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.
A geometric description of human intestine.
Coşkun, Ihsaniye; Yildiz, Hüseyin; Arslan, Kadri; Yildiz, Bahri
2007-01-01
Mathematical models of natural phenomena play a central role in the physical sciences. Moreover, modeling of the organs draws from some beautiful areas of mathematics, such as nonlinear dynamics, multiscale transforms and stability analysis. In this study, a geometric recognition of the separate intestine sections (duodenum, jejunum, ileum, cecum and colon) of the human is presented. The human intestine was considered a tubular shape along a special curve and two male Turkish men were used for the modeling study. The length (cm) and diameter (mm) of the intestines were measured with a digital compass and formulated. These models were compared with their original photographs. It has been concluded that the geometric modeling and experimental work were consistent. These kinds of organ modeling techniques will also profit to medical lecturers to show 3-D figures to their students.
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.
Geometrical description of algebraic structures: Applications to Quantum Mechanics
Carinena, J. F.; Ibort, A.; Marmo, G.; Morandi, G.
2009-05-06
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to quantum mechanics. We will concentrate our attention into quantum theories and we will show how to use in a systematic way the transition from algebraic to geometrical structures to explore their geometry, mainly its Jordan-Lie structure.
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.
Detection and description of geometrically transformed digital images
NASA Astrophysics Data System (ADS)
Mahdian, Babak; Saic, Stanislav
2009-02-01
Geometric transformations such as scaling or rotation are common tools employed by forgery creators. These procedures are typically based on a resampling and interpolation step. The interpolation process brings specific periodic properties into the image. In this paper, we show how to detect these properties. Our aim is to detect all possible geometric transformations in the image being investigated. Furthermore, as the proposed method, as well as other existing detectors, is sensitive to noise, we also briefly show a simple method capable of detecting image noise inconsistencies. Noise is a common tool used to conceal the traces of tampering.
Random geometric graph description of connectedness percolation in rod systems.
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.
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.
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.
Extensor mechanism of the fingers. I. A quantitative geometric study.
Garcia-Elias, M; An, K N; Berglund, L; Linscheid, R L; Cooney, W P; Chao, E Y
1991-11-01
A close-range stereophotogrammetric measurement system was used to determine the three-dimensional geometric characteristics of the extensor assembly in seven human finger specimens and five finger configurations. The numerical data obtained showed that, although changes in length of the different bundles are small, their spatial orientation varies considerably from one to another position. This information should help to improve the accuracy of models derived to understand the extensor assembly behavior in normal and pathological conditions.
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.
Lambert, R K; Paré, P D; Seow, C Y
2004-02-01
Despite considerable investigation, the mechanisms underlying the functional properties of smooth muscle are poorly understood. This can be attributed, at least in part, to a lack of knowledge about the structure and organization of the contractile apparatus inside the muscle cell. Recent observations of the plasticity of smooth muscle and of morphometry of the cell have provided enough information for us to propose a quantitative, although highly simplified, model for the geometric arrangement of contractile units and their collective kinematic functions in smooth muscle, particularly airway smooth muscle. We propose that, to a considerable extent, contractile machinery restructures upon activation of the muscle and adapts to cell geometry at the time of activation. We assume that, under steady-state conditions, the geometric arrangement of contractile units and the filaments within these units determines the kinematic characteristics of the muscle. The model successfully predicts the results of experiments on airway smooth muscle plasticity relating to maximal force generation, maximal velocity of shortening, and the variation of compliance with adapted length. The model is also concordant with morphometric observations that show an increase in myosin filament density when muscle is adapted to a longer length. The model provides a framework for design of experiments to quantitatively test various aspects of smooth muscle plasticity in terms of geometric arrangement of contractile units and the muscle's mechanical properties.
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.
Light beams with general direction and polarization: Global description and geometric phase
NASA Astrophysics Data System (ADS)
Nityananda, R.; Sridhar, S.
2014-02-01
We construct the manifold describing the family of plane monochromatic light waves with all directions, polarizations, phases and intensities. A smooth description of polarization, valid over the entire sphere S2 of directions, is given through the construction of an orthogonal basis pair of complex polarization vectors for each direction; any light beam is then uniquely and smoothly specified by giving its direction and two complex amplitudes. This implies that the space of all light beams is the six dimensional manifold S2×C2∖{0}, the (untwisted) Cartesian product of a sphere and a two dimensional complex vector space minus the origin. A Hopf map (i.e. mapping the two complex amplitudes to the Stokes parameters) then leads to the four dimensional manifold S2×S2 which describes beams with all directions and polarization states. This product of two spheres can be viewed as an ordered pair of two points on a single sphere, in contrast to earlier work in which the same system was represented using Majorana's mapping of the states of a spin one quantum system to an unordered pair of points on a sphere. This is a different manifold, CP2, two dimensional complex projective space, which does not faithfully represent the full space of all directions and polarizations. Following the now-standard framework, we exhibit the fibre bundle whose total space is the set of all light beams of non-zero intensity, and base space S2×S2. We give the U(1) connection which determines the geometric phase as the line integral of a one-form along a closed curve in the total space. Bases are classified as globally smooth, global but singular, and local, with the last type of basis being defined only when the curve traversed by the system is given. Existing as well as new formulae for the geometric phase are presented in this overall framework.
Botton-Divet, Léo; 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.
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
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.
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.
Torres-Rivas, Francisco; Flores-Hidalgo, Manuel Alberto; Glossman-Mitnik, Daniel; Barraza-Jimenez, Diana
2015-10-01
The geometric parameters, local and global chemical reactivity parameters (such as the ionization potential, electron affinity, electronegativity, hardness, softness, chemical potential, and electrophilicity index), as well as the energy levels (HOMO/LUMO) and HOMO-LUMO energy gaps have been determined for the principal carotenoids in higher plants. DFT calculations performed using the B3LYP functional in combination with the 6-31G(d,p) (for geometric parameters) and 6-31 + G(d,p) (for energy parameters) basis sets were carried out to study these structures. The HOMO-LUMO energy gaps obtained with the TPSSh functional were compared with the corresponding energy gaps obtained with B3LYP (when both functionals were used with the 6-31 + G(d,p) basis set). Upon analyzing all of the calculated parameters of the studied molecules, both carotenes were found to be the most reactive, followed by β-cryptoxanthin, zeaxanthin, lutein, violaxanthin, and finally neoxanthin, the least reactive molecule. The results reveal that all of the carotenoids show very high coplanarity in the photochemically active region, resulting in small HOMO-LUMO energy gaps. The calculated local and global chemical reactivity parameters indicate that all of the studied molecules may be classified as soft, as they are good electron donors/acceptors, making these molecules good candidates for use in artificial photosynthetic systems.
Molecular acidity: A quantitative conceptual density functional theory description.
Liu, Shubin; Schauer, Cynthia K; Pedersen, Lee G
2009-10-28
Accurate predictions of molecular acidity using ab initio and density functional approaches are still a daunting task. Using electronic and reactivity properties, one can quantitatively estimate pKa values of acids. In a recent paper [S. B. Liu and L. G. Pedersen, J. Phys. Chem. A 113, 3648 (2009)], we employed the molecular electrostatic potential (MEP) on the nucleus and the sum of valence natural atomic orbital (NAO) energies for the purpose. In this work, we reformulate these relationships on the basis of conceptual density functional theory and compare the results with those from the thermodynamic cycle method. We show that MEP and NAO properties of the dissociating proton of an acid should satisfy the same relationships with experimental pKa data. We employ 27 main groups and first to third row transition metal-water complexes as illustrative examples to numerically verify the validity of these strong linear correlations. Results also show that the accuracy of our approach and that of the conventional method through the thermodynamic cycle are statistically similar.
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.
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.
Nielsen, S P; Xie, X; Bärenholdt, O
2001-01-01
It is well known among clinicians that Colles fracture patients may have normal projected axial bone mineral density and that bone mass is not synonymous with bone strength. The aim of this work was to investigate whether cross-sectional properties of the distal radius in female patients with recent Colles fracture differ from those of a younger group of normal women without fracture. It was hypothesized that patients with Colles fracture had petite distal radii and that cortical thinning and reduced cortical and trabecular volumetric density are dominant features of this fracture type. We used a multilayer high-precision peripheral quantitative computed tomography (pQCT) device with a long-term precision error of 0.1% for a dedicated phantom during the measurement period (152 d). Clinical measurements were made at an ultradistal site rich in trabecular bone and a less ultradistal site rich in cortical bone. The results show that the following pQCT variables were significantly reduced in the nonfractured radius of the Colles fracture cases: mean ultradistal trabecular volumetric density, mean ultradistal and distal cortical volumetric density, mean ultradistal and distal cortical thickness (p < 0.001 for all differences). The outer cortical diameter, cross-sectional bone area, and cortical bending moment of inertia were not statistically different in the two groups. Thus, it would appear that Colles fracture cases did not have petite distal radii. The results suggest that the deforming force of Colles fracture has a transaxial direction (fall on outstretched arm), resulting in a crush fracture, and that it is not a bending force. We suggest that Colles fracture occurs as a result of the combined effect of a fall on the out-stretched arm, low trabecular and cortical volumetric bone density, and reduced cortical thickness.
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.
Quantitative description of collagen fibre network on trabecular bone surfaces based on AFM imaging.
Hua, W-D; Chen, P-P; Xu, M-Q; Ao, Z; Liu, Y; Han, D; He, F
2016-04-01
The collagen fibre network is an important part of extracellular matrix (ECM) on trabecular bone surface. The geometry features of the network can provide us insights into its physical and physiological properties. However, previous researches have not focused on the geometry and the quantitative description of the collagen fibre network on trabecular bone surface. In this study,we developed a procedure to quantitatively describe the network and verified the validity of the procedure. The experiment proceeds as follow. Atomic force microscopy (AFM) was used to acquire submicron resolution images of the trabecular surface. Then, an image analysing procedure was built to extract important parameters, including, fibre orientation, fibre density, fibre width, fibre crossing numbers, the number of holes formed by fibre s, and the area of holes from AFM images. In order to verify the validity of the parameters extracted by image analysing methods, we adopted two other methods, which are statistical geometry model and computer simulation, to calculate those same parameters and check the consistency of the three methods' results. Statistical tests indicate that there is no significant difference between three groups. We conclude that, (a) the ECM on trabecular surface mainly consists of random collagen fibre network with oriented fibres; (b) our method based on image analysing can be used to characterize quantitative geometry features of the collagen fibre network effectively. This method may provide a basis for quantitative investigating the architecture and function of collagen fibre network.
NASA Astrophysics Data System (ADS)
Goto, Shin-itiro
2016-10-01
Contact geometry has been applied to various mathematical sciences, and it has been proposed that a contact manifold and a strictly convex function induce a dually flat space that is used in information geometry. Here, such a dually flat space is related to a Legendre submanifold in a contact manifold. In this paper, contact geometric descriptions of vector fields on dually flat spaces are proposed on the basis of the theory of contact Hamiltonian vector fields. Based on these descriptions, two ways of lifting vector fields on Legendre submanifolds to contact manifolds are given. For some classes of these lifted vector fields, invariant measures in contact manifolds and stability analysis around Legendre submanifolds are explicitly given. Throughout this paper, Legendre duality is explicitly stated. In addition, to show how to apply these general methodologies to applied mathematical disciplines, electric circuit models and some examples taken from nonequilibrium statistical mechanics are analyzed.
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.
NASA Astrophysics Data System (ADS)
Lüdde, H. J.; Achenbach, A.; Kalkbrenner, T.; Jankowiak, H. C.; Kirchner, T.
2016-09-01
Recently, we proposed to calculate electron removal cross sections for ion-molecule collisions in an independent atom model that accounts for geometric screening corrections. The correction coefficients are obtained from using a pixel counting method (PCM) for the exact calculation of the effective cross sectional area that emerges when the molecular cross section is pictured as a structure of (overlapping) atomic cross sections. This structure varies with the relative orientation of the molecule with respect to the projectile beam direction and, accordingly, orientation-independent total cross sections are obtained from averaging the pixel count over many orientations. In this contribution, we apply the PCM to proton collisions from amino acids and DNA and RNA nucleobases. The strength of the screening effect is analyzed by comparing the PCM results with Bragg additivity rule cross sections and with experimental data where available. Work supported by NSERC, Canada.
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.
Yan, Yuan; Shan, Hangyong; Li, Min; Chen, Shu; Liu, Jianyu; Cheng, Yanfang; Ye, Cui; Yang, Zhilin; Lai, Xuandi; Hu, Jianqiang
2015-11-19
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.
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
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.
Nagarajan, Mahesh B.; Coan, Paola; Huber, Markus B.; Diemoz, Paul C.; Wismüller, Axel
2015-01-01
Phase contrast X-ray computed tomography (PCI-CT) has attracted significant interest in recent years for its ability to provide significantly improved image contrast in low absorbing materials such as soft biological tissue. In the research context of cartilage imaging, previous studies have demonstrated the ability of PCI-CT to visualize structural details of human patellar cartilage matrix and capture changes to chondrocyte organization induced by osteoarthritis. This study evaluates the use of geometrical and topological features for volumetric characterization of such chondrocyte patterns in the presence (or absence) of osteoarthritic damage. Geometrical features derived from the scaling index method (SIM) and topological features derived from Minkowski Functionals were extracted from 1392 volumes of interest (VOI) annotated on PCI-CT images of ex vivo human patellar cartilage specimens. These features were subsequently used in a machine learning task with support vector regression to classify VOIs as healthy or osteoarthritic; classification performance was evaluated using the area under the receiver-operating characteristic (ROC) curve (AUC). Our results show that the classification performance of SIM-derived geometrical features (AUC: 0.90 ± 0.09) significantly outperform Minkowski Functionals volume (AUC: 0.54 ± 0.02), surface (AUC: 0.72 ± 0.06), mean breadth (AUC: 0.74 ± 0.06) and Euler characteristic (AUC: 0.78 ± 0.04) (p < 10−4). These results suggest that such geometrical features can provide a detailed characterization of the chondrocyte organization in the cartilage matrix in an automated manner, while also enabling classification of cartilage as healthy or osteoarthritic with high accuracy. Such features could potentially serve as diagnostic imaging markers for evaluating osteoarthritis progression and its response to different therapeutic intervention strategies. PMID:26142112
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
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…
Quantitative descriptions of generalized arousal, an elementary function of the vertebrate brain
Quinkert, Amy Wells; Vimal, Vivek; Weil, Zachary M.; Reeke, George N.; Schiff, Nicholas D.; Banavar, Jayanth R.; Pfaff, Donald W.
2011-01-01
We review a concept of the most primitive, fundamental function of the vertebrate CNS, generalized arousal (GA). Three independent lines of evidence indicate the existence of GA: statistical, genetic, and mechanistic. Here we ask, is this concept amenable to quantitative analysis? Answering in the affirmative, four quantitative approaches have proven useful: (i) factor analysis, (ii) information theory, (iii) deterministic chaos, and (iv) application of a Gaussian equation. It strikes us that, to date, not just one but at least four different quantitative approaches seem necessary for describing different aspects of scientific work on GA. PMID:21555568
Schnell, S; Mendoza, C
1997-02-21
The enzymological principles of the polymerase chain reaction (PCR) and of the quantitative competitive PCR (QC-PCR) are developed, proposing a theoretical framework that will facilitate quantification in experimental methodologies. It is demonstrated that the specificity of the QC-PCR, i.e. the ratio of the target initial velocity to that of the competitor template, remains constant not only during a particular amplification but also for increasing initial competitor concentrations. Linear fitting procedures are thus recommended that will enable a quantitative estimate of the initial target concentration. Finally, expressions for the efficiency of the PCR and QC-PCR are derived that are in agreement with previous experimental inferences.
A classification based framework for quantitative description of large-scale microarray data
Sangurdekar, Dipen P; Srienc, Friedrich; Khodursky, Arkady B
2006-01-01
Genome-wide surveys of transcription depend on gene classifications for the purpose of data interpretation. We propose a new information-theoretical-based method to: assess significance of co-expression within any gene group; quantitatively describe condition-specific gene-class activity; and systematically evaluate conditions in terms of gene-class activity. We applied this technique to describe microarray data tracking Escherichia coli transcriptional responses to more than 30 chemical and physiological perturbations. We correlated the nature and breadth of the responses with the nature of perturbation, identified gene group proxies for the perturbation classes and quantitatively compared closely related physiological conditions. PMID:16626502
A quantitative description of the Na-K-2Cl cotransporter and its conformity to experimental data.
Benjamin, B A; Johnson, E A
1997-09-01
In epithelia, the Na-K-2Cl cotransporter cooperates with other transport mechanisms to produce transepithelial NaCl transport. The reaction cycle for the Na-K-2Cl cotransporter has been established experimentally, but whether it accounts, quantitatively, for experimental findings has yet to be established. The differential equations that describe the reaction cycle were formulated, and the steady-state solutions were obtained by digital computation. Conformity between this description and the experimental data obtained from the literature was explored by automatic searches for the sets of rate constants that yielded statistical best-fits to the experimental data. Fits were obtained from renal epithelial cell lines, HeLa cells, and duck erythrocytes. Results show that the reaction cycle for the Na-K-2Cl cotransporter conforms well, quantitatively, with the experimental data.
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.
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 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.
2004-01-01
A detailed study has been carried out on the dependence of folate binding on the concentration of FBP (folate-binding protein) at pH 5.0, conditions selected to prevent complications arising from the pre-existing self-association of the acceptor. In contrast with the mandatory requirement that reversible interaction of ligand with a single acceptor site should exhibit a unique, rectangular hyperbolic binding curve, results obtained by ultrafiltration for the FBP–folate system required description in terms of (i) a sigmoidal relationship between concentrations of bound and free folate and (ii) an inverse dependence of affinity on FBP concentration. These findings have been attributed to the difficulties in determining the free ligand concentration in the FBP–folate mixtures for which reaction is essentially stoichiometric. This explanation also accounts for the similar published behaviour of the FBP–folate system at neutral pH, which had been attributed erroneously to acceptor self-association, a phenomenon incompatible with the experimental findings because of its prediction of a greater affinity for folate with increasing FBP concentration. PMID:15142039
Zhang, Shuxing; Golbraikh, Alexander; Tropsha, Alexander
2009-01-01
Novel geometrical chemical descriptors have been derived based on the computational geometry of protein-ligand interfaces and Pauling atomic electronegativities (EN). Delaunay tessellation has been applied to a diverse set of 517 X-ray characterized protein-ligand complexes yielding a unique collection of interfacial nearest neighbor atomic quadruplets for each complex. Each quadruplet composition was characterized by a single descriptor calculated as the sum of the EN values for the four participating atom types. We termed these simple descriptors generated from atomic EN values and derived with the Delaunay Tessellation the ENTess descriptors and used them in the variable selection k-Nearest Neighbor quantitative structure-binding affinity relationship (QSBR) studies of 264 diverse protein-ligand complexes with known binding constants. 24 complexes with chemically dissimilar ligands were set aside as an independent validation set, and the remaining dataset of 240 complexes was divided into multiple training and test sets. The best models were characterized by the leave-one-out cross-validated correlation coefficient q2 as high as 0.66 for the training set and the correlation coefficient R2 as high as 0.83 for the test set. High predictive power of these models was confirmed independently by applying them to the validation set of 24 complexes yielding R2 as high as 0.85. We conclude that QSBR models built with the ENTess descriptors can be instrumental for predicting the binding affinity of receptor-ligand complexes. PMID:16640331
NASA Astrophysics Data System (ADS)
Kreisel, A.; Nelson, R.; Berlijn, T.; Ku, W.; Aluru, Ramakrishna; Chi, Shun; Zhou, Haibiao; Singh, Udai Raj; Wahl, Peter; Liang, Ruixing; Hardy, Walter N.; Bonn, D. A.; Hirschfeld, P. J.; Andersen, Brian M.
2016-12-01
Since the discovery of iron-based superconductors, a number of theories have been put forward to explain the qualitative origin of pairing, but there have been few attempts to make quantitative, material-specific comparisons to experimental results. The spin-fluctuation theory of electronic pairing, based on first-principles electronic structure calculations, makes predictions for the superconducting gap. Within the same framework, the surface wave functions may also be calculated, allowing, e.g., for detailed comparisons between theoretical results and measured scanning tunneling topographs and spectra. Here we present such a comparison between theory and experiment on the Fe-based superconductor LiFeAs. Results for the homogeneous surface as well as impurity states are presented as a benchmark test of the theory. For the homogeneous system, we argue that the maxima of topographic image intensity may be located at positions above either the As or Li atoms, depending on tip height and the setpoint current of the measurement. We further report the experimental observation of transitions between As- and Li-registered lattices as functions of both tip height and setpoint bias, in agreement with this prediction. Next, we give a detailed comparison between the simulated scanning tunneling microscopy images of transition-metal defects with experiment. Finally, we discuss possible extensions of the current framework to obtain a theory with true predictive power for scanning tunneling microscopy in Fe-based systems.
Quantitative description for the growth rate of self-induced GaN nanowires
NASA Astrophysics Data System (ADS)
Consonni, V.; Dubrovskii, V. G.; Trampert, A.; Geelhaar, L.; Riechert, H.
2012-04-01
We determine with high precision the growth rate of self-induced GaN nanowires grown by molecular beam epitaxy under various conditions from scanning electron micrographs by taking into account in situ measurements of the initial incubation time, which is needed before the nanowire growth starts. In order to quantitatively describe the dependence of the growth rate on growth time, gallium flux, and growth temperature, we develop a detailed theoretical model of diffusion-induced nanowire growth specifically for the self-induced approach, i.e., without any droplet at the nanowire top. The theoretical fits are in excellent agreement with the experimental data and allow us to deduce important kinetic parameters of the self-induced GaN nanowire growth. The gallium adatom effective diffusion length on the nanowire sidewalls composed of m-plane facets is only 45 nm, which is consistent with our experimental finding that the growth rate initially decreases drastically as the contribution from the adatoms on the planar substrate surface rapidly vanishes. In contrast, the gallium adatom effective diffusion length on the amorphous silicon nitride substrate surface reaches about 100 nm. Furthermore, the nucleation energy on the nanowire sidewalls is found to be 5.44 eV and is larger than on their top facet accounting for the nanowire elongation.
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.
A geometrical model for the description of the AlN shell morphology in GaN-AlN core-shell nanowires
NASA Astrophysics Data System (ADS)
Hestroffer, Karine; Daudin, Bruno
2013-12-01
A geometrical model based on the one formulated by Foxon et al. [J. Cryst. Growth 311, 3423 (2009)] is developed to describe the morphology of AlN shells in GaN-AlN core-shell nanowires grown by plasma-assisted molecular beam epitaxy. The shell aspect ratio is studied as a function of the atomic beam flux incidence angles and of the ratio between Al and N species. The comparison between experimental data and the developed geometrical model suggests the diffusion of about 55% of Al atoms from the side walls to the top surface.
Place, Benjamin J; Morris, Mallory J; Phillips, Melissa M; Sander, Lane C; Rimmer, Catherine A
2014-11-14
Comprehensive, two-dimensional liquid chromatography (LC × LC) is a powerful technique for the separation of complex mixtures. Most studies using LC × LC are focused on qualitative efforts, such as increasing peak capacity. The present study examined the use of LC × LC-UV/vis for the separation and quantitation of polycyclic aromatic hydrocarbons (PAHs). More specifically, this study evaluated the impact of different peak integration approaches on the quantitative performance of the LC × LC method. For well-resolved three-dimensional peaks, parameters such as baseline definition, peak base shape, and peak width determination did not have a significant impact on accuracy and precision. For less-resolved peaks, a dropped baseline and the summation of all slices in the peak improved the accuracy and precision of the integration methods. The computational approaches to three-dimensional peak integration are provided, including fully descriptive, select slice, and summed heights integration methods, each with its own strengths and weaknesses. Overall, the integration methods presented quantify each of the PAHs within acceptable precision and accuracy ranges and have comparable performance to that of single dimension liquid chromatography.
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)
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.
Nagarajan, Mahesh B; Coan, Paola; Huber, Markus B; Diemoz, Paul C; Wismüller, Axel
2015-11-01
Phase-contrast X-ray computed tomography (PCI-CT) has attracted significant interest in recent years for its ability to provide significantly improved image contrast in low absorbing materials such as soft biological tissue. In the research context of cartilage imaging, previous studies have demonstrated the ability of PCI-CT to visualize structural details of human patellar cartilage matrix and capture changes to chondrocyte organization induced by osteoarthritis. This study evaluates the use of geometrical and topological features for volumetric characterization of such chondrocyte patterns in the presence (or absence) of osteoarthritic damage. Geometrical features derived from the scaling index method (SIM) and topological features derived from Minkowski Functionals were extracted from 1392 volumes of interest (VOI) annotated on PCI-CT images of ex vivo human patellar cartilage specimens. These features were subsequently used in a machine learning task with support vector regression to classify VOIs as healthy or osteoarthritic; classification performance was evaluated using the area under the receiver operating characteristic curve (AUC). Our results show that the classification performance of SIM-derived geometrical features (AUC: 0.90 ± 0.09) is significantly better than Minkowski Functionals volume (AUC: 0.54 ± 0.02), surface (AUC: 0.72 ± 0.06), mean breadth (AUC: 0.74 ± 0.06) and Euler characteristic (AUC: 0.78 ± 0.04) (p < 10(-4)). These results suggest that such geometrical features can provide a detailed characterization of the chondrocyte organization in the cartilage matrix in an automated manner, while also enabling classification of cartilage as healthy or osteoarthritic with high accuracy. Such features could potentially serve as diagnostic imaging markers for evaluating osteoarthritis progression and its response to different therapeutic intervention strategies.
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.
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
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.
Wang, Ziyun; Hu, P
2017-02-15
The relation between the surface structure and adsorption energy of adsorbates is of great importance in heterogeneous catalysis. Based on density functional theory calculations, we propose an explicit equation with three chemically meaningful terms, namely the bonding contribution equation, to quantitatively account for the surface structures and the adsorption energies. Successful predictions of oxygen adsorption energies on complex alloy surfaces containing up to 4 components are demonstrated, and the generality of this equation is also tested using different surface sizes and other adsorbates. This work may not only offer a powerful tool to understand the structure-adsorption relation, but may also be used to inversely design novel catalysts.
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.
Friedman, M H
1972-06-01
The description of corneal mechanics and transport developed in part I and used there to describe normal corneal behavior is here applied to corneas whose properties or boundary conditions are abnormal. The predicted effects of changing intraocular pressure, aqueous concentration, and tear tonicity are examined, and these compare favorably with available experimental data. The periodic variation in tear tonicity which accompanies the sleep-wake cycle prevents the cornea from achieving a true steady state, but a time-average steady state, about which corneal behavior oscillates, can be defined. The in vivo effects of endothelial dystrophy and epithelial removal are explained, and it is suggested that the epithelial sodium pump may act homeostatically to maintain corneal thickness in the face of ambient temperature variations. Part II concludes with a discussion, from the standpoint of the present theory, of the role of metabolically coupled water transport in the maintenance of the normal corneal thickness.
NASA Astrophysics Data System (ADS)
Kumazawa, Takao; Ogata, Yosihiko
2013-12-01
The epidemic-type aftershock sequence (ETAS) model is extended for application to nonstationary seismic activity, including transient swarm activity or seismicity anomalies, in a seismogenic region. The time-dependent rates of both background seismicity and aftershock productivity in the ETAS model are optimally estimated from hypocenter data. These rates can provide quantitative evidence for abrupt or gradual changes in shear stress and/or fault strength due to aseismic transient causes such as triggering by remote earthquakes, slow slips, or fluid intrusions within the region. This extended model is applied to data sets from several seismic events including swarms that were induced by the M9.0 Tohoku-Oki earthquake of 2011.
