective function based on distance. It optimizes for 3D orientation and placement. Spatial placement optimization is a general problem and can be applied to object packing or asset relocation.
Phenomenological modeling of geometric metasurfaces.
Ye, Weimin; Guo, Qinghua; Xiang, Yuanjiang; Fan, Dianyuan; Zhang, Shuang
2016-04-01
Metasurfaces, with their superior capability in manipulating the optical wavefront at the subwavelength scale and low manufacturing complexity, have shown great potential for planar photonics and novel optical devices. However, vector field simulation of metasurfaces is so far limited to periodic-structured metasurfaces containing a small number of meta-atoms in the unit cell by using full-wave numerical methods. Here, focusing on achiral meta-atoms only with electric polarizability and thickness far less than the wavelength of light, and ignoring the coupling between meta-atoms, we propose a general phenomenological method to analytically model the metasurfaces based on the assumption that the meta-atoms possess localized resonances with Lorentz-Drude forms, whose exact form can be retrieved from the full wave simulation of a single element. Applied to phase modulated geometric metasurfaces constituted by identical meta-atoms with different orientations, our analytical results show good agreement with full-wave numerical simulations. The proposed theory provides an efficient method to model and design optical devices based on metasurfaces.
Geometric morphology of cellular solids
Schlei, B. R.; Prasad, L.; Skourikhine, A. N.
2001-01-01
We demonstrate how to derive morphological information from micrographs, i.e., grey-level images, of polymeric foams. The segmentation of the images is performed by applying a pulse-coupled neural network. This processing generates blobs of the foams walls/struts and voids, respectively. The contours of the blobs and their corresponding points form the input to a constrained Delaunay tessellation, which provides an unstructured grid of the material under consideration. The subsequently applied Chordal Axis Transform captures the intrinsic shape characteristics, and facilitates the identification and localization of key morphological features. While stochastic features of the polymeric foams struts/walls such as areas, aspect ratios, etc., already can be computed at this stage, the foams voids require further geometric processing. The voids are separated into single foam cells. This shape manipulation leads to a refinement of the initial blob contours, which then requires the repeated application of the constrained Delaunay tessellation and Chordal Axis Transform, respectively. Using minimum enclosing rectangles for each foam cell, finally the stochastic features of the foam voids are computed.
Phenomenological modeling of geometric metasurfaces.
Ye, Weimin; Guo, Qinghua; Xiang, Yuanjiang; Fan, Dianyuan; Zhang, Shuang
2016-04-01
Metasurfaces, with their superior capability in manipulating the optical wavefront at the subwavelength scale and low manufacturing complexity, have shown great potential for planar photonics and novel optical devices. However, vector field simulation of metasurfaces is so far limited to periodic-structured metasurfaces containing a small number of meta-atoms in the unit cell by using full-wave numerical methods. Here, focusing on achiral meta-atoms only with electric polarizability and thickness far less than the wavelength of light, and ignoring the coupling between meta-atoms, we propose a general phenomenological method to analytically model the metasurfaces based on the assumption that the meta-atoms possess localized resonances with Lorentz-Drude forms, whose exact form can be retrieved from the full wave simulation of a single element. Applied to phase modulated geometric metasurfaces constituted by identical meta-atoms with different orientations, our analytical results show good agreement with full-wave numerical simulations. The proposed theory provides an efficient method to model and design optical devices based on metasurfaces. PMID:27137005
The geometric semantics of algebraic quantum mechanics.
Cruz Morales, John Alexander; Zilber, Boris
2015-08-01
In this paper, we will present an ongoing project that aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We argue that this approach provides a geometric semantics for such a formalism by means of establishing a (non-commutative) duality between certain algebraic and geometric objects.
Solving Absolute Value Equations Algebraically and Geometrically
ERIC Educational Resources Information Center
Shiyuan, Wei
2005-01-01
The way in which students can improve their comprehension by understanding the geometrical meaning of algebraic equations or solving algebraic equation geometrically is described. Students can experiment with the conditions of the absolute value equation presented, for an interesting way to form an overall understanding of the concept.
Early Sex Differences in Weighting Geometric Cues
ERIC Educational Resources Information Center
Lourenco, Stella F.; Addy, Dede; Huttenlocher, Janellen; Fabian, Lydia
2011-01-01
When geometric and non-geometric information are both available for specifying location, men have been shown to rely more heavily on geometry compared to women. To shed insight on the nature and developmental origins of this sex difference, we examined how 18- to 24-month-olds represented the geometry of a surrounding (rectangular) space when…
On geometric interpretation of the berry phase
NASA Astrophysics Data System (ADS)
Katanaev, M. O.
2012-03-01
A geometric interpretation of the Berry phase and its Wilczek-Zee non-Abelian generalization are given in terms of connections on principal fiber bundles. It is demonstrated that a principal fiber bundle can be trivial in all cases, while the connection and its holonomy group are nontrivial. Therefore, the main role is played by geometric rather than topological effects.
Parabolas: Connection between Algebraic and Geometrical Representations
ERIC Educational Resources Information Center
Shriki, Atara
2011-01-01
A parabola is an interesting curve. What makes it interesting at the secondary school level is the fact that this curve is presented in both its contexts: algebraic and geometric. Being one of Apollonius' conic sections, the parabola is basically a geometric entity. It is, however, typically known for its algebraic characteristics, in particular…
Second-quantized formulation of geometric phases
Deguchi, Shinichi; Fujikawa, Kazuo
2005-07-15
The level crossing problem and associated geometric terms are neatly formulated by the second-quantized formulation. This formulation exhibits a hidden local gauge symmetry related to the arbitrariness of the phase choice of the complete orthonormal basis set. By using this second-quantized formulation, which does not assume adiabatic approximation, a convenient exact formula for the geometric terms including off-diagonal geometric terms is derived. The analysis of geometric phases is then reduced to a simple diagonalization of the Hamiltonian, and it is analyzed both in the operator and path-integral formulations. If one diagonalizes the geometric terms in the infinitesimal neighborhood of level crossing, the geometric phases become trivial (and thus no monopole singularity) for arbitrarily large but finite time interval T. The integrability of Schroedinger equation and the appearance of the seemingly nonintegrable phases are thus consistent. The topological proof of the Longuet-Higgins' phase-change rule, for example, fails in the practical Born-Oppenheimer approximation where a large but finite ratio of two time scales is involved and T is identified with the period of the slower system. The difference and similarity between the geometric phases associated with level crossing and the exact topological object such as the Aharonov-Bohm phase become clear in the present formulation. A crucial difference between the quantum anomaly and the geometric phases is also noted.
NASA Astrophysics Data System (ADS)
Duerr, Fabian; Meuret, Youri; Thienpont, Hugo
2010-05-01
Scaling down the dimensions of concentrating photovoltaic systems based on plane Fresnel lenses has several promising advantages. By conserving a designed concentration ratio and reducing the aperture size of the lens, the working distance decreases as well. This provides thinner modules and the dimensions of the used solar cells can be scaled down to the millimeter range. An important benefit of this miniaturization process is the avoidance of technically demanding cooling. In this work the design of a plane Fresnel lens is introduced and the basic limitations concerning the achievable concentration ratio are investigated based on geometrical optics. However, accompanied by the down scaling of the prism dimensions, pure ray tracing based on the geometrical optics approximation may no longer be valid for the determination of the concentration ratio. In terms of micro-structured Fresnel lenses for solar concentration, only a qualitative description of this limit - typically a rule of thumb - is provided in the literature. For this reason a quantitative investigation of the influence of the prisms' down scaling and thus the appearing wave optical effects on the obtained concentration ratio is presented. In a final step the introduced monochromatic investigations are extended to a polychromatic analysis. This allows for the prediction of the influence of miniaturization on the effective concentration ratio for a given spectrum and thus the adequate size of the receiver. A better quantitative understanding of the impact of diffraction in micro-structured Fresnel lenses might help to optimize the design of several applications in nonimaging optics.
Watson, Roger
2015-04-01
This article describes the basic tenets of quantitative research. The concepts of dependent and independent variables are addressed and the concept of measurement and its associated issues, such as error, reliability and validity, are explored. Experiments and surveys – the principal research designs in quantitative research – are described and key features explained. The importance of the double-blind randomised controlled trial is emphasised, alongside the importance of longitudinal surveys, as opposed to cross-sectional surveys. Essential features of data storage are covered, with an emphasis on safe, anonymous storage. Finally, the article explores the analysis of quantitative data, considering what may be analysed and the main uses of statistics in analysis.
Students' Geometrical Perception on a Task-Based Dynamic Geometry Platform
ERIC Educational Resources Information Center
Leung, Allen; Lee, Arthur Man Sang
2013-01-01
This paper describes a task-based dynamic geometry platform that is able to record student responses in a collective fashion to pre-designed dragging tasks. The platform provides a new type of data and opens up a quantitative dimension to interpret students' geometrical perception in dynamic geometry environments. The platform is capable of…
Testing the geometric clutch hypothesis.
Lindemann, Charles B
2004-12-01
The Geometric Clutch hypothesis is based on the premise that transverse forces (t-forces) acting on the outer doublets of the eukaryotic axoneme coordinate the action of the dynein motors to produce flagellar and ciliary beating. T-forces result from tension and compression on the outer doublets when a bend is present on the flagellum or cilium. The t-force acts to pry the doublets apart in an active bend, and push the doublets together when the flagellum is passively bent and thus could engage and disengage the dynein motors. Computed simulations of this working mechanism have reproduced the beating pattern of simple cilia and flagella, and of mammalian sperm. Cilia-like beating, with a clearly defined effective and recovery stroke, can be generated using one uniformly applied switching algorithm. When the mechanical properties and dimensions appropriate to a specific flagellum are incorporated into the model the same algorithm can simulate a sea urchin or bull sperm-like beat. The computed model reproduces many of the observed behaviors of real flagella and cilia. The model can duplicate the results of outer arm extraction experiments in cilia and predicted two types of arrest behavior that were verified experimentally in bull sperm. It also successfully predicted the experimentally determined nexin elasticity. Calculations based on live and reactivated sea urchin and bull sperm yielded a value of 0.5 nN/microm for the t-force at the switch-point. This is a force sufficient to overcome the shearing force generated by all the dyneins on one micron of outer doublet. A t-force of this magnitude should produce substantial distortion of the axoneme at the switch-point, especially in spoke or spoke-head deficient motile flagella. This concrete and verifiable prediction is within the grasp of recent advances in imaging technology, specifically cryoelectron microscopy and atomic force microscopy. PMID:15567522
Mobility in geometrically confined membranes
Domanov, Yegor A.; Aimon, Sophie; Toombes, Gilman E. S.; Renner, Marianne; Quemeneur, François; Triller, Antoine; Turner, Matthew S.; Bassereau, Patricia
2011-01-01
Lipid and protein lateral mobility is essential for biological function. Our theoretical understanding of this mobility can be traced to the seminal work of Saffman and Delbrück, who predicted a logarithmic dependence of the protein diffusion coefficient (i) on the inverse of the size of the protein and (ii) on the “membrane size” for membranes of finite size [Saffman P, Delbrück M (1975) Proc Natl Acad Sci USA 72:3111—3113]. Although the experimental proof of the first prediction is a matter of debate, the second has not previously been thought to be experimentally accessible. Here, we construct just such a geometrically confined membrane by forming lipid bilayer nanotubes of controlled radii connected to giant liposomes. We followed the diffusion of individual molecules in the tubular membrane using single particle tracking of quantum dots coupled to lipids or voltage-gated potassium channels KvAP, while changing the membrane tube radius from approximately 250 to 10 nm. We found that both lipid and protein diffusion was slower in tubular membranes with smaller radii. The protein diffusion coefficient decreased as much as 5-fold compared to diffusion on the effectively flat membrane of the giant liposomes. Both lipid and protein diffusion data are consistent with the predictions of a hydrodynamic theory that extends the work of Saffman and Delbrück to cylindrical geometries. This study therefore provides strong experimental support for the ubiquitous Saffman–Delbrück theory and elucidates the role of membrane geometry and size in regulating lateral diffusion. PMID:21768336
Geometric metastability, quivers and holography
Aganagic, Mina; Aganagic, Mina; Beem, Christopher; Freivogel, Ben
2007-09-06
We use large N duality to study brane/anti-brane configurations on a class of Calabi-Yau manifolds. With only branes present, the Calabi-Yau manifolds in question give rise to N=2 ADE quiver theories deformed by superpotential terms. We show that the large N duality conjecture of hep-th/0610249 reproduces correctly the known qualitative features of the brane/anti-brane physics. In the supersymmetric case, the gauge theories have Seiberg dualities which are represented as flops in the geometry. Moreover, the holographic dual geometry encodes the whole RG flow of the gauge theory. In the non-supersymmetric case, the large N duality predicts that the brane/anti-brane theories also enjoy such dualities, and allows one to pick out the good description at a given energy scale.
ERIC Educational Resources Information Center
DuBridge, Lee A.
An appeal for more research to determine how to educate children as effectively as possible is made. Mathematics teachers can readily examine the educational problems of today in their classrooms since learning progress in mathematics can easily be measured and evaluated. Since mathematics teachers have learned to think in quantitative terms and…
Abstract: In toxicology, the role of quantitative assessment of brain morphology can be understood in the context of two types of treatment-related alterations. One type of alteration is specifically associated with treatment and is not observed in control animals. Measurement ...
On geometric factors for neutral particle analyzers.
Stagner, L; Heidbrink, W W
2014-11-01
Neutral particle analyzers (NPA) detect neutralized energetic particles that escape from plasmas. Geometric factors relate the counting rate of the detectors to the intensity of the particle source. Accurate geometric factors enable quick simulation of geometric effects without the need to resort to slower Monte Carlo methods. Previously derived expressions [G. R. Thomas and D. M. Willis, "Analytical derivation of the geometric factor of a particle detector having circular or rectangular geometry," J. Phys. E: Sci. Instrum. 5(3), 260 (1972); J. D. Sullivan, "Geometric factor and directional response of single and multi-element particle telescopes," Nucl. Instrum. Methods 95(1), 5-11 (1971)] for the geometric factor implicitly assume that the particle source is very far away from the detector (far-field); this excludes applications close to the detector (near-field). The far-field assumption does not hold in most fusion applications of NPA detectors. We derive, from probability theory, a generalized framework for deriving geometric factors that are valid for both near and far-field applications as well as for non-isotropic sources and nonlinear particle trajectories.
On geometric factors for neutral particle analyzers
Stagner, L.; Heidbrink, W. W.
2014-11-15
Neutral particle analyzers (NPA) detect neutralized energetic particles that escape from plasmas. Geometric factors relate the counting rate of the detectors to the intensity of the particle source. Accurate geometric factors enable quick simulation of geometric effects without the need to resort to slower Monte Carlo methods. Previously derived expressions [G. R. Thomas and D. M. Willis, “Analytical derivation of the geometric factor of a particle detector having circular or rectangular geometry,” J. Phys. E: Sci. Instrum. 5(3), 260 (1972); J. D. Sullivan, “Geometric factor and directional response of single and multi-element particle telescopes,” Nucl. Instrum. Methods 95(1), 5–11 (1971)] for the geometric factor implicitly assume that the particle source is very far away from the detector (far-field); this excludes applications close to the detector (near-field). The far-field assumption does not hold in most fusion applications of NPA detectors. We derive, from probability theory, a generalized framework for deriving geometric factors that are valid for both near and far-field applications as well as for non-isotropic sources and nonlinear particle trajectories.
Conceptual aspects of geometric quantum computation
NASA Astrophysics Data System (ADS)
Sjöqvist, Erik; Azimi Mousolou, Vahid; Canali, Carlo M.
2016-07-01
Geometric quantum computation is the idea that geometric phases can be used to implement quantum gates, i.e., the basic elements of the Boolean network that forms a quantum computer. Although originally thought to be limited to adiabatic evolution, controlled by slowly changing parameters, this form of quantum computation can as well be realized at high speed by using nonadiabatic schemes. Recent advances in quantum gate technology have allowed for experimental demonstrations of different types of geometric gates in adiabatic and nonadiabatic evolution. Here, we address some conceptual issues that arise in the realizations of geometric gates. We examine the appearance of dynamical phases in quantum evolution and point out that not all dynamical phases need to be compensated for in geometric quantum computation. We delineate the relation between Abelian and non-Abelian geometric gates and find an explicit physical example where the two types of gates coincide. We identify differences and similarities between adiabatic and nonadiabatic realizations of quantum computation based on non-Abelian geometric phases.
Conceptual aspects of geometric quantum computation
NASA Astrophysics Data System (ADS)
Sjöqvist, Erik; Azimi Mousolou, Vahid; Canali, Carlo M.
2016-10-01
Geometric quantum computation is the idea that geometric phases can be used to implement quantum gates, i.e., the basic elements of the Boolean network that forms a quantum computer. Although originally thought to be limited to adiabatic evolution, controlled by slowly changing parameters, this form of quantum computation can as well be realized at high speed by using nonadiabatic schemes. Recent advances in quantum gate technology have allowed for experimental demonstrations of different types of geometric gates in adiabatic and nonadiabatic evolution. Here, we address some conceptual issues that arise in the realizations of geometric gates. We examine the appearance of dynamical phases in quantum evolution and point out that not all dynamical phases need to be compensated for in geometric quantum computation. We delineate the relation between Abelian and non-Abelian geometric gates and find an explicit physical example where the two types of gates coincide. We identify differences and similarities between adiabatic and nonadiabatic realizations of quantum computation based on non-Abelian geometric phases.
Geometric quantum discord under noisy environment
NASA Astrophysics Data System (ADS)
Huang, Zhiming; Qiu, Daowen
2016-05-01
In this work, we mainly analyze the dynamics of geometric quantum discord under a common dissipating environment. Our results indicate that geometric quantum discord is generated when the initial state is a product state. The geometric quantum discord increases from zero to a stable value with the increasing time, and the variations of stable values depend on the system size. For different initial product states, geometric quantum discord has some different behaviors in contrast with entanglement. For initial maximally entangled state, it is shown that geometric quantum discord decays with the increasing dissipated time. It is found that for EPR state, entanglement is more robust than geometric quantum discord, which is a sharp contrast to the existing result that quantum discord is more robust than entanglement in noisy environments. However, for GHZ state and W state, geometric quantum discord is more stable than entanglement. By the comparison of quantum discord and entanglement, we find that a common dissipating environment brings complicated effects on quantum correlation, which may deepen our understanding of physical impacts of decohering environment on quantum correlation. In the end, we analyze the effects of collective dephasing noise and rotating noise to a class of two-qubit X states, and we find that quantum correlation is not altered by the collective noises.
On geometric factors for neutral particle analyzers
NASA Astrophysics Data System (ADS)
Stagner, L.; Heidbrink, W. W.
2014-11-01
Neutral particle analyzers (NPA) detect neutralized energetic particles that escape from plasmas. Geometric factors relate the counting rate of the detectors to the intensity of the particle source. Accurate geometric factors enable quick simulation of geometric effects without the need to resort to slower Monte Carlo methods. Previously derived expressions [G. R. Thomas and D. M. Willis, "Analytical derivation of the geometric factor of a particle detector having circular or rectangular geometry," J. Phys. E: Sci. Instrum. 5(3), 260 (1972); J. D. Sullivan, "Geometric factor and directional response of single and multi-element particle telescopes," Nucl. Instrum. Methods 95(1), 5-11 (1971)] for the geometric factor implicitly assume that the particle source is very far away from the detector (far-field); this excludes applications close to the detector (near-field). The far-field assumption does not hold in most fusion applications of NPA detectors. We derive, from probability theory, a generalized framework for deriving geometric factors that are valid for both near and far-field applications as well as for non-isotropic sources and nonlinear particle trajectories.
Numerical procedure to determine geometric view factors for surfaces occluded by cylinders
NASA Technical Reports Server (NTRS)
Sawyer, P. L.
1978-01-01
A numerical procedure was developed to determine geometric view factors between connected infinite strips occluded by any number of infinite circular cylinders. The procedure requires a two-dimensional cross-sectional model of the configuration of interest. The two-dimensional model consists of a convex polygon enclosing any number of circles. Each side of the polygon represents one strip, and each circle represents a circular cylinder. A description and listing of a computer program based on this procedure are included in this report. The program calculates geometric view factors between individual strips and between individual strips and the collection of occluding cylinders.
Stereo Orthogonal Axonometric Perspective for the Teaching of Descriptive Geometry
ERIC Educational Resources Information Center
Méxas, José Geraldo Franco; Guedes, Karla Bastos; Tavares, Ronaldo da Silva
2015-01-01
Purpose: The purpose of this paper is to present the development of a software for stereo visualization of geometric solids, applied to the teaching/learning of Descriptive Geometry. Design/methodology/approach: The paper presents the traditional method commonly used in computer graphic stereoscopic vision (implemented in C language) and the…
The perception of geometrical structure from congruence
NASA Technical Reports Server (NTRS)
Lappin, Joseph S.; Wason, Thomas D.
1989-01-01
The principle function of vision is to measure the environment. As demonstrated by the coordination of motor actions with the positions and trajectories of moving objects in cluttered environments and by rapid recognition of solid objects in varying contexts from changing perspectives, vision provides real-time information about the geometrical structure and location of environmental objects and events. The geometric information provided by 2-D spatial displays is examined. It is proposed that the geometry of this information is best understood not within the traditional framework of perspective trigonometry, but in terms of the structure of qualitative relations defined by congruences among intrinsic geometric relations in images of surfaces. The basic concepts of this geometrical theory are outlined.
The geometric phase in nonlinear dissipative systems
Ning, C.Z.; Haken, H. )
1992-10-30
In this paper, the authors review the recent progress made in generalizing the concept of the geometric phase to nonlinear dissipative systems. The authors first illustrate the usual form of the parallel transport law with an elementary example of the parallel shift of a line on the complex plane. Important results about the non-adiabatical geometric (Aharonov and Anandan or AA) phase [sup 18] for the Schrodinger equations are reviewed in order to make a comparison with results for dissipative systems. The authors show that a geometric phase can be defined for dissipative systems with the cyclic attractors. Systems undergoing the Hopf bifurcation with a continuous symmetry are shown to possess such cyclic attractors. Examples from laser physics are discussed to exhibit the applicability of our formalism and the widespread existence of the geometric phase in dissipative systems.
Geometric phases in discrete dynamical systems
NASA Astrophysics Data System (ADS)
Cartwright, Julyan H. E.; Piro, Nicolas; Piro, Oreste; Tuval, Idan
2016-10-01
In order to study the behaviour of discrete dynamical systems under adiabatic cyclic variations of their parameters, we consider discrete versions of adiabatically-rotated rotators. Parallelling the studies in continuous systems, we generalize the concept of geometric phase to discrete dynamics and investigate its presence in these rotators. For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number of the system. For the discrete version of the rotated rotator considered by Berry, the rotated standard map, we further explore this connection as well as the role of the geometric phase at the onset of chaos. Further into the chaotic regime, we show that the geometric phase is also related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent.
Geometric symmetries in superfluid vortex dynamics
Kozik, Evgeny; Svistunov, Boris
2010-10-01
Dynamics of quantized vortex lines in a superfluid feature symmetries associated with the geometric character of the complex-valued field, w(z)=x(z)+iy(z), describing the instant shape of the line. Along with a natural set of Noether's constants of motion, which - apart from their rather specific expressions in terms of w(z) - are nothing but components of the total linear and angular momenta of the fluid, the geometric symmetry brings about crucial consequences for kinetics of distortion waves on the vortex lines, the Kelvin waves. It is the geometric symmetry that renders Kelvin-wave cascade local in the wave-number space. Similar considerations apply to other systems with purely geometric degrees of freedom.
The Pentagon Problem: Geometric Reasoning with Technology.
ERIC Educational Resources Information Center
Zbiek, Rose Mary
1996-01-01
Presents an activity, involving pentagons and using a figure manipulator such as The Geometer's Sketchpad, that requires students to reason geometrically without making unsubstantiated assumptions based on diagrams. (MKR)
Quantitative Literacy: Geosciences and Beyond
NASA Astrophysics Data System (ADS)
Richardson, R. M.; McCallum, W. G.
2002-12-01
Quantitative literacy seems like such a natural for the geosciences, right? The field has gone from its origin as a largely descriptive discipline to one where it is hard to imagine failing to bring a full range of mathematical tools to the solution of geological problems. Although there are many definitions of quantitative literacy, we have proposed one that is analogous to the UNESCO definition of conventional literacy: "A quantitatively literate person is one who, with understanding, can both read and represent quantitative information arising in his or her everyday life." Central to this definition is the concept that a curriculum for quantitative literacy must go beyond the basic ability to "read and write" mathematics and develop conceptual understanding. It is also critical that a curriculum for quantitative literacy be engaged with a context, be it everyday life, humanities, geoscience or other sciences, business, engineering, or technology. Thus, our definition works both within and outside the sciences. What role do geoscience faculty have in helping students become quantitatively literate? Is it our role, or that of the mathematicians? How does quantitative literacy vary between different scientific and engineering fields? Or between science and nonscience fields? We will argue that successful quantitative literacy curricula must be an across-the-curriculum responsibility. We will share examples of how quantitative literacy can be developed within a geoscience curriculum, beginning with introductory classes for nonmajors (using the Mauna Loa CO2 data set) through graduate courses in inverse theory (using singular value decomposition). We will highlight six approaches to across-the curriculum efforts from national models: collaboration between mathematics and other faculty; gateway testing; intensive instructional support; workshops for nonmathematics faculty; quantitative reasoning requirement; and individual initiative by nonmathematics faculty.
Machine Learning and Geometric Technique for SLAM
NASA Astrophysics Data System (ADS)
Bernal-Marin, Miguel; Bayro-Corrochano, Eduardo
This paper describes a new approach for building 3D geometric maps using a laser rangefinder, a stereo camera system and a mathematical system the Conformal Geometric Algebra. The use of a known visual landmarks in the map helps to carry out a good localization of the robot. A machine learning technique is used for recognition of objects in the environment. These landmarks are found using the Viola and Jones algorithm and are represented with their position in the 3D virtual map.
Geometrical expression of excess entropy production.
Sagawa, Takahiro; Hayakawa, Hisao
2011-11-01
We derive a geometrical expression of the excess entropy production for quasistatic transitions between nonequilibrium steady states of Markovian jump processes, which can be exactly applied to nonlinear and nonequilibrium situations. The obtained expression is geometrical; the excess entropy production depends only on a trajectory in the parameter space, analogous to the Berry phase in quantum mechanics. Our results imply that vector potentials are needed to construct the thermodynamics of nonequilibrium steady states. PMID:22181372
The Geometric Grids of the Hieratic Numeral.
NASA Astrophysics Data System (ADS)
Aboulfotouh, Hossam M. K.
The paper discusses the geometrical designs of the hieratic numeral signs. It shows the regular-grid-patterns of squares upon which, the shapes of the already decoded hieratic numeral-signs, have been designed. Also, it shows the design of some hieratic numeral signs, based on subdividing the circle; and the hieratic signs of modular notation. It might reveal the basic geometrical level of understanding of anonymous ancient Egyptians who designed them some four thousand years ago.
NASA Technical Reports Server (NTRS)
Parse, Joseph B.; Wert, J. A.
1991-01-01
Inhomogeneities in the spatial distribution of second phase particles in engineering materials are known to affect certain mechanical properties. Progress in this area has been hampered by the lack of a convenient method for quantitative description of the spatial distribution of the second phase. This study intends to develop a broadly applicable method for the quantitative analysis and description of the spatial distribution of second phase particles. The method was designed to operate on a desktop computer. The Dirichlet tessellation technique (geometrical method for dividing an area containing an array of points into a set of polygons uniquely associated with the individual particles) was selected as the basis of an analysis technique implemented on a PC. This technique is being applied to the production of Al sheet by PM processing methods; vacuum hot pressing, forging, and rolling. The effect of varying hot working parameters on the spatial distribution of aluminum oxide particles in consolidated sheet is being studied. Changes in distributions of properties such as through-thickness near-neighbor distance correlate with hot-working reduction.
Acquisition of teleological descriptions
NASA Astrophysics Data System (ADS)
Franke, David W.
1992-03-01
Teleology descriptions capture the purpose of an entity, mechanism, or activity with which they are associated. These descriptions can be used in explanation, diagnosis, and design reuse. We describe a technique for acquiring teleological descriptions expressed in the teleology language TeD. Acquisition occurs during design by observing design modifications and design verification. We demonstrate the acquisition technique in an electronic circuit design.
Schaffner, M
1990-01-01
The skill of writing job descriptions begins with an understanding of the advantages, as well as the basic elements, of a well written description. The end result should be approved and updated as needed. Having a better understanding of this process makes writing the job description a challenge rather than a chore.
Determining Geometrically Stable Domains in Molecular Conformation Sets.
Romanowska, Julia; Nowiński, Krzysztof S; Trylska, Joanna
2012-08-14
Detecting significant conformational changes occurring in biomolecules is a challenging task, especially when considering tens to hundreds of thousands of conformations. Conformational variability can be described by dividing a biomolecule into dynamic domains, i.e., by finding compact fragments that move as coherent units. Typical approaches, based on calculating a dynamical cross-correlation matrix, are limited by their inability to reveal correlated rotations and anticorrelated motions. We propose a geometric approach for finding dynamic domains, where we compare traces of atomic movements in a pairwise manner, and search for their best superposition. A quaternion representation of rotation is used to simplify the complex calculations. The algorithm was implemented in a Java graphical program: Geometrically Stable Substructures (GeoStaS). The program processes PDB and DCD binary files with large structural sets for proteins, nucleic acids, and their complexes. We demonstrate its efficiency in analyzing (a) ensembles of structures generated by NMR experiments and (b) conformation sets from biomolecular simulations, such as molecular dynamics. The results provide a clear description of the molecular movements even for large biomolecules. Compared to a standard dynamic cross-correlation matrix, our algorithm detects the correlations in both translational and rotational motions. PMID:26592104
Rational and efficient geometric definition of pharmacophores is essential for the patent process.
Guérin, Georges-Alexandre; Pratuangdejkul, Jaturong; Alemany, Monica; Launay, Jean-Marie; Manivet, Philippe
2006-11-01
The geometric description of pharmacophores suffers from approximations. No consensus has been clearly established, despite the increasing interest in using pharmacophores in drug design and in patent applications. We therefore propose an original definition of a pharmacophore using spherical coordinates. These coordinates give a precise description of each point using three parameters: distance to a geometric origin and two angles. If necessary, these parameters can be easily and rapidly converted to cartesian coordinates. Our method can guarantee, to the patent applicant, the safe protection of his intellectual property by both improving markedly the readability of a pharmacophore definition and bringing, to the person who is skilled in the art, enough information to understand easily the essence of the invention. PMID:17055408
Introduction to Dynamical Systems and Geometric Mechanics
NASA Astrophysics Data System (ADS)
Maruskin, Jared M.
2012-01-01
Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean space, whereas geometric mechanics explores similar systems that instead evolve on differentiable manifolds. In the study of geometric mechanics, however, additional geometric structures are often present, since such systems arise from the laws of nature that govern the motions of particles, bodies, and even galaxies. In the first part of the text, we discuss linearization and stability of trajectories and fixed points, invariant manifold theory, periodic orbits, PoincarÃ© maps, Floquet theory, the PoincarÃ©-Bendixson theorem, bifurcations, and chaos. The second part of the text begins with a self-contained chapter on differential geometry that introduces notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and differential forms. The final chapters cover Lagrangian and Hamiltonian mechanics from a modern geometric perspective, mechanics on Lie groups, and nonholonomic mechanics via both moving frames and fiber bundle decompositions. The text can be reasonably digested in a single-semester introductory graduate-level course. Each chapter concludes with an application that can serve as a springboard project for further investigation or in-class discussion.
