Geometric Deformations Based on 3D Volume Morphing
Institute of Scientific and Technical Information of China (English)
JIN Xiaogang; WAN Huagen; PENG Qunsheng
2001-01-01
This paper presents a new geometric deformation method based on 3D volume morphing by using a new concept called directional polar coordinate. The user specifies the source control object and the destination control object which act as the embedded spaces.The source and the destination control objects determine a 3D volume morphing which maps the space enclosed in the source control object to that of the destination control object. By embedding the object to be deformed into the source control object, the 3D volume morphing determines the deformed object automatically without the tiring moving of control points.Experiments show that this deformation model is efficient and intuitive, and it can achieve some deformation effects which are difficult to achieve for traditional methods.
Geometric Modeling Applications Interface Program (GMAP). Volume 1. Executive Overview
1989-09-01
Z . Code) 10. SOURCE OF FUNDING NOS. PROGRAM PROJECT TASK WORK UNIT ELEMENT NO. NO. NO. NO. 11. TITLE (Include Security Classification) GEOMETRIC...342f CI FTR560240OOlU September 1989 SECTION 2 SCOPE OF GMAP GMAP focused on the generacion , control, and exchange of computer information to replace
Gómez-Robles, Aida; Martinón-Torres, María; Bermúdez de Castro, José María; Prado-Simón, Leyre; Arsuaga, Juan Luis
2011-12-01
This paper continues the series of articles initiated in 2006 that analyse hominin dental crown morphology by means of geometric morphometric techniques. The detailed study of both upper premolar occlusal morphologies in a comprehensive sample of hominin fossils, including those coming from the Gran Dolina-TD6 and Sima de los Huesos sites from Atapuerca, Spain, complement previous works on lower first and second premolars and upper first molars. A morphological gradient consisting of the change from asymmetric to symmetric upper premolars and a marked reduction of the lingual cusp in recent Homo species has been observed in both premolars. Although percentages of correct classification based on upper premolar morphologies are not very high, significant morphological differences between Neanderthals (and European middle Pleistocene fossils) and modern humans have been identified, especially in upper second premolars. The study of morphological integration between premolar morphologies reveals significant correlations that are weaker between upper premolars than between lower ones and significant correlations between antagonists. These results have important implications for understanding the genetic and functional factors underlying dental phenotypic variation and covariation. Copyright Â© 2011 Elsevier Ltd. All rights reserved.
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Seldin, D.W.; Esser, P.D.; Nichols, A.B.; Ratner, S.J.; Alderson, P.O.
1983-12-01
The utility of a semi-automatic method of measuring left ventricular (LV) volume geometrically from gated blood-pool studies and digital subtraction angiography (DSA) was investigated using computerized edge detection and spatial calibration algorithms. LAO LV volumes determined from gated blood-pool studies were compared to volumes obtained from contrast left ventriculograms in 21 patients and the applicability of this method to DSA was evaluated in 25 additional patients who also had conventional left ventriculography. There was excellent correlation between the two, both for radionuclide studies and for DSA. Computer-based geometric determinations of LV volume appear to be rapid, accurate, and less dependent on subjective operator decisions than previously reported geometric approaches.
A geometric characterization of the upper bound for the span of the Jones polynomial
González-Meneses, J
2009-01-01
Let D be a link diagram with n crossings, s_A and s_B its extreme states and |s_AD| (resp. |s_BD|) the number of simple closed curves that appear when smoothing D according to s_A (resp. s_B). We give a general formula for the sum |s_AD|+|s_BD| for a k-almost alternating diagram D, for any k, characterising this sum as the number of faces in an appropriate triangulation of an appropriate surface with boundary. When D is dealternator connected, the triangulation is especially simple, obtaining that |s_AD|+|s_BD|=n+2-2k. This gives a simple geometric proof of the upper bound of the span of the Jones polynomial for dealternator connected diagrams, a result first obtained by Zhu in 1997. Another upper bound of the span of the Jones polynomial for dealternator connected and dealternator reduced diagrams, discovered historically first by Adams et al in 1992, is obtained as a corollary.
On Geometric Upper Bounds for Positioning Algorithms in Wireless Sensor Networks
Gholami, Mohammad Reza; Wymeersch, Henk; Rydström, Mats
2012-01-01
This paper studies the possibility of upper bounding the position error of an estimate for range based positioning algorithms in wireless sensor networks. In this study, we argue that in certain situations when the measured distances between sensor nodes are positively biased, e.g., in non-line-of-sight conditions, the target node is confined to a closed bounded convex set (a feasible set) which can be derived from the measurements. Then, we formulate two classes of geometric upper bounds with respect to the feasible set. If an estimate is available, either feasible or infeasible, the worst-case position error can be defined as the maximum distance between the estimate and any point in the feasible set (the first bound). Alternatively, if an estimate given by a positioning algorithm is always feasible, we propose to get the maximum length of the feasible set as the worst-case position error (the second bound). These bounds are formulated as nonconvex optimization problems. To progress, we relax the nonconvex ...
The geometric and arithmetic volume of Shimura varieties of orthogonal type
Hörmann, Fritz
2011-01-01
We apply the theory of Borcherds products to calculate arithmetic volumes (heights) of Shimura varieties of orthogonal type up to contributions from very bad primes. The approach is analogous to the well-known computation of their geometric volume by induction, using special cycles. A functorial theory of integral models of toroidal compactifications of those varieties and a theory of arithmetic Chern classes of integral automorphic vector bundles with singular metrics are used. We obtain some evidence in the direction of Kudla's conjectures on relations of heights of special cycles on these varieties to special derivatives of Eisenstein series.
Approximating the volume of unions and intersections of high-dimensional geometric objects
Bringmann, Karl
2008-01-01
We consider the computation of the volume of the union of high-dimensional geometric objects. While showing that this problem is #P-hard already for very simple bodies (i.e., axis-parallel boxes), we give a fast FPRAS for all objects where one can: (1) test whether a given point lies inside the object, (2) sample a point uniformly, (3) calculate the volume of the object in polynomial time. All three oracles can be weak, that is, just approximate. This implies that Klee's measure problem and the hypervolume indicator can be approximated efficiently even though they are #P-hard and hence cannot be solved exactly in time polynomial in the number of dimensions unless P=NP. Our algorithm also allows to approximate efficiently the volume of the union of convex bodies given by weak membership oracles. For the analogous problem of the intersection of high-dimensional geometric objects we prove #P-hardness for boxes and show that there is no multiplicative polynomial-time $2^{d^{1-\\epsilon}}$-approximation for certain...
Geometrical volume effects in the computation of the slope of the Isgur-Wise function
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Lellouch, L. [Southampton Univ. (United Kingdom). Dept. of Physics; Nieves, J. [Southampton Univ. (United Kingdom). Dept. of Physics; Sachrajda, C.T. [Southampton Univ. (United Kingdom). Dept. of Physics; Stella, N. [Southampton Univ. (United Kingdom). Dept. of Physics; Wittig, H. [Southampton Univ. (United Kingdom). Dept. of Physics; Martinelli, G. [Dipartimento di Fisica, Universita di Roma `La Sapienza`, 00185 Rome (Italy); Richards, D.G. [Department of Physics, The University of Edinburgh, Edinburgh EH9 3JZ, Scotland (United Kingdom); UKQCD Collaboration
1995-06-19
We use a method recently suggested for evaluating the slope of the Isgur-Wise function, at the zero-recoil point, on the lattice. The computations are performed in the quenched approximation to lattice QCD, on a 24{sup 3} x48 lattice at {beta}=6.2, using an O(a)-improved action for the fermions. We have found unexpectedly large finite-volume effects in such a calculation. These volume corrections turned out to be purely geometrical and independent of the dynamics of the system. After the study of these effects on a smaller volume and for different quark masses, we give approximate expressions that account for them. Using these approximations we find {xi}{sup `}(1)=-1.7{sup +2}{sub -2} and {xi}{sup `}(1)=-1.4{sup +2}{sub -1} for the slope of the Isgur-Wise function, for two mesons composed of a heavy quark slightly heavier and lighter, respectively, than the charm quark, and in both cases, a light antiquark whose mass is about that of the strange quark. ((orig.)).
Enthalpy, geometric volume and logarithmic correction to entropy for van der Waals black hole
Pradhan, Parthapratim
2016-10-01
If the negative cosmological constant is treated as a dynamical pressure and if the volume is its thermodynamically conjugate variable then the gravitational mass can be expressed as the total gravitational enthalpy rather than the energy. Under these circumtances, a new phenomenon emerges in the context of extended phase space thermodynamics. We examine here these features for the recently discovered van der Waals (VDW) black hole (BH) (Rajagopal A. et al., Phys. Lett. B, 737 (2014) 277) which is analogous to the VDW fluid. We show that the thermodynamic volume is greater than the naive geometric volume. We also show that the Smarr-Gibbs-Duhem relation is satisfied for this BH. Furthermore, by computing the thermal specific heat we find the local thermodynamic stability criterion for this BH. It has been observed that the BH does not possess any kind of second-order phase transition. This is an interesting feature of VDW BH by its own right. Moreover, we also derive the Cosmic-Censorship-Inequality for this class of BH. In addition finally, we compute the logarithmic correction to the entropy of this BH due to the quantum fluctuations around the thermal equilibrium.
Enthalpy, Geometric Volume and Logarithmic correction to Entropy for Van-der-Waals Black Hole
Pradhan, Parthapratim
2016-01-01
If the negative cosmological constant is treated as a dynamical pressure and if the volume be its thermodynamically conjugate variable then the gravitational mass can be expressed as the total gravitational enthalpy rather than the energy. Under these circumstances, a new phenomena emerges in the context of extended phase space thermodynamics. We \\emph{examine} here these features for recently discovered Van-der-Waal (VDW) black hole (BH) \\cite{mann15} which is analogous to the VDW fluid. We show that the thermodynamic volume is \\emph{greater} than the naive geometric volume. We also show that the \\emph{Smarr-Gibbs-Duhem} relation is satisfied for this BH. Furthermore, by computing the thermal specific heat we find the local thermodynamic stability criterion for this BH. It has been observed that the BH does \\emph{not} possess any kind of second order phase transition. This is an interesting feature of VDW BH by its own right. Moreover, we also derive \\emph{Cosmic-Censorship-Inequality} for this class of BH. ...
Directory of Open Access Journals (Sweden)
Arschang eValipour
2012-10-01
Full Text Available Rationale: In clinical trials, homogeneous emphysema patients have responded well to upper lobe volume reduction but not lower lobe volume reduction. Materials/Methods: To understand the physiological basis for this observation, a computer model was developed to simulate the effects of upper and lower lobe lung volume reduction on RV/TLC and lung recoil in homogeneous emphysema.Results: Patients with homogeneous emphysema received either upper or lower lobe volume reduction therapy based on findings of radionucleotide scintigraphy scanning. CT analysis of lobar volumes showed that patients undergoing upper (n=18; -265 mL/site and lower lobe treatment (n=11; -217 mL/site experienced similar reductions in lung volume. However, only upper lobe treatment improved FEV1 (+11.1±14.7% vs -4.4±15.8% and RV/TLC (-5.4± 8.1% vs -2.4±8.6%. Model simulations provided an unexpected explanation for this response. Increases in transpulmonary pressure subsequent to volume reduction increased RV/TLC in upper lobe alveoli, while caudal shifts in airway closure decreased RV/TLC in lower lobe alveoli. Upper lobe treatment, which eliminates apical alveoli with high RV/TLC values, lowers the average RV/TLC of the lung. Conversely, lower lobe treatment, which eliminates caudal alveoli with low RV/TLC values, has less effect. Conclusions: Lower lobe treatment in homogeneous emphysema is uniformly less effective than upper lobe treatment.
Evaluation of geometric efficiency and radiation exposure in z-axis for volume scan.
Kobayashi, Masanao; Koshida, Kichiro; Suzuki, Shoichi; Katada, Kazuhiro
2011-01-01
The International Electrotechnical Commission (IEC) recommended that a display be provided on the operating console of medical computed tomography (CT) scanners when the geometric efficiency (GE) in the z-axis is 70% or less. Taking into account the increase in the number of detector rows and the changes in the scanning method, the present study was conducted to review the GE and to evaluate the exposure dose in the z-axis direction. The GE for a single-rotation scan was calculated in accordance with IEC-606024 Ed. 2. The findings of the present study suggest that 320-row area detector computed tomography volume scan (single axial scan with no table movement in which it just happened to use a very large beam width) extends 18.8 mm beyond the nominal beam collimation, even when the GE is >70%. However, compared with the helical scan, which is the present mainstream of CT examinations, the dose beyond the scan length is narrower in volume scan for a limited scan length of 160 mm or less.
Kim, Euitae; Shidahara, Miho; Tsoumpas, Charalampos; McGinnity, Colm J; Kwon, Jun Soo; Howes, Oliver D; Turkheimer, Federico E
2013-06-01
We validated the use of a novel image-based method for partial volume correction (PVC), structural-functional synergistic resolution recovery (SFS-RR) for the accurate quantification of dopamine synthesis capacity measured using [(18)F]DOPA positron emission tomography. The bias and reliability of SFS-RR were compared with the geometric transfer matrix (GTM) method. Both methodologies were applied to the parametric maps of [(18)F]DOPA utilization rates (ki(cer)). Validation was first performed by measuring repeatability on test-retest scans. The precision of the methodologies instead was quantified using simulated [(18)F]DOPA images. The sensitivity to the misspecification of the full-width-half-maximum (FWHM) of the scanner point-spread-function on both approaches was also assessed. In the in-vivo data, the ki(cer) was significantly increased by application of both PVC procedures while the reliability remained high (intraclass correlation coefficients >0.85). The variability was not significantly affected by either PVC approach (<10% variability in both cases). The corrected ki(cer) was significantly influenced by the FWHM applied in both the acquired and simulated data. This study shows that SFS-RR can effectively correct for partial volume effects to a comparable degree to GTM but with the added advantage that it enables voxelwise analyses, and that the FWHM used can affect the PVC result indicating the importance of accurately calibrating the FWHM used in the recovery model.
Van der Jeught, Sam; Bradu, Adrian; Podoleanu, Adrian Gh; Dirckx, Joris J J
2012-01-01
Large-volume optical coherence tomography (OCT)-setups employ scanning mirrors and suffer from non-linear geometric distortion artifacts in which the degree of distortion is determined by the maximum angles over which the mirrors rotate. In this chapter, we describe a straightforward approach to correct for these distortion artifacts, creating an alternative to previously reported ray-tracing schemes that are unable to apply these corrections in real-time. By implementing the proposed 3D recalibration algorithm on the graphics card of a standard computer, this feature can be applied in real-time. We validate the accuracy of the technique using OCT measurements of a highly curved object within a large imaging volume of 12.35 x 10.13 x 2.36 mm^3. The resulting 3D object shape measurements are compared against high-resolution and aberration-free optical profilometry measurements. Maintaining an optical resolution of <10 micron within the sample, both axially and transversally, we realized a real-time, high-re...
Frandsen, Michael W.; Wessol, Daniel E.; Wheeler, Floyd J.
2001-01-16
Methods and computer executable instructions are disclosed for ultimately developing a dosimetry plan for a treatment volume targeted for irradiation during cancer therapy. The dosimetry plan is available in "real-time" which especially enhances clinical use for in vivo applications. The real-time is achieved because of the novel geometric model constructed for the planned treatment volume which, in turn, allows for rapid calculations to be performed for simulated movements of particles along particle tracks there through. The particles are exemplary representations of neutrons emanating from a neutron source during BNCT. In a preferred embodiment, a medical image having a plurality of pixels of information representative of a treatment volume is obtained. The pixels are: (i) converted into a plurality of substantially uniform volume elements having substantially the same shape and volume of the pixels; and (ii) arranged into a geometric model of the treatment volume. An anatomical material associated with each uniform volume element is defined and stored. Thereafter, a movement of a particle along a particle track is defined through the geometric model along a primary direction of movement that begins in a starting element of the uniform volume elements and traverses to a next element of the uniform volume elements. The particle movement along the particle track is effectuated in integer based increments along the primary direction of movement until a position of intersection occurs that represents a condition where the anatomical material of the next element is substantially different from the anatomical material of the starting element. This position of intersection is then useful for indicating whether a neutron has been captured, scattered or exited from the geometric model. From this intersection, a distribution of radiation doses can be computed for use in the cancer therapy. The foregoing represents an advance in computational times by multiple factors of
Asymmetry in volume between dominant and nondominant upper limbs in young tennis players.
Rogowski, Isabelle; Ducher, Gaële; Brosseau, Olivier; Hautier, Christophe
2008-08-01
This study aimed at demonstrating the asymmetry in volume between the dominant and nondominant upper limbs in tennis players, controlled for maturity status. Upper limb volumes on both sides were calculated in 72 tennis players and 84 control subjects, using the truncated cone method. The participants' maturity status was determined using the predicted age at peak height velocity (PHV). The results showed significant larger side-to-side asymmetry in volume in tennis groups than in control groups. These findings suggested that, even before PHV, specific-sport adaptations occurred in the dominant upper limb in tennis players.
Directory of Open Access Journals (Sweden)
José Gómez-Tames
2014-01-01
Full Text Available Volume conductor models with different geometric representations, such as the parallel layer model (PM, the cylindrical layer model (CM, or the anatomically based model (AM, have been employed during the implementation of bioelectrical models for electrical stimulation (FES. Evaluating their strengths and limitations to predict nerve activation is fundamental to achieve a good trade-off between accuracy and computation time. However, there are no studies aimed at clarifying the following questions. (1 Does the nerve activation differ between CM and PM? (2 How well do CM and PM approximate an AM? (3 What is the effect of the presence of blood vessels and nerve trunk on nerve activation prediction? Therefore, in this study, we addressed these questions by comparing nerve activation between CM, PM, and AM models by FES. The activation threshold was used to evaluate the models under different configurations of superficial electrodes (size and distance, nerve depths, and stimulation sites. Additionally, the influences of the sciatic nerve, femoral artery, and femoral vein were inspected for a human thigh. The results showed that the CM and PM had a high error rate, but the variation of the activation threshold followed the same tendency for electrode size and interelectrode distance variation as AM.
Gómez-Robles, Aida; Bermúdez de Castro, José María; Martinón-Torres, María; Prado-Simón, Leyre; Arsuaga, Juan Luis
2012-09-01
The study of dental morphology by means of geometric morphometric methods allows for a detailed and quantitative comparison of hominin species that is useful for taxonomic assignment and phylogenetic reconstruction. Upper second and third molars have been studied in a comprehensive sample of Plio- and Pleistocene hominins from African, Asian and European sites in order to complete our analysis of the upper postcanine dentition. Intraspecific variation in these two molars is high, but some interspecific trends can be identified. Both molars exhibit a strong reduction of the distal cusps in recent hominin species, namely European Homo heidelbergensis, Homo neanderthalensis and Homo sapiens, but this reduction shows specific patterns and proportions in the three groups. Second molars tend to show four well developed cusps in earlier hominin species and their morphology is only marginally affected by allometric effects. Third molars can be incipiently reduced in earlier species and they evince a significant allometric component, identified both inter- and intraspecifically. European Middle Pleistocene fossils from Sima de los Huesos (SH) show a very strong reduction of these two molars, even more marked than the reduction observed in Neanderthals and in modern human populations. The highly derived shape of SH molars points to an early acquisition of typical Neanderthal dental traits by pre-Neanderthal populations and to a deviation of this population from mean morphologies of other European Middle Pleistocene groups. Copyright © 2012 Elsevier Ltd. All rights reserved.
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Iliadis, Georgios; Misailidou, Despina [Dept. of Radiation Oncology, ' ' Papageorgiou' ' General Hospital, Thessaloniki (Greece); Selviaridis, Panagiotis; Chatzisotiriou, Athanasios [Dept. of Neurosurgery, ' ' AHEPA' ' Hospital, Aristotle Univ. of Thessaloniki, School of Medicine (Greece); Kalogera-Fountzila, Anna [Dept. of Radiology, ' ' AHEPA' ' Hospital, Aristotle Univ. of Thessaloniki, School of Medicine (Greece); Fragkoulidi, Anna; Fountzilas, George [Dept. of Medical Oncology, ' ' Papageorgiou' ' General Hospital, Aristotle Univ. of Thessaloniki, School of Medicine (Greece); Baltas, Dimos; Tselis, Nikolaos; Zamboglou, Nikolaos [Dept. of Radiation Oncology, Klinikum Offenbach (Germany)
2009-11-15
Background and purpose: the importance of tumor volume as a prognostic factor in high-grade gliomas is highly controversial and there are numerous methods estimating this parameter. In this study, a computer-based application was used in order to assess tumor volume from hard copies and a survival analysis was conducted in order to evaluate the prognostic significance of preoperative volumetric data in patients harboring glioblastomas. Patients and methods: 50 patients suffering from glioblastoma were analyzed retrospectively. Tumor volume was determined by the various geometric models as well as by an own specialized software (Volumio). Age, performance status, type of excision, and tumor location were also included in the multivariate analysis. Results: the spheroid and rectangular models overestimated tumor volume, while the ellipsoid model offered the best approximation. Volume failed to attain any statistical significance in prognosis, while age and performance status confirmed their importance in progression-free and overall survival of patients. Conclusion: geometric models provide a rough approximation of tumor volume and should not be used, as accurate determination of size is of paramount importance in order to draw safe conclusions in oncology. Although the significance of volumetry was not disclosed, further studies are definitely required. (orig.)
Maric, Tomislav; Bothe, Dieter
2013-01-01
A new parallelized unsplit geometrical Volume of Fluid (VoF) algorithm with support for arbitrary unstructured meshes and dynamic local Adaptive Mesh Refinement (AMR), as well as for two and three dimensional computation is developed. The geometrical VoF algorithm supports arbitrary unstructured meshes in order to enable computations involving flow domains of arbitrary geometrical complexity. The implementation of the method is done within the framework of the OpenFOAM library for Computational Continuum Mechanics (CCM) using the C++ programming language with modern policy based design for high program code modularity. The development of the geometrical VoF algorithm significantly extends the method base of the OpenFOAM library by geometrical volumetric flux computation for two-phase flow simulations. For the volume fraction advection, a novel unsplit geometrical algorithm is developed, which inherently sustains volume conservation utilizing unique Lagrangian discrete trajectories located in the mesh points. ...
Sattarivand, Mike; Kusano, Maggie; Poon, Ian; Caldwell, Curtis
2012-11-01
Limited spatial resolution of positron emission tomography (PET) often requires partial volume correction (PVC) to improve the accuracy of quantitative PET studies. Conventional region-based PVC methods use co-registered high resolution anatomical images (e.g. computed tomography (CT) or magnetic resonance images) to identify regions of interest. Spill-over between regions is accounted for by calculating regional spread functions (RSFs) in a geometric transfer matrix (GTM) framework. This paper describes a new analytically derived symmetric GTM (sGTM) method that relies on spill-over between RSFs rather than between regions. It is shown that the sGTM is mathematically equivalent to Labbe's method; however it is a region-based method rather than a voxel-based method and it avoids handling large matrices. The sGTM method was validated using two three-dimensional (3D) digital phantoms and one physical phantom. A 3D digital sphere phantom with sphere diameters ranging from 5 to 30 mm and a sphere-to-background uptake ratio of 3-to-1 was used. A 3D digital brain phantom was used with four different anatomical regions and a background region with different activities assigned to each region. A physical sphere phantom with the same geometry and uptake as the digital sphere phantom was manufactured and PET-CT images were acquired. Using these three phantoms, the performance of the sGTM method was assessed against that of the GTM method in terms of accuracy, precision, noise propagation and robustness. The robustness was assessed by applying mis-registration errors and errors in estimates of PET point spread function (PSF). In all three phantoms, the results showed that the sGTM method has accuracy similar to that of the GTM method and within 5%. However, the sGTM method showed better precision and noise propagation than the GTM method, especially for spheres smaller than 13 mm. Moreover, the sGTM method was more robust than the GTM method when mis-registration errors or
Brookes, G B; Fairfax, A J
1982-06-01
Chronic obstructive lesions of the upper airways such as post-traumatic strictures, bilateral vocal cord paralysis and chronic inflammatory foci are uncommon. The functional assessment of the severity and character of an obstruction is important both for diagnosis and management, and may also allow evaluation of the efficacy of medical and surgical treatment. There are limitations of simple spirometric pulmonary function tests, which are evident when assessing upper airways obstruction. The flow volume loop is a graphic recording of airflow during maximal respiration and expiration at different lung volumes, and may be affected in a characteristic way by alterations in the airway resistance. Three unusual cases of chronic upper airway obstruction are presented which illustrate the value of the flow volume loop examination in their management.
An upper-bound estimate for the accuracy of volume-area scaling
Farinotti, D.; Huss, M.
2013-06-01
Volume-area scaling is the most popular method for estimating the ice volume of large glacier samples. Here, a series of resampling experiments based on different sets of synthetic data are presented in order to derive an upper-bound estimate (i.e. a level achieved only with ideal conditions) for the accuracy of its application. We also quantify the maximum accuracy expected when scaling is used for determining the glacier volume change, and area change of a given glacier population. A comprehensive set of measured glacier areas, volumes, area and volume changes is evaluated to investigate the impact of real-world data quality on the so assessed accuracies. For populations larger than a few thousand glaciers, the total ice volume can be recovered within 30% if all measurements available worldwide are used for estimating the scaling coefficients. Assuming no systematic biases in ice volume measurements, their uncertainty is of secondary importance. Knowing the individual areas of a glacier sample for two points in time allows recovering the corresponding ice volume change within 40% for populations larger than a few hundred glaciers, both for steady-state and transient geometries. If ice volume changes can be estimated without bias, glacier area changes derived from volume-area scaling show similar uncertainties as for the volume changes. This paper does not aim at making a final judgement about the suitability of volume-area scaling, but provides the means for assessing the accuracy expected from its application.
A geometric proof of the upper bound on the size of partial spreads in H(4n+1, q²)
Vanhove, Frédéric
2011-01-01
We give a geometric proof of the upper bound of q(2n+1) + 1 on the size of partial spreads in the polar space H(4n + 1, q(2)). This bound is tight and has already been proved in an algebraic way. Our alternative proof also yields a characterization of the partial spreads of maximum size in H(4n + 1, q(2)).
Machado, Marco; Willardson, Jeffrey M.; Silva, Dailson P.; Frigulha, Italo C.; Koch, Alexander J.; Souza, Sergio C.
2012-01-01
In the current study, we examined the relationship between serum creatine kinase (CK) activity following upper body resistance exercise with a 1- or 3-min rest between sets. Twenty men performed two sessions, each consisting of four sets with a 10-repetition maximum load. The results demonstrated significantly greater volume for the 3-min…
Large volume liquid silicone injection in the upper thighs : a never ending story
Hofer, SOP; Damen, A; Nicolai, JPA
2000-01-01
This report concerns a 26-year-old male-to-female transsexual who had received a large volume liquid silicone injection of unknown grade into her upper lateral thighs to gain female contour. She presented at our outpatient clinic 4 years after the silicone injection with complaints of pain and silic
Machado, Marco; Willardson, Jeffrey M.; Silva, Dailson P.; Frigulha, Italo C.; Koch, Alexander J.; Souza, Sergio C.
2012-01-01
In the current study, we examined the relationship between serum creatine kinase (CK) activity following upper body resistance exercise with a 1- or 3-min rest between sets. Twenty men performed two sessions, each consisting of four sets with a 10-repetition maximum load. The results demonstrated significantly greater volume for the 3-min…
Lan, Yihua; Li, Cunhua; Ren, Haozheng; Zhang, Yong; Min, Zhifang
2012-10-01
A new heuristic algorithm based on the so-called geometric distance sorting technique is proposed for solving the fluence map optimization with dose-volume constraints which is one of the most essential tasks for inverse planning in IMRT. The framework of the proposed method is basically an iterative process which begins with a simple linear constrained quadratic optimization model without considering any dose-volume constraints, and then the dose constraints for the voxels violating the dose-volume constraints are gradually added into the quadratic optimization model step by step until all the dose-volume constraints are satisfied. In each iteration step, an interior point method is adopted to solve each new linear constrained quadratic programming. For choosing the proper candidate voxels for the current dose constraint adding, a so-called geometric distance defined in the transformed standard quadratic form of the fluence map optimization model was used to guide the selection of the voxels. The new geometric distance sorting technique can mostly reduce the unexpected increase of the objective function value caused inevitably by the constraint adding. It can be regarded as an upgrading to the traditional dose sorting technique. The geometry explanation for the proposed method is also given and a proposition is proved to support our heuristic idea. In addition, a smart constraint adding/deleting strategy is designed to ensure a stable iteration convergence. The new algorithm is tested on four cases including head-neck, a prostate, a lung and an oropharyngeal, and compared with the algorithm based on the traditional dose sorting technique. Experimental results showed that the proposed method is more suitable for guiding the selection of new constraints than the traditional dose sorting method, especially for the cases whose target regions are in non-convex shapes. It is a more efficient optimization technique to some extent for choosing constraints than the dose
sprotocols
2015-01-01
Authors: David Hevia, Aida Rodriguez-Garcia, Marta Alonso-Gervós, Isabel Quirós-González, Henar M Cimadevilla, Carmen Gómez-Cordovés, Rosa M Sainz & Juan C Mayo ### Abstract The protocol reported here describes a simple, easy, fast and reproducible method aimed to know the geometric parameters of living cells based on confocal laser scanning microscopy combined with 3D reconstruction software. Briefly, the method is based on intrinsic fluorescence properties of acridine orange (AO...
An upper-bound estimate for the accuracy of glacier volume-area scaling
Farinotti, D.; Huss, M.
2013-11-01
Volume-area scaling is the most popular method for estimating the ice volume of large glacier samples. Here, a series of resampling experiments based on different sets of synthetic data is presented in order to derive an upper-bound estimate (i.e. a level achieved only within ideal conditions) for its accuracy. For real-world applications, a lower accuracy has to be expected. We also quantify the maximum accuracy expected when scaling is used for determining the glacier volume change, and area change of a given glacier population. A comprehensive set of measured glacier areas, volumes, area and volume changes is evaluated to investigate the impact of real-world data quality on the so-assessed accuracies. For populations larger than a few thousand glaciers, the total ice volume can be recovered within 30% if all data currently available worldwide are used for estimating the scaling parameters. Assuming no systematic bias in ice volume measurements, their uncertainty is of secondary importance. Knowing the individual areas of a glacier sample for two points in time allows recovering the corresponding ice volume change within 40% for populations larger than a few hundred glaciers, both for steady-state and transient geometries. If ice volume changes can be estimated without bias, glacier area changes derived from volume-area scaling show similar uncertainties to those of the volume changes. This paper does not aim at making a final judgement on the suitability of volume-area scaling as such, but provides the means for assessing the accuracy expected from its application.
Directory of Open Access Journals (Sweden)
Li Minghuan
2013-01-01
Full Text Available Radiation is an important modality for cervical and upper-thoracic esophageal squamous cell carcinoma (ESCC. Delineating the lymph node clinical target volume (CTVn for EC remains a challenging task. The present paper retrospectively analyzes the distribution of affected lymph nodes of cervical and upper thoracic ESCC on CT images to provide a reference for determination of CTVn. The cases of untreated cervical or upper-thoracic ESCC patients with regional lymph node metastases at diagnosis were retrospectively analyzed. CT scans were done to assess the extent of circumferential involvement and the local-regional lymph node status. Based on the CT criteria (cervical, mediastinal and upper abdominal lymph nodes were considered to be positive for malignancy when they were larger than 8-12 mm in short-axis diameter according to different station respectively. Detailed lymph node stations were recorded for every case and the distribution information of loco-regional node metastasis for these patients was analyzed. A total of 256 patients were diagnosed with node metastasis and qualified for the study, including 206 men and 50 women (age range 37-85 years, median 60. This included 205 upper thoracic cases and 51 of cervical lesion. The length of the primary tumors ranged from 1.0 cm to 9.0 cm, median 4.5 cm. The size of the enlarged lymph nodes ranged from 0.8 to 5.0 cm median 1.4 cm, mean 1.61 cm. The number of involved stations ranged from 1 to 7 median 2. The lymph node stations, with an involved probability of 10% or more, included the upper and middle neck, supraclavicular and lower neck, upper paraesophageal and upper paratracheal area for cervical lesions, and the supraclavicular and lower neck, upper paraesophageal, upper paratracheal, lower paratracheal, aortopulmonary and subcarinal areas for upper thoracic EC, respectively. The mid-upper neck nodes were more likely to be involved in cervical EC than thoracic EC (X 2 test, p=0.000. Fewer
The geometric and arithmetic volume of Shimura varieties of orthogonal type
Hörmann, Fritz
2015-01-01
This book outlines a functorial theory of integral models of (mixed) Shimura varieties and of their toroidal compactifications, for odd primes of good reduction. This is the integral version, developed in the author's thesis, of the theory invented by Deligne and Pink in the rational case. In addition, the author develops a theory of arithmetic Chern classes of integral automorphic vector bundles with singular metrics using the work of Burgos, Kramer and Kühn. The main application is calculating arithmetic volumes or "heights" of Shimura varieties of orthogonal type using Borcherds' famous modular forms with their striking product formula-an idea due to Bruinier-Burgos-Kühn and Kudla. This should be seen as an Arakelov analogue of the classical calculation of volumes of orthogonal locally symmetric spaces by Siegel and Weil. In the latter theory, the volumes are related to special values of (normalized) Siegel Eisenstein series. In this book, it is proved that the Arakelov analogues are related to special d...
Vidt, Meghan E; Daly, Melissa; Miller, Michael E; Davis, Cralen C; Marsh, Anthony P; Saul, Katherine R
2012-01-10
Aging is associated with the loss of muscle volume (MV) and force leading to difficulties with activities of daily living. However, the relationship between upper limb MV and joint strength has not been characterized for older adults. Quantifying this relationship may help our understanding of the functional declines of the upper limb that older adults experience. Our objective was to assess the relationship between upper limb MV and maximal isometric joint moment-generating capacity (IJM) in a single cohort of healthy older adults (age ≥ 65 years) for 6 major functional groups (32 muscles). MV was determined from MRI for 18 participants (75.1±4.3 years). IJM at the shoulder (abduction/adduction), elbow (flexion/extension), and wrist (flexion/extension) was measured. MV and IJM measurements were compared to previous reports for young adults (28.6±4.5 years). On average older adults had 16.5% less total upper limb MV compared to young adults. Additionally, older adult wrist extensors composed a significantly increased percentage of upper limb MV. Older adult IJM was reduced across all joints, with significant differences for shoulder abductors (pIJM was accounted for by MV changes (p≤0.027), compared to 81.0% in young adults. We conclude that for older adults, MV and IJM are, on average, reduced but the significant linear relationship between MV and IJM is maintained. These results suggest that older adult MV and IJM cannot be simply scaled from young adults.
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Herschtal, Alan, E-mail: Alan.Herschtal@petermac.org [Department of Biostatistics and Clinical Trials, Peter MacCallum Cancer Centre, Melbourne (Australia); Faculty of Health, Arts and Design, Swinburne University of Technology, Melbourne (Australia); Te Marvelde, Luc [Department of Biostatistics and Clinical Trials, Peter MacCallum Cancer Centre, Melbourne (Australia); Mengersen, Kerrie [School of Mathematical Sciences, Science and Engineering Faculty, Queensland University of Technology, Brisbane (Australia); Foroudi, Farshad [Department of Radiation Oncology, Peter MacCallum Cancer Centre, Melbourne (Australia); The Sir Peter MacCallum Department of Oncology, Faculty of Medicine, Dentistry and Health Sciences, University of Melbourne, Melbourne (Australia); Eade, Thomas [Northern Sydney Cancer Centre, Radiation Oncology Department, Royal North Shore Hospital, St. Leonards, Sydney (Australia); Northern Clinical School, University of Sydney (Australia); Pham, Daniel [Department of Radiation Therapy, Peter MacCallum Cancer Centre, Melbourne (Australia); Caine, Hannah [Northern Sydney Cancer Centre, Radiation Oncology Department, Royal North Shore Hospital, St. Leonards, Sydney (Australia); Kron, Tomas [The Sir Peter MacCallum Department of Oncology, Faculty of Medicine, Dentistry and Health Sciences, University of Melbourne, Melbourne (Australia); Department of Physical Sciences, Peter MacCallum Cancer Centre, Melbourne (Australia)
2015-06-01
Objective: To develop a mathematical tool that can update a patient's planning target volume (PTV) partway through a course of radiation therapy to more precisely target the tumor for the remainder of treatment and reduce dose to surrounding healthy tissue. Methods and Materials: Daily on-board imaging was used to collect large datasets of displacements for patients undergoing external beam radiation therapy for solid tumors. Bayesian statistical modeling of these geometric uncertainties was used to optimally trade off between displacement data collected from previously treated patients and the progressively accumulating data from a patient currently partway through treatment, to optimally predict future displacements for that patient. These predictions were used to update the PTV position and margin width for the remainder of treatment, such that the clinical target volume (CTV) was more precisely targeted. Results: Software simulation of dose to CTV and normal tissue for 2 real prostate displacement datasets consisting of 146 and 290 patients treated with a minimum of 30 fractions each showed that re-evaluating the PTV position and margin width after 8 treatment fractions reduced healthy tissue dose by 19% and 17%, respectively, while maintaining CTV dose. Conclusion: Incorporating patient-specific displacement patterns from early in a course of treatment allows PTV adaptation for the remainder of treatment. This substantially reduces the dose to healthy tissues and thus can reduce radiation therapy–induced toxicities, improving patient outcomes.
Meijer, R.S.; Rietman, J.S.; Geertzen, J.H.B.; Bosmans, J.C.; Dijkstra, P.U.
2004-01-01
We investigated a method of indirect volume measurement that utilized surface measurements and a simplified formula derived from the formula for a frustum (Sitzia's method) to determine limb volumes in patients with breast cancer-related lymphedema of the upper extremity. Repeated measurements of up
Meijer, R.S.; Rietman, J.S.; Geertzen, J.H.B.; Bosmans, J.C.; Dijkstra, P.U.
We investigated a method of indirect volume measurement that utilized surface measurements and a simplified formula derived from the formula for a frustum (Sitzia's method) to determine limb volumes in patients with breast cancer-related lymphedema of the upper extremity. Repeated measurements of
Castro, C
2004-01-01
We construct the Extended Relativity Theory in Born-Clifford-Phase spaces with an upper and lower length scales (infrared/ultraviolet cutoff). The invariance symmetry leads naturally to the real Clifford algebra Cl (2, 6, R ) and complexified Clifford Cl_C ( 4 ) algebra related to Twistors. We proceed with an extensive review of Smith's 8D model based on the Clifford algebra Cl ( 1 ,7) that reproduces at low energies the physics of the Standard Model and Gravity; including the derivation of all the coupling constants, particle masses, mixing angles, ....with high precision. Further results by Smith are discussed pertaining the interplay among Clifford, Jordan, Division and Exceptional Lie algebras within the hierarchy of dimensions D = 26, 27, 28 related to bosonic string, M, F theory. Two Geometric actions are presented like the Clifford-Space extension of Maxwell's Electrodynamics, Brandt's action related the 8D spacetime tangent-bundle involving coordinates and velocities (Finsler geometries) followed by a...
Kishore, Raj; Das, Shreeja; Nussinov, Zohar; Sahu, Kisor K.
2016-06-01
Although the energetics of grain boundaries are more or less understood, their mechanical description remains challenging primarily because of very fast dynamics in the atomic length scale. By contrast, granular dynamics are extraordinarily sluggish. In this study, two dimensional centripetal packings of macroscopic granular particles are employed to investigate the role of geometric aspects of grain boundary formation. Using a novel sampling scheme, the extensive configuration space is well represented by a few prominent structures. Our results suggest that cohesive effects “iron out” any disorder present and enforce a transition towards a “fixed point” basin associated with a universal high density jammed hexagonal structure. Two main conjectures are advanced: (i) the appearance of grain boundary like structures is the manifestation of the kinetic instabilities of the densification process and has its origin in the structural rearrangement and (ii) the departure from six-fold coordination in the final packing is bounded from above by a sixth of the angular dispersion present in the initial configuration. If similar predictive consequences are further developed for three dimensional cases, this may have far reaching consequences in many areas of science and technology.
