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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. Early diagnosis of lymph node metastasis: Importance of intranodal pressures.

    PubMed

    Miura, Yoshinobu; Mikada, Mamoru; Ouchi, Tomoki; Horie, Sachiko; Takeda, Kazu; Yamaki, Teppei; Sakamoto, Maya; Mori, Shiro; Kodama, Tetsuya

    2016-03-01

    Regional lymph node status is an important prognostic indicator of tumor aggressiveness. However, early diagnosis of metastasis using intranodal pressure, at a stage when lymph node size has not changed significantly, has not been investigated. Here, we use an MXH10/Mo-lpr/lpr mouse model of lymph node metastasis to show that intranodal pressure increases in both the subiliac lymph node and proper axillary lymph node, which are connected by lymphatic vessels, when tumor cells are injected into the subiliac lymph node to induce metastasis to the proper axillary lymph node. We found that intranodal pressure in the subiliac lymph node increased at the stage when metastasis was detected by in vivo bioluminescence, but when proper axillary lymph node volume (measured by high-frequency ultrasound imaging) had not increased significantly. Intravenously injected liposomes, encapsulating indocyanine green, were detected in solid tumors by in vivo bioluminescence, but not in the proper axillary lymph node. Basic blood vessel and lymphatic channel structures were maintained in the proper axillary lymph node, although sinus histiocytosis was detected. These results show that intranodal pressure in the proper axillary lymph node increases at early stages when metastatic tumor cells have not fully proliferated. Intranodal pressure may be a useful parameter for facilitating early diagnosis of lymph node metastasis.

  5. 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.

  6. 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.

  7. Intranodal Palisaded Myofibroblastoma Masquerading as N2 Non-Small Cell Lung Carcinoma.

    PubMed

    Yim, Ivan H W; Will, Malcolm B; Dhaliwal, Catharine; Salter, Donald M; Walker, William S

    2016-07-01

    Intranodal palisaded myofibroblastoma is a rare and benign tumor that usually presents in the inguinal region. We report the case of a 68-year-old woman with a right paratracheal mass and right upper lobe non-small cell lung carcinoma initially staged as T1b N2 M0. After mediastinal staging, the right paratracheal mass was found to be an intranodal palisaded myofibroblastoma, which had caused erroneous upstaging of the lung carcinoma to N2 disease. This had the potential of leading to suboptimal treatment of the primary lung carcinoma if formal mediastinal staging had not been performed. To the best of our knowledge, this is the first report in the English literature of an intranodal palisaded myofibroblastoma occurring concurrently with lung cancer. This case highlights the importance of mediastinal staging in lung cancer. Mediastinoscopy remains the gold standard.

  8. 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

  9. Intra-nodal injection of gentamicin for the treatment of suppurated cat scratch disease's lymphadenitis.

    PubMed

    Garnier, Camille; Martin-Blondel, Guillaume; Debuisson, Cécile; Dubois, Damien; Debard, Alexa; Cuzin, Lise; Massip, Patrice; Delobel, Pierre; Marchou, Bruno

    2016-02-01

    Cat scratch disease (CSD)'s lymphadenitis may have a protracted course with painful suppuration necessitating several needle aspirations or surgical drainage. The objective of this study was to evaluate the benefit of an intra-nodal injection of gentamicin add-on oral azithromycin treatment on the outcome of suppurated CSD's lymphadenitis. We performed a retrospective monocentric study including 51 consecutive patients diagnosed between Jan 2009 and Mar 2014 with suppurated CSD who had a positive PCR for Bartonella henselae DNA in pus collected from lymph node by needle aspiration, and who were treated with azithromycin. Among them, 26/51 patients (51%) received oral azithromycin only, of whom 8 patients (31%) were cured and 18 patients (69%) had complications, while 25/51 patients (49%) received an intra-nodal injection of gentamicin add-on oral azithromycin, of whom 16 patients (64 %) were cured and 9 patients (36%) had complications. In univariate analysis, the combined treatment was the only variable related to cure without complications (64 versus 31%, p = 0.01), but this difference did not remain statistically significant in multivariate analysis (OR = 3.84, 95% CI: 0.95-15.56, p = 0.06). Intra-nodal injection of gentamicin add-on oral azithromycin treatment might improve the outcome of patients with suppurated CSD's lymphadenitis, deserving further randomized studies.

  10. ManyClaw: Implementation and Comparison of Intra-Node Parallelism of Clawpack

    NASA Astrophysics Data System (ADS)

    Terrel, A. R.; Mandli, K. T.

    2012-12-01

    Computational methods for geophysical phenomena have in the past seen tremendous increases in ability due to increased hardware capability and advances in the computational methods being used. In the past two decades these avenues for increasing computational power have become intertwined as the most advanced computational methods must be written specifically for the hardware it will run on. This has become a growing concern for many scientists as the effort needed to produce efficient codes on the state-of-the-art machines has become increasingly difficult. Next generation computer architectures will include an order of magnitude more intra-node parallelism. In this context, we have created ManyClaw, a project intended to explore the exploitation of intra-node parallelism in hyperbolic PDE solvers from the Clawpack software package. Clawpack uses a finite volume wave-propagation approach to solving linear and non-linear hyperbolic conservation and balance laws. The basic computational units of Clawpack include the Riemann solver, limiters, and the cell update. The goal of ManyClaw then is to implement each of these components in a number of different ways exploring the best way to exploit as much intra-node parallelism as possible. One result of this effort is that a number of design decisions in ManyClaw differ significantly from Clawpack. Although this was not unexpected, insuring compatibility with the original code through PyClaw, a Python version of Clawpack, has also been undertaken. In this presentation we will focus on a discussion of the scalability of various threading approaches in each of the basic computational units described above. We implemented a number of different Riemann problems with different levels of arithmetic intensity via vectorized Fortran, OpenMP, TBB, and ISPC. The code was factored to allow any threading model to call any of the Riemann problems, limiters, and update routines. Results from Intel MIC and NVidia GPU implementations

  11. Histologic heterogeneity and intranodal shunt flow in lymph nodes from elderly subjects: a cadaveric study.

    PubMed

    Murakami, Gen; Taniguchi, Izumi

    2004-03-01

    Gaps of the superficial cortex of the lymph node provide intranodal shunts that are more often the cause of skip metastasis than are collateral vessels. Examination of lymph nodes from cadavers of elderly subjects often revealed cortical gaps, especially in specific three-dimensional assembled cords; these cortical gaps were readily seen in para-aortic and pelvic nodes. This architecture seemed to be more appropriate for a systemic immune response than a local defense. Evidence of poorly developed cortices, anthracosis, and hyalinization also suggested impaired nodal function. We suspect that this histologic heterogeneity, perhaps a result of aging, affects the nodal trapping of colorimetric/isotopic tracers and metastatic cancer cells. This may have implications for lymphatic mapping of the sentinel lymph node in elderly patients with early-stage cancer.

  12. 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.

  13. 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

  14. 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.

  15. 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

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

    PubMed

    Kong, Tae Wook; Chang, Suk Joon; Kim, Jinoo; Paek, Jiheum; Kim, Su Hyun; Won, Je Hwan; Ryu, Hee Sug

    2016-07-01

    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. 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. 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. 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.

  17. Subtracted geometry

    NASA Astrophysics Data System (ADS)

    Saleem, Zain Hamid

    In this thesis we study a special class of black hole geometries called subtracted geometries. Subtracted geometry black holes are obtained when one omits certain terms from the warp factor of the metric of general charged rotating black holes. The omission of these terms allows one to write the wave equation of the black hole in a completely separable way and one can explicitly see that the wave equation of a massless scalar field in this slightly altered background of a general multi-charged rotating black hole acquires an SL(2, R) x SL(2, R) x SO(3) symmetry. The "subtracted limit" is considered an appropriate limit for studying the internal structure of the non-subtracted black holes because new 'subtracted' black holes have the same horizon area and periodicity of the angular and time coordinates in the near horizon regions as the original black hole geometry it was constructed from. The new geometry is asymptotically conical and is physically similar to that of a black hole in an asymptotically confining box. We use the different nice properties of these geometries to understand various classically and quantum mechanically important features of general charged rotating black holes.

  18. 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…

  19. 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…

  20. 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)

  1. Geometry in the Computer Age.

    ERIC Educational Resources Information Center

    Scott, Paul

    1988-01-01

    Discusses the use of computer graphics in the teaching of geometry. Describes five types of geometry: Euclidean geometry, transformation geometry, coordinate geometry, three-dimensional geometry, and geometry of convex sets. (YP)

  2. 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…

  3. 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…

  4. 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…

  5. 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…

  6. 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…

  7. 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…

  8. 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.

  9. 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'…

  10. Twistors to twisted geometries

    SciTech Connect

    Freidel, Laurent; Speziale, Simone

    2010-10-15

    In a previous paper we showed that the phase space of loop quantum gravity on a fixed graph can be parametrized in terms of twisted geometries, quantities describing the intrinsic and extrinsic discrete geometry of a cellular decomposition dual to the graph. Here we unravel the origin of the phase space from a geometric interpretation of twistors.

  11. 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…

  12. 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…

  13. 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.

  14. 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…

  15. Variable geometry trusses

    NASA Technical Reports Server (NTRS)

    Robertshaw, H. H.; Reinholtz, C. F.

    1989-01-01

    Vibration control and kinematic control with variable-geometry trusses are covered. The analytical approach taken is to model each actuator with lumped masses and model a beam with finite elements, including in each model the generalized reaction forces from the beam on the actuator or vice versa. It is concluded that, from an operational standpoint, the variable-geometry truss actuator is more favorable than the inertia-type actuator. A spatial variable-geometry truss is used to test out rudimentary robotic tasks.

  16. 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)

  17. 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)

  18. 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)

  19. 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.

  20. 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)

  1. 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)

  2. 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)

  3. 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)

  4. 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).

  5. SOC and Fractal Geometry

    NASA Astrophysics Data System (ADS)

    McAteer, R. T. J.

    2013-06-01

    When Mandelbrot, the father of modern fractal geometry, made this seemingly obvious statement he was trying to show that we should move out of our comfortable Euclidean space and adopt a fractal approach to geometry. The concepts and mathematical tools of fractal geometry provides insight into natural physical systems that Euclidean tools cannot do. The benet from applying fractal geometry to studies of Self-Organized Criticality (SOC) are even greater. SOC and fractal geometry share concepts of dynamic n-body interactions, apparent non-predictability, self-similarity, and an approach to global statistics in space and time that make these two areas into naturally paired research techniques. Further, the iterative generation techniques used in both SOC models and in fractals mean they share common features and common problems. This chapter explores the strong historical connections between fractal geometry and SOC from both a mathematical and conceptual understanding, explores modern day interactions between these two topics, and discusses how this is likely to evolve into an even stronger link in the near future.

  6. 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.

  7. 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

  8. Contact Geometry of Curves

    NASA Astrophysics Data System (ADS)

    Vassiliou, Peter J.

    2009-10-01

    Cartan's method of moving frames is briefly recalled in the context of immersed curves in the homogeneous space of a Lie group G. The contact geometry of curves in low dimensional equi-affine geometry is then made explicit. This delivers the complete set of invariant data which solves the G-equivalence problem via a straightforward procedure, and which is, in some sense a supplement to the equivariant method of Fels and Olver. Next, the contact geometry of curves in general Riemannian manifolds (M,g) is described. For the special case in which the isometries of (M,g) act transitively, it is shown that the contact geometry provides an explicit algorithmic construction of the differential invariants for curves in M. The inputs required for the construction consist only of the metric g and a parametrisation of structure group SO(n); the group action is not required and no integration is involved. To illustrate the algorithm we explicitly construct complete sets of differential invariants for curves in the Poincaré half-space H3 and in a family of constant curvature 3-metrics. It is conjectured that similar results are possible in other Cartan geometries.

  9. 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. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

  10. 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…

  11. 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…

  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. 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.

  14. 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.

  15. 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…

  16. 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…

  17. 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.

  18. 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…

  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

    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.

  1. 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)

  2. 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…

  3. 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)

  4. 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

  5. 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)

  6. 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…

  7. 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

  8. Teaching Geometry with Tangrams.

    ERIC Educational Resources Information Center

    Russell, Dorothy S.; Bologna, Elaine M.

    1982-01-01

    Geometry is viewed as the most neglected area of the elementary school mathematics curriculum. Tangram activities provide numerous worthwhile mathematical experiences for children. A method of constructing tangrams through paper folding is followed by suggested spatial visualization, measurement, and additional activities. (MP)

  9. 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".…

  10. 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…

  11. 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)

  12. 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)

  13. 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

  14. 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".…

  15. 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)

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. Emergent geometry, emergent forces

    NASA Astrophysics Data System (ADS)

    Selesnick, S. A.

    2017-10-01

    We give a brief account of some aspects of Finkelstein’s quantum relativity, namely an extension of it that derives elements of macroscopic geometry and the Lagrangians of the standard model including gravity from a presumed quantum version of spacetime. These emerge as collective effects in this quantal substrate. Our treatment, which is largely self-contained, differs mathematically from that originally given by Finkelstein. Dedicated to the memory of David Ritz Finkelstein

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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

  8. 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

  9. 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.

  10. 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.

  11. 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…

  12. 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.