Unifying Geometrical Representations of Gauge Theory
NASA Astrophysics Data System (ADS)
Alsid, Scott; Serna, Mario
2015-01-01
We unify three approaches within the vast body of gauge-theory research that have independently developed distinct representations of a geometrical surface-like structure underlying the vector-potential. The three approaches that we unify are: those who use the compactified dimensions of Kaluza-Klein theory, those who use Grassmannian models (also called gauge theory embedding or models) to represent gauge fields, and those who use a hidden spatial metric to replace the gauge fields. In this paper we identify a correspondence between the geometrical representations of the three schools. Each school was mostly independently developed, does not compete with other schools, and attempts to isolate the gauge-invariant geometrical surface-like structures that are responsible for the resulting physics. By providing a mapping between geometrical representations, we hope physicists can now isolate representation-dependent physics from gauge-invariant physical results and share results between each school. We provide visual examples of the geometrical relationships between each school for electric and magnetic fields. We highlight a first new result: in all three representations a static electric field (electric field from a fixed ring of charge or a sphere of charge) has a hidden gauge-invariant time dependent surface that is underlying the vector potential.
Geometric estimation method for x-ray digital intraoral tomosynthesis
NASA Astrophysics Data System (ADS)
Li, Liang; Yang, Yao; Chen, Zhiqiang
2016-06-01
It is essential for accurate image reconstruction to obtain a set of parameters that describes the x-ray scanning geometry. A geometric estimation method is presented for x-ray digital intraoral tomosynthesis (DIT) in which the detector remains stationary while the x-ray source rotates. The main idea is to estimate the three-dimensional (3-D) coordinates of each shot position using at least two small opaque balls adhering to the detector surface as the positioning markers. From the radiographs containing these balls, the position of each x-ray focal spot can be calculated independently relative to the detector center no matter what kind of scanning trajectory is used. A 3-D phantom which roughly simulates DIT was designed to evaluate the performance of this method both quantitatively and qualitatively in the sense of mean square error and structural similarity. Results are also presented for real data acquired with a DIT experimental system. These results prove the validity of this geometric estimation method.
NASA Astrophysics Data System (ADS)
Goswami, Himangshu Prabal; Agarwalla, Bijay Kumar; Harbola, Upendra
2016-05-01
Cyclic Pancharatnam-Berry (PB) and adiabatic noncyclic geometric (ANG) effects are investigated in a single electron orbital system connected to two metal contacts with externally driven chemical potential and/or temperatures. The PB contribution doesn't affect the density matrix evolution, but has a quantitative effect on the statistics (fluctuations) of electron transfer. The ANG contribution, on the other hand, affects the net flux across the junction. Unlike the PB, the ANG contribution is nonzero when two parameters are identically driven. Closed analytical expressions are derived for the ANG contribution to the flux, and the PB contribution to the first two leading order fluctuations. Fluctuations can be modified by manipulating the relative phases of the drivings. Interestingly, we find that the fluctuations of the pumped charge do not satisfy the steady state fluctuation theorem in presence of nonzero geometric contribution, but can be recovered for a vanishing geometric contribution even in presence of the external driving.
Overview on METEOSAT geometrical image data processing
NASA Technical Reports Server (NTRS)
Diekmann, Frank J.
1994-01-01
Digital Images acquired from the geostationary METEOSAT satellites are processed and disseminated at ESA's European Space Operations Centre in Darmstadt, Germany. Their scientific value is mainly dependent on their radiometric quality and geometric stability. This paper will give an overview on the image processing activities performed at ESOC, concentrating on the geometrical restoration and quality evaluation. The performance of the rectification process for the various satellites over the past years will be presented and the impacts of external events as for instance the Pinatubo eruption in 1991 will be explained. Special developments both in hard and software, necessary to cope with demanding tasks as new image resampling or to correct for spacecraft anomalies, are presented as well. The rotating lens of MET-5 causing severe geometrical image distortions is an example for the latter.
The Geometric Phase of Stock Trading.
Altafini, Claudio
2016-01-01
Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time systems, and even when the cycles in shape space have zero area. A context in which this principle can be applied is stock trading. A zero-area cycle in shape space represents the type of trading operations normally carried out by high-frequency traders (entering and exiting a position on a fast time-scale), while the phase variable represents the cash balance of a trader. Under the assumption that trading impacts stock prices, even zero-area cyclic trading operations can induce geometric phases, i.e., profits or losses, without affecting the stock quote. PMID:27556642
The Geometric Phase of Stock Trading
2016-01-01
Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time systems, and even when the cycles in shape space have zero area. A context in which this principle can be applied is stock trading. A zero-area cycle in shape space represents the type of trading operations normally carried out by high-frequency traders (entering and exiting a position on a fast time-scale), while the phase variable represents the cash balance of a trader. Under the assumption that trading impacts stock prices, even zero-area cyclic trading operations can induce geometric phases, i.e., profits or losses, without affecting the stock quote. PMID:27556642
Connexions for the nuclear geometrical collective model
NASA Astrophysics Data System (ADS)
Rosensteel, G.; Sparks, N.
2015-11-01
The Bohr-Mottelson-Frankfurt model of nuclear rotations and quadrupole vibrations is a foundational model in nuclear structure physics. The model, also called the geometrical collective model or simply GCM(3), has two hidden mathematical structures, one group theoretic and the other differential geometric. Although the group structure has been understood for some time, the geometric structure is a new feature that this paper investigates in some detail. Using the de Rham Laplacian \\triangle =\\star d \\star d for the kinetic energy extends significantly the physical scope of the GCM(3) model. This Laplacian contains a ‘magnetic’ term due to the connexion between base manifold rotational and fibre vortex degrees of freedom. When the connexion specializes to irrotational flow, the Laplacian reduces to the Bohr-Mottelson kinetic energy operator.
Geometric spin echo under zero field
NASA Astrophysics Data System (ADS)
Sekiguchi, Yuhei; Komura, Yusuke; Mishima, Shota; Tanaka, Touta; Niikura, Naeko; Kosaka, Hideo
2016-05-01
Spin echo is a fundamental tool for quantum registers and biomedical imaging. It is believed that a strong magnetic field is needed for the spin echo to provide long memory and high resolution, since a degenerate spin cannot be controlled or addressed under a zero magnetic field. While a degenerate spin is never subject to dynamic control, it is still subject to geometric control. Here we show the spin echo of a degenerate spin subsystem, which is geometrically controlled via a mediating state split by the crystal field, in a nitrogen vacancy centre in diamond. The demonstration reveals that the degenerate spin is protected by inherent symmetry breaking called zero-field splitting. The geometric spin echo under zero field provides an ideal way to maintain the coherence without any dynamics, thus opening the way to pseudo-static quantum random access memory and non-invasive biosensors.
The geometric phase controls ultracold chemistry
Kendrick, B. K.; Hazra, Jisha; Balakrishnan, N.
2015-07-30
In this study, the geometric phase is shown to control the outcome of an ultracold chemical reaction. The control is a direct consequence of the sign change on the interference term between two scattering pathways (direct and looping), which contribute to the reactive collision process in the presence of a conical intersection (point of degeneracy between two Born–Oppenheimer electronic potential energy surfaces). The unique properties of the ultracold energy regime lead to an effective quantization of the scattering phase shift enabling maximum constructive or destructive interference between the two pathways. By taking the O + OH → H + O_{2} reaction as an illustrative example, it is shown that inclusion of the geometric phase modifies ultracold reaction rates by nearly two orders of magnitude. Interesting experimental control possibilities include the application of external electric and magnetic fields that might be used to exploit the geometric phase effect reported here and experimentally switch on or off the reactivity.
The geometric phase controls ultracold chemistry
Kendrick, B. K.; Hazra, Jisha; Balakrishnan, N.
2015-01-01
The geometric phase is shown to control the outcome of an ultracold chemical reaction. The control is a direct consequence of the sign change on the interference term between two scattering pathways (direct and looping), which contribute to the reactive collision process in the presence of a conical intersection (point of degeneracy between two Born–Oppenheimer electronic potential energy surfaces). The unique properties of the ultracold energy regime lead to an effective quantization of the scattering phase shift enabling maximum constructive or destructive interference between the two pathways. By taking the O+OH→H+O2 reaction as an illustrative example, it is shown that inclusion of the geometric phase modifies ultracold reaction rates by nearly two orders of magnitude. Interesting experimental control possibilities include the application of external electric and magnetic fields that might be used to exploit the geometric phase effect reported here and experimentally switch on or off the reactivity. PMID:26224326
The geometric phase controls ultracold chemistry
NASA Astrophysics Data System (ADS)
Kendrick, B. K.; Hazra, Jisha; Balakrishnan, N.
2015-07-01
The geometric phase is shown to control the outcome of an ultracold chemical reaction. The control is a direct consequence of the sign change on the interference term between two scattering pathways (direct and looping), which contribute to the reactive collision process in the presence of a conical intersection (point of degeneracy between two Born-Oppenheimer electronic potential energy surfaces). The unique properties of the ultracold energy regime lead to an effective quantization of the scattering phase shift enabling maximum constructive or destructive interference between the two pathways. By taking the O+OH-->H+O2 reaction as an illustrative example, it is shown that inclusion of the geometric phase modifies ultracold reaction rates by nearly two orders of magnitude. Interesting experimental control possibilities include the application of external electric and magnetic fields that might be used to exploit the geometric phase effect reported here and experimentally switch on or off the reactivity.
The Geometric Phase of Stock Trading.
Altafini, Claudio
2016-01-01
Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time systems, and even when the cycles in shape space have zero area. A context in which this principle can be applied is stock trading. A zero-area cycle in shape space represents the type of trading operations normally carried out by high-frequency traders (entering and exiting a position on a fast time-scale), while the phase variable represents the cash balance of a trader. Under the assumption that trading impacts stock prices, even zero-area cyclic trading operations can induce geometric phases, i.e., profits or losses, without affecting the stock quote.
MM Algorithms for Geometric and Signomial Programming.
Lange, Kenneth; Zhou, Hua
2014-02-01
This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates.
Geometric spin echo under zero field
Sekiguchi, Yuhei; Komura, Yusuke; Mishima, Shota; Tanaka, Touta; Niikura, Naeko; Kosaka, Hideo
2016-01-01
Spin echo is a fundamental tool for quantum registers and biomedical imaging. It is believed that a strong magnetic field is needed for the spin echo to provide long memory and high resolution, since a degenerate spin cannot be controlled or addressed under a zero magnetic field. While a degenerate spin is never subject to dynamic control, it is still subject to geometric control. Here we show the spin echo of a degenerate spin subsystem, which is geometrically controlled via a mediating state split by the crystal field, in a nitrogen vacancy centre in diamond. The demonstration reveals that the degenerate spin is protected by inherent symmetry breaking called zero-field splitting. The geometric spin echo under zero field provides an ideal way to maintain the coherence without any dynamics, thus opening the way to pseudo-static quantum random access memory and non-invasive biosensors. PMID:27193936
Towards quantitative assessment of calciphylaxis
NASA Astrophysics Data System (ADS)
Deserno, Thomas M.; Sárándi, István.; Jose, Abin; Haak, Daniel; Jonas, Stephan; Specht, Paula; Brandenburg, Vincent
2014-03-01
Calciphylaxis is a rare disease that has devastating conditions associated with high morbidity and mortality. Calciphylaxis is characterized by systemic medial calcification of the arteries yielding necrotic skin ulcerations. In this paper, we aim at supporting the installation of multi-center registries for calciphylaxis, which includes a photographic documentation of skin necrosis. However, photographs acquired in different centers under different conditions using different equipment and photographers cannot be compared quantitatively. For normalization, we use a simple color pad that is placed into the field of view, segmented from the image, and its color fields are analyzed. In total, 24 colors are printed on that scale. A least-squares approach is used to determine the affine color transform. Furthermore, the card allows scale normalization. We provide a case study for qualitative assessment. In addition, the method is evaluated quantitatively using 10 images of two sets of different captures of the same necrosis. The variability of quantitative measurements based on free hand photography is assessed regarding geometric and color distortions before and after our simple calibration procedure. Using automated image processing, the standard deviation of measurements is significantly reduced. The coefficients of variations yield 5-20% and 2-10% for geometry and color, respectively. Hence, quantitative assessment of calciphylaxis becomes practicable and will impact a better understanding of this rare but fatal disease.
Telencephalon and geometric space in goldfish.
Vargas, Juan Pedro; Bingman, Verner Peter; Portavella, Manuel; López, Juan Carlos
2006-11-01
Neuroanatomical evidence indicates that the lateral pallium (LP) of ray-finned fishes could be homologous to the hippocampus of mammals and birds. Recent studies have found that hippocampus of mammals and birds is critical for learning geometric properties of space. In this work, we studied the effects of lesions to the lateral pallium of goldfish on the encoding of geometric spatial information. Goldfish with telencephalic lesions were trained to search for a goal in a rectangular-shaped arena containing one different wall that served as the only distinctive environmental feature. Although fish with lateral pallium lesions learned the task even faster than sham and medial pallium (MP)-lesioned animals, subsequent probe trials showed that they were insensitive to geometric information. Sham and medial pallium-lesioned animals could use both geometric and feature information to locate the goal. By contrast, fish with lateral palium lesions relied exclusively on the feature information provided by the wall of a different colour. These results indicate that lesions to the lateral pallium of goldfish, like hippocampal lesions in mammals and birds, selectively impair the encoding of geometric spatial information of environmental space. Thus, the forebrain structures of teleost fish that are neuroanatomically equivalent to the mammalian and avian hippocampus also share a central role in supporting spatial cognition. Present results suggest that the presence of a hippocampal-dependent memory system implicated in the processing of geometric spatial information is an ancient feature of the vertebrate forebrain that has been conserved during the divergent evolution of different vertebrate groups.
Primary School Teacher Candidates' Geometric Habits of Mind
ERIC Educational Resources Information Center
Köse, Nilu¨fer Y.; Tanisli, Dilek
2014-01-01
Geometric habits of mind are productive ways of thinking that support learning and using geometric concepts. Identifying primary school teacher candidates' geometric habits of mind is important as they affect the development of their future students' geometric thinking. Therefore, this study attempts to determine primary school…
Local Geometrical Machinery for Complexity and Control
NASA Astrophysics Data System (ADS)
Ivancevic, Vladimir G.; Reid, Darryn J.
2015-11-01
In this Chapter, we present local geometrical machinery for studying complexity and control, consisting of dynamics on Kähler manifolds, which combine three geometrical structures-Riemannian, symplectic and complex (Hermitian)-in a mutually compatible way. In other words, every Kähler manifold is simultaneously Riemannian, symplectic and complex (Hermitian). It is well known that Riemannian manifolds represent the stage on which Lagrangian dynamics is set, symplectic manifolds represent the stage for Hamiltonian dynamics, and complex (Hermitian) varieties comprise the stage for quantum dynamics. Therefore, Kähler manifolds represent the richest dynamical stage available where Lagrangian, Hamiltonian, and quantum dynamics all dance together.
Geometrical compression of lidar return signals.
Harms, J; Lahmann, W; Weitkamp, C
1978-04-01
The dynamic range of lidar return signals has been calculated for coaxial transmitter-receiver geometries via the spatial distribution of irradiance in the detector plane as a function of distance z. It is shown that the z(-2)dependence from the lidar equation can be converted to almost constant signal amplitude for distances up to 3 km by suitable and realistic choice of the geometric parameters. On the other hand, no signal degradation with respect to the lidar equation occurs at large distances. This geometrical compression of lidar return signal amplitudes is rated superior to electronic compression methods such as gain switching or logarithmic amplification. PMID:20197946
Model-based vision using geometric hashing
NASA Astrophysics Data System (ADS)
Akerman, Alexander, III; Patton, Ronald
1991-04-01
The Geometric Hashing technique developed by the NYU Courant Institute has been applied to various automatic target recognition applications. In particular, I-MATH has extended the hashing algorithm to perform automatic target recognition ofsynthetic aperture radar (SAR) imagery. For this application, the hashing is performed upon the geometric locations of dominant scatterers. In addition to being a robust model-based matching algorithm -- invariant under translation, scale, and 3D rotations of the target -- hashing is of particular utility because it can still perform effective matching when the target is partially obscured. Moreover, hashing is very amenable to a SIMD parallel processing architecture, and thus potentially realtime implementable.
Quantitative representation and description of intravoxel fiber complexity in HARDI
NASA Astrophysics Data System (ADS)
Sun, Chang-yu; Chu, Chun-yu; Liu, Wan-yu; Hsu, Edward W.; Korenberg, Julie R.; Zhu, Yue-min
2015-11-01
Diffusion tensor imaging and high angular resolution diffusion imaging are often used to analyze the fiber complexity of tissues. In these imaging techniques, the most commonly calculated metric is anisotropy, such as fractional anisotropy (FA), generalized anisotropy (GA), and generalized fractional anisotropy (GFA). The basic idea underlying these metrics is to compute the deviation from free or spherical diffusion. However, in many cases, the question is not really to know whether it concerns spherical diffusion. Instead, the main concern is to describe and quantify fiber complexity such as fiber crossing in a voxel. In this context, it would be more direct and effective to compute the deviation from a single fiber bundle instead of a sphere. We propose a new metric, called PEAM (PEAnut Metric), which is based on computing the deviation of orientation diffusion functions (ODFs) from a single fiber bundle ODF represented by a peanut. As an example, the proposed PEAM metric is used to classify intravoxel fiber configurations. The results on simulated data, physical phantom data and real brain data consistently showed that the proposed PEAM provides greater accuracy than FA, GA and GFA and enables parallel and complex fibers to be better distinguished.
Quantitative description of realistic wealth distributions by kinetic trading models
NASA Astrophysics Data System (ADS)
Lammoglia, Nelson; Muñoz, Víctor; Rogan, José; Toledo, Benjamín; Zarama, Roberto; Valdivia, Juan Alejandro
2008-10-01
Data on wealth distributions in trading markets show a power law behavior x-(1+α) at the high end, where, in general, α is greater than 1 (Pareto’s law). Models based on kinetic theory, where a set of interacting agents trade money, yield power law tails if agents are assigned a saving propensity. In this paper we are solving the inverse problem, that is, in finding the saving propensity distribution which yields a given wealth distribution for all wealth ranges. This is done explicitly for two recently published and comprehensive wealth datasets.
Dual Enrollment in a Rural Environment: A Descriptive Quantitative Study
ERIC Educational Resources Information Center
Dodge, Mary Beth
2012-01-01
Dual enrollment is a federally funded program that offers high school students the opportunity to earn both high school and postsecondary credits for the same course. While the phenomenon of concurrent enrollment in postsecondary and college educational programs is not new, political support and public funding has drawn focus to the policies of…
QUANTITATIVE SOIL DESCRIPTIONS FOR ECOREGIONS OF THE UNITED STATES
Researchers have defined ecological regions of the United States based on patterns in the coincidence of terrestrial, aquatic, abiotic and biotic characteristics that are associated with spatial differences in ecosystems. Ecoregions potentially facilitate regional research, monit...
Multimedia content description framework
NASA Technical Reports Server (NTRS)
Bergman, Lawrence David (Inventor); Kim, Michelle Yoonk Yung (Inventor); Li, Chung-Sheng (Inventor); Mohan, Rakesh (Inventor); Smith, John Richard (Inventor)
2003-01-01
A framework is provided for describing multimedia content and a system in which a plurality of multimedia storage devices employing the content description methods of the present invention can interoperate. In accordance with one form of the present invention, the content description framework is a description scheme (DS) for describing streams or aggregations of multimedia objects, which may comprise audio, images, video, text, time series, and various other modalities. This description scheme can accommodate an essentially limitless number of descriptors in terms of features, semantics or metadata, and facilitate content-based search, index, and retrieval, among other capabilities, for both streamed or aggregated multimedia objects.
Quantitative measurement of feline colonic transit
Krevsky, B.; Somers, M.B.; Maurer, A.H.; Malmud, L.S.; Knight, L.C.; Fisher, R.S.
1988-10-01
Colonic transit scintigraphy, a method for quantitatively evaluating the movement of the fecal stream in vivo, was employed to evaluate colonic transit in the cat. Scintigraphy was performed in duplicate in five cats and repeated four times in one cat. After instillation of an 111In marker into the cecum through a surgically implanted silicone cecostomy tube, colonic movement of the instillate was quantitated for 24 h using gamma scintigraphy. Antegrade and retrograde motion of radionuclide was observed. The cecum and ascending colon emptied rapidly, with a half-emptying time of 1.68 +/- 0.56 h (mean +/- SE). After 24 h, 25.1 +/- 5.2% of the activity remained in the transverse colon. The progression of the geometric center was initially rapid, followed later by a delayed phase. Geometric center reproducibility was found to be high when analyzed using simple linear regression (slope = 0.92; r = 0.73; P less than 0.01). Atropine (0.1 mg/kg im) was found to delay cecum and ascending colon emptying and delay progression of the geometric center. These results demonstrate both 1) the ability of colonic transit scintigraphy to detect changes in transit induced by pharmacological manipulation and 2) the fact that muscarinic blockade inhibits antegrade transit of the fecal stream. We conclude that feline colonic transit may be studied in a quantitative and reproducible manner with colonic transit scintigraphy.
Reinforcing Geometric Properties with Shapedoku Puzzles
ERIC Educational Resources Information Center
Wanko, Jeffrey J.; Nickell, Jennifer V.
2013-01-01
Shapedoku is a new type of puzzle that combines logic and spatial reasoning with understanding of basic geometric concepts such as slope, parallelism, perpendicularity, and properties of shapes. Shapedoku can be solved by individuals and, as demonstrated here, can form the basis of a review for geometry students as they create their own. In this…
Geometric Models for Collaborative Search and Filtering
ERIC Educational Resources Information Center
Bitton, Ephrat
2011-01-01
This dissertation explores the use of geometric and graphical models for a variety of information search and filtering applications. These models serve to provide an intuitive understanding of the problem domains and as well as computational efficiencies to our solution approaches. We begin by considering a search and rescue scenario where both…
How Do Young Children Learn Geometric Concepts.
ERIC Educational Resources Information Center
Ohe, Pia
Twenty children (ages 5 and 6) from each of seven cultural groups (Caucasian, Black, Jewish, Puerto Rican, Chinese, Korean-American and native Korean) were given a copying task of 21 geometric shapes to test the cultural invariancy of Piaget's topological-projective-Euclidean concept acquisition sequence. All subjects were either middle or lower…
Geometric Mean--What Does It Mean?
ERIC Educational Resources Information Center
Kalder, Robin S.
2012-01-01
The National Council of Teachers of Mathematics and numerous mathematics educators promote the combination of conceptual understanding and procedural learning in the successful instruction of mathematics. Despite this, when geometric mean is taught in a typical American geometry class, it is taught as a process only despite the many connections…
The geometrical significance of the Laplacian
NASA Astrophysics Data System (ADS)
Styer, Daniel F.
2015-12-01
The Laplacian operator can be defined, not only as a differential operator, but also through its averaging properties. Such a definition lends geometric significance to the operator: a large Laplacian at a point reflects a "nonconformist" (i.e., different from average) character for the function there. This point of view is used to motivate the wave equation for a drumhead.
Geometric interpretations for resonances of plasmonic nanoparticles
NASA Astrophysics Data System (ADS)
Liu, Wei; Oulton, Rupert F.; Kivshar, Yuri S.
2015-07-01
The field of plasmonics can be roughly categorized into two branches: surface plasmon polaritons (SPPs) propagating in waveguides and localized surface plasmons (LSPs) supported by scattering particles. Investigations along these two directions usually employ different approaches, resulting in more or less a dogma that the two branches progress almost independently of each other, with few interactions. Here in this work we interpret LSPs from a Bohr model based geometric perspective relying on SPPs, thus establishing a connection between these two sub-fields. Besides the clear explanations of conventional scattering features of plasmonic nanoparticles, based on this geometric model we further demonstrate other anomalous scattering features (higher order modes supported at lower frequencies, and blueshift of the resonance with increasing particle sizes) and multiple electric resonances of the same order supported at different frequencies, which have been revealed to originate from backward SPP modes and multiple dispersion bands supported in the corresponding plasmonic waveguides, respectively. Inspired by this geometric model, it is also shown that, through solely geometric tuning, the absorption of each LSP resonance can be maximized to reach the single channel absorption limit, provided that the scattering and absorption rates are tuned to be equal.
Geometric Interpretation of the Pauli Spinor.
ERIC Educational Resources Information Center
Frescura, F. A. M.; Hiley, B. J.
1981-01-01
Presents a reexamination of an intuitively geometric view of the nonrelativistic Pauli spinor in a simplified discussion of the connection between the rotation group and special transformations in the plane of projection. This view of the spinor is related to those based on the existence of an istropic or null vector. (SK)
Children's Learning of Geometrical Concepts Through Logo.
ERIC Educational Resources Information Center
Noss, Richard
1987-01-01
Exploratory study aimed to investigate elements of geometrical concepts that children learn through Logo programing. A test designed to assess three components of length and angle was administered to 84 children who had learned Logo for one year and 92 who had not. Data indicated a positive effect of Logo work on some items, but not all.…
Geometric Transformations in Middle School Mathematics Textbooks
ERIC Educational Resources Information Center
Zorin, Barbara
2011-01-01
This study analyzed treatment of geometric transformations in presently available middle grades (6, 7, 8) student mathematics textbooks. Fourteen textbooks from four widely used textbook series were evaluated: two mainline publisher series, Pearson (Prentice Hall) and Glencoe (Math Connects); one National Science Foundation (NSF) funded curriculum…
Modern Geometric Algebra: A (Very Incomplete!) Survey
ERIC Educational Resources Information Center
Suzuki, Jeff
2009-01-01
Geometric algebra is based on two simple ideas. First, the area of a rectangle is equal to the product of the lengths of its sides. Second, if a figure is broken apart into several pieces, the sum of the areas of the pieces equals the area of the original figure. Remarkably, these two ideas provide an elegant way to introduce, connect, and…
If Only Clairaut Had Dynamic Geometric Tools
ERIC Educational Resources Information Center
Chang, Hyewon; Reys, Barbara J.
2013-01-01
Geometry is a major area of study in middle school mathematics, yet middle school and secondary students have difficulty learning important geometric concepts. This article considers Alexis-Claude Clairaut's approach that emphasizes engaging student curiosity about key ideas and theorems instead of directly teaching theorems before their…
Impossible Geometric Constructions: A Calculus Writing Project
ERIC Educational Resources Information Center
Awtrey, Chad
2013-01-01
This article discusses a writing project that offers students the opportunity to solve one of the most famous geometric problems of Greek antiquity; namely, the impossibility of trisecting the angle [pi]/3. Along the way, students study the history of Greek geometry problems as well as the life and achievements of Carl Friedrich Gauss. Included is…
More Meaning from the Geometric Mean.
ERIC Educational Resources Information Center
Dorner, Bryan C.
2003-01-01
Provides classroom suggestions for combining numerical, algebraic, and geometric techniques with the understanding of a simple method for computing square roots. Historical origins of the method illustrate the debt owed to ancient minds living in what are now India, Pakistan, Iraq, and Egypt. (Author/NB)
A Geometric Approach to Fair Division
ERIC Educational Resources Information Center
Barbanel, Julius
2010-01-01
We wish to divide a cake among some collection of people (who may have very different notions of the comparative value of pieces of cake) in a way that is both "fair" and "efficient." We explore the meaning of these terms, introduce two geometric tools to aid our analysis, and present a proof (due to Dietrich Weller) that establishes the existence…
Geometric Determinants of Human Spatial Memory
ERIC Educational Resources Information Center
Hartley, Tom; Trinkler, Iris; Burgess, Neil
2004-01-01
Geometric alterations to the boundaries of a virtual environment were used to investigate the representations underlying human spatial memory. Subjects encountered a cue object in a simple rectangular enclosure, with distant landmarks for orientation. After a brief delay, during which they were removed from the arena, subjects were returned to it…
Quantification and correction of geometric distortions in low-field MRI
NASA Astrophysics Data System (ADS)
Parra Robles, Juan M.; Dominguez, William; Gonzalez, Evelio R.; Berdellans, Ilse
1999-05-01
Geometric distortions are one of the most important degrading factors in MRI. They usually do not greatly affect the clinical relevance of images, but their correction is indispensable for lesion volume measurements, radiotherapy and surgical planning. In this work, the main sources of geometric distortion in Cuban low-field MRI systems are studied. Geometric distortion models and correction algorithms are tested by means of computer simulation using theoretical distributions of the magnetic fields. The real distributions are determined from images of a grid phantom. Calculated static field distributions showed that the system magnetic center is shifted, relative to magnet geometric center. Quantitative measurements provided inhomogeneity values (93 ppm in a spherical region of diameter 256 mm) larger than calibration data (65 ppm) obtained 15 months ago. The shim settings must be readjusted. The temporal behavior of static field was also studied. The magnet heating produces a slow time variation in static field intensity, but field error distribution proved to be stable. In the images, geometric distortions increase with increasing distance from image center and ranged from -6 to 7 mm. The implemented correction procedure reduced distortions from maximally 7 mm to the order of pixel resolution (0.8 - 1 mm).
Can EPR non-locality be geometrical?
Ne`eman, Y. |; Botero, A.
1995-10-01
The presence in Quantum Mechanics of non-local correlations is one of the two fundamentally non-intuitive features of that theory. The non-local correlations themselves fall into two classes: EPR and Geometrical. The non-local characteristics of the geometrical type are well-understood and are not suspected of possibly generating acausal features, such as faster-than-light propagation of information. This has especially become true since the emergence of a geometrical treatment for the relevant gauge theories, i.e. Fiber Bundle geometry, in which the quantum non-localities are seen to correspond to pure homotopy considerations. This aspect is reviewed in section 2. Contrary-wise, from its very conception, the EPR situation was felt to be paradoxical. It has been suggested that the non-local features of EPR might also derive from geometrical considerations, like all other non-local characteristics of QM. In[7], one of the authors was able to point out several plausibility arguments for this thesis, emphasizing in particular similarities between the non-local correlations provided by any gauge field theory and those required by the preservation of the quantum numbers of the original EPR state-vector, throughout its spatially-extended mode. The derivation was, however, somewhat incomplete, especially because of the apparent difference between, on the one hand, the closed spatial loops arising in the analysis of the geometrical non-localities, from Aharonov-Bohm and Berry phases to magnetic monopoles and instantons, and on the other hand, in the EPR case, the open line drawn by the positions of the two moving decay products of the disintegrating particle. In what follows, the authors endeavor to remove this obstacle and show that as in all other QM non-localities, EPR is somehow related to closed loops, almost involving homotopy considerations. They develop this view in section 3.
Subgraphs and network motifs in geometric networks
NASA Astrophysics Data System (ADS)
Itzkovitz, Shalev; Alon, Uri
2005-02-01
Many real-world networks describe systems in which interactions decay with the distance between nodes. Examples include systems constrained in real space such as transportation and communication networks, as well as systems constrained in abstract spaces such as multivariate biological or economic data sets and models of social networks. These networks often display network motifs: subgraphs that recur in the network much more often than in randomized networks. To understand the origin of the network motifs in these networks, it is important to study the subgraphs and network motifs that arise solely from geometric constraints. To address this, we analyze geometric network models, in which nodes are arranged on a lattice and edges are formed with a probability that decays with the distance between nodes. We present analytical solutions for the numbers of all three- and four-node subgraphs, in both directed and nondirected geometric networks. We also analyze geometric networks with arbitrary degree sequences and models with a bias for directed edges in one direction. Scaling rules for scaling of subgraph numbers with system size, lattice dimension, and interaction range are given. Several invariant measures are found, such as the ratio of feedback and feed-forward loops, which do not depend on system size, dimension, or connectivity function. We find that network motifs in many real-world networks, including social networks and neuronal networks, are not captured solely by these geometric models. This is in line with recent evidence that biological network motifs were selected as basic circuit elements with defined information-processing functions.
