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Sample records for geometry reconstrucao intranodal

  1. Intranodal Palisaded Myofibroblastoma: Radiological and Cytological Overview

    PubMed Central

    Altinbas, Namik Kemal; Oz, Ilker; Ustuner, Evren; Gulpinar, Basak; Peker, Elif; Akkaya, Zehra; Peker, Ahmet; Ceyhan, Koray; Yagci, Cemil

    2016-01-01

    Summary Background Intranodal palisaded myofibroblastoma is a benign and very rare mesenchymal neoplasm of the lymph nodes originating from differentiated smooth muscle cells and myofibroblasts. Case Report We report a case of intranodal palisaded myofibroblastoma in an 84-year-old woman with Parkinson’s disease that presented as a left inguinal mass. The diagnosis was made using ultrasound-guided fine needle aspiration biopsy and consequent cytopathological examination that included immunohistochemical analysis. Herein, we discuss the presentation of a rare intranodal palisaded myofibroblastoma with emphasis on its ultrasonographic and cytopathologic features. Conclusions Intranodal palisaded myofibroblastoma should be considered in the differential diagnosis of inguinal lymphadenopathy and the diagnosis is possible with cytopathologic exam and immunohistochemical analysis using ultrasound-guided FNA biopsy, guiding the clinician to nodal excision rather than aggressive measures. PMID:27504146

  2. Intranode data communications in a parallel computer

    DOEpatents

    Archer, Charles J; Blocksome, Michael A; Miller, Douglas R; Ratterman, Joseph D; Smith, Brian E

    2013-07-23

    Intranode data communications in a parallel computer that includes compute nodes configured to execute processes, where the data communications include: allocating, upon initialization of a first process of a compute node, a region of shared memory; establishing, by the first process, a predefined number of message buffers, each message buffer associated with a process to be initialized on the compute node; sending, to a second process on the same compute node, a data communications message without determining whether the second process has been initialized, including storing the data communications message in the message buffer of the second process; and upon initialization of the second process: retrieving, by the second process, a pointer to the second process's message buffer; and retrieving, by the second process from the second process's message buffer in dependence upon the pointer, the data communications message sent by the first process.

  3. Intranode data communications in a parallel computer

    DOEpatents

    Archer, Charles J; Blocksome, Michael A; Miller, Douglas R; Ratterman, Joseph D; Smith, Brian E

    2014-01-07

    Intranode data communications in a parallel computer that includes compute nodes configured to execute processes, where the data communications include: allocating, upon initialization of a first process of a computer node, a region of shared memory; establishing, by the first process, a predefined number of message buffers, each message buffer associated with a process to be initialized on the compute node; sending, to a second process on the same compute node, a data communications message without determining whether the second process has been initialized, including storing the data communications message in the message buffer of the second process; and upon initialization of the second process: retrieving, by the second process, a pointer to the second process's message buffer; and retrieving, by the second process from the second process's message buffer in dependence upon the pointer, the data communications message sent by the first process.

  4. Case report. Peripancreatic intranodal haemangioma mimicking pancreatic neuroendocrine tumour: imaging and pathological findings.

    PubMed

    Karaosmanoglu, A D; Arellano, R; Baker, G

    2011-12-01

    Haemangiomas are common benign tumours that are generally detected within the skin, mucosal surfaces and soft tissues. However, intranodal haemangiomas are extremely rare and are among the benign primary vascular abnormalities of the lymph nodes that include lymphangioma, haemangioendothelioma, angiomyomatous hamartoma and haemangiomas. In this case report, we present the imaging and pathological findings of an intranodal haemangioma in the pancreatic head simulating a pancreatic neuroendocrine tumour. To the best of our knowledge, this is the first report of an intranodal haemangioma in this location.

  5. Intranodal leiomyoma in a young child: report of a rare spindle cell lesion.

    PubMed

    Girhotra, Manish; Virk, Shehbaaz Singh; Verma, Sarika; Bansal, Kalpana; Gupta, Ruchika

    2014-01-01

    ABSTRACT Primary spindle cell lesions of lymph nodes, with the exception of Kaposi's sarcoma, are rare. Intranodal palisaded myofibroblastoma has been described as a spindle cell tumor with prominent amianthoid fibers, intralesional hemorrhage, and intracellular or extracellular inclusions. Another spindle cell lesion, intranodal leiomyoma, has been reported only occasionally. We report the case of a 6-year-old boy with a mass in the neck without other systemic complaints. Excision biopsy of the lymph node revealed a spindle cell tumor with lymph nodal tissue at the periphery. The tumor showed features of smooth muscle differentiation with focally high mitotic index. The classical features of myofibroblastoma were not present. A final pathologic diagnosis of intranodal leiomyoma was rendered. The child has been free of recurrence in the follow-up period. Intranodal leiomyoma is a rare primary spindle cell lesion of the lymph nodes and should be considered in the differential diagnosis of the same.

  6. Axillary intranodal palisaded myofibroblastoma: report of a case associated with chronic mastitis

    PubMed Central

    D'Antonio, Antonio; Addesso, Maria; Amico, Paolo; Fragetta, Filippo

    2014-01-01

    Intranodal palisaded myofibroblastoma is a rare tumour of the lymph node that may be derived from myofibroblasts. The most usual area of presentation is the inguinal lymph nodes, but occurrence within other areas has also been reported. It is characterised by spindle cells, amianthoid-like fibres, and by the proliferation of hemosiderin-containing histiocytes in the lymph node. Although intranodal palisaded myofibroblastoma is benign, it is frequently confused with metastatic lesions, especially when it occurs in atypical sites. We herein report the second case of axillary intranodal palisaded myofibroblastoma occurring in a woman with a granulomatous chronic mastitis. The salient clinicopathological features of this unusual tumour are presented with emphasis to the pathogenesis of the tumour as well as to its histological and immunohistochemical characteristics. Clinicians and pathologists must be aware of this rare tumour to avoid a misdiagnosis of malignancy and assure patient a correct therapeutic management. PMID:25323283

  7. Diagnostic Accuracy of Computer-Aided Assessment of Intranodal Vascularity in Distinguishing Different Causes of Cervical Lymphadenopathy.

    PubMed

    Ying, Michael; Cheng, Sammy C H; Ahuja, Anil T

    2016-08-01

    Ultrasound is useful in assessing cervical lymphadenopathy. Advancement of computer science technology allows accurate and reliable assessment of medical images. The aim of the study described here was to evaluate the diagnostic accuracy of computer-aided assessment of the intranodal vascularity index (VI) in differentiating the various common causes of cervical lymphadenopathy. Power Doppler sonograms of 347 patients (155 with metastasis, 23 with lymphoma, 44 with tuberculous lymphadenitis, 125 reactive) with palpable cervical lymph nodes were reviewed. Ultrasound images of cervical nodes were evaluated, and the intranodal VI was quantified using a customized computer program. The diagnostic accuracy of using the intranodal VI to distinguish different disease groups was evaluated and compared. Metastatic and lymphomatous lymph nodes tend to be more vascular than tuberculous and reactive lymph nodes. The intranodal VI had the highest diagnostic accuracy in distinguishing metastatic and tuberculous nodes with a sensitivity of 80%, specificity of 73%, positive predictive value of 91%, negative predictive value of 51% and overall accuracy of 68% when a cutoff VI of 22% was used. Computer-aided assessment provides an objective and quantitative way to evaluate intranodal vascularity. The intranodal VI is a useful parameter in distinguishing certain causes of cervical lymphadenopathy and is particularly useful in differentiating metastatic and tuberculous lymph nodes. However, it has limited value in distinguishing lymphomatous nodes from metastatic and reactive nodes.

  8. Supraventricular tachycardia in Lown-Ganong-Levine syndrome: atrionodal versus intranodal reentry.

    PubMed

    Josephson, M E; Kastor, J A

    1977-10-01

    The mechanism of the abbreviated atrioventricular (A-V) nodal conduction time and paroxysmal supraventricular tachycardia in the Lown-Ganong-Levine syndrome was evaluated in six patients. In each the A-H interval increased in response to rapid atrial pacing and atrial extrastimuli; typical dual A-V nodal pathways were demonstrated. In five patients studied at two cycle lengths prolongation of conduction and refractoriness of the "fast" pathway was noted at the shorter basic cycle length. Propranolol prolonged conduction and refractoriness of the "fast" pathway in three patients and in one produced Wenckebach conduction during atrial pacing which did not occur prior to its administration. In three patients the atrium did not appear necessary to sustain supraventricular tachycardia. These findings suggest that preferential rapidly conducting A-V nodal fibers and intranodal reentry are the responsible mechanisms in those patients with Lown-Ganong-Levine syndrome and reciprocating tachycardia.

  9. Sinoatrial Node Reentry in a Canine Chronic Left Ventricular Infarct Model: The Role of Intranodal Fibrosis and Heterogeneity of Refractoriness

    PubMed Central

    Glukhov, Alexey V.; Hage, Lori T.; Hansen, Brian J.; Pedraza-Toscano, Adriana; Vargas-Pinto, Pedro; Hamlin, Robert L.; Weiss, Raul; Carnes, Cynthia A.; Billman, George E.; Fedorov, Vadim V.

    2014-01-01

    Background Reentrant arrhythmias involving the sinoatrial node (SAN), namely, SAN reentry, remain one of the most intriguing enigmas of cardiac electrophysiology. The goal of the present study was to elucidate the mechanism of SAN micro-reentry in canine hearts with post myocardial infarction (MI) structural remodeling. Methods and Results In vivo, Holter monitoring revealed ventricular arrhythmias and SAN dysfunctions in post left ventricular MI (6–15 wks) dogs (n=5) compared to control dogs (n=4). In vitro, high resolution near-infrared optical mapping of intramural SAN activation was performed in coronary perfused atrial preparations from MI (n=5) and controls (n=4). Both SAN macro- (slow-fast; 16–28 mm) and micro-reentries (1–3 mm) were observed in 60% of the MI preparations during moderate autonomic stimulation (acetylcholine (0.1 µM) or isoproterenol (0.01-0.1 µM)) after termination of atrial tachypacing (5–8 Hz), a finding not seen in controls. The autonomic stimulation induced heterogeneous changes in the SAN refractoriness; thus, competing atrial and/or SAN pacemaker waves could produce unidirectional blocks and initiate intranodal micro-reentries. The micro-reentry pivot waves were anchored to the longitudinal block region and produced both tachycardia and paradoxical bradycardia (due to exit block), despite an atrial ECG morphology identical to regular sinus rhythm. Intranodal longitudinal conduction blocks coincided with interstitial fibrosis strands that were exaggerated in the MI SAN pacemaker complex (fibrosis density 37±7% MI vs. 23±6% control, P<0.001). Conclusions Both tachy- and bradyarrhythmias can result from SAN micro-reentries. Post-infarction remodeling, including increased intranodal fibrosis and heterogeneity of refractoriness, provides substrates for SAN reentry. PMID:23960214

  10. Afferent lymph-derived T cells and DCs use different chemokine receptor CCR7-dependent routes for entry into the lymph node and intranodal migration.

    PubMed

    Braun, Asolina; Worbs, Tim; Moschovakis, G Leandros; Halle, Stephan; Hoffmann, Katharina; Bölter, Jasmin; Münk, Anika; Förster, Reinhold

    2011-08-14

    Little is known about the molecular mechanisms that determine the entry into the lymph node and intranodal positioning of lymph-derived cells. By injecting cells directly into afferent lymph vessels of popliteal lymph nodes, we demonstrate that lymph-derived T cells entered lymph-node parenchyma mainly from peripheral medullary sinuses, whereas dendritic cells (DCs) transmigrated through the floor of the subcapsular sinus on the afferent side. Transmigrating DCs induced local changes that allowed the concomitant entry of T cells at these sites. Signals mediated by the chemokine receptor CCR7 were absolutely required for the directional migration of both DCs and T cells into the T cell zone but were dispensable for the parenchymal entry of lymph-derived T cells and dendrite probing of DCs. Our findings provide insight into the molecular and structural requirements for the entry into lymph nodes and intranodal migration of lymph-derived cells of the immune system.

  11. Risk factor analysis for massive lymphatic ascites after laparoscopic retroperitonal lymphadenectomy in gynecologic cancers and treatment using intranodal lymphangiography with glue embolization

    PubMed Central

    2016-01-01

    Objective To evaluate risk factors for massive lymphatic ascites after laparoscopic retroperitoneal lymphadenectomy in gynecologic cancer and the feasibility of treatments using intranodal lymphangiography (INLAG) with glue embolization. Methods A retrospective analysis of 234 patients with gynecologic cancer who received laparoscopic retroperitonal lymphadenectomy between April 2006 and November 2015 was done. In June 2014, INLAG with glue embolization was initiated to manage massive lymphatic ascites. All possible clinicopathologic factors related to massive lymphatic ascites were determined in the pre-INLAG group (n=163). Clinical courses between pre-INLAG group and post-INLAG group (n=71) were compared. Results In the pre-INLAG group (n=163), four patients (2.5%) developed massive lymphatic ascites postoperatively. Postoperative lymphatic ascites was associated with liver cirrhosis (three cirrhotic patients, p<0.001). In the post-INLAG group, one patient with massive lymphatic ascites had a congestive heart failure and first received INLAG with glue embolization. She had pelvic drain removed within 7 days after INLAG. The mean duration of pelvic drain and hospital stay decreased after the introduction of INLAG (13.2 days vs. 10.9 days, p=0.001; 15.2 days vs. 12.6 days, p=0.001). There was no evidence of recurrence after this procedure. Conclusion Underlying medical conditions related to the reduced effective circulating volume, such as liver cirrhosis and heart failure, may be associated with massive lymphatic ascites after retroperitoneal lymphadenectomy. INLAG with glue embolization can be an alternative treatment options to treat leaking lymphatic channels in patients with massive lymphatic leakage. PMID:27171674

  12. Molecular Geometry.

    ERIC Educational Resources Information Center

    Desseyn, H. O.; And Others

    1985-01-01

    Compares linear-nonlinear and planar-nonplanar geometry through the valence-shell electron pairs repulsion (V.S.E.P.R.), Mulliken-Walsh, and electrostatic force theories. Indicates that although the V.S.E.P.R. theory has more advantages for elementary courses, an explanation of the best features of the different theories offers students a better…

  13. Enrichment Activities for Geometry.

    ERIC Educational Resources Information Center

    Usiskin, Zalman

    1983-01-01

    Enrichment activities that teach about geometry as they instruct in geometry are given for some significant topics. The facets of geometry included are tessellations, round robin tournaments, geometric theorems on triangles, and connections between geometry and complex numbers. (MNS)

  14. Geometry in Medias Res

    ERIC Educational Resources Information Center

    Cukier, Mimi; Asdourian, Tony; Thakker, Anand

    2012-01-01

    Geometry provides a natural window into what it is like to do mathematics. In the world of geometry, playful experimentation is often more fruitful than following a procedure, and logic plus a few axioms can open new worlds. Nonetheless, teaching a geometry course in a way that combines both rigor and play can be difficult. Many geometry courses…

  15. Learning Geometry through Dynamic Geometry Software

    ERIC Educational Resources Information Center

    Forsythe, Sue

    2007-01-01

    In this article, the author investigates effective teaching and learning of geometrical concepts using dynamic geometry software (DGS). Based from her students' reactions to her project, the author found that her students' understanding of the concepts was better than if they had learned geometry through paper-based tasks. However, mixing computer…

  16. Geometry and Erdkinder.

    ERIC Educational Resources Information Center

    McDonald, Nathaniel J.

    2001-01-01

    Chronicles a teacher's first year teaching geometry at the Hershey Montessori Farm School in Huntsburg, Ohio. Instructional methods relied on Euclid primary readings and combined pure abstract logic with practical applications of geometry on the land. The course included geometry background imparted by Montessori elementary materials as well as…

  17. Developments in special geometry

    NASA Astrophysics Data System (ADS)

    Mohaupt, Thomas; Vaughan, Owen

    2012-02-01

    We review the special geometry of Script N = 2 supersymmetric vector and hypermultiplets with emphasis on recent developments and applications. A new formulation of the local c-map based on the Hesse potential and special real coordinates is presented. Other recent developments include the Euclidean version of special geometry, and generalizations of special geometry to non-supersymmetric theories. As applications we disucss the proof that the local r-map and c-map preserve geodesic completeness, and the construction of four- and five-dimensional static solutions through dimensional reduction over time. The shared features of the real, complex and quaternionic version of special geometry are stressed throughout.

  18. Geometry of multihadron production

    SciTech Connect

    Bjorken, J.D.

    1994-10-01

    This summary talk only reviews a small sample of topics featured at this symposium: Introduction; The Geometry and Geography of Phase space; Space-Time Geometry and HBT; Multiplicities, Intermittency, Correlations; Disoriented Chiral Condensate; Deep Inelastic Scattering at HERA; and Other Contributions.

  19. Geometry + Technology = Proof

    ERIC Educational Resources Information Center

    Lyublinskaya, Irina; Funsch, Dan

    2012-01-01

    Several interactive geometry software packages are available today to secondary school teachers. An example is The Geometer's Sketchpad[R] (GSP), also known as Dynamic Geometry[R] software, developed by Key Curriculum Press. This numeric based technology has been widely adopted in the last twenty years, and a vast amount of creativity has been…

  20. Euclidean Geometry via Programming.

    ERIC Educational Resources Information Center

    Filimonov, Rossen; Kreith, Kurt

    1992-01-01

    Describes the Plane Geometry System computer software developed at the Educational Computer Systems laboratory in Sofia, Bulgaria. The system enables students to use the concept of "algorithm" to correspond to the process of "deductive proof" in the development of plane geometry. Provides an example of the software's capability…

  1. The Beauty of Geometry

    ERIC Educational Resources Information Center

    Morris, Barbara H.

    2004-01-01

    This article describes a geometry project that used the beauty of stained-glass-window designs to teach middle school students about geometric figures and concepts. Three honors prealgebra teachers and a middle school mathematics gifted intervention specialist created a geometry project that covered the curriculum and also assessed students'…

  2. Geometry of membrane fission.

    PubMed

    Frolov, Vadim A; Escalada, Artur; Akimov, Sergey A; Shnyrova, Anna V

    2015-01-01

    Cellular membranes define the functional geometry of intracellular space. Formation of new membrane compartments and maintenance of complex organelles require division and disconnection of cellular membranes, a process termed membrane fission. Peripheral membrane proteins generally control membrane remodeling during fission. Local membrane stresses, reflecting molecular geometry of membrane-interacting parts of these proteins, sum up to produce the key membrane geometries of fission: the saddle-shaped neck and hour-glass hemifission intermediate. Here, we review the fundamental principles behind the translation of molecular geometry into membrane shape and topology during fission. We emphasize the central role the membrane insertion of specialized protein domains plays in orchestrating fission in vitro and in cells. We further compare individual to synergistic action of the membrane insertion during fission mediated by individual protein species, proteins complexes or membrane domains. Finally, we describe how local geometry of fission intermediates defines the functional design of the protein complexes catalyzing fission of cellular membranes.

  3. Flyby Geometry Optimization Tool

    NASA Technical Reports Server (NTRS)

    Karlgaard, Christopher D.

    2007-01-01

    The Flyby Geometry Optimization Tool is a computer program for computing trajectories and trajectory-altering impulsive maneuvers for spacecraft used in radio relay of scientific data to Earth from an exploratory airplane flying in the atmosphere of Mars.

  4. What Is Geometry?

    ERIC Educational Resources Information Center

    Chern, Shiing-Shen

    1990-01-01

    Discussed are the major historical developments of geometry. Euclid, Descartes, Klein's Erlanger Program, Gaus and Riemann, globalization, topology, Elie Cartan, and an application to molecular biology are included as topics. (KR)

  5. Gingerbread-House Geometry.

    ERIC Educational Resources Information Center

    Emenaker, Charles E.

    1999-01-01

    Describes a sixth-grade interdisciplinary geometry unit based on Charles Dickens's "A Christmas Carol". Focuses on finding area, volume, and perimeter, and working with estimation, decimals, and fractions in the context of making gingerbread houses. (ASK)

  6. Facilitating Understandings of Geometry.

    ERIC Educational Resources Information Center

    Pappas, Christine C.; Bush, Sara

    1989-01-01

    Illustrates some learning encounters for facilitating first graders' understanding of geometry. Describes some of children's approaches using Cuisenaire rods and teacher's intervening. Presents six problems involving various combinations of Cuisenaire rods and cubes. (YP)

  7. Proof in Transformation Geometry

    ERIC Educational Resources Information Center

    Bell, A. W.

    1971-01-01

    The first of three articles showing how inductively-obtained results in transformation geometry may be organized into a deductive system. This article discusses two approaches to enlargement (dilatation), one using coordinates and the other using synthetic methods. (MM)

  8. Common Geometry Module

    SciTech Connect

    Tautges, Timothy J.

    2005-01-01

    The Common Geometry Module (CGM) is a code library which provides geometry functionality used for mesh generation and other applications. This functionality includes that commonly found in solid modeling engines, like geometry creation, query and modification; CGM also includes capabilities not commonly found in solid modeling engines, like geometry decomposition tools and support for shared material interfaces. CGM is built upon the ACIS solid modeling engine, but also includes geometry capability developed beside and on top of ACIS. CGM can be used as-is to provide geometry functionality for codes needing this capability. However, CGM can also be extended using derived classes in C++, allowing the geometric model to serve as the basis for other applications, for example mesh generation. CGM is supported on Sun Solaris, SGI, HP, IBM, DEC, Linux and Windows NT platforms. CGM also indudes support for loading ACIS models on parallel computers, using MPI-based communication. Future plans for CGM are to port it to different solid modeling engines, including Pro/Engineer or SolidWorks. CGM is being released into the public domain under an LGPL license; the ACIS-based engine is available to ACIS licensees on request.

  9. Software Geometry in Simulations

    NASA Astrophysics Data System (ADS)

    Alion, Tyler; Viren, Brett; Junk, Tom

    2015-04-01

    The Long Baseline Neutrino Experiment (LBNE) involves many detectors. The experiment's near detector (ND) facility, may ultimately involve several detectors. The far detector (FD) will be significantly larger than any other Liquid Argon (LAr) detector yet constructed; many prototype detectors are being constructed and studied to motivate a plethora of proposed FD designs. Whether it be a constructed prototype or a proposed ND/FD design, every design must be simulated and analyzed. This presents a considerable challenge to LBNE software experts; each detector geometry must be described to the simulation software in an efficient way which allows for multiple authors to easily collaborate. Furthermore, different geometry versions must be tracked throughout their use. We present a framework called General Geometry Description (GGD), written and developed by LBNE software collaborators for managing software to generate geometries. Though GGD is flexible enough to be used by any experiment working with detectors, we present it's first use in generating Geometry Description Markup Language (GDML) files to interface with LArSoft, a framework of detector simulations, event reconstruction, and data analyses written for all LAr technology users at Fermilab. Brett is the other of the framework discussed here, the General Geometry Description (GGD).

  10. Integrable Background Geometries

    NASA Astrophysics Data System (ADS)

    Calderbank, David M. J.

    2014-03-01

    This work has its origins in an attempt to describe systematically the integrable geometries and gauge theories in dimensions one to four related to twistor theory. In each such dimension, there is a nondegenerate integrable geometric structure, governed by a nonlinear integrable differential equation, and each solution of this equation determines a background geometry on which, for any Lie group G, an integrable gauge theory is defined. In four dimensions, the geometry is selfdual conformal geometry and the gauge theory is selfdual Yang-Mills theory, while the lower-dimensional structures are nondegenerate (i.e., non-null) reductions of this. Any solution of the gauge theory on a k-dimensional geometry, such that the gauge group H acts transitively on an ℓ-manifold, determines a (k+ℓ)-dimensional geometry (k+ℓ≤4) fibering over the k-dimensional geometry with H as a structure group. In the case of an ℓ-dimensional group H acting on itself by the regular representation, all (k+ℓ)-dimensional geometries with symmetry group H are locally obtained in this way. This framework unifies and extends known results about dimensional reductions of selfdual conformal geometry and the selfdual Yang-Mills equation, and provides a rich supply of constructive methods. In one dimension, generalized Nahm equations provide a uniform description of four pole isomonodromic deformation problems, and may be related to the {SU}(∞) Toda and dKP equations via a hodograph transformation. In two dimensions, the {Diff}(S^1) Hitchin equation is shown to be equivalent to the hyperCR Einstein-Weyl equation, while the {SDiff}(Σ^2) Hitchin equation leads to a Euclidean analogue of Plebanski's heavenly equations. In three and four dimensions, the constructions of this paper help to organize the huge range of examples of Einstein-Weyl and selfdual spaces in the literature, as well as providing some new ! ones. The nondegenerate reductions have a long ancestry. More ! recently

  11. Origins of cellular geometry

    PubMed Central

    2011-01-01

    Cells are highly complex and orderly machines, with defined shapes and a startling variety of internal organizations. Complex geometry is a feature of both free-living unicellular organisms and cells inside multicellular animals. Where does the geometry of a cell come from? Many of the same questions that arise in developmental biology can also be asked of cells, but in most cases we do not know the answers. How much of cellular organization is dictated by global cell polarity cues as opposed to local interactions between cellular components? Does cellular structure persist across cell generations? What is the relationship between cell geometry and tissue organization? What ensures that intracellular structures are scaled to the overall size of the cell? Cell biology is only now beginning to come to grips with these questions. PMID:21880160

  12. Geometry and Cloaking Devices

    NASA Astrophysics Data System (ADS)

    Ochiai, T.; Nacher, J. C.

    2011-09-01

    Recently, the application of geometry and conformal mappings to artificial materials (metamaterials) has attracted the attention in various research communities. These materials, characterized by a unique man-made structure, have unusual optical properties, which materials found in nature do not exhibit. By applying the geometry and conformal mappings theory to metamaterial science, it may be possible to realize so-called "Harry Potter cloaking device". Although such a device is still in the science fiction realm, several works have shown that by using such metamaterials it may be possible to control the direction of the electromagnetic field at will. We could then make an object hidden inside of a cloaking device. Here, we will explain how to design invisibility device using differential geometry and conformal mappings.

  13. Students Discovering Spherical Geometry Using Dynamic Geometry Software

    ERIC Educational Resources Information Center

    Guven, Bulent; Karatas, Ilhan

    2009-01-01

    Dynamic geometry software (DGS) such as Cabri and Geometers' Sketchpad has been regularly used worldwide for teaching and learning Euclidean geometry for a long time. The DGS with its inductive nature allows students to learn Euclidean geometry via explorations. However, with respect to non-Euclidean geometries, do we need to introduce them to…

  14. Origami, Geometry and Art

    ERIC Educational Resources Information Center

    Wares, Arsalan; Elstak, Iwan

    2017-01-01

    The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and algebra. The activity can be used as a context for illustrating how algebra…

  15. Emergent Hyperbolic Network Geometry.

    PubMed

    Bianconi, Ginestra; Rahmede, Christoph

    2017-02-07

    A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links, triangles, tetrahedra etc.) that have a natural geometric interpretation. As such simplicial complexes are widely used in quantum gravity approaches that involve a discretization of spacetime. Here, by extending our knowledge of growing complex networks to growing simplicial complexes we investigate the nature of the emergent geometry of complex networks and explore whether this geometry is hyperbolic. Specifically we show that an hyperbolic network geometry emerges spontaneously from models of growing simplicial complexes that are purely combinatorial. The statistical and geometrical properties of the growing simplicial complexes strongly depend on their dimensionality and display the major universal properties of real complex networks (scale-free degree distribution, small-world and communities) at the same time. Interestingly, when the network dynamics includes an heterogeneous fitness of the faces, the growing simplicial complex can undergo phase transitions that are reflected by relevant changes in the network geometry.

  16. Sliding vane geometry turbines

    DOEpatents

    Sun, Harold Huimin; Zhang, Jizhong; Hu, Liangjun; Hanna, Dave R

    2014-12-30

    Various systems and methods are described for a variable geometry turbine. In one example, a turbine nozzle comprises a central axis and a nozzle vane. The nozzle vane includes a stationary vane and a sliding vane. The sliding vane is positioned to slide in a direction substantially tangent to an inner circumference of the turbine nozzle and in contact with the stationary vane.

  17. Fractal geometry of music.

    PubMed Central

    Hsü, K J; Hsü, A J

    1990-01-01

    Music critics have compared Bach's music to the precision of mathematics. What "mathematics" and what "precision" are the questions for a curious scientist. The purpose of this short note is to suggest that the mathematics is, at least in part, Mandelbrot's fractal geometry and the precision is the deviation from a log-log linear plot. PMID:11607061

  18. The Helen of Geometry

    ERIC Educational Resources Information Center

    Martin, John

    2010-01-01

    The cycloid has been called the Helen of Geometry, not only because of its beautiful properties but also because of the quarrels it provoked between famous mathematicians of the 17th century. This article surveys the history of the cycloid and its importance in the development of the calculus.

  19. Emergent Hyperbolic Network Geometry

    NASA Astrophysics Data System (ADS)

    Bianconi, Ginestra; Rahmede, Christoph

    2017-02-01

    A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links, triangles, tetrahedra etc.) that have a natural geometric interpretation. As such simplicial complexes are widely used in quantum gravity approaches that involve a discretization of spacetime. Here, by extending our knowledge of growing complex networks to growing simplicial complexes we investigate the nature of the emergent geometry of complex networks and explore whether this geometry is hyperbolic. Specifically we show that an hyperbolic network geometry emerges spontaneously from models of growing simplicial complexes that are purely combinatorial. The statistical and geometrical properties of the growing simplicial complexes strongly depend on their dimensionality and display the major universal properties of real complex networks (scale-free degree distribution, small-world and communities) at the same time. Interestingly, when the network dynamics includes an heterogeneous fitness of the faces, the growing simplicial complex can undergo phase transitions that are reflected by relevant changes in the network geometry.

  20. Emergent Hyperbolic Network Geometry

    PubMed Central

    Bianconi, Ginestra; Rahmede, Christoph

    2017-01-01

    A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links, triangles, tetrahedra etc.) that have a natural geometric interpretation. As such simplicial complexes are widely used in quantum gravity approaches that involve a discretization of spacetime. Here, by extending our knowledge of growing complex networks to growing simplicial complexes we investigate the nature of the emergent geometry of complex networks and explore whether this geometry is hyperbolic. Specifically we show that an hyperbolic network geometry emerges spontaneously from models of growing simplicial complexes that are purely combinatorial. The statistical and geometrical properties of the growing simplicial complexes strongly depend on their dimensionality and display the major universal properties of real complex networks (scale-free degree distribution, small-world and communities) at the same time. Interestingly, when the network dynamics includes an heterogeneous fitness of the faces, the growing simplicial complex can undergo phase transitions that are reflected by relevant changes in the network geometry. PMID:28167818

  1. Gravity is Geometry.

    ERIC Educational Resources Information Center

    MacKeown, P. K.

    1984-01-01

    Clarifies two concepts of gravity--those of a fictitious force and those of how space and time may have geometry. Reviews the position of Newton's theory of gravity in the context of special relativity and considers why gravity (as distinct from electromagnetics) lends itself to Einstein's revolutionary interpretation. (JN)

  2. Geoff Giles and Geometry

    ERIC Educational Resources Information Center

    Fielker, David

    2007-01-01

    Geoff Giles died suddenly in 2005. He was a highly original thinker in the field of geometry teaching. As early as 1964, when teaching at Strathallen School in Perth, he was writing in "MT27" about constructing tessellations by modifying the sides of triangles and (irregular) quadrilaterals to produce what he called "trisides" and "quadrisides".…

  3. Geometry of spinor regularization

    NASA Technical Reports Server (NTRS)

    Hestenes, D.; Lounesto, P.

    1983-01-01

    The Kustaanheimo theory of spinor regularization is given a new formulation in terms of geometric algebra. The Kustaanheimo-Stiefel matrix and its subsidiary condition are put in a spinor form directly related to the geometry of the orbit in physical space. A physically significant alternative to the KS subsidiary condition is discussed. Derivations are carried out without using coordinates.

  4. Making Solid Geometry Solid.

    ERIC Educational Resources Information Center

    Hartz, Viggo

    1981-01-01

    Allowing students to use a polystyrene cutter to fashion their own three-dimensional models is suggested as a means of allowing individuals to experience problems and develop ideas related to solid geometry. A list of ideas that can lead to mathematical discovery is provided. (MP)

  5. Listening to Geometry

    ERIC Educational Resources Information Center

    Cooper, Brett D.; Barger, Rita

    2009-01-01

    The many connections between music and mathematics are well known. The length of a plucked string determines its tone, the time signature of a piece of music is a ratio, and note durations are measured in fractions. One connection commonly overlooked is that between music and geometry--specifically, geometric transformations, including…

  6. GEOMETRY, TENTATIVE GUIDES.

    ERIC Educational Resources Information Center

    KLIER, KATHERINE M.

    PRESENTED IS A FUSED COURSE IN PLANE, SOLID, AND COORDINATE GEOMETRY. ELEMENTARY SET THEORY, LOGIC, AND THE PRINCIPLE OF SEPARATION PROVIDE UNIFYING THREADS THROUGHOUT THE TEXT. THE TWO CURRICULUM GUIDES HAVE BEEN PREPARED FOR USE WITH TWO DIFFERENT TEXTS. EITHER CURRICULUM GUIDE MAY BE USED DEPENDING UPON THE CHOICE OF THE TEACHER AND THE NEEDS…

  7. Core Geometry Manual.

    ERIC Educational Resources Information Center

    Hirata, Li Ann

    Core Geometry is a course offered in the Option Y sequence of the high school mathematics program described by the Hawaii State Department of Education's guidelines. The emphasis of this course is on the general awareness and use of the relationships among points, lines, and figures in planes and space. This sample course is based on the…

  8. The Geometry of Viruses.

    ERIC Educational Resources Information Center

    Case, Christine L.

    1991-01-01

    Presented is an activity in which students make models of viruses, which allows them to visualize the shape of these microorganisms. Included are some background on viruses, the biology and geometry of viruses, directions for building viruses, a comparison of cells and viruses, and questions for students. (KR)

  9. Geometry and physics

    PubMed Central

    Atiyah, Michael; Dijkgraaf, Robbert; Hitchin, Nigel

    2010-01-01

    We review the remarkably fruitful interactions between mathematics and quantum physics in the past decades, pointing out some general trends and highlighting several examples, such as the counting of curves in algebraic geometry, invariants of knots and four-dimensional topology. PMID:20123740

  10. Advanced geometries and regimes

    SciTech Connect

    Bulanov, S. S.; Bulanov, S. V.; Turchetti, G.; Limpouch, J.; Klimo, O.; Psikal, J.; Margarone, D.; Korn, G.

    2013-07-26

    We review and discuss different schemes of laser ion acceleration as well as advanced target geometries in connection with the development of the laser-driven proton source for hadron therapy of oncological diseases, which is a part of the ELIMED project.

  11. Geometry of PDE's. IV

    NASA Astrophysics Data System (ADS)

    Prástaro, Agostino

    2008-02-01

    Following our previous results on this subject [R.P. Agarwal, A. Prástaro, Geometry of PDE's. III(I): Webs on PDE's and integral bordism groups. The general theory, Adv. Math. Sci. Appl. 17 (2007) 239-266; R.P. Agarwal, A. Prástaro, Geometry of PDE's. III(II): Webs on PDE's and integral bordism groups. Applications to Riemannian geometry PDE's, Adv. Math. Sci. Appl. 17 (2007) 267-285; A. Prástaro, Geometry of PDE's and Mechanics, World Scientific, Singapore, 1996; A. Prástaro, Quantum and integral (co)bordism in partial differential equations, Acta Appl. Math. (5) (3) (1998) 243-302; A. Prástaro, (Co)bordism groups in PDE's, Acta Appl. Math. 59 (2) (1999) 111-201; A. Prástaro, Quantized Partial Differential Equations, World Scientific Publishing Co, Singapore, 2004, 500 pp.; A. Prástaro, Geometry of PDE's. I: Integral bordism groups in PDE's, J. Math. Anal. Appl. 319 (2006) 547-566; A. Prástaro, Geometry of PDE's. II: Variational PDE's and integral bordism groups, J. Math. Anal. Appl. 321 (2006) 930-948; A. Prástaro, Th.M. Rassias, Ulam stability in geometry of PDE's, Nonlinear Funct. Anal. Appl. 8 (2) (2003) 259-278; I. Stakgold, Boundary Value Problems of Mathematical Physics, I, The MacMillan Company, New York, 1967; I. Stakgold, Boundary Value Problems of Mathematical Physics, II, Collier-MacMillan, Canada, Ltd, Toronto, Ontario, 1968], integral bordism groups of the Navier-Stokes equation are calculated for smooth, singular and weak solutions, respectively. Then a characterization of global solutions is made on this ground. Enough conditions to assure existence of global smooth solutions are given and related to nullity of integral characteristic numbers of the boundaries. Stability of global solutions are related to some characteristic numbers of the space-like Cauchy dataE Global solutions of variational problems constrained by (NS) are classified by means of suitable integral bordism groups too.

  12. Cylindrical geometry hall thruster

    DOEpatents

    Raitses, Yevgeny; Fisch, Nathaniel J.

    2002-01-01

    An apparatus and method for thrusting plasma, utilizing a Hall thruster with a cylindrical geometry, wherein ions are accelerated in substantially the axial direction. The apparatus is suitable for operation at low power. It employs small size thruster components, including a ceramic channel, with the center pole piece of the conventional annular design thruster eliminated or greatly reduced. Efficient operation is accomplished through magnetic fields with a substantial radial component. The propellant gas is ionized at an optimal location in the thruster. A further improvement is accomplished by segmented electrodes, which produce localized voltage drops within the thruster at optimally prescribed locations. The apparatus differs from a conventional Hall thruster, which has an annular geometry, not well suited to scaling to small size, because the small size for an annular design has a great deal of surface area relative to the volume.

  13. Geometry of thermodynamic control.

    PubMed

    Zulkowski, Patrick R; Sivak, David A; Crooks, Gavin E; DeWeese, Michael R

    2012-10-01

    A deeper understanding of nonequilibrium phenomena is needed to reveal the principles governing natural and synthetic molecular machines. Recent work has shown that when a thermodynamic system is driven from equilibrium then, in the linear response regime, the space of controllable parameters has a Riemannian geometry induced by a generalized friction tensor. We exploit this geometric insight to construct closed-form expressions for minimal-dissipation protocols for a particle diffusing in a one-dimensional harmonic potential, where the spring constant, inverse temperature, and trap location are adjusted simultaneously. These optimal protocols are geodesics on the Riemannian manifold and reveal that this simple model has a surprisingly rich geometry. We test these optimal protocols via a numerical implementation of the Fokker-Planck equation and demonstrate that the friction tensor arises naturally from a first-order expansion in temporal derivatives of the control parameters, without appealing directly to linear response theory.

  14. Freezing in confined geometries

    NASA Technical Reports Server (NTRS)

    Sokol, P. E.; Ma, W. J.; Herwig, K. W.; Snow, W. M.; Wang, Y.; Koplik, Joel; Banavar, Jayanth R.

    1992-01-01

    Results of detailed structural studies, using elastic neutron scattering, of the freezing of liquid O2 and D2 in porous vycor glass, are presented. The experimental studies have been complemented by computer simulations of the dynamics of freezing of a Lennard-Jones liquid in narrow channels bounded by molecular walls. Results point to a new simple physical interpretation of freezing in confined geometries.

  15. E 8 geometry

    NASA Astrophysics Data System (ADS)

    Cederwall, Martin; Rosabal, J. A.

    2015-07-01

    We investigate exceptional generalised diffeomorphisms based on E 8(8) in a geometric setting. The transformations include gauge transformations for the dual gravity field. The surprising key result, which allows for a development of a tensor formalism, is that it is possible to define field-dependent transformations containing connection, which are covariant. We solve for the spin connection and construct a curvature tensor. A geometry for the Ehlers symmetry SL( n + 1) is sketched. Some related issues are discussed.

  16. Poisson-Riemannian geometry

    NASA Astrophysics Data System (ADS)

    Beggs, Edwin J.; Majid, Shahn

    2017-04-01

    We study noncommutative bundles and Riemannian geometry at the semiclassical level of first order in a deformation parameter λ, using a functorial approach. This leads us to field equations of 'Poisson-Riemannian geometry' between the classical metric, the Poisson bracket and a certain Poisson-compatible connection needed as initial data for the quantisation of the differential structure. We use such data to define a functor Q to O(λ2) from the monoidal category of all classical vector bundles equipped with connections to the monoidal category of bimodules equipped with bimodule connections over the quantised algebra. This is used to 'semiquantise' the wedge product of the exterior algebra and in the Riemannian case, the metric and the Levi-Civita connection in the sense of constructing a noncommutative geometry to O(λ2) . We solve our field equations for the Schwarzschild black-hole metric under the assumption of spherical symmetry and classical dimension, finding a unique solution and the necessity of nonassociativity at order λ2, which is similar to previous results for quantum groups. The paper also includes a nonassociative hyperboloid, nonassociative fuzzy sphere and our previously algebraic bicrossproduct model.

  17. Integral geometry and holography

    DOE PAGES

    Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; ...

    2015-10-27

    We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS3/CFT2 correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulkmore » curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS3 whose kinematic space is two-dimensional de Sitter space.« less

  18. Emergent Complex Network Geometry

    PubMed Central

    Wu, Zhihao; Menichetti, Giulia; Rahmede, Christoph; Bianconi, Ginestra

    2015-01-01

    Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant for routing problems, inference and data mining. In real growing networks, topological, structural and geometrical properties emerge spontaneously from their dynamical rules. Nevertheless we still miss a model in which networks develop an emergent complex geometry. Here we show that a single two parameter network model, the growing geometrical network, can generate complex network geometries with non-trivial distribution of curvatures, combining exponential growth and small-world properties with finite spectral dimensionality. In one limit, the non-equilibrium dynamical rules of these networks can generate scale-free networks with clustering and communities, in another limit planar random geometries with non-trivial modularity. Finally we find that these properties of the geometrical growing networks are present in a large set of real networks describing biological, social and technological systems. PMID:25985280

  19. Integral geometry and holography

    SciTech Connect

    Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; Sully, James

    2015-10-27

    We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS3/CFT2 correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS3 whose kinematic space is two-dimensional de Sitter space.

  20. Noncommutative geometry and arithmetics

    NASA Astrophysics Data System (ADS)

    Almeida, P.

    2009-09-01

    We intend to illustrate how the methods of noncommutative geometry are currently used to tackle problems in class field theory. Noncommutative geometry enables one to think geometrically in situations in which the classical notion of space formed of points is no longer adequate, and thus a “noncommutative space” is needed; a full account of this approach is given in [3] by its main contributor, Alain Connes. The class field theory, i.e., number theory within the realm of Galois theory, is undoubtedly one of the main achievements in arithmetics, leading to an important algebraic machinery; for a modern overview, see [23]. The relationship between noncommutative geometry and number theory is one of the many themes treated in [22, 7-9, 11], a small part of which we will try to put in a more down-to-earth perspective, illustrating through an example what should be called an “application of physics to mathematics,” and our only purpose is to introduce nonspecialists to this beautiful area.

  1. Diffusion in quantum geometry

    NASA Astrophysics Data System (ADS)

    Calcagni, Gianluca

    2012-08-01

    The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is controlled by a multiscale fractional diffusion equation, and physically interpreted as a composite stochastic process. The simplest example is a fractional telegraph process, describing quantum spacetimes with a spectral dimension equal to 2 in the ultraviolet and monotonically rising to 4 towards the infrared. The general profile of the spectral dimension of the recently introduced multifractional spaces is constructed for the first time.

  2. Geometrie verstehen: statisch - kinematisch

    NASA Astrophysics Data System (ADS)

    Kroll, Ekkehard

    Dem Allgemeinen steht begrifflich das Besondere gegenüber. In diesem Sinne sind allgemeine Überlegungen zum Verstehen von Mathematik zu ergänzen durch Untersuchungen hinsichtlich des Verstehens der einzelnen mathematischen Disziplinen, insbesondere der Geometrie. Hier haben viele Schülerinnen und Schüler Probleme. Diese rühren hauptsächlich daher, dass eine fertige geometrische Konstruktion in ihrer statischen Präsentation auf Papier nicht mehr die einzelnen Konstruktionsschritte erkennen lässt; zum Nachvollzug müssen sie daher ergänzend in einer Konstruktionsbeschreibung festgehalten werden.

  3. Graded geometry and Poisson reduction

    SciTech Connect

    Cattaneo, A. S.; Zambon, M.

    2009-02-02

    The main result extends the Marsden-Ratiu reduction theorem in Poisson geometry, and is proven by means of graded geometry. In this note we provide the background material about graded geometry necessary for the proof. Further, we provide an alternative algebraic proof for the main result.

  4. Computer-Aided Geometry Modeling

    NASA Technical Reports Server (NTRS)

    Shoosmith, J. N. (Compiler); Fulton, R. E. (Compiler)

    1984-01-01

    Techniques in computer-aided geometry modeling and their application are addressed. Mathematical modeling, solid geometry models, management of geometric data, development of geometry standards, and interactive and graphic procedures are discussed. The applications include aeronautical and aerospace structures design, fluid flow modeling, and gas turbine design.

  5. Teaching of Geometry in Bulgaria

    ERIC Educational Resources Information Center

    Bankov, Kiril

    2013-01-01

    Geometry plays an important role in the school mathematics curriculum all around the world. Teaching of geometry varies a lot (Hoyls, Foxman, & Kuchemann, 2001). Many countries revise the objectives, the content, and the approaches to the geometry in school. Studies of the processes show that there are not common trends of these changes…

  6. Core geometry in perspective

    PubMed Central

    Dillon, Moira R.; Spelke, Elizabeth S.

    2015-01-01

    Research on animals, infants, children, and adults provides evidence that distinct cognitive systems underlie navigation and object recognition. Here we examine whether and how these systems interact when children interpret 2D edge-based perspectival line drawings of scenes and objects. Such drawings serve as symbols early in development, and they preserve scene and object geometry from canonical points of view. Young children show limits when using geometry both in non-symbolic tasks and in symbolic map tasks that present 3D contexts from unusual, unfamiliar points of view. When presented with the familiar viewpoints in perspectival line drawings, however, do children engage more integrated geometric representations? In three experiments, children successfully interpreted line drawings with respect to their depicted scene or object. Nevertheless, children recruited distinct processes when navigating based on the information in these drawings, and these processes depended on the context in which the drawings were presented. These results suggest that children are flexible but limited in using geometric information to form integrated representations of scenes and objects, even when interpreting spatial symbols that are highly familiar and faithful renditions of the visual world. PMID:25441089

  7. Noncommutative geometry of Zitterbewegung

    NASA Astrophysics Data System (ADS)

    Eckstein, Michał; Franco, Nicolas; Miller, Tomasz

    2017-03-01

    Drawing from the advanced mathematics of noncommutative geometry, we model a "classical" Dirac fermion propagating in a curved spacetime. We demonstrate that the inherent causal structure of the model encodes the possibility of Zitterbewegung—the "trembling motion" of the fermion. We recover the well-known frequency of Zitterbewegung as the highest possible speed of change in the fermion's "internal space." Furthermore, we show that the bound does not change in the presence of an external electromagnetic field and derive its explicit analogue when the mass parameter is promoted to a Yukawa field. We explain the universal character of the model and discuss a table-top experiment in the domain of quantum simulation to test its predictions.

  8. Critique of information geometry

    SciTech Connect

    Skilling, John

    2014-12-05

    As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to destination p. Because the only compatible connective H is from≠to asymmetric, H(p;q)≠H(q;p), there can be no compatible geometrical distance (which would necessarily be from=to symmetric). Hence there is no distance relationship compatible with the structure of probability theory. Metrics g and densities sqrt(det(g)) interpreted as prior probabilities follow from the definition of distance, and must fail likewise. Various metrics and corresponding priors have been proposed, Fisher's being the most popular, but all must behave unacceptably. This is illustrated with simple counter-examples.

  9. Magnetism in curved geometries

    NASA Astrophysics Data System (ADS)

    Streubel, Robert; Fischer, Peter; Kronast, Florian; Kravchuk, Volodymyr P.; Sheka, Denis D.; Gaididei, Yuri; Schmidt, Oliver G.; Makarov, Denys

    2016-09-01

    Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisymmetric exchange, i.e. Dzyaloshinskii-Moriya-like interaction. As a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topologically induced magnetization patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered physical properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addition to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. These recent developments ranging from theoretical predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomography approaches are in the focus of this review.

  10. Magnetism in curved geometries

    SciTech Connect

    Streubel, Robert; Fischer, Peter; Kronast, Florian; Kravchuk, Volodymyr P.; Sheka, Denis D.; Gaididei, Yuri; Schmidt, Oliver G.; Makarov, Denys

    2016-08-17

    Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisymmetric exchange, i.e. Dzyaloshinskii–Moriya-like interaction. As a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topologically induced magnetization patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered physical properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addition to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. Finally, these recent developments ranging from theoretical predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomography approaches are in the focus of this review.

  11. Magnetism in curved geometries

    DOE PAGES

    Streubel, Robert; Fischer, Peter; Kronast, Florian; ...

    2016-08-17

    Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisymmetric exchange, i.e. Dzyaloshinskii–Moriya-like interaction. Asmore » a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topologically induced magnetization patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered physical properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addition to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. Finally, these recent developments ranging from theoretical predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomography approaches are in the focus of this review.« less

  12. Generalized Kähler Geometry

    NASA Astrophysics Data System (ADS)

    Gualtieri, Marco

    2014-10-01

    Generalized Kähler geometry is the natural analogue of Kähler geometry, in the context of generalized complex geometry. Just as we may require a complex structure to be compatible with a Riemannian metric in a way which gives rise to a symplectic form, we may require a generalized complex structure to be compatible with a metric so that it defines a second generalized complex structure. We prove that generalized Kähler geometry is equivalent to the bi-Hermitian geometry on the target of a 2-dimensional sigma model with (2, 2) supersymmetry. We also prove the existence of natural holomorphic Courant algebroids for each of the underlying complex structures, and that these split into a sum of transverse holomorphic Dirac structures. Finally, we explore the analogy between pre-quantum line bundles and gerbes in the context of generalized Kähler geometry.