Directory of Open Access Journals (Sweden)
H.-C. Gunga
1999-01-01
Full Text Available Allometric equations are often based on the body mass of an animal because body mass determines many physiological functions. This should also hold for Brachiosaurus brancai and Dicraeosaurus hansemanni, two sauropods from the Upper Jurassic of Tendaguru/Tanzania (East Africa. Widely divergent estimates of body mass for the same specimen can be found in the literature for these two sauropods. Therefore, in order to determine the exact body mass and volume distribution in these sauropods, classical three-dimensional stereophotogrammetry as well as a newly developed laser scanner technique were applied to the mounted skeletons of Brachiosaurus brancai and Dicraeosaurus hansemanni in the Museum für Naturkunde (Berlin, Germany. Thereafter, scaling equations were used to estimate the size of organ systems. In a second step it was tested whether the given data from photogrammetry could be brought in line with the results derived from the allometric equations. These findings are applied to possible ecological problems in the Upper Jurassic of Tendaguru/Tanzania. Der Körpermasse eines Organismus werden oft allometrische Funktionen zugrunde gelegt, da von ihr viele physiologische Funktionen entscheidend abhängen. Dies sollte auch für ausgestorbene Organismen wie Brachiosaurus brancai und Dicraeosaurus hansemanni, zwei Sauropoden aus dem oberen Jura von Tendaguru/Tanzania in Ostafrika gelten. Da zu beiden Sauropoden nur sehr unterschiedliche Massenabschätzungen vorliegen, wurden die Körpermassen und Volumina von Brachiosaurus brancai und Dicraeosaurus hansemanni mit Hilfe der klassischen Photogrammetrie sowie einem neuentwickelten Laserscannerverfahren neu bestimmt. Basierend auf den so gemessenen Körpermassendaten wurden anschließend einige wichtige funktionell-morphologische Größen für eine paläophysiologische Rekonstruktion dieser Sauropoden mit Hilfe der Allometrie berechnet. Die gewonnenen Ergebnisse sind u. a. wichtig für die
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Robert Rietjens
2015-10-01
Full Text Available Introduction: It is unknown whether resistance training intensity or total volume of work affects the acute testosterone response to a greater extent. Purpose: Therefore, the circulating testosterone response was investigated following four resistance training protocols where total volume of work was held constant: moderate intensity (70% 1RM upper body (bench press, bent barbell row, and military press, moderate intensity lower body (squat and deadlift, high intensity (90% 1RM upper body, high intensity lower body. Methods: Total volume of work performed by each participant between protocols was maintained by adjusting the number of sets and or repetitions performed. Ten healthy, resistance trained men volunteered, and performed exercise protocols on separate days in a counterbalanced order. Capillary blood was obtained via finger stick at baseline (pre, immediately following the exercise session (post, and 1h post for the determination of testosterone concentration. Data were analyzed using a factorial ANOVA and significance was accepted at p≤ 0.05. Results: Both moderate intensity resistance protocols (upper and lower body significantly increased testosterone concentration (p=0.026, and p=0.024 respectively, whereas the high intensity protocols elevated testosterone but failed to achieve significance (upper p=0.272, lower p=0.658. No difference was noted in post session testosterone concentration between upper and lower body protocols for either moderate (p=0.248 or high intensity (p=0.990. Conclusion: This may be useful for novice resistance trained individuals because it provides evidence that moderate intensity is sufficient to increase testosterone compared to high intensity protocols that could be associated with a greater risk of injury. Keywords: hormone response, equal total work, high intensity protocol
Directory of Open Access Journals (Sweden)
Ertugrul Gelen
2012-12-01
Full Text Available The purpose of this study was to compare the acute effects of static stretching; dynamic exercises and high volume upper extremity plyometric activity on tennis serve performance. Twenty-six elite young tennis players (15.1 ± 4.2 years, 167.9 ± 5.8 cm and 61.6 ± 8.1 kg performed 4 different warm-up (WU routines in a random order on non-consecutive days. The WU methods consisted of traditional WU (jogging, rally and serve practice (TRAD; traditional WU and static stretching (TRSS; traditional WU and dynamic exercise (TRDE; and traditional WU and high volume upper extremity plyometric activity (TRPLYP. Following each WU session, subjects were tested on a tennis serve ball speed test. TRAD, TRSS, TRDE and TRPLYO were compared by repeated measurement analyses of variance and post-hoc comparisons. In this study a 1 to 3 percent increase in tennis serve ball speed was recorded in TRDE and TRPLYO when compared to TRAD (p 0.05. ICCs for ball speed showed strong reliability (0.82 to 0.93 for the ball speed measurements.The results of this study indicate that dynamic and high volume upper extremity plyometric WU activities are likely beneficial to serve speed of elite junior tennis players.
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Nguyen, T; Mai, N [University of Science, Ho Chi Minh City (Viet Nam); Nguyen, B [Prowess Inc, Concord, CA (United States)
2015-06-15
Purpose: In Proton therapy, especially intensity modulated proton therapy(IMPT), the dose distribution shape is very sensitive to errors due to sharp dose gradients at the Bragg peaks. The concept of the conventional margin is based on the assumption that dose distribution is shifted rather than deformed due to geometrical uncertainties. The goal of this study is to access the validity of the margin concept as well as propose a new approach using Dose Volume Population Histogram (DVPH) in evaluating IMPT plans. Methods: For a prostate case, an intensity modulated proton therapy is optimized based on the conventional PTV based objective function. The plan is evaluated based on the PTV DVH and CTV DVPH (dose volume population histogram) which explicitly taking into account geometric uncertainties. The DVPH is calculated based on 2197 dose distributions at different CTV possible positions for both random and systematic errors. The DVPH with a 90% confidence level is used for the comparison. Results: The minimum dose of the CTV DVPH with a 90% confidence level is only about 18% of the prescribed dose, while the minimum dose of the PTV is 95%. For bladder DVHs, the D50 and D35 is 26% and 30%, compared to 65% and 70% of the prescribed dose from the bladder DVPH with 90% confidence level. Conclusion: The results showed that the PTV concept for ensuring the prescribed dose actually delivered to the CTV is invalid in proton therapy. The good PTV DVH might Result in an underdose to the target and should not be used for IMPT optimization. For OARs, the conventional evaluation approach underestimates dose volume end points. The new concept DVPH has been proved to provide a more accurate DVH evaluation in proton therapy.
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Souza, Fabio Jose Fabricio de Barros; Evangelista, Anne Rosso; Silva, Juliana Veiga; Madeira, Kristian, E-mail: fsouzapneumo@hotmail.com [Universidade do Extremo Sul Catarinense (UNESC), Criciuma, SC (Brazil). Curso de Medicina; Perico, Gregory Vinicius [Unidade Radiologica Criciuma, SC (Brazil)
2016-01-15
Objective: Obstructive sleep apnea syndrome (OSAS) has a high prevalence and carries significant cardiovascular risks. It is important to study new therapeutic approaches to this disease. Positional therapy might be beneficial in reducing the apnea-hypopnea index (AHI). Imaging methods have been employed in order to facilitate the evaluation of the airways of OSAS patients and can be used in order to determine the effectiveness of certain treatments. This study was aimed at determining the influence that upper airway volume, as measured by cervical CT, has in patients diagnosed with OSAS. Methods: This was a quantitative, observational, cross-sectional study. We evaluated 10 patients who had been diagnosed with OSAS by polysomnography and on the basis of the clinical evaluation. All of the patients underwent conventional cervical CT in the supine position. Scans were obtained with the head of the patient in two positions (neutral and at a 44° upward inclination), and the upper airway volume was compared between the two. Results: The mean age, BMI, and neck circumference were 48.9 ± 14.4 years, 30.5 ± 3.5 kg/m{sup 2} , and 40.3 ± 3.4 cm, respectively. The mean AHI was 13.7 ± 10.6 events/h (range, 6.0-41.6 events/h). The OSAS was classified as mild, moderate, and severe in 70%, 20%, and 10% of the patients, respectively. The mean upper airway volume was 7.9 cm{sup 3} greater when the head was at a 44° upward inclination than when it was in the neutral position, and that difference (17.5 ± 11.0%) was statistically significant (p = 0.002). Conclusions: Elevating the head appears to result in a significant increase in the caliber of the upper airways in OSAS patients. (author)
Souza, Fábio José Fabrício de Barros; Evangelista, Anne Rosso; Silva, Juliana Veiga; Périco, Grégory Vinícius; Madeira, Kristian
2016-01-01
Objective : Obstructive sleep apnea syndrome (OSAS) has a high prevalence and carries significant cardiovascular risks. It is important to study new therapeutic approaches to this disease. Positional therapy might be beneficial in reducing the apnea-hypopnea index (AHI). Imaging methods have been employed in order to facilitate the evaluation of the airways of OSAS patients and can be used in order to determine the effectiveness of certain treatments. This study was aimed at determining the influence that upper airway volume, as measured by cervical CT, has in patients diagnosed with OSAS. Methods : This was a quantitative, observational, cross-sectional study. We evaluated 10 patients who had been diagnosed with OSAS by polysomnography and on the basis of the clinical evaluation. All of the patients underwent conventional cervical CT in the supine position. Scans were obtained with the head of the patient in two positions (neutral and at a 44° upward inclination), and the upper airway volume was compared between the two. Results : The mean age, BMI, and neck circumference were 48.9 ± 14.4 years, 30.5 ± 3.5 kg/m2, and 40.3 ± 3.4 cm, respectively. The mean AHI was 13.7 ± 10.6 events/h (range, 6.0-41.6 events/h). The OSAS was classified as mild, moderate, and severe in 70%, 20%, and 10% of the patients, respectively. The mean upper airway volume was 7.9 cm3 greater when the head was at a 44° upward inclination than when it was in the neutral position, and that difference (17.5 ± 11.0%) was statistically significant (p = 0.002). Conclusions : Elevating the head appears to result in a significant increase in the caliber of the upper airways in OSAS patients. PMID:26982042
Mirjalili, Shahab; Ivey, Christopher Blake; Mani, Ali
2016-11-01
The diffuse interface(DI) and volume of fluid(VOF) methods are mass conserving front capturing schemes which can handle large interfacial topology changes in realistic two phase flows. The DI method is a conservative phase field method that tracks an interface with finite thickness spread over a few cells and does not require reinitialization. In addition to having the desirable properties of level set methods for naturally capturing curvature and surface tension forces, the model conserves mass continuously and discretely. The VOF method, which tracks the fractional tagged volume in a cell, is discretely conservative by requiring costly geometric reconstructions of the interface and the fluxes. Both methods however, suffer from inaccuracies in calculation of curvature and surface tension forces. We present a quantitative comparison of these methods in terms of their accuracy, convergence rate, memory, and computational cost using canonical 2D two-phase test cases: damped surface wave, oscillating drop, equilibrium static drop, and dense moving drop. We further compared the models in their ability to handle thin films by looking at the impact of a water drop onto a deep water pool. Considering these results, we suggest qualitative guidelines for using the DI and VOF methods. Supported by ONR.
Choi, Jin Woo; Jeon, Seong Woo; Kwon, Jung Gu; Lee, Dong Wook; Ha, Chang Yoon; Cho, Kwang Bum; Jang, Byung Ik; Park, Jung Bae; Park, Youn Sun
2017-08-01
Nonvariceal upper gastrointestinal bleeding (NVUGIB) is a potentially life-threatening hospital emergency requiring hemodynamic stabilization and resuscitation. This study is carried out to determine whether hospital volume can influence outcome in patients with NVUGIB. This is a retrospective study with a prospective cohort database (KCT 0000514. cris.nih.go.kr). Eight teaching hospitals were divided into two different groups: high-volume centers (HVC, ≥60 NVUGIB patients/year, four clinics) and low-volume centers (LVC, bleeding after treatment, re-bleeding, necessity for surgical/other retreatments, and death within 30 days. Similar baseline characters for patients were observed in both groups. There was a significant difference in the incidence of poor outcome between the HVC and LVC groups (9.06 vs. 13.69%, P = 0.014). The incidence rate of poor outcome in high-risk patients (Rockall score ≥8) in HVC was lower than that in high-risk patients in LVC (16.07 vs. 26.92%, P = 0.048); however, there was no significant difference in poor outcome in the lower-risk patients in either group (8.72 vs. 10.42%, P = 0.370). Significant correlation between hospital volume and outcome in NVUGIB patients was observed. Referral to HVC for the management of high-risk NVUGIB patients should be considered in clinical practice.
Geometrical Bioelectrodynamics
Ivancevic, Vladimir G
2008-01-01
This paper proposes rigorous geometrical treatment of bioelectrodynamics, underpinning two fast-growing biomedical research fields: bioelectromagnetism, which deals with the ability of life to produce its own electromagnetism, and bioelectromagnetics, which deals with the effect on life from external electromagnetism. Keywords: Bioelectrodynamics, exterior geometrical machinery, Dirac-Feynman quantum electrodynamics, functional electrical stimulation
Modulation of Upper Esophageal Sphincter (UES) Relaxation and Opening During Volume Swallowing.
Cock, Charles; Jones, Corinne A; Hammer, Michael J; Omari, Taher I; McCulloch, Timothy M
2016-08-17
UES opening occurs following cricopharyngeus deactivation and submental muscle contraction causing hyolaryngeal elevation and UES distraction. During impedance manometry, the inverse of impedance (admittance) can be used to measure bolus presence and infer UES opening. We hypothesized that the temporal relationship between UES relaxation, opening and hyolaryngeal elevation would change with increasing bolus volume. Simultaneous intramuscular cricopharyngeal (CP) electromyography (EMG), surface submental EMG (SM-EMG), and high-resolution impedance manometry were recorded in eight (aged 27 ± 7 years, 5 M) healthy volunteers, while swallowing 0.9 % saline boluses of 2, 5, 10, and 20 ml. Data were exported and analyzed via Matlab. Statistical analysis comprised repeated measures one-way ANOVA and Pearson correlation. A P value of EMG activity occurs relatively later (P modulation of cricopharyngeal and submental muscle activity. Intrabolus pressures, transmitted from the tongue base and pharynx, play a progressively more important role in sphincter opening with increasing volume. The findings may explain why some healthy elderly and patients with oropharyngeal dysphagia have difficulty swallowing larger while tolerating smaller bolus volumes.
Kim, Min-Ah; Park, Yang-Ho
2014-01-01
The purpose of this study was to assess the pharyngeal airway volume change after bimaxillary surgery in patients with skeletal Class III malocclusion and evaluate the difference in postoperative pharyngeal airway space between upper premolar extraction cases and nonextraction cases. Cone-beam computed tomographic scans were obtained for 23 patients (13 in extraction group and 10 in nonextraction group) who were diagnosed with mandibular prognathism before surgery (T0) and then 2 months (T2) and 6 months after surgery (T3). Using InVivoDental 3-dimensional imaging software, volumetric changes in the pharyngeal airway space were assessed at T0, T2, and T3. The Wilcoxon signed-rank test was used to determine whether there were significant changes in pharyngeal airway volume between time points. The Mann-Whitney U test was used to determine whether there were significant differences in volumetric changes between the extraction and nonextraction groups. Volumes in all subsections of the pharyngeal airway were decreased (P bimaxillary surgery. Copyright © 2014 American Association of Oral and Maxillofacial Surgeons. Published by Elsevier Inc. All rights reserved.
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Balderson, Michael, E-mail: michael.balderson@rmp.uhn.ca; Brown, Derek; Johnson, Patricia; Kirkby, Charles
2016-07-01
The purpose of this work was to compare static gantry intensity-modulated radiation therapy (IMRT) with volume-modulated arc therapy (VMAT) in terms of tumor control probability (TCP) under scenarios involving large geometric misses, i.e., those beyond what are accounted for when margin expansion is determined. Using a planning approach typical for these treatments, a linear-quadratic–based model for TCP was used to compare mean TCP values for a population of patients who experiences a geometric miss (i.e., systematic and random shifts of the clinical target volume within the planning target dose distribution). A Monte Carlo approach was used to account for the different biological sensitivities of a population of patients. Interestingly, for errors consisting of coplanar systematic target volume offsets and three-dimensional random offsets, static gantry IMRT appears to offer an advantage over VMAT in that larger shift errors are tolerated for the same mean TCP. For example, under the conditions simulated, erroneous systematic shifts of 15 mm directly between or directly into static gantry IMRT fields result in mean TCP values between 96% and 98%, whereas the same errors on VMAT plans result in mean TCP values between 45% and 74%. Random geometric shifts of the target volume were characterized using normal distributions in each Cartesian dimension. When the standard deviations were doubled from those values assumed in the derivation of the treatment margins, our model showed a 7% drop in mean TCP for the static gantry IMRT plans but a 20% drop in TCP for the VMAT plans. Although adding a margin for error to a clinical target volume is perhaps the best approach to account for expected geometric misses, this work suggests that static gantry IMRT may offer a treatment that is more tolerant to geometric miss errors than VMAT.
Directory of Open Access Journals (Sweden)
Trunev A. P.
2014-05-01
Full Text Available In this article we have investigated the solutions of Maxwell's equations, Navier-Stokes equations and the Schrödinger associated with the solutions of Einstein's equations for empty space. It is shown that in some cases the geometric instability leading to turbulence on the mechanism of alternating viscosity, which offered by N.N. Yanenko. The mechanism of generation of matter from dark energy due to the geometric turbulence in the Big Bang has been discussed
Institute of Scientific and Technical Information of China (English)
LI Zhijun; LI Runling; WANG Zipan; HAAS Christian; DIECKMANN Gerhard
2016-01-01
During the winter and spring of 2006, we investigated the sea ice physics and marine biology in the northwest Weddell Sea, Antarctica aboard R/VPolarstern. We determined the texture of each ice core and 71 ice crystal thin sections from 27 ice cores. We analyzed 393 ice cores, their temperatures, 348 block density and salinity samples, and 311 chlorophylla (Chla) and phaeophytin samples along the cruise route during the investigation. Based on the vertical distributions of 302 groups of data for the ice porosity and Chla content in the ice at the same position, we obtained new evidence that ice physical parameters influence the Chla content in ice. We collected snow and ice thickness data, and established the effects of the snow and ice thickness on the Chla blooms under the ice, as well as the relationships between the activity of ice algae cells and the brine volume in ice according to the principle of environmental control of the ecological balance. We determined the upper limits for Chla in the brine volume of granular and columnar ice in the Antarctica, thereby demonstrating the effects of ice crystals on brine drainage, and the contributions of the physical properties of sea ice to Chla blooms near the ice bottom and on the ice-water interface in the austral spring. Moreover, we found that the physical properties of sea ice affect ice algae and they are key control elements that modulate marine phytoplankton blooms in the ice-covered waters around Antarctica.
Muniz Oliva, Waldyr
2002-01-01
Geometric Mechanics here means mechanics on a pseudo-riemannian manifold and the main goal is the study of some mechanical models and concepts, with emphasis on the intrinsic and geometric aspects arising in classical problems. The first seven chapters are written in the spirit of Newtonian Mechanics while the last two ones as well as two of the four appendices describe the foundations and some aspects of Special and General Relativity. All the material has a coordinate free presentation but, for the sake of motivation, many examples and exercises are included in order to exhibit the desirable flavor of physical applications.
Ersoy, Orkun; Şen, Erdal; Aydar, Erkan; Tatar, İlkan; Çelik, H. Hamdi
2010-10-01
Volcanic ash particles are important components of explosive eruptions, and their surface textures are the subject of intense research. Characterization of ash surfaces is crucial for understanding the physics of volcanic plumes, remote sensing measurements of ash and aerosols, interfacial processes, modelling transportation and deposition of tephra and characterizing eruptive styles. A number of different methods have been used over the years to arrive at surface area estimates. The more common methods include estimates based on geometric considerations (geometric surface area) and physisorption of gas molecules on the surface of interest (physical surface area). In this study, micro computed tomography (micro-CT), which is a non-destructive method providing three-dimensional data, enabled the measurement of surface area and volume of individual ash particles. Results were compared with the values obtained from SEM stereoscopic imaging and geometric considerations. Surface area estimates of micro-CT and SEM stereoscopic imaging are similar, with surface area/volume ratios (SA/V) of 0.0368 and 0.0467, respectively. Ash particle surface textures show a large deviation from that of simple geometric forms, and an approximation both to spheres and ellipsoids do not seem adequate for the representation of ash surface. SEM stereoscopic and/or micro-CT imaging are here suggested as good candidate techniques for the characterization of textures on macro-pore regions of ash particles.
Frè, Pietro Giuseppe
2013-01-01
‘Gravity, a Geometrical Course’ presents general relativity (GR) in a systematic and exhaustive way, covering three aspects that are homogenized into a single texture: i) the mathematical, geometrical foundations, exposed in a self consistent contemporary formalism, ii) the main physical, astrophysical and cosmological applications, updated to the issues of contemporary research and observations, with glimpses on supergravity and superstring theory, iii) the historical development of scientific ideas underlying both the birth of general relativity and its subsequent evolution. The book is divided in two volumes. Volume One is dedicated to the development of the theory and basic physical applications. It guides the reader from the foundation of special relativity to Einstein field equations, illustrating some basic applications in astrophysics. A detailed account of the historical and conceptual development of the theory is combined with the presentation of its mathematical foundations. Differe...
Bestvina, Mladen; Vogtmann, Karen
2014-01-01
Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and the present volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory. The institute consists of a set of intensive short courses offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The courses begin at an introductory level suitable for graduate students and lead up to currently active topics of research. The articles in this volume include introductions to CAT(0) cube complexes and groups, to modern small cancellation theory, to isometry groups of general CAT(0) spaces, and a discussion of nilpotent genus in the context of mapping class groups and CAT(0) gro...
Chisolm, Eric
2012-01-01
This is an introduction to geometric algebra, an alternative to traditional vector algebra that expands on it in two ways: 1. In addition to scalars and vectors, it defines new objects representing subspaces of any dimension. 2. It defines a product that's strongly motivated by geometry and can be taken between any two objects. For example, the product of two vectors taken in a certain way represents their common plane. This system was invented by William Clifford and is more commonly known as Clifford algebra. It's actually older than the vector algebra that we use today (due to Gibbs) and includes it as a subset. Over the years, various parts of Clifford algebra have been reinvented independently by many people who found they needed it, often not realizing that all those parts belonged in one system. This suggests that Clifford had the right idea, and that geometric algebra, not the reduced version we use today, deserves to be the standard "vector algebra." My goal in these notes is to describe geometric al...
Lloyd, Seth
2012-01-01
This letter analyzes the limits that quantum mechanics imposes on the accuracy to which spacetime geometry can be measured. By applying the fundamental physical bounds to measurement accuracy to ensembles of clocks and signals moving in curved spacetime -- e.g., the global positioning system -- I derive a covariant version of the quantum geometric limit: the total number of ticks of clocks and clicks of detectors that can be contained in a four volume of spacetime of radius r and temporal extent t is less than or equal to rt/\\pi x_P t_P, where x_P, t_P are the Planck length and time. The quantum geometric limit bounds the number of events or `ops' that can take place in a four-volume of spacetime: each event is associated with a Planck-scale area. Conversely, I show that if each quantum event is associated with such an area, then Einstein's equations must hold. The quantum geometric limit is consistent with and complementary to the holographic bound which limits the number of bits that can exist within a spat...
Directory of Open Access Journals (Sweden)
Luciana Baptista Pereira Abi-Ramia
2010-10-01
Full Text Available INTRODUÇÃO: o diagnóstico, o tratamento e o acompanhamento de pacientes portadores da síndrome da apneia obstrutiva do sono (SAOS são essenciais, por se tratar de um distúrbio que pode causar alterações sistêmicas. A efetividade do tratamento da SAOS com aparelhos intrabucais foi demonstrada através de estudos cefalométricos. OBJETIVO: o objetivo deste estudo foi avaliar o efeito do aparelho de avanço mandibular (Twin Block, TB no volume das vias aéreas superiores, por meio de tomografia computadorizada Cone-Beam (CBCT. Dezesseis pacientes (6 homens e 10 mulheres portadores de SAOS leve a moderada, idade média de 47,06 anos, utilizaram um aparelho de avanço mandibular e foram acompanhados por 7 meses, em média. MÉTODOS: foram feitas duas CBCT, sendo uma sem e outra com o aparelho em posição. A segmentação e a obtenção dos volumes das vias aéreas superiores foram realizadas e utilizado o teste t de Student pareado para análise estatística, com 5% de significância. RESULTADOS: houve aumento do volume da via aérea superior com TB quando comparado com o volume sem TB (pINTRODUCTION: Diagnosis, treatment and monitoring of patients with obstructive sleep apnea syndrome (OSAS are crucial because this disorder can cause systemic changes. The effectiveness of OSAS treatment with intraoral devices has been demonstrated through cephalometric studies. OBJECTIVE: The purpose of this study was to evaluate the effect of a mandibular advancement device (Twin Block, TB on the volume of the upper airways by means of Cone-Beam Computed Tomography (CBCT. Sixteen patients (6 men and 10 women with mild to moderate OSAS, mean age 47.06 years, wore a mandibular advancement device and were followed up for seven months on average. METHODS: Two CBCT scans were obtained: one with and one without the device in place. Upper airway volumes were segmented and obtained using Student's paired t-tests for statistical analysis with 5% significance level
Rosário, Henrique Damian; Oliveira, Gustavo Mussi Stefan; Freires, Irlan Almeida; de Souza Matos, Felipe; Paranhos, Luiz Renato
2017-01-01
Postsurgical changes of the airways have become a great point of interest because it has been reported that maxillomandibular advancement surgery can improve or eliminate obstructive sleep apnea; however, its treatment effectiveness is still controversial. The purpose of this systematic review and meta-analysis was to assess the effectiveness of maxillomandibular advancement surgery to increase upper airway volume in adults, comparing before and after treatment. Bibliographic searches of observational studies with no restriction of year or language were performed in the electronic databases PubMed, Scopus, ScienceDirect and SciELO for articles published up to April 2015. After verification of duplicate records, 1860 articles were examined. Of these, ten met the eligibility criteria, of which three were excluded for having poor methodological quality. The other seven articles were included in the systematic review and six in the meta-analysis, representing 83 patients. One study whose data were not given in absolute values was excluded from the meta-analysis. The meta-analysis showed a statistically significant difference between the averages of upper airway volume before and after surgery {7.86 cm(3) [95 % CI (6.22, 9.49), p = 1.00)}. Clinical evidence suggests that the upper airway volume is increased after maxillomandibular advancement surgery.
Pragmatic geometric model evaluation
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
World History (Volume Two): Upper Middle School Textbook for the Full-time Ten Year School System.
Chinese Education, 1981
1981-01-01
Contains a translation of the second volume of a two-volume world history textbook for senior secondary students published in China in 1978. This volume covers the period from 1848 to World War II. Particular attention is given to uprisings, rebellions, revolutions, and the development of the Communist movement. (AM)
Ambrosetti, Antonio; Malchiodi, Andrea
2009-01-01
This volume contains lecture notes on some topics in geometric analysis, a growing mathematical subject which uses analytical techniques, mostly of partial differential equations, to treat problems in differential geometry and mathematical physics. The presentation of the material should be rather accessible to non-experts in the field, since the presentation is didactic in nature. The reader will be provided with a survey containing some of the most exciting topics in the field, with a series of techniques used to treat such problems.
Geometric procedures for civil engineers
Tonias, Elias C
2016-01-01
This book provides a multitude of geometric constructions usually encountered in civil engineering and surveying practice. A detailed geometric solution is provided to each construction as well as a step-by-step set of programming instructions for incorporation into a computing system. The volume is comprised of 12 chapters and appendices that may be grouped in three major parts: the first is intended for those who love geometry for its own sake and its evolution through the ages, in general, and, more specifically, with the introduction of the computer. The second section addresses geometric features used in the book and provides support procedures used by the constructions presented. The remaining chapters and the appendices contain the various constructions. The volume is ideal for engineering practitioners in civil and construction engineering and allied areas.
1980-09-01
The Impacts of Dredge Spoil Placement on the Upper Mississippi River. Luther College, Decorah, Iowa. Meritt, F. S. 1968. Standard Handbook for Civil...L, bend equal to the length of the towboat and tow (Figure 1). I fh± ,L- flection arrle is knoan for a particular condition, a reasonzL3v z;cu- rate
Lee, U-Young; Kim, In-Beom; Kwak, Dai-Soon
2015-08-01
This study used 110 CT images taken from donated Korean cadavers to create 3-D models of the following upper and lower limb bones: the clavicle, scapula, humerus, radius, ulna, hip bone (os coxa), femur, patella (knee cap), tibia, talus, and calcaneus. In addition, the bone volume and surface area were calculated to determine sex differences using discriminant analysis. Significant sex differences were found in all bones with respect to volume and surface area (phip bone>tibia>humerus>scapula), although the order of surface area was different. The largest surface area in men was the femur and in women was the hip bone (psex determination (94%). When using the surface area of multiple bones, the maximum accuracy (99.4%) was achieved. The equation was as follows: (discriminant equation of surface area; femalesex determination.
1980-09-01
the water is chocked with living and dead vegetation. A surface layer of living algae , and rooted and floating plants cover a dense mass of dead and...8217-." -Caya Slough - Dead Slough -. : -Harpers Slough -Upper Mud Hen Cut -Little Louie Slough -Minnesota Slough * -Nelson Cut -DeSota Bay - Greymore Lake...bulrush (Scirpus * spp. . (Also see Table II.) Submerged Vegetation - Table II. Algae - Filamentous algae was noted near Station #3 in the 2nd lake
1980-09-01
watershed. Fertile topsoils are washed into creeks and streams dur- ing rainstorms and spring snowmelt and eventually reach the Mississippi River...second and third years. McMahon and Eckblad (1975) also tried whey and found it was conducive to seed germination and plant growth. They felt whey ...penetrate this crust, therefore enhancing its value. Because the 40 - i Upper Mississippi River is in the heart of America’s dairy country and whey is
A New, Effective and Low-Cost Three-Dimensional Approach for the Estimation of Upper-Limb Volume
Directory of Open Access Journals (Sweden)
Roberto Buffa
2015-05-01
Full Text Available The aim of this research was to validate a new procedure (SkanLab for the three-dimensional estimation of total arm volume. SkanLab is based on a single structured-light Kinect sensor (Microsoft, Redmond, WA, USA and on Skanect (Occipital, San Francisco, CA, USA and MeshLab (Visual Computing Lab, Pisa, Italy software. The volume of twelve plastic cylinders was measured using geometry, as the reference, water displacement and SkanLab techniques (two raters and repetitions. The right total arm volume of thirty adults was measured by water displacement (reference and SkanLab (two raters and repetitions. The bias and limits of agreement (LOA between techniques were determined using the Bland–Altman method. Intra- and inter-rater reliability was assessed using the intraclass correlation coefficient (ICC and the standard error of measurement. The bias of SkanLab in measuring the cylinders volume was −21.9 mL (−5.7% (LOA: −62.0 to 18.2 mL; −18.1% to 6.7% and in measuring the volume of arms’ was −9.9 mL (−0.6% (LOA: −49.6 to 29.8 mL; −2.6% to 1.4%. SkanLab’s intra- and inter-rater reliabilities were very high (ICC >0.99. In conclusion, SkanLab is a fast, safe and low-cost method for assessing total arm volume, with high levels of accuracy and reliability. SkanLab represents a promising tool in clinical applications.
Energy Technology Data Exchange (ETDEWEB)
Spofford, W.O. Jr.; Parker, A.L.; Kneese, A.V. (eds.)
1980-01-01
This two-volume set is based primarily on an RFF forum held in Albuquerque, New Mexico, in October 1976. Most of the papers in the book were presented at this forum. All of them were revised and updated after the forum; some were partly or even wholly rewritten. Some of the papers depend directly on research results reported in others, and therefore major revisions were necessary to integrate these papers. Two new papers were added after the forum was held, as was the appendix and five new discussions. This volume, Vol. I, contains the introductory chapter, 6 other papers (chapters), and an appendix; a separate abstract was prepared for each.
Energy Technology Data Exchange (ETDEWEB)
Spofford, W.O. Jr.; Parker, A.L.; Kneese, A.V. (eds.)
1980-01-01
The two-volume set is based primarily on an RFF forum held in Albuquerque, New Mexico, in October 1976. Most of the papers in the book were presented at this forum. All of them were revised and updated after the forum; some were partly or even wholly rewritten. Some of the papers depend directly on research results reported in others, and therefore major revisions were necessary to integrate these papers. Two new papers were added after the forum was held, as was the appendix, and five new discussions. This volume, Vol. II, contains the 10 other papers (chapters) of the set; a separate abstract was prepared for each.
Croddy, Marshall; Degelman, Charles; Doggett, Keri; Hayes, Bill
This is volume one of a two-volume civics curriculum on law and effective citizenship for upper-elementary students. The lessons, set in American historical eras, engage students in cooperative-learning activities, role plays, simulations, readers theater, stories, and guided discussions, which introduce and reinforce law-related and civic…
Geometric constraint solving with geometric transformation
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper proposes two algorithms for solving geometric constraint systems. The first algorithm is for constrained systems without loops and has linear complexity. The second algorithm can solve constraint systems with loops. The latter algorithm is of quadratic complexity and is complete for constraint problems about simple polygons. The key to it is to combine the idea of graph based methods for geometric constraint solving and geometric transformations coming from rule-based methods.
Geometric Topology and Shape Theory
Segal, Jack
1987-01-01
The aim of this international conference the third of its type was to survey recent developments in Geometric Topology and Shape Theory with an emphasis on their interaction. The volume contains original research papers and carefully selected survey of currently active areas. The main topics and themes represented by the papers of this volume include decomposition theory, cell-like mappings and CE-equivalent compacta, covering dimension versus cohomological dimension, ANR's and LCn-compacta, homology manifolds, embeddings of continua into manifolds, complement theorems in shape theory, approximate fibrations and shape fibrations, fibered shape, exact homologies and strong shape theory.
Federal Laboratory Consortium — Purpose: The mission of the Geometric Design Laboratory (GDL) is to support the Office of Safety Research and Development in research related to the geometric design...
On Geometric Infinite Divisibility
Sandhya, E.; Pillai, R. N.
2014-01-01
The notion of geometric version of an infinitely divisible law is introduced. Concepts parallel to attraction and partial attraction are developed and studied in the setup of geometric summing of random variables.
Geometric Computing Based on Computerized Descriptive Geometric
Institute of Scientific and Technical Information of China (English)
YU Hai-yan; HE Yuan-Jun
2011-01-01
Computer-aided Design （CAD）, video games and other computer graphic related technology evolves substantial processing to geometric elements. A novel geometric computing method is proposed with the integration of descriptive geometry, math and computer algorithm. Firstly, geometric elements in general position are transformed to a special position in new coordinate system. Then a 3D problem is projected to new coordinate planes. Finally, according to 2D/3D correspondence principle in descriptive geometry, the solution is constructed computerized drawing process with ruler and compasses. In order to make this method a regular operation, a two-level pattern is established. Basic Layer is a set algebraic packaged function including about ten Primary Geometric Functions （PGF） and one projection transformation. In Application Layer, a proper coordinate is established and a sequence of PGFs is sought for to get the final results. Examples illustrate the advantages of our method on dimension reduction, regulatory and visual computing and robustness.
Geometrization of Trace Formulas
Frenkel, Edward
2010-01-01
Following our joint work arXiv:1003.4578 with Robert Langlands, we make the first steps toward developing geometric methods for analyzing trace formulas in the case of the function field of a curve defined over a finite field. We also suggest a conjectural framework of geometric trace formulas for curves defined over the complex field, which exploits the categorical version of the geometric Langlands correspondence.
Localized Geometric Query Problems
Augustine, John; Maheshwari, Anil; Nandy, Subhas C; Roy, Sasanka; Sarvattomananda, Swami
2011-01-01
A new class of geometric query problems are studied in this paper. We are required to preprocess a set of geometric objects $P$ in the plane, so that for any arbitrary query point $q$, the largest circle that contains $q$ but does not contain any member of $P$, can be reported efficiently. The geometric sets that we consider are point sets and boundaries of simple polygons.
Field guide to geometrical optics
Greivenkamp, John E
2004-01-01
This Field Guide derives from the treatment of geometrical optics that has evolved from both the undergraduate and graduate programs at the Optical Sciences Center at the University of Arizona. The development is both rigorous and complete, and it features a consistent notation and sign convention. This volume covers Gaussian imagery, paraxial optics, first-order optical system design, system examples, illumination, chromatic effects, and an introduction to aberrations. The appendices provide supplemental material on radiometry and photometry, the human eye, and several other topics.
Exploring New Geometric Worlds
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…
Uhrich, Mark A.; Bragg, Heather M.
2003-01-01
Three real-time, instream water-quality and turbidity-monitoring sites were established in October 1998 in the upper North Santiam River Basin on the North Santiam River, the Breitenbush River, and Blowout Creek, the main tributary inputs to Detroit Lake, a large, controlled reservoir that extends from river mile 61 to 70. Suspended-sediment samples were collected biweekly to monthly at each station. Rating curves provided estimated suspended-sediment concentration in 30-minute increments from log transformations of the instream turbidity monitoring data. Turbidity was found to be a better surrogate than discharge for estimating suspended-sediment concentration. Daily and annual mean suspended-sediment loads were estimated using the estimated suspended-sediment concentrations and corresponding streamflow data. A laboratory method for estimating persistent (residual) turbidity from separate turbidity samples was developed. Turbidity was measured over time for each sample. Turbidity decay curves were derived as the suspended sediment settled. Each curve was used to estimate a turbidity value for a given settling time. Medium to fine clay particle (size clay particle persistent turbidity for each site. The monitored instream 30-minute turbidity values were converted to a calculated persistent turbidity value that would have resulted after 8.5 hours of settling in the laboratory. Persistent turbidities of 10 NTU and above were tabulated for each site. (Water of 10 NTU and above can interfere with or damage treatment filters and result in intake closures at drinking-water facilities.) A method was developed that used the persistent turbidity experiments, turbidity decay curves, and stream discharge to estimate the volume of water containing suspended clay that entered Detroit Lake from the three main tributaries. 'Suspended-clay water' was defined as water having a value of at least 10 NTU after settling the required 8.5 hours. The suspended-clay concentrations of 10
Geometric and unipotent crystals
Berenstein, Arkady; Kazhdan, David
1999-01-01
In this paper we introduce geometric crystals and unipotent crystals which are algebro-geometric analogues of Kashiwara's crystal bases. Given a reductive group G, let I be the set of vertices of the Dynkin diagram of G and T be the maximal torus of G. The structure of a geometric G-crystal on an algebraic variety X consists of a rational morphism \\gamma:X-->T and a compatible family e_i:G_m\\times X-->X, i\\in I of rational actions of the multiplicative group G_m satisfying certain braid-like ...
Geometric and engineering drawing
Morling, K
2010-01-01
The new edition of this successful text describes all the geometric instructions and engineering drawing information that are likely to be needed by anyone preparing or interpreting drawings or designs with plenty of exercises to practice these principles.
Differential geometric structures
Poor, Walter A
2007-01-01
This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.
Bledsoe, Gloria J
1987-01-01
The game of "Guess What" is described as a stimulating vehicle for students to consider the unifying or distinguishing features of geometric figures. Teaching suggestions as well as the gameboard are provided. (MNS)
Saturation and geometrical scaling
Praszalowicz, Michal
2016-01-01
We discuss emergence of geometrical scaling as a consequence of the nonlinear evolution equations of QCD, which generate a new dynamical scale, known as the saturation momentum: Qs. In the kinematical region where no other energy scales exist, particle spectra exhibit geometrical scaling (GS), i.e. they depend on the ratio pT=Qs, and the energy dependence enters solely through the energy dependence of the saturation momentum. We confront the hypothesis of GS in different systems with experimental data.
Proof in geometry with "mistakes in geometric proofs"
Fetisov, A I
2006-01-01
This single-volume compilation of 2 books explores the construction of geometric proofs. It offers useful criteria for determining correctness and presents examples of faulty proofs that illustrate common errors. 1963 editions.
Full Text Available ... Clinical Topics / Procedures F - Z / Upper Endoscopy (EGD) Upper Endoscopy (EGD) The Latest Practice Guidelines Technology Reviews ... the Safety of Your Endoscopic Procedure Brochure Understanding Upper Endoscopy Brochure Make the Best Choice for Your ...
Geometric systematic prostate biopsy.
Chang, Doyoung; Chong, Xue; Kim, Chunwoo; Jun, Changhan; Petrisor, Doru; Han, Misop; Stoianovici, Dan
2017-04-01
The common sextant prostate biopsy schema lacks a three-dimensional (3D) geometric definition. The study objective was to determine the influence of the geometric distribution of the cores on the detection probability of prostate cancer (PCa). The detection probability of significant (>0.5 cm(3)) and insignificant (geometric distribution of the cores was optimized to maximize the probability of detecting significant cancer for various prostate sizes (20-100cm(3)), number of biopsy cores (6-40 cores) and biopsy core lengths (14-40 mm) for transrectal and transperineal biopsies. The detection of significant cancer can be improved by geometric optimization. With the current sextant biopsy, up to 20% of tumors may be missed at biopsy in a 20 cm(3) prostate due to the schema. Higher number and longer biopsy cores are required to sample with an equal detection probability in larger prostates. Higher number of cores increases both significant and insignificant tumor detection probability, but predominantly increases the detection of insignificant tumors. The study demonstrates mathematically that the geometric biopsy schema plays an important clinical role, and that increasing the number of biopsy cores is not necessarily helpful.
Geometric control theory and sub-Riemannian geometry
Boscain, Ugo; Gauthier, Jean-Paul; Sarychev, Andrey; Sigalotti, Mario
2014-01-01
This volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as sub-Riemannian, Finslerian geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume.
Geometric optimization and sums of algebraic functions
Vigneron, Antoine E.
2014-01-01
We present a new optimization technique that yields the first FPTAS for several geometric problems. These problems reduce to optimizing a sum of nonnegative, constant description complexity algebraic functions. We first give an FPTAS for optimizing such a sum of algebraic functions, and then we apply it to several geometric optimization problems. We obtain the first FPTAS for two fundamental geometric shape-matching problems in fixed dimension: maximizing the volume of overlap of two polyhedra under rigid motions and minimizing their symmetric difference. We obtain the first FPTAS for other problems in fixed dimension, such as computing an optimal ray in a weighted subdivision, finding the largest axially symmetric subset of a polyhedron, and computing minimum-area hulls.
PREFACE: Geometrically frustrated magnetism Geometrically frustrated magnetism
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
Mahavira's Geometrical Problems
DEFF Research Database (Denmark)
Høyrup, Jens
2004-01-01
Analysis of the geometrical chapters Mahavira's 9th-century Ganita-sara-sangraha reveals inspiration from several chronological levels of Near-Eastern and Mediterranean mathematics: (1)that known from Old Babylonian tablets, c. 1800-1600 BCE; (2)a Late Babylonian but pre-Seleucid Stratum, probably...
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…
Dietary ecology of Murinae (Muridae, Rodentia): a geometric morphometric approach.
Gómez Cano, Ana Rosa; Hernández Fernández, Manuel; Alvarez-Sierra, M Ángeles
2013-01-01
Murine rodents represent a highly diverse group, which displays great ecological versatility. In the present paper we analyse the relationship between dental morphology, on one hand, using geometric morphometrics based upon the outline of first upper molar and the dietary preference of extant murine genera, on the other. This ecomorphological study of extant murine rodents demonstrates that dietary groups can be distinguished with the use of a quantitative geometric morphometric approach based on first upper molar outline. A discriminant analysis of the geometric morphometric variables of the first upper molars enables us to infer the dietary preferences of extinct murine genera from the Iberian Peninsula. Most of the extinct genera were omnivore; only Stephanomys showed a pattern of dental morphology alike that of the herbivore genera.