A GEOMETRICAL HEIGHT SCALE FOR SUNSPOT PENUMBRAE
Puschmann, K. G.; Ruiz Cobo, B.; MartInez Pillet, V. E-mail: brc@iac.e
2010-09-10
Inversions of spectropolarimetric observations of penumbral filaments deliver the stratification of different physical quantities in an optical depth scale. However, without establishing a geometrical height scale, their three-dimensional geometrical structure cannot be derived. This is crucial in understanding the correct spatial variation of physical properties in the penumbral atmosphere and to provide insights into the mechanism capable of explaining the observed penumbral brightness. The aim of this work is to determine a global geometrical height scale in the penumbra by minimizing the divergence of the magnetic field vector and the deviations from static equilibrium as imposed by a force balance equation that includes pressure gradients, gravity, and the Lorentz force. Optical depth models are derived from the inversion of spectropolarimetric data of an active region observed with the Solar Optical Telescope on board the Hinode satellite. We use a genetic algorithm to determine the boundary condition for the inference of geometrical heights. The retrieved geometrical height scale permits the evaluation of the Wilson depression at each pixel and the correlation of physical quantities at each height. Our results fit into the uncombed penumbral scenario, i.e., a penumbra composed of flux tubes with channeled mass flow and with a weaker and more horizontal magnetic field as compared with the background field. The ascending material is hotter and denser than their surroundings. We do not find evidence of overturning convection or field-free regions in the inner penumbral area analyzed. The penumbral brightness can be explained by the energy transfer of the ascending mass carried by the Evershed flow, if the physical quantities below z = -75 km are extrapolated from the results of the inversion.
Provocative Opinion: Descriptive Chemistry.
ERIC Educational Resources Information Center
Bent, Henry A.; Bent, Brian E.
1987-01-01
Discusses many of the distinctions that chemists draw between theoretical chemistry and descriptive chemistry, along with the tendency for chemical educators to adopt the type of chemistry they feel is most important to teach. Uses examples to argue that theoretical chemistry and descriptive chemistry are, at the bottom line, the same. (TW)
ERIC Educational Resources Information Center
Brand, Josef
1979-01-01
In this experiment in description, students in a high school honors English class were asked to select a surrealistic painting and capture it in writing. Their compositions were given to art students who tried to reproduce the paintings from the written descriptions. (SJL)
Physics 3204. Course Description.
ERIC Educational Resources Information Center
Newfoundland and Labrador Dept. of Education.
A description of the physics 3204 course in Newfoundland and Labrador is provided. The description includes: (1) statement of purpose, including general objectives of science education; (2) a list of six course objectives; (3) course content for units on sound, light, optical instruments, electrostatics, current electricity, Michael Faraday and…
Miller, Larry
2014-01-01
The act of writing a job description can be a daunting and difficult task for many managers. This article focuses on the key concepts of What, How, and Measureable Results as they relate to an employee's job duties. When the answers to these three elements are articulated, they define the core responsibilities of any job that form the basis for an effective job description.
NASA Astrophysics Data System (ADS)
Dubbini, Marco; Benedetti, Gianluca; Lucente, Corrado Claudio
2015-04-01
The need to have three-dimensional digital products of high accuracy and high resolution is now increasingly important for the study of the hydrogeological instability phenomena both from a geomorphological point of view and a geotechnical-geomechanical one. What until now was considered the prerogative of the laser scanner (both air-transported and terrestrial) for data acquisition, in many contexts is to be integrated and often replaced by photogrammetric techniques. The integration of the typical photogrammetry algorithms (Aerial Triangulation, bundle adjustment, collinearity equations, etc.) with Structure from Motion (SFM) algorithms derived from Computer Vision (CV) allows to get products "dense points cloud" of high quality and high resolution with almost complete automation of processes. The use of Remotely Piloted Aerial System (RPAS) equipped with high resolution photogrammetric and positioning sensors, allows to obtain, in a very short time and with low costs, all necessary data for the purpose. Through all stages of the photogrammetric processing, is obtained, as a base product, a dense cloud of points. Subsequently, after the phase of cleaning and classification of data, it will be possible to obtained all the necessary products for studing the geomorphological characterization and, in specific cases, also geotechnical-geomechanical characterization. The high repeatability of surveys, due to the insertion of data always in the same reference system without introducing transformations between coordinate systems, and the high accuracy in the determination of Ground Control Point (GCP) measured and processed with geodetic techniques, mainly by GNSS instrumentation, allows to compare data and models over time. The possibility of the RPAS to carry on board the double frequency satellite positioning systems, so as to define the spatial coordinates of the perspective center with centimetric accuracy, it also allows to obtain repeatability of the data in difficult or absolutely no access areas (high-risk zones and so on). The high repeatability, therefore, makes it possible to perform evaluations of volumes variation and of the surfaces shape. When the data is very dense and, for example in case of rock slopes, you can also define the dip and dip-direction of discontinuity planes (like joints and faults), through specific procedures. With a high radiometric accuracy, when the situation allows it and when the texturing of the model is at a very high resolution, there is also the possibility of determining the "rake" parameter.
Araujo; Araujo
2000-09-01
The understanding of contact line fluctuations in heterogeneous systems of controlled wettability is relevant to many industrial processes. Despite its importance, it is poorly understood. Here, we present results on an experimental study of fluid displacement on modified Hele-Shaw cells with surface defects as heterogeneities. The system wettability is controlled by defect surface coverage. Three different surface coverage regimes were studied. For each one, the morphology and deformation energy of the displacement front is determined. The width front is described in terms of two exponents, the roughness exponent (alpha) and the one that describes its growth (beta). In all cases, it is found that the width increases logarithmically in time up to a characteristic value, where a crossover to a saturation behavior is observed. The crossover time is a function of the surface coverage. For low coverage 0.51
NASA Astrophysics Data System (ADS)
Zhevlakov, A. P.; Zatsepina, M. E.; Kirillovskii, V. K.
2014-06-01
The principles of transformation of a Foucault shadowgram into a quantitative map of wave-front deformation based on creation of a system of isophotes are unveiled. The presented studies and their results prove that there is a high degree of correspondence between a Foucault shadowgram and the geometrical model of a shear interferogram with respect to displaying wave-front deformations.
ERIC Educational Resources Information Center
Ertekin, E.; Solak, S.; Yazici, E.
2010-01-01
The aim of this study is to identify the effects of formalism in teaching on primary and secondary school mathematics teacher trainees' algebraic and geometric interpretations of the notions of linear dependency/independency. Quantitative research methods are drawn in order to determine differences in success levels between algebraic and geometric…
Vallortigara, Giorgio; Pagni, Piero; Sovrano, Valeria Anna
2004-04-01
Research has proved that disoriented children and nonhuman animals can reorient themselves using geometric and nongeometric features of the environment, showing conjoined use of both types of information to different degree depending on species and developmental level. Little is known of the neurobiological bases of these spatial reorientation processes. Here we take advantage of the neuroanatomical peculiarities of the visual system of birds (showing segregation of information between the two sides of the brain to a considerable degree) to investigate the way in which geometric and nongeometric information is encoded and used by the left and right hemispheres. Domestic chicks were trained binocularly in an environment with a distinctive geometry (a rectangular cage) with panels at the corners providing nongeometric cues. Between trials, chicks were passively disoriented to disable dead reckoning. When tested after removal of the panels, left-eyed chicks, but not right-eyed chicks, reoriented using the residual information provided by the geometry of the cage. When tested after removal of geometric information (i.e., in a square-shaped cage), both right- and left-eyed chicks reoriented using the residual nongeometric information provided by the panels. When trained binocularly with only geometric information, at test, left-eyed chicks reoriented better than right-eyed chicks. Finally, when geometric and nongeometric cues provided contradictory information, left-eyed chicks showed more reliance on geometric cues, whereas right-eyed chicks showed more reliance on nongeometric cues. The results suggest separate mechanisms for dealing with spatial reorientation problems, with the right hemisphere taking charge of large-scale geometry of the environment and with both hemispheres taking charge of local, nongeometric cues when available in isolation, but with a predominance of the left hemisphere when competition between geometric and non-geometric information occurs
Geometric modeling for computer aided design
NASA Technical Reports Server (NTRS)
Schwing, James L.
1993-01-01
Over the past several years, it has been the primary goal of this grant to design and implement software to be used in the conceptual design of aerospace vehicles. The work carried out under this grant was performed jointly with members of the Vehicle Analysis Branch (VAB) of NASA LaRC, Computer Sciences Corp., and Vigyan Corp. This has resulted in the development of several packages and design studies. Primary among these are the interactive geometric modeling tool, the Solid Modeling Aerospace Research Tool (smart), and the integration and execution tools provided by the Environment for Application Software Integration and Execution (EASIE). In addition, it is the purpose of the personnel of this grant to provide consultation in the areas of structural design, algorithm development, and software development and implementation, particularly in the areas of computer aided design, geometric surface representation, and parallel algorithms.
a Modular Geometric Model for Underwater Photogrammetry
NASA Astrophysics Data System (ADS)
Maas, H.-G.
2015-04-01
Underwater applications of photogrammetric measurement techniques usually need to deal with multimedia photogrammetry aspects, which are characterized by the necessity of handling optical rays that are broken at interfaces between optical media with different refrative indices according to Snell's Law. This so-called multimedia geometry has to be incorporated into geometric models in order to achieve correct measurement results. The paper shows a flexible yet strict geometric model for the handling of refraction effects on the optical path, which can be implemented as a module into photogrammetric standard tools such as spatial resection, spatial intersection, bundle adjustment or epipolar line computation. The module is especially well suited for applications, where an object in water is observed by cameras in air through one or more plane parallel glass interfaces, as it allows for some simplifications here.
Quantum state discrimination: A geometric approach
NASA Astrophysics Data System (ADS)
Markham, Damian; Miszczak, Jarosław Adam; Puchała, Zbigniew; Życzkowski, Karol
2008-04-01
We analyze the problem of finding sets of quantum states that can be deterministically discriminated. From a geometric point of view, this problem is equivalent to that of embedding a simplex of points whose distances are maximal with respect to the Bures distance (or trace distance). We derive upper and lower bounds for the trace distance and for the fidelity between two quantum states, which imply bounds for the Bures distance between the unitary orbits of both states. We thus show that, when analyzing minimal and maximal distances between states of fixed spectra, it is sufficient to consider diagonal states only. Hence when optimal discrimination is considered, given freedom up to unitary orbits, it is sufficient to consider diagonal states. This is illustrated geometrically in terms of Weyl chambers.
Finsler geometric extension of Einstein gravity
NASA Astrophysics Data System (ADS)
Pfeifer, Christian; Wohlfarth, Mattias N. R.
2012-03-01
We construct gravitational dynamics for Finsler spacetimes in terms of an action integral on the unit tangent bundle. These spacetimes are generalizations of Lorentzian metric manifolds which satisfy necessary causality properties. A coupling procedure for matter fields to Finsler gravity completes our new theory that consistently becomes equivalent to Einstein gravity in the limit of metric geometry. We provide a precise geometric definition of observers and their measurements and show that the transformations, by means of which different observers communicate, form a groupoid that generalizes the usual Lorentz group. Moreover, we discuss the implementation of Finsler spacetime symmetries. We use our results to analyze a particular spacetime model that leads to Finsler geometric refinements of the linearized Schwarzschild solution.
Scale-invariant geometric random graphs.
Xie, Zheng; Rogers, Tim
2016-03-01
We introduce and analyze a class of growing geometric random graphs that are invariant under rescaling of space and time. Directed connections between nodes are drawn according to influence zones that depend on node position in space and time, mimicking the heterogeneity and increased specialization found in growing networks. Through calculations and numerical simulations we explore the consequences of scale invariance for geometric random graphs generated this way. Our analysis reveals a dichotomy between scale-free and Poisson distributions of in- and out-degree, the existence of a random number of hub nodes, high clustering, and unusual percolation behavior. These properties are similar to those of empirically observed web graphs. PMID:27078369
Geometric stability of topological lattice phases
Jackson, T. S.; Möller, Gunnar; Roy, Rahul
2015-01-01
The fractional quantum Hall (FQH) effect illustrates the range of novel phenomena which can arise in a topologically ordered state in the presence of strong interactions. The possibility of realizing FQH-like phases in models with strong lattice effects has attracted intense interest as a more experimentally accessible venue for FQH phenomena which calls for more theoretical attention. Here we investigate the physical relevance of previously derived geometric conditions which quantify deviations from the Landau level physics of the FQHE. We conduct extensive numerical many-body simulations on several lattice models, obtaining new theoretical results in the process, and find remarkable correlation between these conditions and the many-body gap. These results indicate which physical factors are most relevant for the stability of FQH-like phases, a paradigm we refer to as the geometric stability hypothesis, and provide easily implementable guidelines for obtaining robust FQH-like phases in numerical or real-world experiments. PMID:26530311
Topological minimally entangled states via geometric measure
NASA Astrophysics Data System (ADS)
Buerschaper, Oliver; García-Saez, Artur; Orús, Román; Wei, Tzu-Chieh
2014-11-01
Here we show how the Minimally Entangled States (MES) of a 2d system with topological order can be identified using the geometric measure of entanglement. We show this by minimizing this measure for the doubled semion, doubled Fibonacci and toric code models on a torus with non-trivial topological partitions. Our calculations are done either quasi-exactly for small system sizes, or using the tensor network approach in Orús et al (arXiv:1406.0585) for large sizes. As a byproduct of our methods, we see that the minimisation of the geometric entanglement can also determine the number of Abelian quasiparticle excitations in a given model. The results in this paper provide a very efficient and accurate way of extracting the full topological information of a 2d quantum lattice model from the multipartite entanglement structure of its ground states.
The classical geometrization of the electromagnetism
NASA Astrophysics Data System (ADS)
de Araujo Duarte, Celso
2015-08-01
Following the line of the history, if by one side the electromagnetic theory was consolidated on the 19th century, the emergence of the special and the general relativity theories on the 20th century opened possibilities of further developments, with the search for the unification of the gravitation and the electromagnetism on a single unified theory. Some attempts to the geometrization of the electromagnetism emerged in this context, where these first models resided strictly on a classical basis. Posteriorly, they were followed by more complete and embracing quantum field theories. The present work reconsiders the classical viewpoint, with the purpose of showing that at first-order of approximation the electromagnetism constitutes a geometric structure aside other phenomena as gravitation, and that magnetic monopoles do not exist at least up to this order of approximation. Even though being limited, the model is consistent and offers the possibility of an experimental test of validity.
The bouncing ball through a geometrical series
NASA Astrophysics Data System (ADS)
Flores, Sergio; Alfaro, Luis L.; Chavez, Juan E.; Bastarrachea, Aztlan; Hurtado, Jazmin
2008-10-01
The mathematical representation of the physical situation related to a bouncing ball on the floor is an important understanding difficulty for most of the students during the introductory mechanics and mathematics courses. The research group named Physics and mathematics in context from the University of Ciudad Juarez is concerned about the versatility in the change from a mathematical representation to the own physical context of any problem under a traditional instruction. In this case, the main idea is the association of the physical properties of the bouncing ball situation to the nearest mathematical model based on a geometrical series. The proposal of the cognitive development is based on a geometrical series that shows the time the ball takes to stop. In addition, we show the behavior of the ratio of the consecutive heights during the motion.
Robot arm geometric link parameter estimation
NASA Astrophysics Data System (ADS)
Hayati, S. A.
A general method for estimating serial link manipulator geometric parameter errors is proposed in this paper. The positioning accuracy of the end-effector may be increased significantly by updating the nominal link parameters in the control software to represent the physical system more accurately. The proposed method is applicable for serial link manipulators with any combination of revolute or prismatic joints, and is not limited to a specific measurement technique.
Multiphase flow in geometrically simple fracture intersections
Basagaoglu, H.; Meakin, P.; Green, C.T.; Mathew, M.; ,
2006-01-01
A two-dimensional lattice Boltzmann (LB) model with fluid-fluid and solid-fluid interaction potentials was used to study gravity-driven flow in geometrically simple fracture intersections. Simulated scenarios included fluid dripping from a fracture aperture, two-phase flow through intersecting fractures and thin-film flow on smooth and undulating solid surfaces. Qualitative comparisons with recently published experimental findings indicate that for these scenarios the LB model captured the underlying physics reasonably well.
Geometric continuum regularization of quantum field theory
Halpern, M.B. . Dept. of Physics)
1989-11-08
An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs.
Chirality: a relational geometric-physical property.
Gerlach, Hans
2013-11-01
The definition of the term chirality by Lord Kelvin in 1893 and 1904 is analyzed by taking crystallography at that time into account. This shows clearly that chirality is a relational geometric-physical property, i.e., two relations between isometric objects are possible: homochiral or heterochiral. In scientific articles the relational term chirality is often mistaken for the two valued measure for the individual (absolute) sense of chirality, an arbitrary attributive term.
Geometric simulation of structures containing rigid units
NASA Astrophysics Data System (ADS)
Wells, Stephen
2005-03-01
Much insight into the behaviour of the framework silicates can be obtained from the Rigid Unit model. I review results from geometric analyses [1] of framework structures, quantifying the significance of rigid unit motion in thermal disorder and in defect accomodation, and from a method of simulation [2,3] based on a whole-body `geometric potential' rather than on interatomic potentials. I show the application of the geometric potential to the symmetry-constrained generation of hypothetical zeolite frameworks [4], and to the rapid generation of protein conformations using insights from rigid cluster decomposition [5]. 1. Wells, Dove and Tucker, Journal of Applied Crystallography, 37:536--544 (2004). 2. G.D. Gatta and S.A. Wells, Phys. Chem. Min. 31:1--10 (2004). 3. A. Sartbaeva, S. A. Wells, S. A. T. Redfern, J. Phys.: Condens. Matter 16, 8173 (2004) 4. M. M. J. Treacy, I. Rivin, E. Balkovsky, K. H. Randall and M. D. Foster, Micropor. Mesopor. Mater. 74, 121-132 (2004). 5. M.F. Thorpe, Ming Lei, A.J. Rader, Donald J. Jacobs, and Leslie A. Kuhn, Journal of Molecular Graphics and Modelling 19, 1:60 - 69, (2001).
Geometric Phase Effect in Heat Transport
NASA Astrophysics Data System (ADS)
Ren, Jie; Hanggi, Petter; Li, Baowen
2011-03-01
Nonlinear molecular heat-pumping devices, which operate via explicitly modulating at least two parameters, are crucial for energy control in low dimensional nano-scale systems. We have applied slow two-parameter modulations on such a molecular junctions and consequently uncovered an intrinsic heat flux contribution, additional to the known, usual dynamical heat flux (from hot to cold). This additional heat flux derives from a nontrivial geometric origin that relates to a non-vanishing, so termed finite Berry phase. It provides a free lunch for the pumped heat and even can direct heat flux against the temperature bias. In addition we are able to show that this so pumped energy exhibits a novel robust fractional quantization phenomenon. Interestingly, this additional geometric heat pump mechanism is also shown to cause a breakdown of the heat-flux fluctuation theorem, which holds true for the non-driving, stationary heat flux transfer. The validity of this theorem is guaranteed whenever (i) the geometric phase contribution vanishes and (ii) the cyclic protocol preserves the detailed balance symmetry.
Evolutionary Optimization of a Geometrically Refined Truss
NASA Technical Reports Server (NTRS)
Hull, P. V.; Tinker, M. L.; Dozier, G. V.
2007-01-01
Structural optimization is a field of research that has experienced noteworthy growth for many years. Researchers in this area have developed optimization tools to successfully design and model structures, typically minimizing mass while maintaining certain deflection and stress constraints. Numerous optimization studies have been performed to minimize mass, deflection, and stress on a benchmark cantilever truss problem. Predominantly traditional optimization theory is applied to this problem. The cross-sectional area of each member is optimized to minimize the aforementioned objectives. This Technical Publication (TP) presents a structural optimization technique that has been previously applied to compliant mechanism design. This technique demonstrates a method that combines topology optimization, geometric refinement, finite element analysis, and two forms of evolutionary computation: genetic algorithms and differential evolution to successfully optimize a benchmark structural optimization problem. A nontraditional solution to the benchmark problem is presented in this TP, specifically a geometrically refined topological solution. The design process begins with an alternate control mesh formulation, multilevel geometric smoothing operation, and an elastostatic structural analysis. The design process is wrapped in an evolutionary computing optimization toolset.
Interacting geometric priors for robust multimodel fitting.
Pham, Trung Thanh; Chin, Tat-Jun; Schindler, Konrad; Suter, David
2014-10-01
Recent works on multimodel fitting are often formulated as an energy minimization task, where the energy function includes fitting error and regularization terms, such as low-level spatial smoothness and model complexity. In this paper, we introduce a novel energy with high-level geometric priors that consider interactions between geometric models, such that certain preferred model configurations may be induced.We argue that in many applications, such prior geometric properties are available and should be fruitfully exploited. For example, in surface fitting to point clouds, the building walls are usually either orthogonal or parallel to each other. Our proposed energy function is useful in dealing with unknown distributions of data errors and outliers, which are often the factors leading to biased estimation. Furthermore, the energy can be efficiently minimized using the expansion move method. We evaluate the performance on several vision applications using real data sets. Experimental results show that our method outperforms the state-of-the-art methods without significant increase in computation.
The geometric phase controls ultracold chemistry
Kendrick, B. K.; Hazra, Jisha; Balakrishnan, N.
2015-07-30
In this study, the geometric phase is shown to control the outcome of an ultracold chemical reaction. The control is a direct consequence of the sign change on the interference term between two scattering pathways (direct and looping), which contribute to the reactive collision process in the presence of a conical intersection (point of degeneracy between two Born–Oppenheimer electronic potential energy surfaces). The unique properties of the ultracold energy regime lead to an effective quantization of the scattering phase shift enabling maximum constructive or destructive interference between the two pathways. By taking the O + OH → H + O2more » reaction as an illustrative example, it is shown that inclusion of the geometric phase modifies ultracold reaction rates by nearly two orders of magnitude. Interesting experimental control possibilities include the application of external electric and magnetic fields that might be used to exploit the geometric phase effect reported here and experimentally switch on or off the reactivity.« less
A Geometric Theory of Nonlinear Morphoelastic Shells
NASA Astrophysics Data System (ADS)
Sadik, Souhayl; Angoshtari, Arzhang; Goriely, Alain; Yavari, Arash
2016-08-01
Many thin three-dimensional elastic bodies can be reduced to elastic shells: two-dimensional elastic bodies whose reference shape is not necessarily flat. More generally, morphoelastic shells are elastic shells that can remodel and grow in time. These idealized objects are suitable models for many physical, engineering, and biological systems. Here, we formulate a general geometric theory of nonlinear morphoelastic shells that describes both the evolution of the body shape, viewed as an orientable surface, as well as its intrinsic material properties such as its reference curvatures. In this geometric theory, bulk growth is modeled using an evolving referential configuration for the shell, the so-called material manifold. Geometric quantities attached to the surface, such as the first and second fundamental forms, are obtained from the metric of the three-dimensional body and its evolution. The governing dynamical equations for the body are obtained from variational consideration by assuming that both fundamental forms on the material manifold are dynamical variables in a Lagrangian field theory. In the case where growth can be modeled by a Rayleigh potential, we also obtain the governing equations for growth in the form of kinetic equations coupling the evolution of the first and the second fundamental forms with the state of stress of the shell. We apply these ideas to obtain stress-free growth fields of a planar sheet, the time evolution of a morphoelastic circular cylindrical shell subject to time-dependent internal pressure, and the residual stress of a morphoelastic planar circular shell.
Geometric phase effects in ultracold chemistry
NASA Astrophysics Data System (ADS)
Hazra, Jisha; Naduvalath, Balakrishnan; Kendrick, Brian K.
2016-05-01
In molecules, the geometric phase, also known as Berry's phase, originates from the adiabatic transport of the electronic wavefunction when the nuclei follow a closed path encircling a conical intersection between two electronic potential energy surfaces. It is demonstrated that the inclusion of the geometric phase has an important effect on ultracold chemical reaction rates. The effect appears in rotationally and vibrationally resolved integral cross sections as well as cross sections summed over all product quantum states. It arises from interference between scattering amplitudes of two reaction pathways: a direct path and a looping path that encircle the conical intersection between the two lowest adiabatic electronic potential energy surfaces. Illustrative results are presented for the O+ OH --> H+ O2 reaction and for hydrogen exchange in H+ H2 and D+HD reactions. It is also qualitatively demonstrated that the geometric phase effect can be modulated by applying an external electric field allowing the possibility of quantum control of chemical reactions in the ultracold regime. This work was supported in part by NSF Grant PHY-1505557 (N.B.) and ARO MURI Grant No. W911NF-12-1-0476 (N.B.).
Early sex differences in weighting geometric cues.
Lourenco, Stella F; Addy, Dede; Huttenlocher, Janellen; Fabian, Lydia
2011-11-01
When geometric and non-geometric information are both available for specifying location, men have been shown to rely more heavily on geometry compared to women. To shed insight on the nature and developmental origins of this sex difference, we examined how 18- to 24-month-olds represented the geometry of a surrounding (rectangular) space when direct non-geometric information (i.e. a beacon) was also available for localizing a hidden object. Children were tested on a disorientation task with multiple phases. Across experiments, boys relied more heavily than girls on geometry to guide localization, as indicated by their errors during the initial phase of the task, and by their search choices following transformations that left only geometry available, or that, under limited conditions, created a conflict between beacon and geometry. Analyses of search times suggested that girls, like boys, had encoded geometry, and testing in a square space ruled out explanations concerned with motivational and methodological variables. Taken together, the findings provide evidence for an early sex difference in the weighting of geometry. This sex difference, we suggest, reflects subtle variation in how boys and girls approach the problem of combining multiple sources of location information.
Landsat-5 bumper-mode geometric correction
Storey, J.C.; Choate, Michael J.
2004-01-01
The Landsat-5 Thematic Mapper (TM) scan mirror was switched from its primary operating mode to a backup mode in early 2002 in order to overcome internal synchronization problems arising from long-term wear of the scan mirror mechanism. The backup bumper mode of operation removes the constraints on scan start and stop angles enforced in the primary scan angle monitor operating mode, requiring additional geometric calibration effort to monitor the active scan angles. It also eliminates scan timing telemetry used to correct the TM scan geometry. These differences require changes to the geometric correction algorithms used to process TM data. A mathematical model of the scan mirror's behavior when operating in bumper mode was developed. This model includes a set of key timing parameters that characterize the time-varying behavior of the scan mirror bumpers. To simplify the implementation of the bumper-mode model, the bumper timing parameters were recast in terms of the calibration and telemetry data items used to process normal TM imagery. The resulting geometric performance, evaluated over 18 months of bumper-mode operations, though slightly reduced from that achievable in the primary operating mode, is still within the Landsat specifications when the data are processed with the most up-to-date calibration parameters.
Geometrical branching model: Correlations and jets
NASA Astrophysics Data System (ADS)
Hwa, Rudolph C.
1988-04-01
A geometrical model for multiparticle production at low as well as high pT is discussed. Below the threshold of substantial production of jets, the model has geometrical scaling and Koba-Nielsen-Olesen scaling, the latter being a result of Furry branching in multiplicity distribution at each impact parameter. Above the threshold the production of jets is explicitly taken into account by use of perturbative QCD. The separation into soft and hard components is done in the eikonal formalism consistent with unitarity. Geometrical scaling defines the soft component of the eikonal function. The hard component is related to the jet-production cross section; the pT cutoff is not chosen arbitrarily, but is to be determined by σel and σtot. Forward-backward multiplicity correlation can be calculated separately for the cases of no jets and with jets. The emphasis in this paper is on the formalism of the model. The procedure to determine the multiplicity distribution at all s is discussed.
Hardware description languages
NASA Technical Reports Server (NTRS)
Tucker, Jerry H.
1994-01-01
Hardware description languages are special purpose programming languages. They are primarily used to specify the behavior of digital systems and are rapidly replacing traditional digital system design techniques. This is because they allow the designer to concentrate on how the system should operate rather than on implementation details. Hardware description languages allow a digital system to be described with a wide range of abstraction, and they support top down design techniques. A key feature of any hardware description language environment is its ability to simulate the modeled system. The two most important hardware description languages are Verilog and VHDL. Verilog has been the dominant language for the design of application specific integrated circuits (ASIC's). However, VHDL is rapidly gaining in popularity.
Geometric morphometric analysis of mandibular shape diversity in Pan.
Robinson, Chris
2012-07-01
The aim of this research is to determine whether geometric morphometric (GM) techniques can provide insights into how the shape of the mandibular corpus differs between bonobos and chimpanzees and to explore the potential implications of those results for our understanding of hominin evolution. We focused on this region of the mandible because of the relative frequency with which it has been recovered in the hominin fossil record. In addition, no previous study had explored in-depth three-dimensional (3D) mandibular corpus shape differences between adults of the two Pan species using geometric morphometrics. GM methods enable researchers to quantitatively analyze and visualize 3D shape changes in skeletal elements and provide an important compliment to traditional two-dimensional analyses. Eighteen mandibular landmarks were collected using a Microscribe 3DX portable digitizer. Specimen configurations were superimposed using Generalized Procrustes analysis and the projections of the fitted coordinates to tangent space were analyzed using multivariate statistics. The size-adjusted corpus shapes of Pan paniscus and Pan troglodytes could be assigned to species with approximately 93% accuracy and the Procrustes distance between the two species was significant. Analyses of the residuals from a multivariate linear regression of the data on centroid size suggested that much of the shape difference between the species is size-related. Chimpanzee subspecies and a small sample of Australopithecus specimens could be correctly identified to taxon, at best, only 75% of the time, although the Procrustes distances between these taxa were significant. The shape of the mandibular symphysis was identified as especially useful in differentiating Pan species from one another. This suggests that this region of the mandible has the potential to be informative for taxonomic analyses of fossil hominoids, including hominins. The results also have implications for phylogenetic hypotheses of
A survey of the core-congruential formulation for geometrically nonlinear TL finite elements
NASA Technical Reports Server (NTRS)
Felippa, Carlos A.; Crivelli, Luis A.; Haugen, Bjorn
1994-01-01
This article presents a survey of the core-congruential formulation (CCF) for geometrically nonlinear mechanical finite elements based on the total Lagrangian (TL) kinematic description. Although the key ideas behind the CCF can be traced back to Rajasekaran and Murray in 1973, it has not subsequently received serious attention. The CCF is distinguished by a two-phase development of the finite element stiffness equations. The initial phase developed equations for individual particles. These equations are expressed in terms of displacement gradients as degrees of freedom. The second phase involves congruential-type transformations that eventually binds the element particles of an individual element in terms of its node-displacement degrees of freedom. Two versions of the CCF, labeled direct and generalized, are distinguished. The direct CCF (DCCF) is first described in general form and then applied to the derivation of geometrically nonlinear bar, and plane stress elements using the Green-Lagrange strain measure. The more complex generalized CCF (GCCF) is described and applied to the derivation of 2D and 3D Timoshenko beam elements. Several advantages of the CCF, notably the physically clean separation of material and geometric stiffnesses, and its independence with respect to the ultimate choice of shape functions and element degrees of freedom, are noted. Application examples involving very large motions solved with the 3D beam element display the range of applicability of this formulation, which transcends the kinematic limitations commonly attributed to the TL description.