  13. Planetary Image Geometry Library

    NASA Technical Reports Server (NTRS)

    Deen, Robert C.; Pariser, Oleg

    2010-01-01

    The Planetary Image Geometry (PIG) library is a multi-mission library used for projecting images (EDRs, or Experiment Data Records) and managing their geometry for in-situ missions. A collection of models describes cameras and their articulation, allowing application programs such as mosaickers, terrain generators, and pointing correction tools to be written in a multi-mission manner, without any knowledge of parameters specific to the supported missions. Camera model objects allow transformation of image coordinates to and from view vectors in XYZ space. Pointing models, specific to each mission, describe how to orient the camera models based on telemetry or other information. Surface models describe the surface in general terms. Coordinate system objects manage the various coordinate systems involved in most missions. File objects manage access to metadata (labels, including telemetry information) in the input EDRs and RDRs (Reduced Data Records). Label models manage metadata information in output files. Site objects keep track of different locations where the spacecraft might be at a given time. Radiometry models allow correction of radiometry for an image. Mission objects contain basic mission parameters. Pointing adjustment ("nav") files allow pointing to be corrected. The object-oriented structure (C++) makes it easy to subclass just the pieces of the library that are truly mission-specific. Typically, this involves just the pointing model and coordinate systems, and parts of the file model. Once the library was developed (initially for Mars Polar Lander, MPL), adding new missions ranged from two days to a few months, resulting in significant cost savings as compared to rewriting all the application programs for each mission. Currently supported missions include Mars Pathfinder (MPF), MPL, Mars Exploration Rover (MER), Phoenix, and Mars Science Lab (MSL). Applications based on this library create the majority of operational image RDRs for those missions. A

  14. Thermodynamics of Asymptotically Conical Geometries.

    PubMed

    Cvetič, Mirjam; Gibbons, Gary W; Saleem, Zain H

    2015-06-12

    We study the thermodynamical properties of a class of asymptotically conical geometries known as "subtracted geometries." We derive the mass and angular momentum from the regulated Komar integral and the Hawking-Horowitz prescription and show that they are equivalent. By deriving the asymptotic charges, we show that the Smarr formula and the first law of thermodynamics hold. We also propose an analog of Christodulou-Ruffini inequality. The analysis can be generalized to other asymptotically conical geometries.

  15. Investigating Fractal Geometry Using LOGO.

    ERIC Educational Resources Information Center

    Thomas, David A.

    1989-01-01

    Discusses dimensionality in Euclidean geometry. Presents methods to produce fractals using LOGO. Uses the idea of self-similarity. Included are program listings and suggested extension activities. (MVL)

  16. Geometry of blind thrusts

    SciTech Connect

    Kligfield, R.; Geiser, P.; Geiser, J.

    1985-01-01

    Blind thrusts are structures which at no time in their history broke the erosion surface and along which displacement progressively changes upwards. Faults of the stiff layer along which displacement progressively decreases to zero (tip) are one prominent type of blind thrust structure. Shortening above such tips is accommodated entirely by folding whereas shortening below the tip is partitioned between folding and faulting. For these types of faults it is possible to determine the original length of the stiff layer for balancing purposes. A systematic methodology for line length and area restoration is outlined for determining blind thrust geometry. Application of the methodology is particularly suitable for use with microcomputers. If the folded form of the cover is known along with the position of the fault and its tip, then it is possible to locate hanging and footwall cutoffs. If the fault trajectory, tip, and a single hanging wall footwall cutoff pair are known, then the folded form of the cover layer can be determined. In these constructions it is necessary to specify pin lines for balancing purposes. These pin lines may or may not have a zero displacement gradient, depending upon the amount of simple shear deformation. Examples are given from both Laramide structures of the western USA and the Appalachians.

  17. Linguistic geometry for autonomous navigation

    SciTech Connect

    Stilman, B.

    1995-09-01

    To discover the inner properties of human expert heuristics, which were successful in a certain class of complex control systems, we develop a formal theory, the Linguistic Geometry. This paper reports two examples of application of Linguistic Geometry to autonomous navigation of aerospace vehicles that demonstrate dramatic search reduction.

  18. GPS: Geometry, Probability, and Statistics

    ERIC Educational Resources Information Center

    Field, Mike

    2012-01-01

    It might be said that for most occupations there is now less of a need for mathematics than there was say fifty years ago. But, the author argues, geometry, probability, and statistics constitute essential knowledge for everyone. Maybe not the geometry of Euclid, but certainly geometrical ways of thinking that might enable us to describe the world…

  19. CATIA-GDML geometry builder

    NASA Astrophysics Data System (ADS)

    Belogurov, S.; Berchun, Yu; Chernogorov, A.; Malzacher, P.; Ovcharenko, E.; Semennikov, A.

    2011-12-01

    Due to conceptual difference between geometry descriptions in Computer-Aided Design (CAD) systems and particle transport Monte Carlo (MC) codes direct conversion of detector geometry in either direction is not feasible. An original set of tools has been developed for building a GEANT4/ROOT compatible geometry in the CATIA CAD system and exchanging it with mentioned MC packages using GDML file format. A Special structure of a CATIA product tree, a wide range of primitives, different types of multiple volume instantiation, and supporting macros have been implemented.

  20. An improved combinatorial geometry model for arbitrary geometry in DSMC

    NASA Astrophysics Data System (ADS)

    Kargaran, H.; Minuchehr, A.; Zolfaghari, A.

    2017-03-01

    This paper focuses on a new direct simulation Monte Carlo (DSMC) code based on combinatorial geometry (CG) for simulation of any rarefied gas flow. The developed code, called DgSMC-A, has been supplied with an improved CG modeling able to significantly optimize the particle-tracking process, resulting in a highly reduced runtime compared to the conventional codes. The improved algorithm inserts a grid over the geometry and saves those grid elements containing some part of the geometry border. Since only a small part of a grid is engaged with the geometry border, significant time can be saved using the proposed algorithm. Embedding the modified algorithm in the DgSMC-A resulted in a fast, robust and self-governing code needless to any mesh generator. The code completely handles complex geometries created with first-and second-order surfaces. In addition, we developed a new surface area calculator in the CG methodology for complex geometries based on the Monte Carlo method with acceptable accuracy. Several well-known test cases are examined to indicate the code ability to deal with a wide range of realistic problems. Results are also found to be in good agreement with references and experimental data.

  1. Emergent geometry from quantized spacetime

    SciTech Connect

    Yang, Hyun Seok; Sivakumar, M.

    2010-08-15

    We examine the picture of emergent geometry arising from a mass-deformed matrix model. Because of the mass deformation, a vacuum geometry turns out to be a constant curvature spacetime such as d-dimensional sphere and (anti-)de Sitter spaces. We show that the mass-deformed matrix model giving rise to the constant curvature spacetime can be derived from the d-dimensional Snyder algebra. The emergent geometry beautifully confirms all the rationale inferred from the algebraic point of view that the d-dimensional Snyder algebra is equivalent to the Lorentz algebra in (d+1)-dimensional flat spacetime. For example, a vacuum geometry of the mass-deformed matrix model is completely described by a G-invariant metric of coset manifolds G/H defined by the Snyder algebra. We also discuss a nonlinear deformation of the Snyder algebra.

  2. The Common Geometry Module (CGM).

    SciTech Connect

    Tautges, Timothy James

    2004-12-01

    The Common Geometry Module (CGM) is a code library which provides geometry functionality used for mesh generation and other applications. This functionality includes that commonly found in solid modeling engines, like geometry creation, query and modification; CGM also includes capabilities not commonly found in solid modeling engines, like geometry decomposition tools and support for shared material interfaces. CGM is built upon the ACIS solid modeling engine, but also includes geometry capability developed beside and on top of ACIS. CGM can be used as-is to provide geometry functionality for codes needing this capability. However, CGM can also be extended using derived classes in C++, allowing the geometric model to serve as the basis for other applications, for example mesh generation. CGM is supported on Sun Solaris, SGI, HP, IBM, DEC, Linux and Windows NT platforms. CGM also includes support for loading ACIS models on parallel computers, using MPI-based communication. Future plans for CGM are to port it to different solid modeling engines, including Pro/Engineer or SolidWorks. CGM is being released into the public domain under an LGPL license; the ACIS-based engine is available to ACIS licensees on request.

  3. Electrodynamics and Spacetime Geometry: Foundations

    NASA Astrophysics Data System (ADS)

    Cabral, Francisco; Lobo, Francisco S. N.

    2016-11-01

    We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.

  4. Conventionalism and integrable Weyl geometry

    NASA Astrophysics Data System (ADS)

    Pucheu, M. L.

    2015-03-01

    Since the appearance of Einstein's general relativity, gravitation has been associated to the space-time curvature. This theory introduced a geometrodynamic language which became a convenient tool to predict matter behaviour. However, the properties of space-time itself cannot be measurable by experiments. Taking Poincaré idea that the geometry of space-time is merely a convention, we show that the general theory of relativity can be completely reformulated in a more general setting, a generalization of Riemannian geometry, namely, the Weyl integrable geometry. The choice of this new mathematical language implies, among other things, that the path of particles and light rays should now correspond to Weylian geodesies. Such modification in the dynamic of bodies brings a new perception of physical phenomena that we will explore.

  5. Quantum geometry and gravitational entropy

    SciTech Connect

    Simon, Joan; Balasubramanian, Vijay; Czech, Bart Iomiej; Larjo, Klaus; Marolf, Donald; Simon, Joan

    2007-05-29

    Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S5 universes. In this sector we devise a"coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.

  6. Electrodynamics and Spacetime Geometry: Foundations

    NASA Astrophysics Data System (ADS)

    Cabral, Francisco; Lobo, Francisco S. N.

    2017-02-01

    We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.

  7. Geometry, topology, and string theory

    SciTech Connect

    Varadarajan, Uday

    2003-01-01

    A variety of scenarios are considered which shed light upon the uses and limitations of classical geometric and topological notions in string theory. The primary focus is on situations in which D-brane or string probes of a given classical space-time see the geometry quite differently than one might naively expect. In particular, situations in which extra dimensions, non-commutative geometries as well as other non-local structures emerge are explored in detail. Further, a preliminary exploration of such issues in Lorentzian space-times with non-trivial causal structures within string theory is initiated.

  8. Geometry of generalized depolarizing channels

    SciTech Connect

    Burrell, Christian K.

    2009-10-15

    A generalized depolarizing channel acts on an N-dimensional quantum system to compress the 'Bloch ball' in N{sup 2}-1 directions; it has a corresponding compression vector. We investigate the geometry of these compression vectors and prove a conjecture of Dixit and Sudarshan [Phys. Rev. A 78, 032308 (2008)], namely, that when N=2{sup d} (i.e., the system consists of d qubits), and we work in the Pauli basis then the set of all compression vectors forms a simplex. We extend this result by investigating the geometry in other bases; in particular we find precisely when the set of all compression vectors forms a simplex.

  9. Teaching Activity-Based Taxicab Geometry

    ERIC Educational Resources Information Center

    Ada, Tuba

    2013-01-01

    This study aimed on the process of teaching taxicab geometry, a non-Euclidean geometry that is easy to understand and similar to Euclidean geometry with its axiomatic structure. In this regard, several teaching activities were designed such as measuring taxicab distance, defining a taxicab circle, finding a geometric locus in taxicab geometry, and…

  10. Exploring Fractal Geometry with Children.

    ERIC Educational Resources Information Center

    Vacc, Nancy Nesbitt

    1999-01-01

    Heightens the awareness of elementary school teachers, teacher educators, and teacher-education researchers of possible applications of fractal geometry with children and, subsequently, initiates discussion about the appropriateness of including this new mathematics in the elementary curriculum. Presents activities for exploring children's…

  11. General Relativity: Geometry Meets Physics

    ERIC Educational Resources Information Center

    Thomsen, Dietrick E.

    1975-01-01

    Observing the relationship of general relativity and the geometry of space-time, the author questions whether the rest of physics has geometrical explanations. As a partial answer he discusses current research on subatomic particles employing geometric transformations, and cites the existence of geometrical definitions of physical quantities such…

  12. Improving Student Reasoning in Geometry

    ERIC Educational Resources Information Center

    Wong, Bobson; Bukalov, Larisa

    2013-01-01

    In their years of teaching geometry, Wong and Bukalov realized that the greatest challenge has been getting students to improve their reasoning. Many students have difficulty writing formal proofs--a task that requires a good deal of reasoning. Wong and Bukalov reasoned that the solution was to divide the lessons into parallel tasks, allowing…

  13. Generative CAI in Analytical Geometry.

    ERIC Educational Resources Information Center

    Uttal, William R.; And Others

    A generative computer-assisted instruction system is being developed to tutor students in analytical geometry. The basis of this development is the thesis that a generative teaching system can be developed by establishing and then stimulating a simplified, explicit model of the human tutor. The goal attempted is that of a computer environment…

  14. Analogical Reasoning in Geometry Education

    ERIC Educational Resources Information Center

    Magdas, Ioana

    2015-01-01

    The analogical reasoning isn't used only in mathematics but also in everyday life. In this article we approach the analogical reasoning in Geometry Education. The novelty of this article is a classification of geometrical analogies by reasoning type and their exemplification. Our classification includes: analogies for understanding and setting a…

  15. 3DHZETRN: Inhomogeneous Geometry Issues

    NASA Technical Reports Server (NTRS)

    Wilson, John W.; Slaba, Tony C.; Badavi, Francis F.

    2017-01-01

    Historical methods for assessing radiation exposure inside complicated geometries for space applications were limited by computational constraints and lack of knowledge associated with nuclear processes occurring over a broad range of particles and energies. Various methods were developed and utilized to simplify geometric representations and enable coupling with simplified but efficient particle transport codes. Recent transport code development efforts, leading to 3DHZETRN, now enable such approximate methods to be carefully assessed to determine if past exposure analyses and validation efforts based on those approximate methods need to be revisited. In this work, historical methods of representing inhomogeneous spacecraft geometry for radiation protection analysis are first reviewed. Two inhomogeneous geometry cases, previously studied with 3DHZETRN and Monte Carlo codes, are considered with various levels of geometric approximation. Fluence, dose, and dose equivalent values are computed in all cases and compared. It is found that although these historical geometry approximations can induce large errors in neutron fluences up to 100 MeV, errors on dose and dose equivalent are modest (<10%) for the cases studied here.

  16. Teaching Geometry According to Euclid.

    ERIC Educational Resources Information Center

    Hartshorne, Robin

    2000-01-01

    This essay contains some reflections and questions arising from encounters with the text of Euclid's Elements. The reflections arise out of the teaching of a course in Euclidean and non-Euclidean geometry to undergraduates. It is concluded that teachers of such courses should read Euclid and ask questions, then teach a course on Euclid and later…

  17. Math Sense: Algebra and Geometry.

    ERIC Educational Resources Information Center

    Howett, Jerry

    This book is designed to help students gain the range of math skills they need to succeed in life, work, and on standardized tests; overcome math anxiety; discover math as interesting and purposeful; and develop good number sense. Topics covered in this book include algebra and geometry. Lessons are organized around four strands: (1) skill lessons…

  18. Adaptive Geometry Shader Tessellation for Massive Geometry Display

    DTIC Science & Technology

    2015-03-01

    necessary to prepare complex models for use in analysis and visualization tasks. We investigated several avenues for high-speed visualization and worked to...geometry, visualization 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18. NUMBER OF PAGES 22 19a. NAME OF RESPONSIBLE...Introduction and Background 1 2. Approach 2 3. Speed Improvements in the Visual Simulation Laboratory 2 4. Ray Tracing 4 5. Sharing Display Technologies

  19. Geometry-invariant resonant cavities

    PubMed Central

    Liberal, I.; Mahmoud, A. M.; Engheta, N.

    2016-01-01

    Resonant cavities are one of the basic building blocks in various disciplines of science and technology, with numerous applications ranging from abstract theoretical modelling to everyday life devices. The eigenfrequencies of conventional cavities are a function of their geometry, and, thus, the size and shape of a resonant cavity is selected to operate at a specific frequency. Here we demonstrate theoretically the existence of geometry-invariant resonant cavities, that is, resonators whose eigenfrequencies are invariant with respect to geometrical deformations of their external boundaries. This effect is obtained by exploiting the unusual properties of zero-index metamaterials, such as epsilon-near-zero media, which enable decoupling of the temporal and spatial field variations in the lossless limit. This new class of resonators may inspire alternative design concepts, and it might lead to the first generation of deformable resonant devices. PMID:27010103

  20. Hyperbolic geometry of cosmological attractors

    NASA Astrophysics Data System (ADS)

    Carrasco, John Joseph M.; Kallosh, Renata; Linde, Andrei; Roest, Diederik

    2015-08-01

    Cosmological α attractors give a natural explanation for the spectral index ns of inflation as measured by Planck while predicting a range for the tensor-to-scalar ratio r , consistent with all observations, to be measured more precisely in future B-mode experiments. We highlight the crucial role of the hyperbolic geometry of the Poincaré disk or half plane in the supergravity construction. These geometries are isometric under Möbius transformations, which include the shift symmetry of the inflaton field. We introduce a new Kähler potential frame that explicitly preserves this symmetry, enabling the inflaton to be light. Moreover, we include higher-order curvature deformations, which can stabilize a direction orthogonal to the inflationary trajectory. We illustrate this new framework by stabilizing the single superfield α attractors.

  1. Experimental Probes of Spacetime Geometries

    SciTech Connect

    Hewett, JoAnne

    2009-07-10

    A novel approach which exploits the geometry of extra spacetime dimensions has been recently proposed as a means to resolving the hierarchy problem, i.e., the large energy gap that separates the electroweak scale and the scale where gravity becomes strong. I will describe two models of this type: one where the apparent hierarchy is generated by a large volume for the extra dimensions, and a second where the observed hierarchy is created by an exponential warp factor which arises from a non-factorizable geometry. Both scenarios have concrete and distinctive phenomenological tests at the TeV scale. I will describe the classes of low-energy and collider signatures for both models, summarize the present constraints from experiment, and examine the ability of future accelerators to probe their parameter space.

  2. Geometry-invariant resonant cavities

    NASA Astrophysics Data System (ADS)

    Liberal, I.; Mahmoud, A. M.; Engheta, N.

    2016-03-01

    Resonant cavities are one of the basic building blocks in various disciplines of science and technology, with numerous applications ranging from abstract theoretical modelling to everyday life devices. The eigenfrequencies of conventional cavities are a function of their geometry, and, thus, the size and shape of a resonant cavity is selected to operate at a specific frequency. Here we demonstrate theoretically the existence of geometry-invariant resonant cavities, that is, resonators whose eigenfrequencies are invariant with respect to geometrical deformations of their external boundaries. This effect is obtained by exploiting the unusual properties of zero-index metamaterials, such as epsilon-near-zero media, which enable decoupling of the temporal and spatial field variations in the lossless limit. This new class of resonators may inspire alternative design concepts, and it might lead to the first generation of deformable resonant devices.

  3. Information geometry of Boltzmann machines.

    PubMed

    Amari, S; Kurata, K; Nagaoka, H

    1992-01-01

    A Boltzmann machine is a network of stochastic neurons. The set of all the Boltzmann machines with a fixed topology forms a geometric manifold of high dimension, where modifiable synaptic weights of connections play the role of a coordinate system to specify networks. A learning trajectory, for example, is a curve in this manifold. It is important to study the geometry of the neural manifold, rather than the behavior of a single network, in order to know the capabilities and limitations of neural networks of a fixed topology. Using the new theory of information geometry, a natural invariant Riemannian metric and a dual pair of affine connections on the Boltzmann neural network manifold are established. The meaning of geometrical structures is elucidated from the stochastic and the statistical point of view. This leads to a natural modification of the Boltzmann machine learning rule.

  4. Dynamics, Spectral Geometry and Topology

    SciTech Connect

    Burghelea, Dan

    2011-02-10

    The paper is an informal report on joint work with Stefan Haller on Dynamics in relation with Topology and Spectral Geometry. By dynamics one means a smooth vector field on a closed smooth manifold; the elements of dynamics of concern are the rest points, instantons and closed trajectories. One discusses their counting in the case of a generic vector field which has some additional properties satisfied by a still very large class of vector fields.

  5. Core foundations of abstract geometry.

    PubMed

    Dillon, Moira R; Huang, Yi; Spelke, Elizabeth S

    2013-08-27

    Human adults from diverse cultures share intuitions about the points, lines, and figures of Euclidean geometry. Do children develop these intuitions by drawing on phylogenetically ancient and developmentally precocious geometric representations that guide their navigation and their analysis of object shape? In what way might these early-arising representations support later-developing Euclidean intuitions? To approach these questions, we investigated the relations among young children's use of geometry in tasks assessing: navigation; visual form analysis; and the interpretation of symbolic, purely geometric maps. Children's navigation depended on the distance and directional relations of the surface layout and predicted their use of a symbolic map with targets designated by surface distances. In contrast, children's analysis of visual forms depended on the size-invariant shape relations of objects and predicted their use of the same map but with targets designated by corner angles. Even though the two map tasks used identical instructions and map displays, children's performance on these tasks showed no evidence of integrated representations of distance and angle. Instead, young children flexibly recruited geometric representations of either navigable layouts or objects to interpret the same spatial symbols. These findings reveal a link between the early-arising geometric representations that humans share with diverse animals and the flexible geometric intuitions that give rise to human knowledge at its highest reaches. Although young children do not appear to integrate core geometric representations, children's use of the abstract geometry in spatial symbols such as maps may provide the earliest clues to the later construction of Euclidean geometry.

  6. Hyperbolic geometry of complex networks.

    PubMed

    Krioukov, Dmitri; Papadopoulos, Fragkiskos; Kitsak, Maksim; Vahdat, Amin; Boguñá, Marián

    2010-09-01

    We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong clustering in complex networks emerge naturally as simple reflections of the negative curvature and metric property of the underlying hyperbolic geometry. Conversely, we show that if a network has some metric structure, and if the network degree distribution is heterogeneous, then the network has an effective hyperbolic geometry underneath. We then establish a mapping between our geometric framework and statistical mechanics of complex networks. This mapping interprets edges in a network as noninteracting fermions whose energies are hyperbolic distances between nodes, while the auxiliary fields coupled to edges are linear functions of these energies or distances. The geometric network ensemble subsumes the standard configuration model and classical random graphs as two limiting cases with degenerate geometric structures. Finally, we show that targeted transport processes without global topology knowledge, made possible by our geometric framework, are maximally efficient, according to all efficiency measures, in networks with strongest heterogeneity and clustering, and that this efficiency is remarkably robust with respect to even catastrophic disturbances and damages to the network structure.

  7. Network geometry with flavor: From complexity to quantum geometry.

    PubMed

    Bianconi, Ginestra; Rahmede, Christoph

    2016-03-01

    Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d-dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s=-1,0,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d. In d=1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d>1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t. Interestingly the NGF remains fully classical but its

  8. Network geometry with flavor: From complexity to quantum geometry

    NASA Astrophysics Data System (ADS)

    Bianconi, Ginestra; Rahmede, Christoph

    2016-03-01

    Network geometry is attracting increasing attention because it has a wide range of applications, ranging from data mining to routing protocols in the Internet. At the same time advances in the understanding of the geometrical properties of networks are essential for further progress in quantum gravity. In network geometry, simplicial complexes describing the interaction between two or more nodes play a special role. In fact these structures can be used to discretize a geometrical d -dimensional space, and for this reason they have already been widely used in quantum gravity. Here we introduce the network geometry with flavor s =-1 ,0 ,1 (NGF) describing simplicial complexes defined in arbitrary dimension d and evolving by a nonequilibrium dynamics. The NGF can generate discrete geometries of different natures, ranging from chains and higher-dimensional manifolds to scale-free networks with small-world properties, scale-free degree distribution, and nontrivial community structure. The NGF admits as limiting cases both the Bianconi-Barabási models for complex networks, the stochastic Apollonian network, and the recently introduced model for complex quantum network manifolds. The thermodynamic properties of NGF reveal that NGF obeys a generalized area law opening a new scenario for formulating its coarse-grained limit. The structure of NGF is strongly dependent on the dimensionality d . In d =1 NGFs grow complex networks for which the preferential attachment mechanism is necessary in order to obtain a scale-free degree distribution. Instead, for NGF with dimension d >1 it is not necessary to have an explicit preferential attachment rule to generate scale-free topologies. We also show that NGF admits a quantum mechanical description in terms of associated quantum network states. Quantum network states evolve by a Markovian dynamics and a quantum network state at time t encodes all possible NGF evolutions up to time t . Interestingly the NGF remains fully classical but

  9. The Effect of Geometry Instruction with Dynamic Geometry Software; GeoGebra on Van Hiele Geometry Understanding Levels of Students

    ERIC Educational Resources Information Center

    Kutluca, Tamer

    2013-01-01

    The aim of this study is to investigate the effect of dynamic geometry software GeoGebra on Van Hiele geometry understanding level of students at 11th grade geometry course. The study was conducted with pre and posttest control group quasi-experimental method. The sample of the study was 42 eleventh grade students studying in the spring term of…

  10. A Whirlwind Tour of Computational Geometry.

    ERIC Educational Resources Information Center

    Graham, Ron; Yao, Frances

    1990-01-01

    Described is computational geometry which used concepts and results from classical geometry, topology, combinatorics, as well as standard algorithmic techniques such as sorting and searching, graph manipulations, and linear programing. Also included are special techniques and paradigms. (KR)

  11. The fractal geometry of life.

    PubMed

    Losa, Gabriele A

    2009-01-01

    The extension of the concepts of Fractal Geometry (Mandelbrot [1983]) toward the life sciences has led to significant progress in understanding complex functional properties and architectural / morphological / structural features characterising cells and tissues during ontogenesis and both normal and pathological development processes. It has even been argued that fractal geometry could provide a coherent description of the design principles underlying living organisms (Weibel [1991]). Fractals fulfil a certain number of theoretical and methodological criteria including a high level of organization, shape irregularity, functional and morphological self-similarity, scale invariance, iterative pathways and a peculiar non-integer fractal dimension [FD]. Whereas mathematical objects are deterministic invariant or self-similar over an unlimited range of scales, biological components are statistically self-similar only within a fractal domain defined by upper and lower limits, called scaling window, in which the relationship between the scale of observation and the measured size or length of the object can be established (Losa and Nonnenmacher [1996]). Selected examples will contribute to depict complex biological shapes and structures as fractal entities, and also to show why the application of the fractal principle is valuable for measuring dimensional, geometrical and functional parameters of cells, tissues and organs occurring within the vegetal and animal realms. If the criteria for a strict description of natural fractals are met, then it follows that a Fractal Geometry of Life may be envisaged and all natural objects and biological systems exhibiting self-similar patterns and scaling properties may be considered as belonging to the new subdiscipline of "fractalomics".

  12. Cable equation for general geometry.

    PubMed

    López-Sánchez, Erick J; Romero, Juan M

    2017-02-01

    The cable equation describes the voltage in a straight cylindrical cable, and this model has been employed to model electrical potential in dendrites and axons. However, sometimes this equation might give incorrect predictions for some realistic geometries, in particular when the radius of the cable changes significantly. Cables with a nonconstant radius are important for some phenomena, for example, discrete swellings along the axons appear in neurodegenerative diseases such as Alzheimers, Parkinsons, human immunodeficiency virus associated dementia, and multiple sclerosis. In this paper, using the Frenet-Serret frame, we propose a generalized cable equation for a general cable geometry. This generalized equation depends on geometric quantities such as the curvature and torsion of the cable. We show that when the cable has a constant circular cross section, the first fundamental form of the cable can be simplified and the generalized cable equation depends on neither the curvature nor the torsion of the cable. Additionally, we find an exact solution for an ideal cable which has a particular variable circular cross section and zero curvature. For this case we show that when the cross section of the cable increases the voltage decreases. Inspired by this ideal case, we rewrite the generalized cable equation as a diffusion equation with a source term generated by the cable geometry. This source term depends on the cable cross-sectional area and its derivates. In addition, we study different cables with swelling and provide their numerical solutions. The numerical solutions show that when the cross section of the cable has abrupt changes, its voltage is smaller than the voltage in the cylindrical cable. Furthermore, these numerical solutions show that the voltage can be affected by geometrical inhomogeneities on the cable.

  13. Cable equation for general geometry

    NASA Astrophysics Data System (ADS)

    López-Sánchez, Erick J.; Romero, Juan M.

    2017-02-01

    The cable equation describes the voltage in a straight cylindrical cable, and this model has been employed to model electrical potential in dendrites and axons. However, sometimes this equation might give incorrect predictions for some realistic geometries, in particular when the radius of the cable changes significantly. Cables with a nonconstant radius are important for some phenomena, for example, discrete swellings along the axons appear in neurodegenerative diseases such as Alzheimers, Parkinsons, human immunodeficiency virus associated dementia, and multiple sclerosis. In this paper, using the Frenet-Serret frame, we propose a generalized cable equation for a general cable geometry. This generalized equation depends on geometric quantities such as the curvature and torsion of the cable. We show that when the cable has a constant circular cross section, the first fundamental form of the cable can be simplified and the generalized cable equation depends on neither the curvature nor the torsion of the cable. Additionally, we find an exact solution for an ideal cable which has a particular variable circular cross section and zero curvature. For this case we show that when the cross section of the cable increases the voltage decreases. Inspired by this ideal case, we rewrite the generalized cable equation as a diffusion equation with a source term generated by the cable geometry. This source term depends on the cable cross-sectional area and its derivates. In addition, we study different cables with swelling and provide their numerical solutions. The numerical solutions show that when the cross section of the cable has abrupt changes, its voltage is smaller than the voltage in the cylindrical cable. Furthermore, these numerical solutions show that the voltage can be affected by geometrical inhomogeneities on the cable.

  14. The Geometry of Quasar Outflows

    NASA Astrophysics Data System (ADS)

    Ganguly, Rajib

    2012-10-01

    Quasar outflows are important for understanding the accretion and growth processes of the central black hole, but also potentially play a role in feedback to the galaxy, halting star formation and infall of gas. A big uncertainty lies in the geometry and density of these outflows, especially as a function of ionization and velocity. We aim to tackle this using the archival COS M grating spectra of 266 quasars. We separate the geometry of outflows into two parts: the solid angle subtended around the black hole, and the distance of the outflow from the central engine. Large numbers of quasars with high resolution spectra are required for each aspect of this statistical investigation. First, we will determine which/how many absorption-line systems are intrinsic through both partial covering methods and statistical assessments. Second, we will consider the incidence of intrinsic absorbers as a function of quasar property {e.g., radio-loudness, SED shape, black hole mass, bolometric luminosity}. This will reveal what determines the solid angle. This can only be done at moderate redshifts where quasars with a larger range of properties are observable, and hence requires HST/COS. Third, we will use the wide range of diagnostic lines to constrain the physical conditions of the absorbers. We will target the CIII*1175 complex and apply photoionization models to constrain the densities and ionization parameters. This will provide the largest set yet of intrinsic absorbers with systematic distance constraints. In tandem with the solid angles, this work will inform models regarding the geometry of quasar outflows.

  15. Complex geometry and string theory

    NASA Astrophysics Data System (ADS)

    Morozov, A. Y.; Perelomov, A. M.

    1990-06-01

    The analytic properties of string theory are reviewed. It is demonstrated that the theory of strings is connected with contemporary fields of complex geometry. A massless classical point-like particle which moves in Minkowski space of D dimensions is considered. The formulation used to develop string theory is based on the Polyakov approach. In order to find the quantum scattering amplitude in the Polyakov approach, the functional integral over all Riemannian surfaces is calculated. The simplest case of the amplitude of vacuum-vacuum transitions Z of a closed string is considered. The description of linear bundles in the divisor terms is given.

  16. Worldsheet geometries of ambitwistor string

    NASA Astrophysics Data System (ADS)

    Ohmori, Kantaro

    2015-06-01

    Mason and Skinner proposed the ambitwistor string theory which directly reproduces the formulas for the amplitudes of massless particles proposed by Cachazo, He and Yuan. In this paper we discuss geometries of the moduli space of worldsheets associated to the bosonic or the RNS ambitwistor string. Further, we investigate the factorization properties of the amplitudes when an internal momentum is near on-shell in the abstract CFT language. Along the way, we propose the existence of the ambitwistor strings with three or four fermionic worldsheet currents.

  17. Bondi accretion in trumpet geometries

    NASA Astrophysics Data System (ADS)

    Miller, August J.; Baumgarte, Thomas W.

    2017-02-01

    The Bondi solution, which describes the radial inflow of a gas onto a non-rotating black hole, provides a powerful test for numerical relativistic codes. However, the Bondi solution is usually derived in Schwarzschild coordinates, which are not well suited for dynamical spacetime evolutions. Instead, many current numerical relativistic codes adopt moving-puncture coordinates, which render black holes in trumpet geometries. Here we transform the Bondi solution into trumpet coordinates, which result in regular expressions for the fluid flow extending into the black-hole interior. We also evolve these solutions numerically and demonstrate their usefulness for testing and calibrating numerical codes.

  18. Quanta of geometry and unification

    NASA Astrophysics Data System (ADS)

    Chamseddine, Ali H.

    2016-11-01

    This is a tribute to Abdus Salam’s memory whose insight and creative thinking set for me a role model to follow. In this contribution I show that the simple requirement of volume quantization in spacetime (with Euclidean signature) uniquely determines the geometry to be that of a noncommutative space whose finite part is based on an algebra that leads to Pati-Salam grand unified models. The Standard Model corresponds to a special case where a mathematical constraint (order one condition) is satisfied. This provides evidence that Salam was a visionary who was generations ahead of his time.

  19. Geometry: Career Related Units. Teacher's Edition.

    ERIC Educational Resources Information Center

    Pierro, Mike; And Others

    Using six geometry units as resource units, the document explores 22 math-related careers. The authors intend the document to provide senior high school students with career orientation and exploration experiences while they learn geometry skills. The units are to be considered as a part of a geometry course, not a course by themselves. The six…

  20. Preservice Primary School Teachers' Elementary Geometry Knowledge

    ERIC Educational Resources Information Center

    Marchis, Iuliana

    2012-01-01

    Geometrical notions and properties occur in real-world problems, thus Geometry has an important place in school Mathematics curricula. Primary school curricula lays the foundation of Geometry knowledge, pupils learn Geometry notions and properties by exploring their environment. Thus it is very important that primary school teachers have a good…

  1. Students' Misconceptions and Errors in Transformation Geometry

    ERIC Educational Resources Information Center

    Ada, Tuba; Kurtulus, Aytac

    2010-01-01

    This study analyses the students' performances in two-dimensional transformation geometry and explores the mistakes made by the students taking the analytic geometry course given by researchers. An examination was given to students of Education Faculties who have taken the analytic geometry course at Eskisehir Osmangazi University in Turkey. The…

  2. Teaching Geometry: An Experiential and Artistic Approach.

    ERIC Educational Resources Information Center

    Ogletree, Earl J.

    The view that geometry should be taught at every grade level is promoted. Primary and elementary school children are thought to rarely have any direct experience with geometry, except on an incidental basis. Children are supposed to be able to learn geometry rather easily, so long as the method and content are adapted to their development and…

  3. Geometry in the Early Years: A Commentary

    ERIC Educational Resources Information Center

    Dindyal, Jaguthsing

    2015-01-01

    The primary goal of this paper is to provide a commentary on the teaching and learning of geometry in the early years of schooling with the set of papers in this issue as a guiding factor. It is structured around issues about geometry education of young learners, such as: what should we teach in geometry and why; representation of geometrical…

  4. Engaging All Students with "Impossible Geometry"

    ERIC Educational Resources Information Center

    Wiest, Lynda R.; Ayebo, Abraham; Dornoo, Michael D.

    2010-01-01

    Geometry is an area in which Australian students performed particularly poorly on the 2007 Trends in International Mathematics and Science Study (TIMSS). One innovative area of recreational geometry that has rich potential to engage and challenge a wide variety of students is "impossible geometry." An impossible geometric object is a…

  5. Target Detection Using Fractal Geometry

    NASA Technical Reports Server (NTRS)

    Fuller, J. Joseph

    1991-01-01

    The concepts and theory of fractal geometry were applied to the problem of segmenting a 256 x 256 pixel image so that manmade objects could be extracted from natural backgrounds. The two most important measurements necessary to extract these manmade objects were fractal dimension and lacunarity. Provision was made to pass the manmade portion to a lookup table for subsequent identification. A computer program was written to construct cloud backgrounds of fractal dimensions which were allowed to vary between 2.2 and 2.8. Images of three model space targets were combined with these backgrounds to provide a data set for testing the validity of the approach. Once the data set was constructed, computer programs were written to extract estimates of the fractal dimension and lacunarity on 4 x 4 pixel subsets of the image. It was shown that for clouds of fractal dimension 2.7 or less, appropriate thresholding on fractal dimension and lacunarity yielded a 64 x 64 edge-detected image with all or most of the cloud background removed. These images were enhanced by an erosion and dilation to provide the final image passed to the lookup table. While the ultimate goal was to pass the final image to a neural network for identification, this work shows the applicability of fractal geometry to the problems of image segmentation, edge detection and separating a target of interest from a natural background.

  6. Fuzzy Logic for Incidence Geometry.

    PubMed

    Tserkovny, Alex

    The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly used names of landmarks, water areas, and so forth. Unlike single points that are given in Cartesian coordinates, these geographic entities are extended in space and often loosely defined, but people easily perform spatial reasoning with extended geographic objects "as if they were points." Unfortunately, up to date, geographic information systems (GIS) miss the capability of geometric reasoning with extended objects. The aim of the paper is to present a mathematical apparatus for approximate geometric reasoning with extended objects that is usable in GIS. In the paper we discuss the fuzzy logic (Aliev and Tserkovny, 2011) as a reasoning system for geometry of extended objects, as well as a basis for fuzzification of the axioms of incidence geometry. The same fuzzy logic was used for fuzzification of Euclid's first postulate. Fuzzy equivalence relation "extended lines sameness" is introduced. For its approximation we also utilize a fuzzy conditional inference, which is based on proposed fuzzy "degree of indiscernibility" and "discernibility measure" of extended points.

  7. Quanta of geometry: noncommutative aspects.

    PubMed

    Chamseddine, Ali H; Connes, Alain; Mukhanov, Viatcheslav

    2015-03-06

    In the construction of spectral manifolds in noncommutative geometry, a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of real scalar fields naturally appears and implies, by equality with the index formula, the quantization of the volume. We first show that this condition implies that the manifold decomposes into disconnected spheres, which will represent quanta of geometry. We then refine the condition by involving the real structure and two types of geometric quanta, and show that connected spin manifolds with large quantized volume are then obtained as solutions. The two algebras M_{2}(H) and M_{4}(C) are obtained, which are the exact constituents of the standard model. Using the two maps from M_{4} to S^{4} the four-manifold is built out of a very large number of the two kinds of spheres of Planckian volume. We give several physical applications of this scheme such as quantization of the cosmological constant, mimetic dark matter, and area quantization of black holes.

  8. Weyl gravity and Cartan geometry

    NASA Astrophysics Data System (ADS)

    Attard, J.; François, J.; Lazzarini, S.

    2016-04-01

    We point out that the Cartan geometry known as the second-order conformal structure provides a natural differential geometric framework underlying gauge theories of conformal gravity. We are concerned with two theories: the first one is the associated Yang-Mills-like Lagrangian, while the second, inspired by [1], is a slightly more general one that relaxes the conformal Cartan geometry. The corresponding gauge symmetry is treated within the Becchi-Rouet-Stora-Tyutin language. We show that the Weyl gauge potential is a spurious degree of freedom, analogous to a Stueckelberg field, that can be eliminated through the dressing field method. We derive sets of field equations for both the studied Lagrangians. For the second one, they constrain the gauge field to be the "normal conformal Cartan connection.''Finally, we provide in a Lagrangian framework a justification of the identification, in dimension 4, of the Bach tensor with the Yang-Mills current of the normal conformal Cartan connection, as proved in [2].

  9. Fuzzy Logic for Incidence Geometry

    PubMed Central

    2016-01-01

    The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly used names of landmarks, water areas, and so forth. Unlike single points that are given in Cartesian coordinates, these geographic entities are extended in space and often loosely defined, but people easily perform spatial reasoning with extended geographic objects “as if they were points.” Unfortunately, up to date, geographic information systems (GIS) miss the capability of geometric reasoning with extended objects. The aim of the paper is to present a mathematical apparatus for approximate geometric reasoning with extended objects that is usable in GIS. In the paper we discuss the fuzzy logic (Aliev and Tserkovny, 2011) as a reasoning system for geometry of extended objects, as well as a basis for fuzzification of the axioms of incidence geometry. The same fuzzy logic was used for fuzzification of Euclid's first postulate. Fuzzy equivalence relation “extended lines sameness” is introduced. For its approximation we also utilize a fuzzy conditional inference, which is based on proposed fuzzy “degree of indiscernibility” and “discernibility measure” of extended points. PMID:27689133

  10. Differential Geometry Based Multiscale Models

    PubMed Central

    Wei, Guo-Wei

    2010-01-01

    Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atom-istic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier–Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson–Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson–Nernst–Planck equations that

  11. Differential geometry based multiscale models.

    PubMed

    Wei, Guo-Wei

    2010-08-01

    Large chemical and biological systems such as fuel cells, ion channels, molecular motors, and viruses are of great importance to the scientific community and public health. Typically, these complex systems in conjunction with their aquatic environment pose a fabulous challenge to theoretical description, simulation, and prediction. In this work, we propose a differential geometry based multiscale paradigm to model complex macromolecular systems, and to put macroscopic and microscopic descriptions on an equal footing. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum mechanical description of the aquatic environment with the microscopic discrete atomistic description of the macromolecule. Multiscale free energy functionals, or multiscale action functionals are constructed as a unified framework to derive the governing equations for the dynamics of different scales and different descriptions. Two types of aqueous macromolecular complexes, ones that are near equilibrium and others that are far from equilibrium, are considered in our formulations. We show that generalized Navier-Stokes equations for the fluid dynamics, generalized Poisson equations or generalized Poisson-Boltzmann equations for electrostatic interactions, and Newton's equation for the molecular dynamics can be derived by the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows. Comparison is given to classical descriptions of the fluid and electrostatic interactions without geometric flow based micro-macro interfaces. The detailed balance of forces is emphasized in the present work. We further extend the proposed multiscale paradigm to micro-macro analysis of electrohydrodynamics, electrophoresis, fuel cells, and ion channels. We derive generalized Poisson-Nernst-Planck equations that are

  12. Geometry dependence of stellarator turbulence

    NASA Astrophysics Data System (ADS)

    Mynick, H. E.; Xanthopoulos, P.; Boozer, A. H.

    2009-11-01

    Using the nonlinear gyrokinetic code package GENE/GIST [F. Jenko, W. Dorland, M. Kotschenreuther, and B. N. Rogers, Phys. Plasmas 7, 1904 (2000); P. Xanthopoulos, W. A. Cooper, F. Jenko, Yu. Turkin, A. Runov, and J. Geiger, Phys. Plasmas 16, 082303 (2009)], we study the turbulent transport in a broad family of stellarator designs, to understand the geometry dependence of the microturbulence. By using a set of flux tubes on a given flux surface, we construct a picture of the two-dimensional structure of the microturbulence over that surface and relate this to relevant geometric quantities, such as the curvature, local shear, and effective potential in the Schrödinger-like equation governing linear drift modes.

  13. Geometry of spinning Ellis wormholes

    NASA Astrophysics Data System (ADS)

    Chew, Xiao Yan; Kleihaus, Burkhard; Kunz, Jutta

    2016-11-01

    We give a detailed account of the properties of spinning Ellis wormholes, supported by a phantom field. The general set of solutions depends on three parameters, associated with the size of the throat, the rotation, and the symmetry of the solutions. For symmetric wormholes the global charges possess the same values in both asymptotic regions, while this is no longer the case for nonsymmetric wormholes. We present mass formulas for these wormholes, study their quadrupole moments, and discuss the geometry of their throat and their ergoregion. We demonstrate, that these wormholes possess limiting configurations corresponding to an extremal Kerr black hole. Moreover, we analyze the geodesics of these wormholes, and show that they possess bound orbits.

  14. Geometry of minisuperspace in examples

    NASA Astrophysics Data System (ADS)

    Kerbrat, Yvan; Kerbrat-Lunc, Hélène; Śniatycki, Jȩdrzej

    1992-04-01

    Minisuperspace, interpreted as the configuration space for homogeneous cosmologies, has a naturally defined pseudo-Riemannian metric (supermetric) such that solutions of the ADM equations correspond to geodesics of the supermetric parametrized by arc-length (supertime). The supermetric is used to analyse the geometry of minisuperspace. In particular, if the supermetric is incomplete, its prolongations relate different components of minisuperspace. For Robertson-Walker universes with a homogeneous scalar field there exists a C1 prolongation of supermetric relating the positive and the negative curvature models. If the potential vanishes, then this prolongation is C∞. There is no prolongation of supermetric through generic boundary points between the Bianchi VIII and Bianchi IX models.

  15. Geometry-induced capillary emptying.

    PubMed

    Rascón, Carlos; Parry, Andrew O; Aarts, Dirk G A L

    2016-10-24

    When a capillary is half-filled with liquid and turned to the horizontal, the liquid may flow out of the capillary or remain in it. For lack of a better criterion, the standard assumption is that the liquid will remain in a capillary of narrow cross-section, and will flow out otherwise. Here, we present a precise mathematical criterion that determines which of the two outcomes occurs for capillaries of arbitrary cross-sectional shape, and show that the standard assumption fails for certain simple geometries, leading to very rich and counterintuitive behavior. This opens the possibility of creating very sensitive microfluidic devices that respond readily to small physical changes, for instance, by triggering the sudden displacement of fluid along a capillary without the need of any external pumping.

  16. Changing the Structure Boundary Geometry

    SciTech Connect

    Karasev, Viktor; Dzlieva, Elena; Ivanov, Artyom

    2008-09-07

    Analysis of previously obtained results shows that hexagonal crystal lattice is the dominant type of ordering, in particular, in striated glow discharges. We explore the possibility for changing the dust distribution in horizontal cross sections of relatively highly ordered structures in a glow-discharge. Presuming that boundary geometry can affect dust distribution, we used cylindrical coolers held at 0 deg. C and placed against a striation containing a structure, to change the geometry of its outer boundary. By varying the number of coolers, their positions, and their separations from the tube wall, azimuthally asymmetric thermophoretic forces can be used to form polygonal boundaries and vary the angles between their segments (in a horizontal cross section). The corner in the structure's boundary of 60 deg. stimulates formation of hexagonal cells. The structure between the supported parallel boundaries is also characterized by stable hexagonal ordering. We found that a single linear boundary segment does not give rise to any sizable domain, but generates a lattice extending from the boundary (without edge defects). A square lattice can be formed by setting the angle equal to 90 deg. . However, angles of 45 deg. and 135 deg. turned out easier to form. Square lattice was created by forming a near-135 deg. corner with four coolers. It was noted that no grain ordering is observed in the region adjacent to corners of angles smaller than 30 deg. , which do not promote ordering into cells of any shape. Thus, manipulation of a structure boundary can be used to change dust distribution, create structures free of the ubiquitous edge defects that destroy orientation order, and probably change the crystal lattice type.

  17. Local geometry of isoscalar surfaces.

    PubMed

    Dopazo, César; Martín, Jesús; Hierro, Juan

    2007-11-01

    An inert dynamically passive scalar in a constant density fluid forced by a statistically homogeneous field of turbulence has been investigated using the results of a 256(3) grid direct numerical simulation. Mixing characteristics are characterized in terms of either principal curvatures or mean and Gauss curvatures. The most probable small-scale scalar geometries are flat and tilelike isosurfaces. Preliminary correlations between flow and scalar small-scale structures associate highly curved saddle points with large-strain regions and elliptic points with vorticity-dominated zones. The concavity of the scalar profiles along the isosurface normal coordinate xn correlates well with negative mean curvatures, Gauss curvatures displaying any sign, which correspond to scalar minima, tiles, or saddle points; on the other hand, convexity along xn is associated with positive mean curvatures, Gauss curvatures ranging from negative to positive signs, featuring maxima, tiles, or saddle points; inflection points along xn correlate well with small values of the mean curvature and zero or negative values of kg, corresponding to plane isosurfaces or saddle points with curvatures of equal and opposite signs. Small values of the scalar gradient are associated with elliptic points, either concave or convex (kg>0) , for both concave and convex scalar profiles along xn. Large values of the scalar gradient (or, equivalently, scalar fluctuation dissipation rates) are generally connected with small values of the Gauss curvature (either flat or moderate-curvature tilelike local geometries), with both concave and convex scalar profiles along xn equally probable. Vortical local flow structures correlate well with small and moderate values of the scalar gradient, while strain-dominated regions are associated with large values.

  18. Convection in Slab and Spheroidal Geometries

    NASA Technical Reports Server (NTRS)

    Porter, David H.; Woodward, Paul R.; Jacobs, Michael L.

    2000-01-01

    Three-dimensional numerical simulations of compressible turbulent thermally driven convection, in both slab and spheroidal geometries, are reviewed and analyzed in terms of velocity spectra and mixing-length theory. The same ideal gas model is used in both geometries, and resulting flows are compared. The piecewise-parabolic method (PPM), with either thermal conductivity or photospheric boundary conditions, is used to solve the fluid equations of motion. Fluid motions in both geometries exhibit a Kolmogorov-like k(sup -5/3) range in their velocity spectra. The longest wavelength modes are energetically dominant in both geometries, typically leading to one convection cell dominating the flow. In spheroidal geometry, a dipolar flow dominates the largest scale convective motions. Downflows are intensely turbulent and up drafts are relatively laminar in both geometries. In slab geometry, correlations between temperature and velocity fluctuations, which lead to the enthalpy flux, are fairly independent of depth. In spheroidal geometry this same correlation increases linearly with radius over the inner 70 percent by radius, in which the local pressure scale heights are a sizable fraction of the radius. The effects from the impenetrable boundary conditions in the slab geometry models are confused with the effects from non-local convection. In spheroidal geometry nonlocal effects, due to coherent plumes, are seen as far as several pressure scale heights from the lower boundary and are clearly distinguishable from boundary effects.

  19. Riemannian geometry of fluctuation theory: An introduction

    NASA Astrophysics Data System (ADS)

    Velazquez, Luisberis

    2016-05-01

    Fluctuation geometry was recently proposed as a counterpart approach of Riemannian geometry of inference theory (information geometry), which describes the geometric features of the statistical manifold M of random events that are described by a family of continuous distributions dpξ(x|θ). This theory states a connection among geometry notions and statistical properties: separation distance as a measure of relative probabilities, curvature as a measure about the existence of irreducible statistical correlations, among others. In statistical mechanics, fluctuation geometry arises as the mathematical apparatus of a Riemannian extension of Einstein fluctuation theory, which is also closely related to Ruppeiner geometry of thermodynamics. Moreover, the curvature tensor allows to express some asymptotic formulae that account for the system fluctuating behavior beyond the gaussian approximation, while curvature scalar appears as a second-order correction of Legendre transformation between thermodynamic potentials.

  20. Geometry of solar coronal rays

    NASA Astrophysics Data System (ADS)

    Filippov, B. P.; Martsenyuk, O. V.; Platov, Yu. V.; Den, O. E.