  13. Models of molecular geometry.

    PubMed

    Gillespie, Ronald J; Robinson, Edward A

    2005-05-01

    Although the structure of almost any molecule can now be obtained by ab initio calculations chemists still look for simple answers to the question "What determines the geometry of a given molecule?" For this purpose they make use of various models such as the VSEPR model and qualitative quantum mechanical models such as those based on the valence bond theory. The present state of such models, and the support for them provided by recently developed methods for analyzing calculated electron densities, are reviewed and discussed in this tutorial review.

  14. 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.

  15. 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

  16. Proterozoic Geomagnetic Field Geometry

    NASA Astrophysics Data System (ADS)

    Panzik, J. E.; Evans, D. A.

    2011-12-01

    Pre-Mesozoic continental reconstructions and paleoclimatic inferences from paleomagnetism rely critically upon the assumption of a time-averaged geocentric axial dipole (GAD) magnetic field. We have been testing the GAD assumption and localized non-dipole components in a different manner, by observing directional variations within the Matachewan, Mackenzie and Franklin dyke swarms. Large dyke swarms, commonly emplaced within a few million years, provide the necessary broad areal coverage to perform a test of global geomagnetic field geometry. Our analysis varies the quadrupole and octupole values of the generalized paleolatitude equation to determine a minimal angular dispersion and maximum precision of paleopoles from each dyke swarm. As a control, paleomagnetic data from the central Atlantic magmatic province (CAMP) show the sensitivities of our method to non-GAD contributions to the ancient geomagnetic field. Within the uncertainties, CAMP data are consistent with independent estimates of non-GAD contributions derived from global tectonic reconstructions (Torsvik & Van der Voo, 2002). Current results from the three Proterozoic dyke swarms all have best fits that are non-dipolar, but they differ in their optimal quadrupole/ octupole components. Treated together under the hypothesis of a static Proterozoic field geometry, the data allow a pure GAD geodynamo within the uncertainty of the method. Current results were performed using Fisherian statistics, but Bingham statistics will be included to account for the ellipticity of data.

  17. 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.

  18. 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.

  19. Geometry from Gauge Theory

    SciTech Connect

    Correa, Diego H.; Silva, Guillermo A.

    2008-07-28

    We discuss how geometrical and topological aspects of certain (1/2)-BPS type IIB geometries are captured by their dual operators in N = 4 Super Yang-Mills theory. The type IIB solutions are characterized by arbitrary droplet pictures in a plane and we consider, in particular, axially symmetric droplets. The 1-loop anomalous dimension of the dual gauge theory operators probed with single traces is described by some bosonic lattice Hamiltonians. These Hamiltonians are shown to encode the topology of the droplets. In appropriate BMN limits, the Hamiltonians spectrum reproduces the spectrum of near-BPS string excitations propagating along each of the individual edges of the droplet. We also study semiclassical regimes for the Hamiltonians. For droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents.

  20. 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

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. 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

  6. 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)

  7. 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.

  8. Conformal Lorentz geometry revisited

    NASA Astrophysics Data System (ADS)

    Teleman, Kostake

    1996-02-01

    . We also show that Mach's principle on inertial motions receives an explanation in our theory by considering the particular geodesic paths, for which one of the partners of an interacting pair is fixed and sent to infinity. In fact we study a dynamical system (W,L) which presents some formal and topological similarities with a system of two particles interacting gravitationally. (W,L) is the only conformally invariant relativistic two-point dynamical system. At the end we show that W can be naturally regarded as the base of a principal GL(2,C)-bundle which comes with a natural connection. We study this bundle from differential geometric point of view. Physical interpretations will be discussed in a future paper. This text is an improvement of a previous version, which was submitted under the title ``Hypertwistor Geometry.'' [See, K. Teleman, ``Hypertwistor Geometry (abstract),'' 14th International Conference on General Relativity and Gravitation, Florence, Italy, 1995.] The change of the title and many other improvements are due to the valuable comments of the referee, who also suggested the author to avoid hazardous interpretations.

  9. 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…

  10. Sex Differences in Geometry Achievement.

    ERIC Educational Resources Information Center

    Dees, Roberta L.

    The following questions are addressed: (1) Are there sex differences in achievement, either in entering knowledge of geometry in the fall, or in achievement in acquiring standard geometry content by year's end? (2) Are there sex differences in the performance of students on the van Hiele test, either at the beginning or end of the year? and (3)…

  11. 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…

  12. 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.

  13. 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.

  14. 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.

  15. The geometry of our world

    NASA Astrophysics Data System (ADS)

    Lotay, Jason

    2017-04-01

    Jason Lotay explains how mathematicians studying special geometries are collaborating with physicists to explore M-theory, an 11-dimensional description of the world that unifies the various string theories

  16. 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.

  17. Drift waves in stellarator geometry

    SciTech Connect

    Persson, M.; Nadeem, M.; Lewandowski, J.L.V.; Gardner, H.J.

    2000-02-07

    Drift waves are investigated in a real three-dimensional stellarator geometry. A linear system, based on the cold ion fluid model and a ballooning mode formalism, is solved numerically in the geometry of the stellarator H1-NF. The spectra of stable and unstable modes, as well as localization, are discussed. The dependence of the spectrum of the unstable modes on the wavevector, plasma density variation, and the location in the plasma is presented.

  18. 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.

  19. A Comment on Molecular Geometry

    NASA Astrophysics Data System (ADS)

    Gomba, Frank J.

    1999-12-01

    A method of determining the correct molecular geometry of simple molecules and ions with one central atom is proposed. While the usual method of determining the molecular geometry involves first drawing the Lewis structure, this method can be used without doing so. In fact, the Lewis structure need not be drawn at all. The Lewis structure may be drawn as the final step, with the geometry of the simple molecule or ion already established. In the case of diatomic molecules, any atom may be used as the central atom. When hydrogen is present in a multiatom molecule or ion, this method "naturally" eliminates choosing hydrogen; but, any other atom may be used as the central atom to determine the correct geometry. The Lewis structure can then be used to determine the formal charges on the atoms. In this way there is a check on the selection of the central atom, should the correct Lewis structure be desired. Thus, it assumes that one is familiar with both Lewis structures and the valence shell electron pair repulsion (VSEPR) approach to bonding. The approach suggested in this paper will give rapid and accurate molecular geometries, and it is fun !!!

  20. 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.

  1. 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.

  2. DOGBONE GEOMETRY FOR RECIRCULATING ACCELERATORS.

    SciTech Connect

    BERG,J.S.; JOHNSTONE,C.; SUMMERS,D.

    2001-06-18

    Most scenarios for accelerating muons require recirculating acceleration. A racetrack shape for the accelerator requires particles with lower energy in early passes to traverse almost the same length of arc as particles with the highest energy. This extra arc length may lead to excess decays and excess cost. Changing the geometry to a dogbone shape, where there is a single linac and the beam turns completely around at the end of the linac, returning to the same end of the linac from which it exited, addresses this problem. In this design, the arc lengths can be proportional to the particle's momentum. This paper proposes an approximate cost model for a recirculating accelerator, attempts to make cost-optimized designs for both racetrack and dogbone geometries, and demonstrates that the dogbone geometry does appear to be more cost effective.

  3. 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.

  4. Nernst branes from special geometry

    NASA Astrophysics Data System (ADS)

    Dempster, P.; Errington, D.; Mohaupt, T.

    2015-05-01

    We construct new black brane solutions in U(1) gauged N = 2 supergravity with a general cubic prepotential, which have entropy density s ˜ T 1/3 as T → 0 and thus satisfy the Nernst Law. By using the real formulation of special geometry, we are able to obtain analytical solutions in closed form as functions of two parameters, the temperature T and the chemical potential μ. Our solutions interpolate between hyperscaling violating Lifshitz geometries with ( z, θ) = (0 , 2) at the horizon and ( z, θ) = (1 , -1) at infinity. In the zero temperature limit, where the entropy density goes to zero, we recover the extremal Nernst branes of Barisch et al, and the parameters of the near horizon geometry change to ( z, θ) = (3 , 1).

  5. 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.

  6. Individualized Geometry: A Geometry Unit for the Intermediate Grades.

    ERIC Educational Resources Information Center

    Geissler, Dennis; Larson, Richard

    This geometry unit for the intermediate grades is based on the Holt Mathematics Series (levels 3-6), using the concepts of Individually Guided Education (IGE). It is divided into seven levels, one for grade 3 and two each for grades 4-6. Each is designed for both individual and group learning. A vocabulary list is used as a key for activities; a…

  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. RSRM Propellant Grain Geometry Modification

    NASA Technical Reports Server (NTRS)

    Schorr, Andrew A.; Endicott, Joni B.; McCool, Alex (Technical Monitor)

    2000-01-01

    This document is composed of viewgraphs about the RSRM propellant grain geometry modification project, which hopes to improve personnel and system safety by modifying propellant grain geometry to improve structural factors of safety. Using techniques such as Finite Element Analysis to determine blend radii required to reduce localized stresses, and ballistic predictions to ensure that the ballistics, ignition transient and Block Model have not been adversely affected, the project hopes to build and test FSM-10 with a new design, and determine flight effectivity pending successful test evaluation.

  10. 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…

  11. 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…

  12. 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…

  13. 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…

  14. 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…

  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. Foucault pendulum through basic geometry

    NASA Astrophysics Data System (ADS)

    von Bergmann, Jens; von Bergmann, HsingChi

    2007-10-01

    We provide a thorough explanation of the Foucault pendulum that utilizes its underlying geometry on a level suitable for science students not necessarily familiar with calculus. We also explain how the geometrically understood Foucault pendulum can serve as a prototype for more advanced phenomena in physics known as Berry's phase or geometric phases.

  17. 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…

  18. Exploring Bundling Theory with Geometry

    ERIC Educational Resources Information Center

    Eckalbar, John C.

    2006-01-01

    The author shows how instructors might successfully introduce students in principles and intermediate microeconomic theory classes to the topic of bundling (i.e., the selling of two or more goods as a package, rather than separately). It is surprising how much students can learn using only the tools of high school geometry. To be specific, one can…

  19. Instructional Identities of Geometry Students

    ERIC Educational Resources Information Center

    Aaron, Wendy Rose; Herbst, Patricio

    2012-01-01

    We inspect the hypothesis that geometry students may be oriented toward how they expect that the teacher will evaluate them as students or otherwise oriented to how they expect that their work will give them opportunities to do mathematics. The results reported here are based on a mixed-methods analysis of twenty-two interviews with high school…

  20. 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…

  1. 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…

  2. 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…

  3. 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…

  4. 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…

  5. 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…

  6. Signature geometry and quantum engineering

    NASA Astrophysics Data System (ADS)

    Samociuk, Stefan

    2013-09-01

    As the operating frequency of electromagnetic based devices increase, physical design geometry is playing an ever more important role. Evidence is considered in support of a relationship between the dimensionality of primitive geometric forms, such as transistors, and corresponding electromagnetic coupling efficiency. The industry of electronics is defined as the construction of devices by the patterning of primitive forms to physical materials. Examples are given to show the evolution of these primitives, down to nano scales, are requiring exacting geometry and three dimensional content. Consideration of microwave monolithic integrated circuits,(MMIC), photonics and metamaterials,(MM), support this trend and also add new requirements of strict geometric periodicity and multiplicity. Signature geometries,(SG), are characterized by distinctive attributes and examples are given. The transcendent form transcode algorithm, (TTA) is introduced as a multi dimensional SG and its use in designing photonic integrated circuits and metamaterials is discussed . A creative commons licensed research database, TRANSFORM, containing TTA geometries in OASIS file formats is described. An experimental methodology for using the database is given. Multidimensional SG and extraction of three dimensional cross sections as primitive forms is discussed as a foundation for quantum engineering and the exploitation of phenomena other than the electromagnetic.

  7. 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…

  8. Geometry in transition: a model of emergent geometry.

    PubMed

    Delgadillo-Blando, Rodrigo; O'Connor, Denjoe; Ydri, Badis

    2008-05-23

    We study a three matrix model with global SO(3) symmetry containing at most quartic powers of the matrices. We find an exotic line of discontinuous transitions with a jump in the entropy, characteristic of a 1st order transition, yet with divergent critical fluctuations and a divergent specific heat with critical exponent alpha=1/2. The low temperature phase is a geometrical one with gauge fields fluctuating on a round sphere. As the temperature increased the sphere evaporates in a transition to a pure matrix phase with no background geometrical structure. Both the geometry and gauge fields are determined dynamically. It is not difficult to invent higher dimensional models with essentially similar phenomenology. The model presents an appealing picture of a geometrical phase emerging as the system cools and suggests a scenario for the emergence of geometry in the early Universe.

  9. 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

  10. Beyond core knowledge: Natural geometry

    PubMed Central

    Spelke, Elizabeth; Lee, Sang Ah; Izard, Véronique

    2010-01-01

    For many centuries, philosophers and scientists have pondered the origins and nature of human intuitions about the properties of points, lines, and figures on the Euclidean plane, with most hypothesizing that a system of Euclidean concepts either is innate or is assembled by general learning processes. Recent research from cognitive and developmental psychology, cognitive anthropology, animal cognition, and cognitive neuroscience suggests a different view. Knowledge of geometry may be founded on at least two distinct, evolutionarily ancient, core cognitive systems for representing the shapes of large-scale, navigable surface layouts and of small-scale, movable forms and objects. Each of these systems applies to some but not all perceptible arrays and captures some but not all of the three fundamental Euclidean relationships of distance (or length), angle, and direction (or sense). Like natural number (Carey, 2009), Euclidean geometry may be constructed through the productive combination of representations from these core systems, through the use of uniquely human symbolic systems. PMID:20625445

  11. 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.