Geometrization of the physics with teleparallelism. II. Towards a fully geometric Dirac equation
NASA Astrophysics Data System (ADS)
Vargas, José G.; Torr, Douglas G.; Lecompte, Alvaro
1992-04-01
In an accompanying paper (I), it is shown that the basic equations of the theory of Lorentzian connections with teleparallelism (TP) acquire standard forms of physical field equations upon removal of the constraints represented by the Bianchi identities. A classical physical theory results that supersedes general relativity and Maxwell-Lorentz electrodynamics if the connection is viewed as Finslerian. The theory also encompasses a short-range, strong, classical interaction. It has, however, an open end, since the source side of the torsion field equation is not geometric. In this paper, Kaehler's partial geometrization of the Dirac equation is taken as a starting point for the development of fully geometric Dirac equations via the correspondence principle given in I. For this purpose, Kaehler's calculus (where the spinors are differential forms) is generalized so that it also applies when the torsion is not zero. The point is then made that the forms can take values in tangent Clifford algebras rather than in tensor algebras. The basic “Eigenschaft” of the Kaehler calculus also is examined from the physical perspective of dimensional analysis. Geometric Dirac equations of great structural simplicity are finally inferred from the standard Dirac equation by using the aforementioned correspondence principle. The realm of application of the Dirac theory is thus enriched in principle, though only at an abstract level at this point: the standard spinors, which are scalar-valued forms in the Kaehler version of that theory, become Clifford-valued. In addition, the geometrization of the Dirac equation implies a geometrization of the Dirac current. When this current is replaced in the field equations for the torsion, the theory of Paper I becomes fully geometric.
Geometric Approaches to Quadratic Equations from Other Times and Places.
ERIC Educational Resources Information Center
Allaire, Patricia R.; Bradley, Robert E.
2001-01-01
Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)
Chang, Y.M.; Grot, R.A.; Wood, J.T.
1985-06-01
This report presents the description of the laboratory apparatus and preliminary results of the quantitative evaluation of three high-resolution and two low-resolution infrared imaging systems. These systems which are commonly used for building diagnostics are tested under various background temperatures (from -20/sup 0/C to 25/sup 0/C) for their minimum resolvable temperature differences (MRTD) at spatial frequencies from 0.03 to 0.25 cycles per milliradian. The calibration curves of absolute and differential temperature measurements are obtained for three systems. The signal transfer function and line spread function at ambient temperature of another three systems are also measured. Comparisons of the dependence of the MRTD on background temperatures from the measured data with the predicted values given in ASHRAE Standards 101-83 are also included. The dependence of background temperatures for absolute temperature measurements are presented, as well as comparison of measured data and data given by the manufacturer. Horizontal on-axis magnification factors of the geometric transfer function of two systems are also established to calibrate the horizontal axis for the measured line spread function to obtain the modulation transfer function. The variation of the uniformity for horizontal display of these two sensors are also observed. Included are detailed descriptions of laboratory design, equipment setup, and evaluation procedures of each test. 10 refs., 38 figs., 12 tabs.
Behavioral Assembly Required: Particularly for Quantitative Courses
ERIC Educational Resources Information Center
Mazen, Abdelmagid
2008-01-01
This article integrates behavioral approaches into the teaching and learning of quantitative subjects with application to statistics. Focusing on the emotional component of learning, the article presents a system dynamic model that provides descriptive and prescriptive accounts of learners' anxiety. Metaphors and the metaphorizing process are…
Quantitative Measurement of Trans-Fats by Infrared Spectroscopy
ERIC Educational Resources Information Center
Walker, Edward B.; Davies, Don R.; Campbell, Mike
2007-01-01
Trans-fat is a general term, which is mainly used to describe the various trans geometric isomers present in unsaturated fatty acids. Various techniques are now used for a quantitative measurement of the amount of trans-fats present in foods and cooking oil.
Children's Use of Geometric Information in Mapping Tasks
ERIC Educational Resources Information Center
Vasilyeva, Marina; Bowers, Edmond
2006-01-01
Accumulating evidence, particularly from research using the disorientation technique, demonstrates early sensitivity to geometric properties of space. However, it is not known whether children can use geometric cues to interpret a map. The current study examined how 3- to 6-year-olds use geometric features of layouts in solving mapping tasks.…
Lê, François
2016-09-01
Argument This paper challenges the use of the notion of "culture" to describe a particular organization of mathematical knowledge, shared by a few mathematicians over a short period of time in the second half of the nineteenth century. This knowledge relates to "geometrical equations," objects that proved crucial for the mechanisms of encounters between equation theory, substitution theory, and geometry at that time, although they were not well-defined mathematical objects. The description of the mathematical collective activities linked to "geometrical equations," and especially the technical aspects of these activities, is made on the basis of a sociological definition of "culture." More precisely, after an examination of the social organization of the group of mathematicians, I argue that these activities form an intricate system of patterns, symbols, and values, for which I suggest a characterization as a "cultural system."
Lê, François
2016-09-01
Argument This paper challenges the use of the notion of "culture" to describe a particular organization of mathematical knowledge, shared by a few mathematicians over a short period of time in the second half of the nineteenth century. This knowledge relates to "geometrical equations," objects that proved crucial for the mechanisms of encounters between equation theory, substitution theory, and geometry at that time, although they were not well-defined mathematical objects. The description of the mathematical collective activities linked to "geometrical equations," and especially the technical aspects of these activities, is made on the basis of a sociological definition of "culture." More precisely, after an examination of the social organization of the group of mathematicians, I argue that these activities form an intricate system of patterns, symbols, and values, for which I suggest a characterization as a "cultural system." PMID:27573998
NASA Astrophysics Data System (ADS)
Yang, Kun
2016-04-01
We show that an acoustic crystalline wave gives rise to an effect similar to that of a gravitational wave to an electron gas. Applying this idea to a two-dimensional electron gas in the fractional quantum Hall regime, this allows for experimental study of its intra-Landau level dynamical response in the long-wavelength limit. To study such response we generalize Haldane's geometrical description of fractional quantum Hall states to situations where the external metric is time dependent. We show that such time-dependent metric (generated by acoustic wave) couples to collective modes of the system, including a quadrapolar mode at long wavelength, and magnetoroton at finite wavelength. Energies of these modes can be revealed in spectroscopic measurements, controlled by strain-induced Fermi velocity anisotropy. We argue that such geometrical probe provides a potentially highly useful alternative probe of quantum Hall liquids, in addition to the usual electromagnetic response.
On-ground characterization of Rosetta/VIRTIS-M. I. Spectral and geometrical calibrations
Ammannito, E.; Filacchione, G.; Coradini, A.; Capaccioni, F.; Piccioni, G.; De Sanctis, M. C.; Dami, M.; Barbis, A.
2006-09-15
The complete characterization of complex imaging spectrometers, such as VIRTIS-M (visual infrared thermal imaging spectrometer) aboard the Rosetta mission, requires a detailed and prolonged activity starting with the instrument integration and continuing during the entire operational life of the experiment. In this article we report the main experimental activities realized during the on-ground characterizations to evaluate the spectral and geometric performances in order to check the conformance with the technical requirements derived from the scientific goals of the experiment. Spectral calibrations allow to confirm instrumental spectral range, resolution, and sampling; geometric calibrations are necessary to estimate the pixel and slit functions, field of view extension, and possible optical aberrations. Two separate sections are dedicated to each one of these subjects, including the strategy followed to prepare measurements, a basic description of the on-ground experimental setups, and the analysis of the collected data.
Optimization of biotechnological systems through geometric programming
Marin-Sanguino, Alberto; Voit, Eberhard O; Gonzalez-Alcon, Carlos; Torres, Nestor V
2007-01-01
Background In the past, tasks of model based yield optimization in metabolic engineering were either approached with stoichiometric models or with structured nonlinear models such as S-systems or linear-logarithmic representations. These models stand out among most others, because they allow the optimization task to be converted into a linear program, for which efficient solution methods are widely available. For pathway models not in one of these formats, an Indirect Optimization Method (IOM) was developed where the original model is sequentially represented as an S-system model, optimized in this format with linear programming methods, reinterpreted in the initial model form, and further optimized as necessary. Results A new method is proposed for this task. We show here that the model format of a Generalized Mass Action (GMA) system may be optimized very efficiently with techniques of geometric programming. We briefly review the basics of GMA systems and of geometric programming, demonstrate how the latter may be applied to the former, and illustrate the combined method with a didactic problem and two examples based on models of real systems. The first is a relatively small yet representative model of the anaerobic fermentation pathway in S. cerevisiae, while the second describes the dynamics of the tryptophan operon in E. coli. Both models have previously been used for benchmarking purposes, thus facilitating comparisons with the proposed new method. In these comparisons, the geometric programming method was found to be equal or better than the earlier methods in terms of successful identification of optima and efficiency. Conclusion GMA systems are of importance, because they contain stoichiometric, mass action and S-systems as special cases, along with many other models. Furthermore, it was previously shown that algebraic equivalence transformations of variables are sufficient to convert virtually any types of dynamical models into the GMA form. Thus
Aerospace plane guidance using geometric control theory
NASA Technical Reports Server (NTRS)
Van Buren, Mark A.; Mease, Kenneth D.
1990-01-01
A reduced-order method employing decomposition, based on time-scale separation, of the 4-D state space in a 2-D slow manifold and a family of 2-D fast manifolds is shown to provide an excellent approximation to the full-order minimum-fuel ascent trajectory. Near-optimal guidance is obtained by tracking the reduced-order trajectory. The tracking problem is solved as regulation problems on the family of fast manifolds, using the exact linearization methodology from nonlinear geometric control theory. The validity of the overall guidance approach is indicated by simulation.
Crystallization kinetics: A solution for geometrical impingement
NASA Astrophysics Data System (ADS)
Clemente, R. A.; Saleh, A. M.
2002-04-01
Starting from the wrong derivation by Erukhimovitch and Baram of an equation alternative to the classical Kolmogoroff-Johnson-Mehl-Avrami one for the transformed fraction in an infinite specimen, undergoing an isothermal first-order phase transformation, it is shown that a different exact solution of the geometrical problem of impingement can be obtained. Such solution is equivalent to the empirical one already presented by Austin and Rickett more than sixty years ago and allows to better fit experimental results for isothermal transformations. This also suggests that perhaps different statistical derivations could allow to reach the same result.
Geometric Aspects of Biological Sequence Comparison
Stojmirović, Aleksandar
2009-01-01
Abstract We introduce a geometric framework suitable for studying the relationships among biological sequences. In contrast to previous works, our formulation allows asymmetric distances (quasi-metrics), originating from uneven weighting of strings, which may induce non-trivial partial orders on sets of biosequences. The distances considered are more general than traditional generalized string edit distances. In particular, our framework enables non-trivial conversion between sequence similarities, both local and global, and distances. Our constructions apply to a wide class of scoring schemes and require much less restrictive gap penalties than the ones regularly used. Numerous examples are provided to illustrate the concepts introduced and their potential applications. PMID:19361329
A geometric criterion for adiabatic chaos
Kaper, T.J. ); Kovacic, G. )
1994-03-01
Chaos in adiabatic Hamiltonian systems is a recent discovery and a pervasive phenomenon in physics. In this work, a geometric criterion is discussed based on the theory of action from classical mechanics to detect the existence of Smale horseshoe chaos in adiabatic systems. It is used to show that generic adiabatic planar Hamiltonian systems exhibit stochastic dynamics in large regions of phase space. To illustrate the method, results are obtained for three problems concerning relativistic particle dynamics, fluid mechanics, and passage through resonance, results which either could not be obtained with existing methods, or which were difficult and analytically impractical to obtain with them.
Geometric derivation of the chronometric redshift.
Segal, I E
1993-01-01
The chronometric redshift-distance relation z = tan 2(1/2rho), where rho is the distance in radians in the Einstein metric, is derived by an elementary geometric analysis comparable to that in traditional analysis of the expanding universe model. The differential dTt of Einstein time evolution Tt through time t, as applied to the local Minkowski coordinates x, takes the form sec2(1/2t). At the point of observation t = rho, implying that for a sufficiently localized source, observed wave lengths are a factor of sec2(1/2rho) greater than the corresponding emitted wave lengths. PMID:11607440
Geometrical Wake of a Smooth Flat Collimator
Stupakov, G.V.; /SLAC
2011-09-09
A transverse geometrical wake generated by a beam passing through a smooth flat collimator with a gradually varying gap between the upper and lower walls is considered. Based on generalization of the approach recently developed for a smooth circular taper we reduce the electromagnetic problem of the impedance calculation to the solution of two much simpler static problems - a magnetostatic and an electrostatic ones. The solution shows that in the limit of not very large frequencies, the impedance increases with the ratio h/d where h is the width and d is the distance between the collimating jaws. Numerical results are presented for the NLC Post Linac collimator.
State-Space Regularization: Geometric Theory
Chavent, G.; Kunisch, K.
1998-05-15
Regularization of nonlinear ill-posed inverse problems is analyzed for a class of problems that is characterized by mappings which are the composition of a well-posed nonlinear and an ill-posed linear mapping. Regularization is carried out in the range of the nonlinear mapping. In applications this corresponds to the state-space variable of a partial differential equation or to preconditioning of data. The geometric theory of projection onto quasi-convex sets is used to analyze the stabilizing properties of this regularization technique and to describe its asymptotic behavior as the regularization parameter tends to zero.
The minimal geometric deformation approach extended
NASA Astrophysics Data System (ADS)
Casadio, R.; Ovalle, J.; da Rocha, Roldão
2015-11-01
The minimal geometric deformation approach was introduced in order to study the exterior spacetime around spherically symmetric self-gravitating systems, such as stars or similar astrophysical objects, in the Randall-Sundrum brane-world framework. A consistent extension of this approach is developed here, which contains modifications of both the time component and the radial component of a spherically symmetric metric. A modified Schwarzschild geometry is obtained as an example of its simplest application, and a new solution that is potentially useful to describe stars in the brane-world is also presented.
Some Geometrical Aspects of M-Theory
NASA Astrophysics Data System (ADS)
de Azcárraga, José A.; Izquierdo, José M.
2008-06-01
Some geometrical aspects of super-p-brane theory, M-theory, and their connection with supergravity, are reviewed. In particular, the different fractions of preserved supersymmetries are discussed both from the algebraic and the supergravity solutions point of view. We also review the `preon conjecture' according to which states preserving a 31/32 fraction of supersymmetries would be the building blocks of M-theory, and on the failed attempts made so far to find these states in terms of supergravity solutions.
Geometric derivation of the quantum speed limit
Jones, Philip J.; Kok, Pieter
2010-08-15
The Mandelstam-Tamm and Margolus-Levitin inequalities play an important role in the study of quantum-mechanical processes in nature since they provide general limits on the speed of dynamical evolution. However, to date there has been only one derivation of the Margolus-Levitin inequality. In this paper, alternative geometric derivations for both inequalities are obtained from the statistical distance between quantum states. The inequalities are shown to hold for unitary evolution of pure and mixed states, and a counterexample to the inequalities is given for evolution described by completely positive trace-preserving maps. The counterexample shows that there is no quantum speed limit for nonunitary evolution.
NASA Astrophysics Data System (ADS)
Ertekin, E.; Solak, S.; Yazici, E.
2010-12-01
The aim of this study is to identify the effects of formalism in teaching on primary and secondary school mathematics teacher trainees' algebraic and geometric interpretations of the notions of linear dependency/independency. Quantitative research methods are drawn in order to determine differences in success levels between algebraic and geometric interpretations of the linear dependency/independency of vectors presented in two- and three-dimensional space. On the other hand, qualitative research methods were utilized in order to investigate thinking modes involved in the geometric interpretation of the same notion. The participants were a total of 144 teacher trainees registered at the Selçuk University, Education Faculty in 2007-2008 academic year. 33 participants were first year students at Secondary Mathematics Education Department, while 111 were second year students at Primary Mathematics Education Department. The results indicated that correlations between the formal definition of the notions of linear dependency/independency and the items of the test which required algebraic and geometric interpretation were both low. Yet, the correlation for the algebraic dimension of the test was higher than the geometric dimension. Likewise, algebraic mean success score was significantly higher than the geometric mean score.
On the minimum of independent geometrically distributed random variables
NASA Technical Reports Server (NTRS)
Ciardo, Gianfranco; Leemis, Lawrence M.; Nicol, David
1994-01-01
The expectations E(X(sub 1)), E(Z(sub 1)), and E(Y(sub 1)) of the minimum of n independent geometric, modifies geometric, or exponential random variables with matching expectations differ. We show how this is accounted for by stochastic variability and how E(X(sub 1))/E(Y(sub 1)) equals the expected number of ties at the minimum for the geometric random variables. We then introduce the 'shifted geometric distribution' and show that there is a unique value of the shift for which the individual shifted geometric and exponential random variables match expectations both individually and in the minimums.
Finite octree meshing through topologically driven geometric operators
NASA Technical Reports Server (NTRS)
Grice, Kurt R.
1987-01-01
The octree technique is developed into the finite octree, and an overview is given. Modeler requirements are given. The octree discretization is discussed along with geometric communication operators. Geometric communication operators returning topological associativity and geometric communication operators returning spatial data are also discussed and illustrated. The advantages are given of the boundary representation and of geometric communication operators. The implementation plays an important role in the integration with a variety of geometric modelers. The capabilities of closed loop processes within a complete finite element system are presented.
Ritchie, L.T.; Alpert, D.J.; Burke, R.P.; Johnson, J.D.; Ostmeyer, R.M.; Aldrich, D.C.; Blond, R.M.
1984-03-01
The CRAC2 computer code is a revised version of CRAC (Calculation of Reactor Accident Consequences) which was developed for the Reactor Safety Study. This document provides an overview of the CRAC2 code and a description of each of the models used. Significant improvements incorporated into CRAC2 include an improved weather sequence sampling technique, a new evacuation model, and new output capabilities. In addition, refinements have been made to the atmospheric transport and deposition model. Details of the modeling differences between CRAC2 and CRAC are emphasized in the model descriptions.
The Isosceles Three-Body Problem: a Global Geometric Analysis
NASA Astrophysics Data System (ADS)
Chesley, Steven Ross
1998-12-01
This study demonstrates the use of the Poincare map to determine the evolution of areas in the surface of section under a single iteration, rather than scrutinizing a few initial conditions for many iterations as is usually done. This new approach provides details on the underlying structure of what are simply 'chaotic seas' in the traditional surface-of-section plot. Furthermore, since many iterations of the map are not required, the present approach substantially avoids issues of numerical reliability. The isosceles three-body problem has been reduced to a two-dimensional area-preserving Poincare map f depending on two parameters: the mass ratio, and the total angular momentum. The region of allowable motion is divided into subregions according to a symbolic dynamics representation. In this new context one considers how the images of the subregions intersect with their preimages. This leads to an elegant geometric description of the dynamics in the chaotic regions, and to a nearly complete global description of the system. This description immediately provides the existence of various types of motion such as capture-escape, permanent capture, ejection-collision, etc., and their corresponding measures in the map domain. Moreover, this method can be used to show that certain dynamical behaviors are not permitted by the equations of motion. The problem is investigated in three stages. First, the planar (zero angular momentum) case with three equal masses is studied in considerable detail. In this case there exist two important invariant subsets under f. The first is a Cantor set with zero measure. The existence of this chaotic set follows from the fact that f is similar to the Smale horseshoe map in part of the domain. The second subset is an invariant KAM region with positive measure surrounding an elliptic fixed point-the 'main' periodic orbit. The second stage explores the bifurcations in the mass ratio for the planar case. Here the entire chaotic invariant set
Geometric Quality Assessment of LIDAR Data Based on Swath Overlap
NASA Astrophysics Data System (ADS)
Sampath, A.; Heidemann, H. K.; Stensaas, G. L.
2016-06-01
This paper provides guidelines on quantifying the relative horizontal and vertical errors observed between conjugate features in the overlapping regions of lidar data. The quantification of these errors is important because their presence quantifies the geometric quality of the data. A data set can be said to have good geometric quality if measurements of identical features, regardless of their position or orientation, yield identical results. Good geometric quality indicates that the data are produced using sensor models that are working as they are mathematically designed, and data acquisition processes are not introducing any unforeseen distortion in the data. High geometric quality also leads to high geolocation accuracy of the data when the data acquisition process includes coupling the sensor with geopositioning systems. Current specifications (e.g. Heidemann 2014) do not provide adequate means to quantitatively measure these errors, even though they are required to be reported. Current accuracy measurement and reporting practices followed in the industry and as recommended by data specification documents also potentially underestimate the inter-swath errors, including the presence of systematic errors in lidar data. Hence they pose a risk to the user in terms of data acceptance (i.e. a higher potential for Type II error indicating risk of accepting potentially unsuitable data). For example, if the overlap area is too small or if the sampled locations are close to the center of overlap, or if the errors are sampled in flat regions when there are residual pitch errors in the data, the resultant Root Mean Square Differences (RMSD) can still be small. To avoid this, the following are suggested to be used as criteria for defining the inter-swath quality of data: a) Median Discrepancy Angle b) Mean and RMSD of Horizontal Errors using DQM measured on sloping surfaces c) RMSD for sampled locations from flat areas (defined as areas with less than 5 degrees of slope
Quantitative Literacy Provision in the First Year of Medical Studies
ERIC Educational Resources Information Center
Frith, V.
2011-01-01
This article presents a description of and motivation for the quantitative literacy (numeracy) intervention in the first year of medical studies at a South African university. This intervention is a response to the articulation gap between the quantitative literacy of many first-year medical students and the demands of their curriculum.…
A geometric approach to direct minimization
NASA Astrophysics Data System (ADS)
van Voorhis, Troy; Head-Gordon, Martin
The approach presented, geometric direct minimization (GDM), is derived from purely geometrical arguments, and is designed to minimize a function of a set of orthonormal orbitals. The optimization steps consist of sequential unitary transformations of the orbitals, and convergence is accelerated using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) approach in the iterative subspace, together with a diagonal approximation to the Hessian for the remaining degrees of freedom. The approach is tested by implementing the solution of the self-consistent field (SCF) equations and comparing results with the standard direct inversion in the iterative subspace (DIIS) method. It is found that GDM is very robust and converges in every system studied, including several cases in which DIIS fails to find a solution. For main group compounds, GDM convergence is nearly as rapid as DIIS, whereas for transition metalcontaining systems we find that GDM is significantly slower than DIIS. A hybrid procedure where DIIS is used for the first several iterations and GDM is used thereafter is found to provide a robust solution for transition metal-containing systems.
Geometric representation of fundamental particles' inertial mass
Schachter, L.; Spencer, James
2015-07-22
A geometric representation of the (N = 279) masses of quarks, leptons, hadrons and gauge bosons was introduced by employing a Riemann Sphere facilitating the interpretation of the N masses in terms of a single particle, the Masson, which might be in one of the N eigen-states. Geometrically, its mass is the radius of the Riemann Sphere. Dynamically, its derived mass is near the mass of the nucleon regardless of whether it is determined from all N particles of only the hadrons, the mesons or the baryons separately. Ignoring all the other properties of these particles, it is shown that the eigen-values, the polar representation θ_{ν} of the masses on the Sphere, satisfy the symmetry θ_{ν} + θ_{N+1-ν} = π within less than 1% relative error. In addition, these pair correlations include the pairs θ_{γ} + θ_{top} ≃ π and θ_{gluon} + θ_{H} ≃ π as well as pairing the weak gauge bosons with the three neutrinos.
Translating cosmological special relativity into geometric algebra
NASA Astrophysics Data System (ADS)
Horn, Martin Erik
2012-11-01
Geometric algebra and Clifford algebra are important tools to describe and analyze the physics of the world we live in. Although there is enormous empirical evidence that we are living in four dimensional spacetime, mathematical worlds of higher dimensions can be used to present the physical laws of our world in an aesthetical and didactical more appealing way. In physics and mathematics education we are therefore confronted with the question how these high dimensional spaces should be taught. But as an immediate confrontation of students with high dimensional compactified spacetimes would expect too much from them at the beginning of their university studies, it seems reasonable to approach the mathematics and physics of higher dimensions step by step. The first step naturally is the step from four dimensional spacetime of special relativity to a five dimensional spacetime world. As a toy model for this artificial world cosmological special relativity, invented by Moshe Carmeli, can be used. This five dimensional non-compactified approach describes a spacetime which consists not only of one time dimension and three space dimensions. In addition velocity is regarded as a fifth dimension. This model very probably will not represent physics correctly. But it can be used to discuss and analyze the consequences of an additional dimension in a clear and simple way. Unfortunately Carmeli has formulated cosmological special relativity in standard vector notation. Therefore a translation of cosmological special relativity into the mathematical language of Grassmann and Clifford (Geometric algebra) is given and the physics of cosmological special relativity is discussed.
Nanoparticle fabrication by geometrically confined nanosphere lithography
NASA Astrophysics Data System (ADS)
Denomme, Ryan C.; Iyer, Krishna; Kreder, Michael; Smith, Brendan; Nieva, Patricia M.
2013-07-01
Arrays of metal nanoparticles, typically gold or silver, exhibit localized surface plasmon resonance, a phenomenon that has many applications, such as chemical and biological sensing. However, fabrication of metal nanoparticle arrays with high uniformity and repeatability, at a reasonable cost, is difficult. Nanosphere lithography (NSL) has been used before to produce inexpensive nanoparticle arrays through the use of monolayers of self-assembled microspheres as a deposition mask. However, control over the size and location of the arrays, as well as uniformity over large areas is poor, thus limiting its use to research purposes. In this paper, a new NSL method, called here geometrically confined NSL (GCNSL), is presented. In GCNSL, microsphere assembly is confined to geometric patterns defined in photoresist, allowing high-precision and large-scale nanoparticle patterning while still remaining low cost. Using this new method, it is demonstrated that 400 nm polystyrene microspheres can be assembled inside of large arrays of photoresist patterns. Results show that optimal microsphere assembly is achieved with long and narrow rectangular photoresist patterns. The combination of microsphere monolayers and photoresist patterns is then used as a deposition mask to produce silver nanoparticles at precise locations on the substrate with high uniformity, repeatability, and quality.
Geometric and Radiometric Evaluation of Rasat Images
NASA Astrophysics Data System (ADS)
Cam, Ali; Topan, Hüseyin; Oruç, Murat; Özendi, Mustafa; Bayık, Çağlar
2016-06-01
RASAT, the second remote sensing satellite of Turkey, was designed and assembled, and also is being operated by TÜBİTAK Uzay (Space) Technologies Research Institute (Ankara). RASAT images in various levels are available free-of-charge via Gezgin portal for Turkish citizens. In this paper, the images in panchromatic (7.5 m GSD) and RGB (15 m GSD) bands in various levels were investigated with respect to its geometric and radiometric characteristics. The first geometric analysis is the estimation of the effective GSD as less than 1 pixel for radiometrically processed level (L1R) of both panchromatic and RGB images. Secondly, 2D georeferencing accuracy is estimated by various non-physical transformation models (similarity, 2D affine, polynomial, affine projection, projective, DLT and GCP based RFM) reaching sub-pixel accuracy using minimum 39 and maximum 52 GCPs. The radiometric characteristics are also investigated for 8 bits, estimating SNR between 21.8-42.2, and noise 0.0-3.5 for panchromatic and MS images for L1R when the sea is masked to obtain the results for land areas. The analysis show that RASAT images satisfies requirements for various applications. The research is carried out in Zonguldak test site which is mountainous and partly covered by dense forest and urban areas.
Geometrical analysis of cytochrome c unfolding
NASA Astrophysics Data System (ADS)
Urie, Kristopher G.; Pletneva, Ekaterina; Gray, Harry B.; Winkler, Jay R.; Kozak, John J.
2011-01-01
A geometrical model has been developed to study the unfolding of iso-1 cytochrome c. The model draws on the crystallographic data reported for this protein. These data were used to calculate the distance between specific residues in the folded state, and in a sequence of extended states defined by n = 3, 5, 7, 9, 11, 13, and 15 residue units. Exact calculations carried out for each of the 103 residues in the polypeptide chain demonstrate that different regions of the chain have different unfolding histories. Regions where there is a persistence of compact structures can be identified, and this geometrical characterization is fully consistent with analyses of time-resolved fluorescence energy-transfer (TrFET) data using dansyl-derivatized cysteine side-chain probes at positions 39, 50, 66, 85, and 99. The calculations were carried out assuming that different regions of the polypeptide chain unfold synchronously. To test this assumption, lattice Monte Carlo simulations were performed to study systematically the possible importance of asynchronicity. Calculations show that small departures from synchronous dynamics can arise if displacements of residues in the main body of the chain are much more sluggish than near-terminal residues.
Processing geometric representations on SIMD computers
Hung, Y.
1988-01-01
This thesis contributes to designing parallel algorithms to process border and linear quadtree representations on mesh-connected computers (MCCs) and hypercubes. This thesis consists of two parts. The first part studies some primitive operations on mesh-connected computers and hypercubes. These include various routing tasks and several versions of the parallel prefix algorithms. It is shown how general routings can be done in O(n) time on an n {times} n mesh and O(d{sup 2}) on a d-dimensional hypercube (d-cube). Also presented are optimal routing algorithms for some classes of permutation routings. For the parallel prefix problem, the author describes how the initial prefixes can be computed efficiently when the data are mapped into the MCC or the hypercube in some specific manners. The second part deals with processing border codes and linear quadtrees. These include generating border codes and linear quadtrees from a given image, reconstructing the image from its geometric representations, computing various geometric properties, answering the point-in-region query, performing set operations, etc. For linear quadtrees, algorithms are also designed for finding neighbors of equal or larger size for all nodes simultaneously. A connected component-labeling algorithm is also presented.
A Geometric Theory of Growth Mechanics
NASA Astrophysics Data System (ADS)
Yavari, Arash
2010-12-01
In this paper we formulate a geometric theory of the mechanics of growing solids. Bulk growth is modeled by a material manifold with an evolving metric. The time dependence of the metric represents the evolution of the stress-free (natural) configuration of the body in response to changes in mass density and “shape”. We show that the time dependency of the material metric will affect the energy balance and the entropy production inequality; both the energy balance and the entropy production inequality have to be modified. We then obtain the governing equations covariantly by postulating invariance of energy balance under time-dependent spatial diffeomorphisms. We use the principle of maximum entropy production in deriving an evolution equation for the material metric. In the case of isotropic growth, we find those growth distributions that do not result in residual stresses. We then look at Lagrangian field theory of growing elastic solids. We will use the Lagrange-d’Alembert principle with Rayleigh’s dissipation functions to derive the governing equations. We make an explicit connection between our geometric theory and the conventional multiplicative decomposition of the deformation gradient, F= F e F g, into growth and elastic parts. We linearize the nonlinear theory and derive a linearized theory of growth mechanics. Finally, we obtain the stress-free growth distributions in the linearized theory.
Geometrical, response, and gap properties of Lindbladians
NASA Astrophysics Data System (ADS)
Albert, Victor V.; Bradlyn, Barry; Fraas, Martin; Jiang, Liang
We study Lindbladians admitting multi-dimensional steady-state subspaces (SSS) which can be used to store, protect, and process quantum information. We derive an analytical formula for the left eigenmatrices of such Lindbladians corresponding to purely imaginary eigenvalues. This formula resolves how Lindbladian evolution affects perturbative response and geometrical features of the SSS and allows us to generalize recent work to all types of SSS. We show that Hamiltonian and certain jump operator perturbations induce, to first order, exclusively unitary evolution on the SSS. Similarly, the holonomy (generalization of geometric phase) induced on the SSS after adiabatic traversal of a closed path in parameter space is unitary. We derive a new Riemannian metric tensor in parameter space induced by one type of SSS, generalizing the Fubini-Study metric to Lindbladians possessing one or more mixed steady states. We derive a Kubo formula governing linear response of the SSS to Hamiltonian perturbations. Finally, we show that the energy scale governing leakage out of the SSS is different from the conventional Lindbladian dissipative gap.