    2016-02-01

    Coronal helmet streamers are the most prominent large-scale elements of the solar corona observed in white light during total solar eclipses. The base of the streamer is an arcade of loops located above a global polarity inversion line. At an altitude of 1-2 solar radii above the limb, the apices of the arches sharpen, forming cusp structures, above which narrow coronal rays are observed. Lyot coronagraphs, especially those on-board spacecrafts flying beyond the Earth's atmosphere, enable us to observe the corona continuously and at large distances. At distances of several solar radii, the streamers take the form of fairly narrow spokes that diverge radially from the Sun. This radial direction displays a continuous expansion of the corona into the surrounding space, and the formation of the solar wind. However, the solar magnetic field and solar rotation complicate the situation. The rotation curves radial streams into spiral ones, similar to water streams flowing from rotating tubes. The influence of the magnetic field is more complex and multifarious. A thorough study of coronal ray geometries shows that rays are frequently not radial and not straight. Coronal streamers frequently display a curvature whose direction in the meridional plane depends on the phase of the solar cycle. It is evident that this curvature is related to the geometry of the global solar magnetic field, which depends on the cycle phase. Equatorward deviations of coronal streamers at solar minima and poleward deviations at solar maxima can be interpreted as the effects of changes in the general topology of the global solar magnetic field. There are sporadic temporal changes in the coronal rays shape caused by remote coronal mass ejections (CMEs) propagating through the corona. This is also a manifestation of the influence of the magnetic field on plasma flows. The motion of a large-scale flux rope associated with a CME away from the Sun creates changes in the structure of surrounding field

  1. Use of CAD Geometry in MDO

    NASA Technical Reports Server (NTRS)

    Samareh, Jamshid A.

    1996-01-01

    The purpose of this paper is to discuss the use of Computer-Aided Design (CAD) geometry in a Multi-Disciplinary Design Optimization (MDO) environment. Two techniques are presented to facilitate the use of CAD geometry by different disciplines, such as Computational Fluid Dynamics (CFD) and Computational Structural Mechanics (CSM). One method is to transfer the load from a CFD grid to a CSM grid. The second method is to update the CAD geometry for CSM deflection.

  2. Serpentine Geometry Plasma Actuators for Flow Control

    DTIC Science & Technology

    2013-08-23

    Serpentine geometry plasma actuators for flow control Mark Riherd and Subrata Roy Citation: J. Appl. Phys. 114, 083303 (2013); doi: 10.1063...DATES COVERED 00-00-2013 to 00-00-2013 4. TITLE AND SUBTITLE Serpentine geometry plasma actuators for flow control 5a. CONTRACT NUMBER 5b...unclassified c. THIS PAGE unclassified Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18 Serpentine geometry plasma actuators for flow

  3. T-branes and geometry

    NASA Astrophysics Data System (ADS)

    Anderson, Lara B.; Heckman, Jonathan J.; Katz, Sheldon

    2014-05-01

    T-branes are a non-abelian generalization of intersecting branes in which the matrix of normal deformations is nilpotent along some subspace. In this paper we study the geometric remnant of this open string data for six-dimensional F-theory vacua. We show that in the dual M-theory / IIA compactification on a smooth Calabi-Yau threefold X smth, the geometric remnant of T-brane data translates to periods of the three-form potential valued in the intermediate Jacobian of X smth. Starting from a smoothing of a singular Calabi-Yau, we show how to track this data in singular limits using the theory of limiting mixed Hodge structures, which in turn directly points to an emergent Hitchin-like system coupled to defects. We argue that the physical data of an F-theory compactification on a singular threefold involves specifying both a geometry as well as the remnant of three-form potential moduli and flux which is localized on the discriminant. We give examples of T-branes in compact F-theory models with heterotic duals, and comment on the extension of our results to four-dimensional vacua.

  4. Latent geometry of bipartite networks

    NASA Astrophysics Data System (ADS)

    Kitsak, Maksim; Papadopoulos, Fragkiskos; Krioukov, Dmitri

    2017-03-01

    Despite the abundance of bipartite networked systems, their organizing principles are less studied compared to unipartite networks. Bipartite networks are often analyzed after projecting them onto one of the two sets of nodes. As a result of the projection, nodes of the same set are linked together if they have at least one neighbor in common in the bipartite network. Even though these projections allow one to study bipartite networks using tools developed for unipartite networks, one-mode projections lead to significant loss of information and artificial inflation of the projected network with fully connected subgraphs. Here we pursue a different approach for analyzing bipartite systems that is based on the observation that such systems have a latent metric structure: network nodes are points in a latent metric space, while connections are more likely to form between nodes separated by shorter distances. This approach has been developed for unipartite networks, and relatively little is known about its applicability to bipartite systems. Here, we fully analyze a simple latent-geometric model of bipartite networks and show that this model explains the peculiar structural properties of many real bipartite systems, including the distributions of common neighbors and bipartite clustering. We also analyze the geometric information loss in one-mode projections in this model and propose an efficient method to infer the latent pairwise distances between nodes. Uncovering the latent geometry underlying real bipartite networks can find applications in diverse domains, ranging from constructing efficient recommender systems to understanding cell metabolism.

  5. Geometry-induced asymmetric diffusion

    PubMed Central

    Shaw, Robert S.; Packard, Norman; Schröter, Matthias; Swinney, Harry L.

    2007-01-01

    Past work has shown that ions can pass through a membrane more readily in one direction than the other. We demonstrate here in a model and an experiment that for a mixture of small and large particles such asymmetric diffusion can arise solely from an asymmetry in the geometry of the pores of the membrane. Our deterministic simulation considers a two-dimensional gas of elastic disks of two sizes diffusing through a membrane, and our laboratory experiment examines the diffusion of glass beads of two sizes through a metal membrane. In both experiment and simulation, the membrane is permeable only to the smaller particles, and the asymmetric pores lead to an asymmetry in the diffusion rates of these particles. The presence of even a small percentage of large particles can clog a membrane, preventing passage of the small particles in one direction while permitting free flow of the small particles in the other direction. The purely geometric kinetic constraints may play a role in common biological contexts such as membrane ion channels. PMID:17522257

  6. Contour matching by epipolar geometry

    NASA Astrophysics Data System (ADS)

    Hu, Mao-Lin; Zhang, Damin; Wei, Sui

    2003-09-01

    Matching features computed in images is an important process in multiview image analysis. When the motion between two images is large, the matching problem becomes very difficult. In this paper, we propose a contour matching algorithm based on geometric constraints. With the assumption that the contours are obtained from images taken from a moving camera with static scenes, we apply the epipolar constraint between two sets of contours and compute the corresponding points on the contours. From the initial epipolar constraints obtained from comer point matching, candidate contours are selected according to the epipolar geometry, the linear relation among tangent vectors of the contour. In order to reduce the possibility of false matches, the curvature of the contour of match points on a contour is also used as a selection method. The initial epipolar constraint is refined from the matched sets of contours. The algorithm can be applied to a pair or two pairs of images. All of the processes are fully automatic and successfully implemented and tested with various synthetic images.

  7. Noncommutative Riemannian geometry on graphs

    NASA Astrophysics Data System (ADS)

    Majid, Shahn

    2013-07-01

    We show that arising out of noncommutative geometry is a natural family of edge Laplacians on the edges of a graph. The family includes a canonical edge Laplacian associated to the graph, extending the usual graph Laplacian on vertices, and we find its spectrum. We show that for a connected graph its eigenvalues are strictly positive aside from one mandatory zero mode, and include all the vertex degrees. Our edge Laplacian is not the graph Laplacian on the line graph but rather it arises as the noncommutative Laplace-Beltrami operator on differential 1-forms, where we use the language of differential algebras to functorially interpret a graph as providing a 'finite manifold structure' on the set of vertices. We equip any graph with a canonical 'Euclidean metric' and a canonical bimodule connection, and in the case of a Cayley graph we construct a metric compatible connection for the Euclidean metric. We make use of results on bimodule connections on inner calculi on algebras, which we prove, including a general relation between zero curvature and the braid relations.

  8. Eye movements and information geometry.

    PubMed

    Lenz, Reiner

    2016-08-01

    The human visual system uses eye movements to gather visual information. They act as visual scanning processes and can roughly be divided into two different types: small movements around fixation points and larger movements between fixation points. The processes are often modeled as random walks, and recent models based on heavy tail distributions, also known as Levý flights, have been used in these investigations. In contrast to these approaches we do not model the stochastic processes, but we will show that the step lengths of the movements between fixation points follow generalized Pareto distributions (GPDs). We will use general arguments from the theory of extreme value statistics to motivate the usage of the GPD and show empirically that the GPDs provide good fits for measured eye tracking data. In the framework of information geometry the GPDs with a common threshold form a two-dimensional Riemann manifold with the Fisher information matrix as a metric. We compute the Fisher information matrix for the GPDs and introduce a feature vector describing a GPD by its parameters and different geometrical properties of its Fisher information matrix. In our statistical analysis we use eye tracker measurements in a database with 15 observers viewing 1003 images under free-viewing conditions. We use Matlab functions with their standard parameter settings and show that a naive Bayes classifier using the eigenvalues of the Fisher information matrix provides a high classification rate identifying the 15 observers in the database.

  9. PREFACE: Water in confined geometries

    NASA Astrophysics Data System (ADS)

    Rovere, Mauro

    2004-11-01

    The study of water confined in complex systems in solid or gel phases and/or in contact with macromolecules is relevant to many important processes ranging from industrial applications such as catalysis and soil chemistry, to biological processes such as protein folding or ionic transport in membranes. Thermodynamics, phase behaviour and the molecular mobility of water have been observed to change upon confinement depending on the properties of the substrate. In particular, polar substrates perturb the hydrogen bond network of water, inducing large changes in the properties upon freezing. Understanding how the connected random hydrogen bond network of bulk water is modified when water is confined in small cavities inside a substrate material is very important for studies of stability and the enzymatic activity of proteins, oil recovery or heterogeneous catalysis, where water-substrate interactions play a fundamental role. The modifications of the short-range order in the liquid depend on the nature of the water-substrate interaction, hydrophilic or hydrophobic, as well as on its spatial range and on the geometry of the substrate. Despite extensive study, both experimentally and by computer simulation, there remain a number of open problems. In the many experimental studies of confined water, those performed on water in Vycor are of particular interest for computer simulation and theoretical studies since Vycor is a porous silica glass characterized by a quite sharp distribution of pore sizes and a strong capability to absorb water. It can be considered as a good candidate for studying the general behaviour of water in hydrophilic nanopores. But there there have been a number of studies of water confined in more complex substrates, where the interpretation of experiments and computer simulation is more difficult, such as in zeolites or in aerogels or in contact with membranes. Of the many problems to consider we can mention the study of supercooled water. It is

  10. Quantum groups: Geometry and applications

    SciTech Connect

    Chu, Chong -Sun

    1996-05-13

    The main theme of this thesis is a study of the geometry of quantum groups and quantum spaces, with the hope that they will be useful for the construction of quantum field theory with quantum group symmetry. The main tool used is the Faddeev-Reshetikhin-Takhtajan description of quantum groups. A few content-rich examples of quantum complex spaces with quantum group symmetry are treated in details. In chapter 1, the author reviews some of the basic concepts and notions for Hopf algebras and other background materials. In chapter 2, he studies the vector fields of quantum groups. A compact realization of these vector fields as pseudodifferential operators acting on the linear quantum spaces is given. In chapter 3, he describes the quantum sphere as a complex quantum manifold by means of a quantum stereographic projection. A covariant calculus is introduced. An interesting property of this calculus is the existence of a one-form realization of the exterior differential operator. The concept of a braided comodule is introduced and a braided algebra of quantum spheres is constructed. In chapter 4, the author considers the more general higher dimensional quantum complex projective spaces and the quantum Grassman manifolds. Differential calculus, integration and braiding can be introduced as in the one dimensional case. Finally, in chapter 5, he studies the framework of quantum principal bundle and construct the q-deformed Dirac monopole as a quantum principal bundle with a quantum sphere as the base and a U(1) with non-commutative calculus as the fiber. The first Chern class can be introduced and integrated to give the monopole charge.

  11. The slab geometry laser. I - Theory

    NASA Technical Reports Server (NTRS)

    Eggleston, J. M.; Kane, T. J.; Kuhn, K.; Byer, R. L.; Unternahrer, J.

    1984-01-01

    Slab geometry solid-state lasers offer significant performance improvements over conventional rod-geometry lasers. A detailed theoretical description of the thermal, stress, and beam-propagation characteristics of a slab laser is presented. The analysis includes consideration of the effects of the zig-zag optical path, which eliminates thermal and stress focusing and reduces residual birefringence.

  12. Reflection: Its Concepts and Applications in Geometry

    ERIC Educational Resources Information Center

    Man, Yiu Kwong

    2004-01-01

    This paper discusses the basic concepts of reflection and its related concepts in optics. It aims at providing examples on how to apply the principle of reflection in geometry. Explorations of the concepts involved via dynamic geometry software are also included.

  13. The Geometry of the Universe: Part 2

    ERIC Educational Resources Information Center

    Francis, Stephanie

    2009-01-01

    Hyperbolic geometry occurs on hyperbolic planes--the most commonly cited one being a saddle shape. In this article, the author explores negative hyperbolic curvature, and provides a detailed description of how she constructed two hyperbolic paraboloids. Hyperbolic geometry occurs on surfaces that have negative curvature. (Contains 11 figures and 4…

  14. Geometry and Education in the Internet Age.

    ERIC Educational Resources Information Center

    Kortenkamp, Ulrich H.; Richter-Gebert, Jurgen

    This paper discusses the requirements of Interactive Geometry Systems (IGSs) and how they can be fulfilled, explains how a geometry tool can benefit from the Internet, and presents Cinderella's Cafe. Cinderella's Cafe is a new IGS with a high mathematical background that uses the most general mathematical models whenever possible, is highly…

  15. Geometry, Student's Text, Part II, Unit 14.

    ERIC Educational Resources Information Center

    Allen, Frank B.; And Others

    Unit 14 in the SMSG secondary school mathematics series is a student text covering the following topics in geometry: areas of polygonal regions, similarity, circles and spheres, characterization of sets, constructions, areas of circles and sectors, volumes of solids, and plane coordinate geometry. Appendices cover Eratosthenes' measurement of the…

  16. Visual and Analytic Strategies in Geometry

    ERIC Educational Resources Information Center

    Kospentaris, George; Vosniadou, Stella; Kazic, Smaragda; Thanou, Emilian

    2016-01-01

    We argue that there is an increasing reliance on analytic strategies compared to visuospatial strategies, which is related to geometry expertise and not on individual differences in cognitive style. A Visual/Analytic Strategy Test (VAST) was developed to investigate the use of visuo-spatial and analytic strategies in geometry in 30 mathematics…

  17. Geometry, Senior High School Curriculum Guide.

    ERIC Educational Resources Information Center

    Klier, Katherine M., Ed.

    This syllabus presents a fused course in plane, solid, and coordinate geometry for secondary school students. Elementary set theory, logic, and the principles of separation provide unifying threads throughout this approach to geometry. There are actually two curriculum guides included; one for each of two different texts--Henderson, Pingry, and…

  18. Exact geometries from quantum chemical calculations

    NASA Astrophysics Data System (ADS)

    Cremer, Dieter; Kraka, Elfi; He, Yuan

    2001-06-01

    For seventeen molecules, complete basis set (CBS) geometries are obtained for Møller-Plesset perturbation methods at second (MP2), fourth (MP4), and sixth order (MP6) as well as for the Coupled Cluster methods CCD, CCSD, and CCSD( T). The correlation consistent basis sets cc-pVDZ, cc-pVTZ, and cc-pVQZ were systematically applied and calculated geometries extrapolated to the limit of an infinitely large basis set. MP6 equilibrium geometries are more accurate than MP2 or MP4 geometries at the CBS limit and provide AH bond lengths with an accuracy of 0.001 Å. However, AB bonds are always predicted too long because of the lack of sufficient coupling effects between p-electron correlation at MP6. CCSD( T) provides reasonable AB bond lengths although these are in general too short by 0.003 Å. Due to error cancellation very accurate geometries are obtained at the CCSD( T)/cc-pVTZ and CCSD( T)/cc-pVQZ level of theory. With the help of the accurate equilibrium geometries obtained in this work, several experimentally based geometries could be corrected. The effects of HF-optimized basis sets, diffuse functions or the frozen core approximation on geometry optimizations are discussed. It is emphasized that the use of the cc-pVDZ or any other VDZ+P basis set should be avoided in correlation corrected ab initio calculations.

  19. Fractal Geometry in Elementary School Mathematics.

    ERIC Educational Resources Information Center

    Vacc, Nancy Nesbitt

    1992-01-01

    Reports a case study to evaluate whether basic concepts of fractal geometry are teachable to elementary school children and to determine the effectiveness of having an elementary school student present a lesson to inservice and preservice teachers. Concludes that simple concepts of fractal geometry appear appropriate for the elementary school…

  20. Computing Bisectors in a Dynamic Geometry Environment

    ERIC Educational Resources Information Center

    Botana, Francisco

    2013-01-01

    In this note, an approach combining dynamic geometry and automated deduction techniques is used to study the bisectors between points and curves. Usual teacher constructions for bisectors are discussed, showing that inherent limitations in dynamic geometry software impede their thorough study. We show that the interactive sketching of bisectors…

  1. An approach for management of geometry data

    NASA Technical Reports Server (NTRS)

    Dube, R. P.; Herron, G. J.; Schweitzer, J. E.; Warkentine, E. R.

    1980-01-01

    The strategies for managing Integrated Programs for Aerospace Design (IPAD) computer-based geometry are described. The computer model of geometry is the basis for communication, manipulation, and analysis of shape information. IPAD's data base system makes this information available to all authorized departments in a company. A discussion of the data structures and algorithms required to support geometry in IPIP (IPAD's data base management system) is presented. Through the use of IPIP's data definition language, the structure of the geometry components is defined. The data manipulation language is the vehicle by which a user defines an instance of the geometry. The manipulation language also allows a user to edit, query, and manage the geometry. The selection of canonical forms is a very important part of the IPAD geometry. IPAD has a canonical form for each entity and provides transformations to alternate forms; in particular, IPAD will provide a transformation to the ANSI standard. The DBMS schemas required to support IPAD geometry are explained.

  2. Reasoning by Contradiction in Dynamic Geometry

    ERIC Educational Resources Information Center

    Baccaglini-Frank, Anna; Antonini, Samuele; Leung, Allen; Mariotti, Maria Alessandra

    2013-01-01

    This paper addresses contributions that dynamic geometry systems (DGSs) may give in reasoning by contradiction in geometry. We present analyses of three excerpts of students' work and use the notion of pseudo object, elaborated from previous research, to show some specificities of DGS in constructing proof by contradiction. In particular, we…

  3. A Multivariate Model of Achievement in Geometry

    ERIC Educational Resources Information Center

    Bailey, MarLynn; Taasoobshirazi, Gita; Carr, Martha

    2014-01-01

    Previous studies have shown that several key variables influence student achievement in geometry, but no research has been conducted to determine how these variables interact. A model of achievement in geometry was tested on a sample of 102 high school students. Structural equation modeling was used to test hypothesized relationships among…

  4. Making Euclidean Geometry Compulsory: Are We Prepared?

    ERIC Educational Resources Information Center

    Van Putten, Sonja; Howie, Sarah; Stols, Gerrit

    2010-01-01

    This study investigated the attitude towards, as well as the level of understanding of Euclidean geometry in pre-service mathematics education (PME) students. In order to do so, a case study was undertaken within which a one group pre-post-test procedure was conducted around a geometry module, and a representative group of students was interviewed…

  5. Teaching Geometry to Visually Impaired Students

    ERIC Educational Resources Information Center

    Pritchard, Christine K.; Lamb, John H.

    2012-01-01

    NCTM (2000) described geometry as "a means of describing, analyzing, and understanding the world and seeing beauty in its structures" (p. 309). Dossey et al. (2002) captured the essence of this aspect of visualization by stating that geometry fosters in students an ability to "visualize and mentally manipulate geometric objects." (p. 200).…

  6. Historical Digressions in Greek Geometry Lessons.

    ERIC Educational Resources Information Center

    Thomaidis, Yannis

    1991-01-01

    Presents an attempt to combine the history of mathematics of ancient Greece with the course on theoretical geometry taught in Greek secondary schools. Three sections present the history of ancient Greek geometry, geometrical constructions using straightedges and compasses, and an application of Ptolemy's theorem in solving ancient astronomy…

  7. Topics in sub-Riemannian geometry

    NASA Astrophysics Data System (ADS)

    Agrachev, A. A.

    2016-12-01

    Sub-Riemannian geometry is the geometry of spaces with non-holonomic constraints. This paper presents an informal survey of some topics in this area, starting with the construction of geodesic curves and ending with a recent definition of curvature. Bibliography: 28 titles.

  8. Improving African American Achievement in Geometry Honors

    ERIC Educational Resources Information Center

    Mims, Adrian B.

    2010-01-01

    This case study evaluated the significance of implementing an enrichment mathematics course during the summer to rising African American ninth graders entitled, "Geometry Honors Preview." In the past, 60 to 70 percent of African American students in this school district had withdrawn from Geometry Honors by the second academic quarter. This study…

  9. Stop Teaching and Let Students Learn Geometry

    ERIC Educational Resources Information Center

    Bosse, Michael J.; Adu-Gyamfi, Kwaku

    2011-01-01

    For many high school students as well as preservice teachers, geometry can be difficult to learn without experiences that allow them to build their own understanding. The authors' approach to geometry instruction--with its integration of content, multiple representations, real-world examples, reading and writing, communication and collaboration as…

  10. FINAL REPORT: GEOMETRY AND ELEMENTARY PARTICLE PHYSICS

    SciTech Connect

    Singer, Isadore M.

    2008-03-04

    The effect on mathematics of collaborations between high-energy theoretical physics and modern mathematics has been remarkable. Mirror symmetry has revolutionized enumerative geometry, and Seiberg-Witten invariants have greatly simplified the study of four manifolds. And because of their application to string theory, physicists now need to know cohomology theory, characteristic classes, index theory, K-theory, algebraic geometry, differential geometry, and non-commutative geometry. Much more is coming. We are experiencing a deeper contact between the two sciences, which will stimulate new mathematics essential to the physicists’ quest for the unification of quantum mechanics and relativity. Our grant, supported by the Department of Energy for twelve years, has been instrumental in promoting an effective interaction between geometry and string theory, by supporting the Mathematical Physics seminar, postdoc research, collaborations, graduate students and several research papers.

  11. Analogy and Dynamic Geometry System Used to Introduce Three-Dimensional Geometry

    ERIC Educational Resources Information Center

    Mammana, M. F.; Micale, B.; Pennisi, M.

    2012-01-01

    We present a sequence of classroom activities on Euclidean geometry, both plane and space geometry, used to make three dimensional geometry more catchy and simple. The activity consists of a guided research activity that leads the students to discover unexpected properties of two apparently distant geometrical entities, quadrilaterals and…

  12. Drawing Dynamic Geometry Figures Online with Natural Language for Junior High School Geometry

    ERIC Educational Resources Information Center

    Wong, Wing-Kwong; Yin, Sheng-Kai; Yang, Chang-Zhe

    2012-01-01

    This paper presents a tool for drawing dynamic geometric figures by understanding the texts of geometry problems. With the tool, teachers and students can construct dynamic geometric figures on a web page by inputting a geometry problem in natural language. First we need to build the knowledge base for understanding geometry problems. With the…

  13. Geometry-Related Children's Literature Improves the Geometry Achievement and Attitudes of Second-Grade Students

    ERIC Educational Resources Information Center

    McAndrew, Erica M.; Morris, Wendy L.; Fennell, Francis

    2017-01-01

    Use of mathematics-related literature can engage students' interest and increase their understanding of mathematical concepts. A quasi-experimental study of two second-grade classrooms assessed whether daily inclusion of geometry-related literature in the classroom improved attitudes toward geometry and achievement in geometry. Consistent with the…

  14. Visuospatial Working Memory in Intuitive Geometry, and in Academic Achievement in Geometry

    ERIC Educational Resources Information Center

    Giofre, David; Mammarella, Irene C.; Ronconi, Lucia; Cornoldi, Cesare

    2013-01-01

    A study was conducted on the involvement of visuospatial working memory (VSWM) in intuitive geometry and in school performance in geometry at secondary school. A total of 166 pupils were administered: (1) six VSWM tasks, comprising simple storage and complex span tasks; and (2) the intuitive geometry task devised by Dehaene, Izard, Pica, and…

  15. Stokes flow in ellipsoidal geometry

    NASA Astrophysics Data System (ADS)

    Vafeas, Panayiotis; Dassios, George

    2006-09-01

    Particle-in-cell models for Stokes flow through a relatively homogeneous swarm of particles are of substantial practical interest, because they provide a relatively simple platform for the analytical or semianalytical solution of heat and mass transport problems. Despite the fact that many practical applications involve relatively small particles (inorganic, organic, biological) with axisymmetric shapes, the general consideration consists of rigid particles of arbitrary shape. The present work is concerned with some interesting aspects of the theoretical analysis of creeping flow in ellipsoidal, hence nonaxisymmetric domains. More specifically, the low Reynolds number flow of a swarm of ellipsoidal particles in an otherwise quiescent Newtonian fluid, that move with constant uniform velocity in an arbitrary direction and rotate with an arbitrary constant angular velocity, is analyzed with an ellipsoid-in-cell model. The solid internal ellipsoid represents a particle of the swarm. The external ellipsoid contains the ellipsoidal particle and the amount of fluid required to match the fluid volume fraction of the swarm. The nonslip flow condition on the surface of the solid ellipsoid is supplemented by the boundary conditions on the external ellipsoidal surface which are similar to those of the sphere-in-cell model of Happel (self-sufficient in mechanical energy). This model requires zero normal velocity component and shear stress. The boundary value problem is solved with the aim of the potential representation theory. In particular, the Papkovich-Neuber complete differential representation of Stokes flow, valid for nonaxisymmetric geometries, is considered here, which provides the velocity and total pressure fields in terms of harmonic ellipsoidal eigenfunctions. The flexibility of the particular representation is demonstrated by imposing some conditions, which made the calculations possible. It turns out that the velocity of first degree, which represents the leading

  16. Moving KML geometry elements within Google Earth

    NASA Astrophysics Data System (ADS)

    Zhu, Liang-feng; Wang, Xi-feng; Pan, Xin

    2014-11-01

    During the process of modeling and visualizing geospatial information on the Google Earth virtual globe, there is an increasing demand to carry out such operations as moving geospatial objects defined by KML geometry elements horizontally or vertically. Due to the absence of the functionality and user interface for performing the moving transformation, it is either hard or impossible to interactively move multiple geospatial objects only using the existing Google Earth desktop application, especially when the data sets are in large volume. In this paper, we present a general framework and associated implementation methods for moving multiple KML geometry elements within Google Earth. In our proposed framework, we first load KML objects into the Google Earth plug-in, and then extract KML geometry elements from the imported KML objects. Subsequently, we interactively control the movement distance along a specified orientation by employing a custom user interface, calculate the transformed geographic location for each KML geometry element, and adjust geographic coordinates of the points in each KML objects. And finally, transformed KML geometry elements can be displayed in Google Earth for 3D visualization and spatial analysis. A key advantage of the proposed framework is that it provides a simple, uniform and efficient user interface for moving multiple KML geometry elements within Google Earth. More importantly, the proposed framework and associated implementations can be conveniently integrated into other customizable Google Earth applications to support interactively visualizing and analyzing geospatial objects defined by KML geometry elements.

  17. Detection of edges using local geometry

    NASA Technical Reports Server (NTRS)

    Gualtieri, J. A.; Manohar, M.

    1989-01-01

    Researchers described a new representation, the local geometry, for early visual processing which is motivated by results from biological vision. This representation is richer than is often used in image processing. It extracts more of the local structure available at each pixel in the image by using receptive fields that can be continuously rotated and that go to third order spatial variation. Early visual processing algorithms such as edge detectors and ridge detectors can be written in terms of various local geometries and are computationally tractable. For example, Canny's edge detector has been implemented in terms of a local geometry of order two, and a ridge detector in terms of a local geometry of order three. The edge detector in local geometry was applied to synthetic and real images and it was shown using simple interpolation schemes that sufficient information is available to locate edges with sub-pixel accuracy (to a resolution increase of at least a factor of five). This is reasonable even for noisy images because the local geometry fits a smooth surface - the Taylor series - to the discrete image data. Only local processing was used in the implementation so it can readily be implemented on parallel mesh machines such as the MPP. Researchers expect that other early visual algorithms, such as region growing, inflection point detection, and segmentation can also be implemented in terms of the local geometry and will provide sufficiently rich and robust representations for subsequent visual processing.

  18. Geometry of contextuality from Grothendieck's coset space

    NASA Astrophysics Data System (ADS)

    Planat, Michel

    2015-07-01

    The geometry of cosets in the subgroups of the two-generator free group nicely fits, via Grothendieck's dessins d'enfants, the geometry of commutation for quantum observables. In previous work, it was established that dessins stabilize point-line geometries whose incidence structure reflects the commutation of (generalized) Pauli operators. Now we find that the nonexistence of a dessin for which the commutator precisely corresponds to the commutator of quantum observables on all lines of the geometry is a signature of quantum contextuality. This occurs first at index : in Mermin's square and at index in Mermin's pentagram, as expected. Commuting sets of -qubit observables with are found to be contextual as well as most generalized polygons. A geometrical contextuality measure is introduced.

  19. Fractal Geometry in the High School Classroom.

    ERIC Educational Resources Information Center

    Camp, Dane R.

    1995-01-01

    Discusses classroom activities that involve applications of fractal geometry. Includes an activity sheet that explores Pascal's triangle, Sierpinsky's gasket, and modular arithmetic in two and three dimensions. (Author/MKR)

  20. Designing Phoxonic Metamaterials with Fractal Geometry

    NASA Astrophysics Data System (ADS)

    Ni, Sisi; Koh, Cheong Yang; Kooi, Steve; Thomas, Edwin

    2012-02-01

    Recently, the concepts of fractal geometry have been introduced into electromagnetic and plasmonic metamaterials. With their self-similarity, structures based on fractal geometry should exhibit multi-band character with high Q factors due to the scaling law. However, there exist few studies of phononic metamaterials based on fractal geometry. We use COMSOL to investigate the wave propagation in two dimensional systems possessing fractal geometries. The simulations of these systems, guided by our recently developed general design framework, help to understand the role of design in determining the phononic properties of the structures. Proposed structures are being fabricated via standard lithographic or 3D printing techniques. The wave behavior of the structures can be characterized using Brillouin Light Scattering, Scanning Acoustic Microscope and Near-field Scanning Optical Microscopy. Due to their sparse spatial distribution, fractal phononic structures show potential fir ``smart skin'', where multifunctional components can be fabricated on the same platform.

  1. Geometry independence of three-string vertices

    NASA Astrophysics Data System (ADS)

    Maeno, Masahiro

    1989-01-01

    The geometry independence of three-string vertices in both HIKKO's and Witten's string field theories is examined. A careful regularization shows that the anomaly which has been reported by Morris and Mañes vanishes.

  2. Non-Euclidean Geometry and Unreal Numbers.

    ERIC Educational Resources Information Center

    Thwaites, G. N.

    1989-01-01

    This article discusses two of the reasons for the decline of formal Euclidean geometry in recent syllabi: (1) Traditional approach; and (2) Inherent difficulties. Suggested are some reasons and examples as to why the decline should be reversed. (YP)

  3. The Oak Leaf: Connecting Geometry and Biology.

    ERIC Educational Resources Information Center

    Snyder, Judy

    1999-01-01

    Presents an activity that integrates biology and mathematics. Involves students in actual biological research and uses geometry, statistics, and computers to interpret data about the leaves of a tree. (ASK)

  4. Emergence of wave equations from quantum geometry

    SciTech Connect

    Majid, Shahn

    2012-09-24

    We argue that classical geometry should be viewed as a special limit of noncommutative geometry in which aspects which are inter-constrained decouple and appear arbitrary in the classical limit. In particular, the wave equation is really a partial derivative in a unified extra-dimensional noncommutative geometry and arises out of the greater rigidity of the noncommutative world not visible in the classical limit. We provide an introduction to this 'wave operator' approach to noncommutative geometry as recently used[27] to quantize any static spacetime metric admitting a spatial conformal Killing vector field, and in particular to construct the quantum Schwarzschild black hole. We also give an introduction to our related result that every classical Riemannian manifold is a shadow of a slightly noncommutative one wherein the meaning of the classical Ricci tensor becomes very natural as the square of a generalised braiding.

  5. Structure analysis for plane geometry figures

    NASA Astrophysics Data System (ADS)

    Feng, Tianxiao; Lu, Xiaoqing; Liu, Lu; Li, Keqiang; Tang, Zhi

    2013-12-01

    As there are increasing numbers of digital documents for education purpose, we realize that there is not a retrieval application for mathematic plane geometry images. In this paper, we propose a method for retrieving plane geometry figures (PGFs), which often appear in geometry books and digital documents. First, detecting algorithms are applied to detect common basic geometry shapes from a PGF image. Based on all basic shapes, we analyze the structural relationships between two basic shapes and combine some of them to a compound shape to build the PGF descriptor. Afterwards, we apply matching function to retrieve candidate PGF images with ranking. The great contribution of the paper is that we propose a structure analysis method to better describe the spatial relationships in such image composed of many overlapped shapes. Experimental results demonstrate that our analysis method and shape descriptor can obtain good retrieval results with relatively high effectiveness and efficiency.

  6. Geometry of quantum computation with qutrits.

    PubMed

    Li, Bin; Yu, Zu-Huan; Fei, Shao-Ming

    2013-01-01

    Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum computation with n qutrits. We show that the optimal quantum circuits are essentially equivalent to the shortest path between two points in a certain curved geometry of SU(3(n)). As an example, three-qutrit systems are investigated in detail.

  7. Geometry, Representation Theory, and the Langlands Program

    DTIC Science & Technology

    2013-04-01

    AFRL-OSR-VA-TR-2013-0144 Geometry, Representation Theory , and the Langlands Program Kari Vilonen Northwestern University...16/6/2008-31/09/2012 Geometry, Representation Theory , and the Langlands Program FA9550-08-1-0351 Kari Vilonen Northwestern University Evanston, IL...Schmid and Vilonen have mostly carried out the program of determining the Unitary dual of reductive Lie groups using Hodge theory . Kashiwara and

  8. Phase distribution in complex geometry conduits

    SciTech Connect

    Lahey, R.T. Jr.; Lopez de Bertodano, M.; Jones, O.C. Jr.

    1992-12-31

    Some of the most important and challenging problems in two-phase flow today have to do with the understanding and prediction of multidimensional phenomena, in particular, lateral phase distribution in both simple and complex geometry conduits. A prior review paper summarized the state-of-the-art in the understanding of phase distribution phenomena, and the ability to perform mechanistic multidimensional predictions. The purpose of this paper is to update that review, with particular emphasis on complex geometry conduit predictive capabilities.

  9. Orientifolded locally AdS3 geometries

    NASA Astrophysics Data System (ADS)

    Loran, F.; Sheikh-Jabbari, M. M.

    2011-01-01

    Continuing the analysis of [Loran F and Sheikh-Jabbari M M 2010 Phys. Lett. B 693 184-7], we classify all locally AdS3 stationary axi-symmetric unorientable solutions to AdS3 Einstein gravity and show that they are obtained by applying certain orientifold projection on AdS3, BTZ or AdS3 self-dual orbifold, respectively, O-AdS3, O-BTZ and O-SDO geometries. Depending on the orientifold fixed surface, the O-surface, which is either a space-like 2D plane or a cylinder, or a light-like 2D plane or a cylinder, one can distinguish four distinct cases. For the space-like orientifold plane or cylinder cases, these geometries solve AdS3 Einstein equations and are hence locally AdS3 everywhere except at the O-surface, where there is a delta-function source. For the light-like cases, the geometry is a solution to Einstein equations even at the O-surface. We discuss the causal structure for static, extremal and general rotating O-BTZ and O-SDO cases as well as the geodesic motion on these geometries. We also discuss orientifolding Poincaré patch AdS3 and AdS2 geometries as a way to geodesic completion of these spaces and comment on the 2D CFT dual to the O-geometries.

  10. Optimum geometry selection for sensor fusion

    NASA Astrophysics Data System (ADS)

    Kadar, Ivan

    1998-07-01

    A relative sensors-to-target geometry measure-of-merit (MOM), based on the Geometric Dilution of Precision (GDOP) measure, is developed. The method of maximum likelihood estimation is introduced for the solution of the position location problem. A linearized measurement model-based error sensitivity analysis is used to derive an expression for the GDOP MOM. The GDOP MOM relates the sensor measurement errors to the target position errors as a function of sensors-to-target geometry. In order to illustrate the efficacy of GDOP MOM for fusion systems, GDOP functional relationships are computed for bearing-only measuring sensors-to-target geometries. The minimum GDOP and associated specific target-to-sensors geometries are computed and illustrated for both two and three bearing-only measuring sensors. Two and three-dimensional plots of relative error contours provide a geometric insight to sensor placement as a function of geometry induced error dilution. The results can be used to select preferred target- to-sensor(s) geometries for M sensors in this application. The GDOP MOM is general and is readily extendable to other measurement-based sensors and fusion architectures.

  11. An Improvement on SSA Congruence for Geometry and Trigonometry.

    ERIC Educational Resources Information Center

    Yeshurun, Shraga; Kay, David C.

    1983-01-01

    Three ideas are explored: (1) an improvement of the SSA congruence theorem for trigonometry; (2) a discussion of the failure of SSA in spherical geometry; and (3) an extension of SSA to spherical geometry and hyperbolic geometry. (MNS)

  12. Geometry-induced protein pattern formation.

    PubMed

    Thalmeier, Dominik; Halatek, Jacob; Frey, Erwin

    2016-01-19

    Protein patterns are known to adapt to cell shape and serve as spatial templates that choreograph downstream processes like cell polarity or cell division. However, how can pattern-forming proteins sense and respond to the geometry of a cell, and what mechanistic principles underlie pattern formation? Current models invoke mechanisms based on dynamic instabilities arising from nonlinear interactions between proteins but neglect the influence of the spatial geometry itself. Here, we show that patterns can emerge as a direct result of adaptation to cell geometry, in the absence of dynamical instability. We present a generic reaction module that allows protein densities robustly to adapt to the symmetry of the spatial geometry. The key component is an NTPase protein that cycles between nucleotide-dependent membrane-bound and cytosolic states. For elongated cells, we find that the protein dynamics generically leads to a bipolar pattern, which vanishes as the geometry becomes spherically symmetrical. We show that such a reaction module facilitates universal adaptation to cell geometry by sensing the local ratio of membrane area to cytosolic volume. This sensing mechanism is controlled by the membrane affinities of the different states. We apply the theory to explain AtMinD bipolar patterns in [Formula: see text] EcMinDE Escherichia coli. Due to its generic nature, the mechanism could also serve as a hitherto-unrecognized spatial template in many other bacterial systems. Moreover, the robustness of the mechanism enables self-organized optimization of protein patterns by evolutionary processes. Finally, the proposed module can be used to establish geometry-sensitive protein gradients in synthetic biological systems.

  13. Beam geometry selection using sequential beam addition

    SciTech Connect

    Popple, Richard A. Brezovich, Ivan A.; Fiveash, John B.

    2014-05-15

    Purpose: The selection of optimal beam geometry has been of interest since the inception of conformal radiotherapy. The authors report on sequential beam addition, a simple beam geometry selection method, for intensity modulated radiation therapy. Methods: The sequential beam addition algorithm (SBA) requires definition of an objective function (score) and a set of candidate beam geometries (pool). In the first iteration, the optimal score is determined for each beam in the pool and the beam with the best score selected. In the next iteration, the optimal score is calculated for each beam remaining in the pool combined with the beam selected in the first iteration, and the best scoring beam is selected. The process is repeated until the desired number of beams is reached. The authors selected three treatment sites, breast, lung, and brain, and determined beam arrangements for up to 11 beams from a pool comprised of 25 equiangular transverse beams. For the brain, arrangements were additionally selected from a pool of 22 noncoplanar beams. Scores were determined for geometries comprised equiangular transverse beams (EQA), as well as two tangential beams for the breast case. Results: In all cases, SBA resulted in scores superior to EQA. The breast case had the strongest dependence on beam geometry, for which only the 7-beam EQA geometry had a score better than the two tangential beams, whereas all SBA geometries with more than two beams were superior. In the lung case, EQA and SBA scores monotonically improved with increasing number of beams; however, SBA required fewer beams to achieve scores equivalent to EQA. For the brain case, SBA with a coplanar pool was equivalent to EQA, while the noncoplanar pool resulted in slightly better scores; however, the dose-volume histograms demonstrated that the differences were not clinically significant. Conclusions: For situations in which beam geometry has a significant effect on the objective function, SBA can identify

  14. Packing of charged chains on toroidal geometries?

    NASA Astrophysics Data System (ADS)

    Yao, Zhenwei; Olvera de La Cruz, Monica

    2013-03-01

    We study sequential Langmuir adsorption of a flexible charged polyelectrolyte chain on tori. In the regime of monomer-monomer electrostatic interaction dominating over thermal fluctuations, it becomes a generalized Thomson problem. Various patterns of adsorbed chain are found including double spirals, disclination-like structures, Janus tori and uniform wrappings, arising from the long-range electrostatic interaction and the toroidal geometry. Their broken mirror symmetry and energetics are analyzed. In particular, we find a power law for the electrostatic energy; the dependence of the power on the geometry of tori implies a geometric origin. Furthermore, in the regime of large thermal fluctuation, we systematically study random walks on tori that generate chain configurations; the features associated with the toroidal geometry are discussed. This work was funded by grants from the Office of the Director of Defense Research and Engineering (DDR&E) and the Air Force Office of Scientific Research (AFOSR) under Award No. FA9550-10-1-0167.

  15. Gully geometry: what are we measuring?

    NASA Astrophysics Data System (ADS)

    Casalí, J.; Giménez, R.; Campo-Bescós, M. A.

    2015-07-01

    Much of the research on (ephemeral) gully erosion comprises the determination of the geometry of these eroded channels, especially their width and depth. This is not a simple task due to uncertainty generated by the wide range of variability in gully cross section shapes found in the field. However, in the literature, this uncertainty is not recognized so that no criteria for their measurement are indicated. The aim of this work is to make researchers aware of the ambiguity that arises when characterizing the geometry of an ephemeral gully and similar eroded channels. In addition, a measurement protocol is proposed with the ultimate goal of pooling criteria in future works. It is suggested that the geometry of a gully could be characterized through its mean equivalent width and mean equivalent depth, which, together with its length, define an "equivalent prismatic gully" (EPG). The latter would facilitate the comparison between different gullies.

  16. First-order Dyson coordinates and geometry.

    PubMed

    Hermes, Matthew R; Hirata, So

    2013-08-15

    The mathematical constructs of the Dyson coordinates and geometry are introduced. The former are a unitary transformation of the normal coordinates and the anharmonic vibrational counterpart of the Dyson orbitals in electronic structure theory. The first-order Dyson coordinates bring the sums of the harmonic force constants and their first-order diagrammatic perturbation corrections (the first-order Dyson self-energy) to a diagonal form. The first-order Dyson geometry has no counterpart in electronic structure theory. It is the point on the potential energy surface at which the sums of the energy gradients and their first-order diagrammatic perturbation corrections vanish. It agrees with the vibrationally averaged geometry of vibrational self-consistent field (VSCF) theory in the bulk limit. These constructs provide a unified view of the relationship of VSCF and its diagrammatically size-consistent modifications as well as the self-consistent phonon method widely used in solid-state physics.

  17. Interfacial geometry dictates cancer cell tumorigenicity

    NASA Astrophysics Data System (ADS)

    Lee, Junmin; Abdeen, Amr A.; Wycislo, Kathryn L.; Fan, Timothy M.; Kilian, Kristopher A.

    2016-08-01

    Within the heterogeneous architecture of tumour tissue there exists an elusive population of stem-like cells that are implicated in both recurrence and metastasis. Here, by using engineered extracellular matrices, we show that geometric features at the perimeter of tumour tissue will prime a population of cells with a stem-cell-like phenotype. These cells show characteristics of cancer stem cells in vitro, as well as enhanced tumorigenicity in murine models of primary tumour growth and pulmonary metastases. We also show that interfacial geometry modulates cell shape, adhesion through integrin α5β1, MAPK and STAT activity, and initiation of pluripotency signalling. Our results for several human cancer cell lines suggest that interfacial geometry triggers a general mechanism for the regulation of cancer-cell state. Similar to how a growing tumour can co-opt normal soluble signalling pathways, our findings demonstrate how cancer can also exploit geometry to orchestrate oncogenesis.

  18. The Magnetic Field Geometry of Cool Stars

    NASA Astrophysics Data System (ADS)

    See, Victor; Jardine, Moira; Vidotto, Aline; Donati, Jean-Francois; Folsom, Colin; Boro Saikia, Sudeshna; Bouvier, Jerome; Fares, Rim; Gregory, Scott; Hussain, Gaitee; Jeffers, Sandra; Marsden, Stephen; Morin, Julien; Moutou, Claire; do Nascimento, Jose-Dias, Jr.; Petit, Pascal; Rosen, Lisa; Waite, Ian

    2016-06-01

    Zeeman-Doppler imaging has been used to map the large-scale surface magnetic fields of cool stars across a wide range of stellar masses and rotation periods. The derived field geometries are surprising, with many stars showing strong azimuthal fields that are not observed on the Sun. In this poster, using 100 magnetic maps of over 50 stars, we present results showing how the magnetic field geometry of cool stars varies as a function of fundamental parameters. The stellar mass, and hence internal structure, critically influences the field geometry, although this is modified by the stellar rotation rate. We discuss the implications of these results for dynamo theory and the nature of stellar magnetic activity.

  19. Geometric Monte Carlo and black Janus geometries

    NASA Astrophysics Data System (ADS)

    Bak, Dongsu; Kim, Chanju; Kim, Kyung Kiu; Min, Hyunsoo; Song, Jeong-Pil

    2017-04-01

    We describe an application of the Monte Carlo method to the Janus deformation of the black brane background. We present numerical results for three and five dimensional black Janus geometries with planar and spherical interfaces. In particular, we argue that the 5D geometry with a spherical interface has an application in understanding the finite temperature bag-like QCD model via the AdS/CFT correspondence. The accuracy and convergence of the algorithm are evaluated with respect to the grid spacing. The systematic errors of the method are determined using an exact solution of 3D black Janus. This numerical approach for solving linear problems is unaffected initial guess of a trial solution and can handle an arbitrary geometry under various boundary conditions in the presence of source fields.

  20. Pearson's Functions to Describe FSW Weld Geometry

    SciTech Connect

    Lacombe, D.; Coupard, D.; Tcherniaeff, S.; Girot, F.; Gutierrez-Orrantia, M. E.

    2011-01-17

    Friction stir welding (FSW) is a relatively new joining technique particularly for aluminium alloys that are difficult to fusion weld. In this study, the geometry of the weld has been investigated and modelled using Pearson's functions. It has been demonstrated that the Pearson's parameters (mean, standard deviation, skewness, kurtosis and geometric constant) can be used to characterize the weld geometry and the tensile strength of the weld assembly. Pearson's parameters and process parameters are strongly correlated allowing to define a control process procedure for FSW assemblies which make radiographic or ultrasonic controls unnecessary. Finally, an optimisation using a Generalized Gradient Method allows to determine the geometry of the weld which maximises the assembly tensile strength.

  1. Supersymmetric geometries of IIA supergravity III

    NASA Astrophysics Data System (ADS)

    Gran, Ulf; Papadopoulos, George; von Schultz, Christian

    2016-06-01

    We find that (massive) IIA backgrounds that admit a {G}_2ltimes {mathbb{R}}^8 invariant Killing spinor must exhibit a null Killing vector field which leaves the Killing spinor invariant and that the rotation of the Killing vector field satisfies a certain g2 instanton condition. This result together with those in [4] and [5] complete the classification of geometries of all (massive) IIA backgrounds that preserve one supersymmetry. We also explore the geometry of a class of backgrounds which admit a {G}_2ltimes {mathbb{R}}^8 invariant Killing spinor and where in addition an appropriate 1-form bilinear vanishes. In all cases, we express the fluxes of the theory in terms of the geometry.

  2. Coordinate Geometry. Geometry Module for Use in a Mathematics Laboratory Setting.

    ERIC Educational Resources Information Center

    Brotherton, Sheila; And Others

    This is one of a series of geometry modules developed for use by secondary students in a laboratory setting. This module includes: (1) Pythagorean Theorem (with review of radicals); (2) Basic Coordinate Geometry (distance and midpoint, slope, slope of parallels and perpendiculars, and equation of a line); (3) Selecting Coordinates; (4) Coordinate…

  3. The Effect of Dynamic Geometry Software and Physical Manipulatives on Candidate Teachers' Transformational Geometry Success

    ERIC Educational Resources Information Center

    Yilmaz, Gül Kaleli

    2015-01-01

    This study aims to investigate the effects of using Dynamic Geometry Software (DGS) Cabri II Plus and physical manipulatives on the transformational geometry achievement of candidate teachers. In this study, the semi-experimental method was used, consisting of two experimental and one control groups. The samples of this study were 117 students. A…

  4. Using Dynamic Geometry Software to Improve Eight Grade Students' Understanding of Transformation Geometry

    ERIC Educational Resources Information Center

    Guven, Bulent

    2012-01-01

    This study examines the effect of dynamic geometry software (DGS) on students' learning of transformation geometry. A pre- and post-test quasi-experimental design was used. Participants in the study were 68 eighth grade students (36 in the experimental group and 32 in the control group). While the experimental group students were studying the…

  5. Aspects of electrostatics in BTZ geometries

    NASA Astrophysics Data System (ADS)

    Herrera, Y.; Hurovich, V.; Santillán, O.; Simeone, C.

    2015-10-01

    In the present paper the electrostatics of charges in nonrotating BTZ black hole and wormhole spacetimes is studied. Our attention is focused on the self-force of a point charge in the geometry, for which a regularization prescription based on the Haddamard Green function is employed. The differences between the self-force in both cases is a theoretical experiment for distinguishing both geometries, which otherwise are locally indistinguishable. This idea was applied before to four and higher-dimensional black holes by the present and other authors. However, the particularities of the BTZ geometry makes the analysis considerable more complicated than those. First, the BTZ spacetimes are not asymptotically flat but instead asymptotically AdS. In addition, the relative distance d (r ,r +1 ) between two particles located at a radius r and r +1 in the geometry tends to zero when r →∞. This behavior, which is radically different in a flat geometry, changes the analysis of the asymptotic conditions for the electrostatic field. The other problem is that there exist several regularization methods other than the one we are employing, and there does not exist a proof in three dimensions that they are equivalent. However, we focus on the Haddamard method and obtain an expression for the hypothetical self-force in series, and the resulting expansion is convergent to the real solution. We suspect that the convergence is not uniform, and furthermore there are no summation formulas at our disposal. It appears, for points that are far away from the black hole the calculation of the Haddamard self-force requires higher-order summation. These subtleties are carefully analyzed in the paper, and it is shown that they lead to severe problems when calculating the Haddamard self-force for asymptotic points in the geometry.