Dietary ecology of Murinae (Muridae, Rodentia: a geometric morphometric approach.
Directory of Open Access Journals (Sweden)
Ana Rosa Gómez Cano
Full Text Available 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.
Scale effect and geometric shapes of grains
Institute of Scientific and Technical Information of China (English)
GUO Hui; GUO Xing-ming
2007-01-01
The rule-of-mixture approach has become one of the widely spread ways to investigate the mechanical properties of nano-materials and nano-structures, and it is very important for the simulation results to exactly compute phase volume fractions. The nanocrystalline (NC) materials are treated as three-phase composites consisting of grain core phase, grain boundary (GB) phase and triple junction phase, and a two-dimensional three-phase mixture regular polygon model is established to investigate the scale effect of mechanical properties of NC materials due to the geometrical polyhedron characteristics of crystal grain. For different multi-sided geometrical shapes of grains, the corresponding regular polygon model is adopted to obtain more precise phase volume fractions and exactly predict the mechanical properties of NC materials.
Geometric measure theory a beginner's guide
Morgan, Frank
1995-01-01
Geometric measure theory is the mathematical framework for the study of crystal growth, clusters of soap bubbles, and similar structures involving minimization of energy. Morgan emphasizes geometry over proofs and technicalities, and includes a bibliography and abundant illustrations and examples. This Second Edition features a new chapter on soap bubbles as well as updated sections addressing volume constraints, surfaces in manifolds, free boundaries, and Besicovitch constant results. The text will introduce newcomers to the field and appeal to mathematicians working in the field.
Geometric reasoning about assembly tools
Energy Technology Data Exchange (ETDEWEB)
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.
Full Text Available ... Procedure Brochure Understanding Upper Endoscopy Brochure Make the Best Choice for Your Endoscopic Procedure Brochure Members-only ... Procedure Brochure Understanding Upper Endoscopy Brochure Make the Best Choice for Your Endoscopic Procedure Brochure View more ...
Full Text Available ... Endoscopic Submucosal Dissection (ESD) Endoscopic Ultrasound (EUS) Procedures F - Z GI Bleeding Manometry Photodynamic Therapy (PDT) Polypectomy ... Gastrointestinal Glossary of Terms Home / Clinical Topics / Procedures F - Z / Upper Endoscopy (EGD) Upper Endoscopy (EGD) The ...
Directory of Open Access Journals (Sweden)
Márcio Fragoso Vieira
2008-04-01
Full Text Available OBJETIVO: determinar a acurácia do volume do braço fetal aferido pela ultra-sonografia tridimensional (USG3D na predição de peso ao nascimento. MÉTODOS: realizou-se um estudo prospectivo, do tipo corte transversal, com 25 gestantes sem anormalidades estruturais ou cromossomopatias. Os parâmetros bidimensionais (diâmetro biparietal, circunferência abdominal e comprimento do fêmur e o volume do braço fetal pela USG3D foram avaliados em até 48 horas antes do parto. Para o cálculo do volume do braço fetal, utilizou-se o método multiplanar, por meio de múltiplos planos seqüenciais com intervalos de 5,0 mm. Realizaram-se regressões polinomiais para se determinar a melhor equação de predição de peso fetal. A acurácia desta nova fórmula foi comparada com as fórmulas bidimensionais de Shepard e Hadlock. RESULTADOS: o volume do braço fetal foi altamente correlacionado com o peso ao nascimento (r=0,83; p0,05. Em relação à fórmula de Hadlock, apenas o erro médio foi menor, mas não estatisticamente significante (p>0,05. CONCLUSÕES: o volume do braço fetal aferido pela USG3D mostrou acurácia similar às fórmulas bidimensionais na predição do peso ao nascimento. Há necessidade de estudos com maiores casuísticas para se comprovar esses achados.PURPOSE: to evaluate the accuracy of fetal upper arm volume, using three-dimensional ultrasound (3DUS, in the prediction of birth weight. METHODS: this prospective cross-sectional study involved 25 pregnancies without structural or chromosomal anomalies. Bidimensional parameters (biparietal diameter, abdominal circumference and femur length and the 3DUS fetal upper arm volume were obtained in the last 48 hours before delivery. The multiplanar method, using multiple sequential planes with 5.0-mm intervals, was used to calculate fetal upper arm volume. Polynomial regressions were used to determine the best equation in the prediction of fetal weight. The accuracy of this new formula was
Testing algebraic geometric codes
Institute of Scientific and Technical Information of China (English)
CHEN Hao
2009-01-01
Property testing was initially studied from various motivations in 1990's.A code C (∩)GF(r)n is locally testable if there is a randomized algorithm which can distinguish with high possibility the codewords from a vector essentially far from the code by only accessing a very small (typically constant) number of the vector's coordinates.The problem of testing codes was firstly studied by Blum,Luby and Rubinfeld and closely related to probabilistically checkable proofs (PCPs).How to characterize locally testable codes is a complex and challenge problem.The local tests have been studied for Reed-Solomon (RS),Reed-Muller (RM),cyclic,dual of BCH and the trace subcode of algebraicgeometric codes.In this paper we give testers for algebraic geometric codes with linear parameters (as functions of dimensions).We also give a moderate condition under which the family of algebraic geometric codes cannot be locally testable.
Testing algebraic geometric codes
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Property testing was initially studied from various motivations in 1990’s. A code C GF (r)n is locally testable if there is a randomized algorithm which can distinguish with high possibility the codewords from a vector essentially far from the code by only accessing a very small (typically constant) number of the vector’s coordinates. The problem of testing codes was firstly studied by Blum, Luby and Rubinfeld and closely related to probabilistically checkable proofs (PCPs). How to characterize locally testable codes is a complex and challenge problem. The local tests have been studied for Reed-Solomon (RS), Reed-Muller (RM), cyclic, dual of BCH and the trace subcode of algebraicgeometric codes. In this paper we give testers for algebraic geometric codes with linear parameters (as functions of dimensions). We also give a moderate condition under which the family of algebraic geometric codes cannot be locally testable.
Dynamics in geometrical confinement
Kremer, Friedrich
2014-01-01
This book describes the dynamics of low molecular weight and polymeric molecules when they are constrained under conditions of geometrical confinement. It covers geometrical confinement in different dimensionalities: (i) in nanometer thin layers or self supporting films (1-dimensional confinement) (ii) in pores or tubes with nanometric diameters (2-dimensional confinement) (iii) as micelles embedded in matrices (3-dimensional) or as nanodroplets.The dynamics under such conditions have been a much discussed and central topic in the focus of intense worldwide research activities within the last two decades. The present book discusses how the resulting molecular mobility is influenced by the subtle counterbalance between surface effects (typically slowing down molecular dynamics through attractive guest/host interactions) and confinement effects (typically increasing the mobility). It also explains how these influences can be modified and tuned, e.g. through appropriate surface coatings, film thicknesses or pore...
Full Text Available ... Upper Endoscopy (EGD) Upper Endoscopy (EGD) The Latest Practice Guidelines Technology Reviews Articles Videos Events & Products Ensuring the Safety of Your Endoscopic Procedure Brochure Understanding Upper Endoscopy Brochure Make the Best Choice for Your Endoscopic Procedure Brochure Members-only ...
Progressive geometric algorithms
Directory of Open Access Journals (Sweden)
Sander P.A. Alewijnse
2015-01-01
Full Text Available Progressive algorithms are algorithms that, on the way to computing a complete solution to the problem at hand, output intermediate solutions that approximate the complete solution increasingly well. We present a framework for analyzing such algorithms, and develop efficient progressive algorithms for two geometric problems: computing the convex hull of a planar point set, and finding popular places in a set of trajectories.
Geometric Time Delay Interferometry
Vallisneri, Michele
2005-01-01
The space-based gravitational-wave observatory LISA, a NASA-ESA mission to be launched after 2012, will achieve its optimal sensitivity using Time Delay Interferometry (TDI), a LISA-specific technique needed to cancel the otherwise overwhelming laser noise in the inter-spacecraft phase measurements. The TDI observables of the Michelson and Sagnac types have been interpreted physically as the virtual measurements of a synthesized interferometer. In this paper, I present Geometric TDI, a new an...
Geometric unsharpness calculations
Energy Technology Data Exchange (ETDEWEB)
Anderson, D.J. [International Training and Education Group (INTEG), Oakville, Ontario (Canada)
2008-07-15
The majority of radiographers' geometric unsharpness calculations are normally performed with a mathematical formula. However, a majority of codes and standards refer to the use of a nomograph for this calculation. Upon first review, the use of a nomograph appears more complicated but with a few minutes of study and practice it can be just as effective. A review of this article should provide enlightenment. (author)
Geometric Stochastic Resonance
Ghosh, Pulak Kumar; Savel'ev, Sergey E; Nori, Franco
2015-01-01
A Brownian particle moving across a porous membrane subject to an oscillating force exhibits stochastic resonance with properties which strongly depend on the geometry of the confining cavities on the two sides of the membrane. Such a manifestation of stochastic resonance requires neither energetic nor entropic barriers, and can thus be regarded as a purely geometric effect. The magnitude of this effect is sensitive to the geometry of both the cavities and the pores, thus leading to distinctive optimal synchronization conditions.
Geometrically Consistent Mesh Modification
Bonito, A.
2010-01-01
A new paradigm of adaptivity is to execute refinement, coarsening, and smoothing of meshes on manifolds with incomplete information about their geometry and yet preserve position and curvature accuracy. We refer to this collectively as geometrically consistent (GC) mesh modification. We discuss the concept of discrete GC, show the failure of naive approaches, and propose and analyze a simple algorithm that is GC and accuracy preserving. © 2010 Society for Industrial and Applied Mathematics.
Geometric properties of eigenfunctions
Energy Technology Data Exchange (ETDEWEB)
Jakobson, D; Nadirashvili, N [McGill University, Montreal, Quebec (Canada); Toth, John [University of Chicago, Chicago, Illinois (United States)
2001-12-31
We give an overview of some new and old results on geometric properties of eigenfunctions of Laplacians on Riemannian manifolds. We discuss properties of nodal sets and critical points, the number of nodal domains, and asymptotic properties of eigenfunctions in the high-energy limit (such as weak * limits, the rate of growth of L{sup p} norms, and relationships between positive and negative parts of eigenfunctions)
Geometric theory of information
2014-01-01
This book brings together geometric tools and their applications for Information analysis. It collects current and many uses of in the interdisciplinary fields of Information Geometry Manifolds in Advanced Signal, Image & Video Processing, Complex Data Modeling and Analysis, Information Ranking and Retrieval, Coding, Cognitive Systems, Optimal Control, Statistics on Manifolds, Machine Learning, Speech/sound recognition, and natural language treatment which are also substantially relevant for the industry.
Perspective: Geometrically frustrated assemblies
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.
Energy Technology Data Exchange (ETDEWEB)
Adam, C., E-mail: adam@fpaxp1.usc.es [Departamento de Física de Partículas, Universidad de Santiago de Compostela and Instituto Galego de Física de Altas Enerxias (IGFAE), E-15782 Santiago de Compostela (Spain); Haberichter, M. [School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury, CT2 7NF (United Kingdom); Wereszczynski, A. [Institute of Physics, Jagiellonian University, Lojasiewicza 11, Kraków (Poland)
2016-03-10
There exists, in general, no unique definition of the size (volume, area, etc., depending on dimension) of a soliton. Here we demonstrate that the geometric volume (area etc.) of a soliton is singled out in the sense that it exactly coincides with the thermodynamical or continuum-mechanical volume. In addition, this volume may be defined uniquely for rather arbitrary solitons in arbitrary dimensions.
Geometric diffusion of quantum trajectories.
Yang, Fan; Liu, Ren-Bao
2015-07-16
A quantum object can acquire a geometric phase (such as Berry phases and Aharonov-Bohm phases) when evolving along a path in a parameter space with non-trivial gauge structures. Inherent to quantum evolutions of wavepackets, quantum diffusion occurs along quantum trajectories. Here we show that quantum diffusion can also be geometric as characterized by the imaginary part of a geometric phase. The geometric quantum diffusion results from interference between different instantaneous eigenstate pathways which have different geometric phases during the adiabatic evolution. As a specific example, we study the quantum trajectories of optically excited electron-hole pairs in time-reversal symmetric insulators, driven by an elliptically polarized terahertz field. The imaginary geometric phase manifests itself as elliptical polarization in the terahertz sideband generation. The geometric quantum diffusion adds a new dimension to geometric phases and may have applications in many fields of physics, e.g., transport in topological insulators and novel electro-optical effects.
Institute of Scientific and Technical Information of China (English)
刘璐; 李荣荣; 刘梦臖; 张琰; 刘东旭
2015-01-01
Objective To investigate the alveolar bone volume around upper incisors in adult patients with Class Ⅰbimaxillary protrusion and provide a reference for orthodontic diagnosis and treatment planning.Methods Twenty-two cases with Class Ⅰ bimaxillary protrusion (bimaxillary protrusion group)and Eighteen cases with individual normal occlusion (control group)were recruited.Lateral cephalograms and cone beam computed tomography(CBCT)scan-nings were taken respectively and the alveolar bone volume around four upper incisors in each subject were measured by Mimics 16.0.Results In bimaxillary protrusion group,alveolar bone volume around upper incisors decreased com-pared to the control group (P <0.05),apart from labial root apex zone of central incisors,labial root apex and palatal crest zone of the lateral incisors.Besides,alveolar crest zone,middle root zone,palatal alveolar bone,total alveolar bone of the central incisors,labial alveolar bone,palatal alveolar bone,total alveolar bone of the lateral incisors and total alveolar bone volume of four upper incisors in bimaxillary protrusion group were decreased compared to the control group (P <0.001).Conclusion The alveolar bone volume around upper incisors in adult patients with Class Ⅰ bima-xillary protrusion is fewer than that in the subjects with normal occlusion.It should be more cautious in the process of treatment planning,especially retraction or intrusion of the upper incisors.%目的：研究成人安氏Ⅰ类双颌前突患者上颌切牙区牙槽骨体积，为正畸诊断及治疗计划制定提供参考。方法选择安氏Ⅰ类双颌前突患者22例（双颌前突组）及个别正常牙合志愿者18例（对照组），分别拍摄头颅侧位片及锥体束计算机断层扫描（CBCT），利用 Mimics 16．0测量上颌4颗切牙牙槽骨体积。结果双颌前突组上颌切牙区牙槽骨体积除中切牙唇侧根尖区、侧切牙唇侧根尖区及腭侧牙槽嵴顶区外，
Algebraic geometric codes with applications
Institute of Scientific and Technical Information of China (English)
CHEN Hao
2007-01-01
The theory of linear error-correcting codes from algebraic geomet-ric curves (algebraic geometric (AG) codes or geometric Goppa codes) has been well-developed since the work of Goppa and Tsfasman, Vladut, and Zink in 1981-1982. In this paper we introduce to readers some recent progress in algebraic geometric codes and their applications in quantum error-correcting codes, secure multi-party computation and the construction of good binary codes.
Taradaj, J; Halski, T; Rosinczuk, J; Dymarek, R; Laurowski, A; Smykla, A
2016-07-01
The aim of our study was to evaluate the effect of Kinesiology Taping (KT) on the size of lymphoedema and manual dexterity of the upper limb in women after breast cancer treatment. We also examined whether the application of KT can replace the traditional and standard multilayered bandaging in the treatment of upper extremity lymphoedema. Group A comprised of 22 patients who underwent KT as well as pneumatic and manual lymphatic drainage. Then, group B comprised of 23 patients who were treated with quasi-KT as well as pneumatic and manual lymphatic drainage. In contrast, group C had 25 patients subjected only to the standard procedure - pneumatic and manual lymphatic drainage and multilayered bandaging. Patient evaluation items included limb size, grip strength and range of motion. After 4-week therapy, we observed that KT is not an effective method of reducing lymphoedema II and III(0) in women after breast cancer treatment. At this moment, the taping cannot replace the traditional and standard multilayered bandaging in the treatment of upper extremity lymphoedema. © 2015 John Wiley & Sons Ltd.
Institute of Scientific and Technical Information of China (English)
杨飞; 沈婧芳
2011-01-01
本文研究了黎曼流形上一类一般的曲率流问题.利用Perelman在Ricci流下导出体积单调性的方法,在初始流形完备非紧的情况下,获得了这类曲率流的一个单调性的体积公式,推广了Reto Müller在紧致情形的结果.%We consider a kind of general geometric flow problem. By utilizing Perelman's method under the Ricci flow, when the initial manifold is complete and noncompact, we obtain compact.
Geometric Number Systems and Spinors
Sobczyk, Garret
2015-01-01
The real number system is geometrically extended to include three new anticommuting square roots of plus one, each such root representing the direction of a unit vector along the orthonormal coordinate axes of Euclidean 3-space. The resulting geometric (Clifford) algebra provides a geometric basis for the famous Pauli matrices which, in turn, proves the consistency of the rules of geometric algebra. The flexibility of the concept of geometric numbers opens the door to new understanding of the nature of space-time, and of Pauli and Dirac spinors as points on the Riemann sphere, including Lorentz boosts.
Bose, Prosenjit; Morin, Pat; Smid, Michiel
2012-01-01
Highly connected and yet sparse graphs (such as expanders or graphs of high treewidth) are fundamental, widely applicable and extensively studied combinatorial objects. We initiate the study of such highly connected graphs that are, in addition, geometric spanners. We define a property of spanners called robustness. Informally, when one removes a few vertices from a robust spanner, this harms only a small number of other vertices. We show that robust spanners must have a superlinear number of edges, even in one dimension. On the positive side, we give constructions, for any dimension, of robust spanners with a near-linear number of edges.
Corrochano, Eduardo Bayro
2010-01-01
This book presents contributions from a global selection of experts in the field. This useful text offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. Written in an accessible style, the discussion of all applications is enhanced by the inclusion of numerous examples, figures and experimental analysis. Features: provides a thorough discussion of several tasks for image processing, pattern recognition, computer vision, robotics and computer graphics using the geometric algebra framework; int
Shapere, Alfred D
1989-01-01
During the last few years, considerable interest has been focused on the phase that waves accumulate when the equations governing the waves vary slowly. The recent flurry of activity was set off by a paper by Michael Berry, where it was found that the adiabatic evolution of energy eigenfunctions in quantum mechanics contains a phase of geometric origin (now known as 'Berry's phase') in addition to the usual dynamical phase derived from Schrödinger's equation. This observation, though basically elementary, seems to be quite profound. Phases with similar mathematical origins have been identified
Alternative proofs for Kocik's Geometric Diagram for Relativistic Velocity Addition
Sasane, Amol
2015-01-01
A geometric construction for the Poincare formula for relativistic addition of velocities in one dimension was given by Jerzy Kocik in "Geometric Diagram for Relativistic Addition of Velocities", American Journal of Physics, volume 80, page 737, 2012. While the proof given there used Cartesian coordinate geometry, three alternative approaches are given in this article: a trigonometric one, one via Euclidean geometry, and one using projective geometry.
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Bidimensionality and Geometric Graphs
Fomin, Fedor V; Saurabh, Saket
2011-01-01
In this paper we use several of the key ideas from Bidimensionality to give a new generic approach to design EPTASs and subexponential time parameterized algorithms for problems on classes of graphs which are not minor closed, but instead exhibit a geometric structure. In particular we present EPTASs and subexponential time parameterized algorithms for Feedback Vertex Set, Vertex Cover, Connected Vertex Cover, Diamond Hitting Set, on map graphs and unit disk graphs, and for Cycle Packing and Minimum-Vertex Feedback Edge Set on unit disk graphs. Our results are based on the recent decomposition theorems proved by Fomin et al [SODA 2011], and our algorithms work directly on the input graph. Thus it is not necessary to compute the geometric representations of the input graph. To the best of our knowledge, these results are previously unknown, with the exception of the EPTAS and a subexponential time parameterized algorithm on unit disk graphs for Vertex Cover, which were obtained by Marx [ESA 2005] and Alber and...
Manwani, Naresh
2010-01-01
In this paper we present a new algorithm for learning oblique decision trees. Most of the current decision tree algorithms rely on impurity measures to assess the goodness of hyperplanes at each node while learning a decision tree in a top-down fashion. These impurity measures do not properly capture the geometric structures in the data. Motivated by this, our algorithm uses a strategy to assess the hyperplanes in such a way that the geometric structure in the data is taken into account. At each node of the decision tree, we find the clustering hyperplanes for both the classes and use their angle bisectors as the split rule at that node. We show through empirical studies that this idea leads to small decision trees and better performance. We also present some analysis to show that the angle bisectors of clustering hyperplanes that we use as the split rules at each node, are solutions of an interesting optimization problem and hence argue that this is a principled method of learning a decision tree.
Manfredini, Maria; Morbidelli, Daniele; Polidoro, Sergio; Uguzzoni, Francesco
2015-01-01
The analysis of PDEs is a prominent discipline in mathematics research, both in terms of its theoretical aspects and its relevance in applications. In recent years, the geometric properties of linear and nonlinear second order PDEs of elliptic and parabolic type have been extensively studied by many outstanding researchers. This book collects contributions from a selected group of leading experts who took part in the INdAM meeting "Geometric methods in PDEs", on the occasion of the 70th birthday of Ermanno Lanconelli. They describe a number of new achievements and/or the state of the art in their discipline of research, providing readers an overview of recent progress and future research trends in PDEs. In particular, the volume collects significant results for sub-elliptic equations, potential theory and diffusion equations, with an emphasis on comparing different methodologies and on their implications for theory and applications. .
Geometric description of images as topographic maps
Caselles, Vicent
2010-01-01
This volume discusses the basic geometric contents of an image and presents a tree data structure to handle those contents efficiently. The nodes of the tree are derived from connected components of level sets of the intensity, while the edges represent inclusion information. Grain filters, morphological operators simplifying these geometric contents, are analyzed and several applications to image comparison and registration, and to edge and corner detection, are presented. The mathematically inclined reader may be most interested in Chapters 2 to 6, which generalize the topological Morse description to continuous or semicontinuous functions, while mathematical morphologists may more closely consider grain filters in Chapter 3. Computer scientists will find algorithmic considerations in Chapters 6 and 7, the full justification of which may be found in Chapters 2 and 4 respectively. Lastly, all readers can learn more about the motivation for this work in the image processing applications presented in Chapter 8...
Geometric Complexity Theory: Introduction
Sohoni, Ketan D Mulmuley Milind
2007-01-01
These are lectures notes for the introductory graduate courses on geometric complexity theory (GCT) in the computer science department, the university of Chicago. Part I consists of the lecture notes for the course given by the first author in the spring quarter, 2007. It gives introduction to the basic structure of GCT. Part II consists of the lecture notes for the course given by the second author in the spring quarter, 2003. It gives introduction to invariant theory with a view towards GCT. No background in algebraic geometry or representation theory is assumed. These lecture notes in conjunction with the article \\cite{GCTflip1}, which describes in detail the basic plan of GCT based on the principle called the flip, should provide a high level picture of GCT assuming familiarity with only basic notions of algebra, such as groups, rings, fields etc.
The Geometric Transition Revisited
Gwyn, Rhiannon
2007-01-01
Our intention in this article is to review known facts and to summarise recent advances in the understanding of geometric transitions and the underlying open/closed duality in string theory. We aim to present a pedagogical discussion of the gauge theory underlying the Klebanov--Strassler model and review the Gopakumar--Vafa conjecture based on topological string theory. These models are also compared in the T-dual brane constructions. We then summarise a series of papers verifying both models on the supergravity level. An appendix provides extensive background material about conifold geometries. We pay special attention to their complex structures and re-evaluate the supersymmetry conditions on the background flux in constructions with fractional D3-branes on the singular (Klebanov--Strassler) and resolved (Pando Zayas--Tseytlin) conifolds. We agree with earlier results that only the singular solution allows a supersymmetric flux, but point out the importance of using the correct complex structure to reach th...
Kahle, Matthew
2009-01-01
We study the expected topological properties of Cech and Vietoris-Rips complexes built on randomly sampled points in R^d. These are, in some cases, analogues of known results for connectivity and component counts for random geometric graphs. However, an important difference in this setting is that homology is not monotone in the underlying parameter. In the sparse range, we compute the expectation and variance of the Betti numbers, and establish Central Limit Theorems and concentration of measure. In the dense range, we introduce Morse theoretic arguments to bound the expectation of the Betti numbers, which is the main technical contribution of this article. These results provide a detailed probabilistic picture to compare with the topological statistics of point cloud data.
Geometrical Destabilization of Inflation
Renaux-Petel, Sébastien; Turzyński, Krzysztof
2016-09-01
We show the existence of a general mechanism by which heavy scalar fields can be destabilized during inflation, relying on the fact that the curvature of the field space manifold can dominate the stabilizing force from the potential and destabilize inflationary trajectories. We describe a simple and rather universal setup in which higher-order operators suppressed by a large energy scale trigger this instability. This phenomenon can prematurely end inflation, thereby leading to important observational consequences and sometimes excluding models that would otherwise perfectly fit the data. More generally, it modifies the interpretation of cosmological constraints in terms of fundamental physics. We also explain how the geometrical destabilization can lead to powerful selection criteria on the field space curvature of inflationary models.
Evolution of Brain Tumor and Stability of Geometric Invariants
Directory of Open Access Journals (Sweden)
K. Tawbe
2008-01-01
Full Text Available This paper presents a method to reconstruct and to calculate geometric invariants on brain tumors. The geometric invariants considered in the paper are the volume, the area, the discrete Gauss curvature, and the discrete mean curvature. The volume of a tumor is an important aspect that helps doctors to make a medical diagnosis. And as doctors seek a stable calculation, we propose to prove the stability of some invariants. Finally, we study the evolution of brain tumor as a function of time in two or three years depending on patients with MR images every three or six months.
Computing the Expected Value and Variance of Geometric Measures
DEFF Research Database (Denmark)
Staals, Frank; Tsirogiannis, Constantinos
2017-01-01
points in P. This problem is a crucial part of modern ecological analyses; each point in P represents a species in d-dimensional trait space, and the goal is to compute the statistics of a geometric measure on this trait space, when subsets of species are selected under random processes. We present...... efficient exact algorithms for computing the mean and variance of several geometric measures when point sets are selected under one of the described random distributions. More specifically, we provide algorithms for the following measures: the bounding box volume, the convex hull volume, the mean pairwise...
1981-04-01
Overriding considerations including operating range, volume and lining of reservoir, embankment design, intake/outlet arrangements and filling and make up water provisions were studied within the context of minimizing facility costs and optimizing the plant layout. The study led to the selection of a reservoir formed by embankment of compacted rockfill together with an intake/outlet structure located in the embankment. The reservoir floor and upstream slopes of the embankment will have an asphalt lining to prevent leakage. The material and cost estimates presented are based on the requirements for a 2000 MW plant providing 20,000 MWh of storage with a nominal head of 4600 ft.
Full Text Available ... Upper Endoscopy (EGD) The Latest Practice Guidelines Technology Reviews Articles Videos Events & Products Ensuring the Safety of ... S0016-5107(98)70268-8 View more Technology Reviews Members-only content Document Link: ASGE Leading Edge: ...
Full Text Available ... Upper Endoscopy (EGD) The Latest Practice Guidelines Technology Reviews Articles Videos Events & Products Ensuring the Safety of ... S0016-5107(98)70268-8 View more Technology Reviews Members-only content Document Link: ASGE Leading Edge: ...
Full Text Available ... EGD) Upper Endoscopy (EGD) The Latest Practice Guidelines Technology Reviews Articles Videos Events & Products Ensuring the Safety ... 1016/S0016-5107(98)70268-8 View more Technology Reviews Members-only content Document Link: ASGE Leading ...
Full Text Available ... EGD) Upper Endoscopy (EGD) The Latest Practice Guidelines Technology Reviews Articles Videos Events & Products Ensuring the Safety ... 1016/S0016-5107(98)70268-8 View more Technology Reviews Members-only content Document Link: ASGE Leading ...
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Azizi, Fouad; Arredouani, Abdelilah; Mohammad, Ramzi M
2015-01-01
During airway inflammation, airway surface liquid volume (ASLV) expansion may result from the movement of plasma proteins and excess liquid into the airway lumen due to extravasation and elevation of subepithelial hydrostatic pressure. We previously demonstrated that elevation of submucosal hydrostatic pressure increases airway epithelium permeability resulting in ASLV expansion by 500 μL cm−2 h−1. Liquid reabsorption by healthy airway epithelium is regulated by active Na+ transport at a rate of 5 μL cm−2 h−1. Thus, during inflammation the airway epithelium may be submerged by a large volume of luminal liquid. Here, we have investigated the mechanism by which ASLV expansion alters active epithelial Na+ transport, and we have characterized the time course of the change. We used primary cultures of tracheal airway epithelium maintained under air interface (basal ASLV, depth is 7 ± 0.5 μm). To mimic airway flooding, ASLV was expanded to a depth of 5 mm. On switching from basal to expanded ASLV conditions, short-circuit current (Isc, a measure of total transepithelial active ion transport) declined by 90% with a half-time (t1/2) of 1 h. 24 h after the switch, there was no significant change in ATP concentration nor in the number of functional sodium pumps as revealed by [3H]-ouabain binding. However, amiloride-sensitive uptake of 22Na+ was reduced by 70% upon ASLV expansion. This process is reversible since after returning cells back to air interface, Isc recovered with a t1/2 of 5–10 h. These results may have important clinical implications concerning the development of Na+ channels activators and resolution of pulmonary edema. PMID:26333829
Harmonic and geometric analysis
Citti, Giovanna; Pérez, Carlos; Sarti, Alessandro; Zhong, Xiao
2015-01-01
This book presents an expanded version of four series of lectures delivered by the authors at the CRM. Harmonic analysis, understood in a broad sense, has a very wide interplay with partial differential equations and in particular with the theory of quasiconformal mappings and its applications. Some areas in which real analysis has been extremely influential are PDE's and geometric analysis. Their foundations and subsequent developments made extensive use of the Calderón–Zygmund theory, especially the Lp inequalities for Calderón–Zygmund operators (Beurling transform and Riesz transform, among others) and the theory of Muckenhoupt weights. The first chapter is an application of harmonic analysis and the Heisenberg group to understanding human vision, while the second and third chapters cover some of the main topics on linear and multilinear harmonic analysis. The last serves as a comprehensive introduction to a deep result from De Giorgi, Moser and Nash on the regularity of elliptic partial differen...
Geometrical approach to fluid models
Kuvshinov, B. N.; Schep, T. J.
1997-01-01
Differential geometry based upon the Cartan calculus of differential forms is applied to investigate invariant properties of equations that describe the motion of continuous media. The main feature of this approach is that physical quantities are treated as geometrical objects. The geometrical
In Defence of Geometrical Algebra
Blasjo, V.N.E.
2016-01-01
The geometrical algebra hypothesis was once the received interpretation of Greek mathematics. In recent decades, however, it has become anathema to many. I give a critical review of all arguments against it and offer a consistent rebuttal case against the modern consensus. Consequently, I find that the geometrical algebra interpretation should be reinstated as a viable historical hypothesis.
Homological Type of Geometric Transitions
Rossi, Michele
2010-01-01
The present paper gives an account and quantifies the change in topology induced by small and type II geometric transitions, by introducing the notion of the \\emph{homological type} of a geometric transition. The obtained results agree with, and go further than, most results and estimates, given to date by several authors, both in mathematical and physical literature.
Geometrical approach to fluid models
Kuvshinov, B. N.; Schep, T. J.
1997-01-01
Differential geometry based upon the Cartan calculus of differential forms is applied to investigate invariant properties of equations that describe the motion of continuous media. The main feature of this approach is that physical quantities are treated as geometrical objects. The geometrical notio
Transmuted Complementary Weibull Geometric Distribution
Directory of Open Access Journals (Sweden)
Ahmed Z. A fify
2014-12-01
Full Text Available This paper provides a new generalization of the complementary Weibull geometric distribution that introduced by Tojeiro et al. (2014, using the quadratic rank transmutation map studied by Shaw and Buckley (2007. The new distribution is referred to as transmuted complementary Weibull geometric distribution (TCWGD. The TCWG distribution includes as special cases the complementary Weibull geometric distribution (CWGD, complementary exponential geometric distribution(CEGD,Weibull distribution (WD and exponential distribution (ED. Various structural properties of the new distribution including moments, quantiles, moment generating function and RØnyi entropy of the subject distribution are derived. We proposed the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set are used to compare the exibility of the transmuted version versus the complementary Weibull geometric distribution.
Pinto, Nicole; Salassi, James W; Donlin, Ayla; Schroeder, Jan; Rozenek, Ralph
2017-05-30
The purpose of this study was to compare the effects of upper extremity (UE) high intensity interval training (HIIT) to UE continuous training (CT) when training at a similar intensity. 20 participants (mean age = 23 ± 3 yrs) were randomly assigned to either a HIIT (n = 10) or CT (n = 10) group. Participants completed a graded exercise test utilizing arm cranking prior to and following 6 wks (2 sessions · wk-1) of UE training. During sessions, HIIT performed 10 repetitions of 60 s of work at 92.3 ± 1.0% of the arm HRpeak (%aHRpeak) and 60 s of passive recovery (%aHRpeak = 73.0 ± 4.0%) yielding an average training intensity of 82.6 ± 1.5 %aHRpeak. CT exercised for 20 min. at an average intensity of 81.9 ± 2.2 %aHRpeak. Following training HIIT showed greater improvement in V[Combining Dot Above]O2peak compared to CT (Δ = 4.1 ml · min-¹ · kg-¹, 95%CI: 1.3 - 6.9 ml · min-¹ · kg-¹, p = .007). Total exercise time during the post-test GXT was also improved as a result of HIIT (Δ = 1.4 min, 95%CI: 0.4 - 2.3 min, p = .008). Both groups improved peak power output, but no difference was observed between them (Δ = 3.3 W, 95%CI: -3.3 - 9.9 W, p = .305). For a similar time investment, HIIT appeared to improve cardiopulmonary capacity and exercise time to a greater extent than CT and may be a time-efficient alternative for those who incorporate UE aerobic activity into a training program.
Geometrical method of decoupling
Baumgarten, C.
2012-12-01
The computation of tunes and matched beam distributions are essential steps in the analysis of circular accelerators. If certain symmetries—like midplane symmetry—are present, then it is possible to treat the betatron motion in the horizontal, the vertical plane, and (under certain circumstances) the longitudinal motion separately using the well-known Courant-Snyder theory, or to apply transformations that have been described previously as, for instance, the method of Teng and Edwards. In a preceding paper, it has been shown that this method requires a modification for the treatment of isochronous cyclotrons with non-negligible space charge forces. Unfortunately, the modification was numerically not as stable as desired and it was still unclear, if the extension would work for all conceivable cases. Hence, a systematic derivation of a more general treatment seemed advisable. In a second paper, the author suggested the use of real Dirac matrices as basic tools for coupled linear optics and gave a straightforward recipe to decouple positive definite Hamiltonians with imaginary eigenvalues. In this article this method is generalized and simplified in order to formulate a straightforward method to decouple Hamiltonian matrices with eigenvalues on the real and the imaginary axis. The decoupling of symplectic matrices which are exponentials of such Hamiltonian matrices can be deduced from this in a few steps. It is shown that this algebraic decoupling is closely related to a geometric “decoupling” by the orthogonalization of the vectors E→, B→, and P→, which were introduced with the so-called “electromechanical equivalence.” A mathematical analysis of the problem can be traced down to the task of finding a structure-preserving block diagonalization of symplectic or Hamiltonian matrices. Structure preservation means in this context that the (sequence of) transformations must be symplectic and hence canonical. When used iteratively, the decoupling
Geometric features for voxel-based surface recognition
Yarotsky, Dmitry
2017-01-01
We introduce a library of geometric voxel features for CAD surface recognition/retrieval tasks. Our features include local versions of the intrinsic volumes (the usual 3D volume, surface area, integrated mean and Gaussian curvature) and a few closely related quantities. We also compute Haar wavelet and statistical distribution features by aggregating raw voxel features. We apply our features to object classification on the ESB data set and demonstrate accurate results with a small number of s...
Geometrical method of decoupling
Directory of Open Access Journals (Sweden)
C. Baumgarten
2012-12-01
Full Text Available The computation of tunes and matched beam distributions are essential steps in the analysis of circular accelerators. If certain symmetries—like midplane symmetry—are present, then it is possible to treat the betatron motion in the horizontal, the vertical plane, and (under certain circumstances the longitudinal motion separately using the well-known Courant-Snyder theory, or to apply transformations that have been described previously as, for instance, the method of Teng and Edwards. In a preceding paper, it has been shown that this method requires a modification for the treatment of isochronous cyclotrons with non-negligible space charge forces. Unfortunately, the modification was numerically not as stable as desired and it was still unclear, if the extension would work for all conceivable cases. Hence, a systematic derivation of a more general treatment seemed advisable. In a second paper, the author suggested the use of real Dirac matrices as basic tools for coupled linear optics and gave a straightforward recipe to decouple positive definite Hamiltonians with imaginary eigenvalues. In this article this method is generalized and simplified in order to formulate a straightforward method to decouple Hamiltonian matrices with eigenvalues on the real and the imaginary axis. The decoupling of symplectic matrices which are exponentials of such Hamiltonian matrices can be deduced from this in a few steps. It is shown that this algebraic decoupling is closely related to a geometric “decoupling” by the orthogonalization of the vectors E[over →], B[over →], and P[over →], which were introduced with the so-called “electromechanical equivalence.” A mathematical analysis of the problem can be traced down to the task of finding a structure-preserving block diagonalization of symplectic or Hamiltonian matrices. Structure preservation means in this context that the (sequence of transformations must be symplectic and hence canonical. When
Geometric Computing for Freeform Architecture
Wallner, J.
2011-06-03
Geometric computing has recently found a new field of applications, namely the various geometric problems which lie at the heart of rationalization and construction-aware design processes of freeform architecture. We report on our work in this area, dealing with meshes with planar faces and meshes which allow multilayer constructions (which is related to discrete surfaces and their curvatures), triangles meshes with circle-packing properties (which is related to conformal uniformization), and with the paneling problem. We emphasize the combination of numerical optimization and geometric knowledge.
Geometric inequalities for black holes
Energy Technology Data Exchange (ETDEWEB)
Dain, Sergio [Universidad Nacional de Cordoba (Argentina)
2013-07-01
Full text: A geometric inequality in General Relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr-Newman black hole satisfy several important geometric inequalities. Remarkably enough, some of these inequalities also hold for dynamical black holes. This kind of inequalities, which are valid in the dynamical and strong field regime, play an important role in the characterization of the gravitational collapse. They are closed related with the cosmic censorship conjecture. In this talk I will review recent results in this subject. (author)
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
Aythami Jurado-Navarro, Á.; López-Puertas, Manuel; Funke, Bernd; García-Comas, Maya; Gardini, Angela; González-Galindo, Francisco; Stiller, Gabriele P.; von Clarmann, Thomas; Grabowski, Udo; Linden, Andrea
2016-12-01
Global distributions of the CO2 vmr (volume mixing ratio) in the mesosphere and lower thermosphere (from 70 up to ˜ 140 km) have been derived from high-resolution limb emission daytime MIPAS (Michelson Interferometer for Passive Atmospheric Sounding) spectra in the 4.3 µm region. This is the first time that the CO2 vmr has been retrieved in the 120-140 km range. The data set spans from January 2005 to March 2012. The retrieval of CO2 has been performed jointly with the elevation pointing of the line of sight (LOS) by using a non-local thermodynamic equilibrium (non-LTE) retrieval scheme. The non-LTE model incorporates the new vibrational-vibrational and vibrational-translational collisional rates recently derived from the MIPAS spectra by [Jurado-Navarro et al.(2015)]. It also takes advantage of simultaneous MIPAS measurements of other atmospheric parameters (retrieved in previous steps), such as the kinetic temperature (derived up to ˜ 100 km from the CO2 15 µm region of MIPAS spectra and from 100 up to 170 km from the NO 5.3 µm emission of the same MIPAS spectra) and the O3 measurements (up to ˜ 100 km). The latter is very important for calculations of the non-LTE populations because it strongly constrains the O(3P) and O(1D) concentrations below ˜ 100 km. The estimated precision of the retrieved CO2 vmr profiles varies with altitude ranging from ˜ 1 % below 90 km to 5 % around 120 km and larger than 10 % above 130 km. There are some latitudinal and seasonal variations of the precision, which are mainly driven by the solar illumination conditions. The retrieved CO2 profiles have a vertical resolution of about 5-7 km below 120 km and between 10 and 20 km at 120-140 km. We have shown that the inclusion of the LOS as joint fit parameter improves the retrieval of CO2, allowing for a clear discrimination between the information on CO2 concentration and the LOS and also leading to significantly smaller systematic errors. The retrieved CO2 has an improved
Mobile Watermarking against Geometrical Distortions
Directory of Open Access Journals (Sweden)
Jing Zhang
2015-08-01
Full Text Available Mobile watermarking robust to geometrical distortions is still a great challenge. In mobile watermarking, efficient computation is necessary because mobile devices have very limited resources due to power consumption. In this paper, we propose a low-complexity geometrically resilient watermarking approach based on the optimal tradeoff circular harmonic function (OTCHF correlation filter and the minimum average correlation energy Mellin radial harmonic (MACE-MRH correlation filter. By the rotation, translation and scale tolerance properties of the two kinds of filter, the proposed watermark detector can be robust to geometrical attacks. The embedded watermark is weighted by a perceptual mask which matches very well with the properties of the human visual system. Before correlation, a whitening process is utilized to improve watermark detection reliability. Experimental results demonstrate that the proposed watermarking approach is computationally efficient and robust to geometrical distortions.
Geometric structure of gauge theories
Energy Technology Data Exchange (ETDEWEB)
Mangiarotti, L.; Modugno, M.