Albrecht-Buehler, G; Lancaster, R M
1976-11-01
We suggest a method of quantitating the motile actions of surface protrusions in spreading animal cells in culture. Its basis is the determination of the percentage of freshly plated cells which produce particle-free areas around them on a gold particle-coated glass cover slip within 50 min. Studying 3T3 cells with this assay, we found that the presence of Na+, K+, Cl-, and Mg++ or Ca++ in a neutral or slightly alkaline phosphate or bicarbonate buffered solution is sufficient to support the optimal particle removal by the cells for at least 50 min. Two metabolic inhibitors, 2,4-dinitrophenol and Na-azide, inhibit the particle removal. If D-glucose is added along with the inhibitors, particle removal can be restored, whereas the addition of three glucose analogues which are generally believed to be nonmetabolizable cannot restore the activity. Serum is not required for the mechanism(s) of the motile actions of surface protrusions in spreading 3T3 cells. However, it contains components which can neutralize the inhibitory actions of bovine serum albumin and several amino acids, particularly L-cystine or L-cystein and L-methionine. Furthermore, serum codetermines which of the major surface extension, filopodia, lamellipodia, or lobopodia, is predominantly active. We found three distinct classes of extracellular conditions under which the active surface projections are predominantly either lamellipodia, (sheetlike projections), lobopodia (blebs), or filopodia (microspikes). The quantitated dependencies on temperature, pH and the inhibition by cytochalasin B or the particle removal are very similar in all three cases. Preventing the cells from anchoring themselves for 15-20 min before plating in serum-free medium seems to stimulate particle removal threefold.
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.
Wu, Renhua; Longo, Dario Livio; Aime, Silvio; Sun, Phillip Zhe
2015-01-01
Chemical exchange saturation transfer (CEST) MRI holds great promise for imaging pH. However, routine CEST measurement varies not only with pH-dependent chemical exchange rate but also with CEST agent concentration, providing pH-weighted information. Conventional ratiometric CEST imaging normalizes the confounding concentration factor by analyzing the relative CEST effect from different exchangeable groups, requiring CEST agents with multiple chemically distinguishable labile proton sites. Recently, an RF power-based ratiometric CEST MRI approach has been developed for concentration-independent pH MRI using CEST agents with a single exchangeable group. To facilitate quantification and optimization of the new ratiometric analysis, we quantitated RF power-based ratiometric CEST ratio (rCESTR) and derived its signal-to-noise and contrast-to-noise ratio. Using creatine as a representative CEST agent containing a single exchangeable site, our study demonstrated that optimized RF power-based ratiometric analysis provides good pH sensitivity. We showed that rCESTR follows a base-catalyzed exchange relationship with pH independent of creatine concentration. The pH accuracy of RF power-based ratiometric MRI was within 0.15–0.20 pH unit. Furthermore, absolute exchange rate can be obtained from the proposed ratiometric analysis. To summarize, RF power-based ratiometric CEST analysis provides concentration-independent pH-sensitive imaging and complements conventional multiple labile proton groups-based ratiometric CEST analysis. PMID:25807919
Hernández-Castellano, Lorenzo E; Argüello, Anastasio; Almeida, André M; Castro, Noemí; Bendixen, Emøke
2015-01-01
Colostrum intake is a key factor for newborn ruminant survival because the placenta does not allow the transfer of immune components. Therefore, newborn ruminants depend entirely on passive immunity transfer from the mother to the neonate, through the suckling of colostrum. Understanding the importance of specific colostrum proteins has gained significant attention in recent years. However, proteomics studies of sheep colostrum and their uptake in neonate lambs has not yet been presented. The aim of this study was to describe the proteomes of sheep colostrum and lamb blood plasma, using sodium dodecyl sulfate-PAGE for protein separation and in-gel digestion, followed by liquid chromatography-tandem mass spectrometry of resulting tryptic peptides for protein identification. An isobaric tag for relative and absolute quantitation (iTRAQ)-based proteomics approach was subsequently used to provide relative quantification of how neonatal plasma protein concentrations change as an effect of colostrum intake. The results of this study describe the presence of 70 proteins in the ovine colostrum proteome. Furthermore, colostrum intake resulted in an increase of 8 proteins with important immune functions in the blood plasma of lambs. Further proteomic studies will be necessary, particularly using the selected reaction monitoring approach, to describe in detail the role of specific colostrum proteins for immune transfer to the neonate.
Marillet, Simon; Lefranc, Marie-Paule; Boudinot, Pierre; Cazals, Frédéric
2017-01-01
Antibody–antigen complexes challenge our understanding, as analyses to date failed to unveil the key determinants of binding affinity and interaction specificity. We partially fill this gap based on novel quantitative analyses using two standardized databases, the IMGT/3Dstructure-DB and the structure affinity benchmark. First, we introduce a statistical analysis of interfaces which enables the classification of ligand types (protein, peptide, and chemical; cross-validated classification error of 9.6%) and yield binding affinity predictions of unprecedented accuracy (median absolute error of 0.878 kcal/mol). Second, we exploit the contributions made by CDRs in terms of position at the interface and atomic packing properties to show that in general, VH CDR3 and VL CDR3 make dominant contributions to the binding affinity, a fact also shown to be consistent with the enthalpy–entropy compensation associated with preconfiguration of CDR3. Our work suggests that the affinity prediction problem could be partially solved from databases of high resolution crystal structures of complexes with known affinity. PMID:28232828
Representing geometrical knowledge.
Anderson, J A
1997-08-29
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.
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
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.
NASA Astrophysics Data System (ADS)
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.
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…
Bueno, M; Schulte, R; Meylan, S; Villagrasa, C
2015-11-07
The aim of this study was to evaluate the influence of the geometrical detail of the DNA on nanodosimetric parameters of track structure induced by protons and alpha particles of different energies (LET values ranging from 1 to 162.5 keV µm-1) as calculated by Geant4-DNA Monte Carlo simulations.The first geometry considered consisted of a well-structured placement of a realistic description of the DNA double helix wrapped around cylindrical histones (GeomHist) forming a 18 kbp-long chromatin fiber. In the second geometry considered, the DNA was modeled as a total of 1800 ten bp-long homogeneous cylinders (2.3 nm diameter and 3.4 nm height) placed in random positions and orientations (GeomCyl). As for GeomHist, GeomCyl contained a DNA material equivalent to 18 kbp. Geant4-DNA track structure simulations were performed and ionizations were counted in the scoring volumes. For GeomCyl, clusters were defined as the number of ionizations (ν) scored in each 10 bp-long cylinder. For GeomHist, clusters of ionizations scored in the sugar-phosphate groups of the double-helix were revealed by the DBSCAN clustering algorithm according to a proximity criteria among ionizations separated by less than 10 bp. The topology of the ionization clusters formed using GeomHist and GeomCyl geometries were compared in terms of biologically relevant nanodosimetric quantities.The discontinuous modeling of the DNA for GeomCyl led to smaller cluster sizes than for GeomHist. The continuous modeling of the DNA molecule for GeomHist allowed the merging of ionization points by the DBSCAN algorithm giving rise to larger clusters, which were not detectable within the GeomCyl geometry. Mean cluster size (m1) was found to be of the order of 10% higher for GeomHist compared to GeomCyl for LET < 15 keV µm-1. For higher LETs, the difference increased with LET similarly for protons and alpha particles. Both geometries showed the same relationship between m1 and the cumulative relative frequency of
NASA Astrophysics Data System (ADS)
Bueno, M.; Schulte, R.; Meylan, S.; Villagrasa, C.
2015-11-01
The aim of this study was to evaluate the influence of the geometrical detail of the DNA on nanodosimetric parameters of track structure induced by protons and alpha particles of different energies (LET values ranging from 1 to 162.5~\\text{keV}~μ {{\\text{m}}-1} ) as calculated by Geant4-DNA Monte Carlo simulations. The first geometry considered consisted of a well-structured placement of a realistic description of the DNA double helix wrapped around cylindrical histones (GeomHist) forming a 18 kbp-long chromatin fiber. In the second geometry considered, the DNA was modeled as a total of 1800 ten bp-long homogeneous cylinders (2.3 nm diameter and 3.4 nm height) placed in random positions and orientations (GeomCyl). As for GeomHist, GeomCyl contained a DNA material equivalent to 18 kbp. Geant4-DNA track structure simulations were performed and ionizations were counted in the scoring volumes. For GeomCyl, clusters were defined as the number of ionizations (ν) scored in each 10 bp-long cylinder. For GeomHist, clusters of ionizations scored in the sugar-phosphate groups of the double-helix were revealed by the DBSCAN clustering algorithm according to a proximity criteria among ionizations separated by less than 10 bp. The topology of the ionization clusters formed using GeomHist and GeomCyl geometries were compared in terms of biologically relevant nanodosimetric quantities. The discontinuous modeling of the DNA for GeomCyl led to smaller cluster sizes than for GeomHist. The continuous modeling of the DNA molecule for GeomHist allowed the merging of ionization points by the DBSCAN algorithm giving rise to larger clusters, which were not detectable within the GeomCyl geometry. Mean cluster size (m1) was found to be of the order of 10% higher for GeomHist compared to GeomCyl for LET <15~\\text{keV}~μ {{\\text{m}}-1} . For higher LETs, the difference increased with LET similarly for protons and alpha particles. Both geometries showed the same relationship
DeBeer George, S; Metz, M; Szilagyi, R K; Wang, H; Cramer, S P; Lu, Y; Tolman, W B; Hedman, B; Hodgson, K O; Solomon, E I
2001-06-20
To evaluate the importance of the electronic structure of Cu(A) to its electron-transfer (ET) function, a quantitative description of the ground-state wave function of the mixed-valence (MV) binuclear Cu(A) center engineered into Pseudomonas aeruginosa azurin has been developed, using a combination of S K-edge and Cu L-edge X-ray absorption spectroscopies (XAS). Parallel descriptions have been developed for a binuclear thiolate-bridged MV reference model complex ([(L(i)(PrdacoS)Cu)(2)](+)) and a homovalent (II,II) analogue ([L(i)(Pr2tacnS)Cu)(2)](2+), where L(i)(PrdacoS) and L(i)(Pr2tacnS) are macrocyclic ligands with attached thiolates that bridge the Cu ions. Previous studies have qualitatively defined the ground-state wave function of Cu(A) in terms of ligand field effects on the orbital orientation and the presence of a metal--metal bond. The studies presented here provide further evidence for a direct Cu--Cu interaction and, importantly, experimentally quantify the covalency of the ground-state wave function. The experimental results are further supported by DFT calculations. The nature of the ground-state wave function of Cu(A) is compared to that of the well-defined blue copper site in plastocyanin, and the importance of this wave function to the lower reorganization energy and ET function of Cu(A) is discussed. This wave function incorporates anisotropic covalency into the intra- and intermolecular ET pathways in cytochrome c oxidase. Thus, the high covalency of the Cys--Cu bond allows a path through this ligand to become competitive with a shorter His path in the intramolecular ET from Cu(A) to heme a and is particularly important for activating the intermolecular ET path from heme c to Cu(A).
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 morphology of granular materials
NASA Astrophysics Data System (ADS)
Schlei, Bernd R.; Prasad, Lakshman; Skourikhine, Alexei N.
2000-10-01
We present a new method to transform the spectral pixel information of a micrograph into an affine geometric description, which allows us to analyze the morphology of granular materials. We use spectral and pulse-coupled neural network based segmentation techniques to generate blobs, and a newly developed algorithm to extract dilated contours. A constrained Delaunay tessellation of the contour points results in a triangular mesh. This mesh is the basic ingredient of the Chodal Axis Transform, which provides a morphological decomposition of shapes. Such decomposition allows for grain separation and the efficient computation of the statistical features of granular materials.
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.
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…
NASA Astrophysics Data System (ADS)
Matsuzaki, F.; Yoshikawa, N.; Tanaka, M.; Fujimaki, A.; Takai, Y.
2003-10-01
Recently many single flux quantum (SFQ) logic circuits containing several thousands of Josephson junctions have been designed successfully by using digital domain simulation based on the hard ware description language (HDL). In the present HDL-based design of SFQ circuits, a structure-level HDL description has been used, where circuits are made up of basic gate cells. However, in order to analyze large-scale SFQ digital systems, such as a microprocessor, more higher-level circuit abstraction is necessary to reduce the circuit simulation time. In this paper we have investigated the way to describe functionality of the large-scale SFQ digital circuits by a behavior-level HDL description. In this method, the functionality and the timing of the circuit block is defined directly by describing their behavior by the HDL. Using this method, we can dramatically reduce the simulation time of large-scale SFQ digital circuits.
Geometrically Induced Interactions and Bifurcations
NASA Astrophysics Data System (ADS)
Binder, Bernd
2010-01-01
In order to evaluate the proper boundary conditions in spin dynamics eventually leading to the emergence of natural and artificial solitons providing for strong interactions and potentials with monopole charges, the paper outlines a new concept referring to a curvature-invariant formalism, where superintegrability is given by a special isometric condition. Instead of referring to the spin operators and Casimir/Euler invariants as the generator of rotations, a curvature-invariant description is introduced utilizing a double Gudermann mapping function (generator of sine Gordon solitons and Mercator projection) cross-relating two angular variables, where geometric phases and rotations arise between surfaces of different curvature. Applying this stereographic projection to a superintegrable Hamiltonian can directly map linear oscillators to Kepler/Coulomb potentials and/or monopoles with Pöschl-Teller potentials and vice versa. In this sense a large scale Kepler/Coulomb (gravitational, electro-magnetic) wave dynamics with a hyperbolic metric could be mapped as a geodesic vertex flow to a local oscillator singularity (Dirac monopole) with spherical metrics and vice versa. Attracting fixed points and dynamic constraints are given by special isometries with magic precession angles. The nonlinear angular encoding directly provides for a Shannon mutual information entropy measure of the geodesic phase space flow. The emerging monopole patterns show relations to spiral Fresnel holography and Berry/Aharonov-Bohm geometric phases subject to bifurcation instabilities and singularities from phase ambiguities due to a local (entropy) overload. Neutral solitons and virtual patterns emerging and mediating in the overlap region between charged or twisted holographic patterns are visualized and directly assigned to the Berry geometric phase revealing the role of photons, neutrons, and neutrinos binding repulsive charges in Coulomb, strong and weak interaction.
Wrinkled flames and geometrical stretch
NASA Astrophysics Data System (ADS)
Denet, Bruno; Joulin, Guy
2011-07-01
Localized wrinkles of thin premixed flames subject to hydrodynamic instability and geometrical stretch of uniform intensity (S) are studied. A stretch-affected nonlinear and nonlocal equation, derived from an inhomogeneous Michelson-Sivashinsky equation, is used as a starting point, and pole decompositions are used as a tool. Analytical and numerical descriptions of isolated (centered or multicrested) wrinkles with steady shapes (in a frame) and various amplitudes are provided; their number increases rapidly with 1/S>0. A large constant S>0 weakens or suppresses all localized wrinkles (the larger the wrinkles, the easier the suppression), whereas S<0 strengthens them; oscillations of S further restrict their existence domain. Self-similar evolutions of unstable many-crested patterns are obtained. A link between stretch, nonlinearity, and instability with the cutoff size of the wrinkles in turbulent flames is suggested. Open problems are evoked.
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.
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.
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.
Time as a geometric property of space
NASA Astrophysics Data System (ADS)
Chappell, James; Hartnett, John; Iannella, Nicolangelo; Iqbal, Azhar; Abbott, Derek
2016-11-01
The proper description of time remains a key unsolved problem in science. Newton conceived of time as absolute and universal which `flows equably without relation to anything external'. In the nineteenth century, the four-dimensional algebraic structure of the quaternions developed by Hamilton, inspired him to suggest that they could provide a unified representation of space and time. With the publishing of Einstein's theory of special relativity these ideas then lead to the generally accepted Minkowski spacetime formulation in 1908. Minkowski, though, rejected the formalism of quaternions suggested by Hamilton and adopted rather an approach using four-vectors. The Minkowski framework is indeed found to provide a versatile formalism for describing the relationship between space and time in accordance with Einstein's relativistic principles, but nevertheless fails to provide more fundamental insights into the nature of time itself. In order to answer this question we begin by exploring the geometric properties of three-dimensional space that we model using Clifford geometric algebra, which is found to contain sufficient complexity to provide a natural description of spacetime. This description using Clifford algebra is found to provide a natural alternative to the Minkowski formulation as well as providing new insights into the nature of time. Our main result is that time is the scalar component of a Clifford space and can be viewed as an intrinsic geometric property of three-dimensional space without the need for the specific addition of a fourth dimension.
Chiral models: Geometrical aspects
NASA Astrophysics Data System (ADS)
Perelomov, A. M.
1987-02-01
Two-dimensional classical chiral models of field theory are considered, the main attention being paid on geometrical aspects of such theories. A characteristic feature of these models is that the interaction is inserted not by adding the interaction Lagrangian to the free field Lagrangian, but has a purely geometrical origin and is related to the inner curvature of the manifold. These models are in many respects analogous to non-Abelian gauge theories and as became clear recently, they are also important for the superstring theory which nowadays is the most probable candidate for a truly unified theory of all interactions including gravitation.
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…
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…
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
Burgess, Claudia R.
2014-01-01
Designed for a broad audience, including educators, camp directors, afterschool coordinators, and preservice teachers, this investigation aims to help individuals experience mathematics in unconventional and exciting ways by engaging them in the physical activity of building geometric shapes using ropes. Through this engagement, the author…
Morphing of geometric composites via residual swelling.
Pezzulla, Matteo; Shillig, Steven A; Nardinocchi, Paola; Holmes, Douglas P
2015-08-07
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.
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.
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.
CAM - Geometric systems integration
NASA Astrophysics Data System (ADS)
Dunlap, G. C.
The integration of geometric and nongeometric information for efficient use of CAM is examined. Requirements for engineering drawings requested by management are noted to involve large volumes of nongeometric data to define the materials and quantity variables which impinge on the required design, so that the actual design may be the last and smaller step in the CAM process. Geometric classification and coding are noted to offer an alpha/numeric identifier for integrating the engineering design, manufacturing, and quality assurance functions. An example is provided of a turbine gear part coding in terms of polycode and monocode displays, showing a possible covering of more than 10 trillion features. Software is stressed as the key to integration of company-wide data.
Geometric measures of entanglement
Uyanik, K.; Turgut, S.
2010-03-15
The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated entanglement monotone can be defined. The explicit analytical forms of these measures are obtained for bipartite entangled states. Moreover, the three-qubit case is discussed and it is argued that the distance to the W states is a new monotone.
Geometrical deuteron stripping revisited
Neoh, Y. S.; Yap, S. L.
2014-03-05
We investigate the reality of the idea of geometrical deuteron stripping originally envisioned by Serber. By taking into account of realistic deuteron wavefunction, nuclear density, and nucleon stopping mean free path, we are able to estimate inclusive deuteron stripping cross section for deuteron energy up to before pion production. Our semiclassical model contains only one global parameter constant for all nuclei which can be approximated by Woods-Saxon or any other spherically symmetric density distribution.
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.
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.
Quantum computation using geometric algebra
NASA Astrophysics Data System (ADS)
Matzke, Douglas James
This dissertation reports that arbitrary Boolean logic equations and operators can be represented in geometric algebra as linear equations composed entirely of orthonormal vectors using only addition and multiplication Geometric algebra is a topologically based algebraic system that naturally incorporates the inner and anticommutative outer products into a real valued geometric product, yet does not rely on complex numbers or matrices. A series of custom tools was designed and built to simplify geometric algebra expressions into a standard sum of products form, and automate the anticommutative geometric product and operations. Using this infrastructure, quantum bits (qubits), quantum registers and EPR-bits (ebits) are expressed symmetrically as geometric algebra expressions. Many known quantum computing gates, measurement operators, and especially the Bell/magic operators are also expressed as geometric products. These results demonstrate that geometric algebra can naturally and faithfully represent the central concepts, objects, and operators necessary for quantum computing, and can facilitate the design and construction of quantum computing tools.
Geometric diffusion of quantum trajectories
Yang, Fan; Liu, Ren-Bao
2015-01-01
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. PMID:26178745
Wang, W Q; Song, S Q; Li, S H; Gan, Y Y; Wu, J H; Cheng, H Y
2009-01-01
The effect of stratification on dormancy release of grape seeds crossing from the sub- to the supraoptimal range of temperatures and water contents was analysed by modified threshold models. The stratification impacted on dormancy release in three different ways: (i) dormancy was consistently released with prolonged stratification time when stratified at temperatures of <15 degrees C; (ii) at 15 degrees C and 20 degrees C, the stratification effect initially increased, and then decreased with extended time; and (iii) stratification at 25 degrees C only reduced germinable seeds. These behaviours indicated that stratification could not only release primary dormancy but also induce secondary dormancy in grape seed. The rate of dormancy release changed linearly in two phases, while induction increased exponentially with increasing temperature. The thermal time approaches effectively quantified dormancy release only at suboptimal temperature, but a quantitative method to integrate the occurrence of dormancy release and induction at the same time could describe it well at either sub- or supraoptimal temperatures. The regression with the percentage of germinable seeds versus stratification temperature or water content within both the sub- and supraoptimal range revealed how the optimal temperature (T(so)) and water content (W(so)) for stratification changed. The T(so) moved from 10.6 degrees C to 5.3 degrees C with prolonged time, while W(so) declined from >0.40 g H2O g DW(-1) at 5 degrees C to approximately 0.23 g H2O g DW(-1) at 30 degrees C. Dormancy release in grape seeds can occur across a very wide range of conditions, which has important implications for their ability to adapt to a changeable environment in the wild.
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.
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.
Geometric Modeling Applications Interface Program (GMAP). Volume 2. Program Description
1989-09-01
Retirement for Cause ..................................................... 3- 41 3-21 Interrelationship of GMAP Documents...M a 9 2a. ~* .E 0 4) -------- U- 00 004-4 a___ cam 0 0 Z CL cw; 3- 41 CI FTR560240001U September 1989 Initially, GMAP looked at several programs...oteInpcinPanGnrto Sub System Intgratof IBIs.tfaiithPats hinecto AMofa Syservic Rene aoressr bade fo sufaenoaiesuin fluo.ResCInteetrface inspetin. ee eainhp 3.3.21
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
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.
Light polarization: A geometric-algebra approach
NASA Astrophysics Data System (ADS)
Baylis, W. E.; Bonenfant, J.; Derbyshire, J.; Huschilt, J.
1993-06-01
The geometric algebra of three-dimensional space (the ``Pauli algebra'') is known to provide an efficient geometric description of electromagnetic phenomena. Here, it is applied to the three-dimensional Stokes subspace to describe the polarization of an approximately monochromatic collimated beam of electromagnetic radiation. The coherency density ρ is a real element of the algebra whose components are the four Stokes parameters: a scalar representing the total photon flux density plus a three-dimensional vector whose direction and length in the Poincaré sphere give the type and degree of polarization. The detection of the radiation and the incoherent and coherent modification of the polarization by various optical elements are calculated by algebraic multiplication which has faithful representations in 2×2 matrices. One matrix representation of ρ is the coherency matrix with which Jones and Mueller matrices are related whereas another representation is the spin density matrix. However, the calculations are simplest to perform and interpret in the algebraic form independent of any particular matrix representation. It is shown that any possible change in the Stokes parameters can be treated algebraically by a combination of attenuation, depolarization, polarization, and rotation transformations of ρ. The geometric algebra thus unifies Stokes parameters, the Poincaré sphere, Jones and Mueller matrices, and the coherency and density matrices in a single, simple formalism.
Quantitative description and modeling of real networks
NASA Astrophysics Data System (ADS)
Capocci, Andrea; Caldarelli, Guido; de Los Rios, Paolo
2003-10-01
We present data analysis and modeling of two particular cases of study in the field of growing networks. We analyze World Wide Web data set and authorship collaboration networks in order to check the presence of correlation in the data. The results are reproduced with good agreement through a suitable modification of the standard Albert-Barabási model of network growth. In particular, intrinsic relevance of sites plays a role in determining the future degree of the vertex.
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…
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.
Shi, Runhua; McLarty, Jerry W
2009-10-01
In this article, we introduced basic concepts of statistics, type of distributions, and descriptive statistics. A few examples were also provided. The basic concepts presented herein are only a fraction of the concepts related to descriptive statistics. Also, there are many commonly used distributions not presented herein, such as Poisson distributions for rare events and exponential distributions, F distributions, and logistic distributions. More information can be found in many statistics books and publications.
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.
Geometric phase gradient and spin Hall effect of light
NASA Astrophysics Data System (ADS)
Ling, Xiaohui; Zhou, Xinxing; Qiu, Cheng-Wei
2016-10-01
The spin Hall effect (SHE) of light originates from the spin-orbit interaction, which can be explained in terms of two geometric phases: the Rytov-Vladimirskii-Berry phase and the Pancharatnam-Berry phase. Here we present a unified theoretical description of the SHE based on the two types of geometric phase gradients, and observe experimentally the SHE in structured dielectric metasurfaces induced by the PB phase. Unlike the weak real-space spin-Hall shift induced by the SRB phase occurring at interfacial reflection/refraction, the observed SHE occurs in momentum space is large enough to be measured directly.
A Geometrical Version of the Maxwell-Vlasov Hamiltonian Structure
NASA Astrophysics Data System (ADS)
Vittot, Michel; Morrison, Philip
2014-10-01
We present a geometrization of the Hamiltonian approach of classical electrodynamics, via (non-canonical) Poisson structures. This relativistic Hamiltonian framework (introduced by Morrison, Marsden, Weinstein) is a field theory written in terms of differential forms, independently of the gauge potentials. This algebraic and geometric description of the Vlasov kinetics is well suited for a perturbation theory, in a strong inhomogeneous magnetic field (expansion in 1/B, with all the curvature terms...), like in magnetically confined plasmas, and in any coordinates, for instance adapted to a Tokamak (toroidal coordinates, or else...).
Geometric phase shifting digital holography.
Jackin, Boaz Jessie; Narayanamurthy, C S; Yatagai, Toyohiko
2016-06-01
A new phase shifting digital holographic technique using a purely geometric phase in Michelson interferometric geometry is proposed. The geometric phase in the system does not depend upon either optical path length or wavelength, unlike dynamic phase. The amount of geometric phase generated is controllable through a rotating wave plate. The new approach has unique features and major advantages in holographic measurement of transparent and reflecting three-dimensional (3D) objects. Experimental results on surface shape measurement and imaging of 3D objects are presented using the proposed method.
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.
Activities: Geometric Transformations. Part 2.
ERIC Educational Resources Information Center
Eddins, Susan K.; And Others
1994-01-01
Presents a lesson that connects basic transformational concepts with transformations on a Cartesian-coordinate system, culminating with the application of matrix operations to perform geometric transformations. Includes reproducible student worksheets and assessment activities. (MKR)
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
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
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 aspects of Painlevé equations
NASA Astrophysics Data System (ADS)
Kajiwara, Kenji; Noumi, Masatoshi; Yamada, Yasuhiko
2017-02-01
In this paper a comprehensive review is given on the current status of achievements in the geometric aspects of the Painlevé equations, with a particular emphasis on the discrete Painlevé equations. The theory is controlled by the geometry of certain rational surfaces called the spaces of initial values, which are characterized by eight point configuration on {{{P}}}1× {{{P}}}1 and classified according to the degeneration of points. We give a systematic description of the equations and their various properties, such as affine Weyl group symmetries, hypergeometric solutions and Lax pairs under this framework, by using the language of Picard lattice and root systems. We also provide with a collection of basic data; equations, point configurations/root data, Weyl group representations, Lax pairs, and hypergeometric solutions of all possible cases.
Monolithic geometric anti-spring blades
NASA Astrophysics Data System (ADS)
Cella, G.; Sannibale, V.; DeSalvo, R.; Márka, S.; Takamori, A.
2005-03-01
In this article we investigate the principle and properties of a vertical passive seismic noise attenuator conceived for ground based gravitational wave interferometers. This mechanical attenuator based on a particular geometry of cantilever blades called monolithic geometric anti springs (MGAS) permits the design of mechanical harmonic oscillators with very low resonant frequency (below 10 mHz). Here we address the theoretical description of the mechanical device, focusing on the most important quantities for the low-frequency regime, on the distribution of internal stresses, and on the thermal stability. In order to obtain physical insight of the attenuator peculiarities, we devise some simplified models, rather than use the brute force of finite element analysis. Those models have been used to optimize the design of a seismic attenuation system prototype for LIGO advanced configurations and for the next generation of the TAMA interferometer.