  6. Holographic Geometries for Condensed Matter Applications

    NASA Astrophysics Data System (ADS)

    Keränen, V.; Thorlacius, L.

    2015-01-01

    Holographic modeling of strongly correlated many-body systems motivates the study of novel spacetime geometries where the scaling behavior of quantum critical systems is encoded into spacetime symmetries. Einstein-Dilaton-Maxwell theory has planar black brane solutions that exhibit Lifshitz scaling and in some cases hyperscaling violation. Entanglement entropy and Wilson loops in the dual field theory are studied by inserting simple geometric probes involving minimal surfaces into the black brane geometry. Coupling to background matter fields leads to interesting low-energy behavior in holographic models, such as U(1) symmetry breaking and emergent Lifshitz scaling.

  7. Semiclassical geometry of charged black holes

    SciTech Connect

    Frolov, Andrei V.; Kristjansson, Kristjan R.; Thorlacius, Larus

    2005-07-15

    At the classical level, two-dimensional dilaton gravity coupled to an abelian gauge field has charged black hole solutions, which have much in common with four-dimensional Reissner-Nordstroem black holes, including multiple asymptotic regions, timelike curvature singularities, and Cauchy horizons. The black hole spacetime is, however, significantly modified by quantum effects, which can be systematically studied in this two-dimensional context. In particular, the back-reaction on the geometry due to pair-creation of charged fermions destabilizes the inner horizon and replaces it with a spacelike curvature singularity. The semiclassical geometry has the same global topology as an electrically neutral black hole.

  8. Thin shells joining local cosmic string geometries

    NASA Astrophysics Data System (ADS)

    Eiroa, Ernesto F.; Rubín de Celis, Emilio; Simeone, Claudio

    2016-10-01

    In this article we present a theoretical construction of spacetimes with a thin shell that joins two different local cosmic string geometries. We study two types of global manifolds, one representing spacetimes with a thin shell surrounding a cosmic string or an empty region with Minkowski metric, and the other corresponding to wormholes which are not symmetric across the throat located at the shell. We analyze the stability of the static configurations under perturbations preserving the cylindrical symmetry. For both types of geometries we find that the static configurations can be stable for suitable values of the parameters.

  9. Computational fluid dynamics using CATIA created geometry

    NASA Astrophysics Data System (ADS)

    Gengler, Jeanne E.

    1989-07-01

    A method has been developed to link the geometry definition residing on a CAD/CAM system with a computational fluid dynamics (CFD) tool needed to evaluate aerodynamic designs and requiring the memory capacity of a supercomputer. Requirements for surfaces suitable for CFD analysis are discussed. Techniques for developing surfaces and verifying their smoothness are compared, showing the capability of the CAD/CAM system. The utilization of a CAD/CAM system to create a computational mesh is explained, and the mesh interaction with the geometry and input file preparation for the CFD analysis is discussed.

  10. Solc filters in a reflective geometry

    NASA Astrophysics Data System (ADS)

    Messaadi, Abdelghafour; Vargas, Asticio; Sánchez-López, María M.; García-Martínez, Pascuala; Kula, Przemysław; Bennis, Noureddine; Moreno, Ignacio

    2017-04-01

    We present the realization of a bulk optics birefringent Solc filter in a reflective geometry. This geometry reduces by half the number of required retarders, ensures the same spectral retardance function in pairs of retarders, and helps to make more compact filters. The key element is a quarter-wave Fresnel rhomb located in between the set of retarders and a mirror. Two cases are considered: the first Solc filter uses multiple-order quartz retarders, and the second one uses two liquid-crystal retarders. The latter has the advantage of being tunable via an applied voltage. Experimental results show how to filter the spectral content of a supercontinuum laser.

  11. SABRINA - an interactive geometry modeler for MCNP

    SciTech Connect

    West, J.T.; Murphy, J. )

    1988-01-01

    One of the most difficult tasks when analyzing a complex three-dimensional system with Monte Carlo is geometry model development. SABRINA attempts to make the modeling process more user-friendly and less of an obstacle. It accepts both combinatorial solid bodies and MCNP surfaces and produces MCNP cells. The model development process in SABRINA is highly interactive and gives the user immediate feedback on errors. Users can view their geometry from arbitrary perspectives while the model is under development and interactively find and correct modeling errors. An example of a SABRINA display is shown. It represents a complex three-dimensional shape.

  12. Method for Determining Optimum Injector Inlet Geometry

    NASA Technical Reports Server (NTRS)

    Trinh, Huu P. (Inventor); Myers, W. Neill (Inventor)

    2015-01-01

    A method for determining the optimum inlet geometry of a liquid rocket engine swirl injector includes obtaining a throttleable level phase value, volume flow rate, chamber pressure, liquid propellant density, inlet injector pressure, desired target spray angle and desired target optimum delta pressure value between an inlet and a chamber for a plurality of engine stages. The method calculates the tangential inlet area for each throttleable stage. The method also uses correlation between the tangential inlet areas and delta pressure values to calculate the spring displacement and variable inlet geometry of a liquid rocket engine swirl injector.

  13. MRI quantification of human spine cartilage endplate geometry: Comparison with age, degeneration, level, and disc geometry.

    PubMed

    DeLucca, John F; Peloquin, John M; Smith, Lachlan J; Wright, Alexander C; Vresilovic, Edward J; Elliott, Dawn M

    2016-08-01

    Geometry is an important indicator of disc mechanical function and degeneration. While the geometry and associated degenerative changes in the nucleus pulposus and the annulus fibrosus are well-defined, the geometry of the cartilage endplate (CEP) and its relationship to disc degeneration are unknown. The objectives of this study were to quantify CEP geometry in three dimensions using an MRI FLASH imaging sequence and evaluate relationships between CEP geometry and age, degeneration, spinal level, and overall disc geometry. To do so, we assessed the MRI-based measurements for accuracy and repeatability. Next, we measured CEP geometry across a larger sample set and correlated CEP geometric parameters to age, disc degeneration, level, and disc geometry. The MRI-based measures resulted in thicknesses (0.3-1 mm) that are comparable to prior measurements of CEP thickness. CEP thickness was greatest at the anterior/posterior (A/P) margins and smallest in the center. The CEP A/P thickness, axial area, and lateral width decreased with age but were not related to disc degeneration. Age-related, but not degeneration-related, changes in geometry suggest that the CEP may not follow the progression of disc degeneration. Ultimately, if the CEP undergoes significant geometric changes with aging and if these can be related to low back pain, a clinically feasible translation of the FLASH MRI-based measurement of CEP geometry presented in this study may prove a useful diagnostic tool. © 2016 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 34:1410-1417, 2016.

  14. SABRINA: an interactive solid geometry modeling program for Monte Carlo

    SciTech Connect

    West, J.T.

    1985-01-01

    SABRINA is a fully interactive three-dimensional geometry modeling program for MCNP. In SABRINA, a user interactively constructs either body geometry, or surface geometry models, and interactively debugs spatial descriptions for the resulting objects. This enhanced capability significantly reduces the effort in constructing and debugging complicated three-dimensional geometry models for Monte Carlo Analysis.

  15. Alignment of Elementary Geometry Curriculum with Current Standards.

    ERIC Educational Resources Information Center

    Pickreign, Jamar; Capps, Lelon R.

    2000-01-01

    Examines geometry language used in K-6 textbooks and compares the findings to language used in modern mathematics standards documents. Finds a substantial misalignment between the geometry presented in textbooks, the geometry teaching expectations of mathematics education professionals, and the geometry being assessed in student performance…

  16. Project-Based Learning to Explore Taxicab Geometry

    ERIC Educational Resources Information Center

    Ada, Tuba; Kurtulus, Aytac

    2012-01-01

    In Turkey, the content of the geometry course in the Primary School Mathematics Education, which is developed by The Council of Higher Education (YOK), comprises Euclidean and non-Euclidean types of geometry. In this study, primary mathematics teacher candidates compared these two geometries by focusing on Taxicab geometry among non-Euclidean…

  17. Honeycomb Geometry: Applied Mathematics in Nature.

    ERIC Educational Resources Information Center

    Roberts, William J.

    1984-01-01

    Study and exploration of the hexagonal shapes found in honeycombs is suggested as an interesting topic for geometry classes. Students learn that the hexagonal pattern maximizes the enclosed region and minimizes the wax needed for construction, while satisfying the bees' cell-size constraint. (MNS)

  18. Fostering Spatial vs. Metric Understanding in Geometry

    ERIC Educational Resources Information Center

    Kinach, Barbara M.

    2012-01-01

    Learning to reason spatially is increasingly recognized as an essential component of geometry education. Generally taken to be the "ability to represent, generate, transform, communicate, document, and reflect on visual information," "spatial reasoning" uses the spatial relationships between objects to form ideas. Spatial thinking takes a variety…

  19. SPICE: A Means for Determining Observation Geometry

    NASA Astrophysics Data System (ADS)

    Acton, C.; Bachman, N.; Diaz Del Rio, J.; Semenov, B.; Wright, E.; Yamamoto, Y.

    2011-10-01

    The "SPICE"1system is the NASA Planetary Science Division's method of conveniently packaging, archiving, and subsequently accessing observation geometry needed to understand science data returned from robotic spacecraft. This paper provides an overview of "SPICE"-what it is and how it's used- and then offers a glimpse into how it is being extended to better support the space science community.

  20. Learning Geometry by Designing Persian Mosaics

    ERIC Educational Resources Information Center

    Karssenberg, Goossen

    2014-01-01

    To encourage students to do geometry, the art of Islamic geometric ornamentation was chosen as the central theme of a lesson strand which was developed using the newly presented didactical tool called "Learning by Acting". The Dutch students who took these lessons in 2010 to 2013 were challenged to act as if they themselves were Persian…

  1. Discernment of Invariants in Dynamic Geometry Environments

    ERIC Educational Resources Information Center

    Leung, Allen; Baccaglini-Frank, Anna; Mariotti, Maria Alessandra

    2013-01-01

    In this paper, we discuss discernment of invariants in dynamic geometry environments (DGE) based on a combined perspective that puts together the lens of variation and the maintaining dragging strategy developed previously by the authors. We interpret and describe a model of discerning invariants in DGE through types of variation awareness and…

  2. Effectivizing the geometry of the curve complex

    NASA Astrophysics Data System (ADS)

    Aougab, Tarik

    This thesis is devoted to understanding how the geometry of the curve complex of a surface S, the Teichmuller space of S, and of the mapping class group of S explicitly depend on the underlying topology of S. Moreover, this thesis demonstrates that the geometry of the mapping class group, and the tools used to study this geometry such as Masur and Minsky's celebrated distance formula, can be used to answer basic, but surprisingly challenging questions related to the combinatorial properties of curves on surfaces. In particular, we prove that all curve graphs are uniformly hyperbolic, independent of the topology of the underlying surface. We also give effective versions of several results regarding train track splitting sequences, and the subset of the curve graph corresponding to curves which bound disks in a handlebody. Finally, we study the local geometry of a family of curve graphs all related to the same surface, and specifically we give upper and lower bounds on the maximum size of a complete subgraph for these graphs.

  3. Applications of Differential Geometry to Cartography

    ERIC Educational Resources Information Center

    Benitez, Julio; Thome, Nestor

    2004-01-01

    This work introduces an application of differential geometry to cartography. The mathematical aspects of some geographical projections of Earth surface are revealed together with some of its more important properties. An important problem since the discovery of the 'spherical' form of the Earth is how to compose a reliable map of the surface of…

  4. User Interface Design for Dynamic Geometry Software

    ERIC Educational Resources Information Center

    Kortenkamp, Ulrich; Dohrmann, Christian

    2010-01-01

    In this article we describe long-standing user interface issues with Dynamic Geometry Software and common approaches to address them. We describe first prototypes of multi-touch-capable DGS. We also give some hints on the educational benefits of proper user interface design.

  5. Meromorphic Higgs bundles and related geometries

    NASA Astrophysics Data System (ADS)

    Dalakov, Peter

    2016-11-01

    The present note is mostly a survey on the generalised Hitchin integrable system and moduli spaces of meromorphic G-Higgs bundles. We also fill minor gaps in the existing literature, outline a calculation of the infinitesimal period map and review some related geometries.

  6. Hydrophobicity of silver surfaces with microparticle geometry

    NASA Astrophysics Data System (ADS)

    Macko, Ján; Oriňaková, Renáta; Oriňak, Andrej; Kovaľ, Karol; Kupková, Miriam; Erdélyi, Branislav; Kostecká, Zuzana; Smith, Roger M.

    2016-11-01

    The effect of the duration of the current deposition cycle and the number of current pulses on the geometry of silver microstructured surfaces and on the free surface energy, polarizability, hydrophobicity and thus adhesion force of the silver surfaces has been investigated. The changes in surface hydrophobicity were entirely dependent on the size and density of the microparticles on the surface. The results showed that formation of the silver microparticles was related to number of current pulses, while the duration of one current pulse played only a minor effect on the final surface microparticle geometry and thus on the surface tension and hydrophobicity. The conventional geometry of the silver particles has been transformed to the fractal dimension D. The surface hydrophobicity depended predominantly on the length of the dendrites not on their width. The highest silver surface hydrophobicity was observed on a surface prepared by 30 current pulses with a pulse duration of 1 s, the lowest one when deposition was performed by 10 current pulses with a duration of 0.1 s. The partial surface tension coefficients γDS and polarizability kS of the silver surfaces were calculated. Both parameters can be applied in future applications in living cells adhesion prediction and spectral method selection. Silver films with microparticle geometry showed a lower variability in final surface hydrophobicity when compared to nanostructured surfaces. The comparisons could be used to modify surfaces and to modulate human cells and bacterial adhesion on body implants, surgery instruments and clean surfaces.

  7. Asynchronous event-based hebbian epipolar geometry.

    PubMed

    Benosman, Ryad; Ieng, Sio-Hoï; Rogister, Paul; Posch, Christoph

    2011-11-01

    Epipolar geometry, the cornerstone of perspective stereo vision, has been studied extensively since the advent of computer vision. Establishing such a geometric constraint is of primary importance, as it allows the recovery of the 3-D structure of scenes. Estimating the epipolar constraints of nonperspective stereo is difficult, they can no longer be defined because of the complexity of the sensor geometry. This paper will show that these limitations are, to some extent, a consequence of the static image frames commonly used in vision. The conventional frame-based approach suffers from a lack of the dynamics present in natural scenes. We introduce the use of neuromorphic event-based--rather than frame-based--vision sensors for perspective stereo vision. This type of sensor uses the dimension of time as the main conveyor of information. In this paper, we present a model for asynchronous event-based vision, which is then used to derive a general new concept of epipolar geometry linked to the temporal activation of pixels. Practical experiments demonstrate the validity of the approach, solving the problem of estimating the fundamental matrix applied, in a first stage, to classic perspective vision and then to more general cameras. Furthermore, this paper shows that the properties of event-based vision sensors allow the exploration of not-yet-defined geometric relationships, finally, we provide a definition of general epipolar geometry deployable to almost any visual sensor.

  8. From wave geometry to fake supergravity

    NASA Astrophysics Data System (ADS)

    Townsend, Paul K.

    2008-08-01

    The 'Wave Geometry' equation of the pre-WWII Hiroshima program is also the key equation of the current 'fake supergravity' program. I review the status of (fake) supersymmetric domain walls and (fake) pseudo-supersymmetric cosmologies. An extension of the domain-wall/cosmology correspondence to a triple correspondence with instantons shows that 'pseudo-supersymmetry' has another interpretation as the Euclidean supersymmetry.

  9. Solving Geometry Problems via Mechanical Principles

    ERIC Educational Resources Information Center

    Man, Yiu Kwong

    2004-01-01

    The application of physical principles in solving mathematics problems have often been neglected in the teaching of physics or mathematics, especially at the secondary school level. This paper discusses how to apply the mechanical principles to geometry problems via concrete examples, which aims at providing insight and inspirations to physics or…

  10. Transport Code for Regular Triangular Geometry

    SciTech Connect

    1993-06-09

    DIAMANT2 solves the two-dimensional static multigroup neutron transport equation in planar regular triangular geometry. Both regular and adjoint, inhomogeneous and homogeneous problems subject to vacuum, reflective or input specified boundary flux conditions are solved. Anisotropy is allowed for the scattering source. Volume and surface sources are allowed for inhomogeneous problems.

  11. The Valence Bond Interpretation of Molecular Geometry.

    ERIC Educational Resources Information Center

    Smith, Derek W.

    1980-01-01

    Presents ways in which the valence bond (VB) theory describes the bonding and geometry of molecules, following directly from earlier principles laid down by Pauling and others. Two other theories (molecular orbital approach and valence shell electron pair repulsion) are discussed and compared to VB. (CS)

  12. Special Relativity as a Simple Geometry Problem

    ERIC Educational Resources Information Center

    de Abreu, Rodrigo; Guerra, Vasco

    2009-01-01

    The null result of the Michelson-Morley experiment and the constancy of the one-way speed of light in the "rest system" are used to formulate a simple problem, to be solved by elementary geometry techniques using a pair of compasses and non-graduated rulers. The solution consists of a drawing allowing a direct visualization of all the fundamental…

  13. Connecting Functions in Geometry and Algebra

    ERIC Educational Resources Information Center

    Steketee, Scott; Scher, Daniel

    2016-01-01

    One goal of a mathematics education is that students make significant connections among different branches of mathematics. Connections--such as those between arithmetic and algebra, between two-dimensional and three-dimensional geometry, between compass-and-straight-edge constructions and transformations, and between calculus and analytic…

  14. Environment Study with Buckminster Fuller's Geometry

    ERIC Educational Resources Information Center

    Cohen, Martin J.; Petrillo, Joseph

    1972-01-01

    Describes the teaching of geodesic-dome concepts to students in grades 3-5 through the trial use of Energetic and Synergetic Geometry as well as the undertaking of a workshop designed to prepare elementary and secondary school teachers to conduct further experiments. (CC)

  15. The Geometry of the Universe: Part 1

    ERIC Educational Resources Information Center

    Francis, Stephanie

    2009-01-01

    This article describes how the author carries out an investigation into the geometry of the three possible curvatures of the universe. The author begins the investigation by looking on the web and in books. She found that the general consensus was that there were three different possible curvatures of the universe, namely: (1) flat; (2) positive;…

  16. Geometry and the Design of Product Packaging

    ERIC Educational Resources Information Center

    Cherico, Cindy M.

    2011-01-01

    The most common question the author's students ask is, "When will I ever use this in real life?" To address this question in her geometry classes, the author sought to create a project that would incorporate a real-world business situation with their lesson series on the surface area and volume of three-dimensional objects--specifically, prisms,…

  17. Magnetic resonance spectra and statistical geometry

    Technology Transfer Automated Retrieval System (TEKTRAN)

    Methods of statistical geometry are introduced which allow one to estimate, on the basis of computable criteria, the conditions under which maximally informative data may be collected. We note the important role of constraints that introduce curvature into parameter space and discuss the appropriate...

  18. Children's Use of Geometry for Reorientation

    ERIC Educational Resources Information Center

    Lee, Sang Ah; Spelke, Elizabeth S.

    2008-01-01

    Research on navigation has shown that humans and laboratory animals recover their sense of orientation primarily by detecting geometric properties of large-scale surface layouts (e.g. room shape), but the reasons for the primacy of layout geometry have not been clarified. In four experiments, we tested whether 4-year-old children reorient by the…

  19. Determining Fault Geometries From Surface Displacements

    NASA Astrophysics Data System (ADS)

    Volkov, D.; Voisin, C.; Ionescu, I. R.

    2017-02-01

    We introduce a new algorithm for determining the geometry of active parts of faults. This algorithm uses surface measurements of displacement fields and local modeling of the Earth's crust as a half-space elastic medium. The numerical method relies on iterations alternating non-linear steps for recovering the geometry and linear steps for reconstructing slip fields. Our algorithm greatly improves upon past attempts at reconstructing fault profiles. We argue that these past attempts suffered from either the restrictive assumption that the geometry of faults can be derived using only uniformly constant slips or that they relied on arbitrary assumptions on the statistics of the reconstruction error. We test this algorithm on the 2006 Guerrero, Mexico, slow slip event (SSE) and on the 2009 SSE for the same region. These events occurred on a relatively well-known subduction zone, whose geometry was derived from seismicity and gravimetric techniques, see Kostoglodov et al. (Geophys Res Lett 23(23):3385-3388, 1996), Pardo and Suarez (J Geophys Res 100(B7):357-373, 1995), Singh and Pardo (Geophys Res Lett 20(14):1483-1486, 1993), so our results can be compared to known benchmarks. Our derived geometry is found to be consistent with these benchmarks regarding dip and strike angles and the positioning of the North American Trench. In addition, our derived slip distribution is also consistent with previous studies (all done with an assumed fixed geometry), see Larson et al. (Geophys Res Lett 34(13), 2007), Bekaert et al. (J Geophys Res: Solid Earth 120(2):1357-1375, 2015), Radiguet et al. (Geophys J Int 184(2):816-828, 2011, J Geophys Res 2012), Rivet et al. (Geophys Res Lett 38(8), 2011), Vergnolle et al. (J Geophys Res: Solid Earth 115(B8), 2010), Walpersdorf et al. Geophys Res Lett 38(15), 2011), to name a few. We believe that the new computational inverse method introduced in this paper holds great promise for applications to blind inversion cases, where both geometry and

  20. The Study of "Elementary Geometry" (1903) by Godfrey and Siddons (1): Roles of Experimental Tasks in the Teaching of Geometry.

    ERIC Educational Resources Information Center

    Fujita, Taro

    2001-01-01

    Examines the roles of experimental tasks in "Elementary Geometry" (1903) by Godfrey and Siddons, which is considered one of the most important geometry textbooks in the history of geometry teaching. Roles of experimental tasks included preparations for deductive geometry and, even though it is implicit, the verification of geometrical facts.…

  1. Potentials for Spatial Geometry Curriculum Development with Three-Dimensional Dynamic Geometry Software in Lower Secondary Mathematics

    ERIC Educational Resources Information Center

    Miyazaki, Mikio; Kimiho, Chino; Katoh, Ryuhei; Arai, Hitoshi; Ogihara, Fumihiro; Oguchi, Yuichi; Morozumi, Tatsuo; Kon, Mayuko; Komatsu, Kotaro

    2012-01-01

    Three-dimensional dynamic geometry software has the power to enhance students' learning of spatial geometry. The purpose of this research is to clarify what potential using three-dimensional dynamic geometry software can offer us in terms of how to develop the spatial geometry curriculum in lower secondary schools. By focusing on the impacts the…

  2. Predicting the Geometry Knowledge of Pre-Service Elementary Teachers (Sinif Ögretmeni Adaylarinin Geometri Bilgilerinin Yordanmasi)

    ERIC Educational Resources Information Center

    Duatepe Aksu, Asuman

    2013-01-01

    In this study, the aim was to examine the factors that predict the geometry knowledge of pre-service elementary teachers. Data was collected on 387 pre-service elementary teachers from four universities by using a geometry knowledge test, the van Hiele geometric thinking level test, a geometry self efficacy scale and a geometry attitude scale.…

  3. Automatic Conversion of Conceptual Geometry to CFD Geometry for Aircraft Design

    NASA Technical Reports Server (NTRS)

    Li, Wu

    2007-01-01

    Conceptual aircraft design is usually based on simple analysis codes. Its objective is to provide an overall system performance of the developed concept, while preliminary aircraft design uses high-fidelity analysis tools such as computational fluid dynamics (CFD) analysis codes or finite element structural analysis codes. In some applications, such as low-boom supersonic concept development, it is important to be able to explore a variety of drastically different configurations while using CFD analysis to check whether a given configuration can be tailored to have a low-boom ground signature. It poses an extremely challenging problem of integrating CFD analysis in conceptual design. This presentation will discuss a computer code, called iPatch, for automatic conversion of conceptual geometry to CFD geometry. In general, conceptual aircraft geometry is not as well-defined as a CAD geometry model. In particular, a conceptual aircraft geometry model usually does not define the intersection curves for the connecting surfaces. The computer code iPatch eliminates the gap between conceptual geometry and CFD geometry by accomplishing the following three tasks automatically: (1) use bicubic B-splines to extrapolate (if necessary) each surface in a conceptual geometry so that all the independently defined geometry components (such as wing and fuselage) can be intersected to form a watertight CFD geometry, (2) compute the intersection curves of surface patches at any resolution (up to 10-7 accuracy) specified by users, and (3) write the B-spline surface patches and the corresponding boundary points for the watertight CFD geometry in the format that can be directly exported to the meshing tool VGRID in the CFD software TetrUSS. As a result, conceptual designers can get quick feedback on the aerodynamic characteristics of their concepts, which will allow them to understand some subtlety in their concepts and to be able to assess their concepts with a higher degree of

  4. Shadow of noncommutative geometry inspired black hole

    SciTech Connect

    Wei, Shao-Wen; Cheng, Peng; Zhong, Yi; Zhou, Xiang-Nan E-mail: pcheng14@lzu.edu.cn E-mail: zhouxn10@lzu.edu.cn

    2015-08-01

    In this paper, the shadow casted by the rotating black hole inspired by noncommutative geometry is investigated. In addition to the dimensionless spin parameter a/M{sub 0} with M{sub 0} black hole mass and inclination angle i, the dimensionless noncommutative parameter √θ/M{sub 0} is also found to affect the shape of the black hole shadow. The result shows that the size of the shadow slightly decreases with the parameter √θ/M{sub 0}, while the distortion increases with it. Compared to the Kerr black hole, the parameter √θ/M{sub 0} increases the deformation of the shadow. This may offer a way to distinguish noncommutative geometry inspired black hole from Kerr one via astronomical instruments in the near future.

  5. Impacts of Conformational Geometries in Fluorinated Alkanes

    NASA Astrophysics Data System (ADS)

    Brandenburg, Tim; Golnak, Ronny; Nagasaka, Masanari; Atak, Kaan; Sreekantan Nair Lalithambika, Sreeju; Kosugi, Nobuhiro; Aziz, Emad F.

    2016-08-01

    Research of blood substitute formulations and their base materials is of high scientific interest. Especially fluorinated microemulsions based on perfluorocarbons, with their interesting chemical properties, offer opportunities for applications in biomedicine and physical chemistry. In this work, carbon K-edge absorption spectra of liquid perfluoroalkanes and their parent hydrocarbons are presented and compared. Based on soft X-ray absorption, a comprehensive picture of the electronic structure is provided with the aid of time dependent density functional theory. We have observed that conformational geometries mainly influence the chemical and electronic interactions in the presented liquid materials, leading to a direct association of conformational geometries to the dissolving capacity of the presented perfluorocarbons with other solvents like water and possibly gases like oxygen.

  6. A linguistic geometry for space applications

    NASA Technical Reports Server (NTRS)

    Stilman, Boris

    1994-01-01

    We develop a formal theory, the so-called Linguistic Geometry, in order to discover the inner properties of human expert heuristics, which were successful in a certain class of complex control systems, and apply them to different systems. This research relies on the formalization of search heuristics of high-skilled human experts which allow for the decomposition of complex system into the hierarchy of subsystems, and thus solve intractable problems reducing the search. The hierarchy of subsystems is represented as a hierarchy of formal attribute languages. This paper includes a formal survey of the Linguistic Geometry, and new example of a solution of optimization problem for the space robotic vehicles. This example includes actual generation of the hierarchy of languages, some details of trajectory generation and demonstrates the drastic reduction of search in comparison with conventional search algorithms.

  7. Collective neutrino oscillations in nonspherical geometry

    SciTech Connect

    Dasgupta, Basudeb; Dighe, Amol; Mirizzi, Alessandro; Raffelt, Georg

    2008-08-01

    The rich phenomenology of collective neutrino oscillations has been studied only in one-dimensional or spherically symmetric systems. Motivated by the nonspherical example of coalescing neutron stars, presumably the central engines of short gamma-ray bursts, we use the Liouville equation to formulate the problem for general source geometries. Assuming the neutrino ensemble displays self-maintained coherence, the problem once more becomes effectively one-dimensional along the streamlines of the overall neutrino flux. This approach for the first time provides a formal definition of the 'single-angle approximation' frequently used for supernova neutrinos and allows for a natural generalization to nonspherical geometries. We study the explicit example of a disk-shaped source as a proxy for coalescing neutron stars.

  8. Doppler effect in Schwarzschild and Kerr geometries

    NASA Astrophysics Data System (ADS)

    Radosz, A.; Augousti, A. T.; Ostasiewicz, K.

    2008-03-01

    Calculation of the Doppler shift in general relativity involves contributions of gravitational and kinematical origins and for most metrics or trajectories these contributions are coupled. The exact expression for this Doppler shift may simplify for particular symmetries. Here the specific case for a light signal emitted by a distant inertial observer and received by an in-falling observer in a Schwarzschild geometry is discussed. The resulting expression the Doppler shift is composed of simple factors that can be clearly identified with contributions arising from classical kinematical, special relativistic and general relativistic origins. This result turns out to be more general and it holds for a case of an arbitrary radial in-fall in Schwarzschild geometry and for a particular type of in-fall in the case of a Kerr metric.

  9. The universal instability in general geometry

    SciTech Connect

    Helander, P.; Plunk, G. G.

    2015-09-15

    The “universal” instability has recently been revived by Landreman et al. [Phys. Rev. Lett. 114, 095003 (2015)], who showed that it indeed exists in plasma geometries with straight (but sheared) magnetic field lines. Here, it is demonstrated analytically that this instability can be presented in more general sheared and toroidal geometries. In a torus, the universal instability is shown to be closely related to the trapped-electron mode, although the trapped-electron drive is usually dominant. However, this drive can be weakened or eliminated, as in the case in stellarators with the maximum-J property, leaving the parallel Landau resonance to drive a residual mode, which is identified as the universal instability.

  10. Multiscale Talbot effects in Fibonacci geometry

    NASA Astrophysics Data System (ADS)

    Ho, I.-Lin; Chang, Yia-Chung

    2015-04-01

    This article investigates the Talbot effects in Fibonacci geometry by introducing the cut-and-projection construction, which allows for capturing the entire infinite Fibonacci structure in a single computational cell. Theoretical and numerical calculations demonstrate the Talbot foci of Fibonacci geometry at distances that are multiples (τ +2){{({{F}μ }+τ {{F}μ +1})}-1}p/(2q) or (τ +2){{({{L}μ }+τ {{L}μ +1})}-1}p/(2q) of the Talbot distance. Here (p, q) are coprime integers, μ is an integer, τ is the golden mean, and {{F}μ } and {{L}μ } are Fibonacci and Lucas numbers, respectively. The image of a single Talbot focus exhibits a multiscale-interval pattern due to the self-similarity of the scaling Fourier spectrum.

  11. Bending of Light in Ellis Wormhole Geometry

    NASA Astrophysics Data System (ADS)

    Bhattacharya, Amrita; Potapov, Alexander A.

    A recent work by Dey and Sen derived the approximate light deflection angle α by an Ellis wormhole in terms of proper radial distance ℓ that covers the entire spacetime. On the other hand, Bodenner and Will calculated the expressions for light bending in Schwarzschild geometry using various coordinates and showed that they all reduce to a single formula when re-expressed in the coordinate independent language of "circumferential radius" rC identified with the standard radial coordinate rS. We shall argue that the coordinate invariant language for two-way wormholes should be ℓ rather than rS. Hence here we find the exact deflection α in Ellis wormhole geometry first in terms of ℓ and then in terms of rS. We confirm the latter expression using three different methods. We argue that the practical measurement scheme does not necessarily single out either ℓ or rS. Some errors in the literature are corrected.

  12. Emergent Geometry from Entropy and Causality

    NASA Astrophysics Data System (ADS)

    Engelhardt, Netta

    In this thesis, we investigate the connections between the geometry of spacetime and aspects of quantum field theory such as entanglement entropy and causality. This work is motivated by the idea that spacetime geometry is an emergent phenomenon in quantum gravity, and that the physics responsible for this emergence is fundamental to quantum field theory. Part I of this thesis is focused on the interplay between spacetime and entropy, with a special emphasis on entropy due to entanglement. In general spacetimes, there exist locally-defined surfaces sensitive to the geometry that may act as local black hole boundaries or cosmological horizons; these surfaces, known as holographic screens, are argued to have a connection with the second law of thermodynamics. Holographic screens obey an area law, suggestive of an association with entropy; they are also distinguished surfaces from the perspective of the covariant entropy bound, a bound on the total entropy of a slice of the spacetime. This construction is shown to be quite general, and is formulated in both classical and perturbatively quantum theories of gravity. The remainder of Part I uses the Anti-de Sitter/ Conformal Field Theory (AdS/CFT) correspondence to both expand and constrain the connection between entanglement entropy and geometry. The AdS/CFT correspondence posits an equivalence between string theory in the "bulk" with AdS boundary conditions and certain quantum field theories. In the limit where the string theory is simply classical General Relativity, the Ryu-Takayanagi and more generally, the Hubeny-Rangamani-Takayanagi (HRT) formulae provide a way of relating the geometry of surfaces to entanglement entropy. A first-order bulk quantum correction to HRT was derived by Faulkner, Lewkowycz and Maldacena. This formula is generalized to include perturbative quantum corrections in the bulk at any (finite) order. Hurdles to spacetime emergence from entanglement entropy as described by HRT and its quantum

  13. Dewetting processes in a cylindrical geometry.

    PubMed

    Callegari, G; Calvo, A; Hulin, J P

    2005-03-01

    Dewetting of liquid films of water-glycerol solutions of different viscosities has been studied experimentally in PVC cylindrical tubes. In contrast with plane surfaces, the dewetting capillary number Ca(vd) increases with the film thickness ho over a large part of the experimental range and follows a same global trend independent of viscosity as a function of ho. This increase is only partly explained by variations of the capillary driving force predicted in a recent theoretical work for a cylindrical geometry. An additional explanation is suggested, based on different spatial distributions of the viscous dissipation in the dewetting bump in the planar and cylindrical geometries. This mechanism is investigated for films of different thicknesses in a numerical model assuming a polynomial variation of the liquid thickness with distance in the bump region.

  14. Damage experiments in a cylindrical geometry

    SciTech Connect

    Kaul, Ann M

    2010-09-21

    Studying spallation damage with a cylindrical configuration allows for a natural recollection of the damaged material under proper driving conditions. Additionally, the damaged material can come to a complete rest without the application of further stopping forces. Specific areas of research include the damage initiation regime in convergent geometry, behavior of material recollected after damage, and effects of convergent geometry on the material response. Such experiments produce unique strain and shear stress states, motivating improvements in existing computational material models and increasing the predictive capabilities of codes. A LANL/VNIIEF joint experimental series has produced cylindrical aluminum failure initiation data and studied the behavior of material recollected after damage initiation and after complete failure. In addition to post-shot collection of the damaged target material for subsequent metallographic analysis, dynamic in-situ experimental diagnostics include velocimetry and transverse radial radiography. This paper will discuss the current experimental status.

  15. Impacts of Conformational Geometries in Fluorinated Alkanes

    PubMed Central

    Brandenburg, Tim; Golnak, Ronny; Nagasaka, Masanari; Atak, Kaan; Sreekantan Nair Lalithambika, Sreeju; Kosugi, Nobuhiro; Aziz, Emad F.

    2016-01-01

    Research of blood substitute formulations and their base materials is of high scientific interest. Especially fluorinated microemulsions based on perfluorocarbons, with their interesting chemical properties, offer opportunities for applications in biomedicine and physical chemistry. In this work, carbon K-edge absorption spectra of liquid perfluoroalkanes and their parent hydrocarbons are presented and compared. Based on soft X-ray absorption, a comprehensive picture of the electronic structure is provided with the aid of time dependent density functional theory. We have observed that conformational geometries mainly influence the chemical and electronic interactions in the presented liquid materials, leading to a direct association of conformational geometries to the dissolving capacity of the presented perfluorocarbons with other solvents like water and possibly gases like oxygen. PMID:27527753

  16. Schwarzschild geometry emerging from matrix models

    NASA Astrophysics Data System (ADS)

    Blaschke, Daniel N.; Steinacker, Harold

    2010-09-01

    We demonstrate how various geometries can emerge from Yang-Mills-type matrix models with branes, and consider the examples of Schwarzschild and Reissner-Nordström geometries. We provide an explicit embedding of these branes in \\mathds{R}^{2,5} and \\mathds{R}^{4,6}, as well as an appropriate Poisson resp. symplectic structure which determines the non-commutativity of spacetime. The embedding is asymptotically flat with the asymptotically constant θμν for large r, and therefore suitable for a generalization to many-body configurations. This is an illustration of our previous work (Blaschke and Steinacker 2010 Class. Quantum Grav. 27 165010 (arXiv:1003.4132)), where we have shown how the Einstein-Hilbert action can be realized within such matrix models.

  17. Robust optimisation of railway crossing geometry

    NASA Astrophysics Data System (ADS)

    Wan, Chang; Markine, Valeri; Dollevoet, Rolf

    2016-05-01

    This paper presents a methodology for improving the crossing (frog) geometry through the robust optimisation approach, wherein the variability of the design parameters within a prescribed tolerance is included in the optimisation problem. Here, the crossing geometry is defined by parameterising the B-spline represented cross-sectional shape and the longitudinal height profile of the nose rail. The dynamic performance of the crossing is evaluated considering the variation of wheel profiles and track alignment. A multipoint approximation method (MAM) is applied in solving the optimisation problem of minimising the contact pressure during the wheel-rail contact and constraining the location of wheel transition at the crossing. To clarify the difference between the robust optimisation and the normal deterministic optimisation approaches, the optimisation problems are solved in both approaches. The results show that the deterministic optimum fails under slight change of the design variables; the robust optimum, however, has improved and robust performance.

  18. Downstream hydraulic geometry of alluvial rivers

    NASA Astrophysics Data System (ADS)

    Julien, P. Y.

    2015-03-01

    This article presents a three-level approach to the analysis of downstream hydraulic geometry. First, empirical concepts based on field observations of "poised" conditions in irrigation canals are examined. Second, theoretical developments have been made possible by combining basic relationships for the description of flow and sediment transport in alluvial rivers. Third, a relatively new concept of equivalent channel widths is presented. The assumption of equilibrium may describe a perpetual state of change and adjustments. The new concepts define the trade-offs between some hydraulic geometry parameters such as width and slope. The adjustment of river widths and slope typically follows a decreasing exponential function and recent developments indicate how the adjustment time scale can be quantified. Some examples are also presented to illustrate the new concepts presented and the realm of complex river systems.

  19. Inductor Geometry With Improved Energy Density

    SciTech Connect

    Cui, H; Ngo, KDT; Moss, J; Lim, MHF; Rey, E

    2014-10-01

    The "constant-flux" concept is leveraged to achieve high magnetic-energy density, leading to inductor geometries with height significantly lower than that of conventional products. Techniques to shape the core and to distribute the winding turns to shape a desirable field profile are described for the two basic classes of magnetic geometries: those with the winding enclosed by the core and those with the core enclosed by the winding. A relatively constant flux distribution is advantageous not only from the density standpoint, but also from the thermal standpoint via the reduction of hot spots, and from the reliability standpoint via the suppression of flux crowding. In this journal paper on a constant-flux inductor (CFI) with enclosed winding, the foci are operating principle, dc analysis, and basic design procedure. Prototype cores and windings were routed from powder-iron disks and copper sheets, respectively. The design of CFI was validated by the assembled inductor prototype.

  20. Damage experiments in cylindrical geometry update

    SciTech Connect

    Kaul, Anne; Holtkamp, David; Rodriguez, George

    2009-01-01

    Using a cylindrical configuration to study spallation damage allows for a natural recollection of the damaged material under proper driving conditions. Previous experiments provided data about failure initiation in aluminum in a cylindrical geometry and the behavior of material recollected after damage from pressures in the damage initiation regime. The current series of experiments studied the behavior of material recollected after complete failure. Results from the current experiments will be presented.

  1. Coaxial inverted geometry transistor having buried emitter

    NASA Technical Reports Server (NTRS)

    Hruby, R. J.; Cress, S. B.; Dunn, W. R. (Inventor)

    1973-01-01

    The invention relates to an inverted geometry transistor wherein the emitter is buried within the substrate. The transistor can be fabricated as a part of a monolithic integrated circuit and is particularly suited for use in applications where it is desired to employ low actuating voltages. The transistor may employ the same doping levels in the collector and emitter, so these connections can be reversed.

  2. Geodesics and submanifold structures in conformal geometry

    NASA Astrophysics Data System (ADS)

    Belgun, Florin

    2015-05-01

    A conformal structure on a manifold Mn induces natural second order conformally invariant operators, called Möbius and Laplace structures, acting on specific weight bundles of M, provided that n ≥ 3. By extending the notions of Möbius and Laplace structures to the case of surfaces and curves, we develop here the theory of extrinsic conformal geometry for submanifolds, find tensorial invariants of a conformal embedding, and use these invariants to characterize various notions of geodesic submanifolds.

  3. Analytic Coleman-de Luccia Geometries

    SciTech Connect

    Dong, Xi; Harlow, Daniel; /Stanford U., ITP /Stanford U., Phys. Dept.

    2012-02-16

    We present the necessary and sufficient conditions for a Euclidean scale factor to be a solution of the Coleman-de Luccia equations for some analytic potential V ({psi}), with a Lorentzian continuation describing the growth of a bubble of lower-energy vacuum surrounded by higher-energy vacuum. We then give a set of explicit examples that satisfy the conditions and thus are closed-form analytic examples of Coleman-de Luccia geometries.

  4. Effective geometries in self-gravitating polytropes

    SciTech Connect

    Bini, D.; Cherubini, C.; Filippi, S.

    2008-09-15

    Perturbations of a perfect barotropic and irrotational Newtonian self-gravitating fluid are studied using a generalization of the so-called 'effective geometry' formalism. The case of polytropic spherical stars, as described by the Lane-Emden equation, is studied in detail in the known cases of existing explicit solutions. The present formulation gives a natural scenario in which the acoustic analogy has relevance for both stellar and galactic dynamics.

  5. Multilinear Computing and Multilinear Algebraic Geometry

    DTIC Science & Technology

    2016-08-10

    satisfying a polynomial growth condi- tion: for such a given function, computation of its Fenchel dual/conjugate is polynomial-time reducible to...computation of the given function. Hence the computation of a norm or a convex function of polynomial growth is NP-hard if and only if the computation of... growth and that of its Fenchel dual. This paper has been submitted and is available as a preprint (see [19] in Section 4) Semialgebraic geometry of

  6. The Geometry of Noncommutative Space-Time

    NASA Astrophysics Data System (ADS)

    Mendes, R. Vilela

    2016-10-01

    Stabilization, by deformation, of the Poincaré-Heisenberg algebra requires both the introduction of a fundamental lentgh and the noncommutativity of translations which is associated to the gravitational field. The noncommutative geometry structure that follows from the deformed algebra is studied both for the non-commutative tangent space and the full space with gravity. The contact points of this approach with the work of David Finkelstein are emphasized.

  7. The Mechanism of Restructuring in Geometry

    DTIC Science & Technology

    1990-05-01

    The Mechanism of Restructuring in Geometry Stellan Ohlsson The Learning Research and Development Center, University of Pittsburgh, Pittsburgh, PA ...6c. ADDRESS (City, State, and ZIP Code) 7b ADDRESS (City, State, and ZIP Code) 3939 0’Hara Street 800 North Quincy Street Pittsburgh, PA 15260...discovery and the psychology of problem solving. In Mind and cosmos: Essays in contemporary science and philosophy. Vol. III. (pp. 22-40). Pittsburgh, PA

  8. Doubly special relativity and Finsler geometry

    SciTech Connect

    Mignemi, S.

    2007-08-15

    We discuss the recent proposal of implementing doubly special relativity in configuration space by means of Finsler geometry. Although this formalism leads to a consistent description of the dynamics of a particle, it does not seem to give a complete description of the physics. In particular, the Finsler line element is not invariant under the deformed Lorentz transformations of doubly special relativity. We study in detail some simple applications of the formalism.

  9. The Convex Geometry of Linear Inverse Problems

    DTIC Science & Technology

    2010-12-02

    The Convex Geometry of Linear Inverse Problems Venkat Chandrasekaranm, Benjamin Rechtw, Pablo A. Parrilom, and Alan S. Willskym ∗ m Laboratory for...83) = 3r(m1 +m2 − r) + 2(m1 − r − r2) (84) where the second inequality follows from the fact that (a+ b)2 ≤ 2a2 + 2b2. References [1] Aja- Fernandez , S

  10. Extraction electrode geometry for a calutron

    DOEpatents

    Veach, A.M.; Bell, W.A. Jr.

    1975-09-23

    This patent relates to an improved geometry for the extraction electrode and the ground electrode utilized in the operation of a calutron. The improved electrodes are constructed in a partial-picture-frame fashion with the slits of both electrodes formed by two tungsten elongated rods. Additional parallel spaced-apart rods in each electrode are used to establish equipotential surfaces over the rest of the front of the ion source. (auth)

  11. Geometry of basic statistical physics mapping

    NASA Astrophysics Data System (ADS)

    Angelelli, Mario; Konopelchenko, Boris

    2016-09-01

    The geometry of hypersurfaces defined by the relation which generalizes the classical formula for free energy in terms of microstates is studied. The induced metric, the Riemann curvature tensor, the Gauss-Kronecker curvature and its associated entropy are calculated. A special class of ideal statistical hypersurfaces is analyzed in detail. Non-ideal hypersurfaces and singularities similar to those of the phase transitions are considered. The tropical limit of the statistical hypersurfaces and the double scaling tropical limit are discussed too.

  12. Turbulent flow computations in complex geometries

    NASA Astrophysics Data System (ADS)

    Burns, A. D.; Clarke, D. S.; Jones, I. P.; Simcox, S.; Wilkes, N. S.

    The nonstaggered-grid Navier-Stokes algorithm of Rhie and Chow (1983) and its implementation in the FLOW3D code (Burns et al., 1987) are described, with a focus on their application to problems involving complex geometries. Results for the flow in a tile-lined burner and for the flow over an automobile model are presented in extensive graphs and discussed in detail, and the advantages of supercomputer vectorization of the code are considered.

  13. Hessian geometry and the holomorphic anomaly

    NASA Astrophysics Data System (ADS)

    Cardoso, G. L.; Mohaupt, T.

    2016-02-01

    We present a geometrical framework which incorporates higher derivative corrections to the action of N = 2 vector multiplets in terms of an enlarged scalar manifold which includes a complex deformation parameter. This enlarged space carries a deformed version of special Kähler geometry which we characterise. The holomorphic anomaly equation arises in this framework from the integrability condition for the existence of a Hesse potential.

  14. Core systems of geometry in animal minds

    PubMed Central

    Spelke, Elizabeth S.; Lee, Sang Ah

    2012-01-01

    Research on humans from birth to maturity converges with research on diverse animals to reveal foundational cognitive systems in human and animal minds. The present article focuses on two such systems of geometry. One system represents places in the navigable environment by recording the distance and direction of the navigator from surrounding, extended surfaces. The other system represents objects by detecting the shapes of small-scale forms. These two systems show common signatures across animals, suggesting that they evolved in distant ancestral species. As children master symbolic systems such as maps and language, they come productively to combine representations from the two core systems of geometry in uniquely human ways; these combinations may give rise to abstract geometric intuitions. Studies of the ontogenetic and phylogenetic sources of abstract geometry therefore are illuminating of both human and animal cognition. Research on animals brings simpler model systems and richer empirical methods to bear on the analysis of abstract concepts in human minds. In return, research on humans, relating core cognitive capacities to symbolic abilities, sheds light on the content of representations in animal minds. PMID:22927577

  15. Ultrasonic ray models for complex geometries

    NASA Astrophysics Data System (ADS)

    Schumm, A.

    2000-05-01

    Computer Aided Design techniques have become an inherent part of many industrial applications and are also gaining popularity in Nondestructive Testing. In sound field calculations, CAD representations can contribute to one of the generic problem in ultrasonic modeling, the wave propagation in complex geometries. Ray tracing codes were the first to take account of the geometry, providing qualitative information on beam propagation, such as geometrical echoes, multiple sound paths and possible conversions between wave modes. The forward ray tracing approach is intuitive and straightforward and can evolve towards a more quantitative code if transmission, divergence and polarization information is added. If used to evaluate the impulse response of a given geometry, an approximated time-dependent received signal can be obtained after convolution with the excitation signal. The more accurate reconstruction of a sound field after interaction with a geometrical interface according to ray theory requires inverse (or Fermat) ray-tracing to obtain the contribution of each elementary point source to the field at a given observation point. The resulting field of a finite transducer can then be obtained after integration over all point sources. While conceptionally close to classical ray tracing, this approach puts more stringent requirements on the CAD representation employed and is more difficult to extend towards multiple interfaces. In this communication we present examples for both approaches. In a prospective step, the link between both ray techniques is shown, and we illustrate how a combination of both approaches contributes to the solution of an industrial problem.

  16. Tits Satake projections of homogeneous special geometries

    NASA Astrophysics Data System (ADS)

    Fré, Pietro; Gargiulo, Floriana; Rosseel, Jan; Rulik, Ksenya; Trigiante, Mario; Van Proeyen, Antoine

    2007-01-01

    We organize the homogeneous special geometries, describing as well the couplings of D = 6, 5, 4 and 3 supergravities with eight supercharges, in a small number of universality classes. This relates manifolds on which similar types of dynamical solutions can exist. The mathematical ingredient is the Tits Satake projection of real simple Lie algebras, which we extend to all solvable Lie algebras occurring in these homogeneous special geometries. Apart from some exotic cases all the other, 'very special', homogeneous manifolds can be grouped into seven universality classes. The organization of these classes, which capture the essential features of their basic dynamics, commutes with the r- and c-map. Different members are distinguished by different choices of the paint group, a notion discovered in the context of cosmic billiard dynamics of non-maximally supersymmetric supergravities. We comment on the usefulness of this organization in universality class both in relation with cosmic billiard dynamics and with configurations of branes and orbifolds defining special geometry backgrounds.

  17. Core systems of geometry in animal minds.

    PubMed

    Spelke, Elizabeth S; Lee, Sang Ah

    2012-10-05

    Research on humans from birth to maturity converges with research on diverse animals to reveal foundational cognitive systems in human and animal minds. The present article focuses on two such systems of geometry. One system represents places in the navigable environment by recording the distance and direction of the navigator from surrounding, extended surfaces. The other system represents objects by detecting the shapes of small-scale forms. These two systems show common signatures across animals, suggesting that they evolved in distant ancestral species. As children master symbolic systems such as maps and language, they come productively to combine representations from the two core systems of geometry in uniquely human ways; these combinations may give rise to abstract geometric intuitions. Studies of the ontogenetic and phylogenetic sources of abstract geometry therefore are illuminating of both human and animal cognition. Research on animals brings simpler model systems and richer empirical methods to bear on the analysis of abstract concepts in human minds. In return, research on humans, relating core cognitive capacities to symbolic abilities, sheds light on the content of representations in animal minds.