  12. Tin clusters adopt prolate geometries

    NASA Astrophysics Data System (ADS)

    Shvartsburg, Alexandre A.; Jarrold, Martin F.

    1999-08-01

    We have characterized the structures of Snn cations up to n=68 using ion mobility measurements. Up to n~35, tin clusters track the prolate growth pattern previously found for Sin and Gen. However, the detailed size-dependent variations start deviating from those observed for Sin above n=14 and Gen above n=21. Over the n~35-65 size range, tin clusters gradually rearrange towards near-spherical geometries, passing through several intermediate structural families. Two or three isomers are resolved for some sizes in the n=18-49 range. The observed geometries are independent of the He buffer gas temperature between 78 and 378 K and are not affected by collisional annealing.

  13. 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

  14. 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.

  15. 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.

  16. 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.

  17. Extending dark optical trapping geometries.

    PubMed

    Arnold, Aidan S

    2012-07-01

    New counterpropagating geometries are presented for localizing ultracold atoms in the dark regions created by the interference of Laguerre-Gaussian laser beams. In particular dark helices, an "optical revolver," axial lattices of rings, and axial lattices of ring lattices of rings are considered and a realistic scheme for achieving phase stability is explored. The dark nature of these traps will enable their use as versatile tools for low-decoherence atom interferometry with zero differential light shifts.

  18. 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.

  19. The unassigned distance geometry problem

    DOE PAGES

    Duxbury, P. M.; Granlund, L.; Gujarathi, S. R.; ...

    2015-11-19

    Studies of distance geometry problems (DGP) have focused on cases where the vertices at the ends of all or most of the given distances are known or assigned, which we call assigned distance geometry problems (aDGPs). In this contribution we consider the unassigned distance geometry problem (uDGP) where the vertices associated with a given distance are unknown, so the graph structure has to be discovered. uDGPs arises when attempting to find the atomic structure of molecules and nanoparticles using X-ray or neutron diffraction data from non-crystalline materials. Rigidity theory provides a useful foundation for both aDGPs and uDGPs, though itmore » is restricted to generic realizations of graphs, and key results are summarized. Conditions for unique realization are discussed for aDGP and uDGP cases, build-up algorithms for both cases are described and experimental results for uDGP are presented.« less

  20. Geometry of statistical target detection

    NASA Astrophysics Data System (ADS)

    Basener, William F.; Allen, Brian; Bretney, Kristen

    2017-01-01

    This paper presents an investigation into the underlying geometry and performance of various statistical target detection algorithms for hyperspectral imagery, presents results from algorithm testing, and investigates general trends and observable principles for understanding performance. Over the variety of detection algorithms, there is no universally best performing algorithm. In our test, often top performing algorithms on one class of targets obtain mediocre results on another class of targets. However, there are two clear trends: quadratic detectors such as ACE generally performed better than linear ones especially for subpixel targets (our top 15 scoring algorithms were quadratic detectors), and using anomaly detection to prescreen image spectra improved the performance of the quadratic detectors (8 of our top 9 scoring algorithms using anomaly prescreening). We also demonstrate that simple combinations of detection algorithms can outperform single algorithms in practice. In our derivation of detection algorithms, we provide exposition on the underlying mathematical geometry of the algorithms. That geometry is then used to investigate differences in algorithm performance. Tests are conducted using imagery and targets freely available online. The imagery was acquired over Cooke City, Montana, a small town near Yellowstone National Park, using the HyMap V/NIR/SWIR sensor with 126 spectral bands. There are three vehicle and four fabric targets located in the town and surrounding area.

  1. 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.

  2. 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

  3. 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

  4. 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…

  5. 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)

  6. 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.

  7. 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.

  8. 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".

  9. 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.

  10. 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…

  11. 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…

  12. 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…

  13. 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…

  14. 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…

  15. 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…

  16. 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…

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  1. Quanta of Geometry and Unification

    NASA Astrophysics Data System (ADS)

    Chamseddine, Ali H.

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

  2. Regular polygons in taxicab geometry

    NASA Astrophysics Data System (ADS)

    Hanson, J. R.

    2014-10-01

    A polygon of n sides will be called regular in taxicab geometry if it has n equal angles and n sides of equal taxicab length. This paper will show that there are no regular taxicab triangles and no regular taxicab pentagons. The sets of taxicab rectangles and taxicab squares will be shown to be the same, respectively, as the sets of Euclidean rectangles and Euclidean squares. A method of construction for a regular taxicab 2n-gon for any n will be demonstrated.

  3. Geometry of physical dispersion relations

    NASA Astrophysics Data System (ADS)

    Rätzel, Dennis; Rivera, Sergio; Schuller, Frederic P.

    2011-02-01

    To serve as a dispersion relation, a cotangent bundle function must satisfy three simple algebraic properties. These conditions are derived from the inescapable physical requirements that local matter field dynamics must be predictive and allow for an observer-independent notion of positive energy. Possible modifications of the standard relativistic dispersion relation are thereby severely restricted. For instance, the dispersion relations associated with popular deformations of Maxwell theory by Gambini-Pullin or Myers-Pospelov are not admissible. Dispersion relations passing the simple algebraic checks derived here correspond to physically admissible Finslerian refinements of Lorentzian geometry.

  4. 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

  5. Entanglement classification with algebraic geometry

    NASA Astrophysics Data System (ADS)

    Sanz, M.; Braak, D.; Solano, E.; Egusquiza, I. L.

    2017-05-01

    We approach multipartite entanglement classification in the symmetric subspace in terms of algebraic geometry, its natural language. We show that the class of symmetric separable states has the structure of a Veronese variety and that its k-secant varieties are SLOCC invariants. Thus SLOCC classes gather naturally into families. This classification presents useful properties such as a linear growth of the number of families with the number of particles, and nesting, i.e. upward consistency of the classification. We attach physical meaning to this classification through the required interaction length of parent Hamiltonians. We show that the states W N and GHZ N are in the same secant family and that, effectively, the former can be obtained in a limit from the latter. This limit is understood in terms of tangents, leading to a refinement of the previous families. We compute explicitly the classification of symmetric states with N≤slant4 qubits in terms of both secant families and its refinement using tangents. This paves the way to further use of projective varieties in algebraic geometry to solve open problems in entanglement theory.

  6. 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].

  7. Turbine engine variable geometry device

    NASA Technical Reports Server (NTRS)

    Rogo, Casimir (Inventor); Lenz, Herman N. (Inventor)

    1985-01-01

    A variable geometry device for use with the turbine nozzle of a turbine engine of the type having a support housing and a combustion chamber contained within the support housing. A pair of spaced walls in the support housing define an annular and radially extending nozzle passageway. The outer end of the nozzle passageway is open to the combustion chamber while the inner end of the nozzle passageway is open to one or more turbine stages. A plurality of circumferentially spaced nozzle vanes are mounted to one of the spaced walls and protrude across the nozzle passageway. An annular opening is formed around the opposite spaced wall and an annular ring is axially slidably mounted within the opening. A motor is operatively connected to this ring and, upon actuation, axially displaces the ring within the nozzle passageway. In addition, the ring includes a plurality of circumferentially spaced slots which register with the nozzle vanes so that the vane geometry remains the same despite axial displacement of the ring.

  8. 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.

  9. Geometry and the quantum: basics

    NASA Astrophysics Data System (ADS)

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

    2014-12-01

    Motivated by the construction of spectral manifolds in noncommutative geometry, we introduce a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of scalar fields. This commutation relation appears in two versions, one sided and two sided. It implies the quantization of the volume. In the one-sided case it implies that the manifold decomposes into a disconnected sum of spheres which will represent quanta of geometry. The two sided version in dimension 4 predicts the two algebras M 2(ℍ) and M 4(ℂ) which are the algebraic constituents of the Standard Model of particle physics. This taken together with the non-commutative algebra of functions allows one to reconstruct, using the spectral action, the Lagrangian of gravity coupled with the Standard Model. We show that any connected Riemannian Spin 4-manifold with quantized volume > 4 (in suitable units) appears as an irreducible representation of the two-sided commutation relations in dimension 4 and that these representations give a seductive model of the "particle picture" for a theory of quantum gravity in which both the Einstein geometric standpoint and the Standard Model emerge from Quantum Mechanics. Physical applications of this quantization scheme will follow in a separate publication.

  10. 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.

  11. 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.

  12. Quanta of Geometry: Noncommutative Aspects

    NASA Astrophysics Data System (ADS)

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

    2015-03-01

    In the construction of spectral manifolds in noncommutative geometry, a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of real scalar fields naturally appears and implies, by equality with the index formula, the quantization of the volume. We first show that this condition implies that the manifold decomposes into disconnected spheres, which will represent quanta of geometry. We then refine the condition by involving the real structure and two types of geometric quanta, and show that connected spin manifolds with large quantized volume are then obtained as solutions. The two algebras M2(H ) and M4(C ) are obtained, which are the exact constituents of the standard model. Using the two maps from M4 to S4 the four-manifold is built out of a very large number of the two kinds of spheres of Planckian volume. We give several physical applications of this scheme such as quantization of the cosmological constant, mimetic dark matter, and area quantization of black holes.

  13. 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

  14. 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

  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. Kinematic dynamos in spheroidal geometries

    NASA Astrophysics Data System (ADS)

    Ivers, D. J.

    2017-10-01

    The kinematic dynamo problem is solved numerically for a spheroidal conducting fluid of possibly large aspect ratio with an insulating exterior. The solution method uses solenoidal representations of the magnetic field and the velocity by spheroidal toroidal and poloidal fields in a non-orthogonal coordinate system. Scaling of coordinates and fields to a spherical geometry leads to a modified form of the kinematic dynamo problem with a geometric anisotropic diffusion and an anisotropic current-free condition in the exterior, which is solved explicitly. The scaling allows the use of well-developed spherical harmonic techniques in angle. Dynamo solutions are found for three axisymmetric flows in oblate spheroids with semi-axis ratios 1≤a/c≤25. For larger aspect ratios strong magnetic fields may occur in any region of the spheroid, depending on the flow, but the external fields for all three flows are weak and concentrated near the axis or periphery of the spheroid.

  17. 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.

  18. 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.

  19. Geometry-induced capillary emptying

    PubMed Central

    Parry, Andrew O.; Aarts, Dirk G. A. L.

    2016-01-01

    When a capillary is half-filled with liquid and turned to the horizontal, the liquid may flow out of the capillary or remain in it. For lack of a better criterion, the standard assumption is that the liquid will remain in a capillary of narrow cross-section, and will flow out otherwise. Here, we present a precise mathematical criterion that determines which of the two outcomes occurs for capillaries of arbitrary cross-sectional shape, and show that the standard assumption fails for certain simple geometries, leading to very rich and counterintuitive behavior. This opens the possibility of creating very sensitive microfluidic devices that respond readily to small physical changes, for instance, by triggering the sudden displacement of fluid along a capillary without the need of any external pumping. PMID:27791079

  20. 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.

  1. Spinors in Physics and Geometry

    NASA Astrophysics Data System (ADS)

    Trautman, A.; Furlan, G.

    1988-11-01

    The Table of Contents for the full book PDF is as follows: * Preface * Killing Spinors According to O. Hijazi and Applications * Self-Duality Conditions Satisfied by the Spin Connections on Spheres * Maslov Index and Half - Forms * Spin - 3/2 Fields on Black Hole Spacetimes * Indecomposable Conformal Spinors and Operator Product Expansions in a Massless QED Model * Nonlinear Spinor Representations * Nonlinear Wave Equations for Intrinsic Spinor Coordinates * Twistors - "Spinors" of SU(2,2), Their Generalizations and Achievements * Spinors, Reflections and Clifford Algebras: A Review * overline {SL}(n, R) Spinors for Particles, Gravity and Superstrings * Spinors on Compact Riemann Surfaces * Simple Spinors as Urfelder * Applications of Cartan Spinors to Differential Geometry in Higher Dimensions * Killing Spinors on Spheres and Projective Spaces * Spinor Structures on Homogeneous Riemannian Spaces * Classical Strings and Minimal Surfaces * Representing Spinors with Differential Forms * Inequalities for Spinors Norms in Clifford Algebras * The Importance of Spin * The Theory of World Spinors * Final List of Participants

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. Subsectors, Dynkin diagrams and new generalised geometries

    NASA Astrophysics Data System (ADS)

    Strickland-Constable, Charles

    2017-08-01

    We examine how generalised geometries can be associated with a labelled Dynkin diagram built around a gravity line. We present a series of new generalised geometries based on the groups Spin( d, d) × ℝ + for which the generalised tangent space transforms in a spinor representation of the group. In low dimensions these all appear in subsectors of maximal supergravity theories. The case d = 8 provides a geometry for eight-dimensional backgrounds of M theory with only seven-form flux, which have not been included in any previous geometric construction. This geometry is also one of a series of "half-exceptional" geometries, which "geometrise" a six-form gauge field. In the appendix, we consider exam-ples of other algebras appearing in gravitational theories and give a method to derive the Dynkin labels for the "section condition" in general. We argue that generalised geometry can describe restrictions and subsectors of many gravitational theories.

  7. 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.

  8. 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

  9. 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.

  10. 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

  11. 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.

  12. 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.

  13. 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

  14. 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.

  15. 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.