Geometric Observers for Dynamically Evolving Curves
Niethammer, Marc; Vela, Patricio A.; Tannenbaum, Allen
2009-01-01
This paper proposes a deterministic observer design for visual tracking based on nonparametric implicit (level-set) curve descriptions. The observer is continuous discrete with continuous-time system dynamics and discrete-time measurements. Its state-space consists of an estimated curve position augmented by additional states (e.g., velocities) associated with every point on the estimated curve. Multiple simulation models are proposed for state prediction. Measurements are performed through standard static segmentation algorithms and optical-flow computations. Special emphasis is given to the geometric formulation of the overall dynamical system. The discrete-time measurements lead to the problem of geometric curve interpolation and the discrete-time filtering of quantities propagated along with the estimated curve. Interpolation and filtering are intimately linked to the correspondence problem between curves. Correspondences are established by a Laplace-equation approach. The proposed scheme is implemented completely implicitly (by Eulerian numerical solutions of transport equations) and thus naturally allows for topological changes and subpixel accuracy on the computational grid. PMID:18421113
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 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.
Geometric incompatibility in a fault system.
Gabrielov, A; Keilis-Borok, V; Jackson, D D
1996-01-01
Interdependence between geometry of a fault system, its kinematics, and seismicity is investigated. Quantitative measure is introduced for inconsistency between a fixed configuration of faults and the slip rates on each fault. This measure, named geometric incompatibility (G), depicts summarily the instability near the fault junctions: their divergence or convergence ("unlocking" or "locking up") and accumulation of stress and deformations. Accordingly, the changes in G are connected with dynamics of seismicity. Apart from geometric incompatibility, we consider deviation K from well-known Saint Venant condition of kinematic compatibility. This deviation depicts summarily unaccounted stress and strain accumulation in the region and/or internal inconsistencies in a reconstruction of block- and fault system (its geometry and movements). The estimates of G and K provide a useful tool for bringing together the data on different types of movement in a fault system. An analog of Stokes formula is found that allows determination of the total values of G and K in a region from the data on its boundary. The phenomenon of geometric incompatibility implies that nucleation of strong earthquakes is to large extent controlled by processes near fault junctions. The junctions that have been locked up may act as transient asperities, and unlocked junctions may act as transient weakest links. Tentative estimates of K and G are made for each end of the Big Bend of the San Andreas fault system in Southern California. Recent strong earthquakes Landers (1992, M = 7.3) and Northridge (1994, M = 6.7) both reduced K but had opposite impact on G: Landers unlocked the area, whereas Northridge locked it up again. Images Fig. 1 Fig. 2 PMID:11607673
Rendón-Macías, Mario Enrique; Villasís-Keever, Miguel Ángel; Miranda-Novales, María Guadalupe
2016-01-01
Descriptive statistics is the branch of statistics that gives recommendations on how to summarize clearly and simply research data in tables, figures, charts, or graphs. Before performing a descriptive analysis it is paramount to summarize its goal or goals, and to identify the measurement scales of the different variables recorded in the study. Tables or charts aim to provide timely information on the results of an investigation. The graphs show trends and can be histograms, pie charts, "box and whiskers" plots, line graphs, or scatter plots. Images serve as examples to reinforce concepts or facts. The choice of a chart, graph, or image must be based on the study objectives. Usually it is not recommended to use more than seven in an article, also depending on its length.
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.
Geometric similarity between protein-RNA interfaces.
Zhou, Peng; Zou, Jianwei; Tian, Feifei; Shang, Zhicai
2009-12-01
A new method is described to measure the geometric similarity between protein-RNA interfaces quantitatively. The method is based on a procedure that dissects the interface geometry in terms of the spatial relationships between individual amino acid nucleotide pairs. Using this technique, we performed an all-on-all comparison of 586 protein-RNA interfaces deposited in the current Protein Data Bank, as the result, an interface-interface similarity score matrix was obtained. Based upon this matrix, hierarchical clustering was carried out which yielded a complete clustering tree for the 586 protein-RNA interfaces. By investigating the organizing behavior of the clustering tree and the SCOP classification of protein partners in complexes, a geometrically nonredundant, diverse data set (representative data set) consisting of 45 distinct protein-RNA interfaces was extracted for the purpose of studying protein-RNA interactions, RNA regulations, and drug design. We classified protein-RNA interfaces into three types. In type I, the families and interface structural classes of the protein partners, as well as the interface geometries are all similar. In type II, the interface geometries and the interface structural classes are similar, whereas the protein families are different. In type III, only the interface geometries are similar but the protein families and the interface structural classes are distinct. Furthermore, we also show two new RNA recognition themes derived from the representative data set.
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.
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.
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
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.
Geometric scaling as traveling waves.
Munier, S; Peschanski, R
2003-12-05
We show the relevance of the nonlinear Fisher and Kolmogorov-Petrovsky-Piscounov (KPP) equation to the problem of high energy evolution of the QCD amplitudes. We explain how the traveling wave solutions of this equation are related to geometric scaling, a phenomenon observed in deep-inelastic scattering experiments. Geometric scaling is for the first time shown to result from an exact solution of nonlinear QCD evolution equations. Using general results on the KPP equation, we compute the velocity of the wave front, which gives the full high energy dependence of the saturation scale.
Supersymmetric chiral models: Geometrical aspects
NASA Astrophysics Data System (ADS)
Perelomov, A. M.
1989-03-01
We consider classical supersymmetric chiral models of field theory and focus our attention on the geometrical aspects of such theories. A characteristic feature of such models is that the interaction is not introduced by adding the interaction Lagrangian to the free field Lagrangian, but has a purely geometrical origin and is related to the inner curvature of the target manifold. In many aspects these models are analogous to gauge theories and, as became clear recently, they are also important for superstring theory, which nowadays is the most probable candidate for a truly unified theory of all interactions including gravitation.
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…
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.
Geometric Quantum Noise of Spin
NASA Astrophysics Data System (ADS)
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.
Linear patterning of mesenchymal condensations is modulated by geometric constraints.
Klumpers, Darinka D; Mao, Angelo S; Smit, Theo H; Mooney, David J
2014-06-06
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.
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
Serth, J; Panitz, F; Herrmann, H; Alves, J
1998-10-01
Competitive PCR is a frequently used technique for quantitation of DNA and mRNA. However, the application of the most favourable homologous mutated competitors is impeded by the formation of heteroduplex molecules which complicates the data evaluation and may lead to quantitation errors. Moreover, in most cases a single quantitation of an unknown sample requires multiple competitive reactions for identification of the equivalence point. In the present study, a highly efficient and reliable method as well as the underlying theoretical model is described. The mathematical solutions of this model provide the basis for single-tube quantitation using a homologous mutated competitor. For quantitation of Human Papilloma Virus 16-DNA, it is shown that single tube quantitations using simple PAGE separation and video evaluation for signal analysis permit linear detection within more than two orders of magnitude. In addition, repeated single-tube competitive PCRs exhibited good precision (average standard deviation 5%), even if carried out as nested high cycle PCR for quantitation of low abundant sequences (intraassay sensitivity <2 x 10(2) copies). This evaluation method can be applied to any DNA separation and detection method which is capable of resolving the heteroduplex fraction from both homoduplex molecules.
Geometrical Phases in Quantum Mechanics
NASA Astrophysics Data System (ADS)
Christian, Joy Julius
In quantum mechanics, the path-dependent geometrical phase associated with a physical system, over and above the familiar dynamical phase, was initially discovered in the context of adiabatically changing environments. Subsequently, Aharonov and Anandan liberated this phase from the original formulation of Berry, which used Hamiltonians, dependent on curves in a classical parameter space, to represent the cyclic variations of the environments. Their purely quantum mechanical treatment, independent of Hamiltonians, instead used the non-trivial topological structure of the projective space of one-dimensional subspaces of an appropriate Hilbert space. The geometrical phase, in their treatment, results from a parallel transport of the time-dependent pure quantum states along a curve in this space, which is endowed with an abelian connection. Unlike Berry, they were able to achieve this without resort to an adiabatic approximation or to a time-independent eigenvalue equation. Prima facie, these two approaches are conceptually quite different. After a review of both approaches, an exposition bridging this apparent conceptual gap is given; by rigorously analyzing a model composite system, it is shown that, in an appropriate correspondence limit, the Berry phase can be recovered as a special case from the Aharonov-Anandan phase. Moreover, the model composite system is used to show that Berry's correction to the traditional Born-Oppenheimer energy spectra indeed brings the spectra closer to the exact results. Then, an experimental arrangement to measure geometrical phases associated with cyclic and non-cyclic variations of quantum states of an entangled composite system is proposed, utilizing the fundamental ideas of the recently opened field of two-particle interferometry. This arrangement not only resolves the controversy regarding the true nature of the phases associated with photon states, but also unequivocally predicts experimentally accessible geometrical phases in a
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.
Geometric Landau-Zener interferometry.
Gasparinetti, S; Solinas, P; Pekola, J P
2011-11-11
We propose a new type of interferometry, based on geometric phases accumulated by a periodically driven two-level system undergoing multiple Landau-Zener transitions. As a specific example, we study its implementation in a superconducting charge pump. We find that interference patterns appear as a function of the pumping frequency and the phase bias, and clearly manifest themselves in the pumped charge. We also show that the effects described should persist in the presence of realistic decoherence.
Geometrical interpretation of optical absorption
Monzon, J. J.; Barriuso, A. G.; Sanchez-Soto, L. L.; Montesinos-Amilibia, J. M.
2011-08-15
We reinterpret the transfer matrix for an absorbing system in very simple geometrical terms. In appropriate variables, the system appears as performing a Lorentz transformation in a (1 + 3)-dimensional space. Using homogeneous coordinates, we map that action on the unit sphere, which is at the realm of the Klein model of hyperbolic geometry. The effects of absorption appear then as a loxodromic transformation, that is, a rhumb line crossing all the meridians at the same angle.
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.
2016-05-05
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(1). Quantum physics supports this view(2), demonstrating that delocalized electrons make a static macroscopic polarization, an ill-defined quantity in metals(3)-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(4). Here we describe the quantum mechanical design and experimental realization of room-temperature polar metals in thin-film ANiO(3) perovskite nickelates using a strategy based on atomic-scale control of inversion-preserving (centric) displacements(5). 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(6-10), 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.
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.
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)…
Remarks on the geometric quantization of Landau levels
NASA Astrophysics Data System (ADS)
Galasso, Andrea; Spera, Mauro
2016-08-01
In this note, we resume the geometric quantization approach to the motion of a charged particle on a plane, subject to a constant magnetic field perpendicular to the latter, by showing directly that it gives rise to a completely integrable system to which we may apply holomorphic geometric quantization. In addition, we present a variant employing a suitable vertical polarization and we also make contact with Bott’s quantization, enforcing the property “quantization commutes with reduction”, which is known to hold under quite general conditions. We also provide an interpretation of translational symmetry breaking in terms of coherent states and index theory. Finally, we give a representation theoretic description of the lowest Landau level via the use of an S1-equivariant Dirac operator.
A Geometric Crescent Model for Black Hole Images
NASA Astrophysics Data System (ADS)
Kamruddin, Ayman Bin; Dexter, J.
2013-01-01
The Event Horizon Telescope (EHT), a global very long baseline interferometry array operating at millimeter wavelengths, is spatially resolving the immediate environment of black holes for the first time. The current observations of the Galactic center black hole, Sagittarius A* (Sgr A*), have been interpreted in terms of unmotivated geometric models (e.g., a symmetric Gaussian) or detailed calculations involving accretion onto a black hole. The latter are subject to large systematic uncertainties. Motivated by relativistic effects around black holes, we propose a geometric crescent model for black hole images. We show that this simple model provides an excellent statistical description of the existing EHT data of Sgr A*, superior to the Gaussian. It also closely matches physically predicted models, bridging accretion theory and observation. Based on our results, we make predictions for future observations for the accessibility of the black hole shadow, direct evidence for a black hole event horizon.
Geometric Exponents of Dilute Loop Models
NASA Astrophysics Data System (ADS)
Provencher, Guillaume; Saint-Aubin, Yvan; Pearce, Paul A.; Rasmussen, Jørgen
2012-04-01
The fractal dimensions of the hull, the external perimeter and of the red bonds are measured through Monte Carlo simulations for dilute minimal models, and compared with predictions from conformal field theory and SLE methods. The dilute models used are those first introduced by Nienhuis. Their loop fugacity is β=-2 \\cos(π/bar{kappa}) where the parameter bar{kappa} is linked to their description through conformal loop ensembles. It is also linked to conformal field theories through their central charges c(bar{kappa})=13-6(bar{kappa}+bar{kappa}^{-1}) and, for the minimal models of interest here, bar{kappa}=p/p' where p and p' are two coprime integers. The geometric exponents of the hull and external perimeter are studied for the pairs ( p, p')=(1,1),(2,3),(3,4),(4,5),(5,6),(5,7), and that of the red bonds for ( p, p')=(3,4). Monte Carlo upgrades are proposed for these models as well as several techniques to improve their speeds. The measured fractal dimensions are obtained by extrapolation on the lattice size H, V→∞. The extrapolating curves have large slopes; despite these, the measured dimensions coincide with theoretical predictions up to three or four digits. In some cases, the theoretical values lie slightly outside the confidence intervals; explanations of these small discrepancies are proposed.
The geometrical properties researching of surface quality by membership function
NASA Astrophysics Data System (ADS)
Yang, Yufen
2008-12-01
The main content of assessing the machined surface quality of machine components is the geometrical properties of surface quality. The geometrical properties of the two assessing parameters of identical surface quality (surface roughness and surface waviness) exist in the identical substance and there are certain blend and fuzziness, what's more, there is not the concept of the value to describe its varying blend degree, there are, so far, still not practicable methods and measuring tools to separate surface roughness and waviness completely. In contrast, the paper is based on the membership function of fuzzy mathematics to research the geometrical properties of surface roughness and waviness. This method completely broke the traditional one that only adopts numerical values to separate surface roughness and waviness. It can not only directly separate the two assessing parameters from actual surface, measure the actual values of parameters that meet the assessing quality and obtain the actual probability of the blend compositions between the two, but also entirely evaluate the geometrical properties of the actual surface quality, moreover, there will be a quantitative evaluation for the authenticity and reliability of the measured values from measuring systems and instruments.
Geometric Theory of Hinged Devices
NASA Astrophysics Data System (ADS)
Kovalev, M. D.
1995-02-01
This article contains results connected with engineering mechanics. Among them are: a theorem "on the nonuniqueness of a statically determinable truss", a classification of hinged mechanisms and their schemes, and an example of a hinged mechanism with variable number of degrees of freedom. The study of general geometric properties is based on the concept, introduced here, of an abstract hinged device in Rd. This concept formalizes a well-known approach in the theory of mechanisms. The formalization gives rise to a number of interesting mathematical questions.
Geometric methods in quantum computation
NASA Astrophysics Data System (ADS)
Zhang, Jun
Recent advances in the physical sciences and engineering have created great hopes for new computational paradigms and substrates. One such new approach is the quantum computer, which holds the promise of enhanced computational power. Analogous to the way a classical computer is built from electrical circuits containing wires and logic gates, a quantum computer is built from quantum circuits containing quantum wires and elementary quantum gates to transport and manipulate quantum information. Therefore, design of quantum gates and quantum circuits is a prerequisite for any real application of quantum computation. In this dissertation we apply geometric control methods from differential geometry and Lie group representation theory to analyze the properties of quantum gates and to design optimal quantum circuits. Using the Cartan decomposition and the Weyl group, we show that the geometric structure of nonlocal two-qubit gates is a 3-Torus. After further reducing the symmetry, the geometric representation of nonlocal gates is seen to be conveniently visualized as a tetrahedron. Each point in this tetrahedron except on the base corresponds to a different equivalent class of nonlocal gates. This geometric representation is one of the cornerstones for the discussion on quantum computation in this dissertation. We investigate the properties of those two-qubit operations that can generate maximal entanglement. It is an astonishing finding that if we randomly choose a two-qubit operation, the probability that we obtain a perfect entangler is exactly one half. We prove that given a two-body interaction Hamiltonian, it is always possible to explicitly construct a quantum circuit for exact simulation of any arbitrary nonlocal two-qubit gate by turning on the two-body interaction for at most three times, together with at most four local gates. We also provide an analytic approach to construct a universal quantum circuit from any entangling gate supplemented with local gates
Geometric reasoning and spatial understanding
Binford, T.O.
1982-01-01
Progress has been made on extensions to ACRONYM which include: representation and reasoning with time, events, and sequences; collaboration with MIT to develop geometric learning: representation of function, and reasoning between structure and function. A new ribbon finder for ACRONYM is under construction. Work in figure/ground separation is underway as a basis for the ribbon finder. Preliminary results are shown in grouping operations to determine regularities in images. A stereo system has been completed which combines edge-based stereo matching with surface interpolation utilizing correspondence of gray levels. Design of a new stereo vision system is underway.
Graphene with geometrically induced vorticity.
Pachos, Jiannis K; Stone, Michael; Temme, Kristan
2008-04-18
At half filling, the electronic structure of graphene can be modeled by a pair of free two-dimensional Dirac fermions. We explicitly demonstrate that in the presence of a geometrically induced gauge field an everywhere-real Kekulé modulation of the hopping matrix elements can correspond to a nonreal Higgs field with nontrivial vorticity. This provides a natural setting for fractionally charged vortices with localized zero modes. For fullerenelike molecules we employ the index theorem to demonstrate the existence of six low-lying states that do not depend strongly on the Kekulé-induced mass gap.
Evolution: geometrical and dynamical aspects.
Freguglia, Paolo; Bazzani, Armando
2003-01-01
We develop a possible axiomatic approach to the evolution theory that has been previously discussed in Freguglia [2002]. The axioms synthesize the fundamental ideas of evolution theory and allow a geometrical and dynamical interpretation of the generation law. Using the axioms we derive a simple reaction-diffusion model which introduces the species as self-organized stationary distribution of a finite population and simulates the evolution of a phenotypic character under the effect of an external perturbing action. The dynamical properties of the model are briefly presented using numerical simulations.
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.
Science, art and geometrical imagination
NASA Astrophysics Data System (ADS)
Luminet, Jean-Pierre
2011-06-01
From the geocentric, closed world model of Antiquity to the wraparound universe models of relativistic cosmology, the parallel history of space representations in science and art illustrates the fundamental rôle of geometric imagination in innovative findings. Through the analysis of works of various artists and scientists like Plato, Dürer, Kepler, Escher, Grisey or the author, it is shown how the process of creation in science and in the arts rests on aesthetical principles such as symmetry, regular polyhedra, laws of harmonic proportion, tessellations, group theory, etc., as well as on beauty, conciseness and an emotional approach of the world.
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.
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.
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
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 effects in tomographic reconstruction
Barnes, F.L.; Azevedo, S.G.; Martz, H.E. Jr.; Roberson, G.P.; Schneberk, D.J.; Skeate, M.F.
1990-01-08
In x-ray and ion-beam computerized tomography, there are a number of reconstruction effects, manifested as artifacts, that can be attributed to the geometry of the experimental setup and of the object being scanned. In this work, we will examine four geometric effects that are common to first-and third-generation (parallel beam, 180 degree) computerized tomography (CT) scanners and suggest solutions for each problem. The geometric effects focused on in this paper are: X-pattern'' artifacts (believed to be caused by several errors), edge-generated ringing artifacts (due to improper choice of the reconstruction filter and cutoff frequency), circular-ring artifacts (caused by employing uncalibrated detectors), and tuning-fork artifacts (generated by an incorrectly specified center-of-rotation). Examples of four effects are presented. The X-pattern and edge-generated ringing artifacts are presented with actual experimental data introducing the artifact. given the source of the artifact, we present simulated data designed to replicate the artifact. Finally, we suggest ways to reduce or completely remove these artifacts. The circular-ring and tuning-fork artifacts are introduced with actual experimental data as well, while digital signal processing solutions are employed to remove the artifacts from the data. 15 refs., 12 figs.
Image coding with geometric wavelets.
Alani, Dror; Averbuch, Amir; Dekel, Shai
2007-01-01
This paper describes a new and efficient method for low bit-rate image coding which is based on recent development in the theory of multivariate nonlinear piecewise polynomial approximation. It combines a binary space partition scheme with geometric wavelet (GW) tree approximation so as to efficiently capture curve singularities and provide a sparse representation of the image. The GW method successfully competes with state-of-the-art wavelet methods such as the EZW, SPIHT, and EBCOT algorithms. We report a gain of about 0.4 dB over the SPIHT and EBCOT algorithms at the bit-rate 0.0625 bits-per-pixels (bpp). It also outperforms other recent methods that are based on "sparse geometric representation." For example, we report a gain of 0.27 dB over the Bandelets algorithm at 0.1 bpp. Although the algorithm is computationally intensive, its time complexity can be significantely reduced by collecting a "global" GW n-term approximation to the image from a collection of GW trees, each constructed separately over tiles of the image.
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.
Geometric asymmetry driven Janus micromotors.
Zhao, Guanjia; Pumera, Martin
2014-10-07
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.
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.
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.
NASA Technical Reports Server (NTRS)
Meyer, Peter; Green, Robert O.; Chrien, Thomas G.
1993-01-01
Remotely sensed data are affected by system (sensor and platform), and scene related effects. For quantitative investigations the spectral, radiometric characteristics of the system and scene have to be known. The relevant effects and their possible influence on an image have to be specifically determined for every remote sensing system and adequate description parameters need to be updated and reported on a regular basis as they are carried out, e.g., for the AVIRIS system. It is evident that the strength of the influence of similar effects in very dependent on the accessibility of auxiliary information about such sensor systems. Degradation in a spaceborne system can normally be just reported and cannot be corrected. In contrast, an airborne sensor can be evaluated, maintained and improved periodically. Such maintenance efforts are particularly important because airborne systems are exposed to extreme and changing environments. These include tens of takeoffs and landing each year as well as extreme changes in temperature and humidity on the tarmac and in flight. For the AVIRIS system there are environmental stresses such as changes in temperature, air pressure, humidity, vibration of the platform or scene-related reasons like atmospheric conditions, and topography. The information contained in the auxiliary files included with the AVIRIS data can be used to assess these effects and compensate for them. In addition the spectral, radiometer and geometric calibration data contained in the auxiliary file are required for quantitative analysis of the data. The paper describes tools to access the auxiliary information that characterizes the AVIRIS system. These tools allow the examination of parameters that may impact the quality of the measured AVIRIS image. An example of the use of this auxiliary data was carried out with regard to a parametric geocoding approach. Emphasis is placed on the reported auxiliary information that describes the geometric character of the
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.
A geometric crescent model for black hole images
NASA Astrophysics Data System (ADS)
Kamruddin, Ayman Bin; Dexter, Jason
2013-09-01
The Event Horizon Telescope (EHT), a global very long baseline interferometry array operating at millimetre wavelengths, is spatially resolving the immediate environments of black holes for the first time. The current observations of the Galactic centre black hole, Sagittarius A* (Sgr A*), and M87 have been interpreted in terms of either geometric models (e.g. a symmetric Gaussian) or detailed calculations of the appearance of black hole accretion flows. The former are not physically motivated, while the latter are subject to large systematic uncertainties. Motivated by the dominant relativistic effects of Doppler beaming and gravitational lensing in many calculations, we propose a geometric crescent model for black hole images. We show that this simple model provides an excellent statistical description of the existing EHT data of Sgr A* and M87, superior to other geometric models for Sgr A*. It also qualitatively matches physically predicted models, bridging accretion theory and observation. Based on our results, we make predictions for the detectability of the black hole shadow, a signature of strong gravity, in future observations.
Multiple representation approach to geometric model construction from range data
NASA Astrophysics Data System (ADS)
Koivunen, Visa; Vezien, Jean-Marc; Bajcsy, Ruzena
1995-04-01
A method is presented for constructing geometric design data from noisy 3-D sensor measurements of physical parts. In early processing phase, RLTS regression filters stemming from robust estimation theory are used for separating the desired part of the signal in contaminated sensor data from undesired part. Strategies for producing a complete 3-D data set from partial views are studied. Surface triangulation, NURBS, and superellipsoids are employed in model construction to be able to represent efficiently polygonal shapes, free form surfaces and standard primitive solids. Multiple representations are used because there is no single representation that would be most appropriate in all situations. The size of the required control point mesh for spline description is estimated using a surface characterization process. Surfaces of arbitrary topology are modeled using triangulation and trimmed NURBS. A user given tolerance value is driving refinement of the obtained surface model. The resulting model description is a procedural CAD model which can convey structural information in addition to low level geometric primitives. The model is translated to IGES standard product data exchange format to enable data sharing with other processes in concurrent engineering environment. Preliminary results on view registration and integration using simulated data are shown. Examples of model construction using both real and simulated data are also given.
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 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 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.
Geometrical aspects of quantum spaces
Ho, Pei -Ming
1996-05-11
Various geometrical aspects of quantum spaces are presented showing the possibility of building physics on quantum spaces. In the first chapter the authors give the motivations for studying noncommutative geometry and also review the definition of a Hopf algebra and some general features of the differential geometry on quantum groups and quantum planes. In Chapter 2 and Chapter 3 the noncommutative version of differential calculus, integration and complex structure are established for the quantum sphere S_{1}^{2} and the quantum complex projective space CP{sub q}(N), on which there are quantum group symmetries that are represented nonlinearly, and are respected by all the aforementioned structures. The braiding of S_{q}^{2} and CP_{q}(N) is also described. In Chapter 4 the quantum projective geometry over the quantum projective space CP_{q}(N) is developed. Collinearity conditions, coplanarity conditions, intersections and anharmonic ratios is described. In Chapter 5 an algebraic formulation of Reimannian geometry on quantum spaces is presented where Riemannian metric, distance, Laplacian, connection, and curvature have their quantum counterparts. This attempt is also extended to complex manifolds. Examples include the quantum sphere, the complex quantum projective space and the two-sheeted space. The quantum group of general coordinate transformations on some quantum spaces is also given.
Generalized Geometric Quantum Speed Limits
NASA Astrophysics Data System (ADS)
Pires, Diego Paiva; Cianciaruso, Marco; Céleri, Lucas C.; Adesso, Gerardo; Soares-Pinto, Diogo O.
2016-04-01
The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the interpretation of the time-energy uncertainty relations as lower bounds for the minimal evolution time between two distinguishable states of a quantum system, also known as quantum speed limits. We investigate how the nonuniqueness of a bona fide measure of distinguishability defined on the quantum-state space affects the quantum speed limits and can be exploited in order to derive improved bounds. Specifically, we establish an infinite family of quantum speed limits valid for unitary and nonunitary evolutions, based on an elegant information geometric formalism. Our work unifies and generalizes existing results on quantum speed limits and provides instances of novel bounds that are tighter than any established one based on the conventional quantum Fisher information. We illustrate our findings with relevant examples, demonstrating the importance of choosing different information metrics for open system dynamics, as well as clarifying the roles of classical populations versus quantum coherences, in the determination and saturation of the speed limits. Our results can find applications in the optimization and control of quantum technologies such as quantum computation and metrology, and might provide new insights in fundamental investigations of quantum thermodynamics.
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 aspects of ordering phenomena
NASA Astrophysics Data System (ADS)
Cugliandolo, Leticia F.
2017-01-01
A macroscopic system prepared in a disordered phase and quenched across a second-order phase transition into an ordered phase undergoes a coarsening process whereby it orders locally in one of the equilibrium states. The study of the evolution of the morphology of the ordered structures in two dimensions has recently unveiled two interesting and generic features. On the one hand, the dynamics first approach a critical percolating state via the growth of a new lengthscale and satisfying scaling properties with respect to it. The time needed to reach the critical percolating state diverges with the system size, though more weakly than the equilibration time. On the other hand, once the critical percolating structures established, the geometrical and statistical properties at larger scales than the one established by the usual dynamic growing length remain the ones of critical percolation. These observations are common to different microscopic dynamics (single spin flip, local and non-local spin exchange, voter) in pure or weakly disordered systems. We discuss these results and we refer to the relevant publications for details. xml:lang="fr"
Plate Wave Transmission/reflection at Geometric Obstructions: Experiment
NASA Astrophysics Data System (ADS)
Reusser, R. S.; Chimenti, D. E.; Holland, S. D.; Roberts, R. A.