  18. Miss distance geometry estimation for maneuvering bodies

    NASA Astrophysics Data System (ADS)

    Karlin, Baruch E.

    1994-02-01

    The end game of air-to-air missiles is characterized by high velocities (Mach 2 and higher), high accelerations (30 g and higher) and small miss distances (less than 20 m.) Event analysis of this phase requires knowledge of the intercept geometry: minimum-distance time, miss-distance vector, velocities, angles, range and range rate. Separate trajectory estimation for each object is usually unsuitable for this purpose owing to systematic errors. A technique is described for miss-distance geometry estimation which is based on reference trajectory data and on missile-target image offsets photodigitized from high-speed cameras (over 300 fps.) The method includes calculation of the line-of-sight to the reference trajectory and the transformation angles to the required point, estimation of the required trajectory by three-dimensional triangulation, identification of the minimum-distance point, and calculation of the miss-distance parameters. The method is robust and not sensitive to bias errors in the reference trajectory or camera positions. It requires accurate data synchronization. Suitable setups within 15-km ranges give end-game geometry of violently maneuvering bodies with 0.1-0.3 m accuracy.

  19. Geometry of guanidinium groups in arginines.

    PubMed

    Malinska, Maura; Dauter, Miroslawa; Dauter, Zbigniew

    2016-09-01

    The restraints in common usage today have been obtained based on small molecule X-ray crystal structures available 25 years ago and recent reports have shown that the values of bond lengths and valence angles can be, in fact, significantly different from those stored in libraries, for example for the peptide bond or the histidine ring geometry. We showed that almost 50% of outliers found in protein validation reports released in the Protein Data Bank on 23 March 2016 come from geometry of guanidine groups in arginines. Therefore, structures of small molecules and atomic resolution protein crystal structures have been used to derive new target values for the geometry of this group. The most significant difference was found for NE-CZ-NH1 and NE-CZ-NH2 angles, showing that the guanidinium group is not symmetric. The NE-CZ-NH1 angle is larger, 121.5(10)˚, than NE-CZ-NH2, 119.2(10)˚, due to the repulsive interaction between NH1 and CD1 atom.

  20. Discovering Structural Regularity in 3D Geometry

    PubMed Central

    Pauly, Mark; Mitra, Niloy J.; Wallner, Johannes; Pottmann, Helmut; Guibas, Leonidas J.

    2010-01-01

    We introduce a computational framework for discovering regular or repeated geometric structures in 3D shapes. We describe and classify possible regular structures and present an effective algorithm for detecting such repeated geometric patterns in point- or mesh-based models. Our method assumes no prior knowledge of the geometry or spatial location of the individual elements that define the pattern. Structure discovery is made possible by a careful analysis of pairwise similarity transformations that reveals prominent lattice structures in a suitable model of transformation space. We introduce an optimization method for detecting such uniform grids specifically designed to deal with outliers and missing elements. This yields a robust algorithm that successfully discovers complex regular structures amidst clutter, noise, and missing geometry. The accuracy of the extracted generating transformations is further improved using a novel simultaneous registration method in the spatial domain. We demonstrate the effectiveness of our algorithm on a variety of examples and show applications to compression, model repair, and geometry synthesis. PMID:21170292

  1. SPICE Supports Planetary Science Observation Geometry

    NASA Astrophysics Data System (ADS)

    Hall Acton, Charles; Bachman, Nathaniel J.; Semenov, Boris V.; Wright, Edward D.

    2015-11-01

    "SPICE" is an information system, comprising both data and software, providing scientists with the observation geometry needed to plan observations from instruments aboard robotic spacecraft, and to subsequently help in analyzing the data returned from those observations. The SPICE system has been used on the majority of worldwide planetary exploration missions since the time of NASA's Galileo mission to Jupiter. Along with its "free" price tag, portability and the absence of licensing and export restrictions, its stable, enduring qualities help make it a popular choice. But stability does not imply rigidity-improvements and new capabilities are regularly added. This poster highlights recent additions that could be of interest to planetary scientists.Geometry Finder allows one to find all the times or time intervals when a particular geometric condition exists (e.g. occultation) or when a particular geometric parameter is within a given range or has reached a maximum or minimum.Digital Shape Kernel (DSK) provides means to compute observation geometry using accurately modeled target bodies: a tessellated plate model for irregular bodies and a digital elevation model for large, regular bodies.WebGeocalc (WGC) provides a graphical user interface (GUI) to a SPICE "geometry engine" installed at a mission operations facility, such as the one operated by NAIF. A WGC user need have only a computer with a web browser to access this geometry engine. Using traditional GUI widgets-drop-down menus, check boxes, radio buttons and fill-in boxes-the user inputs the data to be used, the kind of calculation wanted, and the details of that calculation. The WGC server makes the specified calculations and returns results to the user's browser.Cosmographia is a mission visualization program. This tool provides 3D visualization of solar system (target) bodies, spacecraft trajectory and orientation, instrument field-of-view "cones" and footprints, and more.The research described in this

  2. Dynamic geometry, brain function modeling, and consciousness.

    PubMed

    Roy, Sisir; Llinás, Rodolfo

    2008-01-01

    Pellionisz and Llinás proposed, years ago, a geometric interpretation towards understanding brain function. This interpretation assumes that the relation between the brain and the external world is determined by the ability of the central nervous system (CNS) to construct an internal model of the external world using an interactive geometrical relationship between sensory and motor expression. This approach opened new vistas not only in brain research but also in understanding the foundations of geometry itself. The approach named tensor network theory is sufficiently rich to allow specific computational modeling and addressed the issue of prediction, based on Taylor series expansion properties of the system, at the neuronal level, as a basic property of brain function. It was actually proposed that the evolutionary realm is the backbone for the development of an internal functional space that, while being purely representational, can interact successfully with the totally different world of the so-called "external reality". Now if the internal space or functional space is endowed with stochastic metric tensor properties, then there will be a dynamic correspondence between events in the external world and their specification in the internal space. We shall call this dynamic geometry since the minimal time resolution of the brain (10-15 ms), associated with 40 Hz oscillations of neurons and their network dynamics, is considered to be responsible for recognizing external events and generating the concept of simultaneity. The stochastic metric tensor in dynamic geometry can be written as five-dimensional space-time where the fifth dimension is a probability space as well as a metric space. This extra dimension is considered an imbedded degree of freedom. It is worth noticing that the above-mentioned 40 Hz oscillation is present both in awake and dream states where the central difference is the inability of phase resetting in the latter. This framework of dynamic

  3. Developing the concept of a parabola in Taxicab geometry

    NASA Astrophysics Data System (ADS)

    Ada, Tuba; Kurtuluş, Aytaç; Bahadır Yanik, H.

    2015-02-01

    The aim of this study was to observe the development process of the concept of a parabola in Taxicab geometry. The study was carried out in two stages. First, some activities related to Euclidean geometry and Taxicab geometry were designed based on concept development and real-life applications, and they were administered to a ninth-grade student. According to the findings, once the student learnt the definition of a parabola in Euclidean geometry, she was able to define a Taxicab parabola using the distance function in Taxicab geometry. Also, she came up with an algebraic definition of a Taxicab parabola based on this geometric definition of the concept of a parabola. Moving from algebraic definition to geometric representation, she configured the concept of a parabola in Taxicab geometry. By means of this application activity, the student had the opportunity to observe and practise the concept of a parabola in a real-life situation based on Euclidean geometry and Taxicab geometry.

  4. Geometry of loop quantum gravity on a graph

    SciTech Connect

    Rovelli, Carlo; Speziale, Simone

    2010-08-15

    We discuss the meaning of geometrical constructions associated to loop quantum gravity states on a graph. In particular, we discuss the 'twisted geometries' and derive a simple relation between these and Regge geometries.

  5. Effects of Measurement Geometry on Spectral Reflectance and Color

    DTIC Science & Technology

    1998-01-01

    calibration of outdoor color imagery were made using integrating sphere and 45°/0° geometry. The differing results are discussed using CIELAB linear... CIELAB color coordinate results were obtained for different measurement geometries. Such results should affect the digital photographic measurements...measurement geometry on spectral reflectance and CIELAB values using integrating sphere and 45°/0° measurement geometries. An example of the phenomenology

  6. Surface grid generation for complex three-dimensional geometries

    NASA Astrophysics Data System (ADS)

    Luh, Raymond Ching-Chung

    1988-10-01

    An outline is presented for the creation of surface grids from primitive geometry data such as obtained from CAD/CAM systems. The general procedure is applicable to any geometry including full aircraft with wing, nacelle, and empennage. When developed in an interactive graphics environment, a code based on this procedure is expected to substantially improve the turn around time for generating surface grids on complex geometries. Results are shown for a general hypersonic airplane geometry.

  7. PREFACE: Algebra, Geometry, and Mathematical Physics 2010

    NASA Astrophysics Data System (ADS)

    Stolin, A.; Abramov, V.; Fuchs, J.; Paal, E.; Shestopalov, Y.; Silvestrov, S.

    2012-02-01

    This proceedings volume presents results obtained by the participants of the 6th Baltic-Nordic workshop 'Algebra, Geometry, and Mathematical Physics (AGMP-6)' held at the Sven Lovén Centre for Marine Sciences in Tjärnö, Sweden on October 25-30, 2010. The Baltic-Nordic Network AGMP 'Algebra, Geometry, and Mathematical Physics' http://www.agmp.eu was created in 2005 on the initiative of two Estonian universities and two Swedish universities: Tallinn University of Technology represented by Eugen Paal (coordinator of the network), Tartu University represented by Viktor Abramov, Lund University represented by Sergei Silvestrov, and Chalmers University of Technology and the University of Gothenburg represented by Alexander Stolin. The goal was to promote international and interdisciplinary cooperation between scientists and research groups in the countries of the Baltic-Nordic region in mathematics and mathematical physics, with special emphasis on the important role played by algebra and geometry in modern physics, engineering and technologies. The main activities of the AGMP network consist of a series of regular annual international workshops, conferences and research schools. The AGMP network also constitutes an important educational forum for scientific exchange and dissimilation of research results for PhD students and Postdocs. The network has expanded since its creation, and nowadays its activities extend beyond countries in the Baltic-Nordic region to universities in other European countries and participants from elsewhere in the world. As one of the important research-dissimilation outcomes of its activities, the network has a tradition of producing high-quality research proceedings volumes after network events, publishing them with various international publishers. The PDF also contains the following: List of AGMP workshops and other AGMP activities Main topics discussed at AGMP-6 Review of AGMP-6 proceedings Acknowledgments List of Conference Participants

  8. Properties and geometry of radio pulsar emission

    NASA Astrophysics Data System (ADS)

    Smits, Johannes Martinus

    2006-10-01

    This thesis consists of a number of studies on the radio emission of pulsars. The central topics are polarisation and multi frequency observations, which both lead to important information on the geometry of the emission. The first chapter introduces different aspects of pulsars that are related to the research that has been done in this thesis. In particular it deals with different aspects concerning the geometry of pulsar emission. Chapter 2 is about the nature of the radio emission. It shows the result of an attempt to confirm and expand on work that has been published by Jenet et al. (2001) on the detection of coherence in pulsar radiation. From an analysis of high time resolution observations, we found that the detection of coherence is consistent with the effects of interstellar scintillation. In chapter 3 a study is carried out on the orthogonal polarisation mode behaviour as a function of frequency of 18 pulsars. By making the assumption that the radiation consists of two 100% polarised completely orthogonal superposed modes, both modes could be separated In chapter 4 PSR B0031-07 is studied at two frequencies using two observations that were carried out simultaneously. It is shown that from the three known drift modes, only one drift mode is seen at high frequency. Based on this result we suggest a geometrical model in which different modes are emitted in concentric rings around the magnetic axis, with each mode having a different radius. The fifth chapter follows the suggestions made in chapter 4 to create a geometrical model of PSR B0031-07 for two of the drift modes. The results can be used to limit the possible geometries of PSR B0031-07. The final chapter consists of documentation of software that was written in C and utilised for this thesis for handling and analysing data files in the EPN format

  9. Cloud geometry effects on atmospheric solar absorption

    SciTech Connect

    Fu, Q.; Cribb, M.C.; Barker, H.W.; Krueger, S.K.; Grossman, A.

    2000-04-15

    A 3D broadband solar radiative transfer scheme is formulated by integrating a Monte Carlo photon transport algorithm with the Fu-Liou radiation model. It is applied to fields of tropical mesoscale convective clouds and subtropical marine boundary layer clouds that were generated by a 2D cloud-resolving model. The effects of cloud geometry on the radiative energy budget are examined by comparing the full-resolution Monte Carlo results with those from the independent column approximation (ICA) that applies the plane-parallel radiation model to each column. For the tropical convective cloud system, it is found that cloud geometry effects always enhance atmospheric solar absorption regardless of solar zenith angle. In a large horizontal domain (512 km), differences in domain-averaged atmospheric absorption between the Monte Carlo and the ICA are less than 4 W m{sup {minus}2} in the daytime. However, for a smaller domain (e.g., 75 km) containing a cluster of deep convective towers, domain-averaged absorption can be enhanced by more than 20 W m{sup {minus}2}. For a subtropical marine boundary layer cloud system during the stratus-to-cumulus transition, calculations show that the ICA works very well for domain-averaged fluxes of the stratocumulus cloud fields even for a very small domain (4.8 km). For the trade cumulus cloud field, the effects of cloud sides and horizontal transport of photons become more significant. Calculations have also been made for both cloud systems including black carbon aerosol and a water vapor continuum. It is found that cloud geometry produces no discernible effects on the absorption enhancement due to the black carbon aerosol and water vapor continuum. The current study indicates that the atmospheric absorption enhancement due to cloud-related 3D photon transport is small. This enhancement could not explain the excess absorption suggested by recent studies.

  10. Galilean geometry in condensed matter systems

    NASA Astrophysics Data System (ADS)

    Geracie, Michael

    In this thesis we present a systematic means to impose Galilean invariance within effective field theory. Recently a number of authors have shown that Galilean invariance has powerful consequences on condensed matter systems. However, unlike the relativistic case, torsion is often a necessary element and is subject to constraints that make it surprisingly difficult to include in a Galilean invariant way. We will review this issue, define the most general torsionful geometries consistent with Galilean invariance and then turn to applications within effective field theory and the quantum Hall effect.

  11. Centriole asymmetry determines algal cell geometry

    PubMed Central

    Marshall, Wallace F.

    2012-01-01

    The mechanisms that determine the shape and organization of cells remain largely unknown. Green algae such as Chlamydomonas provide excellent model systems for studying cell geometry due to their highly reproducible cell organization. Structural and genetic studies suggest that asymmetry of the centriole (basal body) plays a critical determining role in organizing the internal organization of algal cells, through the attachment of microtubule rootlets and other large fiber systems to specific sets of microtubule triplets on the centriole. Thus to understand cell organization, it will be critical to understand how the different triplets of the centriole come to have distinct molecular identities. PMID:23026116

  12. Drift Mode Calculations in Nonaxisymmetric Geometry

    SciTech Connect

    G. Rewoldt; L.-P. Ku; W.A. Cooper; W.M. Tang

    1999-07-01

    A fully kinetic assessment of the stability properties of toroidal drift modes has been obtained for nonaxisymmetric (stellarator) geometry, in the electrostatic limit. This calculation is a comprehensive solution of the linearized gyrokinetic equation, using the lowest-order ''ballooning representation'' for high toroidal mode number instabilities, with a model collision operator. Results for toroidal drift waves destabilized by temperature gradients and/or trapped particle dynamics are presented, using three-dimensional magnetohydrodynamic equilibria generated as part of a design effort for a quasiaxisymmetric stellarator. Comparisons of these results with those obtained for typical tokamak cases indicate that the basic trends are similar.

  13. Entanglement entropy of subtracted geometry black holes

    NASA Astrophysics Data System (ADS)

    Cvetič, Mirjam; Saleem, Zain H.; Satz, Alejandro

    2014-09-01

    We compute the entanglement entropy of minimally coupled scalar fields on subtracted geometry black hole backgrounds, focusing on the logarithmic corrections. We notice that matching between the entanglement entropy of original black holes and their subtracted counterparts is only at the order of the area term. The logarithmic correction term is not only different but also, in general, changes sign in the subtracted case. We apply Harrison transformations to the original black holes and find out the choice of the Harrison parameters for which the logarithmic corrections vanish.

  14. Joule heating in spin Hall geometry

    NASA Astrophysics Data System (ADS)

    Taniguchi, Tomohiro

    2016-07-01

    The theoretical formula for the entropy production rate in the presence of spin current is derived using the spin-dependent transport equation and thermodynamics. This theory is applicable regardless of the source of the spin current, for example, an electric field, a temperature gradient, or the Hall effect. It reproduces the result in a previous work on the dissipation formula when the relaxation time approximation is applied to the spin relaxation rate. By using the developed theory, it is found that the dissipation in the spin Hall geometry has a contribution proportional to the square of the spin Hall angle.

  15. Extending the ADM formalism to Weyl geometry

    SciTech Connect

    Barreto, A. B.; Almeida, T. S.; Romero, C.

    2015-03-26

    In order to treat quantum cosmology in the framework of Weyl spacetimes we take the first step of extending the Arnowitt-Deser-Misner formalism to Weyl geometry. We then obtain an expression of the curvature tensor in terms of spatial quantities by splitting spacetime in (3+l)-dimensional form. We next write the Lagrangian of the gravitation field based in Weyl-type gravity theory. We extend the general relativistic formalism in such a way that it can be applied to investigate the quantum cosmology of models whose spacetimes are endowed with a Weyl geometrical structure.

  16. Foucault pendulum and sub-Riemannian geometry

    NASA Astrophysics Data System (ADS)

    Anzaldo-Meneses, A.; Monroy-Pérez, F.

    2010-08-01

    The well known Foucault nonsymmetrical pendulum is studied as a problem of sub-Riemannian geometry on nilpotent Lie groups. It is shown that in a rotating frame a sub-Riemannian structure can be naturally introduced. For small oscillations, three dimensional horizontal trajectories are computed and displayed in detail. The fiber bundle structure is explicitly shown. The underlying Lie structure is described together with the corresponding holonomy group, which turns out to be given by the center of the Heisenberg group. Other related physical problems that can be treated in a similar way are also mentioned.

  17. Differential geometry, Palatini gravity and reduction

    SciTech Connect

    Capriotti, S.

    2014-01-15

    The present article deals with a formulation of the so called (vacuum) Palatini gravity as a general variational principle. In order to accomplish this goal, some geometrical tools related to the geometry of the bundle of connections of the frame bundle LM are used. A generalization of Lagrange-Poincaré reduction scheme to these types of variational problems allows us to relate it with the Einstein-Hilbert variational problem. Relations with some other variational problems for gravity found in the literature are discussed.

  18. Information theory, spectral geometry, and quantum gravity.

    PubMed

    Kempf, Achim; Martin, Robert

    2008-01-18

    We show that there exists a deep link between the two disciplines of information theory and spectral geometry. This allows us to obtain new results on a well-known quantum gravity motivated natural ultraviolet cutoff which describes an upper bound on the spatial density of information. Concretely, we show that, together with an infrared cutoff, this natural ultraviolet cutoff beautifully reduces the path integral of quantum field theory on curved space to a finite number of ordinary integrations. We then show, in particular, that the subsequent removal of the infrared cutoff is safe.

  19. Twisted spectral geometry for the standard model

    NASA Astrophysics Data System (ADS)

    Martinetti, Pierre

    2015-07-01

    In noncommutative geometry, the spectral triple of a manifold does not generate bosonic fields, for fluctuations of the Dirac operator vanish. A Connes-Moscovici twist forces the commutative algebra to be multiplied by matrices. Keeping the space of spinors untouched, twisted-fluctuations then yield perturbations of the spin connection. Applied to the spectral triple of the Standard Model, a similar twist yields the scalar field needed to stabilize the vacuum and to make the computation of the Higgs mass compatible with its experimental value.

  20. Pulsar Emission Geometry and Accelerating Field Strength

    DTIC Science & Technology

    2011-11-01

    ar X iv :1 11 1. 03 25 v1 [ as tr o- ph .H E ] 1 N ov 2 01 1 2011 Fermi Symposium, Roma., May. 9-12 1 Pulsar Emission Geometry and Accelerating...observations of gamma-ray pulsars have opened a new window to understanding the generation mechanisms of high-energy emission from these systems. The high...the Vela and CTA 1 pulsars with simulated high-energy light curves generated from geometrical representations of the outer gap and slot gap emission

  1. Explorations of Dusty Debris Disk Geometry

    NASA Astrophysics Data System (ADS)

    Dennihy, E.; Debes, J. H.; Clemens, C. J.

    2017-03-01

    As the sample of white dwarfs with signatures of planetary systems has grown, statistical studies have begun to suggest our picture of compact debris disk formation from disrupted planetary bodies is incomplete. Here we present the results of an effort to extend the preferred dust disk model introduced by Jura (2003) to include elliptical geometries. We apply this model to the observed distribution of fractional infrared luminosities, and explore the difference in preferred parameter spaces for a circular and highly elliptical model on a well-studied dusty white dwarf.

  2. Self-acting geometry for noncontact seals

    NASA Technical Reports Server (NTRS)

    Allen, G. P.

    1981-01-01

    Performance ot two self acting seal designs for a liquid oxygen (LOX) turbopump was predicted over ranges of pressure differential and speed. Predictions were compared with test results. Performance of a radial face seal for LOX was predicted up to 448 N/cu cm and 147 m/sec. Performance of a segmented circumferential seal for helium was predicted up to 69 N/cu cm and 189 m/sec. Results confirmed predictions of noncontact operation. Qualitative agreement between test and analysis was found. The LOX face seal evidently operated with mostly liquid in the self acting geometry and mostly gas across the dam.

  3. Target Positioning and Tracking in Degenerate Geometry

    DTIC Science & Technology

    2011-07-01

    estimation accuracy is to use the geometric dilution of precision ( GDOP ) [8]. In a poor geometry with not enough independent measurements and/or nearly...in GDOP may be significant, leading to degenerate cases. Indeed, when a target is close to or crosses the baseline, the 2D solution is no longer...7) is given by (8). The resulting position error is σx = √2/2σ, which is equivalent to having a GDOP of 0.707, the lowest of the 2D solution. A

  4. Information geometry of mean-field approximation.

    PubMed

    Tanaka, T

    2000-08-01

    I present a general theory of mean-field approximation based on information geometry and applicable not only to Boltzmann machines but also to wider classes of statistical models. Using perturbation expansion of the Kullback divergence (or Plefka expansion in statistical physics), a formulation of mean-field approximation of general orders is derived. It includes in a natural way the "naive" mean-field approximation and is consistent with the Thouless-Anderson-Palmer (TAP) approach and the linear response theorem in statistical physics.

  5. An Alternative Approach to Logo-Based Geometry

    ERIC Educational Resources Information Center

    Durmus, Soner; Karakirik, Erol

    2005-01-01

    Geometry is an important branch of mathematics. Geometry curriculum can be enriched by using different Technologies such as graphing calculators and computers. Logo-based different software packages aim to improve conceptual understanding in geometry. The goals of this paper are i) to present theoretical foundations of any computer software…

  6. An Alternative Approach to Logo-Based Geometry

    ERIC Educational Resources Information Center

    Karakirik, Erol; Durmus, Soner

    2005-01-01

    Geometry is an important branch of mathematics. Geometry curriculum can be enriched by using different Technologies such as graphing calculators and computers. Logo-based different software packages aim to improve conceptual understanding in geometry. The goals of this paper are i) to present theoretical foundations of any compute software…

  7. Problem Solving in Calculus with Symbolic Geometry and CAS

    ERIC Educational Resources Information Center

    Todd, Philip; Wiechmann, James

    2008-01-01

    Computer algebra systems (CAS) have been around for a number of years, as has dynamic geometry. Symbolic geometry software is new. It bears a superficial similarity to dynamic geometry software, but differs in that problems may be set up involving symbolic variables and constants, and measurements are given as symbolic expressions. Mathematical…

  8. Developing the Concept of a Parabola in Taxicab Geometry

    ERIC Educational Resources Information Center

    Ada, Tuba; Kurtulus, Aytaç; Yanik, H. Bahadir

    2015-01-01

    The aim of this study was to observe the development process of the concept of a parabola in Taxicab geometry. The study was carried out in two stages. First, some activities related to Euclidean geometry and Taxicab geometry were designed based on concept development and real-life applications, and they were administered to a ninth-grade student.…

  9. A Brief History of Non-Euclidean Geometry

    ERIC Educational Resources Information Center

    Marshall, Daniel; Scott, Paul

    2004-01-01

    Around 300 BC, Euclid wrote "The Elements", a major treatise on the geometry of the time, and what would be considered "geometry" for many years after. Arguably "The Elements" is the second most read book of the western world, falling short only to The Bible. In his book, Euclid states five postulates of geometry which he uses as the foundation…

  10. Early Childhood Teacher Education: The Case of Geometry

    ERIC Educational Resources Information Center

    Clements, Douglas H.; Sarama, Julie

    2011-01-01

    For early childhood, the domain of geometry and spatial reasoning is an important area of mathematics learning. Unfortunately, geometry and spatial thinking are often ignored or minimized in early education. We build a case for the importance of geometry and spatial thinking, review research on professional development for these teachers, and…

  11. Characterizing Student Mathematics Teachers' Levels of Understanding in Spherical Geometry

    ERIC Educational Resources Information Center

    Guven, Bulent; Baki, Adnan

    2010-01-01

    This article presents an exploratory study aimed at the identification of students' levels of understanding in spherical geometry as van Hiele did for Euclidean geometry. To do this, we developed and implemented a spherical geometry course for student mathematics teachers. Six structured, "task-based interviews" were held with eight student…

  12. Imaging molecular geometry with electron momentum spectroscopy.

    PubMed

    Wang, Enliang; Shan, Xu; Tian, Qiguo; Yang, Jing; Gong, Maomao; Tang, Yaguo; Niu, Shanshan; Chen, Xiangjun

    2016-12-22

    Electron momentum spectroscopy is a unique tool for imaging orbital-specific electron density of molecule in momentum space. However, the molecular geometry information is usually veiled due to the single-centered character of momentum space wavefunction of molecular orbital (MO). Here we demonstrate the retrieval of interatomic distances from the multicenter interference effect revealed in the ratios of electron momentum profiles between two MOs with symmetric and anti-symmetric characters. A very sensitive dependence of the oscillation period on interatomic distance is observed, which is used to determine F-F distance in CF4 and O-O distance in CO2 with sub-Ångström precision. Thus, using one spectrometer, and in one measurement, the electron density distributions of MOs and the molecular geometry information can be obtained simultaneously. Our approach provides a new robust tool for imaging molecules with high precision and has potential to apply to ultrafast imaging of molecular dynamics if combined with ultrashort electron pulses in the future.

  13. Study on Pyroelectric Harvesters with Various Geometry

    PubMed Central

    Siao, An-Shen; Chao, Ching-Kong; Hsiao, Chun-Ching

    2015-01-01

    Pyroelectric harvesters convert time-dependent temperature variations into electric current. The appropriate geometry of the pyroelectric cells, coupled with the optimal period of temperature fluctuations, is key to driving the optimal load resistance, which enhances the performance of pyroelectric harvesters. The induced charge increases when the thickness of the pyroelectric cells decreases. Moreover, the induced charge is extremely reduced for the thinner pyroelectric cell when not used for the optimal period. The maximum harvested power is achieved when a 100 μm-thick PZT (Lead zirconate titanate) cell is used to drive the optimal load resistance of about 40 MΩ. Moreover, the harvested power is greatly reduced when the working resistance diverges even slightly from the optimal load resistance. The stored voltage generated from the 75 μm-thick PZT cell is less than that from the 400 μm-thick PZT cell for a period longer than 64 s. Although the thinner PZT cell is advantageous in that it enhances the efficiency of the pyroelectric harvester, the much thinner 75 μm-thick PZT cell and the divergence from the optimal period further diminish the performance of the pyroelectric cell. Therefore, the designers of pyroelectric harvesters need to consider the coupling effect between the geometry of the pyroelectric cells and the optimal period of temperature fluctuations to drive the optimal load resistance. PMID:26270666

  14. Teaching Molecular Geometry with the VSEPR Model

    NASA Astrophysics Data System (ADS)

    Gillespie, Ronald J.

    2004-03-01

    Molecular geometry can be discussed in terms of the VSEPR model at several levels of sophistication—from the empirical model to a more complete model based on the Pauli principle. It is recommended that for most first-year courses VSEPR is presented at the purely empirical level or in the form of the domain version. A more sophisticated version is discussed here, not only because it should be taught in more advanced courses, but because it is important that it is understood by instructors and textbook writers so that incorrect explanations of the VSEPR model are not given. The difficulties associated with the usual treatment of the VB and MO theories in connection with molecular geometry in beginning courses are discussed. It is recommended that the VB and MO theories should be presented only after the VSEPR model either in the general chemistry course or in a following course, particularly in the case of the MO theory, which is not really necessary for the first-year course. The Pauli principle and its importance as the fundamental basis of the VSEPR model should be presented in a higher-level course, such as a quantum mechanics or physical chemistry course, or an inorganic course, in which VSEPR has many applications, for example, in the discussion of noble gas and other high coordination number molecules.

  15. Imaging molecular geometry with electron momentum spectroscopy

    PubMed Central

    Wang, Enliang; Shan, Xu; Tian, Qiguo; Yang, Jing; Gong, Maomao; Tang, Yaguo; Niu, Shanshan; Chen, Xiangjun

    2016-01-01

    Electron momentum spectroscopy is a unique tool for imaging orbital-specific electron density of molecule in momentum space. However, the molecular geometry information is usually veiled due to the single-centered character of momentum space wavefunction of molecular orbital (MO). Here we demonstrate the retrieval of interatomic distances from the multicenter interference effect revealed in the ratios of electron momentum profiles between two MOs with symmetric and anti-symmetric characters. A very sensitive dependence of the oscillation period on interatomic distance is observed, which is used to determine F-F distance in CF4 and O-O distance in CO2 with sub-Ångström precision. Thus, using one spectrometer, and in one measurement, the electron density distributions of MOs and the molecular geometry information can be obtained simultaneously. Our approach provides a new robust tool for imaging molecules with high precision and has potential to apply to ultrafast imaging of molecular dynamics if combined with ultrashort electron pulses in the future. PMID:28004794

  16. An Observer-Based Foundation of Geometry

    NASA Astrophysics Data System (ADS)

    Bahreyni, Newshaw; Knuth, Kevin H.

    2012-02-01

    The fact that some events influence other events enables one to define a partially ordered set (poset) of events, often referred to as a causal set. A chain of events, called observer chain, can be quantified by labeling its events numerically. Other events in a poset may be quantified with respect to an observer chain/chains by projecting them onto the chain, resulting in a pair of numbers. Similarly, pairs of events, called intervals, can be quantified with four numbers. Under certain conditions, this leads to the Minkowski metric, Lorentz transformations and the mathematics of special relativity (Bahreyni & Knuth, APS March Meeting 2011). We exploit the same techniques to demonstrate that geometric concepts can be derived from order-theoretic concepts. We show how chains in a poset can be used to define points and line segments. Subsequent quantification results in the Pythagorean Theorem and the inner product as well as other geometric concepts and measures. Thus the geometry of space, which is assumed to be fundamental, emerges as a result of quantifying a partially ordered set. More importantly, this proposed foundation of geometry is entirely observer-based, which may provide a natural way toward integration with quantum mechanics.

  17. Study on Pyroelectric Harvesters with Various Geometry.

    PubMed

    Siao, An-Shen; Chao, Ching-Kong; Hsiao, Chun-Ching

    2015-08-11

    Pyroelectric harvesters convert time-dependent temperature variations into electric current. The appropriate geometry of the pyroelectric cells, coupled with the optimal period of temperature fluctuations, is key to driving the optimal load resistance, which enhances the performance of pyroelectric harvesters. The induced charge increases when the thickness of the pyroelectric cells decreases. Moreover, the induced charge is extremely reduced for the thinner pyroelectric cell when not used for the optimal period. The maximum harvested power is achieved when a 100 μm-thick PZT (Lead zirconate titanate) cell is used to drive the optimal load resistance of about 40 MΩ. Moreover, the harvested power is greatly reduced when the working resistance diverges even slightly from the optimal load resistance. The stored voltage generated from the 75 μm-thick PZT cell is less than that from the 400 μm-thick PZT cell for a period longer than 64 s. Although the thinner PZT cell is advantageous in that it enhances the efficiency of the pyroelectric harvester, the much thinner 75 μm-thick PZT cell and the divergence from the optimal period further diminish the performance of the pyroelectric cell. Therefore, the designers of pyroelectric harvesters need to consider the coupling effect between the geometry of the pyroelectric cells and the optimal period of temperature fluctuations to drive the optimal load resistance.

  18. Lobed Mixer Optimization for Advanced Ejector Geometries

    NASA Technical Reports Server (NTRS)

    Waitz, Ian A.

    1996-01-01

    The overall objectives are: 1) to pursue analytical, computational, and experimental studies that enhance basic understanding of forced mixing phenomena relevant to supersonic jet noise reduction, and 2) to integrate this enhanced understanding (analytical, computational, and empirical) into a design-oriented model of a mixer-ejector noise suppression system. The work is focused on ejector geometries and flow conditions typical of those being investigated in the NASA High Speed Research Program (HSRP). The research will be carried out in collaboration with the NASA HSRP Nozzle Integrated Technology Development (ITD) Team, and will both contribute to, and benefit from, the results of other HSRP research. The noise suppressor system model that is being developed under this grant is distinct from analytical tools developed by industry because it directly links details of lobe geometry to mixer-ejector performance. In addition, the model provides a 'technology road map to define gaps in the current understanding of various phenomena related to mixer-ejector design and to help prioritize research areas. This report describes research completed in the past year, as well as work proposed for the following year.

  19. A method of plane geometry primitive presentation

    NASA Astrophysics Data System (ADS)

    Jiao, Anbo; Luo, Haibo; Chang, Zheng; Hui, Bin

    2014-11-01

    Point feature and line feature are basic elements in object feature sets, and they play an important role in object matching and recognition. On one hand, point feature is sensitive to noise; on the other hand, there are usually a huge number of point features in an image, which makes it complex for matching. Line feature includes straight line segment and curve. One difficulty in straight line segment matching is the uncertainty of endpoint location, the other is straight line segment fracture problem or short straight line segments joined to form long straight line segment. While for the curve, in addition to the above problems, there is another difficulty in how to quantitatively describe the shape difference between curves. Due to the problems of point feature and line feature, the robustness and accuracy of target description will be affected; in this case, a method of plane geometry primitive presentation is proposed to describe the significant structure of an object. Firstly, two types of primitives are constructed, they are intersecting line primitive and blob primitive. Secondly, a line segment detector (LSD) is applied to detect line segment, and then intersecting line primitive is extracted. Finally, robustness and accuracy of the plane geometry primitive presentation method is studied. This method has a good ability to obtain structural information of the object, even if there is rotation or scale change of the object in the image. Experimental results verify the robustness and accuracy of this method.

  20. Probing the geometry of the Laughlin state

    SciTech Connect

    Johri, Sonika; Papic, Z.; Schmitteckert, P.; Bhatt, R. N.; Haldane, F. D. M.

    2016-02-05

    It has recently been pointed out that phases of matter with intrinsic topological order, like the fractional quantum Hall states, have an extra dynamical degree of freedom that corresponds to quantum geometry. Here we perform extensive numerical studies of the geometric degree of freedom for the simplest example of fractional quantumHall states—the filling v = 1/3 Laughlin state.We perturb the system by a smooth, spatially dependent metric deformation and measure the response of the Hall fluid, finding it to be proportional to the Gaussian curvature of the metric. Further, we generalize the concept of coherent states to formulate the bulk off-diagonal long range order for the Laughlin state, and compute the deformations of the metric in the vicinity of the edge of the system. We introduce a ‘pair amplitude’ operator and show that it can be used to numerically determine the intrinsic metric of the Laughlin state. Furthermore, these various probes are applied to several experimentally relevant settings that can expose the quantum geometry of the Laughlin state, in particular to systems with mass anisotropy and in the presence of an electric field gradient.

  1. Advanced geometries for ballistic neutron guides

    NASA Astrophysics Data System (ADS)

    Schanzer, Christian; Böni, Peter; Filges, Uwe; Hils, Thomas

    2004-08-01

    Sophisticated neutron guide systems take advantage of supermirrors being used to increase the neutron flux. However, the finite reflectivity of supermirrors becomes a major loss mechanism when many reflections occur, e.g. in long neutron guides and for long wavelengths. In order to reduce the number of reflections, ballistic neutron guides have been proposed. Usually linear tapered sections are used to enlarge the cross-section and finally, focus the beam to the sample. The disadvantages of linear tapering are (i) an inhomogeneous phase space at the sample position and (ii) a decreasing flux with increasing distance from the exit of the guide. We investigate the properties of parabolic and elliptic tapering for ballistic neutron guides, using the Monte Carlo program McStas with a new guide component dedicated for such geometries. We show that the maximum flux can indeed be shifted away from the exit of the guide. In addition we explore the possibilities of parabolic and elliptic geometries to create point like sources for dedicated experimental demands.

  2. The CLAS12-RICH hybrid geometry

    NASA Astrophysics Data System (ADS)

    Angelini, Giovanni; CLAS12-RICH Collaboration

    2017-01-01

    A Ring-imaging Cherenkov detector (RICH) has been designed for the CLAS12 spectrometer (JLAB, Hall B) in order to increase the particle identification. Among the approved physics program focused upon 3D imaging of the nucleon, some Semi Inclusive Deep Inelastic Scattering experiments (E12-09-007, E12-09-008, E12-09-009) demand an efficient kaon identification across the momentum range from 3 to 8 GeV/c. The detector exploits a novel elaborated hybrid geometry based on a complex focusing mirror system that will reduce the area instrumented with photon detectors. For forward scattered particles (θ <12°) with momenta p = 3-8 GeV/c, a proximity imaging method with direct Cherenkov light detection will be used. For larger angles of 12° < θ <35° and momenta of p = 3-6 GeV/c, the Cherenkov light will be focused by a spherical mirror, undergo two further passes through the aerogel radiator and will be reflected from planar mirrors before detection. A carefully study on reflections has been performed considering microscopic and macroscopic effects. In addition, a new feature has been introduced in the CLAS12 simulation software in order to generate the geometry of the detector by using a computer-aided design (CAD) file for an accurate geometrical description. U.S. Department of Energy, GWU Columbian College Art and Science Facilitating Fund Award (CCAS CCFF).

  3. Quantitative analysis of blood vessel geometry

    NASA Astrophysics Data System (ADS)

    Fuhrman, Michael G.; Abdul-Karim, Othman; Shah, Sujal; Gilbert, Steven G.; Van Bibber, Richard

    2001-07-01

    Re-narrowing or restenosis of a human coronary artery occurs within six months in one third of balloon angioplasty procedures. Accurate and repeatable quantitative analysis of vessel shape is important to characterize the progression and type of restenosis, and to evaluate effects new therapies might have. A combination of complicated geometry and image variability, and the need for high resolution and large image size makes visual/manual analysis slow, difficult, and prone to error. The image processing and analysis described here was developed to automate feature extraction of the lumen, internal elastic lamina, neointima, external elastic lamina, and tunica adventitia and to enable an objective, quantitative definition of blood vessel geometry. The quantitative geometrical analysis enables the measurement of several features including perimeter, area, and other metrics of vessel damage. Automation of feature extraction creates a high throughput capability that enables analysis of serial sections for more accurate measurement of restenosis dimensions. Measurement results are input into a relational database where they can be statistically analyzed compared across studies. As part of the integrated process, results are also imprinted on the images themselves to facilitate auditing of the results. The analysis is fast, repeatable and accurate while allowing the pathologist to control the measurement process.

  4. New geometries for black hole horizons

    NASA Astrophysics Data System (ADS)

    Armas, Jay; Blau, Matthias

    2015-07-01

    We construct several classes of worldvolume effective actions for black holes by integrating out spatial sections of the worldvolume geometry of asymptotically flat black branes. This provides a generalisation of the blackfold approach for higher-dimensional black holes and yields a map between different effective theories, which we exploit by obtaining new hydrodynamic and elastic transport coefficients via simple integrations. Using Euclidean minimal surfaces in order to decouple the fluid dynamics on different sections of the worldvolume, we obtain local effective theories for ultraspinning Myers-Perry branes and helicoidal black branes, described in terms of a stress-energy tensor, particle currents and non-trivial boost vectors. We then study in detail and present novel compact and non-compact geometries for black hole horizons in higher-dimensional asymptotically flat space-time. These include doubly-spinning black rings, black helicoids and helicoidal p-branes as well as helicoidal black rings and helicoidal black tori in D ≥ 6.

  5. Swimming Vorticella convallaria in various confined geometries

    NASA Astrophysics Data System (ADS)

    Sotelo, Luz; Lee, Donghee; Jung, Sunghwan; Ryu, Sangjin

    2014-11-01

    Vorticella convallaria is a stalked ciliate observed in the sessile form (trophont) or swimming form (telotroch). Trophonts are mainly composed of an inverted bell-shaped cell body generating vortical feeding currents, and a slender stalk attaching the cell body to a substrate. If the surrounding environment is no longer suitable, the trophont transforms into a telotroch by elongating its cell body into a cylindrical shape, resorbing its oral cilia and producing an aboral cilia wreath. After a series of contractions, the telotroch will completely detach from the stalk and swim away to find a better location. While sessile Vorticella has been widely studied because of its stalk contraction and usefulness in waste treatment, Vorticella's swimming has not yet been characterized. The purpose of this study is to describe V. convallaria's swimming modes, both in its trophont and telotroch forms, in different confined geometries. Using video microscopy, we observed Vorticellae swimming in semi-infinite field, in Hele-Shaw configurations, and in capillary tubes. Based on measured swimming displacement and velocity, we investigated how V. convallaria's mobility was affected by the geometry constrictions. We acknolwedge support from the First Award grant of Nebraska EPSCoR.

  6. Probing the geometry of the Laughlin state

    DOE PAGES

    Johri, Sonika; Papic, Z.; Schmitteckert, P.; ...

    2016-02-05

    It has recently been pointed out that phases of matter with intrinsic topological order, like the fractional quantum Hall states, have an extra dynamical degree of freedom that corresponds to quantum geometry. Here we perform extensive numerical studies of the geometric degree of freedom for the simplest example of fractional quantumHall states—the filling v = 1/3 Laughlin state.We perturb the system by a smooth, spatially dependent metric deformation and measure the response of the Hall fluid, finding it to be proportional to the Gaussian curvature of the metric. Further, we generalize the concept of coherent states to formulate the bulkmore » off-diagonal long range order for the Laughlin state, and compute the deformations of the metric in the vicinity of the edge of the system. We introduce a ‘pair amplitude’ operator and show that it can be used to numerically determine the intrinsic metric of the Laughlin state. Furthermore, these various probes are applied to several experimentally relevant settings that can expose the quantum geometry of the Laughlin state, in particular to systems with mass anisotropy and in the presence of an electric field gradient.« less

  7. Non-Abelian bubbles in microstate geometries

    NASA Astrophysics Data System (ADS)

    Ramírez, Pedro F.

    2016-11-01

    We find the first smooth bubbling microstate geometries with non-Abelian fields. The solutions constitute an extension of the BPS three-charge smooth microstates. These consist in general families of regular supersymmetric solutions with non-trivial topology, i.e. bubbles, of {N}=d , d = 5 Super-Einstein-Yang-Mills theory, having the asymptotic charges of a black hole or black ring but with no horizon. The non-Abelian fields make their presence at the very heart of the microstate structure: the physical size of the bubbles is affected by the non-Abelian topological charge they carry, which combines with the Abelian flux threading the bubbles to hold them up. Interestingly the non-Abelian fields carry a set of adjustable continuous parameters that do not alter the asymptotics of the solutions but modify the local geometry. This feature can be used to obtain a classically infinite number of microstate solutions with the asymptotics of a single black hole or black ring.

  8. TES Limb-Geometry Observations of Aerosols

    NASA Technical Reports Server (NTRS)

    Smith, Michael D.

    2003-01-01

    The Thermal Emission Spectrometer (TES) on-board Mars Global Surveyor (MGS) has a pointing mirror that allows observations in the plane of the orbit anywhere from directly nadir to far above either the forward or aft limbs for details about the TES instrument). Nadir-geometry observations are defined as those where the field-of-view contains the surface of Mars (even if the actual observation is at a high emission angle far from true nadir). Limb-geometry observations are defined as those where the line-of-sight of the observations does not intersect the surface. At a number of points along the MGS orbit (typically every 10 deg. or 20 deg. of latitude) a limb sequence is taken, which includes a stack of overlapping TES spectra from just below the limb to more than 120 km above the limb. A typical limb sequence has approx. 20 individual spectra, and the projected size of a TES pixel at the limb is 13 km.

  9. Pulsar Emission Geometry and Accelerating Field Strength

    NASA Technical Reports Server (NTRS)

    DeCesar, Megan E.; Harding, Alice K.; Miller, M. Coleman; Kalapotharakos, Constantinos; Parent, Damien

    2012-01-01

    The high-quality Fermi LAT observations of gamma-ray pulsars have opened a new window to understanding the generation mechanisms of high-energy emission from these systems, The high statistics allow for careful modeling of the light curve features as well as for phase resolved spectral modeling. We modeled the LAT light curves of the Vela and CTA I pulsars with simulated high-energy light curves generated from geometrical representations of the outer gap and slot gap emission models. within the vacuum retarded dipole and force-free fields. A Markov Chain Monte Carlo maximum likelihood method was used to explore the phase space of the magnetic inclination angle, viewing angle. maximum emission radius, and gap width. We also used the measured spectral cutoff energies to estimate the accelerating parallel electric field dependence on radius. under the assumptions that the high-energy emission is dominated by curvature radiation and the geometry (radius of emission and minimum radius of curvature of the magnetic field lines) is determined by the best fitting light curves for each model. We find that light curves from the vacuum field more closely match the observed light curves and multiwavelength constraints, and that the calculated parallel electric field can place additional constraints on the emission geometry

  10. The Calculus of Relativistic Temporal Geometry

    NASA Astrophysics Data System (ADS)

    Mayer, Alexander

    2009-05-01

    Richard Feynman's unpublished 1965 gedanken experiment, discussed on pages 60-62 of A. F. Mayer, On the Geometry of Time in Physics and Cosmology (April 2009), demonstrates that the principles of relativity destroy both Newton's concept of absolute time and the concept of a Newtonian gravitational equipotential surface. According to logic arising from experience, it has long been falsely assumed that no energy cost is incurred for translation over an ideally frictionless level surface in the presence of a vertical acceleration. However, that the speed of light is a limiting velocity implies that while two distinct points on such a surface can be considered to be at the same potential relative to a third point that is not on that surface, a particle translated between two such points must incur energy transfer to the accelerating field. Typically, this manifests as a redshift of electromagnetic radiation as demonstrated by ``Feynman's rocket.'' Accurate calculation of this relativistic transverse gravitational redshift (TGR) for observable phenomena in a real-world astrophysical gravitational field requires the calculus of relativistic temporal geometry. Calculations using this technique accurately predict the following empirically observed but heretofore unexplained natural phenomena: the center-to-limb variation of solar wavelength (˜1 km/ s), the K-effect for massive main sequence stars (˜2-3 km/s), and the excess redshift of white dwarf stars (˜10-15 km/s).

  11. Geometry of Discrete-Time Spin Systems

    NASA Astrophysics Data System (ADS)

    McLachlan, Robert I.; Modin, Klas; Verdier, Olivier

    2016-10-01

    Classical Hamiltonian spin systems are continuous dynamical systems on the symplectic phase space (S^2)^n. In this paper, we investigate the underlying geometry of a time discretization scheme for classical Hamiltonian spin systems called the spherical midpoint method. As it turns out, this method displays a range of interesting geometrical features that yield insights and sets out general strategies for geometric time discretizations of Hamiltonian systems on non-canonical symplectic manifolds. In particular, our study provides two new, completely geometric proofs that the discrete-time spin systems obtained by the spherical midpoint method preserve symplecticity. The study follows two paths. First, we introduce an extended version of the Hopf fibration to show that the spherical midpoint method can be seen as originating from the classical midpoint method on T^*{R}^{2n} for a collective Hamiltonian. Symplecticity is then a direct, geometric consequence. Second, we propose a new discretization scheme on Riemannian manifolds called the Riemannian midpoint method. We determine its properties with respect to isometries and Riemannian submersions, and, as a special case, we show that the spherical midpoint method is of this type for a non-Euclidean metric. In combination with Kähler geometry, this provides another geometric proof of symplecticity.

  12. Thermodynamic geometry: Evolution, correlation and phase transition

    NASA Astrophysics Data System (ADS)

    Bellucci, S.; Tiwari, B. N.

    2011-06-01

    Under the fluctuation of the electric charge and atomic mass, this paper considers the theory of the thin film depletion layer formation of an ensemble of finitely excited, non-empty d/f-orbital heavy materials, from the thermodynamic geometric perspective. At each state of the local adiabatic evolutions, we examine the nature of the thermodynamic parameters, viz., electric charge and mass, changing at each respective embedding. The definition of the intrinsic Riemannian geometry and differential topology offers the properties of (i) local heat capacities, (ii) global stability criterion and (iv) global correlation length. Under the Gaussian fluctuations, such an intrinsic geometric consideration is anticipated to be useful in the statistical coating of the thin film layer of a desired quality-fine high cost material on a low cost durable coatant. From the perspective of everyday applications, thermodynamic geometry is thus intrinsically self-consistent with the theory of local and global economic optimizations. Following the above procedure, the quality of the thin layer depletion could self-consistently be examined to produce quality products economically.

  13. Dimensional flow in discrete quantum geometries

    NASA Astrophysics Data System (ADS)

    Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes

    2015-04-01

    In various theories of quantum gravity, one observes a change in the spectral dimension from the topological spatial dimension d at large length scales to some smaller value at small, Planckian scales. While the origin of such a flow is well understood in continuum approaches, in theories built on discrete structures a firm control of the underlying mechanism is still missing. We shed some light on the issue by presenting a particular class of quantum geometries with a flow in the spectral dimension, given by superpositions of states defined on regular complexes. For particular superposition coefficients parametrized by a real number 0 <α geometries may be considered as fractal only when α =1 , where the "magic number" DS≃2 for the spectral dimension of spacetime, appearing so often in quantum gravity, is reproduced as well. These results apply, in particular, to special superpositions of spin-network states in loop quantum gravity, and they provide more solid indications of dimensional flow in this approach.