Geometrical versus wave optics under gravitational waves
NASA Astrophysics Data System (ADS)
Angélil, Raymond; Saha, Prasenjit
2015-06-01
We present some new derivations of the effect of a plane gravitational wave on a light ray. A simple interpretation of the results is that a gravitational wave causes a phase modulation of electromagnetic waves. We arrive at this picture from two contrasting directions, namely, null geodesics and Maxwell's equations, or geometric and wave optics. Under geometric optics, we express the geodesic equations in Hamiltonian form and solve perturbatively for the effect of gravitational waves. We find that the well-known time-delay formula for light generalizes trivially to massive particles. We also recover, by way of a Hamilton-Jacobi equation, the phase modulation obtained under wave optics. Turning then to wave optics—rather than solving Maxwell's equations directly for the fields, as in most previous approaches—we derive a perturbed wave equation (perturbed by the gravitational wave) for the electromagnetic four-potential. From this wave equation it follows that the four-potential and the electric and magnetic fields all experience the same phase modulation. Applying such a phase modulation to a superposition of plane waves corresponding to a Gaussian wave packet leads to time delays.
Geometric defects in quantum Hall states
NASA Astrophysics Data System (ADS)
Gromov, Andrey
2016-08-01
We describe a geometric (or gravitational) analog of the Laughlin quasiholes in fractional quantum Hall states. Analogously to the quasiholes, these defects can be constructed by an insertion of an appropriate vertex operator into the conformal block representation of a trial wave function; however, unlike the quasiholes these defects are extrinsic and do not correspond to true excitations of the quantum fluid. We construct a wave function in the presence of such defects and explain how to assign an electric charge and a spin to each defect and calculate the adiabatic, non-Abelian statistics of the defects. The defects turn out to be equivalent to the genons in that their adiabatic exchange statistics can be described in terms of representations of the mapping class group of an appropriate higher genus Riemann surface. We present a general construction that, in principle, makes it possible to calculate the statistics of Zn genons for any "parent" topological phase. We illustrate the construction on the example of the Laughlin state and perform an explicit calculation of the braiding matrices. In addition to non-Abelian statistics, geometric defects possess a universal Abelian overall phase, determined by the gravitational anomaly.
Geometrical basis for the Standard Model
Potter, F. )
1994-02-01
The robust character of the Standard Model is confirmed. Examination of its geometrical basis in three equivalent internal symmetry spaces - the unitary plane C[sup 2], the quaternion space Q, and the real space R[sup 4] - as well as the real space R[sup 3] uncovers mathematical properties that predict the physical properties of leptons and quarks. The finite rotational subgroups of the gauge group SU(2)[sub L] [times] U(1)[sub Y] generate exactly three lepton families and four quark families and reveal how quarks and leptons are related. Among the physical properties explained are the mass ratios of the six leptons and eight quarks, the origin of the left-handed preference by the weak interaction, the geometrical source of color symmetry, and the zero neutrino masses. The (u,d) and (c,s) quark families team together to satisfy the triangle anomaly cancellation with the electron family, while the other families pair one-to-one for cancellation. The spontaneously broken symmetry is discrete and needs no Higgs mechanism. Predictions include all massless neutrinos, the top quark at 160 GeV/c[sup 2], the b[prime] quark at 80 GeV/c[sup 2], and the t[prime] quark at 2600 GeV/c[sup 2].
Geometric control of myogenic cell fate
de Juan-Pardo, Elena M; Hoang, Mike Bao-Trong; Conboy, Irina M
2006-01-01
This work combines expertise in stem cell biology and bioengineering to define the system for geometric control of proliferation and differentiation of myogenic progenitor cells. We have created an artificial niche of myogenic progenitor cells, namely, modified extracellular matrix (ECM) substrates with spatially embedded growth or differentiation factors (GF, DF) that predictably direct muscle cell fate in a geometric pattern. Embedded GF and DF signal progenitor cells from specifically defined areas on the ECM successfully competed against culture media for myogenic cell fate determination at a clearly defined boundary. Differentiation of myoblasts into myotubes is induced in growth-promoting medium, myotube formation is delayed in differentiation-promoting medium, and myogenic cells, at different stages of proliferation and differentiation, can be induced to coexist adjacently in identical culture media. This method can be used to identify molecular interactions between cells in different stages of myogenic differentiation, which are likely to be important determinants of tissue repair. The designed ECM niches can be further developed into a vehicle for transplantation of myogenic progenitor cells maintaining their regenerative potential. Additionally, this work may also serve as a general model to engineer synthetic cellular niches to harness the regenerative potential of organ stem cells. PMID:17722537
Comparison of different definitions of the geometric measure of entanglement
NASA Astrophysics Data System (ADS)
Chen, Lin; Aulbach, Martin; Hajdušek, Michal
2014-04-01
Several inequivalent definitions of the geometric measure of entanglement (GM) have been introduced and studied in the past. Here we review several known and new definitions, with the qualifying criterion being that for pure states the measure is a linear or logarithmic function of the maximal fidelity with product states. The entanglement axioms and properties of the measures are studied, and qualitative and quantitative comparisons are made between all definitions. Streltsov et al. [New J. Phys. 12, 123004 (2010), 10.1088/1367-2630/12/12/123004] proved the equivalence of two linear definitions of GM, whereas we show that the corresponding logarithmic definitions are distinct. Certain classes of states such as "maximally correlated states" and isotropic states are particularly valuable for this analysis. A little-known GM definition is found to be the first one to be both normalized and weakly monotonous, thus being a prime candidate for future studies of multipartite entanglement. We also find that a large class of graph states, which includes all cluster states, have a "universal" closest separable state that minimizes the quantum relative entropy, the Bures distance, and the trace distance.
Fundamental Principles of Classical Mechanics: a Geometrical Perspectives
NASA Astrophysics Data System (ADS)
Lam, Kai S.
2014-07-01
Classical mechanics is the quantitative study of the laws of motion for oscopic physical systems with mass. The fundamental laws of this subject, known as Newton's Laws of Motion, are expressed in terms of second-order differential equations governing the time evolution of vectors in a so-called configuration space of a system (see Chapter 12). In an elementary setting, these are usually vectors in 3-dimensional Euclidean space, such as position vectors of point particles; but typically they can be vectors in higher dimensional and more abstract spaces. A general knowledge of the mathematical properties of vectors, not only in their most intuitive incarnations as directed arrows in physical space but as elements of abstract linear vector spaces, and those of linear operators (transformations) on vector spaces as well, is then indispensable in laying the groundwork for both the physical and the more advanced mathematical - more precisely topological and geometrical - concepts that will prove to be vital in our subject. In this beginning chapter we will review these properties, and introduce the all-important related notions of dual spaces and tensor products of vector spaces. The notational convention for vectorial and tensorial indices used for the rest of this book (except when otherwise specified) will also be established...
Automated reconstruction of dendritic and axonal trees by global optimization with geometric priors.
Türetken, Engin; González, Germán; Blum, Christian; Fua, Pascal
2011-09-01
We present a novel probabilistic approach to fully automated delineation of tree structures in noisy 2D images and 3D image stacks. Unlike earlier methods that rely mostly on local evidence, ours builds a set of candidate trees over many different subsets of points likely to belong to the optimal tree and then chooses the best one according to a global objective function that combines image evidence with geometric priors. Since the best tree does not necessarily span all the points, the algorithm is able to eliminate false detections while retaining the correct tree topology. Manually annotated brightfield micrographs, retinal scans and the DIADEM challenge datasets are used to evaluate the performance of our method. We used the DIADEM metric to quantitatively evaluate the topological accuracy of the reconstructions and showed that the use of the geometric regularization yields a substantial improvement. PMID:21573886
Analysis and quantification of errors in the geometric correction of satellite images
NASA Technical Reports Server (NTRS)
Ford, G. E.; Zanelli, C. I.
1985-01-01
The quantitative use of remote sensing satellite images in many applications requires that the geometric distortion inherent in these images be corrected, or rectified, to a desired map projection. The most widely used technique relies on ground control points to empirically determine a mathematical coordinate transformation to correct the geometry. In this paper, using the method of least squares, expressions for the accuracy of the geometric transformation and of the rectification of the satellite image to a map projection are derived. Explicit relations between the global accuracy of the transformation and the number, location, and local accuracy of the ground control points are obtained. The results are applied to the correction of a Landsat MSS image.
ERIC Educational Resources Information Center
Brashers, H. C.
1968-01-01
As the inexperienced writer becomes aware of the issues involved in the composition of effective descriptive prose, he also develops a consistent control over his materials. The persona he chooses, if coherently thought out, can function as an index of many choices, helping him to manipulate the tone, intent, and mood of this style; to regulate…
Parametric modeling for quantitative analysis of pulmonary structure to function relationships
NASA Astrophysics Data System (ADS)
Haider, Clifton R.; Bartholmai, Brian J.; Holmes, David R., III; Camp, Jon J.; Robb, Richard A.
2005-04-01
While lung anatomy is well understood, pulmonary structure-to-function relationships such as the complex elastic deformation of the lung during respiration are less well documented. Current methods for studying lung anatomy include conventional chest radiography, high-resolution computed tomography (CT scan) and magnetic resonance imaging with polarized gases (MRI scan). Pulmonary physiology can be studied using spirometry or V/Q nuclear medicine tests (V/Q scan). V/Q scanning and MRI scans may demonstrate global and regional function. However, each of these individual imaging methods lacks the ability to provide high-resolution anatomic detail, associated pulmonary mechanics and functional variability of the entire respiratory cycle. Specifically, spirometry provides only a one-dimensional gross estimate of pulmonary function, and V/Q scans have poor spatial resolution, reducing its potential for regional assessment of structure-to-function relationships. We have developed a method which utilizes standard clinical CT scanning to provide data for computation of dynamic anatomic parametric models of the lung during respiration which correlates high-resolution anatomy to underlying physiology. The lungs are segmented from both inspiration and expiration three-dimensional (3D) data sets and transformed into a geometric description of the surface of the lung. Parametric mapping of lung surface deformation then provides a visual and quantitative description of the mechanical properties of the lung. Any alteration in lung mechanics is manifest by alterations in normal deformation of the lung wall. The method produces a high-resolution anatomic and functional composite picture from sparse temporal-spatial methods which quantitatively illustrates detailed anatomic structure to pulmonary function relationships impossible for translational methods to provide.
Geometric Toys in the Attic? A Corpus Analysis of Early Exposure to Geometric Shapes
ERIC Educational Resources Information Center
Resnick, Ilyse; Verdine, Brian; Golinkoff, Roberta; Hirsh-Pasek, Kathy
2016-01-01
Preschoolers' experiences with shapes are important because geometry is foundational to aspects of mathematics and it is now part of the Common Core for school-readiness. Exposure to shapes also provides experiences that are key to developing spatial thinking more broadly. Yet achieving a strong conceptual understanding of geometric categories can…
NASA Technical Reports Server (NTRS)
Anuta, P. E.
1975-01-01
Least squares approximation techniques were developed for use in computer aided correction of spatial image distortions for registration of multitemporal remote sensor imagery. Polynomials were first used to define image distortion over the entire two dimensional image space. Spline functions were then investigated to determine if the combination of lower order polynomials could approximate a higher order distortion with less computational difficulty. Algorithms for generating approximating functions were developed and applied to the description of image distortion in aircraft multispectral scanner imagery. Other applications of the techniques were suggested for earth resources data processing areas other than geometric distortion representation.
Huang, Huiqin; Wu, Xiaopeng; Yi, Sheng; Zhou, Zhiwang; Zhu, Jun; Fang, Zhe; Yue, Jianmin; Bao, Shixiang
2009-02-01
Strain AM105 was separated from mangrove sediment in the South China Sea in this research. The morphological and genomic data showed that the strain merits description as a novel species, proposed as Micromonospora rifamycinica. From the acetate ethyl extract of its fermentation broth, two antibiotics against Gram-positive bacteria (including MRSA), rifamycin S and its geometric isomer were isolated. Their structures were elucidated on the basis of spectroscopic analyzes. (1)H and (13)C NMR data of the isomer of rifamycin S were first described in this paper.
NASA Astrophysics Data System (ADS)
van Brummelen, Glen
2006-07-01
In terms of complexity, planetary latitudes are the culmination of Ptolemy's mathematical astronomy. Al-Kashi's remarkable system removes its mathematical flaws, and demonstrates that Muslim astronomers not only mastered this apex of Ptolemaic astronomy, but also perfected its mathematics. The remainder of this paper is devoted first to a brief description of the mathematics of Ptolemy's latitude model, and then to a technical account of the part of the Khaqani Zij devoted to al-Kashi's spherical approach. Al-Kashi's text falls roughly into three sections: a geometrical description of the spherical model, a mathematical discussion of how one might generate planetary positions from it, and a sample calculation for Venus. A translation by Sergei Tourkin of the passage in which al-Kashi describes the geometric structure of his model may be found in an appendix.
Thematic mapper: detailed radiometric and geometric characteristics
Kieffer, Hugh
1983-01-01
Those radiometric characteristics of the Landsat 4 Thematic Mapper (TM) that can be established without absolute calibration of spectral data have been examined. Subscenes of radiometric all raw data (B-data) were examined on an individual detector basis: areas of uniform radiance were used to characterize subtle radiometric differences and noise problems. A variety of anomalies have been discovered with magnitude of a few digital levels or less: the only problem not addressable by ground processing is irregular width of the digital levels. Essentially all of this non-ideal performance is incorporated in the fully processed (P-type) images, but disguised by the geometric resampling procedure. The overall performance of the Thematic Mapper is a great improvement over previous Landsat scanners. The effective resolution in radiance is degraded by about a factor of two by irregular width of the digital levels. Several detectors have a change of gain with a period of several scans, the largest effect is about 4%. These detectors appear to switch between two response levels during scan direction reversal; there is no apparent periodicity to these changes. This can cause small apparent difference between forward and reverse scans for portions of an image. The high-frequency noise level of each detector was characterized by the standard deviation of the first derivative in the sample direction across a flat field. Coherent sinusoidal noise patterns were determined using one-dimensional Fourier transforms. A "stitching" pattern in Band 1 has a period of 13.8 samples with a peak-to-peak amplitude ranging from 1 to 5 DN. Noise with a period of 3.24 samples is pronounced for most detectors in band 1, to a lesser extent in bands 2, 3, and 4, and below background noise levels in bands 5, 6, and 7. The geometric fidelity of the GSFC film writer used for Thematic Mapper (TM) images was assessed by measurement with accuracy bette than three micrometers of a test grid. A set of 55
DNA DAMAGE QUANTITATION BY ALKALINE GEL ELECTROPHORESIS.
SUTHERLAND,B.M.; BENNETT,P.V.; SUTHERLAND, J.C.
2004-03-24
Physical and chemical agents in the environment, those used in clinical applications, or encountered during recreational exposures to sunlight, induce damages in DNA. Understanding the biological impact of these agents requires quantitation of the levels of such damages in laboratory test systems as well as in field or clinical samples. Alkaline gel electrophoresis provides a sensitive (down to {approx} a few lesions/5Mb), rapid method of direct quantitation of a wide variety of DNA damages in nanogram quantities of non-radioactive DNAs from laboratory, field, or clinical specimens, including higher plants and animals. This method stems from velocity sedimentation studies of DNA populations, and from the simple methods of agarose gel electrophoresis. Our laboratories have developed quantitative agarose gel methods, analytical descriptions of DNA migration during electrophoresis on agarose gels (1-6), and electronic imaging for accurate determinations of DNA mass (7-9). Although all these components improve sensitivity and throughput of large numbers of samples (7,8,10), a simple version using only standard molecular biology equipment allows routine analysis of DNA damages at moderate frequencies. We present here a description of the methods, as well as a brief description of the underlying principles, required for a simplified approach to quantitation of DNA damages by alkaline gel electrophoresis.
MartiTracks: A Geometrical Approach for Identifying Geographical Patterns of Distribution
Echeverría-Londoño, Susy; Miranda-Esquivel, Daniel Rafael
2011-01-01
Panbiogeography represents an evolutionary approach to biogeography, using rational cost-efficient methods to reduce initial complexity to locality data, and depict general distribution patterns. However, few quantitative, and automated panbiogeographic methods exist. In this study, we propose a new algorithm, within a quantitative, geometrical framework, to perform panbiogeographical analyses as an alternative to more traditional methods. The algorithm first calculates a minimum spanning tree, an individual track for each species in a panbiogeographic context. Then the spatial congruence among segments of the minimum spanning trees is calculated using five congruence parameters, producing a general distribution pattern. In addition, the algorithm removes the ambiguity, and subjectivity often present in a manual panbiogeographic analysis. Results from two empirical examples using 61 species of the genus Bomarea (2340 records), and 1031 genera of both plants and animals (100118 records) distributed across the Northern Andes, demonstrated that a geometrical approach to panbiogeography is a feasible quantitative method to determine general distribution patterns for taxa, reducing complexity, and the time needed for managing large data sets. PMID:21533259
Random geometric graphs with general connection functions.
Dettmann, Carl P; Georgiou, Orestis
2016-03-01
In the original (1961) Gilbert model of random geometric graphs, nodes are placed according to a Poisson point process, and links formed between those within a fixed range. Motivated by wireless ad hoc networks "soft" or "probabilistic" connection models have recently been introduced, involving a "connection function" H(r) that gives the probability that two nodes at distance r are linked (directly connect). In many applications (not only wireless networks), it is desirable that the graph is connected; that is, every node is linked to every other node in a multihop fashion. Here the connection probability of a dense network in a convex domain in two or three dimensions is expressed in terms of contributions from boundary components for a very general class of connection functions. It turns out that only a few quantities such as moments of the connection function appear. Good agreement is found with special cases from previous studies and with numerical simulations. PMID:27078372
Facial symmetry assessment based on geometric features
NASA Astrophysics Data System (ADS)
Xu, Guoping; Cao, Hanqiang
2015-12-01
Face image symmetry is an important factor affecting the accuracy of automatic face recognition. Selecting high symmetrical face image could improve the performance of the recognition. In this paper, we proposed a novel facial symmetry evaluation scheme based on geometric features, including centroid, singular value, in-plane rotation angle of face and the structural similarity index (SSIM). First, we calculate the value of the four features according to the corresponding formula. Then, we use fuzzy logic algorithm to integrate the value of the four features into a single number which represents the facial symmetry. The proposed method is efficient and can adapt to different recognition methods. Experimental results demonstrate its effectiveness in improving the robustness of face detection and recognition.
Geometrical model of the Baltic artesian basin
NASA Astrophysics Data System (ADS)
Sennikovs, J.; Virbulis, J.; Bethers, U.
2012-04-01
Baltic artesian basin (BAB) is a multi-layer sedimentary basin spanning around 480'000 km2. BAB is located in the territory of Latvia, Lithuania and Estonia, parts of Poland, Russia, Belarus and large area of the Baltic Sea, including island of Gotland. The thickness of sedimentary cover is about 5000 m in the south-western part. Crystalline bedding reaches the surface in the northern and north-western parts. The aim of the present work is development of the model of geometric structure and three dimensional finite element mesh for the hydrogeological model of the whole BAB. The information that is used to build the geometrical structure includes: (1) Stratigraphic information from boreholes in Latvia and Estonia (2) Maps of height isolines of geological layers for Latvia and Lithuania (3) Maps of sub-quaternary deposits in Latvia and Lithuania (4) Maps of fault lines on the crystalline basement surface in Latvia, Lithuania and Estonia (5) Buried valley data from Latvia and Estonia (6) Earth topography data (7) Baltic sea depth data (8) Data from published geological cross-sections, information from books and other sources. Unification of the heterogeneous information from different sources, which are employed for building of the geometrical structure of the model are performed. Special algorithms are developed for this purpose considering the priority, importance and plausibility of each of the data sources. Pre-processing of the borehole information to screen out the outlying borehole data has been performed. Model of geological structure contains 42 layers. It includes aquifers and aquitards from Cambrian up to the Quaternary deposits. Fault displacements are incorporated into the model taking into account data from the published structural maps. Four reconstructed regional erosion surfaces (upper Ordovician, Devonian, Permian and Quaternary) are included into the model Three dimensional mesh of the geological structure is constructed layer-wise. The triangular
Geometric aeolian dune crest migration model
NASA Astrophysics Data System (ADS)
Swanson, T.; Mohrig, D. C.; Kocurek, G.; Pedersen, A.
2012-12-01
We present a geometric aeolian dune crest model that provides a predictive linkage between local lee face sediment deposition and wholesale landform change. The model is driven using an initial condition of 3D dune crest data obtained from a time series of airborne LIDAR surveys of White Sands, NM, and wind observations from nearby Holloman AFB. Transient dune migration is modeled by volume filling of a simple theoretical dune geometry with sediment flux derived using shear velocity dependent transport (Bagnold, 1941) modified by a new incidence angle dependent lee face sediment deposition function styled after Rubin and Hunter (1985). Model calibration is achieved using an azimuthal wind direction correction and threshold values for shear velocity dependent sediment transport. Agreement between observations and model results are presented using a l2 norm representing a global error estimate.
Geometric formulation of the uncertainty principle
NASA Astrophysics Data System (ADS)
Bosyk, G. M.; Osán, T. M.; Lamberti, P. W.; Portesi, M.
2014-03-01
A geometric approach to formulate the uncertainty principle between quantum observables acting on an N-dimensional Hilbert space is proposed. We consider the fidelity between a density operator associated with a quantum system and a projector associated with an observable, and interpret it as the probability of obtaining the outcome corresponding to that projector. We make use of fidelity-based metrics such as angle, Bures, and root infidelity to propose a measure of uncertainty. The triangle inequality allows us to derive a family of uncertainty relations. In the case of the angle metric, we recover the Landau-Pollak inequality for pure states and show, in a natural way, how to extend it to the case of mixed states in arbitrary dimension. In addition, we derive and compare alternative uncertainty relations when using other known fidelity-based metrics.
A geometrical perspective for the bargaining problem.
Wong, Kelvin Kian Loong
2010-01-01
A new treatment to determine the Pareto-optimal outcome for a non-zero-sum game is presented. An equilibrium point for any game is defined here as a set of strategy choices for the players, such that no change in the choice of any single player will increase the overall payoff of all the players. Determining equilibrium for multi-player games is a complex problem. An intuitive conceptual tool for reducing the complexity, via the idea of spatially representing strategy options in the bargaining problem is proposed. Based on this geometry, an equilibrium condition is established such that the product of their gains over what each receives is maximal. The geometrical analysis of a cooperative bargaining game provides an example for solving multi-player and non-zero-sum games efficiently. PMID:20436675
Random geometric graphs with general connection functions
NASA Astrophysics Data System (ADS)
Dettmann, Carl P.; Georgiou, Orestis
2016-03-01
In the original (1961) Gilbert model of random geometric graphs, nodes are placed according to a Poisson point process, and links formed between those within a fixed range. Motivated by wireless ad hoc networks "soft" or "probabilistic" connection models have recently been introduced, involving a "connection function" H (r ) that gives the probability that two nodes at distance r are linked (directly connect). In many applications (not only wireless networks), it is desirable that the graph is connected; that is, every node is linked to every other node in a multihop fashion. Here the connection probability of a dense network in a convex domain in two or three dimensions is expressed in terms of contributions from boundary components for a very general class of connection functions. It turns out that only a few quantities such as moments of the connection function appear. Good agreement is found with special cases from previous studies and with numerical simulations.
A geometric approach to quantum state separation
NASA Astrophysics Data System (ADS)
Bagan, E.; Yerokhin, V.; Shehu, A.; Feldman, E.; Bergou, J. A.
2015-12-01
Probabilistic quantum state transformations can be characterized by the degree of state separation they provide. This, in turn, sets limits on the success rate of these transformations. We consider optimum state separation of two known pure states in the general case where the known states have arbitrary a priori probabilities. The problem is formulated from a geometric perspective and shown to be equivalent to the problem of finding tangent curves within two families of conics that represent the unitarity constraints and the objective functions to be optimized, respectively. We present the corresponding analytical solutions in various forms. In the limit of perfect state separation, which is equivalent to unambiguous state discrimination, the solution exhibits a phenomenon analogous to a second order symmetry breaking phase transition. We also propose a linear optics implementation of separation which is based on the dual rail representation of qubits and single-photon multiport interferometry.
Geometric Mechanics of Curved Crease Origami
NASA Astrophysics Data System (ADS)
Dias, Marcelo A.; Dudte, Levi H.; Mahadevan, L.; Santangelo, Christian D.
2012-09-01
Folding a sheet of paper along a curve can lead to structures seen in decorative art and utilitarian packing boxes. Here we present a theory for the simplest such structure: an annular circular strip that is folded along a central circular curve to form a three-dimensional buckled structure driven by geometrical frustration. We quantify this shape in terms of the radius of the circle, the dihedral angle of the fold, and the mechanical properties of the sheet of paper and the fold itself. When the sheet is isometrically deformed everywhere except along the fold itself, stiff folds result in creases with constant curvature and oscillatory torsion. However, relatively softer folds inherit the broken symmetry of the buckled shape with oscillatory curvature and torsion. Our asymptotic analysis of the isometrically deformed state is corroborated by numerical simulations that allow us to generalize our analysis to study structures with multiple curved creases.
Geometric mechanics of curved crease origami.
Dias, Marcelo A; Dudte, Levi H; Mahadevan, L; Santangelo, Christian D
2012-09-14
Folding a sheet of paper along a curve can lead to structures seen in decorative art and utilitarian packing boxes. Here we present a theory for the simplest such structure: an annular circular strip that is folded along a central circular curve to form a three-dimensional buckled structure driven by geometrical frustration. We quantify this shape in terms of the radius of the circle, the dihedral angle of the fold, and the mechanical properties of the sheet of paper and the fold itself. When the sheet is isometrically deformed everywhere except along the fold itself, stiff folds result in creases with constant curvature and oscillatory torsion. However, relatively softer folds inherit the broken symmetry of the buckled shape with oscillatory curvature and torsion. Our asymptotic analysis of the isometrically deformed state is corroborated by numerical simulations that allow us to generalize our analysis to study structures with multiple curved creases. PMID:23005633
A geometric approach to spectral subtraction
Lu, Yang; Loizou, Philipos C.
2008-01-01
The traditional power spectral subtraction algorithm is computationally simple to implement but suffers from musical noise distortion. In addition, the subtractive rules are based on incorrect assumptions about the cross terms being zero. A new geometric approach to spectral subtraction is proposed in the present paper that addresses these shortcomings of the spectral subtraction algorithm. A method for estimating the cross terms involving the phase differences between the noisy (and clean) signals and noise is proposed. Analysis of the gain function of the proposed algorithm indicated that it possesses similar properties as the traditional MMSE algorithm. Objective evaluation of the proposed algorithm showed that it performed significantly better than the traditional spectral subtractive algorithm. Informal listening tests revealed that the proposed algorithm had no audible musical noise. PMID:19122867
Geometric Phase of a Transported Oscillator
Dittirich, W.
2004-02-25
An oscillator constrained to a plane that is transported along some surface will rotate by an angle dependent only on the path and the surface, not on the speed at which it is transported. This is thus an example of a geometric phase. We analyze this phase using the methods of parallel transport. This concept plays a key role in General Relativity, but it can also be applied in classical mechanics. The Foucault pendulum can be seen as an application of this analysis, where the surface is a sphere and the curve is a line of constant latitude. In view of some considerable confusion and erroneous treatments in the recent literature, we here present a rather simple way for visualizing the motion of the Foucault pendulum using concepts that are based on Frenet's formulae and the methods of parallel displacement.
Geometric Correction System Capabilities, Processing, and Application
Brewster, S.B.
1999-06-30
The U.S. Department of Energy's Remote Sensing Laboratory developed the geometric correction system (GCS) as a state-of-the-art solution for removing distortions from multispectral line scanner data caused by aircraft motion. The system operates on Daedalus AADS-1268 scanner data acquired from fixed-wing and helicopter platforms. The aircraft attitude, altitude, acceleration, and location are recorded and applied to the data, thereby determining the location of the earth with respect to a given datum and projection. The GCS has yielded a positional accuracy of 0.5 meters when used with a 1-meter digital elevation model. Data at this level of accuracy are invaluable in making precise areal estimates and as input into a geographic information system. The combination of high-spatial resolution and accurate geo-rectification makes the GCS a unique tool in identifying and locating environmental conditions, finding targets of interest, and detecting changes as they occur over time.
A Geometrical Approach to Bell's Theorem
NASA Technical Reports Server (NTRS)
Rubincam, David Parry
2000-01-01
Bell's theorem can be proved through simple geometrical reasoning, without the need for the Psi function, probability distributions, or calculus. The proof is based on N. David Mermin's explication of the Einstein-Podolsky-Rosen-Bohm experiment, which involves Stern-Gerlach detectors which flash red or green lights when detecting spin-up or spin-down. The statistics of local hidden variable theories for this experiment can be arranged in colored strips from which simple inequalities can be deduced. These inequalities lead to a demonstration of Bell's theorem. Moreover, all local hidden variable theories can be graphed in such a way as to enclose their statistics in a pyramid, with the quantum-mechanical result lying a finite distance beneath the base of the pyramid.
On the geometric form of volcanoes - Comment
NASA Technical Reports Server (NTRS)
Wood, C. A.
1982-01-01
The model of Lacey et al. (1981) accounting for the geometric regularity and approximate cone shape of volcanoes is discussed. It is pointed out that, contrary to the model, volcano eruptions do not occur randomly in elevation and azimuth, but are commonly restricted to summit vents and a few well defined flank zones, so that the form of a volcano is determined by its vent locations and styles of eruption. Other false predictions of the model include the constancy of lava volumes at all vent elevations, the increase in volcano radius as the square root of time, a critical height for volcano growth, the influence of planetary gravity on volcano height and the negligible influence of ash falls and flows and erosional deposition. It is noted that the model of Shteynberg and Solov'yev, in which cone shape is related to stresses due to increasing cone height, may provide a better understanding of volcano morphology.
Random broadcast on random geometric graphs
Bradonjic, Milan; Elsasser, Robert; Friedrich, Tobias
2009-01-01
In this work, we consider the random broadcast time on random geometric graphs (RGGs). The classic random broadcast model, also known as push algorithm, is defined as: starting with one informed node, in each succeeding round every informed node chooses one of its neighbors uniformly at random and informs it. We consider the random broadcast time on RGGs, when with high probability: (i) RGG is connected, (ii) when there exists the giant component in RGG. We show that the random broadcast time is bounded by {Omicron}({radical} n + diam(component)), where diam(component) is a diameter of the entire graph, or the giant component, for the regimes (i), or (ii), respectively. In other words, for both regimes, we derive the broadcast time to be {Theta}(diam(G)), which is asymptotically optimal.
THEMATIC MAPPER: DETAILED RADIOMETRIC AND GEOMETRIC CHARACTERISTICS.
Kieffer, Hugh
1983-01-01
The paper is in abstract form. It discusses those radiometric characteristics of the Landsat 4 Thematic Mapper (TM) that can be established without absolute calibration or spectral data. Subscenes of radiometrically raw data (B-data) were examined on an individual detector basis; areas of uniform radiance were used to characterize subtle radiometric differences and noise problems. The effective resolution in radiance is degraded by about a factor of two by irregular width of the digital levels. Several detectors have a change of gain with a period of several scans, the largest effect is about 4%. The geometric fidelity of the GSFC filmwriter used for Thematic Mapper (TM) images was assessed by measurement with accuracy better than three micrometers of a test grid.