2010-02-01
This paper reports on the experimental examination of the transmission and reflection characteristics of arbitrarily shaped geometric obstructions in problems of plate wave propagation, such as joints, stiffeners, thickness transitions, and bends. The motivation for this work is noise source location in structures, the specific application being the location of air leaks in spacecraft skins, funded by NASA. In this work, it has been demonstrated that leaks can be located at a distance using array-based sensors which determine direction of signal propagation at the sensor location. The limiting factor in practice is the influence of geometric obstructions between the leak and sensor. This work reports a quantitative examination of the transmission properties of various obstructions such as stiffening ribs. Surface motions arising from a distance source are recorded over a local array of spatial positions using a scanned laser vibrometer. Spatial Fourier analysis is then applied to determine the individual contributions of the constituent mode types to the measured signals. Transmission properties of intervening geometric obstructions are determined by comparison to unobstructed signals. Comparisons to theoretical predictions of transmission characteristics will be presented for selected cases.
The geometric semantics of algebraic quantum mechanics.
Cruz Morales, John Alexander; Zilber, Boris
2015-08-06
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.
Geometric Growing Patterns: What's the Rule?
ERIC Educational Resources Information Center
Hourigan, Mairéad; Leavy, Aisling
2015-01-01
While within a geometric repeating pattern, there is an identifiable core which is made up of objects that repeat in a predictable manner, a geometric growing pattern (also called visual or pictorial growing patterns in other curricula) "is a pattern that is made from a sequence of figures [or objects] that change from one term to the next in…
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…
Geometrical splitting and reduction of Feynman diagrams
NASA Astrophysics Data System (ADS)
Davydychev, Andrei I.
2016-10-01
A geometrical approach to the calculation of N-point Feynman diagrams is reviewed. It is shown that the geometrical splitting yields useful connections between Feynman integrals with different momenta and masses. It is demonstrated how these results can be used to reduce the number of variables in the occurring functions.
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.
Biological Interpretation of Quantitative PET Brain Data
NASA Astrophysics Data System (ADS)
Sossi, Vesna
2002-11-01
The variety of available positron emission tomography (PET) radiotracers and the ability of providing quantitative estimates of radiotracer concentrations make PET an invaluable tool in the in-vivo investigation of biological processes. Mathematical descriptions of the processes under investigation are used to extract relevant kinetic parameters from the time course of radioactivity concentrations. Such kinetic parameters can provide a quantitative description of both, the characteristics of a particular process, and its changes due to various disease states.
Geometric Hamiltonian quantum mechanics and applications
NASA Astrophysics Data System (ADS)
Pastorello, Davide
2016-08-01
Adopting a geometric point of view on Quantum Mechanics is an intriguing idea since, we know that geometric methods are very powerful in Classical Mechanics then, we can try to use them to study quantum systems. In this paper, we summarize the construction of a general prescription to set up a well-defined and self-consistent geometric Hamiltonian formulation of finite-dimensional quantum theories, where phase space is given by the Hilbert projective space (as Kähler manifold), in the spirit of celebrated works of Kibble, Ashtekar and others. Within geometric Hamiltonian formulation quantum observables are represented by phase space functions, quantum states are described by Liouville densities (phase space probability densities), and Schrödinger dynamics is induced by a Hamiltonian flow on the projective space. We construct the star-product of this phase space formulation and some applications of geometric picture are discussed.
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
2011-08-02
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.
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
Analyser-based phase contrast image reconstruction using geometrical optics.
Kitchen, M J; Pavlov, K M; Siu, K K W; Menk, R H; Tromba, G; Lewis, R A
2007-07-21
Analyser-based phase contrast imaging can provide radiographs of exceptional contrast at high resolution (<100 microm), whilst quantitative phase and attenuation information can be extracted using just two images when the approximations of geometrical optics are satisfied. Analytical phase retrieval can be performed by fitting the analyser rocking curve with a symmetric Pearson type VII function. The Pearson VII function provided at least a 10% better fit to experimentally measured rocking curves than linear or Gaussian functions. A test phantom, a hollow nylon cylinder, was imaged at 20 keV using a Si(1 1 1) analyser at the ELETTRA synchrotron radiation facility. Our phase retrieval method yielded a more accurate object reconstruction than methods based on a linear fit to the rocking curve. Where reconstructions failed to map expected values, calculations of the Takagi number permitted distinction between the violation of the geometrical optics conditions and the failure of curve fitting procedures. The need for synchronized object/detector translation stages was removed by using a large, divergent beam and imaging the object in segments. Our image acquisition and reconstruction procedure enables quantitative phase retrieval for systems with a divergent source and accounts for imperfections in the analyser.
Tomlinson, A; Coupland, R E
1990-01-01
The innervation of the adrenal medulla has been investigated in normal Wistar rats from birth to old age and ultrastructural findings compared with biochemical markers of the cholinergic innervation of the adrenal gland and catecholamine storage. Morphological evidence of the immaturity of the innervation during the first postnatal week is provided and using quantitative morphometry the innervation of chromaffin cells is shown to reach a mean total of 5.4 synapses per chromaffin cell during the period 26 days to 12 weeks of age. The variation in contents of synaptic profiles is discussed in the light of recent work that demonstrates a major sensory as well as visceral efferent innervation of the gland. Adrenal medullary neurons usually occur in closely packed groups, intimately associated with Schwann cells. Axodendritic and axosomatic synapses on these neurons are described and the likely origin of axonal processes innervating the neurons discussed. In old age the density of innervation remains the same as in young adult animals even though the medulla shows evidence of hyperplasia and hypertrophy of individual chromaffin cells. Images Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig. 6 Fig. 7 Fig. 8 Fig. 9 Fig. 10 Fig. 11 Fig. 12 Fig. 13 Fig. 14 Fig. 15 Fig. 16 Fig. 17 Fig. 18 Fig. 19 Fig. 20 Fig. 21 Fig. 22 Fig. 23 Fig. 24 Fig. 25 PMID:2384334
NASA Astrophysics Data System (ADS)
Le Pape, Olivier; Chauvet, Florence; Mahévas, Stéphanie; Lazure, Pascal; Guérault, Daniel; Désaunay, Yves
2003-11-01
This study describes the spatial distribution of young-of-the-year sole based on autumnal beam trawl surveys conducted in the Bay of Biscay (France) during a 15-y period. Previous studies showed that habitat suitability for juvenile sole varies according to physical factors such as bathymetry, sediment structure and river plume influence. These factors, which are known exhaustively for the entire Bay of Biscay from static maps (bathymetry and granulometry) or temporal maps based on a hydrodynamic model (the river plume), were used as descriptors in a generalised linear model of habitat suitability in order to characterise the distribution of juvenile 0-group sole according to delta distribution. This model was used to identify the habitats in which juvenile 0-group sole are concentrated. The respective areas of these habitats were determined from a Geographic Information System (GIS), and their respective contribution to the sole population in the Bay of Biscay was calculated in terms of the estimated number of young fish (GIS area×density derived from the model). Despite the great variability of survey data, this quantitative approach emphasises the highly important role of restricted shallow, muddy estuarine areas as nursery grounds of sole in the Bay of Biscay and demonstrates the relation between interannual variations of nursery habitat capacity (with respect to estuarine extent) and sole recruitment.
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.
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.
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…
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.
The promise of geometric morphometrics.
Richtsmeier, Joan T; DeLeon, Valerie Burke; Lele, Subhash R
2002-01-01
Nontraditional or geometric morphometric methods have found wide application in the biological sciences, especially in anthropology, a field with a strong history of measurement of biological form. Controversy has arisen over which method is the "best" for quantifying the morphological difference between forms and for making proper statistical statements about the detected differences. This paper explains that many of these arguments are superfluous to the real issues that need to be understood by those wishing to apply morphometric methods to biological data. Validity, the ability of a method to find the correct answer, is rarely discussed and often ignored. We explain why demonstration of validity is a necessary step in the evaluation of methods used in morphometrics. Focusing specifically on landmark data, we discuss the concepts of size and shape, and reiterate that since no unique definition of size exists, shape can only be recognized with reference to a chosen surrogate for size. We explain why only a limited class of information related to the morphology of an object can be known when landmark data are used. This observation has genuine consequences, as certain morphometric methods are based on models that require specific assumptions, some of which exceed what can be known from landmark data. We show that orientation of an object with reference to other objects in a sample can never be known, because this information is not included in landmark data. Consequently, a descriptor of form difference that contains information on orientation is flawed because that information does not arise from evidence within the data, but instead is a product of a chosen orientation scheme. To illustrate these points, we apply superimposition, deformation, and linear distance-based morphometric methods to the analysis of a simulated data set for which the true differences are known. This analysis demonstrates the relative efficacy of various methods to reveal the true
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.
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 ...
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.
Heat transfer in geometrically similar cylinders
NASA Technical Reports Server (NTRS)
Riekert, P; Held, A
1941-01-01
The power and heat-stress conditions of geometrically similar engines are discussed. The advantages accruing from smaller cylinder dimensions are higher specific horsepower, lower weight per horsepower, lower piston temperature, and less frontal area, with reduced detonation tendency.
Hidden geometric correlations in real multiplex networks
NASA Astrophysics Data System (ADS)
Kleineberg, Kaj-Kolja; Boguñá, Marián; Ángeles Serrano, M.; Papadopoulos, Fragkiskos
2016-11-01
Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are not random combinations of single network layers. Instead, they are organized in specific ways dictated by hidden geometric correlations between the layers. We find that these correlations are significant in different real multiplexes, and form a key framework for answering many important questions. Specifically, we show that these geometric correlations facilitate the definition and detection of multidimensional communities, which are sets of nodes that are simultaneously similar in multiple layers. They also enable accurate trans-layer link prediction, meaning that connections in one layer can be predicted by observing the hidden geometric space of another layer. And they allow efficient targeted navigation in the multilayer system using only local knowledge, outperforming navigation in the single layers only if the geometric correlations are sufficiently strong.
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.
Concepts and Figures in Geometric Reasoning.
ERIC Educational Resources Information Center
Fischbein, Efraim; Nachlieli, Talli
1998-01-01
Opens with the theoretical construct of figural concepts. Argues that geometrical figures are characterized by both conceptual and sensorial properties. Investigates the effects of interaction between conceptual and figural components. Contains 19 references. (DDR)
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.
Geometric sensitivity of ClearPET™ Neuro
NASA Astrophysics Data System (ADS)
Gundlich, Brigitte; Weber, Simone
2007-02-01
ClearPET™ Neuro is a small-animal positron emission tomography (PET) scanner dedicated to brain studies on rats and primates. The design of ClearPET™ Neuro leads to a specific geometric sensitivity, characterized by inhomogeneous and, depending on the measurement setup, even incomplete data. With respect to reconstruction techniques, homogeneous and complete data sets are a 'must' for analytical reconstruction methods, whereas iterative methods take the geometrical sensitivity into account during the reconstruction process. Nevertheless, here a homogeneous geometric sensitivity over the field of view is highly desirable. Therefore, this contribution aims at studying the impact of different scanner geometries and measurement setups on the geometric sensitivity. A data set of coincident events is computed for certain settings that contains each possible crystal combination once. The lines of response are rebinned into normalizing sinograms and backprojected into sensitivity images. Both, normalizing sinograms and sensitivity images mirror the geometric sensitivity and therefore, provide information which setting enables most complete and homogeneous data sets. An optimal measurement setup and scanner geometry in terms of homogeneous geometric sensitivity is found by analyzing the sensitivity images.
Geometric principles in the assembly of α-helical bundles.
Pratap, J V; Luisi, B F; Calladine, C R
2013-06-28
α-Helical coiled coils are usually stabilized by hydrophobic interfaces between the two constituent α-helices, in the form of 'knobs-into-holes' packing of non-polar residues arranged in repeating heptad patterns. Here we examine the corresponding 'hydrophobic cores' that stabilize bundles of four α-helices. In particular, we study three different kinds of bundle, involving four α-helices of identical sequence: two pack in a parallel and one in an anti-parallel orientation. We point out that the simplest way of understanding the packing of these 4-helix bundles is to use Crick's original idea that the helices are held together by 'hydrophobic stripes', which are readily visualized on the cylindrical surface lattice of the α-helices; and that the 'helix-crossing angle'--which determines, in particular, whether supercoiling is left- or right-handed--is fixed by the slope of the lattice lines that contain the hydrophobic residues. In our three examples the constituent α-helices have hydrophobic repeat patterns of 7, 11 and 4 residues, respectively; and we associate the different overall conformations with 'knobs-into-holes' packing along the 7-, 11- and 4-start lines, respectively, of the cylindrical surface lattices of the constituent α-helices. For the first two examples, all four interfaces between adjacent helices are geometrically equivalent; but in the third, one of the four interfaces differs significantly from the others. We provide a geometrical explanation for this non-equivalence in terms of two different but equivalent ways of assembling this bundle, which may possibly constitute a bistable molecular 'switch' with a coaxial throw of about 12 Å. The geometrical ideas that we deploy in this paper provide the simplest and clearest description of the structure of helical bundles. In an appendix, we describe briefly a computer program that we have devised in order to search for 'knobs-into-holes' packing between α-helices in proteins.
Orlando, Ron
2010-01-01
The ability to quantitatively determine changes is an essential component of comparative glycomics. Multiple strategies are available by which this can be accomplished. These include label-free approaches and strategies where an isotopic label is incorporated into the glycans prior to analysis. The focus of this chapter is to describe each of these approaches while providing insight into their strengths and weaknesses, so that glycomic investigators can make an educated choice of the strategy that is best suited for their particular application.
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.
D-brane superpotentials: Geometric and worldsheet approaches
NASA Astrophysics Data System (ADS)
Baumgartl, Marco; Brunner, Ilka; Soroush, Masoud
2011-02-01
From the worldsheet perspective, the superpotential on a D-brane wrapping internal cycles of a Calabi-Yau manifold is given as a generating functional for disk correlation functions. On the other hand, from the geometric point of view, D-brane superpotentials are captured by certain chain integrals. In this work, we explicitly show for branes wrapping internal two-cycles how these two different approaches are related. More specifically, from the worldsheet point of view, D-branes at the Landau-Ginzburg point have a convenient description in terms of matrix factorizations. We use a formula derived by Kapustin and Li to explicitly evaluate disk correlators for families of D2-branes. On the geometry side, we then construct a three-chain whose period gives rise to the effective superpotential and show that the two expressions coincide. Finally, as an explicit example, we choose a particular compact Calabi-Yau hypersurface and compute the effective D2-brane superpotential in different branches of the open moduli space, in both geometric and worldsheet approaches.
Geometric algebra and information geometry for quantum computational software
NASA Astrophysics Data System (ADS)
Cafaro, Carlo
2017-03-01
The art of quantum algorithm design is highly nontrivial. Grover's search algorithm constitutes a masterpiece of quantum computational software. In this article, we use methods of geometric algebra (GA) and information geometry (IG) to enhance the algebraic efficiency and the geometrical significance of the digital and analog representations of Grover's algorithm, respectively. Specifically, GA is used to describe the Grover iterate and the discretized iterative procedure that exploits quantum interference to amplify the probability amplitude of the target-state before measuring the query register. The transition from digital to analog descriptions occurs via Stone's theorem which relates the (unitary) Grover iterate to a suitable (Hermitian) Hamiltonian that controls Schrodinger's quantum mechanical evolution of a quantum state towards the target state. Once the discrete-to-continuos transition is completed, IG is used to interpret Grover's iterative procedure as a geodesic path on the manifold of the parametric density operators of pure quantum states constructed from the continuous approximation of the parametric quantum output state in Grover's algorithm. Finally, we discuss the dissipationless nature of quantum computing, recover the quadratic speedup relation, and identify the superfluity of the Walsh-Hadamard operation from an IG perspective with emphasis on statistical mechanical considerations.
Quantitation of signal transduction.
Krauss, S; Brand, M D
2000-12-01
Conventional qualitative approaches to signal transduction provide powerful ways to explore the architecture and function of signaling pathways. However, at the level of the complete system, they do not fully depict the interactions between signaling and metabolic pathways and fail to give a manageable overview of the complexity that is often a feature of cellular signal transduction. Here, we introduce a quantitative experimental approach to signal transduction that helps to overcome these difficulties. We present a quantitative analysis of signal transduction during early mitogen stimulation of lymphocytes, with steady-state respiration rate as a convenient marker of metabolic stimulation. First, by inhibiting various key signaling pathways, we measure their relative importance in regulating respiration. About 80% of the input signal is conveyed via identifiable routes: 50% through pathways sensitive to inhibitors of protein kinase C and MAP kinase and 30% through pathways sensitive to an inhibitor of calcineurin. Second, we quantify how each of these pathways differentially stimulates functional units of reactions that produce and consume a key intermediate in respiration: the mitochondrial membrane potential. Both the PKC and calcineurin routes stimulate consumption more strongly than production, whereas the unidentified signaling routes stimulate production more than consumption, leading to no change in membrane potential despite increased respiration rate. The approach allows a quantitative description of the relative importance of signal transduction pathways and the routes by which they activate a specific cellular process. It should be widely applicable.
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.
Geometric phases in self-induced transparency
Sen, T; Milovich, J
1991-05-01
We consider the geometric phases arising in the lossless propagation of light pulses through a medium composed of near resonant two-level atoms. A reformulation of the coupled Maxwell-Schroedinger equations allows us to construct conservation laws in a general context. There exist periodic solutions of these equations which lead to the possibility of cyclical evolution of the state vector and the appearance of a geometric phase. We first show that if the ground state is the initial state of the system, then it acquires a geometric phase after the passage of the soliton pulses of McCall and Hahn. More generally if the initial state is a superposition of the two levels, continuous pulse trains can propagate without appreciable loss. We also find in this case that the state vector develops a geometric phase provided the parameters take on the particular values required for cyclical evolution. In both cases we exhibit the geometric character of the calculated phases by showing that they equal half the solid angle subtended by a closed curve traced by the Bloch, vector on the Bloch sphere. We verify a recent assertion of Anandan and Aharonov that the energy uncertainty in the state is directly related to the speed at which the tip of the Bloch vector moves along the curve on the Bloch sphere (or in more general terms the energy uncertainty is related to the speed in the projective Hilbert space).
Geometric modeling of pelvic organs with thickness
NASA Astrophysics Data System (ADS)
Bay, T.; Chen, Z.-W.; Raffin, R.; Daniel, M.; Joli, P.; Feng, Z.-Q.; Bellemare, M.-E.
2012-03-01
Physiological changes in the spatial configuration of the internal organs in the abdomen can induce different disorders that need surgery. Following the complexity of the surgical procedure, mechanical simulations are necessary but the in vivo factor makes complicate the study of pelvic organs. In order to determine a realistic behavior of these organs, an accurate geometric model associated with a physical modeling is therefore required. Our approach is integrated in the partnership between a geometric and physical module. The Geometric Modeling seeks to build a continuous geometric model: from a dataset of 3D points provided by a Segmentation step, surfaces are created through a B-spline fitting process. An energy function is built to measure the bidirectional distance between surface and data. This energy is minimized with an alternate iterative Hoschek-like method. A thickness is added with an offset formulation, and the geometric model is finally exported in a hexahedral mesh. Afterward, the Physical Modeling tries to calculate the properties of the soft tissues to simulate the organs displacements. The physical parameters attached to the data are determined with a feedback loop between finite-elements deformations and ground-truth acquisition (dynamic MRI).
Dynamics of zonal flows: failure of wave-kinetic theory, and new geometrical optics approximations
NASA Astrophysics Data System (ADS)
Parker, Jeffrey B.
2016-12-01
The self-organisation of turbulence into regular zonal flows can be fruitfully investigated with quasi-linear methods and statistical descriptions. A wave-kinetic equation that assumes asymptotically large-scale zonal flows leads to ultraviolet divergence. From an exact description of quasi-linear dynamics emerges two better geometrical optics approximations. These involve not only the mean flow shear but also the second and third derivative of the mean flow. One approximation takes the form of a new wave-kinetic equation, but is only valid when the zonal flow is quasi-static and wave action is conserved.
Extracting dimensional geometric parameters from B-spline surface models of aircraft
NASA Technical Reports Server (NTRS)
Jayaram, U.; Myklebust, Arvid; Gelhausen, P.
1992-01-01
Research that creates techniques to automatically obtain dimensional geometric parameters from the nonuniform B-spline surface description of an object is presented. These techniques have been implemented successfully in the aircraft design software, ACSYNT, a computer-aided design system for conceptual aircraft design created at Virginia Tech and NASA Ames. The techniques created and implemented in this research are also of significance to general-purpose design.
Geometric complexity is increased in in vitro activated platelets.
Bianciardi, Giorgio
2015-06-01
This article investigates the use of computerized fractal analysis for objective characterization of the complexity of platelets in vitro stimulated by low level thrombin (0.02 U mL(-1) ), collected from healthy individuals and observed by means of transmission electron microscopy. Platelet boundaries were extracted by means of automatically image analysis. Local fractal dimension was evaluated by the box-counting technique (measure of geometric complexity of the platelet outline). The results showed that the platelet boundary is fractal when observed by transmission electron microscopy and that, after an in vitro platelet activation test, the shape of platelets present increased geometric complexity in comparison to the no stimulated platelets (P < 0.001), with 100% correct classification. Computerized fractal analysis of platelet shape by transmission electron microscopy can provide accurate, quantitative, data to study platelet activation. The results may play important roles in the evaluation of the platelets status in pathological conditions, like as atherosclerosis and diabetes mellitus, where in in vivo activated platelets have been described.
Young Children's Understanding of Geometric Shapes: The Role of Geometric Models
ERIC Educational Resources Information Center
Elia, Iliada; Gagatsis, Athanasios; Kyriakides, Leonidas
2003-01-01
In this paper, we explore the role of polygonal shapes as geometrical models in teaching mathematics, so as to elicit and interpret children's geometric conceptions and understanding about shapes. Primary pupils were asked to draw a stairway of figures (triangles, squares and rectangles) each one bigger than the preceding one. Pupils use two…
Control of chaos in excitable physiological systems: A geometric analysis.
Christini, David J.; Collins, James J.
1997-12-01
Model-independent chaos control techniques are inherently well-suited for the control of physiological systems for which quantitative system models are unavailable. The proportional perturbation feedback (PPF) control paradigm, which uses electrical stimulation to perturb directly the controlled system variable (e.g., the interbeat or interspike interval), was developed for excitable physiological systems that do not have an easily accessible system parameter. We develop the stable manifold placement (SMP) technique, a PPF-type technique which is simpler and more robust than the original PPF control algorithm. We use the SMP technique to control a simple geometric model of a chaotic system in the neighborhood of an unstable periodic orbit (UPO). We show that while the SMP technique can control a chaotic system that has UPO dynamics which are characterized by one stable manifold and one unstable manifold, the success of the SMP technique is sensitive to UPO parameter estimation errors. (c) 1997 American Institute of Physics.
Studying developmental variation with Geometric Morphometric Image Analysis (GMIA).
Mayer, Christine; Metscher, Brian D; Müller, Gerd B; Mitteroecker, Philipp
2014-01-01
The ways in which embryo development can vary across individuals of a population determine how genetic variation translates into adult phenotypic variation. The study of developmental variation has been hampered by the lack of quantitative methods for the joint analysis of embryo shape and the spatial distribution of cellular activity within the developing embryo geometry. By drawing from the strength of geometric morphometrics and pixel/voxel-based image analysis, we present a new approach for the biometric analysis of two-dimensional and three-dimensional embryonic images. Well-differentiated structures are described in terms of their shape, whereas structures with diffuse boundaries, such as emerging cell condensations or molecular gradients, are described as spatial patterns of intensities. We applied this approach to microscopic images of the tail fins of larval and juvenile rainbow trout. Inter-individual variation of shape and cell density was found highly spatially structured across the tail fin and temporally dynamic throughout the investigated period.
Quantification of Osteon Morphology Using Geometric Histomorphometrics.
Dillon, Scott; Cunningham, Craig; Felts, Paul
2016-03-01
Many histological methods in forensic anthropology utilize combinations of traditional histomorphometric parameters which may not accurately describe the morphology of microstructural features. Here, we report the novel application of a geometric morphometric method suitable when considering structures without anatomically homologous landmarks for the quantification of complete secondary osteon size and morphology. The method is tested for its suitability in the measurement of intact secondary osteons using osteons digitized from transverse femoral diaphyseal sections prepared from two human individuals. The results of methodological testing demonstrate the efficacy of the technique when applied to intact secondary osteons. In providing accurate characterization of micromorphology within the robust mathematical framework of geometric morphometrics, this method may surpass traditional histomorphometric variables currently employed in forensic research and practice. A preliminary study of the intersectional histomorphometric variation within the femoral diaphysis is made using this geometric histomorphometric method to demonstrate its potential.
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.
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
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
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.
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.
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.
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
Geometric uncertainty relation for mixed quantum states
Andersson, Ole Heydari, Hoshang
2014-04-15
In this paper we use symplectic reduction in an Uhlmann bundle to construct a principal fiber bundle over a general space of unitarily equivalent mixed quantum states. The bundle, which generalizes the Hopf bundle for pure states, gives in a canonical way rise to a Riemannian metric and a symplectic structure on the base space. With these we derive a geometric uncertainty relation for observables acting on quantum systems in mixed states. We also give a geometric proof of the classical Robertson-Schrödinger uncertainty relation, and we compare the two. They turn out not to be equivalent, because of the multiple dimensions of the gauge group for general mixed states. We give examples of observables for which the geometric relation provides a stronger estimate than that of Robertson and Schrödinger, and vice versa.
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.
Geometric Computation of Human Gyrification Indexes from Magnetic Resonance Images
2009-04-01
GEOMETRIC COMPUTATION OF HUMAN GYRIFICATION INDEXES FROM MAGNETIC RESONANCE IMAGES By Shu Su Tonya White Marcus Schmidt Chiu-Yen Kao and Guillermo...00-2009 to 00-00-2009 4. TITLE AND SUBTITLE Geometric Computation of Human Gyrification Indexes from Magnetic Resonance Images 5a. CONTRACT NUMBER... Geometric Computation of Gyrification Indexes Chiu-Yen Kao 1 Geometric Computation of Human Gyrification
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 teachers' geometric…
Methods of geometrical integration in accelerator physics
NASA Astrophysics Data System (ADS)
Andrianov, S. N.
2016-12-01
In the paper we consider a method of geometric integration for a long evolution of the particle beam in cyclic accelerators, based on the matrix representation of the operator of particles evolution. This method allows us to calculate the corresponding beam evolution in terms of two-dimensional matrices including for nonlinear effects. The ideology of the geometric integration introduces in appropriate computational algorithms amendments which are necessary for preserving the qualitative properties of maps presented in the form of the truncated series generated by the operator of evolution. This formalism extends both on polarized and intense beams. Examples of practical applications are described.
Classical light beams and geometric phases.
Mukunda, N; Chaturvedi, S; Simon, R
2014-06-01
We present a study of geometric phases in classical wave and polarization optics using the basic mathematical framework of quantum mechanics. Important physical situations taken from scalar wave optics, pure polarization optics, and the behavior of polarization in the eikonal or ray limit of Maxwell's equations in a transparent medium are considered. The case of a beam of light whose propagation direction and polarization state are both subject to change is dealt with, attention being paid to the validity of Maxwell's equations at all stages. Global topological aspects of the space of all propagation directions are discussed using elementary group theoretical ideas, and the effects on geometric phases are elucidated.
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.
Quantum gates and their coexisting geometric phases
Wu Lianao; Bishop, C. Allen; Byrd, Mark S.
2011-08-15
Geometric phases arise naturally in a variety of quantum systems with observable consequences. They also arise in quantum computations when dressed states are used in gating operations. Here we show how they arise in these gating operations and how one may take advantage of the dressed states producing them. Specifically, we show that for a given, but arbitrary Hamiltonian, and at an arbitrary time {tau}, there always exists a set of dressed states such that a given gate operation can be performed by the Hamiltonian up to a phase {phi}. The phase is a sum of a dynamical phase and a geometric phase. We illustrate the dressed phase for several systems.
Geometric Integration of Weakly Dissipative Systems
NASA Astrophysics Data System (ADS)
Modin, K.; Führer, C.; Soöderlind, G.