  14. Imaging molecular geometry with electron momentum spectroscopy

    NASA Astrophysics Data System (ADS)

    Wang, Enliang; Shan, Xu; Tian, Qiguo; Yang, Jing; Gong, Maomao; Tang, Yaguo; Niu, Shanshan; Chen, Xiangjun

    2016-12-01

    Electron momentum spectroscopy is a unique tool for imaging orbital-specific electron density of molecule in momentum space. However, the molecular geometry information is usually veiled due to the single-centered character of momentum space wavefunction of molecular orbital (MO). Here we demonstrate the retrieval of interatomic distances from the multicenter interference effect revealed in the ratios of electron momentum profiles between two MOs with symmetric and anti-symmetric characters. A very sensitive dependence of the oscillation period on interatomic distance is observed, which is used to determine F-F distance in CF4 and O-O distance in CO2 with sub-Ångström precision. Thus, using one spectrometer, and in one measurement, the electron density distributions of MOs and the molecular geometry information can be obtained simultaneously. Our approach provides a new robust tool for imaging molecules with high precision and has potential to apply to ultrafast imaging of molecular dynamics if combined with ultrashort electron pulses in the future.

  15. Measurement of quantum fluctuations in geometry

    SciTech Connect

    Hogan, Craig J.

    2008-05-15

    A particular form for the quantum indeterminacy of relative spacetime position of events is derived from the context of a holographic geometry with a minimum length at the Planck scale. The indeterminacy predicts fluctuations from a classically defined geometry in the form of ''holographic noise'' whose spatial character, absolute normalization, and spectrum are predicted with no parameters. The noise has a distinctive transverse spatial shear signature and a flat power spectral density given by the Planck time. An interferometer signal displays noise due to the uncertainty of relative positions of reflection events. The noise corresponds to an accumulation of phase offset with time that mimics a random walk of those optical elements that change the orientation of a wavefront. It only appears in measurements that compare transverse positions and does not appear at all in purely radial position measurements. A lower bound on holographic noise follows from a covariant upper bound on gravitational entropy. The predicted holographic noise spectrum is estimated to be comparable to measured noise in the currently operating interferometric gravitational-wave detector GEO600. Because of its transverse character, holographic noise is reduced relative to gravitational wave effects in other interferometer designs, such as the LIGO observatories, where beam power is much less in the beam splitter than in the arms.

  16. Students' Learning Experiences When Using a Dynamic Geometry Software Tool in a Geometry Lesson at Secondary School in Ethiopia

    ERIC Educational Resources Information Center

    Denbel, Dejene Girma

    2015-01-01

    Students learning experiences were investigated in geometry lesson when using Dynamic Geometry Software (DGS) tool in geometry learning in 25 Ethiopian secondary students. The research data were drawn from the used worksheets, classroom observations, results of pre- and post-test, a questionnaire and interview responses. I used GeoGebra as a DGS…

  17. The geometry of Bi nanolines on Si(0 0 1)

    NASA Astrophysics Data System (ADS)

    Miwa, R. H.; MacLeod, J. M.; Srivastava, G. P.; McLean, A. B.

    2005-05-01

    A study of the Bi nanoline geometry on Si(0 0 1) has been performed using a combination of ab initio theoretical technique and scanning tunnelling microscopy (STM). Our calculations demonstrate decisively that the recently proposed Haiku geometry is a lower energy configuration than any of the previously proposed line geometries. Furthermore, we have made comparisons between STM constant-current topographs of the lines and Tersoff-Haman STM simulations. Although the Haiku and the Miki geometries both reproduce the main features of the constant-current topographs, the simulated STM images of the Miki geometry have a dark stripe between the dimer rows that does not correspond well with experiment.

  18. The relationship among geometry, working memory, and intelligence in children.

    PubMed

    Giofrè, David; Mammarella, Irene Cristina; Cornoldi, Cesare

    2014-07-01

    Although geometry is one of the main areas of mathematical learning, the cognitive processes underlying geometry-related academic achievement have not been studied in detail. This study explored the relationship among working memory (WM), intelligence (g factor), and geometry in 176 typically developing children attending school in their fourth and fifth grades. Structural equation modeling showed that approximately 40% of the variance in academic achievement and in intuitive geometry (which is assumed to be independent of a person's cultural background) was explained by WM and the g factor. After taking intelligence and WM into account, intuitive geometry was no longer significantly related to academic achievement in geometry. We also found intuitive geometry to be closely related to fluid intelligence (as measured by Raven's colored progressive matrices) and reasoning ability, whereas academic achievement in geometry depended largely on WM. These results were confirmed by a series of regressions in which we estimated the contributions of WM, intelligence, and intuitive geometry to the unique and shared variance explaining academic achievement in geometry. Theoretical and educational implications of the relationship among WM, intelligence, and academic achievement in geometry are discussed.

  19. Geometry of Miura-folded metamaterials

    PubMed Central

    Schenk, Mark; Guest, Simon D.

    2013-01-01

    This paper describes two folded metamaterials based on the Miura-ori fold pattern. The structural mechanics of these metamaterials are dominated by the kinematics of the folding, which only depends on the geometry and therefore is scale-independent. First, a folded shell structure is introduced, where the fold pattern provides a negative Poisson’s ratio for in-plane deformations and a positive Poisson’s ratio for out-of-plane bending. Second, a cellular metamaterial is described based on a stacking of individual folded layers, where the folding kinematics are compatible between layers. Additional freedom in the design of the metamaterial can be achieved by varying the fold pattern within each layer. PMID:23401549

  20. The Bell states in noncommutative algebraic geometry

    NASA Astrophysics Data System (ADS)

    Beil, Charlie

    2014-10-01

    We introduce new mathematical aspects of the Bell states using matrix factorizations, non-noetherian singularities, and noncommutative blowups. A matrix factorization of a polynomial p consists of two matrices ϕ1, ϕ2 such that ϕ1ϕ2 = ϕ2ϕ1 = p id. Using this notion, we show how the Bell states emerge from the separable product of two mixtures, by defining pure states over complex matrices rather than just the complex numbers. We then show in an idealized algebraic setting that pure states are supported on non-noetherian singularities. Moreover, we find that the collapse of a Bell state is intimately related to the representation theory of the noncommutative blowup along its singular support. This presents an exchange in geometry: the nonlocal commutative spacetime of the entangled state emerges from an underlying local noncommutative spacetime.

  1. Hofstadter’s butterfly in quantum geometry

    NASA Astrophysics Data System (ADS)

    Hatsuda, Yasuyuki; Katsura, Hosho; Tachikawa, Yuji

    2016-10-01

    We point out that the recent conjectural solution to the spectral problem for the Hamiltonian H={{{e}}}x+{{{e}}}-x+{{{e}}}p+{{{e}}}-p in terms of the refined topological invariants of a local Calabi-Yau (CY) geometry has an intimate relation with two-dimensional non-interacting electrons moving in a periodic potential under a uniform magnetic field. In particular, we find that the quantum A-period, determining the relation between the energy eigenvalue and the Kähler modulus of the CY, can be found explicitly when the quantum parameter q={{{e}}}{{i}{\\hslash }} is a root of unity, that its branch cuts are given by Hofstadter’s butterfly, and that its imaginary part counts the number of states of the Hofstadter Hamiltonian. The modular double operation, exchanging ℏ and \\widetilde{{\\hslash }}=4{π }2/{\\hslash }, plays an important role.

  2. Fermi liquid viscosity in a finite geometry

    NASA Technical Reports Server (NTRS)

    Jaffe, J. E.

    1979-01-01

    Forced flow of a Fermi liquid is studied for a cell geometry consisting of two planes with a separation on the order of the mean free path. An approximate transport equation is used to derive an integral equation for the velocity profile, which is solved numerically. Results for the total flux through the cell, which determines the dissipation, are given as a function of the Knudsen number kappa (ratio of cell thickness to mean free path). Effects of specular reflection at the boundaries are considered. It is found that the dissipation has a minimum at kappa of 1/2, and behaves linearly for kappa not less than 3. Implications for present experimentation are discussed.

  3. Interactive design of hypersonic waverider geometries

    NASA Technical Reports Server (NTRS)

    Center, K. B.; Sobieczky, H.; Dougherty, F. C.

    1991-01-01

    The paper deals with an inverse design code utilizing the method of oscillating cones; the code integrated into an interactive graphics software package allows manipulation of both the exit-plane shock profile and leading edge of the vehicle. Another interactive feature of the system is the ability to vary freestream conditions and reevaluate the governing conditions. The development of the oscillating cones is shown on five classes each of which is chosen to demonstrate an aspect of improved design flexibility over previous studies. Results are evaluated using a robust flow solver, insuring that the shock shapes specified in the design process are recovered. It is pointed out that the expanded range of waverider geometries that may be generated using the oscillating cones technique may provide insight into visually oriented optimization parameters such as volumetric efficiency and practical planform.

  4. The geometry of spontaneous symmetry breaking

    NASA Astrophysics Data System (ADS)

    Abud, M.; Sartori, G.

    1983-10-01

    The problem of classifying the theoretically allowed patterns of spontaneous symmetry breading, in theories where the ground state is determined as a minimum of a G-invariant potential ( G a compact group of transformations), is analyzed. A detailed, complete, and rigorous justification of a recently proposed approach to the determination of the minima of G-invariant potentials (M. Abud and G. Sartori, Phys. Lett. B104 (1981), 147) is presented. The results are obtained through an analysis of the geometry of the finite-dimensional representations of G, which leads to a complete characterization of the structure of orbit space and its partition in subsets (strata) formed by orbits with the same symmetry under G-transformations (orbit type), and to a new theorem stating that the gradients of complex analytic G-invariant functions annihilate on one-dimensional strata. Polynomial potentials in particular are studied. Conditions for instability of the residual symmetry (second-order phase transitions) are determined.

  5. Consciousness, the brain, and spacetime geometry.

    PubMed

    Hameroff, S

    2001-04-01

    subunit proteins ("tubulins") within certain brain neurons, remain coherent, and recruit more superposed tubulins until a mass-time-energy threshold (related to quantum gravity) is reached. At that point, self-collapse, or objective reduction (OR), abruptly occurs. We equate the pre-reduction, coherent superposition ("quantum computing") phase with pre-conscious processes, and each instantaneous (and non-computable) OR, or self-collapse, with a discrete conscious event. Sequences of OR events give rise to a "stream" of consciousness. Microtubule-associated proteins can "tune" the quantum oscillations of the coherent superposed states; the OR is thus self-organized, or "orchestrated" ("Orch OR"). Each Orch OR event selects (non-computably) microtubule subunit states which regulate synaptic/neural functions using classical signaling. The quantum gravity threshold for self-collapse is relevant to consciousness, according to our arguments, because macroscopic superposed quantum states each have their own spacetime geometries. These geometries are also superposed, and in some way "separated," but when sufficiently separated, the superposition of spacetime geometries becomes significantly unstable and reduces to a single universe state. Quantum gravity determines the limits of the instability; we contend that the actual choice of state made by Nature is non-computable. Thus each Orch OR event is a self-selection of spacetime geometry, coupled to the brain through microtubules and other biomolecules. If conscious experience is intimately connected with the very physics underlying spacetime structure, then Orch OR in microtubules indeed provides us with a completely new and uniquely promising perspective on the difficult problems of consciousness.

  6. Interferometric tests of Planckian quantum geometry models

    DOE PAGES

    Kwon, Ohkyung; Hogan, Craig J.

    2016-04-19

    The effect of Planck scale quantum geometrical effects on measurements with interferometers is estimated with standard physics, and with a variety of proposed extensions. It is shown that effects are negligible in standard field theory with canonically quantized gravity. Statistical noise levels are estimated in a variety of proposals for nonstandard metric fluctuations, and these alternatives are constrained using upper bounds on stochastic metric fluctuations from LIGO. Idealized models of several interferometer system architectures are used to predict signal noise spectra in a quantum geometry that cannot be described by a fluctuating metric, in which position noise arises from holographicmore » bounds on directional information. Lastly, predictions in this case are shown to be close to current and projected experimental bounds.« less

  7. Interferometric tests of Planckian quantum geometry models

    SciTech Connect

    Kwon, Ohkyung; Hogan, Craig J.

    2016-04-19

    The effect of Planck scale quantum geometrical effects on measurements with interferometers is estimated with standard physics, and with a variety of proposed extensions. It is shown that effects are negligible in standard field theory with canonically quantized gravity. Statistical noise levels are estimated in a variety of proposals for nonstandard metric fluctuations, and these alternatives are constrained using upper bounds on stochastic metric fluctuations from LIGO. Idealized models of several interferometer system architectures are used to predict signal noise spectra in a quantum geometry that cannot be described by a fluctuating metric, in which position noise arises from holographic bounds on directional information. Lastly, predictions in this case are shown to be close to current and projected experimental bounds.

  8. Fermi liquid viscosity in a finite geometry

    NASA Technical Reports Server (NTRS)

    Jaffe, J. E.

    1979-01-01

    Forced flow of a Fermi liquid is studied for a cell geometry consisting of two planes with a separation on the order of mean free path. An approximate transport equation is used to derive an integral equation for the velocity profile, which is solved numerically. Results for the total flux through the cell, which determines the dissipation, are given as a function of the Knudsen number N (ratio of cell thickness to mean free path). Effects of specular reflection at the boundaries are considered. It is found that the dissipation has a minimum at N approximately equal to 1/2, and behaves linearly for N greater than or equal to 3. Implications for present experimentation are discussed.

  9. Robot motion planning with virtually modified geometry

    NASA Astrophysics Data System (ADS)

    Baginski, Boris

    1998-07-01

    We present a novel approach to motion planning for robot manipulators in known environments. The key concept is to evaluate complete trajectories between start and goal in the workspace and to reshape them incrementally. The evaluation is based on virtual modifications, especially shrinking and expansion, of the geometry model of the robot. The trajectories are bended in space to be improved with respect to the evaluation. We initialize this planning with a possibly colliding connection, evaluate it in our world model and incrementally decrease the degree of collision for the whole trajectory. The planning is applicable to realistic robot tasks, even problems with a high number of degrees of freedom can be solved easily. The principle of planning with whole trajectories instead of a moving position along a trajectory can be seen as a shift of perspective that may serve as an example for other planning domains.

  10. Geometry in the mechanics of origami

    NASA Astrophysics Data System (ADS)

    Dias, Marcelo A.; Santangelo, Christian D.

    2012-02-01

    We present a mechanical model for curved fold origami in which the bending energies of developable regions are balanced with a phenomenological energy for the crease. The latter energy comes into play as a source of geometric frustration, allowing us to study shape formation by prescribing crease patterns. For a single fold annular configuration, we show how geometry forces a symmetry breaking of the ground state by increasing the width of the ribbon. We extend our model to study multiple fold structures, where we derive geometrical constraints that can be written as recursive relations to build the surface from valley to mountain, and so on. We also suggest a mechanical model for single vertex folds, mapping this problem to an elastica on the sphere.

  11. Deception discovery and employment with linguistic geometry

    NASA Astrophysics Data System (ADS)

    Stilman, Boris; Yakhnis, Vladimir; Curry, Pat; Umanskiy, Oleg

    2005-05-01

    No battle plan survives first contact with the enemy - this is a famous adage attributed to a great many military thinkers from Belisarius to Clausewitz, but which is essentially timeless. Indeed, while the Blue side is trying to anticipate and predict the enemy action, this enemy is actively trying to do the same with respect to Blue while simultaneously trying to deny Blue sufficient information on which to predict Red's actions. It becomes even worse when the Red side is actively engaged in deceptive behavior leading to ambushes and other deceptive schemes causing losses to the Blue side. Linguistic Geometry (LG), a new game-theoretical approach, permits uncovering enemy deceptive schemes via indicators and probes. We will describe the theory behind the LG approach to deception and discuss a specific example of discerning enemy deception via LG algorithms.

  12. Computational algebraic geometry of epidemic models

    NASA Astrophysics Data System (ADS)

    Rodríguez Vega, Martín.

    2014-06-01

    Computational Algebraic Geometry is applied to the analysis of various epidemic models for Schistosomiasis and Dengue, both, for the case without control measures and for the case where control measures are applied. The models were analyzed using the mathematical software Maple. Explicitly the analysis is performed using Groebner basis, Hilbert dimension and Hilbert polynomials. These computational tools are included automatically in Maple. Each of these models is represented by a system of ordinary differential equations, and for each model the basic reproductive number (R0) is calculated. The effects of the control measures are observed by the changes in the algebraic structure of R0, the changes in Groebner basis, the changes in Hilbert dimension, and the changes in Hilbert polynomials. It is hoped that the results obtained in this paper become of importance for designing control measures against the epidemic diseases described. For future researches it is proposed the use of algebraic epidemiology to analyze models for airborne and waterborne diseases.

  13. Geometry and Mechanics of Thin Growing Bilayers

    NASA Astrophysics Data System (ADS)

    Pezzulla, Matteo; Smith, Gabriel; Nardinocchi, Paola; Holmes, Douglas

    We investigate how thin sheets of arbitrary shapes morph under the isotropic in-plane expansion of their top surface, which may represent several stimuli such as nonuniform heating, local swelling and differential growth. Inspired by geometry, an analytical model is presented that rationalizes how the shape of the disk influences morphing, from the initial spherical bending to the final isometric limit. We introduce a new measure of slenderness that describes a sheet in terms of both thickness and plate shape. We find that the mean curvature of the isometric state is three fourth's the natural curvature, which we verify by numerics and experiments. We finally investigate the emergence of a preferred direction of bending in the isometric state, guided by numerical analyses. The scalability of our model suggests that it is suitable to describe the morphing of sheets spanning several orders of magnitude. NSF Grant CMMI-1300860.

  14. Gully geometry: what are we measuring?

    NASA Astrophysics Data System (ADS)

    Casalí, Javier; Giménez, Rafael; Ángel Campo, Miguel

    2014-05-01

    Gully erosion has attracted the attention of many scientists during the last decades, and gullies are an important source of sediment within catchments. For succeeding in gully erosion research, gullies must be properly characterized. Characterization includes the determination of gully morphology and volume, being the definition of gully width (W) and depth (D) -and consequently related variables such as the well-known W/D ratio- key issues toward to this goal. However, and surprisingly, universally accepted criteria (rules or guidance) to define gully morphology are lacking. This because the protocol every researcher follows to measure the eroded channel geometry is generally taken for granted and most of the time even no explanation is given about it. For example, when analyzing a gully cross section we usually just identify gully depth with gully maximum depth. But, is this the right protocol? What does this length really represent? What is its meaning? All this uncertainties can lead to non-comparable results and then important inconsistencies. So, to define universal rules of procedure would allow gully scientists "speak the same language" and then deliver truly comparable gully geometry and volume. On the other hand, there are other misunderstandings. For example, very frequently we characterize or depict a whole gully only through some of its cross sections. Again, is this correct? The problem is even more complex when considering that gully geometry may (largely) change along the channel. The main aim of this presentation is to highlight some (unnoticed) common flaws when measuring and describing gully geometry, hoping ultimately to open a debate on that subject. For this last purpose, a conceptual approach to define gully cross section width and other derived variables is firstly proposed. It is based on the subtraction of a highly detailed digital elevation model of a landscape surface containing the studied gully (DEM1) from a detailed spatial

  15. Generating Composite Overlapping Grids on CAD Geometries

    SciTech Connect

    Henshaw, W.D.

    2002-02-07

    We describe some algorithms and tools that have been developed to generate composite overlapping grids on geometries that have been defined with computer aided design (CAD) programs. This process consists of five main steps. Starting from a description of the surfaces defining the computational domain we (1) correct errors in the CAD representation, (2) determine topology of the patched-surface, (3) build a global triangulation of the surface, (4) construct structured surface and volume grids using hyperbolic grid generation, and (5) generate the overlapping grid by determining the holes and the interpolation points. The overlapping grid generator which is used for the final step also supports the rapid generation of grids for block-structured adaptive mesh refinement and for moving grids. These algorithms have been implemented as part of the Overture object-oriented framework.

  16. Satellite Multiangle Cumulus Geometry Retrieval: Case Study

    SciTech Connect

    Kassianov, Evgueni I.; Ackerman, Thomas P.; Marchand, Roger T.; Ovtchinnikov, Mikhail

    2003-02-08

    Most satellite-based analyses have been conducted using near nadir-viewing sensors. The Multi-angle Imaging SpectroRadiometer (MISR), recently launched on the National Aeronautics and Space Administration (NASA) Terra platform, provides high-resolution measurements of reflectance at nine different viewing angles. In this study, we examine the possible retrieval of detailed cumulus geometry using the new and unique MISR datasets. We suggested one approach and apply it to an early MISR dataset of small marine cumulus clouds. This paper also presents validation analysis of this technique with both independent ground-based radar measurements and a model-output inverse problem. Collocated and coincident MISR data and ground-based observations at the Atmospheric Radiation Measurement (ARM) Tropical Western Pacific (TWP) site form the basis of this validation. Future work will attempt to test the suggested approach with additional MISR scenes.

  17. BOREAS TE-12 SSA Shoot Geometry Data

    NASA Technical Reports Server (NTRS)

    Hall, Forrest G. (Editor); Curd, Shelaine (Editor); Walter-Shea, Elizabeth A.; Mesarch, Mark A.; Cheng, L.; Yang, Litao

    2000-01-01

    The Boreal Ecosystem-Atmospheric Study (BOREAS) TE-12 (Terrestrial Ecology) team collected shoot geometry data in 1993 and 1994 from aspen, jack pine, and black spruce trees. Collections were made at the Southern Study Area Nipawin Fen Site (SSA FEN), Young Jack Pine (YJP), Old Jack Pine (OJP), Old Aspen (OA), Young Aspen (YA), Mixed Site (MIX), and Old Black Spruce (OBS) sites. A caliper was used to measure shoot and needle lengths and widths. A volume displacement procedure was used to measure the weight of the shoot or twig submerged in water. The data files are available on a CD-ROM (see document number 20010000884), or from the Oak Ridge National Laboratory (ORNL) Distributed Active Archive Center (DAAC).

  18. Geometry of aortic heart valves. [prosthetic design

    NASA Technical Reports Server (NTRS)

    Karara, H. M.

    1975-01-01

    Photogrammetric measurements of the surface topography of the aortic valves obtained from silicon rubber molds of freshly excised human aortic valves are presented. The data are part of an investigation into the design of a new prosthetic valve which will be a central-flow device, like the real valve and unlike previous central-occluding prostheses. Since the maximum stress on the heart valve is induced when the valve is closed and subject to diastolic back-pressure, it was decided to determine the valve geometry during diastole. That is, the molds were formed by pouring the rubber down the excised aortas, causing the valves to close. The molds were made under different pressures (20-120 torr); photogrammetry served as a vehicle for the assessment of the mold topography through the following outputs: digital models, surface profiles, and contour maps.

  19. Algebraic geometry realization of quantum Hall soliton

    NASA Astrophysics Data System (ADS)

    Abounasr, R.; Ait Ben Haddou, M.; El Rhalami, A.; Saidi, E. H.

    2005-02-01

    Using the Iqbal-Netzike-Vafa dictionary giving the correspondence between the H2 homology of del Pezzo surfaces and p-branes, we develop a way to approach the system of brane bounds in M-theory on S1. We first review the structure of 10-dimensional quantum Hall soliton (QHS) from the view of M-theory on S1. Then, we show how the D0 dissolution in D2-brane is realized in M-theory language and derive the p-brane constraint equations used to define appropriately the QHS. Finally, we build an algebraic geometry realization of the QHS in type IIA superstring and show how to get its type IIB dual. Other aspects are also discussed.

  20. Exotic geometry in string theory and cosmology

    NASA Astrophysics Data System (ADS)

    Haque, Sheikh Shajid

    One of the main features expected of a quantum theory of gravity is non-locality. Implementing non-locality in quantum field theories turns out to be already challenging both conceptually and technically and requires the use of several techniques, such as string dualities and twists in order to construct and understand the effects of non-locality. This thesis explored these concepts in the construction of quantum field theories with a particular type of non- locality, non-commutative geometry, as an opportunity to study non-locality in a broader context. Another important challenge of theoretical physics is to connect the microscopic structure of spacetime implied by string theory to the empirical fact that the cosmological constant is positive and that the universe is asymptotically de Sitter. Constructing de Sitter space from string theory has proven to be extremely difficult over the years. In this thesis, I will discuss recent work in these areas.

  1. Footprint Geometry and Sessile Drop Resonance

    NASA Astrophysics Data System (ADS)

    Chang, Chun-Ti; Daniel, Susan; Steen, Paul H.

    2016-11-01

    How does a sessile drop resonate if its footprint is square (square drop)? In this talk, we discuss the two distinct families of observed modes in our experiments. One family (spherical modes) is identified with the natural modes of capillary spherical caps, and the other (grid modes) with Faraday waves on a square bath (square Faraday waves). A square drop exhibits grid or spherical modes depending on its volume, and the two families of modes arise depending on how wavenumber selection of footprint geometry and capillarity compete. For square drops, a dominant effect of footprint constraint leads to grid modes which are constrained response; otherwise the drops exhibit spherical modes, the characteristic of sessile drops on flat plates. Chun-Ti Chang takes his new position at National Taiwan University on Aug. 15th, 2016. Until then, Chun-Ti Chang is affiliated with Technical University Dortmund, Germany.

  2. Multiphase flows in confinement with complex geometries

    NASA Astrophysics Data System (ADS)

    Aymard, Benjamin; Pradas, Marc; Vaes, Urbain; Kalliadasis, Serafim

    2016-11-01

    Understanding the dynamics of immiscible fluids in confinement is crucial in numerous applications such as oil recovery, fuel cells and the rapidly growing field of microfluidics. Complexities such as microstructures, chemical-topographical heterogeneities or porous membranes, can often induce non-trivial effects such as critical phenomena and phase transitions . The dynamics of confined multiphase flows may be efficiently described using diffuse-interface theory, leading to the Cahn-Hilliard-Navier-Stokes(CHNS) equations with Cahn wetting boundary conditions. Here we outline an efficient numerical method to solve the CHNS equations using advanced geometry-capturing mesh techniques both in two and three dimensional scenarios. The methodology is applied to two different systems: a droplet on a spatially chemical-topographical heterogeneous substrateand a microfluidic separator.

  3. Black holes and large order quantum geometry

    SciTech Connect

    Huang Minxin; Klemm, Albrecht; Marino, Marcos; Tavanfar, Alireza

    2009-03-15

    We study five-dimensional black holes obtained by compactifying M theory on Calabi-Yau threefolds. Recent progress in solving topological string theory on compact, one-parameter models allows us to test numerically various conjectures about these black holes. We give convincing evidence that a microscopic description based on Gopakumar-Vafa invariants accounts correctly for their macroscopic entropy, and we check that highly nontrivial cancellations--which seem necessary to resolve the so-called entropy enigma in the Ooguri-Strominger-Vafa conjecture--do in fact occur. We also study analytically small 5d black holes obtained by wrapping M2 branes in the fiber of K3 fibrations. By using heterotic/type II duality we obtain exact formulae for the microscopic degeneracies in various geometries, and we compute their asymptotic expansion for large charges.

  4. Special relativity as a simple geometry problem

    NASA Astrophysics Data System (ADS)

    de Abreu, Rodrigo; Guerra, Vasco

    2009-03-01

    The null result of the Michelson-Morley experiment and the constancy of the one-way speed of light in the 'rest system' are used to formulate a simple problem, to be solved by elementary geometry techniques using a pair of compasses and non-graduated rulers. The solution consists of a drawing allowing a direct visualization of all the fundamental effects of standard relativistic kinematics, namely time dilation, length contraction and relativity of simultaneity. Moreover, it also provides an immediate image of other important and more subtle aspects, often passed by in relativity courses, such as the conventionality of simultaneity thesis, possible non-invariance of the one-way speed of light and compatibility between the Lorentz-Poincaré and Einstein-Minkowski philosophies. The geometric scheme so constructed constitutes a powerful tool to clearly illustrate both traditional and not-so-traditional aspects of special relativity teaching.

  5. Simulating Irregular Source Geometries for Ionian Plumes

    SciTech Connect

    McDoniel, W. J.; Goldstein, D. B.; Varghese, P. L.; Trafton, L. M.; Buchta, D. A.; Freund, J.; Kieffer, S. W.

    2011-05-20

    Volcanic plumes on Io respresent a complex rarefied flow into a near-vacuum in the presence of gravity. A 3D Direct Simulation Monte Carlo (DSMC) method is used to investigate the gas dynamics of such plumes, with a focus on the effects of source geometry on far-field deposition patterns. A rectangular slit and a semicircular half annulus are simulated to illustrate general principles, especially the effects of vent curvature on deposition ring structure. Then two possible models for the giant plume Pele are presented. One is a curved line source corresponding to an IR image of a particularly hot region in the volcano's caldera and the other is a large area source corresponding to the entire caldera. The former is seen to produce the features seen in observations of Pele's ring, but with an error in orientation. The latter corrects the error in orientation, but loses some structure. A hybrid simulation of 3D slit flow is also discussed.

  6. Critical geometry of a thermal big bang

    NASA Astrophysics Data System (ADS)

    Afshordi, Niayesh; Magueijo, João

    2016-11-01

    We explore the space of scalar-tensor theories containing two nonconformal metrics, and find a discontinuity pointing to a "critical" cosmological solution. Due to the different maximal speeds of propagation for matter and gravity, the cosmological fluctuations start off inside the horizon even without inflation, and will more naturally have a thermal origin (since there is never vacuum domination). The critical model makes an unambiguous, nontuned prediction for the spectral index of the scalar fluctuations: nS=0.96478 (64 ) . Considering also that no gravitational waves are produced, we have unveiled the most predictive model on offer. The model has a simple geometrical interpretation as a probe 3-brane embedded in an E AdS2×E3 geometry.

  7. Geometry Shapes Evolution of Early Multicellularity

    PubMed Central

    Libby, Eric; Ratcliff, William; Travisano, Michael; Kerr, Ben

    2014-01-01

    Organisms have increased in complexity through a series of major evolutionary transitions, in which formerly autonomous entities become parts of a novel higher-level entity. One intriguing feature of the higher-level entity after some major transitions is a division of reproductive labor among its lower-level units in which reproduction is the sole responsibility of a subset of units. Although it can have clear benefits once established, it is unknown how such reproductive division of labor originates. We consider a recent evolution experiment on the yeast Saccharomyces cerevisiae as a unique platform to address the issue of reproductive differentiation during an evolutionary transition in individuality. In the experiment, independent yeast lineages evolved a multicellular “snowflake-like” cluster formed in response to gravity selection. Shortly after the evolution of clusters, the yeast evolved higher rates of cell death. While cell death enables clusters to split apart and form new groups, it also reduces their performance in the face of gravity selection. To understand the selective value of increased cell death, we create a mathematical model of the cellular arrangement within snowflake yeast clusters. The model reveals that the mechanism of cell death and the geometry of the snowflake interact in complex, evolutionarily important ways. We find that the organization of snowflake yeast imposes powerful limitations on the available space for new cell growth. By dying more frequently, cells in clusters avoid encountering space limitations, and, paradoxically, reach higher numbers. In addition, selection for particular group sizes can explain the increased rate of apoptosis both in terms of total cell number and total numbers of collectives. Thus, by considering the geometry of a primitive multicellular organism we can gain insight into the initial emergence of reproductive division of labor during an evolutionary transition in individuality. PMID:25233196

  8. UNDERSTANDING THE GEOMETRY OF ASTROPHYSICAL MAGNETIC FIELDS

    SciTech Connect

    Broderick, Avery E.; Blandford, Roger D.

    2010-08-01

    Faraday rotation measurements have provided an invaluable technique for probing the properties of astrophysical magnetized plasmas. Unfortunately, typical observations provide information only about the density-weighted average of the magnetic field component parallel to the line of sight. As a result, the magnetic field geometry along the line of sight, and in many cases even the location of the rotating material, is poorly constrained. Frequently, interpretations of Faraday rotation observations are dependent upon underlying models of the magnetic field being probed (e.g., uniform, turbulent, equipartition). However, we show that at sufficiently low frequencies, specifically below roughly 13(RM/1 rad m{sup -2}){sup 1/4}(B/1 G){sup 1/2} MHz, the character of Faraday rotation changes, entering what we term the 'super-adiabatic regime' in which the rotation measure (RM) is proportional to the integrated absolute value of the line-of-sight component of the field. As a consequence, comparing RMs at high frequencies with those in this new regime provides direct information about the geometry of the magnetic field along the line of sight. Furthermore, the frequency defining the transition to this new regime, {nu}{sub SA}, depends directly upon the local electron density and magnetic field strength where the magnetic field is perpendicular to the line of sight, allowing the unambiguous distinction between Faraday rotation within and in front of the emission region. Typical values of {nu}{sub SA} range from 10 kHz (below the ionospheric cutoff, but above the heliospheric cutoff) to 10 GHz, depending upon the details of the Faraday rotating environment. In particular, for resolved active galactic nuclei, including the black holes at the center of the Milky Way (Sgr A*) and M81, {nu}{sub SA} ranges from roughly 10 MHz to 10 GHz, and thus can be probed via existing and up-coming ground-based radio observatories.

  9. Notes on "Quantum Gravity" and Noncommutative Geometry

    NASA Astrophysics Data System (ADS)

    Gracia-Bondía, J. M.

    I hesitated for a long time before giving shape to these notes, originally intended for preliminary reading by the attendees to the Summer School "New paths towards quantum gravity" (Holbaek Bay, Denmark, May 2008). At the end, I decide against just selling my mathematical wares, and for a survey, necessarily very selective, but taking a global phenomenological approach to its subject matter. After all, noncommutative geometry does not purport yet to solve the riddle of quantum gravity; it is more of an insurance policy against the probable failure of the other approaches. The plan is as follows: the introduction invites students to the fruitful doubts and conundrums besetting the application of even classical gravity. Next, the first experiments detecting quantum gravitational states inoculate us a healthy dose of scepticism on some of the current ideologies. In Sect. 1.3 we look at the action for general relativity as a consequence of gauge theory for quantum tensor fields. Section 1.4 briefly deals with the unimodular variants. Section 1.5 arrives at noncommutative geometry. I am convinced that, if this is to play a role in quantum gravity, commutative and noncommutative manifolds must be treated on the same footing, which justifies the place granted to the reconstruction theorem. Together with Sect. 1.3, this part constitutes the main body of the notes. Only very summarily at the end of this section do we point to some approaches to gravity within the noncommutative realm. The last section delivers a last dose of scepticism. My efforts will have been rewarded if someone from the young generation learns to mistrust current mindsets.

  10. The human mind: origin in geometry.

    PubMed

    Abler, William L

    2010-01-01

    Within 53 years after the public acceptance of Mendel's laws (in 1900), the genetic material was identified and described (by Watson and Crick). Today, 53 years after the modern era began in the scientific study of language (with Chomsky's Syntactic structures), there is no agreement as to whether universal grammar exists, or whether language as such exists at all, that is, there is no agreement as to which square is square-one. Under the circumstances, a new approach is justified. It is the goal of this paper to place the scientific study of mind, language and brain onto a theoretical basis, beginning with naturally-occurring human language. The human mind has two major components, one with its antecedents in biology and behaviour the other with its antecedents in geometry. It is the geometric component, consisting of language, tool-use, the mathematical sense, and the sense of truth and falsity, that distinguishes and defines the human being. Thus the constructions of language conform to the commutative, associative and distributive laws, and have their ultimate source in geometry. Equations have a symmetrical deep-structure based on the fact that one side is "equal" to the other: The "equals" symbol represents the axis of symmetry, and functions as a kind of main verb. The deep structure of the ordinary sentence is derived by moving the attachment for the "equals" to one of the branches, generating the asymmetrical Subject-Verb-Object relationship. Tool-use, with its Subject (the tool), Verb (movement of the tool), and Object (the workpiece), and manipulation of mental images, is an extension of the sentence. The sense of truth and falsity shares a common source with the right and wrong answers of arithmetic.

  11. Influence of geometry on liquid oxygen magnetohydrodynamics

    SciTech Connect

    Boulware, Jeffrey C.; Ban, Heng; Jensen, Scott; Wassom, Steve

    2010-11-15

    Magnetic fluid actuators have performed well in industrial applications, but have a limited temperature range due to the freezing point of the carrier fluid. Liquid oxygen (LOX) presents a pure, paramagnetic fluid suitable for use in a cryogenic magnetic fluid system; therefore, it is a potential solution to increasing the thermal range of magnetic fluid technology without the need for magnetic particles. The current study presents experimental work regarding the influence of geometry on the dynamics of a LOX slug in a 1.9 mm quartz tube when pulsed by a solenoid in a closed volume. A numerical analysis calculated the optimal solenoid geometry and balanced the magnetic, damping, and pressure forces to determine optimal slug lengths. Three configurations comprised the experiment: (1) a 24-gauge wire solenoid with an optimized 2.7 cm length slug, (2) a 30-gauge wire solenoid with an optimized 1.3 cm length slug, and (3) a 30-gauge wire solenoid with a nonoptimized 2.5 cm length slug. Typically, the hydrodynamic breakdown limit is calculated and used to determine the system range; however the experiment showed that the hydrodynamic breakdown limit was never reached by the slug. This implied that, instead, the system range should factor in a probabilistic risk of failure calculated as a function of the induced pressure change from its oscillations. The experimental data were also used to establish a nondimensional relationship between the maximum displacement and initial magnetic pressure on the slug. The average initial velocity of the slug was found to be proportional to the initial magnetic pressure, Mason number, and slug length. The results of this study can be used in the design and optimization of a LOX fluid system for space or low-temperature applications. (author)

  12. Fabric geometry distortion during composites processing

    NASA Technical Reports Server (NTRS)

    Chen, Julie

    1994-01-01

    Waviness and tow misalignment are often cited as possible causes of data scatter and lower compression stiffness and strength in textile composites. Strength differences of as much as 40 percent have been seen in composites that appear to have the same basic material and structural properties -- i.e., yarn orientation, yarn size, interlacing geometry. Fabric geometry distortion has been suggested as a possible reason for this discrepancy, but little quantitative data or substantial evidence exists. The focus of this research is to contribute to the present understanding of the causes and effects of geometric distortion in textile composites. The initial part of the study was an attempt to gather qualitative information on a variety of textile structures. Existing and new samples confirmed that structures with a significant direction presence would be more susceptible to distortion due to the compaction process. Thus, uniweaves (fiber vol frac: 54-72 percent) biaxial braids (vf: 34-58 percent) demonstrated very little fabric geometry distortion. In stitched panels, only slight buckling of z-direction stitches was observed, primarily near the surface. In contrast, for structures with high compaction ratios -- e.g., large cylindrical yarns (2.5:1) orpowder towpreg (4:1) -- there were visible distortions where previously smooth and periodic undulations were transformed to abrupt changes in direction. A controlled study of the effect of forming pressure on distortion was conducted on type 162 glass plain weave fabrics. Panels (6 x 6 in) were produced via a resin infusion type setup, but with an EPON 815 epoxy resin. Pressures ranging from hand layup to 200 psi were used (vf: 34-54 percent). Photomicrographs indicated that at pressures up to 50 psi, large changes in thickness were due primarily to resin squeeze out. At higher pressures, when intimate contact was made between the layers, there was some tow flattening and in-plane shifting to optimize nesting. However

  13. Spin precession of Dirac particles in Kerr geometry

    NASA Astrophysics Data System (ADS)

    Farooqui, Anusar

    2017-01-01

    We isolate and study the transformation of the intrinsic spin of Dirac particles as they propagate along timelike geodesics in Kerr geometry. Reference frames play a crucial role in the definition and measurement of the intrinsic spin of test particles. We show how observers located in the outer geometry of Kerr black holes may exploit the symmetries of the geometry to set up reference frames using purely geometric, locally-available information. Armed with these geometrically-defined reference frames, we obtain a closed-form expression for the geometrically-induced spin precession of Dirac particles in the outer geometry of Kerr black holes. We show that the spin of Dirac particles does not precess on the equatorial place of Kerr geometry; and hence, in Schwarzschild geometry.

  14. Development and application of CATIA-GDML geometry builder

    NASA Astrophysics Data System (ADS)

    Belogurov, S.; Berchun, Yu; Chernogorov, A.; Malzacher, P.; Ovcharenko, E.; Schetinin, V.

    2014-06-01

    Due to conceptual difference between geometry descriptions in Computer-Aided Design (CAD) systems and particle transport Monte Carlo (MC) codes direct conversion of detector geometry in either direction is not feasible. The paper presents an update on functionality and application practice of the CATIA-GDML geometry builder first introduced at CHEP2010. This set of CATIAv5 tools has been developed for building a MC optimized GEANT4/ROOT compatible geometry based on the existing CAD model. The model can be exported via Geometry Description Markup Language (GDML). The builder allows also import and visualization of GEANT4/ROOT geometries in CATIA. The structure of a GDML file, including replicated volumes, volume assemblies and variables, is mapped into a part specification tree. A dedicated file template, a wide range of primitives, tools for measurement and implicit calculation of parameters, different types of multiple volume instantiation, mirroring, positioning and quality check have been implemented. Several use cases are discussed.

  15. The Influence of Wildfire on Hillslope Geometry

    NASA Astrophysics Data System (ADS)

    Rengers, F. K.; Inbar, A.; Sheridan, G. J.; Nyman, P.

    2014-12-01

    In southeastern Australia wildfire occurs regularly, resulting in increased hillslope erosion. However, post-wildfire erosion processes differ depending on hillslope aspect. Equatorial (north)-facing slopes are drier than polar (south)-facing slopes and experience overland flow erosion after wildfire. By contrast, overland flow is not an active process on polar-facing slopes, even after high-intensity wildfires. These differences in post-wildfire erosion processes are accompanied by observations that slope angle and curvature also differ by hillslope aspect. An airborne LiDAR dataset flown over our study area in the Kinglake National Park, Victoria shows that the mean slope angle of polar-facing slopes is nearly 5 degrees steeper than equatorial-facing slopes. We have sought to test the hypothesis that aspect differences in post-wildfire erosion processes are sufficient to create differences in hillslope geometry. In order to test this hypothesis, we use a simple 1D model that simulates hillslope evolution over thousands of years. We limit our model to low-drainage area hillslopes where debris-flows are unlikely to occur. Erosion is modeled as nonlinear diffusion regardless of aspect during non-wildfire model years. Wildfire is modeled by changing the erosional processes on each slope aspect to reflect the effects of post-wildfire erosion according to a wildfire recurrence interval. For two years following a model wildfire we allow overland flow erosion to erode equatorial-facing slopes, whereas polar-facing slopes erode according to nonlinear diffusion for only one year following a wildfire. The erosion parameters on the polar-facing slopes are changed during this period to reflect higher post-wildfire erosion. In addition to erosional processes, we use an exponential soil production law to simulate new soil formation every model year. Our preliminary results suggest that changes in erosional magnitude associated with the different wildfire erosional processes are

  16. Circular electrode geometry metal-semiconductor-metal photodetectors

    NASA Technical Reports Server (NTRS)

    Mcadoo, James A. (Inventor); Towe, Elias (Inventor); Bishop, William L. (Inventor); Wang, Liang-Guo (Inventor)

    1995-01-01

    The invention comprises a high speed, metal-semiconductor-metal photodetector which comprises a pair of generally circular, electrically conductive electrodes formed on an optically active semiconductor layer. Various embodiments of the invention include a spiral, intercoiled electrode geometry and an electrode geometry comprised of substantially circular, concentric electrodes which are interposed. These electrode geometries result in photodetectors with lower capacitances, dark currents and lower inductance which reduces the ringing seen in the optical pulse response.

  17. Circular electrode geometry metal-semiconductor-metal photodetectors

    NASA Technical Reports Server (NTRS)

    Mcaddo, James A. (Inventor); Towe, Elias (Inventor); Bishop, William L. (Inventor); Wang, Liang-Guo (Inventor)

    1994-01-01

    The invention comprises a high speed, metal-semiconductor-metal photodetector which comprises a pair of generally circular, electrically conductive electrodes formed on an optically active semiconductor layer. Various embodiments of the invention include a spiral, intercoiled electrode geometry and an electrode geometry comprised of substantially circular, concentric electrodes which are interposed. These electrode geometries result in photodetectors with lower capacitances, dark currents and lower inductance which reduces the ringing seen in the optical pulse response.

  18. Geometry and experience: Einstein's 1921 paper and Hilbert's axiomatic system

    NASA Astrophysics Data System (ADS)

    De Gandt, François

    2006-06-01

    In his 1921 paper Geometrie und Erfahrung, Einstein decribes the new epistemological status of geometry, divorced from any intuitive or a priori content. He calls that "axiomatics", following Hilbert's theoretical developments on axiomatic systems, which started with the stimulus given by a talk by Hermann Wiener in 1891 and progressed until the Foundations of geometry in 1899. Difficult questions arise: how is a theoretical system related to an intuitive empirical content?

  19. Capillary condensation in a square geometry with surface fields

    NASA Astrophysics Data System (ADS)

    Zubaszewska, M.; Gendiar, A.; Drzewiński, A.

    2012-12-01

    We study the influence of wetting on capillary condensation for a simple fluid in a square geometry with surface fields, where the reference system is an infinitely long slit. The corner transfer matrix renormalization group method has been extended to study a two-dimensional Ising model confined in an L×L geometry with equal surface fields. Our results have confirmed that in both geometries the coexistence line shift is governed by the same scaling powers, but their prefactors are different.

  20. Geometry Between the Devil and the Deep Sea

    ERIC Educational Resources Information Center

    Freudenthal, Hans

    1971-01-01

    After a discussion of philosophy and learning processes and theories, the author presents rationale for teaching axiomatics in geometry including traditional and modern transformational approaches. (JG)

  1. Geometry creation for MCNP by Sabrina and XSM

    SciTech Connect

    Van Riper, K.A.

    1994-02-01

    The Monte Carlo N-Particle transport code MCNP is based on a surface description of 3-dimensional geometry. Cells are defined in terms of boolean operations on signed quadratic surfaces. MCNP geometry is entered as a card image file containing coefficients of the surface equations and a list of surfaces and operators describing cells. Several programs are available to assist in creation of the geometry specification, among them Sabrina and the new ``Smart Editor`` code XSM. We briefly describe geometry creation in Sabrina and then discuss XSM in detail. XSM is under development; our discussion is based on the state of XSM as of January 1, 1994.

  2. Generalized Kähler Geometry from Supersymmetric Sigma Models

    NASA Astrophysics Data System (ADS)

    Bredthauer, Andreas; Lindström, Ulf; Persson, Jonas; Zabzine, Maxim

    2006-09-01

    We give a physical derivation of generalized Kähler geometry. Starting from a supersymmetric nonlinear sigma model, we rederive and explain the results of Gualtieri (Generalized complex geometry, DPhil thesis, Oxford University, 2004) regarding the equivalence between generalized Kähler geometry and the bi-hermitean geometry of Gates et al. (Nucl Phys B248:157, 1984). When cast in the language of supersymmetric sigma models, this relation maps precisely to that between the Lagrangian and the Hamiltonian formalisms. We also discuss topological twist in this context.

  3. Graph-based representation for multiview image geometry.

    PubMed

    Maugey, Thomas; Ortega, Antonio; Frossard, Pascal

    2015-05-01

    In this paper, we propose a new geometry representation method for multiview image sets. Our approach relies on graphs to describe the multiview geometry information in a compact and controllable way. The links of the graph connect pixels in different images and describe the proximity between pixels in 3D space. These connections are dependent on the geometry of the scene and provide the right amount of information that is necessary for coding and reconstructing multiple views. Our multiview image representation is very compact and adapts the transmitted geometry information as a function of the complexity of the prediction performed at the decoder side. To achieve this, our graph-based representation (GBR) carefully selects the amount of geometry information needed before coding. This is in contrast with depth coding, which directly compresses with losses the original geometry signal, thus making it difficult to quantify the impact of coding errors on geometry-based interpolation. We present the principles of this GBR and we build an efficient coding algorithm to represent it. We compare our GBR approach to classical depth compression methods and compare their respective view synthesis qualities as a function of the compactness of the geometry description. We show that GBR can achieve significant gains in geometry coding rate over depth-based schemes operating at similar quality. Experimental results demonstrate the potential of this new representation.

  4. On the sigma-model of deformed special geometry

    NASA Astrophysics Data System (ADS)

    Lopes Cardoso, Gabriel; Véliz-Osorio, Alvaro

    2013-07-01

    We discuss the deformed sigma-model that arises when considering four-dimensional N=2 abelian vector multiplets in the presence of an arbitrary chiral background field. In addition, we allow for a class of deformations of special geometry by non-holomorphic terms. We analyze the geometry of the sigma-model in terms of intrinsic torsion classes. We show that, generically, the deformed geometry is non-Kähler. We illustrate our findings with an example. We also express the deformed sigma-model in terms of the Hesse potential that underlies the real formulation of special geometry.

  5. Traffic Light Detection Using Conic Section Geometry

    NASA Astrophysics Data System (ADS)

    Hosseinyalmdary, S.; Yilmaz, A.

    2016-06-01

    Traffic lights detection and their state recognition is a crucial task that autonomous vehicles must reliably fulfill. Despite scientific endeavors, it still is an open problem due to the variations of traffic lights and their perception in image form. Unlike previous studies, this paper investigates the use of inaccurate and publicly available GIS databases such as OpenStreetMap. In addition, we are the first to exploit conic section geometry to improve the shape cue of the traffic lights in images. Conic section also enables us to estimate the pose of the traffic lights with respect to the camera. Our approach can detect multiple traffic lights in the scene, it also is able to detect the traffic lights in the absence of prior knowledge, and detect the traffics lights as far as 70 meters. The proposed approach has been evaluated for different scenarios and the results show that the use of stereo cameras significantly improves the accuracy of the traffic lights detection and pose estimation.

  6. Microparticle column geometry in acoustic stationary fields.

    PubMed

    Hancock, Andrew; Insana, Michael F; Allen, John S

    2003-01-01

    Particles suspended in a fluid will experience forces from stationary acoustic fields. The magnitude of the force depends on the time-averaged energy density of the field and the material properties of the particles and fluid. Forces acting on known particles smaller than 20 microm were studied. Within a 500 kHz acoustic beam generated by a plane-piston circular source, observations were made of the geometry of the particle column that is formed. Varying the acoustic energy altered the column width in a manner predicted by equations for the primary acoustic radiation force from scattering of particles in the long-wavelength limit. The minimum pressures required to trap gas, solid, and liquid particles in a water medium at room temperature were also estimated to within 12%. These results highlight the ability of stationary acoustic fields from a plane-piston radiator to impose nano-Newton-scale forces onto fluid particles with properties similar to biological cells, and suggest that it is possible to accurately quantify these forces.

  7. Two-stream instability in convergent geometry

    SciTech Connect

    Gratton, F.T.; Gnavi, G.

    1987-02-01

    The problem of the instability of counterstreaming beams of charged particles is extended to cylindrical and spherical geometries. For well-focused configurations it can be solved by complex contour integral representations. The effects of the convergence of the flow and the density gradient along the trajectories of the particles are considered. The linear spectrum for the cylindrical case is obtained, together with the proof that the solution has finite energy and satisfies two physical matching conditions through the origin. The properties of the special functions which solve this problem are presented. Although the density of the ideally focused model diverges as 1/r at the origin, the growth rate of the instability, for a system of radius R, is given by ..omega../sup 2//sub p/R/V/sub 0/2xi/sub n/, where V/sub 0/ is the beam velocity, xi/sub n/ are the zeros of the Bessel function of zeroth order, and the plasma frequency ..omega../sub p/ is evaluated at one-half the average density of particles.