Spin dynamics in geometrically frustrated antiferromagnetic pyrochlores
NASA Astrophysics Data System (ADS)
Gardner, J. S.; Ehlers, G.; Bramwell, S. T.; Gaulin, B. D.
2004-03-01
We have studied the spin dynamics of several antiferromagnetic pyrochlore oxides. These magnets are geometrically frustrated and only reach their ground states at temperatures much lower than that expected from mean field theory. Here we present data on the magnetic nature, especially the spin dynamics of Tb2Ti2O7, Gd2Ti2O7 and Y2Mo2O7. In these systems the ground states are found to be very different. Y2Mo2O7 freezes completely into a spin glass-like state, Tb2Ti2O7 is a cooperative paramagnetic and remains dynamic down to 15 mK and Gd2Ti2O7 enters a unique partially ordered state at {\\sim }1 K.
On the geometrization of quantum mechanics
NASA Astrophysics Data System (ADS)
Tavernelli, Ivano
2016-08-01
Nonrelativistic quantum mechanics is commonly formulated in terms of wavefunctions (probability amplitudes) obeying the static and the time-dependent Schrödinger equations (SE). Despite the success of this representation of the quantum world a wave-particle duality concept is required to reconcile the theory with observations (experimental measurements). A first solution to this dichotomy was introduced in the de Broglie-Bohm theory according to which a pilot-wave (solution of the SE) is guiding the evolution of particle trajectories. Here, I propose a geometrization of quantum mechanics that describes the time evolution of particles as geodesic lines in a curved space, whose curvature is induced by the quantum potential. This formulation allows therefore the incorporation of all quantum effects into the geometry of space-time, as it is the case for gravitation in the general relativity.
Efficient broadcast on random geometric graphs
Bradonjic, Milan; Elsasser, Robert; Friedrich, Tobias; Sauerwald, Thomas
2009-01-01
A Randon Geometric Graph (RGG) is constructed by distributing n nodes uniformly at random in the unit square and connecting two nodes if their Euclidean distance is at most r, for some prescribed r. They analyze the following randomized broadcast algorithm on RGGs. At the beginning, there is only one informed node. Then in each round, each informed node chooses a neighbor uniformly at random and informs it. They prove that this algorithm informs every node in the largest component of a RGG in {Omicron}({radical}n/r) rounds with high probability. This holds for any value of r larger than the critical value for the emergence of a giant component. In particular, the result implies that the diameter of the giant component is {Theta}({radical}n/r).
Geometric investigations of a vorticity model equation
NASA Astrophysics Data System (ADS)
Bauer, Martin; Kolev, Boris; Preston, Stephen C.
2016-01-01
This article consists of a detailed geometric study of the one-dimensional vorticity model equation which is a particular case of the generalized Constantin-Lax-Majda equation. Wunsch showed that this equation is the Euler-Arnold equation on Diff (S1) when the latter is endowed with the right-invariant homogeneous H ˙ 1 / 2-metric. In this article we prove that the exponential map of this Riemannian metric is not Fredholm and that the sectional curvature is locally unbounded. Furthermore, we prove a Beale-Kato-Majda-type blow-up criterion, which we then use to demonstrate a link to our non-Fredholmness result. Finally, we extend a blow-up result of Castro-Córdoba to the periodic case and to a much wider class of initial conditions, using a new generalization of an inequality for Hilbert transforms due to Córdoba-Córdoba.
Generalized geometric vacua with eight supercharges
NASA Astrophysics Data System (ADS)
Graña, Mariana; Ntokos, Praxitelis
2016-08-01
We investigate compactifications of type II and M-theory down to AdS 5 with generic fluxes that preserve eight supercharges, in the framework of Exceptional Generalized Geometry. The geometric data and gauge fields on the internal manifold are encoded in a pair of generalized structures corresponding to the vector and hyper-multiplets of the reduced five-dimensional supergravity. Supersymmetry translates into integrability conditions for these structures, generalizing, in the case of type IIB, the Sasaki-Einstein conditions. We show that the ten and eleven-dimensional type IIB and M-theory Killing-spinor equations specialized to a warped AdS 5 background imply the generalized integrability conditions.
Geometric invariance of compressible turbulent boundary layers
NASA Astrophysics Data System (ADS)
Bi, Wei-Tao; Wu, Bin; She, Zhen-Su; Hussain, Fazle
2015-11-01
A symmetry based approach is applied to analyze the mean velocity and temperature fields of compressible, flat plate turbulent boundary layers (CTBL). A Reynolds stress length scale and a turbulent heat flux length scale are identified to possess the same defect scaling law in the CTBL bulk, which is solely owing to the constraint of the wall to the geometry of the wall-attached eddies, but invariant to compressibility and wall heat transfer. This invariance is called the geometric invariance of CTBL eddies and is likely the origin of the Mach number invariance of Morkovin's hypothesis, as well as the similarity of energy and momentum transports. A closure for the turbulent transport by using the invariant lengths is attainted to predict the mean velocity and temperature profiles in the CTBL bulk- superior to the van Driest transformation and the Reynolds analogy based relations for its sound physics and higher accuracy. Additionally, our approach offers a new understanding of turbulent Prandtl number.
A Geometric Representation of Collective Attention Flows
Shi, Peiteng; Huang, Xiaohan; Wang, Jun; Zhang, Jiang; Deng, Su; Wu, Yahui
2015-01-01
With the fast development of Internet and WWW, “information overload” has become an overwhelming problem, and collective attention of users will play a more important role nowadays. As a result, knowing how collective attention distributes and flows among different websites is the first step to understand the underlying dynamics of attention on WWW. In this paper, we propose a method to embed a large number of web sites into a high dimensional Euclidean space according to the novel concept of flow distance, which both considers connection topology between sites and collective click behaviors of users. With this geometric representation, we visualize the attention flow in the data set of Indiana university clickstream over one day. It turns out that all the websites can be embedded into a 20 dimensional ball, in which, close sites are always visited by users sequentially. The distributions of websites, attention flows, and dissipations can be divided into three spherical crowns (core, interim, and periphery). 20% popular sites (Google.com, Myspace.com, Facebook.com, etc.) attracting 75% attention flows with only 55% dissipations (log off users) locate in the central layer with the radius 4.1. While 60% sites attracting only about 22% traffics with almost 38% dissipations locate in the middle area with radius between 4.1 and 6.3. Other 20% sites are far from the central area. All the cumulative distributions of variables can be well fitted by “S”-shaped curves. And the patterns are stable across different periods. Thus, the overall distribution and the dynamics of collective attention on websites can be well exhibited by this geometric representation. PMID:26325390
Geometric morphometric footprint analysis of young women
2013-01-01
Background Most published attempts to quantify footprint shape are based on a small number of measurements. We applied geometric morphometric methods to study shape variation of the complete footprint outline in a sample of 83 adult women. Methods The outline of the footprint, including the toes, was represented by a comprehensive set of 85 landmarks and semilandmarks. Shape coordinates were computed by Generalized Procrustes Analysis. Results The first four principal components represented the major axes of variation in foot morphology: low-arched versus high-arched feet, long and narrow versus short and wide feet, the relative length of the hallux, and the relative length of the forefoot. These shape features varied across the measured individuals without any distinct clusters or discrete types of footprint shape. A high body mass index (BMI) was associated with wide and flat feet, and a high frequency of wearing high-heeled shoes was associated with a larger forefoot area of the footprint and a relatively long hallux. Larger feet had an increased length-to-width ratio of the footprint, a lower-arched foot, and longer toes relative to the remaining foot. Footprint shape differed on average between left and right feet, and the variability of footprint asymmetry increased with BMI. Conclusions Foot shape is affected by lifestyle factors even in a sample of young women (median age 23 years). Geometric morphometrics proved to be a powerful tool for the detailed analysis of footprint shape that is applicable in various scientific disciplines, including forensics, orthopedics, and footwear design. PMID:23886074
Quantitative measures for redox signaling.
Pillay, Ché S; Eagling, Beatrice D; Driscoll, Scott R E; Rohwer, Johann M
2016-07-01
Redox signaling is now recognized as an important regulatory mechanism for a number of cellular processes including the antioxidant response, phosphokinase signal transduction and redox metabolism. While there has been considerable progress in identifying the cellular machinery involved in redox signaling, quantitative measures of redox signals have been lacking, limiting efforts aimed at understanding and comparing redox signaling under normoxic and pathogenic conditions. Here we have outlined some of the accepted principles for redox signaling, including the description of hydrogen peroxide as a signaling molecule and the role of kinetics in conferring specificity to these signaling events. Based on these principles, we then develop a working definition for redox signaling and review a number of quantitative methods that have been employed to describe signaling in other systems. Using computational modeling and published data, we show how time- and concentration- dependent analyses, in particular, could be used to quantitatively describe redox signaling and therefore provide important insights into the functional organization of redox networks. Finally, we consider some of the key challenges with implementing these methods. PMID:27151506
Spacelab J experiment descriptions
Miller, T.Y.
1993-08-01
Brief descriptions of the experiment investigations for the Spacelab J Mission which was launched from the Kennedy Space Center aboard the Endeavour in Sept. 1992 are presented. Experiments cover the following: semiconductor crystals; single crystals; superconducting composite materials; crystal growth; bubble behavior in weightlessness; microgravity environment; health monitoring of Payload Specialists; cultured plant cells; effect of low gravity on calcium metabolism and bone formation; and circadian rhythm. Separate abstracts have been prepared for articles from this report.
Spacelab J experiment descriptions
NASA Technical Reports Server (NTRS)
Miller, Teresa Y. (Editor)
1993-01-01
Brief descriptions of the experiment investigations for the Spacelab J Mission which was launched from the Kennedy Space Center aboard the Endeavour in Sept. 1992 are presented. Experiments cover the following: semiconductor crystals; single crystals; superconducting composite materials; crystal growth; bubble behavior in weightlessness; microgravity environment; health monitoring of Payload Specialists; cultured plant cells; effect of low gravity on calcium metabolism and bone formation; and circadian rhythm.
Management control system description
Bence, P. J.
1990-10-01
This Management Control System (MCS) description describes the processes used to manage the cost and schedule of work performed by Westinghouse Hanford Company (Westinghouse Hanford) for the US Department of Energy, Richland Operations Office (DOE-RL), Richland, Washington. Westinghouse Hanford will maintain and use formal cost and schedule management control systems, as presented in this document, in performing work for the DOE-RL. This MCS description is a controlled document and will be modified or updated as required. This document must be approved by the DOE-RL; thereafter, any significant change will require DOE-RL concurrence. Westinghouse Hanford is the DOE-RL operations and engineering contractor at the Hanford Site. Activities associated with this contract (DE-AC06-87RL10930) include operating existing plant facilities, managing defined projects and programs, and planning future enhancements. This document is designed to comply with Section I-13 of the contract by providing a description of Westinghouse Hanford's cost and schedule control systems used in managing the above activities. 5 refs., 22 figs., 1 tab.
NASA Astrophysics Data System (ADS)
Schneider, M.; Müller, R.; Krawzcyk, H.; Bachmann, M.; Storch, T.; Mogulsky, V.; Hofer, S.
2012-07-01
The German Aerospace Center DLR - namely the Earth Observation Center EOC and the German Space Operations Center GSOC - is responsible for the establishment of the ground segment of the future German hyperspectral satellite mission EnMAP (Environmental Mapping and Analysis Program). The Earth Observation Center has long lasting experiences with air- and spaceborne acquisition, processing, and analysis of hyperspectral image data. In the first part of this paper, an overview of the radiometric in-flight calibration concept including dark value measurements, deep space measurements, internal lamps measurements and sun measurements is presented. Complemented by pre-launch calibration and characterization these analyses will deliver a detailed and quantitative assessment of possible changes of spectral and radiometric characteristics of the hyperspectral instrument, e.g. due to degradation of single elements. A geometric accuracy of 100 m, which will be improved to 30 m with respect to a used reference image, if it exists, will be achieved by ground processing. Therfore, and for the required co-registration accuracy between SWIR and VNIR channels, additional to the radiometric calibration, also a geometric calibration is necessary. In the second part of this paper, the concept of the geometric calibration is presented in detail. The geometric processing of EnMAP scenes will be based on laboratory calibration results. During repeated passes over selected calibration areas images will be acquired. The update of geometric camera model parameters will be done by an adjustment using ground control points, which will be extracted by automatic image matching. In the adjustment, the improvements of the attitude angles (boresight angles), the improvements of the interior orientation (view vector) and the improvements of the position data are estimated. In this paper, the improvement of the boresight angles is presented in detail as an example. The other values and combinations
The geometric factor of a cylindrical plate electrostatic analyzer
NASA Technical Reports Server (NTRS)
Johnstone, A. D.
1971-01-01
A method for calculating the geometric factor of cylindrical plate electrostatic energy analyzers with various detector geometries is described. The effects of the fringe-field are estimated. For a special simple case an exact geometric factor is calculated enabling an estimate of the inaccuracies of the approximations used in other cases. The results of some calculations are presented and a simple approximate expression for the geometric factor is deduced.
Description for rotating C60 fullerenes via an analogue of Gödel-type metric
NASA Astrophysics Data System (ADS)
Cavalcante, Everton; Carvalho, Josevi; Furtado, Claudio
2016-08-01
In this paper a geometric approach to describe a rotating fullerene molecule with Ih symmetry is developed. We study the quantum dynamics of quasiparticles in a continuum limit considering a description of fullerene in a spherical solution of the Gödel-type space-time with a topological defect. Therefore, we study the molecule in a rotating frame. Also we combine the well-known non-Abelian monopole approach with this geometric description, including the case of the presence of the external Aharonov-Bohm flux. The energy levels and the persistent current for this study are obtained, and we show that they depend on the geometrical and topological properties of the fullerene. Also, we verify recovering of the well-known results for limiting cases.
The Need (?) for Descriptive Geometry in a World of 3D Modeling.
ERIC Educational Resources Information Center
Croft, Frank M. Jr.
1998-01-01
Evaluates the use of modern CAD methods to solve geometric problems. Solves descriptive geometry problems using the layout and position of the successive auxiliary views from the projection of three-dimensional figures onto a two-dimensional plane of paper. (CCM)
[A geometrical analysis of the shape of the response surface in ecologico-toxicologic experiments].
Maksimov, V N; Kadomtsev, S V; Korsak, M N; Lifshits, A V
1989-01-01
A new method of working up results of factorial toxicological experiments is put forward and illustrated by a number of examples. It is based on the profound comparison of values of reactions as consequences of toxic influence and aimed at revealing the combinations of toxicant concentrations that break the monotonous character of a surface which graphically depicts the effect of pollutants. The geometrical analysis allows us to have a new vision of numerous results of factorial experiments, gives some complimentary possibilities for quantitative evaluation of impact of pollutants by mean of surface diagrams and for experimental assessment of environmental parameters of natural communities.
Geometry and dynamics of one-norm geometric quantum discord
NASA Astrophysics Data System (ADS)
Huang, Zhiming; Qiu, Daowen; Mateus, Paulo
2016-01-01
We investigate the geometry of one-norm geometric quantum discord and present a geometric interpretation of one-norm geometric quantum discord for a class of two-qubit states. It is found that one-norm geometric quantum discord has geometric behavior different from that described in Lang and Caves (Phys Rev Lett 105:150501, 2010), Li et al. (Phys Rev A 83:022321, 2011) and Yao et al. (Phys Lett A 376:358-364, 2012). We also compare the dynamics of the one-norm geometric quantum discord and other measures of quantum correlations under correlated noise. It is shown that different decoherent channels bring different influences to quantum correlations measured by concurrence, entropic quantum discord and geometric quantum discord, which depend on the memory parameter and decoherence parameter. We lay emphasis on the behaviors such as entanglement sudden death and sudden transition of quantum discord. Finally, we study the dynamical behavior of one-norm geometric quantum discord in one-dimensional anisotropic XXZ model by utilizing the quantum renormalization group method. It is shown that the one-norm geometric quantum discord demonstrates quantum phase transition through renormalization group approach.
Anisotropy without tensors: a novel approach using geometric algebra.
Matos, Sérgio A; Ribeiro, Marco A; Paiva, Carlos R
2007-11-12
The most widespread approach to anisotropic media is dyadic analysis. However, to get a geometrical picture of a dielectric tensor, one has to resort to a coordinate system for a matrix form in order to obtain, for example, the index-ellipsoid, thereby obnubilating the deeper coordinate-free meaning of anisotropy itself. To overcome these shortcomings we present a novel approach to anisotropy: using geometric algebra we introduce a direct geometrical interpretation without the intervention of any coordinate system. By applying this new approach to biaxial crystals we show the effectiveness and insight that geometric algebra can bring to the optics of anisotropic media.
Continuum description of avalanches in granular media.
Aranson, I. S.; Tsimring, L. S.
2000-12-05
A continuum theory of partially fluidized granular flows is proposed. The theory is based on a combination of the mass and momentum conservation equations with the order parameter equation which describes the transition between flowing and static components of the granular system. We apply this model to the dynamics of avalanches in chutes. The theory provides a quantitative description of recent observations of granular flows on rough inclined planes (Daerr and Douady 1999): layer bistability, and the transition from triangular avalanches propagating downhill at small inclination angles to balloon-shaped avalanches also propagating uphill for larger angles.
Geometric phase for collinear conical intersections. I. Geometric phase angle and vector potentials
Li Xuan; Brue, Daniel A.; Blandon, Juan D.; Parker, Gregory A.; Kendrick, Brian K.
2011-02-14
We present a method for properly treating collinear conical intersections in triatomic systems. The general vector potential (gauge theory) approach for including the geometric phase effects associated with collinear conical intersections in hyperspherical coordinates is presented. The current study develops an introductory method in the treatment of collinear conical intersections by using the phase angle method. The geometric phase angle, {eta}, in terms of purely internal coordinates is derived using the example of a spin-aligned quartet lithium triatomic system. A numerical fit and thus an analytical form for the associated vector potentials are explicitly derived for this triatomic A{sub 3} system. The application of this methodology to AB{sub 2} and ABC systems is also discussed.
Rigour in quantitative research.
Claydon, Leica Sarah
2015-07-22
This article which forms part of the research series addresses scientific rigour in quantitative research. It explores the basis and use of quantitative research and the nature of scientific rigour. It examines how the reader may determine whether quantitative research results are accurate, the questions that should be asked to determine accuracy and the checklists that may be used in this process. Quantitative research has advantages in nursing, since it can provide numerical data to help answer questions encountered in everyday practice.
Navia, Denise; Ferreira, Cecília B S; Reis, Aleuny C; Gondim, Manoel G C
2015-09-01
Cryptic diversity has been confirmed for several phytophagous mites in the Eriophyoidea superfamily previously considered as presenting low host specificity. Among generalist eriophyoids is the phytoptid Retracrus johnstoni Keifer, which has been reported in 19 palm species belonging to 11 genera, causing severe damage on some of them. Surprisingly this species was recently reported on another monocot family, Heliconiaceae, infesting Heliconia plants in Costa Rica and Brazil, being the only in the tribe Mackiellini to not be associated with palm trees. This study aimed to investigate the occurrence of cryptic species in R. johnstoni and to clarify the taxonomic status of populations associated with heliconias in the Americas. With this purpose traditional and geometric morphometric analyses were conducted as well as a detailed morphological study. Measurable trait data were analysed via univariate and multivariate analyses. Shapes of specimens from different populations were compared via geometric morphometric landmark methods. Morphometric analysis supported occurrence of at least two cryptic species previously identified as R. johsntoni and suggested occurrence of cryptic species among populations associated with different palm trees. Taxonomic descriptions of two new taxa associated with heliconias, namely Retracrus costaricensis n. sp. Ferreira and Navia and Retracrus heliconiae n. sp. Ferreira and Navia are presented. Morphometric traits that can be useful in the taxonomic identification are noted and their value is discussed. Results of the traditional morphometry and geometric methods were compared and the advantages of their joint use for Eriophyoidea systematics are discussed. PMID:26089124
Navia, Denise; Ferreira, Cecília B S; Reis, Aleuny C; Gondim, Manoel G C
2015-09-01
Cryptic diversity has been confirmed for several phytophagous mites in the Eriophyoidea superfamily previously considered as presenting low host specificity. Among generalist eriophyoids is the phytoptid Retracrus johnstoni Keifer, which has been reported in 19 palm species belonging to 11 genera, causing severe damage on some of them. Surprisingly this species was recently reported on another monocot family, Heliconiaceae, infesting Heliconia plants in Costa Rica and Brazil, being the only in the tribe Mackiellini to not be associated with palm trees. This study aimed to investigate the occurrence of cryptic species in R. johnstoni and to clarify the taxonomic status of populations associated with heliconias in the Americas. With this purpose traditional and geometric morphometric analyses were conducted as well as a detailed morphological study. Measurable trait data were analysed via univariate and multivariate analyses. Shapes of specimens from different populations were compared via geometric morphometric landmark methods. Morphometric analysis supported occurrence of at least two cryptic species previously identified as R. johsntoni and suggested occurrence of cryptic species among populations associated with different palm trees. Taxonomic descriptions of two new taxa associated with heliconias, namely Retracrus costaricensis n. sp. Ferreira and Navia and Retracrus heliconiae n. sp. Ferreira and Navia are presented. Morphometric traits that can be useful in the taxonomic identification are noted and their value is discussed. Results of the traditional morphometry and geometric methods were compared and the advantages of their joint use for Eriophyoidea systematics are discussed.
NASA Astrophysics Data System (ADS)
Horn, Martin Erik
2014-10-01
It is still a great riddle to me why Wolfgang Pauli and P.A.M. Dirac had not fully grasped the meaning of their own mathematical constructions. They invented magnificent, fantastic and very important mathematical features of modern physics, but they only delivered half of the interpretations of their own inventions. Of course, Pauli matrices and Dirac matrices represent operators, which Pauli and Dirac discussed in length. But this is only part of the true meaning behind them, as the non-commutative ideas of Grassmann, Clifford, Hamilton and Cartan allow a second, very far reaching interpretation of Pauli and Dirac matrices. An introduction to this alternative interpretation will be discussed. Some applications of this view on Pauli and Dirac matrices are given, e.g. a geometric algebra picture of the plane wave solution of the Maxwell equation, a geometric algebra picture of special relativity, a toy model of SU(3) symmetry, and some only very preliminary thoughts about a possible geometric meaning of quantum mechanics.
NASA Astrophysics Data System (ADS)
Mayes, R.; Lyford, M. E.; Myers, J. D.
2009-12-01
The Quantitative Reasoning in STEM (QR STEM) project is a state level Mathematics and Science Partnership Project (MSP) with a focus on the mathematics and statistics that underlies the understanding of complex global scientific issues. This session is a companion session to the QR STEM: The Science presentation. The focus of this session is the quantitative reasoning aspects of the project. As students move from understandings that range from local to global in perspective on issues of energy and environment, there is a significant increase in the need for mathematical and statistical conceptual understanding. These understandings must be accessible to the students within the scientific context, requiring the special understandings that are endemic within quantitative reasoning. The QR STEM project brings together interdisciplinary teams of higher education faculty and middle/high school teachers to explore complex problems in energy and environment. The disciplines include life sciences, physics, chemistry, earth science, statistics, and mathematics. These interdisciplinary teams develop open ended performance tasks to implement in the classroom, based on scientific concepts that underpin energy and environment. Quantitative reasoning is broken down into three components: Quantitative Literacy, Quantitative Interpretation, and Quantitative Modeling. Quantitative Literacy is composed of arithmetic concepts such as proportional reasoning, numeracy, and descriptive statistics. Quantitative Interpretation includes algebraic and geometric concepts that underlie the ability to interpret a model of natural phenomena which is provided for the student. This model may be a table, graph, or equation from which the student is to make predictions or identify trends, or from which they would use statistics to explore correlations or patterns in data. Quantitative modeling is the ability to develop the model from data, including the ability to test hypothesis using statistical
Topological and differential geometrical gauge field theory
NASA Astrophysics Data System (ADS)
Saaty, Joseph
between bosons (quantized) and fermions (not quantized). Thus I produced results that were previously unobtainable. Furthermore, since topological charge takes place in Flat Spacetime, I investigated the quantization of the Curved Spacetime version of topological charge (Differential Geometrical Charge) by developing the differential geometrical Gauge Field Theory. It should be noted that the homotopy classification method is not at all applicable to Curved Spacetime. I also modified the Dirac equation in Curved Spacetime by using Einstein's field equation in order to account for the presence of matter. As a result, my method has allowed me to address four cases of topological charge (both spinless and spin one- half, in both Flat and in Curved Spacetime) whereas earlier methods had been blind to all but one of these cases (spinless in Flat Spacetime). (Abstract shortened by UMI.)
A Descriptive Analysis of High School Student Motivators for Success
ERIC Educational Resources Information Center
Booker, Janet Maria
2011-01-01
The purpose of the quantitative descriptive study was to gain an understanding of the motivating factors leading high school students from rural and urban schools to receive a diploma. A revised version of the High School Motivation Scale (Close, 2001; Solberg et al., 2007) generated from SurveyMonkey.com was administered to high school graduates…
Asymptotic geometric phase and purity for phase qubit dispersively coupled to lossy LC circuit
Mohamed, A.-B.A.; Obada, A.-S.F.
2011-09-15
Analytical descriptions of the geometric phases (GPs) for the total system and subsystems are studied for a current biased Josephson phase qubit strongly coupled to a lossy LC circuit in the dispersive limit. It is found that, the GP and purity depend on the damping parameter which leads to the phenomenon of GP death. Coherence parameter delays the phenomenon of a regular sequence of deaths and births of the GP. The asymptotic behavior of the GP and the purity for the qubit-LC resonator state closely follow that for the qubit state, but however, for the LC circuit these asymptotic values are equal to zero. - Highlights: > The model of a current biased Josephson phase qubit, strongly coupled to loss LC circuit, is considered. > Analytical descriptions of the geometric phase (GP) of this model, in the dispersive limit, are studied. > The GP and purity depend on the dissipation which leads to the GP death phenomenon. > Coherence parameter delays the phenomenon of a regular sequence of deaths and births of the GP.
Studying avian encephalization with geometric morphometrics.
Marugán-Lobón, Jesús; Watanabe, Akinobu; Kawabe, Soichiro
2016-08-01
Encephalization is a core concept in comparative neurobiology, aiming to quantify the neurological capacity of organisms. For measuring encephalization, many studies have employed relative brain sizes corrected for expected allometric scaling to body size. Here we highlight the utility of a multivariate geometric morphometric (GM) approach for visualizing and analyzing neuroanatomical shape variation associated with encephalization. GM readily allows the statistical evaluation of covariates, such as size, and many software tools exist for visualizing their effects on shape. Thus far, however, studies using GM have not attempted to translate the meaning of encephalization to shape data. As such, we tested the statistical relationship between size and encephalization quotients (EQs) to brain shape utilizing a broad interspecific sample of avian endocranial data. Although statistically significant, the analyses indicate that allometry accounts for <10% of total neuroanatomical shape variation. Notably, we find that EQs, despite being corrected for allometric scaling based on size, contain size-related neuroanatomical shape changes. In addition, much of what is traditionally considered encephalization comprises clade-specific trends in relative forebrain expansion, particularly driven by landbirds. EQs, therefore, fail to capture 90% of the total neuroanatomical variation after correcting for allometry and shared phylogenetic history. Moving forward, GM techniques provide crucial tools for investigating key drivers of this vast, largely unexplored aspect of avian brain morphology. PMID:27112986
Geometrical beaming of stellar mass ULXs
NASA Astrophysics Data System (ADS)
Middleton, Matthew J.; King, Andrew
2016-10-01
The presence or lack of eclipses in the X-ray light curves of ultraluminous X-ray sources (ULXs) can be directly linked to the accreting system geometry. In the case where the compact object is stellar mass and radiates isotropically, we should expect eclipses by a main-sequence to sub-giant secondary star on the recurrence time-scale of hours to days. X-ray light curves are now available for large numbers of ULXs as a result of the latest XMM-Newton catalogue. We determine the amount of fractional variability that should be injected into an otherwise featureless light curve for a given set of system parameters as a result of eclipses and compare this to the available data. We find that the vast majority of sources for which the variability has been measured to be non-zero and for which available observations meet the criteria for eclipse searches, have fractional variabilities which are too low to derive from eclipses and so must be viewed such that θ ≤ cos- 1(R*/a). This would require that the disc subtends a larger angle than that of the secondary star and is therefore consistent with a conical outflow formed from super-critical accretion rates and implies some level of geometrical beaming in ULXs.
Geometric perturbation theory and plasma physics
Omohundro, S.M.
1985-01-01
Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory, and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure in five different ways. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle-group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a long-standing question posed by Kruskal about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no adhoc elements, which is then applied to gyromotion. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A theory motivated by free electron lasers gives new restrictions on the change of area of projected parallelepipeds under canonical transformations.
Geometrical aspects on the dark matter problem
Capistrano, A.J.S.; Cabral, L.A.
2014-09-15
In the present paper we apply Nash’s theory of perturbative geometry to the study of dark matter gravity in a higher-dimensional space–time. It is shown that the dark matter gravitational perturbations at local scale can be explained by the extrinsic curvature of the standard cosmology. In order to test our model, we use a spherically symmetric metric embedded in a five-dimensional bulk. As a result, considering a sample of 10 low surface brightness and 6 high surface brightness galaxies, we find a very good agreement with the observed rotation curves of smooth hybrid alpha-HI measurements. - Highlights: • The metric perturbation and the embedding lead naturally to a “brane-world”-like higher dimensional structure. • Nash’s theorem as a cornerstone of the formation of geometrical structures. • The dark matter gravitational perturbations at local scale can be explained by the extrinsic curvature. • A good agreement was found with the observed rotation curves of smooth hybrid alpha-HI measurements.
The inertial and geometrical properties of helmets.
Njus, G O; Liu, Y K; Nye, T A
1984-10-01
The center of gravity (CG) and the principal mass moments of inertia about the CG of Army aviator, American football, and bicycle helmets were experimentally determined by a variation of the classic differential weighing and torsional pendulum techniques. In the course of these experiments, an innovative method for three-dimensional (3D) digitization was found. An electronic caliper, which measured length, was used with a computer algorithm to achieve 3D digitization. The results of the above measurements show that the weight of the helmet and the distances from the CG to the orthogonal coordinate axes intercepts with the outer shell surface were highly correlated with its principal mass moments of inertia. A set of regression equations was derived on theoretical considerations and served to unify the experimentally obtained data. Our results indicate that the principal mass moments of inertia of helmets vary linearly with its mass but nonlinearly with size and shape. For a helmet, given its weight and certain geometrical distances, the regression equations estimate the principal mass moments of inertia to within 5% of its experimentally-determined values. For the helmets studied in this series, a modified linear-regression relationship between the principal mass moments of inertia and its mass was found. This result is reasonable because the mass distribution of the current generation of helmets are set primarily by the head size and secondarily by helmet size, shape, and materials.
Geometric stiffening in multibody dynamics formulations
NASA Technical Reports Server (NTRS)
Sharf, Inna
1993-01-01
In this paper we discuss the issue of geometric stiffening as it arises in the context of multibody dynamics. This topic has been treated in a number of previous publications in this journal and appears to be a debated subject. The controversy revolves primarily around the 'correct' methodology for incorporating the stiffening effect into dynamics formulations. The main goal of this work is to present the different approaches that have been developed for this problem through an in-depth review of several publications dealing with this subject. This is done with the goal of contributing to a precise understanding of the existing methodologies for modelling the stiffening effects in multibody systems. Thus, in presenting the material we attempt to illuminate the key characteristics of the various methods as well as show how they relate to each other. In addition, we offer a number of novel insights and clarifying interpretations of these schemes. The paper is completed with a general classification and comparison of the different approaches.