2009-09-01
Some problems in mechanics, e.g. in bearing simulation, contain subsystems that are conservative as well as weakly dissipative subsystems. Our experience is that geometric integration methods are often superior for such systems, as long as the dissipation is weak. Here we develop adaptive methods for dissipative perturbations of Hamiltonian systems. The methods are "geometric" in the sense that the form of the dissipative perturbation is preserved. The methods are linearly explicit, i.e., they require the solution of a linear subsystem. We sketch an analysis in terms of backward error analysis and numerical comparisons with a conventional RK method of the same order is given.
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.
NASA Astrophysics Data System (ADS)
Heller, Marc Andre; Ikeda, Noriaki; Watamura, Satoshi
2017-02-01
We give a systematic derivation of the local expressions of the NS H-flux, geometric F- as well as non-geometric Q- and R-fluxes in terms of bivector β- and two-form B-potentials including vielbeins. They are obtained using a supergeometric method on QP-manifolds by twist of the standard Courant algebroid on the generalized tangent space without flux. Bianchi identities of the fluxes are easily deduced. We extend the discussion to the case of the double space and present a formulation of T-duality in terms of canonical transformations between graded symplectic manifolds. Thus, we find a unified description of geometric as well as non-geometric fluxes and T-duality transformations in double field theory. Finally, the construction is compared to the formerly introduced Poisson Courant algebroid, a Courant algebroid on a Poisson manifold, as a model for R-flux.
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…
A survey of quantitative descriptions of molecular structure.
Guha, Rajarshi; Willighagen, Egon
2012-01-01
Numerical characterization of molecular structure is a first step in many computational analysis of chemical structure data. These numerical representations, termed descriptors, come in many forms, ranging from simple atom counts and invariants of the molecular graph to distribution of properties, such as charge, across a molecular surface. In this article we first present a broad categorization of descriptors and then describe applications and toolkits that can be employed to evaluate them. We highlight a number of issues surrounding molecular descriptor calculations such as versioning and reproducibility and describe how some toolkits have attempted to address these problems.
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.
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…
Descriptive Metadata: Emerging Standards.
ERIC Educational Resources Information Center
Ahronheim, Judith R.
1998-01-01
Discusses metadata, digital resources, cross-disciplinary activity, and standards. Highlights include Standard Generalized Markup Language (SGML); Extensible Markup Language (XML); Dublin Core; Resource Description Framework (RDF); Text Encoding Initiative (TEI); Encoded Archival Description (EAD); art and cultural-heritage metadata initiatives;…
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.
Reshaping Plant Biology: Qualitative and Quantitative Descriptors for Plant Morphology
Balduzzi, Mathilde; Binder, Brad M.; Bucksch, Alexander; Chang, Cynthia; Hong, Lilan; Iyer-Pascuzzi, Anjali S.; Pradal, Christophe; Sparks, Erin E.
2017-01-01
An emerging challenge in plant biology is to develop qualitative and quantitative measures to describe the appearance of plants through the integration of mathematics and biology. A major hurdle in developing these metrics is finding common terminology across fields. In this review, we define approaches for analyzing plant geometry, topology, and shape, and provide examples for how these terms have been and can be applied to plants. In leaf morphological quantifications both geometry and shape have been used to gain insight into leaf function and evolution. For the analysis of cell growth and expansion, we highlight the utility of geometric descriptors for understanding sepal and hypocotyl development. For branched structures, we describe how topology has been applied to quantify root system architecture to lend insight into root function. Lastly, we discuss the importance of using morphological descriptors in ecology to assess how communities interact, function, and respond within different environments. This review aims to provide a basic description of the mathematical principles underlying morphological quantifications. PMID:28217137
Reshaping Plant Biology: Qualitative and Quantitative Descriptors for Plant Morphology.
Balduzzi, Mathilde; Binder, Brad M; Bucksch, Alexander; Chang, Cynthia; Hong, Lilan; Iyer-Pascuzzi, Anjali S; Pradal, Christophe; Sparks, Erin E
2017-01-01
An emerging challenge in plant biology is to develop qualitative and quantitative measures to describe the appearance of plants through the integration of mathematics and biology. A major hurdle in developing these metrics is finding common terminology across fields. In this review, we define approaches for analyzing plant geometry, topology, and shape, and provide examples for how these terms have been and can be applied to plants. In leaf morphological quantifications both geometry and shape have been used to gain insight into leaf function and evolution. For the analysis of cell growth and expansion, we highlight the utility of geometric descriptors for understanding sepal and hypocotyl development. For branched structures, we describe how topology has been applied to quantify root system architecture to lend insight into root function. Lastly, we discuss the importance of using morphological descriptors in ecology to assess how communities interact, function, and respond within different environments. This review aims to provide a basic description of the mathematical principles underlying morphological quantifications.
Integral representation for geometric optics solutions
NASA Astrophysics Data System (ADS)
Hazak, G.; Bernstein, I. B.; Smith, T. M.
1983-03-01
An integral representation of the geometric optics solutions for the field of dressed particles in inhomogeneous plasma is derived. The representation is a natural generalization of the Fourier integral used for homogeneous systems. The set of plane waves is replaced by a complete orthogonal set of 'quasi-plane waves' which in practice may be constructed by using the existing ray tracing codes.
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…
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…
On Arithmetic-Geometric-Mean Polynomials
ERIC Educational Resources Information Center
Griffiths, Martin; MacHale, Des
2017-01-01
We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…
Estimation on Geometric Measure of Quantum Coherence
NASA Astrophysics Data System (ADS)
Zhang, Hai-Jun; Chen, Bin; Li, Ming; Fei, Shao-Ming; Long, Gui-Lu
2017-02-01
We study the geometric measure of quantum coherence recently proposed in [Phys. Rev. Lett. 115, 020403 (2015)]. Both lower and upper bounds of this measure are provided. These bounds are shown to be tight for a class of important coherent states -- maximally coherent mixed states. The trade-off relation between quantum coherence and mixedness for this measure is also discussed.
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)
Geometric Probability and the Areas of Leaves
ERIC Educational Resources Information Center
Hoiberg, Karen Bush; Sharp, Janet; Hodgson, Ted; Colbert, Jim
2005-01-01
This article describes how a group of fifth-grade mathematics students measured irregularly shaped objects using geometric probability theory. After learning how to apply a ratio procedure to find the areas of familiar shapes, students extended the strategy for use with irregularly shaped objects, in this case, leaves. (Contains 2 tables and 8…
Using geometric algebra to study optical aberrations
Hanlon, J.; Ziock, H.
1997-05-01
This paper uses Geometric Algebra (GA) to study vector aberrations in optical systems with square and round pupils. GA is a new way to produce the classical optical aberration spot diagrams on the Gaussian image plane and surfaces near the Gaussian image plane. Spot diagrams of the third, fifth and seventh order aberrations for square and round pupils are developed to illustrate the theory.
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…
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…
Plato alleges that God forever geometrizes
NASA Astrophysics Data System (ADS)
Ne'Eman, Yuval
1996-05-01
Since 1961, the experimental exploration at the fundamental level of physical reality has surprised physists by revealing to them a highly geometric scenery. Like Einstein's (classical) theory of gravity, the “standard model,” describing the strong, weak, and electromagnetic interaction, testifies in favor of Plato's reported allegation.
Geometric Interpretations of Some Psychophysical Results.
ERIC Educational Resources Information Center
Levine, Michael V.
A theory of psychophysics is discussed that enlarges the classical theory in three general ways: (1) the multidimensional nature of perception is made explicit; (2) the transformations of the theory are interpreted geometrically; and (3) attributes are distinguished from sensations and only partially ordered. It is shown that, with the enlarged…
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…
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…
Geometric interpretations for resonances of plasmonic nanoparticles
Liu, Wei; Oulton, Rupert F.; Kivshar, Yuri S.
2015-01-01
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. PMID:26173797
An underlying geometrical manifold for Hamiltonian mechanics
NASA Astrophysics Data System (ADS)
Horwitz, L. P.; Yahalom, A.; Levitan, J.; Lewkowicz, M.
2017-02-01
We show that there exists an underlying manifold with a conformal metric and compatible connection form, and a metric type Hamiltonian (which we call the geometrical picture), that can be put into correspondence with the usual Hamilton-Lagrange mechanics. The requirement of dynamical equivalence of the two types of Hamiltonians, that the momenta generated by the two pictures be equal for all times, is sufficient to determine an expansion of the conformal factor, defined on the geometrical coordinate representation, in its domain of analyticity with coefficients to all orders determined by functions of the potential of the Hamiltonian-Lagrange picture, defined on the Hamilton-Lagrange coordinate representation, and its derivatives. Conversely, if the conformal function is known, the potential of a Hamilton-Lagrange picture can be determined in a similar way. We show that arbitrary local variations of the orbits in the Hamilton-Lagrange picture can be generated by variations along geodesics in the geometrical picture and establish a correspondence which provides a basis for understanding how the instability in the geometrical picture is manifested in the instability of the the original Hamiltonian motion.
Calculation of Geometric Dilution of Precision
NASA Astrophysics Data System (ADS)
Zhu, Jijie
1992-07-01
In this short communication, a very simple closed-form formula for the calculation of the Geometric Dilution of Precision (GDOP) in Global Positioning System (GPS) navigation and in Global Navigation Satellite System (GLONASS) navigation is presented, which requires less than 40 multiplications.
Geometric Representations for Discrete Fourier Transforms
NASA Technical Reports Server (NTRS)
Cambell, C. W.
1986-01-01
Simple geometric representations show symmetry and periodicity of discrete Fourier transforms (DFT's). Help in visualizing requirements for storing and manipulating transform value in computations. Representations useful in any number of dimensions, but particularly in one-, two-, and three-dimensional cases often encountered in practice.
Reflections on representing non-geometric data
NASA Technical Reports Server (NTRS)
Emnett, R. F.; Shu, H. H.
1984-01-01
The American National Standard Y14.26M-1981 on Digital Representation for Communication of Product Definition Data includes an introduction, three sections corresponding to IGES (Initial Graphics Exchange Specification) Version 1.0, and Section 5, which is a constructive, relational, language based representation for geometric and topological entitles.
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.
Geometrical attenuation, frequency dependence of Q, and the absorption band problem
NASA Astrophysics Data System (ADS)
Morozov, Igor B.
2008-10-01
A geometrical attenuation model is proposed as an alternative to the conventional frequency-dependent attenuation law Q(f) = Q0(f/f0)η. The new model provides a straightforward differentiation between the geometrical and effective attenuation (Qe) which incorporates the intrinsic attenuation and small-scale scattering. Unlike the (Q0, η) description, the inversion procedure uses only the spectral amplitude data and does not rely on elaborate theoretical models or restrictive assumptions. Data from over 40 reported studies were transformed to the new parametrization. The levels of geometrical attenuation strongly correlate with crustal tectonic types and decrease with tectonic age. The corrected values of Qe are frequency-independent and generally significantly higher than Q0 and show no significant correlation with tectonic age. Several case studies were revisited in detail, with significant changes in the interpretations. The absorption-band and the `10-Hz transition' are not found in the corrected Qe data, and therefore, these phenomena are interpreted as related to geometrical attenuation. The absorption band could correspond to changes in the dominant mode content of the wavefield as the frequency changes from about 0.1 to 100 Hz. Alternatively, it could also be a pure artefact related to the power-law Q(f) paradigm above. The explicit separation of the geometrical and intrinsic attenuation achieves three goals: (1) it provides an unambiguous, assumption- and model-free description of attenuation, (2) it allows relating the observations to the basic physics and geology and (3) it simplifies the interpretation because of reduced emphasis on the apparent Q(f) dependence. The model also agrees remarkably well with the initial attempts for finite-difference short-period coda waveform modelling. Because of its consistency and direct link to the observations, the approach should also help in building robust and transportable coda magnitudes and in seismic
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
Towards standardized assessment of endoscope optical performance: geometric distortion
NASA Astrophysics Data System (ADS)
Wang, Quanzeng; Desai, Viraj N.; Ngo, Ying Z.; Cheng, Wei-Chung; Pfefer, Joshua
2013-12-01
Technological advances in endoscopes, such as capsule, ultrathin and disposable devices, promise significant improvements in safety, clinical effectiveness and patient acceptance. Unfortunately, the industry lacks test methods for preclinical evaluation of key optical performance characteristics (OPCs) of endoscopic devices that are quantitative, objective and well-validated. As a result, it is difficult for researchers and developers to compare image quality and evaluate equivalence to, or improvement upon, prior technologies. While endoscope OPCs include resolution, field of view, and depth of field, among others, our focus in this paper is geometric image distortion. We reviewed specific test methods for distortion and then developed an objective, quantitative test method based on well-defined experimental and data processing steps to evaluate radial distortion in the full field of view of an endoscopic imaging system. Our measurements and analyses showed that a second-degree polynomial equation could well describe the radial distortion curve of a traditional endoscope. The distortion evaluation method was effective for correcting the image and can be used to explain other widely accepted evaluation methods such as picture height distortion. Development of consensus standards based on promising test methods for image quality assessment, such as the method studied here, will facilitate clinical implementation of innovative endoscopic devices.
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…
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.
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.
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.
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
Geometric Mechanics of Periodic Pleated Origami
NASA Astrophysics Data System (ADS)
Wei, Z. Y.; Guo, Z. V.; Dudte, L.; Liang, H. Y.; Mahadevan, L.
2013-05-01
Origami structures are mechanical metamaterials with properties that arise almost exclusively from the geometry of the constituent folds and the constraint of piecewise isometric deformations. Here we characterize the geometry and planar and nonplanar effective elastic response of a simple periodically folded Miura-ori structure, which is composed of identical unit cells of mountain and valley folds with four-coordinated ridges, defined completely by two angles and two lengths. We show that the in-plane and out-of-plane Poisson’s ratios are equal in magnitude, but opposite in sign, independent of material properties. Furthermore, we show that effective bending stiffness of the unit cell is singular, allowing us to characterize the two-dimensional deformation of a plate in terms of a one-dimensional theory. Finally, we solve the inverse design problem of determining the geometric parameters for the optimal geometric and mechanical response of these extreme structures.
Geometric mechanics of periodic pleated origami.
Wei, Z Y; Guo, Z V; Dudte, L; Liang, H Y; Mahadevan, L
2013-05-24
Origami structures are mechanical metamaterials with properties that arise almost exclusively from the geometry of the constituent folds and the constraint of piecewise isometric deformations. Here we characterize the geometry and planar and nonplanar effective elastic response of a simple periodically folded Miura-ori structure, which is composed of identical unit cells of mountain and valley folds with four-coordinated ridges, defined completely by two angles and two lengths. We show that the in-plane and out-of-plane Poisson's ratios are equal in magnitude, but opposite in sign, independent of material properties. Furthermore, we show that effective bending stiffness of the unit cell is singular, allowing us to characterize the two-dimensional deformation of a plate in terms of a one-dimensional theory. Finally, we solve the inverse design problem of determining the geometric parameters for the optimal geometric and mechanical response of these extreme structures.
Superatoms: Electronic and Geometric Effects on Reactivity.
Reber, Arthur C; Khanna, Shiv N
2017-02-21
The relative role of electronic and geometric effects on the stability of clusters has been a contentious topic for quite some time, with the focus on electronic structure generally gaining the upper hand. In this Account, we hope to demonstrate that both electronic shell filling and geometric shell filling are necessary concepts for an intuitive understanding of the reactivity of metal clusters. This work will focus on the reactivity of aluminum based clusters, although these concepts may be applied to clusters of different metals and ligand protected clusters. First we highlight the importance of electronic shell closure in the stability of metallic clusters. Quantum confinement in small compact metal clusters results in the bunching of quantum states that are reminiscent of the electronic shells in atoms. Clusters with closed electronic shells and large HOMO-LUMO (highest occupied molecular orbital-lowest unoccupied molecular orbital) gaps have enhanced stability and reduced reactivity with O2 due to the need for the cluster to accommodate the spin of molecular oxygen during activation of the molecule. To intuitively understand the reactivity of clusters with protic species such as water and methanol, geometric effects are needed. Clusters with unsymmetrical structures and defects usually result in uneven charge distribution over the surface of the cluster, forming active sites. To reduce reactivity, these sites must be quenched. These concepts can also be applied to ligand protected clusters. Clusters with ligands that are balanced across the cluster are less reactive, while clusters with unbalanced ligands can result in induced active sites. Adatoms on the surface of a cluster that are bound to a ligand result in an activated adatom that reacts readily with protic species, offering a mechanism by which the defects will be etched off returning the cluster to a closed geometric shell. The goal of this Account is to argue that both geometric and electronic shell
Small-on-large geometric anelasticity
NASA Astrophysics Data System (ADS)
Sadik, Souhayl; Yavari, Arash
2016-11-01
In this paper, we are concerned with finding exact solutions for the stress fields of nonlinear solids with non-symmetric distributions of defects (or more generally finite eigenstrains) that are small perturbations of symmetric distributions of defects with known exact solutions. In the language of geometric mechanics, this corresponds to finding a deformation that is a result of a perturbation of the metric of the Riemannian material manifold. We present a general framework that can be used for a systematic analysis of this class of anelasticity problems. This geometric formulation can be thought of as a material analogue of the classical small-on-large theory in nonlinear elasticity. We use the present small-on-large anelasticity theory to find exact solutions for the stress fields of some non-symmetric distributions of screw dislocations in incompressible isotropic solids.
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.
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.
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.
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.
Geometric Phases in Sensing and Control
2003-01-01
this idea with an equal-sided, spring-jointed, four-bar mechanism and then apply the technique to a vibrating ring gyroscope. In physical systems the...Douglas Sparks of Delco Au- tomotive Systems ) . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.4 Equal-Sided Four-Bar Mechanism ...Landsberg in [48, 49]. Many researchers have investigated the role of the geometric phase in mechan - ical systems . In problems of this type, changes
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.
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 Factors in Target Positioning and Tracking
2009-07-01
used in active management of distributed sensor resources and sensor path planning. Keywords: Ranging & Bearing-Only Sensors, Geometry, LOS, GDOP ... GDOP ) A scalar value that characterizes the position solution is the geometrical dilution of precision ( GDOP ) defined as [4, 13]: ))((traceGDOP 11...HRHT (14a) ))((trace 1−= HHT when R = I (14b) For the case with two ranging sensors, the GDOP can be written as: )(sin GDOP 21 2 2 2 2 1
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
Geometric Morphometrics of Rodent Sperm Head Shape
Varea Sánchez, María; Bastir, Markus; Roldan, Eduardo R. S.
2013-01-01
Mammalian spermatozoa, particularly those of rodent species, are extremely complex cells and differ greatly in form and dimensions. Thus, characterization of sperm size and, particularly, sperm shape represents a major challenge. No consensus exists on a method to objectively assess size and shape of spermatozoa. In this study we apply the principles of geometric morphometrics to analyze rodent sperm head morphology and compare them with two traditional morphometry methods, that is, measurements of linear dimensions and dimensions-derived parameters calculated using formulae employed in sperm morphometry assessments. Our results show that geometric morphometrics clearly identifies shape differences among rodent spermatozoa. It is also capable of discriminating between size and shape and to analyze these two variables separately. Thus, it provides an accurate method to assess sperm head shape. Furthermore, it can identify which sperm morphology traits differ between species, such as the protrusion or retraction of the base of the head, the orientation and relative position of the site of flagellum insertion, the degree of curvature of the hook, and other distinct anatomical features and appendices. We envisage that the use of geometric morphometrics may have a major impact on future studies focused on the characterization of sperm head formation, diversity of sperm head shape among species (and underlying evolutionary forces), the effects of reprotoxicants on changes in cell shape, and phenotyping of genetically-modified individuals. PMID:24312234
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.
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.
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).
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.
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.).
Algebraic and geometric spread in finite frames
NASA Astrophysics Data System (ADS)
King, Emily J.
2015-08-01
When searching for finite unit norm tight frames (FUNTFs) of M vectors in FN which yield robust representations, one is concerned with finding frames consisting of frame vectors which are in some sense as spread apart as possible. Algebraic spread and geometric spread are the two most commonly used measures of spread. A frame with optimal algebraic spread is called full spark and is such that any subcollection of N frame vectors is a basis for FN. A Grassmannian frame is a FUNTF which satisfies the Grassmannian packing problem; that is, the frame vectors are optimally geometrically spread given fixed M and N. A particular example of a Grassmannian frame is an equiangular frame, which is such that the absolute value of all inner products of distinct vectors is equal. The relationship between these two types of optimal spread is complicated. The folk knowledge for many years was that equiangular frames were full spark; however, this is now known not to hold for an infinite class of equiangular frames. The exact relationship between these types of spread will be further explored in this talk, as well as Plücker coordinates and coherence, which are measures of how much a frame misses being optimally algebraically or geometrically spread.
Some "Facts" About CAI: A Quantitative Analysis of the 1976 Index to Computer Based Instruction
ERIC Educational Resources Information Center
Kearsley, Greg P.
1976-01-01
Descriptive quantitative data on various aspects of CAI are reported, including subject matter, author languages, instructional strategies, level of instruction, sources, and central processors. (Author)
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.
NASA Astrophysics Data System (ADS)
Kang, Kicheon
2014-02-01
We investigate the local geometric phase induced by Faraday's law of induction in a superconducting charge qubit threaded by an Aharonov-Bohm flux. A quantum-state reconstruction scheme, which is based on measurement of three complementary quantities, that is, the extra charge and two local currents, is introduced. We find that, while the variation of the local phase with magnetic field is determined by Faraday's law, incorporation of the time-reversal symmetry enables complete determination of the local phase. This procedure clearly demonstrates that the local geometric phase is a physical quantity (aside from a global phase factor), in contrast to the standard description of the Aharonov-Bohm effect.
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)
Design of geometric phase measurement in EAST Tokamak
NASA Astrophysics Data System (ADS)
Lan, T.; Liu, H. Q.; Liu, J.; Jie, Y. X.; Wang, Y. L.; Gao, X.; Qin, H.
2016-07-01
The optimum scheme for geometric phase measurement in EAST Tokamak is proposed in this paper. The theoretical values of geometric phase for the probe beams of EAST Polarimeter-Interferometer (POINT) system are calculated by path integration in parameter space. Meanwhile, the influences of some controllable parameters on geometric phase are evaluated. The feasibility and challenge of distinguishing geometric effect in the POINT signal are also assessed in detail.
Topological Quantum Field Theory and the Geometric Langlands Correspondence
NASA Astrophysics Data System (ADS)
Setter, Kevin
In the pioneering work of A. Kapustin and E. Witten, the geometric Langlands program of number theory was shown to be intimately related to duality of GL-twisted N = 4 super Yang-Mills theory compactified on a Riemann surface. In this thesis, we generalize Kapustin-Witten by investigating compactification of the GL-twisted theory to three dimensions on a circle (for various values of the twisting parameter t). By considering boundary conditions in the three-dimensional description, we classify codimension-two surface operators of the GL-twisted theory, generalizing those surface operators studied by S. Gukov and E. Witten. For t = i, we propose a complete description of the 2-category of surface operators in terms of module categories, and, in addition, we determine the monoidal category of line operators which includes Wilson lines as special objects. For t = 1 and t = 0, we discuss surface and line operators in the abelian case. We generalize Kapustin-Witten also by analyzing a separate twisted version of N = 4, the Vafa-Witten theory. After introducing a new four-dimensional topological gauge theory, the gauged 4d A-model, we locate the Vafa-Witten theory as a special case. Compactification of the Vafa-Witten theory on a circle and on a Riemann surface is discussed. Several novel two- and three-dimensional topological gauge theories are studied throughout the thesis and in the appendices. In work unrelated to the main thread of the thesis, we conclude by classifying codimension-one topological defects in two-dimensional sigma models with various amounts of supersymmetry.
Quantitative analysis of qualitative images
NASA Astrophysics Data System (ADS)
Hockney, David; Falco, Charles M.
2005-03-01
We show optical evidence that demonstrates artists as early as Jan van Eyck and Robert Campin (c1425) used optical projections as aids for producing their paintings. We also have found optical evidence within works by later artists, including Bermejo (c1475), Lotto (c1525), Caravaggio (c1600), de la Tour (c1650), Chardin (c1750) and Ingres (c1825), demonstrating a continuum in the use of optical projections by artists, along with an evolution in the sophistication of that use. However, even for paintings where we have been able to extract unambiguous, quantitative evidence of the direct use of optical projections for producing certain of the features, this does not mean that paintings are effectively photographs. Because the hand and mind of the artist are intimately involved in the creation process, understanding these complex images requires more than can be obtained from only applying the equations of geometrical optics.
Design of geometric phase measurement in EAST Tokamak
NASA Astrophysics Data System (ADS)
Lan, Ting; Liu, Haiqing; Liu, Jian; Qin, Hong
2016-10-01
The aim of this work is to propose the optimum scheme for geometric phase measurement in EAST Tokamak. On the one hand, the experimental observation of geometric phase in plasma systems is an essential verification of the geometric phase theory by a new experimental technique. On the other hand, the measurement of geometric phase confirms geometric effect as a new system error in the existing diagnostics. The geometric phase in Faraday rotation angle for linearly polarized electromagnetic waves propagating in non-uniform magnetized plasmas is a good candidate for the first identification of geometric phase in plasma. In this work, the theoretical values of geometric phase for the probe beams of EAST Polarimeter-Interferometer (POINT) system are calculated by path integration in parameter space. Several schemes are proposed for the measurement of the geometric phase in POINT system by amplifying the geometric phase and enhancing the diagnostic resolution. To reach the conditions of the designed scheme for geometric phase measurement, the feasibility of replacing individual retro reflectors (RRs) with retro reflector array (RRA) in POINT system is verified experimentally. Corresponding results are beneficial for geometric phase measurement in EAST Tokamak.
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.
A geometric and algebraic view of MHC-peptide complexes and their binding properties
Cano, Pedro; Fan, Bo
2001-01-01
Background Major histocompatibility complex (MHC) molecules present peptides to T lymphocytes. It is of critical biological and medical importance to elucidate how different MHC alleles bind to a specific set of peptides. Method In this study we approach the problem from the algebraic and geometric point of view to analyse MHC-peptide-binding data accumulated over the years. The space of sequence properties (having a particular amino acid at a particular position) of MHC-peptide complexes conveys a geometric structure to these sequence properties in the form of a distance measure, which reveals the peptide binding requirements imposed by the polymorphic sequence characteristics of the MHC molecules. Results Comparison of the results of this study with our current knowledge of MHC-peptide binding constraints leads to robust agreement. This study provides the tools to quantitate these binding constraints giving a more detailed account of them and opening the way to make peptide binding predictions for MHC alleles for which there is no peptide elution data. In addition, the geometric representation of MHC-peptide complex sequence data gives a distance measure between amino acids in reference to their ability to meet MHC binding requirements. Conclusions The algebraic and geometric view of amino acid sequences provides a theoretical framework to study the function of proteins when there is enough variation in this sequence to account for the variation in their function, as it is the case with MHC molecules in regard to their ability to present peptides. PMID:11472639
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
The Electromagnetic Duality Formulation of Geometric Phases
NASA Astrophysics Data System (ADS)
Zhang, Yuchao; Li, Kang
2015-06-01
This paper focuses on the electromagnetic(EM) duality formulation of geometric phases of Aharonov-Bohm(A-B) effect and Aharonov-Casher(A-C) effect. Through the two four-vector potential formulation of electromagnetic theory, we construct a EM duality formulation for both A-B effect and A-C effect. The He-McKellar-Wilkens(HMW) effect is included as a EM duality counterpart of the A-C effect, and also the EM duality counterpart of the A-B effect is also predicted.
CMOS-integrated geometrically tunable optical filters.
Lerose, Damiana; Hei, Evie Kho Siaw; Ching, Bong Ching; Sterger, Martin; Yaw, Liau Chu; Schulze, Frank Michael; Schmidt, Frank; Schmidt, Andrei; Bach, Konrad
2013-03-10
We present a method for producing monolithically integrated complementary metal-oxide-semiconductor (CMOS) optical filters with different and customer-specific responses. The filters are constituted by a Fabry-Perot resonator formed by two Bragg mirrors separated by a patterned cavity. The filter response can be tuned by changing the geometric parameters of the patterning, and consequently the cavity effective refractive index. In this way, many different filters can be produced at once on a single chip, allowing multichanneling. The filter has been designed, produced, and characterized. The results for a chip with 24 filters are presented.