  8. Topological string theory and enumerative geometry

    NASA Astrophysics Data System (ADS)

    Song, Yun S.

    2001-10-01

    In this thesis we investigate several problems which have their roots in both topological string theory and enumerative geometry. In the former case, underlying theories are topological field theories, whereas the latter case is concerned with intersection theories on moduli spaces. A permeating theme in this thesis is to examine the close interplay between these two complementary fields of study. The main problems addressed are as follows: In considering the Hurwitz enumeration problem of branched covers of compact connected Riemann surfaces, we completely solve the problem in the case of simple Hurwitz numbers. In addition, utilizing the connection between Hurwitz numbers and Hodge integrals, we derive a generating function for the latter on the moduli space overline Mg,2 of 2- pointed, genus- g Deligne-Mumford stable curves. We also investigate Givental's recent conjecture regarding semisimple Frobenius structures and Gromov- Witten invariants, both of which are closely related to topological field theories; we consider the case of a complex projective line P1 as a specific example and verify his conjecture at low genera. In the last chapter, we demonstrate that certain topological open string amplitudes can be computed via relative stable morphisms in the algebraic category.

  9. Formation geometries for multistatic SAR tomography

    NASA Astrophysics Data System (ADS)

    Fasano, Giancarmine; Renga, Alfredo; D'Errico, Marco

    2014-03-01

    This paper analyzes relative orbit design for multi-satellite radar missions aimed at multistatic SAR tomography. To this end, formation requirements and performance parameters are derived by adapting existing models for SAR tomography to single pass techniques. Then, relative trajectory design is carried out on the basis of an analytical relative motion model including secular J2 effects. By properly scaling the differences in orbital parameters, different formation geometries enable uniform sampling of the effective baseline along the whole orbit. The difference among the possible choices lies in latitude coverage, formation stability, and collision avoidance aspects. A numerical example of relative trajectory design is discussed considering L-band as operating frequency. In particular, achievable height resolution and unambiguous height along the orbit are pointed out for a multi-cartwheel, a multi-pendulum, and a multi-helix formation. In view of future implementation of a multi-satellite SAR tomography mission, new concepts aimed at the reduction of required satellites, and long term evolution of designed formations, are also discussed.

  10. Microscopic wormholes and the geometry of entanglement

    NASA Astrophysics Data System (ADS)

    Lobo, Francisco S. N.; Olmo, Gonzalo J.; Rubiera-Garcia, D.

    2014-06-01

    It has recently been suggested that Einstein-Rosen (ER) bridges can be interpreted as maximally entangled states of two black holes that form a complex Einstein-Podolsky-Rosen (EPR) pair. This relationship has been dubbed as the correlation. In this work, we consider the latter conjecture in the context of quadratic Palatini theory. An important result, which stems from the underlying assumptions as regards the geometry on which the theory is constructed, is the fact that all the charged solutions of the quadratic Palatini theory possess a wormhole structure. Our results show that spacetime may have a foam-like microstructure with wormholes generated by fluctuations of the quantum vacuum. This involves the spontaneous creation/annihilation of entangled particle-antiparticle pairs, existing in a maximally entangled state connected by a non-traversable wormhole. Since the particles are produced from the vacuum and therefore exist in a singlet state, they are necessarily entangled with one another. This gives further support to the claim.

  11. Strain Functionals for Characterizing Atomistic Geometries

    NASA Astrophysics Data System (ADS)

    Kober, Edward; Rudin, Sven

    The development of a set of strain tensor functionals that are capable of characterizing arbitrarily ordered atomistic structures is described. This approach defines a Gaussian-weighted neighborhood around each atom and characterizes that local geometry in terms of n-th order strain tensors, which are equivalent to the moments of the neighborhood. Fourth order expansions can distinguish the cubic structures (and deformations thereof), but sixth order expansions are required to fully characterize hexagonal structures. Other methods used to characterize atomic structures, such as the Steinhardt parameters or the centrosymmetry metric, can be derived from this more general approach. These functions are continuous and smooth and much less sensitive to thermal fluctuations than other descriptors based on discrete neighborhoods. They allow material phases, deformations, and a large number of defect structures to be readily identified and classified. Applications to the analysis of shock-loaded samples of Cu, Ta and Ti will be presented. This strain functional basis can also then be used for developing interatomic potential functions, and an initial application to Cu will be presented.

  12. Optimization of RF multipole ion trap geometries

    NASA Astrophysics Data System (ADS)

    Fanghänel, Sven; Asvany, Oskar; Schlemmer, Stephan

    2017-02-01

    Radio-frequency (rf) traps are ideal places to store cold ions for spectroscopic experiments. Specific multipole configurations are suited best for different applications but have to be modified to allow e.g. for a proper overlap of a laser beam waist with the ion cloud. Therefore the corresponding trapping fields should be shaped accordingly. To achieve this goal highly accurate electrical potentials of rf multipole traps and the resulting effective trapping potentials are calculated using the boundary element method (BEM). These calculations are used to evaluate imperfections and to optimize the field geometry. For that purpose the complex fields are reduced to a small set of multipole expansion coefficients. Desirable values for these coefficients are met by systematic changes of real trap dimensions from CAD designs. The effect of misalignment of a linear quadrupole, the optimization of an optically open Paul trap, the influence of steering electrodes (end electrode and ring electrode) on a 22-pole ion trap and the effect of the micro motion on the lowest reachable temperatures in such a trap are discussed.

  13. Linquistic geometry: new technology for decision support

    NASA Astrophysics Data System (ADS)

    Stilman, Boris; Yakhnis, Vladimir

    2003-09-01

    Linguistic Geometry (LG) is a revolutionary gaming approach which is ideally suited for military decision aids for Air, Ground, Naval, and Space-based operations, as well guiding robotic vehicles and traditional entertainment games. When thinking about modern or future military operations, the game metaphor comes to mind right away. Indeed, the air space together with the ground and seas may be viewed as a gigantic three-dimensional game board. Refining this picture, the LG approach is capable of providing an LG hypergame, that is, a system of multiple concurrent interconnected multi-player abstract board games (ABG) of various resolutions and time frames reflecting various kinds of hardware and effects involved in the battlespace and the solution space. By providing a hypergame representation of the battlespace, LG already provides a significant advance in situational awareness. However, the greatest advantage of the LG approach is an ability to provide commanders of campaigns and missions with decision options resulting in attainment of the commander's intent. At each game turn, an LG decision support tool assigns the best actions to each of the multitude of battlespace actors (UAVs, bombers, cruise missiles, etc.). This is done through utilization of algorithms finding winning strategies and tactics, which are the core of the LG approach.

  14. Differential geometry of groups in string theory

    SciTech Connect

    Schmidke, W.B. Jr.

    1990-09-01

    Techniques from differential geometry and group theory are applied to two topics from string theory. The first topic studied is quantum groups, with the example of GL (1{vert bar}1). The quantum group GL{sub q}(1{vert bar}1) is introduced, and an exponential description is derived. The algebra and coproduct are determined using the invariant differential calculus method introduced by Woronowicz and generalized by Wess and Zumino. An invariant calculus is also introduced on the quantum superplane, and a representation of the algebra of GL{sub q}(1{vert bar}1) in terms of the super-plane coordinates is constructed. The second topic follows the approach to string theory introduced by Bowick and Rajeev. Here the ghost contribution to the anomaly of the energy-momentum tensor is calculated as the Ricci curvature of the Kaehler quotient space Diff(S{sup 1})/S{sup 1}. We discuss general Kaehler quotient spaces and derive an expression for their Ricci curvatures. Application is made to the string and superstring diffeomorphism groups, considering all possible choices of subgroup. The formalism is extended to associated holomorphic vector bundles, where the Ricci curvature corresponds to the anomaly for different ghost sea levels. 26 refs.

  15. Optimized Geometry for Superconducting Sensing Coils

    NASA Technical Reports Server (NTRS)

    Eom, Byeong Ho; Pananen, Konstantin; Hahn, Inseob

    2008-01-01

    An optimized geometry has been proposed for superconducting sensing coils that are used in conjunction with superconducting quantum interference devices (SQUIDs) in magnetic resonance imaging (MRI), magnetoencephalography (MEG), and related applications in which magnetic fields of small dipoles are detected. In designing a coil of this type, as in designing other sensing coils, one seeks to maximize the sensitivity of the detector of which the coil is a part, subject to geometric constraints arising from the proximity of other required equipment. In MRI or MEG, the main benefit of maximizing the sensitivity would be to enable minimization of measurement time. In general, to maximize the sensitivity of a detector based on a sensing coil coupled with a SQUID sensor, it is necessary to maximize the magnetic flux enclosed by the sensing coil while minimizing the self-inductance of this coil. Simply making the coil larger may increase its self-inductance and does not necessarily increase sensitivity because it also effectively increases the distance from the sample that contains the source of the signal that one seeks to detect. Additional constraints on the size and shape of the coil and on the distance from the sample arise from the fact that the sample is at room temperature but the coil and the SQUID sensor must be enclosed within a cryogenic shield to maintain superconductivity.

  16. Role of target geometry in phagocytosis

    PubMed Central

    Champion, Julie A.; Mitragotri, Samir

    2006-01-01

    Phagocytosis is a principal component of the body’s innate immunity in which macrophages internalize targets in an actin-dependent manner. Targets vary widely in shape and size and include particles such as pathogens and senescent cells. Despite considerable progress in understanding this complicated process, the role of target geometry in phagocytosis has remained elusive. Previous studies on phagocytosis have been performed using spherical targets, thereby overlooking the role of particle shape. Using polystyrene particles of various sizes and shapes, we studied phagocytosis by alveolar macrophages. We report a surprising finding that particle shape, not size, plays a dominant role in phagocytosis. All shapes were capable of initiating phagocytosis in at least one orientation. However, the local particle shape, measured by tangent angles, at the point of initial contact dictates whether macrophages initiate phagocytosis or simply spread on particles. The local shape determines the complexity of the actin structure that must be created to initiate phagocytosis and allow the membrane to move over the particle. Failure to create the required actin structure results in simple spreading and not internalization. Particle size primarily impacts the completion of phagocytosis in cases where particle volume exceeds the cell volume. PMID:16549762

  17. Uncertainty relations as Hilbert space geometry

    NASA Technical Reports Server (NTRS)

    Braunstein, Samuel L.

    1994-01-01

    Precision measurements involve the accurate determination of parameters through repeated measurements of identically prepared experimental setups. For many parameters there is a 'natural' choice for the quantum observable which is expected to give optimal information; and from this observable one can construct an Heinsenberg uncertainty principle (HUP) bound on the precision attainable for the parameter. However, the classical statistics of multiple sampling directly gives us tools to construct bounds for the precision available for the parameters of interest (even when no obvious natural quantum observable exists, such as for phase, or time); it is found that these direct bounds are more restrictive than those of the HUP. The implication is that the natural quantum observables typically do not encode the optimal information (even for observables such as position, and momentum); we show how this can be understood simply in terms of the Hilbert space geometry. Another striking feature of these bounds to parameter uncertainty is that for a large enough number of repetitions of the measurements all V quantum states are 'minimum uncertainty' states - not just Gaussian wave-packets. Thus, these bounds tell us what precision is achievable as well as merely what is allowed.

  18. Accretion shock geometries in the magnetic variables

    NASA Technical Reports Server (NTRS)

    Stockman, H. S.

    1988-01-01

    The first self consistent shock models for the AM Herculis-type systems successfully identified the dominant physical processes and their signatures. These homogenous shock models predict unpolarized, Rayleigh-Jeans optical spectra with sharp cutoffs and rising polarizations as the shocks become optically thin in the ultraviolet. However, the observed energy distributions are generally flat with intermediate polarizations over a broad optical band. These and other observational evidence support a non-homogenous accretion profile which may extend over a considerable fraction of the stellar surface. Both the fundamental assumptions underlying the canonical 1-D shock model and the extension of this model to inhomogenous accretion shocks were identified, for both radial and linear structures. The observational evidence was also examined for tall shocks and little evidence was found for relative shock heights in excess of h/R(1) greater than or equal to 0.1. For several systems, upper limits to the shock height can be obtained from either x ray or optical data. These lie in the region h/R(1) is approximately 0.01 and are in general agreement with the current physical picture for these systems. The quasi-periodic optical variations observed in several magnetic variables may eventually prove to be a major aid in further understanding their accretion shock geometries.

  19. Statistics and geometry of cosmic voids

    SciTech Connect

    Gaite, José

    2009-11-01

    We introduce new statistical methods for the study of cosmic voids, focusing on the statistics of largest size voids. We distinguish three different types of distributions of voids, namely, Poisson-like, lognormal-like and Pareto-like distributions. The last two distributions are connected with two types of fractal geometry of the matter distribution. Scaling voids with Pareto distribution appear in fractal distributions with box-counting dimension smaller than three (its maximum value), whereas the lognormal void distribution corresponds to multifractals with box-counting dimension equal to three. Moreover, voids of the former type persist in the continuum limit, namely, as the number density of observable objects grows, giving rise to lacunar fractals, whereas voids of the latter type disappear in the continuum limit, giving rise to non-lacunar (multi)fractals. We propose both lacunar and non-lacunar multifractal models of the cosmic web structure of the Universe. A non-lacunar multifractal model is supported by current galaxy surveys as well as cosmological N-body simulations. This model suggests, in particular, that small dark matter halos and, arguably, faint galaxies are present in cosmic voids.

  20. Protonation and geometry of histidine rings.

    PubMed

    Malinska, Maura; Dauter, Miroslawa; Kowiel, Marcin; Jaskolski, Mariusz; Dauter, Zbigniew

    2015-07-01

    The presence of H atoms connected to either or both of the two N atoms of the imidazole moiety in a histidine residue affects the geometry of the five-membered ring. Analysis of the imidazole moieties found in histidine residues of atomic resolution protein crystal structures in the Protein Data Bank (PDB), and in small-molecule structures retrieved from the Cambridge Structural Database (CSD), identified characteristic patterns of bond lengths and angles related to the protonation state of the imidazole moiety. Using discriminant analysis, two functions could be defined, corresponding to linear combinations of the four most sensitive stereochemical parameters, two bond lengths (ND1-CE1 and CE1-NE2) and two endocyclic angles (-ND1- and -NE2-), that uniquely identify the protonation states of all imidazole moieties in the CSD and can be used to predict which N atom(s) of the histidine side chains in protein structures are protonated. Updated geometrical restraint target values are proposed for differently protonated histidine side chains for use in macromolecular refinement.

  1. Footprint geometry and sessile drop resonance

    NASA Astrophysics Data System (ADS)

    Chang, Chun-Ti; Daniel, Susan; Steen, Paul H.

    2017-03-01

    In this work, we examine experimentally the resonance of a sessile drop with a square footprint (square drop) on a flat plate. Two families of modal behaviors are reported. One family is identified with the modes of sessile drops with circular footprints (circular drop), denoted as "spherical modes." The other family is associated with Faraday waves on a square liquid bath (square Faraday waves), denoted as "grid modes." The two families are distinguished based on their dispersion behaviors. By comparing the occurrence of the modes, we recognize spherical modes as the characteristic of sessile drops, and grid modes as the constrained response. Within a broader context, we further discuss the resonance modes of circular sessile drops and free spherical drops, and we recognize various modal behaviors as surface waves under different extents of constraint. From these, we conclude that sessile drops resonate according to how wave-number selection by footprint geometry and capillarity compete. For square drops, a dominant effect of footprint constraint leads to grid modes; otherwise, the drops exhibit spherical modes, the characteristic of sessile drops on flat plates.

  2. High efficiency, variable geometry, centrifugal cryogenic pump

    SciTech Connect

    Forsha, M.D.; Nichols, K.E.; Beale, C.A.

    1994-12-31

    A centrifugal cryogenic pump has been developed which has a basic design that is rugged and reliable with variable speed and variable geometry features that achieve high pump efficiency over a wide range of head-flow conditions. The pump uses a sealless design and rolling element bearings to achieve high reliability and the ruggedness to withstand liquid-vapor slugging. The pump can meet a wide range of variable head, off-design flow requirements and maintain design point efficiency by adjusting the pump speed. The pump also has features that allow the impeller and diffuser blade heights to be adjusted. The adjustable height blades were intended to enhance the pump efficiency when it is operating at constant head, off-design flow rates. For small pumps, the adjustable height blades are not recommended. For larger pumps, they could provide off-design efficiency improvements. This pump was developed for supercritical helium service, but the design is well suited to any cryogenic application where high efficiency is required over a wide range of head-flow conditions.

  3. Effective geometry of a white dwarf

    SciTech Connect

    Bini, D.; Cherubini, C.; Filippi, S.

    2011-03-15

    The ''effective geometry'' formalism is used to study the perturbations of a white dwarf described as a self-gravitating fermion gas with a completely degenerate relativistic equation of state of barotropic type. The quantum nature of the system causes an absence of homological properties, manifested instead by polytropic stars, and requires a parametric study of the solutions both at the numerical and analytical level. We have explicitly derived a compact analytical parametric approximate solution of Pade type, which gives density curves and stellar radii in good accordance with already existing numerical results. After validation of this new type of approximate solutions, we use them to construct the effective acoustic metric governing general perturbations following Chebsch's formalism. Even in this quantum case, the stellar surface exhibits a curvature singularity due to the vanishing of density, as already evidenced in past studies on nonquantum self-gravitating polytropic stars. The equations of the theory are finally numerically integrated in the simpler case of irrotational spherical pulsating perturbations, including the effect of backreaction, in order to have a dynamical picture of the process occurring in the acoustic metric.

  4. Geometry of the infalling causal patch

    NASA Astrophysics Data System (ADS)

    Freivogel, Ben; Jefferson, Robert A.; Kabir, Laurens; Yang, I.-Sheng

    2015-02-01

    The firewall paradox states that an observer falling into an old black hole must see a violation of unitarity, locality, or the equivalence principle. Motivated by this remarkable conflict, we analyze the causal structure of black hole spacetimes in order to determine whether all the necessary ingredients for the paradox fit within a single observer's causal patch. We particularly focus on the question of whether the interior partner modes of the outgoing Hawking quanta can, in principle, be measured by an infalling observer. Since the relevant modes are spread over the entire sphere, we answer a simple geometrical question: can any observer see an entire sphere behind the horizon? We find that for all static black holes in 3 +1 and higher dimensions, with any value of the cosmological constant, no single observer can see both the early Hawking radiation and the interior modes with low angular momentum. We present a detailed description of the causal patch geometry of the Schwarzschild black hole in 3 +1 dimensions, where an infalling observer comes closest to being able to measure the relevant modes.

  5. The Planetary Data System Information Model for Geometry Metadata

    NASA Astrophysics Data System (ADS)

    Guinness, E. A.; Gordon, M. K.

    2014-12-01

    The NASA Planetary Data System (PDS) has recently developed a new set of archiving standards based on a rigorously defined information model. An important part of the new PDS information model is the model for geometry metadata, which includes, for example, attributes of the lighting and viewing angles of observations, position and velocity vectors of a spacecraft relative to Sun and observing body at the time of observation and the location and orientation of an observation on the target. The PDS geometry model is based on requirements gathered from the planetary research community, data producers, and software engineers who build search tools. A key requirement for the model is that it fully supports the breadth of PDS archives that include a wide range of data types from missions and instruments observing many types of solar system bodies such as planets, ring systems, and smaller bodies (moons, comets, and asteroids). Thus, important design aspects of the geometry model are that it standardizes the definition of the geometry attributes and provides consistency of geometry metadata across planetary science disciplines. The model specification also includes parameters so that the context of values can be unambiguously interpreted. For example, the reference frame used for specifying geographic locations on a planetary body is explicitly included with the other geometry metadata parameters. The structure and content of the new PDS geometry model is designed to enable both science analysis and efficient development of search tools. The geometry model is implemented in XML, as is the main PDS information model, and uses XML schema for validation. The initial version of the geometry model is focused on geometry for remote sensing observations conducted by flyby and orbiting spacecraft. Future releases of the PDS geometry model will be expanded to include metadata for landed and rover spacecraft.

  6. Single molecule junction conductance and binding geometry

    NASA Astrophysics Data System (ADS)

    Kamenetska, Maria

    This Thesis addresses the fundamental problem of controlling transport through a metal-organic interface by studying electronic and mechanical properties of single organic molecule-metal junctions. Using a Scanning Tunneling Microscope (STM) we image, probe energy-level alignment and perform STM-based break junction (BJ) measurements on molecules bound to a gold surface. Using Scanning Tunneling Microscope-based break-junction (STM-BJ) techniques, we explore the effect of binding geometry on single-molecule conductance by varying the structure of the molecules, metal-molecule binding chemistry and by applying sub-nanometer manipulation control to the junction. These experiments are performed both in ambient conditions and in ultra high vacuum (UHV) at cryogenic temperatures. First, using STM imaging and scanning tunneling spectroscopy (STS) measurements we explore binding configurations and electronic properties of an amine-terminated benzene derivative on gold. We find that details of metal-molecule binding affect energy-level alignment at the interface. Next, using the STM-BJ technique, we form and rupture metal-molecule-metal junctions ˜104 times to obtain conductance-vs-extension curves and extract most likely conductance values for each molecule. With these measurements, we demonstrated that the control of junction conductance is possible through a choice of metal-molecule binding chemistry and sub-nanometer positioning. First, we show that molecules terminated with amines, sulfides and phosphines bind selectively on gold and therefore demonstrate constant conductance levels even as the junction is elongated and the metal-molecule attachment point is modified. Such well-defined conductance is also obtained with paracyclophane molecules which bind to gold directly through the pi system. Next, we are able to create metal-molecule-metal junctions with more than one reproducible conductance signatures that can be accessed by changing junction geometry. In the

  7. Singularities and the geometry of spacetime

    NASA Astrophysics Data System (ADS)

    Hawking, Stephen

    2014-11-01

    The aim of this essay is to investigate certain aspects of the geometry of the spacetime manifold in the General Theory of Relativity with particular reference to the occurrence of singularities in cosmological solutions and their relation with other global properties. Section 2 gives a brief outline of Riemannian geometry. In Section 3, the General Theory of Relativity is presented in the form of two postulates and two requirements which are common to it and to the Special Theory of Relativity, and a third requirement, the Einstein field equations, which distinguish it from the Special Theory. There does not seem to be any alternative set of field equations which would not have some undeseriable features. Some exact solutions are described. In Section 4, the physical significance of curvature is investigated using the deviation equation for timelike and null curves. The Riemann tensor is decomposed into the Ricci tensor which represents the gravitational effect at a point of matter at that point and the Welyl tensor which represents the effect at a point of gravitational radiation and matter at other points. The two tensors are related by the Bianchi identities which are presented in a form analogous to the Maxwell equations. Some lemmas are given for the occurrence of conjugate points on timelike and null geodesics and their relation with the variation of timelike and null curves is established. Section 5 is concerned with properties of causal relations between points of spacetime. It is shown that these could be used to determine physically the manifold structure of spacetime if the strong causality assumption held. The concepts of a null horizon and a partial Cauchy surface are introduced and are used to prove a number of lemmas relating to the existence of a timelike curve of maximum length between two sets. In Section 6, the definition of a singularity of spacetime is given in terms of geodesic incompleteness. The various energy assumptions needed to prove

  8. A computer program for analyzing channel geometry

    USGS Publications Warehouse

    Regan, R.S.; Schaffranek, R.W.

    1985-01-01

    The Channel Geometry Analysis Program (CGAP) provides the capability to process, analyze, and format cross-sectional data for input to flow/transport simulation models or other computational programs. CGAP allows for a variety of cross-sectional data input formats through use of variable format specification. The program accepts data from various computer media and provides for modification of machine-stored parameter values. CGAP has been devised to provide a rapid and efficient means of computing and analyzing the physical properties of an open-channel reach defined by a sequence of cross sections. CGAP 's 16 options provide a wide range of methods by which to analyze and depict a channel reach and its individual cross-sectional properties. The primary function of the program is to compute the area, width, wetted perimeter, and hydraulic radius of cross sections at successive increments of water surface elevation (stage) from data that consist of coordinate pairs of cross-channel distances and land surface or channel bottom elevations. Longitudinal rates-of-change of cross-sectional properties are also computed, as are the mean properties of a channel reach. Output products include tabular lists of cross-sectional area, channel width, wetted perimeter, hydraulic radius, average depth, and cross-sectional symmetry computed as functions of stage; plots of cross sections; plots of cross-sectional area and (or) channel width as functions of stage; tabular lists of cross-sectional area and channel width computed as functions of stage for subdivisions of a cross section; plots of cross sections in isometric projection; and plots of cross-sectional area at a fixed stage as a function of longitudinal distance along an open-channel reach. A Command Procedure Language program and Job Control Language procedure exist to facilitate program execution on the U.S. Geological Survey Prime and Amdahl computer systems respectively. (Lantz-PTT)

  9. Microtubule guidance tested through controlled cell geometry

    PubMed Central

    Huda, Sabil; Soh, Siowling; Pilans, Didzis; Byrska-Bishop, Marta; Kim, Jiwon; Wilk, Gary; Borisy, Gary G.; Kandere-Grzybowska, Kristiana; Grzybowski, Bartosz A.

    2012-01-01

    Summary In moving cells dynamic microtubules (MTs) target and disassemble substrate adhesion sites (focal adhesions; FAs) in a process that enables the cell to detach from the substrate and propel itself forward. The short-range interactions between FAs and MT plus ends have been observed in several experimental systems, but the spatial overlap of these structures within the cell has precluded analysis of the putative long-range mechanisms by which MTs growing through the cell body reach FAs in the periphery of the cell. In the work described here cell geometry was controlled to remove the spatial overlap of cellular structures thus allowing for unambiguous observation of MT guidance. Specifically, micropatterning of living cells was combined with high-resolution in-cell imaging and gene product depletion by means of RNA interference to study the long-range MT guidance in quantitative detail. Cells were confined on adhesive triangular microislands that determined cell shape and ensured that FAs localized exclusively at the vertices of the triangular cells. It is shown that initial MT nucleation at the centrosome is random in direction, while the alignment of MT trajectories with the targets (i.e. FAs at vertices) increases with an increasing distance from the centrosome, indicating that MT growth is a non-random, guided process. The guided MT growth is dependent on the presence of FAs at the vertices. The depletion of either myosin IIA or myosin IIB results in depletion of F-actin bundles and spatially unguided MT growth. Taken together our findings provide quantitative evidence of a role for long-range MT guidance in MT targeting of FAs. PMID:22992457

  10. New Opportunities in Geometry Education at the Primary School

    ERIC Educational Resources Information Center

    Sinclair, Nathalie; Bruce, Catherine D.

    2015-01-01

    This paper outlines the new opportunities that that will be changing the landscape of geometry education at the primary school level. These include: the research on spatial reasoning and its connection to school mathematics in general and school geometry in particular; the function of drawing in the construction of geometric meaning; the role of…

  11. Connecting Research to Teaching: Evaluating and Writing Dynamic Geometry Tasks

    ERIC Educational Resources Information Center

    Trocki, Aaron

    2014-01-01

    The advent of dynamic geometry software has changed the way students draw, construct, and measure by using virtual tools instead of or along with physical tools. Use of technology in general and of dynamic geometry in particular has gained traction in mathematics education, as evidenced in the Common Core State Standards for Mathematics (CCSSI…

  12. Nonlinear partial differential equations: Integrability, geometry and related topics

    NASA Astrophysics Data System (ADS)

    Krasil'shchik, Joseph; Rubtsov, Volodya

    2017-03-01

    Geometry and Differential Equations became inextricably entwined during the last one hundred fifty years after S. Lie and F. Klein's fundamental insights. The two subjects go hand in hand and they mutually enrich each other, especially after the "Soliton Revolution" and the glorious streak of Symplectic and Poisson Geometry methods in the context of Integrability and Solvability problems for Non-linear Differential Equations.

  13. The Role of Structure in Learning Non-Euclidean Geometry

    ERIC Educational Resources Information Center

    Asmuth, Jennifer A.

    2009-01-01

    How do people learn novel mathematical information that contradicts prior knowledge? The focus of this thesis is the role of structure in the acquisition of knowledge about hyperbolic geometry, a non-Euclidean geometry. In a series of three experiments, I contrast a more holistic structure--training based on closed figures--with a mathematically…

  14. Disruption and Disclosure: Learning To Model Spherical Geometry.

    ERIC Educational Resources Information Center

    Stevenson, Ian

    2001-01-01

    Discusses some aspects of learning to read the process of the variation in congruence and relate it to the original geometry of the sphere since it touches on more general questions about how models are appropriated and used. Presents a learning episode that implemented projective models for both spherical and hyperbolic geometry in Object Logo.…

  15. Generating Conjectures in Dynamic Geometry: The Maintaining Dragging Model

    ERIC Educational Resources Information Center

    Baccaglini-Frank, Anna; Mariotti, Maria Alessandra

    2010-01-01

    Research has shown that the tools provided by dynamic geometry systems (DGSs) impact students' approach to investigating open problems in Euclidean geometry. We particularly focus on cognitive processes that might be induced by certain ways of dragging in Cabri. Building on the work of Arzarello, Olivero and other researchers, we have conceived a…

  16. Teachers Modify Geometry Problems: From Proof to Investigation

    ERIC Educational Resources Information Center

    Leikin, Roza; Grossman, Dorith

    2013-01-01

    We explored transformations that teachers made to modify geometry proof problems into investigation problems and analyzed how these transformations differ in teachers who use a dynamic geometry environment (DGE) in their classes and those who do not. We devised a framework for the analysis of problem transformations and types of teacher-generated…

  17. Using 3D Geometric Models to Teach Spatial Geometry Concepts.

    ERIC Educational Resources Information Center

    Bertoline, Gary R.

    1991-01-01

    An explanation of 3-D Computer Aided Design (CAD) usage to teach spatial geometry concepts using nontraditional techniques is presented. The software packages CADKEY and AutoCAD are described as well as their usefulness in solving space geometry problems. (KR)

  18. Randomized Control Trials on the Dynamic Geometry Approach

    ERIC Educational Resources Information Center

    Jiang, Zhonghong; White, Alexander; Rosenwasser, Alana

    2011-01-01

    The project reported here is conducting repeated randomized control trials of an approach to high school geometry that utilizes Dynamic Geometry (DG) software to supplement ordinary instructional practices. It compares effects of that intervention with standard instruction that does not make use of computer drawing/exploration tools. The basic…

  19. Pivotal Teaching Moments in Technology-Intensive Secondary Geometry Classrooms

    ERIC Educational Resources Information Center

    Cayton, Charity; Hollebrands, Karen; Okumus, Samet; Boehm, Ethan

    2017-01-01

    This study investigates three teachers' uses of a dynamic geometry program (The Geometer's Sketchpad) in their high school geometry classes over a 2-year period. The researchers examine teachers' actions and questions during pivotal teaching moments to characterize mathematics instruction that utilizes technology. Findings support an association…

  20. The role of geometry in 4-vertex origami mechanics

    NASA Astrophysics Data System (ADS)

    Waitukaitis, Scott; Dieleman, Peter; van Hecke, Martin

    Origami offers an interesting design platform metamaterials because it strongly couples mechanics with geometry. Even so, most research carried out so far has been limited to one or two particular patterns. I will discuss the full geometrical space of the most common origami building block, the 4-vertex, and show how exotic geometries can have dramatic effects on the mechanics.

  1. From geometry to algebra: the Euclidean way with technology

    NASA Astrophysics Data System (ADS)

    Ferrarello, Daniela; Flavia Mammana, Maria; Pennisi, Mario

    2016-05-01

    In this paper, we present the results of an experimental classroom activity, history-based with a phylogenetic approach, to achieve algebra properties through geometry. In particular, we used Euclidean propositions, processed them by a dynamic geometry system and translate them into algebraic special products.

  2. Overcoming the Obstacle of Poor Knowledge in Proving Geometry Tasks

    ERIC Educational Resources Information Center

    Magajna, Zlatan

    2013-01-01

    Proving in school geometry is not just about validating the truth of a claim. In the school setting, the main function of the proof is to convince someone that a claim is true by providing an explanation. Students consider proving to be difficult; in fact, they find the very concept of proof demanding. Proving a claim in planar geometry involves…

  3. Geometry and Thermodynamics: Exploring the Internal Energy Landscape

    ERIC Educational Resources Information Center

    Hantsaridou, A. P.; Polatoglou, H. M.

    2006-01-01

    If we look into the past we will discover that the teachers of thermodynamics were always trying to interpret an important part of their science by using geometry. The relation between geometry and thermodynamics is of great interest and importance in teaching thermodynamics. This article examines the way undergraduate students of thermodynamics…

  4. Effects of Spatial Ability and Instructional Program on Geometry Achievement

    ERIC Educational Resources Information Center

    Hannafin, Robert D.; Truxaw, Mary P.; Vermillion, Jennifer R.; Liu, Yingjie

    2008-01-01

    The authors investigated the effects of student spatial ability, as measured by Raven's Progressive Colored Matrices (J. C. Raven, 1938) and type of instructional program on geometry achievement. Sixth-grade students worked through either 6 instructional activities in Geometer's Sketchpad (Key Curriculum Press, 1993), a dynamic geometry program,…

  5. Theory of Alfven wave heating in general toroidal geometry

    SciTech Connect

    Tataronis, J.A.; Salat, A.

    1981-09-01

    A general treatment of Alfven wave heating based on the linearized equations of ideal magnetohydrodynamics (MHD) is given. The conclusion of this study is that the geometry of the plasma equilium could play an important role on the effectiveness of this heating mechanism, and for certain geometries the fundamental equations may not possess solutions which satisfy prescribed boundary conditions.

  6. Simultaneous cast shadows, illumination and geometry inference using hypergraphs.

    PubMed

    Panagopoulos, Alexandros; Wang, Chaohui; Samaras, Dimitris; Paragios, Nikos

    2013-02-01

    The cast shadows in an image provide important information about illumination and geometry. In this paper, we utilize this information in a novel framework in order to jointly recover the illumination environment, a set of geometry parameters, and an estimate of the cast shadows in the scene given a single image and coarse initial 3D geometry. We model the interaction of illumination and geometry in the scene and associate it with image evidence for cast shadows using a higher order Markov Random Field (MRF) illumination model, while we also introduce a method to obtain approximate image evidence for cast shadows. Capturing the interaction between light sources and geometry in the proposed graphical model necessitates higher order cliques and continuous-valued variables, which make inference challenging. Taking advantage of domain knowledge, we provide a two-stage minimization technique for the MRF energy of our model. We evaluate our method in different datasets, both synthetic and real. Our model is robust to rough knowledge of geometry and inaccurate initial shadow estimates, allowing a generic coarse 3D model to represent a whole class of objects for the task of illumination estimation, or the estimation of geometry parameters to refine our initial knowledge of scene geometry, simultaneously with illumination estimation.

  7. Using Dynamic Geometry to Explore Non-Traditional Theorems

    ERIC Educational Resources Information Center

    Wares, Arsalan

    2010-01-01

    The purpose of this article is to provide examples of "non-traditional" theorems that can be explored in a dynamic geometry environment by university and high school students. These theorems were encountered in the dynamic geometry environment. The author believes that teachers can ask their students to construct proofs for these theorems. The…

  8. Automated Preparation of Geometry for Computational Applications Final Report

    DTIC Science & Technology

    2011-01-31

    the GPW exports the CAD geometry to commonly used grid generation tools such as Chimera Grid Tools, Cart3D , and SolidMesh. Export in STL format is...exports the CAD geometry to commonly used grid generation tools such as Chimera Grid Tools and Cart3D and SolidMesh. Export in STL format is also

  9. Ontological Convictions and Epistemological Obstacles in Bolzano's Elementary Geometry

    NASA Astrophysics Data System (ADS)

    Waldegg, Guillermina

    Bernard Bolzano (1781-1848) was a contemporary of the founders of non-Euclidean geometry and of the renovation of projective geometry. However, he did not participate in the movement transforming concepts and methods which crystallized in a new order of geometry at the beginning of the nineteenth century. On the contrary, throughout his life Bolzano tried to demonstrate Euclid's postulate of parallel lines.Two ontological convictions played the role of epistemological obstacle for Bolzano and prevented him even from imagining the possibility that non-Euclidean geometries might exist. In the first place, Bolzano thought that Euclidean geometry had an intrinsic structure and thus geometrical space must be intrinsically Euclidean. Secondly, the description of this structure contained the existence of an objective connection between geometrical truths; a basic truth was, by its nature, simple and general.

  10. Lensless x-ray imaging in reflection geometry

    SciTech Connect

    Roy, S.; Parks, D.H.; Seu, K.A.; Turner, J.J.; Chao, W.; Anderson, E.H.; Cabrini, S.; Kevan, S.D.; Su, R.

    2011-02-03

    Lensless X-ray imaging techniques such as coherent diffraction imaging and ptychography, and Fourier transform holography can provide time-resolved, diffraction-limited images. Nearly all examples of these techniques have focused on transmission geometry, restricting the samples and reciprocal spaces that can be investigated. We report a lensless X-ray technique developed for imaging in Bragg and small-angle scattering geometries, which may also find application in transmission geometries. We demonstrate this by imaging a nanofabricated pseudorandom binary structure in small-angle reflection geometry. The technique can be used with extended objects, places no restriction on sample size, and requires no additional sample masking. The realization of X-ray lensless imaging in reflection geometry opens up the possibility of single-shot imaging of surfaces in thin films, buried interfaces in magnetic multilayers, organic photovoltaic and field-effect transistor devices, or Bragg planes in a single crystal.

  11. Geometry Teaching--Geometrieunterricht. Conference on the Teaching of Geometry (Helsinki, Finland, August 1-4, 1989). Research Report 74.

    ERIC Educational Resources Information Center

    Pehkonen, Erkki, Ed.

    This report contains conference papers on geometry teaching. There were five plenary talks given and a review of Hungarian geometry teaching. The plenary talks addressed background theories of the psychology of learning such as constructivism, perceptional psychology, and motivational psychology. The themes of the 21 short talks were on a varied…

  12. An Analysis of How and Why High School Geometry Teachers Implement Dynamic Geometry Software Tasks for Student Engagement

    ERIC Educational Resources Information Center

    Nirode, Wayne

    2012-01-01

    This study examined teachers' use of student tasks involving dynamic geometry software, in which a figure is constructed then altered while maintaining its constructed properties. Although researchers, professional organizations, and policy makers generally have been proponents of dynamic geometry for instruction, there is little research about…

  13. Teachers' Scaffolding of Students' Learning of Geometry While Using a Dynamic Geometry Program

    ERIC Educational Resources Information Center

    Dove, Anthony; Hollenbrands, Karen

    2014-01-01

    This study examined the scaffolds that three high school mathematics teachers provided to their geometry students as they used technology to explore geometric ideas. Teachers often used structured activities using a dynamic geometry program and provided significant emotive feedback while students worked through the tasks. This provided…

  14. Geometry controlled anomalous diffusion in random fractal geometries: looking beyond the infinite cluster.

    PubMed

    Mardoukhi, Yousof; Jeon, Jae-Hyung; Metzler, Ralf

    2015-11-28

    We investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and the cluster size distribution of the random geometry, thus being of purely geometrical origin. Moreover, we reveal that the convergence scaling law to ergodicity, which is known to be inversely proportional to the observation time T for ergodic diffusion processes, follows a power-law ∼T(-h) with h < 1 due to the fractal structure of the accessible space. These results provide useful measures for differentiating the subdiffusion on random fractals from an otherwise closely related process, namely, fractional Brownian motion. Implications of our results on the analysis of single particle tracking experiments are provided.

  15. The relationship between strain geometry and geometrically necessary dislocations

    NASA Astrophysics Data System (ADS)

    Hansen, Lars; Wallis, David

    2016-04-01

    The kinematics of past deformations are often a primary goal in structural analyses of strained rocks. Details of the strain geometry, in particular, can help distinguish hypotheses about large-scale tectonic phenomena. Microstructural indicators of strain geometry have been heavily utilized to investigate large-scale kinematics. However, many of the existing techniques require structures for which the initial morphology is known, and those structures must undergo the same deformation as imposed macroscopically. Many deformed rocks do not exhibit such convenient features, and therefore the strain geometry is often difficult (if not impossible) to ascertain. Alternatively, crystallographic textures contain information about the strain geometry, but the influence of strain geometry can be difficult to separate from other environmental factors that might affect slip system activity and therefore the textural evolution. Here we explore the ability for geometrically necessary dislocations to record information about the deformation geometry. It is well known that crystallographic slip due to the motion of dislocations yields macroscopic plastic strain, and the mathematics are established to relate dislocation glide on multiple slip systems to the strain tensor of a crystal. This theoretical description generally assumes that dislocations propagate across the entire crystal. However, at any point during the deformation, dislocations are present that have not fully transected the crystal, existing either as free dislocations or as dislocations organized into substructures like subgrain boundaries. These dislocations can remain in the lattice after deformation if the crystal is quenched sufficiently fast, and we hypothesize that this residual dislocation population can be linked to the plastic strain geometry in a quantitative manner. To test this hypothesis, we use high-resolution electron backscatter diffraction to measure lattice curvatures in experimentally deformed

  16. Measuring intranodal pressure and lymph viscosity to elucidate mechanisms of arthritic flare and therapeutic outcomes.

    PubMed

    Bouta, Echoe M; Wood, Ronald W; Perry, Seth W; Brown, Edward B; Ritchlin, Christopher T; Xing, Lianping; Schwarz, Edward M

    2011-12-01

    Rheumatoid arthritis (RA) is a chronic autoimmune disease with episodic flares in affected joints; the etiology of RA is largely unknown. Recent studies in mice demonstrated that alterations in lymphatics from affected joints precede flares. Thus, we aimed to develop novel methods for measuring lymph node pressure and lymph viscosity in limbs of mice. Pressure measurements were performed by inserting a glass micropipette connected to a pressure transducer into popliteal lymph nodes (PLN) or axillary lymph nodes (ALN) of mice; subsequently, we determined that the lymphatic pressures of water were 9 and 12 cm, respectively. We are also developing methods for measuring lymph viscosity in lymphatic vessels afferent to PLN, which can be measured by multiphoton fluorescence recovery after photobleaching (MP-FRAP) of fluorescein isothiocyanate-labeled bovine serum albumin (FITC-BSA) injected into the hind footpad. These results demonstrate the potential of lymph node pressure and lymph viscosity measurements, and future studies to test these outcomes as biomarkers of arthritic flare are warranted.

  17. Simplifying and speeding the management of intra-node cache coherence

    DOEpatents

    Blumrich, Matthias A [Ridgefield, CT; Chen, Dong [Croton on Hudson, NY; Coteus, Paul W [Yorktown Heights, NY; Gara, Alan G [Mount Kisco, NY; Giampapa, Mark E [Irvington, NY; Heidelberger, Phillip [Cortlandt Manor, NY; Hoenicke, Dirk [Ossining, NY; Ohmacht, Martin [Yorktown Heights, NY

    2012-04-17

    A method and apparatus for managing coherence between two processors of a two processor node of a multi-processor computer system. Generally the present invention relates to a software algorithm that simplifies and significantly speeds the management of cache coherence in a message passing parallel computer, and to hardware apparatus that assists this cache coherence algorithm. The software algorithm uses the opening and closing of put/get windows to coordinate the activated required to achieve cache coherence. The hardware apparatus may be an extension to the hardware address decode, that creates, in the physical memory address space of the node, an area of virtual memory that (a) does not actually exist, and (b) is therefore able to respond instantly to read and write requests from the processing elements.

  18. Lymph Nodes and Cancer Metastasis: New Perspectives on the Role of Intranodal Lymphatic Sinuses

    PubMed Central

    Ji, Rui-Cheng

    2016-01-01

    The lymphatic system is essential for transporting interstitial fluid, soluble antigen, and immune cells from peripheral tissues to lymph nodes (LNs). Functional integrity of LNs is dependent on intact lymphatics and effective lymph drainage. Molecular mechanisms that facilitate interactions between tumor cells and lymphatic endothelial cells (LECs) during tumor progression still remain to be identified. The cellular and molecular structures of LNs are optimized to trigger a rapid and efficient immune response, and to participate in the process of tumor metastasis by stimulating lymphangiogenesis and establishing a premetastatic niche in LNs. Several molecules, e.g., S1P, CCR7-CCL19/CCL21, CXCL12/CXCR4, IL-7, IFN-γ, TGF-β, and integrin α4β1 play an important role in controlling the activity of LN stromal cells including LECs, fibroblastic reticular cells (FRCs) and follicular dendritic cells (DCs). The functional stromal cells are critical for reconstruction and remodeling of the LN that creates a unique microenvironment of tumor cells and LECs for cancer metastasis. LN metastasis is a major determinant for the prognosis of most human cancers and clinical management. Ongoing work to elucidate the function and molecular regulation of LN lymphatic sinuses will provide insight into cancer development mechanisms and improve therapeutic approaches for human malignancy. PMID:28036019

  19. [Geometry of the hip joint: methodology and guidelines].

    PubMed

    Gaspar, Drago; Crnković, Tomislav

    2013-03-01

    An hip fracture is an significant personal, family and health issue of people older than 65 years. In the first year of the fracture up to 30% of the injured die and about 50% of them never regain their formal degree of independence in fulfilling day-to-day activities. Estimations are that throughout 30 years in the world there will be around 6 million hip fractures per year which is about four times the todays amount. Todays predictions of hip fractures based on the hip geometry have shown us that the hip geometry is an independent variable of the bone mineral density. The hip geometry is more resistant to the effect of various factors than the bone mineral density and the changes throu life are a lot slower. The uniqueness and the sensitivity of the hip geometry in predicting a fracture is high and acceptable in research results of most authors. In this review we present the previous relevant knowledge about the measures and factors which determines the hip geometry and the accepted amount of pictorial methods of hip display. We have compared the methodology and the patients of eleven randomly picked writings on predicting hip fracture based on the hip geometry. We highlight the need of further refinement of the methodology and the more balanced selection of patients for a greater conformity in future writings. The hip geometry has shown it self as an useful diagnostical instrument but there is still more room for its improvement.

  20. Classification of Near-Horizon Geometries of Extremal Black Holes.

    PubMed

    Kunduri, Hari K; Lucietti, James

    2013-01-01

    Any spacetime containing a degenerate Killing horizon, such as an extremal black hole, possesses a well-defined notion of a near-horizon geometry. We review such near-horizon geometry solutions in a variety of dimensions and theories in a unified manner. We discuss various general results including horizon topology and near-horizon symmetry enhancement. We also discuss the status of the classification of near-horizon geometries in theories ranging from vacuum gravity to Einstein-Maxwell theory and supergravity theories. Finally, we discuss applications to the classification of extremal black holes and various related topics. Several new results are presented and open problems are highlighted throughout.

  1. Accurate Excited State Geometries within Reduced Subspace TDDFT/TDA.

    PubMed

    Robinson, David

    2014-12-09

    A method for the calculation of TDDFT/TDA excited state geometries within a reduced subspace of Kohn-Sham orbitals has been implemented and tested. Accurate geometries are found for all of the fluorophore-like molecules tested, with at most all valence occupied orbitals and half of the virtual orbitals included but for some molecules even fewer orbitals. Efficiency gains of between 15 and 30% are found for essentially the same level of accuracy as a standard TDDFT/TDA excited state geometry optimization calculation.

  2. Nozzle and wing geometry effects on OTW aerodynamic characteristics

    NASA Technical Reports Server (NTRS)

    Vonglahn, U.; Groesbeck, D.

    1976-01-01

    The effects of nozzle geometry and wing size on the aerodynamic performance of several 5:1 aspect ratio slot nozzles are presented for over-the-wing (OTW) configurations. Nozzle geometry variables include roof angle, sidewall cutback, and nozzle chordwise location. Wing variables include chord size, and flap deflection. Several external deflectors also were included for comparison. The data indicate that good flow turning may not necessarily provide the best aerodynamic performance. The results suggest that a variable exhaust nozzle geometry offers the best solution for a viable OTW configuration.

  3. A spin foam model for general Lorentzian 4-geometries

    NASA Astrophysics Data System (ADS)

    Conrady, Florian; Hnybida, Jeff

    2010-09-01

    We derive simplicity constraints for the quantization of general Lorentzian 4-geometries. Our method is based on the correspondence between coherent states and classical bivectors and the minimization of associated uncertainties. For triangulations with spacelike triangles, this scheme agrees with the master constraint method of the model by Engle, Pereira, Rovelli and Livine (EPRL). When it is applied to general triangulations of Lorentzian geometries, we obtain new constraints that include the EPRL constraints as a special case. They imply a discrete area spectrum for both spacelike and timelike surfaces. We use these constraints to define a spin foam model for general Lorentzian 4-geometries.

  4. Unstructured Cartesian/prismatic grid generation for complex geometries

    NASA Technical Reports Server (NTRS)

    Karman, Steve L., Jr.

    1995-01-01

    The generation of a hybrid grid system for discretizing complex three dimensional (3D) geometries is described. The primary grid system is an unstructured Cartesian grid automatically generated using recursive cell subdivision. This grid system is sufficient for computing Euler solutions about extremely complex 3D geometries. A secondary grid system, using triangular-prismatic elements, may be added for resolving the boundary layer region of viscous flows near surfaces of solid bodies. This paper describes the grid generation processes used to generate each grid type. Several example grids are shown, demonstrating the ability of the method to discretize complex geometries, with very little pre-processing required by the user.

  5. Variable geometry inlet design for scram jet engine

    NASA Technical Reports Server (NTRS)

    Guinan, Daniel P. (Inventor); Drake, Alan (Inventor); Andreadis, Dean (Inventor); Beckel, Stephen A. (Inventor)

    2005-01-01

    The present invention relates to an improved variable geometry inlet for a scram jet engine having at least one combustor module. The variable geometry inlet comprises each combustor module having two sidewalls. Each of the sidewalls has a central portion with a thickness and a tapered profile forward of the central portion. The tapered profile terminates in a sharp leading edge. The variable geometry inlet further comprises each module having a lower wall and a movable cowl flap positioned forward of the lower wall. The movable cowl flap has a leading edge and the leading edges of the sidewalls intersect the leading edge of the cowl flap.

  6. Evolutionary algorithm for optimization of nonimaging Fresnel lens geometry.

    PubMed

    Yamada, N; Nishikawa, T

    2010-06-21

    In this study, an evolutionary algorithm (EA), which consists of genetic and immune algorithms, is introduced to design the optical geometry of a nonimaging Fresnel lens; this lens generates the uniform flux concentration required for a photovoltaic cell. Herein, a design procedure that incorporates a ray-tracing technique in the EA is described, and the validity of the design is demonstrated. The results show that the EA automatically generated a unique geometry of the Fresnel lens; the use of this geometry resulted in better uniform flux concentration with high optical efficiency.