Geometric morphometrics of hominoid infraspinous fossa shape.
Green, David J; Serrins, Jesse D; Seitelman, Brielle; Martiny, Amy R; Gunz, Philipp
2015-01-01
Recent discoveries of early hominin scapulae from Ethiopia (Dikika, Woranso-Mille) and South Africa (Malapa) have motivated new examinations of the relationship between scapular morphology and locomotor function. In particular, infraspinous fossa shape has been shown to significantly differ among hominoids. However, this region presents relatively few homologous landmarks, such that traditional distance and angle-based methods may oversimplify this three-dimensional structure. To more thoroughly assess infraspinous fossa shape variation as it relates to function among adult hominoid representatives, we considered two geometric morphometric (GM) approaches--one employing five homologous landmarks ("wireframe") and another with 83 sliding semilandmarks along the border of the infraspinous fossa. We identified several differences in infraspinous fossa shape with traditional approaches, particularly in superoinferior fossa breadth and scapular spine orientation. The wireframe analysis reliably captured the range of shape variation in the sample, which reflects the relatively straightforward geometry of the infraspinous fossa. Building on the traditional approach, the GM results highlighted how the orientation of the medial portion of the infraspinous fossa differed relative to both the axillary border and spine. These features distinguished Pan from Gorilla in a way that traditional analyses had not been able to discern. Relative to the wireframe method, the semilandmark approach further distinguished Pongo from Homo, highlighting aspects of infraspinous fossa morphology that may be associated with climbing behaviors in hominoid taxa. These results highlight the ways that GM methods can enhance our ability to evaluate complex aspects of shape for refining and testing hypotheses about functional morphology.
Geometric Explanation for AN Accelerating Universe
NASA Astrophysics Data System (ADS)
Bacinich, Edward J.
2004-01-01
The appearance and interpretation of an accelerating universe may be an observed distortion resulting from a universe defined by spherical geometry. The annihilation of Planck and anti-Planck mass is paramount in explaining the Big-Bang [1]. In a model similar to the standard model of a Riemannian-Friedmann-Lemaitre hypersphere, the primordial energy of the Big-Bang is released in the form of electromagnetic-like radiation that expands radiantly in every 4D direction from time zero in the structure of hyper-waves carried by Planck and anti-Planck bosons. The resulting geometry shows that time is synonymous with the lightspeed expansion of our universe. In this model we find that time is not parallel but radiant. This implies that time is a vector - where every place we observe has a unique time direction (angle) with a magnitude (age) and a light cone. The result of this condition is the illusion that the further back we look from our position in spacetime, space appears to be contracted and time appears to run slower both exponentially and logarithmically. Simply stated, we can not rely on observations unless we understand the geometric distortions inherent in curved photon paths.
Effect of geometrical frustration on inverse freezing.
Schmidt, M; Morais, C V; Zimmer, F M
2016-01-01
The interplay between geometrical frustration (GF) and inverse freezing (IF) is studied within a cluster approach. The model considers first-neighbor (J_{1}) and second-neighbor (J_{2}) intracluster antiferromagnetic interactions between Ising spins on a checkerboard lattice and long-range disordered couplings (J) among clusters. We obtain phase diagrams of temperature versus J_{1}/J in two cases: the absence of J_{2} interaction and the isotropic limit J_{2}=J_{1}, where GF takes place. An IF reentrant transition from the spin-glass (SG) to paramagnetic (PM) phase is found for a certain range of J_{1}/J in both cases. The J_{1} interaction leads to a SG state with high entropy at the same time that can introduce a low-entropy PM phase. In addition, it is observed that the cluster size plays an important role. The GF increases the PM phase entropy, but larger clusters can give an entropic advantage for the SG phase that favors IF. Therefore, our results suggest that disordered systems with antiferromagnetic clusters can exhibit an IF transition even in the presence of GF. PMID:26871062
Geometric modeling for computer aided design
NASA Technical Reports Server (NTRS)
Schwing, James L.; Olariu, Stephen
1995-01-01
The primary goal of this grant has been the design and implementation of software to be used in the conceptual design of aerospace vehicles particularly focused on the elements of geometric design, graphical user interfaces, and the interaction of the multitude of software typically used in this engineering environment. This has resulted in the development of several analysis packages and design studies. These include two major software systems currently used in the conceptual level design of aerospace vehicles. These tools are SMART, the Solid Modeling Aerospace Research Tool, and EASIE, the Environment for Software Integration and Execution. Additional software tools were designed and implemented to address the needs of the engineer working in the conceptual design environment. SMART provides conceptual designers with a rapid prototyping capability and several engineering analysis capabilities. In addition, SMART has a carefully engineered user interface that makes it easy to learn and use. Finally, a number of specialty characteristics have been built into SMART which allow it to be used efficiently as a front end geometry processor for other analysis packages. EASIE provides a set of interactive utilities that simplify the task of building and executing computer aided design systems consisting of diverse, stand-alone, analysis codes. Resulting in a streamlining of the exchange of data between programs reducing errors and improving the efficiency. EASIE provides both a methodology and a collection of software tools to ease the task of coordinating engineering design and analysis codes.
The Geometric Solution of Laplace's Equation
NASA Astrophysics Data System (ADS)
Bakhoum, Ezzat Gamal
In 1891, J.J. Thomson--the discoverer of the electron--stated a formula that relates the first derivative of the electric field intensity to the mean curvature of an equipotential surface. That formula was later proved by others, but remained unexploited in any practical purpose to this date. This dissertation presents a numerical method based on Thomson's formula for the rapid solution of Laplace's equation, the governing equation of field theory. The presented method is based on geometric construction principles. Specifically, the method uses the concept of representing equipotential surfaces by polynomials for the rapid tracing of these surfaces; and is therefore fundamentally different from previously-known techniques which are based on discretizing the domain or the boundary of the problem. The new method is especially suited for problems which have complicated or irregular boundaries as well as problems in exterior domains. Previously, such types of problems have required a number of computations of O(N.M), where N is the number of points taken on the boundary of the problem and M is the number of points inside the domain at which the solution is to be computed. The new method requires an O(M) computations only; and is therefore significantly faster than the previous techniques. Applications include problems of electrostatics, cosmology, biomedical engineering, nuclear and particle physics, etc.
The inertial and geometrical properties of helmets.
Njus, G O; Liu, Y K; Nye, T A
1984-10-01
The center of gravity (CG) and the principal mass moments of inertia about the CG of Army aviator, American football, and bicycle helmets were experimentally determined by a variation of the classic differential weighing and torsional pendulum techniques. In the course of these experiments, an innovative method for three-dimensional (3D) digitization was found. An electronic caliper, which measured length, was used with a computer algorithm to achieve 3D digitization. The results of the above measurements show that the weight of the helmet and the distances from the CG to the orthogonal coordinate axes intercepts with the outer shell surface were highly correlated with its principal mass moments of inertia. A set of regression equations was derived on theoretical considerations and served to unify the experimentally obtained data. Our results indicate that the principal mass moments of inertia of helmets vary linearly with its mass but nonlinearly with size and shape. For a helmet, given its weight and certain geometrical distances, the regression equations estimate the principal mass moments of inertia to within 5% of its experimentally-determined values. For the helmets studied in this series, a modified linear-regression relationship between the principal mass moments of inertia and its mass was found. This result is reasonable because the mass distribution of the current generation of helmets are set primarily by the head size and secondarily by helmet size, shape, and materials. PMID:6513769
Geometric Modeling of Inclusions as Ellipsoids
NASA Technical Reports Server (NTRS)
Bonacuse, Peter J.
2008-01-01
Nonmetallic inclusions in gas turbine disk alloys can have a significant detrimental impact on fatigue life. Because large inclusions that lead to anomalously low lives occur infrequently, probabilistic approaches can be utilized to avoid the excessively conservative assumption of lifing to a large inclusion in a high stress location. A prerequisite to modeling the impact of inclusions on the fatigue life distribution is a characterization of the inclusion occurrence rate and size distribution. To help facilitate this process, a geometric simulation of the inclusions was devised. To make the simulation problem tractable, the irregularly sized and shaped inclusions were modeled as arbitrarily oriented, three independent dimensioned, ellipsoids. Random orientation of the ellipsoid is accomplished through a series of three orthogonal rotations of axes. In this report, a set of mathematical models for the following parameters are described: the intercepted area of a randomly sectioned ellipsoid, the dimensions and orientation of the intercepted ellipse, the area of a randomly oriented sectioned ellipse, the depth and width of a randomly oriented sectioned ellipse, and the projected area of a randomly oriented ellipsoid. These parameters are necessary to determine an inclusion s potential to develop a propagating fatigue crack. Without these mathematical models, computationally expensive search algorithms would be required to compute these parameters.
Exploring Eucladoceros ecomorphology using geometric morphometrics.
Curran, Sabrina C
2015-01-01
An increasingly common method for reconstructing paleoenvironmental parameters of hominin sites is ecological functional morphology (ecomorphology). This study provides a geometric morphometric study of cervid rearlimb morphology as it relates to phylogeny, size, and ecomorphology. These methods are then applied to an extinct Pleistocene cervid, Eucladoceros, which is found in some of the earliest hominin-occupied sites in Eurasia. Variation in cervid postcranial functional morphology associated with different habitats can be summarized as trade-offs between joint stability versus mobility and rapid movement versus power-generation. Cervids in open habitats emphasize limb stability to avoid joint dislocation during rapid flight from predators. Closed-adapted cervids require more joint mobility to rapidly switch directions in complex habitats. Two skeletal features (of the tibia and calcaneus) have significant phylogenetic signals, while two (the femur and third phalanx) do not. Additionally, morphology of two of these features (tibia and third phalanx) were correlated with body size. For the tibial analysis (but not the third phalanx) this correlation was ameliorated when phylogeny was taken into account. Eucladoceros specimens from France and Romania fall on the more open side of the habitat continuum, a result that is at odds with reconstructions of their diet as browsers, suggesting that they may have had a behavioral regime unlike any extant cervid.
Attentional biases in geometric form perception.
Latimer, C; Stevens, C; Irish, M; Webber, L
2000-08-01
This paper reports the operation of robust attentional bias to the top and right during perception of small, single geometric forms. Same/different judgements of successively presented standard and comparison forms are faster when local differences are located at top and right rather than in other regions of the forms. The bias persists when form size is reduced to approximately one degree of visual angle, and it is unaffected by saccadic eye movements and by instructions to attend to other reliably differentiating regions of the forms. Results lend support in various degrees to two of the possible explanations of the bias: (1) a static, skewed distribution of attentional resources around eye fixation; and (2) biased, covert scanning that commences invariably at the top and right of stimulus forms. Origins of the bias in terms of possible left-hemispheric capacity for constructing representations of visual stimuli from parts, as well as in terms of reading experience and prevailing optic flow during locomotion through space are considered. Recent investigations of conditions under which the bias can be maintained or reduced are mentioned.
Geometric investigation of a gaming active device
NASA Astrophysics Data System (ADS)
Menna, Fabio; Remondino, Fabio; Battisti, Roberto; Nocerino, Erica
2011-07-01
3D imaging systems are widely available and used for surveying, modeling and entertainment applications, but clear statements regarding their characteristics, performances and limitations are still missing. The VDI/VDE and the ASTME57 committees are trying to set some standards but the commercial market is not reacting properly. Since many new users are approaching these 3D recording methodologies, clear statements and information clarifying if a package or system satisfies certain requirements before investing are fundamental for those users who are not really familiar with these technologies. Recently small and portable consumer-grade active sensors came on the market, like TOF rangeimaging cameras or low-cost triangulation-based range sensor. A quite interesting active system was produced by PrimeSense and launched on the market thanks to the Microsoft Xbox project with the name of Kinect. The article reports the geometric investigation of the Kinect active sensors, considering its measurement performances, the accuracy of the retrieved range data and the possibility to use it for 3D modeling application.
Geometric phase of a qubit driven by a phase noise laser under non-Markovian dynamics
Berrada, K.
2014-01-15
Robustness of the geometric phase (GP) with respect to the environmental effects is a basic condition for an effective quantum computation. Here, we study quantitatively the GP of a two-level atom system driven by a phase noise laser under non-Markovian dynamics in terms of different parameters involved in the whole system. We find that with the change of the damping coupling, the GP is very sensitive to its properties exhibiting long collapse and revival phenomena, which play a significant role in enhancing the stabilization and control of the system dynamics. Moreover, we show that the GP can be considered as a tool for testing and characterizing the nature of the qubit–environment coupling. Due to the significance of how a system is quantum correlated with its environment in the construction of a scalable quantum computer, the entanglement dynamics between the qubit with its environment under external classical noise is evaluated and investigated during the time evolution. -- Highlights: •Geometric phase under noise phase laser. •Dynamics of the geometric phase under non-Markovian dynamics in the presence of classical noise. •Solution of master equation of the system in terms atomic inversion. •Nonlocal correlation between the system and its environment under non-Markovianity.
Analysis of geometrical relations between multiple sclerosis lesions and brain vasculature
NASA Astrophysics Data System (ADS)
Kozinska, Dorota E.; Holland, Christopher; Krissian, Karl; Westin, Carl-Fredrik; Guttmann, Charles R. G.
2004-04-01
Due to histological evidence of the fundamental role of the cerebral vessels in white matter abnormalities, recently there has been an increased interest in analyzing the relationship between brain white matter lesions in multiple sclerosis (MS) and brain vasculature. We developed a method for visualization and measurement of geometrical relationships between MS lesions and the brain vessels imaged with magnetic resonance (MR) imaging techniques. Using MR images we create surface models of lesions and vessels that constitute a base for quantitative analysis. In this work we analyze correlation between basic lesion geometrical characteristics and two features: 1) distances to vessels, and 2) vessel caliber. For the former, we compute a distance map from the vessel structure, such that each voxel stores its distance vector to the closest vessel. This allows the measurements of Euclidean distances to the closest vessels. For the latter, we compute a radius map in which each voxel stores the radius of its closest vessel. It is used to measure distribution of lesions with respect to the vessel caliber. We compute and analyze relations between the basic geometrical characteristics of lesions and the closest vessels locations and calibers. To demonstrate the feasibility of the developed technique we present results from the study of 3 MS cases.
Ballyns, Jeffrey J; Cohen, Daniel L; Malone, Evan; Maher, Suzanne A; Potter, Hollis G; Wright, Timothy; Lipson, Hod; Bonassar, Lawrence J
2010-08-01
Quantification of shape fidelity of complex geometries for tissue-engineered constructs has not been thoroughly investigated. The objective of this study was to quantitatively describe geometric fidelities of various approaches to the fabrication of anatomically shaped meniscal constructs. Ovine menisci (n = 4) were imaged using magnetic resonance imaging (MRI) and microcomputed tomography (microCT). Acrylonitrile butadiene styrene plastic molds were designed from each imaging modality and three-dimensional printed on a Stratasys FDM 3000. Silastic impression molds were fabricated directly from ovine menisci. These molds were used to generate shaped constructs using 2% alginate with 2% CaSO(4). Solid freeform fabrication was conducted on a custom open-architecture three-dimensional printing platform. Printed samples were made using 2% alginate with 0.75% CaSO(4). Hydrogel constructs were scanned via laser triangulation distance sensor. The point cloud images were analyzed to acquire computational measurements for key points of interest (e.g., height, width, and volume). Silastic molds were within + or - 10% error with respect to the native tissue for seven key measurements, microCT molds for six of seven, microCT prints for four of seven, MRI molds for five of seven, and MRI prints for four of seven. This work shows the ability to generate and quantify anatomically shaped meniscal constructs of high geometric fidelity and lends insight into the relative geometric fidelities of several tissue engineering techniques.
NASA Astrophysics Data System (ADS)
Lim, Cheolwoong; Yan, Bo; Kang, Huixiao; Song, Zhibin; Lee, Wen Chao; De Andrade, Vincent; De Carlo, Francesco; Yin, Leilei; Kim, Youngsik; Zhu, Likun
2016-10-01
To investigate geometric and electrochemical characteristics of Li ion battery electrode with different packing densities, lithium cobalt oxide (LiCoO2) cathode electrodes were fabricated from a 94:3:3 (wt%) mixture of LiCoO2, polymeric binder, and super-P carbon black and calendered to different densities. A synchrotron X-ray nano-computed tomography system with a spatial resolution of 58.2 nm at the Advanced Photon Source of the Argonne National Laboratory was employed to obtain three dimensional morphology data of the electrodes. The morphology data were quantitatively analyzed to characterize their geometric properties, such as porosity, tortuosity, specific surface area, and pore size distribution. The geometric and electrochemical analysis reveal that high packing density electrodes have smaller average pore size and narrower pore size distribution, which improves the electrical contact between carbon-binder matrix and LiCoO2 particles. The better contact improves the capacity and rate capability by reducing the possibility of electrically isolated LiCoO2 particles and increasing the electrochemically active area. The results show that increase of packing density results in higher tortuosity, but electrochemically active area is more crucial to cell performance than tortuosity at up to 3.6 g/cm3 packing density and 4 C rate.
Geometrical Formation of Compound Starch Grains in Rice Implements Voronoi Diagram.
Matsushima, Ryo; Maekawa, Masahiko; Sakamoto, Wataru
2015-11-01
Starch forms transparent grains, called starch grains (SGs), in amyloplasts. One of the major morphological SG forms in Poaceae, called a compound SG, is formed by assemblies of small starch granules in an amyloplast. Starch granules assemble as a well-ordered structure; however, the mechanism that regulates this organization has not been identified. In this study, we examined how starch granules grow and converge into the final SG morphology. First, we found that the number of starch granules in an amyloplast is almost constant from the early developmental stage until endosperm maturity. Next, we quantitatively evaluated the geometrical similarities between starch granules and a Voronoi diagram, which is a mathematical tessellation of space based on the distance to a specific set of points in the space. The in silico growth simulation showed that the geometrical patterns of compound SGs resembling a Voronoi diagram is determined by physical interactions among the free-growing starch granules and the amyloplast envelope membrane. The geometrical similarity between compound SGs and a Voronoi diagram is likely a result of maximum loading and storage of starch in the amyloplast. The simulation described in this study provides a greater understanding of how compound SGs are formed and also has the potential to explain morphological variations of SGs.
Geometric design of a multisensor structured light range digitizer
NASA Astrophysics Data System (ADS)
Commean, Paul K.; Smith, Kirk E.; Bhatia, Gulab H.; Vannier, Michael W.
1994-04-01
An optical noncontact 3-D range digitizer based on projection of 2-D structured light patterns and multiplexed charge injection device (CID) camera sensors has been developed. The system acquires digitized data in 0.75 s and allows 360-deg examination of the subject's head and facial surface features in less than 1 s, making it suitable for digitizing children as well as adults. The resultant 3-D surface data is suitable for computer graphics display and manipulation, numerically controlled replication, and further processing such as surface measurement extraction. The digitizer uses a set of six stationary sensors positioned about the subject. A sensor consists of a pattern projector and a solid state video camera. This device allows quantitative volume measurements and employs no harmful ionizing radiation. The cost of a scan with this technology is substantially less than that of alternative means of collecting 3-D surface data sets, such as by stereometric, moirÃ© fringe, and single-point digitization. This system was geometrically designed such that any surface of the head or facial area was independently digitized by a minimum of two sensors and to capture areas normally occluded with other techniques. The dimensions of the structure were derived to satisfy physical constraints placed on its overall size. The camera and projector orientations in space, the distance from the lens centers to the center of the digitizing volume, and the lens focal lengths were determined analytically. To reduce cost, a standard lens nearest the analytical value was used. Based on the standard size lens, the field of view was calculated.
The Case for Descriptive Writing.
ERIC Educational Resources Information Center
Hauck, Marian K.
An approach to teaching descriptive writing and its values are discussed. Benefits derived from a descriptive writing unit are said to be the following: (1) Descriptive writing is fun; (2) It enables the instructor to demonstrate that the first word that pops into the writer's mind is often not the best one; (3) There is no easier way in which to…
Three Approaches to Descriptive Research.
ERIC Educational Resources Information Center
Svensson, Lennart
This report compares three approaches to descriptive research, focusing on the kinds of descriptions developed and on the methods used to develop the descriptions. The main emphasis in all three approaches is on verbal data. In these approaches the importance of interpretation and its intuitive nature are emphasized. The three approaches, however,…
Geometric deviation modeling by kinematic matrix based on Lagrangian coordinate
NASA Astrophysics Data System (ADS)
Liu, Weidong; Hu, Yueming; Liu, Yu; Dai, Wanyi
2015-09-01
Typical representation of dimension and geometric accuracy is limited to the self-representation of dimension and geometric deviation based on geometry variation thinking, yet the interactivity affection of geometric variation and gesture variation of multi-rigid body is not included. In this paper, a kinematic matrix model based on Lagrangian coordinate is introduced, with the purpose of unified model for geometric variation and gesture variation and their interactive and integrated analysis. Kinematic model with joint, local base and movable base is built. The ideal feature of functional geometry is treated as the base body; the fitting feature of functional geometry is treated as the adjacent movable body; the local base of the kinematic model is fixed onto the ideal geometry, and the movable base of the kinematic model is fixed onto the fitting geometry. Furthermore, the geometric deviation is treated as relative location or rotation variation between the movable base and the local base, and it's expressed by the Lagrangian coordinate. Moreover, kinematic matrix based on Lagrangian coordinate for different types of geometry tolerance zones is constructed, and total freedom for each kinematic model is discussed. Finally, the Lagrangian coordinate library, kinematic matrix library for geometric deviation modeling is illustrated, and an example of block and piston fits is introduced. Dimension and geometric tolerances of the shaft and hole fitting feature are constructed by kinematic matrix and Lagrangian coordinate, and the results indicate that the proposed kinematic matrix is capable and robust in dimension and geometric tolerances modeling.
Growing and Growing: Promoting Functional Thinking with Geometric Growing Patterns
ERIC Educational Resources Information Center
Markworth, Kimberly A.
2010-01-01
Design research methodology is used in this study to develop an empirically-substantiated instruction theory about students' development of functional thinking in the context of geometric growing patterns. The two research questions are: (1) How does students' functional thinking develop in the context of geometric growing patterns? (2) What are…
A Note on a Geometric Interpretation of the Correlation Coefficient.
ERIC Educational Resources Information Center
Marks, Edmond
1982-01-01
An alternate geometric interpretation of the correlation coefficient to that given in most statistics texts for psychology and education is presented. This interpretation is considered to be more consistent with the statistical model for the data, and richer in geometric meaning. (Author)
Creativity and Motivation for Geometric Tasks Designing in Education
ERIC Educational Resources Information Center
Rumanová, Lucia; Smiešková, Edita
2015-01-01
In this paper we focus on creativity needed for geometric tasks designing, visualization of geometric problems and use of ICT. We present some examples of various problems related to tessellations. Altogether 21 students--pre-service teachers participated in our activity within a geometry course at CPU in Nitra, Slovakia. Our attempt was to…
On an Assumption of Geometric Foundation of Numbers
ERIC Educational Resources Information Center
Anatriello, Giuseppina; Tortoriello, Francesco Saverio; Vincenzi, Giovanni
2016-01-01
In line with the latest positions of Gottlob Frege, this article puts forward the hypothesis that the cognitive bases of mathematics are geometric in nature. Starting from the geometry axioms of the "Elements" of Euclid, we introduce a geometric theory of proportions along the lines of the one introduced by Grassmann in…
Geometric Scaling from Dokshitzer-Gribov-Lipatov-Altarelli-Parisi Evolution
Caola, Fabrizio; Forte, Stefano
2008-07-11
We show that the geometric scaling of the total virtual photon-proton cross section data can be explained using standard linear Dokshitzer-Gribov-Altarelli-Parisi perturbative evolution with generic boundary conditions in a wide kinematic region. This allows us to single out the region where geometric scaling may provide evidence for parton saturation.
Geometric quadratic stochastic operator on countable infinite set
Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar
2015-02-03
In this paper we construct the family of Geometric quadratic stochastic operators defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. Such operators can be reinterpreted in terms of of evolutionary operator of free population. We show that Geometric quadratic stochastic operators are regular transformations.
Active Learning Environment with Lenses in Geometric Optics
ERIC Educational Resources Information Center
Tural, Güner
2015-01-01
Geometric optics is one of the difficult topics for students within physics discipline. Students learn better via student-centered active learning environments than the teacher-centered learning environments. So this study aimed to present a guide for middle school teachers to teach lenses in geometric optics via active learning environment…
Children's Strategies in Imagining Spatio-Geometrical Transformations.
ERIC Educational Resources Information Center
McGillicuddy-De Lisi, Ann V.; De Lisi, Richard
1981-01-01
Seventy-five children, 6 to 13 years of age, were assigned to one of five groups on the basis of Piagetian tests of spatial-geometrical knowledge. Subjects imagined and executed three transformations of geometric figures: square-enlargement, diamond enlargement and transformation of a small diamond into a large square. (CM)
Homothetic Transformations and Geometric Loci: Properties of Triangles and Quadrilaterals
ERIC Educational Resources Information Center
Mammana, Maria Flavia
2016-01-01
In this paper, we use geometric transformations to find some interesting properties related with geometric loci. In particular, given a triangle or a cyclic quadrilateral, the locus generated by the centroid or by the orthocentre (for triangles) or by the anticentre (for cyclic quadrilaterals) when one vertex moves on the circumcircle of the…
Geometric Potential and Transport in Photonic Topological Crystals
Szameit, Alexander; Dreisow, Felix; Heinrich, Matthias; Keil, Robert; Nolte, Stefan; Tuennermann, Andreas; Longhi, Stefano
2010-04-16
We report on the experimental realization of an optical analogue of a quantum geometric potential for light wave packets constrained on thin dielectric guiding layers fabricated in silica by the femtosecond laser writing technology. We further demonstrate the optical version of a topological crystal, with the observation of Bloch oscillations and Zener tunneling of a purely geometric nature.
Prospective Middle School Mathematics Teachers' Preconceptions of Geometric Translations
ERIC Educational Resources Information Center
Yanik, H. Bahadir
2011-01-01
This article reports an analysis of 44 prospective middle school mathematics teachers' pre-existing knowledge of rigid geometric transformations, specifically the geometric translations. The main data source for this study was the participants' responses to the tasks that were presented during semi-structured clinical interviews. The findings of…
Li, Yan-Li; Meng, Yi-Fan; Zhang, Zi-Mou; Jiang, Yong
2014-08-01
Atomic force microscopy (AFM), which provides true 3D surface topography, can also be used to determine the geometric parameters of proteins quantitatively at a single molecular level. In this paper, two different kinds of Escherichia coli MutS (MutS) protein were observed using AFM, and the geometric parameters of the proteins such as height, perimeter, area, and volume were measured. On the basis of these measurements, the molecular weight, association constant, oligomeric state, and orientation of MutS proteins on a mica surface were deduced. The oligomerization mechanism of MutS was analyzed in detail, and the results show that two different kinds of interactions between MutS protein may be involved in oligomerization. Our results also show that AFM imaging is an accurate method for analyzing the geometric structures of a single protein quantitatively at a single-molecule level.
Technical note: Revisiting the geometric theorems for volume averaging
NASA Astrophysics Data System (ADS)
Wood, Brian D.
2013-12-01
The geometric theorems reported by Quintard and Whitaker [5, Appendix B] are re-examined. We show (1) The geometrical theorems can be interpreted in terms of the raw spatial moments of the pore structure within the averaging volume. (2) For the case where the first spatial moment is aligned with the center of mass of the averaging volume, the geometric theorems can be expressed in terms of the central moments of the porous medium. (3) When the spatial moments of the pore structure are spatially stationary, the geometrical theorems allow substantial simplification of nonlocal terms arising in the averaged equations. (4) In the context of volume averaging, the geometric theorems of Quintard and Whitaker [5, Appendix B] are better interpreted as statements regarding the spatial stationarity of specific volume averaged quantities rather than an explicit statement about the media disorder.
Entanglement dynamics via geometric phases in quantum spin chains
Castro, C. S.; Sarandy, M. S.
2011-04-15
We introduce a connection between entanglement induced by interaction and geometric phases acquired by a composite quantum spin system. We begin by analyzing the evaluation of cyclic (Aharonov-Anandan) and noncyclic (Mukunda-Simon) geometric phases for general spin chains evolving in the presence of time-independent magnetic fields. Then, by considering Heisenberg chains, we show that the interaction geometric phase, namely, the total geometric phase with subtraction of free spin contributions, is directly related to the global (Meyer-Wallach) entanglement exhibited by an initially separable state during its evolution in Hilbert space. This is analytically shown for N=2 spins and numerically illustrated for larger chains. This relationship promotes the interaction geometric phase to an indicator of global entanglement in the system, which may constitute a useful tool for quantum tasks based on entanglement as a resource to their performance.
A geometric representation scheme suitable for shape optimization
NASA Technical Reports Server (NTRS)
Tortorelli, Daniel A.
1990-01-01
A geometric representation scheme is outlined which utilizes the natural design variable concept. A base configuration with distinct topological features is created. This configuration is then deformed to define components with similar topology but different geometry. The values of the deforming loads are the geometric entities used in the shape representation. The representation can be used for all geometric design studies; it is demonstrated here for structural optimization. This technique can be used in parametric design studies, where the system response is defined as functions of geometric entities. It can also be used in shape optimization, where the geometric entities of an original design are modified to maximize performance and satisfy constraints. Two example problems are provided. A cantilever beam is elongated to meet new design specifications and then optimized to reduce volume and satisfy stress constraints. A similar optimization problem is presented for an automobile crankshaft section. The finite element method is used to perform the analyses.
Li Xinhua; Zhang Da; Liu, Bob
2011-01-15
Purpose: To study the sensitivity of a geometric calibration method using projection matrices for digital tomosynthesis systems. Methods: A generic geometric calibration method for tomographic imaging systems has been presented in our previous work. The method involves a scan of a calibration phantom with multiple markers. Their locations in projection images are detected and are associated with their 3D coordinates to compute 3x4 projection matrices, which can be used in subsequent image reconstruction. The accuracy of geometric calibration may be affected by errors in the input data of marker positions. The effects of errors may depend on the number of markers and the volume surrounded by them in 3D space. This work analyzed the sensitivity of the calibration method to the above factors. A 6 cm CIRS breast research phantom and a prototype breast tomosynthesis system were used for our tests. A high contrast ring and two small speck groups were reconstructed in various testing cases for comparison. To achieve quantitative assessment, a 15x15 point detection mask was adopted for detecting signals and for computing changes between testing cases and the regular geometric calibration. Results: When 3D coordinates and 2D projections of markers were accurate, all tested numbers of markers, 6-44, provided similar high quality reconstructions of the ring and the two speck groups. Errors in marker positions resulted in image degradations and signal changes, which increased with fewer markers and smaller volume surrounded by markers in the 3D object space. Signal changes of small specks were more significant than those of the ring. Errors in marker projections produced drastic image degradations. Coplanar marker placement caused a failure in projection matrix computation. Conclusions: For practical geometric calibration phantom design, ample markers are desired. They need to have a large volumetric coverage in the 3D space and be far from being coplanar. Precise
Digital polarization holography advancing geometrical phase optics.