1985-06-01
In the framework of the adjoint forms over the jet spaces of connections and using a canonical jet shift differential, we give a geometrical interpretation of the Yang--Mills equations both in a direct and Lagrangian formulation.
Effects of Forest Cover Change on Flood Characteristics in the Upper Citarum Watershed
Directory of Open Access Journals (Sweden)
Bambang Dwi Dasanto
2015-02-01
Full Text Available Information on the effect of forest cover changes on streamflow (river discharge in large-scale catchment is important to be studied. The rate of forest cover change in the Upper Citarum Watershed as a large-scale catchment is high enough to drive streamflow change, such as increase of discharge level, or flood volume. Within the research area, flood would occur when the volume of streamflow exceeded the canal capacity and inundated areas that were normally dry. Therefore, this research focused on identifying the effects of forest cover change on flood events and its distribution. The research consisted of 2 main stages; firstly, building geometric data of river and performing frequency analysis of historical and scenario discharges using an approach of probability distribution; and, secondly, flood inundation mapping using HEC-RAS model. The results showed that forest reduction have affected water yield in the downstream of Upper Citarum Watershed. In each return period, this reduction have increased river discharge level and affected the spread of flooded areas. In 2-year return period, the extent of flood as an impact of forest reduction was estimated to decrease slowly. However, in the return period of more than 2 years, the spread of flooded areas increased sharply. These proved that forest cover reduction would always increase the discharge value, but it did not always expand the inundated area.Keywords: geometric data, forest cover, water yield, return period
Geometric phases in graphitic cones
Energy Technology Data Exchange (ETDEWEB)
Furtado, Claudio [Departamento de Fisica, CCEN, Universidade Federal da Paraiba, Cidade Universitaria, 58051-970 Joao Pessoa, PB (Brazil)], E-mail: furtado@fisica.ufpb.br; Moraes, Fernando [Departamento de Fisica, CCEN, Universidade Federal da Paraiba, Cidade Universitaria, 58051-970 Joao Pessoa, PB (Brazil); Carvalho, A.M. de M [Departamento de Fisica, Universidade Estadual de Feira de Santana, BR116-Norte, Km 3, 44031-460 Feira de Santana, BA (Brazil)
2008-08-04
In this Letter we use a geometric approach to study geometric phases in graphitic cones. The spinor that describes the low energy states near the Fermi energy acquires a phase when transported around the apex of the cone, as found by a holonomy transformation. This topological result can be viewed as an analogue of the Aharonov-Bohm effect. The topological analysis is extended to a system with n cones, whose resulting configuration is described by an effective defect00.
Determining Geometric Accuracy in Turning
Institute of Scientific and Technical Information of China (English)
Kwong; Chi; Kit; A; Geddam
2002-01-01
Mechanical components machined to high levels of ac cu racy are vital to achieve various functional requirements in engineering product s. In particular, the geometric accuracy of turned components play an important role in determining the form, fit and function of mechanical assembly requiremen ts. The geometric accuracy requirements of turned components are usually specifi ed in terms of roundness, straightness, cylindricity and concentricity. In pract ice, the accuracy specifications achievable are infl...
The Geometric Gravitational Internal Problem
González-Martin, G R
2000-01-01
In a geometric unified theory there is an energy momentum equation, apart from the field equations and equations of motion. The general relativity Einstein equation with cosmological constant follows from this energy momentum equation for empty space. For non empty space we obtain a generalized Einstein equation, relating the Einstein tensor to a geometric stress energy tensor. The matching exterior solution is in agreement with the standard relativity tests. Furthermore, there is a Newtonian limit where we obtain Poisson's equation.
Geometric symmetries in light nuclei
Bijker, Roelof
2016-01-01
The algebraic cluster model is is applied to study cluster states in the nuclei 12C and 16O. The observed level sequences can be understood in terms of the underlying discrete symmetry that characterizes the geometrical configuration of the alpha-particles, i.e. an equilateral triangle for 12C, and a regular tetrahedron for 16O. The structure of rotational bands provides a fingerprint of the underlying geometrical configuration of alpha-particles.
Geometric inequalities methods of proving
Sedrakyan, Hayk
2017-01-01
This unique collection of new and classical problems provides full coverage of geometric inequalities. Many of the 1,000 exercises are presented with detailed author-prepared-solutions, developing creativity and an arsenal of new approaches for solving mathematical problems. This book can serve teachers, high-school students, and mathematical competitors. It may also be used as supplemental reading, providing readers with new and classical methods for proving geometric inequalities. .
Antenna with Dielectric Having Geometric Patterns
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.
Geometric Lattice Structure of Covering-Based Rough Sets through Matroids
Directory of Open Access Journals (Sweden)
Aiping Huang
2012-01-01
relationship among them. First, a geometric lattice structure of covering-based rough sets is established through the transversal matroid induced by a covering. Then its characteristics, such as atoms, modular elements, and modular pairs, are studied. We also construct a one-to-one correspondence between this type of geometric lattices and transversal matroids in the context of covering-based rough sets. Second, we present three sufficient and necessary conditions for two types of covering upper approximation operators to be closure operators of matroids. We also represent two types of matroids through closure axioms and then obtain two geometric lattice structures of covering-based rough sets. Third, we study the relationship among these three geometric lattice structures. Some core concepts such as reducible elements in covering-based rough sets are investigated with geometric lattices. In a word, this work points out an interesting view, namely, geometric lattice, to study covering-based rough sets.
Developments and retrospectives in Lie theory geometric and analytic methods
Penkov, Ivan; Wolf, Joseph
2014-01-01
This volume reviews and updates a prominent series of workshops in representation/Lie theory, and reflects the widespread influence of those workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, and mathematical physics. Many of the contributors have had leading roles in both the classical and modern developments of Lie theory and its applications. This Work, entitled Developments and Retrospectives in Lie Theory, and comprising 26 articles, is organized in two volumes: Algebraic Methods and Geometric and Analytic Methods. This is the Geometric and Analytic Methods volume. The Lie Theory Workshop series, founded by Joe Wolf and Ivan Penkov and joined shortly thereafter by Geoff Mason, has been running for over two decades. Travel to the workshops has usually been supported by the NSF, and local universities have provided hospitality. The workshop talks have been seminal in describing new perspectives in the field covering broad areas of current re...
Sigma models for genuinely non-geometric backgrounds
Chatzistavrakidis, Athanasios; Lechtenfeld, Olaf
2015-01-01
The existence of genuinely non-geometric backgrounds, i.e. ones without geometric dual, is an important question in string theory. In this paper we examine this question from a sigma model perspective. First we construct a particular class of Courant algebroids as protobialgebroids with all types of geometric and non-geometric fluxes. For such structures we apply the mathematical result that any Courant algebroid gives rise to a 3D topological sigma model of the AKSZ type and we discuss the corresponding 2D field theories. It is found that these models are always geometric, even when both 2-form and 2-vector fields are neither vanishing nor inverse of one another. Taking a further step, we suggest an extended class of 3D sigma models, whose world volume is embedded in phase space, which allow for genuinely non-geometric backgrounds. Adopting the doubled formalism such models can be related to double field theory, albeit from a world sheet perspective.
Geometric scalar theory of gravity
Energy Technology Data Exchange (ETDEWEB)
Novello, M.; Bittencourt, E.; Goulart, E.; Salim, J.M.; Toniato, J.D. [Instituto de Cosmologia Relatividade Astrofisica ICRA - CBPF Rua Dr. Xavier Sigaud 150 - 22290-180 Rio de Janeiro - Brazil (Brazil); Moschella, U., E-mail: novello@cbpf.br, E-mail: eduhsb@cbpf.br, E-mail: Ugo.Moschella@uninsubria.it, E-mail: egoulart@cbpf.br, E-mail: jsalim@cbpf.br, E-mail: toniato@cbpf.br [Università degli Studi dell' Insubria - Dipartamento di Fisica e Matematica Via Valleggio 11 - 22100 Como - Italy (Italy)
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.
Geometric identities in stereological particle analysis
DEFF Research Database (Denmark)
Kötzer, S.; Jensen, Eva Bjørn Vedel; Baddeley, A.
We review recent findings about geometric identities in integral geometry and geometric tomography, and their statistical application to stereological particle analysis. Open questions are discussed.......We review recent findings about geometric identities in integral geometry and geometric tomography, and their statistical application to stereological particle analysis. Open questions are discussed....
Geometric orbit datum and orbit covers
Institute of Scientific and Technical Information of China (English)
梁科; 侯自新
2001-01-01
Vogan conjectured that the parabolic induction of orbit data is independent of the choice of the parabolic subgroup. In this paper we first give the parabolic induction of orbit covers, whose relationship with geometric orbit datum is also induced. Hence we show a geometric interpretation of orbit data and finally prove the conjugation for geometric orbit datum using geometric method.
Geometric formula for prism deflection
Indian Academy of Sciences (India)
Apoorva G Wagh; Veer Chand Rakhecha
2004-08-01
While studying neutron deflections produced by a magnetic prism, we have stumbled upon a simple `geometric' formula. For a prism of refractive index close to unity, the deflection simply equals the product of the refractive power − 1 and the base-to-height ratio of the prism, regardless of the apex angle. The base and height of the prism are measured respectively along and perpendicular to the direction of beam propagation within the prism. The geometric formula greatly simplifies the optimisation of prism parameters to suit any specific experiment.
A Geometric Formulation of Supersymmetry
Freedman, Daniel Z; Van Proeyen, Antoine
2016-01-01
The scalar fields of supersymmetric models are coordinates of a geometric space. We propose a formulation of supersymmetry that is covariant with respect to reparametrizations of this target space. Employing chiral multiplets as an example, we introduce modified supersymmetry variations and redefined auxiliary fields that transform covariantly under reparametrizations. The resulting action and transformation laws are manifestly covariant and highlight the geometric structure of the supersymmetric theory. The covariant methods are developed first for general theories (not necessarily supersymmetric) whose scalar fields are coordinates of a Riemannian target space.
Height and Tilt Geometric Texture
DEFF Research Database (Denmark)
Andersen, Vedrana; Desbrun, Mathieu; Bærentzen, Jakob Andreas
2009-01-01
We propose a new intrinsic representation of geometric texture over triangle meshes. Our approach extends the conventional height field texture representation by incorporating displacements in the tangential plane in the form of a normal tilt. This texture representation offers a good practical...... compromise between functionality and simplicity: it can efficiently handle and process geometric texture too complex to be represented as a height field, without having recourse to full blown mesh editing algorithms. The height-and-tilt representation proposed here is fully intrinsic to the mesh, making...
Geometric integration for particle accelerators
Energy Technology Data Exchange (ETDEWEB)
Forest, Etienne [High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba, Ibaraki 305-0801 (Japan)
2006-05-12
This paper is a very personal view of the field of geometric integration in accelerator physics-a field where often work of the highest quality is buried in lost technical notes or even not published; one has only to think of Simon van der Meer Nobel prize work on stochastic cooling-unpublished in any refereed journal. So I reconstructed the relevant history of geometrical integration in accelerator physics as much as I could by talking to collaborators and using my own understanding of the field. The reader should not be too surprised if this account is somewhere between history, science and perhaps even fiction.
Geometric pumping in autophoretic channels
Michelin, Sebastien; De Canio, Gabriele; Lobato-Dauzier, Nicolas; Lauga, Eric
2015-01-01
Many microfluidic devices use macroscopic pressure differentials to overcome viscous friction and generate flows in microchannels. In this work, we investigate how the chemical and geometric properties of the channel walls can drive a net flow by exploiting the autophoretic slip flows induced along active walls by local concentration gradients of a solute species. We show that chemical patterning of the wall is not required to generate and control a net flux within the channel, rather channel geometry alone is sufficient. Using numerical simulations, we determine how geometric characteristics of the wall influence channel flow rate, and confirm our results analytically in the asymptotic limit of lubrication theory.
Asymptotic geometric analysis, part I
Artstein-Avidan, Shiri
2015-01-01
The authors present the theory of asymptotic geometric analysis, a field which lies on the border between geometry and functional analysis. In this field, isometric problems that are typical for geometry in low dimensions are substituted by an "isomorphic" point of view, and an asymptotic approach (as dimension tends to infinity) is introduced. Geometry and analysis meet here in a non-trivial way. Basic examples of geometric inequalities in isomorphic form which are encountered in the book are the "isomorphic isoperimetric inequalities" which led to the discovery of the "concentration phenomen
An introduction to geometrical physics
Aldrovandi, R
1995-01-01
This book stresses the unifying power of the geometrical framework in bringing together concepts from the different areas of physics. Common underpinnings of optics, elasticity, gravitation, relativistic fields, particle mechanics and other subjects are underlined. It attempts to extricate the notion of space currently in the physical literature from the metric connotation.The book's goal is to present mathematical ideas associated with geometrical physics in a rather introductory language. Included are many examples from elementary physics and also, for those wishing to reach a higher level o
Urbanisation and 3d Spatial - a Geometric Approach
Duncan, E. E.; Rahman, A. Abdul
2013-09-01
Urbanisation creates immense competition for space, this may be attributed to an increase in population owing to domestic and external tourism. Most cities are constantly exploring all avenues in maximising its limited space. Hence, urban or city authorities need to plan, expand and use such three dimensional (3D) space above, on and below the city space. Thus, difficulties in property ownership and the geometric representation of the 3D city space is a major challenge. This research, investigates the concept of representing a geometric topological 3D spatial model capable of representing 3D volume parcels for man-made constructions above and below the 3D surface volume parcel. A review of spatial data models suggests that the 3D TIN (TEN) model is significant and can be used as a unified model. The concepts, logical and physical models of 3D TIN for 3D volumes using tetrahedrons as the base geometry is presented and implemented to show man-made constructions above and below the surface parcel within a user friendly graphical interface. Concepts for 3D topology and 3D analysis are discussed. Simulations of this model for 3D cadastre are implemented. This model can be adopted by most countries to enhance and streamline geometric 3D property ownership for urban centres. 3D TIN concept for spatial modelling can be adopted for the LA_Spatial part of the Land Administration Domain Model (LADM) (ISO/TC211, 2012), this satisfies the concept of 3D volumes.
Energy Technology Data Exchange (ETDEWEB)
Kubas, A.; Mornex, F.; D' Hombres, A.; Lorchel, F.; Chapet, O. [Centre hospitalier Lyon-Sud, Service de Radiotherapie-oncologie Rhone-Alpes, 69 - Pierre-Benite (France); Merle, P. [Hopital de l' Hotel-Dieu, Service d' Hepatogastroenterologie, 69 - Lyon (France)
2008-12-15
Purpose: To evaluate the amplitude of motion and the variations of volume of the tumor, the liver and upper abdominal organs induced by breathing during the irradiation of hepatocellular carcinoma (H.C.C.). Material and methods: Two scanners were performed in inhale and in exhale not forced in 20 patients with a H.C.C.. The liver (left/right lobes), the tumor, the duodenum, the two kidneys and the pancreas were delineated on each acquisition. The superposition of the two spirals made it possible to measure the displacements and variations of volume of these structures in the cranio caudal (C.C.), lateral (Lat), and anteroposterior (A.P.) directions. Results:The mean displacement of the tumour in C.C., Lat and A.P. was of 19.7 {+-} 8.3 mm, 4.5 {+-} 2.3 mm, and 8.9 {+-} 6.5 mm. The greatest amplitude of movement was obtained in C.C. for the right and left hepatic lobes (19 {+-} 6.5 mm, 10 {+-} 5.6 mm), the duodenum(12.6 {+-} 6.4 mm), the kidneys right and left (15.5 {+-} 6.1 mm, 16.2 {+-} 10 mm) and the pancreas (13.2 {+-} 6 mm). No significant variation of volume was observed for these organs. Conclusion: The movements of the tumour, the liver and the abdominal organs, induced by breathing are significant. The respiratory gating appears essential in particular with the development of new techniques of irradiation such as the intensity-modulated radiotherapy (I.M.R.T.) or the stereotactic body radiation therapy (S.B.R.T.). (authors)
Towards the Amplituhedron Volume
Ferro, Livia; Orta, Andrea; Parisi, Matteo
2015-01-01
It has been recently conjectured that scattering amplitudes in planar N=4 super Yang-Mills are given by the volume of the (dual) amplituhedron. In this paper we show some interesting connections between the tree-level amplituhedron and a special class of differential equations. In particular we demonstrate how the amplituhedron volume for NMHV amplitudes is determined by these differential equations. The new formulation allows for a straightforward geometric description, without any reference to triangulations. Finally we discuss possible implications for volumes related to generic N^kMHV amplitudes.
In Defence of Geometrical Algebra
Blasjo, V.N.E.
2016-01-01
The geometrical algebra hypothesis was once the received interpretation of Greek mathematics. In recent decades, however, it has become anathema to many. I give a critical review of all arguments against it and offer a consistent rebuttal case against the modern consensus. Consequently, I find that
Metastable vacua and geometric deformations
Amariti, A; Girardello, L; Mariotti, A
2008-01-01
We study the geometric interpretation of metastable vacua for systems of D3 branes at non isolated toric deformable singularities. Using the L^{aba} examples, we investigate the relations between the field theoretic susy breaking and restoration and the complex deformations of the CY singularities.
Geometric hashing and object recognition
Stiller, Peter F.; Huber, Birkett
1999-09-01
We discuss a new geometric hashing method for searching large databases of 2D images (or 3D objects) to match a query built from geometric information presented by a single 3D object (or single 2D image). The goal is to rapidly determine a small subset of the images that potentially contain a view of the given object (or a small set of objects that potentially match the item in the image). Since this must be accomplished independent of the pose of the object, the objects and images, which are characterized by configurations of geometric features such as points, lines and/or conics, must be treated using a viewpoint invariant formulation. We are therefore forced to characterize these configurations in terms of their 3D and 2D geometric invariants. The crucial relationship between the 3D geometry and its 'residual' in 2D is expressible as a correspondence (in the sense of algebraic geometry). Computing a set of generating equations for the ideal of this correspondence gives a complete characterization of the view of independent relationships between an object and all of its possible images. Once a set of generators is in hand, it can be used to devise efficient recognition algorithms and to give an efficient geometric hashing scheme. This requires exploiting the form and symmetry of the equations. The result is a multidimensional access scheme whose efficiency we examine. Several potential directions for improving this scheme are also discussed. Finally, in a brief appendix, we discuss an alternative approach to invariants for generalized perspective that replaces the standard invariants by a subvariety of a Grassmannian. The advantage of this is that one can circumvent many annoying general position assumptions and arrive at invariant equations (in the Plucker coordinates) that are more numerically robust in applications.
Geometric Transformations in Engineering Geometry
Directory of Open Access Journals (Sweden)
I. F. Borovikov
2015-01-01
Full Text Available Recently, for business purposes, in view of current trends and world experience in training engineers, research and faculty staff there has been a need to transform traditional courses of descriptive geometry into the course of engineering geometry in which the geometrical transformations have to become its main section. On the basis of critical analysis the paper gives suggestions to improve a presentation technique of this section both in the classroom and in academic literature, extend an application scope of geometrical transformations to solve the position and metric tasks and simulation of surfaces, as well as to design complex engineering configurations, which meet a number of pre-specified conditions.The article offers to make a number of considerable amendments to the terms and definitions used in the existing courses of descriptive geometry. It draws some conclusions and makes the appropriate proposals on feasibility of coordination in teaching the movement transformation in the courses of analytical and descriptive geometry. This will provide interdisciplinary team teaching and allow students to be convinced that a combination of analytical and graphic ways to solve geometric tasks is useful and reasonable.The traditional sections of learning courses need to be added with a theory of projective and bi-rational transformations. In terms of application simplicity and convenience it is enough to consider the central transformations when solving the applied tasks. These transformations contain a beam of sub-invariant (low-invariant straight lines on which the invariant curve induces non-involution and involution projectivities. The expediency of nonlinear transformations application is shown in the article by a specific example of geometric modeling of the interfacing surface "spar-blade".Implementation of these suggestions will contribute to a real transformation of a traditional course of descriptive geometry to the engineering geometry
Geometric modeling of subcellular structures, organelles, and multiprotein complexes
Feng, Xin; Xia, Kelin; Tong, Yiying; Wei, Guo-Wei
2013-01-01
SUMMARY Recently, the structure, function, stability, and dynamics of subcellular structures, organelles, and multi-protein complexes have emerged as a leading interest in structural biology. Geometric modeling not only provides visualizations of shapes for large biomolecular complexes but also fills the gap between structural information and theoretical modeling, and enables the understanding of function, stability, and dynamics. This paper introduces a suite of computational tools for volumetric data processing, information extraction, surface mesh rendering, geometric measurement, and curvature estimation of biomolecular complexes. Particular emphasis is given to the modeling of cryo-electron microscopy data. Lagrangian-triangle meshes are employed for the surface presentation. On the basis of this representation, algorithms are developed for surface area and surface-enclosed volume calculation, and curvature estimation. Methods for volumetric meshing have also been presented. Because the technological development in computer science and mathematics has led to multiple choices at each stage of the geometric modeling, we discuss the rationales in the design and selection of various algorithms. Analytical models are designed to test the computational accuracy and convergence of proposed algorithms. Finally, we select a set of six cryo-electron microscopy data representing typical subcellular complexes to demonstrate the efficacy of the proposed algorithms in handling biomolecular surfaces and explore their capability of geometric characterization of binding targets. This paper offers a comprehensive protocol for the geometric modeling of subcellular structures, organelles, and multiprotein complexes. PMID:23212797
Geometrical and fluidic tuning of periodically modulated thin metal films
DEFF Research Database (Denmark)
Gilardi, Giovanni; Xiao, Sanshui; Beccherelli, Romeo;
2012-01-01
We numerically demonstrate near-zero transmission of light through two-dimensional arrays of isolated gold rings. The analysis of the device as an optofluidic sensor is presented to demonstrate the tuning of the device in relation to variations of volume and refractive index of an isotropic fluid...... positioned over the structure. We also evaluate the performance of the device with respect to geometrical parameters of the rings....
Geometrical Phases in Quantum Mechanics
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
Guiding light via geometric phases
Slussarenko, Sergei; Jisha, Chandroth P; Piccirillo, Bruno; Santamato, Enrico; Assanto, Gaetano; Marrucci, Lorenzo
2015-01-01
Known methods for transverse confinement and guidance of light can be grouped into a few basic mechanisms, the most common being metallic reflection, total internal reflection and photonic-bandgap (or Bragg) reflection. All of them essentially rely on changes of the refractive index, that is on scalar properties of light. Recently, processes based on "geometric Berry phases", such as manipulation of polarization states or deflection of spinning-light rays, have attracted considerable interest in the contexts of singular optics and structured light. Here, we disclose a new approach to light waveguiding, using geometric Berry phases and exploiting polarization states and their handling. This can be realized in structured three-dimensional anisotropic media, in which the optic axis lies orthogonal to the propagation direction and is modulated along it and across the transverse plane, so that the refractive index remains constant but a phase distortion can be imposed on a beam. In addition to a complete theoretic...
A Geometrical Method of Decoupling
Baumgarten, Christian
2012-01-01
In a preceeding paper the real Dirac matrices have been introduced to coupled linear optics and a recipe to decouple positive definite Hamiltonians has been given. In this article a geometrical method is presented which allows to decouple regular {\\it and} irregular systems with the same straightforward method and to compute the eigenvalues and eigenvectors of Hamiltonian matrices with both, real and imaginary eigenvalues. It is shown that the algebraic decoupling is closely related to a geometric "decoupling" by the orthogonalization of the vectors $\\vec E$, $\\vec B$ and $\\vec p$, that were introduced with the so-called "electromechanical equivalence" (EMEQ). When used iteratively, the decoupling algorithm can also be applied to n-dimensional non-dissipative systems.
Geometrical Aspects of Venus Transit
Bertuola, Alberto C; Magalhães, N S; Filho, Victo S
2016-01-01
We obtained two astronomical values, the Earth-Venus distance and Venus diameter, by means of a geometrical treatment of photos taken of Venus transit in June of 2012. Here we presented the static and translational modelsthat were elaborated taking into account the Earth and Venus orbital movements. An additional correction was also added by considering the Earth rotation movement. The results obtained were compared with the values of reference from literature, showing very good concordance.
Geometric Hyperplanes: Desargues Encodes Doily
Saniga, Metod
2011-01-01
It is shown that the structure of the generalized quadrangle of order two is fully encoded in the properties of the Desargues configuration. A point of the quadrangle is represented by a geometric hyperplane of the Desargues configuration and its line by a set of three hyperplanes such that one of them is the complement of the symmetric difference of the remaining two and they all share a pair of non-collinear points.
Geometrical interpretation of optical absorption
Energy Technology Data Exchange (ETDEWEB)
Monzon, J. J.; Barriuso, A. G.; Sanchez-Soto, L. L. [Departamento de Optica, Facultad de Fisica, Universidad Complutense, E-28040 Madrid (Spain); Montesinos-Amilibia, J. M. [Departamento de Geometria y Topologia, Facultad de Matematicas, Universidad Complutense, E-28040 Madrid (Spain)
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
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.
Some geometrical iteration methods for nonlinear equations
Institute of Scientific and Technical Information of China (English)
LU Xing-jiang; QIAN Chun
2008-01-01
This paper describes geometrical essentials of some iteration methods (e.g. Newton iteration,secant line method,etc.) for solving nonlinear equations and advances some geomet-rical methods of iteration that are flexible and efficient.
Institute of Scientific and Technical Information of China (English)
王丽君; 郭业松; 张兰芳; 黄生富; 何侠; 张宜勤
2016-01-01
目的：探讨鼻咽癌IMRT的CTV中Ⅱb 区的上界，并寻找个体化缩减Ⅱb 区范围的标准。方法回顾分析2012—2014年收治的142例（ AJCC 2010分期标准Ⅰ、Ⅱ、Ⅲ、Ⅳ期分别为8、37、41、56例）初治鼻咽癌患者采用IMRT情况。根据影像阅片研究鼻咽癌颈部淋巴结分布规律。比较缩减Ⅱb 区范围者与未缩减者腮腺剂量参数差异并t检验及t＇检验。结果咽后外侧淋巴结和Ⅱb 区淋巴结是最常见受累淋巴结，转移率分别为75�4％和67�6％。在Ⅱb 区受累患者中51�0％出现了高位阳性淋巴结，6�3％阳性淋巴结上界超过了RTOG分区定义的Ⅱb 区上界。对符合拟定标准患者缩减Ⅱb 区范围是安全的，优化靶区后可显著降低腮腺D50、V26（ P＝0�000）。结论在勾画鼻咽癌颈部CTV时，原则上Ⅱb 区上界应至侧颅底，但对符合拟定标准者可个体化缩减Ⅱb 区上界，以更好地保护腮腺。%Objective To explore the upper bound of Ⅱb region in the clinical target volume ( CTV ) for intensity⁃modulated radiotherapy ( IMRT ) for nasopharyngeal carcinoma ( NPC ) , and to establish a standard for personalized reduction in the range ofⅡb region. Methods A retrospective analysis was performed on the IMRT results of 142 patients newly diagnosed with NPC who were admitted to our hospital from 2012 to 2014. According to the American Joint Committee on Cancer 2010 staging system, there were 8 patients with stageⅠ disease, 37 stage Ⅱ, 41 stage Ⅲ, and 56 stage Ⅳ. The distribution pattern of cervical lymph nodes in NPC was studied based on the imaging results. Comparison of the dose to parotid glands between patients with and without reduction in the range ofⅡb region was made by t test and t'test. Results The metastasis rates of the most common diseased lymph nodes, lateral retropharyngeal lymph node and Ⅱb lymph node, were 75�4% and 67�6%, respectively. In the patients
Adiabatic geometric phases in hydrogenlike atoms
Sjöqvist, Erik; Yi, X. X.; Åberg, J.
2005-01-01
We examine the effect of spin-orbit coupling on geometric phases in hydrogenlike atoms exposed to a slowly varying magnetic field. The marginal geometric phases associated with the orbital angular momentum and the intrinsic spin fulfill a sum rule that explicitly relates them to the corresponding geometric phase of the whole system. The marginal geometric phases in the Zeeman and Paschen-Back limit are analyzed. We point out the existence of nodal points in the marginal phases that may be det...
Development of a Geometric Spatial Visualization Tool
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)…
Exact Solutions for Einstein's Hyperbolic Geometric Flow
Institute of Scientific and Technical Information of China (English)
HE Chun-Lei
2008-01-01
In this paper we investigate the Einstein's hyperbolic geometric flow and obtain some interesting exact solutions for this kind of flow. Many interesting properties of these exact solutions have also been analyzed and we believe that these properties of Einstein's hyperbolic geometric flow are very helpful to understanding the Einstein equations and the hyperbolic geometric flow.
Generalized geometrically convex functions and inequalities.
Noor, Muhammad Aslam; Noor, Khalida Inayat; Safdar, Farhat
2017-01-01
In this paper, we introduce and study a new class of generalized functions, called generalized geometrically convex functions. We establish several basic inequalities related to generalized geometrically convex functions. We also derive several new inequalities of the Hermite-Hadamard type for generalized geometrically convex functions. Several special cases are discussed, which can be deduced from our main results.
Fey, David L.; Church, Stan E.; Finney, Christopher J.
1999-01-01
Metal-mining related wastes in the Boulder River basin study area in northern Jefferson County, Montana have been implicated in their detrimental effects on water quality with regard to acid-generation and toxic-metal solubilization. Flotation-mill tailings in the meadow below the Buckeye mine, hereafter referred to as the Buckeye mill-tailings site, have been identified as significant contributors to water quality degradation of Basin Creek, Montana. Basin Creek is one of three tributaries to the Boulder River in the study area; bed sediments and waters draining from the Buckeye mine have also been implicated. Geochemical analysis of 35 tailings cores and six bed-sediment samples was undertaken to determine the concentrations of Ag, As, Cd, Cu, Pb,and Zn present in these materials. These elements are environmentally significant, in that they can be toxic to fish and/or the invertebrate organisms that constitute their food. A suite of one-inch cores of dispersed flotation-mill tailings and underlying premining material was taken from a large, flat area north of Basin Creek near the site of the Buckeye mine. Thirty-five core samples were taken and divided into 204 subsamples. The samples were analyzed by ICP-AES (inductively coupled plasma-atomic emission spectroscopy) using a mixed-acid digestion. Results of the core analyses show that the elements listed above are present at moderate to very high concentrations (arsenic to 63,000 ppm, silver to 290 ppm, cadmium to 370 ppm, copper to 4,800 ppm, lead to 93,000 ppm, and zinc to 23,000 ppm). Volume calculations indicate that an estimated 8,400 metric tons of contaminated material are present at the site. Six bed-sediment samples were also subjected to the mixed-acid total digestion, and a warm (50°C) 2M HCl-1% H2O2 leach and analyzed by ICP-AES. Results indicate that bed sediments of Basin Creek are only slightly impacted by past mining above the Buckeye-Enterprise complex, moderately impacted at the upper (eastern
Polar Metals by Geometric Design
Energy Technology Data Exchange (ETDEWEB)
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.
A history of geometrical methods
Coolidge, Julian Lowell
2013-01-01
Full and authoritative, this history of the techniques for dealing with geometric questions begins with synthetic geometry and its origins in Babylonian and Egyptian mathematics; reviews the contributions of China, Japan, India, and Greece; and discusses the non-Euclidean geometries. Subsequent sections cover algebraic geometry, starting with the precursors and advancing to the great awakening with Descartes; and differential geometry, from the early work of Huygens and Newton to projective and absolute differential geometry. The author's emphasis on proofs and notations, his comparisons betwe
Science, Art and Geometrical Imagination
Luminet, J -P
2009-01-01
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 role of geometric imagination in innovative findings. Through the analysis of works of various artists and scientists like Plato, Durer, Kepler, Escher, Grisey or the present 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 beauty, conciseness and emotional approach of the world.
Science, art and geometrical imagination
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.
Geometric Rationalization for Freeform Architecture
Jiang, Caigui
2016-06-20
The emergence of freeform architecture provides interesting geometric challenges with regards to the design and manufacturing of large-scale structures. To design these architectural structures, we have to consider two types of constraints. First, aesthetic constraints are important because the buildings have to be visually impressive. Sec- ond, functional constraints are important for the performance of a building and its e cient construction. This thesis contributes to the area of architectural geometry. Specifically, we are interested in the geometric rationalization of freeform architec- ture with the goal of combining aesthetic and functional constraints and construction requirements. Aesthetic requirements typically come from designers and architects. To obtain visually pleasing structures, they favor smoothness of the building shape, but also smoothness of the visible patterns on the surface. Functional requirements typically come from the engineers involved in the construction process. For exam- ple, covering freeform structures using planar panels is much cheaper than using non-planar ones. Further, constructed buildings have to be stable and should not collapse. In this thesis, we explore the geometric rationalization of freeform archi- tecture using four specific example problems inspired by real life applications. We achieve our results by developing optimization algorithms and a theoretical study of the underlying geometrical structure of the problems. The four example problems are the following: (1) The design of shading and lighting systems which are torsion-free structures with planar beams based on quad meshes. They satisfy the functionality requirements of preventing light from going inside a building as shad- ing systems or reflecting light into a building as lighting systems. (2) The Design of freeform honeycomb structures that are constructed based on hex-dominant meshes with a planar beam mounted along each edge. The beams intersect without
Hubbard model with geometrical frustration
Energy Technology Data Exchange (ETDEWEB)
Lee, Hunpyo
2009-10-15
At first we present the details of the dual fermion (DF), the cluster extension of dynamical mean field theory (CDMFT) and continuous-time quantum Monte Carlo (CT QMC) methods. Using a panoply of these methods we explore the Hubbard model on the triangular and hyperkagome lattice. We find a first-order transition and continuous transition on the triangular and hyper-kagome lattice, respectively. Moreover, we find the reentrant behavior due to competition between the magnetic correlation and itinerancy of electrons by source of geometrical frustration on both lattices. (orig.)
Buildings, spiders, and geometric Satake
Fontaine, Bruce; Kuperberg, Greg
2011-01-01
Let G be a simple algebraic group. Labelled trivalent graphs called webs can be used to product invariants in tensor products of minuscule representations. For each web, we construct a configuration space of points in the affine Grassmannian. Via the geometric Satake correspondence, we relate these configuration spaces to the invariant vectors coming from webs. In the case G = SL(3), non-elliptic webs yield a basis for the invariant spaces. The non-elliptic condition, which is equivalent to the condition that the dual diskoid of the web is CAT(0), is explained by the fact that affine buildings are CAT(0).
Cosmological parameters from large scale structure - geometric versus shape information
Hamann, Jan; Lesgourgues, Julien; Rampf, Cornelius; Wong, Yvonne Y Y
2010-01-01
The matter power spectrum as derived from large scale structure (LSS) surveys contains two important and distinct pieces of information: an overall smooth shape and the imprint of baryon acoustic oscillations (BAO). We investigate the separate impact of these two types of information on cosmological parameter estimation, and show that for the simplest cosmological models, the broad-band shape information currently contained in the SDSS DR7 halo power spectrum (HPS) is by far superseded by geometric information derived from the baryonic features. An immediate corollary is that contrary to popular beliefs, the upper limit on the neutrino mass m_\
Manipulation of the geometric and electronic parameters of metal nanocatalysts
Laskar, Moitree
Metal nanoparticles find wide use in the field of catalysis owing to their high surface to volume ratio. The catalytic activity depends on the interaction between the molecular substrate and catalyst surface. This substrate-catalyst interaction can be regulated by manipulating the geometric and electronic parameters of these nanoparticles. The shape and size of the nanoparticles dictate the geometric parameters whereas their composition controls the electronics of these catalysts. Manipulation of these parameters can be used to tune catalytic activities; hence, a better understanding of their regulation will help in designing efficient catalysts. The synthesis and characterization of a series of monometallic Pd and core shell Au Pd nanoparticles with varying shapes and sizes will be discussed in this presentation. These nanocrystals were used to catalyze two model reactions: selective hydrogenation of 2-hexyne and oxidation of formic acid. Comparison of their catalytic activities by varying one parameter at a time (either size or shape) helps to identify the effect of geometric parameters on catalysis. Additionally, comparison of particles with varying composition but same geometric features provides insight into how the electronics underlying the catalysis can be manipulated through nanostructure architecture. We find that a balance in binding interaction between the substrate and catalyst surface is necessary to design an efficient catalyst and can be achieved with shape-controlled core shell nanocrystals.
A Geometric Model of Multiaxial Warp-knitted Preform for Composite Reinforcement
Institute of Scientific and Technical Information of China (English)
周荣星; 李炜; 陈南梁; 冯勋伟
2003-01-01
A new geometric model of Multiaxial Warp-Knitted (MWK) performs, which is based on the experimental observations and analysis of basic stitch, is developed to relate the geometric parameters and process variables. The fiber volume fraction and fibre orientation of MWK reinforced composites are described in terms of structural and processing parameters in the model. And this model provides a basis for the prediction of mechanical behavior of the MWK reinforced composites.
GEOMETRIC TURBULENCE IN GENERAL RELATIVITY
Directory of Open Access Journals (Sweden)
Trunev A. P.
2015-03-01
Full Text Available The article presents the simulation results of the metric of elementary particles, atoms, stars and galaxies in the general theory of relativity and Yang-Mills theory. We have shown metrics and field equations describing the transition to turbulence. The problems of a unified field theory with the turbulent fluctuations of the metric are considered. A transition from the Einstein equations to the diffusion equation and the Schrödinger equation in quantum mechanics is shown. Ther are examples of metrics in which the field equations are reduced to a single equation, it changes type depending on the equation of state. These examples can be seen as a transition to the geometric turbulence. It is shown that the field equations in general relativity can be reduced to a hyperbolic, elliptic or parabolic type. The equation of parabolic type describing the perturbations of the gravitational field on the scale of stars, galaxies and clusters of galaxies, which is a generalization of the theory of gravitation Newton-Poisson in case of Riemannian geometry, taking into account the curvature of space-time has been derived. It was found that the geometric turbulence leads to an exchange between regions of different scale. Under turbulent exchange material formed of two types of clusters, having positive and negative energy density that corresponds to the classical and quantum particle motion respectively. These results allow us to answer the question about the origin of the quantum theory
Geometric decompositions of collective motion
Mischiati, Matteo; Krishnaprasad, P. S.
2017-04-01
Collective motion in nature is a captivating phenomenon. Revealing the underlying mechanisms, which are of biological and theoretical interest, will require empirical data, modelling and analysis techniques. Here, we contribute a geometric viewpoint, yielding a novel method of analysing movement. Snapshots of collective motion are portrayed as tangent vectors on configuration space, with length determined by the total kinetic energy. Using the geometry of fibre bundles and connections, this portrait is split into orthogonal components each tangential to a lower dimensional manifold derived from configuration space. The resulting decomposition, when interleaved with classical shape space construction, is categorized into a family of kinematic modes-including rigid translations, rigid rotations, inertia tensor transformations, expansions and compressions. Snapshots of empirical data from natural collectives can be allocated to these modes and weighted by fractions of total kinetic energy. Such quantitative measures can provide insight into the variation of the driving goals of a collective, as illustrated by applying these methods to a publicly available dataset of pigeon flocking. The geometric framework may also be profitably employed in the control of artificial systems of interacting agents such as robots.
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.
Measurement error in geometric morphometrics.
Fruciano, Carmelo
2016-06-01
Geometric morphometrics-a set of methods for the statistical analysis of shape once saluted as a revolutionary advancement in the analysis of morphology -is now mature and routinely used in ecology and evolution. However, a factor often disregarded in empirical studies is the presence and the extent of measurement error. This is potentially a very serious issue because random measurement error can inflate the amount of variance and, since many statistical analyses are based on the amount of "explained" relative to "residual" variance, can result in loss of statistical power. On the other hand, systematic bias can affect statistical analyses by biasing the results (i.e. variation due to bias is incorporated in the analysis and treated as biologically-meaningful variation). Here, I briefly review common sources of error in geometric morphometrics. I then review the most commonly used methods to measure and account for both random and non-random measurement error, providing a worked example using a real dataset.
NPP VIIRS Geometric Performance Status
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 Methods in Physics : XXXII Workshop
Bieliavsky, Pierre; Odesskii, Alexander; Odzijewicz, Anatol; Schlichenmaier, Martin; Voronov, Theodore; Geometric Methods in Physics
2014-01-01
The Białowieża Workshops on Geometric Methods in Physics, which are hosted in the unique setting of the Białowieża natural forest in Poland, are among the most important meetings in the field. Every year some 80 to 100 participants from both the mathematics and physics world join to discuss new developments and to exchange ideas. The current volume was produced on the occasion of the 32nd meeting in 2013. It is now becoming a tradition that the Workshop is followed by a School on Geometry and Physics, which consists of advanced lectures for graduate students and young researchers. Selected speakers at the 2013 Workshop were asked to contribute to this book, and their work was supplemented by additional review articles. The selection shows that, despite its now long tradition, the workshop remains at the cutting edge of research. The 2013 Workshop also celebrated the 75th birthday of Daniel Sternheimer, and on this occasion the discussion mainly focused on his contributions to mathematical physics such as ...
Geometrical modeling of fibrous materials under compression
Maze, Benoit; Tafreshi, Hooman Vahedi; 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.
Geometrical shock dynamics for magnetohydrodynamic fast shocks
Mostert, W.