  16. Latent geometry of bipartite networks.

    PubMed

    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.

  17. Combinatorics, geometry, and mathematical physics

    SciTech Connect

    Chen, W.Y.C.; Louck, J.D.

    1998-11-01

    This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). Combinatorics and geometry have been among the most active areas of mathematics over the past few years because of newly discovered inter-relations between them and their potential for applications. In this project, the authors set out to identify problems in physics, chemistry, and biology where these methods could impact significantly. In particular, the experience suggested that the areas of unitary symmetry and discrete dynamical systems could be brought more strongly under the purview of combinatorial methods. Unitary symmetry deals with the detailed description of the quantum mechanics of many-particle systems, and discrete dynamical systems with chaotic systems. The depth and complexity of the mathematics in these physical areas of research suggested that not only could significant advances be made in these areas, but also that here would be a fertile feedback of concept and structure to enrich combinatorics itself by setting new directions. During the three years of this project, the goals have been realized beyond expectation, and in this report the authors set forth these advancements and justify their optimism.

  18. 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.

  19. 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

  20. 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.

  1. 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).…

  2. Trigonometry and Analytic Geometry: Curriculum Guide.

    ERIC Educational Resources Information Center

    Harlandale Independent School District, San Antonio, TX. Career Education Center.

    The guide (one-quarter trigonometry course; two-quarter analytic geometry course) provides both subject matter and career preparation assistance for advanced mathematics teachers. It is arranged in vertical columns relating curriculum concepts in trigonometry and analytic geometry to curriculum performance objectives, career concepts and teaching…

  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. 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…

  6. Cognitive Styles, Dynamic Geometry and Measurement Performance

    ERIC Educational Resources Information Center

    Pitta-Pantazi, Demetra; Christou, Constantinos

    2009-01-01

    This paper reports the outcomes of an empirical study undertaken to investigate the effect of students' cognitive styles on achievement in measurement tasks in a dynamic geometry learning environment, and to explore the ability of dynamic geometry learning in accommodating different cognitive styles and enhancing students' learning. A total of 49…

  7. 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…

  8. 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…

  9. 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.

  10. 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.

  11. 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…

  12. 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…

  13. 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…

  14. 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…

  15. 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…

  16. 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…

  17. 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…

  18. 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.

  19. Teaching Molecular Geometry with the VSEPR Model

    ERIC Educational Resources Information Center

    Gillespie, Ronald J.

    2004-01-01

    The first introduction to molecular geometry should be through the simple and easily understood VSEPR model, as the Valence Bond Theory and MO Theory suffer from limitations as far as understanding molecular geometry is concerned. The VSEPR model gives a perfectly satisfactory description of the bonding that follows directly from the Lewis model…

  20. 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.

  1. 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.

  2. 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.

  3. 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…

  4. 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…

  5. 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…

  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. 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…

  8. 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.

  9. 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…

  10. 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…

  11. Poisson geometry from a Dirac perspective

    NASA Astrophysics Data System (ADS)

    Meinrenken, Eckhard

    2017-07-01

    We present proofs of classical results in Poisson geometry using techniques from Dirac geometry. This article is based on mini-courses at the Poisson summer school in Geneva, June 2016, and at the workshop Quantum Groups and Gravity at the University of Waterloo, April 2016.

  12. 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.

  13. 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.

  14. 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…

  15. 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…

  16. 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…

  17. 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…

  18. 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…

  19. 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…

  20. 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…

  1. 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

  2. basement reservoir geometry and properties

    NASA Astrophysics Data System (ADS)

    Walter, bastien; Geraud, yves; Diraison, marc

    2017-04-01

    Basement reservoirs are nowadays frequently investigated for deep-seated fluid resources (e.g. geothermal energy, groundwater, hydrocarbons). The term 'basement' generally refers to crystalline and metamorphic formations, where matrix porosity is negligible in fresh basement rocks. Geothermal production of such unconventional reservoirs is controlled by brittle structures and altered rock matrix, resulting of a combination of different tectonic, hydrothermal or weathering phenomena. This work aims to characterize the petro-structural and petrophysical properties of two basement surface analogue case studies in geological extensive setting (the Albert Lake rift in Uganda; the Ifni proximal margin of the South West Morocco Atlantic coast). Different datasets, using field structural study, geophysical acquisition and laboratory petrophysical measurements, were integrated to describe the multi-scale geometry of the porous network of such fractured and weathered basement formations. This study points out the multi-scale distribution of all the features constituting the reservoir, over ten orders of magnitude from the pluri-kilometric scale of the major tectonics structures to the infra-millimetric scale of the secondary micro-porosity of fractured and weathered basements units. Major fault zones, with relatively thick and impermeable fault core structures, control the 'compartmentalization' of the reservoir by dividing it into several structural blocks. The analysis of these fault zones highlights the necessity for the basement reservoirs to be characterized by a highly connected fault and fracture system, where structure intersections represent the main fluid drainage areas between and within the reservoir's structural blocks. The suitable fluid storage areas in these reservoirs correspond to the damage zone of all the fault structures developed during the tectonic evolution of the basement and the weathered units of the basement roof developed during pre

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. Interactive graphics for quick-geometry modeling

    NASA Technical Reports Server (NTRS)

    Townsend, J. C.

    1984-01-01

    The QUICK-geometry system is a method for defining configuration shapes in completely analytical form. It was developed for use when the analytical definition of aircraft geometry is advantageous or necessary for the solution of the flow around it. While the QUICK-geometry system provides a convenient and flexible method for generating configurations with completely analytical definitions, experience showed that it can be difficult to match a previously defined configuration with a QUICK-geometry definition. Therefore, the National Aeronautics and Space Administration (NASA) and other users developed computer programs that aid in the generation of QUICK inputs. A NASA-developed set of such programs which recently were upgraded extensively to improve its usability and portability are described.

  8. 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)

  9. 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)

  10. 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.

  11. 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.

  12. 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.

  13. 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)

  14. MRI Quantification of Human Spine Cartilage Endplate Geometry: Comparison With Age, Degeneration, Level, and Disc Geometry

    PubMed Central

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

    2017-01-01

    Geometry is an important indicator of disc mechanical function and degeneration. While the geometry and associated degenerative changes in the nucleus pulposus and the annulus fibrosus are well-defined, the geometry of the cartilage endplate (CEP) and its relationship to disc degeneration are unknown. The objectives of this study were to quantify CEP geometry in three dimensions using an MRI FLASH imaging sequence and evaluate relationships between CEP geometry and age, degeneration, spinal level, and overall disc geometry. To do so, we assessed the MRI-based measurements for accuracy and repeatability. Next, we measured CEP geometry across a larger sample set and correlated CEP geometric parameters to age, disc degeneration, level, and disc geometry. The MRI-based measures resulted in thicknesses (0.3–1 mm) that are comparable to prior measurements of CEP thickness. CEP thickness was greatest at the anterior/posterior (A/P) margins and smallest in the center. The CEP A/P thickness, axial area, and lateral width decreased with age but were not related to disc degeneration. Age-related, but not degeneration-related, changes in geometry suggest that the CEP may not follow the progression of disc degeneration. Ultimately, if the CEP undergoes significant geometric changes with aging and if these can be related to low back pain, a clinically feasible translation of the FLASH MRI-based measurement of CEP geometry presented in this study may prove a useful diagnostic tool. PMID:27232974

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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)

  20. 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)

  1. Geometry-induced protein pattern formation

    PubMed Central

    Thalmeier, Dominik; Halatek, Jacob; Frey, Erwin

    2016-01-01

    Protein patterns are known to adapt to cell shape and serve as spatial templates that choreograph downstream processes like cell polarity or cell division. However, how can pattern-forming proteins sense and respond to the geometry of a cell, and what mechanistic principles underlie pattern formation? Current models invoke mechanisms based on dynamic instabilities arising from nonlinear interactions between proteins but neglect the influence of the spatial geometry itself. Here, we show that patterns can emerge as a direct result of adaptation to cell geometry, in the absence of dynamical instability. We present a generic reaction module that allows protein densities robustly to adapt to the symmetry of the spatial geometry. The key component is an NTPase protein that cycles between nucleotide-dependent membrane-bound and cytosolic states. For elongated cells, we find that the protein dynamics generically leads to a bipolar pattern, which vanishes as the geometry becomes spherically symmetrical. We show that such a reaction module facilitates universal adaptation to cell geometry by sensing the local ratio of membrane area to cytosolic volume. This sensing mechanism is controlled by the membrane affinities of the different states. We apply the theory to explain AtMinD bipolar patterns in Δ EcMinDE Escherichia coli. Due to its generic nature, the mechanism could also serve as a hitherto-unrecognized spatial template in many other bacterial systems. Moreover, the robustness of the mechanism enables self-organized optimization of protein patterns by evolutionary processes. Finally, the proposed module can be used to establish geometry-sensitive protein gradients in synthetic biological systems. PMID:26739566

  2. What is inverse-geometry CT?

    PubMed

    Schmidt, Taly Gilat

    2011-01-01

    Inverse-geometry computed tomography (IGCT) systems are being developed to provide improved volumetric imaging. In conventional multislice CT systems, x-rays are emitted from a small area and irradiate a large-area detector. In an IGCT system, x-ray sources are distributed over a large area, with each beam irradiating a small-area detector. Therefore, in the inverse geometry, a series of narrow x-ray beams are switched on and off while the gantry rotates. In conventional CT geometry, cone-beam and scatter artifacts increase with the imaged volume thickness. An inverse geometry may be less susceptible to scatter effects, because only a fraction of the field of view is irradiated at one time. The distributed source in the inverse geometry potentially improves sampling, leading to reduced cone-beam artifacts. In the inverse geometry, the tube current may be adjusted separately for each source location, which potentially reduces dose. Multiple IGCT prototypes have been constructed and tested on phantoms. A gantry-based IGCT system with one-second gantry rotation was developed, and images of phantoms and small animals were successfully acquired. Clinical feasibility with acceptable noise levels and scan times has not yet been shown. Overall, results from prototype systems suggest that the inverse geometry will enable imaging of a thick volume (∼16 cm) while potentially reducing cone-beam artifacts, scatter effects, and radiation dose. The magnitude of these benefits will depend on the specific IGCT implementation and need to be quantified relative to comparable multislice scanners. Copyright © 2011 Society of Cardiovascular Computed Tomography. Published by Elsevier Inc. All rights reserved.

  3. 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.

  4. Twisted geometries, twistors, and conformal transformations

    NASA Astrophysics Data System (ADS)

    Lângvik, Miklos; Speziale, Simone

    2016-07-01

    The twisted geometries of spin network states are described by simple twistors, isomorphic to null twistors with a timelike direction singled out. The isomorphism depends on the Immirzi parameter γ and reduces to the identity for γ =∞ . Using this twistorial representation, we study the action of the conformal group SU(2,2) on the classical phase space of loop quantum gravity, described by twisted geometry. The generators of translations and conformal boosts do not preserve the geometric structure, whereas the dilatation generator does. It corresponds to a one-parameter family of embeddings of T*SL(2,C) in twistor space, and its action preserves the intrinsic geometry while changing the extrinsic one—that is the boosts among polyhedra. We discuss the implication of this action from a dynamical point of view and compare it with a discretization of the dilatation generator of the continuum phase space, given by the Lie derivative of the group character. At leading order in the continuum limit, the latter reproduces the same transformation of the extrinsic geometry, while also rescaling the areas and volumes and preserving the angles associated with the intrinsic geometry. Away from the continuum limit, its action has an interesting nonlinear structure but is in general incompatible with the closure constraint needed for the geometric interpretation. As a side result, we compute the precise relation between the extrinsic geometry used in twisted geometries and the one defined in the gauge-invariant parametrization by Dittrich and Ryan and show that the secondary simplicity constraints they posited coincide with those dynamically derived in the toy model of [Classical Quantum Gravity 32, 195015 (2015)].

  5. 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

  6. Topology Changing Transitions in Bubbling Geometries

    SciTech Connect

    Horava, Petr; Shepard, Peter G.

    2005-02-15

    Topological transitions in bubbling half-BPS Type IIB geometries with SO(4) x SO(4) symmetry can be decomposed into a sequence of n elementary transitions. The half-BPS solution that describes the elementary transition is seeded by a phase space distribution of fermions filling two diagonal quadrants. We study the geometry of this solution in some detail. We show that this solution can be interpreted as a time dependent geometry, interpolating between two asymptotic pp-waves in the far past and the far future. The singular solution at the transition can be resolved in two different ways, related by the particle-hole duality in the effective fermion description. Some universal features of the topology change are governed by two-dimensional Type 0B string theory, whose double scaling limit corresponds to the Penrose limit of AdS_5 x S5 at topological transition. In addition, we present the full class of geometries describing the vicinity of the most general localized classical singularity that can occur in this class of half-BPS bubbling geometries.

  7. Topology Changing Transitions in Bubbling Geometries

    SciTech Connect

    Horava, Petr; Shepard, Peter G.

    2005-02-15

    Topological transitions in bubbling half-BPS Type IIB geometries with SO(4) x SO(4) symmetry can be decomposed into a sequence of n elementary transitions. The half-BPS solution that describes the elementary transition is seeded by a phase space distribution of fermions filling two diagonal quadrants. We study the geometry of this solution in some detail. We show that this solution can be interpreted as a time dependent geometry, interpolating between two asymptotic pp-waves in the far past and the far future. The singular solution at the transition can be resolved in two different ways, related by the particle-hole duality in the effective fermion description. Some universal features of the topology change are governed by two-dimensional Type 0B string theory, whose double scaling limit corresponds to the Penrose limit of AdS_5 x S^5 at topological transition. In addition, we present the full class of geometries describing the vicinity of the most general localized classical singularity that can occur in this class of half-BPS bubbling geometries.