In the Realm of Geometric Transitions
Alexander, S
2004-09-09
We complete the duality cycle by constructing the geometric transition duals in the type IIB, type I and heterotic theories. We show that in the type IIB theory the background on the closed string side is a Kahler deformed conifold, as expected, even though the mirror type IIA backgrounds are non-Kahler (both before and after the transition). On the other hand, the Type I and heterotic backgrounds are non-Kahler. Therefore, on the heterotic side these backgrounds give rise to new torsional manifolds that have not been studied before. We show the consistency of these backgrounds by verifying the torsional equation.
Minimal representations, geometric quantization, and unitarity.
Brylinski, R; Kostant, B
1994-01-01
In the framework of geometric quantization we explicitly construct, in a uniform fashion, a unitary minimal representation pio of every simply-connected real Lie group Go such that the maximal compact subgroup of Go has finite center and Go admits some minimal representation. We obtain algebraic and analytic results about pio. We give several results on the algebraic and symplectic geometry of the minimal nilpotent orbits and then "quantize" these results to obtain the corresponding representations. We assume (Lie Go)C is simple. PMID:11607478
Advances in Geometric Acoustic Propagation Modeling Methods
NASA Astrophysics Data System (ADS)
Blom, P. S.; Arrowsmith, S.
2013-12-01
Geometric acoustics provides an efficient numerical method to model propagation effects. At leading order, one can identify ensonified regions and calculate celerities of the predicted arrivals. Beyond leading order, the solution of the transport equation provides a means to estimate the amplitude of individual acoustic phases. The auxiliary parameters introduced in solving the transport equation have been found to provide a means of identifying ray paths connecting source and receiver, or eigenrays, for non-planar propagation. A detailed explanation of the eigenray method will be presented as well as an application to predicting azimuth deviations for infrasonic data recorded during the Humming Roadrunner experiment of 2012.
FOLD LENS FLUX ANOMALIES: A GEOMETRIC APPROACH
Goldberg, David M.; Chessey, Mary K.; Harris, Wendy B.; Richards, Gordon T.
2010-06-01
We develop a new approach for studying flux anomalies in quadruply imaged fold lens systems. We show that in the absence of substructure, microlensing, or differential absorption, the expected flux ratios of a fold pair can be tightly constrained using only geometric arguments. We apply this technique to 11 known quadruple lens systems in the radio and infrared and compare our estimates to the Monte Carlo based results of Keeton et al. We show that a robust estimate for a flux ratio from a smoothly varying potential can be found, and at long wavelengths those lenses deviating from this ratio almost certainly contain significant substructure.
Fold Lens Flux Anomalies: A Geometric Approach
NASA Astrophysics Data System (ADS)
Goldberg, David M.; Chessey, Mary K.; Harris, Wendy B.; Richards, Gordon T.
2010-06-01
We develop a new approach for studying flux anomalies in quadruply imaged fold lens systems. We show that in the absence of substructure, microlensing, or differential absorption, the expected flux ratios of a fold pair can be tightly constrained using only geometric arguments. We apply this technique to 11 known quadruple lens systems in the radio and infrared and compare our estimates to the Monte Carlo based results of Keeton et al. We show that a robust estimate for a flux ratio from a smoothly varying potential can be found, and at long wavelengths those lenses deviating from this ratio almost certainly contain significant substructure.
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.
Geometric extension through Schwarzschild R = 0
NASA Astrophysics Data System (ADS)
Lynden-Bell, D.; Katz, J.
1990-12-01
A very simple conservation theorem pertaining to embeddings of Tolman solutions into flat space has been found which, in nonsingular regions of space-time, follows from Einstein's equations and the equations that define the embedding. If the conservation is extended to cover the singular 'surface' r = 0, it furnishes the requisite physical and geometrical supplement to Einstein's equations at the singularity; by thus bridging the singular region, a unique extension is found beyond the singularity. The passage of an extended particle through the singularity is illustrated by a classical toy model that demonstrates both the expected crushing and the emergence into extended space.
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.
Overview of geometrical room acoustic modeling techniques.
Savioja, Lauri; Svensson, U Peter
2015-08-01
Computerized room acoustics modeling has been practiced for almost 50 years up to date. These modeling techniques play an important role in room acoustic design nowadays, often including auralization, but can also help in the construction of virtual environments for such applications as computer games, cognitive research, and training. This overview describes the main principles, landmarks in the development, and state-of-the-art for techniques that are based on geometrical acoustics principles. A focus is given to their capabilities to model the different aspects of sound propagation: specular vs diffuse reflections, and diffraction.
Geometric formalism for DNA quadruplex folding.
Webba da Silva, Mateus
2007-01-01
Understanding the control of self-assembly and stereochemical properties of DNA higher order architectural folds is of fundamental importance in biology as well as biochemical technological applications. Guanine-rich DNA sequences can form tetrahelical architectures termed quadruplexes. A formalism is presented describing the interdependency of a set of structural descriptors as a geometric basis for folding of unimolecular quadruplex topologies. It represents a standard for interpretation of structural characteristics of quadruplexes, and is comprehensive in explicitly harmonizing the results of published literature with a unified language. The formalism is a fundamental step towards prediction of unimolecular quadruplex folding topologies from primary sequence.
Supersymmetric QCD vacua and geometrical engineering
Tatar, Radu; Wetenhall, Ben
2008-02-15
We consider the geometrical engineering constructions for the N=1 supersymmetric QCD vacua recently proposed by Giveon and Kutasov. After 1 T-duality, the geometries with wrapped D5 branes become N=1 brane configurations with NS branes and D4 branes. The field theories encoded by the geometries contain extra massive adjoint fields for the flavor group. After performing a flop, the geometries contain branes, antibranes and branes wrapped on nonholomorphic 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 nonsupersymmetric vacua.
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.
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…
Andrew integrated reservoir description
Todd, S.P.
1996-12-31
The Andrew field is an oil and gas accumulation in Palaeocene deep marine sands in the Central North Sea. It is currently being developed with mainly horizontal oil producers. Because of the field`s relatively small reserves (mean 118 mmbbls), the performance of each of the 10 or so horizontal wells is highly important. Reservoir description work at sanction time concentrated on supporting the case that the field could be developed commercially with the minimum number of wells. The present Integrated Reservoir Description (IRD) is focussed on delivering the next level of detail that will impact the understanding of the local reservoir architecture and dynamic performance of each well. Highlights of Andrew IRD Include: (1) Use of a Reservoir Uncertainty Statement (RUS) developed at sanction time to focus the descriptive effort of both asset, support and contract petrotechnical staff, (2) High resolution biostratigraphic correlation to support confident zonation of the reservoir, (3) Detailed sedimentological analysis of the core including the use of dipmeter to interpret channel/sheet architecture to provide new insights into reservoir heterogeneity; (4) Integrated petrographical and petrophysical investigation of the controls on Sw-Height and relative permeability of water; (5) Fluids description using oil geochemistry and Residual Salt Analysis Sr isotope studies. Andrew IRD has highlighted several important risks to well performance, including the influence of more heterolithic intervals on gas breakthrough and the controls on water coning exerted by suppressed water relative permeability in the transition zone.
Andrew integrated reservoir description
Todd, S.P.
1996-01-01
The Andrew field is an oil and gas accumulation in Palaeocene deep marine sands in the Central North Sea. It is currently being developed with mainly horizontal oil producers. Because of the field's relatively small reserves (mean 118 mmbbls), the performance of each of the 10 or so horizontal wells is highly important. Reservoir description work at sanction time concentrated on supporting the case that the field could be developed commercially with the minimum number of wells. The present Integrated Reservoir Description (IRD) is focussed on delivering the next level of detail that will impact the understanding of the local reservoir architecture and dynamic performance of each well. Highlights of Andrew IRD Include: (1) Use of a Reservoir Uncertainty Statement (RUS) developed at sanction time to focus the descriptive effort of both asset, support and contract petrotechnical staff, (2) High resolution biostratigraphic correlation to support confident zonation of the reservoir, (3) Detailed sedimentological analysis of the core including the use of dipmeter to interpret channel/sheet architecture to provide new insights into reservoir heterogeneity; (4) Integrated petrographical and petrophysical investigation of the controls on Sw-Height and relative permeability of water; (5) Fluids description using oil geochemistry and Residual Salt Analysis Sr isotope studies. Andrew IRD has highlighted several important risks to well performance, including the influence of more heterolithic intervals on gas breakthrough and the controls on water coning exerted by suppressed water relative permeability in the transition zone.
Geometric spin Hall effect of light with inhomogeneous polarization
NASA Astrophysics Data System (ADS)
Ling, Xiaohui; Zhou, Xinxing; Yi, Xunong
2017-01-01
The spin Hall effect of light originates from spin-orbit interaction of light, which manifests two types of geometric phases. In this paper, we report the observation of a geometric spin Hall effect by generating a light beam with inhomogeneous polarization distribution. Unlike the previously reported geometric spin Hall effect observed in a tilted beam-detector system, which is believed to result from an effective spin-redirection Berry geometric phase, the geometric spin Hall effect demonstrated here is attributed to an effective, spatially varying Pancharatnam-Berry geometric phase generated by the inhomogeneous polarization geometry. Our further experiments show that the geometric spin Hall effect can be tuned by tailoring the polarization geometry of light, demonstrating the spin states of photons can be steered with a great flexibility.
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.
Geometric-optical illusions at isoluminance.
Hamburger, Kai; Hansen, Thorsten; Gegenfurtner, Karl R
2007-12-01
The idea of a largely segregated processing of color and form was initially supported by observations that geometric-optical illusions vanish under isoluminance. However, this finding is inconsistent with some psychophysical studies and also with physiological evidence showing that color and luminance are processed together by largely overlapping sets of neurons in the LGN, in V1, and in extrastriate areas. Here we examined the strength of nine geometric-optical illusions under isoluminance (Delboeuf, Ebbinghaus, Hering, Judd, Müller-Lyer, Poggendorff, Ponzo, Vertical, Zöllner). Subjects interactively manipulated computer-generated line drawings to counteract the illusory effect. In all cases, illusions presented under isoluminance (both for colors drawn from the cardinal L-M or S-(L+M) directions of DKL color space) were as effective as the luminance versions (both for high and low contrast). The magnitudes of the illusion effects were highly correlated across subjects for the different conditions. In two additional experiments we determined that the strong illusions observed under isoluminance were not due to individual deviations from the photometric point of isoluminance or due to chromatic aberrations. Our findings show that our conscious percept is affected similarly for both isoluminance and luminance conditions, suggesting that the joint processing for chromatic and luminance defined contours may extend well beyond early visual areas.
Geometrical effects in X-mode scattering
Bretz, N.
1986-10-01
One technique to extend microwave scattering as a probe of long wavelength density fluctuations in magnetically confined plasmas is to consider the launching and scattering of extraordinary (X-mode) waves nearly perpendicular to the field. When the incident frequency is less than the electron cyclotron frequency, this mode can penetrate beyond the ordinary mode cutoff at the plasma frequency and avoid significant distortions from density gradients typical of tokamak plasmas. In the more familiar case, where the incident and scattered waves are ordinary, the scattering is isotropic perpendicular to the field. However, because the X-mode polarization depends on the frequency ratios and the ray angle to the magnetic field, the coupling between the incident and scattered waves is complicated. This geometrical form factor must be unfolded from the observed scattering in order to interpret the scattering due to density fluctuations alone. The geometrical factor is calculated here for the special case of scattering perpendicular to the magnetic field. For frequencies above the ordinary mode cutoff the scattering is relatively isotropic, while below cutoff there are minima in the forward and backward directions which go to zero at approximately half the ordinary mode cutoff density.
Geometric Modelling of Octagonal Lamp Poles
NASA Astrophysics Data System (ADS)
Chan, T. O.; Lichti, D. D.
2014-06-01
Lamp poles are one of the most abundant highway and community components in modern cities. Their supporting parts are primarily tapered octagonal cones specifically designed for wind resistance. The geometry and the positions of the lamp poles are important information for various applications. For example, they are important to monitoring deformation of aged lamp poles, maintaining an efficient highway GIS system, and also facilitating possible feature-based calibration of mobile LiDAR systems. In this paper, we present a novel geometric model for octagonal lamp poles. The model consists of seven parameters in which a rotation about the z-axis is included, and points are constrained by the trigonometric property of 2D octagons after applying the rotations. For the geometric fitting of the lamp pole point cloud captured by a terrestrial LiDAR, accurate initial parameter values are essential. They can be estimated by first fitting the points to a circular cone model and this is followed by some basic point cloud processing techniques. The model was verified by fitting both simulated and real data. The real data includes several lamp pole point clouds captured by: (1) Faro Focus 3D and (2) Velodyne HDL-32E. The fitting results using the proposed model are promising, and up to 2.9 mm improvement in fitting accuracy was realized for the real lamp pole point clouds compared to using the conventional circular cone model. The overall result suggests that the proposed model is appropriate and rigorous.
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.
Geometrical Monte Carlo simulation of atmospheric turbulence
NASA Astrophysics Data System (ADS)
Yuksel, Demet; Yuksel, Heba
2013-09-01
Atmospheric turbulence has a significant impact on the quality of a laser beam propagating through the atmosphere over long distances. Turbulence causes intensity scintillation and beam wander from propagation through turbulent eddies of varying sizes and refractive index. This can severely impair the operation of target designation and Free-Space Optical (FSO) communications systems. In addition, experimenting on an FSO communication system is rather tedious and difficult. The interferences of plentiful elements affect the result and cause the experimental outcomes to have bigger error variance margins than they are supposed to have. Especially when we go into the stronger turbulence regimes the simulation and analysis of the turbulence induced beams require delicate attention. We propose a new geometrical model to assess the phase shift of a laser beam propagating through turbulence. The atmosphere along the laser beam propagation path will be modeled as a spatial distribution of spherical bubbles with refractive index discontinuity calculated from a Gaussian distribution with the mean value being the index of air. For each statistical representation of the atmosphere, the path of rays will be analyzed using geometrical optics. These Monte Carlo techniques will assess the phase shift as a summation of the phases that arrive at the same point at the receiver. Accordingly, there would be dark and bright spots at the receiver that give an idea regarding the intensity pattern without having to solve the wave equation. The Monte Carlo analysis will be compared with the predictions of wave theory.
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.
Geometric Phases in Single Molecule Magnets
NASA Astrophysics Data System (ADS)
Fenochio, Brian Canchola
The characterization of the material properties of Single Molecule Magnets (SMMs) has grown in importance over the last few decades with the rise of novel applications such as high-density magnetic storage and quantum computation. Many of the applications require the probing of SMMs with spectroscopic methods that make use of electromagnetic radiation. The interaction with these time-dependent fields leads to energy shifts, which can be attributed to the geometric phase acquired by the system or the Bloch-Siegert shift. We model an SMM by a giant spin Hamiltonian, and use Floquet perturbation theory to find the geometric phase shifts. The locations where the phase shift between two levels is zero is useful for performing accurate spectroscopies, whereas the regions where relative phase differences exist are useful in applications like quantum computing. Using the same giant spin Hamiltonian, we can use Floquet theory and Salwen perturbation theory to determine the Bloch-Siegert shift and derive a modified version of the Rabi formula for transition probabilities between the energy states Ealpha → Ealpha+/-1, Ealpha → Ealpha+/-3, and Ealpha → Ealpha+/-5 , where alpha is the index of an arbitrary initial state. The shifted eigenvalues and modified transition probabilities can be useful in spectroscopies where accurate values for the energy-splitting between magnetic states needs to be determined.
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 acoustics and transonic helicopter sound
NASA Technical Reports Server (NTRS)
Isom, Morris; Purcell, Timothy W.; Strawn, Roger C.
1987-01-01
A new method is presented for predicting the impulsive noise generated by a transonic rotor blade. The method is a combined approach involving computational fluid dynamics and geometrical acoustics. A full-potential finite-difference method is used to obtain the pressure field close to the blade. A Kirchhoff integral formulation is then used to extend these finite-difference results into the far field. This Kirchhoff formula is based on geometrical acoustics approximations. It requires initial data across a plane at the sonic radius in a blade-fixed coordinate system. This data is provided by the finite-difference solution. Acoustic pressure predictions show good agreement with hover experimental data for cases with hover tip Mach numbers of 0.88 through 0.96. The cases above 0.92 tip Mach number are dominated by non-linear transonic effects seen as strong shocks on and off the blade tip. This paper gives the first successful predictions of far-field acoustic pressures for high-speed impulsive noise over a range of Mach numbers after delocalization.
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
Topological and geometric measurements of force-chain structure
NASA Astrophysics Data System (ADS)
Giusti, Chad; Papadopoulos, Lia; Owens, Eli T.; Daniels, Karen E.; Bassett, Danielle S.
2016-09-01
Developing quantitative methods for characterizing structural properties of force chains in densely packed granular media is an important step toward understanding or predicting large-scale physical properties of a packing. A promising framework in which to develop such methods is network science, which can be used to translate particle locations and force contacts into a graph in which particles are represented by nodes and forces between particles are represented by weighted edges. Recent work applying network-based community-detection techniques to extract force chains opens the door to developing statistics of force-chain structure, with the goal of identifying geometric and topological differences across packings, and providing a foundation on which to build predictions of bulk material properties from mesoscale network features. Here we discuss a trio of related but fundamentally distinct measurements of the mesoscale structure of force chains in two-dimensional (2D) packings, including a statistic derived using tools from algebraic topology, which together provide a tool set for the analysis of force chain architecture. We demonstrate the utility of this tool set by detecting variations in force-chain architecture with pressure. Collectively, these techniques can be generalized to 3D packings, and to the assessment of continuous deformations of packings under stress or strain.
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.
Topological and geometric measurements of force-chain structure.
Giusti, Chad; Papadopoulos, Lia; Owens, Eli T; Daniels, Karen E; Bassett, Danielle S
2016-09-01
Developing quantitative methods for characterizing structural properties of force chains in densely packed granular media is an important step toward understanding or predicting large-scale physical properties of a packing. A promising framework in which to develop such methods is network science, which can be used to translate particle locations and force contacts into a graph in which particles are represented by nodes and forces between particles are represented by weighted edges. Recent work applying network-based community-detection techniques to extract force chains opens the door to developing statistics of force-chain structure, with the goal of identifying geometric and topological differences across packings, and providing a foundation on which to build predictions of bulk material properties from mesoscale network features. Here we discuss a trio of related but fundamentally distinct measurements of the mesoscale structure of force chains in two-dimensional (2D) packings, including a statistic derived using tools from algebraic topology, which together provide a tool set for the analysis of force chain architecture. We demonstrate the utility of this tool set by detecting variations in force-chain architecture with pressure. Collectively, these techniques can be generalized to 3D packings, and to the assessment of continuous deformations of packings under stress or strain.
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...
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.
X-ray scattering from freestanding polymer films with geometrically curved surfaces.
Lee, D R; Shin, K; Seeck, O H; Kim, Hyunjung; Seo, Y-S; Tolan, M; Rafailovich, M H; Sokolov, J; Sinha, S K
2003-05-09
We show that the x-ray surface scattering from a freestanding polymer film exhibits features that cannot be explained by the usual stochastic formalism for surfaces with random height fluctuations. Instead, a geometric description of the film morphology assuming two curved surfaces characterized by a radius of curvature and a lateral cutoff length successfully accounts for the phase difference between the Kiessig fringes of the nominal "specular" and "off-specular" components of the scattering. The formalism allows one to distinguish unambiguously between conformal and anticonformal curvature morphologies at long length scales.
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.
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…
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.…
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.
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.
Reasoning about scene descriptions
DiManzo, M.; Adorni, G.; Giunchiglia, F.
1986-07-01
When a scene is described by means of natural language sentences, many details are usually omitted, because they are not in the focus of the conversation. Moreover, natural language is not the best tool to define precisely positions and spatial relationships. The process of interpreting ambiguous statements and inferring missing details involves many types of knowledge, from linguistics to physics. This paper is mainly concerned with the problem of modeling the process of understanding descriptions of static scenes. The specific topics covered by this work are the analysis of the meaning of spatial prepositions, the problem of the reference system and dimensionality, the activation of expectations about unmentioned objects, the role of default knowledge about object positions and its integration with contextual information sources, and the problem of space representation. The issue of understanding dynamic scenes descriptions is briefly approached in the last section.
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
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.
Quantitative geometric analysis of rib, costal cartilage and sternum from childhood to teenagehood.
Sandoz, Baptiste; Badina, Alina; Laporte, Sébastien; Lambot, Karene; Mitton, David; Skalli, Wafa
2013-09-01
Better understanding of the effects of growth on children's bones and cartilage is necessary for clinical and biomechanical purposes. The aim of this study is to define the 3D geometry of children's rib cages: including sternum, ribs and costal cartilage. Three-dimensional reconstructions of 960 ribs, 518 costal cartilages and 113 sternebrae were performed on thoracic CT scans of 48 children, aged 4 months to 15 years. The geometry of the sternum was detailed and nine parameters were used to describe the ribs and rib cages. A "costal index" was defined as the ratio between cartilage length and whole rib length to evaluate the cartilage ratio for each rib level. For all children, the costal index decreased from rib level 1 to 3 and increased from level 3 to 7. For all levels, the cartilage accounted for 45-60 % of the rib length, and was longer for the first years of life. The mean costal index decreased by 21 % for subjects over 3-year old compared to those under three (p < 10(-4)). The volume of the sternebrae was found to be highly age dependent. Such data could be useful to define the standard geometry of the pediatric thorax and help to detect clinical abnormalities.
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
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.
Geometrical shock dynamics of fast magnetohydrodynamic shocks
NASA Astrophysics Data System (ADS)
Mostert, Wouter; Pullin, Dale I.; Samtaney, Ravi; Wheatley, Vincent
2016-11-01
We extend the theory of geometrical shock dynamics (GSD, Whitham 1958), to two-dimensional fast magnetohydrodynamic (MHD) shocks moving in the presence of nonuniform magnetic fields of general orientation and strength. The resulting generalized area-Mach number rule is adapted to MHD shocks moving in two spatial dimensions. A partially-spectral numerical scheme developed from that of Schwendeman (1993) is described. This is applied to the stability of plane MHD fast shocks moving into a quiescent medium containing a uniform magnetic field whose field lines are inclined to the plane-shock normal. In particular, we consider the time taken for an initially planar shock subject to an initial perturbed magnetosonic Mach number distribution, to first form shock-shocks. Supported by KAUST OCRF Award No. URF/1/2162-01.
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.
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.
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 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.
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.
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.
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 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 calibration of rotational kaleidoscopic instrument
NASA Astrophysics Data System (ADS)
Havran, Vlastimil; Němcová, Šárka; Čáp, Jiří; Hošek, Jan; Bittner, Jiří; Macúchová, Karolina
2016-11-01
The measurement of spatially varying surface reflectance is required for faithful reproduction of real world to allow for predictive look of computer generated images. One such proposed method uses a rotational kaleidoscopic imaging, where illumination and imaging paths are realized by subimages on kaleidoscopic mirrors and illumination is carried out by a DLP projector. We describe a novel geometric calibration method for a rotational kaleidoscope that is necessary to get aligned and accurate data from measurement. The calibration has two stages. The first stage mechanically adjusts the camera, the projector, and the autocollimator against the kaleidoscope mirrors. The second stage is based on the software. By random perturbation of camera and projector in corresponding mathematical model of the kaleidoscope we estimate better real positions of camera and projector in a physical setup, comparing the computed images from the software simulator and the acquired images from the physical setup.
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.
On the geometrization of quantum mechanics
Tavernelli, Ivano
2016-08-15
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.
A Geometric Classification of Jaw Deformities
Gateno, Jaime; Alfi, David; Xia, James J.; Teichgraeber, John F.
2015-01-01
In the United States, the most widely used classification system for jaw deformities is the one provided by the International Classification of Diseases, Clinical Modification (ICD-CM), a taxonomy scheme that is based on the World Health Organization's International Classification of Diseases (ICD). The last iteration of ICD-CM, version 10, sorts jaw deformities according to geometry, into 3 groups: anomalies of jaw size, anomalies of jaw-cranial base relationship, or unspecified. Yet these deformities can affect 6 different geometric attributes: size, position, orientation, shape, symmetry, and completeness. In clinical practice and in teaching we have found the ICD-CM classification to be incomplete and disjointed. With this in mind, we have developed a better classification system. The purpose of this paper is to present it. PMID:26608152
Geometrical-numerical approach to diffraction phenomena.
Bosch, S; Ferré-Borrull, J
2001-02-15
The calculation of diffracted fields is considered by means of a geometrical analysis of the incoming wave into semiperiodic zones in the aperture plane, followed by a numerical process for addition of the contributions corresponding to the semiperiodic zones. This general approach constitutes a novel interpretation of diffraction phenomena that permits exact evaluation of the mathematical expressions of diffraction theory and overcomes the limitations of any approximation. The method is illustrated by analysis of two important configuration in optics: the pinhole camera, for which we deduce the optimum radius for imaging, and the diffraction of a spherical converging wave through a circular aperture, from which we determine the limit of the validity of the Fraunhofer approximation (i.e., of the Airy pattern) and the influence of the obliquity factor.
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.
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.
A geometrical perspective for the bargaining problem.
Wong, Kelvin Kian Loong
2010-04-26
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.
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.
Coifman, R R; Lafon, S; Lee, A B; Maggioni, M; Nadler, B; Warner, F; Zucker, S W
2005-05-24
In the companion article, a framework for structural multiscale geometric organization of subsets of R(n) and of graphs was introduced. Here, diffusion semigroups are used to generate multiscale analyses in order to organize and represent complex structures. We emphasize the multiscale nature of these problems and build scaling functions of Markov matrices (describing local transitions) that lead to macroscopic descriptions at different scales. The process of iterating or diffusing the Markov matrix is seen as a generalization of some aspects of the Newtonian paradigm, in which local infinitesimal transitions of a system lead to global macroscopic descriptions by integration. This article deals with the construction of fast-order N algorithms for data representation and for homogenization of heterogeneous structures.
Wigner rotation and Thomas precession: geometric phases and related physical theories
NASA Astrophysics Data System (ADS)
Brezov, Danail S.; Mladenova, Clementina D.; Mladenov, Ivaïlo M.
2015-06-01
We use a vector parameter description of the Lorentz groups in ℝ2,1 and ℝ3,1 to obtain an exact expression for the Thomas factor as a geometric phase. The effect of phase accumulation in Thomas-Wigner precession phenomena is seen as a manifestation of the hyperbolic solid angle theorem. On the infinitesimal level, our description involves affine connections on the noncompact Hopf fibrations U(1) → SU(1, 1) → Δ and SU(2) → PSL(2,ℂ) → H 3. The associated gauge field is a restriction of the familiar Yang-Mills anti-instanton. We also consider the dual compact case, and we discuss generalizations to arbitrary dimensions and applications in various branches of theoretical physics.
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.
Discrimination of geometric angles by adult humans.
Reichert, James F; Kelly, Debbie M
2012-03-01
Men and women learned to discriminate between two different size angles presented to them as objects within a real-world task. During Experiment 1, participants in group 50 were trained to choose a 50° angle and participants in group 75 were trained to choose a 75° angle. During testing, both groups were provided with a choice between their training angle and one of a set of test angles that was either smaller or larger than the training angle. Results showed a generalized pattern of responding, with group 50 showing increased responding to test angles smaller than 50° and group 75 showing increased responding to test angles larger than 75°. Further analysis of the response patterns revealed that participants in group 50 showed evidence of absolute learning, whereas participants in group 75 showed evidence of relational learning. During Experiment 2, a third group of participants (group 25) trained to choose a smaller angle (25°) was included in addition to group 50 and group 75. Participants were trained with three angles present and tested with just two, one being their training angle and the other being one of a set of novel test angles. Similar to the participants from Experiment 1, group 75 showed evidence of relational learning. Group 50, for which no relational rule could be applied during training, showed an absolute learning pattern with no response shift to test angles smaller or larger than their training angle. Group 25 showed evidence of absolute responding that was more pronounced than that found for the smallest training angle during Experiment 1. These findings suggest differential learning of geometric angles based on amplitude with smaller angles perceived as more distinct and thus more resistant to broader generalization than larger angles. Implications of these results are that certain geometric properties may be subject to different learning processes based on the specific magnitude of that property.