2016-12-12
We describe a formulation of two-dimensional geometrical shock dynamics (GSD) suitable for ideal magnetohydrodynamic (MHD) fast shocks under magnetic fields of general strength and orientation. The resulting area–Mach-number–shock-angle relation is then incorporated into a numerical method using pseudospectral differentiation. The MHD-GSD model is verified by comparison with results from nonlinear finite-volume solution of the complete ideal MHD equations applied to a shock implosion flow in the presence of an oblique and spatially varying magnetic field ahead of the shock. Results from application of the MHD-GSD equations to the stability of fast MHD shocks in two dimensions are presented. It is shown that the time to formation of triple points for both perturbed MHD and gas-dynamic shocks increases as (Formula presented.), where (Formula presented.) is a measure of the initial Mach-number perturbation. Symmetry breaking in the MHD case is demonstrated. In cylindrical converging geometry, in the presence of an azimuthal field produced by a line current, the MHD shock behaves in the mean as in Pullin et al. (Phys. Fluids, vol. 26, 2014, 097103), but suffers a greater relative pressure fluctuation along the shock than the gas-dynamic shock. © 2016 Cambridge University Press
Geometric Methods in Physics : XXXIII Workshop
Bieliavsky, Pierre; Odzijewicz, Anatol; Schlichenmaier, Martin; Voronov, Theodore
2015-01-01
This book presents a selection of papers based on the XXXIII Białowieża Workshop on Geometric Methods in Physics, 2014. The Białowieża Workshops are among the most important meetings in the field and attract researchers from both mathematics and physics. The articles gathered here are mathematically rigorous and have important physical implications, addressing the application of geometry in classical and quantum physics. Despite their long tradition, the workshops remain at the cutting edge of ongoing research. For the last several years, each Białowieża Workshop has been followed by a School on Geometry and Physics, where advanced lectures for graduate students and young researchers are presented; some of the lectures are reproduced here. The unique atmosphere of the workshop and school is enhanced by its venue, framed by the natural beauty of the Białowieża forest in eastern Poland. The volume will be of interest to researchers and graduate students in mathematical physics, theoretical physics and m...
Surface and Volume Grid Generation in Parametric Form
Yu, Tzuyi; Soni, Bharat K.; Benjamin, Ted; Williams, Robert
1996-01-01
The algorithm for surface modeling and volume grid generation using parametric Non-Uniform Rational B-splines (NURBS) geometric representation are presented. The enhanced re-parameterization algorithm which can yield a desired physical distribution on the curve, surface, and volume is also presented. This approach bridges the gap between computer aided design surface/volume definition and surface/volume grid generation.
Dimensional, Geometrical, and Physical Constraints in Skull Growth
Weickenmeier, Johannes; Fischer, Cedric; Carter, Dennis; Kuhl, Ellen; Goriely, Alain
2017-06-01
After birth, the skull grows and remodels in close synchrony with the brain to allow for an increase in intracranial volume. Increase in skull area is provided primarily by bone accretion at the sutures. Additional remodeling, to allow for a change in curvatures, occurs by resorption on the inner surface of the bone plates and accretion on their outer surfaces. When a suture fuses too early, normal skull growth is disrupted, leading to a deformed final skull shape. The leading theory assumes that the main stimulus for skull growth is provided by mechanical stresses. Based on these ideas, we first discuss the dimensional, geometrical, and kinematic synchrony between brain, skull, and suture growth. Second, we present two mechanical models for skull growth that account for growth at the sutures and explain the various observed dysmorphologies. These models demonstrate the particular role of physical and geometrical constraints taking place in skull growth.
CIME course on Ricci Flow and Geometric Applications
Mantegazza, Carlo
2016-01-01
Presenting some impressive recent achievements in differential geometry and topology, this volume focuses on results obtained using techniques based on Ricci flow. These ideas are at the core of the study of differentiable manifolds. Several very important open problems and conjectures come from this area and the techniques described herein are used to face and solve some of them. The book's four chapters are based on lectures given by leading researchers in the field of geometric analysis and low-dimensional geometry/topology, respectively offering an introduction to: the differentiable sphere theorem (G. Besson), the geometrization of 3-manifolds (M. Boileau), the singularities of 3-dimensional Ricci flows (C. Sinestrari), and Kahler-Ricci flow (G. Tian). The lectures will be particularly valuable to young researchers interested in differential manifolds.
Deformed Spacetime Geometrizing Interactions in Four and Five Dimensions
Cardone, Fabio
2007-01-01
This volume provides a detailed discussion of the mathematical aspects and the physical applications of a new geometrical structure of space-time, based on a generalization ("deformation") of the usual Minkowski space, as supposed to be endowed with a metric whose coefficients depend on the energy. Such a formalism (Deformed Special Relativity, DSR) allows one to account for breakdown of local Lorentz invariance in the usual, special-relativistic meaning (however, Lorentz invariance is recovered in a generalized sense) to provide an effective geometrical description of the four fundamental interactions (electromagnetic, weak, strong and gravitational) Moreover, the four-dimensional energy-dependent space-time is just a manifestation of a larger, five-dimensional space in which energy plays the role of a fifth (non-compactified) dimension. This new five-dimensional scheme (Deformed Relativity in Five Dimensions, DR5) represents a true generalization of the usual Kaluza-Klein (KK) formalism. The mathematical pr...
Image-Based Geometric Modeling and Mesh Generation
2013-01-01
As a new interdisciplinary research area, “image-based geometric modeling and mesh generation” integrates image processing, geometric modeling and mesh generation with finite element method (FEM) to solve problems in computational biomedicine, materials sciences and engineering. It is well known that FEM is currently well-developed and efficient, but mesh generation for complex geometries (e.g., the human body) still takes about 80% of the total analysis time and is the major obstacle to reduce the total computation time. It is mainly because none of the traditional approaches is sufficient to effectively construct finite element meshes for arbitrarily complicated domains, and generally a great deal of manual interaction is involved in mesh generation. This contributed volume, the first for such an interdisciplinary topic, collects the latest research by experts in this area. These papers cover a broad range of topics, including medical imaging, image alignment and segmentation, image-to-mesh conversion,...
Defying geometric similarity: Shape centralization in male UK offshore workers.
Stewart, Arthur D; Ledingham, Robert J; Furnace, Graham; Williams, Hector; Nevill, Alan M
2017-05-06
Applying geometric similarity predictions of body dimensions to specific occupational groups has the potential to reveal useful ergonomic and health implications. This study assessed a representative sample of the male UK offshore workforce, and examined how body dimensions from sites typifying musculoskeletal development or fat accumulation, differed from predicted values. A cross sectional sample was obtained across seven weight categories using quota sampling, to match the wider workforce. In total, 588 UK offshore workers, 84 from each of seven weight categories, were measured for stature, mass and underwent 3D body scans which yielded 22 dimensional measurements. Each measurement was modeled using a body-mass power law (adjusting for age), to derive its exponent, which was compared against that predicted from geometric similarity. Mass scaled to stature (1.73) (CI: 1.44-2.02). Arm and leg volume increased by mass(0.8) , and torso volume increased by mass(1.1) in contrast to mass (1.0) predicted by geometric similarity. Neck girth increased by mass (0.33) as expected, while torso girth and depth dimensions increased by mass(0.53-0.72) , all substantially greater than assumed by geometric similarity. After controlling for age, offshore workers experience spectacular "super-centralization" of body shape, with greatest gains in abdominal depth and girth dimensions in areas of fat accumulation, and relative dimensional loss in limbs. These findings are consistent with the antecedents of sarcopenic obesity, and should be flagged as a health concern for this workforce, and for future targeted research and lifestyle interventions. © 2016 Wiley Periodicals, Inc.
Effects of Forest Cover Change on Flood Characteristics in the Upper Citarum Watershed
Directory of Open Access Journals (Sweden)
Bambang Dwi Dasanto
2014-12-01
Full Text Available Information on the effect of forest cover changes on streamflow (river discharge in large-scale catchment is important to be studied. The rate of forest cover change in the Upper Citarum Watershed as a large-scale catchment is high enough to drive streamflow change, such as increase of discharge level, or flood volume. Within the research area, flood would occur when the volume of streamflow exceeded the canal capacity and inundated areas that were normally dry. Therefore, this research focused on identifying the effects of forest cover change on flood events and its distribution. The research consisted of 2 main stages; firstly, building geometric data of river and performing frequency analysis of historical and scenario discharges using an approach of probability distribution; and, secondly, flood inundation mapping using HEC-RAS model. The results showed that forest reduction have affected water yield in the downstream of Upper Citarum Watershed. In each return period, this reduction have increased river discharge level and affected the spread of flooded areas. In 2-year return period, the extent of flood as an impact of forest reduction was estimated to decrease slowly. However, in the return period of more than 2 years, the spread of flooded areas increased sharply. These proved that forest cover reduction would always increase the discharge value, but it did not always expand the inundated area.
Geometrical charged-particle optics
Rose, Harald H
2009-01-01
This reference monograph covers all theoretical aspects of modern geometrical charged-particle optics. It is intended as a guide for researchers, who are involved in the design of electron optical instruments and beam-guiding systems for charged particles, and as a tutorial for graduate students seeking a comprehensive treatment. Procedures for calculating the properties of systems with arbitrarily curved axes are outlined in detail and methods are discussed for designing and optimizing special components such as aberration correctors, spectrometers, energy filters, monochromators, ion traps, electron mirrors and cathode lenses. Also addressed is the design of novel electron optical components enabling sub-Angstroem spatial resolution and sub-0.1eV energy resolution. Relativistic motion and spin precession of the electron is treated in a concise way by employing a covariant five-dimensional procedure.
On chromatic and geometrical calibration
DEFF Research Database (Denmark)
Folm-Hansen, Jørgen
1999-01-01
of non-uniformity of the illumination of the image plane. Only the image deforming aberrations and the non-uniformity of illumination are included in the calibration models. The topics of the pinhole camera model and the extension to the Direct Linear Transform (DLT) are described. It is shown how......The main subject of the present thesis is different methods for the geometrical and chromatic calibration of cameras in various environments. For the monochromatic issues of the calibration we present the acquisition of monochrome images, the classic monochrome aberrations and the various sources...... the DLT can be extended with non-linear models of the common lens aberrations/errors some of them caused by manufacturing defects like decentering and thin prism distortion. The relation between a warping and the non-linear defects are shown. The issue of making a good resampling of an image by using...
Geometrical charged-particle optics
Rose, Harald
2012-01-01
This second edition is an extended version of the first edition of Geometrical Charged-Particle Optics. The updated reference monograph is intended as a guide for researchers and graduate students who are seeking a comprehensive treatment of the design of instruments and beam-guiding systems of charged particles and their propagation in electromagnetic fields. Wave aspects are included in this edition for explaining electron holography, the Aharanov-Bohm effect and the resolution of electron microscopes limited by diffraction. Several methods for calculating the electromagnetic field are presented and procedures are outlined for calculating the properties of systems with arbitrarily curved axis. Detailed methods are presented for designing and optimizing special components such as aberration correctors, spectrometers, energy filters monochromators, ion traps, electron mirrors and cathode lenses. In particular, the optics of rotationally symmetric lenses, quadrupoles, and systems composed of these elements are...
Phenomenological modeling of Geometric Metasurfaces
Ye, Weimin; Xiang, Yuanjiang; Fan, Dianyuan; Zhang, Shuang
2015-01-01
Metasurfaces, with their superior capability in manipulating the optical wavefront at the subwavelength scale and low manufacturing complexity, have shown great potential for planar photonics and novel optical devices. However, vector field simulation of metasurfaces is so far limited to periodic-structured metasurfaces containing a small number of meta-atoms in the unit cell by using full-wave numerical methods. Here, we propose a general phenomenological method to analytically model metasurfaces made up of arbitrarily distributed meta-atoms based on the assumption that the meta-atoms possess localized resonances with Lorentz-Drude forms, whose exact form can be retrieved from the full wave simulation of a single element. Applied to phase modulated geometric metasurfaces, our analytical results show good agreement with full-wave numerical simulations. The proposed theory provides an efficient method to model and design optical devices based on metasurfaces.
LUNGEOMETRY- GEOMETRICAL INVESTIGATION OF LUNGE
Directory of Open Access Journals (Sweden)
R.Vinodh Rajkumar
2015-02-01
Full Text Available Physiotherapists must learn the biomechanics of lunge in detail to clearly understand its significance in human life and implement effective training measures to overcome the limiting factors of proper lunge of their clientele. To understand the biomechanical value of every movement, interesting experimental learning methods must be employed to kindle the Physiotherapists to actively take part in research activities from the under-graduate level onwards. Lungeometry is a novel, simple and inexpensive experimental investigation of lunge, applying basic geometrical methods taking near normal lower limb length dimensions and rationale approaches into consideration. Lungeometry can give a foundation to learn other forms of lunges like forward lunge, weighted lunges, lateral lunges. This model of learning biomechanics of movements using fundamental geometry techniques is expected to strongly connect with any futuristic Physiotherapy curricular structure.
Geometric interpretation of phyllotaxis transition
Okabe, Takuya
2012-01-01
The original problem of phyllotaxis was focused on the regular arrangements of leaves on mature stems represented by common fractions such as 1/2, 1/3, 2/5, 3/8, 5/13, etc. The phyllotaxis fraction is not fixed for each plant but it may undergo stepwise transitions during ontogeny, despite contrasting observation that the arrangement of leaf primordia at shoot apical meristems changes continuously. No explanation has been given so far for the mechanism of the phyllotaxis transition, excepting suggestion resorting to genetic programs operating at some specific stages. Here it is pointed out that varying length of the leaf trace acts as an important factor to control the transition by analyzing Larson's diagram of the procambial system of young cottonwood plants. The transition is interpreted as a necessary consequence of geometric constraints that the leaf traces cannot be fitted into a fractional pattern unless their length is shorter than the denominator times the internode.
Elastic scattering in geometrical model
Plebaniak, Zbigniew; Wibig, Tadeusz
2016-10-01
The experimental data on proton-proton elastic and inelastic scattering emerging from the measurements at the Large Hadron Collider, calls for an efficient model to fit the data. We have examined the optical, geometrical picture and we have found the simplest, linear dependence of this model parameters on the logarithm of the interaction energy with the significant change of the respective slopes at one point corresponding to the energy of about 300 GeV. The logarithmic dependence observed at high energies allows one to extrapolate the proton-proton elastic, total (and inelastic) cross sections to ultra high energies seen in cosmic rays events which makes a solid justification of the extrapolation to very high energy domain of cosmic rays and could help us to interpret the data from an astrophysical and a high energy physics point of view.
Microlocal Analysis of the Geometric Separation Problem
Donoho, David L
2010-01-01
Image data are often composed of two or more geometrically distinct constituents; in galaxy catalogs, for instance, one sees a mixture of pointlike structures (galaxy superclusters) and curvelike structures (filaments). It would be ideal to process a single image and extract two geometrically `pure' images, each one containing features from only one of the two geometric constituents. This seems to be a seriously underdetermined problem, but recent empirical work achieved highly persuasive separations. We present a theoretical analysis showing that accurate geometric separation of point and curve singularities can be achieved by minimizing the $\\ell_1$ norm of the representing coefficients in two geometrically complementary frames: wavelets and curvelets. Driving our analysis is a specific property of the ideal (but unachievable) representation where each content type is expanded in the frame best adapted to it. This ideal representation has the property that important coefficients are clustered geometrically ...
Geometric solitons of Hamiltonian flows on manifolds
Energy Technology Data Exchange (ETDEWEB)
Song, Chong, E-mail: songchong@xmu.edu.cn [School of Mathematical Sciences, Xiamen University, Xiamen 361005 (China); Sun, Xiaowei, E-mail: sunxw@cufe.edu.cn [School of Applied Mathematics, Central University of Finance and Economics, Beijing 100081 (China); Wang, Youde, E-mail: wyd@math.ac.cn [Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190 (China)
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.
Rusak, Z.; Luijten, J.; Kooijman, A.
2015-01-01
The present invention relates a wearable exoskeleton for a user having a torso with an upper limb to support motion of the said upper limb. The wearable exoskeleton comprises a first fixed frame mountable to the torso, an upper arm brace and a first group of actuators for moving the upper arm brace
Rusak, Z.; Luijten, J.; Kooijman, A.
2015-01-01
The present invention relates a wearable exoskeleton for a user having a torso with an upper limb to support motion of the said upper limb. The wearable exoskeleton comprises a first fixed frame mountable to the torso, an upper arm brace and a first group of actuators for moving the upper arm brace
Institute of Scientific and Technical Information of China (English)
马利民; 王金星; 蒋向前; 李柱; 徐振高
2004-01-01
Geometrical Product Specification and verification (GPS) is an ISO standard system coveting standards of size, dimension,geometrical tolerance and surface texture of geometrical product. ISO/TC213 on the GPS has been working towards coordination of the previous standards in tolerance and related metrology in order to publish the next generation of the GPS language. This paper introduces the geometrical product specification model for design, manufacturing and verification based on the improved GPS and its new concepts,i.e., surface models, geometrical features and operations. An application example for the geometrical product specification model is then given.
Geometric Photonic Spin Hall Effect with Metapolarization
2014-01-01
We develop a geometric photonic spin Hall effect (PSHE) which manifests as spin-dependent shift in momentum space. It originates from an effective space-variant Pancharatnam-Berry (PB) phase created by artificially engineering the polarization distribution of the incident light. Unlikely the previously reported PSHE involving the light-matter interaction, the resulting spin-dependent splitting in the geometric PSHE is purely geometrically depend upon the polarization distribution of light whi...
A Geometric Approach to Noncommutative Principal Bundles
Wagner, Stefan
2011-01-01
From a geometrical point of view it is, so far, not sufficiently well understood what should be a "noncommutative principal bundle". Still, there is a well-developed abstract algebraic approach using the theory of Hopf algebras. An important handicap of this approach is the ignorance of topological and geometrical aspects. The aim of this thesis is to develop a geometrically oriented approach to the noncommutative geometry of principal bundles based on dynamical systems and the representation theory of the corresponding transformation group.
Guide to Geometric Algebra in Practice
Dorst, Leo
2011-01-01
This highly practical "Guide to Geometric Algebra in Practice" reviews algebraic techniques for geometrical problems in computer science and engineering, and the relationships between them. The topics covered range from powerful new theoretical developments, to successful applications, and the development of new software and hardware tools. This title: provides hands-on review exercises throughout the book, together with helpful chapter summaries; presents a concise introductory tutorial to conformal geometric algebra (CGA) in the appendices; examines the application of CGA for the d
Report on Workshop on Geometric Scattering
DEFF Research Database (Denmark)
As part of the activities of MaPhySto a workshop on geometric scattering was organized at University of Aarhus, November 5-7, 1998. The workshop was narrowly focused on geometric scattering, and in particular the use of geometric scattering in understanding the structure of the scattering operator...... for the quantum mechanical many-body problem. A number of other questions were also discussed in detail, including the resonances and various geometric questions. This report includes the program of the workshop, a collection of previews, abstracts, and reports on the lectures, with extensive references....
Higher-Dimensional Geometric $\\sigma$-Models
Vasilic, M
1999-01-01
Geometric $\\sigma$-models have been defined as purely geometric theories of scalar fields coupled to gravity. By construction, these theories possess arbitrarily chosen vacuum solutions. Using this fact, one can build a Kaluza--Klein geometric $\\sigma$-model by specifying the vacuum metric of the form $M^4\\times B^d$. The obtained higher dimensional theory has vanishing cosmological constant but fails to give massless gauge fields after the dimensional reduction. In this paper, a modified geometric $\\sigma$-model is suggested, which solves the above problem.
Adiabatic geometric phases in hydrogenlike atoms
Sjöqvist, Erik; Yi, X. X.; Åberg, Johan
2005-11-01
We examine the effect of spin-orbit coupling on geometric phases in hydrogenlike atoms exposed to a slowly varying magnetic field. The marginal geometric phases associated with the orbital angular momentum and the intrinsic spin fulfill a sum rule that explicitly relates them to the corresponding geometric phase of the whole system. The marginal geometric phases in the Zeeman and Paschen-Back limits are analyzed. We point out the existence of nodal points in the marginal phases that may be detected by topological means.
Adiabatic geometric phases in hydrogenlike atoms
Sjöqvist, E; Sj\\"{o}qvist, Erik
2005-01-01
We examine the effect of spin-orbit coupling on geometric phases in hydrogenlike atoms exposed to a slowly varying magnetic field. The marginal geometric phases associated with the orbital angular momentum and the intrinsic spin fulfill a sum rule that explicitly relates them to the corresponding geometric phase of the whole system. The marginal geometric phases in the Zeeman and Paschen-Back limit are analyzed. We point out the existence of nodal points in the marginal phases that may be detected by topological means.
Gingival hyperplasia by upper airway obstruction
Díaz Soriano, Ana; Docente Departamento Académico de Estomatología Biosocial.; Lévano Torres, Víctor; Docente Departamento Académico Médico Quirúrgico.; Pastor Yataco, Shamila; Alumnos del 3er año de Odontología de la UNMSM.; Vallejos Pulido, Arturo; Alumnos del 3er año de Odontología de la UNMSM.; Huamanyauri Gonzales, Lizbeth; Alumnos del 3er año de Odontología de la UNMSM.
2014-01-01
The effects of mouth breathing are the introduction of cold air, dry and dusty in the mouth and pharynx, the lost functions of heating, humedificacion and filtering the air entering the nose increases the oral mucosa irritation and pharyngeal. A case of a female patient 15 years old who comes for consultation of Periodontology with increase in volume and gingival redness in the upper anterior sector of upper airway obstruction caused by deviated septum right turbinate hypertrophy and maxillar...
1980-09-10
Platyhelminthes : Trematoda). This point somewhat coun- ters the idea of this population’s viability. Partially reviewed by Fuller (1974), Nearctic...materials. phylogeny ( phylogenies ), phylogenetic--the history of the evolu- tion of a taxon. PL--United States federal Public Law. plankter (plankters...infestation with flukes, a group of parasitic flatworms ( Platyhelminthes : Trematoda). UM -- Upper Mississippi. Unionicolidae, unionicolid -- the
Body circumferences: clinical implications emerging from a new geometric model
Directory of Open Access Journals (Sweden)
Gallagher Dympna
2008-10-01
Full Text Available Abstract Background Body volume expands with the positive energy balance associated with the development of adult human obesity and this "growth" is captured by two widely used clinical metrics, waist circumference and body mass index (BMI. Empirical correlations between circumferences, BMI, and related body compartments are frequently reported but fail to provide an important common conceptual foundation that can be related to key clinical observations. A two-phase program was designed to fill this important gap: a geometric model linking body volume with circumferences and BMI was developed and validated in cross-sectional cohorts; and the model was applied to the evaluation of longitudinally monitored subjects during periods of voluntary weight loss. Concepts emerging from the developed model were then used to examine the relations between the evaluated clinical measures and body composition. Methods Two groups of healthy adults (n = 494 and 1499 were included in the cross-sectional model development/testing phase and subjects in two previous weight loss studies were included in the longitudinal model evaluation phase. Five circumferences (arm, waist, hip, thigh, and calf; average of sum, C, height (H, BMI, body volume (V; underwater weighing, and the volumes of major body compartments (whole-body magnetic resonance imaging were measured. Results The evaluation of a humanoid geometric model based a cylinder confirmed that V derived from C and H was highly correlated with measured V [R2 both males and females, 0.97; p 0.5. The scaling of individual circumferences to V/H varied, with waist the highest (V/H~0.6 and calf the lowest (V/H~0.3, indicating that the largest and smallest between-subject "growth" with greater body volume occurs in the abdominal area and lower extremities, respectively. A stepwise linear regression model including all five circumferences2 showed that each contributed independently to V/H. These cross
Discrete geometric structures for architecture
Pottmann, Helmut
2010-06-13
The emergence of freeform structures in contemporary architecture raises numerous challenging research problems, most of which are related to the actual fabrication and are a rich source of research topics in geometry and geometric computing. The talk will provide an overview of recent progress in this field, with a particular focus on discrete geometric structures. Most of these result from practical requirements on segmenting a freeform shape into planar panels and on the physical realization of supporting beams and nodes. A study of quadrilateral meshes with planar faces reveals beautiful relations to discrete differential geometry. In particular, we discuss meshes which discretize the network of principal curvature lines. Conical meshes are among these meshes; they possess conical offset meshes at a constant face/face distance, which in turn leads to a supporting beam layout with so-called torsion free nodes. This work can be generalized to a variety of multilayer structures and laid the ground for an adapted curvature theory for these meshes. There are also efforts on segmenting surfaces into planar hexagonal panels. Though these are less constrained than planar quadrilateral panels, this problem is still waiting for an elegant solution. Inspired by freeform designs in architecture which involve circles and spheres, we present a new kind of triangle mesh whose faces\\' in-circles form a packing, i.e., the in-circles of two triangles with a common edge have the same contact point on that edge. These "circle packing (CP) meshes" exhibit an aesthetic balance of shape and size of their faces. They are closely tied to sphere packings on surfaces and to various remarkable structures and patterns which are of interest in art, architecture, and design. CP meshes constitute a new link between architectural freeform design and computational conformal geometry. Recently, certain timber structures motivated us to study discrete patterns of geodesics on surfaces. This
Rotational Crofton formulae for flagged intrinsic volumes
DEFF Research Database (Denmark)
Auneau, Jeremy Michel
, and the integration is over all sections containing the fixed point origo. Our main result is a local stereological analogue to the well-known Crofton formula. More precisely, we derive geometric formulae that relate new flagged intrinsic volumes of a set with the flagged intrinsic volumes of its sections...
Volume of a doubly truncated hyperbolic tetrahedron
Kolpakov, Alexander
2012-01-01
The present paper regards the volume function of a doubly truncated hyperbolic tetrahedron. Starting from the previous results of J. Murakami, U. Yano and A. Ushijima, we have developed a unified approach to expressing the volume in different geometric cases by dilogarithm functions and to treat properly the many analytic strata of the latter. Finally, several numeric examples are given.
3D geometric split-merge segmentation of brain MRI datasets.
Marras, Ioannis; Nikolaidis, Nikolaos; Pitas, Ioannis
2014-05-01
In this paper, a novel method for MRI volume segmentation based on region adaptive splitting and merging is proposed. The method, called Adaptive Geometric Split Merge (AGSM) segmentation, aims at finding complex geometrical shapes that consist of homogeneous geometrical 3D regions. In each volume splitting step, several splitting strategies are examined and the most appropriate is activated. A way to find the maximal homogeneity axis of the volume is also introduced. Along this axis, the volume splitting technique divides the entire volume in a number of large homogeneous 3D regions, while at the same time, it defines more clearly small homogeneous regions within the volume in such a way that they have greater probabilities of survival at the subsequent merging step. Region merging criteria are proposed to this end. The presented segmentation method has been applied to brain MRI medical datasets to provide segmentation results when each voxel is composed of one tissue type (hard segmentation). The volume splitting procedure does not require training data, while it demonstrates improved segmentation performance in noisy brain MRI datasets, when compared to the state of the art methods.
Simulating geometrically complex blast scenarios
Directory of Open Access Journals (Sweden)
Ian G. Cullis
2016-04-01
Full Text Available The effects of blast waves generated by energetic and non-energetic sources are of continuing interest to the ballistics research community. Modern conflicts are increasingly characterised by asymmetric urban warfare, with improvised explosive devices (IEDs often playing a dominant role on the one hand and an armed forces requirement for minimal collateral effects from their weapons on the other. These problems are characterised by disparate length- and time-scales and may also be governed by complex physics. There is thus an increasing need to be able to rapidly assess and accurately predict the effects of energetic blast in topologically complex scenarios. To this end, this paper presents a new QinetiQ-developed advanced computational package called EAGLE-Blast, which is capable of accurately resolving the generation, propagation and interaction of blast waves around geometrically complex shapes such as vehicles and buildings. After a brief description of the numerical methodology, various blast scenario simulations are described and the results compared with experimental data to demonstrate the validation of the scheme and its ability to describe these complex scenarios accurately and efficiently. The paper concludes with a brief discussion on the use of the code in supporting the development of algorithms for fast running engineering models.
Generalized Geometric Quantum Speed Limits
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.
Simulating geometrically complex blast scenarios
Institute of Scientific and Technical Information of China (English)
Ian G. CULLIS; Nikos NIKIFORAKIS; Peter FRANKL; Philip BLAKELY; Paul BENNETT; Paul GREENWOOD
2016-01-01
The effects of blast waves generated by energetic and non-energetic sources are of continuing interest to the ballistics research community. Modern conflicts are increasingly characterised by asymmetric urban warfare, with improvised explosive devices (IEDs) often playing a dominant role on the one hand and an armed forces requirement for minimal collateral effects from their weapons on the other. These problems are characterised by disparate length-and time-scales and may also be governed by complex physics. There is thus an increasing need to be able to rapidly assess and accurately predict the effects of energetic blast in topologically complex scenarios. To this end, this paper presents a new QinetiQ-developed advanced computational package called EAGLE-Blast, which is capable of accurately resolving the generation, propagation and interaction of blast waves around geometrically complex shapes such as vehicles and buildings. After a brief description of the numerical methodology, various blast scenario simulations are described and the results compared with experimental data to demonstrate the validation of the scheme and its ability to describe these complex scenarios accurately and efficiently. The paper concludes with a brief discussion on the use of the code in supporting the development of algorithms for fast running engineering models.
Geometric Reasoning for Automated Planning
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.
Generalized Geometric Quantum Speed Limits
Directory of Open Access Journals (Sweden)
Diego Paiva Pires
2016-06-01
Full Text Available 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.
Geometrical aspects of quantum spaces
Energy Technology Data Exchange (ETDEWEB)
Ho, P.M. [Lawrence Berkeley Lab., CA (United States). Theoretical Physics Group
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{sub 1}{sup 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{sub q}{sup 2} and CP{sub q}(N) is also described. In Chapter 4 the quantum projective geometry over the quantum projective space CP{sub 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.
Geometrical splitting and reduction of Feynman diagrams
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.
Parabolas: Connection between Algebraic and Geometrical Representations
Shriki, Atara
2011-01-01
A parabola is an interesting curve. What makes it interesting at the secondary school level is the fact that this curve is presented in both its contexts: algebraic and geometric. Being one of Apollonius' conic sections, the parabola is basically a geometric entity. It is, however, typically known for its algebraic characteristics, in particular…
Some technical issues in geometric modeling
Energy Technology Data Exchange (ETDEWEB)
Peterson, D.P.
1983-01-01
The full impact of CAD/CAM will not be felt until geometric modeling systems support dimensioning and tolerancing, have sophisticated user interfaces, and are capable of routinely handling many representation conversions. The attainment of these capabilities requires a joint effort among users, implementors, and theoreticians of geometric modeling.
Geometric Growing Patterns: What's the Rule?
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…
Sudan-decoding generalized geometric Goppa codes
DEFF Research Database (Denmark)
Heydtmann, Agnes Eileen
2003-01-01
Generalized geometric Goppa codes are vector spaces of n-tuples with entries from different extension fields of a ground field. They are derived from evaluating functions similar to conventional geometric Goppa codes, but allowing evaluation in places of arbitrary degree. A decoding scheme...
A Framework for Analyzing Geometric Pattern Tasks
Friel, Susan N.; Markworth, Kimberly A.
2009-01-01
Teachers can use geometric patterns to promote students' understanding of functional relationships. In this article, the authors first look at a problem-solving process that supports the use of figural reasoning to explore and interpret geometric pattern tasks and generalize function rules. Second, the authors discuss a framework for…
On geometric Langlands theory and stacks
Poirier, Cécile Florence Christine
2008-01-01
R.Langlands conjectured the existence of a bridge between two parts of number theory. This correspondence, called 'Langlands conjecture' was proved by L. Lafforgue who obtained a Fields medal for his work. G. Laumon gave a geometric translation of a part of the theorem, called 'geometric Langlands c
Geometrical optics and the diffraction phenomenon
Energy Technology Data Exchange (ETDEWEB)
Timofeev, Aleksandr V [Russian Research Centre ' Kurchatov Institute' , Moscow (Russian Federation)
2005-06-30
This note outlines the principles of the geometrical optics of inhomogeneous waves whose description necessitates the use of complex values of the wave vector. Generalizing geometrical optics to inhomogeneous waves permits including in its scope the analysis of the diffraction phenomenon. (methodological notes)
Variance optimal stopping for geometric Levy processes
DEFF Research Database (Denmark)
Gad, Kamille Sofie Tågholt; Pedersen, Jesper Lund
2015-01-01
The main result of this paper is the solution to the optimal stopping problem of maximizing the variance of a geometric Lévy process. We call this problem the variance problem. We show that, for some geometric Lévy processes, we achieve higher variances by allowing randomized stopping. Furthermore...
Geometrical description of denormalized thermodynamic manifold
Institute of Scientific and Technical Information of China (English)
Wu Li-Ping; Sun Hua-Fei; Cao Li-Mei
2009-01-01
In view of differential geometry,the state space of thermodynamic parameters is investigated. Here the geometrical structures of the denormalized thermodynamic manifold are considered. The relation of their geometrical metrics is obtained. Moreover an example is used to illustrate our conclusions.
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 phases in discrete dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Cartwright, Julyan H.E., E-mail: julyan.cartwright@csic.es [Instituto Andaluz de Ciencias de la Tierra, CSIC–Universidad de Granada, E-18100 Armilla, Granada (Spain); Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071 Granada (Spain); Piro, Nicolas, E-mail: nicolas.piro@epfl.ch [École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne (Switzerland); Piro, Oreste, E-mail: piro@imedea.uib-csic.es [Departamento de Física, Universitat de les Illes Balears, E-07122 Palma de Mallorca (Spain); Tuval, Idan, E-mail: ituval@imedea.uib-csic.es [Mediterranean Institute for Advanced Studies, CSIC–Universitat de les Illes Balears, E-07190 Mallorca (Spain)
2016-10-14
In order to study the behaviour of discrete dynamical systems under adiabatic cyclic variations of their parameters, we consider discrete versions of adiabatically-rotated rotators. Parallelling the studies in continuous systems, we generalize the concept of geometric phase to discrete dynamics and investigate its presence in these rotators. For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number of the system. For the discrete version of the rotated rotator considered by Berry, the rotated standard map, we further explore this connection as well as the role of the geometric phase at the onset of chaos. Further into the chaotic regime, we show that the geometric phase is also related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent. - Highlights: • We extend the concept of geometric phase to maps. • For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number. • For the rotated standard map, we explore the role of the geometric phase at the onset of chaos. • We show that the geometric phase is related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent.
Geometric integrators for stochastic rigid body dynamics
Tretyakov, Mikhail
2016-01-05
Geometric integrators play an important role in simulating dynamical systems on long time intervals with high accuracy. We will illustrate geometric integration ideas within the stochastic context, mostly on examples of stochastic thermostats for rigid body dynamics. The talk will be mainly based on joint recent work with Rusland Davidchak and Tom Ouldridge.
Geometric Control of Patterned Linear Systems
Hamilton, Sarah C
2012-01-01
This monograph is aiming at researchers of systems control, especially those interested in multiagent systems, distributed and decentralized control, and structured systems. The book assumes no prior background in geometric control theory; however, a first year graduate course in linear control systems is desirable. Since not all control researchers today are exposed to geometric control theory, the book also adopts a tutorial style by way of examples that illustrate the geometric and abstract algebra concepts used in linear geometric control. In addition, the matrix calculations required for the studied control synthesis problems of linear multivariable control are illustrated via a set of running design examples. As such, some of the design examples are of higher dimension than one may typically see in a text; this is so that all the geometric features of the design problem are illuminated.
Rule-based transformations for geometric modelling
Directory of Open Access Journals (Sweden)
Thomas Bellet
2011-02-01
Full Text Available The context of this paper is the use of formal methods for topology-based geometric modelling. Topology-based geometric modelling deals with objects of various dimensions and shapes. Usually, objects are defined by a graph-based topological data structure and by an embedding that associates each topological element (vertex, edge, face, etc. with relevant data as their geometric shape (position, curve, surface, etc. or application dedicated data (e.g. molecule concentration level in a biological context. We propose to define topology-based geometric objects as labelled graphs. The arc labelling defines the topological structure of the object whose topological consistency is then ensured by labelling constraints. Nodes have as many labels as there are different data kinds in the embedding. Labelling constraints ensure then that the embedding is consistent with the topological structure. Thus, topology-based geometric objects constitute a particular subclass of a category of labelled graphs in which nodes have multiple labels.
Rule-based transformations for geometric modelling
Bellet, Thomas; Gall, Pascale Le; 10.4204/EPTCS.48.5
2011-01-01
The context of this paper is the use of formal methods for topology-based geometric modelling. Topology-based geometric modelling deals with objects of various dimensions and shapes. Usually, objects are defined by a graph-based topological data structure and by an embedding that associates each topological element (vertex, edge, face, etc.) with relevant data as their geometric shape (position, curve, surface, etc.) or application dedicated data (e.g. molecule concentration level in a biological context). We propose to define topology-based geometric objects as labelled graphs. The arc labelling defines the topological structure of the object whose topological consistency is then ensured by labelling constraints. Nodes have as many labels as there are different data kinds in the embedding. Labelling constraints ensure then that the embedding is consistent with the topological structure. Thus, topology-based geometric objects constitute a particular subclass of a category of labelled graphs in which nodes hav...
Aftershock Statistics explained from Geometric Reductionism
Mignan, Arnaud
2016-04-01
The decay of aftershocks has recently been shown to follow a stretched exponential function instead of the Omori law (Mignan, Geophys. Res. Lett., 2015). This triggers a complete re-investigation of aftershock statistics in Southern California and a new physical interpretation of these results: (1) After verifying the stretched exponential behavior of aftershocks in time, I show that aftershocks follow a pure exponential in space. I then (re)demonstrate that K(M) = exp(α(M-mmin-ΔmB)) with K the aftershock production by mainshock magnitude M, α the Gutenberg-Richter distribution slope and ΔmB Båth's parameter. Based on these observations, I propose the Recursive Aftershock Stretched Exponential (RASE) model. (2) I investigate the origin of aftershocks using geometric reductionism made possible by the Non-Critical Precursory Accelerating Seismicity Theory postulate, which states that spatial density switches from δb0 for background seismicity to δbp for activated events (such as foreshocks, induced seismicity and here aftershocks) when the static stress field σ(r) exceeds the threshold σ(rA*) ∝ Δσ* with r the distance to source. The postulate explains the exponential spatial distribution (assuming that aftershocks fill a noisy fractal network within rA*) and aftershock production (assuming a constant stress drop) with K(M) = δbp.V(M), V being the volume of a rounded cuboid centred on the fault of length l ∝ exp(αM), and with radius rA*. Finally the observed stretching factor β ≈ 0.4 is explained topologically from the fractal dimension D ≈ 1.5.
Winter, Samantha Lee; Forrest, Sarah Michelle; Wallace, Joanne; Challis, John H
2017-08-08
The purpose of this study was to validate a new geometric solids model, developed to address the lack of female specific models for body segment inertial parameter estimation. A second aim was to determine the effect of reducing the number of geometric solids used to model the limb segments on model accuracy. The 'full' model comprised 56 geometric solids, the 'reduced' 31, and the 'basic' 16. Predicted whole-body inertial parameters were compared with direct measurements (reaction board, scales), and predicted segmental parameters with those estimated from whole-body DXA scans for 28 females. The percentage root mean square error (%RMSE) for whole-body volume was geometric solids are required to more accurately model the trunk.
Energy Technology Data Exchange (ETDEWEB)
1994-08-01
This report comprises appendices A--J which support the Y-12 Plant`s remedial action report involving Chestnut Ridge Operable Unit 2 (filled coal ash pond/Upper McCoy Branch). The appendices cover the following: Sampling fish from McCoy Branch; well and piezometer logs; ecological effects of contaminants in McCoy Branch 1989-1990; heavy metal bioaccumulation data; microbes in polluted sediments; and baseline human health risk assessment data.
Geometrical Aberration Suppression for Large Aperture Sub-THz Lenses
Rachon, M.; Liebert, K.; Siemion, A.; Bomba, J.; Sobczyk, A.; Knap, W.; Coquillat, D.; Suszek, J.; Sypek, M.
2017-03-01
Advanced THz setups require high performance optical elements with large numerical apertures and small focal lengths. This is due to the high absorption of humid air and relatively low efficiency of commercially available detectors. Here, we propose a new type of double-sided sub-THz diffractive optical element with suppressed geometrical aberration for narrowband applications (0.3 THz). One side of the element is designed as thin structure in non-paraxial approach which is the exact method, but only for ideally flat elements. The second side will compensate phase distribution differences between ideal thin structure and real volume one. The computer-aided optimization algorithm is performed to design an additional phase distribution of correcting layer assuming volume designing of the first side of the element. The experimental evaluation of the proposed diffractive component created by 3D printing technique shows almost two times larger performance in comparison with uncorrected basic diffractive lens.
Geometrical Aberration Suppression for Large Aperture Sub-THz Lenses
Rachon, M.; Liebert, K.; Siemion, A.; Bomba, J.; Sobczyk, A.; Knap, W.; Coquillat, D.; Suszek, J.; Sypek, M.
2016-11-01
Advanced THz setups require high performance optical elements with large numerical apertures and small focal lengths. This is due to the high absorption of humid air and relatively low efficiency of commercially available detectors. Here, we propose a new type of double-sided sub-THz diffractive optical element with suppressed geometrical aberration for narrowband applications (0.3 THz). One side of the element is designed as thin structure in non-paraxial approach which is the exact method, but only for ideally flat elements. The second side will compensate phase distribution differences between ideal thin structure and real volume one. The computer-aided optimization algorithm is performed to design an additional phase distribution of correcting layer assuming volume designing of the first side of the element. The experimental evaluation of the proposed diffractive component created by 3D printing technique shows almost two times larger performance in comparison with uncorrected basic diffractive lens.
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.