  8. GEMPAK: An arbitrary aircraft geometry generator

    NASA Technical Reports Server (NTRS)

    Stack, S. H.; Edwards, C. L. W.; Small, W. J.

    1977-01-01

    A computer program, GEMPAK, has been developed to aid in the generation of detailed configuration geometry. The program was written to allow the user as much flexibility as possible in his choices of configurations and the detail of description desired and at the same time keep input requirements and program turnaround and cost to a minimum. The program consists of routines that generate fuselage and planar-surface (winglike) geometry and a routine that will determine the true intersection of all components with the fuselage. This paper describes the methods by which the various geometries are generated and provides input description with sample input and output. Also included are descriptions of the primary program variables and functions performed by the various routines. The FORTRAN program GEMPAK has been used extensively in conjunction with interfaces to several aerodynamic and plotting computer programs and has proven to be an effective aid in the preliminary design phase of aircraft configurations.

  9. Geometry optimization of branchings in vascular networks

    NASA Astrophysics Data System (ADS)

    Khamassi, Jamel; Bierwisch, Claas; Pelz, Peter

    2016-06-01

    Progress has been made in developing manufacturing technologies which enable the fabrication of artificial vascular networks for tissue cultivation. However, those networks are rudimentary designed with respect to their geometry. This restricts long-term biological functionality of vascular cells which depends on geometry-related fluid mechanical stimuli and the avoidance of vessel occlusion. In the present work, a bioinspired geometry optimization for branchings in artificial vascular networks has been conducted. The analysis could be simplified by exploiting self-similarity properties of the system. Design rules in the form of two geometrical parameters, i.e., the branching angle and the radius ratio of the daughter branches, are derived using the wall shear stress as command variable. The numerical values of these parameters are within the range of experimental observations. Those design rules are not only beneficial for tissue engineering applications. Moreover, they can be used as indicators for diagnoses of vascular diseases or for the layout of vascular grafts.

  10. 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.

  11. 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.

  12. 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.

  13. Novel nanophotonics geometries for sensing applications

    NASA Astrophysics Data System (ADS)

    Smolyaninov, Igor I.; Davis, Christopher C.

    2004-10-01

    We describe our latest experimental and theoretical results on two promising nanophotonics geometries for sensor applications. These geometries are based on various combinations of nanohole and/or microdroplet arrays on the surfaces of metal films which support propagation of surface plasmon-polaritons. These novel geometries exhibit large enhancements of local electromagnetic field, which can be used in various nonlinear optical sensing arrangements. For example, liquid microdroplets on the gold film surface support surface plasmon whispering gallery modes. Local field enhancement due to excitation of such modes is determined by combination of both cavity electrodynamics and surface plasmon-polariton related effects. In addition, individual microdroplets have interesting imaging properties, which may be used in high-resolution visualization of individual viruses and cells.

  14. Remarks on Contact and Jacobi Geometry

    NASA Astrophysics Data System (ADS)

    Bruce, Andrew James; Grabowska, Katarzyna; Grabowski, Janusz

    2017-07-01

    We present an approach to Jacobi and contact geometry that makes many facts, presented in the literature in an overcomplicated way, much more natural and clear. The key concepts are Kirillov manifolds and linear Kirillov structures, i.e., homogeneous Poisson manifolds and, respectively, homogeneous linear Poisson manifolds. The difference with the existing literature is that the homogeneity of the Poisson structure is related to a principal GL(1,R)-bundle structure on the manifold and not just to a vector field. This allows for working with Jacobi bundle structures on nontrivial line bundles and drastically simplifies the picture of Jacobi and contact geometry. Our results easily reduce to various basic theorems of Jacobi and contact geometry when the principal bundle structure is trivial, while giving new insights into the theory.

  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. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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…

  1. 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…

  2. 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…

  3. 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…

  4. Performance on Middle School Geometry Problems with Geometry Clues Matched to Three Different Cognitive Styles

    ERIC Educational Resources Information Center

    Anderson, Karen L.; Casey, M. Beth; Thompson, William L.; Burrage, Marie S.; Pezaris, Elizabeth; Kosslyn, Stephen M.

    2008-01-01

    This study investigated the relationship between 3 ability-based cognitive styles (verbal deductive, spatial imagery, and object imagery) and performance on geometry problems that provided different types of clues. The purpose was to determine whether students with a specific cognitive style outperformed other students, when the geometry problems…

  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. 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.

  7. Fields and Laplacians on Quantum Geometries

    NASA Astrophysics Data System (ADS)

    Thürigen, Johannes

    2015-01-01

    In fundamentally discrete approaches to quantum gravity such as loop quantum gravity, spin-foam models, group field theories or Regge calculus observables are functions on discrete geometries. We present a bra-ket formalism of function spaces and discrete calculus on abstract simplicial complexes equipped with geometry and apply it to the mentioned theories of quantum gravity. In particular we focus on the quantum geometric Laplacian and discuss as an example the expectation value of the heat kernel trace from which the spectral dimension follows.

  8. 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.

  9. 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.

  10. Path Deviation Equations in AP-Geometry

    NASA Astrophysics Data System (ADS)

    Wanas, M. I.; Kahil, M. E.

    2006-02-01

    Recently, it has been shown that Absolute Parallelism (AP) geometry admits paths that are naturally quantized. These paths have been used to describe the motion of spinning particles in a background gravitational field. In case of a weak static gravitational field limits, the paths are applied successfully to interpret the discrepancy in the motion of thermal neutrons in the Earth's gravitational field (COW-experiment). The aim of the present work is to explore the properties of the deviation equations corresponding to these paths. In the present work the deviation equations are derived and compared to the geodesic deviation equation of the Riemannian geometry.

  11. Computational fluid dynamics using CATIA created geometry

    SciTech Connect

    Gengler, J.E.

    1989-01-01

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

  12. 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.

  13. 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.

  14. 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.

  15. 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.

  16. Information geometry and the renormalization group.

    PubMed

    Maity, Reevu; Mahapatra, Subhash; Sarkar, Tapobrata

    2015-11-01

    Information theoretic geometry near critical points in classical and quantum systems is well understood for exactly solvable systems. Here, we show that renormalization group flow equations can be used to construct the information metric and its associated quantities near criticality for both classical and quantum systems in a universal manner. We study this metric in various cases and establish its scaling properties in several generic examples. Scaling relations on the parameter manifold involving scalar quantities are studied, and scaling exponents are identified. The meaning of the scalar curvature and the invariant geodesic distance in information geometry is established and substantiated from a renormalization group perspective.

  17. 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.

  18. 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…

  19. 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.

  20. 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…

  1. 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…

  2. 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.

  3. From Circle to Hyperbola in Taxicab Geometry

    ERIC Educational Resources Information Center

    Berger, Ruth I.

    2015-01-01

    This "Activity for Students" article presents a taxicab geometry problem that engages students in plotting points and observing surprising shapes and underlining reasons for the appearance of figures when working with street grids. With this activity, teachers can provide an extra challenge by writing additional problems introducing a…

  4. 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…

  5. 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)

  6. The Convex Geometry of Linear Inverse Problems

    DTIC Science & Technology

    2010-12-02

    equator. Via elementary trigonometry , the solid angle that K subtends is given by π/2− sin−1(h). Hence, if h(β) is the largest number such that β caps of...1107–1130. [34] Harris, J., Algebraic Geometry: A First Course . Springer. [35] Haupt, J., Bajwa, W., Raz, G., and Nowak, R. (2008). Toeplitz

  7. 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)

  8. 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…

  9. 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…

  10. On the Geometry of Constant Returns.

    ERIC Educational Resources Information Center

    Jehle, Geoffrey A.

    2002-01-01

    States that often constant returns to scale are also much more and that many important results depend on the very special properties of this class of production function. Offers a unified set of simple proofs, employing only familiar diagrams and high school geometry, for most of the crucial analytical properties of constant returns production.…

  11. Reshaping Mathematics for Understanding Motion Geometry.

    ERIC Educational Resources Information Center

    Slovin, Hannah; Venenciano, Linda; Ishihara, Melanie; Beppu, Cynthia

    This book introduces concepts of geometry that students use throughout middle-grade and higher-level mathematics courses. These concepts, presented through the study of transformations, provide a framework for other important topics such as number, measurement, proportional reasoning, and graphing on the coordinate plane. The book is designed for…

  12. 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)

  13. 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,…

  14. 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…

  15. 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…

  16. 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…

  17. 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.

  18. 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…

  19. 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.

  20. 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…

  1. 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…

  2. 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.

  3. 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.

  4. 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)

  5. 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…

  6. 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.

  7. 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)

  8. 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.

  9. 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…

  10. 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.

  11. Quilts and Tangrams: Linking Literature and Geometry.

    ERIC Educational Resources Information Center

    Bohning, Gerry; Williams, Rebecca

    1997-01-01

    Suggests that by making quilt squares with tangrams, children link geometry and children's literature. Provides background on quilts and tangrams, and provides guidelines for teachers. Points out that children gain communication and mathematical thinking skills as they manipulate and explore relationships among pieces. Contains an annotated…

  12. 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;…

  13. 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…

  14. 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,…

  15. Magnetic resonance spectra and statistical geometry

    USDA-ARS?s Scientific Manuscript database

    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...

  16. On the granular stress-geometry equation

    NASA Astrophysics Data System (ADS)

    DeGiuli, Eric; Schoof, Christian

    2014-01-01

    Using discrete calculus, we derive the missing stress-geometry equation for rigid granular materials in two dimensions, in the mean-field approximation. We show that i) the equation imposes that the voids cannot carry stress, ii) stress transmission is generically elliptic and has a quantitative relation to anisotropic elasticity, and iii) the packing fabric plays an essential role.

  17. 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…

  18. 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;…

  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. Determining Fault Geometries From Surface Displacements

    NASA Astrophysics Data System (ADS)

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

    2017-04-01

    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

  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. 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…

  3. 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.…

  4. 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.…

  5. From geometry to algebra and vice versa: Realistic mathematics education principles for analyzing geometry tasks

    NASA Astrophysics Data System (ADS)

    Jupri, Al

    2017-04-01

    In this article we address how Realistic Mathematics Education (RME) principles, including the intertwinement and the reality principles, are used to analyze geometry tasks. To do so, we carried out three phases of a small-scale study. First we analyzed four geometry problems - considered as tasks inviting the use of problem solving and reasoning skills - theoretically in the light of the RME principles. Second, we tested two problems to 31 undergraduate students of mathematics education program and other two problems to 16 master students of primary mathematics education program. Finally, we analyzed student written work and compared these empirical to the theoretical results. We found that there are discrepancies between what we expected theoretically and what occurred empirically in terms of mathematization and of intertwinement of mathematical concepts from geometry to algebra and vice versa. We conclude that the RME principles provide a fruitful framework for analyzing geometry tasks that, for instance, are intended for assessing student problem solving and reasoning skills.

  6. 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

  7. Impacts of Conformational Geometries in Fluorinated Alkanes.

    PubMed

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

    2016-08-16

    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.

  8. 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

  9. 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.

  10. 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.

  11. 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.

  12. Tectonic wedges: geometry and kinematic interpretation

    NASA Astrophysics Data System (ADS)

    Martinez-Torres, L. M.; Ramon-Lluch, R.; Eguiluz, L.

    1994-10-01

    The geometry of several tectonic wedge combinations was studied in an outcrop in the Basque Basin, Western Pyrenees. Three types of tectonic wedges were distinguished: simple, double and triple wedge. On the surface the geometry of the observed tectonic wedges is always highly elemental: emergent thrust, horse or klippe. The final stage in the evolution of a tectonic wedge is its delamination. This can occur by the spreading of the thrusts which conform the wedge, or by the development of back thrusts associated to them. The relative age of the back thrust with respect to the thrust indicates whether the original structure was a simple thrust or a tectonic wedge. If this criterion is applied to the Pyrenean Orogen, this range corresponds to a tectonic wedge.

  13. Stages as models of scene geometry.

    PubMed

    Nedović, Vladimir; Smeulders, Arnold W M; Redert, André; Geusebroek, Jan-Mark

    2010-09-01

    Reconstruction of 3D scene geometry is an important element for scene understanding, autonomous vehicle and robot navigation, image retrieval, and 3D television. We propose accounting for the inherent structure of the visual world when trying to solve the scene reconstruction problem. Consequently, we identify geometric scene categorization as the first step toward robust and efficient depth estimation from single images. We introduce 15 typical 3D scene geometries called stages, each with a unique depth profile, which roughly correspond to a large majority of broadcast video frames. Stage information serves as a first approximation of global depth, narrowing down the search space in depth estimation and object localization. We propose different sets of low-level features for depth estimation, and perform stage classification on two diverse data sets of television broadcasts. Classification results demonstrate that stages can often be efficiently learned from low-dimensional image representations.