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
Hierarchical structure description of spatiotemporal chaos.
Liu, Jian; She, Zhen-Su; Guo, Hongyu; Li, Liang; Ouyang, Qi
2004-09-01
We develop a hierarchical structure (HS) analysis for quantitative description of statistical states of spatially extended systems. Examples discussed here include an experimental reaction-diffusion system with Belousov-Zhabotinsky kinetics, the two-dimensional complex Ginzburg-Landau equation, and the modified FitzHugh-Nagumon equation, which all show complex dynamics of spirals and defects. We demonstrate that the spatial-temporal fluctuation fields in the above-mentioned systems all display the HS similarity property originally proposed for the study of fully developed turbulence [Phys. Rev. Lett. 72, 336 (1994)
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.
Generalizations of fuzzy linguistic control points in geometric design
NASA Astrophysics Data System (ADS)
Sallehuddin, M. H.; Wahab, A. F.; Gobithaasan, R. U.
2014-07-01
Control points are geometric primitives that play an important role in designing the geometry curve and surface. When these control points are blended with some basis functions, there are several geometric models such as Bezier, B-spline and NURBS(Non-Uniform Rational B-Spline) will be produced. If the control points are defined by the theory of fuzzy sets, then fuzzy geometric models are produced. But the fuzzy geometric models can only solve the problem of uncertainty complex. This paper proposes a new definition of fuzzy control points with linguistic terms. When the fuzzy control points with linguistic terms are blended with basis functions, then a fuzzy linguistic geometric model is produced. This paper ends with some numerical examples illustrating linguistic control attributes of fuzzy geometric models.
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.
Geometric quantum gates that are robust against stochastic control errors
Zhu Shiliang; Zanardi, Paolo
2005-08-15
The realistic application of geometric quantum computation is crucially dependent on an unproved robustness conjecture, claiming that geometric quantum gates are more resilient against random noise than dynamic gates. We propose a suitable model that allows a direct and fair comparison between geometrical and dynamical operations. In the presence of stochastic control errors we find that the maximum of gate fidelity corresponds to quantum gates with a vanishing dynamical phase. This is a clear evidence for the robustness of nonadiabatic geometric quantum computation. The predictions here presented can be experimentally tested in almost all of the already existing quantum computer candidates.
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.
Comparison of geometrical and diffraction optical transfer functions
NASA Astrophysics Data System (ADS)
Mahajan, Virendra N.; Díaz, José Antonio
2015-09-01
The geometrical and diffraction point-spread functions of an optical imaging system have been reviewed and compared in the past [V. N. Mahajan, "Comparison of geometrical and diffraction point-spread functions," SPIE Proc. 3729, 434-445 (1999)]. In this paper, we review and compare its corresponding optical transfer functions. While the truth lies with the diffraction OTF, it is considered easier and quicker to calculate the geometrical OTF, especially for large aberrations. We briefly describe the theory of the two OTFs, and explore the range of spatial frequencies and the magnitude of the primary aberrations over which the geometrical OTF may provide a reasonable approximation of the diffraction OTF.
NASA Technical Reports Server (NTRS)
Wu, M.-L. C.
1986-01-01
Techniques are presented and their application illustrated for analysis of remotely sensed data collected with an aircraft carrying a multispectral cloud radiometer and an advanced microwave moisture sounder. The instruments were used on NASA high altitude flights to perform cloud field experiments. Sample IR and microwave brightness temperature data are provided as functions of the ice water path and of the ice water content. Quantitative models are described for deriving the cloud ice (or liquid) water content and the cloud geometric thickness from the radiometric data.
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.
The Genre of Technical Description.
ERIC Educational Resources Information Center
Jordan, Michael P.
1986-01-01
Summarizes recent research into systems of lexical and grammatical cohesion in technical description. Discusses various methods by which technical writers "re-enter" the topic of description back into the text in successive sentences. (HTH)
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…
MCO Monitoring activity description
SEXTON, R.A.
1998-11-09
Spent Nuclear Fuel remaining from Hanford's N-Reactor operations in the 1970s has been stored under water in the K-Reactor Basins. This fuel will be repackaged, dried and stored in a new facility in the 200E Area. The safety basis for this process of retrieval, drying, and interim storage of the spent fuel has been established. The monitoring of MCOS in dry storage is a currently identified issue in the SNF Project. This plan outlines the key elements of the proposed monitoring activity. Other fuel stored in the K-Reactor Basins, including SPR fuel, will have other monitoring considerations and is not addressed by this activity description.
Geometrical analysis of the LiCN vibrational dynamics: a stability geometrical indicator.
Vergel, A; Benito, R M; Losada, J C; Borondo, F
2014-02-01
The vibrational dynamics of the LiNC/LiCN molecular system is examined making use of the Riemannian geometry. Stability and chaoticity are analyzed, in this context, by means of the Jacobi-Levi-Civita equations, derived from the Jacobi metric, and its solutions. A dynamical indicator, called stability geometrical indicator, is introduced in order to ascertain the dynamical characteristics of stability and chaos in the molecule under study.
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.
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,…
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.
Efficient Geometric Sound Propagation Using Visibility Culling
NASA Astrophysics Data System (ADS)
Chandak, Anish
2011-07-01
Simulating propagation of sound can improve the sense of realism in interactive applications such as video games and can lead to better designs in engineering applications such as architectural acoustics. In this thesis, we present geometric sound propagation techniques which are faster than prior methods and map well to upcoming parallel multi-core CPUs. We model specular reflections by using the image-source method and model finite-edge diffraction by using the well-known Biot-Tolstoy-Medwin (BTM) model. We accelerate the computation of specular reflections by applying novel visibility algorithms, FastV and AD-Frustum, which compute visibility from a point. We accelerate finite-edge diffraction modeling by applying a novel visibility algorithm which computes visibility from a region. Our visibility algorithms are based on frustum tracing and exploit recent advances in fast ray-hierarchy intersections, data-parallel computations, and scalable, multi-core algorithms. The AD-Frustum algorithm adapts its computation to the scene complexity and allows small errors in computing specular reflection paths for higher computational efficiency. FastV and our visibility algorithm from a region are general, object-space, conservative visibility algorithms that together significantly reduce the number of image sources compared to other techniques while preserving the same accuracy. Our geometric propagation algorithms are an order of magnitude faster than prior approaches for modeling specular reflections and two to ten times faster for modeling finite-edge diffraction. Our algorithms are interactive, scale almost linearly on multi-core CPUs, and can handle large, complex, and dynamic scenes. We also compare the accuracy of our sound propagation algorithms with other methods. Once sound propagation is performed, it is desirable to listen to the propagated sound in interactive and engineering applications. We can generate smooth, artifact-free output audio signals by applying
Geometrical Constraints on Dark Energy Models
NASA Astrophysics Data System (ADS)
Lazkoz, Ruth
2007-11-01
This contribution intends to give a pedagogical introduction to the topic of dark energy (the mysterious agent supposed to drive the observed late time acceleration of the Universe) and to various observational tests which require only assumptions on the geometry of the Universe. Those tests are the supernovae luminosity, the CMB shift, the direct Hubble data, and the baryon acoustic oscillations test. An historical overview of Cosmology is followed by some generalities on FRW spacetimes (the best large-scale description of the Universe), and then the test themselves are discussed. A convenient section on statistical inference is included as well.
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
Geometric strategies for neuroanatomic analysis from MRI
Duncan, James S.; Papademetris, Xenophon; Yang, Jing; Jackowski, Marcel; Zeng, Xiaolan; Staib, Lawrence H.
2010-01-01
In this paper, we describe ongoing work in the Image Processing and Analysis Group (IPAG) at Yale University specifically aimed at the analysis of structural information as represented within magnetic resonance images (MRI) of the human brain. Specifically, we will describe our applied mathematical approaches to the segmentation of cortical and subcortical structure, the analysis of white matter fiber tracks using diffusion tensor imaging (DTI), and the intersubject registration of neuroanatomical (aMRI) data sets. Many of our methods rally around the use of geometric constraints, statistical (MAP) estimation, and the use of level set evolution strategies. The analysis of gray matter structure and connecting white matter paths combined with the ability to bring all information into a common space via intersubject registration should provide us with a rich set of data to investigate structure and variation in the human brain in neuropsychiatric disorders, as well as provide a basis for current work in the development of integrated brain function–structure analysis. PMID:15501099
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.
On pool spreading around tanks: geometrical considerations.
Brambilla, Sara; Manca, Davide
2008-10-01
The paper discusses a straightforward approach for evaluating the distance covered by a spreading liquid pool, when the axisymmetric hypothesis is no longer valid. This distance is evaluated by a three-steps methodology: the pre-processing of input data (bund radius, if present, and radial velocity); the simulation of pool spreading by a model based on the axisymmetric hypothesis; and the post-processing of results. The paper reports some geometrical correlations to pre- and post-process the data, with regard to four case-studies. Some numerical examples are also presented to prove that the pre-processed input data and post-processed results differ from those based on the axisymmetric hypothesis. Finally, we validate our modeling approach with the experimental data of Cronin and Evans [P.S. Cronin, J.A. Evans, A series of experiments to study the spreading of liquid pools with different bund arrangements, HSE Contract Research Report 405/2002, Advantica Technologies Limited, 2002].
Geometric Model of a Coronal Cavity
NASA Technical Reports Server (NTRS)
Kucera, Therese A.; Gibson, S. E.; Ratawicki, D.; Dove, J.; deToma, G.; Hao, J.; Hudson, H. S.; Marque, C.; McIntosh, P. S.; Reeves, K. K.; Schmidt, D. J.; Sterling, A. C.; Tripathi, D. K.; Williams, D. R.; Zhang, M.
2010-01-01
We observed a coronal cavity from August 8-18 2007 during a multi-instrument observing campaign organized under the auspices of the International Heliophysical Year (IHY). Here we present initial efforts to model the cavity with a geometrical streamer-cavity model. The model is based the white-light streamer mode] of Gibson et a]. (2003 ), which has been enhanced by the addition of a cavity and the capability to model EUV and X-ray emission. The cavity is modeled with an elliptical cross-section and Gaussian fall-off in length and width inside the streamer. Density and temperature can be varied in the streamer and cavity and constrained via comparison with data. Although this model is purely morphological, it allows for three-dimensional, multi-temperature analysis and characterization of the data, which can then provide constraints for future physical modeling. Initial comparisons to STEREO/EUVI images of the cavity and streamer show that the model can provide a good fit to the data. This work is part of the effort of the International Space Science Institute International Team on Prominence Cavities
Effect of geometrical frustration on inverse freezing
NASA Astrophysics Data System (ADS)
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 (J1) and second-neighbor (J2) 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 J1/J in two cases: the absence of J2 interaction and the isotropic limit J2=J1 , where GF takes place. An IF reentrant transition from the spin-glass (SG) to paramagnetic (PM) phase is found for a certain range of J1/J in both cases. The J1 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.
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 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.
Generalized Bergman kernels and geometric quantization
NASA Astrophysics Data System (ADS)
Tuynman, G. M.
1987-03-01
In geometric quantization it is well known that, if f is an observable and F a polarization on a symplectic manifold (M,ω), then the condition ``Xf leaves F invariant'' (where Xf denotes the Hamiltonian vector field associated to f ) is sufficient to guarantee that one does not have to compute the BKS kernel explicitly in order to know the corresponding quantum operator. It is shown in this paper that this condition on f can be weakened to ``Xf leaves F+F° invariant''and the corresponding quantum operator is then given implicitly by formula (4.8); in particular when F is a (positive) Kähler polarization, all observables can be quantized ``directly'' and moreover, an ``explicit'' formula for the corresponding quantum operator is derived (Theorem 5.8). Applying this to the phase space R2n one obtains a quantization prescription which ressembles the normal ordering of operators in quantum field theory. When we translate this prescription to the usual position representation of quantum mechanics, the result is (a.o) that the operator associated to a classical potential is multiplication by a function which is essentially the convolution of the potential function with a Gaussian function of width ℏ, instead of multiplication by the potential itself.
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.
Geometric median for missing rainfall data imputation
NASA Astrophysics Data System (ADS)
Burhanuddin, Siti Nur Zahrah Amin; Deni, Sayang Mohd; Ramli, Norazan Mohamed
2015-02-01
Missing data is a common problem faced by researchers in environmental studies. Environmental data, particularly, rainfall data are highly vulnerable to be missed, which is due to several reasons, such as malfunction instrument, incorrect measurements, and relocation of stations. Rainfall data are also affected by the presence of outliers due to the temporal and spatial variability of rainfall measurements. These problems may harm the quality of rainfall data and subsequently, produce inaccuracy in the results of analysis. Thus, this study is aimed to propose an imputation method that is robust towards the presence of outliers for treating the missing rainfall data. Geometric median was applied to estimate the missing values based on the available rainfall data from neighbouring stations. The method was compared with several conventional methods, such as normal ratio and inverse distance weighting methods, in order to evaluate its performance. Thirteen rainfall stations in Peninsular Malaysia were selected for the application of the imputation methods. The results indicated that the proposed method provided the most accurate estimation values compared to both conventional methods based on the least mean absolute error. The normal ratio was found to be the worst method in estimating the missing rainfall values.
Fold Lens Flux Anomalies: A Geometric Approach
NASA Astrophysics Data System (ADS)
Harris, Wendy B.; Chessey, M. K.; Goldberg, D. M.; Richards, G. T.
2010-01-01
Strong gravitational lensing of quasars is a powerful tool to learn about the distribution of dark matter in lensing galaxies. Multiply imaged quasar systems have symmetries which allow for an understanding of the lensing galaxy without detailed mass reconstructions. Keeton et al. (2005) defined a useful expression for the flux anomaly of "fold'' lenses, which we might naively expect to have the same flux: Rfold=(fA-fB)/(fA+fB), where "A'' and "B'' represent the positive and negative parity images straddling a critical curve. We show that the geometric configuration of the images greatly constrains the possible flux anomalies allowable from a smooth galaxy potential. Using gravlens, we create a number of simple galaxies from various mass models to put our solution to the test, and find that simulated flux anomalies are reproduced to an accuracy of |δ R| < 0.04. We then apply our approach to a radio sample of 9 well-studied fold lenses and quickly identify those with significant substructure.
Geometric conditions for violation of Bell's inequality
Mendas, Istok P.
2005-03-01
The geometric conditions for violation of Bell's inequality, in its original form dealing with a pair of spin one-half particles formed in the singlet spin state, are discussed. The parameters x{sub 1}, x{sub 2}, and x{sub 3} are introduced as the cosines of angles {theta}{sub ab}=angle(a,b), {theta}{sub ac}=angle(a,c), and {theta}{sub bc}=angle(b,c) between the unit vectors a, b, and c defining the orientation of the corresponding Stern-Gerlach magnets. A Monte Carlo experiment shows that in order to obtain violation, the three parameters must belong to a definite region in the parametric space that encompasses 1/3 of all possible triplets of unit vectors generated randomly from the isotropic distribution in the ordinary space. By introducing a measure of violation D{identical_to}|x{sub 1}-x{sub 2}|+x{sub 3}-1, it is found that 0{<=}D{<=}1/2 and that the maximal violation D=1/2 is obtained only in two isolated cases, when the relevant angles are {theta}{sub ab}=2{pi}/3, {theta}{sub ac}={theta}{sub bc}={pi}/3, or when {theta}{sub ab}={theta}{sub bc}={pi}/3, {theta}{sub ac}=2{pi}/3. In both cases the unit vectors a, b, and c are coplanar.
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
2016-08-08
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.
Geometrical features underlying the perception of collinearity.
Morgan, Michael; Dillenburger, Barbara
2016-11-01
The magnitude of the Poggendorff bias in perceived collinearity was measured with a 2AFC task and roving pedestal, and was found to be in the region of 6-8deg, within the range of previous estimates. Further measurements dissected the bias into several components: (1) The small (∼1deg) repulsion of the orientation of the pointer from the parallel, probably localized in the part of the line near the intersection (2) A small (<1deg) location bias affecting the intersection of pointers and inducing lines; and (3) A larger (>1deg) bias in the orientation of virtual lines crossing the gap between two parallels, towards the orientation of the parallels, or equivalently (4) An orthogonal bias in actively constructing a virtual line across the gap. We conclude that orientation repulsion by itself is an inadequate explanation of the Poggendorff effect, and that a full explanation must take account of the way in which observers construct virtual lines in visual space in order to carry out elementary geometrical tasks such as extrapolation.
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.
Geometric facial gender scoring: objectivity of perception.
Gilani, Syed Zulqarnain; Rooney, Kathleen; Shafait, Faisal; Walters, Mark; Mian, Ajmal
2014-01-01
Gender score is the cognitive judgement of the degree of masculinity or femininity of a face which is considered to be a continuum. Gender scores have long been used in psychological studies to understand the complex psychosocial relationships between people. Perceptual scores for gender and attractiveness have been employed for quality assessment and planning of cosmetic facial surgery. Various neurological disorders have been linked to the facial structure in general and the facial gender perception in particular. While, subjective gender scoring by human raters has been a tool of choice for psychological studies for many years, the process is both time and resource consuming. In this study, we investigate the geometric features used by the human cognitive system in perceiving the degree of masculinity/femininity of a 3D face. We then propose a mathematical model that can mimic the human gender perception. For our experiments, we obtained 3D face scans of 64 subjects using the 3dMDface scanner. The textureless 3D face scans of the subjects were then observed in different poses and assigned a gender score by 75 raters of a similar background. Our results suggest that the human cognitive system employs a combination of Euclidean and geodesic distances between biologically significant landmarks of the face for gender scoring. We propose a mathematical model that is able to automatically assign an objective gender score to a 3D face with a correlation of up to 0.895 with the human subjective scores.
Geometrical modeling of fibrous materials under compression
NASA Astrophysics Data System (ADS)
Maze, Benoit; Vahedi Tafreshi, Hooman; Pourdeyhimi, Behnam
2007-10-01
Many fibrous materials such as nonwovens are consolidated via compaction rolls in a so-called calendering process. Hot rolls compress the fiber assembly and cause fiber-to-fiber bonding resulting in a strong yet porous structure. In this paper, we describe an algorithm for generating three dimensional virtual fiberwebs and simulating the geometrical changes that happen to the structure during the calendering process. Fibers are assumed to be continuous filaments with square cross sections lying randomly in the x or y direction. The fibers are assumed to be flexible to allow bending over one another during the compression process. Lateral displacement is not allowed during the compaction process. The algorithm also does not allow the fibers to interpenetrate or elongate and so the mass of the fibers is conserved. Bending of the fibers is modeled either by considering a constant "slope of bending" or constant "span of bending." The influence of the bending parameters on the propagation of compression through the material's thickness is discussed. In agreement with our experimental observations, it was found that the average solid volume fraction profile across the thickness becomes U shaped after the calendering. The application of these virtual structures in studying transport phenomena in fibrous materials is also demonstrated.
Oscillating Filaments. I. Oscillation and Geometrical Fragmentation
NASA Astrophysics Data System (ADS)
Gritschneder, Matthias; Heigl, Stefan; Burkert, Andreas
2017-01-01
We study the stability of filaments in equilibrium between gravity and internal as well as external pressure using the grid-based AMR code RAMSES. A homogeneous, straight cylinder below a critical line mass is marginally stable. However, if the cylinder is bent, such as with a slight sinusoidal perturbation, an otherwise stable configuration starts to oscillate, is triggered into fragmentation, and collapses. This previously unstudied behavior allows a filament to fragment at any given scale, as long as it has slight bends. We call this process “geometrical fragmentation.” In our realization, the spacing between the cores matches the wavelength of the sinusoidal perturbation, whereas up to now, filaments were thought to be only fragmenting on the characteristic scale set by the mass-to-line ratio. Using first principles, we derive the oscillation period as well as the collapse timescale analytically. To enable a direct comparison with observations, we study the line-of-sight velocity for different inclinations. We show that the overall oscillation pattern can hide the infall signature of cores.
Floating-point geometry: toward guaranteed geometric computations with approximate arithmetics
NASA Astrophysics Data System (ADS)
Bajard, Jean-Claude; Langlois, Philippe; Michelucci, Dominique; Morin, Géraldine; Revol, Nathalie
2008-08-01
Geometric computations can fail because of inconsistencies due to floating-point inaccuracy. For instance, the computed intersection point between two curves does not lie on the curves: it is unavoidable when the intersection point coordinates are non rational, and thus not representable using floating-point arithmetic. A popular heuristic approach tests equalities and nullities up to a tolerance ɛ. But transitivity of equality is lost: we can have A approx B and B approx C, but A not approx C (where A approx B means ||A - B|| < ɛ for A,B two floating-point values). Interval arithmetic is another, self-validated, alternative; the difficulty is to limit the swell of the width of intervals with computations. Unfortunately interval arithmetic cannot decide equality nor nullity, even in cases where it is decidable by other means. A new approach, developed in this paper, consists in modifying the geometric problems and algorithms, to account for the undecidability of the equality test and unavoidable inaccuracy. In particular, all curves come with a non-zero thickness, so two curves (generically) cut in a region with non-zero area, an inner and outer representation of which is computable. This last approach no more assumes that an equality or nullity test is available. The question which arises is: which geometric problems can still be solved with this last approach, and which cannot? This paper begins with the description of some cases where every known arithmetic fails in practice. Then, for each arithmetic, some properties of the problems they can solve are given. We end this work by proposing the bases of a new approach which aims to fulfill the geometric computations requirements.
The geometric signature: Quantifying landslide-terrain types from digital elevation models
Pike, R.J.
1988-01-01
Topography of various types and scales can be fingerprinted by computer analysis of altitude matrices (digital elevation models, or DEMs). The critical analytic tool is the geometric signature, a set of measures that describes topographic form well enough to distinguish among geomorphically disparate landscapes. Different surficial processes create topography with diagnostic forms that are recognizable in the field. The geometric signature abstracts those forms from contour maps or their DEMs and expresses them numerically. This multivariate characterization enables once-in-tractable problems to be addressed. The measures that constitute a geometric signature express different but complementary attributes of topographic form. Most parameters used here are statistical estimates of central tendency and dispersion for five major categories of terrain geometry; altitude, altitude variance spectrum, slope between slope reversals, and slope and its curvature at fixed slope lengths. As an experimental application of geometric signatures, two mapped terrain types associated with different processes of shallow landsliding in Marin County, California, were distinguished consistently by a 17-variable description of topography from 21??21 DEMs (30-m grid spacing). The small matrix is a statistical window that can be used to scan large DEMs by computer, thus potentially automating the mapping of contrasting terrain types. The two types in Marin County host either (1) slow slides: earth flows and slump-earth flows, or (2) rapid flows: debris avalanches and debris flows. The signature approach should adapt to terrain taxonomy and mapping in other areas, where conditions differ from those in Central California. ?? 1988 International Association for Mathematical Geology.
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.
Establishment of Imaging Spectroscopy of Nuclear Gamma-Rays based on Geometrical Optics.
Tanimori, Toru; Mizumura, Yoshitaka; Takada, Atsushi; Miyamoto, Shohei; Takemura, Taito; Kishimoto, Tetsuro; Komura, Shotaro; Kubo, Hidetoshi; Kurosawa, Shunsuke; Matsuoka, Yoshihiro; Miuchi, Kentaro; Mizumoto, Tetsuya; Nakamasu, Yuma; Nakamura, Kiseki; Parker, Joseph D; Sawano, Tatsuya; Sonoda, Shinya; Tomono, Dai; Yoshikawa, Kei
2017-02-03
Since the discovery of nuclear gamma-rays, its imaging has been limited to pseudo imaging, such as Compton Camera (CC) and coded mask. Pseudo imaging does not keep physical information (intensity, or brightness in Optics) along a ray, and thus is capable of no more than qualitative imaging of bright objects. To attain quantitative imaging, cameras that realize geometrical optics is essential, which would be, for nuclear MeV gammas, only possible via complete reconstruction of the Compton process. Recently we have revealed that "Electron Tracking Compton Camera" (ETCC) provides a well-defined Point Spread Function (PSF). The information of an incoming gamma is kept along a ray with the PSF and that is equivalent to geometrical optics. Here we present an imaging-spectroscopic measurement with the ETCC. Our results highlight the intrinsic difficulty with CCs in performing accurate imaging, and show that the ETCC surmounts this problem. The imaging capability also helps the ETCC suppress the noise level dramatically by ~3 orders of magnitude without a shielding structure. Furthermore, full reconstruction of Compton process with the ETCC provides spectra free of Compton edges. These results mark the first proper imaging of nuclear gammas based on the genuine geometrical optics.
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.
Establishment of Imaging Spectroscopy of Nuclear Gamma-Rays based on Geometrical Optics
NASA Astrophysics Data System (ADS)
Tanimori, Toru; Mizumura, Yoshitaka; Takada, Atsushi; Miyamoto, Shohei; Takemura, Taito; Kishimoto, Tetsuro; Komura, Shotaro; Kubo, Hidetoshi; Kurosawa, Shunsuke; Matsuoka, Yoshihiro; Miuchi, Kentaro; Mizumoto, Tetsuya; Nakamasu, Yuma; Nakamura, Kiseki; Parker, Joseph D.; Sawano, Tatsuya; Sonoda, Shinya; Tomono, Dai; Yoshikawa, Kei
2017-02-01
Since the discovery of nuclear gamma-rays, its imaging has been limited to pseudo imaging, such as Compton Camera (CC) and coded mask. Pseudo imaging does not keep physical information (intensity, or brightness in Optics) along a ray, and thus is capable of no more than qualitative imaging of bright objects. To attain quantitative imaging, cameras that realize geometrical optics is essential, which would be, for nuclear MeV gammas, only possible via complete reconstruction of the Compton process. Recently we have revealed that “Electron Tracking Compton Camera” (ETCC) provides a well-defined Point Spread Function (PSF). The information of an incoming gamma is kept along a ray with the PSF and that is equivalent to geometrical optics. Here we present an imaging-spectroscopic measurement with the ETCC. Our results highlight the intrinsic difficulty with CCs in performing accurate imaging, and show that the ETCC surmounts this problem. The imaging capability also helps the ETCC suppress the noise level dramatically by ~3 orders of magnitude without a shielding structure. Furthermore, full reconstruction of Compton process with the ETCC provides spectra free of Compton edges. These results mark the first proper imaging of nuclear gammas based on the genuine geometrical optics.
Establishment of Imaging Spectroscopy of Nuclear Gamma-Rays based on Geometrical Optics
Tanimori, Toru; Mizumura, Yoshitaka; Takada, Atsushi; Miyamoto, Shohei; Takemura, Taito; Kishimoto, Tetsuro; Komura, Shotaro; Kubo, Hidetoshi; Kurosawa, Shunsuke; Matsuoka, Yoshihiro; Miuchi, Kentaro; Mizumoto, Tetsuya; Nakamasu, Yuma; Nakamura, Kiseki; Parker, Joseph D.; Sawano, Tatsuya; Sonoda, Shinya; Tomono, Dai; Yoshikawa, Kei
2017-01-01
Since the discovery of nuclear gamma-rays, its imaging has been limited to pseudo imaging, such as Compton Camera (CC) and coded mask. Pseudo imaging does not keep physical information (intensity, or brightness in Optics) along a ray, and thus is capable of no more than qualitative imaging of bright objects. To attain quantitative imaging, cameras that realize geometrical optics is essential, which would be, for nuclear MeV gammas, only possible via complete reconstruction of the Compton process. Recently we have revealed that “Electron Tracking Compton Camera” (ETCC) provides a well-defined Point Spread Function (PSF). The information of an incoming gamma is kept along a ray with the PSF and that is equivalent to geometrical optics. Here we present an imaging-spectroscopic measurement with the ETCC. Our results highlight the intrinsic difficulty with CCs in performing accurate imaging, and show that the ETCC surmounts this problem. The imaging capability also helps the ETCC suppress the noise level dramatically by ~3 orders of magnitude without a shielding structure. Furthermore, full reconstruction of Compton process with the ETCC provides spectra free of Compton edges. These results mark the first proper imaging of nuclear gammas based on the genuine geometrical optics. PMID:28155870
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.