Geometric characterization of polymeric macrofibers
Directory of Open Access Journals (Sweden)
A. R. E. Cáceres
Full Text Available ABSTRACTThe geometric characteristics of synthetic macrofibers are important because they affect the behavior of fiber-reinforced concrete (FRC. Because there is a lack of specific, relevant publications in Brazil, the European standard EN14889-2:2006 was adopted as a reference to perform the characterization. Thus, an experimental plan was developed to assess the adequacy of testing procedures for the qualification of synthetic macrofibers for use in FRC. Two types of macrofibers were evaluated. The length measurement was performed using two methods: the caliper method, which is a manual measurement, and the digital image analysis method using the ImageJ software for image processing. These aforementioned methods were used to determine the diameter together with the density method, which is an indirect method that uses the developed length obtained by one of the previous methods. The statistical analyses revealed that the length results are similar regardless of the method used. However, the macrofibers must be pre-stretched to maximize the accuracy of caliper measurements. The caliper method for diameter determination has the disadvantage of underestimating the macrofiber cross-section because of the pressure applied by the load claws. In contrast, the digital image analysis method obtains the projected diameter in a single plane, which overestimate the diameter because the macrofibers are oriented with the pressure of the scanner cover. Thus, these techniques may result in false projections of the diameters that will depend on the level of torsion in the macrofibers. It was concluded that both the caliper method using previously stretched macrofibers and the digital imaging method can be used to measure length. The density method presented the best results for the diameter determination because these results were not affected by the method chosen to determine the length.
US Fish and Wildlife Service, Department of the Interior — The Upper Kenai Corridor study describes and evaluates the Upper Kenai River and the land which embraces it. It also places the river corridor in its regional...
Upper limb arterial thromboembolism
DEFF Research Database (Denmark)
Andersen, L V; Lip, Gregory Y.H.; Lindholt, J S;
2013-01-01
The aim of this review is to focus on risk factors, risk-modifying drugs and prognosis for upper limb arterial thromboembolism, and the relationship between upper limb arterial thromboembolism and atrial fibrillation (AF).......The aim of this review is to focus on risk factors, risk-modifying drugs and prognosis for upper limb arterial thromboembolism, and the relationship between upper limb arterial thromboembolism and atrial fibrillation (AF)....
Geometrical modulus of a casting and its influence on solidification process
Directory of Open Access Journals (Sweden)
F. Havlicek
2011-10-01
Full Text Available Object: The work analyses the importance of the known criterion for evaluating the controlled solidification of castings, so called geometrical modulus defined by N. Chvorinov as the first one. Geometrical modulus influences the solidification process. The modulus has such specificity that during the process of casting formation it is not a constant but its initial value decreases with the solidification progress because the remaining melt volume can decrease faster than its cooling surface.Methodology: The modulus is determined by a simple calculation from the ratio of the casting volume after pouring the metal in the mould to the cooled mould surface. The solidified metal volume and the cooled surface too are changed during solidification. That calculation is much more complicated. Results were checked up experimentally by measuring the temperatures in the cross-section of heavy steel castings during cooling them.Results: The given experimental results have completed the original theoretical calculations by Chvorinov and recent researches done with use of numerical calculations. The contribution explains how the geometrical modulus together with the thermal process in the casting causes the higher solidification rate in the axial part of the casting cross-section and shortening of solidification time. Practical implications: Change of the geometrical modulus negatively affects the casting internal quality. Melt feeding by capillary filtration in the dendritic network in the casting central part decreases and in such a way the shrinkage porosity volume increases. State of stress character in the casting is changed too and it increases.
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.
Conceptual aspects of geometric quantum computation
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.
The Geometric Field at a Josephson Junction
Atanasov, Victor
2016-01-01
A geometric potential from the kinetic term of a constrained to a curved hyper-plane of space-time quantum superconducting condensate is derived. An energy conservation relation involving the geometric field at every material point in the superconductor is demonstrated. At a Josephson junction the energy conservation relation implies the possibility to transform electric energy into geometric field energy, that is curvature of space-time. Experimental procedures to verify that the Josephson junction can act as a voltage-to-curvature converter are discussed.
A physics perspective on geometric Langlands duality
Schlesinger, Karl-Georg
2009-01-01
We review the approach to the geometric Langlands program for algebraic curves via S-duality of an N=4 supersymmetric four dimensional gauge theory, initiated by Kapustin and Witten in 2006. We sketch some of the central further developments. Placing this four dimensional gauge theory into a six dimensional framework, as advocated by Witten, holds the promise to lead to a formulation which makes geometric Langlands duality a manifest symmetry (like coavariance in differential geometry). Furthermore, it leads to an approach toward geometric Langlands duality for algebraic surfaces, reproducing and extending the recent results of Braverman and Finkelberg.
A Geometric Characterization of Arithmetic Varieties
Indian Academy of Sciences (India)
Kapil Hari Paranjape
2002-08-01
A result of Belyi can be stated as follows. Every curve defined over a number field can be expressed as a cover of the projective line with branch locus contained in a rigid divisor. We define the notion of geometrically rigid divisors in surfaces and then show that every surface defined over a number field can be expressed as a cover of the projective plane with branch locus contained in a geometrically rigid divisor in the plane. The main result is the characterization of arithmetically defined divisors in the plane as geometrically rigid divisors in the plane.
Murugan, Karmani; Choonara, Yahya E; Kumar, Pradeep; du Toit, Lisa C; Pillay, Viness
2017-09-01
This study aimed to highlight a statistic design to precisely engineer homogenous geometric copper nanoparticles (CuNPs) for enhanced intracellular drug delivery as a function of geometrical structure. CuNPs with a dual functionality comprising geometric attributes for enhanced cell uptake and exerting cytotoxic activity on proliferating cells were synthesized as a novel drug delivery system. This paper investigated the defined concentrations of two key surfactants used in the reaction to mutually control and manipulate nano-shape and optimisation of the geometric nanosystems. A statistical experimental design comprising a full factorial model served as a refining factor to achieve homogenous geometric nanoparticles using a one-pot method for the systematic optimisation of the geometric CuNPs. Shapes of the nanoparticles were investigated to determine the result of the surfactant variation as the aim of the study and zeta potential was studied to ensure the stability of the system and establish a nanosystem of low aggregation potential. After optimisation of the nano-shapes, extensive cellular internalisation studies were conducted to elucidate the effect of geometric CuNPs on uptake rates, in addition to the vital toxicity assays to further understand the cellular effect of geometric CuNPs as a drug delivery system. In addition to geometry; volume, surface area, orientation to the cell membrane and colloidal stability is also addressed. The outcomes of the study demonstrated the success of homogenous geometric NP formation, in addition to a stable surface charge. The findings of the study can be utilized for the development of a drug delivery system for promoted cellular internalisation and effective drug delivery. Copyright © 2017 Elsevier B.V. All rights reserved.
Transition curves for highway geometric design
Kobryń, Andrzej
2017-01-01
This book provides concise descriptions of the various solutions of transition curves, which can be used in geometric design of roads and highways. It presents mathematical methods and curvature functions for defining transition curves. .
Exotic geometric structures on Kodaira surfaces
McKay, Benjamin
2012-01-01
On all compact complex surfaces (modulo finite unramified coverings), we classify all of the locally homogeneous geometric structures which are locally isomorphic to the exotic homogeneous surfaces of Lie.
Geometric Photonic Spin Hall Effect with Metapolarization
Ling, Xiaohui; Yi, Xunong; Luo, Hailu; Wen, Shuangchun
2014-01-01
We develop a geometric photonic spin Hall effect (PSHE) which manifests as spin-dependent shift in momentum space. It originates from an effective space-variant Pancharatnam-Berry (PB) phase created by artificially engineering the polarization distribution of the incident light. Unlikely the previously reported PSHE involving the light-matter interaction, the resulting spin-dependent splitting in the geometric PSHE is purely geometrically depend upon the polarization distribution of light which can be tailored by assembling its circular polarization basis with suitably magnitude and phase. This metapolarization idea enables us to manipulate the geometric PSHE by suitably tailoring the polarization geometry of light. Our scheme provides great flexibility in the design of various polarization geometry and polarization-dependent application, and can be extrapolated to other physical system, such as electron beam or atom beam, with the similar spin-orbit coupling underlying.
5th Dagstuhl Seminar on Geometric Modelling
Brunnett, Guido; Farin, Gerald; Goldman, Ron
2004-01-01
In 19 articles presented by leading experts in the field of geometric modelling the state-of-the-art on representing, modeling, and analyzing curves, surfaces as well as other 3-dimensional geometry is given. The range of applications include CAD/CAM-systems, computer graphics, scientific visualization, virtual reality, simulation and medical imaging. The content of this book is based on selected lectures given at a workshop held at IBFI Schloss Dagstuhl, Germany. Topics treated are: – curve and surface modelling – non-manifold modelling in CAD – multiresolution analysis of complex geometric models – surface reconstruction – variational design – computational geometry of curves and surfaces – 3D meshing – geometric modelling for scientific visualization – geometric models for biomedical applications
Hidden geometric correlations in real multiplex networks
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.
Study on the Grey Polynomial Geometric Programming
Institute of Scientific and Technical Information of China (English)
LUODang
2005-01-01
In the model of geometric programming, values of parameters cannot be gotten owing to data fluctuation and incompletion. But reasonable bounds of these parameters can be attained. This is to say, parameters of this model can be regarded as interval grey numbers. When the model contains grey numbers, it is hard for common programming method to solve them. By combining the common programming model with the grey system theory,and using some analysis strategies, a model of grey polynomial geometric programming, a model of 8 positioned geometric programming and their quasi-optimum solution or optimum solution are put forward. At the same time, we also developed an algorithm for the problem.This approach brings a new way for the application research of geometric programming. An example at the end of this paper shows the rationality and feasibility of the algorithm.
A geometric approach to acyclic orientations
Ehrenborg, Richard
2009-01-01
The set of acyclic orientations of a connected graph with a given sink has a natural poset structure. We give a geometric proof of a result of Jim Propp: this poset is the disjoint union of distributive lattices.
Concepts and Figures in Geometric Reasoning.
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)
Geometric continuum mechanics and induced beam theories
R Eugster, Simon
2015-01-01
This research monograph discusses novel approaches to geometric continuum mechanics and introduces beams as constraint continuous bodies. In the coordinate free and metric independent geometric formulation of continuum mechanics as well as for beam theories, the principle of virtual work serves as the fundamental principle of mechanics. Based on the perception of analytical mechanics that forces of a mechanical system are defined as dual quantities to the kinematical description, the virtual work approach is a systematic way to treat arbitrary mechanical systems. Whereas this methodology is very convenient to formulate induced beam theories, it is essential in geometric continuum mechanics when the assumptions on the physical space are relaxed and the space is modeled as a smooth manifold. The book addresses researcher and graduate students in engineering and mathematics interested in recent developments of a geometric formulation of continuum mechanics and a hierarchical development of induced beam theories.
Three-dimensional Transient Analysis in the Upper Plenum of MONJU with MARS-LMR
Energy Technology Data Exchange (ETDEWEB)
Lee, Kwi-Lim; Jeong, Jae-Ho; Ha, Kwi-Seok [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2015-10-15
The JAEA had provided a detailed geometrical data of the reactor vessel upper plenum, and time-dependent inlet conditions of the flow rate and temperature at the reactor core top surface for the transient analysis. The KAERI(Korea Atomic Energy Research Institute) had studied a numerical analysis of thermal stratification in an upper plenum of the MONJU using the MARS-LMR code. Three-dimensional analysis results have a good agreement with the experimental data and also show a better estimation than that of the one-dimensional analysis. Three-dimensional thermal hydraulic analyses are implemented in MARS-LMR code to validate the thermal-hydraulic models of the MARS-LMR code and identify important phenomena such as buoyancy effect and thermal stratification. The results of a 3-D analysis show a better estimation than that of a 1-D analysis. In the steady-state calculation, the total flow rate through UFHs is larger than that of the LFHs unlike a result of a 1-D calculation due to a dominant radial-flow instead of an over-flow by a geometrical interruption of an axially located fuel handling system. In the transient calculation, the sodium keeps overflowing an inner barrel during a simulation time of 3600 sec in the 3-D analysis. As a result, sodium over UFHs steadily continues to be cooled in the 3-D analysis. However, a calculated temperature at the 9th node near the top of an inner barrel is lower than an experimental data. It is considered to be caused by a modeling of an over-flow region as one dimensional volume, because the overflow region has a multi-dimensional flow.
Geometric Modelling by Recursively Cutting Vertices
Institute of Scientific and Technical Information of China (English)
吕伟; 梁友栋; 等
1989-01-01
In this paper,a new method for curve and surface modelling is introduced which generates curves and surfaces by recursively cutting and grinding polygons and polyhedra.It is a generalization of the existing corner-cutting methods.A lot of properties,such as geometric continuity,representation,shape-preserving,and the algorithm are studied which show that such curves and surfaces are suitable for geometric designs in CAD,computer graphics and their application fields.
Mechanisms of geometrical seismic attenuation
Directory of Open Access Journals (Sweden)
Igor B. Morozov
2011-07-01
Full Text Available In several recent reports, we have explained the frequency dependence of the apparent seismic quality-factor (Q observed in many studies according to the effects of geometrical attenuation, which was defined as the zero-frequency limit of the temporal attenuation coefficient. In particular, geometrical attenuation was found to be positive for most waves traveling within the lithosphere. Here, we present three theoretical models that illustrate the origin of this geometrical attenuation, and we investigate the causes of its preferential positive values. In addition, we discuss the physical basis and limitations of both the conventional and new attenuation models. For waves in media with slowly varying properties, geometrical attenuation is caused by variations in the wavefront curvature, which can be both positive (for defocusing and negative (for focusing. In media with velocity/density contrasts, incoherent reflectivity leads to geometrical-attenuation coefficients which are proportional to the mean squared reflectivity and are always positive. For «coherent» reflectivity, the geometrical attenuation is approximately zero, and the attenuation process can be described according to the concept of «scattering Q». However, the true meaning of this parameter is in describing the mean reflectivity within the medium, and not that of the traditional resonator quality factor known in mechanics. The general conclusion from these models is that non-zero and often positive levels of geometrical attenuation are common in realistic, heterogeneous media, both observationally and theoretically. When transformed into the conventional Q-factor form, this positive geometrical attenuation leads to Q values that quickly increase with frequency. These predictions show that the positive frequency-dependent Q observed in many datasets might represent artifacts of the transformations of the attenuation coefficients into Q.
A Toolbox for Geometric Grain Boundary Characterization
Glowinski, Krzysztof; Morawiec, Adam
Properties of polycrystalline materials are affected by grain boundary networks. The most basic aspect of boundary analysis is boundary geometry. This paper describes a package of computer programs for geometric boundary characterization based on macroscopic boundary parameters. The program allows for determination whether a boundary can be classified as near-tilt, -twist, -symmetric et cetera. Since calculations on experimental, i.e., error affected data are assumed, the program also provides distances to the nearest geometrically characteristic boundaries. The software has a number of other functions helpful in grain boundary analysis. One of them is the determination of planes of all characteristic boundaries for a given misorientation. The resulting diagrams of geometrically characteristic boundaries can be linked to experimentally determined grain boundary distributions. In computations, all symmetrically equivalent representations of boundaries are taken into account. Cubic and hexagonal holohedral crystal symmetries are allowed.
2012-01-01
Este libro, Problemas de Geometría, junto con otros dos, Problemas de Matemáticas y Problemas de Geometría Analítica y Diferencial, están dedicados a la presentación y resolución de problemas que se planteaban hace unas décadas, en la preparación para ingreso en las carreras de ingeniería técnica superior. Incluye 744 problemas que se presentan en dos grandes grupos: • Geometría del plano, con 523 problemas referentes a lugares geométricos, rectas, ángulos, triángulos y su construcción, cuadr...
Spherical projections and liftings in geometric tomography
DEFF Research Database (Denmark)
Goodey, Paul; Kiderlen, Markus; Weil, Wolfgang
2011-01-01
We consider a variety of integral transforms arising in Geometric Tomography. It will be shown that these can be put into a common framework using spherical projection and lifting operators. These operators will be applied to support functions and surface area measures of convex bodies and to rad......We consider a variety of integral transforms arising in Geometric Tomography. It will be shown that these can be put into a common framework using spherical projection and lifting operators. These operators will be applied to support functions and surface area measures of convex bodies...... and to radial functions of star bodies. We then investigate averages of lifted projections and show that they correspond to self-adjoint intertwining operators. We obtain formulas for the eigenvalues of these operators and use them to ascertain circumstances under which tomographic measurements determine...... the original bodies. This approach via mean lifted projections leads us to some unexpected relationships between seemingly disparate geometric constructions....
An Underlying Geometrical Manifold for Hamiltonian Mechanics
Horwitz, L P; Levitan, J; Lewkowicz, M
2015-01-01
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 Hamilton-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 pictu...
Duality orbits of non-geometric fluxes
Energy Technology Data Exchange (ETDEWEB)
Dibitetto, G.; Roest, D. [Centre for Theoretical Physics, University of Groningen, Nijenborgh 4, 9747 AG Groningen (Netherlands); Fernandez-Melgarejo, J.J. [Grupo de Fisica Teorica y Cosmologia, Dept. de Fisica, University of Murcia, Campus de Espinardo, 30100-Murcia (Spain); Marques, D. [Institut de Physique Theorique, CEA/ Saclay, 91191 Gif-sur-Yvette Cedex (France)
2012-11-15
Compactifications in duality covariant constructions such as generalised geometry and double field theory have proven to be suitable frameworks to reproduce gauged supergravities containing non-geometric fluxes. However, it is a priori unclear whether these approaches only provide a reformulation of old results, or also contain new physics. To address this question, we classify the T- and U-duality orbits of gaugings of (half-)maximal supergravities in dimensions seven and higher. It turns out that all orbits have a geometric supergravity origin in the maximal case, while there are non-geometric orbits in the half-maximal case. We show how the latter are obtained from compactifications of double field theory. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
The Geometric Phase of Stock Trading.
Altafini, Claudio
2016-01-01
Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of this paper is to show that geometric phases can exist also for discrete-time systems, and even when the cycles in shape space have zero area. A context in which this principle can be applied is stock trading. A zero-area cycle in shape space represents the type of trading operations normally carried out by high-frequency traders (entering and exiting a position on a fast time-scale), while the phase variable represents the cash balance of a trader. Under the assumption that trading impacts stock prices, even zero-area cyclic trading operations can induce geometric phases, i.e., profits or losses, without affecting the stock quote.
Geometrical families of mechanically stable granular packings
Gao, Guo-Jie; Blawzdziewicz, Jerzy; O'Hern, Corey S.
2009-12-01
We enumerate and classify nearly all of the possible mechanically stable (MS) packings of bidipserse mixtures of frictionless disks in small sheared systems. We find that MS packings form continuous geometrical families, where each family is defined by its particular network of particle contacts. We also monitor the dynamics of MS packings along geometrical families by applying quasistatic simple shear strain at zero pressure. For small numbers of particles (N16 , we observe an increase in the period and random splittings of the trajectories caused by bifurcations in configuration space. We argue that the ratio of the splitting and contraction rates in large systems will determine the distribution of MS-packing geometrical families visited in steady state. This work is part of our long-term research program to develop a master-equation formalism to describe macroscopic slowly driven granular systems in terms of collections of small subsystems.
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.
Singularity Analysis of Geometric Constraint Systems
Institute of Scientific and Technical Information of China (English)
彭小波; 陈立平; 周凡利; 周济
2002-01-01
Singularity analysis is an important subject of the geometric constraint sat-isfaction problem. In this paper, three kinds of singularities are described and corresponding identification methods are presented for both under-constrained systems and over-constrained systems. Another special but common singularity for under-constrained geometric systems, pseudo-singularity, is analyzed. Pseudo-singularity is caused by a variety of constraint match ing of under-constrained systems and can be removed by improving constraint distribution. To avoid pseudo-singularity and decide redundant constraints adaptively, a differentiation algo rithm is proposed in the paper. Its correctness and efficiency have been validated through its practical applications in a 2D/3D geometric constraint solver CBA.
Understanding geometric algebra for electromagnetic theory
Arthur, John W
2011-01-01
"This book aims to disseminate geometric algebra as a straightforward mathematical tool set for working with and understanding classical electromagnetic theory. It's target readership is anyone who has some knowledge of electromagnetic theory, predominantly ordinary scientists and engineers who use it in the course of their work, or postgraduate students and senior undergraduates who are seeking to broaden their knowledge and increase their understanding of the subject. It is assumed that the reader is not a mathematical specialist and is neither familiar with geometric algebra or its application to electromagnetic theory. The modern approach, geometric algebra, is the mathematical tool set we should all have started out with and once the reader has a grasp of the subject, he or she cannot fail to realize that traditional vector analysis is really awkward and even misleading by comparison"--Provided by publisher.
Energy Technology Data Exchange (ETDEWEB)
Blendl, C.; Selbach, M.; Uphoff, C. [Fachhochschule Koeln (Germany). Inst. fuer Medien- und Phototechnik; Fiebich, M.; Voigt, J.M. [Fachhochschule Giessen (DE). Inst. fuer Medizinische Physik und Strahlenschutz (IMPS)
2012-01-15
Purpose: The study aims at investigating how far image quality (MTF and NPS) differs in between CT, CBCT and DVT units and how far the geometrical 3 D accuracy and the HU calibration differ in respect to surgical or radio therapeutic planning. Materials and Methods: X ray image stacks have been made using a new designed test device which contains structures for measuring MTF, NPS, the 3 D accuracy and the Hounsfield calibration (jaw or skull program). The image stacks of the transversal images were analyzed with a dedicated computer program. Results: The MTF values are correlated with the physical resolution (CT and DVT) and are influenced by the used Kernel (CT). The NPS values are limited to an intra system comparison due to the insufficient HU accuracy. The 3 D accuracy is comparable in between the system types. Conclusions: The values of image quality are not yet correlated with dose values: NPS. Investigations to an appropriate dosimetry are ongoing to establish the ratio between dose and image quality (ALARA principle). No fundamental difference between the systems can be stated in respect radio therapeutic planning: improper HU calibration accuracy in CBCT and DVT units. The geometric 3 D accuracy of high performance DVT systems is greater than that of CT Systems. (orig.)
The effect of photometric and geometric context on photometric and geometric lightness effects.
Lee, Thomas Y; Brainard, David H
2014-01-24
We measured the lightness of probe tabs embedded at different orientations in various contextual images presented on a computer-controlled stereo display. Two background context planes met along a horizontal roof-like ridge. Each plane was a graphic rendering of a set of achromatic surfaces with the simulated illumination for each plane controlled independently. Photometric context was varied by changing the difference in simulated illumination intensity between the two background planes. Geometric context was varied by changing the angle between them. We parsed the data into separate photometric effects and geometric effects. For fixed geometry, varying photometric context led to linear changes in both the photometric and geometric effects. Varying geometric context did not produce a statistically reliable change in either the photometric or geometric effects.
High-fidelity geometric modeling for biomedical applications
Energy Technology Data Exchange (ETDEWEB)
Yu, Zeyun [Univ. of California, San Diego, CA (United States). Dept. of Mathematics; Holst, Michael J. [Univ. of California, San Diego, CA (United States). Dept. of Mathematics; Andrew McCammon, J. [Univ. of California, San Diego, CA (United States). Dept. of Chemistry and Biochemistry; Univ. of California, San Diego, CA (United States). Dept. of Pharmacology
2008-05-19
In this paper, we describe a combination of algorithms for high-fidelity geometric modeling and mesh generation. Although our methods and implementations are application-neutral, our primary target application is multiscale biomedical models that range in scales across the molecular, cellular, and organ levels. Our software toolchain implementing these algorithms is general in the sense that it can take as input a molecule in PDB/PQR forms, a 3D scalar volume, or a user-defined triangular surface mesh that may have very low quality. The main goal of our work presented is to generate high quality and smooth surface triangulations from the aforementioned inputs, and to reduce the mesh sizes by mesh coarsening. Tetrahedral meshes are also generated for finite element analysis in biomedical applications. Experiments on a number of bio-structures are demonstrated, showing that our approach possesses several desirable properties: feature-preservation, local adaptivity, high quality, and smoothness (for surface meshes). Finally, the availability of this software toolchain will give researchers in computational biomedicine and other modeling areas access to higher-fidelity geometric models.
Primary School Teacher Candidates' Geometric Habits of Mind
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…
Christodoulou, Marios; De Lorenzo, Tommaso
2016-11-01
Black holes that have nearly evaporated are often thought of as small objects, due to their tiny exterior area. However, the horizon bounds large spacelike hypersurfaces. A compelling geometric perspective on the evolution of the interior geometry was recently shown to be provided by a generally covariant definition of the volume inside a black hole using maximal surfaces. In this article, we expand on previous results and show that finding the maximal surfaces in an arbitrary spherically symmetric spacetime is equivalent to a 1 +1 geodesic problem. We then study the effect of Hawking radiation on the volume by computing the volume of maximal surfaces inside the apparent horizon of an evaporating black hole as a function of time at infinity: while the area is shrinking, the volume of these surfaces grows monotonically with advanced time, up to when the horizon has reached Planckian dimensions. The physical relevance of these results for the information paradox and the remnant scenarios are discussed.
Numerical Study of Urban Canyon Microclimate Related to Geometrical Parameters
Directory of Open Access Journals (Sweden)
Andrea de Lieto Vollaro
2014-11-01
Full Text Available In this study a microclimate analysis on a particular urban configuration: the—street canyon—has been carried out. The analysis, conducted by performing numerical simulations using the finite volumes commercial code ANSYS-Fluent, shows the flow field in an urban environment, taking into account three different aspect ratios (H/W. This analysis can be helpful in the study on urban microclimate and on the heat exchanges with the buildings. Fluid-dynamic fields on vertical planes within the canyon, have been evaluated. The results show the importance of the geometrical configuration, in relation to the ratio between the height (H of the buildings and the width (W of the road. This is a very important subject from the point of view of “Smart Cities”, considering the urban canyon as a subsystem of a larger one (the city, which is affected by climate changes.
Model-based vision using geometric hashing
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.
The geometric phase in quantum physics
Energy Technology Data Exchange (ETDEWEB)
Bohm, A.
1993-03-01
After an explanatory introduction, a quantum system in a classical time-dependent environment is discussed; an example is a magnetic moment in a classical magnetic field. At first, the general abelian case is discussed in the adiabatic approximation. Then the geometric phase for nonadiabatic change of the environment (Anandan--Aharonov phase) is introduced, and after that general cyclic (nonadiabatic) evolution is discussed. The mathematics of fiber bundles is introduced, and some of its results are used to describe the relation between the adiabatic Berry phase and the geometric phase for general cyclic evolution of a pure state. The discussion is restricted to the abelian, U(1) phase.
Geometric measure theory a beginner's guide
Morgan, Frank
2008-01-01
Geometric measure theory provides the framework to understand the structure of a crystal, a soap bubble cluster, or a universe. Measure Theory: A Beginner's Guide is essential to any student who wants to learn geometric measure theory, and will appeal to researchers and mathematicians working in the field. Morgan emphasizes geometry over proofs and technicalities providing a fast and efficient insight into many aspects of the subject.New to the 4th edition:* Abundant illustrations, examples, exercises, and solutions.* The latest results on soap bubble clusters, including
Satellite Video Stabilization with Geometric Distortion
Directory of Open Access Journals (Sweden)
WANG Xia
2016-02-01
Full Text Available There is an exterior orientation difference in each satellite video frame, and the corresponding points have different image locations in adjacent frames images which has geometric distortion. So the projection model, affine model and other classical image stabilization registration model cannot accurately describe the relationship between adjacent frames. This paper proposes a new satellite video image stabilization method with geometric distortion to solve the problem, based on the simulated satellite video, we verify the feasibility and accuracy of proposed satellite video stabilization method.
Adiabatic geometric phases and response functions
Jain, S R; Jain, Sudhir R.; Pati, Arun K.
1998-01-01
Treating a many-body Fermi system in terms of a single particle in a deforming mean field. We relate adiabatic geometric phase to susceptibility for the noncyclic case, and to its derivative for the cyclic case. Employing the semiclassical expression of susceptibility, the expression for geometric phase for chaotic quantum system immediately follows. Exploiting the well-known association of the absorptive part of susceptibility with dissipation, our relations may provide a quantum mechanical origin of the damping of collective excitations in Fermi systems.
Classical Light Beams and Geometric Phases
Mukunda, N; Simon, R
2013-01-01
We present a study of geometric phases in classical wave and polarisation optics using the basic mathematical framework of quantum mechanics. Important physical situations taken from scalar wave optics, pure polarisation optics, and the behaviour of polarisation 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 polarisation 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.
Workshop on Topology and Geometric Group Theory
Fowler, James; Lafont, Jean-Francois; Leary, Ian
2016-01-01
This book presents articles at the interface of two active areas of research: classical topology and the relatively new field of geometric group theory. It includes two long survey articles, one on proofs of the Farrell–Jones conjectures, and the other on ends of spaces and groups. In 2010–2011, Ohio State University (OSU) hosted a special year in topology and geometric group theory. Over the course of the year, there were seminars, workshops, short weekend conferences, and a major conference out of which this book resulted. Four other research articles complement these surveys, making this book ideal for graduate students and established mathematicians interested in entering this area of research.
A lexicographic shellability characterization of geometric lattices
Davidson, Ruth
2011-01-01
Geometric lattices are characterized as those finite, atomic lattices such that every atom ordering induces a lexicographic shelling given by an edge labeling known as a minimal labeling. This new characterization fits into a similar paradigm as McNamara's characterization of supersolvable lattices as those lattices admitting a different type of lexicographic shelling, namely one in which each maximal chain is labeled with a permutation of {1,...,n}. Geometric lattices arise as the intersection lattices of central hyperplane arrangements and more generally as the lattices of flats for matroids.
Geometry modeling and grid generation using 3D NURBS control volume
Yu, Tzu-Yi; Soni, Bharat K.; Shih, Ming-Hsin
1995-01-01
The algorithms for volume grid generation using NURBS geometric representation are presented. The parameterization algorithm is enhanced to yield a desired physical distribution on the curve, surface and volume. This approach bridges the gap between CAD surface/volume definition and surface/volume grid generation. Computational examples associated with practical configurations have shown the utilization of these algorithms.
Geometric calibration of high-resolution remote sensing sensors
Institute of Scientific and Technical Information of China (English)
LIANG Hong-you; GU Xing-fa; TAO Yu; QIAO Chao-fei
2007-01-01
This paper introduces the applications of high-resolution remote sensing imagery and the necessity of geometric calibration for remote sensing sensors considering assurance of the geometric accuracy of remote sensing imagery. Then the paper analyzes the general methodology of geometric calibration. Taking the DMC sensor geometric calibration as an example, the paper discusses the whole calibration procedure. Finally, it gave some concluding remarks on geometric calibration of high-resolution remote sensing sensors.
Energy Technology Data Exchange (ETDEWEB)
1994-08-01
This document is a report on the remedial investigation (RI) of Chestnut Ridge Operable Unit (OU) 2 at the Oak Ridge Y-12 Plant. Chestnut Ridge OU 2 consists of Upper McCoy Branch (UMB), the Filled Coal Ash Pond (FCAP), and the area surrounding the Sluice Channel formerly associated with coal ash disposal in the FCAP. Chestnut Ridge OU 2 is located within the U.S. Department of Energy`s (DOE`s) Oak Ridge Reservation in Anderson County, Tennessee, approximately 24 miles west of Knoxville. The pond is an 8.5-acre area on the southern slope of Chestnut Ridge, 0.5 mile south of the main Y-12 Plant and geographically separated from the Y-12 Plant by Chestnut Ridge. The elevation of the FCAP is {approximately} 950 ft above mean sea level (msl), and it is relatively flat and largely vegetated. Two small ponds are usually present at the northeast and northwest comers of the FCAP. The Sluice Channel Area extends {approximately}1000 ft from the northern margin of the FCAP to the crest of Chestnut Ridge, which has an elevation of {approximately}1100 ft above msl. The Sluice Channel Area is largely vegetated also. McCoy Branch runs from the top of Chestnut Ridge across the FCAP into Rogers Quarry and out of the quarry where it runs a short distance into Milton Hill Lake at McCoy Embayment, termed UMB. The portion south of Rogers Quarry, within Chestnut Ridge OU 4, is termed Lower McCoy Branch. The DOE Oak Ridge Y-12 Plant disposed of coal ash from its steam plant operations as a slurry that was discharged into an ash retention impoundment; this impoundment is the FCAP. The FCAP was built in 1955 to serve as a settling basin after coal ash slurried over Chestnut Ridge from the Y-12 Plant. The FCAP was constructed by building an earthen dam across the northern tributary of McCoy Branch. The dam was designed to hold 20 years of Y-12 steam plant ash. By July 1967, ash had filled up the impoundment storage behind the dam to within 4 ft of the top.
[Upper extremity arterial diseases].
Becker, F
2007-02-01
Compared to lower limb arterial diseases, upper limb arterial diseases look rare, heterogeneous with various etiologies and a rather vague clinical picture, but with a negligible risk of amputation. Almost all types of arterial diseases can be present in the upper limb, but the anatomical and hemodynamic conditions particular to the upper limb often confuse the issue. Thus, atherosclerosis affects mainly the subclavian artery in its proximal segment where the potential of collateral pathway is high making the symptomatic forms not very frequent whereas the prevalence of subclavian artery stenosis or occlusion is relatively high. The clinical examination and the etiologies are discussed according to the clinical, anatomical and hemodynamic context.
Ambient Occlusion Effects for Combined Volumes and Tubular Geometry
Schott, M.
2013-06-01
This paper details a method for interactive direct volume rendering that computes ambient occlusion effects for visualizations that combine both volumetric and geometric primitives, specifically tube-shaped geometric objects representing streamlines, magnetic field lines or DTI fiber tracts. The algorithm extends the recently presented the directional occlusion shading model to allow the rendering of those geometric shapes in combination with a context providing 3D volume, considering mutual occlusion between structures represented by a volume or geometry. Stream tube geometries are computed using an effective spline-based interpolation and approximation scheme that avoids self-intersection and maintains coherent orientation of the stream tube segments to avoid surface deforming twists. Furthermore, strategies to reduce the geometric and specular aliasing of the stream tubes are discussed.
Geometric foundation of spin and isospin
Hannibal, L
1996-01-01
Various theories of spinning particles are interpreted as realizing elements of an underlying geometric theory. Classical particles are described by trajectories on the Poincare group. Upon quantization an eleven-dimensional Kaluza-Klein type theory is obtained which incorporates spin and isospin in a local SL(2,C) x U(1) x SU(2) theory with broken U(1)x SU(2) part.
Reinforcing Geometric Properties with Shapedoku Puzzles
Wanko, Jeffrey J.; Nickell, Jennifer V.
2013-01-01
Shapedoku is a new type of puzzle that combines logic and spatial reasoning with understanding of basic geometric concepts such as slope, parallelism, perpendicularity, and properties of shapes. Shapedoku can be solved by individuals and, as demonstrated here, can form the basis of a review for geometry students as they create their own. In this…
Robust Geometric Control of a Distillation Column
DEFF Research Database (Denmark)
Kymmel, Mogens; Andersen, Henrik Weisberg
1987-01-01
A frequency domain method, which makes it possible to adjust multivariable controllers with respect to both nominal performance and robustness, is presented. The basic idea in the approach is that the designer assigns objectives such as steady-state tracking, maximum resonance peaks, bandwidth, m...... is used to examine and improve geometric control of a binary distillation column....
An underlying geometrical manifold for Hamiltonian mechanics
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.
Using geometric algebra to study optical aberrations
Energy Technology Data Exchange (ETDEWEB)
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.
Geometric singular perturbation theory in biological practice
Hek, G.
2010-01-01
Geometric singular perturbation theory is a useful tool in the analysis of problems with a clear separation in time scales. It uses invariant manifolds in phase space in order to understand the global structure of the phase space or to construct orbits with desired properties. This paper explains an
Saturation and geometrical scaling in small systems
Praszalowicz, Michal
2016-01-01
Saturation and geometrical scaling (GS) of gluon distributions are a consequence of the non-linear evolution equations of QCD. We argue that in pp GS holds for the inelastic cross-section rather than for the multiplicity distributions. We also discuss possible fluctuations of the proton saturation scale in pA collisions at the LHC.
Geometric Interpretations of Some Psychophysical Results.
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…
Geometric Algorithms for Part Orienting and Probing
Panahi, F.
2015-01-01
In this thesis, detailed solutions are presented to several problems dealing with geometric shape and orientation of an object in the field of robotics and automation. We first have considered a general model for shape variations that allows variation along the entire boundary of an object, both in
On Arithmetic-Geometric-Mean Polynomials
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…
Geometric properties of optimal photonic crystals
DEFF Research Database (Denmark)
Sigmund, Ole; Hougaard, Kristian G.
2008-01-01
on numerical optimization studies, we have discovered some surprisingly simple geometric properties of optimal planar band gap structures. We conjecture that optimal structures for gaps between bands n and n+1 correspond to n elliptic rods with centers defined by the generators of an optimal centroidal Voronoi...
Geometric Mean--What Does It Mean?
Kalder, Robin S.
2012-01-01
The National Council of Teachers of Mathematics and numerous mathematics educators promote the combination of conceptual understanding and procedural learning in the successful instruction of mathematics. Despite this, when geometric mean is taught in a typical American geometry class, it is taught as a process only despite the many connections…
Geometric Total Variation for Texture Deformation
DEFF Research Database (Denmark)
Bespalov, Dmitriy; Dahl, Anders Lindbjerg; Shokoufandeh, Ali
2010-01-01
of features in texture images leads to significant improvements in localization of these features, when textures undergo geometrical transformations. Accurate localization of features in the presense of unkown deformations is a crucial property for texture characterization methods, and we intend to expoit...
Geometric Abstract Art and Public Health Data
Centers for Disease Control (CDC) Podcasts
2016-10-18
Dr. Salaam Semaan, a CDC behavioral scientist, discusses the similarities between geometric abstract art and public health data analysis. Created: 10/18/2016 by National Center for Emerging and Zoonotic Infectious Diseases (NCEZID). Date Released: 10/18/2016.
Modern Geometric Algebra: A (Very Incomplete!) Survey
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…
Robust topology optimization accounting for geometric imperfections
DEFF Research Database (Denmark)
Schevenels, M.; Jansen, M.; Lombaert, Geert
2013-01-01
performance. As a consequence, the actual structure may be far from optimal. In this paper, a robust approach to topology optimization is presented, taking into account two types of geometric imperfections: variations of (1) the crosssections and (2) the locations of structural elements. The first type...... of imperfections) and a vertical load carrying system (for the second type). © 2013 Taylor & Francis Group, London....
A Geometric Approach to Fair Division
Barbanel, Julius
2010-01-01
We wish to divide a cake among some collection of people (who may have very different notions of the comparative value of pieces of cake) in a way that is both "fair" and "efficient." We explore the meaning of these terms, introduce two geometric tools to aid our analysis, and present a proof (due to Dietrich Weller) that establishes the existence…
Geometric Reductivity--A Quotient Space Approach
Sastry, Pramathanath
2010-01-01
We give another proof that a reductive algebraic group is geometrically reductive. We show that a quotient of the semi-stable locus (by a linear action of a reductive algebraic group on a projective scheme) exists, and from this Haboush's Theorem (Mumford's Conjecture) follows.
Wooden Geometric Puzzles: Design and Hardness Proofs
Alt, H.; Bodlaender, H.L.; Kreveld, M.J. van; Rote, G.; Tel, G.
2007-01-01
We discuss some new geometric puzzles and the complexity of their extension to arbitrary sizes. For gate puzzles and two-layer puzzles we prove NP-completeness of solving them. Not only the solution of puzzles leads to interesting questions, but also puzzle design gives rise to interesting
Wooden Geometric Puzzles: Design and Hardness Proofs
Alt, H.; Bodlaender, H.L.; Kreveld, M.J. van; Rote, G.; Tel, G.
2008-01-01
We discuss some new geometric puzzles and the complexity of their extension to arbitrary sizes. For gate puzzles and two-layer puzzles we prove NP-completeness of solving them. Not only the solution of puzzles leads to interesting questions, but also puzzle design gives rise to interesting
Geometric and Texture Inpainting by Gibbs Sampling
DEFF Research Database (Denmark)
Gustafsson, David Karl John; Pedersen, Kim Steenstrup; Nielsen, Mads
2007-01-01
This paper discuss a method suitable for inpainting both large scale geometric structures and more stochastic texture components. Image inpainting concerns the problem of reconstructing the intensity contents inside regions of missing data. Common techniques for solving this problem are methods...
How Do Young Children Learn Geometric Concepts.
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…
Geometrical Factors in the Perception of Sacredness.
Costa, Marco; Bonetti, Leonardo
2016-06-28
Geometrical and environmental factors in the perception of sacredness, dominance, and attractiveness were assessed by 137 participants in five tests. In the first test, a two-alternative forced-choice paradigm was used to test the perception of sacredness, dominance, and attractiveness in geometrical figures differing in shape, verticality, size, and symmetry. Verticality, symmetry, and convexity were found to be important factors in the perception of sacredness. In the second test, participants had to mark the point inside geometrical surfaces that was perceived as most sacred, dominant, and attractive. The top and the center areas were associated with sacredness, dominance, and attractiveness. In the third test, peaks and elevated regions in landscapes were evaluated as more sacred, dominant, and attractive than valley regions. In the fourth test, three figures sharing the same area but differing in horizontal and vertical orientation were evaluated on eight scales. The vertical figure was evaluated as more sacred, dominant, and attractive than the horizontal figure. The fifth test demonstrated the significant role of space seclusion and inaccessibility in the perception of sacredness. Geometrical factors in the perception of sacredness, dominance, and attractiveness were largely overlapping.
Geometric inequalities in sub-Riemannian groups
Montefalcone, Francescopaolo
2012-01-01
Let G be a sub-Riemannian k-step Carnot group of homogeneous dimension Q. In this paper, we shall prove several geometric inequalities concerning smooth hypersurfaces (i.e. codimension one submanifolds) immersed in G, endowed with the H-perimeter measure.
Deformable image registration with geometric changes
Institute of Scientific and Technical Information of China (English)
Yu LIU; Bo ZHU
2015-01-01
Geometric changes present a number of difficulties in deformable image registration. In this paper, we propose a global deformation framework to model geometric changes whilst promoting a smooth transformation between source and target images. To achieve this, we have developed an innovative model which significantly reduces the side effects of geometric changes in image registration, and thus improves the registration accuracy. Our key contribution is the introduction of a sparsity-inducing norm, which is typically L1 norm regularization targeting regions where geometric changes occur. This preserves the smoothness of global transformation by eliminating local transformation under different conditions. Numerical solutions are discussed and analyzed to guarantee the stability and fast convergence of our algorithm. To demonstrate the effectiveness and utility of this method, we evaluate it on both synthetic data and real data from traumatic brain injury (TBI). We show that the transformation estimated from our model is able to reconstruct the target image with lower instances of error than a standard elastic registration model.