  7. Graph-drawing algorithms geometries versus molecular mechanics in fullereness

    NASA Astrophysics Data System (ADS)

    Kaufman, M.; Pisanski, T.; Lukman, D.; Borštnik, B.; Graovac, A.

    1996-09-01

    The algorithms of Kamada-Kawai (KK) and Fruchterman-Reingold (FR) have been recently generalized (Pisanski et al., Croat. Chem. Acta 68 (1995) 283) in order to draw molecular graphs in three-dimensional space. The quality of KK and FR geometries is studied here by comparing them with the molecular mechanics (MM) and the adjacency matrix eigenvectors (AME) algorithm geometries. In order to compare different layouts of the same molecule, an appropriate method has been developed. Its application to a series of experimentally detected fullerenes indicates that the KK, FR and AME algorithms are able to reproduce plausible molecular geometries.

  8. Connections in sub-Riemannian geometry of parallelizable distributions

    NASA Astrophysics Data System (ADS)

    Youssef, Nabil L.; Taha, Ebtsam H.

    The notion of a parallelizable distribution has been introduced and investigated. A non-integrable parallelizable distribution carries a natural sub-Riemannian structure. The geometry of this structure has been studied from the bi-viewpoint of absolute parallelism geometry and sub-Riemannian geometry. Two remarkable linear connections have been constructed on a sub-Riemannian parallelizable distribution, namely, the Weitzenböck connection and the sub-Riemannian connection. The obtained results have been applied to two concrete examples: the spheres S3 and S7.

  9. Multigrid Methods for Aerodynamic Problems in Complex Geometries

    NASA Technical Reports Server (NTRS)

    Caughey, David A.

    1995-01-01

    Work has been directed at the development of efficient multigrid methods for the solution of aerodynamic problems involving complex geometries, including the development of computational methods for the solution of both inviscid and viscous transonic flow problems. The emphasis is on problems of complex, three-dimensional geometry. The methods developed are based upon finite-volume approximations to both the Euler and the Reynolds-Averaged Navier-Stokes equations. The methods are developed for use on multi-block grids using diagonalized implicit multigrid methods to achieve computational efficiency. The work is focused upon aerodynamic problems involving complex geometries, including advanced engine inlets.

  10. Determination of electron-nucleus collisions geometry with forward neutrons

    DOE PAGES

    Zheng, L.; Aschenauer, E.; Lee, J. H.

    2014-12-29

    There are a large number of physics programs one can explore in electron-nucleus collisions at a future electron-ion collider. Collision geometry is very important in these studies, while the measurement for an event-by-event geometric control is rarely discussed in the prior deep-inelastic scattering experiments off a nucleus. This paper seeks to provide some detailed studies on the potential of tagging collision geometries through forward neutron multiplicity measurements with a zero degree calorimeter. As a result, this type of geometry handle, if achieved, can be extremely beneficial in constraining nuclear effects for the electron-nucleus program at an electron-ion collider.

  11. Unit cell geometry of 3-D braided structures

    NASA Technical Reports Server (NTRS)

    Du, Guang-Wu; Ko, Frank K.

    1993-01-01

    The traditional approach used in modeling of composites reinforced by three-dimensional (3-D) braids is to assume a simple unit cell geometry of a 3-D braided structure with known fiber volume fraction and orientation. In this article, we first examine 3-D braiding methods in the light of braid structures, followed by the development of geometric models for 3-D braids using a unit cell approach. The unit cell geometry of 3-D braids is identified and the relationship of structural parameters such as yarn orientation angle and fiber volume fraction with the key processing parameters established. The limiting geometry has been computed by establishing the point at which yarns jam against each other. Using this factor makes it possible to identify the complete range of allowable geometric arrangements for 3-D braided preforms. This identified unit cell geometry can be translated to mechanical models which relate the geometrical properties of fabric preforms to the mechanical responses of composite systems.

  12. Aircraft geometry verification with enhanced computer-generated displays

    NASA Technical Reports Server (NTRS)

    Cozzolongo, J. V.

    1982-01-01

    A method for visual verification of aerodynamic geometries using computer-generated, color-shaded images is described. The mathematical models representing aircraft geometries are created for use in theoretical aerodynamic analyses and in computer-aided manufacturing. The aerodynamic shapes are defined using parametric bi-cubic splined patches. This mathematical representation is then used as input to an algorithm that generates a color-shaded image of the geometry. A discussion of the techniques used in the mathematical representation of the geometry and in the rendering of the color-shaded display is presented. The results include examples of color-shaded displays, which are contrasted with wire-frame-type displays. The examples also show the use of mapped surface pressures in terms of color-shaded images of V/STOL fighter/attack aircraft and advanced turboprop aircraft.

  13. Slab-geometry Nd:glass laser performance studies

    NASA Technical Reports Server (NTRS)

    Eggleston, J. M.; Kane, T. J.; Byer, R. L.; Unternahrer, J.

    1982-01-01

    It is noted that slab-geometry solid-state lasers potentially provide significant performance improvements relative to conventional rod-geometry lasers. Experimental measurements that use an Nd:glass test-bed slab laser are presented. A comparison is made between the results and computer-model predictions of the slab-geometry approach. The computer model calculates and displays the temperature and stress fields in the slab, and on the basis of these predicts birefringence and index-of-refraction distributions. The effect that these distributions have on optical propagation is determined in a polarization-sensitive ray-tracing section of the model. Calculations are also made of stress-induced surface curvature and the resulting focusing effects. The measurements are found to be in good agreement with the computer-model predictions. It is concluded that the slab configuration offers significant laser-performance advantages in comparison with the traditional rod-laser geometry.

  14. Elastic Geometry and Storyknifing: A Yup'ik Eskimo Example.

    ERIC Educational Resources Information Center

    Lipka, Jerry; Wildfeuer, Sandra; Wahlberg, Nastasia; George, Mary; Ezran, Dafna R.

    2001-01-01

    Introduces elastic geometry, or topology, into the elementary classroom through the study of connecting the intuitive, visual, and spatial components of storyknifing as well as other everyday and ethnomathematical activities. (ASK)

  15. Axiomatics of Geometry in School and in Science.

    ERIC Educational Resources Information Center

    Zeitler, Herbert

    1990-01-01

    Geometric axioms are discussed in terms of philosophy, history, refinements, and basic concepts. The triumphs and limitations of the formalism theory are included. Described is the status of high school geometry internationally. (KR)

  16. Measuring Space-Time Geometry over the Ages

    SciTech Connect

    Stebbins, Albert; /Fermilab

    2012-05-01

    Theorists are often told to express things in the 'observational plane'. One can do this for space-time geometry, considering 'visual' observations of matter in our universe by a single observer over time, with no assumptions about isometries, initial conditions, nor any particular relation between matter and geometry, such as Einstein's equations. Using observables as coordinates naturally leads to a parametrization of space-time geometry in terms of other observables, which in turn prescribes an observational program to measure the geometry. Under the assumption of vorticity-free matter flow we describe this observational program, which includes measurements of gravitational lensing, proper motion, and redshift drift. Only 15% of the curvature information can be extracted without long time baseline observations, and this increases to 35% with observations that will take decades. The rest would likely require centuries of observations. The formalism developed is exact, non-perturbative, and more general than the usual cosmological analysis.

  17. Aircraft geometry verification with enhanced computer generated displays

    NASA Technical Reports Server (NTRS)

    Cozzolongo, J. V.

    1982-01-01

    A method for visual verification of aerodynamic geometries using computer generated, color shaded images is described. The mathematical models representing aircraft geometries are created for use in theoretical aerodynamic analyses and in computer aided manufacturing. The aerodynamic shapes are defined using parametric bi-cubic splined patches. This mathematical representation is then used as input to an algorithm that generates a color shaded image of the geometry. A discussion of the techniques used in the mathematical representation of the geometry and in the rendering of the color shaded display is presented. The results include examples of color shaded displays, which are contrasted with wire frame type displays. The examples also show the use of mapped surface pressures in terms of color shaded images of V/STOL fighter/attack aircraft and advanced turboprop aircraft.

  18. Geometry Projects Linking Mathematics, Literacy, Art, and Technology.

    ERIC Educational Resources Information Center

    Little, Catherine

    1999-01-01

    Describes a geometry project for students using the Geometer's Sketchpad. Students choose from constructing an instruction manual, writing and illustrating a children's picture book, or creating a piece of art in the Escher style. (ASK)

  19. Triangle Geometry Processing for Surface Modeling and Cartesian Grid Generation

    NASA Technical Reports Server (NTRS)

    Aftosmis, Michael J. (Inventor); Melton, John E. (Inventor); Berger, Marsha J. (Inventor)

    2002-01-01

    Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.

  20. MUVES-S2 Adaptive Geometry User Guide

    DTIC Science & Technology

    2015-09-01

    ARL-TR-7438 ● SEP 2015 US Army Research Laboratory MUVES-S2 Adaptive Geometry User Guide by Matthew C Rothwell and James...return it to the originator. ARL-TR-7438 ● SEP 2015 US Army Research Laboratory MUVES-S2 Adaptive Geometry User Guide by...DATE (DD-MM-YYYY) September 2015 2. REPORT TYPE Final 3. DATES COVERED (From - To) 1–30 June 2014 4. TITLE AND SUBTITLE MUVES-S2 Adaptive

  1. Movement Timing and Invariance Arise from Several Geometries

    PubMed Central

    Bennequin, Daniel; Fuchs, Ronit; Berthoz, Alain; Flash, Tamar

    2009-01-01

    Human movements show several prominent features; movement duration is nearly independent of movement size (the isochrony principle), instantaneous speed depends on movement curvature (captured by the 2/3 power law), and complex movements are composed of simpler elements (movement compositionality). No existing theory can successfully account for all of these features, and the nature of the underlying motion primitives is still unknown. Also unknown is how the brain selects movement duration. Here we present a new theory of movement timing based on geometrical invariance. We propose that movement duration and compositionality arise from cooperation among Euclidian, equi-affine and full affine geometries. Each geometry posses a canonical measure of distance along curves, an invariant arc-length parameter. We suggest that for continuous movements, the actual movement duration reflects a particular tensorial mixture of these canonical parameters. Near geometrical singularities, specific combinations are selected to compensate for time expansion or compression in individual parameters. The theory was mathematically formulated using Cartan's moving frame method. Its predictions were tested on three data sets: drawings of elliptical curves, locomotion and drawing trajectories of complex figural forms (cloverleaves, lemniscates and limaçons, with varying ratios between the sizes of the large versus the small loops). Our theory accounted well for the kinematic and temporal features of these movements, in most cases better than the constrained Minimum Jerk model, even when taking into account the number of estimated free parameters. During both drawing and locomotion equi-affine geometry was the most dominant geometry, with affine geometry second most important during drawing; Euclidian geometry was second most important during locomotion. We further discuss the implications of this theory: the origin of the dominance of equi-affine geometry, the possibility that the brain

  2. Triangle geometry processing for surface modeling and cartesian grid generation

    DOEpatents

    Aftosmis, Michael J [San Mateo, CA; Melton, John E [Hollister, CA; Berger, Marsha J [New York, NY

    2002-09-03

    Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.

  3. The geometry of the 37-tile microwave antenna support structure

    NASA Technical Reports Server (NTRS)

    Finley, L. A.

    1980-01-01

    The geometry of the support structure for a proposed parabolic shaped microwave antenna is examined. The surface of the antenna is comprised of 37 hexagonal shaped tiles, each connected to a truss module. The units are joined together to form a rigidized, faceted, concave parabolic surface. The geometry specifications are described through an explanation of the structural components which make up the antenna, a description of the coordinate system devised to identify the structure, and a presentation of the nondimensional results.

  4. Optimization and experimental validation of electrostatic adhesive geometry

    NASA Astrophysics Data System (ADS)

    Ruffatto, D.; Shah, J.; Spenko, M.

    This paper introduces a method to optimize the electrode geometry of electrostatic adhesives for robotic gripping, attachment, and manipulation applications. Electrostatic adhesion is achieved by applying a high voltage potential, on the order of kV, to a set of electrodes, which generates an electric field. The electric field polarizes the substrate material and creates an adhesion force. Previous attempts at creating electro-static adhesives have shown them to be effective, but researchers have made no effort to optimize the electrode configuration and geometry. We have shown that by optimizing the geometry of the electrode configuration, the electric field strength, and therefore the adhesion force, is enhanced. To accomplish this, Comsol Multiphysics was utilized to evaluate the average electric field generated by a given electrode geometry. Several electrode patterns were evaluated, including parallel conductors, concentric circles, Hilbert curves (a fractal geometry) and spirals. The arrangement of the electrodes in concentric circles with varying electrode widths proved to be the most effective. The most effective sizing was to use the smallest gap spacing allowable coupled with a variable electrode width. These results were experimentally validated on several different surfaces including drywall, wood, tile, glass, and steel. A new manufacturing process allowing for the fabrication of thin, conformal electro-static adhesive pads was utilized. By combining the optimized electrode geometry with the new fabrication process we are able to demonstrate a marked improvement of up to 500% in shear pressure when compared to previously published values.

  5. PREFACE: Nonlinearity and Geometry: connections with integrability Nonlinearity and Geometry: connections with integrability

    NASA Astrophysics Data System (ADS)

    Cieslinski, Jan L.; Ferapontov, Eugene V.; Kitaev, Alexander V.; Nimmo, Jonathan J. C.

    2009-10-01

    Geometric ideas are present in many areas of modern theoretical physics and they are usually associated with the presence of nonlinear phenomena. Integrable nonlinear systems play a prime role both in geometry itself and in nonlinear physics. One can mention general relativity, exact solutions of the Einstein equations, string theory, Yang-Mills theory, instantons, solitons in nonlinear optics and hydrodynamics, vortex dynamics, solvable models of statistical physics, deformation quantization, and many others. Soliton theory now forms a beautiful part of mathematics with very strong physical motivations and numerous applications. Interactions between mathematics and physics associated with integrability issues are very fruitful and stimulating. For instance, spectral theories of linear quantum mechanics turned out to be crucial for studying nonlinear integrable systems. The modern theory of integrable nonlinear partial differential and difference equations, or the `theory of solitons', is deeply rooted in the achievements of outstanding geometers of the end of the 19th and the beginning of the 20th century, such as Luigi Bianchi (1856-1928) and Jean Gaston Darboux (1842-1917). Transformations of surfaces and explicit constructions developed by `old' geometers were often rediscovered or reinterpreted in a modern framework. The great progress of recent years in so-called discrete geometry is certainly due to strong integrable motivations. A very remarkable feature of the results of the classical integrable geometry is the quite natural (although nontrivial) possibility of their discretization. This special issue is dedicated to Jean Gaston Darboux and his pioneering role in the development of the geometric ideas of modern soliton theory. The most famous aspects of his work are probably Darboux transformations and triply orthogonal systems of surfaces, whose role in modern mathematical physics cannot be overestimated. Indeed, Darboux transformations play a central

  6. The Geometry of Almost Einstein (2, 3, 5) Distributions

    NASA Astrophysics Data System (ADS)

    Sagerschnig, Katja; Willse, Travis

    2017-01-01

    We analyze the classic problem of existence of Einstein metrics in a given conformal structure for the class of conformal structures inducedf Nurowski's construction by (oriented) (2, 3, 5) distributions. We characterize in two ways such conformal structures that admit an almost Einstein scale: First, they are precisely the oriented conformal structures c that are induced by at least two distinct oriented (2, 3, 5) distributions; in this case there is a 1-parameter family of such distributions that induce c. Second, they are characterized by the existence of a holonomy reduction to SU(1, 2), SL(3, R), or a particular semidirect product SL(2, R) ltimes Q_+, according to the sign of the Einstein constant of the corresponding metric. Via the curved orbit decomposition formalism such a reduction partitions the underlying manifold into several submanifolds and endows each ith a geometric structure. This establishes novel links between (2, 3, 5) distributions and many other geometries - several classical geometries among them - including: Sasaki-Einstein geometry and its paracomplex and null-complex analogues in dimension 5; Kähler-Einstein geometry and its paracomplex and null-complex analogues, Fefferman Lorentzian conformal structures, and para-Fefferman neutral conformal structures in dimension 4; CR geometry and the point geometry of second-order ordinary differential equations in dimension 3; and projective geometry in dimension 2. We describe a generalized Fefferman construction that builds from a 4-dimensional Kähler-Einstein or para-Kähler-Einstein structure a family of (2, 3, 5) distributions that induce the same (Einstein) conformal structure. We exploit some of these links to construct new examples, establishing the existence of nonflat almost Einstein (2, 3, 5) conformal structures for which the Einstein constant is positive and negative.

  7. Unit cell geometry of multiaxial preforms for structural composites

    NASA Technical Reports Server (NTRS)

    Ko, Frank; Lei, Charles; Rahman, Anisur; Du, G. W.; Cai, Yun-Jia

    1993-01-01

    The objective of this study is to investigate the yarn geometry of multiaxial preforms. The importance of multiaxial preforms for structural composites is well recognized by the industry but, to exploit their full potential, engineering design rules must be established. This study is a step in that direction. In this work the preform geometry for knitted and braided preforms was studied by making a range of well designed samples and studying them by photo microscopy. The structural geometry of the preforms is related to the processing parameters. Based on solid modeling and B-spline methodology a software package is developed. This computer code enables real time structural representations of complex fiber architecture based on the rule of preform manufacturing. The code has the capability of zooming and section plotting. These capabilities provide a powerful means to study the effect of processing variables on the preform geometry. the code also can be extended to an auto mesh generator for downstream structural analysis using finite element method. This report is organized into six sections. In the first section the scope and background of this work is elaborated. In section two the unit cell geometries of braided and multi-axial warp knitted preforms is discussed. The theoretical frame work of yarn path modeling and solid modeling is presented in section three. The thin section microscopy carried out to observe the structural geometry of the preforms is the subject in section four. The structural geometry is related to the processing parameters in section five. Section six documents the implementation of the modeling techniques into the computer code MP-CAD. A user manual for the software is also presented here. The source codes and published papers are listed in the Appendices.

  8. A Novel Framework for Learning Geometry-Aware Kernels.

    PubMed

    Pan, Binbin; Chen, Wen-Sheng; Xu, Chen; Chen, Bo

    2016-05-01

    The data from real world usually have nonlinear geometric structure, which are often assumed to lie on or close to a low-dimensional manifold in a high-dimensional space. How to detect this nonlinear geometric structure of the data is important for the learning algorithms. Recently, there has been a surge of interest in utilizing kernels to exploit the manifold structure of the data. Such kernels are called geometry-aware kernels and are widely used in the machine learning algorithms. The performance of these algorithms critically relies on the choice of the geometry-aware kernels. Intuitively, a good geometry-aware kernel should utilize additional information other than the geometric information. In many applications, it is required to compute the out-of-sample data directly. However, most of the geometry-aware kernel methods are restricted to the available data given beforehand, with no straightforward extension for out-of-sample data. In this paper, we propose a framework for more general geometry-aware kernel learning. The proposed framework integrates multiple sources of information and enables us to develop flexible and effective kernel matrices. Then, we theoretically show how the learned kernel matrices are extended to the corresponding kernel functions, in which the out-of-sample data can be computed directly. Under our framework, a novel family of geometry-aware kernels is developed. Especially, some existing geometry-aware kernels can be viewed as instances of our framework. The performance of the kernels is evaluated on dimensionality reduction, classification, and clustering tasks. The empirical results show that our kernels significantly improve the performance.

  9. Geometry optimization for micro-pressure sensor considering dynamic interference

    SciTech Connect

    Yu, Zhongliang; Zhao, Yulong Li, Lili; Tian, Bian; Li, Cun

    2014-09-15

    Presented is the geometry optimization for piezoresistive absolute micro-pressure sensor. A figure of merit called the performance factor (PF) is defined as a quantitative index to describe the comprehensive performances of a sensor including sensitivity, resonant frequency, and acceleration interference. Three geometries are proposed through introducing islands and sensitive beams into typical flat diaphragm. The stress distributions of sensitive elements are analyzed by finite element method. Multivariate fittings based on ANSYS simulation results are performed to establish the equations about surface stress, deflection, and resonant frequency. Optimization by MATLAB is carried out to determine the dimensions of the geometries. Convex corner undercutting is evaluated. Each PF of the three geometries with the determined dimensions is calculated and compared. Silicon bulk micromachining is utilized to fabricate the prototypes of the sensors. The outputs of the sensors under both static and dynamic conditions are tested. Experimental results demonstrate the rationality of the defined performance factor and reveal that the geometry with quad islands presents the highest PF of 210.947 Hz{sup 1/4}. The favorable overall performances enable the sensor more suitable for altimetry.

  10. Parametric Deformation of Discrete Geometry for Aerodynamic Shape Design

    NASA Technical Reports Server (NTRS)

    Anderson, George R.; Aftosmis, Michael J.; Nemec, Marian

    2012-01-01

    We present a versatile discrete geometry manipulation platform for aerospace vehicle shape optimization. The platform is based on the geometry kernel of an open-source modeling tool called Blender and offers access to four parametric deformation techniques: lattice, cage-based, skeletal, and direct manipulation. Custom deformation methods are implemented as plugins, and the kernel is controlled through a scripting interface. Surface sensitivities are provided to support gradient-based optimization. The platform architecture allows the use of geometry pipelines, where multiple modelers are used in sequence, enabling manipulation difficult or impossible to achieve with a constructive modeler or deformer alone. We implement an intuitive custom deformation method in which a set of surface points serve as the design variables and user-specified constraints are intrinsically satisfied. We test our geometry platform on several design examples using an aerodynamic design framework based on Cartesian grids. We examine inverse airfoil design and shape matching and perform lift-constrained drag minimization on an airfoil with thickness constraints. A transport wing-fuselage integration problem demonstrates the approach in 3D. In a final example, our platform is pipelined with a constructive modeler to parabolically sweep a wingtip while applying a 1-G loading deformation across the wingspan. This work is an important first step towards the larger goal of leveraging the investment of the graphics industry to improve the state-of-the-art in aerospace geometry tools.

  11. Tuning spin transport properties and molecular magnetoresistance through contact geometry

    SciTech Connect

    Ulman, Kanchan; Narasimhan, Shobhana; Delin, Anna

    2014-01-28

    Molecular spintronics seeks to unite the advantages of using organic molecules as nanoelectronic components, with the benefits of using spin as an additional degree of freedom. For technological applications, an important quantity is the molecular magnetoresistance. In this work, we show that this parameter is very sensitive to the contact geometry. To demonstrate this, we perform ab initio calculations, combining the non-equilibrium Green's function method with density functional theory, on a dithienylethene molecule placed between spin-polarized nickel leads of varying geometries. We find that, in general, the magnetoresistance is significantly higher when the contact is made to sharp tips than to flat surfaces. Interestingly, this holds true for both resonant and tunneling conduction regimes, i.e., when the molecule is in its “closed” and “open” conformations, respectively. We find that changing the lead geometry can increase the magnetoresistance by up to a factor of ∼5. We also introduce a simple model that, despite requiring minimal computational time, can recapture our ab initio results for the behavior of magnetoresistance as a function of bias voltage. This model requires as its input only the density of states on the anchoring atoms, at zero bias voltage. We also find that the non-resonant conductance in the open conformation of the molecule is significantly impacted by the lead geometry. As a result, the ratio of the current in the closed and open conformations can also be tuned by varying the geometry of the leads, and increased by ∼400%.

  12. Cooperative solutions coupling a geometry engine and adaptive solver codes

    NASA Technical Reports Server (NTRS)

    Dickens, Thomas P.

    1995-01-01

    Follow-on work has progressed in using Aero Grid and Paneling System (AGPS), a geometry and visualization system, as a dynamic real time geometry monitor, manipulator, and interrogator for other codes. In particular, AGPS has been successfully coupled with adaptive flow solvers which iterate, refining the grid in areas of interest, and continuing on to a solution. With the coupling to the geometry engine, the new grids represent the actual geometry much more accurately since they are derived directly from the geometry and do not use refits to the first-cut grids. Additional work has been done with design runs where the geometric shape is modified to achieve a desired result. Various constraints are used to point the solution in a reasonable direction which also more closely satisfies the desired results. Concepts and techniques are presented, as well as examples of sample case studies. Issues such as distributed operation of the cooperative codes versus running all codes locally and pre-calculation for performance are discussed. Future directions are considered which will build on these techniques in light of changing computer environments.

  13. Emergent fuzzy geometry and fuzzy physics in four dimensions

    NASA Astrophysics Data System (ADS)

    Ydri, Badis; Rouag, Ahlam; Ramda, Khaled

    2017-03-01

    A detailed Monte Carlo calculation of the phase diagram of bosonic mass-deformed IKKT Yang-Mills matrix models in three and six dimensions with quartic mass deformations is given. Background emergent fuzzy geometries in two and four dimensions are observed with a fluctuation given by a noncommutative U (1) gauge theory very weakly coupled to normal scalar fields. The geometry, which is determined dynamically, is given by the fuzzy spheres SN2 and SN2 × SN2 respectively. The three and six matrix models are effectively in the same universality class. For example, in two dimensions the geometry is completely stable, whereas in four dimensions the geometry is stable only in the limit M ⟶ ∞, where M is the mass of the normal fluctuations. The behaviors of the eigenvalue distribution in the two theories are also different. We also sketch how we can obtain a stable fuzzy four-sphere SN2 × SN2 in the large N limit for all values of M as well as models of topology change in which the transition between spheres of different dimensions is observed. The stable fuzzy spheres in two and four dimensions act precisely as regulators which is the original goal of fuzzy geometry and fuzzy physics. Fuzzy physics and fuzzy field theory on these spaces are briefly discussed.

  14. An adaptive Cartesian grid generation method for Dirty geometry

    NASA Astrophysics Data System (ADS)

    Wang, Z. J.; Srinivasan, Kumar

    2002-07-01

    Traditional structured and unstructured grid generation methods need a water-tight boundary surface grid to start. Therefore, these methods are named boundary to interior (B2I) approaches. Although these methods have achieved great success in fluid flow simulations, the grid generation process can still be very time consuming if non-water-tight geometries are given. Significant user time can be taken to repair or clean a dirty geometry with cracks, overlaps or invalid manifolds before grid generation can take place. In this paper, we advocate a different approach in grid generation, namely the interior to boundary (I2B) approach. With an I2B approach, the computational grid is first generated inside the computational domain. Then this grid is intelligently connected to the boundary, and the boundary grid is a result of this connection. A significant advantage of the I2B approach is that dirty geometries can be handled without cleaning or repairing, dramatically reducing grid generation time. An I2B adaptive Cartesian grid generation method is developed in this paper to handle dirty geometries without geometry repair. Comparing with a B2I approach, the grid generation time with the I2B approach for a complex automotive engine can be reduced by three orders of magnitude. Copyright

  15. Aerodynamic Optimization of Rocket Control Surface Geometry Using Cartesian Methods and CAD Geometry

    NASA Technical Reports Server (NTRS)

    Nelson, Andrea; Aftosmis, Michael J.; Nemec, Marian; Pulliam, Thomas H.

    2004-01-01

    Aerodynamic design is an iterative process involving geometry manipulation and complex computational analysis subject to physical constraints and aerodynamic objectives. A design cycle consists of first establishing the performance of a baseline design, which is usually created with low-fidelity engineering tools, and then progressively optimizing the design to maximize its performance. Optimization techniques have evolved from relying exclusively on designer intuition and insight in traditional trial and error methods, to sophisticated local and global search methods. Recent attempts at automating the search through a large design space with formal optimization methods include both database driven and direct evaluation schemes. Databases are being used in conjunction with surrogate and neural network models as a basis on which to run optimization algorithms. Optimization algorithms are also being driven by the direct evaluation of objectives and constraints using high-fidelity simulations. Surrogate methods use data points obtained from simulations, and possibly gradients evaluated at the data points, to create mathematical approximations of a database. Neural network models work in a similar fashion, using a number of high-fidelity database calculations as training iterations to create a database model. Optimal designs are obtained by coupling an optimization algorithm to the database model. Evaluation of the current best design then gives either a new local optima and/or increases the fidelity of the approximation model for the next iteration. Surrogate methods have also been developed that iterate on the selection of data points to decrease the uncertainty of the approximation model prior to searching for an optimal design. The database approximation models for each of these cases, however, become computationally expensive with increase in dimensionality. Thus the method of using optimization algorithms to search a database model becomes problematic as the

  16. Geometry of Superluminal Light-Echo Pair Events

    NASA Astrophysics Data System (ADS)

    Nemiroff, Robert J.

    2017-01-01

    Light echoes, shadows, and ionization fronts can and do move faster than light, both in the lab and out in the cosmos. In general, though, a single observer cannot tell the speed of such echoes without distance information -- unless a very specific geometry arises: the radial component crosses c. The observer then sees this crossing location as the site where a pair of bright light echoes is created or annihilated. This pair event tells the observer that a precise speed occurs, a speed that does not scale with distance and so can potentially be leveraged to reveal geometry and distance information. A few simple scattering surface geometries are shown illuminated by a point flash, including linear and circular filaments. In practice, useful astronomical flash sources include novae and supernovae, although in theory any uniquely varying source of stellar variability could be sufficient.

  17. Efficient road geometry identification from digital vector data

    NASA Astrophysics Data System (ADS)

    Andrášik, Richard; Bíl, Michal

    2016-07-01

    A new method for the automatic identification of road geometry from digital vector data is presented. The method is capable of efficiently identifying circular curves with their radii and tangents (straight sections). The average error of identification ranged from 0.01 to 1.30 % for precisely drawn data and 4.81 % in the case of actual road data with noise in the location of vertices. The results demonstrate that the proposed method is faster and more precise than commonly used techniques. This approach can be used by road administrators to complete their databases with information concerning the geometry of roads. It can also be utilized by transport engineers or traffic safety analysts to investigate the possible dependence of traffic accidents on road geometries. The method presented is applicable as well to railroads and rivers or other line features.

  18. Measurement of proton momentum distributions using a direct geometry instrument

    NASA Astrophysics Data System (ADS)

    Senesi, R.; Kolesnikov, A. I.; Andreani, C.

    2014-12-01

    We report the results of inelastic neutron scattering measurements on bulk water and ice using the direct geometry SEQUOIA chopper spectrometer at the Spallation Neutron Source (USA), with incident energy Ei= 6 eV. In this set up the measurements allow to access the Deep Inelastic Neutron Scattering regime. The scattering is centred at the proton recoil energy given by the impulse approximation, and the shape of the recoil peak conveys information on the proton momentum distribution in the system. The comparison with the performance of inverse geometry instruments, such as VESUVIO at the ISIS source (UK), shows that complementary information can be accessed by the use of direct and inverse geometry instruments. Analysis of the neutron Compton profiles shows that the proton kinetic energy in ice at 271 K is larger than in room temperature liquid water, in agreement with previous measurements on VESUVIO.

  19. Geometry of quantum Hall states: Gravitational anomaly and transport coefficients

    SciTech Connect

    Can, Tankut; Laskin, Michael; Wiegmann, Paul B.

    2015-11-15

    We show that universal transport coefficients of the fractional quantum Hall effect (FQHE) can be understood as a response to variations of spatial geometry. Some transport properties are essentially governed by the gravitational anomaly. We develop a general method to compute correlation functions of FQH states in a curved space, where local transformation properties of these states are examined through local geometric variations. We introduce the notion of a generating functional and relate it to geometric invariant functionals recently studied in geometry. We develop two complementary methods to study the geometry of the FQHE. One method is based on iterating a Ward identity, while the other is based on a field theoretical formulation of the FQHE through a path integral formalism.

  20. Global geometry of two-dimensional charged black holes

    SciTech Connect

    Frolov, Andrei V.; Kristjansson, Kristjan R.; Thorlacius, Larus

    2006-06-15

    The semiclassical geometry of charged black holes is studied in the context of a two-dimensional dilaton gravity model where effects due to pair-creation of charged particles can be included in a systematic way. The classical mass-inflation instability of the Cauchy horizon is amplified and we find that gravitational collapse of charged matter results in a spacelike singularity that precludes any extension of the spacetime geometry. At the classical level, a static solution describing an eternal black hole has timelike singularities and multiple asymptotic regions. The corresponding semiclassical solution, on the other hand, has a spacelike singularity and a Penrose diagram like that of an electrically neutral black hole. Extremal black holes are destabilized by pair-creation of charged particles. There is a maximally charged solution for a given black hole mass but the corresponding geometry is not extremal. Our numerical data exhibits critical behavior at the threshold for black hole formation.

  1. Generalization of the electronic susceptibility for arbitrary molecular geometries.

    PubMed

    Scherrer, Arne; Dreßler, Christian; Ahlert, Paul; Sebastiani, Daniel

    2016-04-14

    We generalize the explicit representation of the electronic susceptibility χ[R](r, r') for arbitrary molecular geometries R. The electronic susceptibility is a response function that yields the response of the molecular electronic charge density at linear order to an arbitrary external perturbation. We address the dependence of this response function on the molecular geometry. The explicit representation of the molecular geometry dependence is achieved by means of a Taylor expansion in the nuclear coordinates. Our approach relies on a recently developed low-rank representation of the response function χ[R](r, r') which allows a highly condensed storage of the expansion and an efficient application within dynamical chemical environments. We illustrate the performance and accuracy of our scheme by computing the vibrationally induced variations of the response function of a water molecule and its resulting Raman spectrum.

  2. Tissue characterization using terahertz pulsed imaging in reflection geometry

    NASA Astrophysics Data System (ADS)

    Huang, S. Y.; Wang, Y. X. J.; Yeung, D. K. W.; Ahuja, A. T.; Zhang, Y.-T.; Pickwell-MacPherson, E.

    2009-01-01

    Terahertz pulsed imaging (TPI™) is a non-ionizing and non-destructive imaging technique that has been recently used to study a wide range of biological materials. The severe attenuation of terahertz radiation in samples with high water content means that biological samples need to be very thin if they are to be measured in transmission geometry. To overcome this limitation, samples could be measured in reflection geometry and this is the most feasible way in which TPI could be performed in a clinical setting. In this study, we therefore used TPI in reflection geometry to characterize the terahertz properties of several organ samples freshly harvested from laboratory rats. We observed differences in the measured time domain responses and determined the frequency-dependent optical properties to characterize the samples further. We found statistically significant differences between the tissue types. These results show that TPI has the potential to accurately differentiate between tissue types non-invasively.

  3. Extreme localized exhumation at syntaxes initiated by subduction geometry

    NASA Astrophysics Data System (ADS)

    Bendick, Rebecca; Ehlers, Todd A.

    2014-08-01

    Some of the highest and most localized rates of lithospheric deformation in the world are observed at the transition between adjacent plate boundary subduction segments. The initiating perturbation of this deformation has long been attributed to vigorous erosional processes as observed at Nanga Parbat and Namche Barwa in the Himalaya and at Mount St. Elias in Alaska. However, an erosion-dominated mechanism ignores the 3-D geometry of curved subducting plates. Here we present an alternative explanation for rapid exhumation at these locations based on the 3-D thermomechanical evolution of collisions between plates with nonplanar geometries. Comparison of model predictions with existing data reproduces the defining characteristics of these mountains and offers an explanation for their spatial correlation with arc termini. These results demonstrate a "bottom-up" tectonic rather than "top-down" erosional initiation of feedbacks between erosion and tectonic deformation; hence, the importance of 3-D subduction geometry.

  4. A novel small-angle neutron scattering detector geometry

    PubMed Central

    Kanaki, Kalliopi; Jackson, Andrew; Hall-Wilton, Richard; Piscitelli, Francesco; Kirstein, Oliver; Andersen, Ken H.

    2013-01-01

    A novel 2π detector geometry for small-angle neutron scattering (SANS) applications is presented and its theoretical performance evaluated. Such a novel geometry is ideally suited for a SANS instrument at the European Spallation Source (ESS). Motivated by the low availability and high price of 3He, the new concept utilizes gaseous detectors with 10B as the neutron converter. The shape of the detector is inspired by an optimization process based on the properties of the conversion material. Advantages over the detector geometry traditionally used on SANS instruments are discussed. The angular and time resolutions of the proposed detector concept are shown to satisfy the requirements of the particular SANS instrument. PMID:24046504

  5. Finite-size effects and percolation properties of Poisson geometries

    NASA Astrophysics Data System (ADS)

    Larmier, C.; Dumonteil, E.; Malvagi, F.; Mazzolo, A.; Zoia, A.

    2016-07-01

    Random tessellations of the space represent a class of prototype models of heterogeneous media, which are central in several applications in physics, engineering, and life sciences. In this work, we investigate the statistical properties of d -dimensional isotropic Poisson geometries by resorting to Monte Carlo simulation, with special emphasis on the case d =3 . We first analyze the behavior of the key features of these stochastic geometries as a function of the dimension d and the linear size L of the domain. Then, we consider the case of Poisson binary mixtures, where the polyhedra are assigned two labels with complementary probabilities. For this latter class of random geometries, we numerically characterize the percolation threshold, the strength of the percolating cluster, and the average cluster size.

  6. Kinetics of binding and geometry of cells on molecular biochips

    NASA Astrophysics Data System (ADS)

    Chechetkin, V. R.

    2007-07-01

    We examine how the shape of cells and the geometry of experiment affect the reaction diffusion kinetics at the binding between target and probe molecules on molecular biochips. In particular, we compare the binding kinetics for the probes immobilized on surface of the hemispherical and flat circular cells, the limit of thin slab of analyte solution over probe cell as well as hemispherical gel pads and cells printed in gel slab over a substrate. It is shown that hemispherical geometry provides significantly faster binding kinetics and ensures more spatially homogeneous distribution of local (from a pixel) signals over a cell in the transient regime. The advantage of using thin slabs with small volume of analyte solution may be hampered by the much longer binding kinetics needing the auxiliary mixing devices. Our analysis proves that the shape of cells and the geometry of experiment should be included to the list of essential factors at biochip designing.

  7. Attenuation correction factors for cylindrical, disc and box geometry

    NASA Astrophysics Data System (ADS)

    Agarwal, Chhavi; Poi, Sanhita; Mhatre, Amol; Goswami, A.; Gathibandhe, M.

    2009-08-01

    In the present study, attenuation correction factors have been experimentally determined for samples having cylindrical, disc and box geometry and compared with the attenuation correction factors calculated by Hybrid Monte Carlo (HMC) method [ C. Agarwal, S. Poi, A. Goswami, M. Gathibandhe, R.A. Agrawal, Nucl. Instr. and. Meth. A 597 (2008) 198] and with the near-field and far-field formulations available in literature. It has been observed that the near-field formulae, although said to be applicable at close sample-detector geometry, does not work at very close sample-detector configuration. The advantage of the HMC method is that it is found to be valid for all sample-detector geometries.

  8. Cell dipole behaviour revealed by ECM sub-cellular geometry

    NASA Astrophysics Data System (ADS)

    Mandal, Kalpana; Wang, Irène; Vitiello, Elisa; Orellana, Laura Andreina Chacòn; Balland, Martial

    2014-12-01

    Cells sense and respond to their mechanical environment by exerting forces on their surroundings. The way forces are modulated by extra-cellular matrix (ECM) properties plays a key role in tissue homoeostasis. Using highly resolved micropatterns that constrain cells into the same square envelope but vary the adhesive geometry, here we investigate how the adhesive micro-environment affects the architecture of actin cytoskeleton and the orientation of traction forces. Our data demonstrate that local adhesive changes can trigger orientational ordering of stress fibres throughout the cell, suggesting that cells are capable of integrating information on ECM geometry at the whole-cell level. Finally, we show that cells tend to generate highly polarized force pattern, that is, unidirectional pinching, in response to adequate adhesive conditions. Hence, the geometry of adhesive environment can induce cellular orientation, a process which may have significant implications for the formation and mechanical properties of tissues.

  9. Perception of global facial geometry is modulated through experience

    PubMed Central

    2015-01-01

    Identification of personally familiar faces is highly efficient across various viewing conditions. While the presence of robust facial representations stored in memory is considered to aid this process, the mechanisms underlying invariant identification remain unclear. Two experiments tested the hypothesis that facial representations stored in memory are associated with differential perceptual processing of the overall facial geometry. Subjects who were personally familiar or unfamiliar with the identities presented discriminated between stimuli whose overall facial geometry had been manipulated to maintain or alter the original facial configuration (see Barton, Zhao & Keenan, 2003). The results demonstrate that familiarity gives rise to more efficient processing of global facial geometry, and are interpreted in terms of increased holistic processing of facial information that is maintained across viewing distances. PMID:25825678

  10. Martian Surface Properties: Inferences from Resolved Differences in Crater Geometries

    NASA Technical Reports Server (NTRS)

    Valiant, G. J.; Stewart, S. T.

    2004-01-01

    Impact craters are a natural probe of planetary sub-surfaces, both from the excavated material and from crater geometries, which are sensitive to material properties of the target. One of the most intriguing aspects of Martian craters is the morphology of the ejecta blankets. All fresh and many older Martian craters larger than a few km are surrounded by ejecta blankets which appear fluidized, with morphologies believed to form by entrainment of liquid water. In addition to the ejecta morphology, quantitative information about the subsurface composition may be derived from geometrical measurements, e.g., rim uplift height and ejecta blanket volumes. In order to use craters to derive subsurface composition or test rampart morphology formation hypotheses, accurate measurements with quantified error estimates are required. We have developed and tested a toolkit for measurements of crater geometry using the MOLA altimetry data. Here, we present the results from geometry measurements on fresh craters in Lunae Planum and Utopia Planitia.

  11. Symplectic geometry spectrum regression for prediction of noisy time series

    NASA Astrophysics Data System (ADS)

    Xie, Hong-Bo; Dokos, Socrates; Sivakumar, Bellie; Mengersen, Kerrie

    2016-05-01

    We present the symplectic geometry spectrum regression (SGSR) technique as well as a regularized method based on SGSR for prediction of nonlinear time series. The main tool of analysis is the symplectic geometry spectrum analysis, which decomposes a time series into the sum of a small number of independent and interpretable components. The key to successful regularization is to damp higher order symplectic geometry spectrum components. The effectiveness of SGSR and its superiority over local approximation using ordinary least squares are demonstrated through prediction of two noisy synthetic chaotic time series (Lorenz and Rössler series), and then tested for prediction of three real-world data sets (Mississippi River flow data and electromyographic and mechanomyographic signal recorded from human body).

  12. Spark Ignition: Effects of Fluid Dynamics and Electrode Geometry

    NASA Astrophysics Data System (ADS)

    Bane, Sally; Ziegler, Jack; Shepherd, Joseph

    2010-11-01

    The concept of minimum ignition energy (MIE) has traditionally formed the basis for studying ignition hazards of fuels, and standard test methods for determining the MIE use a capacitive spark discharge as the ignition source. Developing the numerical tools necessary to quantitatively predict ignition is a challenging research problem and remains primarily an experimental issue. In this work a two-dimensional model of spark discharge in air and spark ignition was developed using the non-reactive and reactive Navier-Stokes equations. The simulations were performed with three different electrode geometries to investigate the effect of the geometry on the fluid mechanics of the evolving spark kernel and on flame formation. The computational results were compared with high-speed schlieren visualization of spark and ignition kernels. It was found that the electrode geometry had a significant effect on the fluid motion following spark discharge and hence influences the ignition process and the required spark energy.

  13. Track geometry estimation from car-body vibration

    NASA Astrophysics Data System (ADS)

    Tsunashima, Hitoshi; Naganuma, Yasukuni; Kobayashi, Takahito

    2014-05-01

    Track maintenance works based on track geometry recordings are essential to enhance the safety and comfort of railway transportation. The track condition monitoring system is mainly used for the choice of area needing track tamping works for the purpose of the good riding comfort. An advantage of car-body acceleration measurement devices is their simple structures, which make it easier to carry out maintenance. However, the car-body acceleration waveform is considerably different from track geometry. This paper demonstrates the possibility to estimate the track geometry of Shinkansen tracks using car-body motions only. In an inverse problem to estimate track irregularity from car-body motions, a Kalman Filter (KF) was applied to solve the problem. Estimation results showed that track irregularity estimation in vertical direction is possible with acceptable accuracy for real use.

  14. Integrating particle physical geometry into composting degradation kinetics.

    PubMed

    Wang, Yongjiang; Ai, Ping

    2016-01-01

    The study was carried out to integrate physical geometry of compost particle with degradation kinetics to model biological reactions, which revealing additional dynamic approaches. A sphere and its circumscribing cube were used to represent compost particles. An inner sphere, representing anaerobic zone, was introduced to describe variations of substrate volume without sufficient oxygen supply. Degradation of soluble substrates and hydrolysis of insoluble substrates were associated with the particle geometry. Transportation of soluble substrates produced from hydrolysis was expressed using Fick's law. Through the integration of degradation kinetics with geometry models, degradation models could describe varying volume of composting materials involving aerobic or anaerobic digestion and transportation of soluble substrates in a unit compost particle.

  15. Volume Diffusion Growth Kinetics and Step Geometry in Crystal Growth

    NASA Technical Reports Server (NTRS)

    Mazuruk, Konstantin; Ramachandran, Narayanan

    1998-01-01

    The role of step geometry in two-dimensional stationary volume diff4sion process used in crystal growth kinetics models is investigated. Three different interface shapes: a) a planar interface, b) an equidistant hemispherical bumps train tAx interface, and c) a train of right angled steps, are used in this comparative study. The ratio of the super-saturation to the diffusive flux at the step position is used as a control parameter. The value of this parameter can vary as much as 50% for different geometries. An approximate analytical formula is derived for the right angled steps geometry. In addition to the kinetic models, this formula can be utilized in macrostep growth models. Finally, numerical modeling of the diffusive and convective transport for equidistant steps is conducted. In particular, the role of fluid flow resulting from the advancement of steps and its contribution to the transport of species to the steps is investigated.

  16. Dielectric flashover with triple point shielding in a coaxial geometry.

    PubMed

    Benwell, A; Kovaleski, S D; Gahl, J

    2007-11-01

    Increasing performance of vacuum insulator barriers is a common goal in pulsed power. Insulating performance is continually being improved while new methods are developed. Triple point shielding techniques have been shown to increase flashover voltage, but the role of cathode versus anode shielding is still not fully understood. Open circuit flashover characteristics were obtained for a coaxial geometry to view the effects of triple point shielding for this geometry. The tests included applying various combinations of triple point shields on zero and +45 degrees insulators. Shielding was tested at the cathode triple point outside of the dielectric and at the anode triple point inside the dielectric. The role of anode versus cathode triple point shielding was examined. Flashover voltage was observed to increase when either a cathode or anode triple point shield was applied; however, adding a shield to both regions lowered the flashover threshold. Both triple point regions were found to be important and dependent on each other for some coaxial geometries.

  17. Tunneling into microstate geometries: quantum effects stop gravitational collapse

    NASA Astrophysics Data System (ADS)

    Bena, Iosif; Mayerson, Daniel R.; Puhm, Andrea; Vercnocke, Bert

    2016-07-01

    Collapsing shells form horizons, and when the curvature is small classical general relativity is believed to describe this process arbitrarily well. On the other hand, quantum information theory based (fuzzball/firewall) arguments suggest the existence of some structure at the black hole horizon. This structure can only form if classical general relativity stops being the correct description of the collapsing shell before it reaches the horizon size. We present strong evidence that classical general relativity can indeed break down prematurely, by explicitly computing the quantum tunneling amplitude of a collapsing shell of branes into smooth horizonless microstate geometries. We show that the amplitude for tunneling into microstate geometries with a large number of topologically non-trivial cycles is parametrically larger than e - S BH , which indicates that the shell can tunnel into a horizonless configuration long before the horizon has any chance to form. We also use this technology to investigate the tunneling of M2 branes into LLM bubbling geometries.

  18. Guidelines for Surveying Bankfull Channel Geometry and Developing Regional Hydraulic-Geometry Relations for Streams of New York State

    USGS Publications Warehouse

    Powell, Rocky O.; Miller, Sarah J.; Westergard, Britt E.; Mulvihill, Christiane I.; Baldigo, Barry P.; Gallagher, Anne S.; Starr, Richard R.

    2004-01-01

    Many disturbed streams within New York State are being restored in an effort to provide bank and bed stability and thereby decrease sedimentation and erosion. Efforts to identify and provide accurate indicators for stable-channel characteristics for ungaged streams have been hampered by the lack of regional equations or relations that relate drainage area to bankfull discharge and to channel depth, width, and cross-sectional area (bankfull hydraulic-geometry relations). Regional equations are needed to confirm bankfull hydraulic-geometry, assess stream stability, evaluate restoration needs, and verify restoration design for ungaged streams that lack stage-to-discharge ratings or historic peak-flow records. This report presents guidelines for surveying bankfull channel geometry at USGS stream gages and developing regional hydraulic-geometry relations (equations) for wadeable streams in New York. It summarizes methods to (1) compile and assess existing hydrologic, geometric, photographic, and topographic data, (2) conduct stream-reconnaissance inspections, (3) identify channel-bankfull characteristics, (4) conduct longitudinal and cross-section surveys, (5) measure stream discharge, (6) develop and refine bankfull hydraulic-geometry equations, and (7) analyze and assure data completeness and quality. The techniques primarily address wadeable streams with either active or discontinued surface-water and crest-stage gages. The relations can be applied to ungaged or actively gaged streams that are wadeable, and may be extended to non-wadeable streams (with some limitations) if they have drainage areas comparable to those used to develop the relations.

  19. Investigation of Surface Phenomena in Shocked Tin in Converging Geometry

    SciTech Connect

    Rousculp, Christopher L.; Oro, David Michael; Griego, Jeffrey Randall; Turchi, Peter John; Reinovsky, Robert Emil; Bradley, Joseph Thomas; Cheng, Baolian; Freeman, Matthew Stouten; Patten, Austin Randall

    2016-04-14

    There is a great interest in RMI as source of ejecta from metal shells. Previous experiments have explored wavelength amplitude (kA) variation but they have a small range of drive pressures and are in planer geometry. Simulations, both MD and hydro, have explored RMI in planer geometry. The ejecta source model from RMI is an area of active algorithm and code development in ASCI-IC Lagrangian Applications Project. PHELIX offers precise, reproducible variable driver for Hydro and material physics diagnoses with proton radiography.

  20. Geometry and Symmetric Coherent States of Three Qubits Systems

    NASA Astrophysics Data System (ADS)

    Guo, Xiao-Kan

    2016-06-01

    In this paper, we first generalize the previous results that relate 1- and 2-qubit geometries to complex and quaternionic Möbius transformations respectively, to the case of 3-qubit states under octonionic Möbius transformations. This completes the correspondence between the qubit geometries and the four normed division algebras. Thereby, new systems of symmetric coherent states with 2 and 3 qubits can be constructed by mapping the spin coherent states to their antipodal symmetric ponits on the generalized Bloch spheres via Möbius transformations in corresponding dimensions. Finally, potential applications of the normed division algebras in physics are discussed.