  14. Non-local geometry inside Lifshitz horizon

    NASA Astrophysics Data System (ADS)

    Hu, Qi; Lee, Sung-Sik

    2017-07-01

    Based on the quantum renormalization group, we derive the bulk geometry that emerges in the holographic dual of the fermionic U( N ) vector model at a nonzero charge density. The obstruction that prohibits the metallic state from being smoothly deformable to the direct product state under the renormalization group flow gives rise to a horizon at a finite radial coordinate in the bulk. The region outside the horizon is described by the Lifshitz geometry with a higher-spin hair determined by microscopic details of the boundary theory. On the other hand, the interior of the horizon is not described by any Riemannian manifold, as it exhibits an algebraic non-locality. The non-local structure inside the horizon carries the information on the shape of the filled Fermi sea.

  15. 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.

  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. 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.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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

  3. 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.

  4. 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.

  5. Geometry-driven photorealistic facial expression synthesis.

    PubMed

    Zhang, Qingshan; Liu, Zicheng; Guo, Baining; Terzopoulos, Demetri; Shum, Heung-Yeung

    2006-01-01

    Expression mapping (also called performance driven animation) has been a popular method for generating facial animations. A shortcoming of this method is that it does not generate expression details such as the wrinkles due to skin deformations. In this paper, we provide a solution to this problem. We have developed a geometry-driven facial expression synthesis system. Given feature point positions (the geometry) of a facial expression, our system automatically synthesizes a corresponding expression image that includes photorealistic and natural looking expression details. Due to the difficulty of point tracking, the number of feature points required by the synthesis system is, in general, more than what is directly available from a performance sequence. We have developed a technique to infer the missing feature point motions from the tracked subset by using an example-based approach. Another application of our system is expression editing where the user drags feature points while the system interactively generates facial expressions with skin deformation details.

  6. Laplacians on discrete and quantum geometries

    NASA Astrophysics Data System (ADS)

    Calcagni, Gianluca; Oriti, Daniele; Thürigen, Johannes

    2013-06-01

    We extend discrete calculus for arbitrary (p-form) fields on embedded lattices to abstract discrete geometries based on combinatorial complexes. We then provide a general definition of discrete Laplacian using both the primal cellular complex and its combinatorial dual. The precise implementation of geometric volume factors is not unique and, comparing the definition with a circumcentric and a barycentric dual, we argue that the latter is, in general, more appropriate because it induces a Laplacian with more desirable properties. We give the expression of the discrete Laplacian in several different sets of geometric variables, suitable for computations in different quantum gravity formalisms. Furthermore, we investigate the possibility of transforming from position to momentum space for scalar fields, thus setting the stage for the calculation of heat kernel and spectral dimension in discrete quantum geometries.

  7. Determining fault geometries from surface displacements

    NASA Astrophysics Data System (ADS)

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

    2016-12-01

    We study in this paper a half space linear elasticity model for surface displacements caused by slip along underground faults. We prove uniqueness of the fault location and (piecewise planar) geometry and of the slip field for a given surface displacement field.We then introduce a reconstruction algorithm for the realistic case where only a finite number of surface measurements are available.After showing how this algorithm performs on simulated data and assessing the effect of noise, we apply it to measured data. The data was recorded during slow slip events in Guerrero, Mexico. Since this is a well studied subduction zone, it is possible to compareour inferred fault geometry to other reconstructions (obtained using different techniques), found in the literature.

  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. 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.

  10. The spectrum of static subtracted geometries

    NASA Astrophysics Data System (ADS)

    Andrade, Tomás; Castro, Alejandra; Cohen-Maldonado, Diego

    2017-05-01

    Subtracted geometries are black hole solutions of the four dimensional STU model with rather interesting ties to asymptotically flat black holes. A peculiar feature is that the solutions to the Klein-Gordon equation on this subtracted background can be organized according to representations of the conformal group SO(2, 2). We test if this behavior persists for the linearized fluctuations of gravitational and matter fields on static, electrically charged backgrounds of this kind. We find that there is a subsector of the modes that do display conformal symmetry, while some modes do not. We also discuss two different effective actions that describe these subtracted geometries and how the spectrum of quasinormal modes is dramatically different depending upon the action used.

  11. 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)

  12. Casimir energies of cavities: The geometry question

    NASA Astrophysics Data System (ADS)

    Abalo, Iroko Komi Elom

    The question of how the Casimir effect relates to a system's geometry is of fundamental interest. In this thesis, we present new results for interior Casimir self-energies of various integrable geometries and show interesting systematic relations between these energies. In particular, we consider prisms with triangular cross sections (equilateral, hemiequilateral, and right isosceles triangles), triangular polygons of the same cross sections, and three tetrahedra. The triangular prisms are of infinite or finite lengths. These geometries are integrable and unique in the sense that the Laplacian eigenvalues may be found using the method of images. We obtain interior Casimir energies for these cavities subject to Dirichlet and Neumann boundary conditions. In addition to these boundary conditions, we also obtain electromagnetic Casimir energies for the infinite prisms. These energies are regularized using various consistent methods, one of which is regularization by point-splitting. Summing these modes explicitly using a cylinder kernel formulation, we show that the correct Weyl divergences are obtained. We also give closed-form results for the infinite triangular prisms. In order to understand the geometry dependence of these energies, we rederive well-known results for rectangular parallelepipeds (including the cube) and infinite rectangular prisms. The analysis of these self-energies yields intriguing results. By plotting the scaled energies against the appropriately chosen isoperimetric or isoareal quotients, we observe interesting patterns, which hint towards a systematic functional dependence. In addition to the calculation of new Casimir energies, this constitutes a significant contribution to the theoretical understanding of self-energies and has interesting implications.

  13. 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.

  14. Scaling of Entanglement Entropy and Hyperbolic Geometry

    NASA Astrophysics Data System (ADS)

    Matsueda, Hiroaki

    2013-09-01

    Various scaling relations of the entanglement entropy are reviewed. Based on the scaling, I would like to point out similarity of mathematical formulation among recent topics in wide research area. In particular, the scaling plays crucial roles in identifying a quantum system with a physically different classical system. Close connection between the scaling and hyperbolic geometry and contrast between bulk/edge correspondence and compactification for the identification are also addressed.

  15. Orientifolds of matrix theory and noncommutative geometry

    NASA Astrophysics Data System (ADS)

    Kim, Nakwoo

    1999-06-01

    We study explicit solutions for orientifolds of matrix theory compactified on a noncommutative torus. As quotients of the torus, a cylinder, Klein bottle, and Möbius strip are applicable as orientifolds. We calculate the solutions using the Connes-Douglas-Schwarz projective module solution, and investigate the twisted gauge bundle on quotient spaces as well. These solutions are of Yang-Mills theory on a noncommutative torus with proper boundary conditions which define the geometry of the dual space.

  16. Gyrokinetic Simulations of Microinstabilities in Stellarator Geometry

    SciTech Connect

    J.L.V. Lewandowski

    2003-08-29

    A computational study of microinstabilities in general geometry is presented. The ion gyrokinetic is solved as an initial value problem. The advantage of this approach is the accurate treatment of some important kinetic effects. The magnetohydrodynamic equilibrium is obtained from a three-dimensional local equilibrium model. The use of a local magnetohydrodynamic equilibrium model allows for a computationally-efficient systematic study of the impact of the magnetic structure on microinstabilities.

  17. Sheared-flow Modes in Toroidal Geometry

    SciTech Connect

    J.L.V. Lewandowski; T.S. Hahm; W.W. Lee; Z. Lin

    1999-10-01

    Using a Fourier-Bessel representation for the fluctuating (turbulent) electrostatic potential, an equation governing the sheared-flow modes in toroidal geometry is derived from the gyrokinetic Poisson equation, where both the adiabatic and non-adiabatic responses of the electrons are taken into account. It is shown that the principal geometrical effect on sheared-flow modes of the electrostatic potential is due to the flux-surface average of 1/B, where B is the magnetic field strength.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. 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.

  3. 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.

  4. 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.

  5. Spallation Damage Experiments in Cylindrical Geometry

    DTIC Science & Technology

    2005-06-01

    calculation after the onset of damage suspect. Figure 3. Calculated velocity (m/s) of liner to target impact as a function of radius (m). Figure...SPALLATION DAMAGE EXPERIMENTS IN CYLINDRICAL GEOMETRY Ann M. Kaul Los Alamos National Laboratory, P.O. Box 1663, MS-B259 Los Alamos, NM 87544...USA) Abstract Spallation damage is the process of damage in a ductile material caused by void nucleation, growth and coalescence due to

  6. 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.

  7. 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

  8. 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.

  9. Electrodynamics and spacetime geometry: Astrophysical applications

    NASA Astrophysics Data System (ADS)

    Cabral, Francisco; Lobo, Francisco S. N.

    2017-07-01

    After a brief review of the foundations of (pre-metric) electromagnetism, we explore some physical consequences of electrodynamics in curved spacetime. In general, new electromagnetic couplings and related phenomena are induced by the spacetime curvature. The applications of astrophysical interest considered here correspond essentially to the following geometries: the Schwarzschild spacetime and the spacetime around a rotating spherical mass in the weak field and slow rotation regime. In the latter, we use the Parameterised Post-Newtonian (PPN) formalism. We also explore the hypothesis that the electric and magnetic properties of vacuum reflect the spacetime isometries. Therefore, the permittivity and permeability tensors should not be considered homogeneous and isotropic a priori. For spherical geometries we consider the effect of relaxing the homogeneity assumption in the constitutive relations between the fields and excitations. This affects the generalized Gauss and Maxwell-Ampère laws, where the electric permittivity and magnetic permeability in vacuum depend on the radial coordinate in accordance with the local isometries of space. For the axially symmetric geometries we relax both the assumptions of homogeneity and isotropy. We explore simple solutions and discuss the physical implications related to different phenomena, such as the decay of electromagnetic fields in the presence of gravity, magnetic terms in Gauss law due to the gravitomagnetism of the spacetime around rotating objects, a frame-dragging effect on electric fields and the possibility of a spatial (radial) variability of the velocity of light in vacuum around spherical astrophysical objects for strong gravitational fields.

  10. Managing search complexity in linguistic geometry.

    PubMed

    Stilman, B

    1997-01-01

    This paper is a new step in the development of linguistic geometry. This formal theory is intended to discover and generalize the inner properties of human expert heuristics, which have been successful in a certain class of complex control systems, and apply them to different systems. In this paper, we investigate heuristics extracted in the form of hierarchical networks of planning paths of autonomous agents. Employing linguistic geometry tools the dynamic hierarchy of networks is represented as a hierarchy of formal attribute languages. The main ideas of this methodology are shown in the paper on two pilot examples of the solution of complex optimization problems. The first example is a problem of strategic planning for the air combat, in which concurrent actions of four vehicles are simulated as serial interleaving moves. The second example is a problem of strategic planning for the space comb of eight autonomous vehicles (with interleaving moves) that requires generation of the search tree of the depth 25 with the branching factor 30. This is beyond the capabilities of modern and conceivable future computers (employing conventional approaches). In both examples the linguistic geometry tools showed deep and highly selective searches in comparison with conventional search algorithms. For the first example a sketch of the proof of optimality of the solution is considered.

  11. Dynamics and geometry near resonant bifurcations

    NASA Astrophysics Data System (ADS)

    Broer, Henk W.; Holtman, Sijbo J.; Vegter, Gert; Vitolo, Renato

    2011-02-01

    This paper provides an overview of the universal study of families of dynamical systems undergoing a Hopf-Neĭmarck-Sacker bifurcation as developed in [1-4]. The focus is on the local resonance set, i.e., regions in parameter space for which periodic dynamics occurs. A classification of the corresponding geometry is obtained by applying Poincaré-Takens reduction, Lyapunov-Schmidt reduction and contact-equivalence singularity theory, equivariant under an appropriate cyclic group. It is a classical result that the local geometry of these sets in the nondegenerate case is given by an Arnol'd resonance tongue. In a mildly degenerate situation a more complicated geometry given by a singular perturbation of a Whitney umbrella is encountered. Our approach also provides a skeleton for the local resonant Hopf-Neĭmarck-Sacker dynamics in the form of planar Poincaré-Takens vector fields. To illustrate our methods a leading example is used: A periodically forced generalized Duffing-Van der Pol oscillator.

  12. 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.

  13. 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.

  14. Mapping the internal geometry of tactile space.

    PubMed

    Longo, Matthew R; Golubova, Olga

    2017-10-01

    A large body of research has shown spatial distortions in the perception of tactile distances on the skin. For example, perceived tactile distance is increased on sensitive compared to less sensitive skin regions, and larger for stimuli oriented along the medio-lateral axis than the proximo-distal axis of the limbs. In this study we aimed to investigate the spatial coherence of these distortions by reconstructing the internal geometry of tactile space using multidimensional scaling (MDS). Participants made verbal estimates of the perceived distance between 2 touches applied sequentially to locations on their left hand. In Experiment 1 we constructed perceptual maps of the dorsum of the left hand, which showed a good fit to the actual configuration of stimulus locations. Critically, these maps also showed clear evidence of spatial distortion, being stretched along the medio-lateral hand axis. Experiment 2 replicated this result and showed that no such distortion is apparent on the palmar surface of the hand. These results show that distortions in perceived tactile distance can be characterized by geometrically simple and coherent deformations of tactile space. We suggest that the internal geometry of tactile space is shaped by the geometry of receptive fields in somatosensory cortex. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

  15. Interactions between pool geometry and hydraulics

    USGS Publications Warehouse

    Thompson, D.M.; Nelson, J.M.; Wohl, E.E.