Toeplitz Quantization and Asymptotic Expansions: Geometric Construction
Directory of Open Access Journals (Sweden)
Miroslav Englis
2009-02-01
Full Text Available For a real symmetric domain G_R/K_R, with complexification G_C/K_C, we introduce the concept of ''star-restriction'' (a real analogue of the ''star-products'' for quantization of Kähler manifolds and give a geometric construction of the G_R-invariant differential operators yielding its asymptotic expansion.
Wooden Geometric Puzzles: Design and Hardness Proofs
Alt, H.; Bodlaender, H.L.; Kreveld, M.J. van; Rote, G.; Tel, G.
2007-01-01
We discuss some new geometric puzzles and the complexity of their extension to arbitrary sizes. For gate puzzles and two-layer puzzles we prove NP-completeness of solving them. Not only the solution of puzzles leads to interesting questions, but also puzzle design gives rise to interesting theoretic
Wooden Geometric Puzzles: Design and Hardness Proofs
Alt, H.; Bodlaender, H.L.; Kreveld, M.J. van; Rote, G.; Tel, G.
2008-01-01
We discuss some new geometric puzzles and the complexity of their extension to arbitrary sizes. For gate puzzles and two-layer puzzles we prove NP-completeness of solving them. Not only the solution of puzzles leads to interesting questions, but also puzzle design gives rise to interesting theoretic
Geometric Mechanics of Periodic Pleated Origami
Wei, Zhiyan; Dudte, Levi; Liang, Haiyi; Mahadevan, L
2012-01-01
Origami is the archetype of a structural material with unusual mechanical properties that arise almost exclusively from the geometry of its constituent folds and forms the basis for mechanical metamaterials with an extreme deformation response. Here we consider a simple periodically folded structure Miura-ori, which is composed of identical unit cells of mountain and valley folds with four-coordinated ridges, de?fined completely by 2 angles and 2 lengths. We use the geometrical properties of a Miura-ori plate to characterize its elastic response to planar and non-planar piece- wise isometric deformations and calculate the two-dimensional stretching and bending response of a Miura-ori sheet, and show that the in-plane and out-of-plane Poisson's ratios are equal in magnitude, but opposite in sign. Our geometric approach also allows us to solve the inverse design problem of determining the geometric parameters that achieve the optimal geometric and mechanical response of such structures.
A Geometric Approach to Fair Division
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…
Can EPR non-locality be geometrical?
Energy Technology Data Exchange (ETDEWEB)
Ne`eman, Y. [Tel-Aviv Univ. (Israel). Raymond and Beverly Sackler Faculty of Exact Sciences]|[Univ. of Texas, Austin, TX (United States). Center for Particle Physics; Botero, A. [Texas Univ., Austin, TX (United States)
1995-10-01
The presence in Quantum Mechanics of non-local correlations is one of the two fundamentally non-intuitive features of that theory. The non-local correlations themselves fall into two classes: EPR and Geometrical. The non-local characteristics of the geometrical type are well-understood and are not suspected of possibly generating acausal features, such as faster-than-light propagation of information. This has especially become true since the emergence of a geometrical treatment for the relevant gauge theories, i.e. Fiber Bundle geometry, in which the quantum non-localities are seen to correspond to pure homotopy considerations. This aspect is reviewed in section 2. Contrary-wise, from its very conception, the EPR situation was felt to be paradoxical. It has been suggested that the non-local features of EPR might also derive from geometrical considerations, like all other non-local characteristics of QM. In[7], one of the authors was able to point out several plausibility arguments for this thesis, emphasizing in particular similarities between the non-local correlations provided by any gauge field theory and those required by the preservation of the quantum numbers of the original EPR state-vector, throughout its spatially-extended mode. The derivation was, however, somewhat incomplete, especially because of the apparent difference between, on the one hand, the closed spatial loops arising in the analysis of the geometrical non-localities, from Aharonov-Bohm and Berry phases to magnetic monopoles and instantons, and on the other hand, in the EPR case, the open line drawn by the positions of the two moving decay products of the disintegrating particle. In what follows, the authors endeavor to remove this obstacle and show that as in all other QM non-localities, EPR is somehow related to closed loops, almost involving homotopy considerations. They develop this view in section 3.
U.S. Department of Health & Human Services — Affordable Care Act Federal Upper Limits (FUL) based on the weighted average of the most recently reported monthly average manufacturer price (AMP) for...
... to diagnose conditions such as cancer celiac disease gastritis Doctors also use upper GI endoscopy to treat ... Bhutani MS. Esophagogastroduodenoscopy. Medscape website. emedicine.medscape.com/article/1851864-overview#a17 . Updated June 3, 2013. Accessed ...
Upper gastrointestinal bleeding.
Feinman, Marcie; Haut, Elliott R
2014-02-01
Upper gastrointestinal (GI) bleeding remains a commonly encountered diagnosis for acute care surgeons. Initial stabilization and resuscitation of patients is imperative. Stable patients can have initiation of medical therapy and localization of the bleeding, whereas persistently unstable patients require emergent endoscopic or operative intervention. Minimally invasive techniques have surpassed surgery as the treatment of choice for most upper GI bleeding. Copyright © 2014 Elsevier Inc. All rights reserved.
Upper GI Bleeding in Children What is upper GI Bleeding? Irritation and ulcers of the lining of the esophagus, stomach or duodenum can result in upper GI bleeding. When this occurs the child may vomit ...
Upper GI Bleeding in Children What is upper GI Bleeding? Irritation and ulcers of the lining of the esophagus, stomach or duodenum can result in upper GI bleeding. When this occurs the child may vomit blood ...
Geometrical metrology on vacuum cast silicone rubber form using computed tomography
DEFF Research Database (Denmark)
Pacurar, Ramona; Müller, Pavel; De Chiffre, Leonardo
An investigation on geometrical measurements of silicone rubber cake form and polyamide molds using three measuring techniques - CMM, optical scanner and CT scanner - was carried out. The only measurand was diameter of a cone measured at specified levels. An uncertainty budget for all three techn...... and measuring of complicated features. In connection with the silicone rubber form, CT scanning could be also used for example for failure analysis, 3D volume analysis and other non-destructive and metrological analysis....
Seeing and feeling volumes: The influence of shape on volume perception.
Kahrimanovic, Mirela; Bergmann Tiest, Wouter M; Kappers, Astrid M L
2010-07-01
The volume of common objects can be perceived visually, haptically or by a combination of both senses. The present study shows large effects of the object's shape on volume perception within all these modalities, with an average bias of 36%. In all conditions, the volume of a tetrahedron was overestimated compared to that of a cube or a sphere, and the volume of a cube was overestimated compared to that of a sphere. Additional analyses revealed that the biases could be explained by the dependence of the volume judgment on different geometric properties. During visual volume perception, the strategies depended on the objects that were compared and they were also subject-dependent. However, analysis of the haptic and bimodal data showed more consistent results and revealed that surface area of the stimuli influenced haptic as well as bimodal volume perception. This suggests that bimodal volume perception is more influenced by haptic input than by visual information.
Geometric VOF-PLIC simulations of Hollow Cone Sprays
Nelson, Thomas; Benson, Michael; Vanpoppel, Brett; Bravo, Luis; USMA Team Spray Collaboration; ARL Vehicle Combustion Lab Collaboration; Stanford University Collaboration
2014-11-01
This work examines a Computational Fluid Dynamics (CFD) approach to provide temporally resolved simulations of a novel pressure swirl atomizer presently studied at Stanford University. In a pressure swirl atomizer, the liquid spreads out to form an air-cored vortex within the nozzle and an emerging thin annular film. Due to instabilities the film breaks up to form a hollow cone spray. The numerical simulations focus on the near field nozzle flow physics and primary atomization of the spray. An incompressible flow formulation is adopted with a geometric unsplit Volume of Fluid (VOF) method to track the interface between two immiscible fluids in interfacial flow simulations. Here, the interface is modeled via an advection equation implicitly tracked using a discrete indicator function, f, with values representing the volume fraction of the tagged fluid within a cell. An Adaptive Mesh Refinement (AMR) scheme is also employed to efficiently capture the shear layers near the liquid-gas interface. The study is carried out for two atomizers with 2 mm and 3 mm diameters at intermediate Re = 2.6-3.9 × 103, We = 0.11-0.17 × 105. An in depth comparison is then provided between the CFD results and measurements obtained via shadowgraphy and CT scans.
A framework for geometric reasoning about tools in assembly
Energy Technology Data Exchange (ETDEWEB)
Wilson, R.H.
1995-12-31
When assembling a product, humans, robots, and other automation employ a variety of tools to manipulate, attach, and test parts and subassemblies. This paper proposes a framework lo represent and reason about geometric accessibility constraints for a wide variety of 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 an instance of the FINDPLACE problem. In addition, we present more efficient methods lo integrate the framework into assembly planning. For tools that are applied either before or after their target parts are mated, one method preprocesses a single tool application for all possible states of assembly of a product. For tools applied after their target parts are mated, a complementary method guarantees polynomial-time assembly planning. We describe experiments with an initial implementation of the framework and a library of seven tools.
Scale-invariant geometric random graphs
Xie, Zheng
2015-01-01
We introduce and analyze a class of growing geometric random graphs that are invariant under rescaling of space and time. Directed connections between nodes are drawn according to an influence zone that depends on node position in space and time, capturing the heterogeneity and increased specialization found in growing networks. Through calculations and numerical simulations we explore the consequences of scale-invariance for geometric graphs generated this way. Our analysis reveals a dichotomy between scale-free and Poisson distributions of in- and out-degree, the existence of a random number of hub nodes, high clustering, and unusual percolation behaviour. Moreover, we show how these properties provide a good fit to those of empirically observed web graphs.
Langlands Program, Trace Formulas, and their Geometrization
Frenkel, Edward
2012-01-01
The Langlands Program relates Galois representations and automorphic representations of reductive algebraic groups. The trace formula is a powerful tool in the study of this connection and the Langlands Functoriality Conjecture. After giving an introduction to the Langlands Program and its geometric version, which applies to curves over finite fields and over the complex field, I give a survey of my recent joint work with Robert Langlands and Ngo Bao Chau (arXiv:1003.4578 and arXiv:1004.5323) on a new approach to proving the Functoriality Conjecture using the trace formulas, and on the geometrization of the trace formulas. In particular, I discuss the connection of the latter to the categorification of the Langlands correspondence.
Geometrical dynamics of Born-Infeld objects
Energy Technology Data Exchange (ETDEWEB)
Cordero, Ruben [Departamento de Fisica, Escuela Superior de Fisica y Matematicas del I.P.N., Unidad Adolfo Lopez Mateos, Edificio 9, 07738 Mexico, D.F. (Mexico); Molgado, Alberto [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Col. Villas San Sebastian, Colima (Mexico); Rojas, Efrain [Facultad de Fisica e Inteligencia Artificial, Universidad Veracruzana, 91000 Xalapa, Veracruz (Mexico)
2007-03-21
We present a geometrically inspired study of the dynamics of Dp-branes. We focus on the usual non-polynomial Dirac-Born-Infeld action for the worldvolume swept out by the brane in its evolution in general background spacetimes. We emphasize the form of the resulting equations of motion which are quite simple and resemble Newton's second law, complemented with a conservation law for a worldvolume bicurrent. We take a closer look at the classical Hamiltonian analysis which is supported by the ADM framework of general relativity. The constraints and their algebra are identified as well as the geometrical role they play in phase space. In order to illustrate our results, we review the dynamics of a D1-brane immersed in a AdS{sub 3} x S{sup 3} background spacetime. We exhibit the mechanical properties of Born-Infeld objects paving the way to a consistent quantum formulation.
Advanced Geometric Modeler with Hybrid Representation
Institute of Scientific and Technical Information of China (English)
杨长贵; 陈玉健; 等
1996-01-01
An advanced geometric modeler GEMS4.0 has been developed,in which feature representation is used at the highest level abstraction of a product model.Boundary representation is used at the bottom level,while CSG model is adopted at the median level.A BRep data structure capable of modeling non-manifold is adopted.UNRBS representation is used for all curved surfaces,Quadric surfaces have dual representations consisting of their geometric data such as radius,center point,and center axis.Boundary representation of free form surfaces is easily built by sweeping and skinning method with NURBS geometry.Set operations on curved solids with boundary representation are performed by an evaluation process consisting of four steps.A file exchange facility is provided for the conversion between product data described by STEP and product information generated by GEMS4.0.
GEOMETRICALLY INVARIANT WATERMARKING BASED ON RADON TRANSFORMATION
Institute of Scientific and Technical Information of China (English)
Cai Lian; Du Sidan; Gao Duntang
2005-01-01
The weakness of classical watermarking methods is the vulnerability to geometrical distortions that widely occur during normal use of the media. In this letter, a new imagewatermarking method is presented to resist Rotation, Scale and Translation (RST) attacks. The watermark is embedded into a domain obtained by taking Radon transform of a circular area selected from the original image, and then extracting Two-Dimensional (2-D) Fourier magnitude of the Radon transformed image. Furthermore, to prevent the watermarked image from degrading due to inverse Radon transform, watermark signal is inversely Radon transformed individually.Experimental results demonstrate that the proposed scheme is able to withstand a variety of attacks including common geometric attacks.
A Video Watermarking Against Geometrical Distortions
Institute of Scientific and Technical Information of China (English)
NIUXiamu; SCHMUCKERMartin; BUSCHChristoph; SUNShenghe
2003-01-01
A video watermarking with robustness against frame's geometrical distortions (rotation, aspect ratio, scaling, translation shearing, and bending) is proposed. The watermark information is embedded into pixels along the temporal axis within a Watermark minimum segment (WMS). Since the geometrical distortions operations for every frame along the time axis in a video sequence are the same at a very short interval, the watermark information can be detected from watermarked frames in each WMS subjected to the distortions. Furthermore, adaptive embedding method is proposed for gaining a good quality of the watermarked video. Experimental results show that the proposed technique is robust against common attacks such as rotation, aspect ratio, scaling, translation shearing, and bending of frames, MPEG-2 lossy compression, and color-space conversion.
The bouncing ball through a geometrical series
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.
Mixed State Geometric Phase from Thomas Rotations
Lévai, Peter
2003-01-01
It is shown that Uhlmann's parallel transport of purifications along a path of mixed states represented by $2\\times 2$ density matrices is just the path ordered product of Thomas rotations. These rotations are invariant under hyperbolic translations inside the Bloch sphere that can be regarded as the Poincar\\'e ball model of hyperbolic geometry. A general expression for the mixed state geometric phase for an {\\it arbitrary} geodesic triangle in terms of the Bures fidelities is derived. The formula gives back the solid angle result well-known from studies of the pure state geometric phase. It is also shown that this mixed state anholonomy can be reinterpreted as the pure state non-Abelian anholonomy of entangled states living in a suitable restriction of the quaternionic Hopf bundle. In this picture Uhlmann's parallel transport is just Pancharatnam transport of quaternionic spinors.
Geometric Computations on Indecisive and Uncertain Points
Jorgensen, Allan; Phillips, Jeff M
2012-01-01
We study computing geometric problems on uncertain points. An uncertain point is a point that does not have a fixed location, but rather is described by a probability distribution. When these probability distributions are restricted to a finite number of locations, the points are called indecisive points. In particular, we focus on geometric shape-fitting problems and on building compact distributions to describe how the solutions to these problems vary with respect to the uncertainty in the points. Our main results are: (1) a simple and efficient randomized approximation algorithm for calculating the distribution of any statistic on uncertain data sets; (2) a polynomial, deterministic and exact algorithm for computing the distribution of answers for any LP-type problem on an indecisive point set; and (3) the development of shape inclusion probability (SIP) functions which captures the ambient distribution of shapes fit to uncertain or indecisive point sets and are admissible to the two algorithmic constructi...
Geometrical multiresolution adaptive transforms theory and applications
Lisowska, Agnieszka
2014-01-01
Modern image processing techniques are based on multiresolution geometrical methods of image representation. These methods are efficient in sparse approximation of digital images. There is a wide family of functions called simply ‘X-lets’, and these methods can be divided into two groups: the adaptive and the nonadaptive. This book is devoted to the adaptive methods of image approximation, especially to multismoothlets. Besides multismoothlets, several other new ideas are also covered. Current literature considers the black and white images with smooth horizon function as the model for sparse approximation but here, the class of blurred multihorizon is introduced, which is then used in the approximation of images with multiedges. Additionally, the semi-anisotropic model of multiedge representation, the introduction of the shift invariant multismoothlet transform and sliding multismoothlets are also covered. Geometrical Multiresolution Adaptive Transforms should be accessible to both mathematicians and com...
Spectral statistics of random geometric graphs
Dettmann, Carl P; Knight, Georgie
2016-01-01
We study the spectrum of random geometric graphs using random matrix theory. We look at short range correlations in the level spacings via the nearest neighbour and next nearest neighbour spacing distribution and long range correlations via the spectral rigidity $\\Delta_3$ statistic. These correlations in the level spacings give information about localisation of eigenvectors, level of community structure and the level of randomness within the networks. We find that the spectral statistics of random geometric graphs fits the universality of random matrix theory. In particular, the short range correlations are very close to those found in the Gaussian orthogonal ensemble of random matrix theory. For long range correlations we find deviations from Gaussian orthogonal ensemble statistics towards Poisson. We compare with previous results for Erd\\H{o}s-R\\'{e}nyi, Barab{\\'a}si-Albert and Watts-Strogatz random graphs where similar random matrix theory universality has been found.
Gilman, Robert H; Miasnikov, Alexei
2007-01-01
Each relational structure X has an associated Gaifman graph, which endows X with the properties of a graph. Suppose that X is infinite, connected and of bounded degree. A first-order sentence in the language of X is almost surely true (resp. a.s. false) for finite substructures of X if for every element x in X, the fraction of substructures of the ball of radius n around x which satisfy the sentence approaches 1 (resp. 0) as n approaches infinity. Suppose further that, for every finite substructure, X has a disjoint isomorphic substructure. Then every sentence is a.s. true or a.s. false for finite substructures of X. This is one form of the geometric zero-one law. We formulate it also in a form that does not mention the ambient infinite structure. In addition, we investigate various questions related to the geometric zero-one law.
Geometric reconstruction methods for electron tomography
Alpers, Andreas; König, Stefan; Pennington, Robert S; Boothroyd, Chris B; Houben, Lothar; Dunin-Borkowski, Rafal E; Batenburg, Kees Joost
2012-01-01
Electron tomography is becoming an increasingly important tool in materials science for studying three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is seriously affected by the problems of missing wedge artefacts and nonlinear projection intensities due to diffraction effects. The former refers to the fact that data cannot be acquired over the full $180^\\circ$ tilt range; the latter implies that for some orientations, crystalline structures can show strong contrast changes. To overcome these problems we introduce four algorithms from the mathematical fields of geometric and discrete tomography. The algorithms incorporate geometric prior knowledge (mainly convexity and homogeneity), which also in principle considerably reduces the number of tilt angles required. Results are discussed for the reconstruction of an InAs nanowire.
Theoretical discussions on the geometrical phase analysis
Energy Technology Data Exchange (ETDEWEB)
Rouviere, J.L. [CEA-Grenoble, Departement de Recherche Fondamentale sur la Matiere Condensee, SP2M, 17 rue des Martyrs, 38054 Grenoble Cedex 9 (France)]. E-mail: rouvierej@cea.fr; Sarigiannidou, E. [CEA-Grenoble, Departement de Recherche Fondamentale sur la Matiere Condensee, SP2M, 17 rue des Martyrs, 38054 Grenoble Cedex 9 (France)
2005-12-15
The Geometrical phase analysis, which is a very efficient method to measure deformation from High resolution transmission electron microscopy images, is studied from a theoretical point of view. We point out that the basic property of this method is its ability to measure local reciprocal lattice parameters with a high level of accuracy. We attempt to provide some insights into (a) different formula used in the geometrical phase analysis such as the well-known relation between phase and displacement: P{sub g}(r)=-2{pi}g.u(r), (b) the two different definitions of strain, each of which corresponding to a different lattice reference and (c) the meaning of a continuous displacement in a dot-like high resolution image. The case of one-dimensional analysis is also presented. Finally, we show that the method is able to give the position of the dot that is nearest to a given pixel in the image.
Geometrical geodesy techniques in Goddard earth models
Lerch, F. J.
1974-01-01
The method for combining geometrical data with satellite dynamical and gravimetry data for the solution of geopotential and station location parameters is discussed. Geometrical tracking data (simultaneous events) from the global network of BC-4 stations are currently being processed in a solution that will greatly enhance of geodetic world system of stations. Previously the stations in Goddard earth models have been derived only from dynamical tracking data. A linear regression model is formulated from combining the data, based upon the statistical technique of weighted least squares. Reduced normal equations, independent of satellite and instrumental parameters, are derived for the solution of the geodetic parameters. Exterior standards for the evaluation of the solution and for the scale of the earth's figure are discussed.
Geometric Correction for Braille Document Images
Directory of Open Access Journals (Sweden)
Padmavathi.S
2016-04-01
Full Text Available Braille system has been used by the visually impair ed people for reading.The shortage of Braille books has caused a need for conversion of Braille t o text. This paper addresses the geometric correction of a Braille document images. Due to the standard measurement of the Braille cells, identification of Braille characters could be achie ved by simple cell overlapping procedure. The standard measurement varies in a scaled document an d fitting of the cells become difficult if the document is tilted. This paper proposes a line fitt ing algorithm for identifying the tilt (skew angle. The horizontal and vertical scale factor is identified based on the ratio of distance between characters to the distance between dots. Th ese are used in geometric transformation matrix for correction. Rotation correction is done prior to scale correction. This process aids in increased accuracy. The results for various Braille documents are tabulated.
Geometrical vs wave optics under gravitational waves
Angélil, Raymond
2015-01-01
We present some new derivations of the effect of a plane gravitational wave on a light ray. A simple interpretation of the results is that a gravitational wave causes a phase modulation of electromagnetic waves. We arrive at this picture from two contrasting directions, namely null geodesics and Maxwell's equations, or, geometric and wave optics. Under geometric optics, we express the geodesic equations in Hamiltonian form and solve perturbatively for the effect of gravitational waves. We find that the well-known time-delay formula for light generalizes trivially to massive particles. We also recover, by way of a Hamilton-Jacobi equation, the phase modulation obtained under wave optics. Turning then to wave optics, rather than solving Maxwell's equations directly for the fields, as in most previous approaches, we derive a perturbed wave equation (perturbed by the gravitational wave) for the electromagnetic four-potential. From this wave equation it follows that the four-potential and the electric and magnetic...
New computation methods for geometrical optics
Lin, Psang Dain
2014-01-01
This book employs homogeneous coordinate notation to compute the first- and second-order derivative matrices of various optical quantities. It will be one of the important mathematical tools for automatic optical design. The traditional geometrical optics is based on raytracing only. It is very difficult, if possible, to compute the first- and second-order derivatives of a ray and optical path length with respect to system variables, since they are recursive functions. Consequently, current commercial software packages use a finite difference approximation methodology to estimate these derivatives for use in optical design and analysis. Furthermore, previous publications of geometrical optics use vector notation, which is comparatively awkward for computations for non-axially symmetrical systems.
Color fringe projection profilometry using geometric constraints
Cheng, Teng; Du, Qingyu; Jiang, Yaxi
2017-09-01
A recently proposed phase unwrapping method using geometric constraints performs well without requiring additional camera, more patterns or global search. The major limitation of this technique is the confined measurement depth range (MDR) within 2π in phase domain. To enlarge the MDR, this paper proposes using color fringes for three-dimensional (3D) shape measurement. Each six fringe periods encoded with six different colors are treated as one group. The local order within one group can be identified with reference to the color distribution. Then the phase wrapped period-by-period is converted into the phase wrapped group-by-group. The geometric constraints of the fringe projection system are used to determine the group order. Such that the MDR is extended from 2π to 12π by six times. Experiment results demonstrate the success of the proposed method to measure two isolated objects with large MDR.
Finsler geometric extension of Einstein gravity
Pfeifer, Christian
2011-01-01
We construct gravitational dynamics for Finsler spacetimes in terms of an action integral on the unit tangent bundle. These spacetimes are generalizations of Lorentzian metric manifolds which satisfy necessary causality properties. A coupling procedure for matter fields to Finsler gravity completes our new theory that consistently becomes equivalent to Einstein gravity in the limit of metric geometry. We provide a precise geometric definition of observers and their measurements, and show that the transformations by means of which different observers communicate form a groupoid that generalizes the usual Lorentz group. Moreover, we discuss the implementation of Finsler spacetime symmetries. We use our results to analyze a particular spacetime model that leads to Finsler geometric refinements of the linearized Schwarzschild solution.
Finsler geometric extension of Einstein gravity
Pfeifer, Christian; Wohlfarth, Mattias N. R.
2012-03-01
We construct gravitational dynamics for Finsler spacetimes in terms of an action integral on the unit tangent bundle. These spacetimes are generalizations of Lorentzian metric manifolds which satisfy necessary causality properties. A coupling procedure for matter fields to Finsler gravity completes our new theory that consistently becomes equivalent to Einstein gravity in the limit of metric geometry. We provide a precise geometric definition of observers and their measurements and show that the transformations, by means of which different observers communicate, form a groupoid that generalizes the usual Lorentz group. Moreover, we discuss the implementation of Finsler spacetime symmetries. We use our results to analyze a particular spacetime model that leads to Finsler geometric refinements of the linearized Schwarzschild solution.
Geometric dynamical observables in rare gas crystals
Energy Technology Data Exchange (ETDEWEB)
Casetti, L. [Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa (Italy); Macchi, A. [Istituto Nazionale di Fisica della Materia (INFM), Unita di Firenze, Largo Enrico Fermi 2, 50125 Firenze (Italy)
1997-03-01
We present a detailed description of how a differential geometric approach to Hamiltonian dynamics can be used for determining the existence of a crossover between different dynamical regimes in a realistic system, a model of a rare gas solid. Such a geometric approach allows us to locate the energy threshold between weakly and strongly chaotic regimes, and to estimate the largest Lyapunov exponent. We show how standard methods of classical statistical mechanics, i.e., Monte Carlo simulations, can be used for our computational purposes. Finally we consider a Lennard-Jones crystal modeling solid xenon. The value of the energy threshold turns out to be in excellent agreement with the numerical estimate based on the crossover between slow and fast relaxation to equilibrium obtained in a previous work by molecular dynamics simulations. {copyright} {ital 1997} {ital The American Physical Society}
Geometric dynamical observables in rare gas crystals
Casetti, L; Casetti, Lapo; Macchi, Alessandro
1996-01-01
We present a detailed description of how a differential geometric approach to Hamiltonian dynamics can be used for determining the existence of a crossover between different dynamical regimes in a realistic system, a model of a rare gas solid. Such a geometric approach allows to locate the energy threshold between weakly and strongly chaotic regimes, and to estimate the largest Lyapunov exponent. We show how standard mehods of classical statistical mechanics, i.e. Monte Carlo simulations, can be used for our computational purposes. Finally we consider a Lennard Jones crystal modeling solid Xenon. The value of the energy threshold turns out to be in excellent agreement with the numerical estimate based on the crossover between slow and fast relaxation to equilibrium obtained in a previous work by molecular dynamics simulations.
Topological minimally entangled states via geometric measure
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.
Bootstrap Percolation on Random Geometric Graphs
Bradonjić, Milan
2012-01-01
Bootstrap percolation has been used effectively to model phenomena as diverse as emergence of magnetism in materials, spread of infection, diffusion of software viruses in computer networks, adoption of new technologies, and emergence of collective action and cultural fads in human societies. It is defined on an (arbitrary) network of interacting agents whose state is determined by the state of their neighbors according to a threshold rule. In a typical setting, bootstrap percolation starts by random and independent "activation" of nodes with a fixed probability $p$, followed by a deterministic process for additional activations based on the density of active nodes in each neighborhood ($\\th$ activated nodes). Here, we study bootstrap percolation on random geometric graphs in the regime when the latter are (almost surely) connected. Random geometric graphs provide an appropriate model in settings where the neighborhood structure of each node is determined by geographical distance, as in wireless {\\it ad hoc} ...
Battisacco, E.; Franca, M. J.; Schleiss, A. J.
2016-11-01
Dams trap sediment in the upstream reservoir, which may lead to river bed armoring, streambank erosion and failure, channel incision and reduction of the morphological diversity in the downstream river reaches. The replenishment of sediment is a mitigation measure for this problem to be applied in river reaches downstream of dams. Previously performed field experiments always used one single volume of sediment replenishment. To explore different alternatives, the replenished volume was here divided in four deposits with the motivation to influence also the morphological evolution downstream. Six different geometrical configurations together with three submergence conditions of sediment replenishment were tested for the first time in a laboratory experiment and are herein discussed. The results of the sediment replenishment mitigation technique are described in terms of occupied surface of the flume bed and the temporal evolution of erosion and transport of the introduced sediments. It is shown that, under our experimental conditions, complete submersion of the replenishment volume results in complete erosion of the placed sediment, with a high persistence of the added material along the channel length. The geometrical configuration of the replenishment volume plays a key role for the evolution of bed-forms downstream. Parallel configurations lead to a wider spread of material across the channel. Alternated configurations are suitable to produce sediment clustering and high persistence of placed material in the channel. Observed periodic mounds, considered as the initiating condition for alternate bars, follow a wavelength related to the length of the replenishment when the replenishment volumes are alternating.
Geometric method for stability of non-linear elastic thin shells
Ivanova, Jordanka
2002-01-01
PREFACE This book deals with the new developments and applications of the geometric method to the nonlinear stability problem for thin non-elastic shells. There are no other published books on this subject except the basic ones of A. V. Pogorelov (1966,1967,1986), where variational principles defined over isometric surfaces, are postulated, and applied mainly to static and dynamic problems of elastic isotropic thin shells. A. V. Pogorelov (Harkov, Ukraine) was the first to provide in his monographs the geometric construction of the deformed shell surface in a post-critical stage and deriving explicitely the asymptotic formulas for the upper and lower critical loads. In most cases, these formulas were presented in a closed analytical form, and confirmed by experimental data. The geometric method by Pogorelov is one of the most important analytical methods developed during the last century. Its power consists in its ability to provide a clear geometric picture of the postcritical form of a deformed shell surfac...
Pose measurement method based on geometrical constraints
Institute of Scientific and Technical Information of China (English)
Zimiao Zhang; Changku Sun; Pengfei Sun; Peng Wang
2011-01-01
@@ The pose estimation method based on geometric constraints is studied.The coordinates of the five feature points in the camera coordinate system are calculated to obtain the pose of an object on the basis of the geometric constraints formed by the connective lines of the feature points and the coordinates of the feature points on the CCD image plane; during the solution process,the scaling and orthography projection model is used to approximate the perspective projection model.%The pose estimation method based on geometric constraints is studied. The coordinates of the five feature points in the camera coordinate system are calculated to obtain the pose of an object on the basis of the geometric constraints formed by the connective lines of the feature points and the coordinates of the feature points on the CCD image plane; during the solution process, the scaling and orthography projection model is used to approximate the perspective projection model. The initial values of the coordinates of the five feature points in the camera coordinate system are obtained to ensure the accuracy and convergence rate of the non-linear algorithm. In accordance with the perspective projection characteristics of the circular feature landmarks, we propose an approach that enables the iterative acquisition of accurate target poses through the correction of the perspective projection coordinates of the circular feature landmark centers. Experimental results show that the translation positioning accuracy reaches ±0.05 mm in the measurement range of 0-40 mm, and the rotation positioning accuracy reaches ±0.06° in the measurement range of 4°-60°.
Protein Folding: A New Geometric Analysis
Simmons, Walter A.; Joel L. Weiner
2008-01-01
A geometric analysis of protein folding, which complements many of the models in the literature, is presented. We examine the process from unfolded strand to the point where the strand becomes self-interacting. A central question is how it is possible that so many initial configurations proceed to fold to a unique final configuration. We put energy and dynamical considerations temporarily aside and focus upon the geometry alone. We parameterize the structure of an idealized protein using the ...
A new geometric approach to Sturmian words
Matomäki, Kaisa
2012-01-01
We introduce a new geometric approach to Sturmian words by means of a mapping that associates certain lines in the n x n -grid and sets of finite Sturmian words of length n. Using this mapping, we give new proofs of the formulas enumerating the finite Sturmian words and the palindromic finite Sturmian words of a given length. We also give a new proof for the well-known result that a factor of a Sturmian word has precisely two return words.
Geometrical characterization of micro end milling tools
DEFF Research Database (Denmark)
Borsetto, Francesca; Bariani, Paolo; Bissacco, Giuliano
2005-01-01
Performance of the milling process is directly affected by the accuracy of tool geometry. Development of methods suitable for dimensional characterization of such tools, with low measurement uncertainties is therefore of relevance. The present article focuses on the geometrical characterization o...... of a flat micro end milling tool with a nominal mill diameter of 200 microns. An experimental investigation was carried out involving two different non-contact systems...
Geometrical characterization of micro end milling tools
DEFF Research Database (Denmark)
Borsetto, Francesca; Bariani, Paolo; Bissacco, Giuliano;
2005-01-01
Performance of the milling process is directly affected by the accuracy of tool geometry. Development of methods suitable for dimensional characterization of such tools, with low measurement uncertainties is therefore of relevance. The present article focuses on the geometrical characterization...... of a flat micro end milling tool with a nominal mill diameter of 200 microns. An experimental investigation was carried out involving two different non-contact systems...
Geometrical product specifications. Datums and coordinate systems
Glukhov, V. I.; Ivleva, I. A.; Zlatkina, O. Y.
2017-06-01
The work is devoted to the relevant topic such as the technical products quality improvement due to the geometrical specifications accuracy. The research purpose is to ensure the quality indicators on the basis of the systematic approach to the values normalization and geometrical specifications accuracy in the workpiece coordinate systems in the process of design. To achieve the goal two tasks are completed such as the datum features classification according to the number of linear and angular freedom degrees constraints, called the datums informativeness, and the rectangular coordinate systems identification, materialized by workpiece datums sets. The datum features informativeness characterizes the datums functional purpose to limit product workpiece linear and angular degrees of freedom. The datum features informativeness numerically coincides with the kinematic pairs classes and couplings in mechanics. The datum features informativeness identifies the coordinate system without the location redundancy. Each coordinate plane of a rectangular coordinate system has different informativeness 3 + 2 + 1. Each coordinate axis also has different informativeness 4+2+Θ (zero). It is possible to establish the associated workpiece position with three linear and three angular coordinates relative to two axes with the informativeness 4 and 2. is higher, the more informativeness of the coordinate axis or a coordinate plane is, the higher is the linear and angular coordinates accuracy, the coordinate being plotted along the coordinate axis or plane. The systematic approach to the geometrical products specifications positioning in coordinate systems is the scientific basis for a natural transition to the functional dimensions of features position - coordinating dimensions and the size of the features form - feature dimensions of two measures: linear and angular ones. The products technical quality improving is possible due to the coordinate systems introduction materialized by
Geometric Measure Theory and Minimal Surfaces
Bombieri, Enrico
2011-01-01
W.K. ALLARD: On the first variation of area and generalized mean curvature.- F.J. ALMGREN Jr.: Geometric measure theory and elliptic variational problems.- E. GIUSTI: Minimal surfaces with obstacles.- J. GUCKENHEIMER: Singularities in soap-bubble-like and soap-film-like surfaces.- D. KINDERLEHRER: The analyticity of the coincidence set in variational inequalities.- M. MIRANDA: Boundaries of Caciopoli sets in the calculus of variations.- L. PICCININI: De Giorgi's measure and thin obstacles.
Noncommutative Geometric Gauge Theory from Superconnections
Lee, Chang-Yeong
1996-01-01
Noncommutative geometric gauge theory is reconstructed based on the superconnection concept. The bosonic action of the Connes-Lott model including the symmetry breaking Higgs sector is obtained by using a new generalized derivative, which consists of the usual 1-form exterior derivative plus an extra element called the matrix derivative, for the curvatures. We first derive the matrix derivative based on superconnections and then show how the matrix derivative can give rise to spontaneous symm...
Chirality: a relational geometric-physical property.
Gerlach, Hans
2013-11-01
The definition of the term chirality by Lord Kelvin in 1893 and 1904 is analyzed by taking crystallography at that time into account. This shows clearly that chirality is a relational geometric-physical property, i.e., two relations between isometric objects are possible: homochiral or heterochiral. In scientific articles the relational term chirality is often mistaken for the two valued measure for the individual (absolute) sense of chirality, an arbitrary attributive term.
Geometric stochastic resonance in a double cavity
Ghosh, Pulak K; Marchesoni, Fabio; Savel'ev, Sergey E; Nori, Franco; 10.1103/PhysRevE.84.011109
2012-01-01
Geometric stochastic resonance of particles diffusing across a porous membrane subject to oscillating forces is characterized as a synchronization process. Noninteracting particle currents through a symmetric membrane pore are driven either perpendicular or parallel to the membrane, whereas harmonic-mixing spectral current components are generated by the combined action of perpendicular and parallel drives. In view of potential applications to the transport of colloids and biological molecules through narrow pores, we also consider the role of particle repulsion as a controlling factor.
A geometrical approach to structural change modeling
Stijepic, Denis
2013-01-01
We propose a model for studying the dynamics of economic structures. The model is based on qualitative information regarding structural dynamics, in particular, (a) the information on the geometrical properties of trajectories (and their domains) which are studied in structural change theory and (b) the empirical information from stylized facts of structural change. We show that structural change is path-dependent in this model and use this fact to restrict the number of future structural cha...
Geometric problems in molecular biology and robotics.
Parsons, D; Canny, J
1994-01-01
Some of the geometric problems of interest to molecular biologists have macroscopic analogues in the field of robotics. Two examples of such analogies are those between protein docking and model-based perception, and between ring closure and inverse kinematics. Molecular dynamics simulation, too, has much in common with the study of robot dynamics. In this paper we give a brief survey of recent work on these and related problems.
Geometric treatment of the gravitomagnetic clock effect
Tartaglia, A
2000-01-01
We have developed a general geometric treatment of the GCE valid for any stationary axisymmetric metric. The method is based on the remark that the world lines of objects rotating along spacely circular trajectories are in any case, for those kind of metrics, helices drawn on the flat bidimensional surface of a cylinder. Applying the obtained formulas to the special cases of the Kerr and weak field metric for a spinning body, known results for time delays and synchrony defects are recovered.
Implicitization of surfaces via geometric tropicalization
Cueto, Maria Angelica
2011-01-01
In this paper we describe tropical methods for implicitization of surfaces. We construct the corresponding tropical surfaces via the theory of geometric tropicalization due to Hacking, Keel and Tevelev, which we enrich with a formula for computing tropical multiplicities of regular points in any dimension. We extend previous results for tropical implicitization of generic surfaces due to Sturmfels, Tevelev and Yu and provide methods for the non-generic case.
The Minimal Geometric Deformation Approach Extended
Casadio, Roberto; da Rocha, Roldao
2015-01-01
The minimal geometric deformation approach was introduced in order to study the exterior space-time around spherically symmetric self-gravitating systems, like stars or similar astrophysical objects as well, in the Randall-Sundrum brane-world framework. A consistent extension of this approach is developed here, which contains modifications of both the time component and the radial component of a spherically symmetric metric. A modified Schwarzschild geometry is obtained as an example of its simplest application.
Geometrical model of multidimensional orbital motion
Energy Technology Data Exchange (ETDEWEB)
Jacak, D [Institute of Mathematics and Computer Science, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw (Poland)], E-mail: dorota.jacak@pwr.wroc.pl
2008-05-15
We consider a geometrical n-dimensional model of orbital-type rotation, for n{>=}4. The vectors generating this process are defined and the Fibonacci sequence is found in representation of their lengths. Within the dimension analysis of Planck units, we consider an example of the multidimensional whirl and define a sequence of formal fields. Special attention is paid to the three subsequent elements of this sequence, called here magnetic, electric and energy fields, which allow for some physical interpretations.
Geometrical effective action and Wilsonian flows
Pawlowski, J M
2003-01-01
A gauge invariant flow equation is derived by applying a Wilsonian momentum cut-off to gauge invariant field variables. The construction makes use of the geometrical effective action for gauge theories in the Vilkovisky-DeWitt framework. The approach leads to modified Nielsen identities that pose non-trivial constraints on consistent truncations. We also evaluate the relation of the present approach to gauge fixed formulations as well as discussing possible applications.
Integrating geometric activity images in ANN classification
De Genst, William; Gautama, Sidharta; Bellens, Rik; Canters, Frank
2005-10-01
In this paper we demonstrate how the interaction between innovative methods in the field of computer vision and methods for multi-spectral image classification can help in extracting detailed land-cover / land-use information from Very High Resolution (VHR) satellite imagery. We introduce the novel concept of "geometric activity images", which we define as images encoding the strength of the relationship between a pixel and surrounding features detected through dedicated computer vision methods. These geometric activity images are used as alternatives to more traditional texture images that better describe the geometry of man-made structures and that can be included as additional information in a non-parametric supervised classification framework. We present a number of findings resulting from the integration of geometric activity images and multi-spectral bands in an artificial neural network classification. The geometric activity images we use result from the use of a ridge detector for straight line detection, calculated for different window sizes and for all multi-spectral bands and band-ratio images in a VHR scene. A selection of the most relevant bands to use for classification is carried out using band selection based on a genetic algorithm. Sensitivity analysis is used to assess the importance of each input variable. An application of the proposed methods to part of a Quickbird image taken over the suburban fringe of the city of Ghent (Belgium) shows that we are able to identify roads with much higher accuracy than when using more traditional multi-spectral image classification techniques.