De Sio, Luciano; Roberts, David E; Liao, Zhi; Nersisyan, Sarik; Uskova, Olena; Wickboldt, Lloyd; Tabiryan, Nelson; Steeves, Diane M; Kimball, Brian R
2016-08-01
Geometrical phase or the fourth generation (4G) optics enables realization of optical components (lenses, prisms, gratings, spiral phase plates, etc.) by patterning the optical axis orientation in the plane of thin anisotropic films. Such components exhibit near 100% diffraction efficiency over a broadband of wavelengths. The films are obtained by coating liquid crystalline (LC) materials over substrates with patterned alignment conditions. Photo-anisotropic materials are used for producing desired alignment conditions at the substrate surface. We present and discuss here an opportunity of producing the widest variety of "free-form" 4G optical components with arbitrary spatial patterns of the optical anisotropy axis orientation with the aid of a digital spatial light polarization converter (DSLPC). The DSLPC is based on a reflective, high resolution spatial light modulator (SLM) combined with an "ad hoc" optical setup. The most attractive feature of the use of a DSLPC for photoalignment of nanometer thin photo-anisotropic coatings is that the orientation of the alignment layer, and therefore of the fabricated LC or LC polymer (LCP) components can be specified on a pixel-by-pixel basis with high spatial resolution. By varying the optical magnification or de-magnification the spatial resolution of the photoaligned layer can be adjusted to an optimum for each application. With a simple "click" it is possible to record different optical components as well as arbitrary patterns ranging from lenses to invisible labels and other transparent labels that reveal different images depending on the side from which they are viewed. PMID:27505793
Neutron Studies of Geometrically Frustrated Magnets
NASA Astrophysics Data System (ADS)
Gardner, Jason
2004-03-01
Antiferromagnetically coupled spins residing on a network of corner sharing triangles (Kagome) or tetrahedra (pyrochlore) have attracted much attention in recent years [1-4] and often display phenomena known broadly as geometrical frustration. Because of their low propensity to order, even for classical spins, antiferromagnetic materials based on a pyrochlore lattice appear to be excellent systems for studying exotic ground states. It has also been shown that ferromagnetically coupled spins can be frustrated on such a lattice, if there is considerable local Ising anisotropy. Detailed neutron scattering measurements (elastic and inelastic scattering) taken on the antiferromagnets, Tb_2Ti_2O7 and Gd_2Ti_2O_7, and the ferromagnet, Ho_2Ti_2O_7, will be presented. The neutron data will be backed up with bulk property results. Evidence of short-range magnetic correlations, frozen moments and long-range magnetic ordering in different parts of applied field and temperature space will be discussed. Tb_2Ti_2O7 is a cooperative paramagnet with an effective paramagnetic moment of 9.7 μ_B, has be shown to magnetically order in modest fields and temperatures, however in zero field the system does not order above 15 mK. Ho_2Ti_2O7 is known as a "dipolar spin ice" [3-4] compound and this will be discussed in some detail. If time permits I will present new results on the magnetic ordering of Gd_2Ti_2O7 in zero field. [1] Magnetic Systems with Competing Interactions, edited by H.T. Diep (World Scientific, Singapore, 1994) and Can. J. Phys. 79, (2001). [2] J. S. Gardner et al., Phys. Rev. Lett., 82, 1012, (1999). [3] S. T. Bramwell and M. P. Gingras, Science, 294, 1495, (2001). [4] A. P. Ramirez et al., Nature, 399, 333 (1999).
Geometric characterization of the Arjuna orbital domain
NASA Astrophysics Data System (ADS)
de la Fuente Marcos, C.; de la Fuente Marcos, R.
2015-01-01
Arjuna-type orbits are characterized by being Earth-like, having both low-eccentricity and low-inclination. Objects following these trajectories experience repeated trappings in the 1:1 commensurability with the Earth and can become temporary Trojans, horseshoe librators, quasi-satellites, and even transient natural satellites. Here, we review what we know about this peculiar dynamical group and use a Monte Carlo simulation to characterize geometrically the Arjuna orbital domain, studying its visibility both from the ground and with the European Space Agency Gaia spacecraft. The visibility analysis from the ground together with the discovery circumstances of known objects are used as proxies to estimate the current size of this population. The impact cross-section of the Earth for minor bodies in this resonant group is also investigated. We find that, for ground-based observations, the solar elongation at perigee of nearly half of these objects is less than 90\\degr. They are best observed by space-borne telescopes, but Gaia is not going to improve significantly the current discovery rate for members of this class. Our results suggest that the size of this population may have been underestimated by current models. On the other hand, their intrinsically low encounter velocities with the Earth induce a 10-1000-fold increase in the impact cross-section with respect to what is typical for objects in the Apollo or Aten asteroid populations. We estimate that their probability of capture as transient natural satellites of our planet is about 8 %.
Aftershock Statistics explained from Geometric Reductionism
NASA Astrophysics Data System (ADS)
Mignan, Arnaud
2016-04-01
The decay of aftershocks has recently been shown to follow a stretched exponential function instead of the Omori law (Mignan, Geophys. Res. Lett., 2015). This triggers a complete re-investigation of aftershock statistics in Southern California and a new physical interpretation of these results: (1) After verifying the stretched exponential behavior of aftershocks in time, I show that aftershocks follow a pure exponential in space. I then (re)demonstrate that K(M) = exp(α(M-mmin-ΔmB)) with K the aftershock production by mainshock magnitude M, α the Gutenberg-Richter distribution slope and ΔmB Båth's parameter. Based on these observations, I propose the Recursive Aftershock Stretched Exponential (RASE) model. (2) I investigate the origin of aftershocks using geometric reductionism made possible by the Non-Critical Precursory Accelerating Seismicity Theory postulate, which states that spatial density switches from δb0 for background seismicity to δbp for activated events (such as foreshocks, induced seismicity and here aftershocks) when the static stress field σ(r) exceeds the threshold σ(rA*) ∝ Δσ* with r the distance to source. The postulate explains the exponential spatial distribution (assuming that aftershocks fill a noisy fractal network within rA*) and aftershock production (assuming a constant stress drop) with K(M) = δbp.V(M), V being the volume of a rounded cuboid centred on the fault of length l ∝ exp(αM), and with radius rA*. Finally the observed stretching factor β ≈ 0.4 is explained topologically from the fractal dimension D ≈ 1.5.
Geometric perturbation theory and plasma physics
Omohundro, S.M.
1985-04-04
Modern differential geometric techniques are used to unify the physical asymptotics underlying mechanics, wave theory and statistical mechanics. The approach gives new insights into the structure of physical theories and is suited to the needs of modern large-scale computer simulation and symbol manipulation systems. A coordinate-free formulation of non-singular perturbation theory is given, from which a new Hamiltonian perturbation structure is derived and related to the unperturbed structure. The theory of perturbations in the presence of symmetry is developed, and the method of averaging is related to reduction by a circle group action. The pseudo-forces and magnetic Poisson bracket terms due to reduction are given a natural asymptotic interpretation. Similar terms due to changing reference frames are related to the method of variation of parameters, which is also given a Hamiltonian formulation. These methods are used to answer a question about nearly periodic systems. The answer leads to a new secular perturbation theory that contains no ad hoc elements. Eikonal wave theory is given a Hamiltonian formulation that generalizes Whitham's Lagrangian approach. The evolution of wave action density on ray phase space is given a Hamiltonian structure using a Lie-Poisson bracket. The relationship between dissipative and Hamiltonian systems is discussed. A new type of attractor is defined which attracts both forward and backward in time and is shown to occur in infinite-dimensional Hamiltonian systems with dissipative behavior. The theory of Smale horseshoes is applied to gyromotion in the neighborhood of a magnetic field reversal and the phenomenon of reinsertion in area-preserving horseshoes is introduced. The central limit theorem is proved by renormalization group techniques. A natural symplectic structure for thermodynamics is shown to arise asymptotically from the maximum entropy formalism.
Martínez, Fernando; Sardanyés, Josep; Elena, Santiago F; Daròs, José-Antonio
2011-07-01
The tremendous evolutionary potential of RNA viruses allows them to thrive despite host defense mechanisms and endows them with properties such as emergence, host switching, and virulence. The frequency of mutant viruses after an infectious process results from the interplay between the error rate of the viral replicase, from purifying mechanisms acting after transcription on aberrant RNAs, and from the amplification dynamics of virus RNA positive (+) and negative (-) strands. Two extreme scenarios describing viral RNA amplification are the geometric growth, in which each RNA strand serves as template for the synthesis of complementary strands with the same efficiency, and the stamping machine, where a strand is reiteratively used as template to synthesize multiple copies of the complementary. The resulting mutation frequencies are completely different, being geometric growth largely more mutagenic than stamping machine. In this work we evaluate the contribution of geometric growth and stamping machine to the overall genome amplification of the plant (+)-strand RNA virus turnip mosaic virus (TuMV). By means of transfection experiments of Nicotiana benthamiana protoplasts with a TuMV cDNA infectious clone and by using strand-specific quantitative real-time PCR, we determined the amplification dynamics of viral (+) and (-) RNA during a single-cell infectious process. A mathematical model describing the amplification of each viral strand was fitted to the data. Analyses of the model parameters showed that TuMV (+) and (-) RNA amplification occurs through a mixed strategy with ∼93% of genomes produced via stamping machine and only ∼7% resulting from geometric growth. PMID:21515574
Description Of Scoliotic Deformity Pattern By Harmonic Functions
NASA Astrophysics Data System (ADS)
Drerup, Burkhard; Hierholzer, Eberhard
1989-04-01
Frontal radiographs of scoliotic deformity of the spine reveal a characteristic pattern of lateral deviation, lateral tilt and axial rotation of vertebrae. In order to study interrelations between deformation parameters 478 radiographs of idiopathic scolioses, 23 of scolioses after Wilms-tumor treatment and 18 of scolioses following poliomyelitis were digitized. From these the curves of lateral deviation, tilt and rotation are calculated and fitted by Fourier series. By restriction to the first harmonic, analysis reduces to the analysis of a single phase and amplitude for each curve. Justification of this simplification will be discussed. Results provide a general geometric description of scoliotic deformity.
NASA Astrophysics Data System (ADS)
Ben-Menahem, Yemima
This paper deals with the dependence of directionality in the course of events-or our claims concerning such directionality-on the modes of description we use in speaking of the events in question. I argue that criteria of similarity and individuation play a crucial role in assessments of directionality. This is an extension of Davidson's claim regarding the difference between causal and explanatory contexts. The argument is based on a characterisation of notions of necessity and contingency that differ from their modal logic counterparts on the one hand, and from causality and chance on the other. I show that some types of directionality are perfectly compatible with both determinism and indeterminism at the microscopic level, and that there is no likelihood of, or advantage to, reducing such directionality to other laws or causal processes.
NASA Astrophysics Data System (ADS)
Dunajewski, Adam; Dusza, Jacek J.; Rosado Muñoz, Alfredo
2014-11-01
The article presents a proposal for the description of human gait as a periodic and symmetric process. Firstly, the data for researches was obtained in the Laboratory of Group SATI in the School of Engineering of University of Valencia. Then, the periodical model - Mean Double Step (MDS) was made. Finally, on the basis of MDS, the symmetrical models - Left Mean Double Step and Right Mean Double Step (LMDS and RMDS) could be created. The method of various functional extensions was used. Symmetrical gait models can be used to calculate the coefficients of asymmetry at any time or phase of the gait. In this way it is possible to create asymmetry, function which better describes human gait dysfunction. The paper also describes an algorithm for calculating symmetric models, and shows exemplary results based on the experimental data.
NASA Technical Reports Server (NTRS)
Simmons, Reid; Apfelbaum, David
2005-01-01
Task Description Language (TDL) is an extension of the C++ programming language that enables programmers to quickly and easily write complex, concurrent computer programs for controlling real-time autonomous systems, including robots and spacecraft. TDL is based on earlier work (circa 1984 through 1989) on the Task Control Architecture (TCA). TDL provides syntactic support for hierarchical task-level control functions, including task decomposition, synchronization, execution monitoring, and exception handling. A Java-language-based compiler transforms TDL programs into pure C++ code that includes calls to a platform-independent task-control-management (TCM) library. TDL has been used to control and coordinate multiple heterogeneous robots in projects sponsored by NASA and the Defense Advanced Research Projects Agency (DARPA). It has also been used in Brazil to control an autonomous airship and in Canada to control a robotic manipulator.
NASA Technical Reports Server (NTRS)
Papageorgiou, Demetrios T.
1996-01-01
In this article we review recent results on the breakup of cylindrical jets of a Newtonian fluid. Capillary forces provide the main driving mechanism and our interest is in the description of the flow as the jet pinches to form drops. The approach is to describe such topological singularities by constructing local (in time and space) similarity solutions from the governing equations. This is described for breakup according to the Euler, Stokes or Navier-Stokes equations. It is found that slender jet theories can be applied when viscosity is present, but for inviscid jets the local shape of the jet at breakup is most likely of a non-slender geometry. Systems of one-dimensional models of the governing equations are solved numerically in order to illustrate these differences.
YUCCA MOUNTAIN SITE DESCRIPTION
A.M. Simmons
2004-04-16
The ''Yucca Mountain Site Description'' summarizes, in a single document, the current state of knowledge and understanding of the natural system at Yucca Mountain. It describes the geology; geochemistry; past, present, and projected future climate; regional hydrologic system; and flow and transport within the unsaturated and saturated zones at the site. In addition, it discusses factors affecting radionuclide transport, the effect of thermal loading on the natural system, and tectonic hazards. The ''Yucca Mountain Site Description'' is broad in nature. It summarizes investigations carried out as part of the Yucca Mountain Project since 1988, but it also includes work done at the site in earlier years, as well as studies performed by others. The document has been prepared under the Office of Civilian Radioactive Waste Management quality assurance program for the Yucca Mountain Project. Yucca Mountain is located in Nye County in southern Nevada. The site lies in the north-central part of the Basin and Range physiographic province, within the northernmost subprovince commonly referred to as the Great Basin. The basin and range physiography reflects the extensional tectonic regime that has affected the region during the middle and late Cenozoic Era. Yucca Mountain was initially selected for characterization, in part, because of its thick unsaturated zone, its arid to semiarid climate, and the existence of a rock type that would support excavation of stable openings. In 1987, the United States Congress directed that Yucca Mountain be the only site characterized to evaluate its suitability for development of a geologic repository for high-level radioactive waste and spent nuclear fuel.
Geometric morphometric analysis of the use of mandibular gonial eversion in sex determination.
Oettlé, A C; Pretorius, E; Steyn, M
2009-01-01
Physical anthropologists are continually looking for new ways to determine sex from skeletal remains. Determination of sex is done either metrically or descriptively (morphologically). Many characteristics cannot be metrically assessed and descriptive characteristics cannot always be objectively compared. Geometric morphometrics is a relatively new method that provides a mechanism to quantify descriptive morphological characteristics and provides statistics to interpret findings. In this study gonial eversion as a sexually dimorphic trait was re-evaluated, with the use of geometric morphometrics. Twenty-eight adult black female mandibles and 46 adult black male mandibles from South Africa were used. Photographs were taken of the posterior aspect of each mandible with a digital camera in a fixed position. The mandibles were positioned so as to optimise the demonstration of the gonial eversion.The captured electronic images (in jpg format) were then analysed with the tps series of programs (thin-plate spline analysis of digitized landmarks). Statistical analysis revealed that 71.4% of females and 73.9% of males could be accurately sexed by using the shape of the posterior aspect of the mandible. The males had a more variable shape, while the females were more similar to each other. A smaller gonial eversion involving the lower part of the mandibular ramus was seen in the females while the males tend to have a uniform and much wider curve involving the whole ramus. There was, however, considerable overlap between the sexes. Although different tendencies exist between the gonial eversion of the mandible of males and females, the extent of these differences is not adequate to predict the sex of a single individual.
Implications of Polishing Techniques in Quantitative X-Ray Microanalysis
Rémond, Guy; Nockolds, Clive; Phillips, Matthew; Roques-Carmes, Claude
2002-01-01
Specimen preparation using abrasives results in surface and subsurface mechanical (stresses, strains), geometrical (roughness), chemical (contaminants, reaction products) and physical modifications (structure, texture, lattice defects). The mechanisms involved in polishing with abrasives are presented to illustrate the effects of surface topography, surface and subsurface composition and induced lattice defects on the accuracy of quantitative x-ray microanalysis of mineral materials with the electron probe microanalyzer (EPMA). PMID:27446758
Miniaturization of Fresnel lenses for solar concentration: a quantitative investigation.
Duerr, Fabian; Meuret, Youri; Thienpont, Hugo
2010-04-20
Sizing down the dimensions of solar concentrators for photovoltaic applications offers a number of promising advantages. It provides thinner modules and smaller solar cells, which reduces thermal issues. In this work a plane Fresnel lens design is introduced that is first analyzed with geometrical optics. Because of miniaturization, pure ray tracing may no longer be valid to determine the concentration performance. Therefore, a quantitative wave optical analysis of the miniaturization's influence on the obtained concentration performance is presented. This better quantitative understanding of the impact of diffraction in microstructured Fresnel lenses might help to optimize the design of several applications in nonimaging optics. PMID:20411014
Random geometric prior forest for multiclass object segmentation.
Liu, Xiao; Song, Mingli; Tao, Dacheng; Bu, Jiajun; Chen, Chun
2015-10-01
Recent advances in object detection have led to the development of segmentation by detection approaches that integrate top-down geometric priors for multiclass object segmentation. A key yet under-addressed issue in utilizing top-down cues for the problem of multiclass object segmentation by detection is efficiently generating robust and accurate geometric priors. In this paper, we propose a random geometric prior forest scheme to obtain object-adaptive geometric priors efficiently and robustly. In the scheme, a testing object first searches for training neighbors with similar geometries using the random geometric prior forest, and then the geometry of the testing object is reconstructed by linearly combining the geometries of its neighbors. Our scheme enjoys several favorable properties when compared with conventional methods. First, it is robust and very fast because its inference does not suffer from bad initializations, poor local minimums or complex optimization. Second, the figure/ground geometries of training samples are utilized in a multitask manner. Third, our scheme is object-adaptive but does not require the labeling of parts or poselets, and thus, it is quite easy to implement. To demonstrate the effectiveness of the proposed scheme, we integrate the obtained top-down geometric priors with conventional bottom-up color cues in the frame of graph cut. The proposed random geometric prior forest achieves the best segmentation results of all of the methods tested on VOC2010/2012 and is 90 times faster than the current state-of-the-art method. PMID:25974937
Geometric control of vimentin intermediate filaments.
Shabbir, Shagufta H; Cleland, Megan M; Goldman, Robert D; Mrksich, Milan
2014-02-01
Significant efforts have addressed the role of vimentin intermediate filaments (VIF) in cell motility, shape, adhesion and their connections to microfilaments (MF) and microtubules (MT). The present work uses micropatterned substrates to control the shapes of mouse fibroblasts and demonstrates that the cytoskeletal elements are dependent on each other and that unlike MF, VIF are globally controlled. For example, both square and circle shaped cells have a similar VIF distribution while MF distributions in these two shapes are quite different and depend on the curvature of the shape. Furthermore, in asymmetric and polarized shaped cells VIF avoid the sharp edges where MF are highly localized. Experiments with vimentin null mouse embryonic fibroblasts (MEFs) adherent to polarized (teardrop) and un-polarized (dumbbell) patterns show that the absence of VIF alters microtubule organization and perturbs cell polarity. The results of this study also demonstrate the utility of patterned substrates for quantitative studies of cytoskeleton organization in adherent cells.
Geometric and potential driving formation and evolution of biomolecular surfaces.
Bates, P W; Chen, Zhan; Sun, Yuhui; Wei, Guo-Wei; Zhao, Shan
2009-08-01
This paper presents new geometrical flow equations for the theoretical modeling of biomolecular surfaces in the context of multiscale implicit solvent models. To account for the local variations near the biomolecular surfaces due to interactions between solvent molecules, and between solvent and solute molecules, we propose potential driven geometric flows, which balance the intrinsic geometric forces that would occur for a surface separating two homogeneous materials with the potential forces induced by the atomic interactions. Stochastic geometric flows are introduced to account for the random fluctuation and dissipation in density and pressure near the solvent-solute interface. Physical properties, such as free energy minimization (area decreasing) and incompressibility (volume preserving), are realized by some of our geometric flow equations. The proposed approach for geometric and potential forces driving the formation and evolution of biological surfaces is illustrated by extensive numerical experiments and compared with established minimal molecular surfaces and molecular surfaces. Local modification of biomolecular surfaces is demonstrated with potential driven geometric flows. High order geometric flows are also considered and tested in the present work for surface generation. Biomolecular surfaces generated by these approaches are typically free of geometric singularities. As the speed of surface generation is crucial to implicit solvent model based molecular dynamics, four numerical algorithms, a semi-implicit scheme, a Crank-Nicolson scheme, and two alternating direction implicit (ADI) schemes, are constructed and tested. Being either stable or conditionally stable but admitting a large critical time step size, these schemes overcome the stability constraint of the earlier forward Euler scheme. Aided with the Thomas algorithm, one of the ADI schemes is found to be very efficient as it balances the speed and accuracy.
QuantitativeT2: interactive quantitative T2 MRI witnessed in mouse glioblastoma.
Ali, Tonima Sumya; Bjarnason, Thorarin Albert; Senger, Donna L; Dunn, Jeff F; Joseph, Jeffery T; Mitchell, Joseph Ross
2015-07-01
The aim of this study was to establish an advanced analytical platform for complex in vivo pathologies. We have developed a software program, QuantitativeT2, for voxel-based real-time quantitative T2 magnetic resonance imaging. We analyzed murine brain tumors to confirm feasibility of our method for neurological conditions. Anesthetized mice (with invasive gliomas, and controls) were imaged on a 9.4 Tesla scanner using a Carr-Purcell-Meiboom-Gill sequence. The multiecho T2 decays from axial brain slices were analyzed using QuantitativeT2. T2 distribution histograms demonstrated substantial characteristic differences between normal and pathological brain tissues. Voxel-based quantitative maps of tissue water fraction (WF) and geometric mean T2 (gmT2) revealed the heterogeneous alterations to water compartmentalization caused by pathology. The numeric distribution of WF and gmT2 indicated the extent of tumor infiltration. Relative evaluations between in vivo scans and ex vivo histology indicated that the T2s between 30 and 150 ms were related to cellular density and the integrity of the extracellular matrix. Overall, QuantitativeT2 has demonstrated significant advancements in qT2 analysis with real-time operation. It is interactive with an intuitive workflow; can analyze data from many MR manufacturers; and is released as open-source code to encourage examination, improvement, and expansion of this method. PMID:26213695
Hsieh, Y L; Zeng, G L; Gullberg, G T
1998-02-01
The spatially varying geometric response of the collimator-detector system in single photon emission computed tomography (SPECT) causes loss in resolution, shape distortions, reconstructed density nonuniformity, and quantitative inaccuracies. A projection space image reconstruction algorithm is used to correct these reconstruction artifacts. The projectors F use strip functions to calculate pixels more "natural" for modeling the two-dimensional (2-D) geometric response of the SPECT collimator transaxially to the axis of rotation. These projectors are defined by summing the intersection of an array of multiple strips rotated at equal angles to approximate the ideal system geometric response of the collimator. Two projection models were evaluated for modeling the system geometric response function. For one projector each strip is of equal weight, for the other projector a Gaussian weighting is used. Parallel beam and fan beam projections of a physical three-dimensional (3-D) Hoffman brain phantom and a Jaszczak cold rod phantom were used to evaluate the geometric response correction. Reconstructions were obtained by using the singular value decomposition (SVD) method and the iterative conjugate gradient algorithm to solve for q in the imaging equation FGq = p, where p is the projection measurement. The projector F included the new models for the geometric response, whereas, the backprojector G did not always model the geometric response in order to increase the computational speed. The final reconstruction was obtained by sampling the backprojection Gq at a discrete array of points. Reconstructions produced by the two proposed projectors showed improved resolution when compared against a unit-strip "natural" pixel model, the conventional image pixelized model with ray tracing to calculate the geometric response, and the filtered backprojection algorithm. When the reconstruction is displayed on fine grid points, the continuity and resolution of the image is preserved
Geometric effects on stress wave propagation.
Johnson, K L; Trim, M W; Horstemeyer, M F; Lee, N; Williams, L N; Liao, J; Rhee, H; Prabhu, R
2014-02-01
The present study, through finite element simulations, shows the geometric effects of a bioinspired solid on pressure and impulse mitigation for an elastic, plastic, and viscoelastic material. Because of the bioinspired geometries, stress wave mitigation became apparent in a nonintuitive manner such that potential real-world applications in human protective gear designs are realizable. In nature, there are several toroidal designs that are employed for mitigating stress waves; examples include the hyoid bone on the back of a woodpecker's jaw that extends around the skull to its nose and a ram's horn. This study evaluates four different geometries with the same length and same initial cross-sectional diameter at the impact location in three-dimensional finite element analyses. The geometries in increasing complexity were the following: (1) a round cylinder, (2) a round cylinder that was tapered to a point, (3) a round cylinder that was spiraled in a two dimensional plane, and (4) a round cylinder that was tapered and spiraled in a two-dimensional plane. The results show that the tapered spiral geometry mitigated the greatest amount of pressure and impulse (approximately 98% mitigation) when compared to the cylinder regardless of material type (elastic, plastic, and viscoelastic) and regardless of input pressure signature. The specimen taper effectively mitigated the stress wave as a result of uniaxial deformational processes and an induced shear that arose from its geometry. Due to the decreasing cross-sectional area arising from the taper, the local uniaxial and shear stresses increased along the specimen length. The spiral induced even greater shear stresses that help mitigate the stress wave and also induced transverse displacements at the tip such that minimal wave reflections occurred. This phenomenon arose although only longitudinal waves were introduced as the initial boundary condition (BC). In nature, when shearing occurs within or between materials
Spin relaxation in geometrically frustrated pyrochlores
NASA Astrophysics Data System (ADS)
Dunsiger, Sarah Ruth
This thesis describes muSR experiments which focus on systems where the magnetic ions occupy the vertices of edge or corner sharing triangular units, in particular the pyrochlores A2B2O7. The scientific interest in pyrochlores is based on the fact that they display novel magnetic behaviour at low temperatures due to geometrical frustration. The ground state of these systems is sensitively dependent on such factors as the range of the spin-spin interactions, disorder, anisotropy, thermal and quantum fluctuations. For example, Y2Mo2O7 shows many features reminiscent of a conventional spin glass, even though this material has nominally zero chemical disorder. It is found that the muon spin polarisation obeys a time-field scaling relation which indicates that the spin-spin autocorrelation function has a power law form in time, in stark contrast with the exponential form often assumed for conventional magnets above their transition temperature. Gd2Ti2O7 shows long range order, but only at a temperature much lower than its Curie-Weiss temperature, a signature of a frustrated system. In the paramagnetic regime, it is well described by an isotropic Heisenberg Hamiltonian with nearest neighbour couplings in the presence of a Zeeman interaction, from which the spin-spin autocorrelation function may be calculated as a power series in time. The muon spin relaxation rate decreases with magnetic field as the Zeeman energy becomes comparable with the exchange coupling between Gd spins. Thus, an independent measure of the exchange coupling or equivalently the Gd spin fluctuation rate is extracted. By contrast, Tb2Ti2O7 has been identified as a type of cooperative paramagnet. Short range correlations develop below 50 K. However, there is no long range ordering down to very low temperatures (0.075 K). The Tb3+ ion is subject to strong crystal electric field effects: point charge calculations indicate that this system is Ising like at low temperatures. Thus this system may be
Geometrical parameters of E+S pairs
NASA Technical Reports Server (NTRS)
Rampazzo, Roberto; Sulentic, Jack W.
1990-01-01
Local environmental conditions (i.e., density and angular momentum properties of protogalactic clouds) are thought to be factors affecting the ultimate morphology of a galaxy. The existence of significant numbers of mixed morphology (E/SO+S) pairs of galaxies would represent a direct challenge to this idea unless all early-type components are formed by mergers. The authors wished to isolate candidate E+S pairs for detailed study. The authors have observed 22 pairs of mixed morphology galaxies (containing at least one early-type component) selected from a catalog of Sulentic (1988: unpublished) based upon the ESO sky survey. The observed sample and relevant morphological and interaction characteristics are summarized in tabular form. The authors report the relevant geometrical properties of the galaxies in another table. They list the maximum values measured for the ellipticity and the a(4)/a shape parameter together with the total measured twisting along the profile beyond the seeing disk (they set an inner limit of 3 arcsed). An asterisk indicates objects in which a(4)/a is neither predominantly boxy nor disky. They found a large number of true mixed pairs with 13/22 E+S pairs in the present sample. The remaining objects include 5 disk pairs (composed of SO and S members) and 3 early-type pairs comprising E and SO members. They estimate that between 25 and 50 percent of the pairs in any complete sample will be of the E+S type. This suggests that 100 to 200 such pairs exist on the sky brighter than m sub pg = 16.0. They found no global evidence for a difference between E members of this sample and those in more general samples (e.g., Bender et al. 1989). In particular, they found that about 30 percent of the early-type galaxies cannot be classified either predominantly boxy or disky because the a(4)/a profile shows both of these features at a comparable level or does not show any significant trend. Isophotal twisting is observed with a range and distribution
Geometrical Pumping with a Bose-Einstein Condensate.
Lu, H-I; Schemmer, M; Aycock, L M; Genkina, D; Sugawa, S; Spielman, I B
2016-05-20
We realized a quantum geometric "charge" pump for a Bose-Einstein condensate (BEC) in the lowest Bloch band of a novel bipartite magnetic lattice. Topological charge pumps in filled bands yield quantized pumping set by the global-topological-properties of the bands. In contrast, our geometric charge pump for a BEC occupying just a single crystal momentum state exhibits nonquantized charge pumping set by local-geometrical-properties of the band structure. Like topological charge pumps, for each pump cycle we observed an overall displacement (here, not quantized) and a temporal modulation of the atomic wave packet's position in each unit cell, i.e., the polarization. PMID:27258857
Estimation of spreading fire geometrical characteristics using near infrared stereovision
NASA Astrophysics Data System (ADS)
Rossi, L.; Toulouse, T.; Akhloufi, M.; Pieri, A.; Tison, Y.
2013-03-01
In fire research and forest firefighting, there is a need of robust metrological systems able to estimate the geometrical characteristics of outdoor spreading fires. In recent years, we assist to an increased interest in wildfire research to develop non destructive techniques based on computer vision. This paper presents a new approach for the estimation of fire geometrical characteristics using near infrared stereovision. Spreading fire information like position, rate of spread, height and surface, are estimated from the computed 3D fire points. The proposed system permits to track fire spreading on a ground area of 5mx10m. Keywords: near infrared, stereovision, spreading fire, geometrical characteristics
An overview of the thematic mapper geometric correction system
NASA Technical Reports Server (NTRS)
Beyer, E. P.
1983-01-01
Geometric accuracy specifications for LANDSAT 4 are reviewed and the processing concepts which form the basis of NASA's thematic mapper geometric correction system are summarized for both the flight and ground segments. The flight segment includes the thematic mapper instrument, attitude measurement devices, attitude control, and ephemeris processing. For geometric correction the ground segment uses mirror scan correction data, payload correction data, and control point information to determine where TM detector samples fall on output map projection systems. Then the raw imagery is reformatted and resampled to produce image samples on a selected output projection grid system.
Auto-focusing accelerating hyper-geometric laser beams
NASA Astrophysics Data System (ADS)
Kovalev, A. A.; Kotlyar, V. V.; Porfirev, A. P.
2016-02-01
We derive a new solution to the paraxial wave equation that defines a two-parameter family of three-dimensional structurally stable vortex annular auto-focusing hyper-geometric (AH) beams, with their complex amplitude expressed via a degenerate hyper-geometric function. The AH beams are found to carry an orbital angular momentum and be auto-focusing, propagating on an accelerating path toward a focus, where the annular intensity pattern is ‘sharply’ reduced in diameter. An explicit expression for the complex amplitude of vortex annular auto-focusing hyper-geometric-Gaussian beams is derived. The experiment has been shown to be in good agreement with theory.