    1998-01-01

    An experimental and computational research approach was used to determine interactions between pool geometry and hydraulics. A 20-m-long, 1.8-m-wide flume was used to investigate the effect of four different geometric aspects of pool shape on flow velocity. Plywood sections were used to systematically alter constriction width, pool depth, pool length, and pool exit-slope gradient, each at two separate levels. Using the resulting 16 unique geometries with measured pool velocities in four-way factorial analyses produced an empirical assessment of the role of the four geometric aspects on the pool flow patterns and hence the stability of the pool. To complement the conclusions of these analyses, a two-dimensional computational flow model was used to investigate the relationships between pool geometry and flow patterns over a wider range of conditions. Both experimental and computational results show that constriction and depth effects dominate in the jet section of the pool and that pool length exhibits an increasing effect within the recirculating-eddy system. The pool exit slope appears to force flow reattachment. Pool length controls recirculating-eddy length and vena contracta strength. In turn, the vena contracta and recirculating eddy control velocities throughout the pool.

  16. 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.

  17. 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.

  18. 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

  19. 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

  20. 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

  1. The Investigating Spirit: Resurrection in the Geometry Classroom.

    ERIC Educational Resources Information Center

    Blanton, F. Lamar

    1981-01-01

    Although traditional instructional methods and textbooks mitigate against it, investigation can be a viable alternative strategy in the geometry classroom. Many theorems in geometry, such as Euclidean space, lend themselves easily to student experimentation. (Author/SJL)

  2. 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.

  3. Characterizing student mathematics teachers' levels of understanding in spherical geometry

    NASA Astrophysics Data System (ADS)

    Guven, Bulent; Baki, Adnan

    2010-12-01

    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 mathematics teachers at particular times through the course to determine the spherical geometry learning levels. After identifying the properties of spherical geometry levels, we developed Understandings in Spherical Geometry Test to test whether or not the levels form hierarchy, and 58 student mathematics teachers took the test. The outcomes seemed to support our theoretical perspective that there are some understanding levels in spherical geometry that progress through a hierarchical order as van Hiele levels in Euclidean 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. Using Geometry Description Markup Language to store the geometry of FNAL E-906

    NASA Astrophysics Data System (ADS)

    Hague, Tyler

    2009-10-01

    The primary goal of FNAL E-906 is to investigate the ratio of d(bar)/u(bar) in the nucleon sea. To do this, the Drell-Yan cross section ratio will be measured in proton-proton and proton-deuterium collisions. FNAL E-906 is utilizing Geometry Description Markup Language (GDML) to describe the geometry of the spectrometer. GDML is capable of describing the spectrometer in great detail and is fully functional with GEANT4 and ROOT. By using this we will have a common geometry input for all of our software codes including two Monte Carlo simulations, primary data analysis code, and a ROOT-based event display. The use of such a language creates the need for an easy way to read it and extract data, as well as to update the geometry when changes are made. A tool has been developed to convert a GDML file into an experiment-specific, easy to read ASCII file. Another tool is in development to create a simple interface to update a GDML file without knowledge of the language. These tools use ROOT's geometry tree to traverse the volumes described in GDML. This poster will describe the advantages of using GDML and its implementation.

  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. Surface grid generation for complex three-dimensional geometries

    NASA Technical Reports Server (NTRS)

    Luh, Raymond Ching-Chung

    1988-01-01

    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 base 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.

  8. 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

  9. Surface grid generation for complex three-dimensional geometries

    NASA Technical Reports Server (NTRS)

    Luh, Raymond Ching-Chung

    1988-01-01

    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.

  10. Femoral articular geometry and patellofemoral stability.

    PubMed

    Iranpour, Farhad; Merican, Azhar M; Teo, Seow Hui; Cobb, Justin P; Amis, Andrew A

    2017-06-01

    Patellofemoral instability is a major cause of anterior knee pain. The aim of this study was to examine how the medial and lateral stability of the patellofemoral joint in the normal knee changes with knee flexion and measure its relationship to differences in femoral trochlear geometry. Twelve fresh-frozen cadaveric knees were used. Five components of the quadriceps and the iliotibial band were loaded physiologically with 175N and 30N, respectively. The force required to displace the patella 10mm laterally and medially at 0°, 20°, 30°, 60° and 90° knee flexion was measured. Patellofemoral contact points at these knee flexion angles were marked. The trochlea cartilage geometry at these flexion angles was visualized by Computed Tomography imaging of the femora in air with no overlying tissue. The sulcus, medial and lateral facet angles were measured. The facet angles were measured relative to the posterior condylar datum. The lateral facet slope decreased progressively with flexion from 23°±3° (mean±S.D.) at 0° to 17±5° at 90°. While the medial facet angle increased progressively from 8°±8° to 36°±9° between 0° and 90°. Patellar lateral stability varied from 96±22N at 0°, to 77±23N at 20°, then to 101±27N at 90° knee flexion. Medial stability varied from 74±20N at 0° to 170±21N at 90°. There were significant correlations between the sulcus angle and the medial facet angle with medial stability (r=0.78, p<0.0001). These results provide objective evidence relating the changes of femoral profile geometry with knee flexion to patellofemoral stability. Copyright © 2017 Elsevier B.V. All rights reserved.

  11. 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

  12. 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

  13. 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.

  14. 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…

  15. 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…

  16. 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…

  17. 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.…

  18. 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…

  19. The fractal forest: fractal geometry and applications in forest science.

    Treesearch

    Nancy D. Lorimer; Robert G. Haight; Rolfe A. Leary

    1994-01-01

    Fractal geometry is a tool for describing and analyzing irregularity. Because most of what we measure in the forest is discontinuous, jagged, and fragmented, fractal geometry has potential for improving the precision of measurement and description. This study reviews the literature on fractal geometry and its applications to forest measurements.

  20. 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…

  1. 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…

  2. Flips, Turns, and Tessellations: Teaching Geometry with Logo.

    ERIC Educational Resources Information Center

    Pereira, Peter

    Some mathematics educators feel that too little geometry is taught in elementary schools. This may have serious effects as many students arrive in the traditional high school geometry course without essential backgrounds in informal geometry. The result of this lack of preparation is often lower scores on standardized tests. In this situation,…

  3. 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.…

  4. 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…

  5. 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…

  6. 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.

  7. The NASA-IGES geometry data visualizer

    NASA Technical Reports Server (NTRS)

    Blake, Matthew W.; Jasinskyj, Lonhyn; Chou, Jin J.

    1992-01-01

    NIGESview, an interactive software tool for reading, viewing, and translating geometry data available in the Initial Graphics Exchange Specification (IGES) format, is described. NIGESview is designed to read a variety of IGES entities, translate some of the entities, graphically view the data, and output a file in a specific IGES format. The software provides a modern graphical user interface and is designed in a modular fashion so developers can utilize all or part of the code in their grid generation software for computational fluid dynamics.

  8. 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.

  9. Reactive-infiltration instability in radial geometry

    NASA Astrophysics Data System (ADS)

    Grodzki, Piotr; Szymczak, Piotr

    2015-04-01

    A planar dissolution front propagating through a homogeneous porous matrix is unstable with respect to small variations in local permeability; regions of high permeability dissolve faster because of enhanced transport of reactants, which leads to increased rippling of the front. This phenomenon, usually referred to known as reactive-infiltration instability is an important mechanism for pattern development in geology, with a range of morphologies and scales, from cave systems running for hundreds of miles to laboratory acidization on the scale of centimeters. In general, this instability is characterized by two length scales: the diffusive length (D/v) and the reactant penetration length (v/r), where v is the Darcy velocity, D - the diffusion constant and r - the dissolution rate. If the latter scale is much smaller than the former one can adopt the so-called thin front limit, where the interface is treated as a discontinuity in porosity, with a completely dissolved phase on one side and an undissolved phase on the other. Linear stability analysis for this case has been carried out by Chadam et al. [1], and the corresponding dispersion relation shows that long wavelengths are unstable, whereas short wavelengths are stabilized by diffusion. In their derivation, Chadam et al. have considered a linear geometry with a uniform pressure gradient applied along one of the directions. However, in many cases (e.g. in the acidization techniques used in oil industry) the reactive fluids are injected through a well and thus the relevant geometry is radial rather than linear. Motivated by this, we have carried out the linear stability analysis of the reactive-infiltration problem in radial geometry, with the fluid injection at the centre of the system. We stay within the thin-front limit and derive the corresponding dispersion relation, which shows the stable regions for both the long-wavelength and short-wavelength modes, and the unstable region in between. Next, we study how

  10. 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

  11. Metamaterial electromagnetic concentrators with arbitrary geometries.

    PubMed

    Yang, Jingjing; Huang, Ming; Yang, Chengfu; Xiao, Zhe; Peng, Jinhui

    2009-10-26

    The electromagnetic concentrators play an important role in the harnessing of light in solar cells or similar devices, where high field intensities are required. The material parameters for two-dimensional (2D) metamaterial-assisted electromagnetic concentrators with arbitrary geometries are derived based on transformation-optical approach. Enhancements in field intensities of the 2D concentrator have been shown by full-wave simulation. All theoretical and numerical results validate the material parameters for the 2D concentrator with irregular cross section we developed.

  12. 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.

  13. The Local Geometry of Multiattribute Tradeoff Preferences

    PubMed Central

    McGeachie, Michael; Doyle, Jon

    2011-01-01

    Existing representations for multiattribute ceteris paribus preference statements have provided useful treatments and clear semantics for qualitative comparisons, but have not provided similarly clear representations or semantics for comparisons involving quantitative tradeoffs. We use directional derivatives and other concepts from elementary differential geometry to interpret conditional multiattribute ceteris paribus preference comparisons that state bounds on quantitative tradeoff ratios. This semantics extends the familiar economic notion of marginal rate of substitution to multiple continuous or discrete attributes. The same geometric concepts also provide means for interpreting statements about the relative importance of different attributes. PMID:21528018

  14. Subaperture stitching tolerancing for annular ring geometry.

    PubMed

    Smith, Greg A; Burge, James H

    2015-09-20

    Subaperture stitching is an economical way to extend small-region, high-resolution interferometric metrology to cover large-aperture optics. Starting from system geometry and measurement noise knowledge, this work derives an analytical expression for how noise in an annular ring of subapertures leads to large-scale errors in the computed stitched surface. These errors scale as sin(πp/M)(-2) where p is the number of sine periods around the annular full-aperture and M is the number of subaperture measurements. Understanding how low-spatial-frequency surface errors arise from subaperture noise is necessary for tolerancing systems which use subaperture stitching.

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. Hyperbolic geometry of Kuramoto oscillator networks

    NASA Astrophysics Data System (ADS)

    Chen, Bolun; Engelbrecht, Jan R.; Mirollo, Renato

    2017-09-01

    Kuramoto oscillator networks have the special property that their trajectories are constrained to lie on the (at most) 3D orbits of the Möbius group acting on the state space T N (the N-fold torus). This result has been used to explain the existence of the N-3 constants of motion discovered by Watanabe and Strogatz for Kuramoto oscillator networks. In this work we investigate geometric consequences of this Möbius group action. The dynamics of Kuramoto phase models can be further reduced to 2D reduced group orbits, which have a natural geometry equivalent to the unit disk \

  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. 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.

  3. Phenomenology of effective geometries from quantum gravity

    NASA Astrophysics Data System (ADS)

    Torromé, Ricardo Gallego; Letizia, Marco; Liberati, Stefano

    2015-12-01

    In a recent paper [M. Assanioussi, A. Dapor, and J. Lewandowski, Phys. Lett. B 751, 302 (2015)] a general mechanism for the emergence of cosmological spacetime geometry from a quantum gravity setting was devised and a departure from standard dispersion relations for an elementary particle was predicted. We elaborate here on this approach extending the results obtained in that paper and showing that generically such a framework will not lead to higher order modified dispersion relations in the matter sector. Furthermore, we shall discuss possible phenomenological constraints to this scenario showing that spacetime will have to be classical to a very high degree by now in order to be consistent with current observations.

  4. 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.

  5. Geometry program for aerodynamic lifting surface theory

    NASA Technical Reports Server (NTRS)

    Medan, R. T.

    1973-01-01

    A computer program that provides the geometry and boundary conditions appropriate for an analysis of a lifting, thin wing with control surfaces in linearized, subsonic, steady flow is presented. The kernel function method lifting surface theory is applied. The data which is generated by the program is stored on disk files or tapes for later use by programs which calculate an influence matrix, plot the wing planform, and evaluate the loads on the wing. In addition to processing data for subsequent use in a lifting surface analysis, the program is useful for computing area and mean geometric chords of the wing and control surfaces.

  6. 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

  7. 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.

  8. 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.

  9. 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).

  10. 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.

  11. 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.

  12. Linear and ring polymers in confined geometries

    NASA Astrophysics Data System (ADS)

    Usatenko, Zoryana; Kuterba, Piotr; Chamati, Hassan; Romeis, Dirk

    2017-03-01

    A short overview of the theoretical and experimental works on the polymer-colloid mixtures is given. The behaviour of a dilute solution of linear and ring polymers in confined geometries like slit of two parallel walls or in the solution of mesoscopic colloidal particles of big size with different adsorbing or repelling properties in respect to polymers is discussed. Besides, we consider the massive field theory approach in fixed space dimensions d = 3 for the investigation of the interaction between long flexible polymers and mesoscopic colloidal particles of big size and for the calculation of the correspondent depletion interaction potentials and the depletion forces between confining walls. The presented results indicate the interesting and nontrivial behavior of linear and ring polymers in confined geometries and give possibility better to understand the complexity of physical effects arising from confinement and chain topology which plays a significant role in the shaping of individual chromosomes and in the process of their segregation, especially in the case of elongated bacterial cells. The possibility of using linear and ring polymers for production of new types of nano- and micro-electromechanical devices is analyzed.