Geometrical Methods for Power Network Analysis
Bellucci, Stefano; Gupta, Neeraj
2013-01-01
This book is a short introduction to power system planning and operation using advanced geometrical methods. The approach is based on well-known insights and techniques developed in theoretical physics in the context of Riemannian manifolds. The proof of principle and robustness of this approach is examined in the context of the IEEE 5 bus system. This work addresses applied mathematicians, theoretical physicists and power engineers interested in novel mathematical approaches to power network theory.
DEFF Research Database (Denmark)
Josipovic, Mirjana; Persson, Gitte Bjørnsen Fredberg; Dueck, Jenny;
2016-01-01
BACKGROUND AND PURPOSE: Deep inspiration breath hold (DIBH) increases lung volume and can potentially reduce treatment-related toxicity in locally advanced lung cancer. We estimated geometric uncertainties in visually guided voluntary DIBH and derived the appropriate treatment margins for different...... image-guidance strategies. MATERIAL AND METHODS: Seventeen patients were included prospectively. An optical marker-based respiratory monitoring with visual guidance enabled comfortable DIBHs, adjusted to each patient's performance. All patients had three consecutive DIBH CTs at each of the treatment...... fractions 2, 16 and 31. DIBH reproducibility was evaluated as inter- and intra-fractional variations in lung volume, tumour position and differential motion between primary tumour and mediastinal lymph nodes. RESULTS: Lung volume increased by median 60% in DIBH. Inter- and intra-fractional lung volume...
Edit propagation using geometric relationship functions
Guerrero, Paul
2014-03-01
We propose a method for propagating edit operations in 2D vector graphics, based on geometric relationship functions. These functions quantify the geometric relationship of a point to a polygon, such as the distance to the boundary or the direction to the closest corner vertex. The level sets of the relationship functions describe points with the same relationship to a polygon. For a given query point, we first determine a set of relationships to local features, construct all level sets for these relationships, and accumulate them. The maxima of the resulting distribution are points with similar geometric relationships. We show extensions to handle mirror symmetries, and discuss the use of relationship functions as local coordinate systems. Our method can be applied, for example, to interactive floorplan editing, and it is especially useful for large layouts, where individual edits would be cumbersome. We demonstrate populating 2D layouts with tens to hundreds of objects by propagating relatively few edit operations. © 2014 ACM 0730-0301/2014/03- ART15 $15.00.
Stabilization of LCD devices via geometric alteration.
Jeon, Il; Yoon, MinSung; Lee, Je-Hoon
2013-02-20
Glass bending in LCD displays is an inherent problem that has challenged many engineers. As a solution to this problem, we propose a methodology that can tackle the root of the phenomenon in terms of linear elastic beam theory. Using this hypothesis, we devised a background theory and a solution. In this paper, we present a glass panel to which geometrical changes, such as furrow, groove, and curb have been applied. These geometrical changes are applied to the nonactive area of the glass panel. To confirm the validity of our approach, we conducted simulation tests as well as hands-on experiments to observe the thermo-mechanical behavior of the device under various conditions. The simulation results using the Ansys simulator show that the proposed technique can reduce the deformation level of panel bending by 40%. In the experiment using a bare cell with polarizer films attached and with performing the high temperature reliability test, the deformation level of panel bending is reduced by half compared to the reference glass panel without any geometric alteration.
Geometric absorption of electromagnetic angular momentum
Konz, C.; Benford, Gregory
2003-10-01
Circularly polarized electromagnetic fields carry both energy and angular momentum. We investigate the conditions under which a circularly polarized wave field transfers angular momentum to a perfectly conducting macroscopic object, using exact electromagnetic wave theory in a steady-state calculation. We find that axisymmetric perfect conductors cannot absorb or radiate angular momentum when illuminated. However, any asymmetry allows absorption. A rigorous, steady-state solution of the boundary value problem for the reflection from a perfectly conducting infinite wedge shows that waves convey angular momentum at the edges of asymmetries. Conductors can also radiate angular momentum, so their geometric absorption coefficient for angular momentum can be negative. Such absorption or radiation depends solely on the specific geometry of the conductor. The geometric absorption coefficient can be as high as 0.8, and the coefficient for radiation can be -0.4, larger than typical material absorption coefficients. We apply the results to recent experiments which spun roof-shaped aluminum sheets with polarized microwave beams. Applications of geometric, instead of material, absorption can be quite varied. Though experiments testing these ideas will be simpler at microwavelengths, the ideas work for optical ones as well.
Geometry and topology of geometric limits I
Ohshika, Ken'ichi
2010-01-01
In this paper, we are concerned with hyperbolic 3-manifolds $\\hyperbolic^3/G$ such that $G$ are geometric limits of Kleinian surface groups isomorphic to $\\pi_1(S)$ for a finite-type hyperbolic surface $S$. In the first of the three main theorems, we shall show that such a hyperbolic 3-manifold is uniformly bi-Lipschitz homeomorphic to a model manifold which has a structure called brick decomposition and is embedded in $S \\times (0,1)$. Conversely, any such manifold admitting a brick decomposition with reasonable conditions is bi-Lipschitz homeomorphic to a hyperbolic manifold corresponding to some geometric limit of quasi-Fuchsian groups. Finally, it will be shown that we can define end invariants for hyperbolic 3-manifolds appearing as geometric limits of Kleinian surface groups, and that the homeomorphism type and the end invariants determine the isometric type of a manifold, which is analogous to the ending lamination theorem for the case of finitely generated Kleinian groups.
Salt bridges: geometrically specific, designable interactions.
Donald, Jason E; Kulp, Daniel W; DeGrado, William F
2011-03-01
Salt bridges occur frequently in proteins, providing conformational specificity and contributing to molecular recognition and catalysis. We present a comprehensive analysis of these interactions in protein structures by surveying a large database of protein structures. Salt bridges between Asp or Glu and His, Arg, or Lys display extremely well-defined geometric preferences. Several previously observed preferences are confirmed, and others that were previously unrecognized are discovered. Salt bridges are explored for their preferences for different separations in sequence and in space, geometric preferences within proteins and at protein-protein interfaces, co-operativity in networked salt bridges, inclusion within metal-binding sites, preference for acidic electrons, apparent conformational side chain entropy reduction on formation, and degree of burial. Salt bridges occur far more frequently between residues at close than distant sequence separations, but, at close distances, there remain strong preferences for salt bridges at specific separations. Specific types of complex salt bridges, involving three or more members, are also discovered. As we observe a strong relationship between the propensity to form a salt bridge and the placement of salt-bridging residues in protein sequences, we discuss the role that salt bridges might play in kinetically influencing protein folding and thermodynamically stabilizing the native conformation. We also develop a quantitative method to select appropriate crystal structure resolution and B-factor cutoffs. Detailed knowledge of these geometric and sequence dependences should aid de novo design and prediction algorithms.
Geometric Deep Learning: Going beyond Euclidean data
Bronstein, Michael M.; Bruna, Joan; LeCun, Yann; Szlam, Arthur; Vandergheynst, Pierre
2017-07-01
Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging, regulatory networks in genetics, and meshed surfaces in computer graphics. In many applications, such geometric data are large and complex (in the case of social networks, on the scale of billions), and are natural targets for machine learning techniques. In particular, we would like to use deep neural networks, which have recently proven to be powerful tools for a broad range of problems from computer vision, natural language processing, and audio analysis. However, these tools have been most successful on data with an underlying Euclidean or grid-like structure, and in cases where the invariances of these structures are built into networks used to model them. Geometric deep learning is an umbrella term for emerging techniques attempting to generalize (structured) deep neural models to non-Euclidean domains such as graphs and manifolds. The purpose of this paper is to overview different examples of geometric deep learning problems and present available solutions, key difficulties, applications, and future research directions in this nascent field.
Facades structure detection by geometric moment
Jiang, Diqiong; Chen, Hui; Song, Rui; Meng, Lei
2017-06-01
This paper proposes a novel method for extracting facades structure from real-world pictures by using local geometric moment. Compared with existing methods, the proposed method has advantages of easy-to-implement, low computational cost, and robustness to noises, such as uneven illumination, shadow, and shade from other objects. Besides, our method is faster and has a lower space complexity, making it feasible for mobile devices and the situation where real-time data processing is required. Specifically, a facades structure modal is first proposed to support the use of our special noise reduction method, which is based on a self-adapt local threshold with Gaussian weighted average for image binarization processing and the feature of the facades structure. Next, we divide the picture of the building into many individual areas, each of which represents a door or a window in the picture. Subsequently we calculate the geometric moment and centroid for each individual area, for identifying those collinear ones based on the feature vectors, each of which is thereafter replaced with a line. Finally, we comprehensively analyze all the geometric moment and centroid to find out the facades structure of the building. We compare our result with other methods and especially report the result from the pictures taken in bad environmental conditions. Our system is designed for two application, i.e, the reconstruction of facades based on higher resolution ground-based on imagery, and the positional system based on recognize the urban building.
Time as a geometric property of space
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.
Time as a geometric property of space
Directory of Open Access Journals (Sweden)
James Michael Chappell
2016-11-01
Full Text Available The proper description of time remains a key unsolved problem in science. Newton conceived of time as absolute and universal which it `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.
DEFF Research Database (Denmark)
af Rosenschöld, Per Munck; Aznar, Marianne C; Nygaard, Ditte E;
2010-01-01
Proton therapy of lung cancer holds the potential for a reduction of the volume of irradiated normal lung tissue. In this work we investigate the robustness of intensity modulated proton therapy (IMPT) plans to motion, and evaluate a geometrical tumour tracking method to compensate for tumour...
Institute of Scientific and Technical Information of China (English)
李永; 安云强; 刘兆会; 李婷; 尹红霞; 黄亚奇
2013-01-01
Objective To propose a magnetic resonance imaging ( MRI) procedure for 3D volume scanning to study the effect of fluid shift on the cross section of the upper airway as well as the neck circumference, and to test the feasibility of this strategy. A new thought was provided for exploring the effects of body posture changes on the respiratory functions during sleep. Methods A procedure using 3D - SPGR scanning from the top of nasal cavity to laryngeal prominence of two subjects was conducted under two conditions: the control test with subjects lying supine, and after fluid redistribution resulting from elevating both legs for 8 min. The coordinates of the neck and the upper airway boundaries were extracted directly from the selected axial images to calculate the neck circumference and the cross-sectional area of the upper airway. Results The images showed clearly the changes in the neck circumference and the cross-sectional area and shape of the upper airway. The results indicated that the fluid shift caused by raising legs could narrow the upper airway and increase the neck size, which were consistent with currently published experimental results by other investigators. Conclusions Using the 3D volume MRI technique to study the effects of fluid shift on the upper airway patency, we can easily and accurately measure the changes in the neck size and the cross-sectional area and shape of the upper airway. This method could provide an effective way to investigate the effects of body posture changes on the respiratory functions during sleep,as well as the mechanism behind the correlation between fluid-retaining related diseases and obstructive sleep apnea.%目的 提出用磁共振三维容积成像方式研究流体迁移对人体上气道截面及颈围影响的方法并验证其可行性,为探讨体位改变对睡眠呼吸功能的影响提供新的思路.方法 使用三维扰相梯度回波序列(3 D-SPGR)容积扫描方式,对2位受试者头颈部自鼻腔顶部
Geometric Approach to Lie Symmetry of Discrete Time Toda Equation
Institute of Scientific and Technical Information of China (English)
JIA Xiao-Yu; WANG Na
2009-01-01
By using the extended Harrison and Estabrook geometric approach,we investigate the Lie symmetry of discrete time Toda equation from the geometric point of view.Its one-dimensional continuous symmetry group is presented.
Geometrical approach to the evaluation of multileg Feynman diagrams
Energy Technology Data Exchange (ETDEWEB)
Davydychev, A.I. [Department of Physics, University of Mainz, Mainz (Germany); Delbourgo, R. [Physics Department, University of Tasmania, Hobart, Tasmania (Australia)
1998-10-01
A connection between one-loop N-point Feynman diagrams and certain geometrical quantities in non-Euclidean geometry is discussed. A geometrical way to calculate the corresponding Feynman integrals is considered. (author)
Geometric Approaches to Quadratic Equations from Other Times and Places.
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)
Nonvariceal Upper Gastrointestinal Bleeding.
Rahman, Syed Irfan-Ur; Saeian, Kia
2016-04-01
In the intensive care unit, vigilance is needed to manage nonvariceal upper gastrointestinal bleeding. A focused history and physical examination must be completed to identify inciting factors and the need for hemodynamic stabilization. Although not universally used, risk stratification tools such as the Blatchford and Rockall scores can facilitate triage and management. Urgent evaluation for nonvariceal upper gastrointestinal bleeds requires prompt respiratory assessment, and identification of hemodynamic instability with fluid resuscitation and blood transfusions if necessary. Future studies are needed to evaluate the indication, safety, and efficacy of emerging endoscopic techniques. Copyright © 2016 Elsevier Inc. All rights reserved.
Espinoza, Gabriela Mabel; Prost, Angela Michelle
2016-05-01
Reconstruction of the upper eyelid is complicated because the eyelid must retain mobility, flexibility, function, and a suitable mucosal surface over the delicate cornea. Defects of the upper eyelid may be due to congenital defects or traumatic injury or follow oncologic resection. This article focuses on reconstruction due to loss of tissue. Multiple surgeries may be needed to reach the desired results, addressing loss of tissue and then loss of function. Each defect is unique and the laxity and availability of surrounding tissue vary. Knowing the most common techniques for repair assists surgeons in the multifaceted planning that takes place.
Application of geometric midline yield criterion to analysis of three-dimensional forging
Institute of Scientific and Technical Information of China (English)
ZHAO De-wen; WANG Gen-ji; LIU Xiang-hua; WANG Guo-dong
2008-01-01
A kinematically admissible continuous velocity field was proposed for the analysis of three-dimensional forging. The linear yield criterion expressed by geometric midline of error triangle between Tresca and Twin shear stress yield loci on the π-plane, called GM yield criterion for short, was firstly applied to analysis of the velocity field for the forging. The analytical solution of the forging force with the effects of external zone and bulging parameter is obtained by strain rate inner product. Compression tests of pure lead are performed to compare the calculated results with the measured ones. The results show that the calculated total pressures are higher than the measured ones whilst the relative error is no more than 9.5%. It is implied that the velocity field is reasonable and the geometric midline yield criterion is available. The solution is still an upper-bound one.
Design of geometric phase measurement in EAST Tokamak
Lan, T; Liu, J; Jie, Y X; Wang, Y L; Gao, X; Qin, H
2016-01-01
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.
Geometrical and Monte Carlo projectors in 3D PET reconstruction
Aguiar, Pablo; Rafecas López, Magdalena; Ortuno, Juan Enrique; Kontaxakis, George; Santos, Andrés; Pavía, Javier; Ros, Domènec
2010-01-01
Purpose: In the present work, the authors compare geometrical and Monte Carlo projectors in detail. The geometrical projectors considered were the conventional geometrical Siddon ray-tracer (S-RT) and the orthogonal distance-based ray-tracer (OD-RT), based on computing the orthogonal distance from the center of image voxel to the line-of-response. A comparison of these geometrical projectors was performed using different point spread function (PSF) models. The Monte Carlo-based method under c...
Sequential unilateral lung volume reduction for emphysema - Stretching the benefit.
Khorramnia, Sadie; Holsworth, Lynda; Mestitz, Hugh; Westall, Glen P; Williams, Trevor J; Gooi, Julian H; Snell, Gregory I
2017-01-01
Bronchoscopic Lung Volume Reduction (BLVR) and Surgical Lung Volume Reduction (SLVR) and are two different approaches used to remodel severely emphysematous lungs to improve lung function and quality-of-life. We present a case initially referred for lung transplantation, where sequential left upper lobe BLVR and 7 years later right upper lobe SLVR, providing enduring physiological and functional improvement. The potential for sustained benefit via sequential unilateral lung volume reduction is under-appreciated.
An Upper Limit of AC Huffman Code Length in JPEG Compression
Horie, Kenichi
2009-01-01
A strategy for computing upper code-length limits of AC Huffman codes for an 8x8 block in JPEG Baseline coding is developed. The method is based on a geometric interpretation of the DCT, and the calculated limits are as close as 14% to the maximum code-lengths. The proposed strategy can be adapted to other transform coding methods, e.g., MPEG 2 and 4 video compressions, to calculate close upper code length limits for the respective processing blocks.
A Geometric Approach to the Six Trigonometric Ratios.
Bonsangue, Martin V.
1993-01-01
Geometric interpretations and derivations of the six trigonometric relationships are demonstrated. Selected for discussion are limiting values, geometric verification of trigonometric identities, a one-dimensional illustration of the Pythagorean relationships, and the geometric derivation of infinite-series relationships. (DE)
Geometric Error Analysis in Applied Calculus Problem Solving
Usman, Ahmed Ibrahim
2017-01-01
The paper investigates geometric errors students made as they tried to use their basic geometric knowledge in the solution of the Applied Calculus Optimization Problem (ACOP). Inaccuracies related to the drawing of geometric diagrams (visualization skills) and those associated with the application of basic differentiation concepts into ACOP…
Identifying and Fostering Higher Levels of Geometric Thinking
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…
Some Asymptotic Inference in Multinomial Nonlinear Models (a Geometric Approach)
Institute of Scientific and Technical Information of China (English)
WEIBOCHENG
1996-01-01
A geometric framework is proposed for multinomlat nonlinear modelsbased on a modified vemlon of the geometric structure presented by Bates & Watts[4]. We use this geometric framework to study some asymptotic inference in terms ofcurvtures for multlnomial nonlinear models. Our previous results [15] for ordlnary nonlinear regression models are extended to multlnomlal nonlinear models.
Non-adiabatic geometrical quantum gates in semiconductor quantum dots
Solinas, P; Zanghì, N; Rossi, F; Solinas, Paolo; Zanardi, Paolo; Zanghì, Nino; Rossi, Fausto
2003-01-01
In this paper we study the implementation of non-adiabatic geometrical quantum gates with in semiconductor quantum dots. Different quantum information enconding/manipulation schemes exploiting excitonic degrees of freedom are discussed. By means of the Aharanov-Anandan geometrical phase one can avoid the limitations of adiabatic schemes relying on adiabatic Berry phase; fast geometrical quantum gates can be in principle implemented
Geometric properties of solutions to the total variation denoising problem
Chambolle, Antonin; Duval, Vincent; Peyré, Gabriel; Poon, Clarice
2017-01-01
This article studies the denoising performance of total variation (TV) image regularization. More precisely, we study geometrical properties of the solution to the so-called Rudin-Osher-Fatemi total variation denoising method. The first contribution of this paper is a precise mathematical definition of the ‘extended support’ (associated to the noise-free image) of TV denoising. It is intuitively the region which is unstable and will suffer from the staircasing effect. We highlight in several practical cases, such as the indicator of convex sets, that this region can be determined explicitly. Our second and main contribution is a proof that the TV denoising method indeed restores an image which is exactly constant outside a small tube surrounding the extended support. The radius of this tube shrinks toward zero as the noise level vanishes, and we are able to determine, in some cases, an upper bound on the convergence rate. For indicators of so-called ‘calibrable’ sets (such as disks or properly eroded squares), this extended support matches the edges, so that discontinuities produced by TV denoising cluster tightly around the edges. In contrast, for indicators of more general shapes or for complicated images, this extended support can be larger. Beside these main results, our paper also proves several intermediate results about fine properties of TV regularization, in particular for indicators of calibrable and convex sets, which are of independent interest.
Interferometric Constraints on Quantum Geometrical Shear Noise Correlations
Energy Technology Data Exchange (ETDEWEB)
Chou, Aaron; Glass, Henry; Gustafson, H. Richard; Hogan, Craig J.; Kamai, Brittany L.; Kwon, Ohkyung; Lanza, Robert; McCuller, Lee; Meyer, Stephan S.; Richardson, Jonathan W.; Stoughton, Chris; Tomlin, Ray; Weiss, Rainer
2017-03-24
Final measurements and analysis are reported from the first-generation Holometer, the first instrument capable of measuring correlated variations in space-time position at strain noise power spectral densities smaller than a Planck time. The apparatus consists of two co-located, but independent and isolated, 40 m power-recycled Michelson interferometers, whose outputs are cross-correlated to 25 MHz. The data are sensitive to correlations of differential position across the apparatus over a broad band of frequencies up to and exceeding the inverse light crossing time, 7.6 MHz. By measuring with Planck precision the correlation of position variations at spacelike separations, the Holometer searches for faint, irreducible correlated position noise backgrounds predicted by some models of quantum space-time geometry. The first-generation optical layout is sensitive to quantum geometrical noise correlations with shear symmetry---those that can be interpreted as a fundamental noncommutativity of space-time position in orthogonal directions. General experimental constraints are placed on parameters of a set of models of spatial shear noise correlations, with a sensitivity that exceeds the Planck-scale holographic information bound on position states by a large factor. This result significantly extends the upper limits placed on models of directional noncommutativity by currently operating gravitational wave observatories.
Interferometric constraints on quantum geometrical shear noise correlations
Chou, Aaron; Glass, Henry; Gustafson, H. Richard; Hogan, Craig J.; Kamai, Brittany L.; Kwon, Ohkyung; Lanza, Robert; McCuller, Lee; Meyer, Stephan S.; Richardson, Jonathan W.; Stoughton, Chris; Tomlin, Ray; Weiss, Rainer
2017-08-01
Final measurements and analysis are reported from the first-generation Holometer, the first instrument capable of measuring correlated variations in space-time position at strain noise power spectral densities smaller than a Planck time. The apparatus consists of two co-located, but independent and isolated, 40 m power-recycled Michelson interferometers, whose outputs are cross-correlated to 25 MHz. The data are sensitive to correlations of differential position across the apparatus over a broad band of frequencies up to and exceeding the inverse light crossing time, 7.6 MHz. By measuring with Planck precision the correlation of position variations at spacelike separations, the Holometer searches for faint, irreducible correlated position noise backgrounds predicted by some models of quantum space-time geometry. The first-generation optical layout is sensitive to quantum geometrical noise correlations with shear symmetry—those that can be interpreted as a fundamental noncommutativity of space-time position in orthogonal directions. General experimental constraints are placed on parameters of a set of models of spatial shear noise correlations, with a sensitivity that exceeds the Planck-scale holographic information bound on position states by a large factor. This result significantly extends the upper limits placed on models of directional noncommutativity by currently operating gravitational wave observatories.
Volume of a vortex and the Bradlow bound
Adam, C.; Speight, J. M.; Wereszczynski, A.
2017-06-01
We demonstrate that the geometric volume of a soliton coincides with the thermodynamical volume also for field theories with higher-dimensional vacuum manifolds (e.g., for gauged scalar field theories supporting vortices or monopoles), generalizing the recent results of Ref. [C. Adam, M. Haberichter, and A. Wereszczynski, Phys. Lett. B 754, 18 (2016)., 10.1016/j.physletb.2016.01.009]. We apply this observation to understand Bradlow-type bounds for general Abelian gauge theories supporting vortices, as well as some thermodynamical aspects of said theories. In the case of SDiff Bogomolny-Prasad-Sommerfield (BPS) models (being examples of perfect fluid models) we show that the base-space independent geometric volume (area) of the vortex is exactly equal to the Bradlow volume (a minimal volume for which BPS soliton solutions exist). This volume can be finite for compactons or infinite for infinitely extended solitons (in flat Minkowski space-time).
Postoperative upper airway problems
African Journals Online (AJOL)
QuickSilver
2003-06-09
Jun 9, 2003 ... REVIEW ARTICLE. Southern African Journal of Anaesthesia & Analgesia - May 2003. 12. Postoperative upper airway problems way. A number of factors, some avoidable, influence the incidence ... debilitating pain, inability to swallow and temporary voice changes, and are a ..... decrease airway resistance.
Optimization of biotechnological systems through geometric programming
Directory of Open Access Journals (Sweden)
Torres Nestor V
2007-09-01
Full Text Available Abstract 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
Is Geometric Frustration-Induced Disorder a Recipe for High Ionic Conductivity?
Düvel, Andre; Heitjans, Paul; Fedorov, Pavel; Scholz, Gudrun; Cibin, Giannantonio; Chadwick, Alan V; Pickup, David M; Ramos, Silvia; Sayle, Lewis W L; Sayle, Emma K L; Sayle, Thi X T; Sayle, Dean C
2017-04-26
Ionic conductivity is ubiquitous to many industrially important applications such as fuel cells, batteries, sensors, and catalysis. Tunable conductivity in these systems is therefore key to their commercial viability. Here, we show that geometric frustration can be exploited as a vehicle for conductivity tuning. In particular, we imposed geometric frustration upon a prototypical system, CaF2, by ball milling it with BaF2, to create nanostructured Ba1-xCaxF2 solid solutions and increased its ionic conductivity by over 5 orders of magnitude. By mirroring each experiment with MD simulation, including "simulating synthesis", we reveal that geometric frustration confers, on a system at ambient temperature, structural and dynamical attributes that are typically associated with heating a material above its superionic transition temperature. These include structural disorder, excess volume, pseudovacancy arrays, and collective transport mechanisms; we show that the excess volume correlates with ionic conductivity for the Ba1-xCaxF2 system. We also present evidence that geometric frustration-induced conductivity is a general phenomenon, which may help explain the high ionic conductivity in doped fluorite-structured oxides such as ceria and zirconia, with application for solid oxide fuel cells. A review on geometric frustration [ Nature 2015 , 521 , 303 ] remarks that classical crystallography is inadequate to describe systems with correlated disorder, but that correlated disorder has clear crystallographic signatures. Here, we identify two possible crystallographic signatures of geometric frustration: excess volume and correlated "snake-like" ionic transport; the latter infers correlated disorder. In particular, as one ion in the chain moves, all the other (correlated) ions in the chain move simultaneously. Critically, our simulations reveal snake-like chains, over 40 Å in length, which indicates long-range correlation in our disordered systems. Similarly, collective
Hierarchical Geometric Constraint Model for Parametric Feature Based Modeling
Institute of Scientific and Technical Information of China (English)
高曙明; 彭群生
1997-01-01
A new geometric constraint model is described,which is hierarchical and suitable for parametric feature based modeling.In this model,different levels of geometric information are repesented to support various stages of a design process.An efficient approach to parametric feature based modeling is also presented,adopting the high level geometric constraint model.The low level geometric model such as B-reps can be derived automatically from the hig level geometric constraint model,enabling designers to perform their task of detailed design.
Geometric transition in Non-perturbative Topological string
Sugimoto, Yuji
2016-01-01
We study a geometric transition in non-perturbative topological string. We consider two cases. One is the geometric transition from the closed topological string on the local $\\mathcal{B}_{3}$ to the closed topological string on the resolved conifold. The other is the geometric transition from the closed topological string on the local $\\mathcal{B}_{3}$ to the open topological string on the resolved conifold with a toric A-brane. We find that, in both cases, the geometric transition can be applied for the non-perturbative topological string. We also find the corrections of the value of K\\"ahler parameters at which the geometric transition occurs.
Knowledge-based geometric modeling in construction
DEFF Research Database (Denmark)
Bonev, Martin; Hvam, Lars
2012-01-01
a considerably high amount of their recourses is required for designing and specifying the majority of their product assortment. As design decisions are hereby based on knowledge and experience about behaviour and applicability of construction techniques and materials for a predefined design situation, smart...... tools need to be developed, to support these activities. In order to achieve a higher degree of design automation, this study proposes a framework for using configuration systems within the CAD environment together with suitable geometric modeling techniques on the example of a Danish manufacturer...
Some Geometrical Aspects of M-Theory
de Azcárraga, José A.; Izquierdo, José M.
2008-06-01
Some geometrical aspects of super-p-brane theory, M-theory, and their connection with supergravity, are reviewed. In particular, the different fractions of preserved supersymmetries are discussed both from the algebraic and the supergravity solutions point of view. We also review the `preon conjecture' according to which states preserving a 31/32 fraction of supersymmetries would be the building blocks of M-theory, and on the failed attempts made so far to find these states in terms of supergravity solutions.
Aerospace plane guidance using geometric control theory
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.
The Geometric Nature of the Fundamental Lemma
Nadler, David
2010-01-01
The Fundamental Lemma is a somewhat obscure combinatorial identity introduced by Robert P. Langlands as an ingredient in the theory of automorphic representations. After many years of deep contributions by mathematicians working in representation theory, number theory, algebraic geometry, and algebraic topology, a proof of the Fundamental Lemma was recently completed by Ngo Bau Chau, for which he was awarded a Fields Medal. Our aim here is to touch on some of the beautiful ideas contributing to the Fundamental Lemma and its proof. We highlight the geometric nature of the problem which allows one to attack a question in p-adic analysis with the tools of algebraic geometry.
Evaluation of Design Methods for Geometric Control
DEFF Research Database (Denmark)
Kymmel, Mogens; Beran, M.; Foldager, L.;
1985-01-01
Geometric control can produce desirable control by decoupling the input disturbances from the selected output variables. The basic principle for this method was originally introduced by Wonham. The mathematical complexity involved, however, makes the method very hard to get accepted by the chemical...... community. The paper evaluates Wonham's original method together with three other methods, i.e. eigenvalue/eigenvector methods by Shah et al, the graph theory by Schizas and Evans and the simplified method by KÃ¼mmel et al. The evaluation considers the basic potential of the methods, the prerequisite...... of the designer, transparency, computer demand, and potential for pole shift....
Robust topology optimization accounting for geometric imperfections
DEFF Research Database (Denmark)
Schevenels, M.; Jansen, M.; Lombaert, Geert
2013-01-01
performance. As a consequence, the actual structure may be far from optimal. In this paper, a robust approach to topology optimization is presented, taking into account two types of geometric imperfections: variations of (1) the crosssections and (2) the locations of structural elements. The first type...... is modeled by means of a scalar non-Gaussian random field, which is represented as a translation process. The underlying Gaussian field is simulated by means of the EOLE method. The second type of imperfections is modeled as a Gaussian vector-valued random field, which is simulated directly by means...
A geometrical introduction to screw theory
Minguzzi, E
2012-01-01
Since the addition of applied forces must take into account the line of action, applied forces do not belong to a vector space. Screw theory removes this geometrical limitation and solves other mechanical problems by unifying, in a single concept, the translational and rotational degrees of freedom. Although venerable this theory is little known. By introducing some innovations, I show how screw theory can help us to rapidly develop several standard and less standard results in classical mechanics. The connection with the Lie algebra of the group of rigid maps is clarified.
Minimal representations, geometric quantization, and unitarity.
Brylinski, R; Kostant, B
1994-06-21
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.
Non-geometric branes are DFT monopoles
Bakhmatov, Ilya; Musaev, Edvard T
2016-01-01
The double field theory monopole solution by Berman and Rudolph is shown to reproduce non-geometric backgrounds with non-vanishing Q- and R-flux upon an appropriate choice of physical and dual coordinates. The obtained backgrounds depend non-trivially on dual coordinates and have only trivial monodromies. Upon smearing the solutions along the dual coordinates one reproduces the known $5^2_2$ solution for the Q-brane and co-dimension 1 solution for the R-brane. The T-duality invariant magnetic charge is explicitly calculated for all these backgrounds and is found to be equal to the magnetic charge of (unsmeared) NS5-brane.
The Electromagnetic Duality Formulation of Geometric Phases
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.
Geometric and numerical foundations of movements
Mansard, Nicolas; Lasserre, Jean-Bernard
2017-01-01
This book aims at gathering roboticists, control theorists, neuroscientists, and mathematicians, in order to promote a multidisciplinary research on movement analysis. It follows the workshop “ Geometric and Numerical Foundations of Movements ” held at LAAS-CNRS in Toulouse in November 2015[1]. Its objective is to lay the foundations for a mutual understanding that is essential for synergetic development in motion research. In particular, the book promotes applications to robotics --and control in general-- of new optimization techniques based on recent results from real algebraic geometry.
Geometric Models of the Relativistic Harmonic Oscillator
Cotaescu, I I
1997-01-01
A family of relativistic geometric models is defined as a generalization of the actual anti-de Sitter (1+1) model of the relativistic harmonic oscillator. It is shown that all these models lead to the usual harmonic oscillator in the non-relativistic limit, even though their relativistic behavior is quite different. Among quantum models we find a set of models with countable energy spectra, and another one having only a finite number of energy levels and in addition a continuous spectrum.
Geometric Formulation of Gauge Theory of Gravity
Institute of Scientific and Technical Information of China (English)
WUNing; ZHANGDa-Hua; RUANTu-Nan
2003-01-01
DitTerential geometric formulation of quantum gauge theory of gravity is studied in this paper. The quantum gauge theory of gravity is formulated completely in the framework of traditional quantum field theory. In order to study the relationship between quantum gauge theory of gravity and traditional quantum gravity which is formulated in curved space, it is important to set up the geometry picture of quantum gauge theory of gravity. The correspondence between quantum gauge theory of gravity and differential geometry is discussed and the geometry picture of quantum gauge theory of gravity is studied.
Geometric Formulation of Gauge Theory of Gravity
Institute of Scientific and Technical Information of China (English)
WU Ning; ZHANG Da-Hua; RUAN Tu-Nan
2003-01-01
Differential geometric formulation of quantum gauge theory of gravity is studied in this paper. The quantumgauge theory of gravity is formulated completely in the framework of traditional quantum field theory. In order to studythe relationship between quantum gauge theory of gravity and traditional quantum gravity which is formulated in curvedspace, it is important to set up the geometry picture of quantum gauge theory of gravity. The correspondence betweenquantum gauge theory of gravity and differential geometry is discussed and the geometry picture of quantum gaugetheory of gravity is studied.
Conformal invariants topics in geometric function theory
Ahlfors, Lars V
2010-01-01
Most conformal invariants can be described in terms of extremal properties. Conformal invariants and extremal problems are therefore intimately linked and form together the central theme of this classic book which is primarily intended for students with approximately a year's background in complex variable theory. The book emphasizes the geometric approach as well as classical and semi-classical results which Lars Ahlfors felt every student of complex analysis should know before embarking on independent research. At the time of the book's original appearance, much of this material had never ap
More On Gauge Theory And Geometric Langlands
Witten, Edward
2015-01-01
The geometric Langlands correspondence was described some years ago in terms of $S$-duality of $\\N=4$ super Yang-Mills theory. Some additional matters relevant to this story are described here. The main goal is to explain directly why an $A$-brane of a certain simple kind can be an eigenbrane for the action of 't Hooft operators. To set the stage, we review some facts about Higgs bundles and the Hitchin fibration. We consider only the simplest examples, in which many technical questions can be avoided.
Geometric properties of optimal photonic crystals
DEFF Research Database (Denmark)
Sigmund, Ole; Hougaard, Kristian G.
2008-01-01
Photonic crystals can be designed to control and confine light. Since the introduction of the concept by Yablonovitch and John two decades ago, there has been a quest for the optimal structure, i.e., the periodic arrangement of dielectric and air that maximizes the photonic band gap. Based...... on numerical optimization studies, we have discovered some surprisingly simple geometric properties of optimal planar band gap structures. We conjecture that optimal structures for gaps between bands n and n+1 correspond to n elliptic rods with centers defined by the generators of an optimal centroidal Voronoi...
1995-01-01
El método de las coordenadas, además de tener un conjunto de aplicaciones de amplio espectro -cronología, geógrafa, topógrafa, ﬁsica, geometría....- y de permitir la trascripción algebraica de determinados problemas geométricos, se fundamenta en ideas que son clave a la hora de comprender la eficacia de las matemáticas como herramienta de las ciencias. La tesis que aquí se sostiene es que esas ideas claves no se transparentan restringiendo la utilización del método de las coordenadas al est...
Geometric calibration of ERS satellite SAR images
DEFF Research Database (Denmark)
Mohr, Johan Jacob; Madsen, Søren Nørvang
2001-01-01
Geometric calibration of the European Remote Sensing (ERS) Satellite synthetic aperture radar (SAR) slant range images is important in relation to mapping areas without ground reference points and also in relation to automated processing. The relevant SAR system parameters are discussed...... on a seven-year ERS-1 and a four-year ERS-2 time series, the long term stability is found to be sufficient to allow a single calibration covering the entire mission period. A descending and an ascending orbit tandem pair of the ESA calibration site on Flevoland, suitable for calibration of ERS SAR processors...
A geometric interpretation of integrable motions
Clementi, C; Clementi, Cecilia; Pettini, Marco
2001-01-01
Integrability, one of the classic issues in galactic dynamics and in general in celestial mechanics, is here revisited in a Riemannian geometric framework, where newtonian motions are seen as geodesics of suitable ``mechanical'' manifolds. The existence of constants of motion that entail integrability is associated with the existence of Killing tensor fields on the mechanical manifolds. Such tensor fields correspond to hidden symmetries of non-Noetherian kind. Explicit expressions for Killing tensor fields are given for the N=2 Toda model, and for a modified Henon-Heiles model, recovering the already known analytic expressions of the second conserved quantity besides energy for each model respectively.
Geometric Algebra Model of Distributed Representations
Patyk, Agnieszka
2010-01-01
Formalism based on GA is an alternative to distributed representation models developed so far --- Smolensky's tensor product, Holographic Reduced Representations (HRR) and Binary Spatter Code (BSC). Convolutions are replaced by geometric products, interpretable in terms of geometry which seems to be the most natural language for visualization of higher concepts. This paper recalls the main ideas behind the GA model and investigates recognition test results using both inner product and a clipped version of matrix representation. The influence of accidental blade equality on recognition is also studied. Finally, the efficiency of the GA model is compared to that of previously developed models.
Geometric measure theory and real analysis
2014-01-01
In 2013, a school on Geometric Measure Theory and Real Analysis, organized by G. Alberti, C. De Lellis and myself, took place at the Centro De Giorgi in Pisa, with lectures by V. Bogachev, R. Monti, E. Spadaro and D. Vittone. The book collects the notes of the courses. The courses provide a deep and up to date insight on challenging mathematical problems and their recent developments: infinite-dimensional analysis, minimal surfaces and isoperimetric problems in the Heisenberg group, regularity of sub-Riemannian geodesics and the regularity theory of minimal currents in any dimension and codimension.
ERC Workshop on Geometric Partial Differential Equations
Novaga, Matteo; Valdinoci, Enrico
2013-01-01
This book is the outcome of a conference held at the Centro De Giorgi of the Scuola Normale of Pisa in September 2012. The aim of the conference was to discuss recent results on nonlinear partial differential equations, and more specifically geometric evolutions and reaction-diffusion equations. Particular attention was paid to self-similar solutions, such as solitons and travelling waves, asymptotic behaviour, formation of singularities and qualitative properties of solutions. These problems arise in many models from Physics, Biology, Image Processing and Applied Mathematics in general, and have attracted a lot of attention in recent years.
Multiscale Geometric Analysis: Theory, Applications, and Opportunities
2007-11-02
eiωΦν(x,t) ( a0ν(x, t) + a1ν(x, t) ω + a2ν(x, t) ω2 + . . . ) • Plug into wave equation – Eikonal equations ∂tΦν + λν(x,∇xΦ) = 0. λν(x, k) are the...space ẋ(t) = ∇kλν(x, k), x(0) = x0,k̇(t) = −∇xλν(x, k), k(0) = k0. • Eikonal equations from geometric optics ∂tΦν + λν(x,∇xΦ) = 0. Φ is constant
Geometric massive higher spins and current exchanges
Francia, Dario
2008-01-01
Generalised Fierz-Pauli mass terms allow to describe massive higher-spin fields on flat background by means of simple quadratic deformations of the corresponding geometric, massless Lagrangians. In this framework there is no need for auxiliary fields. We briefly review the construction in the bosonic case and study the interaction of these massive fields with external sources, computing the corresponding propagators. In the same fashion as for the massive graviton, but differently from theories where auxiliary fields are present, the structure of the current exchange is completely determined by the form of the mass term itself.
The minimal geometric deformation approach extended
Casadio, R.; Ovalle, J.; da Rocha, Roldão
2015-11-01
The minimal geometric deformation approach was introduced in order to study the exterior spacetime around spherically symmetric self-gravitating systems, such as stars or similar astrophysical objects, in the Randall-Sundrum brane-world framework. A consistent extension of this approach is developed here, which contains modifications of both the time component and the radial component of a spherically symmetric metric. A modified Schwarzschild geometry is obtained as an example of its simplest application, and a new solution that is potentially useful to describe stars in the brane-world is also presented.
Parabolic non-diffracting beams: geometrical approach
Sosa-Sánchez, Citlalli Teresa; Silva-Ortigoza, Gilberto; Alejandro Juárez-Reyes, Salvador; de Jesús Cabrera-Rosas, Omar; Espíndola-Ramos, Ernesto; Julián-Macías, Israel; Ortega-Vidals, Paula
2017-08-01
The aim of this work is to present a geometrical characterization of parabolic non-diffracting beams. To this end, we compute the corresponding angular spectrum of the separable non-diffracting parabolic beams in order to determine the one-parameter family of solutions of the eikonal equation associated with this type of beam. Using this information, we compute the corresponding wavefronts and caustic, and find that qualitatively the caustic corresponds to the maximum of the intensity pattern and the wavefronts are deformations of conical surfaces.
Toroidal Precession as a Geometric Phase
Energy Technology Data Exchange (ETDEWEB)
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.
Non-Riemannian geometrical optics in QED
Garcia de Andrade, L C
2003-01-01
A non-minimal photon-torsion axial coupling in the quantum electrodynamics (QED) framework is considered. The geometrical optics in Riemannian-Cartan spacetime is considering and a plane wave expansion of the electromagnetic vector potential is considered leading to a set of the equations for the ray congruence. Since we are interested mainly on the torsion effects in this first report we just consider the Riemann-flat case composed of the Minkowskian spacetime with torsion. It is also shown that in torsionic de Sitter background the vacuum polarisation does alter the propagation of individual photons, an effect which is absent in Riemannian spaces.