Auperrin, Audrey; Delille, Rémi; Lesueur, Denis; Bruyère, Karine; Masson, Catherine; Drazétic, Pascal
2014-03-21
The present study aims at providing quantitative data for the personalisation of geometrical and mechanical characteristics of the adult cranial bone to be applied to head FE models. A set of 351 cranial bone samples, harvested from 21 human skulls, were submitted to three-point bending tests at 10 mm/min. For each of them, an apparent elastic modulus was calculated using the beam's theory and a density-dependant beam inertia. Thicknesses, apparent densities and percentage of ash weight were also measured. Distributions of characteristics among the different skull bones show their symmetry and their significant differences between skull areas. A data analysis was performed to analyse potential relationship between thicknesses, densities and the apparent elastic modulus. A specific regression was pointed out to estimate apparent elastic modulus from the product of thickness by apparent density. These results offer quantitative tools in view of personalising head FE models and thus improve definition of local injury criteria for this body part.
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.
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…
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…
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.
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…
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…
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.
Developing a Network of and for Geometric Reasoning
ERIC Educational Resources Information Center
Mamolo, Ami; Ruttenberg-Rozen, Robyn; Whiteley, Walter
2015-01-01
In this article, we develop a theoretical model for restructuring mathematical tasks, usually considered advanced, with a network of spatial visual representations designed to support geometric reasoning for learners of disparate ages, stages, strengths, and preparation. Through our geometric reworking of the well-known "open box…
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…
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…
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)
Survival benefits in mimicry: a quantitative framework.
Mikaberidze, Alexey; Haque, Masudul
2009-08-07
Mimicry is a resemblance between species that benefits at least one of the species. It is a ubiquitous evolutionary phenomenon particularly common among prey species, in which case the advantage involves better protection from predation. We formulate a mathematical description of predation, to investigate benefits and disadvantages of mimicry. The basic setup involves differential equations for quantities representing predator behavior, namely, the probabilities for attacking prey at the next encounter. Using this framework, we present new quantitative results, and also provide a unified description of a significant fraction of the quantitative mimicry literature. The new results include "temporary" mutualism between prey species, and an optimal density at which the survival benefit is greatest for the mimic. The formalism leads naturally to extensions in several directions, such as the interplay of mimicry with population dynamics, studies of spatiotemporal patterns, etc. We demonstrate this extensibility by presenting some explorations on spatiotemporal pattern dynamics.
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 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.
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 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.
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.
Older Adults’ Pain Descriptions
McDonald, Deborah Dillon
2008-01-01
The purpose of this study was to describe the types of pain information described by older adults with chronic osteoarthritis pain. Pain descriptions were obtained from older adults’ who participated in a posttest only double blind study testing how the phrasing of healthcare practitioners’ pain questions affected the amount of communicated pain information. The 207 community dwelling older adults were randomized to respond to either the open-ended or closed-ended pain question. They viewed and orally responded to a computer displayed videotape of a practitioner asking them the respective pain question. All then viewed and responded to the general follow up question, ““What else can you tell me?” and lastly, “What else can you tell me about your pain, aches, soreness or discomfort?” Audio-taped responses were transcribed and content analyzed by trained, independent raters using 16 a priori criteria from the American Pain Society (2002) Guidelines for the Management of Pain in Osteoarthritis, Rheumatoid Arthritis, and Juvenile Chronic Arthritis. Older adults described important but limited types of information primarily about pain location, timing, and intensity. Pain treatment information was elicited after repeated questioning. Therefore, practitioners need to follow up older adults’ initial pain descriptions with pain questions that promote a more complete pain management discussion. Routine use of a multidimensional pain assessment instrument that measures information such as functional interference, current pain treatments, treatment effects, and side effects would be one way of insuring a more complete pain management discussion with older adults. PMID:19706351
Quantitative analysis to guide orphan drug development.
Lesko, L J
2012-08-01
The development of orphan drugs for rare diseases has made impressive strides in the past 10 years. There has been a surge in orphan drug designations, but new drug approvals have not kept up. This article presents a three-pronged hierarchical strategy for quantitative analysis of data at the descriptive, mechanistic, and systems levels of the biological system that could represent a standardized and rational approach to orphan drug development. Examples are provided to illustrate the concept.
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.
Geometrical and FEA study on Millipede Forming
NASA Astrophysics Data System (ADS)
Kong, Lingran; Tang, Di; Ding, Shichao; Zhang, Yuankun
2013-12-01
Millipede Forming is an innovative sheet metal forming approach that has been proposed and developed in Australia. U-channels, Z-channels or tubular products can be made by Millipede Forming. While a strip moves through an optimal transitional surface between the entry to exit of a forming stand, the redundant longitudinal membrane strain can be significantly reduced compared to the conventional roll forming, which is the essential principle to obtaining high quality products. The incremental forming process studied has demonstrated major advantages on space efficiency, power consumption and materials sensitivities. The purpose of this study is to investigate the effects of main geometrical parameters and their optimization, in order to minimize the redundant longitudinal strains into elastic to avoid the redundant plastic deformations at flange during forming. In this study, a mild-steel U-channel sample with 10 mm flange width, fabricated by Millipede Forming in a forming length of 200 mm has been studied. Theoretical longitudinal membrane strains at profile's edge of different transitional surfaces and downhill pass are also analyzed. The results showed that obtaining an optimal transitional surface is essential and necessary in controlling the peak longitudinal strain to an acceptable amount and that by increasing downhill pass, longitudinal strain can be significantly reduced. The optimized transitional surface and downhill pass flow were simulated by Abaqus, and the peak longitudinal strain was finally less than 0.2% through a very short forming length of 200 mm. The results prove that Millipede Forming can achieve a better product quality in a much shorter forming distance than conventional roll forming.
Geometric view of adaptive optics control
NASA Astrophysics Data System (ADS)
Wiberg, Donald M.; Max, Claire E.; Gavel, Donald T.
2005-05-01
The objective of an astronomical adaptive optics control system is to minimize the residual wave-front error remaining on the science-object wave fronts after being compensated for atmospheric turbulence and telescope aberrations. Minimizing the mean square wave-front residual maximizes the Strehl ratio and the encircled energy in pointlike images and maximizes the contrast and resolution of extended images. We prove the separation principle of optimal control for application to adaptive optics so as to minimize the mean square wave-front residual. This shows that the residual wave-front error attributable to the control system can be decomposed into three independent terms that can be treated separately in design. The first term depends on the geometry of the wave-front sensor(s), the second term depends on the geometry of the deformable mirror(s), and the third term is a stochastic term that depends on the signal-to-noise ratio. The geometric view comes from understanding that the underlying quantity of interest, the wave-front phase surface, is really an infinite-dimensional vector within a Hilbert space and that this vector space is projected into subspaces we can control and measure by the deformable mirrors and wave-front sensors, respectively. When the control and estimation algorithms are optimal, the residual wave front is in a subspace that is the union of subspaces orthogonal to both of these projections. The method is general in that it applies both to conventional (on-axis, ground-layer conjugate) adaptive optics architectures and to more complicated multi-guide-star- and multiconjugate-layer architectures envisaged for future giant telescopes. We illustrate the approach by using a simple example that has been worked out previously [J. Opt. Soc. Am. A73, 1171 (1983)] for a single-conjugate, static atmosphere case and follow up with a discussion of how it is extendable to general adaptive optics architectures.
Geometrically consistent approach to stochastic DBI inflation
Lorenz, Larissa; Martin, Jerome; Yokoyama, Jun'ichi
2010-07-15
Stochastic effects during inflation can be addressed by averaging the quantum inflaton field over Hubble-patch-sized domains. The averaged field then obeys a Langevin-type equation into which short-scale fluctuations enter as a noise term. We solve the Langevin equation for an inflaton field with a Dirac-Born-Infeld (DBI) kinetic term perturbatively in the noise and use the result to determine the field value's probability density function (PDF). In this calculation, both the shape of the potential and the warp factor are arbitrary functions, and the PDF is obtained with and without volume effects due to the finite size of the averaging domain. DBI kinetic terms typically arise in string-inspired inflationary scenarios in which the scalar field is associated with some distance within the (compact) extra dimensions. The inflaton's accessible range of field values therefore is limited because of the extra dimensions' finite size. We argue that in a consistent stochastic approach the inflaton's PDF must vanish for geometrically forbidden field values. We propose to implement these extra-dimensional spatial restrictions into the PDF by installing absorbing (or reflecting) walls at the respective boundaries in field space. As a toy model, we consider a DBI inflaton between two absorbing walls and use the method of images to determine its most general PDF. The resulting PDF is studied in detail for the example of a quartic warp factor and a chaotic inflaton potential. The presence of the walls is shown to affect the inflaton trajectory for a given set of parameters.
Laurette, I; Zeng, G L; Welch, A; Christian, P E; Gullberg, G T
2000-11-01
The qualitative and quantitative accuracy of SPECT images is degraded by physical factors of attenuation, Compton scatter and spatially varying collimator geometric response. This paper presents a 3D ray-tracing technique for modelling attenuation, scatter and geometric response for SPECT imaging in an inhomogeneous attenuating medium. The model is incorporated into a three-dimensional projector-backprojector and used with the maximum-likelihood expectation-maximization algorithm for reconstruction of parallel-beam data. A transmission map is used to define the inhomogeneous attenuating and scattering object being imaged. The attenuation map defines the probability of photon attenuation between the source and the scattering site, the scattering angle at the scattering site and the probability of attenuation of the scattered photon between the scattering site and the detector. The probability of a photon being scattered through a given angle and being detected in the emission energy window is approximated using a Gaussian function. The parameters of this Gaussian function are determined using physical measurements of parallel-beam scatter line spread functions from a non-uniformly attenuating phantom. The 3D ray-tracing scatter projector-backprojector produces the scatter and primary components. Then, a 3D ray-tracing projector-backprojector is used to model the geometric response of the collimator. From Monte Carlo and physical phantom experiments, it is shown that the best results are obtained by simultaneously correcting attenuation, scatter and geometric response, compared with results obtained with only one or two of the three corrections. It is also shown that a 3D scatter model is more accurate than a 2D model. A transmission map is useful for obtaining measurements of attenuation and scatter in SPECT data, which can be used together with a model of the geometric response of the collimator to obtain corrected images with quantitative and diagnostically
Ultrasonic geometrical characterization of periodically corrugated surfaces.
Liu, Jingfei; Declercq, Nico F
2013-04-01
Accurate characterization of the characteristic dimensions of a periodically corrugated surface using ultrasonic imaging technique is investigated both theoretically and experimentally. The possibility of accurately characterizing the characteristic dimensions is discussed. The condition for accurate characterization and the quantitative relationship between the accuracy and its determining parameters are given. The strategies to avoid diffraction effects instigated by the periodical nature of a corrugated surface are also discussed. Major causes of erroneous measurements are theoretically discussed and experimentally illustrated. A comparison is made between the presented results and the optical measurements, revealing acceptable agreement. This work realistically exposes the capability of the proposed ultrasonic technique to accurately characterize the lateral and vertical characteristic dimensions of corrugated surfaces. Both the general principles developed theoretically as well as the proposed practical techniques may serve as useful guidelines to peers.
Microgravity Environment Description Handbook
NASA Technical Reports Server (NTRS)
DeLombard, Richard; McPherson, Kevin; Hrovat, Kenneth; Moskowitz, Milton; Rogers, Melissa J. B.; Reckart, Timothy
1997-01-01
The Microgravity Measurement and Analysis Project (MMAP) at the NASA Lewis Research Center (LeRC) manages the Space Acceleration Measurement System (SAMS) and the Orbital Acceleration Research Experiment (OARE) instruments to measure the microgravity environment on orbiting space laboratories. These laboratories include the Spacelab payloads on the shuttle, the SPACEHAB module on the shuttle, the middeck area of the shuttle, and Russia's Mir space station. Experiments are performed in these laboratories to investigate scientific principles in the near-absence of gravity. The microgravity environment desired for most experiments would have zero acceleration across all frequency bands or a true weightless condition. This is not possible due to the nature of spaceflight where there are numerous factors which introduce accelerations to the environment. This handbook presents an overview of the major microgravity environment disturbances of these laboratories. These disturbances are characterized by their source (where known), their magnitude, frequency and duration, and their effect on the microgravity environment. Each disturbance is characterized on a single page for ease in understanding the effect of a particular disturbance. The handbook also contains a brief description of each laboratory.
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.
Capability of geometric features to classify ships in SAR imagery
NASA Astrophysics Data System (ADS)
Lang, Haitao; Wu, Siwen; Lai, Quan; Ma, Li
2016-10-01
Ship classification in synthetic aperture radar (SAR) imagery has become a new hotspot in remote sensing community for its valuable potential in many maritime applications. Several kinds of ship features, such as geometric features, polarimetric features, and scattering features have been widely applied on ship classification tasks. Compared with polarimetric features and scattering features, which are subject to SAR parameters (e.g., sensor type, incidence angle, polarization, etc.) and environment factors (e.g., sea state, wind, wave, current, etc.), geometric features are relatively independent of SAR and environment factors, and easy to be extracted stably from SAR imagery. In this paper, the capability of geometric features to classify ships in SAR imagery with various resolution has been investigated. Firstly, the relationship between the geometric feature extraction accuracy and the SAR imagery resolution is analyzed. It shows that the minimum bounding rectangle (MBR) of ship can be extracted exactly in terms of absolute precision by the proposed automatic ship-sea segmentation method. Next, six simple but effective geometric features are extracted to build a ship representation for the subsequent classification task. These six geometric features are composed of length (f1), width (f2), area (f3), perimeter (f4), elongatedness (f5) and compactness (f6). Among them, two basic features, length (f1) and width (f2), are directly extracted based on the MBR of ship, the other four are derived from those two basic features. The capability of the utilized geometric features to classify ships are validated on two data set with different image resolutions. The results show that the performance of ship classification solely by geometric features is close to that obtained by the state-of-the-art methods, which obtained by a combination of multiple kinds of features, including scattering features and geometric features after a complex feature selection process.
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
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
Geometric Perturbation Theory and Plasma Physics
NASA Astrophysics Data System (ADS)
Omohundro, Stephen Malvern
1985-12-01
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 ad hoc 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. 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
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.
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.
Geometric measure of quantum discord with weak measurements
NASA Astrophysics Data System (ADS)
Li, Lei; Wang, Qing-Wen; Shen, Shu-Qian; Li, Ming
2016-01-01
Super quantum discord based on weak measurements was introduced by Singh and Pati (Ann Phys 343:141-152, 2014). We propose a geometric way of quantifying quantum discord with weak measurements. It is shown that this geometric measure of quantum discord with weak measurements (GQDW) is linearly dependent on geometric measure of quantum discord (Dakic et al. in Phys Rev Lett 105:190502, 2010) and only captures partial quantumness of the states. It is found that the quantum correlation can be extracted by a sequence of infinitesimal weak measurements. Finally, the level surfaces of GQDW for Bell-diagonal states are depicted and the results are demonstrated by explicit example.
Witnessed entanglement and the geometric measure of quantum discord
NASA Astrophysics Data System (ADS)
Debarba, Tiago; Maciel, Thiago O.; Vianna, Reinaldo O.
2012-08-01
We establish relations between geometric quantum discord and entanglement quantifiers obtained by means of optimal witness operators. In particular, we prove a relation between negativity and geometric discord in the Hilbert-Schmidt norm, which has been conjectured before [D. Girolami and G. Adesso, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.84.052110 84, 052110 (2011)]. We also show that, redefining the geometric discord with the trace norm, better bounds can be obtained. We illustrate our results numerically for Werner states and for families of bound entangled states.
Calculus students' ability to solve geometric related-rates problems
NASA Astrophysics Data System (ADS)
Martin, Tami
2000-09-01
This study assessed the ability of university students enrolled in an introductory calculus course to solve related-rates problems set in geometric contexts. Students completed a problem-solving test and a test of performance on the individual steps involved in solving such problems. Each step was characterised as primarily relying on procedural knowledge or conceptual understanding. Results indicated that overall performance on the geometric related-rates problems was poor. The poorest performance was on steps linked to conceptual understanding, specifically steps involving the translation of prose to geometric and symbolic representations. Overall performance was most strongly related to performance on the procedural steps.
Measurement of geometric dephasing using a superconducting qubit
Berger, S.; Pechal, M.; Kurpiers, P.; Abdumalikov, A. A.; Eichler, C.; Mlynek, J. A.; Shnirman, A.; Gefen, Yuval; Wallraff, A.; Filipp, S.
2015-01-01
A quantum system interacting with its environment is subject to dephasing, which ultimately destroys the information it holds. Here we use a superconducting qubit to experimentally show that this dephasing has both dynamic and geometric origins. It is found that geometric dephasing, which is present even in the adiabatic limit and when no geometric phase is acquired, can either reduce or restore coherence depending on the orientation of the path the qubit traces out in its projective Hilbert space. It accompanies the evolution of any system in Hilbert space subjected to noise. PMID:26515812
Trusting Description: Authenticity, Accountability, and Archival Description Standards
ERIC Educational Resources Information Center
MacNeil, Heather
2009-01-01
It has been suggested that one of the purposes of archival description is to establish grounds for presuming the authenticity of the records being described. The article examines the implications of this statement by examining the relationship between and among authenticity, archival description, and archival accountability, assessing how this…
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
Determination of tire cross-sectional geometric characteristics from a digitally scanned image
NASA Technical Reports Server (NTRS)
Danielson, Kent T.
1995-01-01
A semi-automated procedure is described for the accurate determination of geometrical characteristics using a scanned image of the tire cross-section. The procedure can be useful for cases when CAD drawings are not available or when a description of the actual cured tire is desired. Curves representing the perimeter of the tire cross-section are determined by an edge tracing scheme, and the plyline and cord-end positions are determined by locations of color intensities. The procedure provides an accurate description of the perimeter of the tire cross-section and the locations of plylines and cord-ends. The position, normals, and curvatures of the cross-sectional surface are included in this description. The locations of the plylines provide the necessary information for determining the ply thicknesses and relative position to a reference surface. Finally, the locations of the cord-ends provide a means to calculate the cord-ends per inch (epi). Menu driven software has been developed to facilitate the procedure using the commercial code, PV-Wave by Visual Numerics, Inc., to display the images. From a single user interface, separate modules are executed for image enhancement, curve fitting the edge trace of the cross-sectional perimeter, and determining the plyline and cord-end locations. The code can run on SUN or SGI workstations and requires the use of a mouse to specify options or identify items on the scanned image.
A microscopic description of black hole evaporation via holography
NASA Astrophysics Data System (ADS)
Berkowitz, Evan; Hanada, Masanori; Maltz, Jonathan
2016-07-01
We propose a description of how a large, cold black hole (black zero-brane) in type IIA superstring theory evaporates into freely propagating D0-branes, by solving the dual gauge theory quantitatively. The energy spectrum of emitted D0-branes is parametrically close to thermal when the black hole is large. The black hole, while initially cold, gradually becomes an extremely hot and stringy object as it evaporates. As it emits D0-branes, its emission rate speeds up and it evaporates completely without leaving any remnant. Hence this system provides us with a concrete holographic description of black hole evaporation without information loss.
NPP VIIRS Early On-Orbit Geometric Performance
NASA Technical Reports Server (NTRS)
Wolfe, Robert E.; Lin, Guoqing; Nishihama, Masahiro; Tewari, Krishna; Montano, Enrique
2012-01-01
The NASA/NOAA Visible Infrared Imager Radiometer Suite (VIIRS) instrument on-board the Suomi National Polar-orbiting Partnership (NPP) satellite was launched in October, 2011. The instrument geometric performance includes sensor spatial response, band-to-band co-registration (BBR), and geolocation accuracy and precision. The geometric performance is an important aspect of sensor data record (SDR) calibration and validation. In this paper we will discuss geometric performance parameter characterization using the first seven-month of VIIRS' earth and lunar data, and compare with the at-launch performance using ground testing data and analysis of numerical modeling results as the first step in on-orbit geometric calibration and validation.
Shield support selection based on geometric characteristics of coal seam
K. Goshtasbi; K. Oraee; F. Khakpour-yeganeh
2006-01-15
The most initial investment in longwall face equipping is the cost of powered support. Selection of proper shields for powered supports is based on load, geometric characterization of coal seams and economical considerations.
RESEARCH PAPERS : The reciprocity properties of geometrical spreading
NASA Astrophysics Data System (ADS)
Snieder, Roel; Chapman, Chris
1998-01-01
Reciprocity is an important property of acoustic and elastic waves. In this work it is explicity verified that acoustic waves also satisfy the reciprocity theorem in a ray-geometric approximation. This is achieved by deriving a reciprocity relation for the geometric spreading. The analysis is based on integrating the equations of dynamic ray tracing from the source to a receiver and in the reverse direction. It is shown that for a point source the geometric spreading for rays travelling in opposite directions differs by a factor depending on the velocities at the endpoints of the ray. This factor depends on the number of dimensions that one considers. Since the equations of kinematic and dynamic ray tracing are the same for elastic waves and acoustic waves, the derived reciprocity relations for the geometrical spreading hold for elastic waves as well. The results obtained are used to correct some errors in the derivation of an averaging theorem by Snieder & Lomax (1996).
Geometric phases in neutrino oscillations with nonlinear refraction
NASA Astrophysics Data System (ADS)
Johns, Lucas; Fuller, George M.
2017-02-01
Neutrinos propagating in dense astrophysical environments sustain nonlinear refractive effects due to neutrino-neutrino forward scattering. We study geometric phases in neutrino oscillations that arise out of cyclic evolution of the potential generated by these forward-scattering processes. We perform several calculations, exact and perturbative, that illustrate the robustness of such phases, and of geometric effects more broadly, in the flavor evolution of neutrinos. The scenarios we consider are highly idealized in order to make them analytically tractable, but they suggest the possible presence of complicated geometric effects in realistic astrophysical settings. We also point out that in the limit of extremely high neutrino densities, the nonlinear potential in three flavors naturally gives rise to non-Abelian geometric phases. This paper is intended to be accessible to neutrino experts and nonspecialists alike.
Geometric analysis and restitution of digital multispectral scanner data arrays
NASA Technical Reports Server (NTRS)
Baker, J. R.; Mikhail, E. M.
1975-01-01
An investigation was conducted to define causes of geometric defects within digital multispectral scanner (MSS) data arrays, to analyze the resulting geometric errors, and to investigate restitution methods to correct or reduce these errors. Geometric transformation relationships for scanned data, from which collinearity equations may be derived, served as the basis of parametric methods of analysis and restitution of MSS digital data arrays. The linearization of these collinearity equations is presented. Algorithms considered for use in analysis and restitution included the MSS collinearity equations, piecewise polynomials based on linearized collinearity equations, and nonparametric algorithms. A proposed system for geometric analysis and restitution of MSS digital data arrays was used to evaluate these algorithms, utilizing actual MSS data arrays. It was shown that collinearity equations and nonparametric algorithms both yield acceptable results, but nonparametric algorithms possess definite advantages in computational efficiency. Piecewise polynomials were found to yield inferior results.
Geometric curvature and phase of the Rabi model
Mao, Lijun; Huai, Sainan; Guo, Liping; Zhang, Yunbo
2015-11-15
We study the geometric curvature and phase of the Rabi model. Under the rotating-wave approximation (RWA), we apply the gauge independent Berry curvature over a surface integral to calculate the Berry phase of the eigenstates for both single and two-qubit systems, which is found to be identical with the system of spin-1/2 particle in a magnetic field. We extend the idea to define a vacuum-induced geometric curvature when the system starts from an initial state with pure vacuum bosonic field. The induced geometric phase is related to the average photon number in a period which is possible to measure in the qubit–cavity system. We also calculate the geometric phase beyond the RWA and find an anomalous sudden change, which implies the breakdown of the adiabatic theorem and the Berry phases in an adiabatic cyclic evolution are ill-defined near the anti-crossing point in the spectrum.
The arithmetico-geometric sequence: an application of linear algebra
NASA Astrophysics Data System (ADS)
Orosi, Greg
2016-07-01
In this paper, we present a linear algebra-based derivation of the analytic formula for the sum of the first nth terms of the arithmetico-geometric sequence. Furthermore, the advantage of the derivation is briefly discussed.
Measurement of a vacuum-induced geometric phase
Gasparinetti, Simone; Berger, Simon; Abdumalikov, Abdufarrukh A.; Pechal, Marek; Filipp, Stefan; Wallraff, Andreas J.
2016-01-01
Berry’s geometric phase naturally appears when a quantum system is driven by an external field whose parameters are slowly and cyclically changed. A variation in the coupling between the system and the external field can also give rise to a geometric phase, even when the field is in the vacuum state or any other Fock state. We demonstrate the appearance of a vacuum-induced Berry phase in an artificial atom, a superconducting transmon, interacting with a single mode of a microwave cavity. As we vary the phase of the interaction, the artificial atom acquires a geometric phase determined by the path traced out in the combined Hilbert space of the atom and the quantum field. Our ability to control this phase opens new possibilities for the geometric manipulation of atom-cavity systems also in the context of quantum information processing. PMID:27386533
On an assumption of geometric foundation of numbers
NASA Astrophysics Data System (ADS)
Anatriello, Giuseppina; Saverio Tortoriello, Francesco; Vincenzi, Giovanni
2016-04-01
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 Ausdehnungslehre in 1844. Assuming as axioms, the cognitive contents of the theorems of Pappus and Desargues, through their configurations, in an Euclidean plane a natural field structure can be identified that reveals the purely geometric nature of complex numbers. Reasoning based on figures is becoming a growing interdisciplinary field in logic, philosophy and cognitive sciences, and is also of considerable interest in the field of education, moreover, recently, it has been emphasized that the mutual assistance that geometry and complex numbers give is poorly pointed out in teaching and that a unitary vision of geometrical aspects and calculation can be clarifying.
Logic synthesis from DDL description
NASA Technical Reports Server (NTRS)
Shiva, S. G.
1980-01-01
The implementation of DDLTRN and DDLSIM programs on SEL-2 computer system is reported. These programs were tested with DDL descriptions of various complexity. An algorithm to synthesize the combinational logic using the cells available in the standard IC cell library was formulated. The algorithm is implemented as a FORTRAN program and a description of the program is given.
Mission data system framework description
NASA Technical Reports Server (NTRS)
Meyer, K.; Rinker, G.; Dvorak, D.; Rosmussen, R.; Reinholttz, K.
2002-01-01
This document provides an overall description of the MDS Framework technology. Since the purpose is to provide a general reference for the frameworks, the descriptions are organized as compendium. This document does not provide guidance for how the MDS technology should be used.
"Geometric" planetology and origin of the Moon
NASA Astrophysics Data System (ADS)
Kochemasov, Gennady G.
2010-05-01
The comparative wave planetology [1 & othres] demonstrates graphically its main conceptual point: orbits make structures. The structures are produced by a warping action of stationary waves induced in bodies by non-circular orbits with periodically changing bodies' accelerations. A geometric model of tectonic granulation of planets is a schematic row of even circles adorned with granules radius of which increases in direction from Sun to the outer planets. It was shown that the granule radii are inversely proportional to the orbital frequencies of planets. Thus, there is a following row of these radii: Mercury πR/16, Venus πR/6, Earth πR/4, Mars πR/2, asteroids πR/1. It was also shown that these radii well correlate with planetary surface "ruggedness". This observation led to a conception of the "relief-forming potential of planets"[2]. So, this potential is rather weak in Mercury and Venus, rather high in Mars and intermediate in Earth. Certainly, orbital eccentricities were even higher at the earlier period of planet formation, at debris zones of their accretion causing scattering debris material. This scattering was small at Mercury' and Venus' zones, large at the Mars' zone and intermediate at the Earth's zone. Consequently, gravity kept debris in the first zones, allowed them escape in the martian zone, and allowed to have separated debris sub zone in the vicinity of the Earth's zone or around not fully consolidated (accreted) Earth. Rejecting the giant impact hypotheses of Moon formation as contradicting the fact of the ubiquitous wave induced tectonic dichotomy of celestial bodies (Theorem1 [3]) one should concentrate at hypotheses dealing with formation of the satellite from primordial debris in a near-Earth heliocentric orbit or in a circumterrestrial orbit from debris wave separated from the Earth' zone of accretion. Wave scattering of primordial material from an accretion zone or from a not fully accreted (consolidated) body is a normal process