  13. 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.

  14. 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.

  15. A rough end for smooth microstate geometries

    DOE PAGES

    Marolf, Donald; Michel, Ben; Puhm, Andrea

    2017-05-03

    Supersymmetric microstate geometries with five non-compact dimensions have recently been shown by Eperon, Reall, and Santos (ERS) to exhibit a non-linear instability featuring the growth of excitations at an “evanescent ergosurface” of infinite redshift. We argue that this growth may be treated as adiabatic evolution along a family of exactly supersymmetric solutions in the limit where the excitations are Aichelburg-Sexl-like shockwaves. In the 2-charge system such solutions may be constructed explicitly, incorpo-rating full backreaction, and are in fact special cases of known microstate geometries. In a near-horizon limit, they reduce to Aichelburg-Sexl shockwaves in AdS3 × S3 propagating along onemore » of the angular directions of the sphere. Noting that the ERS analysis is valid in the limit of large microstate angular momentum j, we use the above identification to interpret their instability as a transition from rare smooth microstates with large angular momentum to more typical microstates with smaller angular momentum. This entropic driving terminates when the angular momentum decreases to j~√n1n5 where the density of microstates is maximal. Finally, we argue that, at this point, the large stringy corrections to such microstates will render them non-linearly stable. We identify a possible mechanism for this stabilization and detail an illustrative toy model.« less

  16. Variable geometry device for turbine compressor outlet

    NASA Technical Reports Server (NTRS)

    Rogo, Casimir (Inventor); Lenz, Herman N. (Inventor)

    1985-01-01

    A variable geometry device is provided for use with the compressor outlet of a turbine engine. The turbine engine includes a support housing, a compressor contained within the support housing and having a compressed air outlet and in which a pair of spaced walls define an annular and radially extending diffuser passageway. The inner end of the diffuser passageway is open to the compressed outlet while the outer end of the diffuser passageway is open to the combustion chamber for the turbine engine. A plurality of circumferentially spaced diffuser vanes are mounted to one of the diffuser walls and protrude across the diffuser passageway. An annular recessed channel is formed around the opposite diffuser wall and an annular ring is mounted within the channel. A motor is operatively connected to this ring and, upon actuation, displaces the ring transversely across the diffuser passageway to variably restrict the diffuser passageway. In addition, the ring includes a plurality of slots which register with the diffuser vanes so that the vane geometry remains the same despite axial displacement of the ring.

  17. Wobbling geometry in a simple triaxial rotor

    NASA Astrophysics Data System (ADS)

    Shi, Wen-Xian; Chen, Qi-Bo

    2015-05-01

    The spectroscopic properties and angular momentum geometry of the wobbling motion of a simple triaxial rotor are investigated within the triaxial rotor model. The obtained exact solutions of energy spectra and reduced quadrupole transition probabilities are compared to the approximate analytic solutions from the harmonic approximation formula and Holstein-Primakoff formula. It is found that the low lying wobbling bands can be well described by the analytic formulae. The evolution of the angular momentum geometry as well as the K-distribution with respect to the rotation and the wobbling phonon excitation are studied in detail. It is demonstrated that with the increase of the wobbling phonon number, the triaxial rotor changes its wobbling motions along the axis with the largest moment of inertia to the axis with the smallest moment of inertia. In this process, a specific evolutionary track that can be used to depict the motion of a triaxial rotating nucleus is proposed. Supported by President's Undergraduate Research Fellowship (PURF), Peking University, Major State 973 Program of China (2013CB834400), National Natural Science Foundation of China (11175002, 11335002, 11375015, 11345004, 11461141002), National Fund for Fostering Talents of Basic Science (NFFTBS) (J1103206) and Research Fund for the Doctoral Program of Higher Education (20110001110087)

  18. A rough end for smooth microstate geometries

    NASA Astrophysics Data System (ADS)

    Marolf, Donald; Michel, Ben; Puhm, Andrea

    2017-05-01

    Supersymmetric microstate geometries with five non-compact dimensions have recently been shown by Eperon, Reall, and Santos (ERS) to exhibit a non-linear instability featuring the growth of excitations at an "evanescent ergosurface" of infinite redshift. We argue that this growth may be treated as adiabatic evolution along a family of exactly supersymmetric solutions in the limit where the excitations are Aichelburg-Sexl-like shockwaves. In the 2-charge system such solutions may be constructed explicitly, incorpo-rating full backreaction, and are in fact special cases of known microstate geometries. In a near-horizon limit, they reduce to Aichelburg-Sexl shockwaves in AdS 3 × S 3 propagating along one of the angular directions of the sphere. Noting that the ERS analysis is valid in the limit of large microstate angular momentum j, we use the above identification to interpret their instability as a transition from rare smooth microstates with large angular momentum to more typical microstates with smaller angular momentum. This entropic driving terminates when the angular momentum decreases to j˜ √{n_1{n}_5} where the density of microstates is maximal. We argue that, at this point, the large stringy corrections to such microstates will render them non-linearly stable. We identify a possible mechanism for this stabilization and detail an illustrative toy model.

  19. 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.

  20. 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.

  1. 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

  2. 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.

  3. 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

  4. Integral-geometry morphological image analysis

    NASA Astrophysics Data System (ADS)

    Michielsen, K.; De Raedt, H.

    2001-07-01

    This paper reviews a general method to characterize the morphology of two- and three-dimensional patterns in terms of geometrical and topological descriptors. Based on concepts of integral geometry, it involves the calculation of the Minkowski functionals of black-and-white images representing the patterns. The result of this approach is an objective, numerical characterization of a given pattern. We briefly review the basic elements of morphological image processing, a technique to transform images to patterns that are amenable to further morphological image analysis. The image processing technique is applied to electron microscope images of nano-ceramic particles and metal-oxide precipitates. The emphasis of this review is on the practical aspects of the integral-geometry-based morphological image analysis but we discuss its mathematical foundations as well. Applications to simple lattice structures, triply periodic minimal surfaces, and the Klein bottle serve to illustrate the basic steps of the approach. More advanced applications include random point sets, percolation and complex structures found in block copolymers.

  5. 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.

  6. 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.

  7. 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

  8. 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.

  9. New General Tools for Constrained Geometry Optimizations.

    PubMed

    De Vico, Luca; Olivucci, Massimo; Lindh, Roland

    2005-09-01

    A modification of the constrained geometry optimization method by Anglada and Bofill (Anglada, J. M.; Bofill, J. M. J. Comput. Chem. 1997, 18, 992-1003) is designed and implemented. The changes include the choice of projection, quasi-line-search, and the use of a Rational Function optimization approach rather than a reduced-restricted-quasi-Newton-Raphson method in the optimization step. Furthermore, we show how geometrical constrains can be implemented in an approach based on nonredundant curvilinear coordinates avoiding the inclusion of the constraints in the set of redundant coordinates used to define the internal coordinates. The behavior of the new implementation is demonstrated in geometry optimizations featuring single or multiple geometrical constraints (bond lengths, angles, etc.), optimizations on hyperspherical cross sections (as in the computation of steepest descent paths), and location of energy minima on the intersection subspace of two potential energy surfaces (i.e. minimum energy crossing points). In addition, a novel scheme to determine the crossing point geometrically nearest to a given molecular structure is proposed.

  10. Lower leg musculoskeletal geometry and sprint performance.

    PubMed

    Karamanidis, Kiros; Albracht, Kirsten; Braunstein, Bjoern; Moreno Catala, Maria; Goldmann, Jan-Peter; Brüggemann, Gert-Peter

    2011-05-01

    The purpose of this study was to investigate whether sprint performance is related to lower leg musculoskeletal geometry within a homogeneous group of highly trained 100-m sprinters. Using a cluster analysis, eighteen male sprinters were divided into two groups based on their personal best (fast: N=11, 10.30±0.07s; slow: N=7, 10.70±0.08s). Calf muscular fascicle arrangement and Achilles tendon moment arms (calculated by the gradient of tendon excursion versus ankle joint angle) were analyzed for each athlete using ultrasonography. Achilles tendon moment arm, foot and ankle skeletal geometry, fascicle arrangement as well as the ratio of fascicle length to Achilles tendon moment arm showed no significant (p>0.05) correlation with sprint performance, nor were there any differences in the analyzed musculoskeletal parameters between the fast and slow sprinter group. Our findings provide evidence that differences in sprint ability in world-class athletes are not a result of differences in the geometrical design of the lower leg even when considering both skeletal and muscular components.

  11. Extraction of human stomach using computational geometry

    NASA Astrophysics Data System (ADS)

    Aisaka, Kazuo; Arai, Kiyoshi; Tsutsui, Kumiko; Hashizume, Akihide

    1991-06-01

    This paper presents a method for extracting the profile of the stomach by computational geometry. The stomach is difficult to recognize from an X-ray because of its elasticity. Global information of the stomach shape is required for recognition. The method has three steps. In the first step, the edge is enhanced, and then edge pieces are found as candidates for the border. Because the resulting border is almost always incomplete, a method for connecting the pieces is required. The second step uses computational geometry to create the global structure from the edge pieces. A Delaunay graph is drawn from the end points of the pieces. This enables us to decide which pieces are most likely to connect. The third step uses the shape of a stomach to find the best sequence of pieces. The knowledge is described in simple LISP functions. Because a Delaunay graph is planar, we can reduce the number of candidate pieces while searching for the most likely sequence. We applied this method to seven stomach pictures taken by the double contrast method and found the greater curvature in six cases. Enhancing the shape knowledge will increase the number of recognizable parts.

  12. 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.

  13. 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.

  14. Splitting a colon geometry with multiplanar clipping

    NASA Astrophysics Data System (ADS)

    Ahn, David K.; Vining, David J.; Ge, Yaorong; Stelts, David R.

    1998-06-01

    Virtual colonoscopy, a recent three-dimensional (3D) visualization technique, has provided radiologists with a unique diagnostic tool. Using this technique, a radiologist can examine the internal morphology of a patient's colon by navigating through a surface-rendered model that is constructed from helical computed tomography image data. Virtual colonoscopy can be used to detect early forms of colon cancer in a way that is less invasive and expensive compared to conventional endoscopy. However, the common approach of 'flying' through the colon lumen to visually search for polyps is tedious and time-consuming, especially when a radiologist loses his or her orientation within the colon. Furthermore, a radiologist's field of view is often limited by the 3D camera position located inside the colon lumen. We have developed a new technique, called multi-planar geometry clipping, that addresses these problems. Our algorithm divides a complex colon anatomy into several smaller segments, and then splits each of these segments in half for display on a static medium. Multi-planar geometry clipping eliminates virtual colonoscopy's dependence upon expensive, real-time graphics workstations by enabling radiologists to globally inspect the entire internal surface of the colon from a single viewpoint.

  15. Prediction of melt geometry in laser cutting

    NASA Astrophysics Data System (ADS)

    Tani, Giovanni; Tomesani, Luca; Campana, Giampaolo

    2003-03-01

    In this paper, an analytical model for the evaluation of the melt film geometry in laser cutting of steels is developed. Using as basis, a previous model for kerf geometry estimation developed by the authors, with both reactive and non-reactive process gases, the film thickness and velocity were determined as a function of the kerf depth in the cutting plate. Two criteria were then adopted to predict the quality of the laser cutting operation: the first is based on a minimum acceptable value of the ejection speed of the melt from the bottom of the kerf, the second on the occlusion of the kerf itself due to an excess of molten material in the boundary layer at the kerf width. These criteria determined a feasibility region in the domain of the process and material variables, such as cutting speed, assistant gas pressure, laser beam power and material characteristics. These factors may be successfully used to build a process-planning tool for parameters optimisation and setting, in order to achieve a satisfactory process quality. The model response is in excellent agreement with the feasibility regions reported from experimental data by various authors and demonstrates a relationship between the occurrence of dross adhesion and the two different mechanisms predicted for such a phenomenon were: unsatisfactory ejection speed of the melt film from the bottom of the kerf and occlusion of the kerf.

  16. Emergent community agglomeration from data set geometry

    NASA Astrophysics Data System (ADS)

    Zhao, Chenchao; Song, Jun S.

    2017-04-01

    In the statistical learning language, samples are snapshots of random vectors drawn from some unknown distribution. Such vectors usually reside in a high-dimensional Euclidean space, and thus the "curse of dimensionality" often undermines the power of learning methods, including community detection and clustering algorithms, that rely on Euclidean geometry. This paper presents the idea of effective dissimilarity transformation (EDT) on empirical dissimilarity hyperspheres and studies its effects using synthetic and gene expression data sets. Iterating the EDT turns a static data distribution into a dynamical process purely driven by the empirical data set geometry and adaptively ameliorates the curse of dimensionality, partly through changing the topology of a Euclidean feature space Rn into a compact hypersphere Sn. The EDT often improves the performance of hierarchical clustering via the automatic grouping information emerging from global interactions of data points. The EDT is not restricted to hierarchical clustering, and other learning methods based on pairwise dissimilarity should also benefit from the many desirable properties of EDT.

  17. 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.

  18. 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.

  19. 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

  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.